Finite Group Databasebeta

← #11888607

Subgroups — #11888607

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594995C211yesmaximal, characteristic, complemented
2#10594834C211yesmaximal, characteristic, complemented
3#10592832C211yesmaximal, characteristic, complemented
4C3×#5134C211yesmaximal, characteristic, complemented
5C3×#5127C211yesmaximal, characteristic, complemented
6#10591182C211yesmaximal, characteristic, complemented
7#10591126C211yesmaximal, characteristic, complemented
8#10590898C211yesmaximal, characteristic, complemented
9#10590825C211yesmaximal, characteristic, complemented
10#10590823C211yesmaximal, characteristic, complemented
11#10590774C211yesmaximal, characteristic, complemented
12#10590752C211yesmaximal, characteristic, complemented
13#10590746C211yesmaximal, characteristic, complemented
14#10590708C211yesmaximal, characteristic, complemented
15#10590690C211yesmaximal, characteristic, complemented
16#80819—31nomaximal
17#79500—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×C32×M16C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C3×#930C2211yescharacteristic
23C3×C4×#67C2211yescharacteristic
24C3×#924C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27#63980—21no—
28#63975—21no—
29#67⋊Dic3—21no—
30#63958—21no—
31#63908C2211yescharacteristic
32#63894C2211yescharacteristic
33Dic3×D12C2211yescharacteristic
34#63891—21no—
35#63883—21no—
36#63869C2211yescharacteristic
37#63866C2211yescharacteristic
38#63861—21no—
39#63857C2211yescharacteristic
40#63853—21no—
41#63841C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic
46#63643C2211yescharacteristic
47#63643C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#818C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#815C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55#63573C2211yescharacteristic
56#63573C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59#63566C2211yescharacteristic
60#63564C2211yescharacteristic
61#5631—31no—
62#5618—31no—
63#5565—31no—
64#5551—31no—
65C3×#468—31no—
66C3×#435—31no—
67#5172—31no—
68#5162—31no—
69#5134D311yescharacteristic, complemented
70#5133—31no—
71#5133—31no—
72#5133—61no—
73#5127D311yescharacteristic, complemented
74#5114—31no—
75#5113—31no—
76#5043—31no—
77#5037—31no—
78#4891—31no—
79#4888—31no—
80#4847—31no—
81#4841—31no—
82#4804—31no—
83#4797—31no—
84#4785—31no—
85#4778—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—
94C22×C3⋊Dic3—21no—
95#3828—22no—
96#3828—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#625—21no—
107C2×#624—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110#3799—22no—
111#3799—41no—
112C32×M16—41no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4D411yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×#204—41no—
130C3×D3×C8—41no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3716—41no—
143#3714—22no—
144#3307—91noSylow
145C2×#239—31no—
146C2×#235—31no—
147C2×#235—31no—
148C2×#235—31no—
149C2×#235—61no—
150C2×C3×SD16—31no—
151C2×C3×M16—21no—
152C2×C3×M16C2×D311yescharacteristic
153C2×C3×M16C2×D311yescharacteristic
154C22×C3×C8—31no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C3×C4×D4—31no—
158#944—31no—
159#939—61no—
160#939—61no—
161#938—31no—
162#938—61no—
163D4×Dic3—31no—
164D4×Dic3—61no—
165C2×#214—31no—
166C2×#213—31no—
167#930—31no—
168#930C2×D311yescharacteristic
169C4×#67C2×D311yescharacteristic
170#926—31no—
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—61no—
174#924—31no—
175#924C2×D311yescharacteristic
176C2×D24—31no—
177C2×#204—31no—
178C2×#204C2×D311yescharacteristic
179C2×D3×C8C2×D311yescharacteristic
180#898—61no—
181#897—31no—
182#894—61no—
183#893—31no—
184#892—31no—
185D3×C4⋊C4—61no—
186D3×C4⋊C4—61no—
187#890—31no—
188#886—61no—
189#884—61no—
190#883—61no—
191#883—61no—
192#883—61no—
193#883—61no—
194#67⋊C4—61no—
195#879—61no—
196C4×D12—31no—
197C4×D12—31no—
198#870—31no—
199#869—31no—
200C3×#107—31no—
201C3×C4⋊C8—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8—31no—
206C3×#97—31no—
207#835—31no—
208#835—31no—
209#830C2×D311yescharacteristic
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—61no—
216#821—61no—
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8C2×D311yescharacteristic
219#818C2×D311yescharacteristic
220#817—31no—
221#817—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—61no—
230#816—61no—
231#816C2×D311yescharacteristic
232#815C2×D311yescharacteristic
233Dic3⋊C8C2×D311yescharacteristic
234#810—31no—
235#809—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—
250C2×C3⋊Dic3—81no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)#4112yes—
253C4×C3⋊D3—42no—
254#634—21no—
255#634—21no—
256C3×#67—41no—
257C3×#67—42no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#626—42no—
271#625—81no—
272#624—42no—
273#624—42no—
274D3×Dic3—81no—
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—31no—
286#465—91no—
287#461—91no—
288#449—91no—
289#449—91no—
290#442—91no—
291#435—31no—
292#417—91no—
293#416—91no—
294C2×C3×Q8—31no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C2×#67—21no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—121no—
309C2×#67D1211yescharacteristic
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—121no—
314#239—62no—
315#239—121no—
316#235—62no—
317#235—62no—
318#235—62no—
319#235—64no—
320#235—121no—
321#235—121no—
322#235—121no—
323#235—122no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12C22×D311yescharacteristic
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—121no—
337C2×C4×D3C22×D311yescharacteristic
338C2×Dic6—31no—
339C2×Dic6—31no—
340C2×Dic6—61no—
341C2×Dic6C22×D311yescharacteristic
342C3×SD16—121no—
343C3×M16—41no—
344C3×M16—41no—
345C3×M16—42no—
346C2×C3×C8—21no—
347C2×C3×C8—21no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8—121no—
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C2×C3×C8C22×D311yescharacteristic
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—61no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—31no—
364#217—21no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217D1211yescharacteristic
370#214—121no—
371#213—62no—
372(C2×D3)⋊C4—21no—
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)⋊C4D1211yescharacteristic
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—121no—
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4D1211yescharacteristic
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D24—62no—
409#204—41no—
410#204—121no—
411D3×C8—41no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—22no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
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—21no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—41no—
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—91no—
438C2×#41—91no—
439C2×SD16—31no—
440C2×SD16—91no—
441C2×D8—91no—
442C2×M16D3211yescharacteristic
443C22×C8—31no—
444C4⋊Q8—91no—
445#126—181no—
446#125—91no—
447#123—181no—
448#123—181no—
449#123—181no—
450C22⋊Q8—31no—
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—91no—
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#102—91no—
477C22⋊C8—31no—
478C22⋊C8—31no—
479#97—31no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—61no—
483C23×C3C2×D1211yescharacteristic
484C23×C3D3×D411yescharacteristic
485C22×D3—21no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—121no—
489C22×D3C2×D1211yescharacteristic
490C3×Q8—61no—
491C3×Q8—61no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—121no—
495C3×D4—122no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4C2×D1211yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516#67—41no—
517#67—42no—
518#67—122no—
519#67—122no—
520#67—122no—
521#67—124no—
522#67—241no—
523#67—241no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—121no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—241no—
537C2×Dic3—241no—
538C2×Dic3—241no—
539C2×Dic3—242no—
540C2×Dic3C2×D1211yescharacteristic
541C2×Dic3C2×D1211yescharacteristic
542C2×Dic3C2×D1211yescharacteristic
543D12—21no—
544D12—21no—
545D12—32no—
546D12—32no—
547D12—62no—
548D12—61no—
549D12—61no—
550D12—121no—
551D12—122no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—122no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3—122no—
558C4×D3—122no—
559C4×D3—122no—
560C4×D3—124no—
561C4×D3—241no—
562Dic6—21no—
563Dic6—21no—
564Dic6—62no—
565Dic6—61no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—121no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—21no—
574C3×C8—41no—
575C3×C8—41no—
576C3×C8—61no—
577C3×C8—61no—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C2×C32—41no—
581C2×C32#54611yescharacteristic
582C2×C32#57511yescharacteristic
583C2×C32#57711yescharacteristic
584C3⋊D3—42no—
585C3×D3—41no—
586C3×D3—81no—
587#41—182no—
588#41—182no—
589#41—361no—
590#41—361no—
591C2×Q8—31no—
592C2×Q8—91no—
593C2×D4—31no—
594C2×D4—31no—
595C2×D4—61no—
596C2×D4—91no—
597C2×D4—181no—
598C2×D4—181no—
599C2×D4—181no—
600C22×C4—31no—
601C22×C4—181no—
602C22×C4—181no—
603C22×C4—181no—
604C22×C4—181no—
605C22×C4—181no—
606C22×C4C2×D3211yescharacteristic
607SD16—121no—
608SD16—361no—
609D8—182no—
610M16—41no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—121no—
614C2×C8C2×D3211yescharacteristic
615C2×C8C2×D3211yescharacteristic
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—61no—
620C4⋊C4—91no—
621C4⋊C4—91no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C22⋊C4—31no—
629C22⋊C4—31no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C42—31no—
638C42—181no—
639C22×C3—22no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3C22×D1211yescharacteristic
656C22×C3C2×D3×D411yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—62no—
664C2×D3—62no—
665C2×D3—122no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—241no—
671C2×D3—241no—
672C3×C4—22no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4#100411yescharacteristic
684C3×C4#100411yescharacteristic
685C3×C4D3×#4111yescharacteristic
686C3×C4D3×#4111yescharacteristic
687Dic3—21no—
688Dic3—21no—
689Dic3—21no—
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—122no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—121no—
700Dic3—241no—
701Dic3—241no—
702C32#330711yescharacteristic, complemented, Sylow
703C23—31no—
704C23—61no—
705C23—181no—
706C23D3×D1211yescharacteristic
707Q8—61no—
708Q8—61no—
709Q8—181no—
710Q8—181no—
711D4—61no—
712D4—61no—
713D4—92no—
714D4—121no—
715D4—122no—
716D4—181no—
717D4—362no—
718D4—362no—
719D4—721no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—362no—
734C2×C4—362no—
735C2×C4—362no—
736C2×C4—721no—
737C2×C4—721no—
738C2×C4D3×D1211yescharacteristic
739C2×C4C22×D3211yescharacteristic
740C8—21no—
741C8—21no—
742C8—61no—
743C8—61no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—42no—
748C2×C3—41no—
749C2×C3—41no—
750C2×C3—121no—
751C2×C3—241no—
752C2×C3#555411yescharacteristic
753C2×C3#561011yescharacteristic
754C2×C3#574811yescharacteristic
755C2×C3#575111yescharacteristic
756C2×C3#577311yescharacteristic
757C2×C3#577811yescharacteristic
758D3—41no—
759D3—81no—
760D3—122no—
761D3—122no—
762D3—242no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—182no—
773C22—361no—
774C22—361no—
775C22C2×D3×D1211yescharacteristic
776C4—21no—
777C4—61no—
778C4—61no—
779C4—61no—
780C4—121no—
781C4—121no—
782C4—121no—
783C4—361no—
784C4—361no—
785C4—361no—
786C4#6430611yescharacteristic
787C4#6433011yescharacteristic
788C3—21no—
789C3#7950011yescharacteristic, complemented
790C3#8081911yescharacteristic, complemented
791C2—41no—
792C2—121no—
793C2—241no—
794C2—362no—
795C2#1059471211yescharacteristic
796C2#1059471511yescharacteristic
797C2#1059507511yescharacteristic
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. #10594995C2semidirect
2. #10594834C2semidirect
3. #10592832C2semidirect
4. C3×#5134C2semidirect
5. C3×#5127C2semidirect
6. #10591182C2semidirect
7. #10591126C2semidirect
8. #10590898C2semidirect
9. #10590825C2semidirect
10. #10590823C2semidirect
11. #10590774C2semidirect
12. #10590752C2semidirect
13. #10590746C2semidirect
14. #10590708C2semidirect
15. #10590690C2semidirect
69. #5134D3semidirect
73. #5127D3semidirect
702. C32#3307semidirect
789. C3#79500semidirect
790. C3#80819semidirect

Maximal subgroups

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

subgroupindex
#105949952
#105948342
#105928322
C3×#51342
C3×#51272
#105911822
#105911262
#105908982
#105908252
#105908232
#105907742
#105907522
#105907462
#105907082
#105906902
#808193
#795003