Finite Group Databasebeta

← #11878363

Subgroups — #11878363

Order 1152.

832 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595044C211yesmaximal, characteristic
2#10594884C211yesmaximal, characteristic, complemented
3#10592421C211yesmaximal, characteristic, complemented
4C3×#4733C211yesmaximal, characteristic, complemented
5C3×#4727C211yesmaximal, characteristic, complemented
6#10591173C211yesmaximal, characteristic, complemented
7#10591126C211yesmaximal, characteristic, complemented
8#10590949C211yesmaximal, characteristic, complemented
9#10590851C211yesmaximal, characteristic, complemented
10#10590849C211yesmaximal, characteristic, complemented
11#10590834C211yesmaximal, characteristic, complemented
12#10590833C211yesmaximal, characteristic, complemented
13#10590825C211yesmaximal, characteristic, complemented
14#10590822C211yesmaximal, characteristic, complemented
15#10590710C211yesmaximal, characteristic, complemented
16#80238—31nomaximal
17#78681—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22#64133C2211yescharacteristic
23C3×#924C2211yescharacteristic
24C2×C3×Dic12C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28#63980—21no—
29#63980—21no—
30#63969—21no—
31#63959—21no—
32#63908—21no—
33#63908C2211yescharacteristic
34#63908C2211yescharacteristic
35#63884—21no—
36#63857C2211yescharacteristic
37#63856—21no—
38#63856C2211yescharacteristic
39#63856C2211yescharacteristic
40#63856C2211yescharacteristic
41#63841C2211yescharacteristic
42#63839—21no—
43C2×#3719C2211yescharacteristic
44C2×#3716C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46#63645C2211yescharacteristic
47#63645C2211yescharacteristic
48#63643C2211yescharacteristic
49#63643C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×#816C2211yescharacteristic
55#63573C2211yescharacteristic
56#63573C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63566C2211yescharacteristic
60#63563C2211yescharacteristic
61#5833—31no—
62#5833—31no—
63#5825—31no—
64#5628—31no—
65C3×#452—31no—
66C3×#408—31no—
67#5239—31no—
68#5188—31no—
69#5186—31no—
70#5174—31no—
71#5170—31no—
72#5137—31no—
73#5134—31no—
74#5116—31no—
75#5114—31no—
76#5043—31no—
77#4816—31no—
78#4814—31no—
79#4784—31no—
80#4778—31no—
81#4739—31no—
82#4738—31no—
83#4737—31no—
84#4733—31no—
85#4733D311yescharacteristic, complemented
86#4727D311yescharacteristic, complemented
87#4723—31no—
88#4722—31no—
89#4722—31no—
90#4722—61no—
91#4721—31no—
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3—21no—
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67D411yescharacteristic
97C2×C3×#67D411yescharacteristic
98C3×#235—41no—
99C3×#235—41no—
100C3×#235—41no—
101C3×#235—41no—
102C2×C3×D12D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6D411yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#627—21no—
111C2×#625—21no—
112C2×#625—21no—
113C2×D3×Dic3—21no—
114D3×Dic6—41no—
115D3×Dic6—41no—
116C2×C32×C8C2311yescharacteristic
117C2×C32×C8C2311yescharacteristic
118#3757—21no—
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123#3750—21no—
124C3×#217—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×Dic12—41no—
130C3×#204—41no—
131C3×ΓL(1,𝔽25)—41no—
132C3×D3×C8—41no—
133#3724—21no—
134#3724—21no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144Dic32—21no—
145#3719—41no—
146#3716—41no—
147#3201—91noSylow
148C2×C3×#41—31no—
149C2×C3×#41—31no—
150C2×D3×Q8—31no—
151C2×#235C2×D311yescharacteristic
152C2×#235C2×D311yescharacteristic
153C22×Dic6—31no—
154C2×C3×Q16—31no—
155C2×C3×SD16—31no—
156C2×C3×M16—31no—
157C22×C3×C8—31no—
158C3×C22⋊Q8—31no—
159#946—31no—
160#946—31no—
161#946—31no—
162#946—61no—
163#944—61no—
164C2×#216—31no—
165#939—61no—
166#939—61no—
167#939—61no—
168#939—61no—
169#938—31no—
170#938—31no—
171#938—61no—
172#936—61no—
173#935—61no—
174#935—61no—
175C2×#214—31no—
176#930—31no—
177#930—31no—
178#930—61no—
179#926—31no—
180C2×C4⋊Dic3—31no—
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—61no—
183#924—31no—
184#924—31no—
185#924—31no—
186#924—31no—
187#924—31no—
188#924—31no—
189#924—61no—
190#924—61no—
191#924C2×D311yescharacteristic
192C2×Dic12—31no—
193C2×Dic12C2×D311yescharacteristic
194C2×#204—31no—
195C2×#204C2×D311yescharacteristic
196C2×ΓL(1,𝔽25)C2×D311yescharacteristic
197C2×D3×C8C2×D311yescharacteristic
198#897—31no—
199#894—61no—
200#892—31no—
201#888—61no—
202#885—61no—
203#883—61no—
204C3×#103—31no—
205C3×#102—31no—
206C3×C22⋊C8—21no—
207C3×C22⋊C8—31no—
208C3×C22⋊C8—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8C2×D311yescharacteristic
211C3×C22⋊C8C2×D311yescharacteristic
212#835—31no—
213#835—31no—
214#835—31no—
215#832—31no—
216#830C2×D311yescharacteristic
217#821—31no—
218#821C2×D311yescharacteristic
219(C2×D3)⋊C8C2×D311yescharacteristic
220(C2×D3)⋊C8C2×D311yescharacteristic
221#818—31no—
222#818—31no—
223#818—31no—
224#818—31no—
225#818—61no—
226#818—61no—
227#817—31no—
228#817—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232#816—31no—
233#816—31no—
234#816—31no—
235#816—31no—
236#816—61no—
237#816—61no—
238#816C2×D311yescharacteristic
239#808—31no—
240#808—31no—
241C23×C32C2×D411yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—81no—
254#634—21no—
255#634—21no—
256C3×#67—41no—
257C3×#67—41no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—41no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—42no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276C3×Dic6—41no—
277#627—42no—
278#625—81no—
279#625—81no—
280D3×Dic3—42no—
281C32×C8—21no—
282C32×C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#537—91no—
286#536—91no—
287#485—91no—
288#484—91no—
289#483—91no—
290#482—91no—
291#470—91no—
292#468—91no—
293#467—91no—
294#465—91no—
295#452—31no—
296#452—91no—
297#451—91no—
298#448—91no—
299#408—31no—
300C3×#41—121no—
301C3×#41—121no—
302C3×#41—121no—
303C3×#41—121no—
304C2×C3×Q8—31no—
305C2×C3×Q8—31no—
306C2×C3×Q8—31no—
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—31no—
311C2×C3×D4—61no—
312C22×C3×C4—21no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—61no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C2×#67—21no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67D1211yescharacteristic
324C2×#67D1211yescharacteristic
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—121no—
329D3×Q8—121no—
330D3×Q8—121no—
331#235—41no—
332#235—41no—
333#235—41no—
334#235—41no—
335C2×D12D1211yescharacteristic
336C2×D12C22×D311yescharacteristic
337C2×C4×D3—21no—
338C2×C4×D3—61no—
339C2×C4×D3C22×D311yescharacteristic
340C2×C4×D3C22×D311yescharacteristic
341C2×Dic6—31no—
342C2×Dic6—31no—
343C2×Dic6—61no—
344C2×Dic6—61no—
345C2×Dic6—61no—
346C2×Dic6—121no—
347C2×Dic6—121no—
348C2×Dic6D1211yescharacteristic
349C2×Dic6C22×D311yescharacteristic
350C2×Dic6C22×D311yescharacteristic
351C3×Q16—121no—
352C3×SD16—121no—
353C3×M16—121no—
354C2×C3×C8—21no—
355C2×C3×C8—21no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C2×C3×C8—121no—
359C2×C3×C8C22×D311yescharacteristic
360C2×C3×C8C22×D311yescharacteristic
361C2×C3×C8C22×D311yescharacteristic
362C2×C3×C8C22×D311yescharacteristic
363C3×C4⋊C4—31no—
364C3×C4⋊C4—61no—
365C3×C22⋊C4—61no—
366#217—21no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—61no—
376#217—121no—
377#216—121no—
378#214—121no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—121no—
399C4⋊Dic3C22×D311yescharacteristic
400Dic3⋊C4—21no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—121no—
411C4×Dic3—61no—
412C4×Dic3—61no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415Dic12—41no—
416Dic12—121no—
417#204—41no—
418#204—121no—
419ΓL(1,𝔽25)—41no—
420D3×C8—41no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32C22×D411yescharacteristic
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C32×C4—21no—
435C32×C4H(5,𝔽2)11yescharacteristic
436C32×C4H(5,𝔽2)11yescharacteristic
437C3⋊Dic3—41no—
438C3⋊Dic3—41no—
439C3⋊Dic3—41no—
440C3⋊Dic3—41no—
441C3×Dic3—21no—
442C3×Dic3—21no—
443C3×Dic3—41no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C2×#41—31no—
447C2×#41—31no—
448C22×Q8—91no—
449C2×Q16—31no—
450C2×Q16—91no—
451C2×SD16—31no—
452C2×SD16—91no—
453C2×M16—31no—
454C22×C8—31no—
455C4⋊Q8—181no—
456#124—181no—
457#123—181no—
458#123—181no—
459C22⋊Q8—31no—
460C22⋊Q8—91no—
461C22⋊Q8—91no—
462C22⋊Q8—91no—
463C22⋊Q8—91no—
464C22⋊Q8—91no—
465C22⋊Q8—181no—
466#121—91no—
467#121—91no—
468#121—181no—
469#121—181no—
470#121—181no—
471#117—91no—
472C2×C4⋊C4—91no—
473#107—91no—
474#107—91no—
475#106—91no—
476#106—91no—
477#103—31no—
478#103—91no—
479#103—91no—
480#103—91no—
481#103—91no—
482#103—91no—
483#102—31no—
484#102—91no—
485C22⋊C8—31no—
486C22⋊C8—31no—
487C22⋊C8—31no—
488C22⋊C8D3211yescharacteristic
489C23×C3—21no—
490C23×C3—31no—
491C23×C3—31no—
492C23×C3—61no—
493C23×C3C2×D1211yescharacteristic
494C23×C3D3×D411yescharacteristic
495C22×D3—21no—
496C22×D3C2×D1211yescharacteristic
497C22×D3C2×D1211yescharacteristic
498C3×Q8—61no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×Q8—61no—
502C3×Q8—121no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—121no—
506C3×D4—121no—
507C3×D4—121no—
508C3×D4—122no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—122no—
527C2×C3×C4C2×D1211yescharacteristic
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531#67—41no—
532#67—41no—
533#67—42no—
534#67—241no—
535#67—241no—
536#67—241no—
537#67—241no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—121no—
550C2×Dic3—121no—
551C2×Dic3—121no—
552C2×Dic3—121no—
553C2×Dic3—122no—
554C2×Dic3—241no—
555C2×Dic3—241no—
556C2×Dic3—242no—
557C2×Dic3C2×D1211yescharacteristic
558C2×Dic3C2×D1211yescharacteristic
559D12—21no—
560D12—21no—
561D12—41no—
562C4×D3—21no—
563C4×D3—21no—
564C4×D3—21no—
565C4×D3—21no—
566C4×D3—42no—
567C4×D3—122no—
568Dic6—21no—
569Dic6—21no—
570Dic6—21no—
571Dic6—21no—
572Dic6—41no—
573Dic6—61no—
574Dic6—61no—
575Dic6—61no—
576Dic6—61no—
577Dic6—121no—
578Dic6—121no—
579Dic6—122no—
580Dic6—122no—
581C3×C8—21no—
582C3×C8—21no—
583C3×C8—21no—
584C3×C8—21no—
585C3×C8—41no—
586C3×C8—41no—
587C3×C8—61no—
588C3×C8—61no—
589C3⋊C8—21no—
590C3⋊C8—21no—
591C2×C32—41no—
592C2×C32#53411yescharacteristic
593C2×C32#57711yescharacteristic
594C2×C32#57811yescharacteristic
595C3×D3—41no—
596C3×D3—41no—
597C3×D3—81no—
598#41—121no—
599#41—121no—
600#41—121no—
601#41—121no—
602C2×Q8—31no—
603C2×Q8—31no—
604C2×Q8—31no—
605C2×Q8—91no—
606C2×Q8—181no—
607C2×Q8—361no—
608C2×Q8—361no—
609C2×D4—31no—
610C2×D4—31no—
611C2×D4—31no—
612C2×D4—31no—
613C2×D4—61no—
614C2×D4—181no—
615C2×D4—181no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—61no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4C2×D3211yescharacteristic
622Q16—121no—
623Q16—361no—
624SD16—121no—
625SD16—361no—
626M16—121no—
627C2×C8—31no—
628C2×C8—31no—
629C2×C8—121no—
630C2×C8C2×D3211yescharacteristic
631C2×C8C2×D3211yescharacteristic
632C4⋊C4—31no—
633C4⋊C4—61no—
634C4⋊C4—91no—
635C4⋊C4—91no—
636C4⋊C4—91no—
637C4⋊C4—181no—
638C4⋊C4—181no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C22⋊C4—61no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C42—181no—
653C22×C3—22no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—61no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—61no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3C22×D1211yescharacteristic
673C22×C3C2×D3×D411yescharacteristic
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—21no—
677C2×D3—21no—
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—41no—
688C3×C4—61no—
689C3×C4—61no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4#100411yescharacteristic
694C3×C4#100411yescharacteristic
695C3×C4#100411yescharacteristic
696C3×C4#100411yescharacteristic
697Dic3—21no—
698Dic3—21no—
699Dic3—41no—
700Dic3—41no—
701Dic3—41no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—121no—
707Dic3—121no—
708Dic3—121no—
709Dic3—121no—
710Dic3—241no—
711Dic3—241no—
712Dic3—241no—
713Dic3—241no—
714C32#320111yescharacteristic, complemented, Sylow
715C23—31no—
716C23—31no—
717C23—61no—
718C23D3×D1211yescharacteristic
719Q8—61no—
720Q8—61no—
721Q8—61no—
722Q8—61no—
723Q8—121no—
724Q8—181no—
725Q8—181no—
726Q8—362no—
727D4—61no—
728D4—61no—
729D4—121no—
730D4—121no—
731D4—121no—
732D4—122no—
733D4—721no—
734D4—721no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—31no—
738C2×C4—31no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—122no—
747C2×C4—181no—
748C2×C4—181no—
749C2×C4—181no—
750C2×C4—181no—
751C2×C4—362no—
752C2×C4—721no—
753C2×C4D3×D1211yescharacteristic
754C2×C4C22×D3211yescharacteristic
755C8—21no—
756C8—21no—
757C8—61no—
758C8—61no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—42no—
763C2×C3—41no—
764C2×C3—41no—
765C2×C3—121no—
766C2×C3—121no—
767C2×C3—241no—
768C2×C3#549311yescharacteristic
769C2×C3#558911yescharacteristic
770C2×C3#575111yescharacteristic
771C2×C3#575311yescharacteristic
772C2×C3#577111yescharacteristic
773C2×C3#577811yescharacteristic
774D3—41no—
775D3—41no—
776D3—81no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—61no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22C2×D3×D1211yescharacteristic
790C4—21no—
791C4—61no—
792C4—61no—
793C4—121no—
794C4—121no—
795C4—121no—
796C4—361no—
797C4—361no—
798C4—361no—
799C4—361no—
800C4#6431311yescharacteristic
801C4#6431311yescharacteristic
802C3—21no—
803C3#7868111yescharacteristic, complemented
804C3#8023811yescharacteristic, complemented
805C2—41no—
806C2—121no—
807C2—121no—
808C2—241no—
809C2#1059429011yescharacteristic
810C2#1059469211yescharacteristic
811C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595044C2
hypercenterC22⋊C8D32
hypocenterC32#3201
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10594884C2semidirect
3. #10592421C2semidirect
4. C3×#4733C2semidirect
5. C3×#4727C2semidirect
6. #10591173C2semidirect
7. #10591126C2semidirect
8. #10590949C2semidirect
9. #10590851C2semidirect
10. #10590849C2semidirect
11. #10590834C2semidirect
12. #10590833C2semidirect
13. #10590825C2semidirect
14. #10590822C2semidirect
15. #10590710C2semidirect
85. #4733D3semidirect
86. #4727D3semidirect
714. C32#3201semidirect
803. C3#78681semidirect
804. C3#80238semidirect

Maximal subgroups

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

subgroupindex
#105950442
#105948842
#105924212
C3×#47332
C3×#47272
#105911732
#105911262
#105909492
#105908512
#105908492
#105908342
#105908332
#105908252
#105908222
#105907102
#802383
#786813