Finite Group Databasebeta

← #11889401

Subgroups — #11889401

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 777 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596012C211yesmaximal, characteristic
2C3×D4×Dic6C211yesmaximal, characteristic
3C3×#5011C211yesmaximal, characteristic
4#10591187C211yesmaximal, characteristic, complemented
5#10591186C211yesmaximal, characteristic, complemented
6#10591186C211yesmaximal, characteristic, complemented
7#10591127C211yesmaximal, characteristic, complemented
8#10591126C211yesmaximal, characteristic, complemented
9#10591121C211yesmaximal, characteristic, complemented
10#10591100C211yesmaximal, characteristic, complemented
11C2×#63566C211yesmaximal, characteristic, complemented
12#10590388C211yesmaximal, characteristic, complemented
13#10590383C211yesmaximal, characteristic, complemented
14#10590302C211yesmaximal, characteristic, complemented
15#10590289C211yesmaximal, characteristic, complemented
16#83552—31nomaximal
17#79511—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21#64144—21no—
22#64135C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24#64133C2211yescharacteristic
25#64133C2211yescharacteristic
26#64098—21no—
27#64088—21no—
28#64086—21no—
29#64079C2211yescharacteristic
30C4×#634C2211yescharacteristic
31C3×D4×Dic3—21no—
32C3×#924C2211yescharacteristic
33C3×#924C2211yescharacteristic
34C2×C3×#208C2211yescharacteristic
35C22×C3×C3⋊C8C2211yescharacteristic
36C3×#888—21no—
37C3×#878—21no—
38C3×#878—21no—
39C3×#869C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C2×#3719C2211yescharacteristic
44C3×#830C2211yescharacteristic
45C3×#830C2211yescharacteristic
46C3×C4⋊(C3⋊C8)C2211yescharacteristic
47C3×#803C2211yescharacteristic
48#63575C2211yescharacteristic
49#63573C2211yescharacteristic
50#63573C2211yescharacteristic
51#63567C2211yescharacteristic
52#63566C2211yescharacteristic
53#63566C2211yescharacteristic
54#63566C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61C3×D4×Q8—31no—
62#5541—31no—
63#5541—31no—
64#5541—61no—
65D4×Dic6D311yescharacteristic
66C3×#435—31no—
67#5228—31no—
68#5228—31no—
69#5225—31no—
70C2×#835—31no—
71#5137—31no—
72#5120—31no—
73#5116—31no—
74C2×#816—31no—
75#5090—31no—
76#5082—31no—
77#5052—31no—
78#5051—31no—
79#5045—31no—
80#5043—31no—
81#5030—31no—
82#5022—31no—
83#5011D311yescharacteristic
84#4849—31no—
85#4829—31no—
86#4739—31no—
87#4739—31no—
88#4723—31no—
89#4721—31no—
90#4716—31no—
91#4703—31no—
92C2×C32×D4D411yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×#634C2311yescharacteristic
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C2×C3×Dic6—22no—
100C2×C3×Dic6—22no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6—41no—
104C2×C3×Dic6—41no—
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C32×C4⋊C4D411yescharacteristic
109C32×C22⋊C4D411yescharacteristic
110C32×C22⋊C4D411yescharacteristic
111C32×C42C2311yescharacteristic
112#3757—21no—
113#3757—21no—
114#3757—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120#3750—21no—
121#3750—21no—
122#3750—21no—
123#3750—21no—
124C4×C3⋊Dic3—21no—
125C4×C3⋊Dic3—21no—
126C3×#217—21no—
127C3×#217—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3—21no—
135C3×#208—41no—
136C2×C3×C3⋊C8—41no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3719—22no—
142#3719—41no—
143#3719—41no—
144#3312—91noSylow
145C22×C3×Q8—31no—
146C22×C3×Q8—31no—
147C22×Dic6C2×D311yescharacteristic
148C22×Dic6C2×D311yescharacteristic
149C2×C3×M16—31no—
150C22×C3×C8—31no—
151C3×C4⋊Q8—31no—
152C3×C4⋊Q8—61no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—61no—
156C3×C22⋊Q8—61no—
157C3×C4×Q8—31no—
158C3×C4×D4—21no—
159C3×C4×D4—61no—
160C3×C4×D4C2×D311yescharacteristic
161C3×C4×D4C2×D311yescharacteristic
162C2×#216—31no—
163C2×#216—31no—
164C2×#216—31no—
165#935—62no—
166#935—61no—
167#935—61no—
168D4×Dic3—21no—
169#926—31no—
170#926—31no—
171#926—61no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—61no—
175#924—31no—
176#924—31no—
177#924—31no—
178#924—31no—
179#924—61no—
180#924—61no—
181#924C2×D311yescharacteristic
182#924C2×D311yescharacteristic
183C2×#208C2×D311yescharacteristic
184C22×C3⋊C8C2×D311yescharacteristic
185C2×Dic12—31no—
186C2×Dic12—31no—
187C2×Dic12—31no—
188#889—62no—
189#889—61no—
190#889—61no—
191#888—21no—
192#879—62no—
193#879—61no—
194#879—61no—
195#878—21no—
196#878—21no—
197#877—62no—
198#877—61no—
199#877—61no—
200#870—31no—
201#870—31no—
202#870—61no—
203#869C2×D311yescharacteristic
204C4×Dic6—31no—
205C4×Dic6—31no—
206C4×Dic6—61no—
207C4×Dic6C2×D311yescharacteristic
208C3×C4⋊C8—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8—31no—
211C3×#97—31no—
212#835—31no—
213#835—31no—
214#835—31no—
215#835—31no—
216#835—31no—
217#835—31no—
218#835—31no—
219#835—31no—
220#835—31no—
221#830C2×D311yescharacteristic
222#830C2×D311yescharacteristic
223#818—31no—
224#817—31no—
225#817—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232#816—31no—
233#816—31no—
234#816—31no—
235#816—31no—
236#810—31no—
237#808—31no—
238#808—31no—
239#807—31no—
240C4⋊(C3⋊C8)C2×D311yescharacteristic
241#803C2×D311yescharacteristic
242C23×C32C2×D411yescharacteristic
243C23×C32C2×D411yescharacteristic
244C32×D4—22no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—42no—
259#634—21no—
260#634—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—42no—
266C2×C3×Dic3—42no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—42no—
273C3×Dic6—42no—
274C3×Dic6#4112yes—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280D4×Q8—31no—
281#491—91no—
282#485—91no—
283#483—91no—
284#479—91no—
285#470—91no—
286#467—91no—
287#462—91no—
288#451—91no—
289#451—91no—
290#441—91no—
291#435—31no—
292#419—91no—
293C2×#103—91no—
294C2×C3×Q8—31no—
295C2×C3×Q8—31no—
296C2×C3×Q8—31no—
297C2×C3×Q8—62no—
298C2×C3×Q8—62no—
299C2×C3×Q8—61no—
300C2×C3×Q8—61no—
301C2×C3×Q8—121no—
302C2×C3×Q8—121no—
303C2×C3×D4—21no—
304C2×C3×D4D1211yescharacteristic
305C2×C3×D4#6711yescharacteristic
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—62no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C2×Dic6—22no—
320C2×Dic6—22no—
321C2×Dic6—21no—
322C2×Dic6—21no—
323C2×Dic6—31no—
324C2×Dic6—31no—
325C2×Dic6—41no—
326C2×Dic6—41no—
327C2×Dic6—61no—
328C2×Dic6C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C3×M16—121no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—121no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4D1211yescharacteristic
345C3×C4⋊C4#6711yescharacteristic
346C3×C22⋊C4—21no—
347C3×C22⋊C4—21no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4D1211yescharacteristic
351C3×C22⋊C4D1211yescharacteristic
352C3×C22⋊C4#6711yescharacteristic
353C3×C22⋊C4#6711yescharacteristic
354C3×C42—21no—
355C3×C42—61no—
356C3×C42C22×D311yescharacteristic
357C3×C42C22×D311yescharacteristic
358#217—21no—
359#217—21no—
360#217—62no—
361#217—62no—
362#217—62no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—61no—
369#216—62no—
370#216—121no—
371#216—121no—
372C4⋊Dic3—21no—
373C4⋊Dic3—21no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—62no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—62no—
391Dic3⋊C4—62no—
392Dic3⋊C4—62no—
393Dic3⋊C4—62no—
394Dic3⋊C4—62no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405C4×Dic3—21no—
406C4×Dic3—62no—
407C4×Dic3—62no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—61no—
411C4×Dic3—61no—
412#208—41no—
413C2×C3⋊C8—41no—
414C2×C3⋊C8C22×D311yescharacteristic
415C2×C3⋊C8C22×D311yescharacteristic
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418Dic12—62no—
419Dic12—121no—
420Dic12—121no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32#13712yes—
427C22×C32C22×D411yescharacteristic
428C32×C4—21no—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4—21no—
432C32×C4C2×#4111yescharacteristic
433C32×C4H(5,𝔽2)11yescharacteristic
434C3⋊Dic3—41no—
435C3⋊Dic3—41no—
436C3⋊Dic3—41no—
437C3⋊Dic3—41no—
438C3×Dic3—22no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C22×Q8—31no—
443C22×Q8—31no—
444C2×Q16—91no—
445C2×Q16—91no—
446C2×Q16—91no—
447C2×M16—31no—
448C22×C8—31no—
449C4⋊Q8—31no—
450C4⋊Q8—61no—
451#126—181no—
452#125—91no—
453#125—181no—
454#123—181no—
455C22⋊Q8—31no—
456C22⋊Q8—31no—
457C22⋊Q8—61no—
458C22⋊Q8—61no—
459C22⋊Q8—91no—
460C22⋊Q8—91no—
461C4×Q8—31no—
462C4×Q8—91no—
463C4×D4—61no—
464C4×D4D3211yescharacteristic
465#117—91no—
466#117—181no—
467C2×C4⋊C4—91no—
468#107—91no—
469#106—91no—
470#106—91no—
471C4⋊C8—31no—
472#103—91no—
473#103—91no—
474#103—91no—
475#103—91no—
476#103—91no—
477#103—91no—
478#103—91no—
479#103—91no—
480#103—91no—
481#103—91no—
482C22⋊C8—31no—
483C22⋊C8—31no—
484#97—31no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3C2×D1211yescharacteristic
488C23×C3C2×D1211yescharacteristic
489C23×C3C2×#6711yescharacteristic
490C23×C3C2×#6711yescharacteristic
491C3×Q8—32no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×Q8—122no—
498C3×Q8—122no—
499C3×D4—22no—
500C3×D4—22no—
501C3×D4—42no—
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—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—122no—
524C2×C3×C4—122no—
525C2×C3×C4C2×D1211yescharacteristic
526C2×C3×C4C2×D1211yescharacteristic
527C2×C3×C4C2×D1211yescharacteristic
528C2×C3×C4C2×D1211yescharacteristic
529C2×C3×C4C2×#6711yescharacteristic
530C2×C3×C4C2×#6711yescharacteristic
531C2×C3×C4C2×#6711yescharacteristic
532C2×C3×C4C2×#6711yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—42no—
540C2×Dic3—42no—
541C2×Dic3—62no—
542C2×Dic3—62no—
543C2×Dic3—62no—
544C2×Dic3—62no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—124no—
554C2×Dic3—122no—
555C2×Dic3—122no—
556Dic6—21no—
557Dic6—21no—
558Dic6—21no—
559Dic6—21no—
560Dic6—21no—
561Dic6—42no—
562Dic6—42no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—61no—
567Dic6—121no—
568Dic6—121no—
569Dic6#23712yes—
570C3×C8—61no—
571C3×C8—61no—
572C3×C8—61no—
573C3×C8—61no—
574C3⋊C8—21no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C2×C32—22no—
579C2×C32—41no—
580C2×C32#54611yescharacteristic
581C2×C32C2×#13711yescharacteristic
582C2×C32#57811yescharacteristic
583C2×Q8—31no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×Q8—62no—
587C2×Q8—62no—
588C2×Q8—61no—
589C2×Q8—61no—
590C2×Q8—91no—
591C2×Q8—121no—
592C2×Q8—121no—
593C2×D4#62611yescharacteristic
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—181no—
597C22×C4C2×D3211yescharacteristic
598C22×C4C2×D3211yescharacteristic
599Q16—182no—
600Q16—361no—
601Q16—361no—
602M16—121no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8—31no—
607C2×C8—121no—
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—91no—
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#62611yescharacteristic
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4#62611yescharacteristic
630C22⋊C4#62611yescharacteristic
631C42—61no—
632C42—181no—
633C42—181no—
634C42C2×D3211yescharacteristic
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—22no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3#90912yes—
653C22×C3#94212yes—
654C22×C3C22×D1211yescharacteristic
655C22×C3C22×#6711yescharacteristic
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—62no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4C2×#23711yescharacteristic
675C3×C4#100411yescharacteristic
676C3×C4#100411yescharacteristic
677C3×C4D3×#4111yescharacteristic
678Dic3—22no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3—122no—
683Dic3—122no—
684Dic3—122no—
685Dic3—122no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694C32#331211yescharacteristic, complemented, Sylow
695C23C2×#62611yescharacteristic
696C23C2×#62611yescharacteristic
697Q8—32no—
698Q8—61no—
699Q8—61no—
700Q8—61no—
701Q8—61no—
702Q8—61no—
703Q8—122no—
704Q8—122no—
705Q8—181no—
706Q8—181no—
707D4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—122no—
717C2×C4—122no—
718C2×C4—181no—
719C2×C4—181no—
720C2×C4—181no—
721C2×C4—181no—
722C2×C4—362no—
723C2×C4C2×#62611yescharacteristic
724C2×C4C2×#62611yescharacteristic
725C2×C4C2×#62611yescharacteristic
726C2×C4C2×#62611yescharacteristic
727C2×C4C22×D3211yescharacteristic
728C8—61no—
729C8—61no—
730C8—61no—
731C8—61no—
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—41no—
739C2×C3—41no—
740C2×C3—81no—
741C2×C3#555411yescharacteristic
742C2×C3C2×#90911yescharacteristic
743C2×C3#575311yescharacteristic
744C2×C3#580611yescharacteristic
745C2×C3C2×#94211yescharacteristic
746C2×C3#583811yescharacteristic
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22#6383312yes—
753C22C22×#62611yescharacteristic
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—62no—
759C4—121no—
760C4—121no—
761C4—121no—
762C4—361no—
763C4—361no—
764C4—361no—
765C4—361no—
766C4D3×#23711yescharacteristic
767C4#6431311yescharacteristic
768C3—21no—
769C3#7951111yescharacteristic, complemented
770C3#8355211yescharacteristic, complemented
771C2—22no—
772C2—41no—
773C2C2×#6383311yescharacteristic
774C2#1059524611yescharacteristic
775C2#1059545011yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
4. #10591187C2semidirect
5. #10591186C2semidirect
6. #10591186C2semidirect
7. #10591127C2semidirect
8. #10591126C2semidirect
9. #10591121C2semidirect
10. #10591100C2semidirect
11. C2×#63566C2semidirect
12. #10590388C2semidirect
13. #10590383C2semidirect
14. #10590302C2semidirect
15. #10590289C2semidirect
694. C32#3312semidirect
769. C3#79511semidirect
770. C3#83552semidirect

Maximal subgroups

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

subgroupindex
#105960122
C3×D4×Dic62
C3×#50112
#105911872
#105911862
#105911272
#105911262
#105911212
#105911002
C2×#635662
#105903882
#105903832
#105903022
#105902892
#835523
#795113