Finite Group Databasebeta

← #11884263

Subgroups — #11884263

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 901 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595067C211yesmaximal, characteristic, complemented
2#10594834C211yesmaximal, characteristic, complemented
3C2×#63829C211yesmaximal, characteristic, complemented
4C2×#63794C211yesmaximal, characteristic, complemented
5#10592433C211yesmaximal, characteristic, complemented
6C3×#4733C211yesmaximal, characteristic, complemented
7C3×#4730C211yesmaximal, characteristic, complemented
8#10591177C211yesmaximal, characteristic, complemented
9#10590966C211yesmaximal, characteristic, complemented
10#10590946C211yesmaximal, characteristic, complemented
11#10590899C211yesmaximal, characteristic, complemented
12#10590849C211yesmaximal, characteristic, complemented
13#10590770C211yesmaximal, characteristic, complemented
14#10590752C211yesmaximal, characteristic, complemented
15#10590746C211yesmaximal, characteristic, complemented
16#80264—31nomaximal
17#79496—31nomaximal
18C2×#3828C2211yescharacteristic, complemented
19C2×C3×#235C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22#64139C2211yescharacteristic
23C2×#3745C2211yescharacteristic
24C2×#3744C2211yescharacteristic
25C3×C4×#67C2211yescharacteristic
26C3×#924C2211yescharacteristic, complemented
27C22×C3×C3⋊C8C2211yescharacteristic, complemented
28C2×C3×Dic12C2211yescharacteristic, complemented
29C2×C3×#204C2211yescharacteristic
30C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
31#63983—21no—
32#63975—21no—
33#63971—21no—
34#63958—21no—
35D3×(C2×D3)⋊C4—21no—
36#63894C2211yescharacteristic, complemented
37Dic3×D12C2211yescharacteristic
38#63883—21no—
39#63866C2211yescharacteristic, complemented
40#63864C2211yescharacteristic
41#63857C2211yescharacteristic
42#63856C2211yescharacteristic
43#63853—21no—
44#63850—21no—
45C2×#3719C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic, complemented
48#63829—24no—
49C2×#3716C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51#63794—24no—
52C32×C22⋊C8C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63643C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×#816C2211yescharacteristic, complemented
58C3×#815C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60#63573C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63564C2211yescharacteristic
63#5829—31no—
64C2×#950—31no—
65C2×#914—31no—
66C2×#908—31no—
67C2×#904—31no—
68#5631—31no—
69#5551—31no—
70#5550—31no—
71C3×#452—31no—
72C3×#435—31no—
73#5190—31no—
74#5187—31no—
75#5162—31no—
76#5137—31no—
77#5114—31no—
78#5048—31no—
79#4844—31no—
80#4841—31no—
81#4819—31no—
82#4816—31no—
83#4785—31no—
84#4776—31no—
85#4734—31no—
86#4734—31no—
87#4734—61no—
88#4733—31no—
89#4733D311yescharacteristic, complemented
90#4731—31no—
91#4730D311yescharacteristic, complemented
92#4715—31no—
93#4711—31no—
94C22×D32—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98#3828—22no—
99#3828—41no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3—21no—
103C2×#634C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67D411yescharacteristic
106C3×#235—22no—
107C3×#235—41no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#626—21no—
115C2×#624—21no—
116C2×#624—21no—
117C2×D3×Dic3—21no—
118D3×D12—22no—
119D3×D12—41no—
120#3799—22no—
121#3799—41no—
122C2×C32×C8C2311yescharacteristic
123C2×C32×C8C2311yescharacteristic
124#3752—21no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3745—22no—
127#3744—41no—
128C3×#217—21no—
129C3×#217D411yescharacteristic
130C3×(C2×D3)⋊C4D411yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8—22no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×Dic12—41no—
139C3×#204—22no—
140C3×ΓL(1,𝔽25)—22no—
141#3724—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146#3722—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151#3719—22no—
152#3717—22no—
153#3717—22no—
154#3716—22no—
155#3714D414yescomplemented
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×#239—31no—
159C2×D3×D4—31no—
160C2×#235—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—61no—
164C2×#235C2×D311yescharacteristic
165C22×D12—31no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C2×C3×M16—31no—
169C22×C3×C8—31no—
170C3×C22⋊Q8—31no—
171C3×C4×D4—31no—
172#950—64no—
173#947—31no—
174#946—31no—
175#944—31no—
176C2×#216—31no—
177C2×#215—31no—
178C2×#215—31no—
179#939—61no—
180#938—61no—
181#937—61no—
182#937—61no—
183D4×Dic3—31no—
184C2×#214—31no—
185C2×#213—31no—
186#930—31no—
187#930—31no—
188#930—61no—
189#929—61no—
190C4×#67C2×D311yescharacteristic
191C2×(C2×D3)⋊C4—61no—
192#924—31no—
193#924—31no—
194#924C2×D311yescharacteristic, complemented
195C22×C3⋊C8C2×D311yescharacteristic, complemented
196#914—64no—
197#908—64no—
198C2×Dic12—31no—
199C2×Dic12C2×D311yescharacteristic, complemented
200#904—64no—
201C2×D24—31no—
202C2×D24—31no—
203C2×D24—31no—
204C2×D24—61no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—31no—
209C2×#204—31no—
210C2×#204—61no—
211C2×#204C2×D311yescharacteristic
212C2×ΓL(1,𝔽25)C2×D311yescharacteristic
213#897—31no—
214#894—61no—
215#894—61no—
216#893—31no—
217D3×C4⋊C4—61no—
218D3×C4⋊C4—61no—
219#884—61no—
220#884—61no—
221#883—61no—
222#883—61no—
223#883—61no—
224D3×C22⋊C4—61no—
225#875—31no—
226C4×D12—31no—
227C4×D12—31no—
228#869—31no—
229C3×C4⋊C8—31no—
230C3×#103—31no—
231C3×#102—31no—
232C3×C22⋊C8—21no—
233C3×C22⋊C8—31no—
234C3×C22⋊C8C2×D311yescharacteristic, complemented
235C3×C22⋊C8C2×D311yescharacteristic, complemented
236C3×#97—31no—
237#835—31no—
238#821—31no—
239#821—31no—
240#821—31no—
241#821—61no—
242#821C2×D311yescharacteristic
243(C2×D3)⋊C8C2×D311yescharacteristic
244#817—31no—
245#816—31no—
246#816—31no—
247#816—31no—
248#816—61no—
249#816C2×D311yescharacteristic, complemented
250#815C2×D311yescharacteristic, complemented
251Dic3⋊C8C2×D311yescharacteristic, complemented
252#809—31no—
253#808—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266#638—42no—
267#638—81no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)C2×D412yes—
274C4×C3⋊D3—42no—
275#634—21no—
276#634—21no—
277C3×#67—41no—
278C3×#67—42no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12C2×D412yes—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—42no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294#626—42no—
295#626—42no—
296#624—42no—
297#624—42no—
298D3×Dic3—81no—
299C32×C8—21no—
300C32×C8—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—91no—
306#546—91no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—91no—
311#461—91no—
312#452—31no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—31no—
318C23×D3—61no—
319C23×D3—61no—
320C3×#41—62no—
321C3×#41—121no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—61no—
327C22×C3×C4—21no—
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C2×#67—21no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—121no—
340C2×#67—121no—
341C2×#67D1211yescharacteristic
342C22×Dic3—61no—
343#239—62no—
344#239—121no—
345D3×D4—62no—
346D3×D4—121no—
347#235—22no—
348#235—41no—
349#235—62no—
350#235—62no—
351#235—62no—
352#235—122no—
353#235—121no—
354#235—121no—
355#235—121no—
356#235—122no—
357C2×D12—31no—
358C2×D12—31no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—61no—
362C2×D12—61no—
363C2×D12—62no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—121no—
367C2×D12C22×D311yescharacteristic
368C2×C4×D3—21no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—121no—
377C2×C4×D3C22×D311yescharacteristic
378C2×Dic6—31no—
379C2×Dic6—31no—
380C2×Dic6—61no—
381C2×Dic6C22×D311yescharacteristic
382C2×Dic6C22×D311yescharacteristic
383C3×Q16—121no—
384C3×SD16—62no—
385C3×M16—62no—
386C2×C3×C8—21no—
387C2×C3×C8—21no—
388C2×C3×C8—31no—
389C2×C3×C8—31no—
390C2×C3×C8—62no—
391C2×C3×C8C22×D311yescharacteristic
392C2×C3×C8C22×D311yescharacteristic
393C2×C3×C8C22×D311yescharacteristic
394C2×C3×C8C22×D311yescharacteristic
395C3×C4⋊C4—31no—
396C3×C4⋊C4—31no—
397C3×C4⋊C4—61no—
398C3×C22⋊C4—31no—
399C3×C22⋊C4—31no—
400C3×C22⋊C4—61no—
401C3×C42—31no—
402#217—21no—
403#217—61no—
404#217—61no—
405#217—61no—
406#217D1211yescharacteristic
407#216—62no—
408#215—62no—
409#215—62no—
410#214—62no—
411#213—34no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—121no—
424(C2×D3)⋊C4D1211yescharacteristic
425C4⋊Dic3—31no—
426C4⋊Dic3—31no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3—61no—
431C4⋊Dic3C22×D311yescharacteristic
432Dic3⋊C4—21no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4D1211yescharacteristic
439C4×Dic3C22×D311yescharacteristic
440C2×C3⋊C8—22no—
441C2×C3⋊C8C22×D311yescharacteristic
442C2×C3⋊C8C22×D311yescharacteristic
443Dic12—41no—
444Dic12—62no—
445D24—34no—
446D24—62no—
447D24—62no—
448D24—122no—
449#204—22no—
450#204—62no—
451#204—62no—
452#204—62no—
453#204—121no—
454#204—121no—
455#204—122no—
456ΓL(1,𝔽25)—22no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32C22×D411yescharacteristic
461C2×C3⋊D3—22no—
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3×D3—21no—
468C2×C3×D3—22no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473D32—84no—
474C32×C4—21no—
475C32×C4C22×D411yescharacteristic
476C32×C4H(5,𝔽2)11yescharacteristic
477C3⋊Dic3—41no—
478C3⋊Dic3—41no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—41no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C2×#41—31no—
486C2×#41—91no—
487C2×#41—91no—
488C22×D4—91no—
489AGL(1,ℤ/8)—184no—
490#135—184no—
491C2×Q16—31no—
492C2×Q16—91no—
493C2×SD16—31no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×D8—91no—
499C2×D8—91no—
500C2×M16—31no—
501C22×C8—31no—
502C4⋊Q8—91no—
503#124—91no—
504#123—181no—
505#123—181no—
506#123—181no—
507C22⋊Q8—31no—
508C22⋊Q8—91no—
509C22⋊Q8—91no—
510#121—91no—
511#121—181no—
512#121—181no—
513#120—181no—
514C4×D4—31no—
515C4×D4—91no—
516C4×D4—91no—
517C2×C4⋊C4—181no—
518C2×C22⋊C4—181no—
519#106—91no—
520C4⋊C8—31no—
521#103—31no—
522#103—91no—
523#103—91no—
524#102—31no—
525#102—91no—
526#102—91no—
527C22⋊C8—31no—
528C22⋊C8D3211yescharacteristic, complemented
529#97—31no—
530C23×C3—21no—
531C23×C3—31no—
532C23×C3—61no—
533C23×C3C2×D1211yescharacteristic
534C23×C3D3×D411yescharacteristic
535C22×D3—21no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—121no—
541C22×D3—121no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—241no—
547C22×D3—241no—
548C22×D3C2×D1211yescharacteristic
549C3×Q8—61no—
550C3×Q8—61no—
551C3×Q8—61no—
552C3×Q8—61no—
553C3×D4—32no—
554C3×D4—61no—
555C3×D4—121no—
556C3×D4—122no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—31no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—122no—
574C2×C3×C4C2×D1211yescharacteristic
575C2×C3×C4D3×D411yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578#67—41no—
579#67—42no—
580#67—122no—
581#67—122no—
582#67—122no—
583#67—122no—
584#67—124no—
585#67—241no—
586#67—241no—
587#67—242no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3—241no—
598C2×Dic3C2×D1211yescharacteristic
599C2×Dic3C2×D1211yescharacteristic
600C2×Dic3C2×D1211yescharacteristic
601D12—21no—
602D12—32no—
603D12—32no—
604D12—62no—
605D12—61no—
606D12—61no—
607D12—61no—
608D12—61no—
609D12—61no—
610D12—61no—
611D12—121no—
612D12—121no—
613D12—121no—
614D12—122no—
615D12—122no—
616D12D3×D412yes—
617C4×D3—21no—
618C4×D3—21no—
619C4×D3—42no—
620C4×D3—122no—
621C4×D3—122no—
622C4×D3—122no—
623C4×D3—122no—
624C4×D3—122no—
625C4×D3—122no—
626C4×D3—124no—
627C4×D3—241no—
628Dic6—21no—
629Dic6—21no—
630Dic6—21no—
631Dic6—21no—
632Dic6—62no—
633Dic6—61no—
634Dic6—61no—
635Dic6—61no—
636Dic6—61no—
637Dic6—121no—
638C3×C8—21no—
639C3×C8—21no—
640C3×C8—21no—
641C3×C8—21no—
642C3×C8—32no—
643C3×C8—41no—
644C3×C8—41no—
645C3×C8—61no—
646C3⋊C8—21no—
647C3⋊C8D3×D412yes—
648C2×C32—41no—
649C2×C32D4211yescharacteristic
650C2×C32#57511yescharacteristic
651C2×C32#57711yescharacteristic
652C3⋊D3—42no—
653C3⋊D3—81no—
654C3×D3—41no—
655C3×D3—42no—
656C24—181no—
657#41—62no—
658#41—121no—
659#41—182no—
660#41—182no—
661#41—361no—
662#41—361no—
663C2×Q8—31no—
664C2×Q8—31no—
665C2×Q8—91no—
666C2×D4—31no—
667C2×D4—31no—
668C2×D4—61no—
669C2×D4—91no—
670C2×D4—91no—
671C2×D4—181no—
672C2×D4—182no—
673C2×D4—181no—
674C2×D4—181no—
675C2×D4—181no—
676C2×D4—361no—
677C22×C4—31no—
678C22×C4—61no—
679C22×C4—181no—
680C22×C4—181no—
681C22×C4—181no—
682C22×C4—181no—
683C22×C4C2×D3211yescharacteristic
684Q16—121no—
685Q16—182no—
686SD16—62no—
687SD16—182no—
688SD16—182no—
689SD16—182no—
690SD16—361no—
691D8—94no—
692D8—182no—
693M16—62no—
694C2×C8—31no—
695C2×C8—31no—
696C2×C8—62no—
697C2×C8C2×D3211yescharacteristic
698C2×C8C2×D3211yescharacteristic
699C4⋊C4—31no—
700C4⋊C4—31no—
701C4⋊C4—61no—
702C4⋊C4—91no—
703C4⋊C4—181no—
704C4⋊C4—181no—
705C4⋊C4—181no—
706C4⋊C4—181no—
707C22⋊C4—31no—
708C22⋊C4—31no—
709C22⋊C4—61no—
710C22⋊C4—181no—
711C22⋊C4—181no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C42—31no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—62no—
731C22×C3—61no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3C22×D1211yescharacteristic
735C22×C3C2×D3×D411yescharacteristic
736C2×D3—21no—
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—22no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—62no—
743C2×D3—62no—
744C2×D3—122no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—241no—
756C2×D3—241no—
757C2×D3—241no—
758C2×D3—241no—
759C2×D3—241no—
760C2×D3—244no—
761C2×D3—244no—
762C3×C4—21no—
763C3×C4—21no—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—41no—
767C3×C4—61no—
768C3×C4—61no—
769C3×C4—61no—
770C3×C4—121no—
771C3×C4—121no—
772C3×C4—121no—
773C3×C4C2×D3×D411yescharacteristic
774C3×C4C2×D3×D411yescharacteristic
775C3×C4#100411yescharacteristic
776C3×C4#100911yescharacteristic
777Dic3—21no—
778Dic3—21no—
779Dic3—21no—
780Dic3—41no—
781Dic3—41no—
782Dic3—41no—
783Dic3—122no—
784Dic3—121no—
785Dic3—121no—
786Dic3—121no—
787Dic3—121no—
788Dic3—241no—
789C32#326711yescharacteristic, complemented, Sylow
790C23—31no—
791C23—61no—
792C23—181no—
793C23—181no—
794C23—362no—
795C23—362no—
796C23—721no—
797C23D3×D1211yescharacteristic
798Q8—61no—
799Q8—61no—
800Q8—61no—
801Q8—61no—
802Q8—181no—
803Q8—181no—
804D4—32no—
805D4—61no—
806D4—92no—
807D4—121no—
808D4—122no—
809D4—181no—
810D4—181no—
811D4—181no—
812D4—362no—
813D4—362no—
814D4—362no—
815D4—721no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—31no—
819C2×C4—31no—
820C2×C4—31no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—122no—
827C2×C4—181no—
828C2×C4—181no—
829C2×C4—362no—
830C2×C4—362no—
831C2×C4—362no—
832C2×C4—721no—
833C2×C4D3×D1211yescharacteristic
834C2×C4C22×D3211yescharacteristic
835C8—21no—
836C8—21no—
837C8—32no—
838C8—61no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—21no—
842C2×C3—41no—
843C2×C3—41no—
844C2×C3—81no—
845C2×C3—122no—
846C2×C3—121no—
847C2×C3D4×D1211yescharacteristic
848C2×C3#559011yescharacteristic
849C2×C3#574811yescharacteristic
850C2×C3#575111yescharacteristic
851C2×C3#576811yescharacteristic
852C2×C3#577811yescharacteristic
853D3—41no—
854D3—42no—
855D3—122no—
856D3—122no—
857D3—242no—
858D3—241no—
859D3—241no—
860D3—481no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—61no—
865C22—61no—
866C22—61no—
867C22—62no—
868C22—121no—
869C22—121no—
870C22—182no—
871C22—361no—
872C22—361no—
873C22—361no—
874C22—361no—
875C22—361no—
876C22—724no—
877C22C2×D3×D1211yescharacteristic
878C4—21no—
879C4—61no—
880C4—61no—
881C4—61no—
882C4—121no—
883C4—121no—
884C4—121no—
885C4—361no—
886C4—361no—
887C4D32×D411yescharacteristic
888C4#6431411yescharacteristic
889C3—21no—
890C3#7949611yescharacteristic, complemented
891C3#8026411yescharacteristic, complemented
892C2—41no—
893C2—121no—
894C2—122no—
895C2—362no—
896C2—721no—
897C2#1059427711yescharacteristic
898C2#1059467611yescharacteristic
899C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10595067C2semidirect
2. #10594834C2semidirect
3. C2×#63829C2semidirect
4. C2×#63794C2semidirect
5. #10592433C2semidirect
6. C3×#4733C2semidirect
7. C3×#4730C2semidirect
8. #10591177C2semidirect
9. #10590966C2semidirect
10. #10590946C2semidirect
11. #10590899C2semidirect
12. #10590849C2semidirect
13. #10590770C2semidirect
14. #10590752C2semidirect
15. #10590746C2semidirect
18. C2×#3828C22semidirect
26. C3×#924C22semidirect
27. C22×C3×C3⋊C8C22semidirect
28. C2×C3×Dic12C22semidirect
36. #63894C22semidirect
39. #63866C22semidirect
45. C2×#3719C22semidirect
47. C2×#3717C22semidirect
52. C32×C22⋊C8C22semidirect
53. #63648C22semidirect
54. #63643C22semidirect
57. C3×#816C22semidirect
58. C3×#815C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. #63573C22semidirect
61. #63566C22semidirect
89. #4733D3semidirect
91. #4730D3semidirect
155. #3714D4semidirect
194. #924C2×D3semidirect
195. C22×C3⋊C8C2×D3semidirect
199. C2×Dic12C2×D3semidirect
234. C3×C22⋊C8C2×D3semidirect
235. C3×C22⋊C8C2×D3semidirect
249. #816C2×D3semidirect
250. #815C2×D3semidirect
251. Dic3⋊C8C2×D3semidirect
528. C22⋊C8D32semidirect
789. C32#3267semidirect
890. C3#79496semidirect
891. C3#80264semidirect

Maximal subgroups

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

subgroupindex
#105950672
#105948342
C2×#638292
C2×#637942
#105924332
C3×#47332
C3×#47302
#105911772
#105909662
#105909462
#105908992
#105908492
#105907702
#105907522
#105907462
#802643
#794963