Finite Group Databasebeta

← C73×#59845 #32969249

Subgroups — C73×#59845 #32969249

Order 18688.

2262 conjugacy classes of subgroups.

The subgroup lattice has 1586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#556×C73C211yesmaximal, characteristic, complemented
2C2×#551×C73C211yesmaximal, characteristic, complemented
3C73×#2723C211yesmaximal, characteristic, complemented
4C73×#2698C211yesmaximal, characteristic, complemented
5C73×#2674C211yesmaximal, characteristic, complemented
6C73×#2670C211yesmaximal, characteristic
7C73×#2599C211yesmaximal, characteristic, complemented
8C73×#2598C211yesmaximal, characteristic, complemented
9C73×#2560C211yesmaximal, characteristic, complemented
10C73×#2557C211yesmaximal, characteristic, complemented
11C73×#2554C211yesmaximal, characteristic, complemented
12C73×#2521C211yesmaximal, characteristic, complemented
13C73×#2521C211yesmaximal, characteristic, complemented
14C73×#2492C211yesmaximal, characteristic, complemented
15C73×#2480C211yesmaximal, characteristic, complemented
16C73×#2477C211yesmaximal, characteristic, complemented
17C73×#2472C211yesmaximal, characteristic, complemented
18C73×#2472C211yesmaximal, characteristic, complemented
19C73×#2470C211yesmaximal, characteristic, complemented
20C73×#2467C211yesmaximal, characteristic, complemented
21C73×#2465C211yesmaximal, characteristic, complemented
22C73×#2461C211yesmaximal, characteristic, complemented
23C73×#2459C211yesmaximal, characteristic, complemented
24C73×#2458C211yesmaximal, characteristic, complemented
25C73×#2367C211yesmaximal, characteristic, complemented
26C73×#2362C211yesmaximal, characteristic, complemented
27C73×#2358C211yesmaximal, characteristic, complemented
28C73×#2342C211yesmaximal, characteristic, complemented
29C4×#126×C73C211yesmaximal, characteristic, complemented
30C4×#124×C73C211yesmaximal, characteristic, complemented
31C73×#2293C211yesmaximal, characteristic, complemented
32#556×C73—28no—
33#551×C73—28no—
34C2×C4⋊Q8×C73C2211yescharacteristic, complemented
35C2×#126×C73C2211yescharacteristic
36C2×#126×C73C2211yescharacteristic
37C2×#126×C73C2211yescharacteristic
38C2×#126×C73C2211yescharacteristic, complemented
39C2×#126×C73C2211yescharacteristic, complemented
40C2×#124×C73C2211yescharacteristic
41C2×#124×C73C2211yescharacteristic
42C2×#124×C73C2211yescharacteristic
43C2×#124×C73C2211yescharacteristic
44C2×#124×C73C2211yescharacteristic
45C2×#123×C73C2211yescharacteristic
46C2×#123×C73C2211yescharacteristic
47C2×#123×C73C2211yescharacteristic
48C2×C22⋊Q8×C73C2211yescharacteristic
49C2×C22⋊Q8×C73C2211yescharacteristic
50C2×C22⋊Q8×C73C2211yescharacteristic
51C2×C22⋊Q8×C73C2211yescharacteristic
52C2×C22⋊Q8×C73C2211yescharacteristic, complemented
53C2×#120×C73C2211yescharacteristic
54C2×#120×C73C2211yescharacteristic
55C2×C4×Q8×C73C2211yescharacteristic, complemented
56C2×C4×Q8×C73C2211yescharacteristic, complemented
57C2×C4×Q8×C73C2211yescharacteristic, complemented
58C2×C4×D4×C73C2211yescharacteristic
59C2×C4×D4×C73C2211yescharacteristic
60C2×C4×D4×C73C2211yescharacteristic
61C2×C4×D4×C73C2211yescharacteristic
62C2×#117×C73C2211yescharacteristic
63C2×#117×C73C2211yescharacteristic
64C2×#117×C73C2211yescharacteristic
65C2×#117×C73C2211yescharacteristic, complemented
66C22×C22⋊C4×C73C2211yescharacteristic
67C22×C22⋊C4×C73C2211yescharacteristic
68C22×C22⋊C4×C73C2211yescharacteristic
69#400×C73C2211yescharacteristic, complemented
70#400×C73C2211yescharacteristic, complemented
71#399×C73C2211yescharacteristic, complemented
72#399×C73C2211yescharacteristic, complemented
73#398×C73C2211yescharacteristic, complemented
74#398×C73C2211yescharacteristic, complemented
75#397×C73C2211yescharacteristic
76#397×C73C2211yescharacteristic
77#397×C73C2211yescharacteristic
78#397×C73C2211yescharacteristic
79#397×C73C2211yescharacteristic
80#397×C73C2211yescharacteristic, complemented
81#396×C73C2211yescharacteristic
82#396×C73C2211yescharacteristic, complemented
83#395×C73C2211yescharacteristic, complemented
84#395×C73C2211yescharacteristic, complemented
85#395×C73C2211yescharacteristic, complemented
86#394×C73C2211yescharacteristic
87#394×C73C2211yescharacteristic
88#394×C73C2211yescharacteristic
89#394×C73C2211yescharacteristic
90#394×C73C2211yescharacteristic
91#394×C73C2211yescharacteristic
92#394×C73C2211yescharacteristic, complemented
93#393×C73C2211yescharacteristic
94#393×C73C2211yescharacteristic
95#393×C73C2211yescharacteristic
96#393×C73C2211yescharacteristic, complemented
97#393×C73C2211yescharacteristic, complemented
98#392×C73C2211yescharacteristic
99#392×C73C2211yescharacteristic
100#392×C73C2211yescharacteristic
101#391×C73C2211yescharacteristic, complemented
102#391×C73C2211yescharacteristic, complemented
103#391×C73C2211yescharacteristic, complemented
104#391×C73C2211yescharacteristic, complemented
105#391×C73C2211yescharacteristic, complemented
106#390×C73C2211yescharacteristic
107#390×C73C2211yescharacteristic
108#390×C73C2211yescharacteristic
109#390×C73C2211yescharacteristic
110#390×C73C2211yescharacteristic
111#390×C73C2211yescharacteristic, complemented
112#389×C73C2211yescharacteristic, complemented
113#389×C73C2211yescharacteristic, complemented
114#389×C73C2211yescharacteristic, complemented
115#388×C73C2211yescharacteristic
116#388×C73C2211yescharacteristic
117#388×C73C2211yescharacteristic
118#388×C73C2211yescharacteristic
119#388×C73C2211yescharacteristic
120#388×C73C2211yescharacteristic
121#388×C73C2211yescharacteristic
122#388×C73C2211yescharacteristic
123#388×C73C2211yescharacteristic
124#388×C73C2211yescharacteristic
125#388×C73C2211yescharacteristic
126#388×C73C2211yescharacteristic
127#388×C73C2211yescharacteristic
128#388×C73C2211yescharacteristic
129#388×C73C2211yescharacteristic
130#388×C73C2211yescharacteristic, complemented
131#388×C73C2211yescharacteristic, complemented
132#388×C73C2211yescharacteristic, complemented
133#388×C73C2211yescharacteristic, complemented
134#388×C73C2211yescharacteristic, complemented
135#388×C73C2211yescharacteristic, complemented
136#388×C73C2211yescharacteristic, complemented
137#388×C73C2211yescharacteristic, complemented
138#388×C73C2211yescharacteristic, complemented
139#388×C73C2211yescharacteristic, complemented
140#387×C73C2211yescharacteristic, complemented
141#387×C73C2211yescharacteristic, complemented
142#387×C73C2211yescharacteristic, complemented
143#387×C73C2211yescharacteristic, complemented
144#387×C73C2211yescharacteristic, complemented
145#387×C73C2211yescharacteristic, complemented
146#387×C73C2211yescharacteristic, complemented
147#387×C73C2211yescharacteristic, complemented
148#387×C73C2211yescharacteristic, complemented
149#386×C73C2211yescharacteristic
150#386×C73C2211yescharacteristic
151#386×C73C2211yescharacteristic
152#386×C73C2211yescharacteristic
153#386×C73C2211yescharacteristic
154#386×C73C2211yescharacteristic
155#386×C73C2211yescharacteristic
156#386×C73C2211yescharacteristic, complemented
157#386×C73C2211yescharacteristic, complemented
158#385×C73C2211yescharacteristic
159#385×C73C2211yescharacteristic
160#385×C73C2211yescharacteristic
161#385×C73C2211yescharacteristic
162#385×C73C2211yescharacteristic
163#385×C73C2211yescharacteristic
164#385×C73C2211yescharacteristic, complemented
165#383×C73C2211yescharacteristic, complemented
166#382×C73C2211yescharacteristic, complemented
167#381×C73C2211yescharacteristic
168#380×C73C2211yescharacteristic
169#380×C73C2211yescharacteristic
170#379×C73C2211yescharacteristic
171#379×C73C2211yescharacteristic
172C4×C4⋊C4×C73C2211yescharacteristic, complemented
173C4×C4⋊C4×C73C2211yescharacteristic, complemented
174C4×C4⋊C4×C73C2211yescharacteristic, complemented
175C4×C4⋊C4×C73C2211yescharacteristic, complemented
176C4×C4⋊C4×C73C2211yescharacteristic, complemented
177C4×C22⋊C4×C73C2211yescharacteristic
178C4×C22⋊C4×C73C2211yescharacteristic
179C4×C22⋊C4×C73C2211yescharacteristic
180C4×C22⋊C4×C73C2211yescharacteristic
181C4×C22⋊C4×C73C2211yescharacteristic
182C4×C22⋊C4×C73C2211yescharacteristic
183C4×C22⋊C4×C73C2211yescharacteristic
184C4×C22⋊C4×C73C2211yescharacteristic
185C4×C22⋊C4×C73C2211yescharacteristic, complemented
186C4×C22⋊C4×C73C2211yescharacteristic, complemented
187C4×C22⋊C4×C73C2211yescharacteristic, complemented
188C43×C73C2211yescharacteristic, complemented
189C25×C73C2311yescharacteristic
190C22×Q8×C73C2311yescharacteristic
191C22×Q8×C73C2311yescharacteristic
192C22×Q8×C73C2311yescharacteristic
193C22×Q8×C73C2311yescharacteristic
194C22×D4×C73C2311yescharacteristic
195C22×D4×C73C2311yescharacteristic
196C22×D4×C73C2311yescharacteristic
197C22×D4×C73C2311yescharacteristic
198C22×D4×C73C2311yescharacteristic
199C22×D4×C73C2311yescharacteristic
200C22×D4×C73C2311yescharacteristic
201C23×C4×C73C2311yescharacteristic
202C23×C4×C73C2311yescharacteristic
203C23×C4×C73C2311yescharacteristic
204C23×C4×C73C2311yescharacteristic
205C23×C4×C73C2311yescharacteristic
206C23×C4×C73C2311yescharacteristic
207C23×C4×C73C2311yescharacteristic
208C23×C4×C73C2311yescharacteristic
209C4⋊Q8×C73—24no—
210#126×C73—24no—
211#126×C73—24no—
212#126×C73—24no—
213#126×C73—24no—
214#126×C73D418yescomplemented
215#124×C73—24no—
216#124×C73—24no—
217#124×C73—24no—
218#124×C73—24no—
219#124×C73—24no—
220#123×C73—24no—
221#123×C73—24no—
222#123×C73—24no—
223C22⋊Q8×C73—24no—
224C22⋊Q8×C73—24no—
225C22⋊Q8×C73—24no—
226C22⋊Q8×C73—24no—
227C22⋊Q8×C73—24no—
228#120×C73—24no—
229#120×C73—24no—
230C4×Q8×C73—24no—
231C4×Q8×C73—24no—
232C4×Q8×C73—24no—
233C4×D4×C73—24no—
234C4×D4×C73—24no—
235C4×D4×C73—24no—
236C4×D4×C73—24no—
237#117×C73—24no—
238#117×C73—24no—
239#117×C73—24no—
240#117×C73—24no—
241C2×C4⋊C4×C73C2311yescharacteristic
242C2×C4⋊C4×C73C2311yescharacteristic
243C2×C4⋊C4×C73C2311yescharacteristic
244C2×C4⋊C4×C73C2311yescharacteristic
245C2×C4⋊C4×C73C2311yescharacteristic
246C2×C4⋊C4×C73C2311yescharacteristic
247C2×C4⋊C4×C73C2311yescharacteristic
248C2×C4⋊C4×C73C2311yescharacteristic
249C2×C4⋊C4×C73C2311yescharacteristic
250C2×C4⋊C4×C73C2311yescharacteristic
251C2×C4⋊C4×C73C2311yescharacteristic
252C2×C4⋊C4×C73C2311yescharacteristic
253C2×C4⋊C4×C73C2311yescharacteristic
254C2×C4⋊C4×C73C2311yescharacteristic
255C2×C4⋊C4×C73C2311yescharacteristic
256C2×C4⋊C4×C73C2311yescharacteristic
257C2×C4⋊C4×C73C2311yescharacteristic
258C2×C4⋊C4×C73C2311yescharacteristic
259C2×C4⋊C4×C73C2311yescharacteristic
260C2×C4⋊C4×C73C2311yescharacteristic
261C2×C4⋊C4×C73C2311yescharacteristic
262C2×C4⋊C4×C73C2311yescharacteristic
263C2×C4⋊C4×C73C2311yescharacteristic
264C2×C4⋊C4×C73C2311yescharacteristic
265C2×C4⋊C4×C73C2311yescharacteristic
266C2×C4⋊C4×C73C2311yescharacteristic
267C2×C4⋊C4×C73C2311yescharacteristic
268C2×C4⋊C4×C73C2311yescharacteristic
269C2×C4⋊C4×C73C2311yescharacteristic
270C2×C22⋊C4×C73—24no—
271C2×C22⋊C4×C73—24no—
272C2×C22⋊C4×C73—24no—
273C2×C22⋊C4×C73C2311yescharacteristic
274C2×C22⋊C4×C73C2311yescharacteristic
275C2×C22⋊C4×C73C2311yescharacteristic
276C2×C22⋊C4×C73C2311yescharacteristic
277C2×C22⋊C4×C73C2311yescharacteristic
278C2×C22⋊C4×C73C2311yescharacteristic
279C2×C22⋊C4×C73C2311yescharacteristic
280C2×C22⋊C4×C73C2311yescharacteristic
281C2×C22⋊C4×C73C2311yescharacteristic
282C2×C22⋊C4×C73C2311yescharacteristic
283C2×C22⋊C4×C73C2311yescharacteristic
284C2×C22⋊C4×C73C2311yescharacteristic
285C2×C22⋊C4×C73C2311yescharacteristic
286C2×C22⋊C4×C73C2311yescharacteristic
287C2×C22⋊C4×C73C2311yescharacteristic
288C2×C22⋊C4×C73C2311yescharacteristic
289C2×C22⋊C4×C73C2311yescharacteristic
290C2×C22⋊C4×C73C2311yescharacteristic
291C2×C22⋊C4×C73C2311yescharacteristic
292C2×C22⋊C4×C73C2311yescharacteristic
293C2×C22⋊C4×C73C2311yescharacteristic
294C2×C22⋊C4×C73C2311yescharacteristic
295C2×C22⋊C4×C73C2311yescharacteristic
296C2×C22⋊C4×C73C2311yescharacteristic
297C2×C22⋊C4×C73C2311yescharacteristic
298C2×C22⋊C4×C73C2311yescharacteristic
299C2×C22⋊C4×C73C2311yescharacteristic
300C2×C22⋊C4×C73C2311yescharacteristic
301C2×C22⋊C4×C73C2311yescharacteristic
302C2×C22⋊C4×C73C2311yescharacteristic
303C2×C22⋊C4×C73C2311yescharacteristic
304C2×C22⋊C4×C73C2311yescharacteristic
305C2×C22⋊C4×C73C2311yescharacteristic
306C2×C22⋊C4×C73C2311yescharacteristic
307C2×C22⋊C4×C73C2311yescharacteristic
308C2×C22⋊C4×C73C2311yescharacteristic
309C2×C22⋊C4×C73C2311yescharacteristic
310C2×C22⋊C4×C73C2311yescharacteristic
311C2×C22⋊C4×C73C2311yescharacteristic
312C2×C22⋊C4×C73C2311yescharacteristic
313C2×C22⋊C4×C73C2311yescharacteristic
314C2×C22⋊C4×C73C2311yescharacteristic
315C2×C22⋊C4×C73C2311yescharacteristic
316C2×C22⋊C4×C73C2311yescharacteristic
317C2×C22⋊C4×C73C2311yescharacteristic
318C2×C22⋊C4×C73C2311yescharacteristic
319C2×C22⋊C4×C73C2311yescharacteristic
320C2×C22⋊C4×C73C2311yescharacteristic
321C2×C22⋊C4×C73C2311yescharacteristic
322C2×C22⋊C4×C73C2311yescharacteristic
323C2×C42×C73C2311yescharacteristic
324C2×C42×C73C2311yescharacteristic
325C2×C42×C73C2311yescharacteristic
326C2×C42×C73C2311yescharacteristic
327C2×C42×C73C2311yescharacteristic
328C2×C42×C73C2311yescharacteristic
329C2×C42×C73C2311yescharacteristic
330C2×C42×C73C2311yescharacteristic
331C2×C42×C73C2311yescharacteristic
332C2×C42×C73C2311yescharacteristic
333C2×C42×C73C2311yescharacteristic
334C2×C42×C73C2311yescharacteristic
335C2×C42×C73C2311yescharacteristic
336C2×C42×C73C2311yescharacteristic
337C2×C42×C73C2311yescharacteristic
338C2×C42×C73C2311yescharacteristic
339C2×C42×C73C2311yescharacteristic
340C2×C42×C73C2311yescharacteristic
341#95×C73C2311yescharacteristic
342#95×C73C2311yescharacteristic
343#95×C73C2311yescharacteristic
344#95×C73C2311yescharacteristic
345#95×C73C2311yescharacteristic
346#95×C73C2311yescharacteristic
347#95×C73C2311yescharacteristic
348#95×C73C2311yescharacteristic
349#95×C73C2311yescharacteristic
350#95×C73C2311yescharacteristic
351#95×C73C2311yescharacteristic
352#95×C73C2311yescharacteristic
353#95×C73C2311yescharacteristic
354#95×C73C2311yescharacteristic
355#95×C73C2311yescharacteristic
356#95×C73C2311yescharacteristic
357#95×C73C2311yescharacteristic
358#95×C73C2311yescharacteristic
359#95×C73C2311yescharacteristic
360#95×C73C2311yescharacteristic
361#95×C73C2311yescharacteristic
362#95×C73C2311yescharacteristic
363#95×C73C2311yescharacteristic
364#95×C73C2311yescharacteristic
365#95×C73C2311yescharacteristic
366#95×C73C2311yescharacteristic
367#95×C73C2311yescharacteristic
368#95×C73C2311yescharacteristic
369#95×C73C2311yescharacteristic
370#95×C73C2311yescharacteristic
371#95×C73C2311yescharacteristic
372#95×C73C2311yescharacteristic
373#95×C73C2311yescharacteristic
374#95×C73C2311yescharacteristic
375#95×C73C2311yescharacteristic
376#95×C73C2311yescharacteristic
377#95×C73C2311yescharacteristic
378#95×C73C2311yescharacteristic
379C24×C73—22no—
380C24×C73—22no—
381C24×C73—22no—
382C24×C73—41no—
383C24×C73—41no—
384C24×C73—41no—
385C24×C73—41no—
386C24×C73C2411yescharacteristic
387C24×C73C2411yescharacteristic
388C24×C73C2411yescharacteristic
389C24×C73C2411yescharacteristic
390C24×C73C2411yescharacteristic
391C2×Q8×C73—22no—
392C2×Q8×C73—22no—
393C2×Q8×C73—22no—
394C2×Q8×C73—22no—
395C2×Q8×C73—22no—
396C2×Q8×C73—22no—
397C2×Q8×C73—22no—
398C2×Q8×C73—41no—
399C2×Q8×C73—41no—
400C2×Q8×C73—41no—
401C2×Q8×C73—41no—
402C2×Q8×C73—41no—
403C2×D4×C73—22no—
404C2×D4×C73—22no—
405C2×D4×C73—22no—
406C2×D4×C73—22no—
407C2×D4×C73—22no—
408C2×D4×C73—22no—
409C2×D4×C73—22no—
410C2×D4×C73—22no—
411C2×D4×C73—22no—
412C2×D4×C73—22no—
413C2×D4×C73—41no—
414C2×D4×C73—41no—
415C2×D4×C73—41no—
416C2×D4×C73—41no—
417C2×D4×C73—41no—
418C2×D4×C73—41no—
419C2×D4×C73—41no—
420C2×D4×C73—41no—
421C2×D4×C73—41no—
422C2×D4×C73—41no—
423C2×D4×C73—41no—
424C22×C4×C73—22no—
425C22×C4×C73—22no—
426C22×C4×C73—22no—
427C22×C4×C73—22no—
428C22×C4×C73—22no—
429C22×C4×C73—22no—
430C22×C4×C73—22no—
431C22×C4×C73—22no—
432C22×C4×C73—22no—
433C22×C4×C73—22no—
434C22×C4×C73—22no—
435C22×C4×C73—22no—
436C22×C4×C73—41no—
437C22×C4×C73—41no—
438C22×C4×C73—41no—
439C22×C4×C73—41no—
440C22×C4×C73—41no—
441C22×C4×C73—41no—
442C22×C4×C73—41no—
443C22×C4×C73—41no—
444C22×C4×C73—41no—
445C22×C4×C73—41no—
446C22×C4×C73—41no—
447C22×C4×C73—41no—
448C22×C4×C73C2411yescharacteristic
449C22×C4×C73C2411yescharacteristic
450C22×C4×C73C2411yescharacteristic
451C22×C4×C73C2411yescharacteristic
452C22×C4×C73C2411yescharacteristic
453C22×C4×C73C2411yescharacteristic
454C22×C4×C73C2411yescharacteristic
455C22×C4×C73C2411yescharacteristic
456C22×C4×C73C2411yescharacteristic
457C22×C4×C73C2411yescharacteristic
458C22×C4×C73C2411yescharacteristic
459C22×C4×C73C2411yescharacteristic
460C22×C4×C73C2411yescharacteristic
461C22×C4×C73C2411yescharacteristic
462C22×C4×C73C2411yescharacteristic
463C22×C4×C73C2411yescharacteristic
464C22×C4×C73C2411yescharacteristic
465C22×C4×C73C2411yescharacteristic
466C22×C4×C73C2411yescharacteristic
467C22×C4×C73C2411yescharacteristic
468C22×C4×C73C2411yescharacteristic
469C22×C4×C73C2411yescharacteristic
470C22×C4×C73C2411yescharacteristic
471C22×C4×C73C2411yescharacteristic
472C22×C4×C73C2411yescharacteristic
473C22×C4×C73C2411yescharacteristic
474C4⋊C4×C73—22no—
475C4⋊C4×C73—22no—
476C4⋊C4×C73—22no—
477C4⋊C4×C73—22no—
478C4⋊C4×C73—22no—
479C4⋊C4×C73—22no—
480C4⋊C4×C73—22no—
481C4⋊C4×C73—22no—
482C4⋊C4×C73—22no—
483C4⋊C4×C73—22no—
484C4⋊C4×C73—22no—
485C4⋊C4×C73—22no—
486C4⋊C4×C73—22no—
487C4⋊C4×C73—22no—
488C4⋊C4×C73—22no—
489C4⋊C4×C73—22no—
490C4⋊C4×C73—22no—
491C4⋊C4×C73—22no—
492C4⋊C4×C73—41no—
493C4⋊C4×C73—41no—
494C4⋊C4×C73—41no—
495C4⋊C4×C73—41no—
496C4⋊C4×C73—41no—
497C4⋊C4×C73—41no—
498C4⋊C4×C73—41no—
499C4⋊C4×C73—41no—
500C4⋊C4×C73C2×D414yes—
501C4⋊C4×C73C2×D414yes—
502C4⋊C4×C73C2×D414yes—
503C22⋊C4×C73—22no—
504C22⋊C4×C73—22no—
505C22⋊C4×C73—22no—
506C22⋊C4×C73—22no—
507C22⋊C4×C73—22no—
508C22⋊C4×C73—22no—
509C22⋊C4×C73—22no—
510C22⋊C4×C73—22no—
511C22⋊C4×C73—22no—
512C22⋊C4×C73—22no—
513C22⋊C4×C73—22no—
514C22⋊C4×C73—22no—
515C22⋊C4×C73—22no—
516C22⋊C4×C73—22no—
517C22⋊C4×C73—22no—
518C22⋊C4×C73—22no—
519C22⋊C4×C73—22no—
520C22⋊C4×C73—22no—
521C22⋊C4×C73—22no—
522C22⋊C4×C73—22no—
523C22⋊C4×C73—22no—
524C22⋊C4×C73—22no—
525C22⋊C4×C73—22no—
526C22⋊C4×C73—22no—
527C22⋊C4×C73—22no—
528C22⋊C4×C73—22no—
529C22⋊C4×C73—22no—
530C22⋊C4×C73—22no—
531C22⋊C4×C73—22no—
532C22⋊C4×C73—22no—
533C22⋊C4×C73—22no—
534C22⋊C4×C73—41no—
535C22⋊C4×C73—41no—
536C22⋊C4×C73—41no—
537C22⋊C4×C73—41no—
538C22⋊C4×C73—41no—
539C22⋊C4×C73—41no—
540C22⋊C4×C73—41no—
541C22⋊C4×C73—41no—
542C22⋊C4×C73—41no—
543C22⋊C4×C73—41no—
544C22⋊C4×C73—41no—
545C22⋊C4×C73—41no—
546C22⋊C4×C73—41no—
547C22⋊C4×C73—41no—
548C22⋊C4×C73C2×D414yes—
549C22⋊C4×C73C2×D414yes—
550C22⋊C4×C73C2×D414yes—
551C22⋊C4×C73#4114yes—
552C22⋊C4×C73#4114yes—
553C42×C73—22no—
554C42×C73—22no—
555C42×C73—22no—
556C42×C73—22no—
557C42×C73—22no—
558C42×C73—22no—
559C42×C73—22no—
560C42×C73—22no—
561C42×C73—22no—
562C42×C73—22no—
563C42×C73—22no—
564C42×C73—41no—
565C42×C73—41no—
566C42×C73—41no—
567C42×C73—41no—
568C42×C73—41no—
569C42×C73—41no—
570C42×C73C2×D414yes—
571C23×C73—21no—
572C23×C73—21no—
573C23×C73—21no—
574C23×C73—21no—
575C23×C73—21no—
576C23×C73—21no—
577C23×C73—21no—
578C23×C73—21no—
579C23×C73—21no—
580C23×C73—21no—
581C23×C73—21no—
582C23×C73—21no—
583C23×C73—21no—
584C23×C73—21no—
585C23×C73—21no—
586C23×C73—21no—
587C23×C73—21no—
588C23×C73—21no—
589C23×C73—21no—
590C23×C73—21no—
591C23×C73—21no—
592C23×C73—21no—
593C23×C73—21no—
594C23×C73—21no—
595C23×C73—21no—
596C23×C73—21no—
597C23×C73—21no—
598C23×C73—21no—
599C23×C73—21no—
600C23×C73—21no—
601C23×C73—21no—
602C23×C73—21no—
603C23×C73—44no—
604C23×C73—44no—
605C23×C73—44no—
606C23×C73—82no—
607C23×C73—82no—
608C23×C73—82no—
609C23×C73—82no—
610C23×C73C22×D412yes—
611C23×C73C2×#4112yes—
612C23×C73C2×#4112yes—
613C23×C73C2511yescharacteristic
614Q8×C73—44no—
615Q8×C73—44no—
616Q8×C73—44no—
617Q8×C73—82no—
618D4×C73—44no—
619D4×C73—44no—
620D4×C73—44no—
621D4×C73—44no—
622D4×C73—82no—
623D4×C73—82no—
624D4×C73—82no—
625C2×C4×C73—21no—
626C2×C4×C73—21no—
627C2×C4×C73—21no—
628C2×C4×C73—21no—
629C2×C4×C73—21no—
630C2×C4×C73—21no—
631C2×C4×C73—21no—
632C2×C4×C73—21no—
633C2×C4×C73—21no—
634C2×C4×C73—21no—
635C2×C4×C73—21no—
636C2×C4×C73—21no—
637C2×C4×C73—21no—
638C2×C4×C73—21no—
639C2×C4×C73—21no—
640C2×C4×C73—21no—
641C2×C4×C73—21no—
642C2×C4×C73—21no—
643C2×C4×C73—21no—
644C2×C4×C73—21no—
645C2×C4×C73—21no—
646C2×C4×C73—21no—
647C2×C4×C73—21no—
648C2×C4×C73—21no—
649C2×C4×C73—21no—
650C2×C4×C73—21no—
651C2×C4×C73—21no—
652C2×C4×C73—21no—
653C2×C4×C73—21no—
654C2×C4×C73—21no—
655C2×C4×C73—21no—
656C2×C4×C73—21no—
657C2×C4×C73—21no—
658C2×C4×C73—21no—
659C2×C4×C73—21no—
660C2×C4×C73—21no—
661C2×C4×C73—21no—
662C2×C4×C73—21no—
663C2×C4×C73—21no—
664C2×C4×C73—21no—
665C2×C4×C73—21no—
666C2×C4×C73—21no—
667C2×C4×C73—21no—
668C2×C4×C73—21no—
669C2×C4×C73—21no—
670C2×C4×C73—21no—
671C2×C4×C73—21no—
672C2×C4×C73—21no—
673C2×C4×C73—21no—
674C2×C4×C73—21no—
675C2×C4×C73—21no—
676C2×C4×C73—21no—
677C2×C4×C73—21no—
678C2×C4×C73—21no—
679C2×C4×C73—21no—
680C2×C4×C73—21no—
681C2×C4×C73—21no—
682C2×C4×C73—21no—
683C2×C4×C73—21no—
684C2×C4×C73—21no—
685C2×C4×C73—21no—
686C2×C4×C73—21no—
687C2×C4×C73—21no—
688C2×C4×C73—21no—
689C2×C4×C73—21no—
690C2×C4×C73—21no—
691C2×C4×C73—21no—
692C2×C4×C73—21no—
693C2×C4×C73—44no—
694C2×C4×C73—44no—
695C2×C4×C73—44no—
696C2×C4×C73—44no—
697C2×C4×C73—82no—
698C2×C4×C73—82no—
699C2×C4×C73—82no—
700C2×C4×C73—82no—
701C2×C4×C73C22×D412yes—
702C2×C4×C73C22×D412yes—
703C2×C4×C73C22×D412yes—
704C2×C4×C73C22×D412yes—
705C2×C4×C73C22×D412yes—
706C2×C4×C73C22×D412yes—
707C2×C4×C73C2×#4112yes—
708C2×C4×C73C2×#4112yes—
709C2×C4×C73C2×#4112yes—
710C2×C4×C73C2×#4112yes—
711C22×C73—22no—
712C22×C73—22no—
713C22×C73—22no—
714C22×C73—22no—
715C22×C73—22no—
716C22×C73—22no—
717C22×C73—22no—
718C22×C73—22no—
719C22×C73—22no—
720C22×C73—41no—
721C22×C73—41no—
722C22×C73—41no—
723C22×C73—41no—
724C22×C73—41no—
725C22×C73—41no—
726C22×C73—41no—
727C22×C73—41no—
728C22×C73—41no—
729C22×C73—41no—
730C22×C73—41no—
731C22×C73—41no—
732C22×C73—41no—
733C22×C73—41no—
734C22×C73—41no—
735C22×C73—41no—
736C22×C73—41no—
737C22×C73—41no—
738C22×C73—41no—
739C22×C73—41no—
740C22×C73—41no—
741C22×C73—41no—
742C22×C73—41no—
743C22×C73—41no—
744C22×C73—41no—
745C22×C73—41no—
746C22×C73—88no—
747C22×C73C23×D411yescharacteristic
748C22×C73C22×#4111yescharacteristic
749C22×C73C22×#4111yescharacteristic
750C22×C73#58511yescharacteristic
751C22×C73#58511yescharacteristic
752C22×C73#58511yescharacteristic
753C22×C73#58511yescharacteristic
754C4×C73—22no—
755C4×C73—22no—
756C4×C73—22no—
757C4×C73—22no—
758C4×C73—22no—
759C4×C73—22no—
760C4×C73—22no—
761C4×C73—22no—
762C4×C73—22no—
763C4×C73—22no—
764C4×C73—41no—
765C4×C73—41no—
766C4×C73—41no—
767C4×C73—41no—
768C4×C73—41no—
769C4×C73—41no—
770C4×C73—41no—
771C4×C73—41no—
772C4×C73—41no—
773C4×C73—41no—
774C4×C73—41no—
775C4×C73—41no—
776C4×C73—41no—
777C4×C73—41no—
778C4×C73—41no—
779C4×C73—41no—
780#59845C7311yesmaximal, characteristic, direct product factor, Sylow
781C2×C73—42no—
782C2×C73—42no—
783C2×C73—42no—
784C2×C73—81no—
785C2×C73—81no—
786C2×C73D4×#4111yescharacteristic
787C2×C73D4×#4111yescharacteristic
788C2×C73#347511yescharacteristic
789C2×C73#350011yescharacteristic
790C2×C73#351011yescharacteristic
791C2×C73#352111yescharacteristic
792C2×C73#356811yescharacteristic
793C2×#556C2×C7311yescharacteristic, complemented
794C2×#551C2×C7311yescharacteristic, complemented
795#2723C2×C7311yescharacteristic, complemented
796#2698C2×C7311yescharacteristic, complemented
797#2674C2×C7311yescharacteristic, complemented
798#2670C2×C7311yescharacteristic
799#2599C2×C7311yescharacteristic, complemented
800#2598C2×C7311yescharacteristic, complemented
801#2560C2×C7311yescharacteristic, complemented
802#2557C2×C7311yescharacteristic, complemented
803#2554C2×C7311yescharacteristic, complemented
804#2521C2×C7311yescharacteristic, complemented
805#2521C2×C7311yescharacteristic, complemented
806#2492C2×C7311yescharacteristic, complemented
807#2480C2×C7311yescharacteristic, complemented
808#2477C2×C7311yescharacteristic, complemented
809#2472C2×C7311yescharacteristic, complemented
810#2472C2×C7311yescharacteristic, complemented
811#2470C2×C7311yescharacteristic, complemented
812#2467C2×C7311yescharacteristic, complemented
813#2465C2×C7311yescharacteristic, complemented
814#2461C2×C7311yescharacteristic, complemented
815#2459C2×C7311yescharacteristic, complemented
816#2458C2×C7311yescharacteristic, complemented
817#2367C2×C7311yescharacteristic, complemented
818#2362C2×C7311yescharacteristic, complemented
819#2358C2×C7311yescharacteristic, complemented
820#2342C2×C7311yescharacteristic, complemented
821C4×#126C2×C7311yescharacteristic, complemented
822C4×#124C2×C7311yescharacteristic, complemented
823#2293C2×C7311yescharacteristic, complemented
824C73#5984511yescharacteristic, direct product factor, Sylow
825#556—28no—
826#551—28no—
827C2×C4⋊Q8C22×C7311yescharacteristic, complemented
828C2×#126C22×C7311yescharacteristic
829C2×#126C22×C7311yescharacteristic
830C2×#126C22×C7311yescharacteristic
831C2×#126C22×C7311yescharacteristic, complemented
832C2×#126C22×C7311yescharacteristic, complemented
833C2×#124C22×C7311yescharacteristic
834C2×#124C22×C7311yescharacteristic
835C2×#124C22×C7311yescharacteristic
836C2×#124C22×C7311yescharacteristic
837C2×#124C22×C7311yescharacteristic
838C2×#123C22×C7311yescharacteristic
839C2×#123C22×C7311yescharacteristic
840C2×#123C22×C7311yescharacteristic
841C2×C22⋊Q8C22×C7311yescharacteristic
842C2×C22⋊Q8C22×C7311yescharacteristic
843C2×C22⋊Q8C22×C7311yescharacteristic
844C2×C22⋊Q8C22×C7311yescharacteristic
845C2×C22⋊Q8C22×C7311yescharacteristic, complemented
846C2×#120C22×C7311yescharacteristic
847C2×#120C22×C7311yescharacteristic
848C2×C4×Q8C22×C7311yescharacteristic, complemented
849C2×C4×Q8C22×C7311yescharacteristic, complemented
850C2×C4×Q8C22×C7311yescharacteristic, complemented
851C2×C4×D4C22×C7311yescharacteristic
852C2×C4×D4C22×C7311yescharacteristic
853C2×C4×D4C22×C7311yescharacteristic
854C2×C4×D4C22×C7311yescharacteristic
855C2×#117C22×C7311yescharacteristic
856C2×#117C22×C7311yescharacteristic
857C2×#117C22×C7311yescharacteristic
858C2×#117C22×C7311yescharacteristic, complemented
859C22×C22⋊C4C22×C7311yescharacteristic
860C22×C22⋊C4C22×C7311yescharacteristic
861C22×C22⋊C4C22×C7311yescharacteristic
862#400C22×C7311yescharacteristic, complemented
863#400C22×C7311yescharacteristic, complemented
864#399C22×C7311yescharacteristic, complemented
865#399C22×C7311yescharacteristic, complemented
866#398C22×C7311yescharacteristic, complemented
867#398C22×C7311yescharacteristic, complemented
868#397C22×C7311yescharacteristic
869#397C22×C7311yescharacteristic
870#397C22×C7311yescharacteristic
871#397C22×C7311yescharacteristic
872#397C22×C7311yescharacteristic
873#397C22×C7311yescharacteristic, complemented
874#396C22×C7311yescharacteristic
875#396C22×C7311yescharacteristic, complemented
876#395C22×C7311yescharacteristic, complemented
877#395C22×C7311yescharacteristic, complemented
878#395C22×C7311yescharacteristic, complemented
879#394C22×C7311yescharacteristic
880#394C22×C7311yescharacteristic
881#394C22×C7311yescharacteristic
882#394C22×C7311yescharacteristic
883#394C22×C7311yescharacteristic
884#394C22×C7311yescharacteristic
885#394C22×C7311yescharacteristic, complemented
886#393C22×C7311yescharacteristic
887#393C22×C7311yescharacteristic
888#393C22×C7311yescharacteristic
889#393C22×C7311yescharacteristic, complemented
890#393C22×C7311yescharacteristic, complemented
891#392C22×C7311yescharacteristic
892#392C22×C7311yescharacteristic
893#392C22×C7311yescharacteristic
894#391C22×C7311yescharacteristic, complemented
895#391C22×C7311yescharacteristic, complemented
896#391C22×C7311yescharacteristic, complemented
897#391C22×C7311yescharacteristic, complemented
898#391C22×C7311yescharacteristic, complemented
899#390C22×C7311yescharacteristic
900#390C22×C7311yescharacteristic
901#390C22×C7311yescharacteristic
902#390C22×C7311yescharacteristic
903#390C22×C7311yescharacteristic
904#390C22×C7311yescharacteristic, complemented
905#389C22×C7311yescharacteristic, complemented
906#389C22×C7311yescharacteristic, complemented
907#389C22×C7311yescharacteristic, complemented
908#388C22×C7311yescharacteristic
909#388C22×C7311yescharacteristic
910#388C22×C7311yescharacteristic
911#388C22×C7311yescharacteristic
912#388C22×C7311yescharacteristic
913#388C22×C7311yescharacteristic
914#388C22×C7311yescharacteristic
915#388C22×C7311yescharacteristic
916#388C22×C7311yescharacteristic
917#388C22×C7311yescharacteristic
918#388C22×C7311yescharacteristic
919#388C22×C7311yescharacteristic
920#388C22×C7311yescharacteristic
921#388C22×C7311yescharacteristic
922#388C22×C7311yescharacteristic
923#388C22×C7311yescharacteristic, complemented
924#388C22×C7311yescharacteristic, complemented
925#388C22×C7311yescharacteristic, complemented
926#388C22×C7311yescharacteristic, complemented
927#388C22×C7311yescharacteristic, complemented
928#388C22×C7311yescharacteristic, complemented
929#388C22×C7311yescharacteristic, complemented
930#388C22×C7311yescharacteristic, complemented
931#388C22×C7311yescharacteristic, complemented
932#388C22×C7311yescharacteristic, complemented
933#387C22×C7311yescharacteristic, complemented
934#387C22×C7311yescharacteristic, complemented
935#387C22×C7311yescharacteristic, complemented
936#387C22×C7311yescharacteristic, complemented
937#387C22×C7311yescharacteristic, complemented
938#387C22×C7311yescharacteristic, complemented
939#387C22×C7311yescharacteristic, complemented
940#387C22×C7311yescharacteristic, complemented
941#387C22×C7311yescharacteristic, complemented
942#386C22×C7311yescharacteristic
943#386C22×C7311yescharacteristic
944#386C22×C7311yescharacteristic
945#386C22×C7311yescharacteristic
946#386C22×C7311yescharacteristic
947#386C22×C7311yescharacteristic
948#386C22×C7311yescharacteristic
949#386C22×C7311yescharacteristic, complemented
950#386C22×C7311yescharacteristic, complemented
951#385C22×C7311yescharacteristic
952#385C22×C7311yescharacteristic
953#385C22×C7311yescharacteristic
954#385C22×C7311yescharacteristic
955#385C22×C7311yescharacteristic
956#385C22×C7311yescharacteristic
957#385C22×C7311yescharacteristic, complemented
958#383C22×C7311yescharacteristic, complemented
959#382C22×C7311yescharacteristic, complemented
960#381C22×C7311yescharacteristic
961#380C22×C7311yescharacteristic
962#380C22×C7311yescharacteristic
963#379C22×C7311yescharacteristic
964#379C22×C7311yescharacteristic
965C4×C4⋊C4C22×C7311yescharacteristic, complemented
966C4×C4⋊C4C22×C7311yescharacteristic, complemented
967C4×C4⋊C4C22×C7311yescharacteristic, complemented
968C4×C4⋊C4C22×C7311yescharacteristic, complemented
969C4×C4⋊C4C22×C7311yescharacteristic, complemented
970C4×C22⋊C4C22×C7311yescharacteristic
971C4×C22⋊C4C22×C7311yescharacteristic
972C4×C22⋊C4C22×C7311yescharacteristic
973C4×C22⋊C4C22×C7311yescharacteristic
974C4×C22⋊C4C22×C7311yescharacteristic
975C4×C22⋊C4C22×C7311yescharacteristic
976C4×C22⋊C4C22×C7311yescharacteristic
977C4×C22⋊C4C22×C7311yescharacteristic
978C4×C22⋊C4C22×C7311yescharacteristic, complemented
979C4×C22⋊C4C22×C7311yescharacteristic, complemented
980C4×C22⋊C4C22×C7311yescharacteristic, complemented
981C43C22×C7311yescharacteristic, complemented
982C25C23×C7311yescharacteristic
983C22×Q8C23×C7311yescharacteristic
984C22×Q8C23×C7311yescharacteristic
985C22×Q8C23×C7311yescharacteristic
986C22×Q8C23×C7311yescharacteristic
987C22×D4C23×C7311yescharacteristic
988C22×D4C23×C7311yescharacteristic
989C22×D4C23×C7311yescharacteristic
990C22×D4C23×C7311yescharacteristic
991C22×D4C23×C7311yescharacteristic
992C22×D4C23×C7311yescharacteristic
993C22×D4C23×C7311yescharacteristic
994C23×C4C23×C7311yescharacteristic
995C23×C4C23×C7311yescharacteristic
996C23×C4C23×C7311yescharacteristic
997C23×C4C23×C7311yescharacteristic
998C23×C4C23×C7311yescharacteristic
999C23×C4C23×C7311yescharacteristic
1000C23×C4C23×C7311yescharacteristic
1001C23×C4C23×C7311yescharacteristic
1002C4⋊Q8—24no—
1003#126—24no—
1004#126—24no—
1005#126—24no—
1006#126—24no—
1007#126D4×C7318yescomplemented
1008#124—24no—
1009#124—24no—
1010#124—24no—
1011#124—24no—
1012#124—24no—
1013#123—24no—
1014#123—24no—
1015#123—24no—
1016C22⋊Q8—24no—
1017C22⋊Q8—24no—
1018C22⋊Q8—24no—
1019C22⋊Q8—24no—
1020C22⋊Q8—24no—
1021#120—24no—
1022#120—24no—
1023C4×Q8—24no—
1024C4×Q8—24no—
1025C4×Q8—24no—
1026C4×D4—24no—
1027C4×D4—24no—
1028C4×D4—24no—
1029C4×D4—24no—
1030#117—24no—
1031#117—24no—
1032#117—24no—
1033#117—24no—
1034C2×C4⋊C4C23×C7311yescharacteristic
1035C2×C4⋊C4C23×C7311yescharacteristic
1036C2×C4⋊C4C23×C7311yescharacteristic
1037C2×C4⋊C4C23×C7311yescharacteristic
1038C2×C4⋊C4C23×C7311yescharacteristic
1039C2×C4⋊C4C23×C7311yescharacteristic
1040C2×C4⋊C4C23×C7311yescharacteristic
1041C2×C4⋊C4C23×C7311yescharacteristic
1042C2×C4⋊C4C23×C7311yescharacteristic
1043C2×C4⋊C4C23×C7311yescharacteristic
1044C2×C4⋊C4C23×C7311yescharacteristic
1045C2×C4⋊C4C23×C7311yescharacteristic
1046C2×C4⋊C4C23×C7311yescharacteristic
1047C2×C4⋊C4C23×C7311yescharacteristic
1048C2×C4⋊C4C23×C7311yescharacteristic
1049C2×C4⋊C4C23×C7311yescharacteristic
1050C2×C4⋊C4C23×C7311yescharacteristic
1051C2×C4⋊C4C23×C7311yescharacteristic
1052C2×C4⋊C4C23×C7311yescharacteristic
1053C2×C4⋊C4C23×C7311yescharacteristic
1054C2×C4⋊C4C23×C7311yescharacteristic
1055C2×C4⋊C4C23×C7311yescharacteristic
1056C2×C4⋊C4C23×C7311yescharacteristic
1057C2×C4⋊C4C23×C7311yescharacteristic
1058C2×C4⋊C4C23×C7311yescharacteristic
1059C2×C4⋊C4C23×C7311yescharacteristic
1060C2×C4⋊C4C23×C7311yescharacteristic
1061C2×C4⋊C4C23×C7311yescharacteristic
1062C2×C4⋊C4C23×C7311yescharacteristic
1063C2×C22⋊C4—24no—
1064C2×C22⋊C4—24no—
1065C2×C22⋊C4—24no—
1066C2×C22⋊C4C23×C7311yescharacteristic
1067C2×C22⋊C4C23×C7311yescharacteristic
1068C2×C22⋊C4C23×C7311yescharacteristic
1069C2×C22⋊C4C23×C7311yescharacteristic
1070C2×C22⋊C4C23×C7311yescharacteristic
1071C2×C22⋊C4C23×C7311yescharacteristic
1072C2×C22⋊C4C23×C7311yescharacteristic
1073C2×C22⋊C4C23×C7311yescharacteristic
1074C2×C22⋊C4C23×C7311yescharacteristic
1075C2×C22⋊C4C23×C7311yescharacteristic
1076C2×C22⋊C4C23×C7311yescharacteristic
1077C2×C22⋊C4C23×C7311yescharacteristic
1078C2×C22⋊C4C23×C7311yescharacteristic
1079C2×C22⋊C4C23×C7311yescharacteristic
1080C2×C22⋊C4C23×C7311yescharacteristic
1081C2×C22⋊C4C23×C7311yescharacteristic
1082C2×C22⋊C4C23×C7311yescharacteristic
1083C2×C22⋊C4C23×C7311yescharacteristic
1084C2×C22⋊C4C23×C7311yescharacteristic
1085C2×C22⋊C4C23×C7311yescharacteristic
1086C2×C22⋊C4C23×C7311yescharacteristic
1087C2×C22⋊C4C23×C7311yescharacteristic
1088C2×C22⋊C4C23×C7311yescharacteristic
1089C2×C22⋊C4C23×C7311yescharacteristic
1090C2×C22⋊C4C23×C7311yescharacteristic
1091C2×C22⋊C4C23×C7311yescharacteristic
1092C2×C22⋊C4C23×C7311yescharacteristic
1093C2×C22⋊C4C23×C7311yescharacteristic
1094C2×C22⋊C4C23×C7311yescharacteristic
1095C2×C22⋊C4C23×C7311yescharacteristic
1096C2×C22⋊C4C23×C7311yescharacteristic
1097C2×C22⋊C4C23×C7311yescharacteristic
1098C2×C22⋊C4C23×C7311yescharacteristic
1099C2×C22⋊C4C23×C7311yescharacteristic
1100C2×C22⋊C4C23×C7311yescharacteristic
1101C2×C22⋊C4C23×C7311yescharacteristic
1102C2×C22⋊C4C23×C7311yescharacteristic
1103C2×C22⋊C4C23×C7311yescharacteristic
1104C2×C22⋊C4C23×C7311yescharacteristic
1105C2×C22⋊C4C23×C7311yescharacteristic
1106C2×C22⋊C4C23×C7311yescharacteristic
1107C2×C22⋊C4C23×C7311yescharacteristic
1108C2×C22⋊C4C23×C7311yescharacteristic
1109C2×C22⋊C4C23×C7311yescharacteristic
1110C2×C22⋊C4C23×C7311yescharacteristic
1111C2×C22⋊C4C23×C7311yescharacteristic
1112C2×C22⋊C4C23×C7311yescharacteristic
1113C2×C22⋊C4C23×C7311yescharacteristic
1114C2×C22⋊C4C23×C7311yescharacteristic
1115C2×C22⋊C4C23×C7311yescharacteristic
1116C2×C42C23×C7311yescharacteristic
1117C2×C42C23×C7311yescharacteristic
1118C2×C42C23×C7311yescharacteristic
1119C2×C42C23×C7311yescharacteristic
1120C2×C42C23×C7311yescharacteristic
1121C2×C42C23×C7311yescharacteristic
1122C2×C42C23×C7311yescharacteristic
1123C2×C42C23×C7311yescharacteristic
1124C2×C42C23×C7311yescharacteristic
1125C2×C42C23×C7311yescharacteristic
1126C2×C42C23×C7311yescharacteristic
1127C2×C42C23×C7311yescharacteristic
1128C2×C42C23×C7311yescharacteristic
1129C2×C42C23×C7311yescharacteristic
1130C2×C42C23×C7311yescharacteristic
1131C2×C42C23×C7311yescharacteristic
1132C2×C42C23×C7311yescharacteristic
1133C2×C42C23×C7311yescharacteristic
1134#95C23×C7311yescharacteristic
1135#95C23×C7311yescharacteristic
1136#95C23×C7311yescharacteristic
1137#95C23×C7311yescharacteristic
1138#95C23×C7311yescharacteristic
1139#95C23×C7311yescharacteristic
1140#95C23×C7311yescharacteristic
1141#95C23×C7311yescharacteristic
1142#95C23×C7311yescharacteristic
1143#95C23×C7311yescharacteristic
1144#95C23×C7311yescharacteristic
1145#95C23×C7311yescharacteristic
1146#95C23×C7311yescharacteristic
1147#95C23×C7311yescharacteristic
1148#95C23×C7311yescharacteristic
1149#95C23×C7311yescharacteristic
1150#95C23×C7311yescharacteristic
1151#95C23×C7311yescharacteristic
1152#95C23×C7311yescharacteristic
1153#95C23×C7311yescharacteristic
1154#95C23×C7311yescharacteristic
1155#95C23×C7311yescharacteristic
1156#95C23×C7311yescharacteristic
1157#95C23×C7311yescharacteristic
1158#95C23×C7311yescharacteristic
1159#95C23×C7311yescharacteristic
1160#95C23×C7311yescharacteristic
1161#95C23×C7311yescharacteristic
1162#95C23×C7311yescharacteristic
1163#95C23×C7311yescharacteristic
1164#95C23×C7311yescharacteristic
1165#95C23×C7311yescharacteristic
1166#95C23×C7311yescharacteristic
1167#95C23×C7311yescharacteristic
1168#95C23×C7311yescharacteristic
1169#95C23×C7311yescharacteristic
1170#95C23×C7311yescharacteristic
1171#95C23×C7311yescharacteristic
1172C24—22no—
1173C24—22no—
1174C24—22no—
1175C24—41no—
1176C24—41no—
1177C24—41no—
1178C24—41no—
1179C24C24×C7311yescharacteristic
1180C24C24×C7311yescharacteristic
1181C24C24×C7311yescharacteristic
1182C24C24×C7311yescharacteristic
1183C24C24×C7311yescharacteristic
1184C2×Q8—22no—
1185C2×Q8—22no—
1186C2×Q8—22no—
1187C2×Q8—22no—
1188C2×Q8—22no—
1189C2×Q8—22no—
1190C2×Q8—22no—
1191C2×Q8—41no—
1192C2×Q8—41no—
1193C2×Q8—41no—
1194C2×Q8—41no—
1195C2×Q8—41no—
1196C2×D4—22no—
1197C2×D4—22no—
1198C2×D4—22no—
1199C2×D4—22no—
1200C2×D4—22no—
1201C2×D4—22no—
1202C2×D4—22no—
1203C2×D4—22no—
1204C2×D4—22no—
1205C2×D4—22no—
1206C2×D4—41no—
1207C2×D4—41no—
1208C2×D4—41no—
1209C2×D4—41no—
1210C2×D4—41no—
1211C2×D4—41no—
1212C2×D4—41no—
1213C2×D4—41no—
1214C2×D4—41no—
1215C2×D4—41no—
1216C2×D4—41no—
1217C22×C4—22no—
1218C22×C4—22no—
1219C22×C4—22no—
1220C22×C4—22no—
1221C22×C4—22no—
1222C22×C4—22no—
1223C22×C4—22no—
1224C22×C4—22no—
1225C22×C4—22no—
1226C22×C4—22no—
1227C22×C4—22no—
1228C22×C4—22no—
1229C22×C4—41no—
1230C22×C4—41no—
1231C22×C4—41no—
1232C22×C4—41no—
1233C22×C4—41no—
1234C22×C4—41no—
1235C22×C4—41no—
1236C22×C4—41no—
1237C22×C4—41no—
1238C22×C4—41no—
1239C22×C4—41no—
1240C22×C4—41no—
1241C22×C4C24×C7311yescharacteristic
1242C22×C4C24×C7311yescharacteristic
1243C22×C4C24×C7311yescharacteristic
1244C22×C4C24×C7311yescharacteristic
1245C22×C4C24×C7311yescharacteristic
1246C22×C4C24×C7311yescharacteristic
1247C22×C4C24×C7311yescharacteristic
1248C22×C4C24×C7311yescharacteristic
1249C22×C4C24×C7311yescharacteristic
1250C22×C4C24×C7311yescharacteristic
1251C22×C4C24×C7311yescharacteristic
1252C22×C4C24×C7311yescharacteristic
1253C22×C4C24×C7311yescharacteristic
1254C22×C4C24×C7311yescharacteristic
1255C22×C4C24×C7311yescharacteristic
1256C22×C4C24×C7311yescharacteristic
1257C22×C4C24×C7311yescharacteristic
1258C22×C4C24×C7311yescharacteristic
1259C22×C4C24×C7311yescharacteristic
1260C22×C4C24×C7311yescharacteristic
1261C22×C4C24×C7311yescharacteristic
1262C22×C4C24×C7311yescharacteristic
1263C22×C4C24×C7311yescharacteristic
1264C22×C4C24×C7311yescharacteristic
1265C22×C4C24×C7311yescharacteristic
1266C22×C4C24×C7311yescharacteristic
1267C4⋊C4—22no—
1268C4⋊C4—22no—
1269C4⋊C4—22no—
1270C4⋊C4—22no—
1271C4⋊C4—22no—
1272C4⋊C4—22no—
1273C4⋊C4—22no—
1274C4⋊C4—22no—
1275C4⋊C4—22no—
1276C4⋊C4—22no—
1277C4⋊C4—22no—
1278C4⋊C4—22no—
1279C4⋊C4—22no—
1280C4⋊C4—22no—
1281C4⋊C4—22no—
1282C4⋊C4—22no—
1283C4⋊C4—22no—
1284C4⋊C4—22no—
1285C4⋊C4—41no—
1286C4⋊C4—41no—
1287C4⋊C4—41no—
1288C4⋊C4—41no—
1289C4⋊C4—41no—
1290C4⋊C4—41no—
1291C4⋊C4—41no—
1292C4⋊C4—41no—
1293C4⋊C4C2×D4×C7314yes—
1294C4⋊C4C2×D4×C7314yes—
1295C4⋊C4C2×D4×C7314yes—
1296C22⋊C4—22no—
1297C22⋊C4—22no—
1298C22⋊C4—22no—
1299C22⋊C4—22no—
1300C22⋊C4—22no—
1301C22⋊C4—22no—
1302C22⋊C4—22no—
1303C22⋊C4—22no—
1304C22⋊C4—22no—
1305C22⋊C4—22no—
1306C22⋊C4—22no—
1307C22⋊C4—22no—
1308C22⋊C4—22no—
1309C22⋊C4—22no—
1310C22⋊C4—22no—
1311C22⋊C4—22no—
1312C22⋊C4—22no—
1313C22⋊C4—22no—
1314C22⋊C4—22no—
1315C22⋊C4—22no—
1316C22⋊C4—22no—
1317C22⋊C4—22no—
1318C22⋊C4—22no—
1319C22⋊C4—22no—
1320C22⋊C4—22no—
1321C22⋊C4—22no—
1322C22⋊C4—22no—
1323C22⋊C4—22no—
1324C22⋊C4—22no—
1325C22⋊C4—22no—
1326C22⋊C4—22no—
1327C22⋊C4—41no—
1328C22⋊C4—41no—
1329C22⋊C4—41no—
1330C22⋊C4—41no—
1331C22⋊C4—41no—
1332C22⋊C4—41no—
1333C22⋊C4—41no—
1334C22⋊C4—41no—
1335C22⋊C4—41no—
1336C22⋊C4—41no—
1337C22⋊C4—41no—
1338C22⋊C4—41no—
1339C22⋊C4—41no—
1340C22⋊C4—41no—
1341C22⋊C4C2×D4×C7314yes—
1342C22⋊C4C2×D4×C7314yes—
1343C22⋊C4C2×D4×C7314yes—
1344C22⋊C4#41×C7314yes—
1345C22⋊C4#41×C7314yes—
1346C42—22no—
1347C42—22no—
1348C42—22no—
1349C42—22no—
1350C42—22no—
1351C42—22no—
1352C42—22no—
1353C42—22no—
1354C42—22no—
1355C42—22no—
1356C42—22no—
1357C42—41no—
1358C42—41no—
1359C42—41no—
1360C42—41no—
1361C42—41no—
1362C42—41no—
1363C42C2×D4×C7314yes—
1364C23—21no—
1365C23—21no—
1366C23—21no—
1367C23—21no—
1368C23—21no—
1369C23—21no—
1370C23—21no—
1371C23—21no—
1372C23—21no—
1373C23—21no—
1374C23—21no—
1375C23—21no—
1376C23—21no—
1377C23—21no—
1378C23—21no—
1379C23—21no—
1380C23—21no—
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—44no—
1397C23—44no—
1398C23—44no—
1399C23—82no—
1400C23—82no—
1401C23—82no—
1402C23—82no—
1403C23C22×D4×C7312yes—
1404C23C2×#41×C7312yes—
1405C23C2×#41×C7312yes—
1406C23C25×C7311yescharacteristic
1407Q8—44no—
1408Q8—44no—
1409Q8—44no—
1410Q8—82no—
1411D4—44no—
1412D4—44no—
1413D4—44no—
1414D4—44no—
1415D4—82no—
1416D4—82no—
1417D4—82no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—44no—
1487C2×C4—44no—
1488C2×C4—44no—
1489C2×C4—44no—
1490C2×C4—82no—
1491C2×C4—82no—
1492C2×C4—82no—
1493C2×C4—82no—
1494C2×C4C22×D4×C7312yes—
1495C2×C4C22×D4×C7312yes—
1496C2×C4C22×D4×C7312yes—
1497C2×C4C22×D4×C7312yes—
1498C2×C4C22×D4×C7312yes—
1499C2×C4C22×D4×C7312yes—
1500C2×C4C2×#41×C7312yes—
1501C2×C4C2×#41×C7312yes—
1502C2×C4C2×#41×C7312yes—
1503C2×C4C2×#41×C7312yes—
1504C22—22no—
1505C22—22no—
1506C22—22no—
1507C22—22no—
1508C22—22no—
1509C22—22no—
1510C22—22no—
1511C22—22no—
1512C22—22no—
1513C22—41no—
1514C22—41no—
1515C22—41no—
1516C22—41no—
1517C22—41no—
1518C22—41no—
1519C22—41no—
1520C22—41no—
1521C22—41no—
1522C22—41no—
1523C22—41no—
1524C22—41no—
1525C22—41no—
1526C22—41no—
1527C22—41no—
1528C22—41no—
1529C22—41no—
1530C22—41no—
1531C22—41no—
1532C22—41no—
1533C22—41no—
1534C22—41no—
1535C22—41no—
1536C22—41no—
1537C22—41no—
1538C22—41no—
1539C22—88no—
1540C22C23×D4×C7311yescharacteristic
1541C22C22×#41×C7311yescharacteristic
1542C22C22×#41×C7311yescharacteristic
1543C22#585×C7311yescharacteristic
1544C22#585×C7311yescharacteristic
1545C22#585×C7311yescharacteristic
1546C22#585×C7311yescharacteristic
1547C4—22no—
1548C4—22no—
1549C4—22no—
1550C4—22no—
1551C4—22no—
1552C4—22no—
1553C4—22no—
1554C4—22no—
1555C4—22no—
1556C4—22no—
1557C4—41no—
1558C4—41no—
1559C4—41no—
1560C4—41no—
1561C4—41no—
1562C4—41no—
1563C4—41no—
1564C4—41no—
1565C4—41no—
1566C4—41no—
1567C4—41no—
1568C4—41no—
1569C4—41no—
1570C4—41no—
1571C4—41no—
1572C4—41no—
1573C2—42no—
1574C2—42no—
1575C2—42no—
1576C2—81no—
1577C2—81no—
1578C2D4×#41×C7311yescharacteristic
1579C2D4×#41×C7311yescharacteristic
1580C2C73×#347511yescharacteristic
1581C2C73×#350011yescharacteristic
1582C2C73×#351011yescharacteristic
1583C2C73×#352111yescharacteristic
1584C2C73×#356811yescharacteristic
subgroupG/H
center, socleC23×C73C25
commutator, Frattini, cosocleC23C25×C73
prime radicalC73×#2670C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#556×C73C2semidirect
2. C2×#551×C73C2semidirect
3. C73×#2723C2semidirect
4. C73×#2698C2semidirect
5. C73×#2674C2semidirect
7. C73×#2599C2semidirect
8. C73×#2598C2semidirect
9. C73×#2560C2semidirect
10. C73×#2557C2semidirect
11. C73×#2554C2semidirect
12. C73×#2521C2semidirect
13. C73×#2521C2semidirect
14. C73×#2492C2semidirect
15. C73×#2480C2semidirect
16. C73×#2477C2semidirect
17. C73×#2472C2semidirect
18. C73×#2472C2semidirect
19. C73×#2470C2semidirect
20. C73×#2467C2semidirect
21. C73×#2465C2semidirect
22. C73×#2461C2semidirect
23. C73×#2459C2semidirect
24. C73×#2458C2semidirect
25. C73×#2367C2semidirect
26. C73×#2362C2semidirect
27. C73×#2358C2semidirect
28. C73×#2342C2semidirect
29. C4×#126×C73C2semidirect
30. C4×#124×C73C2semidirect
31. C73×#2293C2semidirect
34. C2×C4⋊Q8×C73C22semidirect
38. C2×#126×C73C22semidirect
39. C2×#126×C73C22semidirect
52. C2×C22⋊Q8×C73C22semidirect
55. C2×C4×Q8×C73C22semidirect
56. C2×C4×Q8×C73C22semidirect
57. C2×C4×Q8×C73C22semidirect
65. C2×#117×C73C22semidirect
69. #400×C73C22semidirect
70. #400×C73C22semidirect
71. #399×C73C22semidirect
72. #399×C73C22semidirect
73. #398×C73C22semidirect
74. #398×C73C22semidirect
80. #397×C73C22semidirect
82. #396×C73C22semidirect
83. #395×C73C22semidirect
84. #395×C73C22semidirect
85. #395×C73C22semidirect
92. #394×C73C22semidirect
96. #393×C73C22semidirect
97. #393×C73C22semidirect
101. #391×C73C22semidirect
102. #391×C73C22semidirect
103. #391×C73C22semidirect
104. #391×C73C22semidirect
105. #391×C73C22semidirect
111. #390×C73C22semidirect
112. #389×C73C22semidirect
113. #389×C73C22semidirect
114. #389×C73C22semidirect
130. #388×C73C22semidirect
131. #388×C73C22semidirect
132. #388×C73C22semidirect
133. #388×C73C22semidirect
134. #388×C73C22semidirect
135. #388×C73C22semidirect
136. #388×C73C22semidirect
137. #388×C73C22semidirect
138. #388×C73C22semidirect
139. #388×C73C22semidirect
140. #387×C73C22semidirect
141. #387×C73C22semidirect
142. #387×C73C22semidirect
143. #387×C73C22semidirect
144. #387×C73C22semidirect
145. #387×C73C22semidirect
146. #387×C73C22semidirect
147. #387×C73C22semidirect
148. #387×C73C22semidirect
156. #386×C73C22semidirect
157. #386×C73C22semidirect
164. #385×C73C22semidirect
165. #383×C73C22semidirect
166. #382×C73C22semidirect
172. C4×C4⋊C4×C73C22semidirect
173. C4×C4⋊C4×C73C22semidirect
174. C4×C4⋊C4×C73C22semidirect
175. C4×C4⋊C4×C73C22semidirect
176. C4×C4⋊C4×C73C22semidirect
185. C4×C22⋊C4×C73C22semidirect
186. C4×C22⋊C4×C73C22semidirect
187. C4×C22⋊C4×C73C22semidirect
188. C43×C73C22semidirect
214. #126×C73D4semidirect
780. #59845C73direct (N × H)
793. C2×#556C2×C73semidirect
794. C2×#551C2×C73semidirect
795. #2723C2×C73semidirect
796. #2698C2×C73semidirect
797. #2674C2×C73semidirect
799. #2599C2×C73semidirect
800. #2598C2×C73semidirect
801. #2560C2×C73semidirect
802. #2557C2×C73semidirect
803. #2554C2×C73semidirect
804. #2521C2×C73semidirect
805. #2521C2×C73semidirect
806. #2492C2×C73semidirect
807. #2480C2×C73semidirect
808. #2477C2×C73semidirect
809. #2472C2×C73semidirect
810. #2472C2×C73semidirect
811. #2470C2×C73semidirect
812. #2467C2×C73semidirect
813. #2465C2×C73semidirect
814. #2461C2×C73semidirect
815. #2459C2×C73semidirect
816. #2458C2×C73semidirect
817. #2367C2×C73semidirect
818. #2362C2×C73semidirect
819. #2358C2×C73semidirect
820. #2342C2×C73semidirect
821. C4×#126C2×C73semidirect
822. C4×#124C2×C73semidirect
823. #2293C2×C73semidirect
824. C73#59845direct (N × H)
827. C2×C4⋊Q8C22×C73semidirect
831. C2×#126C22×C73semidirect
832. C2×#126C22×C73semidirect
845. C2×C22⋊Q8C22×C73semidirect
848. C2×C4×Q8C22×C73semidirect
849. C2×C4×Q8C22×C73semidirect
850. C2×C4×Q8C22×C73semidirect
858. C2×#117C22×C73semidirect
862. #400C22×C73semidirect
863. #400C22×C73semidirect
864. #399C22×C73semidirect
865. #399C22×C73semidirect
866. #398C22×C73semidirect
867. #398C22×C73semidirect
873. #397C22×C73semidirect
875. #396C22×C73semidirect
876. #395C22×C73semidirect
877. #395C22×C73semidirect
878. #395C22×C73semidirect
885. #394C22×C73semidirect
889. #393C22×C73semidirect
890. #393C22×C73semidirect
894. #391C22×C73semidirect
895. #391C22×C73semidirect
896. #391C22×C73semidirect
897. #391C22×C73semidirect
898. #391C22×C73semidirect
904. #390C22×C73semidirect
905. #389C22×C73semidirect
906. #389C22×C73semidirect
907. #389C22×C73semidirect
923. #388C22×C73semidirect
924. #388C22×C73semidirect
925. #388C22×C73semidirect
926. #388C22×C73semidirect
927. #388C22×C73semidirect
928. #388C22×C73semidirect
929. #388C22×C73semidirect
930. #388C22×C73semidirect
931. #388C22×C73semidirect
932. #388C22×C73semidirect
933. #387C22×C73semidirect
934. #387C22×C73semidirect
935. #387C22×C73semidirect
936. #387C22×C73semidirect
937. #387C22×C73semidirect
938. #387C22×C73semidirect
939. #387C22×C73semidirect
940. #387C22×C73semidirect
941. #387C22×C73semidirect
949. #386C22×C73semidirect
950. #386C22×C73semidirect
957. #385C22×C73semidirect
958. #383C22×C73semidirect
959. #382C22×C73semidirect
965. C4×C4⋊C4C22×C73semidirect
966. C4×C4⋊C4C22×C73semidirect
967. C4×C4⋊C4C22×C73semidirect
968. C4×C4⋊C4C22×C73semidirect
969. C4×C4⋊C4C22×C73semidirect
978. C4×C22⋊C4C22×C73semidirect
979. C4×C22⋊C4C22×C73semidirect
980. C4×C22⋊C4C22×C73semidirect
981. C43C22×C73semidirect
1007. #126D4×C73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#556×C732
C2×#551×C732
C73×#27232
C73×#26982
C73×#26742
C73×#26702
C73×#25992
C73×#25982
C73×#25602
C73×#25572
C73×#25542
C73×#25212
C73×#24922
C73×#24802
C73×#24772
C73×#24722
C73×#24702
C73×#24672
C73×#24652
C73×#24612
C73×#24592
C73×#24582
C73×#23672
C73×#23622
C73×#23582
C73×#23422
C4×#126×C732
C4×#124×C732
C73×#22932
#5984573