Finite Group Databasebeta

← #33112319

Subgroups — #33112319

Order 18688.

776 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22610730C211yesmaximal, characteristic, complemented
2#22610730C211yesmaximal, characteristic, complemented
3#22610546C211yesmaximal, characteristic, complemented
4#22610546C211yesmaximal, characteristic, complemented
5#22610497C211yesmaximal, characteristic, complemented
6#22610497C211yesmaximal, characteristic, complemented
7#22610229C211yesmaximal, characteristic, complemented
8#22610229C211yesmaximal, characteristic, complemented
9#22610224C211yesmaximal, characteristic, complemented
10#22610224C211yesmaximal, characteristic, complemented
11#22610116C211yesmaximal, characteristic, complemented
12#22610111C211yesmaximal, characteristic, complemented
13#22610002C211yesmaximal, characteristic, complemented
14#22609915C211yesmaximal, characteristic, complemented
15C73×#2392C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18C2×C4⋊#10596831C2211yescharacteristic
19C2×C4⋊#10596831C2211yescharacteristic
20C2×C4⋊#10596831C2211yescharacteristic
21C2×C4⋊#10596831C2211yescharacteristic
22C2×C22⋊#10596831C2211yescharacteristic
23C2×C22⋊#10596831C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26C2×C22⋊#10596831C2211yescharacteristic
27C2×C22⋊#10596831C2211yescharacteristic
28C2×C22⋊#10596831C2211yescharacteristic
29C2×C22⋊#10596831C2211yescharacteristic
30C2×C22⋊#10596831C2211yescharacteristic
31C2×C22⋊#10596831C2211yescharacteristic
32C2×#14556502C2211yescharacteristic
33C2×#14556502C2211yescharacteristic
34#17988342C2211yescharacteristic
35#17988342C2211yescharacteristic
36#17988342C2211yescharacteristic
37#17988342C2211yescharacteristic
38#17988342C2211yescharacteristic
39#17988342C2211yescharacteristic
40#17988342C2211yescharacteristic
41#17988342C2211yescharacteristic
42#17988342C2211yescharacteristic
43#17988342C2211yescharacteristic
44C2×C4×D4×C73C2211yescharacteristic
45C2×C4×D4×C73C2211yescharacteristic
46C2×C4×D4×C73C2211yescharacteristic
47C2×#117×C73C2211yescharacteristic
48#398×C73C411yescharacteristic
49#397×C73C411yescharacteristic
50#396×C73C411yescharacteristic
51#396×C73C411yescharacteristic
52#394×C73C411yescharacteristic
53#394×C73C411yescharacteristic
54#394×C73C411yescharacteristic
55#392×C73C411yescharacteristic
56C4×C4⋊C4×C73C2211yescharacteristic
57C4×C22⋊C4×C73C2211yescharacteristic
58C4×C22⋊C4×C73C2211yescharacteristic
59C2×#11924012—41no—
60C2×#11924012—41no—
61C2×#11924012—41no—
62C22×#10596831—41no—
63C22×#10596831—41no—
64C22×#10596831—41no—
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73C4⋊#10596831—41no—
74C4⋊#10596831—41no—
75C4⋊#10596831—41no—
76C4⋊#10596831—41no—
77C22⋊#10596831—41no—
78C22⋊#10596831—41no—
79C22⋊#10596831—41no—
80C22⋊#10596831—41no—
81C22⋊#10596831—41no—
82C22⋊#10596831—41no—
83C22⋊#10596831—41no—
84C22⋊#10596831—41no—
85C22⋊#10596831—41no—
86C22⋊#10596831—41no—
87#14556502—41no—
88#14556502—41no—
89C22×D4×C73C2×C411yescharacteristic
90C22×D4×C73C2×C411yescharacteristic
91C22×D4×C73C2×C411yescharacteristic
92C23×C4×C73C2311yescharacteristic
93C23×C4×C73C2311yescharacteristic
94C23×C4×C73C2311yescharacteristic
95C4×D4×C73—41no—
96C4×D4×C73—41no—
97C4×D4×C73—41no—
98C4×D4×C73—41no—
99C4×D4×C73—41no—
100C4×D4×C73—41no—
101#117×C73—41no—
102#117×C73—41no—
103C2×C4⋊C4×C73C2×C411yescharacteristic
104C2×C4⋊C4×C73C2×C411yescharacteristic
105C2×C4⋊C4×C73C2×C411yescharacteristic
106C2×C4⋊C4×C73C2×C411yescharacteristic
107C2×C4⋊C4×C73C2×C411yescharacteristic
108C2×C4⋊C4×C73C2×C411yescharacteristic
109C2×C4⋊C4×C73C2×C411yescharacteristic
110C2×C22⋊C4×C73C2×C411yescharacteristic
111C2×C22⋊C4×C73C2×C411yescharacteristic
112C2×C22⋊C4×C73C2×C411yescharacteristic
113C2×C22⋊C4×C73C2×C411yescharacteristic
114C2×C22⋊C4×C73C2×C411yescharacteristic
115C2×C22⋊C4×C73C2×C411yescharacteristic
116C2×C22⋊C4×C73C2×C411yescharacteristic
117C2×C22⋊C4×C73C2×C411yescharacteristic
118C2×C22⋊C4×C73C2×C411yescharacteristic
119C2×C22⋊C4×C73C2×C411yescharacteristic
120C2×C22⋊C4×C73C2×C411yescharacteristic
121C2×C22⋊C4×C73C2×C411yescharacteristic
122C2×C42×C73C2311yescharacteristic
123C2×C42×C73C2311yescharacteristic
124C2×C42×C73C2311yescharacteristic
125C2×C42×C73C2311yescharacteristic
126#95×C73C2×C411yescharacteristic
127#95×C73C2×C411yescharacteristic
128#95×C73C2×C411yescharacteristic
129#95×C73C2×C411yescharacteristic
130#95×C73C2×C411yescharacteristic
131#95×C73C2×C411yescharacteristic
132#11924012—44no—
133C2×#10596831—21no—
134C2×#10596831—21no—
135C2×#10596831—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831—21no—
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—44no—
158C24×C73C22×C411yescharacteristic
159C24×C73C22×C411yescharacteristic
160C24×C73C22×C411yescharacteristic
161C2×D4×C73—22no—
162C2×D4×C73—22no—
163C2×D4×C73—41no—
164C2×D4×C73—41no—
165C2×D4×C73—41no—
166C2×D4×C73—41no—
167C2×D4×C73—41no—
168C2×D4×C73—41no—
169C2×D4×C73—41no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73C22×C411yescharacteristic
189C22×C4×C73C22×C411yescharacteristic
190C22×C4×C73C22×C411yescharacteristic
191C22×C4×C73C22×C411yescharacteristic
192C22×C4×C73C22×C411yescharacteristic
193C22×C4×C73C22×C411yescharacteristic
194C22×C4×C73C22×C411yescharacteristic
195C22×C4×C73C22×C411yescharacteristic
196C22×C4×C73C22×C411yescharacteristic
197C22×C4×C73C22×C411yescharacteristic
198C22×C4×C73C22×C411yescharacteristic
199C22×C4×C73C2411yescharacteristic
200C4⋊C4×C73—41no—
201C4⋊C4×C73—41no—
202C4⋊C4×C73—41no—
203C4⋊C4×C73—41no—
204C4⋊C4×C73—41no—
205C4⋊C4×C73—41no—
206C4⋊C4×C73—41no—
207C22⋊C4×C73—22no—
208C22⋊C4×C73—41no—
209C22⋊C4×C73—41no—
210C22⋊C4×C73—41no—
211C22⋊C4×C73—41no—
212C22⋊C4×C73—41no—
213C22⋊C4×C73—41no—
214C22⋊C4×C73—41no—
215C22⋊C4×C73—41no—
216C22⋊C4×C73—41no—
217C22⋊C4×C73—41no—
218C22⋊C4×C73—41no—
219C42×C73—21no—
220C42×C73—21no—
221C42×C73—21no—
222C42×C73—21no—
223C42×C73—21no—
224C42×C73—21no—
225C42×C73—21no—
226C42×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73#13112yes—
248C23×C73C23×C411yescharacteristic
249D4×C73—44no—
250D4×C73—44no—
251D4×C73—44no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73H(5,𝔽2)11yescharacteristic
298C2×C4×C73H(5,𝔽2)11yescharacteristic
299C2×C4×C73H(5,𝔽2)11yescharacteristic
300C2×C4×C73H(5,𝔽2)11yescharacteristic
301C2×C4×C73H(5,𝔽2)11yescharacteristic
302C2×C4×C732−1+411yescharacteristic
303#10596831—41no—
304#10596831—41no—
305#10596831—41no—
306#10596831—41no—
307#10596831—41no—
308#10596831—41no—
309#10596831—41no—
310#10596831—41no—
311C22×C73—22no—
312C22×C73—22no—
313C22×C73—22no—
314C22×C73—41no—
315C22×C73—41no—
316C22×C73—41no—
317C22×C73—41no—
318C22×C73—41no—
319C22×C73—41no—
320C22×C73—41no—
321C22×C73—41no—
322C22×C73—41no—
323C22×C73—41no—
324C22×C73—41no—
325C22×C73—41no—
326C22×C73—41no—
327C22×C73—41no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—41no—
331C22×C73—41no—
332C22×C73#51811yescharacteristic
333C22×C73#51811yescharacteristic
334C22×C73#52011yescharacteristic
335C22×C73C2×#13111yescharacteristic
336C22×C73#56811yescharacteristic
337C22×C73#56811yescharacteristic
338C22×C73#56811yescharacteristic
339C4×C73—41no—
340C4×C73—41no—
341C4×C73—41no—
342C4×C73—41no—
343C4×C73—41no—
344C4×C73—41no—
345C4×C73—41no—
346C4×C73—41no—
347C4×C73—41no—
348C4×C73—41no—
349C4×C73—41no—
350C4×C73#56011yescharacteristic
351C4×C73#56011yescharacteristic
352C4×C73#56211yescharacteristic
353C4×C73#56211yescharacteristic
354#23335—731nomaximal, Sylow
355C2×C73—42no—
356C2×C73—81no—
357C2×C73—81no—
358C2×C73#237711yescharacteristic
359C2×C73#297611yescharacteristic
360C2×C73#297611yescharacteristic
361C2×C73#297811yescharacteristic
362C2×C73#298011yescharacteristic
363C2×C73#299211yescharacteristic
364C2×C73#299511yescharacteristic
365#2392D7311yescharacteristic
366#1955—731no—
367#1955—731no—
368#1924—731no—
369#1924—731no—
370#1917—731no—
371#1917—731no—
372#1870—731no—
373#1870—731no—
374#1869—731no—
375#1869—731no—
376#1851—731no—
377#1850—731no—
378#1818—731no—
379#1798—731no—
380C73#2333511yescharacteristic, complemented, Sylow
381C22×M16—731no—
382C23×C8—731no—
383C2×C4×D4C2×D7311yescharacteristic
384C2×C4×D4C2×D7311yescharacteristic
385C2×C4×D4C2×D7311yescharacteristic
386C2×#117C2×D7311yescharacteristic
387C2×C4⋊C8—731no—
388C2×C4⋊C8—731no—
389C2×C4⋊C8—731no—
390C2×C4⋊C8—731no—
391C2×C22⋊C8—731no—
392C2×C22⋊C8—731no—
393C2×C22⋊C8—731no—
394C2×C22⋊C8—731no—
395C2×C22⋊C8—731no—
396C2×C22⋊C8—731no—
397C2×C22⋊C8—731no—
398C2×C22⋊C8—731no—
399C2×C22⋊C8—731no—
400C2×C22⋊C8—731no—
401C2×#97—731no—
402C2×#97—731no—
403#398Dic7311yescharacteristic
404#397Dic7311yescharacteristic
405#396Dic7311yescharacteristic
406#396Dic7311yescharacteristic
407#394Dic7311yescharacteristic
408#394Dic7311yescharacteristic
409#394Dic7311yescharacteristic
410#392Dic7311yescharacteristic
411C4×C4⋊C4C2×D7311yescharacteristic
412C4×C22⋊C4C2×D7311yescharacteristic
413C4×C22⋊C4C2×D7311yescharacteristic
414#336—731no—
415#336—731no—
416#336—731no—
417#336—731no—
418#336—731no—
419#336—731no—
420#336—731no—
421#336—731no—
422#336—731no—
423#336—731no—
424C22×D4C2×Dic7311yescharacteristic
425C22×D4C2×Dic7311yescharacteristic
426C22×D4C2×Dic7311yescharacteristic
427C23×C4C22×D7311yescharacteristic
428C23×C4C22×D7311yescharacteristic
429C23×C4C22×D7311yescharacteristic
430C2×M16—2921no—
431C2×M16—2921no—
432C2×M16—2921no—
433C22×C8—2921no—
434C22×C8—2921no—
435C22×C8—2921no—
436C22×C8—731no—
437C22×C8—731no—
438C22×C8—731no—
439C22×C8—731no—
440C22×C8—731no—
441C22×C8—731no—
442C22×C8—731no—
443C22×C8—731no—
444C4×D4—41no—
445C4×D4—41no—
446C4×D4—41no—
447C4×D4—41no—
448C4×D4—41no—
449C4×D4—41no—
450#117—41no—
451#117—41no—
452C2×C4⋊C4C2×Dic7311yescharacteristic
453C2×C4⋊C4C2×Dic7311yescharacteristic
454C2×C4⋊C4C2×Dic7311yescharacteristic
455C2×C4⋊C4C2×Dic7311yescharacteristic
456C2×C4⋊C4C2×Dic7311yescharacteristic
457C2×C4⋊C4C2×Dic7311yescharacteristic
458C2×C4⋊C4C2×Dic7311yescharacteristic
459C2×C22⋊C4C2×Dic7311yescharacteristic
460C2×C22⋊C4C2×Dic7311yescharacteristic
461C2×C22⋊C4C2×Dic7311yescharacteristic
462C2×C22⋊C4C2×Dic7311yescharacteristic
463C2×C22⋊C4C2×Dic7311yescharacteristic
464C2×C22⋊C4C2×Dic7311yescharacteristic
465C2×C22⋊C4C2×Dic7311yescharacteristic
466C2×C22⋊C4C2×Dic7311yescharacteristic
467C2×C22⋊C4C2×Dic7311yescharacteristic
468C2×C22⋊C4C2×Dic7311yescharacteristic
469C2×C22⋊C4C2×Dic7311yescharacteristic
470C2×C22⋊C4C2×Dic7311yescharacteristic
471C2×C42C22×D7311yescharacteristic
472C2×C42C22×D7311yescharacteristic
473C2×C42C22×D7311yescharacteristic
474C2×C42C22×D7311yescharacteristic
475C4⋊C8—2921no—
476C4⋊C8—2921no—
477C4⋊C8—2921no—
478C4⋊C8—2921no—
479C22⋊C8—2921no—
480C22⋊C8—2921no—
481C22⋊C8—2921no—
482C22⋊C8—2921no—
483C22⋊C8—2921no—
484C22⋊C8—2921no—
485C22⋊C8—2921no—
486C22⋊C8—2921no—
487C22⋊C8—2921no—
488C22⋊C8—2921no—
489#97—2921no—
490#97—2921no—
491#95C2×Dic7311yescharacteristic
492#95C2×Dic7311yescharacteristic
493#95C2×Dic7311yescharacteristic
494#95C2×Dic7311yescharacteristic
495#95C2×Dic7311yescharacteristic
496#95C2×Dic7311yescharacteristic
497C24C22×Dic7311yescharacteristic
498C24C22×Dic7311yescharacteristic
499C24C22×Dic7311yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—41no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4C22×Dic7311yescharacteristic
528C22×C4C22×Dic7311yescharacteristic
529C22×C4C22×Dic7311yescharacteristic
530C22×C4C22×Dic7311yescharacteristic
531C22×C4C22×Dic7311yescharacteristic
532C22×C4C22×Dic7311yescharacteristic
533C22×C4C22×Dic7311yescharacteristic
534C22×C4C22×Dic7311yescharacteristic
535C22×C4C22×Dic7311yescharacteristic
536C22×C4C22×Dic7311yescharacteristic
537C22×C4C22×Dic7311yescharacteristic
538C22×C4C23×D7311yescharacteristic
539M16—2924no—
540C2×C8—2924no—
541C2×C8—1461no—
542C2×C8—1461no—
543C2×C8—1461no—
544C2×C8—1461no—
545C2×C8—1461no—
546C2×C8—1461no—
547C2×C8—1461no—
548C2×C8—1461no—
549C2×C8—1461no—
550C2×C8—1461no—
551C2×C8—1461no—
552C2×C8—1461no—
553C2×C8—1461no—
554C2×C8—1461no—
555C2×C8—1461no—
556C2×C8—1461no—
557C2×C8—1461no—
558C2×C8—1461no—
559C2×C8—1461no—
560C2×C8—1461no—
561C2×C8—1461no—
562C2×C8—1461no—
563C2×C8—1461no—
564C2×C8—1461no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C22⋊C4—22no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—41no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23#1455659812yes—
613C23C23×Dic7311yescharacteristic
614D4—44no—
615D4—44no—
616D4—44no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4#1455663611yescharacteristic
663C2×C4#1455663611yescharacteristic
664C2×C4#1455663611yescharacteristic
665C2×C4#1455663611yescharacteristic
666C2×C4#1455663711yescharacteristic
667C2×C4#1455663811yescharacteristic
668C8—2921no—
669C8—2921no—
670C8—2921no—
671C8—2921no—
672C8—2921no—
673C8—2921no—
674C8—2921no—
675C8—2921no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22#1798906211yescharacteristic
698C22#1798906211yescharacteristic
699C22#1798907011yescharacteristic
700C22C2×#1455659811yescharacteristic
701C22#1798935411yescharacteristic
702C22#1798935411yescharacteristic
703C22#1798935411yescharacteristic
704C4—41no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4#1798932511yescharacteristic
716C4#1798932511yescharacteristic
717C4#1798933211yescharacteristic
718C4#1798933211yescharacteristic
719C2—42no—
720C2—81no—
721C2—81no—
722C2#2261308811yescharacteristic
723C2#2261897911yescharacteristic
724C2#2261897911yescharacteristic
725C2#2261899311yescharacteristic
726C2#2261900211yescharacteristic
727C2#2261907011yescharacteristic
728C2#2261910111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#2392C2
prime radical#392×C73C4
cosocleC22×C4×C73C24
hypercenter#2392D73
hypocenterC73#23335
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #2392

Complements

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

NH ≅ G/Ntype
1. #22610730C2semidirect
2. #22610730C2semidirect
3. #22610546C2semidirect
4. #22610546C2semidirect
5. #22610497C2semidirect
6. #22610497C2semidirect
7. #22610229C2semidirect
8. #22610229C2semidirect
9. #22610224C2semidirect
10. #22610224C2semidirect
11. #22610116C2semidirect
12. #22610111C2semidirect
13. #22610002C2semidirect
14. #22609915C2semidirect
380. C73#23335semidirect

Maximal subgroups

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

subgroupindex
#226107302
#226105462
#226104972
#226102292
#226102242
#226101162
#226101112
#226100022
#226099152
C73×#23922
#2333573