Finite Group Databasebeta

← #34028057

Subgroups — #34028057

Order 18688.

878 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626460C211yesmaximal, characteristic, complemented
2#22626444C211yesmaximal, characteristic
3#22626115C211yesmaximal, characteristic, complemented
4#22626044C211yesmaximal, characteristic, complemented
5#22626037C211yesmaximal, characteristic, complemented
6#22626034C211yesmaximal, characteristic, complemented
7#22625994C211yesmaximal, characteristic, complemented
8#22625993C211yesmaximal, characteristic, complemented
9#22625896C211yesmaximal, characteristic
10#22625894C211yesmaximal, characteristic
11#22625732C211yesmaximal, characteristic, complemented
12#22625702C211yesmaximal, characteristic
13#22625701C211yesmaximal, characteristic
14#102×#64408C211yesmaximal, characteristic
15#476×D73C211yesmaximal, characteristic
16C2×Q8×#64408—21no—
17C2×D4×#64408C2211yescharacteristic
18C2×D4×#64408C2211yescharacteristic
19C2×#14556660C2211yescharacteristic
20C2×#14556659C2211yescharacteristic
21C2×#14556653C2211yescharacteristic
22C2×#14556653C2211yescharacteristic
23#17989546C2211yescharacteristic
24C2×#14556645C2211yescharacteristic
25C2×C8×#64408C2211yescharacteristic
26(C2×#64408)⋊Q8—21no—
27#17989538C2211yescharacteristic
28#17989538C2211yescharacteristic
29#17989538C2211yescharacteristic
30#17989538C2211yescharacteristic
31#17989536—21no—
32#17989536—21no—
33#17989534—21no—
34#17989534—21no—
35#17989531C2211yescharacteristic
36#17989529—21no—
37C4⋊C4×#64408C2211yescharacteristic
38C4⋊C4×#64408C2211yescharacteristic
39C4×C4⋊#64408C2211yescharacteristic
40C4×C4⋊#64408C2211yescharacteristic
41C2×(C2×#64408)⋊C4—21no—
42#17989461C2211yescharacteristic
43#17989461C2211yescharacteristic
44#17989460C2211yescharacteristic
45#17989460C2211yescharacteristic
46#17989460C2211yescharacteristic
47#17989460C2211yescharacteristic
48#17989460C2211yescharacteristic
49#17989460C2211yescharacteristic
50#17989452C2211yescharacteristic
51#17989452C2211yescharacteristic
52C4⋊Q8×D73C2211yescharacteristic
53C4×D4×D73C2211yescharacteristic
54#17988878C411yescharacteristic, complemented
55#17988877C411yescharacteristic, complemented
56#17988876C411yescharacteristic, complemented
57#17988876C411yescharacteristic, complemented
58#17988875C411yescharacteristic, complemented
59#17988875C411yescharacteristic, complemented
60#17988874C411yescharacteristic, complemented
61#106×D73C2211yescharacteristic
62#106×D73C2211yescharacteristic
63C4⋊C8×D73C2211yescharacteristic
64#102×D73C2211yescharacteristic
65#102×D73C2211yescharacteristic
66#476×C73C411yescharacteristic, complemented
67C23×#64408—21no—
68C23×#64408—21no—
69C2×#11924036C2311yescharacteristic
70C2×#11924036C2311yescharacteristic
71Q8×#64408—44no—
72D4×#64408—22no—
73D4×#64408—22no—
74D4×#64408—41no—
75D4×#64408—41no—
76C2×C4⋊#64408—21no—
77C2×C4⋊#64408—21no—
78C2×C4⋊#64408—21no—
79C2×C4⋊#64408—21no—
80C2×C4⋊#64408D411yescharacteristic
81C2×C4⋊#64408D411yescharacteristic
82C2×C4⋊#64408C2311yescharacteristic
83C2×C4⋊#64408C2311yescharacteristic
84C2×C4⋊#64408C2311yescharacteristic
85C2×C4⋊#64408C2311yescharacteristic
86C2×C22⋊#64408—21no—
87C2×C22⋊#64408—21no—
88C2×C4×#64408—21no—
89C2×C4×#64408—21no—
90C2×C4×#64408—21no—
91C2×C4×#64408C2311yescharacteristic
92C2×C4×#64408C2311yescharacteristic
93#14556660—41no—
94#14556659—41no—
95#14556653—22no—
96#14556653Q814yescomplemented
97#14556646—21no—
98#14556646—21no—
99#14556645—41no—
100C8×#64408—41no—
101(C2×#64408)⋊C4—21no—
102(C2×#64408)⋊C4—21no—
103(C2×#64408)⋊C4—21no—
104(C2×#64408)⋊C4—21no—
105(C2×#64408)⋊C4—21no—
106(C2×#64408)⋊C4—21no—
107(C2×#64408)⋊C4—21no—
108(C2×#64408)⋊C4—21no—
109(C2×#64408)⋊C4—21no—
110(C2×#64408)⋊C4D411yescharacteristic
111(C2×#64408)⋊C4D411yescharacteristic
112C2×Q8×D73—21no—
113C2×D4×D73C2311yescharacteristic
114C22×C4×D73—21no—
115C2×C8×D73C2311yescharacteristic
116C2×C8×D73C2311yescharacteristic
117#14556591C2×C411yescharacteristic, complemented
118#14556590—21no—
119#14556590C2×C411yescharacteristic, complemented
120#14556590C2×C411yescharacteristic, complemented
121#14556589—21no—
122C4×D292C2×C411yescharacteristic
123D4×Dic73C2×C411yescharacteristic
124#14556553C2×C411yescharacteristic
125C4×C22⋊D73—21no—
126#14556551—21no—
127C4⋊C4×D73—21no—
128C4⋊C4×D73C2311yescharacteristic
129C4⋊C4×D73C2311yescharacteristic
130C4⋊C4×D73C2311yescharacteristic
131C22⋊C4×D73—21no—
132C42×D73C2311yescharacteristic
133#14556523C2×C411yescharacteristic, complemented
134#14556523C2×C411yescharacteristic, complemented
135#14556522C2×C411yescharacteristic, complemented
136#14556522C2×C411yescharacteristic, complemented
137#14556522C2×C411yescharacteristic, complemented
138#14556522C2×C411yescharacteristic, complemented
139C4⋊#10596831C2×C411yescharacteristic, complemented
140#14556520C2×C411yescharacteristic, complemented
141#14556520C2×C411yescharacteristic, complemented
142#14556513C2×C411yescharacteristic
143#14556513C2×C411yescharacteristic
144#14556512C2×C411yescharacteristic
145#14556512C2×C411yescharacteristic
146#14556511C2×C411yescharacteristic
147#14556511C2×C411yescharacteristic
148C4⋊Q8×C73C2×C411yescharacteristic, complemented
149C4×D4×C73C2×C411yescharacteristic
150#106×C73C2×C411yescharacteristic, complemented
151#106×C73C2×C411yescharacteristic, complemented
152C4⋊C8×C73C2×C411yescharacteristic, complemented
153#102×C73C2×C411yescharacteristic
154#102×C73C2×C411yescharacteristic
155C22×#64408—21no—
156C22×#64408—21no—
157C22×#64408—21no—
158C22×#64408—21no—
159C22×#64408—42no—
160C22×#64408—42no—
161C22×#64408—42no—
162C22×#64408—42no—
163C22×#64408—81no—
164C22×#64408—81no—
165C22×#64408C2×D411yescharacteristic
166C22×#64408C2×D411yescharacteristic
167C22×#64408C2×D411yescharacteristic
168C22×#64408C2×D411yescharacteristic
169#11924036—21no—
170#11924036—21no—
171#11924036—21no—
172#11924036C2×Q812yes—
173C2×#10596833—21no—
174C2×#10596833—21no—
175C4⋊#64408—22no—
176C4⋊#64408—21no—
177C4⋊#64408—21no—
178C4⋊#64408—21no—
179C4⋊#64408—21no—
180C4⋊#64408—21no—
181C4⋊#64408—21no—
182C4⋊#64408—21no—
183C4⋊#64408—41no—
184C4⋊#64408—42no—
185C4⋊#64408—42no—
186C4⋊#64408—81no—
187C4⋊#64408—81no—
188C4⋊#64408C2×Q812yes—
189C22⋊#64408—42no—
190C22⋊#64408—42no—
191C4×#64408—21no—
192C4×#64408—21no—
193C4×#64408—21no—
194C4×#64408—21no—
195C4×#64408—42no—
196C4×#64408—42no—
197C4×#64408—42no—
198C23×D73—21no—
199C2×Dic146—21no—
200C2×Dic146—21no—
201C2×Dic146—21no—
202Q8×D73—42no—
203Q8×D73—42no—
204C2×D292C22×C411yescharacteristic
205C2×C22⋊D73—21no—
206D4×D73—21no—
207D4×D73—21no—
208D4×D73C2×Q812yes—
209D4×D73#4112yes—
210C22×Dic73—21no—
211C2×C4×D73—21no—
212C2×C4×D73—21no—
213C2×C4×D73—21no—
214C2×C4×D73—21no—
215C2×C4×D73—21no—
216C2×C4×D73—81no—
217C2×C4×D73—81no—
218C2×C4×D73C2×D411yescharacteristic
219C2×C4×D73C2×D411yescharacteristic
220C2×C4×D73C2411yescharacteristic
221C2×#10596831C22×C411yescharacteristic
222C2×#10596831C22×C411yescharacteristic
223C8×D73—21no—
224C8×D73—21no—
225C8×D73—21no—
226C8×D73—21no—
227C4⋊Dic73—21no—
228C4⋊Dic73C22×C411yescharacteristic
229C4⋊Dic73C22×C411yescharacteristic
230C4⋊Dic73C22×C411yescharacteristic
231#11924007—21no—
232#11924007—21no—
233#11924007—21no—
234#11924007—21no—
235#11924007—21no—
236C22⋊Dic73—21no—
237#11924005—21no—
238#11924005—21no—
239C4×Dic73C22×C411yescharacteristic
240C4×Dic73#4111yescharacteristic
241C4×Dic73#4111yescharacteristic
242C2×Q8×C73—21no—
243C2×D4×C73C22×C411yescharacteristic
244C22×C4×C73—21no—
245C2×C8×C73C22×C411yescharacteristic
246C2×C8×C73C22×C411yescharacteristic
247C4⋊C4×C73—21no—
248C4⋊C4×C73C22×C411yescharacteristic
249C4⋊C4×C73C22×C411yescharacteristic
250C4⋊C4×C73C22×C411yescharacteristic
251C22⋊C4×C73—21no—
252C42×C73C22×C411yescharacteristic
253C23×C73—21no—
254C22×D73—21no—
255C22×D73—22no—
256C22×D73—22no—
257C22×D73—41no—
258C22×D73—41no—
259C22×D73—41no—
260C22×D73—41no—
261C22×D73C22×D411yescharacteristic
262C2×#64408—21no—
263C2×#64408—21no—
264C2×#64408—21no—
265C2×#64408—21no—
266C2×#64408—21no—
267C2×#64408—22no—
268C2×#64408—21no—
269C2×#64408—21no—
270C2×#64408—21no—
271C2×#64408—21no—
272C2×#64408—21no—
273C2×#64408—21no—
274C2×#64408—41no—
275C2×#64408—41no—
276C2×#64408—41no—
277C2×#64408—41no—
278C2×#64408—41no—
279C2×#64408—41no—
280C2×#64408—41no—
281C2×#64408—41no—
282C2×#64408—41no—
283C2×#64408—41no—
284C2×#64408—41no—
285C2×#64408—84no—
286C2×#64408—84no—
287C2×#64408AGL(1,ℤ/8)12yes—
288Q8×C73—42no—
289D4×C73—21no—
290D4×C73C4×Q812yescomplemented
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—81no—
295C2×C4×C73C4×D411yescharacteristic
296C2×C4×C73C4×D411yescharacteristic
297C2×C4×C73C23×C411yescharacteristic
298C22⋊D73—22no—
299C22⋊D73—22no—
300C2×Dic73—21no—
301C2×Dic73—21no—
302C2×Dic73—21no—
303C2×Dic73—81no—
304C2×Dic73C4×D411yescharacteristic
305C2×Dic73C4×D411yescharacteristic
306C2×Dic73C2×#4111yescharacteristic
307D292—21no—
308D292C4×Q812yescomplemented
309C4×D73—21no—
310C4×D73—21no—
311C4×D73—21no—
312C4×D73—21no—
313C4×D73—41no—
314C4×D73—41no—
315C4×D73—41no—
316C4×D73—41no—
317C4×D73—41no—
318C4×D73—41no—
319C4×D73—81no—
320C4×D73—81no—
321C4×D73C22×Q811yescharacteristic
322C4×D73C2×#4111yescharacteristic
323C4×D73H(5,𝔽2)11yescharacteristic
324C4×D732−1+411yescharacteristic
325Dic146—42no—
326Dic146—42no—
327Dic146—42no—
328#10596833—22no—
329#10596833—41no—
330C8×C73—21no—
331C8×C73—21no—
332#10596831—21no—
333#10596831—21no—
334C22×C73—22no—
335C22×C73—41no—
336C22×C73—41no—
337C22×C73C2×C4×D411yescharacteristic
338C2×D73—22no—
339C2×D73—41no—
340C2×D73—41no—
341C2×D73—42no—
342C2×D73—42no—
343C2×D73—42no—
344C2×D73—42no—
345C2×D73#54611yescharacteristic
346C2×D73D4×Q811yescharacteristic
347C2×D73C2×AGL(1,ℤ/8)11yescharacteristic
348C2×D73#57511yescharacteristic
349C2×D73#57711yescharacteristic
350C2×D73#57711yescharacteristic
351#64408—22no—
352#64408—42no—
353#64408—41no—
354#64408—41no—
355#64408—41no—
356#64408—81no—
357#64408—81no—
358#64408—81no—
359C4×C73—21no—
360C4×C73—21no—
361C4×C73—41no—
362C4×C73—41no—
363C4×C73—41no—
364C4×C73C2×C4×Q811yescharacteristic
365C4×C73#52011yescharacteristic
366Dic73—21no—
367Dic73—21no—
368Dic73—41no—
369Dic73—41no—
370Dic73—41no—
371Dic73#55211yescharacteristic
372Dic73#55411yescharacteristic
373#22975—731nomaximal, Sylow
374C2×C73—42no—
375C2×C73#236011yescharacteristic
376C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
377C2×C73#294911yescharacteristic
378D73—42no—
379D73#330611yescharacteristic
380D73#331111yescharacteristic
381D73#338411yescharacteristic
382D73#338811yescharacteristic
383C2×#476—731no—
384#2365—731no—
385#2349—731no—
386#1993—731no—
387#1949—731no—
388#1944—731no—
389#1941—731no—
390#1920—731no—
391#1919—731no—
392#1864—731no—
393#1862—731no—
394#1771—731no—
395#1762—731no—
396#1762—731no—
397C4×#102—731no—
398C73#2297511yescharacteristic, complemented, Sylow
399C2×C4⋊Q8—731no—
400C2×C4×Q8—1461no—
401C2×C4×D4—731no—
402C2×C4×D4—731no—
403C2×C4×D4—731no—
404#476—731no—
405#476—731no—
406#476—731no—
407#476—731no—
408#476—731no—
409#476—731no—
410#476—731no—
411#476#6440811yescharacteristic, complemented
412C2×#107—731no—
413C2×#106—731no—
414C2×#106—731no—
415C2×#106—731no—
416C2×C4⋊C8—731no—
417C2×#102—731no—
418C2×#102—731no—
419C2×#102—731no—
420C2×#102—731no—
421C2×#97—731no—
422C2×#97—731no—
423C2×C4×C8—731no—
424#391—1461no—
425#389—731no—
426#389—731no—
427#389—731no—
428#389—731no—
429#387—1461no—
430#387—1461no—
431#385—1461no—
432#385—1461no—
433#382—731no—
434#380—1461no—
435C4×C4⋊C4—731no—
436C4×C4⋊C4—731no—
437C4×C4⋊C4—731no—
438C4×C4⋊C4—731no—
439C2×#95—1461no—
440#340—731no—
441#340—731no—
442#340—731no—
443#340—731no—
444#340—731no—
445#340—731no—
446#340—731no—
447#340—731no—
448#336—731no—
449#336—731no—
450C22×Q8—1461no—
451C22×D4—731no—
452C23×C4—1461no—
453C23×C4—1461no—
454C23×C4—1461no—
455C22×C8—731no—
456C22×C8—731no—
457C22×C8—731no—
458C22×C8—731no—
459C4⋊Q8—731no—
460C4⋊Q8—731no—
461C4⋊Q8—731no—
462C4⋊Q8—1461no—
463C4⋊Q8—1461no—
464C4⋊Q8C2×#6440811yescharacteristic, complemented
465C4×Q8—2924no—
466C4×D4—2921no—
467C4×D4—2921no—
468C4×D4—731no—
469C4×D4—731no—
470C4×D4—731no—
471C4×D4—1461no—
472C4×D4—1461no—
473C4×D4—1462no—
474C4×D4—1462no—
475C4×D4C2×#6440811yescharacteristic
476C2×C4⋊C4—731no—
477C2×C4⋊C4—731no—
478C2×C4⋊C4—731no—
479C2×C4⋊C4—731no—
480C2×C4⋊C4—731no—
481C2×C4⋊C4—731no—
482C2×C4⋊C4—731no—
483C2×C4⋊C4—731no—
484C2×C4⋊C4—731no—
485C2×C4⋊C4—1461no—
486C2×C4⋊C4—1461no—
487C2×C4⋊C4—1461no—
488C2×C4⋊C4—1461no—
489C2×C4⋊C4—1461no—
490C2×C22⋊C4—1461no—
491C2×C22⋊C4—1461no—
492C2×C22⋊C4—1461no—
493C2×C42—731no—
494C2×C42—731no—
495C2×C42—731no—
496C2×C42—1461no—
497C2×C42—1461no—
498C2×C42—1461no—
499#107—2921no—
500#106—2921no—
501#106—731no—
502#106—731no—
503#106—731no—
504#106—731no—
505#106—731no—
506#106—731no—
507#106C2×#6440811yescharacteristic, complemented
508#106C2×#6440811yescharacteristic, complemented
509C4⋊C8—731no—
510C4⋊C8—731no—
511C4⋊C8—731no—
512C4⋊C8C2×#6440811yescharacteristic, complemented
513#102—734no—
514#102—731no—
515#102—731no—
516#102—731no—
517#102—731no—
518#102—731no—
519#102—731no—
520#102—1462no—
521#102C2×#6440811yescharacteristic
522#102C2×#6440811yescharacteristic
523#97—2921no—
524#97—1461no—
525#97—1461no—
526C4×C8—2921no—
527#95—731no—
528#95—731no—
529#95—1461no—
530#95—1461no—
531#95—1461no—
532#95—1461no—
533#95—1461no—
534#95—1461no—
535#95—1461no—
536#95—1461no—
537#95—1461no—
538C24—1461no—
539C2×Q8—21no—
540C2×Q8—2922no—
541C2×Q8—2922no—
542C2×Q8—1461no—
543C2×Q8—1461no—
544C2×Q8—1461no—
545C2×D4—732no—
546C2×D4—732no—
547C2×D4—731no—
548C2×D4—1461no—
549C2×D4—1461no—
550C2×D4—1461no—
551C2×D4C22×#6440811yescharacteristic
552C22×C4—21no—
553C22×C4—2922no—
554C22×C4—2922no—
555C22×C4—2922no—
556C22×C4—2922no—
557C22×C4—5841no—
558C22×C4—5841no—
559C22×C4—5841no—
560C22×C4—5841no—
561C22×C4—731no—
562C22×C4—731no—
563C22×C4—731no—
564C22×C4—731no—
565C22×C4—731no—
566C22×C4—731no—
567C22×C4—731no—
568C22×C4—1461no—
569C22×C4—1461no—
570C22×C4—1461no—
571C22×C4—1461no—
572C22×C4—1461no—
573C22×C4—1461no—
574C22×C4—1461no—
575C22×C4—1461no—
576C22×C4—1461no—
577C22×C4—1461no—
578C2×C8—732no—
579C2×C8—731no—
580C2×C8—731no—
581C2×C8—1461no—
582C2×C8—1461no—
583C2×C8—1461no—
584C2×C8—1461no—
585C2×C8—1461no—
586C2×C8—1461no—
587C2×C8—1461no—
588C2×C8—1461no—
589C2×C8—1461no—
590C2×C8C22×#6440811yescharacteristic
591C2×C8C22×#6440811yescharacteristic
592C4⋊C4—21no—
593C4⋊C4—2922no—
594C4⋊C4—2922no—
595C4⋊C4—2921no—
596C4⋊C4—5841no—
597C4⋊C4—5841no—
598C4⋊C4—732no—
599C4⋊C4—731no—
600C4⋊C4—731no—
601C4⋊C4—731no—
602C4⋊C4—1461no—
603C4⋊C4—1461no—
604C4⋊C4—1461no—
605C4⋊C4—1461no—
606C4⋊C4—1461no—
607C4⋊C4—1461no—
608C4⋊C4—1461no—
609C4⋊C4—1461no—
610C4⋊C4—1461no—
611C4⋊C4—1461no—
612C4⋊C4—1461no—
613C4⋊C4—1461no—
614C4⋊C4—1462no—
615C4⋊C4—1461no—
616C4⋊C4C22×#6440811yescharacteristic
617C4⋊C4C22×#6440811yescharacteristic
618C4⋊C4C22×#6440811yescharacteristic
619C22⋊C4—21no—
620C22⋊C4—2922no—
621C22⋊C4—2922no—
622C22⋊C4—1461no—
623C22⋊C4—1461no—
624C22⋊C4—1461no—
625C42—2922no—
626C42—2922no—
627C42—2922no—
628C42—731no—
629C42—731no—
630C42—731no—
631C42—1461no—
632C42—1461no—
633C42—1461no—
634C42—1461no—
635C42C22×#6440811yescharacteristic
636C23—21no—
637C23—2921no—
638C23—2921no—
639C23—2921no—
640C23—2921no—
641C23—731no—
642C23—1462no—
643C23—1462no—
644C23—1461no—
645Q8—42no—
646Q8—2922no—
647Q8—2922no—
648Q8—2922no—
649D4—21no—
650D4—732no—
651D4—1462no—
652D4—1462no—
653D4—1461no—
654D4Q8×#6440812yescomplemented
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—81no—
659C2×C4—2921no—
660C2×C4—2921no—
661C2×C4—2921no—
662C2×C4—2921no—
663C2×C4—2921no—
664C2×C4—2921no—
665C2×C4—2921no—
666C2×C4—2921no—
667C2×C4—2921no—
668C2×C4—2921no—
669C2×C4—2921no—
670C2×C4—2921no—
671C2×C4—2921no—
672C2×C4—2921no—
673C2×C4—2921no—
674C2×C4—2921no—
675C2×C4—2921no—
676C2×C4—5841no—
677C2×C4—5841no—
678C2×C4—5844no—
679C2×C4—5841no—
680C2×C4—5844no—
681C2×C4—731no—
682C2×C4—731no—
683C2×C4—731no—
684C2×C4—731no—
685C2×C4—731no—
686C2×C4—732no—
687C2×C4—731no—
688C2×C4—731no—
689C2×C4—1461no—
690C2×C4—1461no—
691C2×C4—1461no—
692C2×C4—1461no—
693C2×C4—1461no—
694C2×C4—1461no—
695C2×C4—1461no—
696C2×C4—1461no—
697C2×C4—1461no—
698C2×C4—1461no—
699C2×C4—1461no—
700C2×C4—1461no—
701C2×C4—1462no—
702C2×C4—1461no—
703C2×C4—1461no—
704C2×C4—1461no—
705C2×C4—1461no—
706C2×C4—1461no—
707C2×C4—1461no—
708C2×C4D4×#6440811yescharacteristic
709C2×C4D4×#6440811yescharacteristic
710C2×C4C23×#6440811yescharacteristic
711C8—21no—
712C8—21no—
713C8—2921no—
714C8—1462no—
715C8—1461no—
716C8—1461no—
717C22—22no—
718C22—41no—
719C22—41no—
720C22—2922no—
721C22—2922no—
722C22—2922no—
723C22—2922no—
724C22—2921no—
725C22—2921no—
726C22—731no—
727C22—731no—
728C22—731no—
729C22—731no—
730C22—731no—
731C22—731no—
732C22—1462no—
733C22C2×D4×#6440811yescharacteristic
734C4—21no—
735C4—21no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—2922no—
740C4—2921no—
741C4—2921no—
742C4—2921no—
743C4—2921no—
744C4—2921no—
745C4—2921no—
746C4—5841no—
747C4—5841no—
748C4—5841no—
749C4—731no—
750C4—731no—
751C4—1462no—
752C4—1461no—
753C4—1461no—
754C4C2×Q8×#6440811yescharacteristic
755C4#1798965611yescharacteristic
756C2—42no—
757C2—2922no—
758C2—731no—
759C2—731no—
760C2—731no—
761C2—731no—
762C2#2262645511yescharacteristic
763C2AGL(1,ℤ/8)×#6440811yescharacteristic
764C2#2262669111yescharacteristic
subgroupG/H
centerC22C2×D4×#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
Fitting#476×C73C4
socleC22×C73C2×C4×D4
prime radicalC2×D4×D73C23
cosocleC2×C4×D73C24
hypercenter#476#64408
hypocenterC73#22975
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #22626460C2semidirect
3. #22626115C2semidirect
4. #22626044C2semidirect
5. #22626037C2semidirect
6. #22626034C2semidirect
7. #22625994C2semidirect
8. #22625993C2semidirect
11. #22625732C2semidirect
54. #17988878C4semidirect
55. #17988877C4semidirect
56. #17988876C4semidirect
57. #17988876C4semidirect
58. #17988875C4semidirect
59. #17988875C4semidirect
60. #17988874C4semidirect
66. #476×C73C4semidirect
96. #14556653Q8semidirect
117. #14556591C2×C4semidirect
119. #14556590C2×C4semidirect
120. #14556590C2×C4semidirect
133. #14556523C2×C4semidirect
134. #14556523C2×C4semidirect
135. #14556522C2×C4semidirect
136. #14556522C2×C4semidirect
137. #14556522C2×C4semidirect
138. #14556522C2×C4semidirect
139. C4⋊#10596831C2×C4semidirect
140. #14556520C2×C4semidirect
141. #14556520C2×C4semidirect
148. C4⋊Q8×C73C2×C4semidirect
150. #106×C73C2×C4semidirect
151. #106×C73C2×C4semidirect
152. C4⋊C8×C73C2×C4semidirect
290. D4×C73C4×Q8semidirect
308. D292C4×Q8semidirect
398. C73#22975semidirect
411. #476#64408semidirect
464. C4⋊Q8C2×#64408semidirect
507. #106C2×#64408semidirect
508. #106C2×#64408semidirect
512. C4⋊C8C2×#64408semidirect
654. D4Q8×#64408semidirect

Maximal subgroups

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

subgroupindex
#226264602
#226264442
#226261152
#226260442
#226260372
#226260342
#226259942
#226259932
#226258962
#226258942
#226257322
#226257022
#226257012
#102×#644082
#476×D732
#2297573