Finite Group Databasebeta

← #11888695

Subgroups — #11888695

Order 1152.

850 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594562C211yesmaximal, characteristic, complemented
2#10594381C211yesmaximal, characteristic, complemented
3#10592563C211yesmaximal, characteristic, complemented
4C3×#4871C211yesmaximal, characteristic, complemented
5C3×#4862C211yesmaximal, characteristic, complemented
6#10590968C211yesmaximal, characteristic, complemented
7#10590956C211yesmaximal, characteristic, complemented
8#10590760C211yesmaximal, characteristic, complemented
9#10590737C211yesmaximal, characteristic, complemented
10#10590617C211yesmaximal, characteristic, complemented
11#10590607C211yesmaximal, characteristic, complemented
12#10590589C211yesmaximal, characteristic, complemented
13#10590585C211yesmaximal, characteristic, complemented
14#10590562C211yesmaximal, characteristic, complemented
15#10590450C211yesmaximal, characteristic, complemented
16#81432—31nomaximal
17#81188—31nomaximal
18C2×#3796C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic
22#64106C2211yescharacteristic
23#64104C2211yescharacteristic
24C3×#897C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#890C2211yescharacteristic
28#63909—21no—
29#63909C2211yescharacteristic
30#63906—21no—
31#63904—21no—
32C4×#626C2211yescharacteristic
33#63897—21no—
34#63894C2211yescharacteristic
35#63891—21no—
36#63890—21no—
37D3×C4⋊Dic3—21no—
38#63866C2211yescharacteristic
39#63849C2211yescharacteristic
40#63848—21no—
41C2×#3717C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C32×#106C2211yescharacteristic
45#63637C2211yescharacteristic
46#63636C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic
54C3×#807C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic
60#63554C2211yescharacteristic
61#5695—31no—
62#5631—31no—
63#5555—31no—
64#5514—31no—
65C3×#483—31no—
66C3×#478—31no—
67#5069—31no—
68#5049—31no—
69#5014—31no—
70#4966—31no—
71#4888—31no—
72#4886—31no—
73#4871D311yescharacteristic, complemented
74#4869—31no—
75#4868—31no—
76#4864—31no—
77#4864—31no—
78#4864—61no—
79#4862D311yescharacteristic, complemented
80#4841—31no—
81#4836—31no—
82#4818—31no—
83#4810—31no—
84#4804—31no—
85#4797—31no—
86#4781—31no—
87#4781—31no—
88#4772—31no—
89#4771—31no—
90#4734—31no—
91#4728—31no—
92C2×C4⋊(C3⋊D3)—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#626—21no—
102C2×#626—21no—
103C2×#626D411yescharacteristic
104C2×#625—21no—
105C2×#624—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3796—22no—
109#3796—41no—
110#3795—22no—
111#3795—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3752—21no—
116#3752—21no—
117C4⋊(C3⋊Dic3)—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119#3744—41no—
120C8×C3⋊D3—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3D411yescharacteristic
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141#3717—41no—
142#3714—22no—
143#3711—41no—
144#3307—91noSylow
145C2×#239—31no—
146C2×#237—31no—
147C2×#237—31no—
148C2×#235—31no—
149C3×#125—31no—
150C3×C22⋊Q8—31no—
151C3×C4×D4—31no—
152C2×C3×C4⋊C4—31no—
153#944—31no—
154C2×#215—31no—
155C2×#213—31no—
156#930—31no—
157#930—61no—
158#930—61no—
159C4×#67—31no—
160C4×#67—61no—
161C2×C4⋊Dic3—61no—
162C2×#208—31no—
163C2×D24—31no—
164C2×#204—31no—
165C2×#204—31no—
166C2×#204—31no—
167C2×#204—61no—
168C2×ΓL(1,𝔽25)—31no—
169C2×D3×C8—31no—
170C2×D3×C8—31no—
171C2×D3×C8—61no—
172#898—61no—
173#898—61no—
174#897—31no—
175#897—31no—
176#897—61no—
177#897C2×D311yescharacteristic
178#895—31no—
179#895—31no—
180#895—31no—
181#895—61no—
182#895—61no—
183#894—61no—
184#894—61no—
185#894—61no—
186#893—31no—
187#893—61no—
188#893C2×D311yescharacteristic
189#892—31no—
190#892—31no—
191D3×C4⋊C4—61no—
192D3×C4⋊C4C2×D311yescharacteristic
193#890C2×D311yescharacteristic
194#886—61no—
195#886—61no—
196#884—61no—
197#883—61no—
198C4×D12—31no—
199C4×D12—31no—
200#869—31no—
201C3×#107—31no—
202C3×#106—21no—
203C3×#106—31no—
204C3×#106C2×D311yescharacteristic
205C3×#106C2×D311yescharacteristic
206C3×C4⋊C8—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×C22⋊C8—31no—
212#835—31no—
213#832—31no—
214#821C2×D311yescharacteristic
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8C2×D311yescharacteristic
218#816—31no—
219#816—31no—
220#816C2×D311yescharacteristic
221#815—31no—
222Dic3⋊C8C2×D311yescharacteristic
223#810—31no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—61no—
229#810C2×D311yescharacteristic
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#809C2×D311yescharacteristic
235#808C2×D311yescharacteristic
236#807C2×D311yescharacteristic
237#803—31no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3C2×D411yescharacteristic
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—81no—
250C4×C3⋊D3—21no—
251C4×C3⋊D3—21no—
252#634—21no—
253#634—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12#4112yes—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—42no—
265C3×C4×D3—81no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268#626—41no—
269#626—42no—
270#626—42no—
271#625—42no—
272#624—81no—
273D3×Dic3—42no—
274D3×Dic3—42no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—91no—
280#547—91no—
281#491—91no—
282#485—91no—
283#483—31no—
284#478—31no—
285#468—91no—
286#465—91no—
287#461—91no—
288#449—91no—
289#449—91no—
290#442—91no—
291#435—91no—
292#417—91no—
293#416—91no—
294C2×C3×Q8—31no—
295C2×C3×D4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—61no—
298C22×C3×C4—61no—
299C2×#67—31no—
300C2×#67—61no—
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—61no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306#239—62no—
307#239—121no—
308#237—62no—
309#237—62no—
310#237—121no—
311#237—121no—
312#235—62no—
313#235—121no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—121no—
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—31no—
327C2×C4×D3—31no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6—61no—
337C2×Dic6C22×D311yescharacteristic
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—31no—
358#217—31no—
359#215—121no—
360#213—62no—
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—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—121no—
377(C2×D3)⋊C4—121no—
378C4⋊Dic3—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—121no—
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—31no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3C22×D311yescharacteristic
396#208—121no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402D24—62no—
403#204—121no—
404#204—121no—
405#204—122no—
406#204—121no—
407ΓL(1,𝔽25)—121no—
408D3×C8—121no—
409D3×C8—121no—
410D3×C8—122no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—21no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3×D3—22no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C32×C4—41no—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—41no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C2×#41—91no—
437C2×#41—91no—
438C2×SD16—91no—
439C2×SD16—91no—
440C2×D8—91no—
441C2×M16—91no—
442C22×C8—91no—
443C4⋊Q8—91no—
444#126—181no—
445#125—31no—
446#123—181no—
447#123—181no—
448#123—181no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451#121—91no—
452#121—91no—
453#121—181no—
454#121—181no—
455C4×D4—31no—
456C4×D4—91no—
457C4×D4—91no—
458C4×D4—181no—
459#117—91no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4—181no—
462#107—31no—
463#106—31no—
464#106D3211yescharacteristic
465C4⋊C8—31no—
466#103—31no—
467#103—31no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476C22⋊C8—31no—
477C22⋊C8—91no—
478#97—91no—
479C23×C3—31no—
480C23×C3—61no—
481C22×D3—21no—
482C22×D3—31no—
483C22×D3—31no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—121no—
488C22×D3D3×D411yescharacteristic
489C3×Q8—61no—
490C3×Q8—61no—
491C3×D4—32no—
492C3×D4—61no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—122no—
509C2×C3×C4—241no—
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—121no—
513#67—122no—
514#67—122no—
515#67—122no—
516#67—122no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—121no—
526C2×Dic3—122no—
527C2×Dic3—122no—
528C2×Dic3D3×D411yescharacteristic
529C2×Dic3D3×D411yescharacteristic
530C2×Dic3D3×D411yescharacteristic
531D12—21no—
532D12—61no—
533D12—61no—
534D12—61no—
535D12—61no—
536D12—121no—
537D12—121no—
538D12—121no—
539D12—122no—
540D12—122no—
541D12—241no—
542D12—241no—
543D12—242no—
544D12#23912yes—
545C4×D3—21no—
546C4×D3—21no—
547C4×D3—42no—
548C4×D3—61no—
549C4×D3—61no—
550C4×D3—61no—
551C4×D3—61no—
552C4×D3—81no—
553C4×D3—121no—
554C4×D3—121no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3—241no—
558C4×D3—241no—
559Dic6—21no—
560Dic6—21no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—121no—
566Dic6—121no—
567C3×C8—22no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—121no—
577C2×C32#54611yescharacteristic
578C2×C32#57511yescharacteristic
579C2×C32#57711yescharacteristic
580C3⋊D3—41no—
581C3⋊D3—81no—
582C3×D3—41no—
583C3×D3—42no—
584#41—182no—
585#41—182no—
586#41—361no—
587#41—361no—
588C2×Q8—31no—
589C2×Q8—91no—
590C2×D4—31no—
591C2×D4—91no—
592C2×D4—91no—
593C2×D4—181no—
594C2×D4—181no—
595C2×D4—181no—
596C2×D4—181no—
597C22×C4—31no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—91no—
601C22×C4—181no—
602C22×C4—181no—
603C22×C4—181no—
604SD16—361no—
605SD16—361no—
606D8—182no—
607M16—361no—
608C2×C8—31no—
609C2×C8—31no—
610C2×C8—91no—
611C2×C8—361no—
612C2×C8C2×D3211yescharacteristic
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—91no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4C2×D3211yescharacteristic
624C4⋊C4C2×D3211yescharacteristic
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—91no—
628C22⋊C4—91no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—31no—
635C42—181no—
636C22×C3—21no—
637C22×C3—62no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
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—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—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—241no—
667C2×D3—241no—
668C2×D3—241no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—81no—
679C3×C4—81no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4C2×#23911yescharacteristic
684C3×C4D3×#4111yescharacteristic
685C3×C4#100911yescharacteristic
686C3×C4#100911yescharacteristic
687Dic3—21no—
688Dic3—21no—
689Dic3—21no—
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—61no—
694Dic3—61no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3—241no—
699C32#330711yescharacteristic, complemented, Sylow
700C23—31no—
701C23—61no—
702C23—91no—
703C23—181no—
704Q8—61no—
705Q8—61no—
706Q8—181no—
707Q8—181no—
708D4—32no—
709D4—61no—
710D4—181no—
711D4—181no—
712D4—361no—
713D4—362no—
714D4—362no—
715D4—362no—
716D4—721no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—91no—
728C2×C4—122no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—241no—
733C2×C4—362no—
734C2×C4—362no—
735C2×C4—721no—
736C2×C4C22×D3211yescharacteristic
737C8—21no—
738C8—61no—
739C8—61no—
740C8—181no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—122no—
745C2×C3—121no—
746C2×C3#563011yescharacteristic
747C2×C3#565411yescharacteristic
748C2×C3#576211yescharacteristic
749C2×C3#577011yescharacteristic
750C2×C3#577311yescharacteristic
751C2×C3#577711yescharacteristic
752D3—41no—
753D3—42no—
754D3—122no—
755D3—121no—
756D3—121no—
757D3—241no—
758D3—241no—
759D3—481no—
760C22—61no—
761C22—62no—
762C22—61no—
763C22—61no—
764C22—121no—
765C22—121no—
766C22—181no—
767C22—181no—
768C22—181no—
769C22—361no—
770C22—361no—
771C22—361no—
772C22D32×D411yescharacteristic
773C4—41no—
774C4—41no—
775C4—61no—
776C4—61no—
777C4—61no—
778C4—121no—
779C4—121no—
780C4—121no—
781C4—181no—
782C4—361no—
783C4#6430811yescharacteristic
784C4D3×#23911yescharacteristic
785C3—21no—
786C3#8118811yescharacteristic, complemented
787C3#8143211yescharacteristic, complemented
788C2—121no—
789C2—122no—
790C2—361no—
791C2—721no—
792C2#1059462011yescharacteristic
793C2#1059474411yescharacteristic
794C2#1059475311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
hypercenter#106D32
hypocenterC32#3307
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
1. #10594562C2semidirect
2. #10594381C2semidirect
3. #10592563C2semidirect
4. C3×#4871C2semidirect
5. C3×#4862C2semidirect
6. #10590968C2semidirect
7. #10590956C2semidirect
8. #10590760C2semidirect
9. #10590737C2semidirect
10. #10590617C2semidirect
11. #10590607C2semidirect
12. #10590589C2semidirect
13. #10590585C2semidirect
14. #10590562C2semidirect
15. #10590450C2semidirect
73. #4871D3semidirect
79. #4862D3semidirect
699. C32#3307semidirect
786. C3#81188semidirect
787. C3#81432semidirect

Maximal subgroups

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

subgroupindex
#105945622
#105943812
#105925632
C3×#48712
C3×#48622
#105909682
#105909562
#105907602
#105907372
#105906172
#105906072
#105905892
#105905852
#105905622
#105904502
#814323
#811883