Finite Group Databasebeta

← #11888611

Subgroups — #11888611

Order 1152.

867 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595248C211yesmaximal, characteristic, complemented
2#10594437C211yesmaximal, characteristic, complemented
3#10592471C211yesmaximal, characteristic, complemented
4C3×#4781C211yesmaximal, characteristic, complemented
5C3×#4763C211yesmaximal, characteristic, complemented
6#10591457C211yesmaximal, characteristic, complemented
7#10591430C211yesmaximal, characteristic, complemented
8#10591414C211yesmaximal, characteristic, complemented
9#10590843C211yesmaximal, characteristic, complemented
10#10590752C211yesmaximal, characteristic, complemented
11#10590737C211yesmaximal, characteristic, complemented
12#10590674C211yesmaximal, characteristic, complemented
13#10590588C211yesmaximal, characteristic, complemented
14#10590562C211yesmaximal, characteristic, complemented
15#10590526C211yesmaximal, characteristic, complemented
16#81188—31nomaximal
17#80108—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21#64101C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×#890C2211yescharacteristic
27#63978—21no—
28#63966—21no—
29C2×Dic3⋊Dic3—21no—
30#63962—21no—
31#63916C2211yescharacteristic
32C4×#626C2211yescharacteristic
33#63898—21no—
34Dic3×D12C2211yescharacteristic
35#63890—21no—
36D3×C4⋊Dic3C2211yescharacteristic
37#63886—21no—
38#63871C2211yescharacteristic
39#63866C2211yescharacteristic
40#63862—21no—
41#63857C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63643C2211yescharacteristic
47#63637C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#807C2211yescharacteristic
54#63573C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic
60#63554C2211yescharacteristic
61#5824—31no—
62#5695—31no—
63#5618—31no—
64#5555—31no—
65C3×#478—31no—
66C3×#449—31no—
67#5232—31no—
68#5171—31no—
69#5162—31no—
70#5158—31no—
71#5152—31no—
72#5069—31no—
73#5042—31no—
74#5014—31no—
75#4888—31no—
76#4886—31no—
77#4864—31no—
78#4862—31no—
79#4841—31no—
80#4836—31no—
81#4815—31no—
82#4797—31no—
83#4781—31no—
84#4781D311yescharacteristic, complemented
85#4772—31no—
86#4772—31no—
87#4772—61no—
88#4771—31no—
89#4763D311yescharacteristic, complemented
90#4728—31no—
91#4721—31no—
92C2×C32×D4C2311yescharacteristic
93C2×#638—21no—
94C22×C3⋊Dic3—21no—
95#3830—22no—
96#3830—41no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C3×#237—22no—
103C3×#237—41no—
104C2×C3×D12—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#626—21no—
109C2×#626D411yescharacteristic
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C8×C3⋊D3—41no—
119C3×#217—21no—
120C3×#213—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×#204—41no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722—21no—
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142#3716—41no—
143#3711—41no—
144#3307—91noSylow
145C2×C3×#41—31no—
146C2×#237—31no—
147C2×#237—31no—
148C2×#237—61no—
149C2×#237C2×D311yescharacteristic
150C2×C3×SD16—31no—
151C2×C3×D8—31no—
152C3×#125—31no—
153C3×#121—31no—
154C3×C4×D4—31no—
155#946—31no—
156#944—31no—
157#939—61no—
158#939—61no—
159#938—31no—
160#935—61no—
161D4×Dic3—31no—
162D4×Dic3—61no—
163D4×Dic3C2×D311yescharacteristic
164C2×#214—31no—
165C2×#213C2×D311yescharacteristic
166#930—61no—
167#929—61no—
168C4×#67—31no—
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—61no—
171#924—31no—
172C2×Dic3⋊C4—61no—
173C2×#208—31no—
174C2×#204—31no—
175C2×#204C2×D311yescharacteristic
176C2×ΓL(1,𝔽25)—31no—
177C2×D3×C8—31no—
178C2×D3×C8—31no—
179C2×D3×C8—61no—
180#898—61no—
181#897—31no—
182#897—31no—
183#895—31no—
184#895—61no—
185#895C2×D311yescharacteristic
186#894—61no—
187#893—61no—
188#892—31no—
189#892—31no—
190#892—61no—
191D3×C4⋊C4—31no—
192#890C2×D311yescharacteristic
193#886—61no—
194#886—61no—
195#886—61no—
196#879—61no—
197C4×D12—31no—
198C4×D12—31no—
199#869—31no—
200C3×#107—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#102—21no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic
207C3×#102C2×D311yescharacteristic
208C3×C22⋊C8—31no—
209#835—31no—
210#835—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—61no—
215#832C2×D311yescharacteristic
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8C2×D311yescharacteristic
219#817—31no—
220#817C2×D311yescharacteristic
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226#815—31no—
227Dic3⋊C8C2×D311yescharacteristic
228#810—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—61no—
233#810C2×D311yescharacteristic
234#809—31no—
235#808—31no—
236#807C2×D311yescharacteristic
237#803—31no—
238C23×C32—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4#4112yes—
244C2×C32×C4—21no—
245C2×C32×C4C2411yescharacteristic
246#638—42no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—42no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C4×C3⋊D3—21no—
252C4×C3⋊D3—21no—
253#634—21no—
254#634—21no—
255C3×#67—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—42no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—41no—
272#626—81no—
273D3×Dic3—81no—
274D3×Dic3—81no—
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—91no—
284#478—31no—
285#468—91no—
286#465—91no—
287#461—91no—
288#449—31no—
289#449—91no—
290#442—91no—
291#435—91no—
292#417—91no—
293#416—91no—
294C3×#41—62no—
295C3×#41—121no—
296C2×C3×Q8—31no—
297C2×C3×D4—21no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C2×#67—21no—
307C2×#67—31no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—121no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—121no—
319#237—22no—
320#237—41no—
321#237—64no—
322#237—62no—
323#237—62no—
324#237—121no—
325#237—121no—
326#237—122no—
327C2×D12—21no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12C22×D311yescharacteristic
331C2×C4×D3—31no—
332C2×C4×D3—31no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3C22×D311yescharacteristic
337C2×Dic6—31no—
338C2×Dic6—31no—
339C2×Dic6—61no—
340C2×Dic6C22×D311yescharacteristic
341C3×SD16—121no—
342C3×D8—62no—
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—31no—
358#217—21no—
359#217—31no—
360#217—61no—
361#217—61no—
362#217—61no—
363#214—121no—
364#213—22no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
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—
377C4⋊Dic3—21no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—31no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—121no—
399C4×Dic3C22×D311yescharacteristic
400#208—121no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406#204—41no—
407#204—121no—
408ΓL(1,𝔽25)—121no—
409D3×C8—121no—
410D3×C8—121no—
411D3×C8—122no—
412C22×C32—22no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—31no—
438C2×#41—91no—
439C2×SD16—31no—
440C2×SD16—91no—
441C2×D8—31no—
442C2×M16—91no—
443C22×C8—91no—
444C4⋊Q8—91no—
445#126—181no—
446#125—31no—
447#123—181no—
448#123—181no—
449#123—181no—
450C22⋊Q8—91no—
451C22⋊Q8—91no—
452#121—31no—
453#121—91no—
454#121—181no—
455#121—181no—
456C4×D4—31no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—181no—
460#117—91no—
461C2×C4⋊C4—91no—
462C2×C4⋊C4—181no—
463#107—31no—
464#106—31no—
465#106—91no—
466C4⋊C8—31no—
467#103—31no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102D3211yescharacteristic
477C22⋊C8—31no—
478C22⋊C8—91no—
479#97—91no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3—41no—
484C23×C3—61no—
485C22×D3—21no—
486C22×D3—31no—
487C22×D3—31no—
488C22×D3—61no—
489C22×D3D3×D411yescharacteristic
490C3×Q8—61no—
491C3×Q8—61no—
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—22no—
495C3×D4—41no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—122no—
499C3×D4—122no—
500C3×D4#23712yes—
501C3×D4#23912yes—
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—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—122no—
515C2×C3×C4—122no—
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—42no—
519#67—121no—
520#67—122no—
521#67—122no—
522#67—124no—
523#67—241no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—42no—
530C2×Dic3—42no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—121no—
537C2×Dic3—121no—
538C2×Dic3—122no—
539C2×Dic3—122no—
540C2×Dic3—124no—
541C2×Dic3—241no—
542C2×Dic3—241no—
543C2×Dic3D3×D411yescharacteristic
544C2×Dic3D3×D411yescharacteristic
545C2×Dic3D3×D411yescharacteristic
546D12—21no—
547D12—21no—
548D12—42no—
549D12—121no—
550D12—241no—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—62no—
554C4×D3—62no—
555C4×D3—61no—
556C4×D3—61no—
557C4×D3—61no—
558C4×D3—61no—
559C4×D3—241no—
560C4×D3—241no—
561Dic6—21no—
562Dic6—21no—
563Dic6—62no—
564Dic6—61no—
565Dic6—61no—
566Dic6—61no—
567Dic6—61no—
568Dic6—121no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—41no—
572C3×C8—61no—
573C3×C8—61no—
574C3⋊C8—21no—
575C3⋊C8—21no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C3⋊C8—121no—
579C2×C32—42no—
580C2×C32#54611yescharacteristic
581C2×C32#57511yescharacteristic
582C2×C32#57711yescharacteristic
583C3⋊D3—41no—
584C3×D3—41no—
585C3×D3—81no—
586#41—62no—
587#41—121no—
588#41—182no—
589#41—361no—
590C2×Q8—31no—
591C2×Q8—91no—
592C2×D4—31no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—91no—
596C2×D4—181no—
597C2×D4—181no—
598C2×D4C2×D3211yescharacteristic
599C22×C4—31no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—91no—
603C22×C4—181no—
604C22×C4—181no—
605C22×C4—181no—
606SD16—121no—
607SD16—361no—
608D8—62no—
609M16—361no—
610C2×C8—31no—
611C2×C8—31no—
612C2×C8—91no—
613C2×C8—361no—
614C2×C8C2×D3211yescharacteristic
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—91no—
620C4⋊C4—91no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4C2×D3211yescharacteristic
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—91no—
630C22⋊C4—91no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C42—31no—
637C42—181no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—21no—
641C22×C3—42no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3C2×D3×D411yescharacteristic
655C22×C3C2×D3×D411yescharacteristic
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—62no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—121no—
670C2×D3—121no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—81no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4C2×#23711yescharacteristic
683C3×C4#100411yescharacteristic
684C3×C4C2×#23911yescharacteristic
685C3×C4#100911yescharacteristic
686Dic3—21no—
687Dic3—21no—
688Dic3—21no—
689Dic3—41no—
690Dic3—41no—
691Dic3—41no—
692Dic3—62no—
693Dic3—61no—
694Dic3—61no—
695Dic3—122no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—121no—
700Dic3—241no—
701C32#330711yescharacteristic, complemented, Sylow
702C23—21no—
703C23—31no—
704C23—61no—
705C23—91no—
706Q8—61no—
707Q8—61no—
708Q8—181no—
709Q8—181no—
710D4—21no—
711D4—61no—
712D4—61no—
713D4—122no—
714D4—122no—
715D4—361no—
716D4—362no—
717D4—721no—
718D4#379612yes—
719C2×C4—21no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—91no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—181no—
734C2×C4—181no—
735C2×C4—362no—
736C2×C4—721no—
737C2×C4—721no—
738C2×C4C22×D3211yescharacteristic
739C8—21no—
740C8—61no—
741C8—61no—
742C8—181no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—42no—
747C2×C3—42no—
748C2×C3—82no—
749C2×C3—121no—
750C2×C3—241no—
751C2×C3#559111yescharacteristic
752C2×C3#563011yescharacteristic
753C2×C3#577011yescharacteristic
754C2×C3#577011yescharacteristic
755C2×C3#577311yescharacteristic
756C2×C3#577311yescharacteristic
757D3—41no—
758D3—81no—
759D3—122no—
760D3—121no—
761D3—121no—
762C22—22no—
763C22—41no—
764C22—41no—
765C22—61no—
766C22—61no—
767C22—61no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—181no—
772C22—181no—
773C22—181no—
774C22D32×D411yescharacteristic
775C4—41no—
776C4—61no—
777C4—61no—
778C4—61no—
779C4—121no—
780C4—121no—
781C4—121no—
782C4—181no—
783C4—361no—
784C4—361no—
785C4C2×#379611yescharacteristic
786C4#6431411yescharacteristic
787C3—21no—
788C3#8010811yescharacteristic, complemented
789C3#8118811yescharacteristic, complemented
790C2—42no—
791C2—121no—
792C2—241no—
793C2—361no—
794C2#1059406311yescharacteristic
795C2#1059472811yescharacteristic
796C2#1059475711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595248C2semidirect
2. #10594437C2semidirect
3. #10592471C2semidirect
4. C3×#4781C2semidirect
5. C3×#4763C2semidirect
6. #10591457C2semidirect
7. #10591430C2semidirect
8. #10591414C2semidirect
9. #10590843C2semidirect
10. #10590752C2semidirect
11. #10590737C2semidirect
12. #10590674C2semidirect
13. #10590588C2semidirect
14. #10590562C2semidirect
15. #10590526C2semidirect
84. #4781D3semidirect
89. #4763D3semidirect
701. C32#3307semidirect
788. C3#80108semidirect
789. C3#81188semidirect

Maximal subgroups

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

subgroupindex
#105952482
#105944372
#105924712
C3×#47812
C3×#47632
#105914572
#105914302
#105914142
#105908432
#105907522
#105907372
#105906742
#105905882
#105905622
#105905262
#811883
#801083