Finite Group Databasebeta

← #11889233

Subgroups — #11889233

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595411C211yesmaximal, characteristic, complemented
2#10595246C211yesmaximal, characteristic
3#10592872C211yesmaximal, characteristic, complemented
4C3×#5169C211yesmaximal, characteristic, complemented
5C3×#5164C211yesmaximal, characteristic, complemented
6#10591604C211yesmaximal, characteristic, complemented
7#10591598C211yesmaximal, characteristic, complemented
8#10591591C211yesmaximal, characteristic, complemented
9#10591424C211yesmaximal, characteristic, complemented
10#10591421C211yesmaximal, characteristic, complemented
11#10591408C211yesmaximal, characteristic, complemented
12#10590895C211yesmaximal, characteristic, complemented
13#10590739C211yesmaximal, characteristic, complemented
14#10590708C211yesmaximal, characteristic, complemented
15#10590651C211yesmaximal, characteristic, complemented
16#80162—31nomaximal
17#79801—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21#64155C2211yescharacteristic, complemented
22C2×#3756C2211yescharacteristic, complemented
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic, complemented
25C2×C3×#215C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic
27#63978—21no—
28#63977—21no—
29#63962—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63918C2211yescharacteristic, complemented
32#63916C2211yescharacteristic
33C4×#626C2211yescharacteristic
34#63860C2211yescharacteristic
35#63858—21no—
36#63857C2211yescharacteristic
37#63852—21no—
38#63849C2211yescharacteristic, complemented
39#63848—21no—
40#63841C2211yescharacteristic
41#63837—21no—
42C2×#3711C2211yescharacteristic
43C2×#3710C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63647C2211yescharacteristic, complemented
46#63643C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#818C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61#5806—31no—
62#5641—31no—
63#5584—31no—
64#5554—31no—
65C3×#450—31no—
66C3×#440—31no—
67#5215—31no—
68#5173—31no—
69#5173—31no—
70#5173—61no—
71#5171—31no—
72#5169D311yescharacteristic, complemented
73#5166—31no—
74#5164D311yescharacteristic, complemented
75#5052—31no—
76#5028—31no—
77#5008—31no—
78#4888—31no—
79#4885—31no—
80#4816—31no—
81#4807—31no—
82#4784—31no—
83#4772—31no—
84#4772—31no—
85#4770—31no—
86#4765—31no—
87#4761—31no—
88#4728—31no—
89#4723—31no—
90#4714—31no—
91#4706—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C22×C3⋊Dic3—21no—
97#3830—22no—
98#3830—41no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C3×D3×D4—22no—
104C3×D3×D4—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×#627—21no—
108C2×#626—21no—
109C2×#626D411yescharacteristic
110C32×SD16—22no—
111C2×C32×C8C2311yescharacteristic
112#3756—41no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#215—41no—
119C3×(C2×D3)⋊C4—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3D411yescharacteristic
132#3722—21no—
133#3722D411yescharacteristic
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141Dic32—21no—
142#3711—41no—
143#3710—41no—
144#3311—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#237—31no—
148C2×#237—61no—
149C2×D3×D4C2×D311yescharacteristic
150C2×C3×SD16—21no—
151C2×C3×SD16—31no—
152C2×C3×SD16C2×D311yescharacteristic
153C2×C3×SD16C2×D311yescharacteristic
154C3×C22⋊Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×D4—31no—
157#953—61no—
158C2×#217—61no—
159#946—31no—
160#946—31no—
161#946—61no—
162#946C2×D311yescharacteristic
163Q8×Dic3C2×D311yescharacteristic, complemented
164C2×#216—31no—
165C2×#216—31no—
166C2×#216—61no—
167C2×#215C2×D311yescharacteristic
168#939—61no—
169#938—31no—
170#936—31no—
171#935—61no—
172D4×Dic3C2×D311yescharacteristic
173#930—61no—
174C4×#67—31no—
175C2×(C2×D3)⋊C4—61no—
176#926—31no—
177#924—31no—
178C2×#208—31no—
179C2×ΓL(1,𝔽25)—31no—
180C2×D3×C8—31no—
181C2×D3×C8—31no—
182#898—61no—
183#898—61no—
184#898—61no—
185#897—31no—
186#895—31no—
187#892—31no—
188#892—31no—
189#892—31no—
190#888—31no—
191#887—61no—
192#886—61no—
193#885—61no—
194#882—61no—
195#879—61no—
196#875—31no—
197#875—61no—
198C4×D12—31no—
199#869—31no—
200C4×Dic6—61no—
201C3×#107—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—31no—
207C3×#97—31no—
208#835C2×D311yescharacteristic, complemented
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—61no—
214#832C2×D311yescharacteristic
215#832C2×D311yescharacteristic
216#821—31no—
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—61no—
221(C2×D3)⋊C8C2×D311yescharacteristic
222#818C2×D311yescharacteristic, complemented
223#817—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228#816—61no—
229#815C2×D311yescharacteristic, complemented
230Dic3⋊C8—31no—
231#810—31no—
232#810—31no—
233#809—31no—
234#808—31no—
235#808—31no—
236#808—31no—
237C4⋊(C3⋊C8)—31no—
238C23×C32—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C32×D4—21no—
248C32×D4#4112yes—
249C2×C32×C4—21no—
250C2×C32×C4C2411yescharacteristic
251#638—42no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—42no—
255C2×C3⋊Dic3C2×D411yescharacteristic
256C4×C3⋊D3—21no—
257C4×C3⋊D3—21no—
258#634—21no—
259#634—21no—
260C3×#67—42no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—81no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12—21no—
270C3×C4×D3—21no—
271C3×C4×D3—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—31no—
290#440—31no—
291#435—91no—
292#418—91no—
293#416—91no—
294C24×C3—61no—
295C23×D3—21no—
296C2×C3×Q8—21no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C2×C3×D4—62no—
303C2×C3×D4—121no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C22×C3×C4—31no—
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—61no—
316C22×Dic3—61no—
317C22×Dic3—121no—
318#237—62no—
319#237—62no—
320#237—122no—
321#237—121no—
322#237—121no—
323#237—122no—
324D3×D4—22no—
325D3×D4—41no—
326C2×D12—31no—
327C2×D12—61no—
328C2×D12C22×D311yescharacteristic
329C2×C4×D3—31no—
330C2×C4×D3—31no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C3×SD16—22no—
339C3×SD16—22no—
340C3×SD16—42no—
341C3×SD16—121no—
342C2×C3×C8—21no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—31no—
355C3×C42—61no—
356#217—21no—
357#217—31no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#216—121no—
364#216—121no—
365#216—122no—
366#215—41no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
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—61no—
380(C2×D3)⋊C4—121no—
381C4⋊Dic3—21no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—31no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—121no—
398C4×Dic3—21no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3C22×D311yescharacteristic
404#208—121no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410ΓL(1,𝔽25)—121no—
411D3×C8—121no—
412D3×C8—121no—
413C22×C32—22no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—84no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—21no—
431C3⋊Dic3—41no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—31no—
441C2×Q16—91no—
442C2×SD16—31no—
443C2×SD16D3211yescharacteristic
444C2×M16—91no—
445C22×C8—91no—
446C4⋊Q8—91no—
447#126—181no—
448#126—181no—
449#124—91no—
450#124—181no—
451#123—181no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454C22⋊Q8—91no—
455#121—91no—
456#121—181no—
457#120—181no—
458C4×Q8—31no—
459C4×Q8—181no—
460C4×D4—31no—
461C4×D4—91no—
462#117—91no—
463#117—91no—
464C2×C22⋊C4—181no—
465#107—31no—
466#106—91no—
467#106—91no—
468C4⋊C8—91no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8—91no—
481#97—31no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—41no—
486C23×C3—61no—
487C23×C3—122no—
488C23×C3—122no—
489C23×C3—241no—
490C22×D3—21no—
491C22×D3—31no—
492C22×D3—31no—
493C22×D3—42no—
494C22×D3—42no—
495C22×D3—61no—
496C22×D3—81no—
497C22×D3D3×D411yescharacteristic
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—41no—
503C3×Q8—41no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—22no—
507C3×D4—41no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—122no—
511C3×D4#23512yes—
512C3×D4#23712yes—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—41no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—241no—
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—42no—
529#67—121no—
530#67—122no—
531#67—122no—
532#67—124no—
533#67—241no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—81no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—122no—
548C2×Dic3—122no—
549C2×Dic3—124no—
550C2×Dic3D3×D411yescharacteristic
551C2×Dic3D3×D411yescharacteristic
552C2×Dic3D3×D411yescharacteristic
553D12—21no—
554D12—21no—
555D12—121no—
556D12—241no—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—61no—
560C4×D3—61no—
561C4×D3—61no—
562C4×D3—61no—
563C4×D3—121no—
564C4×D3—121no—
565Dic6—62no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—61no—
570Dic6—121no—
571Dic6—122no—
572Dic6—122no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—41no—
576C3×C8—61no—
577C3×C8—61no—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—121no—
583C2×C32—42no—
584C2×C32#54611yescharacteristic
585C2×C32#57511yescharacteristic
586C2×C32#57711yescharacteristic
587C3⋊D3—41no—
588C3×D3—41no—
589C3×D3—81no—
590C24—61no—
591#41—182no—
592#41—361no—
593C2×Q8—91no—
594C2×Q8—181no—
595C2×Q8C2×D3211yescharacteristic
596C2×D4—31no—
597C2×D4—61no—
598C2×D4—62no—
599C2×D4—91no—
600C2×D4—121no—
601C2×D4—181no—
602C2×D4—181no—
603C2×D4C2×D3211yescharacteristic
604C22×C4—31no—
605C22×C4—61no—
606C22×C4—91no—
607C22×C4—181no—
608Q16—361no—
609SD16—22no—
610SD16—121no—
611M16—361no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—91no—
615C2×C8—361no—
616C2×C8C2×D3211yescharacteristic
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—91no—
623C4⋊C4—91no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
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—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—31no—
639C42—61no—
640C42—181no—
641C42—181no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—21no—
645C22×C3—42no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—244no—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C2×D3×D411yescharacteristic
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—84no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—81no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4C2×#23511yescharacteristic
689C3×C4C2×#23711yescharacteristic
690C3×C4#100411yescharacteristic
691C3×C4#100911yescharacteristic
692Dic3—21no—
693Dic3—21no—
694Dic3—21no—
695Dic3—41no—
696Dic3—41no—
697Dic3—41no—
698Dic3—61no—
699Dic3—61no—
700Dic3—121no—
701Dic3—122no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—241no—
707C32#331111yescharacteristic, complemented, Sylow
708C23—21no—
709C23—31no—
710C23—61no—
711C23—91no—
712C23—122no—
713C23—122no—
714C23—241no—
715Q8—21no—
716Q8—21no—
717Q8—181no—
718Q8—181no—
719Q8—362no—
720D4—21no—
721D4—61no—
722D4—61no—
723D4—122no—
724D4—361no—
725D4—362no—
726D4—721no—
727D4#380412yes—
728C2×C4—21no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—91no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—241no—
743C2×C4—362no—
744C2×C4C22×D3211yescharacteristic
745C8—21no—
746C8—61no—
747C8—61no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—42no—
753C2×C3—42no—
754C2×C3—82no—
755C2×C3—121no—
756C2×C3—241no—
757C2×C3#555011yescharacteristic
758C2×C3#559111yescharacteristic
759C2×C3#576211yescharacteristic
760C2×C3#577311yescharacteristic
761C2×C3#577511yescharacteristic
762C2×C3#577711yescharacteristic
763D3—41no—
764D3—81no—
765D3—121no—
766D3—121no—
767D3—241no—
768C22—22no—
769C22—41no—
770C22—41no—
771C22—61no—
772C22—61no—
773C22—61no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—181no—
778C22—181no—
779C22—181no—
780C22—244no—
781C22D32×D411yescharacteristic
782C4—41no—
783C4—61no—
784C4—61no—
785C4—61no—
786C4—121no—
787C4—121no—
788C4—121no—
789C4—181no—
790C4—361no—
791C4—361no—
792C4#6431411yescharacteristic
793C4C2×#380411yescharacteristic
794C3—21no—
795C3#7980111yescharacteristic, complemented
796C3#8016211yescharacteristic, complemented
797C2—42no—
798C2—121no—
799C2—241no—
800C2—361no—
801C2#1059474411yescharacteristic
802C2#1059474911yescharacteristic
803C2#1059513511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595246C2
hypercenterC2×SD16D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10595411C2semidirect
3. #10592872C2semidirect
4. C3×#5169C2semidirect
5. C3×#5164C2semidirect
6. #10591604C2semidirect
7. #10591598C2semidirect
8. #10591591C2semidirect
9. #10591424C2semidirect
10. #10591421C2semidirect
11. #10591408C2semidirect
12. #10590895C2semidirect
13. #10590739C2semidirect
14. #10590708C2semidirect
15. #10590651C2semidirect
21. #64155C22semidirect
22. C2×#3756C22semidirect
24. C3×Q8×Dic3C22semidirect
31. #63918C22semidirect
38. #63849C22semidirect
43. C2×#3710C22semidirect
45. #63647C22semidirect
46. #63643C22semidirect
47. C3×#835C22semidirect
52. C3×#818C22semidirect
53. C3×#815C22semidirect
54. #63574C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63567C22semidirect
72. #5169D3semidirect
74. #5164D3semidirect
163. Q8×Dic3C2×D3semidirect
208. #835C2×D3semidirect
222. #818C2×D3semidirect
229. #815C2×D3semidirect
707. C32#3311semidirect
795. C3#79801semidirect
796. C3#80162semidirect

Maximal subgroups

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

subgroupindex
#105954112
#105952462
#105928722
C3×#51692
C3×#51642
#105916042
#105915982
#105915912
#105914242
#105914212
#105914082
#105908952
#105907392
#105907082
#105906512
#801623
#798013