Finite Group Databasebeta

← #14729813

Subgroups — #14729813

Order 2816.

1000 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079176C211yesmaximal, characteristic, complemented
2#13078616C211yesmaximal, characteristic, complemented
3#13078071C211yesmaximal, characteristic, complemented
4#13067900C211yesmaximal, characteristic, complemented
5#13067886C211yesmaximal, characteristic, complemented
6#13067844C211yesmaximal, characteristic, complemented
7#13067830C211yesmaximal, characteristic, complemented
8#13067726C211yesmaximal, characteristic, complemented
9#13067705C211yesmaximal, characteristic, complemented
10#13067699C211yesmaximal, characteristic, complemented
11#13067688C211yesmaximal, characteristic, complemented
12#13067273C211yesmaximal, characteristic, complemented
13#13066998C211yesmaximal, characteristic, complemented
14C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
15C11×#3475C211yesmaximal, characteristic, complemented
16C11×#556C2211yescharacteristic
17C11×#555C2211yescharacteristic
18C11×#554C2211yescharacteristic
19C11×#553—21no—
20C11×#552—21no—
21C11×#552—21no—
22C11×#551—22no—
23C11×#547C2211yescharacteristic
24C11×#546—21no—
25C11×#533C2211yescharacteristic
26C11×#529—22no—
27C11×#529—21no—
28C11×#525—21no—
29C4×C11×#41—21no—
30C4×C11×#41C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C11×#117—21no—
33C2×#67003—21no—
34#10623008C2211yescharacteristic
35#10622830—21no—
36#10622701C2211yescharacteristic, complemented
37#10622698C2211yescharacteristic, complemented
38#10622694C2211yescharacteristic, complemented
39#10622692C2211yescharacteristic, complemented
40#10622661—22no—
41#10622644C2211yescharacteristic, complemented
42#10622641—21no—
43#10622640C2211yescharacteristic, complemented
44C4×#4325—22no—
45#10622632C2211yescharacteristic, complemented
46#10622629—21no—
47#10622628C2211yescharacteristic
48#10622628C2211yescharacteristic
49#10622628C2211yescharacteristic, complemented
50C4×#4323—21no—
51C4×#4323—21no—
52#10622620C2211yescharacteristic
53#10622620C2211yescharacteristic
54#10622615—21no—
55#10622580—21no—
56#10622538C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic
58C2×C4×C11⋊C8C2211yescharacteristic
59#10622185C2211yescharacteristic, complemented
60#10622185C2211yescharacteristic, complemented
61#10622184C2211yescharacteristic, complemented
62#10622184C2211yescharacteristic, complemented
63Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
64Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
65D4⋊(C11⋊C8)C2211yescharacteristic
66D4⋊(C11⋊C8)C2211yescharacteristic
67D4⋊(C11⋊C8)C2211yescharacteristic
68D4⋊(C11⋊C8)C2211yescharacteristic
69D4⋊(C11⋊C8)C2211yescharacteristic, complemented
70D4⋊(C11⋊C8)C2211yescharacteristic, complemented
71C2×C11×#41—21no—
72C2×C11×#41D411yescharacteristic
73C22×D4×C11D411yescharacteristic
74C23×C4×C11—21no—
75C2×#4339—21no—
76C11×C4⋊Q8C2311yescharacteristic
77C11×C4⋊Q8C2311yescharacteristic
78C11×#126—22no—
79C11×#126—22no—
80C11×#126—22no—
81C11×#125—22no—
82C11×#125—21no—
83C11×#125—21no—
84C11×#124—22no—
85C11×#124—21no—
86C11×#123—22no—
87C11×#123—22no—
88C11×#123—22no—
89C11×#123—22no—
90C11×C22⋊Q8—21no—
91C11×C22⋊Q8—21no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—21no—
94C11×C22⋊Q8—21no—
95C11×C22⋊Q8D412yes—
96C11×#121—22no—
97C11×#121—21no—
98C11×#121—21no—
99C11×#121—21no—
100C11×#120—22no—
101C4×Q8×C11—21no—
102C4×Q8×C11—21no—
103C4×Q8×C11D411yescharacteristic
104C4×Q8×C11D412yes—
105C4×Q8×C11C2311yescharacteristic
106C4×D4×C11—22no—
107C4×D4×C11—22no—
108C4×D4×C11—22no—
109C4×D4×C11—21no—
110C4×D4×C11—21no—
111C4×D4×C11—21no—
112C4×D4×C11—21no—
113C4×D4×C11—21no—
114C4×D4×C11D411yescharacteristic
115C4×D4×C11D411yescharacteristic
116C4×D4×C11D411yescharacteristic
117C4×D4×C11C2311yescharacteristic
118C4×D4×C11C2311yescharacteristic
119C4×D4×C11C2311yescharacteristic
120C11×#117—22no—
121C11×#117—22no—
122C11×#117—22no—
123C11×#117—21no—
124C11×#117—21no—
125C11×#117—21no—
126C11×#117—21no—
127C11×#117—21no—
128C11×#117D411yescharacteristic
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4D411yescharacteristic
132C2×C11×C22⋊C4—22no—
133C2×C11×C22⋊C4—21no—
134C2×C42×C11—22no—
135C2×C42×C11—21no—
136C2×C42×C11C2311yescharacteristic
137#67003—44no—
138C2×#4326—21no—
139C2×#4325—21no—
140C2×#4325—22no—
141C2×#4324—21no—
142C2×#4323—21no—
143C2×#4323—21no—
144C2×#4323—21no—
145#66983—21no—
146#66983—21no—
147C22×C11⋊C8—21no—
148C22×C11⋊C8—21no—
149#66928—21no—
150#66927C2311yescharacteristic
151C4×D44—21no—
152C4×D44—21no—
153#66922C2311yescharacteristic
154#66899—22no—
155#66896—21no—
156#66896—21no—
157C22⋊(C11⋊C8)—21no—
158#66874—21no—
159#66874—21no—
160#66873—21no—
161#66873—21no—
162#66873—21no—
163#66873—21no—
164#66873—22no—
165#66872—22no—
166#66871—21no—
167#66871—21no—
168C4⋊(C11⋊C8)—21no—
169C4⋊(C11⋊C8)C2311yescharacteristic
170C4⋊(C11⋊C8)C2311yescharacteristic
171C4⋊(C11⋊C8)C2311yescharacteristic
172C4⋊(C11⋊C8)C2311yescharacteristic
173C4×C11⋊C8—21no—
174C4×C11⋊C8—21no—
175C4×C11⋊C8C2311yescharacteristic
176C4×C11⋊C8C2311yescharacteristic
177#18522—111nomaximal, Sylow
178C24×C11—21no—
179C11×#41—22no—
180C11×#41—22no—
181C11×#41—42no—
182C11×#41—42no—
183C2×Q8×C11—21no—
184C2×Q8×C11C2×D411yescharacteristic
185C2×Q8×C11C2×D412yes—
186C2×D4×C11—22no—
187C2×D4×C11—22no—
188C2×D4×C11—21no—
189C2×D4×C11—22no—
190C2×D4×C11—21no—
191C2×D4×C11—41no—
192C2×D4×C11C2×D411yescharacteristic
193C2×D4×C11C2×D411yescharacteristic
194C2×D4×C11C2×D411yescharacteristic
195C22×C4×C11—22no—
196C22×C4×C11—21no—
197C22×C4×C11—22no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—42no—
206C22×C4×C11—42no—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C2×C22⋊D11—41no—
211#4339—42no—
212#4339—42no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—21no—
216C2×C4×D11—41no—
217C2×Dic22—21no—
218C11×C4⋊C4—22no—
219C11×C4⋊C4—22no—
220C11×C4⋊C4—22no—
221C11×C4⋊C4—22no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—22no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—22no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4C2×D411yescharacteristic
231C11×C4⋊C4C2×D411yescharacteristic
232C11×C4⋊C4C2×D412yes—
233C11×C4⋊C4C2×D411yescharacteristic
234C11×C4⋊C4C2×D411yescharacteristic
235C11×C22⋊C4—22no—
236C11×C22⋊C4—22no—
237C11×C22⋊C4—22no—
238C11×C22⋊C4—22no—
239C11×C22⋊C4—22no—
240C11×C22⋊C4—22no—
241C11×C22⋊C4—21no—
242C11×C22⋊C4—22no—
243C11×C22⋊C4—21no—
244C11×C22⋊C4—21no—
245C11×C22⋊C4—21no—
246C11×C22⋊C4—21no—
247C11×C22⋊C4—21no—
248C11×C22⋊C4—21no—
249C42×C11—22no—
250C42×C11—22no—
251C42×C11—21no—
252C42×C11—22no—
253C42×C11—21no—
254C42×C11—21no—
255C42×C11C2×D411yescharacteristic
256C42×C11C2×D411yescharacteristic
257C42×C11C2×D411yescharacteristic
258C42×C11C2411yescharacteristic
259#4326—42no—
260#4325—42no—
261#4325—44no—
262#4324—42no—
263#4323—42no—
264#4323—42no—
265#4323—42no—
266(C2×D11)⋊C4—41no—
267(C2×D11)⋊C4—41no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—42no—
277C2×C11⋊C8—42no—
278#3475D1111yescharacteristic, complemented
279#3167—111no—
280#3100—111no—
281#3035—111no—
282#1654—111no—
283#1652—111no—
284#1646—111no—
285#1644—111no—
286#1628—111no—
287#1625—111no—
288#1624—111no—
289#1622—111no—
290#1542—111no—
291#1476—111no—
292C2×D4⋊C8—111no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11—81no—
299C23×C11#12011yescharacteristic
300C22×D11—41no—
301Q8×C11—21no—
302Q8×C11—21no—
303Q8×C11—42no—
304Q8×C11—41no—
305Q8×C11—41no—
306D4×C11—21no—
307D4×C11—21no—
308D4×C11—21no—
309D4×C11—21no—
310D4×C11—21no—
311D4×C11—42no—
312D4×C11—44no—
313D4×C11—42no—
314D4×C11—82no—
315D4×C11#13512yescomplemented
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—21no—
325C2×C4×C11—41no—
326C2×C4×C11—44no—
327C2×C4×C11—42no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11—42no—
337C2×C4×C11—81no—
338C2×C4×C11—82no—
339C2×C4×C11#12011yescharacteristic
340C2×C4×C11#12011yescharacteristic
341C2×C4×C11#12011yescharacteristic
342C2×C4×C11#13512yes—
343C2×C4×C11AGL(1,ℤ/8)12yes—
344C2×C4×C11C22×D411yescharacteristic
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C22×D411yescharacteristic
347C22⋊D11—82no—
348C2×Dic11—41no—
349D44—42no—
350D44—41no—
351D44—41no—
352D44—41no—
353D44—41no—
354C4×D11—82no—
355Dic22—41no—
356Dic22—41no—
357C11⋊C8—22no—
358C11⋊C8—41no—
359C11⋊C8—41no—
360C11⋊C8—41no—
361C11⋊C8—41no—
362C11⋊C8—41no—
363C2×#135—221no—
364#556C2×D1111yescharacteristic
365#555C2×D1111yescharacteristic
366#554C2×D1111yescharacteristic
367#553—21no—
368#552—21no—
369#552—21no—
370#551—22no—
371#547C2×D1111yescharacteristic
372#546—21no—
373#533C2×D1111yescharacteristic
374#532—111no—
375#529—22no—
376#529—21no—
377#525—21no—
378C4×#41—21no—
379C4×#41C2×D1111yescharacteristic
380C2×C4×D4C2×D1111yescharacteristic
381C2×#117—21no—
382#498—111no—
383#492—111no—
384#487—111no—
385#486—111no—
386#480—221no—
387#474—111no—
388#474—111no—
389#465—222no—
390#464—221no—
391#463—221no—
392#462—111no—
393#461—111no—
394#460—111no—
395#459—111no—
396#459—111no—
397#459—111no—
398#447—221no—
399C4×SD16—222no—
400C4×D8—221no—
401C4×D8—221no—
402#431—111no—
403C2×C4⋊C8—111no—
404#416—221no—
405C2×C4×C8—111no—
406#333—111no—
407#333—111no—
408#332—111no—
409#332—111no—
410Q8⋊C8—111no—
411Q8⋊C8—111no—
412D4⋊C8—111no—
413D4⋊C8—111no—
414D4⋊C8—111no—
415D4⋊C8—111no—
416D4⋊C8—111no—
417D4⋊C8—111no—
418C22×C11—21no—
419C22×C11—21no—
420C22×C11—22no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—84no—
430C22×C11#44912yes—
431C22×C11C2×#12011yescharacteristic
432C2×D11—81no—
433C2×D11—81no—
434C2×D11—81no—
435C4×C11—21no—
436C4×C11—21no—
437C4×C11—21no—
438C4×C11—41no—
439C4×C11—41no—
440C4×C11—41no—
441C4×C11—41no—
442C4×C11—42no—
443C4×C11—41no—
444C4×C11—42no—
445C4×C11#44912yes—
446C4×C11C2×#13511yescharacteristic
447C4×C11C2×#13511yescharacteristic
448C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
449C4×C11#57511yescharacteristic
450Dic11—81no—
451C2×#41—21no—
452C2×#41—221no—
453C2×#41C22⋊D1111yescharacteristic
454C22×D4C22⋊D1111yescharacteristic
455C23×C4—21no—
456#135—444no—
457C2×Q16—221no—
458C2×SD16—221no—
459C2×SD16—222no—
460C2×SD16—221no—
461C2×D8—221no—
462C2×D8—221no—
463C2×D8—221no—
464C22×C8—221no—
465C22×C8—221no—
466C4⋊Q8—111no—
467C4⋊Q8C22×D1111yescharacteristic
468C4⋊Q8C22×D1111yescharacteristic
469#127—111no—
470#126—22no—
471#126—22no—
472#126—22no—
473#125—22no—
474#125—21no—
475#125—21no—
476#124—22no—
477#124—21no—
478#124—221no—
479#123—22no—
480#123—22no—
481#123—22no—
482#123—22no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8—22no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8C22⋊D1112yes—
489#121—22no—
490#121—21no—
491#121—21no—
492#121—21no—
493#121—221no—
494#121—221no—
495#120—22no—
496C4×Q8—21no—
497C4×Q8—21no—
498C4×Q8C22⋊D1111yescharacteristic
499C4×Q8C22⋊D1112yes—
500C4×Q8C22×D1111yescharacteristic
501C4×D4—22no—
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—221no—
510C4×D4—221no—
511C4×D4C22⋊D1111yescharacteristic
512C4×D4C22⋊D1111yescharacteristic
513C4×D4C22⋊D1111yescharacteristic
514C4×D4C22×D1111yescharacteristic
515C4×D4C22×D1111yescharacteristic
516C4×D4C22×D1111yescharacteristic
517#117—22no—
518#117—22no—
519#117—22no—
520#117—21no—
521#117—21no—
522#117—21no—
523#117—21no—
524#117—21no—
525#117C22⋊D1111yescharacteristic
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4C22⋊D1111yescharacteristic
529C2×C22⋊C4—22no—
530C2×C22⋊C4—21no—
531C2×C42—22no—
532C2×C42—21no—
533C2×C42C22×D1111yescharacteristic
534#107—221no—
535#107—221no—
536#106—222no—
537C4⋊C8—111no—
538C4⋊C8—111no—
539C4⋊C8—111no—
540C4⋊C8—111no—
541C4⋊C8—221no—
542#103—222no—
543#103—221no—
544#103—221no—
545#102—221no—
546#102—221no—
547#102—221no—
548#102—221no—
549#102—221no—
550#102—221no—
551#102—222no—
552C22⋊C8—221no—
553C4×C8—111no—
554C4×C8—111no—
555C4×C8—221no—
556C4×C8—221no—
557C2×C11—22no—
558C2×C11—42no—
559C2×C11—81no—
560C2×C11—81no—
561C2×C11C2×#44911yescharacteristic
562C2×C11#300211yescharacteristic
563C2×C11#301811yescharacteristic
564D11—161no—
565C24—21no—
566#41—22no—
567#41—22no—
568#41—42no—
569#41—42no—
570#41—442no—
571#41—442no—
572C2×Q8—21no—
573C2×Q8—221no—
574C2×Q8C2×C22⋊D1111yescharacteristic
575C2×Q8C2×C22⋊D1112yes—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—41no—
582C2×D4—221no—
583C2×D4—221no—
584C2×D4—221no—
585C2×D4—441no—
586C2×D4C2×C22⋊D1111yescharacteristic
587C2×D4C2×C22⋊D1111yescharacteristic
588C2×D4C2×C22⋊D1111yescharacteristic
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—441no—
602C22×C4C2×C22⋊D1111yescharacteristic
603C22×C4C2×C22⋊D1111yescharacteristic
604C22×C4C2×C22⋊D1111yescharacteristic
605Q16—442no—
606SD16—444no—
607SD16—442no—
608SD16—442no—
609D8—442no—
610D8—442no—
611D8—442no—
612C2×C8—221no—
613C2×C8—221no—
614C2×C8—221no—
615C2×C8—221no—
616C2×C8—221no—
617C2×C8—221no—
618C2×C8—442no—
619C2×C8—442no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—21no—
627C4⋊C4—22no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—221no—
633C4⋊C4—221no—
634C4⋊C4C2×C22⋊D1111yescharacteristic
635C4⋊C4C2×C22⋊D1111yescharacteristic
636C4⋊C4C2×C22⋊D1112yes—
637C4⋊C4C2×C22⋊D1111yescharacteristic
638C4⋊C4C2×C22⋊D1111yescharacteristic
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—21no—
646C22⋊C4—22no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—441no—
654C22⋊C4—441no—
655C42—22no—
656C42—22no—
657C42—21no—
658C42—21no—
659C42—22no—
660C42—21no—
661C42C2×C22⋊D1111yescharacteristic
662C42C2×C22⋊D1111yescharacteristic
663C42C2×C22⋊D1111yescharacteristic
664C42C23×D1111yescharacteristic
665C11#1852211yescharacteristic, complemented, Sylow
666C23—21no—
667C23—21no—
668C23—21no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—441no—
673C23#6700611yescharacteristic
674Q8—21no—
675Q8—21no—
676Q8—42no—
677Q8—41no—
678Q8—41no—
679Q8—441no—
680Q8—441no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—42no—
687D4—44no—
688D4—42no—
689D4—82no—
690D4—442no—
691D4—441no—
692D4—441no—
693D4—441no—
694D4—441no—
695D4—882no—
696D4#6700312yescomplemented
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—41no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—81no—
719C2×C4—82no—
720C2×C4—441no—
721C2×C4—882no—
722C2×C4#6700212yes—
723C2×C4#6700312yes—
724C2×C4#6700611yescharacteristic
725C2×C4#6700611yescharacteristic
726C2×C4#6700611yescharacteristic
727C2×C4C22×C22⋊D1111yescharacteristic
728C2×C4C22×C22⋊D1111yescharacteristic
729C2×C4C22×C22⋊D1111yescharacteristic
730C8—222no—
731C8—441no—
732C8—441no—
733C8—441no—
734C8—441no—
735C8—441no—
736C22—21no—
737C22—21no—
738C22—22no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—84no—
748C22—881no—
749C22—881no—
750C22—881no—
751C22#1062285112yes—
752C22C2×#6700611yescharacteristic
753C4—21no—
754C4—21no—
755C4—21no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—42no—
761C4—41no—
762C4—42no—
763C4—881no—
764C4#1062285112yes—
765C4C2×#6700211yescharacteristic
766C4C2×#6700311yescharacteristic
767C4C2×#6700311yescharacteristic
768C4#1062335311yescharacteristic
769C2—22no—
770C2—42no—
771C2—81no—
772C2—81no—
773C2—1761no—
774C2C2×#1062285111yescharacteristic
775C2#1307783411yescharacteristic
776C2#1307796511yescharacteristic
subgroupG/H
centerC2×C4#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3475C2
socleC22×C11C2×#120
hypercenter#3475D11
hypocenterC11#18522
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. #13079176C2semidirect
2. #13078616C2semidirect
3. #13078071C2semidirect
4. #13067900C2semidirect
5. #13067886C2semidirect
6. #13067844C2semidirect
7. #13067830C2semidirect
8. #13067726C2semidirect
9. #13067705C2semidirect
10. #13067699C2semidirect
11. #13067688C2semidirect
12. #13067273C2semidirect
13. #13066998C2semidirect
14. C2×D4⋊(C11⋊C8)C2semidirect
15. C11×#3475C2semidirect
36. #10622701C22semidirect
37. #10622698C22semidirect
38. #10622694C22semidirect
39. #10622692C22semidirect
41. #10622644C22semidirect
43. #10622640C22semidirect
45. #10622632C22semidirect
49. #10622628C22semidirect
59. #10622185C22semidirect
60. #10622185C22semidirect
61. #10622184C22semidirect
62. #10622184C22semidirect
63. Q8⋊(C11⋊C8)C22semidirect
64. Q8⋊(C11⋊C8)C22semidirect
69. D4⋊(C11⋊C8)C22semidirect
70. D4⋊(C11⋊C8)C22semidirect
278. #3475D11semidirect
315. D4×C11#135semidirect
665. C11#18522semidirect
696. D4#67003semidirect

Maximal subgroups

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

subgroupindex
#130791762
#130786162
#130780712
#130679002
#130678862
#130678442
#130678302
#130677262
#130677052
#130676992
#130676882
#130672732
#130669982
C2×D4⋊(C11⋊C8)2
C11×#34752
#1852211