Finite Group Databasebeta

← C73×#59801 #32969205

Subgroups — C73×#59801 #32969205

Order 18688.

2422 conjugacy classes of subgroups.

The subgroup lattice has 1568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#552×C73C211yesmaximal, characteristic, complemented
2C2×#547×C73C211yesmaximal, characteristic
3C73×#2713C211yesmaximal, characteristic, complemented
4C73×#2694C211yesmaximal, characteristic, complemented
5C73×#2689C211yesmaximal, characteristic, complemented
6C73×#2681C211yesmaximal, characteristic, complemented
7C73×#2559C211yesmaximal, characteristic, complemented
8C73×#2558C211yesmaximal, characteristic, complemented
9C73×#2556C211yesmaximal, characteristic, complemented
10C73×#2553C211yesmaximal, characteristic, complemented
11C73×#2550C211yesmaximal, characteristic, complemented
12C73×#2549C211yesmaximal, characteristic, complemented
13C73×#2488C211yesmaximal, characteristic, complemented
14C73×#2484C211yesmaximal, characteristic, complemented
15C73×#2473C211yesmaximal, characteristic, complemented
16C73×#2470C211yesmaximal, characteristic, complemented
17C73×#2466C211yesmaximal, characteristic, complemented
18C73×#2465C211yesmaximal, characteristic, complemented
19C73×#2449C211yesmaximal, characteristic, complemented
20C73×#2443C211yesmaximal, characteristic, complemented
21C73×#2425C211yesmaximal, characteristic, complemented
22C73×#2413C211yesmaximal, characteristic, complemented
23C73×#2406C211yesmaximal, characteristic, complemented
24C73×#2406C211yesmaximal, characteristic, complemented
25C73×#2360C211yesmaximal, characteristic, complemented
26C73×#2359C211yesmaximal, characteristic, complemented
27C73×#2359C211yesmaximal, characteristic, complemented
28C73×#2339C211yesmaximal, characteristic, complemented
29C4×#123×C73C211yesmaximal, characteristic, complemented
30C73×#2297C211yesmaximal, characteristic, complemented
31C2×#389×C73C211yesmaximal, characteristic, complemented
32C22×#41×C73C2211yescharacteristic
33C22×#41×C73C2211yescharacteristic
34#552×C73—28no—
35#547×C73—28no—
36C2×C4⋊Q8×C73C2211yescharacteristic
37C2×#126×C73C2211yescharacteristic
38C2×#126×C73C2211yescharacteristic
39C2×#125×C73C2211yescharacteristic
40C2×#125×C73C2211yescharacteristic
41C2×#125×C73C2211yescharacteristic
42C2×#123×C73C2211yescharacteristic
43C2×#123×C73C2211yescharacteristic
44C2×#123×C73C2211yescharacteristic
45C2×#123×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×#121×C73C2211yescharacteristic
56C2×#121×C73C2211yescharacteristic
57C2×C4×Q8×C73C2211yescharacteristic
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
65C22×C4⋊C4×C73C2211yescharacteristic
66C22×C4⋊C4×C73C2211yescharacteristic
67C22×C4⋊C4×C73C2211yescharacteristic
68C22×C4⋊C4×C73C2211yescharacteristic
69C22×C4⋊C4×C73C2211yescharacteristic
70C22×C42×C73C2211yescharacteristic
71#400×C73C2211yescharacteristic
72#400×C73C2211yescharacteristic
73#400×C73C2211yescharacteristic
74#400×C73C2211yescharacteristic
75#399×C73C2211yescharacteristic
76#399×C73C2211yescharacteristic
77#398×C73C2211yescharacteristic
78#398×C73C2211yescharacteristic
79#398×C73C2211yescharacteristic
80#398×C73C2211yescharacteristic
81#398×C73C2211yescharacteristic
82#398×C73C2211yescharacteristic
83#398×C73C2211yescharacteristic
84#397×C73C2211yescharacteristic
85#397×C73C2211yescharacteristic
86#397×C73C2211yescharacteristic
87#396×C73C2211yescharacteristic
88#396×C73C2211yescharacteristic
89#396×C73C2211yescharacteristic
90#396×C73C2211yescharacteristic
91#395×C73C2211yescharacteristic
92#395×C73C2211yescharacteristic
93#395×C73C2211yescharacteristic
94#395×C73C2211yescharacteristic
95#395×C73C2211yescharacteristic
96#394×C73C2211yescharacteristic
97#394×C73C2211yescharacteristic
98#394×C73C2211yescharacteristic
99#394×C73C2211yescharacteristic
100#394×C73C2211yescharacteristic
101#394×C73C2211yescharacteristic
102#393×C73C2211yescharacteristic
103#391×C73C2211yescharacteristic
104#391×C73C2211yescharacteristic
105#391×C73C2211yescharacteristic
106#391×C73C2211yescharacteristic
107#391×C73C2211yescharacteristic
108#390×C73C2211yescharacteristic
109#390×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#389×C73C2211yescharacteristic
120#389×C73C2211yescharacteristic
121#389×C73C2211yescharacteristic
122#389×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#387×C73C2211yescharacteristic
134#387×C73C2211yescharacteristic
135#387×C73C2211yescharacteristic
136#387×C73C2211yescharacteristic
137#387×C73C2211yescharacteristic
138#387×C73C2211yescharacteristic
139#387×C73C2211yescharacteristic
140#387×C73C2211yescharacteristic
141#387×C73C2211yescharacteristic
142#387×C73C2211yescharacteristic
143#386×C73C2211yescharacteristic
144#386×C73C2211yescharacteristic
145#386×C73C2211yescharacteristic
146#386×C73C2211yescharacteristic
147#386×C73C2211yescharacteristic
148#386×C73C2211yescharacteristic
149#386×C73C2211yescharacteristic
150#386×C73C2211yescharacteristic
151#386×C73C2211yescharacteristic
152#386×C73C2211yescharacteristic
153#385×C73C2211yescharacteristic
154#385×C73C2211yescharacteristic
155#385×C73C2211yescharacteristic
156#385×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#382×C73C2211yescharacteristic
168#381×C73C2211yescharacteristic
169#381×C73C2211yescharacteristic
170#381×C73C2211yescharacteristic
171#381×C73C2211yescharacteristic
172#380×C73C2211yescharacteristic
173#380×C73C2211yescharacteristic
174C4×C4⋊C4×C73C2211yescharacteristic
175C4×C4⋊C4×C73C2211yescharacteristic
176C4×C4⋊C4×C73C2211yescharacteristic
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
186C2×#95×C73C2211yescharacteristic
187C2×#95×C73C2211yescharacteristic
188C2×#95×C73C2211yescharacteristic
189C2×#41×C73—24no—
190C2×#41×C73—24no—
191C2×#41×C73—24no—
192C2×#41×C73—24no—
193C2×#41×C73—42no—
194C2×#41×C73—42no—
195C22×Q8×C73C2311yescharacteristic
196C22×Q8×C73C2311yescharacteristic
197C22×Q8×C73C2311yescharacteristic
198C22×D4×C73C2311yescharacteristic
199C22×D4×C73C2311yescharacteristic
200C22×D4×C73C2311yescharacteristic
201C22×D4×C73C2311yescharacteristic
202C22×D4×C73C2311yescharacteristic
203C22×D4×C73C2311yescharacteristic
204C23×C4×C73C2311yescharacteristic
205C23×C4×C73C2311yescharacteristic
206C23×C4×C73C2311yescharacteristic
207C23×C4×C73C2311yescharacteristic
208C23×C4×C73C2311yescharacteristic
209C23×C4×C73C2311yescharacteristic
210C23×C4×C73C2311yescharacteristic
211C23×C4×C73C2311yescharacteristic
212C23×C4×C73C2311yescharacteristic
213C23×C4×C73C2311yescharacteristic
214C23×C4×C73C2311yescharacteristic
215C23×C4×C73C2311yescharacteristic
216C23×C4×C73C2311yescharacteristic
217C23×C4×C73C2311yescharacteristic
218C4⋊Q8×C73—24no—
219#126×C73—24no—
220#126×C73—24no—
221#125×C73—24no—
222#125×C73—24no—
223#125×C73—24no—
224#123×C73—24no—
225#123×C73—24no—
226#123×C73—24no—
227#123×C73—24no—
228#123×C73—24no—
229#123×C73—24no—
230#123×C73—42no—
231#123×C73D418yes—
232C22⋊Q8×C73—24no—
233C22⋊Q8×C73—24no—
234C22⋊Q8×C73—24no—
235C22⋊Q8×C73—24no—
236C22⋊Q8×C73—24no—
237#121×C73—24no—
238#121×C73—24no—
239C4×Q8×C73—24no—
240C4×D4×C73—24no—
241C4×D4×C73—24no—
242C4×D4×C73—24no—
243C4×D4×C73—42no—
244#117×C73—24no—
245#117×C73—24no—
246#117×C73—24no—
247C2×C4⋊C4×C73—24no—
248C2×C4⋊C4×C73—24no—
249C2×C4⋊C4×C73—24no—
250C2×C4⋊C4×C73—24no—
251C2×C4⋊C4×C73—42no—
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×C4⋊C4×C73C2311yescharacteristic
286C2×C4⋊C4×C73C2311yescharacteristic
287C2×C4⋊C4×C73C2311yescharacteristic
288C2×C4⋊C4×C73C2311yescharacteristic
289C2×C4⋊C4×C73C2311yescharacteristic
290C2×C4⋊C4×C73C2311yescharacteristic
291C2×C4⋊C4×C73C2311yescharacteristic
292C2×C4⋊C4×C73C2311yescharacteristic
293C2×C4⋊C4×C73C2311yescharacteristic
294C2×C4⋊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×C22⋊C4×C73C2311yescharacteristic
324C2×C22⋊C4×C73C2311yescharacteristic
325C2×C22⋊C4×C73C2311yescharacteristic
326C2×C22⋊C4×C73C2311yescharacteristic
327C2×C22⋊C4×C73C2311yescharacteristic
328C2×C22⋊C4×C73C2311yescharacteristic
329C2×C42×C73—42no—
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
341C2×C42×C73C2311yescharacteristic
342C2×C42×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
379#95×C73C2311yescharacteristic
380#95×C73C2311yescharacteristic
381#95×C73C2311yescharacteristic
382#95×C73C2311yescharacteristic
383#95×C73C2311yescharacteristic
384#95×C73C2311yescharacteristic
385C24×C73C2411yescharacteristic
386C24×C73C2411yescharacteristic
387C24×C73C2411yescharacteristic
388C24×C73C2411yescharacteristic
389#41×C73—416no—
390#41×C73—416no—
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—41no—
398C2×Q8×C73—41no—
399C2×Q8×C73—41no—
400C2×D4×C73—22no—
401C2×D4×C73—22no—
402C2×D4×C73—22no—
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×C73C2×D414yes—
417C2×D4×C73#4114yes—
418C22×C4×C73—22no—
419C22×C4×C73—22no—
420C22×C4×C73—22no—
421C22×C4×C73—22no—
422C22×C4×C73—22no—
423C22×C4×C73—22no—
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—22no—
437C22×C4×C73—22no—
438C22×C4×C73—22no—
439C22×C4×C73—22no—
440C22×C4×C73—22no—
441C22×C4×C73—22no—
442C22×C4×C73—22no—
443C22×C4×C73—22no—
444C22×C4×C73—22no—
445C22×C4×C73—22no—
446C22×C4×C73—22no—
447C22×C4×C73—22no—
448C22×C4×C73—41no—
449C22×C4×C73—41no—
450C22×C4×C73—41no—
451C22×C4×C73—41no—
452C22×C4×C73—41no—
453C22×C4×C73—41no—
454C22×C4×C73—41no—
455C22×C4×C73—41no—
456C22×C4×C73—41no—
457C22×C4×C73—41no—
458C22×C4×C73—41no—
459C22×C4×C73C2×D414yes—
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
474C22×C4×C73C2411yescharacteristic
475C22×C4×C73C2411yescharacteristic
476C22×C4×C73C2411yescharacteristic
477C22×C4×C73C2411yescharacteristic
478C22×C4×C73C2411yescharacteristic
479C22×C4×C73C2411yescharacteristic
480C22×C4×C73C2411yescharacteristic
481C22×C4×C73C2411yescharacteristic
482C22×C4×C73C2411yescharacteristic
483C22×C4×C73C2411yescharacteristic
484C22×C4×C73C2411yescharacteristic
485C22×C4×C73C2411yescharacteristic
486C22×C4×C73C2411yescharacteristic
487C4⋊C4×C73—22no—
488C4⋊C4×C73—22no—
489C4⋊C4×C73—22no—
490C4⋊C4×C73—22no—
491C4⋊C4×C73—22no—
492C4⋊C4×C73—22no—
493C4⋊C4×C73—22no—
494C4⋊C4×C73—22no—
495C4⋊C4×C73—22no—
496C4⋊C4×C73—22no—
497C4⋊C4×C73—22no—
498C4⋊C4×C73—22no—
499C4⋊C4×C73—22no—
500C4⋊C4×C73—22no—
501C4⋊C4×C73—22no—
502C4⋊C4×C73—22no—
503C4⋊C4×C73—22no—
504C4⋊C4×C73—22no—
505C4⋊C4×C73—22no—
506C4⋊C4×C73—22no—
507C4⋊C4×C73—22no—
508C4⋊C4×C73—22no—
509C4⋊C4×C73—22no—
510C4⋊C4×C73—22no—
511C4⋊C4×C73—22no—
512C4⋊C4×C73—22no—
513C4⋊C4×C73—22no—
514C4⋊C4×C73—22no—
515C4⋊C4×C73—22no—
516C4⋊C4×C73—22no—
517C4⋊C4×C73—22no—
518C4⋊C4×C73—41no—
519C4⋊C4×C73—41no—
520C4⋊C4×C73—41no—
521C4⋊C4×C73—41no—
522C4⋊C4×C73—41no—
523C4⋊C4×C73—41no—
524C4⋊C4×C73—41no—
525C4⋊C4×C73—41no—
526C4⋊C4×C73—41no—
527C4⋊C4×C73C2×D414yes—
528C4⋊C4×C73C2×D414yes—
529C4⋊C4×C73#4114yescomplemented
530C22⋊C4×C73—22no—
531C22⋊C4×C73—22no—
532C22⋊C4×C73—22no—
533C22⋊C4×C73—22no—
534C22⋊C4×C73—22no—
535C22⋊C4×C73—22no—
536C22⋊C4×C73—22no—
537C22⋊C4×C73—22no—
538C22⋊C4×C73—22no—
539C22⋊C4×C73—22no—
540C22⋊C4×C73—22no—
541C22⋊C4×C73—22no—
542C22⋊C4×C73—22no—
543C22⋊C4×C73—22no—
544C22⋊C4×C73—22no—
545C22⋊C4×C73—22no—
546C22⋊C4×C73—22no—
547C22⋊C4×C73—22no—
548C22⋊C4×C73—22no—
549C22⋊C4×C73—22no—
550C22⋊C4×C73—22no—
551C22⋊C4×C73—22no—
552C22⋊C4×C73—22no—
553C22⋊C4×C73—22no—
554C22⋊C4×C73—41no—
555C22⋊C4×C73—41no—
556C22⋊C4×C73—41no—
557C22⋊C4×C73—41no—
558C22⋊C4×C73—41no—
559C22⋊C4×C73—41no—
560C22⋊C4×C73—41no—
561C22⋊C4×C73C2×D414yes—
562C22⋊C4×C73C2×D414yes—
563C22⋊C4×C73C2×D414yes—
564C42×C73—22no—
565C42×C73—22no—
566C42×C73—22no—
567C42×C73—22no—
568C42×C73—22no—
569C42×C73—22no—
570C42×C73—22no—
571C42×C73—41no—
572C42×C73—41no—
573C42×C73—41no—
574C42×C73—41no—
575C42×C73—41no—
576C42×C73—41no—
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×C73C22×D412yes—
601C23×C73C22×D412yes—
602C23×C73C2×#4112yes—
603C23×C73C2×#4112yes—
604C23×C73H(5,𝔽2)12yes—
605C23×C73C2511yescharacteristic
606Q8×C73—44no—
607Q8×C73—44no—
608Q8×C73—44no—
609D4×C73—28no—
610D4×C73—28no—
611D4×C73—44no—
612D4×C73—44no—
613D4×C73—44no—
614D4×C73—44no—
615C2×C4×C73—28no—
616C2×C4×C73—28no—
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—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—44no—
688C2×C4×C73—44no—
689C2×C4×C73—44no—
690C2×C4×C73—44no—
691C2×C4×C73—44no—
692C2×C4×C73—44no—
693C2×C4×C73—44no—
694C2×C4×C73—44no—
695C2×C4×C73—44no—
696C2×C4×C73—44no—
697C2×C4×C73—44no—
698C2×C4×C73—82no—
699C2×C4×C73C22×D412yes—
700C2×C4×C73C22×D412yes—
701C2×C4×C73C22×D412yes—
702C2×C4×C73C22×D412yes—
703C2×C4×C73C22×D412yes—
704C2×C4×C73C2×#4112yes—
705C2×C4×C73C2×#4112yes—
706C2×C4×C73C2×#4112yes—
707C2×C4×C73C2×#4112yes—
708C2×C4×C732−1+412yes—
709C2×C4×C732−1+412yes—
710C22×C73—22no—
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—22no—
721C22×C73—22no—
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#54614yes—
738C22×C73C23×D411yescharacteristic
739C22×C73C22×#4111yescharacteristic
740C22×C73C22×#4111yescharacteristic
741C22×C73C2×H(5,𝔽2)11yescharacteristic
742C22×C73C2×2−1+411yescharacteristic
743C22×C73C2×2−1+411yescharacteristic
744C22×C73#58511yescharacteristic
745C4×C73—22no—
746C4×C73—22no—
747C4×C73—22no—
748C4×C73—22no—
749C4×C73—22no—
750C4×C73—22no—
751C4×C73—22no—
752C4×C73—22no—
753C4×C73—22no—
754C4×C73—22no—
755C4×C73—22no—
756C4×C73—41no—
757C4×C73—41no—
758C4×C73—41no—
759C4×C73—41no—
760C4×C73—41no—
761C4×C73—41no—
762C4×C73—41no—
763C4×C73—41no—
764C4×C73—41no—
765C4×C73—41no—
766C4×C73—41no—
767C4×C73—41no—
768C4×C73—41no—
769C4×C73—41no—
770C4×C73—41no—
771C4×C73—41no—
772#59801C7311yesmaximal, characteristic, direct product factor, Sylow
773C2×C73—24no—
774C2×C73—42no—
775C2×C73—42no—
776C2×C73—81no—
777C2×C73C2×#54611yescharacteristic
778C2×C73D4×#4111yescharacteristic
779C2×C73#348211yescharacteristic
780C2×C73#349211yescharacteristic
781C2×C73#349911yescharacteristic
782C2×C73#351511yescharacteristic
783C2×C73#353511yescharacteristic
784C2×#552C2×C7311yescharacteristic, complemented
785C2×#547C2×C7311yescharacteristic
786#2713C2×C7311yescharacteristic, complemented
787#2694C2×C7311yescharacteristic, complemented
788#2689C2×C7311yescharacteristic, complemented
789#2681C2×C7311yescharacteristic, complemented
790#2559C2×C7311yescharacteristic, complemented
791#2558C2×C7311yescharacteristic, complemented
792#2556C2×C7311yescharacteristic, complemented
793#2553C2×C7311yescharacteristic, complemented
794#2550C2×C7311yescharacteristic, complemented
795#2549C2×C7311yescharacteristic, complemented
796#2488C2×C7311yescharacteristic, complemented
797#2484C2×C7311yescharacteristic, complemented
798#2473C2×C7311yescharacteristic, complemented
799#2470C2×C7311yescharacteristic, complemented
800#2466C2×C7311yescharacteristic, complemented
801#2465C2×C7311yescharacteristic, complemented
802#2449C2×C7311yescharacteristic, complemented
803#2443C2×C7311yescharacteristic, complemented
804#2425C2×C7311yescharacteristic, complemented
805#2413C2×C7311yescharacteristic, complemented
806#2406C2×C7311yescharacteristic, complemented
807#2406C2×C7311yescharacteristic, complemented
808#2360C2×C7311yescharacteristic, complemented
809#2359C2×C7311yescharacteristic, complemented
810#2359C2×C7311yescharacteristic, complemented
811#2339C2×C7311yescharacteristic, complemented
812C4×#123C2×C7311yescharacteristic, complemented
813#2297C2×C7311yescharacteristic, complemented
814C2×#389C2×C7311yescharacteristic, complemented
815C73#5980111yescharacteristic, direct product factor, Sylow
816C22×#41C22×C7311yescharacteristic
817C22×#41C22×C7311yescharacteristic
818#552—28no—
819#547—28no—
820C2×C4⋊Q8C22×C7311yescharacteristic
821C2×#126C22×C7311yescharacteristic
822C2×#126C22×C7311yescharacteristic
823C2×#125C22×C7311yescharacteristic
824C2×#125C22×C7311yescharacteristic
825C2×#125C22×C7311yescharacteristic
826C2×#123C22×C7311yescharacteristic
827C2×#123C22×C7311yescharacteristic
828C2×#123C22×C7311yescharacteristic
829C2×#123C22×C7311yescharacteristic
830C2×#123C22×C7311yescharacteristic
831C2×#123C22×C7311yescharacteristic
832C2×#123C22×C7311yescharacteristic
833C2×#123C22×C7311yescharacteristic
834C2×C22⋊Q8C22×C7311yescharacteristic
835C2×C22⋊Q8C22×C7311yescharacteristic
836C2×C22⋊Q8C22×C7311yescharacteristic
837C2×C22⋊Q8C22×C7311yescharacteristic
838C2×C22⋊Q8C22×C7311yescharacteristic
839C2×#121C22×C7311yescharacteristic
840C2×#121C22×C7311yescharacteristic
841C2×C4×Q8C22×C7311yescharacteristic
842C2×C4×D4C22×C7311yescharacteristic
843C2×C4×D4C22×C7311yescharacteristic
844C2×C4×D4C22×C7311yescharacteristic
845C2×C4×D4C22×C7311yescharacteristic
846C2×#117C22×C7311yescharacteristic
847C2×#117C22×C7311yescharacteristic
848C2×#117C22×C7311yescharacteristic
849C22×C4⋊C4C22×C7311yescharacteristic
850C22×C4⋊C4C22×C7311yescharacteristic
851C22×C4⋊C4C22×C7311yescharacteristic
852C22×C4⋊C4C22×C7311yescharacteristic
853C22×C4⋊C4C22×C7311yescharacteristic
854C22×C42C22×C7311yescharacteristic
855#400C22×C7311yescharacteristic
856#400C22×C7311yescharacteristic
857#400C22×C7311yescharacteristic
858#400C22×C7311yescharacteristic
859#399C22×C7311yescharacteristic
860#399C22×C7311yescharacteristic
861#398C22×C7311yescharacteristic
862#398C22×C7311yescharacteristic
863#398C22×C7311yescharacteristic
864#398C22×C7311yescharacteristic
865#398C22×C7311yescharacteristic
866#398C22×C7311yescharacteristic
867#398C22×C7311yescharacteristic
868#397C22×C7311yescharacteristic
869#397C22×C7311yescharacteristic
870#397C22×C7311yescharacteristic
871#396C22×C7311yescharacteristic
872#396C22×C7311yescharacteristic
873#396C22×C7311yescharacteristic
874#396C22×C7311yescharacteristic
875#395C22×C7311yescharacteristic
876#395C22×C7311yescharacteristic
877#395C22×C7311yescharacteristic
878#395C22×C7311yescharacteristic
879#395C22×C7311yescharacteristic
880#394C22×C7311yescharacteristic
881#394C22×C7311yescharacteristic
882#394C22×C7311yescharacteristic
883#394C22×C7311yescharacteristic
884#394C22×C7311yescharacteristic
885#394C22×C7311yescharacteristic
886#393C22×C7311yescharacteristic
887#391C22×C7311yescharacteristic
888#391C22×C7311yescharacteristic
889#391C22×C7311yescharacteristic
890#391C22×C7311yescharacteristic
891#391C22×C7311yescharacteristic
892#390C22×C7311yescharacteristic
893#390C22×C7311yescharacteristic
894#389C22×C7311yescharacteristic
895#389C22×C7311yescharacteristic
896#389C22×C7311yescharacteristic
897#389C22×C7311yescharacteristic
898#389C22×C7311yescharacteristic
899#389C22×C7311yescharacteristic
900#389C22×C7311yescharacteristic
901#389C22×C7311yescharacteristic
902#389C22×C7311yescharacteristic
903#389C22×C7311yescharacteristic
904#389C22×C7311yescharacteristic
905#389C22×C7311yescharacteristic
906#389C22×C7311yescharacteristic
907#388C22×C7311yescharacteristic
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#387C22×C7311yescharacteristic
918#387C22×C7311yescharacteristic
919#387C22×C7311yescharacteristic
920#387C22×C7311yescharacteristic
921#387C22×C7311yescharacteristic
922#387C22×C7311yescharacteristic
923#387C22×C7311yescharacteristic
924#387C22×C7311yescharacteristic
925#387C22×C7311yescharacteristic
926#387C22×C7311yescharacteristic
927#386C22×C7311yescharacteristic
928#386C22×C7311yescharacteristic
929#386C22×C7311yescharacteristic
930#386C22×C7311yescharacteristic
931#386C22×C7311yescharacteristic
932#386C22×C7311yescharacteristic
933#386C22×C7311yescharacteristic
934#386C22×C7311yescharacteristic
935#386C22×C7311yescharacteristic
936#386C22×C7311yescharacteristic
937#385C22×C7311yescharacteristic
938#385C22×C7311yescharacteristic
939#385C22×C7311yescharacteristic
940#385C22×C7311yescharacteristic
941#385C22×C7311yescharacteristic
942#385C22×C7311yescharacteristic
943#385C22×C7311yescharacteristic
944#385C22×C7311yescharacteristic
945#385C22×C7311yescharacteristic
946#385C22×C7311yescharacteristic
947#385C22×C7311yescharacteristic
948#385C22×C7311yescharacteristic
949#385C22×C7311yescharacteristic
950#385C22×C7311yescharacteristic
951#382C22×C7311yescharacteristic
952#381C22×C7311yescharacteristic
953#381C22×C7311yescharacteristic
954#381C22×C7311yescharacteristic
955#381C22×C7311yescharacteristic
956#380C22×C7311yescharacteristic
957#380C22×C7311yescharacteristic
958C4×C4⋊C4C22×C7311yescharacteristic
959C4×C4⋊C4C22×C7311yescharacteristic
960C4×C4⋊C4C22×C7311yescharacteristic
961C4×C22⋊C4C22×C7311yescharacteristic
962C4×C22⋊C4C22×C7311yescharacteristic
963C4×C22⋊C4C22×C7311yescharacteristic
964C4×C22⋊C4C22×C7311yescharacteristic
965C4×C22⋊C4C22×C7311yescharacteristic
966C4×C22⋊C4C22×C7311yescharacteristic
967C4×C22⋊C4C22×C7311yescharacteristic
968C4×C22⋊C4C22×C7311yescharacteristic
969C4×C22⋊C4C22×C7311yescharacteristic
970C2×#95C22×C7311yescharacteristic
971C2×#95C22×C7311yescharacteristic
972C2×#95C22×C7311yescharacteristic
973C2×#41—24no—
974C2×#41—24no—
975C2×#41—24no—
976C2×#41—24no—
977C2×#41—42no—
978C2×#41—42no—
979C22×Q8C23×C7311yescharacteristic
980C22×Q8C23×C7311yescharacteristic
981C22×Q8C23×C7311yescharacteristic
982C22×D4C23×C7311yescharacteristic
983C22×D4C23×C7311yescharacteristic
984C22×D4C23×C7311yescharacteristic
985C22×D4C23×C7311yescharacteristic
986C22×D4C23×C7311yescharacteristic
987C22×D4C23×C7311yescharacteristic
988C23×C4C23×C7311yescharacteristic
989C23×C4C23×C7311yescharacteristic
990C23×C4C23×C7311yescharacteristic
991C23×C4C23×C7311yescharacteristic
992C23×C4C23×C7311yescharacteristic
993C23×C4C23×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#125—24no—
1006#125—24no—
1007#125—24no—
1008#123—24no—
1009#123—24no—
1010#123—24no—
1011#123—24no—
1012#123—24no—
1013#123—24no—
1014#123—42no—
1015#123D4×C7318yes—
1016C22⋊Q8—24no—
1017C22⋊Q8—24no—
1018C22⋊Q8—24no—
1019C22⋊Q8—24no—
1020C22⋊Q8—24no—
1021#121—24no—
1022#121—24no—
1023C4×Q8—24no—
1024C4×D4—24no—
1025C4×D4—24no—
1026C4×D4—24no—
1027C4×D4—42no—
1028#117—24no—
1029#117—24no—
1030#117—24no—
1031C2×C4⋊C4—24no—
1032C2×C4⋊C4—24no—
1033C2×C4⋊C4—24no—
1034C2×C4⋊C4—24no—
1035C2×C4⋊C4—42no—
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×C4⋊C4C23×C7311yescharacteristic
1064C2×C4⋊C4C23×C7311yescharacteristic
1065C2×C4⋊C4C23×C7311yescharacteristic
1066C2×C4⋊C4C23×C7311yescharacteristic
1067C2×C4⋊C4C23×C7311yescharacteristic
1068C2×C4⋊C4C23×C7311yescharacteristic
1069C2×C4⋊C4C23×C7311yescharacteristic
1070C2×C4⋊C4C23×C7311yescharacteristic
1071C2×C4⋊C4C23×C7311yescharacteristic
1072C2×C4⋊C4C23×C7311yescharacteristic
1073C2×C4⋊C4C23×C7311yescharacteristic
1074C2×C4⋊C4C23×C7311yescharacteristic
1075C2×C4⋊C4C23×C7311yescharacteristic
1076C2×C4⋊C4C23×C7311yescharacteristic
1077C2×C4⋊C4C23×C7311yescharacteristic
1078C2×C4⋊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×C42—42no—
1114C2×C42C23×C7311yescharacteristic
1115C2×C42C23×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
1127#95C23×C7311yescharacteristic
1128#95C23×C7311yescharacteristic
1129#95C23×C7311yescharacteristic
1130#95C23×C7311yescharacteristic
1131#95C23×C7311yescharacteristic
1132#95C23×C7311yescharacteristic
1133#95C23×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
1169C24C24×C7311yescharacteristic
1170C24C24×C7311yescharacteristic
1171C24C24×C7311yescharacteristic
1172C24C24×C7311yescharacteristic
1173#41—416no—
1174#41—416no—
1175C2×Q8—22no—
1176C2×Q8—22no—
1177C2×Q8—22no—
1178C2×Q8—22no—
1179C2×Q8—22no—
1180C2×Q8—22no—
1181C2×Q8—41no—
1182C2×Q8—41no—
1183C2×Q8—41no—
1184C2×D4—22no—
1185C2×D4—22no—
1186C2×D4—22no—
1187C2×D4—22no—
1188C2×D4—22no—
1189C2×D4—22no—
1190C2×D4—22no—
1191C2×D4—22no—
1192C2×D4—22no—
1193C2×D4—22no—
1194C2×D4—22no—
1195C2×D4—22no—
1196C2×D4—22no—
1197C2×D4—41no—
1198C2×D4—41no—
1199C2×D4—41no—
1200C2×D4C2×D4×C7314yes—
1201C2×D4#41×C7314yes—
1202C22×C4—22no—
1203C22×C4—22no—
1204C22×C4—22no—
1205C22×C4—22no—
1206C22×C4—22no—
1207C22×C4—22no—
1208C22×C4—22no—
1209C22×C4—22no—
1210C22×C4—22no—
1211C22×C4—22no—
1212C22×C4—22no—
1213C22×C4—22no—
1214C22×C4—22no—
1215C22×C4—22no—
1216C22×C4—22no—
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—22no—
1230C22×C4—22no—
1231C22×C4—22no—
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×C4—41no—
1242C22×C4—41no—
1243C22×C4C2×D4×C7314yes—
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
1267C22×C4C24×C7311yescharacteristic
1268C22×C4C24×C7311yescharacteristic
1269C22×C4C24×C7311yescharacteristic
1270C22×C4C24×C7311yescharacteristic
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—22no—
1286C4⋊C4—22no—
1287C4⋊C4—22no—
1288C4⋊C4—22no—
1289C4⋊C4—22no—
1290C4⋊C4—22no—
1291C4⋊C4—22no—
1292C4⋊C4—22no—
1293C4⋊C4—22no—
1294C4⋊C4—22no—
1295C4⋊C4—22no—
1296C4⋊C4—22no—
1297C4⋊C4—22no—
1298C4⋊C4—22no—
1299C4⋊C4—22no—
1300C4⋊C4—22no—
1301C4⋊C4—22no—
1302C4⋊C4—41no—
1303C4⋊C4—41no—
1304C4⋊C4—41no—
1305C4⋊C4—41no—
1306C4⋊C4—41no—
1307C4⋊C4—41no—
1308C4⋊C4—41no—
1309C4⋊C4—41no—
1310C4⋊C4—41no—
1311C4⋊C4C2×D4×C7314yes—
1312C4⋊C4C2×D4×C7314yes—
1313C4⋊C4#41×C7314yescomplemented
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—22no—
1328C22⋊C4—22no—
1329C22⋊C4—22no—
1330C22⋊C4—22no—
1331C22⋊C4—22no—
1332C22⋊C4—22no—
1333C22⋊C4—22no—
1334C22⋊C4—22no—
1335C22⋊C4—22no—
1336C22⋊C4—22no—
1337C22⋊C4—22no—
1338C22⋊C4—41no—
1339C22⋊C4—41no—
1340C22⋊C4—41no—
1341C22⋊C4—41no—
1342C22⋊C4—41no—
1343C22⋊C4—41no—
1344C22⋊C4—41no—
1345C22⋊C4C2×D4×C7314yes—
1346C22⋊C4C2×D4×C7314yes—
1347C22⋊C4C2×D4×C7314yes—
1348C42—22no—
1349C42—22no—
1350C42—22no—
1351C42—22no—
1352C42—22no—
1353C42—22no—
1354C42—22no—
1355C42—41no—
1356C42—41no—
1357C42—41no—
1358C42—41no—
1359C42—41no—
1360C42—41no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
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—
1384C23C22×D4×C7312yes—
1385C23C22×D4×C7312yes—
1386C23C2×#41×C7312yes—
1387C23C2×#41×C7312yes—
1388C23H(5,𝔽2)×C7312yes—
1389C23C25×C7311yescharacteristic
1390Q8—44no—
1391Q8—44no—
1392Q8—44no—
1393D4—28no—
1394D4—28no—
1395D4—44no—
1396D4—44no—
1397D4—44no—
1398D4—44no—
1399C2×C4—28no—
1400C2×C4—28no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
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—44no—
1472C2×C4—44no—
1473C2×C4—44no—
1474C2×C4—44no—
1475C2×C4—44no—
1476C2×C4—44no—
1477C2×C4—44no—
1478C2×C4—44no—
1479C2×C4—44no—
1480C2×C4—44no—
1481C2×C4—44no—
1482C2×C4—82no—
1483C2×C4C22×D4×C7312yes—
1484C2×C4C22×D4×C7312yes—
1485C2×C4C22×D4×C7312yes—
1486C2×C4C22×D4×C7312yes—
1487C2×C4C22×D4×C7312yes—
1488C2×C4C2×#41×C7312yes—
1489C2×C4C2×#41×C7312yes—
1490C2×C4C2×#41×C7312yes—
1491C2×C4C2×#41×C7312yes—
1492C2×C42−1+4×C7312yes—
1493C2×C42−1+4×C7312yes—
1494C22—22no—
1495C22—22no—
1496C22—22no—
1497C22—22no—
1498C22—22no—
1499C22—22no—
1500C22—22no—
1501C22—22no—
1502C22—22no—
1503C22—22no—
1504C22—22no—
1505C22—22no—
1506C22—41no—
1507C22—41no—
1508C22—41no—
1509C22—41no—
1510C22—41no—
1511C22—41no—
1512C22—41no—
1513C22—41no—
1514C22—41no—
1515C22—41no—
1516C22—41no—
1517C22—41no—
1518C22—41no—
1519C22—41no—
1520C22—41no—
1521C22#546×C7314yes—
1522C22C23×D4×C7311yescharacteristic
1523C22C22×#41×C7311yescharacteristic
1524C22C22×#41×C7311yescharacteristic
1525C22C2×H(5,𝔽2)×C7311yescharacteristic
1526C22C2×2−1+4×C7311yescharacteristic
1527C22C2×2−1+4×C7311yescharacteristic
1528C22#585×C7311yescharacteristic
1529C4—22no—
1530C4—22no—
1531C4—22no—
1532C4—22no—
1533C4—22no—
1534C4—22no—
1535C4—22no—
1536C4—22no—
1537C4—22no—
1538C4—22no—
1539C4—22no—
1540C4—41no—
1541C4—41no—
1542C4—41no—
1543C4—41no—
1544C4—41no—
1545C4—41no—
1546C4—41no—
1547C4—41no—
1548C4—41no—
1549C4—41no—
1550C4—41no—
1551C4—41no—
1552C4—41no—
1553C4—41no—
1554C4—41no—
1555C4—41no—
1556C2—24no—
1557C2—42no—
1558C2—42no—
1559C2—81no—
1560C2C2×#546×C7311yescharacteristic
1561C2D4×#41×C7311yescharacteristic
1562C2C73×#348211yescharacteristic
1563C2C73×#349211yescharacteristic
1564C2C73×#349911yescharacteristic
1565C2C73×#351511yescharacteristic
1566C2C73×#353511yescharacteristic
subgroupG/H
center, socleC23×C73C25
commutator, Frattini, cosocleC23C25×C73
prime radicalC2×#547×C73C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#552×C73C2semidirect
3. C73×#2713C2semidirect
4. C73×#2694C2semidirect
5. C73×#2689C2semidirect
6. C73×#2681C2semidirect
7. C73×#2559C2semidirect
8. C73×#2558C2semidirect
9. C73×#2556C2semidirect
10. C73×#2553C2semidirect
11. C73×#2550C2semidirect
12. C73×#2549C2semidirect
13. C73×#2488C2semidirect
14. C73×#2484C2semidirect
15. C73×#2473C2semidirect
16. C73×#2470C2semidirect
17. C73×#2466C2semidirect
18. C73×#2465C2semidirect
19. C73×#2449C2semidirect
20. C73×#2443C2semidirect
21. C73×#2425C2semidirect
22. C73×#2413C2semidirect
23. C73×#2406C2semidirect
24. C73×#2406C2semidirect
25. C73×#2360C2semidirect
26. C73×#2359C2semidirect
27. C73×#2359C2semidirect
28. C73×#2339C2semidirect
29. C4×#123×C73C2semidirect
30. C73×#2297C2semidirect
31. C2×#389×C73C2semidirect
529. C4⋊C4×C73#41semidirect
772. #59801C73direct (N × H)
784. C2×#552C2×C73semidirect
786. #2713C2×C73semidirect
787. #2694C2×C73semidirect
788. #2689C2×C73semidirect
789. #2681C2×C73semidirect
790. #2559C2×C73semidirect
791. #2558C2×C73semidirect
792. #2556C2×C73semidirect
793. #2553C2×C73semidirect
794. #2550C2×C73semidirect
795. #2549C2×C73semidirect
796. #2488C2×C73semidirect
797. #2484C2×C73semidirect
798. #2473C2×C73semidirect
799. #2470C2×C73semidirect
800. #2466C2×C73semidirect
801. #2465C2×C73semidirect
802. #2449C2×C73semidirect
803. #2443C2×C73semidirect
804. #2425C2×C73semidirect
805. #2413C2×C73semidirect
806. #2406C2×C73semidirect
807. #2406C2×C73semidirect
808. #2360C2×C73semidirect
809. #2359C2×C73semidirect
810. #2359C2×C73semidirect
811. #2339C2×C73semidirect
812. C4×#123C2×C73semidirect
813. #2297C2×C73semidirect
814. C2×#389C2×C73semidirect
815. C73#59801direct (N × H)
1313. C4⋊C4#41×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#552×C732
C2×#547×C732
C73×#27132
C73×#26942
C73×#26892
C73×#26812
C73×#25592
C73×#25582
C73×#25562
C73×#25532
C73×#25502
C73×#25492
C73×#24882
C73×#24842
C73×#24732
C73×#24702
C73×#24662
C73×#24652
C73×#24492
C73×#24432
C73×#24252
C73×#24132
C73×#24062
C73×#23602
C73×#23592
C73×#23392
C4×#123×C732
C73×#22972
C2×#389×C732
#5980173