Finite Group Databasebeta

← #11887320

Subgroups — #11887320

Order 1152.

877 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#10594633C211yesmaximal, characteristic
2#10594550C211yesmaximal, characteristic, complemented
3#10592551C211yesmaximal, characteristic, complemented
4C3×#4866C211yesmaximal, characteristic, complemented
5C3×#4862C211yesmaximal, characteristic, complemented
6#10590970C211yesmaximal, characteristic, complemented
7#10590946C211yesmaximal, characteristic, complemented
8#10590868C211yesmaximal, characteristic, complemented
9#10590718C211yesmaximal, characteristic, complemented
10#10590610C211yesmaximal, characteristic, complemented
11D3×#809C211yesmaximal, characteristic, complemented
12#10590579C211yesmaximal, characteristic, complemented
13#10590578C211yesmaximal, characteristic, complemented
14#10590538C211yesmaximal, characteristic, complemented
15#10590435C211yesmaximal, characteristic, complemented
16#81445—31nomaximal
17#81381—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21#64102C2211yescharacteristic
22#64096C2211yescharacteristic, complemented
23C3×#897C2211yescharacteristic
24C3×#895C2211yescharacteristic
25C3×#892C2211yescharacteristic, complemented
26C3×D3×C4⋊C4C2211yescharacteristic
27#63922—21no—
28#63921—21no—
29#63916—21no—
30#63905—21no—
31C4×#625C2211yescharacteristic
32#63872C2211yescharacteristic, complemented
33#63867—21no—
34#63863C2211yescharacteristic
35#63862—21no—
36#63857C2211yescharacteristic
37#63857C2211yescharacteristic, complemented
38#63855—21no—
39#63854—21no—
40C2×#3719C2211yescharacteristic, complemented
41C2×#3716C2211yescharacteristic
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#106C2211yescharacteristic, complemented
45C8×C3⋊Dic3C2211yescharacteristic, complemented
46#63637C2211yescharacteristic, complemented
47#63636C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#808C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic
61#5630—31no—
62#5612—31no—
63#5529—31no—
64#5513—31no—
65C3×#483—31no—
66C3×#482—31no—
67#5051—31no—
68#5041—31no—
69#5002—31no—
70C2×#809—31no—
71#4891—31no—
72#4887—31no—
73#4871—31no—
74#4866D311yescharacteristic, complemented
75#4864—31no—
76#4862D311yescharacteristic, complemented
77#4852—31no—
78#4852—31no—
79#4852—61no—
80#4808—31no—
81#4804—31no—
82#4800—31no—
83#4798—31no—
84#4776—31no—
85D3×#102—31no—
86#4768—31no—
87#4767—31no—
88#4733—31no—
89#4731—31no—
90#67⋊C8—31no—
91#67⋊C8—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#625D411yescharacteristic
105C2×#624—21no—
106D3×D12—22no—
107D3×D12—41no—
108#3799—22no—
109#3799—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3752—21no—
114#3750—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118#3744—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129#3724D411yescharacteristic
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140#3719—41no—
141#3716—41no—
142D3×C3⋊C8—41no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C3×C22⋊Q8—31no—
150C3×#121—31no—
151C3×#117—31no—
152C2×C3×C4⋊C4—31no—
153#947—31no—
154C2×#216—31no—
155#938—61no—
156#937—61no—
157#936—31no—
158C2×#214—31no—
159#929—61no—
160C4×#67—31no—
161C4×#67—31no—
162#926—61no—
163#924—31no—
164#924—31no—
165C22×C3⋊C8—31no—
166C22×C3⋊C8—31no—
167C2×Dic12—31no—
168C2×#204—31no—
169C2×#204—31no—
170C2×#204—31no—
171C2×#204—61no—
172C2×D3×C8—31no—
173C2×D3×C8—31no—
174#898—61no—
175#897—31no—
176#897—31no—
177#897C2×D311yescharacteristic
178#895—61no—
179#895C2×D311yescharacteristic
180#894—61no—
181#893—31no—
182#893—31no—
183#893—61no—
184#892C2×D311yescharacteristic, complemented
185D3×C4⋊C4C2×D311yescharacteristic
186#890—31no—
187#890—31no—
188#889—61no—
189#887—31no—
190#887—31no—
191#887—61no—
192#883—61no—
193#883—61no—
194#882—61no—
195D3×C22⋊C4—61no—
196D3×C22⋊C4—61no—
197#879—61no—
198#872—61no—
199#870—61no—
200C3×#107—31no—
201C3×#106—21no—
202C3×#106—31no—
203C3×#106C2×D311yescharacteristic, complemented
204C3×#106C2×D311yescharacteristic, complemented
205C3×#103—31no—
206C3×#103—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8—31no—
211#835—31no—
212#832—31no—
213#821—31no—
214#821—31no—
215#821C2×D311yescharacteristic
216(C2×D3)⋊C8C2×D311yescharacteristic
217(C2×D3)⋊C8C2×D311yescharacteristic, complemented
218#816C2×D311yescharacteristic, complemented
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3—61no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—61no—
228#810C2×D311yescharacteristic, complemented
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—61no—
235#809C2×D311yescharacteristic
236#808C2×D311yescharacteristic, complemented
237#807C2×D311yescharacteristic, complemented
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)#4112yes—
253C4×C3⋊D3—81no—
254#634—21no—
255#634—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—81no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—42no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—42no—
272#626—42no—
273#625—22no—
274#624—42no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280#546—91no—
281#488—91no—
282#483—31no—
283#482—31no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×Q8—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—61no—
302C2×#67—31no—
303C2×#67—31no—
304C2×#67—61no—
305C2×#67—61no—
306#239—62no—
307#239—121no—
308D3×D4—62no—
309D3×D4—121no—
310#235—62no—
311#235—121no—
312C2×D12—21no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—61no—
316C2×D12—62no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12—121no—
320C2×D12C22×D311yescharacteristic
321C2×C4×D3—21no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—121no—
327C2×C4×D3C22×D311yescharacteristic
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6—31no—
330C2×Dic6—31no—
331C2×Dic6—61no—
332C2×Dic6C22×D311yescharacteristic
333C2×C3×C8—21no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C42—61no—
352#217—31no—
353#217—31no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#216—121no—
359#214—121no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—31no—
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—
371(C2×D3)⋊C4—121no—
372C4⋊Dic3—21no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—31no—
381Dic3⋊C4—31no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—121no—
389C4×Dic3—21no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—121no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8—121no—
400C2×C3⋊C8—121no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403Dic12—121no—
404#204—62no—
405#204—62no—
406#204—64no—
407#204—121no—
408D3×C8—121no—
409D3×C8—121no—
410C22×C32C22×D411yescharacteristic
411C2×C3⋊D3—22no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3#13512yes—
423D32—84no—
424C32×C4—41no—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C2×#41—91no—
437C22×D4—91no—
438C2×Q16—91no—
439C2×SD16—91no—
440C2×SD16—91no—
441C22×C8—91no—
442C22×C8—91no—
443#126—181no—
444#125—91no—
445#125—181no—
446#124—91no—
447#123—181no—
448#123—181no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451C22⋊Q8—91no—
452#121—31no—
453#121—181no—
454#120—181no—
455C4×Q8—91no—
456C4×D4—91no—
457C4×D4—91no—
458#117—31no—
459#117—181no—
460C2×C4⋊C4—31no—
461C2×C22⋊C4—181no—
462#107—31no—
463#106—31no—
464#106D3211yescharacteristic, complemented
465C4⋊C8—91no—
466#103—31no—
467#103—31no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—31no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476C22⋊C8—31no—
477C22⋊C8—31no—
478C4×C8—91no—
479C23×C3—31no—
480C23×C3—31no—
481C23×C3—61no—
482C22×D3—21no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—121no—
486C22×D3—122no—
487C22×D3—122no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—241no—
491C22×D3—241no—
492C22×D3D3×D411yescharacteristic
493C22×D3D3×D411yescharacteristic
494C3×Q8—61no—
495C3×Q8—61no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—241no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—122no—
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—62no—
519#67—62no—
520#67—122no—
521#67—122no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—121no—
534C2×Dic3D3×D411yescharacteristic
535C2×Dic3D3×D411yescharacteristic
536D12—21no—
537D12—21no—
538D12—32no—
539D12—32no—
540D12—62no—
541D12—61no—
542D12—61no—
543D12—81no—
544D12—121no—
545D12—122no—
546D12—122no—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—42no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—241no—
555C4×D3—241no—
556C4×D3—242no—
557Dic6—21no—
558Dic6—21no—
559Dic6—62no—
560Dic6—61no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—121no—
565C3×C8—22no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—121no—
575C2×C32#54611yescharacteristic
576C2×C32C2×#13511yescharacteristic
577C2×C32#57711yescharacteristic
578C3⋊D3—42no—
579C3×D3—22no—
580C3×D3—41no—
581C3×D3—81no—
582C24—181no—
583#41—182no—
584#41—361no—
585C2×Q8—31no—
586C2×Q8—91no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—91no—
590C2×D4—91no—
591C2×D4—181no—
592C2×D4—182no—
593C2×D4—181no—
594C2×D4—361no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—61no—
598C22×C4—181no—
599C22×C4—181no—
600Q16—361no—
601SD16—182no—
602SD16—361no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—91no—
606C2×C8—361no—
607C2×C8—361no—
608C2×C8C2×D3211yescharacteristic
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—91no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4C2×D3211yescharacteristic
620C4⋊C4C2×D3211yescharacteristic
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—91no—
625C22⋊C4—91no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C42—61no—
632C42—91no—
633C42—181no—
634C22×C3—21no—
635C22×C3—32no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3C2×D3×D411yescharacteristic
645C22×C3C2×D3×D411yescharacteristic
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—62no—
655C2×D3—62no—
656C2×D3—122no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—241no—
662C2×D3—241no—
663C2×D3—244no—
664C2×D3—244no—
665C2×D3#91612yes—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—81no—
675C3×C4—81no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4D3×#4111yescharacteristic
680C3×C4D3×#4111yescharacteristic
681C3×C4#100911yescharacteristic
682C3×C4#100911yescharacteristic
683Dic3—21no—
684Dic3—21no—
685Dic3—41no—
686Dic3—41no—
687Dic3—41no—
688Dic3—62no—
689Dic3—61no—
690Dic3—61no—
691Dic3—61no—
692Dic3—61no—
693Dic3—121no—
694Dic3—122no—
695Dic3—121no—
696Dic3—121no—
697C32#329611yescharacteristic, complemented, Sylow
698C23—31no—
699C23—31no—
700C23—61no—
701C23—181no—
702C23—362no—
703C23—362no—
704C23—721no—
705Q8—61no—
706Q8—61no—
707Q8—181no—
708Q8—181no—
709D4—61no—
710D4—61no—
711D4—92no—
712D4—182no—
713D4—181no—
714D4—241no—
715D4—362no—
716D4—362no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—91no—
729C2×C4—91no—
730C2×C4—122no—
731C2×C4—181no—
732C2×C4—362no—
733C2×C4—721no—
734C2×C4C22×D3211yescharacteristic
735C8—21no—
736C8—61no—
737C8—61no—
738C8—181no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—62no—
743C2×C3—121no—
744C2×C3—241no—
745C2×C3#565411yescharacteristic
746C2×C3#565411yescharacteristic
747C2×C3C2×#91611yescharacteristic
748C2×C3D3×#13511yescharacteristic
749C2×C3#577511yescharacteristic
750C2×C3#577811yescharacteristic
751D3—22no—
752D3—41no—
753D3—81no—
754D3—122no—
755D3—122no—
756D3—242no—
757C22—32no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—182no—
767C22—361no—
768C22—361no—
769C22—724no—
770C22D32×D411yescharacteristic
771C4—41no—
772C4—41no—
773C4—61no—
774C4—61no—
775C4—121no—
776C4—121no—
777C4—121no—
778C4—181no—
779C4—181no—
780C4—361no—
781C4#6430611yescharacteristic
782C4#6432011yescharacteristic
783C3—21no—
784C3#8138111yescharacteristic, complemented
785C3#8144511yescharacteristic, complemented
786C2—62no—
787C2—121no—
788C2—241no—
789C2—362no—
790C2#1059461611yescharacteristic
791C2D3×#91611yescharacteristic
792C2#1059475411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#10594633C2
hypercenter#106D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594550C2semidirect
3. #10592551C2semidirect
4. C3×#4866C2semidirect
5. C3×#4862C2semidirect
6. #10590970C2semidirect
7. #10590946C2semidirect
8. #10590868C2semidirect
9. #10590718C2semidirect
10. #10590610C2semidirect
11. D3×#809C2semidirect
12. #10590579C2semidirect
13. #10590578C2semidirect
14. #10590538C2semidirect
15. #10590435C2semidirect
22. #64096C22semidirect
25. C3×#892C22semidirect
32. #63872C22semidirect
37. #63857C22semidirect
40. C2×#3719C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. C32×#106C22semidirect
45. C8×C3⋊Dic3C22semidirect
46. #63637C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#816C22semidirect
52. C3×#810C22semidirect
54. C3×#808C22semidirect
55. C3×#807C22semidirect
56. #63572C22semidirect
57. #63565C22semidirect
74. #4866D3semidirect
76. #4862D3semidirect
184. #892C2×D3semidirect
203. C3×#106C2×D3semidirect
204. C3×#106C2×D3semidirect
217. (C2×D3)⋊C8C2×D3semidirect
218. #816C2×D3semidirect
228. #810C2×D3semidirect
236. #808C2×D3semidirect
237. #807C2×D3semidirect
464. #106D32semidirect
697. C32#3296semidirect
784. C3#81381semidirect
785. C3#81445semidirect

Maximal subgroups

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

subgroupindex
#105946332
#105945502
#105925512
C3×#48662
C3×#48622
#105909702
#105909462
#105908682
#105907182
#105906102
D3×#8092
#105905792
#105905782
#105905382
#105904352
#814453
#813813