Finite Group Databasebeta

← #14775854

Subgroups — #14775854

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078402C211yesmaximal, characteristic
2#13077560C211yesmaximal, characteristic, complemented
3#13077183C211yesmaximal, characteristic
4#13069591C211yesmaximal, characteristic, complemented
5#13069390C211yesmaximal, characteristic, complemented
6#13069370C211yesmaximal, characteristic, complemented
7#13069366C211yesmaximal, characteristic, complemented
8#13069218C211yesmaximal, characteristic, complemented
9#13068894C211yesmaximal, characteristic
10#13068892C211yesmaximal, characteristic
11#13068468C211yesmaximal, characteristic, complemented
12#13068462C211yesmaximal, characteristic
13#13068459C211yesmaximal, characteristic
14#13068420C211yesmaximal, characteristic
15C11×#1922C211yesmaximal, characteristic, complemented
16C2×#66960C2211yescharacteristic
17C2×#66954C2211yescharacteristic
18#10623053C2211yescharacteristic
19#10623048C2211yescharacteristic
20C11×#427C2211yescharacteristic
21C11×#424C2211yescharacteristic
22C11×#405C2211yescharacteristic
23C2×#66889C2211yescharacteristic
24C2×#66886C2211yescharacteristic
25#10622735C2211yescharacteristic
26#10622731C2211yescharacteristic
27M16×Dic11C2211yescharacteristic
28#10622726C2211yescharacteristic
29C2×#66883C2211yescharacteristic
30#10622715C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35#10622615C2211yescharacteristic
36#10622612C2211yescharacteristic
37#10622612C2211yescharacteristic
38#10622611C2211yescharacteristic
39C42×Dic11C2211yescharacteristic
40C2×#66869C2211yescharacteristic
41#10622504C411yescharacteristic, complemented
42#10622503C411yescharacteristic, complemented
43#10622490C411yescharacteristic, complemented
44#10622488C411yescharacteristic, complemented
45#10622484C411yescharacteristic, complemented
46#10622483C411yescharacteristic, complemented
47#10622470C411yescharacteristic, complemented
48#10622467C411yescharacteristic, complemented
49#10622452—21no—
50#10622452—21no—
51#10622450—21no—
52D11×C4⋊C8—21no—
53#10622314—21no—
54#10622314—21no—
55#10622292—21no—
56C8×Dic22—21no—
57C11×#341C2211yescharacteristic
58C11×#339C2211yescharacteristic
59C11×#339C2211yescharacteristic
60C11×#336C2211yescharacteristic
61#10622196C2211yescharacteristic
62#10622193C2211yescharacteristic
63#10622170C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622162C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×#4339C2311yescharacteristic
68C2×C11×M16C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×#117C2311yescharacteristic
73C11×#117C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75#66979C2311yescharacteristic
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11C2311yescharacteristic
79C2×C4×Dic11C2311yescharacteristic
80C2×#4318C2311yescharacteristic
81C2×#4318C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84#66960—22no—
85#66960—41no—
86#66954—22no—
87#66954—41no—
88C2×#4313—21no—
89C2×#4313—21no—
90C2×C8×D11—21no—
91C2×C8×D11—21no—
92#66946C2×C411yescharacteristic
93#66946C2×C411yescharacteristic
94#66943C2×C411yescharacteristic
95#66943C2×C411yescharacteristic
96#66941C2×C411yescharacteristic
97#66941C2×C411yescharacteristic
98#66940C2×C411yescharacteristic
99#66940C2×C411yescharacteristic
100(C22⋊D11)⋊C4—21no—
101(C22⋊D11)⋊C4—21no—
102#66931—21no—
103#66931—21no—
104#66925—21no—
105C42×D11—21no—
106C4×Dic22—21no—
107C4×Dic22—21no—
108C11×#107C2×C411yescharacteristic
109C11×#107C2×C411yescharacteristic
110C11×#106C2×C411yescharacteristic
111C11×#106C2×C411yescharacteristic
112C11×C4⋊C8—21no—
113C11×C4⋊C8—21no—
114C11×#97—21no—
115C4×C8×C11—21no—
116#66889Q814yescomplemented
117#66886—41no—
118#66885C2×C411yescharacteristic
119#66885C2×C411yescharacteristic
120#66883—41no—
121#66880C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66879—21no—
124#66879—21no—
125#66879—41no—
126#66879—41no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8C2×C411yescharacteristic
132Dic11⋊C8C2×C411yescharacteristic
133Dic11⋊C8C2×C411yescharacteristic
134Dic11⋊C8C2×C411yescharacteristic
135Dic11⋊C8D411yescharacteristic
136Dic11⋊C8D411yescharacteristic
137Dic11⋊C8D411yescharacteristic
138Dic11⋊C8D411yescharacteristic
139C8×Dic11—21no—
140C8×Dic11—21no—
141#66874C2×C411yescharacteristic
142#66874C2×C411yescharacteristic
143#66873C2×C411yescharacteristic
144#66873C2×C411yescharacteristic
145#66872C2×C411yescharacteristic
146#66872C2×C411yescharacteristic
147#66871C2×C411yescharacteristic
148#66871C2×C411yescharacteristic
149#66869—22no—
150C4⋊(C11⋊C8)—21no—
151C4⋊(C11⋊C8)—21no—
152C4⋊(C11⋊C8)—21no—
153C4⋊(C11⋊C8)—21no—
154#22983—111nomaximal, Sylow
155C22×C4×C11—21no—
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—21no—
158C22×Dic11—21no—
159C22×Dic11#4111yescharacteristic
160C22×Dic11#4111yescharacteristic
161#4339—21no—
162#4339—21no—
163#4339C2×Q812yes—
164#4339#4112yes—
165C2×D44C22×C411yescharacteristic
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22C22×C411yescharacteristic
172C11×M16—21no—
173C11×M16—21no—
174C11×M16—21no—
175C11×M16C2×Q812yes—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11C22×C411yescharacteristic
183C2×C8×C11C22×C411yescharacteristic
184C2×C8×C11C2×D411yescharacteristic
185C2×C8×C11C2×D411yescharacteristic
186C11×C4⋊C4C22×C411yescharacteristic
187C11×C4⋊C4C22×C411yescharacteristic
188C11×C4⋊C4C22×C411yescharacteristic
189C11×C4⋊C4C22×C411yescharacteristic
190C11×C22⋊C4—21no—
191C11×C22⋊C4—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C22⋊Dic11—21no—
197(C2×D11)⋊C4—21no—
198(C2×D11)⋊C4—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11C22×C411yescharacteristic
202C4⋊Dic11C22×C411yescharacteristic
203Dic11⋊C4—21no—
204Dic11⋊C4—21no—
205Dic11⋊C4—21no—
206Dic11⋊C4—21no—
207Dic11⋊C4—21no—
208Dic11⋊C4—21no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—42no—
214C4×Dic11—42no—
215C4×Dic11C22×C411yescharacteristic
216C4×Dic11C22×C411yescharacteristic
217C4×Dic11C2×D411yescharacteristic
218C4×Dic11C2×D411yescharacteristic
219C4×Dic11C2×Q812yes—
220#4318—21no—
221#4318—21no—
222#4318—21no—
223#4318—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8C22×C411yescharacteristic
231C2×C11⋊C8C22×C411yescharacteristic
232C2×C11⋊C8C2×D411yescharacteristic
233C2×C11⋊C8C2×D411yescharacteristic
234#4313—42no—
235#4313—42no—
236C8×D11—42no—
237C8×D11—42no—
238#3076—111no—
239#2962—111no—
240#2906—111no—
241#1994—111no—
242#1950—111no—
243#1946—111no—
244#1946—111no—
245#1922—111no—
246#1922D1111yescharacteristic, complemented
247#1866—111no—
248#1866—111no—
249#1767—111no—
250#1765—111no—
251#1765—111no—
252C4×#104—111no—
253C23×C11C2×#4111yescharacteristic
254C22×D11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11C23×C411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×Q811yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C22⋊D11—22no—
269C22⋊D11—22no—
270C2×Dic11—21no—
271C2×Dic11—22no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—22no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11C4×D411yescharacteristic
279C2×Dic11C4×D411yescharacteristic
280C2×Dic11C4×D411yescharacteristic
281C2×Dic11C4×D411yescharacteristic
282D44—21no—
283D44C4×Q812yes—
284C4×D11—22no—
285C4×D11—22no—
286C4×D11—42no—
287C4×D11—81no—
288Dic22—21no—
289Dic22—42no—
290Dic22—81no—
291Dic22C4×Q812yes—
292C8×C11—21no—
293C8×C11—21no—
294C8×C11—21no—
295C8×C11—21no—
296C8×C11—22no—
297C8×C11—41no—
298C11⋊C8—21no—
299C11⋊C8—21no—
300C11⋊C8—21no—
301C11⋊C8—21no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C2×#131—111no—
305C2×#131—111no—
306#533—111no—
307C4×#41—111no—
308#479—111no—
309#479—111no—
310#478—111no—
311#478—111no—
312#477—111no—
313#476—111no—
314#475—111no—
315#474—111no—
316#446—221no—
317#446—221no—
318#446—221no—
319C8×Q8—221no—
320C2×#108—111no—
321C2×#108—111no—
322#427—111no—
323#427C2×D1111yescharacteristic
324#424—111no—
325#424—111no—
326#424—111no—
327#424—221no—
328#424—221no—
329#424C2×D1111yescharacteristic
330#423—111no—
331#423—221no—
332C2×C4⋊C8—111no—
333C2×C4⋊C8—111no—
334C2×C4⋊C8—221no—
335C2×#104—111no—
336C2×#104—111no—
337#416—111no—
338#416—111no—
339#405—111no—
340#405C2×D1111yescharacteristic
341C4×M16—111no—
342C2×#97—111no—
343C2×#97—111no—
344C43—111no—
345#341—111no—
346#341C2×D1111yescharacteristic
347#339—111no—
348#339—111no—
349#339—111no—
350#339—111no—
351#339C2×D1111yescharacteristic
352#339C2×D1111yescharacteristic
353#336—111no—
354#336C2×D1111yescharacteristic
355C22×C11—21no—
356C22×C11—21no—
357C22×C11C2×C4×D411yescharacteristic
358C22×C11#55211yescharacteristic
359C22×C11#55411yescharacteristic
360C2×D11—22no—
361C2×D11—41no—
362C2×D11—41no—
363C4×C11—42no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11C2×C4×Q811yescharacteristic
369C4×C11#52011yescharacteristic
370C4×C11#54611yescharacteristic
371C4×C11D4×Q811yescharacteristic
372Dic11—22no—
373Dic11—21no—
374Dic11—21no—
375Dic11—21no—
376Dic11—42no—
377Dic11—41no—
378Dic11—41no—
379Dic11#44412yes—
380C2×#41—111no—
381#131—222no—
382#131—222no—
383#131—441no—
384#131—441no—
385C2×M16—111no—
386C2×M16—111no—
387C2×M16—221no—
388C2×M16—221no—
389C2×M16C22×D1111yescharacteristic
390C2×M16C22×D1111yescharacteristic
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—221no—
394C22×C8—221no—
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397C4⋊Q8—111no—
398C4⋊Q8—111no—
399#125—111no—
400#125—111no—
401C22⋊Q8—221no—
402C22⋊Q8—221no—
403C4×Q8—111no—
404C4×Q8—111no—
405C4×Q8—221no—
406C4×Q8—221no—
407C4×D4—111no—
408C4×D4—111no—
409C4×D4—221no—
410C4×D4—221no—
411#117—111no—
412#117—221no—
413#117C22×D1111yescharacteristic
414#117C22×D1111yescharacteristic
415C2×C42—111no—
416C2×C42—111no—
417C2×C42—221no—
418C2×C42—221no—
419C2×C42—221no—
420C2×C42C22×D1111yescharacteristic
421#108—441no—
422#108—441no—
423#107—111no—
424#107—111no—
425#107C4×D1111yescharacteristic
426#107C4×D1111yescharacteristic
427#106—111no—
428#106—111no—
429#106C4×D1111yescharacteristic
430#106C4×D1111yescharacteristic
431C4⋊C8—21no—
432C4⋊C8—21no—
433C4⋊C8—111no—
434C4⋊C8—111no—
435C4⋊C8—111no—
436C4⋊C8—111no—
437C4⋊C8—111no—
438C4⋊C8—111no—
439C4⋊C8—111no—
440C4⋊C8—111no—
441C4⋊C8—221no—
442C4⋊C8—221no—
443C4⋊C8—221no—
444C4⋊C8—221no—
445C4⋊C8—221no—
446C4⋊C8—221no—
447C4⋊C8—221no—
448C4⋊C8—221no—
449#104—114no—
450#104—222no—
451#103—111no—
452#103—111no—
453#103—111no—
454#103—111no—
455#102—111no—
456#102—111no—
457#102—111no—
458#102—111no—
459#97—21no—
460#97—221no—
461#97—221no—
462#97—441no—
463#97—441no—
464C4×C8—21no—
465C4×C8—221no—
466C4×C8—221no—
467C2×C11—21no—
468C2×C11—21no—
469C2×C11#236011yescharacteristic
470C2×C11C2×#44411yescharacteristic
471C2×C11#295611yescharacteristic
472D11—42no—
473#41—112no—
474#41—112no—
475#41—221no—
476#41—221no—
477C2×Q8—111no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×D4—111no—
481C2×D4—221no—
482C22×C4—21no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4C23×D1111yescharacteristic
490M16—21no—
491M16—21no—
492M16—21no—
493M16—221no—
494M16—221no—
495M16—221no—
496M16—221no—
497M16—442no—
498M16—442no—
499M16Q8×D1112yes—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—111no—
507C2×C8—111no—
508C2×C8—111no—
509C2×C8—111no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—442no—
517C2×C8—442no—
518C2×C8C2×C4×D1111yescharacteristic
519C2×C8C2×C4×D1111yescharacteristic
520C2×C8D4×D1111yescharacteristic
521C2×C8D4×D1111yescharacteristic
522C4⋊C4—111no—
523C4⋊C4—111no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4C2×C4×D1111yescharacteristic
533C4⋊C4C2×C4×D1111yescharacteristic
534C4⋊C4C2×C4×D1111yescharacteristic
535C4⋊C4C2×C4×D1111yescharacteristic
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—221no—
539C22⋊C4—221no—
540C22⋊C4—221no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—111no—
546C42—111no—
547C42—111no—
548C42—111no—
549C42—112no—
550C42—221no—
551C42—221no—
552C42—221no—
553C42—221no—
554C42—442no—
555C42—442no—
556C11#2298311yescharacteristic, complemented, Sylow
557C23—221no—
558C23#41×D1111yescharacteristic
559Q8—112no—
560Q8—221no—
561Q8—442no—
562Q8—881no—
563D4—112no—
564D4—222no—
565D4—222no—
566D4—221no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—111no—
575C2×C4—111no—
576C2×C4—111no—
577C2×C4—111no—
578C2×C4—222no—
579C2×C4—221no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—222no—
585C2×C4—442no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—881no—
590C2×C4C22×C4×D1111yescharacteristic
591C2×C4C2×D4×D1111yescharacteristic
592C2×C4C2×Q8×D1111yescharacteristic
593C2×C4#41×D1111yescharacteristic
594C2×C4#6704211yescharacteristic
595C2×C4#6704311yescharacteristic
596C8—21no—
597C8—21no—
598C8—22no—
599C8—21no—
600C8—21no—
601C8—41no—
602C8—221no—
603C8—221no—
604C8—221no—
605C8—221no—
606C8—441no—
607C8—441no—
608C22—21no—
609C22—21no—
610C22—222no—
611C22—441no—
612C22—441no—
613C22C4×D4×D1111yescharacteristic
614C22#1062322111yescharacteristic
615C22#1062323911yescharacteristic
616C4—42no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—112no—
622C4—221no—
623C4—222no—
624C4—221no—
625C4—221no—
626C4—442no—
627C4—441no—
628C4—441no—
629C4#1062305411yescharacteristic
630C4C4×Q8×D1111yescharacteristic
631C4#1062316311yescharacteristic
632C4#1062318511yescharacteristic
633C2—21no—
634C2—21no—
635C2—442no—
636C2#1307162411yescharacteristic
637C2D11×#44411yescharacteristic
638C2#1307752111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1922C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C23
cosocleC22×C4×C11C24
hypercenter#1922D11
hypocenterC11#22983
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1922

Complements

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

NH ≅ G/Ntype
2. #13077560C2semidirect
4. #13069591C2semidirect
5. #13069390C2semidirect
6. #13069370C2semidirect
7. #13069366C2semidirect
8. #13069218C2semidirect
11. #13068468C2semidirect
15. C11×#1922C2semidirect
41. #10622504C4semidirect
42. #10622503C4semidirect
43. #10622490C4semidirect
44. #10622488C4semidirect
45. #10622484C4semidirect
46. #10622483C4semidirect
47. #10622470C4semidirect
48. #10622467C4semidirect
116. #66889Q8semidirect
246. #1922D11semidirect
556. C11#22983semidirect

Maximal subgroups

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

subgroupindex
#130784022
#130775602
#130771832
#130695912
#130693902
#130693702
#130693662
#130692182
#130688942
#130688922
#130684682
#130684622
#130684592
#130684202
C11×#19222
#2298311