Finite Group Databasebeta

← #11887321

Subgroups — #11887321

Order 1152.

868 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594630C211yesmaximal, characteristic
2#10594337C211yesmaximal, characteristic, complemented
3#10592561C211yesmaximal, characteristic, complemented
4C3×#4866C211yesmaximal, characteristic, complemented
5C3×#4852C211yesmaximal, characteristic, complemented
6#10590960C211yesmaximal, characteristic, complemented
7#10590943C211yesmaximal, characteristic, complemented
8#10590863C211yesmaximal, characteristic, complemented
9#10590721C211yesmaximal, characteristic, complemented
10#10590608C211yesmaximal, characteristic, complemented
11#10590593C211yesmaximal, characteristic, complemented
12#10590542C211yesmaximal, characteristic, complemented
13#10590532C211yesmaximal, characteristic, complemented
14#10590525C211yesmaximal, characteristic, complemented
15#10590514C211yesmaximal, characteristic, complemented
16#81381—31nomaximal
17#79677—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20#64106C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C2×C3×#204C2211yescharacteristic
23C3×#895C2211yescharacteristic
24C3×#893C2211yescharacteristic
25C3×#892C2211yescharacteristic, complemented
26C3×#887C2211yescharacteristic, complemented
27#63922—21no—
28D3×(C2×D3)⋊C4—21no—
29#63908—21no—
30C4×#626C2211yescharacteristic
31#63891—21no—
32#63874—21no—
33#63871C2211yescharacteristic
34#63869C2211yescharacteristic, complemented
35#63867—21no—
36#63860C2211yescharacteristic
37#63859—21no—
38#63856C2211yescharacteristic, complemented
39#63853—21no—
40C2×#3719C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic
42C2×#3710C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#106C2211yescharacteristic, complemented
45#63647C2211yescharacteristic
46#63643C2211yescharacteristic, complemented
47#63637C2211yescharacteristic, complemented
48#63635C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×C8×Dic3C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#809C2211yescharacteristic
55C3×#807C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61#5612—31no—
62#5581—31no—
63#5554—31no—
64#5529—31no—
65C3×#482—31no—
66C3×C4×SD16—31no—
67#5173—31no—
68#5169—31no—
69#5041—31no—
70#5028—31no—
71#5009—31no—
72#5002—31no—
73#4891—31no—
74#4887—31no—
75#4866D311yescharacteristic, complemented
76#4862—31no—
77#4862—31no—
78#4862—61no—
79#4852D311yescharacteristic, complemented
80#4813—31no—
81#4807—31no—
82#4776—31no—
83#4772—31no—
84D3×#102—31no—
85D3×#102—31no—
86#4768—31no—
87#4767—31no—
88#4733—31no—
89#67⋊C8—31no—
90#4697—31no—
91C8×D12—31no—
92C22×D32—21no—
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#626D411yescharacteristic
103C2×#625—21no—
104C2×#625—21no—
105C2×D3×Dic3—21no—
106#3802—22no—
107#3802—41no—
108#3795—22no—
109#3795—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3752—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×#204—22no—
129#3724—21no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135#3722D411yescharacteristic
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140#3719—41no—
141#3715—41no—
142#3710—41no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C2×#237—31no—
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×#235—31no—
149C2×C3×SD16—31no—
150C3×#121—31no—
151C3×C4×Q8—31no—
152C3×C4×D4—31no—
153C3×#117—31no—
154#946—31no—
155#946—31no—
156C2×#216—31no—
157C2×#215—31no—
158#938—61no—
159#937—61no—
160#936—31no—
161C2×#214—31no—
162#930—61no—
163C4×#67—31no—
164C2×(C2×D3)⋊C4—61no—
165#924—31no—
166C22×C3⋊C8—31no—
167C2×Dic12—31no—
168C2×#204C2×D311yescharacteristic
169C2×D3×C8—31no—
170C2×D3×C8—31no—
171C2×D3×C8—31no—
172#897—31no—
173#897—31no—
174#897—31no—
175#897—61no—
176#895C2×D311yescharacteristic
177#894—61no—
178#893C2×D311yescharacteristic
179#892C2×D311yescharacteristic, complemented
180D3×C4⋊C4—31no—
181D3×C4⋊C4—31no—
182D3×C4⋊C4—61no—
183#890—31no—
184#889—61no—
185#887C2×D311yescharacteristic, complemented
186#886—61no—
187#883—61no—
188#883—61no—
189#882—61no—
190D3×C22⋊C4—61no—
191#879—61no—
192#876—61no—
193#875—31no—
194C4×D12—31no—
195#872—61no—
196#872—61no—
197#870—31no—
198#870—61no—
199C3×#107—31no—
200C3×#106—21no—
201C3×#106C2×D311yescharacteristic, complemented
202C3×#106C2×D311yescharacteristic, complemented
203C3×#103—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C22⋊C8—31no—
208C3×C4×C8—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#821—31no—
213#821—31no—
214#821C2×D311yescharacteristic
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—61no—
218(C2×D3)⋊C8C2×D311yescharacteristic, complemented
219#816—31no—
220#816—31no—
221#816—31no—
222#816—61no—
223Dic3⋊C8—31no—
224C8×Dic3C2×D311yescharacteristic, complemented
225#810—31no—
226#810—31no—
227#810—31no—
228#810—61no—
229#810C2×D311yescharacteristic, complemented
230#809—31no—
231#809C2×D311yescharacteristic
232#809C2×D311yescharacteristic
233#808—31no—
234#808—31no—
235#808—61no—
236#807C2×D311yescharacteristic, complemented
237C4⋊(C3⋊C8)—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
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⋊Dic3—21no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C4×C3⋊D3—21no—
252C4×C3⋊D3—21no—
253C4×C3⋊D3—42no—
254#634—21no—
255#634—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—81no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—81no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—22no—
272#625—42no—
273#625—42no—
274D3×Dic3—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—91no—
283#482—31no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—31no—
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—31no—
299C2×C3×D4—61no—
300C22×C3×C4—31no—
301C22×C3×C4—61no—
302C2×#67—31no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C22×Dic3—61no—
308#237—62no—
309#237—121no—
310D3×D4—62no—
311D3×D4—62no—
312D3×D4—121no—
313D3×D4—121no—
314#235—62no—
315#235—121no—
316C2×D12—21no—
317C2×D12—31no—
318C2×D12C22×D311yescharacteristic
319C2×D12C22×D311yescharacteristic
320C2×C4×D3—21no—
321C2×C4×D3—31no—
322C2×C4×D3—31no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—121no—
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6—31no—
330C2×Dic6—31no—
331C2×Dic6—61no—
332C2×Dic6C22×D311yescharacteristic
333C3×SD16—62no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—31no—
351C3×C42—61no—
352C3×C42—61no—
353#217—31no—
354#217—61no—
355#217—61no—
356#217—61no—
357#216—121no—
358#215—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—31no—
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—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—121no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—121no—
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—31no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—121no—
395C4×Dic3—21no—
396C4×Dic3—21no—
397C4×Dic3C22×D311yescharacteristic
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—121no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404Dic12—121no—
405#204—22no—
406D3×C8—121no—
407D3×C8—121no—
408D3×C8—121no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3#13512yes—
413C2×C3×D3—22no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422D32—84no—
423C32×C4—41no—
424C32×C4—41no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3⋊Dic3—21no—
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—91no—
436C22×D4—91no—
437C2×Q16—91no—
438C2×SD16—31no—
439C2×SD16—91no—
440C22×C8—91no—
441C22×C8—91no—
442#126—181no—
443#125—91no—
444#125—181no—
445#124—91no—
446#123—181no—
447#123—181no—
448C22⋊Q8—91no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451#121—31no—
452#121—181no—
453#120—181no—
454C4×Q8—31no—
455C4×D4—31no—
456C4×D4—91no—
457#117—31no—
458#117—181no—
459C2×C4⋊C4—91no—
460C2×C22⋊C4—181no—
461#107—31no—
462#106—91no—
463#106D3211yescharacteristic, complemented
464C4⋊C8—91no—
465#103—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—31no—
471#102—31no—
472#102—91no—
473#102—91no—
474#102—91no—
475C22⋊C8—31no—
476C22⋊C8—91no—
477C4×C8—31no—
478C23×C3—31no—
479C23×C3—61no—
480C23×C3—61no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—31no—
484C22×D3—31no—
485C22×D3—61no—
486C22×D3—122no—
487C22×D3—122no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—241no—
491C22×D3—241no—
492C22×D3D3×D411yescharacteristic
493C3×Q8—61no—
494C3×Q8—61no—
495C3×D4—32no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—241no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—241no—
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—62no—
518#67—122no—
519#67—122no—
520#67—122no—
521#67—122no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—121no—
532C2×Dic3—121no—
533C2×Dic3—122no—
534C2×Dic3D3×D411yescharacteristic
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537D12—21no—
538D12—21no—
539D12—21no—
540D12—62no—
541D12—81no—
542D12#23512yes—
543C4×D3—21no—
544C4×D3—21no—
545C4×D3—61no—
546C4×D3—61no—
547C4×D3—61no—
548C4×D3—61no—
549C4×D3—81no—
550C4×D3—121no—
551C4×D3—121no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—122no—
555C4×D3—242no—
556Dic6—21no—
557Dic6—21no—
558Dic6—61no—
559Dic6—61no—
560Dic6—61no—
561Dic6—61no—
562Dic6—121no—
563Dic6—121no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—41no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C3⋊C8—61no—
572C3⋊C8—61no—
573C3⋊C8—121no—
574C2×C32#54611yescharacteristic
575C2×C32C2×#13511yescharacteristic
576C2×C32#57711yescharacteristic
577C3⋊D3—22no—
578C3×D3—42no—
579C3×D3—41no—
580C3×D3—81no—
581C24—181no—
582#41—182no—
583#41—361no—
584C2×Q8—31no—
585C2×Q8—91no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—91no—
590C2×D4—181no—
591C2×D4—182no—
592C2×D4—181no—
593C2×D4—361no—
594C22×C4—31no—
595C22×C4—61no—
596C22×C4—91no—
597C22×C4—181no—
598C22×C4—181no—
599Q16—361no—
600SD16—62no—
601SD16—361no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—91no—
605C2×C8—361no—
606C2×C8—361no—
607C2×C8C2×D3211yescharacteristic
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4C2×D3211yescharacteristic
619C4⋊C4C2×D3211yescharacteristic
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—91no—
624C22⋊C4—91no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C42—31no—
631C42—61no—
632C42—61no—
633C22×C3—21no—
634C22×C3—62no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3C2×D3×D411yescharacteristic
644C22×C3C2×D3×D411yescharacteristic
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—22no—
649C2×D3—32no—
650C2×D3—32no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—62no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—244no—
664C2×D3—244no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—81no—
675C3×C4—81no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4C2×#23511yescharacteristic
679C3×C4D3×#4111yescharacteristic
680C3×C4#100911yescharacteristic
681C3×C4#100911yescharacteristic
682Dic3—21no—
683Dic3—21no—
684Dic3—21no—
685Dic3—41no—
686Dic3—41no—
687Dic3—61no—
688Dic3—61no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—241no—
695Dic3—241no—
696C32#329611yescharacteristic, complemented, Sylow
697C23—31no—
698C23—61no—
699C23—61no—
700C23—91no—
701C23—362no—
702C23—362no—
703C23—721no—
704Q8—61no—
705Q8—61no—
706Q8—181no—
707Q8—181no—
708D4—32no—
709D4—61no—
710D4—61no—
711D4—61no—
712D4—182no—
713D4—241no—
714D4—362no—
715D4—362no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—91no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—241no—
731C2×C4—362no—
732C2×C4—362no—
733C2×C4C22×D3211yescharacteristic
734C8—21no—
735C8—61no—
736C8—61no—
737C8—181no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—121no—
742C2×C3—122no—
743C2×C3—241no—
744C2×C3#555011yescharacteristic
745C2×C3#565411yescharacteristic
746C2×C3#576211yescharacteristic
747C2×C3D3×#13511yescharacteristic
748C2×C3D3×#13511yescharacteristic
749C2×C3#577511yescharacteristic
750D3—42no—
751D3—41no—
752D3—62no—
753D3—62no—
754D3—81no—
755D3—122no—
756C22—61no—
757C22—62no—
758C22—61no—
759C22—61no—
760C22—92no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—181no—
767C22—181no—
768C22—724no—
769C22D32×D411yescharacteristic
770C4—41no—
771C4—41no—
772C4—61no—
773C4—61no—
774C4—61no—
775C4—121no—
776C4—121no—
777C4—181no—
778C4—361no—
779C4—361no—
780C4D3×#23511yescharacteristic
781C4#6432011yescharacteristic
782C3—21no—
783C3#7967711yescharacteristic, complemented
784C3#8138111yescharacteristic, complemented
785C2—121no—
786C2—122no—
787C2—182no—
788C2—241no—
789C2#1059461911yescharacteristic
790C2#1059474711yescharacteristic
791C2#1059474911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#10594630C2
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. #10594337C2semidirect
3. #10592561C2semidirect
4. C3×#4866C2semidirect
5. C3×#4852C2semidirect
6. #10590960C2semidirect
7. #10590943C2semidirect
8. #10590863C2semidirect
9. #10590721C2semidirect
10. #10590608C2semidirect
11. #10590593C2semidirect
12. #10590542C2semidirect
13. #10590532C2semidirect
14. #10590525C2semidirect
15. #10590514C2semidirect
25. C3×#892C22semidirect
26. C3×#887C22semidirect
34. #63869C22semidirect
38. #63856C22semidirect
40. C2×#3719C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. C32×#106C22semidirect
46. #63643C22semidirect
47. #63637C22semidirect
48. #63635C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×C8×Dic3C22semidirect
52. C3×#810C22semidirect
55. C3×#807C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
75. #4866D3semidirect
79. #4852D3semidirect
179. #892C2×D3semidirect
185. #887C2×D3semidirect
201. C3×#106C2×D3semidirect
202. C3×#106C2×D3semidirect
218. (C2×D3)⋊C8C2×D3semidirect
224. C8×Dic3C2×D3semidirect
229. #810C2×D3semidirect
236. #807C2×D3semidirect
463. #106D32semidirect
696. C32#3296semidirect
783. C3#79677semidirect
784. C3#81381semidirect

Maximal subgroups

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

subgroupindex
#105946302
#105943372
#105925612
C3×#48662
C3×#48522
#105909602
#105909432
#105908632
#105907212
#105906082
#105905932
#105905422
#105905322
#105905252
#105905142
#813813
#796773