Finite Group Databasebeta

← C73×#59840 #32969244

Subgroups — C73×#59840 #32969244

Order 18688.

2132 conjugacy classes of subgroups.

The subgroup lattice has 1476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#556×C73C211yesmaximal, characteristic, complemented
2C2×#552×C73C211yesmaximal, characteristic, complemented
3C73×#2721C211yesmaximal, characteristic, complemented
4C73×#2680C211yesmaximal, characteristic, complemented
5C73×#2677C211yesmaximal, characteristic, complemented
6C73×#2674C211yesmaximal, characteristic, complemented
7C73×#2599C211yesmaximal, characteristic, complemented
8C73×#2599C211yesmaximal, characteristic, complemented
9C73×#2560C211yesmaximal, characteristic, complemented
10C73×#2557C211yesmaximal, characteristic
11C73×#2556C211yesmaximal, characteristic, complemented
12C73×#2553C211yesmaximal, characteristic, complemented
13C73×#2550C211yesmaximal, characteristic, complemented
14C73×#2549C211yesmaximal, characteristic, complemented
15C73×#2521C211yesmaximal, characteristic, complemented
16C73×#2519C211yesmaximal, characteristic, complemented
17C73×#2479C211yesmaximal, characteristic, complemented
18C73×#2478C211yesmaximal, characteristic, complemented
19C73×#2478C211yesmaximal, characteristic, complemented
20C73×#2462C211yesmaximal, characteristic, complemented
21C73×#2462C211yesmaximal, characteristic, complemented
22C73×#2461C211yesmaximal, characteristic
23C73×#2455C211yesmaximal, characteristic
24C73×#2449C211yesmaximal, characteristic, complemented
25C73×#2362C211yesmaximal, characteristic, complemented
26C73×#2360C211yesmaximal, characteristic, complemented
27C73×#2359C211yesmaximal, characteristic, complemented
28C73×#2359C211yesmaximal, characteristic, complemented
29C4×C4⋊Q8×C73C211yesmaximal, characteristic, complemented
30C4×#126×C73C211yesmaximal, characteristic, complemented
31C73×#2293C211yesmaximal, characteristic, complemented
32#556×C73—28no—
33#552×C73—28no—
34C2×C4⋊Q8×C73C2211yescharacteristic
35C2×C4⋊Q8×C73C2211yescharacteristic
36C2×#126×C73C2211yescharacteristic
37C2×#126×C73C2211yescharacteristic
38C2×#126×C73C2211yescharacteristic
39C2×#126×C73C2211yescharacteristic
40C2×#126×C73C2211yescharacteristic
41C2×#125×C73C2211yescharacteristic
42C2×#125×C73C2211yescharacteristic
43C2×#125×C73C2211yescharacteristic
44C2×#124×C73C2211yescharacteristic
45C2×#124×C73C2211yescharacteristic
46C2×#123×C73C2211yescharacteristic
47C2×#123×C73C2211yescharacteristic
48C2×#123×C73C2211yescharacteristic
49C2×#123×C73C2211yescharacteristic
50C2×C22⋊Q8×C73C2211yescharacteristic
51C2×C22⋊Q8×C73C2211yescharacteristic
52C2×C22⋊Q8×C73C2211yescharacteristic
53C2×C22⋊Q8×C73C2211yescharacteristic
54C2×C22⋊Q8×C73C2211yescharacteristic
55C2×C22⋊Q8×C73C2211yescharacteristic
56C2×C4×Q8×C73C2211yescharacteristic
57C2×C4×Q8×C73C2211yescharacteristic
58C2×C4×Q8×C73C2211yescharacteristic
59C2×C4×Q8×C73C2211yescharacteristic
60C2×C4×D4×C73C2211yescharacteristic
61C2×C4×D4×C73C2211yescharacteristic
62C2×C4×D4×C73C2211yescharacteristic
63C2×#117×C73C2211yescharacteristic
64C2×#117×C73C2211yescharacteristic
65C2×#117×C73C2211yescharacteristic
66C2×#117×C73C2211yescharacteristic
67C2×#117×C73C2211yescharacteristic
68C22×C4⋊C4×C73C2211yescharacteristic
69#399×C73C2211yescharacteristic
70#399×C73C2211yescharacteristic
71#399×C73C2211yescharacteristic
72#399×C73C2211yescharacteristic
73#398×C73C2211yescharacteristic
74#398×C73C2211yescharacteristic
75#398×C73C2211yescharacteristic
76#398×C73C2211yescharacteristic
77#398×C73C2211yescharacteristic
78#398×C73C2211yescharacteristic
79#398×C73C2211yescharacteristic
80#398×C73C2211yescharacteristic
81#398×C73C2211yescharacteristic
82#397×C73C2211yescharacteristic
83#397×C73C2211yescharacteristic
84#397×C73C2211yescharacteristic
85#397×C73C2211yescharacteristic
86#397×C73C2211yescharacteristic
87#396×C73C2211yescharacteristic
88#396×C73C2211yescharacteristic
89#395×C73C2211yescharacteristic
90#395×C73C2211yescharacteristic
91#395×C73C2211yescharacteristic
92#395×C73C2211yescharacteristic
93#395×C73C2211yescharacteristic
94#395×C73C2211yescharacteristic
95#394×C73C2211yescharacteristic
96#394×C73C2211yescharacteristic
97#394×C73C2211yescharacteristic
98#393×C73C2211yescharacteristic
99#393×C73C2211yescharacteristic
100#392×C73C2211yescharacteristic
101#391×C73C2211yescharacteristic
102#391×C73C2211yescharacteristic
103#391×C73C2211yescharacteristic
104#391×C73C2211yescharacteristic
105#390×C73C2211yescharacteristic
106#390×C73C2211yescharacteristic
107#389×C73C2211yescharacteristic
108#389×C73C2211yescharacteristic
109#389×C73C2211yescharacteristic
110#389×C73C2211yescharacteristic
111#389×C73C2211yescharacteristic
112#389×C73C2211yescharacteristic
113#389×C73C2211yescharacteristic
114#389×C73C2211yescharacteristic
115#389×C73C2211yescharacteristic
116#389×C73C2211yescharacteristic
117#389×C73C2211yescharacteristic
118#389×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
131#388×C73C2211yescharacteristic
132#388×C73C2211yescharacteristic
133#388×C73C2211yescharacteristic
134#388×C73C2211yescharacteristic
135#388×C73C2211yescharacteristic
136#387×C73C2211yescharacteristic
137#387×C73C2211yescharacteristic
138#387×C73C2211yescharacteristic
139#387×C73C2211yescharacteristic
140#387×C73C2211yescharacteristic
141#387×C73C2211yescharacteristic
142#387×C73C2211yescharacteristic
143#387×C73C2211yescharacteristic
144#387×C73C2211yescharacteristic
145#387×C73C2211yescharacteristic
146#387×C73C2211yescharacteristic
147#387×C73C2211yescharacteristic
148#387×C73C2211yescharacteristic
149#387×C73C2211yescharacteristic
150#387×C73C2211yescharacteristic
151#387×C73C2211yescharacteristic
152#387×C73C2211yescharacteristic
153#386×C73C2211yescharacteristic
154#386×C73C2211yescharacteristic
155#386×C73C2211yescharacteristic
156#386×C73C2211yescharacteristic
157#385×C73C2211yescharacteristic
158#385×C73C2211yescharacteristic
159#385×C73C2211yescharacteristic
160#385×C73C2211yescharacteristic
161#385×C73C2211yescharacteristic
162#385×C73C2211yescharacteristic
163#385×C73C2211yescharacteristic
164#385×C73C2211yescharacteristic
165#385×C73C2211yescharacteristic
166#385×C73C2211yescharacteristic
167#384×C73C2211yescharacteristic
168#383×C73C2211yescharacteristic
169#382×C73C2211yescharacteristic
170#380×C73C2211yescharacteristic
171C4×C4⋊C4×C73C2211yescharacteristic
172C4×C4⋊C4×C73C2211yescharacteristic
173C4×C4⋊C4×C73C2211yescharacteristic
174C4×C4⋊C4×C73C2211yescharacteristic
175C4×C4⋊C4×C73C2211yescharacteristic
176C4×C4⋊C4×C73C2211yescharacteristic
177C4×C4⋊C4×C73C2211yescharacteristic
178C4×C4⋊C4×C73C2211yescharacteristic
179C4×C4⋊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
186C4×C22⋊C4×C73C2211yescharacteristic
187C2×#95×C73C2211yescharacteristic
188C43×C73C2211yescharacteristic
189C22×Q8×C73C2311yescharacteristic
190C22×Q8×C73C2311yescharacteristic
191C22×Q8×C73C2311yescharacteristic
192C22×Q8×C73C2311yescharacteristic
193C22×D4×C73C2311yescharacteristic
194C22×D4×C73C2311yescharacteristic
195C22×D4×C73C2311yescharacteristic
196C23×C4×C73C2311yescharacteristic
197C23×C4×C73C2311yescharacteristic
198C23×C4×C73C2311yescharacteristic
199C23×C4×C73C2311yescharacteristic
200C23×C4×C73C2311yescharacteristic
201C23×C4×C73C2311yescharacteristic
202C23×C4×C73C2311yescharacteristic
203C4⋊Q8×C73—24no—
204C4⋊Q8×C73—24no—
205#126×C73—24no—
206#126×C73—24no—
207#126×C73—24no—
208#126×C73—24no—
209#126×C73D418yescomplemented
210#125×C73—24no—
211#125×C73—24no—
212#125×C73—24no—
213#124×C73—24no—
214#124×C73—24no—
215#123×C73—24no—
216#123×C73—24no—
217#123×C73—24no—
218#123×C73—24no—
219C22⋊Q8×C73—24no—
220C22⋊Q8×C73—24no—
221C22⋊Q8×C73—24no—
222C22⋊Q8×C73—24no—
223C22⋊Q8×C73—24no—
224C22⋊Q8×C73—24no—
225C4×Q8×C73—24no—
226C4×Q8×C73—24no—
227C4×Q8×C73—24no—
228C4×Q8×C73—24no—
229C4×D4×C73—24no—
230C4×D4×C73—24no—
231C4×D4×C73—24no—
232#117×C73—24no—
233#117×C73—24no—
234#117×C73—24no—
235#117×C73—24no—
236#117×C73—24no—
237C2×C4⋊C4×C73—24no—
238C2×C4⋊C4×C73C2311yescharacteristic
239C2×C4⋊C4×C73C2311yescharacteristic
240C2×C4⋊C4×C73C2311yescharacteristic
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×C4⋊C4×C73C2311yescharacteristic
271C2×C4⋊C4×C73C2311yescharacteristic
272C2×C4⋊C4×C73C2311yescharacteristic
273C2×C4⋊C4×C73C2311yescharacteristic
274C2×C4⋊C4×C73C2311yescharacteristic
275C2×C4⋊C4×C73C2311yescharacteristic
276C2×C4⋊C4×C73C2311yescharacteristic
277C2×C4⋊C4×C73C2311yescharacteristic
278C2×C4⋊C4×C73C2311yescharacteristic
279C2×C4⋊C4×C73C2311yescharacteristic
280C2×C4⋊C4×C73C2311yescharacteristic
281C2×C4⋊C4×C73C2311yescharacteristic
282C2×C4⋊C4×C73C2311yescharacteristic
283C2×C4⋊C4×C73C2311yescharacteristic
284C2×C4⋊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×C42×C73C2311yescharacteristic
318C2×C42×C73C2311yescharacteristic
319C2×C42×C73C2311yescharacteristic
320C2×C42×C73C2311yescharacteristic
321C2×C42×C73C2311yescharacteristic
322C2×C42×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
337#95×C73C2311yescharacteristic
338#95×C73C2311yescharacteristic
339#95×C73C2311yescharacteristic
340#95×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×C73C2411yescharacteristic
380C24×C73C2411yescharacteristic
381C24×C73C2411yescharacteristic
382C2×Q8×C73—22no—
383C2×Q8×C73—22no—
384C2×Q8×C73—22no—
385C2×Q8×C73—22no—
386C2×Q8×C73—22no—
387C2×Q8×C73—22no—
388C2×Q8×C73—22no—
389C2×Q8×C73—22no—
390C2×Q8×C73—41no—
391C2×Q8×C73—41no—
392C2×Q8×C73—41no—
393C2×Q8×C73—41no—
394C2×D4×C73—22no—
395C2×D4×C73—22no—
396C2×D4×C73—22no—
397C2×D4×C73—22no—
398C2×D4×C73—22no—
399C2×D4×C73—22no—
400C2×D4×C73—41no—
401C2×D4×C73—41no—
402C2×D4×C73—41no—
403C22×C4×C73—22no—
404C22×C4×C73—22no—
405C22×C4×C73—22no—
406C22×C4×C73—22no—
407C22×C4×C73—22no—
408C22×C4×C73—22no—
409C22×C4×C73—22no—
410C22×C4×C73—22no—
411C22×C4×C73—22no—
412C22×C4×C73—22no—
413C22×C4×C73—22no—
414C22×C4×C73—22no—
415C22×C4×C73—22no—
416C22×C4×C73—41no—
417C22×C4×C73—41no—
418C22×C4×C73—41no—
419C22×C4×C73—41no—
420C22×C4×C73—41no—
421C22×C4×C73—41no—
422C22×C4×C73—41no—
423C22×C4×C73—41no—
424C22×C4×C73C2411yescharacteristic
425C22×C4×C73C2411yescharacteristic
426C22×C4×C73C2411yescharacteristic
427C22×C4×C73C2411yescharacteristic
428C22×C4×C73C2411yescharacteristic
429C22×C4×C73C2411yescharacteristic
430C22×C4×C73C2411yescharacteristic
431C22×C4×C73C2411yescharacteristic
432C22×C4×C73C2411yescharacteristic
433C22×C4×C73C2411yescharacteristic
434C22×C4×C73C2411yescharacteristic
435C22×C4×C73C2411yescharacteristic
436C22×C4×C73C2411yescharacteristic
437C22×C4×C73C2411yescharacteristic
438C22×C4×C73C2411yescharacteristic
439C22×C4×C73C2411yescharacteristic
440C22×C4×C73C2411yescharacteristic
441C22×C4×C73C2411yescharacteristic
442C22×C4×C73C2411yescharacteristic
443C22×C4×C73C2411yescharacteristic
444C22×C4×C73C2411yescharacteristic
445C22×C4×C73C2411yescharacteristic
446C22×C4×C73C2411yescharacteristic
447C22×C4×C73C2411yescharacteristic
448C22×C4×C73C2411yescharacteristic
449C22×C4×C73C2411yescharacteristic
450C22×C4×C73C2411yescharacteristic
451C22×C4×C73C2411yescharacteristic
452C4⋊C4×C73—22no—
453C4⋊C4×C73—22no—
454C4⋊C4×C73—22no—
455C4⋊C4×C73—22no—
456C4⋊C4×C73—22no—
457C4⋊C4×C73—22no—
458C4⋊C4×C73—22no—
459C4⋊C4×C73—22no—
460C4⋊C4×C73—22no—
461C4⋊C4×C73—22no—
462C4⋊C4×C73—22no—
463C4⋊C4×C73—22no—
464C4⋊C4×C73—22no—
465C4⋊C4×C73—22no—
466C4⋊C4×C73—22no—
467C4⋊C4×C73—22no—
468C4⋊C4×C73—22no—
469C4⋊C4×C73—22no—
470C4⋊C4×C73—22no—
471C4⋊C4×C73—22no—
472C4⋊C4×C73—22no—
473C4⋊C4×C73—22no—
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—41no—
489C4⋊C4×C73—41no—
490C4⋊C4×C73—41no—
491C4⋊C4×C73—41no—
492C4⋊C4×C73—41no—
493C4⋊C4×C73—41no—
494C4⋊C4×C73—41no—
495C4⋊C4×C73C2×D414yes—
496C4⋊C4×C73C2×D414yes—
497C4⋊C4×C73C2×D414yes—
498C4⋊C4×C73#4114yes—
499C22⋊C4×C73—22no—
500C22⋊C4×C73—22no—
501C22⋊C4×C73—22no—
502C22⋊C4×C73—22no—
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—41no—
524C22⋊C4×C73—41no—
525C22⋊C4×C73—41no—
526C22⋊C4×C73—41no—
527C22⋊C4×C73C2×D414yes—
528C22⋊C4×C73C2×D414yes—
529C22⋊C4×C73C2×D414yes—
530C22⋊C4×C73#4114yes—
531C42×C73—22no—
532C42×C73—22no—
533C42×C73—22no—
534C42×C73—22no—
535C42×C73—22no—
536C42×C73—22no—
537C42×C73—22no—
538C42×C73—22no—
539C42×C73—22no—
540C42×C73—22no—
541C42×C73—22no—
542C42×C73—22no—
543C42×C73—22no—
544C42×C73—22no—
545C42×C73—22no—
546C42×C73—41no—
547C42×C73—41no—
548C42×C73—41no—
549C42×C73—41no—
550C42×C73C2×D414yes—
551C23×C73—21no—
552C23×C73—21no—
553C23×C73—21no—
554C23×C73—21no—
555C23×C73—21no—
556C23×C73—21no—
557C23×C73—21no—
558C23×C73—21no—
559C23×C73—21no—
560C23×C73—21no—
561C23×C73—21no—
562C23×C73—21no—
563C23×C73—21no—
564C23×C73—21no—
565C23×C73—21no—
566C23×C73—21no—
567C23×C73—21no—
568C23×C73—21no—
569C23×C73—21no—
570C23×C73C22×D412yes—
571C23×C73C2×#4112yes—
572C23×C73C2511yescharacteristic
573Q8×C73—44no—
574Q8×C73—44no—
575Q8×C73—44no—
576Q8×C73—44no—
577D4×C73—44no—
578D4×C73—44no—
579D4×C73—44no—
580C2×C4×C73—21no—
581C2×C4×C73—21no—
582C2×C4×C73—21no—
583C2×C4×C73—21no—
584C2×C4×C73—21no—
585C2×C4×C73—21no—
586C2×C4×C73—21no—
587C2×C4×C73—21no—
588C2×C4×C73—21no—
589C2×C4×C73—21no—
590C2×C4×C73—21no—
591C2×C4×C73—21no—
592C2×C4×C73—21no—
593C2×C4×C73—21no—
594C2×C4×C73—21no—
595C2×C4×C73—21no—
596C2×C4×C73—21no—
597C2×C4×C73—21no—
598C2×C4×C73—21no—
599C2×C4×C73—21no—
600C2×C4×C73—21no—
601C2×C4×C73—21no—
602C2×C4×C73—21no—
603C2×C4×C73—21no—
604C2×C4×C73—21no—
605C2×C4×C73—21no—
606C2×C4×C73—21no—
607C2×C4×C73—21no—
608C2×C4×C73—21no—
609C2×C4×C73—21no—
610C2×C4×C73—21no—
611C2×C4×C73—21no—
612C2×C4×C73—21no—
613C2×C4×C73—21no—
614C2×C4×C73—21no—
615C2×C4×C73—21no—
616C2×C4×C73—21no—
617C2×C4×C73—21no—
618C2×C4×C73—21no—
619C2×C4×C73—21no—
620C2×C4×C73—21no—
621C2×C4×C73—21no—
622C2×C4×C73—21no—
623C2×C4×C73—21no—
624C2×C4×C73—21no—
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—44no—
652C2×C4×C73—44no—
653C2×C4×C73—44no—
654C2×C4×C73—44no—
655C2×C4×C73—44no—
656C2×C4×C73—44no—
657C2×C4×C73—82no—
658C2×C4×C73C22×D412yes—
659C2×C4×C73C22×D412yes—
660C2×C4×C73C22×D412yes—
661C2×C4×C73C22×D412yes—
662C2×C4×C73C22×D412yes—
663C2×C4×C73C22×D412yes—
664C2×C4×C73C2×#4112yes—
665C2×C4×C73C2×#4112yes—
666C2×C4×C73C2×#4112yes—
667C2×C4×C73C2×#4112yes—
668C2×C4×C73C2×#4112yes—
669C2×C4×C732−1+412yes—
670C2×C4×C732−1+412yes—
671C22×C73—22no—
672C22×C73—22no—
673C22×C73—22no—
674C22×C73—22no—
675C22×C73—22no—
676C22×C73—22no—
677C22×C73—41no—
678C22×C73—41no—
679C22×C73—41no—
680C22×C73—41no—
681C22×C73—41no—
682C22×C73—41no—
683C22×C73—41no—
684C22×C73—41no—
685C22×C73—41no—
686C22×C73—41no—
687C22×C73—41no—
688C22×C73—41no—
689C22×C73—41no—
690C22×C73—41no—
691C22×C73—41no—
692C22×C73C23×D411yescharacteristic
693C22×C73C22×#4111yescharacteristic
694C22×C73C22×#4111yescharacteristic
695C22×C73C2×2−1+411yescharacteristic
696C22×C73C2×2−1+411yescharacteristic
697C22×C73#58511yescharacteristic
698C22×C73#58511yescharacteristic
699C4×C73—22no—
700C4×C73—22no—
701C4×C73—22no—
702C4×C73—22no—
703C4×C73—22no—
704C4×C73—22no—
705C4×C73—22no—
706C4×C73—22no—
707C4×C73—22no—
708C4×C73—22no—
709C4×C73—22no—
710C4×C73—22no—
711C4×C73—22no—
712C4×C73—41no—
713C4×C73—41no—
714C4×C73—41no—
715C4×C73—41no—
716C4×C73—41no—
717C4×C73—41no—
718C4×C73—41no—
719C4×C73—41no—
720C4×C73—41no—
721C4×C73—41no—
722C4×C73—41no—
723C4×C73—41no—
724C4×C73—41no—
725C4×C73—41no—
726C4×C73—41no—
727#59840C7311yesmaximal, characteristic, direct product factor, Sylow
728C2×C73—42no—
729C2×C73—42no—
730C2×C73—81no—
731C2×C73D4×#4111yescharacteristic
732C2×C73D4×#4111yescharacteristic
733C2×C73#348211yescharacteristic
734C2×C73#349511yescharacteristic
735C2×C73#349911yescharacteristic
736C2×C73#350711yescharacteristic
737C2×C73#356411yescharacteristic
738C2×#556C2×C7311yescharacteristic, complemented
739C2×#552C2×C7311yescharacteristic, complemented
740#2721C2×C7311yescharacteristic, complemented
741#2680C2×C7311yescharacteristic, complemented
742#2677C2×C7311yescharacteristic, complemented
743#2674C2×C7311yescharacteristic, complemented
744#2599C2×C7311yescharacteristic, complemented
745#2599C2×C7311yescharacteristic, complemented
746#2560C2×C7311yescharacteristic, complemented
747#2557C2×C7311yescharacteristic
748#2556C2×C7311yescharacteristic, complemented
749#2553C2×C7311yescharacteristic, complemented
750#2550C2×C7311yescharacteristic, complemented
751#2549C2×C7311yescharacteristic, complemented
752#2521C2×C7311yescharacteristic, complemented
753#2519C2×C7311yescharacteristic, complemented
754#2479C2×C7311yescharacteristic, complemented
755#2478C2×C7311yescharacteristic, complemented
756#2478C2×C7311yescharacteristic, complemented
757#2462C2×C7311yescharacteristic, complemented
758#2462C2×C7311yescharacteristic, complemented
759#2461C2×C7311yescharacteristic
760#2455C2×C7311yescharacteristic
761#2449C2×C7311yescharacteristic, complemented
762#2362C2×C7311yescharacteristic, complemented
763#2360C2×C7311yescharacteristic, complemented
764#2359C2×C7311yescharacteristic, complemented
765#2359C2×C7311yescharacteristic, complemented
766C4×C4⋊Q8C2×C7311yescharacteristic, complemented
767C4×#126C2×C7311yescharacteristic, complemented
768#2293C2×C7311yescharacteristic, complemented
769C73#5984011yescharacteristic, direct product factor, Sylow
770#556—28no—
771#552—28no—
772C2×C4⋊Q8C22×C7311yescharacteristic
773C2×C4⋊Q8C22×C7311yescharacteristic
774C2×#126C22×C7311yescharacteristic
775C2×#126C22×C7311yescharacteristic
776C2×#126C22×C7311yescharacteristic
777C2×#126C22×C7311yescharacteristic
778C2×#126C22×C7311yescharacteristic
779C2×#125C22×C7311yescharacteristic
780C2×#125C22×C7311yescharacteristic
781C2×#125C22×C7311yescharacteristic
782C2×#124C22×C7311yescharacteristic
783C2×#124C22×C7311yescharacteristic
784C2×#123C22×C7311yescharacteristic
785C2×#123C22×C7311yescharacteristic
786C2×#123C22×C7311yescharacteristic
787C2×#123C22×C7311yescharacteristic
788C2×C22⋊Q8C22×C7311yescharacteristic
789C2×C22⋊Q8C22×C7311yescharacteristic
790C2×C22⋊Q8C22×C7311yescharacteristic
791C2×C22⋊Q8C22×C7311yescharacteristic
792C2×C22⋊Q8C22×C7311yescharacteristic
793C2×C22⋊Q8C22×C7311yescharacteristic
794C2×C4×Q8C22×C7311yescharacteristic
795C2×C4×Q8C22×C7311yescharacteristic
796C2×C4×Q8C22×C7311yescharacteristic
797C2×C4×Q8C22×C7311yescharacteristic
798C2×C4×D4C22×C7311yescharacteristic
799C2×C4×D4C22×C7311yescharacteristic
800C2×C4×D4C22×C7311yescharacteristic
801C2×#117C22×C7311yescharacteristic
802C2×#117C22×C7311yescharacteristic
803C2×#117C22×C7311yescharacteristic
804C2×#117C22×C7311yescharacteristic
805C2×#117C22×C7311yescharacteristic
806C22×C4⋊C4C22×C7311yescharacteristic
807#399C22×C7311yescharacteristic
808#399C22×C7311yescharacteristic
809#399C22×C7311yescharacteristic
810#399C22×C7311yescharacteristic
811#398C22×C7311yescharacteristic
812#398C22×C7311yescharacteristic
813#398C22×C7311yescharacteristic
814#398C22×C7311yescharacteristic
815#398C22×C7311yescharacteristic
816#398C22×C7311yescharacteristic
817#398C22×C7311yescharacteristic
818#398C22×C7311yescharacteristic
819#398C22×C7311yescharacteristic
820#397C22×C7311yescharacteristic
821#397C22×C7311yescharacteristic
822#397C22×C7311yescharacteristic
823#397C22×C7311yescharacteristic
824#397C22×C7311yescharacteristic
825#396C22×C7311yescharacteristic
826#396C22×C7311yescharacteristic
827#395C22×C7311yescharacteristic
828#395C22×C7311yescharacteristic
829#395C22×C7311yescharacteristic
830#395C22×C7311yescharacteristic
831#395C22×C7311yescharacteristic
832#395C22×C7311yescharacteristic
833#394C22×C7311yescharacteristic
834#394C22×C7311yescharacteristic
835#394C22×C7311yescharacteristic
836#393C22×C7311yescharacteristic
837#393C22×C7311yescharacteristic
838#392C22×C7311yescharacteristic
839#391C22×C7311yescharacteristic
840#391C22×C7311yescharacteristic
841#391C22×C7311yescharacteristic
842#391C22×C7311yescharacteristic
843#390C22×C7311yescharacteristic
844#390C22×C7311yescharacteristic
845#389C22×C7311yescharacteristic
846#389C22×C7311yescharacteristic
847#389C22×C7311yescharacteristic
848#389C22×C7311yescharacteristic
849#389C22×C7311yescharacteristic
850#389C22×C7311yescharacteristic
851#389C22×C7311yescharacteristic
852#389C22×C7311yescharacteristic
853#389C22×C7311yescharacteristic
854#389C22×C7311yescharacteristic
855#389C22×C7311yescharacteristic
856#389C22×C7311yescharacteristic
857#388C22×C7311yescharacteristic
858#388C22×C7311yescharacteristic
859#388C22×C7311yescharacteristic
860#388C22×C7311yescharacteristic
861#388C22×C7311yescharacteristic
862#388C22×C7311yescharacteristic
863#388C22×C7311yescharacteristic
864#388C22×C7311yescharacteristic
865#388C22×C7311yescharacteristic
866#388C22×C7311yescharacteristic
867#388C22×C7311yescharacteristic
868#388C22×C7311yescharacteristic
869#388C22×C7311yescharacteristic
870#388C22×C7311yescharacteristic
871#388C22×C7311yescharacteristic
872#388C22×C7311yescharacteristic
873#388C22×C7311yescharacteristic
874#387C22×C7311yescharacteristic
875#387C22×C7311yescharacteristic
876#387C22×C7311yescharacteristic
877#387C22×C7311yescharacteristic
878#387C22×C7311yescharacteristic
879#387C22×C7311yescharacteristic
880#387C22×C7311yescharacteristic
881#387C22×C7311yescharacteristic
882#387C22×C7311yescharacteristic
883#387C22×C7311yescharacteristic
884#387C22×C7311yescharacteristic
885#387C22×C7311yescharacteristic
886#387C22×C7311yescharacteristic
887#387C22×C7311yescharacteristic
888#387C22×C7311yescharacteristic
889#387C22×C7311yescharacteristic
890#387C22×C7311yescharacteristic
891#386C22×C7311yescharacteristic
892#386C22×C7311yescharacteristic
893#386C22×C7311yescharacteristic
894#386C22×C7311yescharacteristic
895#385C22×C7311yescharacteristic
896#385C22×C7311yescharacteristic
897#385C22×C7311yescharacteristic
898#385C22×C7311yescharacteristic
899#385C22×C7311yescharacteristic
900#385C22×C7311yescharacteristic
901#385C22×C7311yescharacteristic
902#385C22×C7311yescharacteristic
903#385C22×C7311yescharacteristic
904#385C22×C7311yescharacteristic
905#384C22×C7311yescharacteristic
906#383C22×C7311yescharacteristic
907#382C22×C7311yescharacteristic
908#380C22×C7311yescharacteristic
909C4×C4⋊C4C22×C7311yescharacteristic
910C4×C4⋊C4C22×C7311yescharacteristic
911C4×C4⋊C4C22×C7311yescharacteristic
912C4×C4⋊C4C22×C7311yescharacteristic
913C4×C4⋊C4C22×C7311yescharacteristic
914C4×C4⋊C4C22×C7311yescharacteristic
915C4×C4⋊C4C22×C7311yescharacteristic
916C4×C4⋊C4C22×C7311yescharacteristic
917C4×C4⋊C4C22×C7311yescharacteristic
918C4×C22⋊C4C22×C7311yescharacteristic
919C4×C22⋊C4C22×C7311yescharacteristic
920C4×C22⋊C4C22×C7311yescharacteristic
921C4×C22⋊C4C22×C7311yescharacteristic
922C4×C22⋊C4C22×C7311yescharacteristic
923C4×C22⋊C4C22×C7311yescharacteristic
924C4×C22⋊C4C22×C7311yescharacteristic
925C2×#95C22×C7311yescharacteristic
926C43C22×C7311yescharacteristic
927C22×Q8C23×C7311yescharacteristic
928C22×Q8C23×C7311yescharacteristic
929C22×Q8C23×C7311yescharacteristic
930C22×Q8C23×C7311yescharacteristic
931C22×D4C23×C7311yescharacteristic
932C22×D4C23×C7311yescharacteristic
933C22×D4C23×C7311yescharacteristic
934C23×C4C23×C7311yescharacteristic
935C23×C4C23×C7311yescharacteristic
936C23×C4C23×C7311yescharacteristic
937C23×C4C23×C7311yescharacteristic
938C23×C4C23×C7311yescharacteristic
939C23×C4C23×C7311yescharacteristic
940C23×C4C23×C7311yescharacteristic
941C4⋊Q8—24no—
942C4⋊Q8—24no—
943#126—24no—
944#126—24no—
945#126—24no—
946#126—24no—
947#126D4×C7318yescomplemented
948#125—24no—
949#125—24no—
950#125—24no—
951#124—24no—
952#124—24no—
953#123—24no—
954#123—24no—
955#123—24no—
956#123—24no—
957C22⋊Q8—24no—
958C22⋊Q8—24no—
959C22⋊Q8—24no—
960C22⋊Q8—24no—
961C22⋊Q8—24no—
962C22⋊Q8—24no—
963C4×Q8—24no—
964C4×Q8—24no—
965C4×Q8—24no—
966C4×Q8—24no—
967C4×D4—24no—
968C4×D4—24no—
969C4×D4—24no—
970#117—24no—
971#117—24no—
972#117—24no—
973#117—24no—
974#117—24no—
975C2×C4⋊C4—24no—
976C2×C4⋊C4C23×C7311yescharacteristic
977C2×C4⋊C4C23×C7311yescharacteristic
978C2×C4⋊C4C23×C7311yescharacteristic
979C2×C4⋊C4C23×C7311yescharacteristic
980C2×C4⋊C4C23×C7311yescharacteristic
981C2×C4⋊C4C23×C7311yescharacteristic
982C2×C4⋊C4C23×C7311yescharacteristic
983C2×C4⋊C4C23×C7311yescharacteristic
984C2×C4⋊C4C23×C7311yescharacteristic
985C2×C4⋊C4C23×C7311yescharacteristic
986C2×C4⋊C4C23×C7311yescharacteristic
987C2×C4⋊C4C23×C7311yescharacteristic
988C2×C4⋊C4C23×C7311yescharacteristic
989C2×C4⋊C4C23×C7311yescharacteristic
990C2×C4⋊C4C23×C7311yescharacteristic
991C2×C4⋊C4C23×C7311yescharacteristic
992C2×C4⋊C4C23×C7311yescharacteristic
993C2×C4⋊C4C23×C7311yescharacteristic
994C2×C4⋊C4C23×C7311yescharacteristic
995C2×C4⋊C4C23×C7311yescharacteristic
996C2×C4⋊C4C23×C7311yescharacteristic
997C2×C4⋊C4C23×C7311yescharacteristic
998C2×C4⋊C4C23×C7311yescharacteristic
999C2×C4⋊C4C23×C7311yescharacteristic
1000C2×C4⋊C4C23×C7311yescharacteristic
1001C2×C4⋊C4C23×C7311yescharacteristic
1002C2×C4⋊C4C23×C7311yescharacteristic
1003C2×C4⋊C4C23×C7311yescharacteristic
1004C2×C4⋊C4C23×C7311yescharacteristic
1005C2×C4⋊C4C23×C7311yescharacteristic
1006C2×C4⋊C4C23×C7311yescharacteristic
1007C2×C4⋊C4C23×C7311yescharacteristic
1008C2×C4⋊C4C23×C7311yescharacteristic
1009C2×C4⋊C4C23×C7311yescharacteristic
1010C2×C4⋊C4C23×C7311yescharacteristic
1011C2×C4⋊C4C23×C7311yescharacteristic
1012C2×C4⋊C4C23×C7311yescharacteristic
1013C2×C4⋊C4C23×C7311yescharacteristic
1014C2×C4⋊C4C23×C7311yescharacteristic
1015C2×C4⋊C4C23×C7311yescharacteristic
1016C2×C4⋊C4C23×C7311yescharacteristic
1017C2×C4⋊C4C23×C7311yescharacteristic
1018C2×C4⋊C4C23×C7311yescharacteristic
1019C2×C4⋊C4C23×C7311yescharacteristic
1020C2×C4⋊C4C23×C7311yescharacteristic
1021C2×C4⋊C4C23×C7311yescharacteristic
1022C2×C4⋊C4C23×C7311yescharacteristic
1023C2×C22⋊C4C23×C7311yescharacteristic
1024C2×C22⋊C4C23×C7311yescharacteristic
1025C2×C22⋊C4C23×C7311yescharacteristic
1026C2×C22⋊C4C23×C7311yescharacteristic
1027C2×C22⋊C4C23×C7311yescharacteristic
1028C2×C22⋊C4C23×C7311yescharacteristic
1029C2×C22⋊C4C23×C7311yescharacteristic
1030C2×C22⋊C4C23×C7311yescharacteristic
1031C2×C22⋊C4C23×C7311yescharacteristic
1032C2×C22⋊C4C23×C7311yescharacteristic
1033C2×C22⋊C4C23×C7311yescharacteristic
1034C2×C22⋊C4C23×C7311yescharacteristic
1035C2×C22⋊C4C23×C7311yescharacteristic
1036C2×C22⋊C4C23×C7311yescharacteristic
1037C2×C22⋊C4C23×C7311yescharacteristic
1038C2×C22⋊C4C23×C7311yescharacteristic
1039C2×C22⋊C4C23×C7311yescharacteristic
1040C2×C22⋊C4C23×C7311yescharacteristic
1041C2×C22⋊C4C23×C7311yescharacteristic
1042C2×C22⋊C4C23×C7311yescharacteristic
1043C2×C22⋊C4C23×C7311yescharacteristic
1044C2×C22⋊C4C23×C7311yescharacteristic
1045C2×C22⋊C4C23×C7311yescharacteristic
1046C2×C22⋊C4C23×C7311yescharacteristic
1047C2×C22⋊C4C23×C7311yescharacteristic
1048C2×C22⋊C4C23×C7311yescharacteristic
1049C2×C22⋊C4C23×C7311yescharacteristic
1050C2×C22⋊C4C23×C7311yescharacteristic
1051C2×C22⋊C4C23×C7311yescharacteristic
1052C2×C22⋊C4C23×C7311yescharacteristic
1053C2×C22⋊C4C23×C7311yescharacteristic
1054C2×C22⋊C4C23×C7311yescharacteristic
1055C2×C42C23×C7311yescharacteristic
1056C2×C42C23×C7311yescharacteristic
1057C2×C42C23×C7311yescharacteristic
1058C2×C42C23×C7311yescharacteristic
1059C2×C42C23×C7311yescharacteristic
1060C2×C42C23×C7311yescharacteristic
1061C2×C42C23×C7311yescharacteristic
1062C2×C42C23×C7311yescharacteristic
1063C2×C42C23×C7311yescharacteristic
1064C2×C42C23×C7311yescharacteristic
1065C2×C42C23×C7311yescharacteristic
1066C2×C42C23×C7311yescharacteristic
1067C2×C42C23×C7311yescharacteristic
1068C2×C42C23×C7311yescharacteristic
1069C2×C42C23×C7311yescharacteristic
1070C2×C42C23×C7311yescharacteristic
1071C2×C42C23×C7311yescharacteristic
1072C2×C42C23×C7311yescharacteristic
1073C2×C42C23×C7311yescharacteristic
1074C2×C42C23×C7311yescharacteristic
1075#95C23×C7311yescharacteristic
1076#95C23×C7311yescharacteristic
1077#95C23×C7311yescharacteristic
1078#95C23×C7311yescharacteristic
1079#95C23×C7311yescharacteristic
1080#95C23×C7311yescharacteristic
1081#95C23×C7311yescharacteristic
1082#95C23×C7311yescharacteristic
1083#95C23×C7311yescharacteristic
1084#95C23×C7311yescharacteristic
1085#95C23×C7311yescharacteristic
1086#95C23×C7311yescharacteristic
1087#95C23×C7311yescharacteristic
1088#95C23×C7311yescharacteristic
1089#95C23×C7311yescharacteristic
1090#95C23×C7311yescharacteristic
1091#95C23×C7311yescharacteristic
1092#95C23×C7311yescharacteristic
1093#95C23×C7311yescharacteristic
1094#95C23×C7311yescharacteristic
1095#95C23×C7311yescharacteristic
1096#95C23×C7311yescharacteristic
1097#95C23×C7311yescharacteristic
1098#95C23×C7311yescharacteristic
1099#95C23×C7311yescharacteristic
1100#95C23×C7311yescharacteristic
1101#95C23×C7311yescharacteristic
1102#95C23×C7311yescharacteristic
1103#95C23×C7311yescharacteristic
1104#95C23×C7311yescharacteristic
1105#95C23×C7311yescharacteristic
1106#95C23×C7311yescharacteristic
1107#95C23×C7311yescharacteristic
1108#95C23×C7311yescharacteristic
1109#95C23×C7311yescharacteristic
1110#95C23×C7311yescharacteristic
1111#95C23×C7311yescharacteristic
1112#95C23×C7311yescharacteristic
1113#95C23×C7311yescharacteristic
1114#95C23×C7311yescharacteristic
1115#95C23×C7311yescharacteristic
1116#95C23×C7311yescharacteristic
1117C24C24×C7311yescharacteristic
1118C24C24×C7311yescharacteristic
1119C24C24×C7311yescharacteristic
1120C2×Q8—22no—
1121C2×Q8—22no—
1122C2×Q8—22no—
1123C2×Q8—22no—
1124C2×Q8—22no—
1125C2×Q8—22no—
1126C2×Q8—22no—
1127C2×Q8—22no—
1128C2×Q8—41no—
1129C2×Q8—41no—
1130C2×Q8—41no—
1131C2×Q8—41no—
1132C2×D4—22no—
1133C2×D4—22no—
1134C2×D4—22no—
1135C2×D4—22no—
1136C2×D4—22no—
1137C2×D4—22no—
1138C2×D4—41no—
1139C2×D4—41no—
1140C2×D4—41no—
1141C22×C4—22no—
1142C22×C4—22no—
1143C22×C4—22no—
1144C22×C4—22no—
1145C22×C4—22no—
1146C22×C4—22no—
1147C22×C4—22no—
1148C22×C4—22no—
1149C22×C4—22no—
1150C22×C4—22no—
1151C22×C4—22no—
1152C22×C4—22no—
1153C22×C4—22no—
1154C22×C4—41no—
1155C22×C4—41no—
1156C22×C4—41no—
1157C22×C4—41no—
1158C22×C4—41no—
1159C22×C4—41no—
1160C22×C4—41no—
1161C22×C4—41no—
1162C22×C4C24×C7311yescharacteristic
1163C22×C4C24×C7311yescharacteristic
1164C22×C4C24×C7311yescharacteristic
1165C22×C4C24×C7311yescharacteristic
1166C22×C4C24×C7311yescharacteristic
1167C22×C4C24×C7311yescharacteristic
1168C22×C4C24×C7311yescharacteristic
1169C22×C4C24×C7311yescharacteristic
1170C22×C4C24×C7311yescharacteristic
1171C22×C4C24×C7311yescharacteristic
1172C22×C4C24×C7311yescharacteristic
1173C22×C4C24×C7311yescharacteristic
1174C22×C4C24×C7311yescharacteristic
1175C22×C4C24×C7311yescharacteristic
1176C22×C4C24×C7311yescharacteristic
1177C22×C4C24×C7311yescharacteristic
1178C22×C4C24×C7311yescharacteristic
1179C22×C4C24×C7311yescharacteristic
1180C22×C4C24×C7311yescharacteristic
1181C22×C4C24×C7311yescharacteristic
1182C22×C4C24×C7311yescharacteristic
1183C22×C4C24×C7311yescharacteristic
1184C22×C4C24×C7311yescharacteristic
1185C22×C4C24×C7311yescharacteristic
1186C22×C4C24×C7311yescharacteristic
1187C22×C4C24×C7311yescharacteristic
1188C22×C4C24×C7311yescharacteristic
1189C22×C4C24×C7311yescharacteristic
1190C4⋊C4—22no—
1191C4⋊C4—22no—
1192C4⋊C4—22no—
1193C4⋊C4—22no—
1194C4⋊C4—22no—
1195C4⋊C4—22no—
1196C4⋊C4—22no—
1197C4⋊C4—22no—
1198C4⋊C4—22no—
1199C4⋊C4—22no—
1200C4⋊C4—22no—
1201C4⋊C4—22no—
1202C4⋊C4—22no—
1203C4⋊C4—22no—
1204C4⋊C4—22no—
1205C4⋊C4—22no—
1206C4⋊C4—22no—
1207C4⋊C4—22no—
1208C4⋊C4—22no—
1209C4⋊C4—22no—
1210C4⋊C4—22no—
1211C4⋊C4—22no—
1212C4⋊C4—22no—
1213C4⋊C4—22no—
1214C4⋊C4—22no—
1215C4⋊C4—22no—
1216C4⋊C4—22no—
1217C4⋊C4—22no—
1218C4⋊C4—22no—
1219C4⋊C4—22no—
1220C4⋊C4—22no—
1221C4⋊C4—22no—
1222C4⋊C4—22no—
1223C4⋊C4—22no—
1224C4⋊C4—22no—
1225C4⋊C4—22no—
1226C4⋊C4—41no—
1227C4⋊C4—41no—
1228C4⋊C4—41no—
1229C4⋊C4—41no—
1230C4⋊C4—41no—
1231C4⋊C4—41no—
1232C4⋊C4—41no—
1233C4⋊C4C2×D4×C7314yes—
1234C4⋊C4C2×D4×C7314yes—
1235C4⋊C4C2×D4×C7314yes—
1236C4⋊C4#41×C7314yes—
1237C22⋊C4—22no—
1238C22⋊C4—22no—
1239C22⋊C4—22no—
1240C22⋊C4—22no—
1241C22⋊C4—22no—
1242C22⋊C4—22no—
1243C22⋊C4—22no—
1244C22⋊C4—22no—
1245C22⋊C4—22no—
1246C22⋊C4—22no—
1247C22⋊C4—22no—
1248C22⋊C4—22no—
1249C22⋊C4—22no—
1250C22⋊C4—22no—
1251C22⋊C4—22no—
1252C22⋊C4—22no—
1253C22⋊C4—22no—
1254C22⋊C4—22no—
1255C22⋊C4—22no—
1256C22⋊C4—22no—
1257C22⋊C4—22no—
1258C22⋊C4—22no—
1259C22⋊C4—22no—
1260C22⋊C4—22no—
1261C22⋊C4—41no—
1262C22⋊C4—41no—
1263C22⋊C4—41no—
1264C22⋊C4—41no—
1265C22⋊C4C2×D4×C7314yes—
1266C22⋊C4C2×D4×C7314yes—
1267C22⋊C4C2×D4×C7314yes—
1268C22⋊C4#41×C7314yes—
1269C42—22no—
1270C42—22no—
1271C42—22no—
1272C42—22no—
1273C42—22no—
1274C42—22no—
1275C42—22no—
1276C42—22no—
1277C42—22no—
1278C42—22no—
1279C42—22no—
1280C42—22no—
1281C42—22no—
1282C42—22no—
1283C42—22no—
1284C42—41no—
1285C42—41no—
1286C42—41no—
1287C42—41no—
1288C42C2×D4×C7314yes—
1289C23—21no—
1290C23—21no—
1291C23—21no—
1292C23—21no—
1293C23—21no—
1294C23—21no—
1295C23—21no—
1296C23—21no—
1297C23—21no—
1298C23—21no—
1299C23—21no—
1300C23—21no—
1301C23—21no—
1302C23—21no—
1303C23—21no—
1304C23—21no—
1305C23—21no—
1306C23—21no—
1307C23—21no—
1308C23C22×D4×C7312yes—
1309C23C2×#41×C7312yes—
1310C23C25×C7311yescharacteristic
1311Q8—44no—
1312Q8—44no—
1313Q8—44no—
1314Q8—44no—
1315D4—44no—
1316D4—44no—
1317D4—44no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—44no—
1390C2×C4—44no—
1391C2×C4—44no—
1392C2×C4—44no—
1393C2×C4—44no—
1394C2×C4—44no—
1395C2×C4—82no—
1396C2×C4C22×D4×C7312yes—
1397C2×C4C22×D4×C7312yes—
1398C2×C4C22×D4×C7312yes—
1399C2×C4C22×D4×C7312yes—
1400C2×C4C22×D4×C7312yes—
1401C2×C4C22×D4×C7312yes—
1402C2×C4C2×#41×C7312yes—
1403C2×C4C2×#41×C7312yes—
1404C2×C4C2×#41×C7312yes—
1405C2×C4C2×#41×C7312yes—
1406C2×C4C2×#41×C7312yes—
1407C2×C42−1+4×C7312yes—
1408C2×C42−1+4×C7312yes—
1409C22—22no—
1410C22—22no—
1411C22—22no—
1412C22—22no—
1413C22—22no—
1414C22—22no—
1415C22—41no—
1416C22—41no—
1417C22—41no—
1418C22—41no—
1419C22—41no—
1420C22—41no—
1421C22—41no—
1422C22—41no—
1423C22—41no—
1424C22—41no—
1425C22—41no—
1426C22—41no—
1427C22—41no—
1428C22—41no—
1429C22—41no—
1430C22C23×D4×C7311yescharacteristic
1431C22C22×#41×C7311yescharacteristic
1432C22C22×#41×C7311yescharacteristic
1433C22C2×2−1+4×C7311yescharacteristic
1434C22C2×2−1+4×C7311yescharacteristic
1435C22#585×C7311yescharacteristic
1436C22#585×C7311yescharacteristic
1437C4—22no—
1438C4—22no—
1439C4—22no—
1440C4—22no—
1441C4—22no—
1442C4—22no—
1443C4—22no—
1444C4—22no—
1445C4—22no—
1446C4—22no—
1447C4—22no—
1448C4—22no—
1449C4—22no—
1450C4—41no—
1451C4—41no—
1452C4—41no—
1453C4—41no—
1454C4—41no—
1455C4—41no—
1456C4—41no—
1457C4—41no—
1458C4—41no—
1459C4—41no—
1460C4—41no—
1461C4—41no—
1462C4—41no—
1463C4—41no—
1464C4—41no—
1465C2—42no—
1466C2—42no—
1467C2—81no—
1468C2D4×#41×C7311yescharacteristic
1469C2D4×#41×C7311yescharacteristic
1470C2C73×#348211yescharacteristic
1471C2C73×#349511yescharacteristic
1472C2C73×#349911yescharacteristic
1473C2C73×#350711yescharacteristic
1474C2C73×#356411yescharacteristic
subgroupG/H
center, socleC23×C73C25
commutator, Frattini, cosocleC23C25×C73
prime radical#392×C73C22
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×#552×C73C2semidirect
3. C73×#2721C2semidirect
4. C73×#2680C2semidirect
5. C73×#2677C2semidirect
6. C73×#2674C2semidirect
7. C73×#2599C2semidirect
8. C73×#2599C2semidirect
9. C73×#2560C2semidirect
11. C73×#2556C2semidirect
12. C73×#2553C2semidirect
13. C73×#2550C2semidirect
14. C73×#2549C2semidirect
15. C73×#2521C2semidirect
16. C73×#2519C2semidirect
17. C73×#2479C2semidirect
18. C73×#2478C2semidirect
19. C73×#2478C2semidirect
20. C73×#2462C2semidirect
21. C73×#2462C2semidirect
24. C73×#2449C2semidirect
25. C73×#2362C2semidirect
26. C73×#2360C2semidirect
27. C73×#2359C2semidirect
28. C73×#2359C2semidirect
29. C4×C4⋊Q8×C73C2semidirect
30. C4×#126×C73C2semidirect
31. C73×#2293C2semidirect
209. #126×C73D4semidirect
727. #59840C73direct (N × H)
738. C2×#556C2×C73semidirect
739. C2×#552C2×C73semidirect
740. #2721C2×C73semidirect
741. #2680C2×C73semidirect
742. #2677C2×C73semidirect
743. #2674C2×C73semidirect
744. #2599C2×C73semidirect
745. #2599C2×C73semidirect
746. #2560C2×C73semidirect
748. #2556C2×C73semidirect
749. #2553C2×C73semidirect
750. #2550C2×C73semidirect
751. #2549C2×C73semidirect
752. #2521C2×C73semidirect
753. #2519C2×C73semidirect
754. #2479C2×C73semidirect
755. #2478C2×C73semidirect
756. #2478C2×C73semidirect
757. #2462C2×C73semidirect
758. #2462C2×C73semidirect
761. #2449C2×C73semidirect
762. #2362C2×C73semidirect
763. #2360C2×C73semidirect
764. #2359C2×C73semidirect
765. #2359C2×C73semidirect
766. C4×C4⋊Q8C2×C73semidirect
767. C4×#126C2×C73semidirect
768. #2293C2×C73semidirect
769. C73#59840direct (N × H)
947. #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×#552×C732
C73×#27212
C73×#26802
C73×#26772
C73×#26742
C73×#25992
C73×#25602
C73×#25572
C73×#25562
C73×#25532
C73×#25502
C73×#25492
C73×#25212
C73×#25192
C73×#24792
C73×#24782
C73×#24622
C73×#24612
C73×#24552
C73×#24492
C73×#23622
C73×#23602
C73×#23592
C4×C4⋊Q8×C732
C4×#126×C732
C73×#22932
#5984073