Finite Group Databasebeta

← #11888609

Subgroups — #11888609

Order 1152.

848 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#10594887C211yesmaximal, characteristic, complemented
2#10594843C211yesmaximal, characteristic, complemented
3#10592833C211yesmaximal, characteristic, complemented
4C3×#5133C211yesmaximal, characteristic, complemented
5C3×#5127C211yesmaximal, characteristic, complemented
6#10591163C211yesmaximal, characteristic, complemented
7#10591124C211yesmaximal, characteristic, complemented
8#10590968C211yesmaximal, characteristic, complemented
9#10590954C211yesmaximal, characteristic, complemented
10#10590898C211yesmaximal, characteristic, complemented
11#10590847C211yesmaximal, characteristic, complemented
12#10590767C211yesmaximal, characteristic, complemented
13#10590760C211yesmaximal, characteristic, complemented
14#10590746C211yesmaximal, characteristic, complemented
15#10590710C211yesmaximal, characteristic, complemented
16#79500—31nomaximal
17#78895—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×C32×M16C2211yescharacteristic
21#64139C2211yescharacteristic
22#64133C2211yescharacteristic
23C2×#3744C2211yescharacteristic
24C3×C4×#67C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27#63978—21no—
28#63970—21no—
29#63969—21no—
30#63952—21no—
31#63909C2211yescharacteristic
32#63905—21no—
33#63894C2211yescharacteristic
34Dic3×D12C2211yescharacteristic
35D3×Dic3⋊C4—21no—
36#63869C2211yescharacteristic
37#63866C2211yescharacteristic
38#63856C2211yescharacteristic
39#63854—21no—
40#63848—21no—
41#63841C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44#63648C2211yescharacteristic
45#63645C2211yescharacteristic
46#63643C2211yescharacteristic
47C3×#830C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#815C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55#63573C2211yescharacteristic
56#63573C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63566C2211yescharacteristic
60#63563C2211yescharacteristic
61#5824—31no—
62#5565—31no—
63#5551—31no—
64#5514—31no—
65C3×#435—31no—
66C3×#417—31no—
67#5238—31no—
68#5134—31no—
69#5134—31no—
70#5134—61no—
71#5133D311yescharacteristic, complemented
72#5127D311yescharacteristic, complemented
73#5114—31no—
74#5113—31no—
75#4971—31no—
76#4847—31no—
77#4841—31no—
78#4818—31no—
79#4814—31no—
80#4807—31no—
81#4797—31no—
82#4785—31no—
83#4781—31no—
84#4772—31no—
85#4766—31no—
86#4734—31no—
87#4734—31no—
88#4723—31no—
89#4721—31no—
90#4711—31no—
91#4703—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67D411yescharacteristic
98C22×C3×Dic3—21no—
99C3×#235—22no—
100C3×#235—41no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#625—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795—41no—
112C32×M16—41no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115#3757—21no—
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120#3744—41no—
121C3×#217D411yescharacteristic
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4D411yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D3×C8—41no—
131#3724—21no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3717—41no—
143#3714—22no—
144#3307—91noSylow
145C2×C3×#41—31no—
146C2×#237—31no—
147C2×#235—31no—
148C2×#235C2×D311yescharacteristic
149C2×C3×M16—21no—
150C2×C3×M16C2×D311yescharacteristic
151C2×C3×M16C2×D311yescharacteristic
152C22×C3×C8—31no—
153C3×C4×D4—31no—
154C2×C3×C4⋊C4—31no—
155#946—31no—
156#944—31no—
157C2×#215—31no—
158#939—61no—
159#939—61no—
160#938—61no—
161#935—61no—
162D4×Dic3—31no—
163C2×#213—31no—
164#930—31no—
165#930—31no—
166#930—31no—
167#930—61no—
168#930—61no—
169#929—61no—
170C4×#67—61no—
171C4×#67C2×D311yescharacteristic
172#926—31no—
173C2×C4⋊Dic3C2×D311yescharacteristic
174#924—31no—
175#924—31no—
176#924—31no—
177#924—61no—
178C2×Dic3⋊C4—61no—
179C2×D24—31no—
180C2×#204—31no—
181C2×#204—31no—
182C2×#204—31no—
183C2×#204—61no—
184C2×D3×C8C2×D311yescharacteristic
185#898—61no—
186#898—61no—
187#895—31no—
188#894—61no—
189#893—31no—
190#892—31no—
191D3×C4⋊C4—61no—
192#890—31no—
193#883—61no—
194#883—61no—
195#883—61no—
196#67⋊C4—61no—
197C4×D12—31no—
198C4×D12—31no—
199#870—31no—
200#869—31no—
201C3×C4⋊C8—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—31no—
207C3×C22⋊C8—31no—
208C3×#97—31no—
209#835—31no—
210#832—31no—
211#830C2×D311yescharacteristic
212#821—31no—
213#821—31no—
214#821—31no—
215#821—61no—
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8C2×D311yescharacteristic
219#818—31no—
220#818—31no—
221#818—61no—
222#817—31no—
223#817—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—61no—
230#816C2×D311yescharacteristic
231#816C2×D311yescharacteristic
232#815C2×D311yescharacteristic
233Dic3⋊C8C2×D311yescharacteristic
234#810—31no—
235#810—31no—
236#808—31no—
237#808—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246#638—42no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252#634—21no—
253#634—21no—
254C3×#67—41no—
255C3×#67—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—81no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—42no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#626—81no—
271#625—42no—
272#624—81no—
273D3×Dic3—42no—
274D3×Dic3—42no—
275C32×C8—21no—
276C32×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—91no—
285#468—91no—
286#465—91no—
287#461—91no—
288#449—91no—
289#449—91no—
290#442—91no—
291#435—31no—
292#417—31no—
293#416—91no—
294C3×#41—62no—
295C3×#41—121no—
296C2×C3×Q8—31no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C22×C3×C4—21no—
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—21no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—121no—
313C2×#67D1211yescharacteristic
314C22×Dic3—21no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317#237—62no—
318#237—121no—
319#235—22no—
320#235—41no—
321#235—62no—
322#235—121no—
323C2×D12—31no—
324C2×D12—31no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12C22×D311yescharacteristic
328C2×C4×D3—21no—
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
338C3×M16—41no—
339C3×M16—41no—
340C3×M16—42no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8—121no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—31no—
356C3×C42—31no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—121no—
363#217D1211yescharacteristic
364#215—121no—
365#213—62no—
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—121no—
376(C2×D3)⋊C4D1211yescharacteristic
377C4⋊Dic3—21no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—121no—
399Dic3⋊C4D1211yescharacteristic
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405D24—62no—
406#204—121no—
407#204—121no—
408#204—122no—
409#204—121no—
410D3×C8—41no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32C22×D411yescharacteristic
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—21no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3⋊Dic3—41no—
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C2×#41—31no—
437C2×#41—91no—
438C2×SD16—91no—
439C2×SD16—91no—
440C2×D8—91no—
441C2×M16D3211yescharacteristic
442C22×C8—31no—
443C4⋊Q8—91no—
444#126—181no—
445#125—91no—
446#123—181no—
447#123—181no—
448#123—181no—
449C22⋊Q8—91no—
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—91no—
463#106—91no—
464#106—91no—
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—31no—
478#97—31no—
479C23×C3—21no—
480C23×C3—31no—
481C23×C3—61no—
482C23×C3C2×D1211yescharacteristic
483C23×C3D3×D411yescharacteristic
484C22×D3—21no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—121no—
488C22×D3C2×D1211yescharacteristic
489C3×Q8—61no—
490C3×Q8—61no—
491C3×D4—32no—
492C3×D4—61no—
493C3×D4—121no—
494C3×D4—122no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—122no—
512C2×C3×C4—241no—
513C2×C3×C4C2×D1211yescharacteristic
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—41no—
518#67—42no—
519#67—122no—
520#67—122no—
521#67—122no—
522#67—122no—
523#67—242no—
524#67—241no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—81no—
535C2×Dic3—121no—
536C2×Dic3—121no—
537C2×Dic3—121no—
538C2×Dic3—122no—
539C2×Dic3—122no—
540C2×Dic3C2×D1211yescharacteristic
541C2×Dic3C2×D1211yescharacteristic
542C2×Dic3C2×D1211yescharacteristic
543D12—21no—
544D12—61no—
545D12—61no—
546D12—61no—
547D12—61no—
548D12—121no—
549D12—121no—
550D12—241no—
551D12#23512yes—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—42no—
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—21no—
571C3×C8—21no—
572C3×C8—41no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C2×C32—41no—
578C2×C32#54611yescharacteristic
579C2×C32#57511yescharacteristic
580C2×C32#57711yescharacteristic
581C3⋊D3—81no—
582C3×D3—41no—
583C3×D3—42no—
584#41—62no—
585#41—121no—
586#41—182no—
587#41—361no—
588C2×Q8—31no—
589C2×Q8—91no—
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—61no—
593C2×D4—91no—
594C2×D4—181no—
595C2×D4—181no—
596C2×D4—181no—
597C22×C4—31no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—181no—
601C22×C4—181no—
602C22×C4—181no—
603C22×C4C2×D3211yescharacteristic
604SD16—361no—
605SD16—361no—
606D8—182no—
607M16—41no—
608C2×C8—31no—
609C2×C8—31no—
610C2×C8—121no—
611C2×C8C2×D3211yescharacteristic
612C2×C8C2×D3211yescharacteristic
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—91no—
618C4⋊C4—91no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C22⋊C4—31no—
626C22⋊C4—31no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—31no—
635C42—181no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—62no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3C22×D1211yescharacteristic
653C22×C3C2×D3×D411yescharacteristic
654C2×D3—22no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—41no—
659C2×D3—41no—
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—21no—
672C3×C4—21no—
673C3×C4—41no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4C2×#23511yescharacteristic
681C3×C4#100411yescharacteristic
682C3×C4#100411yescharacteristic
683C3×C4D3×#4111yescharacteristic
684Dic3—21no—
685Dic3—21no—
686Dic3—21no—
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697Dic3—241no—
698Dic3—241no—
699C32#330711yescharacteristic, complemented, Sylow
700C23—31no—
701C23—61no—
702C23—181no—
703C23D3×D1211yescharacteristic
704Q8—61no—
705Q8—61no—
706Q8—181no—
707Q8—181no—
708D4—32no—
709D4—61no—
710D4—121no—
711D4—122no—
712D4—181no—
713D4—181no—
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—122no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—241no—
732C2×C4—362no—
733C2×C4—362no—
734C2×C4—721no—
735C2×C4D3×D1211yescharacteristic
736C2×C4C22×D3211yescharacteristic
737C8—21no—
738C8—21no—
739C8—61no—
740C8—61no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—41no—
745C2×C3—41no—
746C2×C3—81no—
747C2×C3—121no—
748C2×C3—122no—
749C2×C3#549011yescharacteristic
750C2×C3#555411yescharacteristic
751C2×C3#574811yescharacteristic
752C2×C3#575111yescharacteristic
753C2×C3#577511yescharacteristic
754C2×C3#577711yescharacteristic
755D3—42no—
756D3—41no—
757D3—241no—
758D3—241no—
759D3—481no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—61no—
764C22—62no—
765C22—61no—
766C22—61no—
767C22—121no—
768C22—121no—
769C22—361no—
770C22—361no—
771C22—361no—
772C22C2×D3×D1211yescharacteristic
773C4—21no—
774C4—61no—
775C4—61no—
776C4—61no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4—361no—
781C4—361no—
782C4—361no—
783C4D3×#23511yescharacteristic
784C4#6433011yescharacteristic
785C3—21no—
786C3#7889511yescharacteristic, complemented
787C3#7950011yescharacteristic, complemented
788C2—41no—
789C2—121no—
790C2—122no—
791C2—721no—
792C2#1059471111yescharacteristic
793C2#1059471311yescharacteristic
794C2#1059507311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10594887C2semidirect
2. #10594843C2semidirect
3. #10592833C2semidirect
4. C3×#5133C2semidirect
5. C3×#5127C2semidirect
6. #10591163C2semidirect
7. #10591124C2semidirect
8. #10590968C2semidirect
9. #10590954C2semidirect
10. #10590898C2semidirect
11. #10590847C2semidirect
12. #10590767C2semidirect
13. #10590760C2semidirect
14. #10590746C2semidirect
15. #10590710C2semidirect
71. #5133D3semidirect
72. #5127D3semidirect
699. C32#3307semidirect
786. C3#78895semidirect
787. C3#79500semidirect

Maximal subgroups

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

subgroupindex
#105948872
#105948432
#105928332
C3×#51332
C3×#51272
#105911632
#105911242
#105909682
#105909542
#105908982
#105908472
#105907672
#105907602
#105907462
#105907102
#795003
#788953