Finite Group Databasebeta

← #11887267

Subgroups — #11887267

Order 1152.

983 conjugacy classes of subgroups.

The subgroup lattice has 843 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596101C211yesmaximal, characteristic
2#10594825C211yesmaximal, characteristic, complemented
3C3×#5051C211yesmaximal, characteristic, complemented
4C3×#5043C211yesmaximal, characteristic, complemented
5#10591602C211yesmaximal, characteristic, complemented
6#10591579C211yesmaximal, characteristic, complemented
7#10591560C211yesmaximal, characteristic, complemented
8#10591539C211yesmaximal, characteristic, complemented
9#10591183C211yesmaximal, characteristic, complemented
10#10591148C211yesmaximal, characteristic, complemented
11C2×#63564C211yesmaximal, characteristic, complemented
12#10590523C211yesmaximal, characteristic, complemented
13#10590483C211yesmaximal, characteristic, complemented
14#10590451C211yesmaximal, characteristic, complemented
15#10590435C211yesmaximal, characteristic, complemented
16#81445—31nomaximal
17#80775—31nomaximal
18C2×#3832C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21#64156C2211yescharacteristic
22C4×#638C2211yescharacteristic
23#64104—21no—
24#64104C2211yescharacteristic
25#64103—21no—
26#64102C2211yescharacteristic
27#64091—21no—
28C22⋊C4×C3⋊D3—21no—
29C2×C3×#216C2211yescharacteristic, complemented
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C3×#924C2211yescharacteristic
32C22×C3×C3⋊C8C2211yescharacteristic
33#63966—21no—
34#63955—21no—
35#63872C2211yescharacteristic, complemented
36#63871C2211yescharacteristic, complemented
37#63849C2211yescharacteristic, complemented
38#63848—21no—
39#63846—21no—
40#63843C2211yescharacteristic, complemented
41C2×#3717C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C2×#3710C2211yescharacteristic, complemented
44C3×#835C2211yescharacteristic, complemented
45C3×#835C2211yescharacteristic, complemented
46C3×#835C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic
48C3×#810C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52#63572C2211yescharacteristic, complemented
53#63564C2211yescharacteristic
54#63564C2211yescharacteristic
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61#5642—31no—
62#5630—31no—
63#5630—31no—
64#5630—61no—
65#5513—31no—
66C3×#483—31no—
67C3×#467—31no—
68#5187—31no—
69#5185—31no—
70C2×#821—31no—
71C8×#67—31no—
72#5051D311yescharacteristic, complemented
73#5046—31no—
74#5043D311yescharacteristic, complemented
75C2×#809—31no—
76#4891—31no—
77#4885—31no—
78#4871—31no—
79#4866—31no—
80#4864—31no—
81#4852—31no—
82#4808—31no—
83#4807—31no—
84#4804—31no—
85#4804—31no—
86#4800—31no—
87#4800—31no—
88#4798—31no—
89#4788—31no—
90#4731—31no—
91#67⋊C8—31no—
92C23×C3⋊D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638D411yescharacteristic
96#3832—22no—
97#3832—41no—
98C2×C4⋊(C3⋊D3)—22no—
99C2×C4⋊(C3⋊D3)—21no—
100C2×C4⋊(C3⋊D3)—21no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)—41no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3—21no—
107C2×C4×C3⋊D3C2311yescharacteristic
108C22×C3×Dic3—21no—
109C2×C3×Dic6C2311yescharacteristic
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113#3757D411yescharacteristic
114#3752—21no—
115#3752—21no—
116#3752—21no—
117#3752—21no—
118#3752D411yescharacteristic
119#3750D411yescharacteristic
120C4×C3⋊Dic3C2311yescharacteristic
121C3×#217—21no—
122C3×#216—41no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C2×C3×C3⋊C8—41no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139Dic32—21no—
140Dic32—21no—
141#3717—22no—
142#3717—41no—
143#3710—41no—
144#3296—91noSylow
145C2×#239—31no—
146C2×#239—31no—
147C2×#239—61no—
148C22×D12—31no—
149C22×D12—31no—
150C22×D12—61no—
151C2×C3×Q16—31no—
152C22×C3×C8—31no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8C2×D311yescharacteristic
156C3×C22⋊Q8C2×D311yescharacteristic
157C2×C3×C4⋊C4—31no—
158#947—31no—
159#947—31no—
160#947—61no—
161#946—31no—
162Q8×Dic3—31no—
163C2×#216C2×D311yescharacteristic, complemented
164C2×#215—31no—
165C2×#215—31no—
166#929—61no—
167C4×#67—31no—
168C4×#67—31no—
169C4×#67—61no—
170#926—61no—
171C2×C4⋊Dic3C2×D311yescharacteristic
172#924C2×D311yescharacteristic
173C22×C3⋊C8C2×D311yescharacteristic
174C2×#204—31no—
175C2×#204—31no—
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178#898—61no—
179#898—61no—
180#897—31no—
181#895—31no—
182#895—31no—
183#895—61no—
184#895—61no—
185#895—61no—
186#895—62no—
187#894—61no—
188#894—61no—
189#894—62no—
190#893—31no—
191#893—31no—
192#893—61no—
193#892—31no—
194#892—31no—
195#890—31no—
196#890—31no—
197#890—61no—
198#889—61no—
199#887—31no—
200#886—61no—
201#882—61no—
202#882—61no—
203#882—62no—
204D3×C22⋊C4—61no—
205D3×C22⋊C4—61no—
206D3×C22⋊C4—62no—
207#877—61no—
208C3×#107—31no—
209C3×#106—31no—
210C3×#106—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×C22⋊C8—31no—
216#835C2×D311yescharacteristic, complemented
217#835C2×D311yescharacteristic, complemented
218#835C2×D311yescharacteristic, complemented
219#830C2×D311yescharacteristic
220#821—31no—
221#821—31no—
222#821—31no—
223#821—31no—
224#821—31no—
225#821—31no—
226(C2×D3)⋊C8—31no—
227(C2×D3)⋊C8—31no—
228Dic3⋊C8—31no—
229Dic3⋊C8—31no—
230C8×Dic3—31no—
231C8×Dic3—31no—
232#810C2×D311yescharacteristic, complemented
233#809—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#809—31no—
238#809—31no—
239#808C2×D311yescharacteristic, complemented
240#808C2×D311yescharacteristic, complemented
241#807C2×D311yescharacteristic, complemented
242C23×C32C2×D411yescharacteristic
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3—42no—
246C22×C3⋊D3—42no—
247C22×C3⋊D3—81no—
248C22×C3⋊D3C2×D411yescharacteristic
249C32×Q8—21no—
250C32×Q8—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257#638—22no—
258C2×C3⋊Dic3C2×D411yescharacteristic
259C2×C3⋊Dic3C2×D411yescharacteristic
260C2×C3⋊Dic3C2×D411yescharacteristic
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)—21no—
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—42no—
265C4⋊(C3⋊D3)—42no—
266C4⋊(C3⋊D3)—81no—
267C4⋊(C3⋊D3)#4112yes—
268C4×C3⋊D3—21no—
269C4×C3⋊D3—21no—
270C4×C3⋊D3—42no—
271C4×C3⋊D3—81no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—42no—
277C3×Dic6—21no—
278C3×Dic6—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283#552—91no—
284#546—91no—
285#488—91no—
286#483—31no—
287#482—91no—
288#478—91no—
289#467—31no—
290#465—91no—
291#464—91no—
292#452—91no—
293#450—91no—
294C4×SD16—91no—
295C8×D4—91no—
296#416—91no—
297C2×#102—91no—
298C23×D3—62no—
299C23×D3—61no—
300C23×D3—61no—
301C2×C3×Q8—21no—
302C2×C3×Q8—31no—
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×Q8C22×D311yescharacteristic
305C22×C3×C4—21no—
306C22×C3×C4—61no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—31no—
310C2×#67—31no—
311C2×#67—61no—
312C22×Dic3—21no—
313#239—62no—
314#239—62no—
315#239—122no—
316#239—121no—
317#239—121no—
318#239—122no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—62no—
326C2×D12—62no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12—62no—
330C2×D12—62no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—62no—
336C2×D12—122no—
337C2×D12—121no—
338C2×D12—121no—
339C2×D12—122no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—62no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—62no—
349C2×Dic6C22×D311yescharacteristic
350C3×Q16—121no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C2×C3×C8—121no—
356C3×C4⋊C4—22no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C22⋊C4—22no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—61no—
371#217—21no—
372#217—31no—
373#217—31no—
374#217—61no—
375#216—41no—
376#215—62no—
377#215—121no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—62no—
394(C2×D3)⋊C4—62no—
395(C2×D3)⋊C4—62no—
396(C2×D3)⋊C4—62no—
397C4⋊Dic3—21no—
398C4⋊Dic3—61no—
399C4⋊Dic3—61no—
400C4⋊Dic3—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3C22×D311yescharacteristic
403C4⋊Dic3C22×D311yescharacteristic
404C4⋊Dic3C22×D311yescharacteristic
405Dic3⋊C4—21no—
406Dic3⋊C4—31no—
407Dic3⋊C4—31no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413C4×Dic3—31no—
414C4×Dic3—31no—
415C4×Dic3—61no—
416C4×Dic3—61no—
417C4×Dic3—61no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420C2×C3⋊C8—41no—
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425#204—62no—
426#204—121no—
427D3×C8—121no—
428D3×C8—121no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32#13512yes—
432C22×C32C22×D411yescharacteristic
433C2×C3⋊D3—22no—
434C2×C3⋊D3—21no—
435C2×C3⋊D3—21no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3—41no—
438C2×C3⋊D3—41no—
439C2×C3⋊D3—41no—
440C2×C3⋊D3—41no—
441C2×C3⋊D3—41no—
442C2×C3⋊D3—84no—
443C32×C4—21no—
444C32×C4—41no—
445C32×C4—41no—
446C32×C4C2×#4111yescharacteristic
447C32×C4H(5,𝔽2)11yescharacteristic
448C3⋊Dic3—21no—
449C3⋊Dic3—21no—
450C3⋊Dic3—21no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C2×#41—91no—
456C22×D4—91no—
457C2×Q16—31no—
458C2×SD16—91no—
459C2×SD16—91no—
460C22×C8—31no—
461C22×C8—91no—
462#126—181no—
463#125—91no—
464#125—181no—
465#124—91no—
466#123—181no—
467#123—181no—
468C22⋊Q8—31no—
469C22⋊Q8—91no—
470C22⋊Q8D3211yescharacteristic
471#121—91no—
472#121—181no—
473#120—181no—
474C4×Q8—91no—
475C4×D4—91no—
476C4×D4—91no—
477#117—91no—
478#117—181no—
479C2×C4⋊C4—31no—
480C2×C22⋊C4—181no—
481#107—31no—
482#106—31no—
483#106—31no—
484C4⋊C8—91no—
485#103—31no—
486#103—31no—
487#103—31no—
488#103—31no—
489#102—91no—
490#102—91no—
491#102—91no—
492#102—91no—
493#102—91no—
494#102—91no—
495C22⋊C8—31no—
496C22⋊C8—91no—
497C4×C8—91no—
498C23×C3—21no—
499C23×C3D3×D411yescharacteristic
500C23×C3D3×D411yescharacteristic
501C22×D3—31no—
502C22×D3—31no—
503C22×D3—61no—
504C22×D3—62no—
505C22×D3—61no—
506C22×D3—61no—
507C22×D3—62no—
508C22×D3—61no—
509C22×D3—61no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—124no—
513C22×D3—124no—
514C22×D3—122no—
515C22×D3—122no—
516C22×D3—241no—
517C22×D3—241no—
518C22×D3—242no—
519C3×Q8—21no—
520C3×Q8—21no—
521C3×Q8—21no—
522C3×Q8—21no—
523C3×Q8—41no—
524C3×Q8—41no—
525C3×Q8—61no—
526C3×Q8—61no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—122no—
546C2×C3×C4D3×D411yescharacteristic
547C2×C3×C4D3×D411yescharacteristic
548C2×C3×C4C23×D311yescharacteristic
549C2×C3×C4C23×D311yescharacteristic
550#67—62no—
551#67—62no—
552#67—122no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—42no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567D12—32no—
568D12—32no—
569D12—62no—
570D12—62no—
571D12—61no—
572D12—61no—
573D12—61no—
574D12—61no—
575D12—61no—
576D12—61no—
577D12—121no—
578D12—121no—
579D12—122no—
580D12—122no—
581D12—122no—
582D12—122no—
583D12—124no—
584D12—124no—
585D12—241no—
586D12—241no—
587D12—242no—
588C4×D3—61no—
589C4×D3—61no—
590C4×D3—61no—
591C4×D3—61no—
592C4×D3—121no—
593C4×D3—121no—
594C4×D3—122no—
595C4×D3—122no—
596C4×D3—124no—
597C4×D3—241no—
598C4×D3—241no—
599C4×D3—242no—
600Dic6—21no—
601Dic6—21no—
602C3×C8—61no—
603C3×C8—61no—
604C3×C8—61no—
605C3×C8—61no—
606C3⋊C8—21no—
607C3⋊C8—21no—
608C3⋊C8—21no—
609C3⋊C8—21no—
610C2×C32—22no—
611C2×C32#54611yescharacteristic
612C2×C32C2×#13511yescharacteristic
613C2×C32#57711yescharacteristic
614C3⋊D3—42no—
615C3⋊D3—41no—
616C3⋊D3—81no—
617C24—181no—
618#41—182no—
619#41—361no—
620C2×Q8—31no—
621C2×Q8C2×D3211yescharacteristic
622C2×D4—91no—
623C2×D4—91no—
624C2×D4—91no—
625C2×D4—182no—
626C2×D4—181no—
627C2×D4—181no—
628C2×D4—181no—
629C2×D4—361no—
630C22×C4—61no—
631C22×C4—91no—
632C22×C4—181no—
633C22×C4—181no—
634C22×C4C2×D3211yescharacteristic
635Q16—121no—
636SD16—182no—
637SD16—361no—
638C2×C8—31no—
639C2×C8—31no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—121no—
643C2×C8—361no—
644C4⋊C4—21no—
645C4⋊C4—31no—
646C4⋊C4—31no—
647C4⋊C4—31no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—91no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4C2×D3211yescharacteristic
656C22⋊C4—21no—
657C22⋊C4—61no—
658C22⋊C4—91no—
659C22⋊C4—91no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C42—91no—
667C42—181no—
668C42—181no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—22no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3#91612yes—
678C22×C3#91912yes—
679C22×C3C2×D3×D411yescharacteristic
680C22×C3C2×D3×D411yescharacteristic
681C2×D3—64no—
682C2×D3—61no—
683C2×D3—62no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—62no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—122no—
694C2×D3—122no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—122no—
700C2×D3—122no—
701C2×D3—122no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—244no—
709C2×D3—244no—
710C2×D3—248no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—41no—
716C3×C4—42no—
717C3×C4—42no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4#100411yescharacteristic
727C3×C4D3×#4111yescharacteristic
728C3×C4D3×#4111yescharacteristic
729C3×C4#100911yescharacteristic
730Dic3—41no—
731Dic3—41no—
732Dic3—41no—
733Dic3—41no—
734Dic3—61no—
735Dic3—61no—
736Dic3—61no—
737Dic3—61no—
738Dic3—61no—
739Dic3—61no—
740Dic3—121no—
741Dic3—121no—
742Dic3—121no—
743C32#329611yescharacteristic, complemented, Sylow
744C23—91no—
745C23—181no—
746C23—181no—
747C23—362no—
748C23—362no—
749C23—721no—
750C23#381111yescharacteristic
751Q8—21no—
752Q8—21no—
753Q8—61no—
754Q8—61no—
755D4—92no—
756D4—182no—
757D4—181no—
758D4—181no—
759D4—181no—
760D4—362no—
761D4—362no—
762D4—721no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—91no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—122no—
775C2×C4—181no—
776C2×C4—181no—
777C2×C4—362no—
778C2×C4—721no—
779C2×C4#381111yescharacteristic
780C2×C4C22×D3211yescharacteristic
781C8—61no—
782C8—61no—
783C8—61no—
784C8—61no—
785C2×C3—22no—
786C2×C3—22no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—42no—
791C2×C3#561011yescharacteristic
792C2×C3#565411yescharacteristic
793C2×C3C2×#91611yescharacteristic
794C2×C3C2×#91911yescharacteristic
795C2×C3#577011yescharacteristic
796C2×C3#577811yescharacteristic
797D3—124no—
798D3—121no—
799D3—122no—
800D3—121no—
801D3—122no—
802D3—241no—
803D3—242no—
804D3—241no—
805D3—241no—
806C22—21no—
807C22—21no—
808C22—181no—
809C22—181no—
810C22—182no—
811C22—181no—
812C22—361no—
813C22—361no—
814C22—361no—
815C22—361no—
816C22—361no—
817C22—724no—
818C22#6395012yes—
819C22C2×#381111yescharacteristic
820C4—21no—
821C4—41no—
822C4—41no—
823C4—121no—
824C4—121no—
825C4—121no—
826C4—121no—
827C4—181no—
828C4—181no—
829C4—181no—
830C4#6431211yescharacteristic
831C4#6431411yescharacteristic
832C3—21no—
833C3#8077511yescharacteristic, complemented
834C3#8144511yescharacteristic, complemented
835C2—22no—
836C2—361no—
837C2—362no—
838C2—721no—
839C2#1059516311yescharacteristic
840C2C2×#6395011yescharacteristic
841C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10596101C2
hypercenterC22⋊Q8D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10594825C2semidirect
3. C3×#5051C2semidirect
4. C3×#5043C2semidirect
5. #10591602C2semidirect
6. #10591579C2semidirect
7. #10591560C2semidirect
8. #10591539C2semidirect
9. #10591183C2semidirect
10. #10591148C2semidirect
11. C2×#63564C2semidirect
12. #10590523C2semidirect
13. #10590483C2semidirect
14. #10590451C2semidirect
15. #10590435C2semidirect
29. C2×C3×#216C22semidirect
35. #63872C22semidirect
36. #63871C22semidirect
37. #63849C22semidirect
40. #63843C22semidirect
43. C2×#3710C22semidirect
44. C3×#835C22semidirect
45. C3×#835C22semidirect
46. C3×#835C22semidirect
48. C3×#810C22semidirect
49. C3×#808C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. #63572C22semidirect
59. #63557C22semidirect
60. #63553C22semidirect
72. #5051D3semidirect
74. #5043D3semidirect
163. C2×#216C2×D3semidirect
216. #835C2×D3semidirect
217. #835C2×D3semidirect
218. #835C2×D3semidirect
232. #810C2×D3semidirect
239. #808C2×D3semidirect
240. #808C2×D3semidirect
241. #807C2×D3semidirect
743. C32#3296semidirect
833. C3#80775semidirect
834. C3#81445semidirect

Maximal subgroups

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

subgroupindex
#105961012
#105948252
C3×#50512
C3×#50432
#105916022
#105915792
#105915602
#105915392
#105911832
#105911482
C2×#635642
#105905232
#105904832
#105904512
#105904352
#814453
#807753