Finite Group Databasebeta

← #11870343

Subgroups — #11870343

Order 1152.

875 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594990C211yesmaximal, characteristic, complemented
2#10594923C211yesmaximal, characteristic
3#10592426C211yesmaximal, characteristic, complemented
4C3×#4735C211yesmaximal, characteristic, complemented
5C3×#4723C211yesmaximal, characteristic, complemented
6#10591101C211yesmaximal, characteristic, complemented
7#10591090C211yesmaximal, characteristic, complemented
8#10590957C211yesmaximal, characteristic, complemented
9#10590956C211yesmaximal, characteristic, complemented
10#10590713C211yesmaximal, characteristic, complemented
11#10590688C211yesmaximal, characteristic, complemented
12#10590686C211yesmaximal, characteristic, complemented
13#10590685C211yesmaximal, characteristic, complemented
14#10590651C211yesmaximal, characteristic, complemented
15#10590649C211yesmaximal, characteristic, complemented
16#81521—31nomaximal
17#81328—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic
22C3×#930C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C3×#924C2211yescharacteristic
26#63971—21no—
27#63958—21no—
28#63952—21no—
29#63952—21no—
30#63916C2211yescharacteristic
31#63910—21no—
32#63900C2211yescharacteristic
33#63900C2211yescharacteristic
34#63900C2211yescharacteristic
35#63896—21no—
36#63894—21no—
37#63871C2211yescharacteristic
38#63849C2211yescharacteristic
39#63849C2211yescharacteristic
40#63844—21no—
41C32×C22⋊C8C2211yescharacteristic
42#63657C2211yescharacteristic
43#63647C2211yescharacteristic
44#63647C2211yescharacteristic
45C3×#821C2211yescharacteristic
46C3×#821C2211yescharacteristic
47C3×#818C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53#63576C2211yescharacteristic
54#63574C2211yescharacteristic
55#63574C2211yescharacteristic
56#63574C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61#5629—31no—
62#5608—31no—
63#5523—31no—
64#5504—31no—
65C3×#485—31no—
66C3×#481—31no—
67#5043—31no—
68#5035—31no—
69#5003—31no—
70#4971—31no—
71#4885—31no—
72#4881—31no—
73#4868—31no—
74#4863—31no—
75#4862—31no—
76#4861—31no—
77D3×#106—31no—
78D3×#106—31no—
79#4815—31no—
80#4805—31no—
81#4804—31no—
82#4803—31no—
83#4784—31no—
84#4777—31no—
85#4772—31no—
86#4771—31no—
87#4735D311yescharacteristic, complemented
88#4727—31no—
89#4727—31no—
90#4727—61no—
91#4723D311yescharacteristic, complemented
92C22×C32×C4C2311yescharacteristic
93C2×#638D411yescharacteristic
94C2×#638D411yescharacteristic
95#3828—22no—
96#3828—22no—
97C2×C4⋊(C3⋊D3)D411yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×#634D411yescharacteristic
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#624—21no—
108C2×#624—21no—
109C2×#624—21no—
110C2×D3×Dic3—21no—
111#3796—22no—
112#3796—22no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117#3743—22no—
118C8×C3⋊D3—22no—
119C3×#217—21no—
120C3×#217—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131#3724—21no—
132#3724—21no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141#3099—91noSylow
142C2×#239—31no—
143C2×#237—31no—
144C2×#235—31no—
145C2×#235—31no—
146C2×#235—61no—
147C3×C22⋊Q8—31no—
148C3×#121—31no—
149C3×#117—31no—
150C2×C3×C4⋊C4—31no—
151#946—31no—
152#939—61no—
153#938—31no—
154#938—61no—
155#930C2×D311yescharacteristic
156C4×#67—61no—
157C4×#67—61no—
158#926C2×D311yescharacteristic
159C2×C4⋊Dic3C2×D311yescharacteristic
160#924C2×D311yescharacteristic
161C2×ΓL(1,𝔽25)—31no—
162C2×ΓL(1,𝔽25)—31no—
163C2×ΓL(1,𝔽25)—61no—
164C2×D3×C8—31no—
165C2×D3×C8—31no—
166C2×D3×C8—61no—
167#897—31no—
168#896—61no—
169#895—31no—
170#895—61no—
171#893—61no—
172#892—31no—
173#892—31no—
174#892—31no—
175#892—31no—
176D3×C4⋊C4—31no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—31no—
179D3×C4⋊C4—31no—
180D3×C4⋊C4—31no—
181D3×C4⋊C4—31no—
182#887—61no—
183#884—61no—
184#884—61no—
185#884—61no—
186#67⋊C4—61no—
187#67⋊C4—61no—
188#878—61no—
189C4×D12—61no—
190C4×Dic6—61no—
191C3×#107—31no—
192C3×#106—31no—
193C3×#106—31no—
194C3×#106—31no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×#102—31no—
199C3×C22⋊C8—21no—
200C3×C22⋊C8C2×D311yescharacteristic
201C3×C22⋊C8C2×D311yescharacteristic
202#835—31no—
203#835—31no—
204#832—31no—
205#832—31no—
206#830—31no—
207#830—31no—
208#830—61no—
209#821C2×D311yescharacteristic
210#821C2×D311yescharacteristic
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—61no—
216(C2×D3)⋊C8—61no—
217#818C2×D311yescharacteristic
218#817C2×D311yescharacteristic
219#817C2×D311yescharacteristic
220#817C2×D311yescharacteristic
221#816C2×D311yescharacteristic
222#816C2×D311yescharacteristic
223#810—31no—
224#810—31no—
225#809—31no—
226#809—31no—
227#808—31no—
228#808—31no—
229#808—31no—
230#808—31no—
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3⋊D3C2×D411yescharacteristic
237C22×C3⋊D3C2×D411yescharacteristic
238C22×C3×D3—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2411yescharacteristic
243#638—22no—
244#638—22no—
245C2×C3⋊Dic3C2×D411yescharacteristic
246C2×C3⋊Dic3C2×D411yescharacteristic
247C4⋊(C3⋊D3)—22no—
248C4×C3⋊D3—21no—
249C4×C3⋊D3—21no—
250C4×C3⋊D3#4112yes—
251C4×C3⋊D3#4112yes—
252#634—22no—
253C3×#67—81no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—81no—
262C3×D12—21no—
263C3×D12—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266#626—42no—
267#626—81no—
268#624—81no—
269#624—81no—
270#624—81no—
271D3×Dic3—42no—
272C32×C8—21no—
273C32×C8—21no—
274C3⋊(C3⋊C8)—21no—
275C3⋊(C3⋊C8)—21no—
276#537—91no—
277#520—91no—
278#485—31no—
279#485—91no—
280#483—91no—
281#483—91no—
282#482—91no—
283#482—91no—
284#481—31no—
285#481—91no—
286#428—91no—
287C2×#106—91no—
288#417—91no—
289#416—91no—
290#408—91no—
291C2×C3×Q8—31no—
292C2×C3×D4—31no—
293C2×C3×D4—61no—
294C22×C3×C4—21no—
295C22×C3×C4—61no—
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C2×#67—21no—
299C2×#67—31no—
300C2×#67—31no—
301C2×#67—31no—
302C2×#67—31no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C22×Dic3—21no—
308C22×Dic3—61no—
309#239—62no—
310#239—62no—
311#237—62no—
312#237—62no—
313#235—62no—
314#235—62no—
315#235—62no—
316#235—62no—
317#235—122no—
318#235—122no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×Dic6—31no—
339C2×Dic6—31no—
340C2×Dic6—61no—
341C2×Dic6C22×D311yescharacteristic
342C2×C3×C8—21no—
343C2×C3×C8—21no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C42—61no—
360#217—21no—
361#217—21no—
362#217—61no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371C4⋊Dic3—21no—
372C4⋊Dic3—61no—
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387C4×Dic3—21no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8—61no—
398ΓL(1,𝔽25)—62no—
399ΓL(1,𝔽25)—62no—
400ΓL(1,𝔽25)—122no—
401D3×C8—62no—
402D3×C8—62no—
403D3×C8—122no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—21no—
407C22×C32C22×D411yescharacteristic
408C2×C3⋊D3—21no—
409C2×C3⋊D3—21no—
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—21no—
413C2×C3⋊D3#12312yes—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C32×C4—21no—
418C32×C4C2×#4111yescharacteristic
419C32×C4C2×#4111yescharacteristic
420C3⋊Dic3—21no—
421C3⋊Dic3#12312yes—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C2×#41—91no—
430C2×#41—91no—
431C2×M16—91no—
432C22×C8—91no—
433C22⋊Q8—31no—
434C22⋊Q8—91no—
435C22⋊Q8—181no—
436#121—31no—
437#121—91no—
438#121—181no—
439#121—181no—
440#121—181no—
441C4×Q8—181no—
442C4×D4—181no—
443C4×D4—181no—
444C4×D4—181no—
445#117—31no—
446#117—91no—
447#117—91no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—91no—
450C2×C4⋊C4—91no—
451C2×C4⋊C4—91no—
452#107—31no—
453#107—91no—
454#106—31no—
455#106—31no—
456#106—31no—
457#106—91no—
458#106—91no—
459#106—91no—
460#103—31no—
461#103—31no—
462#103—91no—
463#103—91no—
464#102—31no—
465#102—31no—
466#102—91no—
467#102—91no—
468C22⋊C8—91no—
469C22⋊C8—91no—
470C22⋊C8—91no—
471C22⋊C8D3211yescharacteristic
472C23×C3—21no—
473C23×C3—61no—
474C23×C3D3×D411yescharacteristic
475C23×C3D3×D411yescharacteristic
476C22×D3—21no—
477C22×D3—31no—
478C22×D3—31no—
479C22×D3—31no—
480C22×D3—31no—
481C22×D3—61no—
482C22×D3—61no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×D4—61no—
486C3×D4—61no—
487C3×D4—241no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—241no—
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508#67—62no—
509#67—62no—
510#67—62no—
511#67—62no—
512#67—81no—
513#67—122no—
514#67—122no—
515#67—122no—
516#67—241no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—81no—
531C2×Dic3—122no—
532D12—21no—
533D12—21no—
534D12—62no—
535D12—62no—
536D12—122no—
537D12—122no—
538D12—241no—
539C4×D3—32no—
540C4×D3—32no—
541C4×D3—32no—
542C4×D3—32no—
543C4×D3—62no—
544C4×D3—62no—
545C4×D3—61no—
546C4×D3—61no—
547C4×D3—61no—
548C4×D3—61no—
549C4×D3—121no—
550C4×D3—121no—
551C4×D3—122no—
552C4×D3—241no—
553C4×D3—241no—
554C4×D3—241no—
555C4×D3—241no—
556C4×D3—241no—
557C4×D3—241no—
558Dic6—21no—
559Dic6—21no—
560Dic6—62no—
561Dic6—62no—
562Dic6—122no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—41no—
568C3×C8—41no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—61no—
573C3⋊C8—121no—
574C3⋊C8—121no—
575C2×C32—41no—
576C2×C32C2×#12311yescharacteristic
577C2×C32#57711yescharacteristic
578C2×C32#57711yescharacteristic
579C3⋊D3—22no—
580C3⋊D3—41no—
581C3×D3—81no—
582#41—182no—
583#41—182no—
584#41—182no—
585#41—182no—
586C2×Q8—31no—
587C2×Q8—91no—
588C2×D4—31no—
589C2×D4—61no—
590C2×D4—91no—
591C2×D4—91no—
592C2×D4—91no—
593C2×D4—181no—
594C2×D4—181no—
595C22×C4—61no—
596C22×C4—91no—
597C22×C4—91no—
598C22×C4—181no—
599C22×C4—181no—
600C22×C4—181no—
601C22×C4—181no—
602C22×C4C2×D3211yescharacteristic
603M16—182no—
604C2×C8—91no—
605C2×C8—91no—
606C2×C8—182no—
607C2×C8C2×D3211yescharacteristic
608C2×C8C2×D3211yescharacteristic
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C42—61no—
629C42—181no—
630C42—181no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3C2×D3×D411yescharacteristic
645C22×C3C2×D3×D411yescharacteristic
646C2×D3—32no—
647C2×D3—32no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—62no—
652C2×D3—61no—
653C2×D3—61no—
654C2×D3—61no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—41no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4D3×#4111yescharacteristic
680C3×C4D3×#4111yescharacteristic
681C3×C4D3×#4111yescharacteristic
682C3×C4D3×#4111yescharacteristic
683Dic3—32no—
684Dic3—32no—
685Dic3—41no—
686Dic3—41no—
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3—41no—
691Dic3—41no—
692Dic3—62no—
693Dic3—61no—
694Dic3—61no—
695Dic3—121no—
696C32#309911yescharacteristic, complemented, Sylow
697C23—61no—
698C23—91no—
699C23—91no—
700C23#380211yescharacteristic
701Q8—61no—
702Q8—61no—
703Q8—182no—
704D4—61no—
705D4—61no—
706D4—182no—
707D4—182no—
708D4—182no—
709D4—241no—
710D4—362no—
711D4—721no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—91no—
722C2×C4—92no—
723C2×C4—92no—
724C2×C4—91no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4—241no—
728C2×C4—362no—
729C2×C4—721no—
730C2×C4—721no—
731C2×C4—721no—
732C2×C4#380211yescharacteristic
733C2×C4C22×D3211yescharacteristic
734C8—21no—
735C8—21no—
736C8—181no—
737C8—181no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—41no—
742C2×C3—41no—
743C2×C3—81no—
744C2×C3—241no—
745C2×C3D3×#12311yescharacteristic
746C2×C3D3×#12311yescharacteristic
747C2×C3#576211yescharacteristic
748C2×C3#577011yescharacteristic
749C2×C3#577511yescharacteristic
750C2×C3#577811yescharacteristic
751D3—62no—
752D3—62no—
753D3—81no—
754D3—122no—
755D3—121no—
756D3—121no—
757D3—241no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—92no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22—181no—
766C22—181no—
767C22—181no—
768C22—181no—
769C22—181no—
770C22C2×#380211yescharacteristic
771C4—21no—
772C4—92no—
773C4—121no—
774C4—121no—
775C4—121no—
776C4—121no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4—181no—
781C4#6431211yescharacteristic
782C4#6431211yescharacteristic
783C3—21no—
784C3#8132811yescharacteristic, complemented
785C3#8152111yescharacteristic, complemented
786C2—41no—
787C2—182no—
788C2—241no—
789C2—361no—
790C2#1059429511yescharacteristic
791C2#1059468611yescharacteristic
792C2#1059471911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10594923C2
hypercenterC22⋊C8D32
hypocenterC32#3099
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
1. #10594990C2semidirect
3. #10592426C2semidirect
4. C3×#4735C2semidirect
5. C3×#4723C2semidirect
6. #10591101C2semidirect
7. #10591090C2semidirect
8. #10590957C2semidirect
9. #10590956C2semidirect
10. #10590713C2semidirect
11. #10590688C2semidirect
12. #10590686C2semidirect
13. #10590685C2semidirect
14. #10590651C2semidirect
15. #10590649C2semidirect
87. #4735D3semidirect
91. #4723D3semidirect
696. C32#3099semidirect
784. C3#81328semidirect
785. C3#81521semidirect

Maximal subgroups

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

subgroupindex
#105949902
#105949232
#105924262
C3×#47352
C3×#47232
#105911012
#105910902
#105909572
#105909562
#105907132
#105906882
#105906862
#105906852
#105906512
#105906492
#815213
#813283