Finite Group Databasebeta

← #11887224

Subgroups — #11887224

Order 1152.

892 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#10595078C211yesmaximal, characteristic
2#10594939C211yesmaximal, characteristic, complemented
3#10592432C211yesmaximal, characteristic, complemented
4C3×#4737C211yesmaximal, characteristic, complemented
5C3×#67⋊C8C211yesmaximal, characteristic, complemented
6#10591175C211yesmaximal, characteristic, complemented
7#10591105C211yesmaximal, characteristic, complemented
8#10590946C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590863C211yesmaximal, characteristic, complemented
11#10590861C211yesmaximal, characteristic, complemented
12#10590852C211yesmaximal, characteristic, complemented
13#10590774C211yesmaximal, characteristic, complemented
14#10590758C211yesmaximal, characteristic, complemented
15#10590674C211yesmaximal, characteristic, complemented
16#81381—31nomaximal
17#79440—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20#64133C2211yescharacteristic, complemented
21C2×#3746C2211yescharacteristic, complemented
22C2×#3744C2211yescharacteristic
23C3×#930C2211yescharacteristic
24C3×C4×#67C2211yescharacteristic
25C3×#926C2211yescharacteristic, complemented
26C22×C3×C3⋊C8C2211yescharacteristic, complemented
27C2×C3×D3×C8C2211yescharacteristic
28#63983—21no—
29#63969—21no—
30#63958—21no—
31#63956—21no—
32#63921—21no—
33#63894C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic
35#63877—21no—
36#63869C2211yescharacteristic, complemented
37#63867—21no—
38#63860C2211yescharacteristic
39#63857C2211yescharacteristic
40#63857C2211yescharacteristic
41#63853—21no—
42#63844C2211yescharacteristic, complemented
43C2×#3716C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63643C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#818C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63563C2211yescharacteristic
61#5612—31no—
62#5550—31no—
63#5541—31no—
64#5529—31no—
65C3×#482—31no—
66C3×C8×D4—31no—
67#5116—31no—
68#5114—31no—
69#5113—31no—
70C2×#821—31no—
71#5041—31no—
72#5002—31no—
73#4891—31no—
74#4887—31no—
75#4862—31no—
76#4852—31no—
77#4847—31no—
78#4845—31no—
79#4776—31no—
80D3×#102—31no—
81#4768—31no—
82#4767—31no—
83#4737D311yescharacteristic, complemented
84#4733—31no—
85#4733—31no—
86#4733—61no—
87#4731—31no—
88#67⋊C8D311yescharacteristic, complemented
89#4721—31no—
90#4697—31no—
91C4×#204—31no—
92C22×D32—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95#3828—22no—
96#3828—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×#634C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×#626—21no—
106C2×#624—21no—
107C2×D3×Dic3—21no—
108D3×D12—22no—
109D3×D12—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112#3757—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3746—41no—
116#3744—22no—
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4D411yescharacteristic
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8—41no—
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—
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3716—41no—
144#3296—91noSylow
145C2×D3×D4—31no—
146C2×#235—31no—
147C2×#235—31no—
148C2×#235—61no—
149C22×D12—31no—
150C22×C3×C8—31no—
151C22×C3×C8—31no—
152C3×#121—31no—
153C3×C4×D4—31no—
154C3×#117—31no—
155#938—61no—
156#937—61no—
157#937—61no—
158#936—31no—
159#935—61no—
160C2×#214—31no—
161#930C2×D311yescharacteristic
162C4×#67C2×D311yescharacteristic
163#926C2×D311yescharacteristic, complemented
164C2×C4⋊Dic3—31no—
165#924—31no—
166#924—31no—
167#924—31no—
168#924—31no—
169#924—61no—
170C22×C3⋊C8C2×D311yescharacteristic, complemented
171C2×Dic12—31no—
172C2×Dic12—31no—
173C2×Dic12—61no—
174C2×#204—31no—
175C2×#204—31no—
176C2×#204—31no—
177C2×#204—61no—
178C2×D3×C8C2×D311yescharacteristic
179#897—31no—
180#897—31no—
181#894—61no—
182#893—31no—
183D3×C4⋊C4—31no—
184#890—31no—
185#889—61no—
186#887—31no—
187#884—61no—
188#883—61no—
189#883—61no—
190D3×C22⋊C4—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×#107—31no—
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—21no—
207C3×C22⋊C8—31no—
208C3×C22⋊C8C2×D311yescharacteristic, complemented
209C3×C22⋊C8C2×D311yescharacteristic, complemented
210C3×C4×C8—31no—
211#832—31no—
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#818C2×D311yescharacteristic, complemented
222#817—31no—
223#817C2×D311yescharacteristic, complemented
224#816—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—61no—
230Dic3⋊C8C2×D311yescharacteristic, complemented
231C8×Dic3C2×D311yescharacteristic, complemented
232#810—31no—
233#810—31no—
234#810—31no—
235#809—31no—
236#809—31no—
237#808—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—42no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)#4112yes—
255C4×C3⋊D3—42no—
256#634—21no—
257#634—21no—
258#634—21no—
259#634—21no—
260C3×#67—22no—
261C3×#67—81no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
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#626—42no—
273#624—81no—
274D3×Dic3—42no—
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—31no—
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—91no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C22×C3×C4—21no—
300C22×C3×C4—31no—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C2×#67—21no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—121no—
308C2×#67D1211yescharacteristic
309C22×Dic3—61no—
310D3×D4—62no—
311D3×D4—121no—
312#235—62no—
313#235—62no—
314#235—122no—
315#235—121no—
316#235—121no—
317#235—122no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—61no—
321C2×D12—62no—
322C2×D12—61no—
323C2×D12—121no—
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—121no—
331C2×C4×D3C22×D311yescharacteristic
332C2×Dic6—31no—
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—121no—
343C2×C3×C8—121no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—31no—
357C3×C42—61no—
358#217—21no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—121no—
366#217D1211yescharacteristic
367#214—121no—
368(C2×D3)⋊C4—21no—
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)⋊C4D1211yescharacteristic
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3C22×D311yescharacteristic
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—121no—
397Dic3⋊C4D1211yescharacteristic
398C4×Dic3—21no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—41no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—121no—
406Dic12—121no—
407Dic12—122no—
408#204—62no—
409#204—62no—
410#204—122no—
411#204—121no—
412D3×C8—41no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—22no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3#13512yes—
426D32—84no—
427C32×C4—21no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—41no—
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—91no—
441C2×Q16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C22×C8—31no—
445C22×C8—31no—
446#126—181no—
447#125—91no—
448#125—181no—
449#124—91no—
450#123—181no—
451#123—181no—
452C22⋊Q8—91no—
453C22⋊Q8—91no—
454C22⋊Q8—91no—
455#121—31no—
456#121—181no—
457#120—181no—
458C4×Q8—91no—
459C4×D4—31no—
460C4×D4—91no—
461#117—31no—
462#117—181no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—181no—
465#107—31no—
466#106—31no—
467#106—91no—
468C4⋊C8—31no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8D3211yescharacteristic, complemented
481C4×C8—31no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—61no—
485C23×C3C2×D1211yescharacteristic
486C23×C3D3×D411yescharacteristic
487C22×D3—21no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—121no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—241no—
496C22×D3—241no—
497C22×D3C2×D1211yescharacteristic
498C3×D4—62no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4—241no—
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×C4C2×D1211yescharacteristic
519C2×C3×C4D3×D411yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522#67—22no—
523#67—81no—
524#67—122no—
525#67—122no—
526#67—122no—
527#67—124no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—122no—
541C2×Dic3C2×D1211yescharacteristic
542C2×Dic3C2×D1211yescharacteristic
543C2×Dic3C2×D1211yescharacteristic
544D12—21no—
545D12—21no—
546D12—32no—
547D12—32no—
548D12—62no—
549D12—61no—
550D12—61no—
551D12—121no—
552D12—122no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3—124no—
558C4×D3—122no—
559C4×D3—241no—
560C4×D3—241no—
561Dic6—62no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—61no—
570Dic6—121no—
571Dic6—121no—
572Dic6—121no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—41no—
578C3×C8—41no—
579C3×C8—61no—
580C3×C8—61no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C2×C32—41no—
584C2×C32#54611yescharacteristic
585C2×C32C2×#13511yescharacteristic
586C2×C32#57711yescharacteristic
587C3⋊D3—42no—
588C3×D3—22no—
589C3×D3—81no—
590C24—181no—
591#41—182no—
592#41—361no—
593C2×Q8—91no—
594C2×Q8—91no—
595C2×D4—31no—
596C2×D4—31no—
597C2×D4—61no—
598C2×D4—91no—
599C2×D4—181no—
600C2×D4—182no—
601C2×D4—181no—
602C2×D4—361no—
603C22×C4—31no—
604C22×C4—181no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4C2×D3211yescharacteristic
608Q16—361no—
609SD16—182no—
610SD16—361no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—121no—
614C2×C8—121no—
615C2×C8C2×D3211yescharacteristic
616C2×C8C2×D3211yescharacteristic
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—91no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C22⋊C4—31no—
630C22⋊C4—31no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C42—31no—
640C42—61no—
641C42—181no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—32no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3C22×D1211yescharacteristic
659C22×C3C2×D3×D411yescharacteristic
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—62no—
666C2×D3—62no—
667C2×D3—122no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—241no—
673C2×D3—241no—
674C2×D3—244no—
675C2×D3—244no—
676C2×D3#90412yes—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—41no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4#100411yescharacteristic
689C3×C4D3×#4111yescharacteristic
690C3×C4D3×#4111yescharacteristic
691C3×C4#100911yescharacteristic
692Dic3—21no—
693Dic3—21no—
694Dic3—21no—
695Dic3—41no—
696Dic3—41no—
697Dic3—41no—
698Dic3—122no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—241no—
706Dic3—241no—
707C32#329611yescharacteristic, complemented, Sylow
708C23—31no—
709C23—61no—
710C23—181no—
711C23—362no—
712C23—362no—
713C23—721no—
714C23D3×D1211yescharacteristic
715Q8—181no—
716Q8—181no—
717Q8—181no—
718Q8—181no—
719D4—62no—
720D4—61no—
721D4—61no—
722D4—92no—
723D4—181no—
724D4—241no—
725D4—362no—
726D4—362no—
727C2×C4—21no—
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—181no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—362no—
741C2×C4—362no—
742C2×C4—721no—
743C2×C4D3×D1211yescharacteristic
744C2×C4C22×D3211yescharacteristic
745C8—21no—
746C8—21no—
747C8—61no—
748C8—61no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—41no—
753C2×C3—41no—
754C2×C3—62no—
755C2×C3—81no—
756C2×C3—241no—
757C2×C3#555411yescharacteristic
758C2×C3#565411yescharacteristic
759C2×C3C2×#90411yescharacteristic
760C2×C3#575111yescharacteristic
761C2×C3D3×#13511yescharacteristic
762C2×C3#577511yescharacteristic
763D3—22no—
764D3—81no—
765D3—122no—
766D3—122no—
767D3—242no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—32no—
772C22—61no—
773C22—61no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—182no—
778C22—361no—
779C22—361no—
780C22—724no—
781C22C2×D3×D1211yescharacteristic
782C4—21no—
783C4—61no—
784C4—61no—
785C4—61no—
786C4—121no—
787C4—121no—
788C4—121no—
789C4—361no—
790C4—361no—
791C4—361no—
792C4#6431211yescharacteristic
793C4#6431411yescharacteristic
794C3—21no—
795C3#7944011yescharacteristic, complemented
796C3#8138111yescharacteristic, complemented
797C2—41no—
798C2—62no—
799C2—241no—
800C2—362no—
801C2#1059429311yescharacteristic
802C2D3×#90411yescharacteristic
803C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595078C2
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. #10592432C2semidirect
4. C3×#4737C2semidirect
5. C3×#67⋊C8C2semidirect
6. #10591175C2semidirect
7. #10591105C2semidirect
8. #10590946C2semidirect
9. D3×#821C2semidirect
10. #10590863C2semidirect
11. #10590861C2semidirect
12. #10590852C2semidirect
13. #10590774C2semidirect
14. #10590758C2semidirect
15. #10590674C2semidirect
20. #64133C22semidirect
21. C2×#3746C22semidirect
25. C3×#926C22semidirect
26. C22×C3×C3⋊C8C22semidirect
36. #63869C22semidirect
42. #63844C22semidirect
44. C32×C22⋊C8C22semidirect
46. #63643C22semidirect
50. C3×#818C22semidirect
51. C3×#817C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63573C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63567C22semidirect
83. #4737D3semidirect
88. #67⋊C8D3semidirect
163. #926C2×D3semidirect
170. C22×C3⋊C8C2×D3semidirect
208. C3×C22⋊C8C2×D3semidirect
209. C3×C22⋊C8C2×D3semidirect
221. #818C2×D3semidirect
223. #817C2×D3semidirect
230. Dic3⋊C8C2×D3semidirect
231. C8×Dic3C2×D3semidirect
480. C22⋊C8D32semidirect
707. C32#3296semidirect
795. C3#79440semidirect
796. C3#81381semidirect

Maximal subgroups

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

subgroupindex
#105950782
#105949392
#105924322
C3×#47372
C3×#67⋊C82
#105911752
#105911052
#105909462
D3×#8212
#105908632
#105908612
#105908522
#105907742
#105907582
#105906742
#813813
#794403