Finite Group Databasebeta

← #11887232

Subgroups — #11887232

Order 1152.

878 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595067C211yesmaximal, characteristic
2#10594939C211yesmaximal, characteristic, complemented
3#10592813C211yesmaximal, characteristic, complemented
4C3×#5113C211yesmaximal, characteristic, complemented
5C3×C8×#67C211yesmaximal, characteristic, complemented
6#10591173C211yesmaximal, characteristic, complemented
7#10591136C211yesmaximal, characteristic, complemented
8#10590946C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590872C211yesmaximal, characteristic, complemented
11#10590848C211yesmaximal, characteristic, complemented
12#10590813C211yesmaximal, characteristic, complemented
13#10590772C211yesmaximal, characteristic, complemented
14#10590744C211yesmaximal, characteristic, complemented
15#10590675C211yesmaximal, characteristic, complemented
16#79440—31nomaximal
17#78845—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic, complemented
21#64139C2211yescharacteristic
22#64133C2211yescharacteristic, complemented
23C2×#3744C2211yescharacteristic
24C3×C4×#67C2211yescharacteristic
25C3×#926C2211yescharacteristic, complemented
26C2×C3×D3×C8C2211yescharacteristic
27#63983—21no—
28#63971—21no—
29#63969—21no—
30#63956—21no—
31D3×(C2×D3)⋊C4—21no—
32Dic3×D12C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63877—21no—
35#63869C2211yescharacteristic, complemented
36#63867—21no—
37#63864C2211yescharacteristic
38#63857C2211yescharacteristic
39#63856C2211yescharacteristic
40#63850—21no—
41#63844C2211yescharacteristic, complemented
42C2×#3719C2211yescharacteristic, complemented
43C2×#3716C2211yescharacteristic
44#63648C2211yescharacteristic
45#63644C2211yescharacteristic, complemented
46#63643C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63563C2211yescharacteristic
61#5829—31no—
62#5550—31no—
63#5541—31no—
64#5529—31no—
65C3×C8×D4—31no—
66C3×#416—31no—
67#5239—31no—
68#5116—31no—
69#5114—31no—
70#5114—31no—
71#5114—61no—
72#5113D311yescharacteristic, complemented
73C2×#821—31no—
74C8×#67D311yescharacteristic, complemented
75#5003—31no—
76#4847—31no—
77#4845—31no—
78#4813—31no—
79#4805—31no—
80#4800—31no—
81#4798—31no—
82#4776—31no—
83D3×#102—31no—
84#4763—31no—
85#4758—31no—
86#4737—31no—
87#4733—31no—
88#4731—31no—
89#4721—31no—
90#4697—31no—
91C4×#204—31no—
92C22×D32—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67D411yescharacteristic
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×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108D3×D12—22no—
109D3×D12—41no—
110C2×C32×C8—41no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113#3757—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3744—41no—
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4D411yescharacteristic
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D3×C8—41no—
130#3724—21no—
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#3719—41no—
143#3716—22no—
144#3296—91noSylow
145C2×C3×#41—31no—
146C2×D3×D4—31no—
147C2×#235C2×D311yescharacteristic
148C22×D12—31no—
149C22×C3×C8—21no—
150C22×C3×C8—31no—
151C22×C3×C8C2×D311yescharacteristic, complemented
152C22×C3×C8C2×D311yescharacteristic, complemented
153C3×C4×D4—31no—
154C3×#117—31no—
155#947—31no—
156#946—31no—
157C2×#216—31no—
158#939—61no—
159#937—61no—
160#937—61no—
161#935—61no—
162D4×Dic3—31no—
163C2×#214—31no—
164#930—31no—
165#930—31no—
166#930—61no—
167#929—61no—
168C4×#67C2×D311yescharacteristic
169C2×(C2×D3)⋊C4—61no—
170#926C2×D311yescharacteristic, complemented
171C2×C4⋊Dic3—31no—
172#924—31no—
173#924—31no—
174#924—31no—
175#924—31no—
176#924—61no—
177C2×Dic12—31no—
178C2×#204—31no—
179C2×#204—31no—
180C2×#204—31no—
181C2×#204—61no—
182C2×D3×C8C2×D311yescharacteristic
183#897—31no—
184#894—61no—
185D3×C4⋊C4—31no—
186#890—31no—
187#889—61no—
188#887—31no—
189#884—61no—
190#883—61no—
191D3×C22⋊C4—61no—
192#879—61no—
193#879—61no—
194#877—61no—
195#875—31no—
196C4×D12—31no—
197#872—61no—
198#870—31no—
199#870—61no—
200C4×Dic6—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×C4×C8—31no—
209#835—31no—
210#832—31no—
211#830C2×D311yescharacteristic, complemented
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—61no—
218#821C2×D311yescharacteristic
219#821C2×D311yescharacteristic
220(C2×D3)⋊C8C2×D311yescharacteristic
221#818—31no—
222#817—31no—
223#817—31no—
224#817—31no—
225#817—61no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—61no—
230#816C2×D311yescharacteristic, complemented
231#816C2×D311yescharacteristic, complemented
232Dic3⋊C8C2×D311yescharacteristic, complemented
233C8×Dic3C2×D311yescharacteristic, complemented
234#809—31no—
235#809—31no—
236#808—31no—
237#807—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249#638—81no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255#634—21no—
256#634—21no—
257C3×#67—22no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—42no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#626—42no—
273D3×Dic3—42no—
274D3×Dic3—81no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280#546—91no—
281#488—91no—
282#483—91no—
283#482—91no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—31no—
292#416—31no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—31no—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—21no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—121no—
312C2×#67D1211yescharacteristic
313C22×Dic3—61no—
314C22×Dic3—61no—
315D3×D4—62no—
316D3×D4—121no—
317#235—22no—
318#235—41no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—62no—
323C2×D12—61no—
324C2×D12—121no—
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3C22×D311yescharacteristic
330C2×Dic6—31no—
331C2×Dic6—31no—
332C2×Dic6—61no—
333C2×Dic6C22×D311yescharacteristic
334C2×C3×C8—21no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8—41no—
339C2×C3×C8—41no—
340C2×C3×C8—42no—
341C2×C3×C8—121no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—31no—
351C3×C22⋊C4—61no—
352C3×C42—31no—
353C3×C42—61no—
354#217—21no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—121no—
361#217D1211yescharacteristic
362#216—121no—
363#214—62no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
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—121no—
374(C2×D3)⋊C4D1211yescharacteristic
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
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—121no—
398Dic3⋊C4D1211yescharacteristic
399C4×Dic3—21no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—121no—
406#204—62no—
407#204—121no—
408#204—121no—
409#204—122no—
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—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3#13512yes—
424D32—84no—
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—31no—
438C22×D4—91no—
439C2×Q16—91no—
440C2×SD16—91no—
441C2×SD16—91no—
442C22×C8—31no—
443C22×C8D3211yescharacteristic, complemented
444#126—181no—
445#125—91no—
446#125—181no—
447#124—91no—
448#123—181no—
449#123—181no—
450C22⋊Q8—91no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453#121—91no—
454#121—181no—
455#120—181no—
456C4×Q8—91no—
457C4×D4—31no—
458C4×D4—91no—
459#117—31no—
460#117—181no—
461C2×C4⋊C4—91no—
462C2×C22⋊C4—181no—
463#107—91no—
464#106—91no—
465#106—91no—
466C4⋊C8—31no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—31no—
478C22⋊C8—31no—
479C4×C8—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×D3—122no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—241no—
494C22×D3—241no—
495C22×D3C2×D1211yescharacteristic
496C3×Q8—61no—
497C3×Q8—61no—
498C3×D4—32no—
499C3×D4—62no—
500C3×D4—61no—
501C3×D4—122no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—122no—
519C2×C3×C4C2×D1211yescharacteristic
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—22no—
524#67—42no—
525#67—122no—
526#67—241no—
527#67—241no—
528#67—242no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—122no—
542C2×Dic3—241no—
543C2×Dic3C2×D1211yescharacteristic
544C2×Dic3C2×D1211yescharacteristic
545C2×Dic3C2×D1211yescharacteristic
546D12—21no—
547D12—61no—
548D12—61no—
549D12—61no—
550D12—61no—
551D12—121no—
552D12—121no—
553D12—122no—
554D12#23512yes—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—42no—
558C4×D3—122no—
559C4×D3—241no—
560Dic6—21no—
561Dic6—21no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—121no—
567Dic6—121no—
568C3×C8—22no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—41no—
574C3×C8—61no—
575C3×C8—61no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C2×C32—41no—
579C2×C32#54611yescharacteristic
580C2×C32C2×#13511yescharacteristic
581C2×C32#57711yescharacteristic
582C3⋊D3—81no—
583C3×D3—22no—
584C3×D3—42no—
585C24—181no—
586#41—62no—
587#41—121no—
588C2×Q8—31no—
589C2×Q8—91no—
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—61no—
593C2×D4—91no—
594C2×D4—181no—
595C2×D4—182no—
596C2×D4—181no—
597C2×D4—361no—
598C22×C4—31no—
599C22×C4—61no—
600C22×C4—181no—
601C22×C4—181no—
602C22×C4C2×D3211yescharacteristic
603Q16—361no—
604SD16—182no—
605SD16—361no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—41no—
609C2×C8—121no—
610C2×C8C2×D3211yescharacteristic
611C2×C8C2×D3211yescharacteristic
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—91no—
616C4⋊C4—91no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C22⋊C4—31no—
625C22⋊C4—31no—
626C22⋊C4—61no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—31no—
635C42—61no—
636C42—181no—
637C22×C3—22no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—32no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—62no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3C22×D1211yescharacteristic
654C22×C3C2×D3×D411yescharacteristic
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—22no—
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—
669C2×D3—244no—
670C2×D3—244no—
671C2×D3#90412yes—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—41no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4C2×#23511yescharacteristic
684C3×C4#100411yescharacteristic
685C3×C4#100411yescharacteristic
686C3×C4D3×#4111yescharacteristic
687Dic3—21no—
688Dic3—21no—
689Dic3—21no—
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—241no—
700Dic3—241no—
701Dic3—241no—
702C32#329611yescharacteristic, complemented, Sylow
703C23—31no—
704C23—61no—
705C23—181no—
706C23—362no—
707C23—362no—
708C23—721no—
709C23D3×D1211yescharacteristic
710Q8—61no—
711Q8—61no—
712Q8—181no—
713Q8—181no—
714D4—32no—
715D4—62no—
716D4—61no—
717D4—122no—
718D4—181no—
719D4—181no—
720D4—362no—
721D4—721no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—122no—
733C2×C4—181no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—362no—
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—62no—
751C2×C3—122no—
752C2×C3#549011yescharacteristic
753C2×C3#555411yescharacteristic
754C2×C3C2×#90411yescharacteristic
755C2×C3#575111yescharacteristic
756C2×C3D3×#13511yescharacteristic
757C2×C3#577011yescharacteristic
758D3—22no—
759D3—42no—
760D3—241no—
761D3—241no—
762D3—481no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—32no—
767C22—61no—
768C22—61no—
769C22—62no—
770C22—121no—
771C22—121no—
772C22—361no—
773C22—361no—
774C22—361no—
775C22—724no—
776C22C2×D3×D1211yescharacteristic
777C4—21no—
778C4—61no—
779C4—61no—
780C4—61no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—361no—
785C4—361no—
786C4—361no—
787C4D3×#23511yescharacteristic
788C4#6433011yescharacteristic
789C3—21no—
790C3#7884511yescharacteristic, complemented
791C3#7944011yescharacteristic, complemented
792C2—41no—
793C2—62no—
794C2—122no—
795C2—721no—
796C2D3×#90411yescharacteristic
797C2#1059467911yescharacteristic
798C2#1059507311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10595067C2
hypercenterC22×C8D32
hypocenterC32#3296
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
2. #10594939C2semidirect
3. #10592813C2semidirect
4. C3×#5113C2semidirect
5. C3×C8×#67C2semidirect
6. #10591173C2semidirect
7. #10591136C2semidirect
8. #10590946C2semidirect
9. D3×#821C2semidirect
10. #10590872C2semidirect
11. #10590848C2semidirect
12. #10590813C2semidirect
13. #10590772C2semidirect
14. #10590744C2semidirect
15. #10590675C2semidirect
20. C22×C32×C8C22semidirect
22. #64133C22semidirect
25. C3×#926C22semidirect
35. #63869C22semidirect
41. #63844C22semidirect
42. C2×#3719C22semidirect
45. #63644C22semidirect
46. #63643C22semidirect
47. C3×#830C22semidirect
51. C3×#816C22semidirect
52. C3×#816C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
57. #63566C22semidirect
72. #5113D3semidirect
74. C8×#67D3semidirect
151. C22×C3×C8C2×D3semidirect
152. C22×C3×C8C2×D3semidirect
170. #926C2×D3semidirect
211. #830C2×D3semidirect
230. #816C2×D3semidirect
231. #816C2×D3semidirect
232. Dic3⋊C8C2×D3semidirect
233. C8×Dic3C2×D3semidirect
443. C22×C8D32semidirect
702. C32#3296semidirect
790. C3#78845semidirect
791. C3#79440semidirect

Maximal subgroups

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

subgroupindex
#105950672
#105949392
#105928132
C3×#51132
C3×C8×#672
#105911732
#105911362
#105909462
D3×#8212
#105908722
#105908482
#105908132
#105907722
#105907442
#105906752
#794403
#788453