Finite Group Databasebeta

← #11889235

Subgroups — #11889235

Order 1152.

899 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595254C211yesmaximal, characteristic
2#10594565C211yesmaximal, characteristic, complemented
3#10592469C211yesmaximal, characteristic, complemented
4C3×#4772C211yesmaximal, characteristic, complemented
5C3×#4757C211yesmaximal, characteristic, complemented
6#10591467C211yesmaximal, characteristic, complemented
7#10591461C211yesmaximal, characteristic, complemented
8#10591408C211yesmaximal, characteristic, complemented
9#10590893C211yesmaximal, characteristic, complemented
10#10590856C211yesmaximal, characteristic, complemented
11#10590847C211yesmaximal, characteristic, complemented
12#10590726C211yesmaximal, characteristic, complemented
13#10590536C211yesmaximal, characteristic, complemented
14#10590526C211yesmaximal, characteristic, complemented
15#10590424C211yesmaximal, characteristic, complemented
16#79801—31nomaximal
17#78855—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21#64101C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic, complemented
25C3×#892C2211yescharacteristic, complemented
26C3×#887C2211yescharacteristic, complemented
27#63981—21no—
28#63978—21no—
29#63966—21no—
30C2×#3722—21no—
31#63918C2211yescharacteristic, complemented
32C4×#627—21no—
33#63909C2211yescharacteristic
34C4×#626C2211yescharacteristic
35#63871C2211yescharacteristic
36#63871C2211yescharacteristic
37#63868—21no—
38#63864C2211yescharacteristic
39#63862—21no—
40#63856C2211yescharacteristic, complemented
41#63852—21no—
42C2×#3718C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63648C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#816C2211yescharacteristic, complemented
50C3×#816C2211yescharacteristic, complemented
51C3×#815C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#807C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#5829—31no—
62#5584—31no—
63#5554—31no—
64#5533—31no—
65C3×#440—31no—
66C3×#416—31no—
67#5239—31no—
68#5173—31no—
69#5169—31no—
70#5114—31no—
71#5111—31no—
72#5028—31no—
73#5008—31no—
74#5003—31no—
75#4888—31no—
76#4885—31no—
77#4816—31no—
78#4816—31no—
79#4815—31no—
80#4807—31no—
81#4798—31no—
82#4794—31no—
83#4776—31no—
84#4772D311yescharacteristic, complemented
85#4770—31no—
86#4770—31no—
87#4770—61no—
88#4761—31no—
89#4757D311yescharacteristic, complemented
90#4714—31no—
91#4706—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95D4×C3⋊D3—22no—
96D4×C3⋊D3—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C3×#237—22no—
103C3×#237—41no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#627—21no—
108C2×#626—21no—
109C2×#626D411yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4×C3⋊Dic3—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116#3743—41no—
117C3×#217—21no—
118C3×#214—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×C4⋊Dic3C2311yescharacteristic
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×D3×C8—41no—
129#3724—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722—21no—
139#3722D411yescharacteristic
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142#3718—41no—
143#3717—41no—
144#3311—91noSylow
145C2×C3×#41—31no—
146C2×#237C2×D311yescharacteristic
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C2×C3×SD16—31no—
151C22×C3×C8—31no—
152C3×C4×Q8—31no—
153C3×C4×D4—31no—
154C3×#117—31no—
155#947—31no—
156#946—31no—
157#946—31no—
158#946—31no—
159C2×#216—31no—
160C2×#216—31no—
161C2×#215—31no—
162#939—61no—
163#937—61no—
164D4×Dic3C2×D311yescharacteristic
165C2×#214C2×D311yescharacteristic
166#930—31no—
167#930—61no—
168#929—61no—
169C4×#67—31no—
170C2×(C2×D3)⋊C4—61no—
171C2×(C2×D3)⋊C4—61no—
172#924—31no—
173C2×#204—31no—
174C2×ΓL(1,𝔽25)—31no—
175C2×ΓL(1,𝔽25)—31no—
176C2×ΓL(1,𝔽25)—61no—
177C2×D3×C8C2×D311yescharacteristic, complemented
178#898—61no—
179#898—61no—
180#897—31no—
181#897—31no—
182#895—31no—
183#892—31no—
184#892—31no—
185#892—61no—
186#892C2×D311yescharacteristic, complemented
187#888—31no—
188#887C2×D311yescharacteristic, complemented
189#886—61no—
190#885—61no—
191#882—61no—
192#879—61no—
193#876—61no—
194#875—31no—
195#875—61no—
196C4×D12—31no—
197#869—31no—
198C4×Dic6—61no—
199C4×Dic6—61no—
200C3×#107—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#102—21no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic
207C3×#102C2×D311yescharacteristic
208C3×#97—31no—
209#835—31no—
210#832—31no—
211#832—31no—
212#832—61no—
213#832C2×D311yescharacteristic
214#830—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—61no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222#817—31no—
223#816—31no—
224#816C2×D311yescharacteristic, complemented
225#816C2×D311yescharacteristic, complemented
226#815C2×D311yescharacteristic, complemented
227Dic3⋊C8—31no—
228#810C2×D311yescharacteristic, complemented
229#809—31no—
230#809—31no—
231#809—31no—
232#809—61no—
233#808—31no—
234#808—31no—
235#808—31no—
236#807C2×D311yescharacteristic, complemented
237C4⋊(C3⋊C8)—31no—
238C23×C32—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—42no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—81no—
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249#638—42no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4×C3⋊D3—21no—
255C4×C3⋊D3—21no—
256C3×#67—42no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—42no—
262C2×C3×Dic3—81no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#627—42no—
273#626—41no—
274#626—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—91no—
281#489—91no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290#440—31no—
291#435—91no—
292#418—91no—
293#416—31no—
294C23×D3—61no—
295C23×D3—61no—
296C23×D3—121no—
297C3×#41—62no—
298C3×#41—121no—
299C2×C3×Q8—31no—
300C2×C3×Q8—31no—
301C2×C3×D4—21no—
302C2×C3×D4—61no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C2×#67—21no—
309C2×#67—31no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—121no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316#237—22no—
317#237—41no—
318D3×D4—64no—
319D3×D4—62no—
320D3×D4—62no—
321D3×D4—121no—
322D3×D4—121no—
323D3×D4—122no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—31no—
327C2×D12—61no—
328C2×D12—61no—
329C2×C4×D3—31no—
330C2×C4×D3—31no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6C22×D311yescharacteristic
336C2×Dic6C22×D311yescharacteristic
337C3×SD16—62no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8—121no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—31no—
353C3×C42—61no—
354C3×C42—61no—
355#217—21no—
356#217—31no—
357#217—61no—
358#216—121no—
359#216—121no—
360#215—121no—
361#214—22no—
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—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—121no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
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—21no—
397C4×Dic3—21no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—121no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407#204—121no—
408ΓL(1,𝔽25)—121no—
409ΓL(1,𝔽25)—121no—
410ΓL(1,𝔽25)—122no—
411D3×C8—41no—
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—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—84no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—31no—
439C22×D4—91no—
440C2×Q16—91no—
441C2×SD16—31no—
442C2×SD16—91no—
443C2×M16—91no—
444C22×C8—31no—
445C4⋊Q8—91no—
446#126—181no—
447#126—181no—
448#124—91no—
449#124—181no—
450#123—181no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453C22⋊Q8—91no—
454#121—91no—
455#121—181no—
456#120—181no—
457C4×Q8—31no—
458C4×Q8—181no—
459C4×D4—31no—
460C4×D4—91no—
461#117—31no—
462#117—91no—
463C2×C22⋊C4—181no—
464#107—31no—
465#106—91no—
466#106—91no—
467C4⋊C8—91no—
468#103—31no—
469#103—31no—
470#103—31no—
471#103—91no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102D3211yescharacteristic
478C22⋊C8—91no—
479C22⋊C8—91no—
480#97—31no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—41no—
485C22×D3—31no—
486C22×D3—31no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—121no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—124no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—242no—
497C22×D3—241no—
498C22×D3—241no—
499C22×D3—242no—
500C22×D3D3×D411yescharacteristic
501C3×Q8—61no—
502C3×Q8—61no—
503C3×Q8—61no—
504C3×Q8—61no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—22no—
508C3×D4—41no—
509C3×D4—122no—
510C3×D4#23512yes—
511C3×D4#23512yes—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—41no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—122no—
526C2×C3×C4—241no—
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—42no—
530#67—121no—
531#67—122no—
532#67—122no—
533#67—124no—
534#67—241no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—42no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—81no—
546C2×Dic3—121no—
547C2×Dic3D3×D411yescharacteristic
548C2×Dic3D3×D411yescharacteristic
549C2×Dic3D3×D411yescharacteristic
550D12—62no—
551D12—61no—
552D12—61no—
553D12—61no—
554D12—61no—
555D12—121no—
556D12—121no—
557D12—241no—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—62no—
561C4×D3—62no—
562C4×D3—61no—
563C4×D3—61no—
564C4×D3—61no—
565C4×D3—61no—
566Dic6—21no—
567Dic6—21no—
568Dic6—21no—
569Dic6—21no—
570Dic6—122no—
571Dic6—122no—
572C3×C8—21no—
573C3×C8—21no—
574C3×C8—41no—
575C3×C8—61no—
576C3×C8—61no—
577C3⋊C8—21no—
578C3⋊C8—21no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—121no—
582C2×C32—42no—
583C2×C32#54611yescharacteristic
584C2×C32#57511yescharacteristic
585C2×C32#57711yescharacteristic
586C3⋊D3—41no—
587C3⋊D3—81no—
588C3×D3—41no—
589C24—181no—
590#41—62no—
591#41—121no—
592C2×Q8—31no—
593C2×Q8—31no—
594C2×Q8—181no—
595C2×D4—61no—
596C2×D4—91no—
597C2×D4—91no—
598C2×D4—181no—
599C2×D4—181no—
600C2×D4—182no—
601C2×D4—361no—
602C2×D4C2×D3211yescharacteristic
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—91no—
607Q16—361no—
608SD16—62no—
609SD16—361no—
610M16—361no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—91no—
614C2×C8—121no—
615C2×C8C2×D3211yescharacteristic
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—61no—
619C4⋊C4—91no—
620C4⋊C4—91no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4C2×D3211yescharacteristic
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—91no—
629C22⋊C4—91no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C42—31no—
638C42—61no—
639C42—61no—
640C42—181no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—21no—
644C22×C3—42no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3C2×D3×D411yescharacteristic
655C22×C3C2×D3×D411yescharacteristic
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—62no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—122no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—241no—
676C2×D3—241no—
677C2×D3—244no—
678C2×D3—244no—
679C2×D3—248no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—81no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4C2×#23511yescharacteristic
693C3×C4C2×#23511yescharacteristic
694C3×C4#100411yescharacteristic
695C3×C4#100911yescharacteristic
696Dic3—21no—
697Dic3—21no—
698Dic3—21no—
699Dic3—41no—
700Dic3—41no—
701Dic3—41no—
702Dic3—41no—
703Dic3—62no—
704Dic3—61no—
705Dic3—61no—
706Dic3—121no—
707Dic3—121no—
708Dic3—241no—
709C32#331111yescharacteristic, complemented, Sylow
710C23—21no—
711C23—31no—
712C23—91no—
713C23—181no—
714C23—362no—
715C23—362no—
716C23—721no—
717Q8—61no—
718Q8—61no—
719Q8—61no—
720Q8—61no—
721Q8—362no—
722D4—21no—
723D4—122no—
724D4—181no—
725D4—181no—
726D4—361no—
727D4—362no—
728D4—721no—
729D4#379812yes—
730C2×C4—21no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—31no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—91no—
741C2×C4—122no—
742C2×C4—181no—
743C2×C4—181no—
744C2×C4—181no—
745C2×C4—241no—
746C2×C4C22×D3211yescharacteristic
747C8—21no—
748C8—61no—
749C8—61no—
750C8—181no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—42no—
755C2×C3—42no—
756C2×C3—82no—
757C2×C3—121no—
758C2×C3#549011yescharacteristic
759C2×C3#555011yescharacteristic
760C2×C3#576811yescharacteristic
761C2×C3#577011yescharacteristic
762C2×C3#577511yescharacteristic
763C2×C3#577711yescharacteristic
764D3—41no—
765D3—122no—
766D3—121no—
767D3—121no—
768D3—242no—
769D3—241no—
770D3—241no—
771C22—22no—
772C22—41no—
773C22—41no—
774C22—61no—
775C22—61no—
776C22—61no—
777C22—181no—
778C22—181no—
779C22—181no—
780C22—361no—
781C22—361no—
782C22—361no—
783C22—724no—
784C22D32×D411yescharacteristic
785C4—41no—
786C4—61no—
787C4—61no—
788C4—61no—
789C4—121no—
790C4—121no—
791C4—121no—
792C4—121no—
793C4—181no—
794C4—361no—
795C4C2×#379811yescharacteristic
796C4#6431411yescharacteristic
797C3—21no—
798C3#7885511yescharacteristic, complemented
799C3#7980111yescharacteristic, complemented
800C2—42no—
801C2—121no—
802C2—361no—
803C2—721no—
804C2#1059418611yescharacteristic
805C2#1059473611yescharacteristic
806C2#1059474611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595254C2
hypercenter#102D32
hypocenterC32#3311
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
2. #10594565C2semidirect
3. #10592469C2semidirect
4. C3×#4772C2semidirect
5. C3×#4757C2semidirect
6. #10591467C2semidirect
7. #10591461C2semidirect
8. #10591408C2semidirect
9. #10590893C2semidirect
10. #10590856C2semidirect
11. #10590847C2semidirect
12. #10590726C2semidirect
13. #10590536C2semidirect
14. #10590526C2semidirect
15. #10590424C2semidirect
24. C2×C3×D3×C8C22semidirect
25. C3×#892C22semidirect
26. C3×#887C22semidirect
31. #63918C22semidirect
40. #63856C22semidirect
42. C2×#3718C22semidirect
49. C3×#816C22semidirect
50. C3×#816C22semidirect
51. C3×#815C22semidirect
52. C3×#810C22semidirect
53. C3×#807C22semidirect
54. #63574C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
84. #4772D3semidirect
89. #4757D3semidirect
177. C2×D3×C8C2×D3semidirect
186. #892C2×D3semidirect
188. #887C2×D3semidirect
224. #816C2×D3semidirect
225. #816C2×D3semidirect
226. #815C2×D3semidirect
228. #810C2×D3semidirect
236. #807C2×D3semidirect
709. C32#3311semidirect
798. C3#78855semidirect
799. C3#79801semidirect

Maximal subgroups

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

subgroupindex
#105952542
#105945652
#105924692
C3×#47722
C3×#47572
#105914672
#105914612
#105914082
#105908932
#105908562
#105908472
#105907262
#105905362
#105905262
#105904242
#798013
#788553