Finite Group Databasebeta

← #14744014

Subgroups — #14744014

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081619C211yesmaximal, characteristic, complemented
2#13081489C211yesmaximal, characteristic
3#13080492C211yesmaximal, characteristic
4#13068294C211yesmaximal, characteristic, complemented
5#13068122C211yesmaximal, characteristic, complemented
6#13068072C211yesmaximal, characteristic, complemented
7#13068007C211yesmaximal, characteristic, complemented
8#13067979C211yesmaximal, characteristic
9#13067865C211yesmaximal, characteristic
10#13067857C211yesmaximal, characteristic, complemented
11#13067829C211yesmaximal, characteristic
12#13067774C211yesmaximal, characteristic, complemented
13#13067464C211yesmaximal, characteristic, complemented
14SD16⋊(C11⋊C8)C211yesmaximal, characteristic
15C11×#3386C211yesmaximal, characteristic
16C11×#557C2211yescharacteristic
17D4×Q8×C11C2211yescharacteristic
18#10623101C2211yescharacteristic
19#10623074C2211yescharacteristic
20C11×#501—21no—
21C11×#500C2211yescharacteristic
22C11×#478—21no—
23C11×#477—21no—
24C11×#475C2211yescharacteristic
25C11×#474C2211yescharacteristic
26C11×#446C2211yescharacteristic
27C11×#440—21no—
28C4×C11×SD16C2211yescharacteristic
29#10622841—21no—
30C2×#66899—21no—
31SD16×Dic11—21no—
32#10622706C2211yescharacteristic
33#10622705—21no—
34#10622705C2211yescharacteristic
35#10622703—21no—
36#10622703C2211yescharacteristic
37#10622703C2211yescharacteristic
38#10622694C2211yescharacteristic
39#10622691C2211yescharacteristic
40#10622664—21no—
41#10622657—21no—
42#10622644—21no—
43#10622644C2211yescharacteristic
44C4×#4326—21no—
45C4×#4326C2211yescharacteristic
46Q8×C11⋊C8C2211yescharacteristic
47#10622634C2211yescharacteristic
48#10622634C2211yescharacteristic
49D4×C11⋊C8C2211yescharacteristic
50#10622620C2211yescharacteristic
51#10622471—21no—
52#10622412—21no—
53#10622376—21no—
54#10622293C2211yescharacteristic
55C8×Dic22C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58Q8⋊(C11⋊C8)C2211yescharacteristic
59Q8⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622124C2211yescharacteristic
62#10622122C2211yescharacteristic
63#10622119C2211yescharacteristic
64#10622117C2211yescharacteristic
65#10622096C2211yescharacteristic
66#10622093C2211yescharacteristic
67C22×Q8×C11—21no—
68C2×C11×SD16D411yescharacteristic
69C11×C4⋊Q8—21no—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×#125—21no—
74C11×#125—41no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—41no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11C2311yescharacteristic
80C4×Q8×C11C2311yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11C2311yescharacteristic
83Q8×Dic11—21no—
84C2×#4326—21no—
85C2×#4326—21no—
86C2×#4326—21no—
87C2×#4326—21no—
88C2×#4326—21no—
89C2×#4326D411yescharacteristic
90D4×Dic11—21no—
91C2×C4⋊Dic11—21no—
92#66977—21no—
93C22×C11⋊C8—21no—
94#66943—21no—
95#66943—21no—
96#66943—41no—
97#66931—41no—
98#66922—21no—
99#66922C2311yescharacteristic
100#66922C2311yescharacteristic
101C4×Dic22—21no—
102C4×Dic22C2311yescharacteristic
103C11×#107—21no—
104C11×#107—21no—
105C11×#107—21no—
106C11×#106—21no—
107C11×#106D411yescharacteristic
108C11×C4⋊C8—21no—
109C11×C4⋊C8C2311yescharacteristic
110C11×#103—21no—
111C11×#103D411yescharacteristic
112C11×#102—21no—
113C11×#102D411yescharacteristic
114C11×#97—21no—
115C4×C8×C11C2311yescharacteristic
116#66899—21no—
117#66899—21no—
118#66899—21no—
119#66899—21no—
120#66899—21no—
121#66899—21no—
122#66899D411yescharacteristic
123#66896—21no—
124C22⋊(C11⋊C8)—21no—
125#66881—21no—
126#66881—21no—
127Dic11⋊C8—21no—
128C8×Dic11—21no—
129#66874—21no—
130#66874—41no—
131#66874D411yescharacteristic
132#66871—21no—
133#66871—21no—
134#66871—21no—
135#66871—41no—
136#66871D411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19815—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—41no—
148C2×Q8×C11—42no—
149C2×Q8×C11—81no—
150C2×Q8×C11C2×D411yescharacteristic
151C2×Q8×C11C2×D411yescharacteristic
152C2×D4×C11C2×D411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—41no—
155C22×Dic11—41no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22C2×D411yescharacteristic
159C11×SD16Q1614yescomplemented
160C2×C8×C11—21no—
161C2×C8×C11C2×D411yescharacteristic
162C2×C8×C11C2×D411yescharacteristic
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—41no—
170C11×C4⋊C4—41no—
171C11×C4⋊C4—41no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4C2×D411yescharacteristic
174C11×C4⋊C4C2×D411yescharacteristic
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C22⋊C4—21no—
177C11×C22⋊C4—41no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—41no—
181C42×C11C2411yescharacteristic
182C22⋊Dic11—41no—
183#4326—41no—
184#4326—42no—
185#4326—81no—
186#4326—81no—
187#4326—81no—
188#4326—81no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—41no—
194C4⋊Dic11—41no—
195C4⋊Dic11—41no—
196C4⋊Dic11C2×D411yescharacteristic
197Dic11⋊C4—21no—
198Dic11⋊C4—41no—
199Dic11⋊C4—41no—
200C4×Dic11—21no—
201C4×Dic11—41no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—81no—
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209#3395—111no—
210#3386D1111yescharacteristic
211#3381—111no—
212#3299—111no—
213#1723—111no—
214#1692—111no—
215#1684—111no—
216#1674—111no—
217#1669—111no—
218#1649—111no—
219#1648—111no—
220#1644—111no—
221#1636—111no—
222#1584—111no—
223SD16⋊C8—111no—
224C23×C11—21no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—82no—
233Q8×C11C2×Q1612yes—
234D4×C11—21no—
235D4×C11C2×Q1612yes—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—82no—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—161no—
254Dic22—21no—
255Dic22—21no—
256Dic22—41no—
257Dic22—41no—
258Dic22—81no—
259C8×C11—21no—
260C8×C11—41no—
261C8×C11C2×Q1612yes—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268#557—111no—
269#557C2×D1111yescharacteristic
270#554—111no—
271D4×Q8C2×D1111yescharacteristic
272#501—21no—
273#500—111no—
274#500C2×D1111yescharacteristic
275#499—221no—
276#498—111no—
277#494—111no—
278#494—221no—
279#487—111no—
280#487—111no—
281#484—221no—
282#479—221no—
283#478—21no—
284#478—221no—
285#477—21no—
286#477—111no—
287#477—111no—
288#475C2×D1111yescharacteristic
289#474—111no—
290#474C2×D1111yescharacteristic
291#467—221no—
292#462—111no—
293#462—111no—
294#462—111no—
295#462—221no—
296#462—221no—
297#451—221no—
298#446C2×D1111yescharacteristic
299C8×Q8—111no—
300C8×Q8—111no—
301#440—21no—
302C4×Q16—111no—
303C4×Q16—221no—
304C4×SD16—221no—
305C4×SD16C2×D1111yescharacteristic
306C8×D4—111no—
307C2×#103—221no—
308#335—111no—
309#335—111no—
310#333—111no—
311#332—111no—
312#332—111no—
313#332—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316Q8⋊C8—111no—
317D4⋊C8—111no—
318#322—111no—
319C22×C11—22no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11D4211yescharacteristic
323C4×C11—22no—
324C4×C11—21no—
325C4×C11—41no—
326C4×C11—41no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—81no—
330C4×C11—81no—
331C4×C11C22×Q1611yescharacteristic
332C4×C11#57511yescharacteristic
333C4×C11#57611yescharacteristic
334C4×C11#57811yescharacteristic
335Dic11—41no—
336Dic11—41no—
337Dic11—81no—
338Dic11—81no—
339C22×Q8—21no—
340C2×Q16—111no—
341C2×Q16—221no—
342C2×Q16—221no—
343C2×Q16—221no—
344C2×Q16—221no—
345C2×Q16—221no—
346C2×SD16C22⋊D1111yescharacteristic
347C22×C8—221no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—111no—
351C4⋊Q8—111no—
352C4⋊Q8—221no—
353C4⋊Q8C22×D1111yescharacteristic
354C4⋊Q8C22×D1111yescharacteristic
355#125—21no—
356#125—41no—
357#125—221no—
358#125—221no—
359#125—441no—
360C22⋊Q8—21no—
361C22⋊Q8—41no—
362C22⋊Q8—221no—
363C22⋊Q8—441no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—111no—
367C4×Q8—221no—
368C4×Q8—221no—
369C4×Q8C22×D1111yescharacteristic
370C4×Q8C22×D1111yescharacteristic
371C4×D4—21no—
372C4×D4—221no—
373C4×D4C22×D1111yescharacteristic
374C2×C4⋊C4—221no—
375#107—21no—
376#107—21no—
377#107—21no—
378#107—111no—
379#107—221no—
380#107—221no—
381#107—221no—
382#107—441no—
383#106—21no—
384#106—221no—
385#106—221no—
386#106C22⋊D1111yescharacteristic
387C4⋊C8—21no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8C22×D1111yescharacteristic
394#103—21no—
395#103—111no—
396#103—111no—
397#103—221no—
398#103—221no—
399#103—221no—
400#103—221no—
401#103—221no—
402#103—221no—
403#103—221no—
404#103—441no—
405#103C22⋊D1111yescharacteristic
406#102—21no—
407#102—221no—
408#102C22⋊D1111yescharacteristic
409C22⋊C8—221no—
410#97—21no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—221no—
414C4×C8—221no—
415C4×C8C22×D1111yescharacteristic
416C2×C11—42no—
417C2×C11#326811yescharacteristic
418C2×C11D4×Q1611yescharacteristic
419C2×C11#328911yescharacteristic
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—41no—
423C2×Q8—42no—
424C2×Q8—81no—
425C2×Q8—111no—
426C2×Q8—221no—
427C2×Q8—221no—
428C2×Q8D4×D1111yescharacteristic
429C2×Q8C2×C22⋊D1111yescharacteristic
430C2×D4C2×C22⋊D1111yescharacteristic
431C22×C4—21no—
432C22×C4—41no—
433C22×C4—441no—
434Q16—441no—
435Q16—442no—
436Q16—881no—
437Q16—881no—
438Q16—881no—
439Q16—881no—
440SD16#432614yescomplemented
441C2×C8—21no—
442C2×C8—111no—
443C2×C8—111no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—881no—
449C2×C8C2×C22⋊D1111yescharacteristic
450C2×C8C2×C22⋊D1111yescharacteristic
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—111no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—441no—
468C4⋊C4—441no—
469C4⋊C4—441no—
470C4⋊C4—441no—
471C4⋊C4—441no—
472C4⋊C4D4×D1111yescharacteristic
473C4⋊C4C2×C22⋊D1111yescharacteristic
474C4⋊C4C2×C22⋊D1111yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—41no—
477C22⋊C4—441no—
478C42—21no—
479C42—21no—
480C42—41no—
481C42—221no—
482C42—441no—
483C42C23×D1111yescharacteristic
484C11#1981511yescharacteristic, complemented, Sylow
485C23—21no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—82no—
494Q8—221no—
495Q8—221no—
496Q8—441no—
497Q8—441no—
498Q8—881no—
499Q8C2×#432612yes—
500D4—21no—
501D4C2×#432612yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—82no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—1761no—
517C2×C4C2×D4×D1111yescharacteristic
518C2×C4#6703711yescharacteristic
519C2×C4C22×C22⋊D1111yescharacteristic
520C8—21no—
521C8—41no—
522C8—221no—
523C8—221no—
524C8—441no—
525C8—441no—
526C8—441no—
527C8—441no—
528C8C2×#432612yes—
529C22—22no—
530C22—41no—
531C22—41no—
532C22D4×C22⋊D1111yescharacteristic
533C4—22no—
534C4—21no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—81no—
540C4—81no—
541C4—441no—
542C4—441no—
543C4—881no—
544C4—881no—
545C4#1062330411yescharacteristic
546C4#1062330511yescharacteristic
547C4C22×#432611yescharacteristic
548C4#1062336911yescharacteristic
549C2—42no—
550C2#1308015011yescharacteristic
551C2D4×#432611yescharacteristic
552C2#1308038711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3386C2
socleC22×C11D42
prime radicalC2×D4×C11C2×D4
hypercenter#3386D11
hypocenterC11#19815
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3386

Complements

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

NH ≅ G/Ntype
1. #13081619C2semidirect
4. #13068294C2semidirect
5. #13068122C2semidirect
6. #13068072C2semidirect
7. #13068007C2semidirect
10. #13067857C2semidirect
12. #13067774C2semidirect
13. #13067464C2semidirect
159. C11×SD16Q16semidirect
440. SD16#4326semidirect
484. C11#19815semidirect

Maximal subgroups

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

subgroupindex
#130816192
#130814892
#130804922
#130682942
#130681222
#130680722
#130680072
#130679792
#130678652
#130678572
#130678292
#130677742
#130674642
SD16⋊(C11⋊C8)2
C11×#33862
#1981511