Finite Group Databasebeta

← #14730971

Subgroups — #14730971

Order 2816.

998 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079953C211yesmaximal, characteristic, complemented
2#13078938C211yesmaximal, characteristic, complemented
3#13078715C211yesmaximal, characteristic, complemented
4#13067844C211yesmaximal, characteristic, complemented
5#13067844C211yesmaximal, characteristic, complemented
6#13067830C211yesmaximal, characteristic, complemented
7#13067823C211yesmaximal, characteristic, complemented
8#13067816C211yesmaximal, characteristic, complemented
9#13067809C211yesmaximal, characteristic, complemented
10#13067795C211yesmaximal, characteristic, complemented
11#13067795C211yesmaximal, characteristic, complemented
12#13067311C211yesmaximal, characteristic, complemented
13#13067076C211yesmaximal, characteristic, complemented
14C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
15C11×#3519C211yesmaximal, characteristic
16C11×#555C2211yescharacteristic
17C11×#554C2211yescharacteristic
18C11×#553—21no—
19C11×#553—21no—
20C11×#550C2211yescharacteristic
21C11×#546—22no—
22C11×#546—21no—
23D42×C11—21no—
24D42×C11C2211yescharacteristic
25C11×#540—21no—
26C11×#538—22no—
27C11×#532C2211yescharacteristic
28C11×#529C2211yescharacteristic
29C11×#525—21no—
30C2×C11×#121—21no—
31C11×#518—21no—
32C2×C4×D4×C11C2211yescharacteristic
33#10623001C2211yescharacteristic, complemented
34#10622846—22no—
35#10622831—21no—
36#10622694C2211yescharacteristic, complemented
37#10622694C2211yescharacteristic, complemented
38#10622683C2211yescharacteristic, complemented
39#10622683C2211yescharacteristic, complemented
40#10622676—21no—
41#10622669—22no—
42#10622667—21no—
43#10622664—21no—
44#10622654—21no—
45#10622644C2211yescharacteristic, complemented
46#10622633C2211yescharacteristic, complemented
47#10622632C2211yescharacteristic
48#10622632C2211yescharacteristic, complemented
49#10622632C2211yescharacteristic, complemented
50#10622631—21no—
51#10622631—21no—
52#10622620C2211yescharacteristic
53#10622620C2211yescharacteristic, complemented
54#10622620C2211yescharacteristic, complemented
55#10622583—21no—
56#10622539C2211yescharacteristic, complemented
57C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
58C2×C4×C11⋊C8C2211yescharacteristic, complemented
59#10622184C2211yescharacteristic, complemented
60#10622184C2211yescharacteristic, complemented
61#10622182C2211yescharacteristic, complemented
62#10622182C2211yescharacteristic, complemented
63Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
64Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
65D4⋊(C11⋊C8)C2211yescharacteristic
66D4⋊(C11⋊C8)C2211yescharacteristic
67D4⋊(C11⋊C8)C2211yescharacteristic, complemented
68D4⋊(C11⋊C8)C2211yescharacteristic, complemented
69D4⋊(C11⋊C8)C2211yescharacteristic, complemented
70D4⋊(C11⋊C8)C2211yescharacteristic, complemented
71C2×C11×#41—21no—
72C2×C11×#41D412yes—
73C22×D4×C11—22no—
74C22×D4×C11—21no—
75C22×D4×C11—21no—
76C22×D4×C11D411yescharacteristic
77C23×C4×C11—21no—
78C11×C4⋊Q8C2311yescharacteristic
79C11×#127—21no—
80C11×#127C2311yescharacteristic
81C11×#126—22no—
82C11×#126—21no—
83C11×#125—21no—
84C11×#125D411yescharacteristic
85C11×#124—22no—
86C11×#124D411yescharacteristic
87C11×#124D412yes—
88C11×#123—22no—
89C11×#123—22no—
90C11×#123—22no—
91C11×#123—21no—
92C11×C22⋊Q8—21no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8D411yescharacteristic
95C11×#121—22no—
96C11×#121—22no—
97C11×#121—22no—
98C11×#121—22no—
99C11×#121—21no—
100C11×#121—22no—
101C11×#121—21no—
102C11×#121—21no—
103C11×#121—21no—
104C11×#121—21no—
105C11×#121—21no—
106C11×#121—21no—
107C11×#121D411yescharacteristic
108C11×#120—22no—
109C11×#120—22no—
110C11×#120—22no—
111C4×Q8×C11C2311yescharacteristic
112C4×D4×C11—22no—
113C4×D4×C11—22no—
114C4×D4×C11—22no—
115C4×D4×C11—21no—
116C4×D4×C11—21no—
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C4×D4×C11—21no—
120C4×D4×C11—21no—
121C4×D4×C11—21no—
122C4×D4×C11D411yescharacteristic
123C4×D4×C11D411yescharacteristic
124C4×D4×C11C2311yescharacteristic
125C4×D4×C11C2311yescharacteristic
126C4×D4×C11C2311yescharacteristic
127C11×#117—21no—
128C11×#117—21no—
129C11×#117—21no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4D411yescharacteristic
132C2×C11×C22⋊C4—22no—
133C2×C11×C22⋊C4—22no—
134C2×C11×C22⋊C4—21no—
135C2×C42×C11C2311yescharacteristic
136C2×#4326—21no—
137C2×#4324—21no—
138C2×#4324—21no—
139C2×#4324—21no—
140#66979—21no—
141#66977—21no—
142#66977—21no—
143C22×C11⋊C8—21no—
144C22×C11⋊C8—21no—
145#66923—21no—
146#66922C2311yescharacteristic
147#66922C2311yescharacteristic
148C4×Dic22—21no—
149C4×Dic22—21no—
150#66899—22no—
151#66899—22no—
152#66899—21no—
153#66896—21no—
154#66896—21no—
155#66896—22no—
156#66896—22no—
157#66896—21no—
158C22⋊(C11⋊C8)—21no—
159#66874—21no—
160#66874—21no—
161#66874—21no—
162#66874—21no—
163#66872—21no—
164#66871—21no—
165#66871—21no—
166#66871—21no—
167C4⋊(C11⋊C8)—21no—
168C4⋊(C11⋊C8)C2311yescharacteristic
169C4⋊(C11⋊C8)C2311yescharacteristic
170C4⋊(C11⋊C8)C2311yescharacteristic
171C4⋊(C11⋊C8)C2311yescharacteristic
172#66867—21no—
173C4×C11⋊C8—21no—
174C4×C11⋊C8C2311yescharacteristic
175C4×C11⋊C8C2311yescharacteristic
176#18628—111nomaximal, Sylow
177C24×C11—22no—
178C24×C11—21no—
179C11×#41—44no—
180C11×#41—81no—
181C11×#41—81no—
182C2×Q8×C11C2×D411yescharacteristic
183C2×Q8×C11C2×D412yes—
184C2×D4×C11—22no—
185C2×D4×C11—22no—
186C2×D4×C11—22no—
187C2×D4×C11—21no—
188C2×D4×C11—22no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11—41no—
196C2×D4×C11—42no—
197C2×D4×C11—42no—
198C2×D4×C11—81no—
199C2×D4×C11—81no—
200C2×D4×C11—84no—
201C2×D4×C11C2×D411yescharacteristic
202C2×D4×C11C2×D411yescharacteristic
203C2×D4×C11C2×D411yescharacteristic
204C2×D4×C11C2×D412yes—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—22no—
213C22×C4×C11—21no—
214C22×C4×C11—81no—
215C22×C4×C11—81no—
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C2×Dic22—21no—
220C2×Dic22—21no—
221C11×C4⋊C4—22no—
222C11×C4⋊C4—22no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
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×D411yescharacteristic
233C11×C4⋊C4C2×D411yescharacteristic
234C11×C22⋊C4—22no—
235C11×C22⋊C4—22no—
236C11×C22⋊C4—22no—
237C11×C22⋊C4—22no—
238C11×C22⋊C4—22no—
239C11×C22⋊C4—21no—
240C11×C22⋊C4—21no—
241C11×C22⋊C4—21no—
242C11×C22⋊C4—21no—
243C11×C22⋊C4—22no—
244C11×C22⋊C4—21no—
245C11×C22⋊C4—21no—
246C11×C22⋊C4—22no—
247C11×C22⋊C4—21no—
248C11×C22⋊C4—21no—
249C11×C22⋊C4—21no—
250C42×C11—22no—
251C42×C11—21no—
252C42×C11C2×D411yescharacteristic
253C42×C11C2×D411yescharacteristic
254C42×C11C2×D411yescharacteristic
255C42×C11C2411yescharacteristic
256C22⋊Dic11—41no—
257#4326—81no—
258#4324—42no—
259#4324—42no—
260#4324—81no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265Dic11⋊C4—41no—
266Dic11⋊C4—41no—
267C4×Dic11—41no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—42no—
275C2×C11⋊C8—81no—
276#3519D1111yescharacteristic
277#3248—111no—
278#3131—111no—
279#3110—111no—
280#1646—111no—
281#1646—111no—
282#1644—111no—
283#1643—111no—
284#1642—111no—
285#1641—111no—
286#1639—111no—
287#1639—111no—
288#1551—111no—
289#1494—111no—
290C2×D4⋊C8—111no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—22no—
295C23×C11—42no—
296C23×C11—44no—
297C23×C11—42no—
298C23×C11—81no—
299C23×C11—82no—
300C23×C11—82no—
301C23×C11#12011yescharacteristic
302Q8×C11—21no—
303Q8×C11—21no—
304Q8×C11—42no—
305D4×C11—21no—
306D4×C11—21no—
307D4×C11—21no—
308D4×C11—21no—
309D4×C11—21no—
310D4×C11—42no—
311D4×C11—42no—
312D4×C11—44no—
313D4×C11—42no—
314D4×C11—44no—
315D4×C11—41no—
316D4×C11—41no—
317D4×C11—41no—
318D4×C11—41no—
319D4×C11—82no—
320D4×C11—82no—
321D4×C11—82no—
322D4×C11—82no—
323D4×C11#13512yes—
324C2×C4×C11—22no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—22no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—81no—
342C2×C4×C11—81no—
343C2×C4×C11—82no—
344C2×C4×C11—81no—
345C2×C4×C11—82no—
346C2×C4×C11—82no—
347C2×C4×C11#12011yescharacteristic
348C2×C4×C11#12011yescharacteristic
349C2×C4×C11#12011yescharacteristic
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C22×D411yescharacteristic
353C2×Dic11—41no—
354C2×Dic11—41no—
355Dic22—41no—
356Dic22—41no—
357Dic22—41no—
358Dic22—41no—
359C11⋊C8—41no—
360C11⋊C8—41no—
361C11⋊C8—41no—
362C11⋊C8—41no—
363C11⋊C8—41no—
364C11⋊C8—41no—
365#555C2×D1111yescharacteristic
366#554C2×D1111yescharacteristic
367#553—21no—
368#553—21no—
369#550C2×D1111yescharacteristic
370#546—22no—
371#546—21no—
372D42—21no—
373D42C2×D1111yescharacteristic
374#540—21no—
375#538—22no—
376#533—111no—
377#532C2×D1111yescharacteristic
378#529C2×D1111yescharacteristic
379#525—21no—
380C2×#121—21no—
381#518—21no—
382C2×C4×D4C2×D1111yescharacteristic
383#488—222no—
384#487—111no—
385#487—111no—
386#486—111no—
387#486—111no—
388#484—221no—
389#479—221no—
390#475—111no—
391#474—111no—
392#474—111no—
393#474—111no—
394#467—221no—
395#465—221no—
396#464—221no—
397#462—111no—
398#461—111no—
399#461—111no—
400#461—111no—
401#450—221no—
402#440—221no—
403#440—221no—
404#432—111no—
405C2×C4⋊C8—111no—
406#416—222no—
407C2×C4×C8—111no—
408#333—111no—
409#333—111no—
410#331—111no—
411#331—111no—
412Q8⋊C8—111no—
413Q8⋊C8—111no—
414D4⋊C8—111no—
415D4⋊C8—111no—
416D4⋊C8—111no—
417D4⋊C8—111no—
418D4⋊C8—111no—
419D4⋊C8—111no—
420C22×C11—21no—
421C22×C11—21no—
422C22×C11—22no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—42no—
428C22×C11—41no—
429C22×C11—42no—
430C22×C11—41no—
431C22×C11—42no—
432C22×C11—41no—
433C22×C11—41no—
434C22×C11—84no—
435C22×C11—164no—
436C22×C11#45512yes—
437C22×C11C2×#12011yescharacteristic
438C4×C11—21no—
439C4×C11—21no—
440C4×C11—21no—
441C4×C11—21no—
442C4×C11—41no—
443C4×C11—41no—
444C4×C11—41no—
445C4×C11—41no—
446C4×C11—41no—
447C4×C11—42no—
448C4×C11C2×#13511yescharacteristic
449C4×C11#57511yescharacteristic
450C4×C11#57611yescharacteristic
451C4×C11#57711yescharacteristic
452Dic11—81no—
453Dic11—81no—
454C2×#41—21no—
455C2×#41C22⋊D1112yes—
456C22×D4—22no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C22⋊D1111yescharacteristic
460C23×C4—21no—
461C2×Q16—221no—
462C2×SD16—221no—
463C2×SD16—221no—
464C2×SD16—221no—
465C22×C8—221no—
466C22×C8—221no—
467C4⋊Q8—111no—
468C4⋊Q8—111no—
469C4⋊Q8C22×D1111yescharacteristic
470#127—21no—
471#127C22×D1111yescharacteristic
472#126—22no—
473#126—21no—
474#125—21no—
475#125—221no—
476#125C22⋊D1111yescharacteristic
477#124—22no—
478#124C22⋊D1111yescharacteristic
479#124C22⋊D1112yes—
480#123—22no—
481#123—22no—
482#123—22no—
483#123—21no—
484C22⋊Q8—21no—
485C22⋊Q8—22no—
486C22⋊Q8—221no—
487C22⋊Q8—221no—
488C22⋊Q8C22⋊D1111yescharacteristic
489#121—22no—
490#121—22no—
491#121—22no—
492#121—22no—
493#121—21no—
494#121—22no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121—21no—
500#121—21no—
501#121C22⋊D1111yescharacteristic
502#120—22no—
503#120—22no—
504#120—22no—
505C4×Q8—221no—
506C4×Q8—221no—
507C4×Q8C22×D1111yescharacteristic
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4C22⋊D1111yescharacteristic
519C4×D4C22⋊D1111yescharacteristic
520C4×D4C22×D1111yescharacteristic
521C4×D4C22×D1111yescharacteristic
522C4×D4C22×D1111yescharacteristic
523#117—21no—
524#117—21no—
525#117—21no—
526#117—221no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4C22⋊D1111yescharacteristic
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—21no—
532C2×C42C22×D1111yescharacteristic
533#107—221no—
534#107—221no—
535#107—221no—
536#106—221no—
537C4⋊C8—111no—
538C4⋊C8—111no—
539C4⋊C8—111no—
540C4⋊C8—111no—
541C4⋊C8—221no—
542#103—222no—
543#103—222no—
544#103—221no—
545#103—221no—
546#103—221no—
547#103—221no—
548#103—221no—
549#102—222no—
550#102—222no—
551#102—221no—
552#102—221no—
553#102—221no—
554C22⋊C8—221no—
555#97—221no—
556C4×C8—111no—
557C4×C8—111no—
558C4×C8—221no—
559C2×C11—22no—
560C2×C11—42no—
561C2×C11—81no—
562C2×C11—82no—
563C2×C11—81no—
564C2×C11#300211yescharacteristic
565C2×C11#301211yescharacteristic
566C2×C11C2×#45511yescharacteristic
567C24—22no—
568C24—21no—
569#41—44no—
570#41—81no—
571#41—81no—
572C2×Q8—221no—
573C2×Q8—221no—
574C2×Q8C2×C22⋊D1111yescharacteristic
575C2×Q8C2×C22⋊D1112yes—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—84no—
593C2×D4C2×C22⋊D1111yescharacteristic
594C2×D4C2×C22⋊D1111yescharacteristic
595C2×D4C2×C22⋊D1111yescharacteristic
596C2×D4C2×C22⋊D1112yes—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4C2×C22⋊D1111yescharacteristic
609C22×C4C2×C22⋊D1111yescharacteristic
610C22×C4C2×C22⋊D1111yescharacteristic
611Q16—881no—
612SD16—442no—
613SD16—442no—
614SD16—881no—
615C2×C8—221no—
616C2×C8—221no—
617C2×C8—221no—
618C2×C8—221no—
619C2×C8—221no—
620C2×C8—221no—
621C2×C8—442no—
622C2×C8—881no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—221no—
633C4⋊C4—221no—
634C4⋊C4—221no—
635C4⋊C4—221no—
636C4⋊C4—441no—
637C4⋊C4—441no—
638C4⋊C4C2×C22⋊D1111yescharacteristic
639C4⋊C4C2×C22⋊D1111yescharacteristic
640C4⋊C4C2×C22⋊D1111yescharacteristic
641C4⋊C4C2×C22⋊D1111yescharacteristic
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—22no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—441no—
659C42—22no—
660C42—21no—
661C42—441no—
662C42C2×C22⋊D1111yescharacteristic
663C42C2×C22⋊D1111yescharacteristic
664C42C2×C22⋊D1111yescharacteristic
665C42C23×D1111yescharacteristic
666C11#1862811yescharacteristic, complemented, Sylow
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—42no—
672C23—44no—
673C23—42no—
674C23—81no—
675C23—82no—
676C23—82no—
677C23#6700611yescharacteristic
678Q8—21no—
679Q8—21no—
680Q8—42no—
681Q8—441no—
682Q8—441no—
683Q8—441no—
684Q8—441no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—21no—
690D4—42no—
691D4—42no—
692D4—44no—
693D4—42no—
694D4—44no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4#6700312yes—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—81no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4#6700611yescharacteristic
730C2×C4#6700611yescharacteristic
731C2×C4#6700611yescharacteristic
732C2×C4C22×C22⋊D1111yescharacteristic
733C2×C4C22×C22⋊D1111yescharacteristic
734C2×C4C22×C22⋊D1111yescharacteristic
735C8—441no—
736C8—441no—
737C8—441no—
738C8—441no—
739C8—441no—
740C8—441no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—41no—
750C22—42no—
751C22—41no—
752C22—42no—
753C22—41no—
754C22—41no—
755C22—84no—
756C22—164no—
757C22#1062285512yes—
758C22C2×#6700611yescharacteristic
759C4—21no—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—42no—
769C4—881no—
770C4—881no—
771C4C2×#6700311yescharacteristic
772C4#1062335311yescharacteristic
773C4#1062336611yescharacteristic
774C4#1062336711yescharacteristic
775C2—22no—
776C2—42no—
777C2—81no—
778C2—81no—
779C2—82no—
780C2#1307783411yescharacteristic
781C2#1307792011yescharacteristic
782C2C2×#1062285511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3519C2
socleC22×C11C2×#120
hypercenter#3519D11
hypocenterC11#18628
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3519

Complements

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

NH ≅ G/Ntype
1. #13079953C2semidirect
2. #13078938C2semidirect
3. #13078715C2semidirect
4. #13067844C2semidirect
5. #13067844C2semidirect
6. #13067830C2semidirect
7. #13067823C2semidirect
8. #13067816C2semidirect
9. #13067809C2semidirect
10. #13067795C2semidirect
11. #13067795C2semidirect
12. #13067311C2semidirect
13. #13067076C2semidirect
14. C2×D4⋊(C11⋊C8)C2semidirect
33. #10623001C22semidirect
36. #10622694C22semidirect
37. #10622694C22semidirect
38. #10622683C22semidirect
39. #10622683C22semidirect
45. #10622644C22semidirect
46. #10622633C22semidirect
48. #10622632C22semidirect
49. #10622632C22semidirect
53. #10622620C22semidirect
54. #10622620C22semidirect
56. #10622539C22semidirect
57. C2×C4⋊(C11⋊C8)C22semidirect
58. C2×C4×C11⋊C8C22semidirect
59. #10622184C22semidirect
60. #10622184C22semidirect
61. #10622182C22semidirect
62. #10622182C22semidirect
63. Q8⋊(C11⋊C8)C22semidirect
64. Q8⋊(C11⋊C8)C22semidirect
67. D4⋊(C11⋊C8)C22semidirect
68. D4⋊(C11⋊C8)C22semidirect
69. D4⋊(C11⋊C8)C22semidirect
70. D4⋊(C11⋊C8)C22semidirect
666. C11#18628semidirect

Maximal subgroups

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

subgroupindex
#130799532
#130789382
#130787152
#130678442
#130678302
#130678232
#130678162
#130678092
#130677952
#130673112
#130670762
C2×D4⋊(C11⋊C8)2
C11×#35192
#1862811