Finite Group Databasebeta

← #14736217

Subgroups — #14736217

Order 2816.

618 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079198C211yesmaximal, characteristic, complemented
2#13078404C211yesmaximal, characteristic
3#41×C11⋊C8C211yesmaximal, characteristic
4#13068076C211yesmaximal, characteristic, complemented
5#13068072C211yesmaximal, characteristic, complemented
6#13068069C211yesmaximal, characteristic, complemented
7#13068065C211yesmaximal, characteristic, complemented
8#13068018C211yesmaximal, characteristic, complemented
9#13068013C211yesmaximal, characteristic, complemented
10#13067984C211yesmaximal, characteristic, complemented
11#13067979C211yesmaximal, characteristic, complemented
12C2×#10622117C211yesmaximal, characteristic, complemented
13#13067274C211yesmaximal, characteristic, complemented
14#13067273C211yesmaximal, characteristic, complemented
15C11×#3076C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#479—21no—
20C11×#478—21no—
21C11×#477C2211yescharacteristic
22C11×#476C2211yescharacteristic
23C11×#475C2211yescharacteristic
24C11×#474C2211yescharacteristic
25C11×#427—21no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#416—21no—
28#10622846—21no—
29#10622706C2211yescharacteristic
30#10622705C2211yescharacteristic
31#10622694C2211yescharacteristic
32#10622691C2211yescharacteristic
33#10622664—21no—
34#10622664—21no—
35C4×#4326—21no—
36C4×#4326—21no—
37Q8×C11⋊C8C2211yescharacteristic
38Q8×C11⋊C8C2211yescharacteristic
39#10622635—21no—
40#10622634C2211yescharacteristic
41#10622633C2211yescharacteristic
42D4×C11⋊C8—21no—
43D4×C11⋊C8—21no—
44D4×C11⋊C8C2211yescharacteristic
45D4×C11⋊C8C2211yescharacteristic
46#10622622—21no—
47#10622621C2211yescharacteristic
48#10622620C2211yescharacteristic
49#10622611—21no—
50#10622538—21no—
51#10622538C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×C4×C11⋊C8—21no—
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58#10622184C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622117C2211yescharacteristic
64#10622117C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C22×C8×C11—21no—
69C11×C4⋊Q8C2311yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×#125—21no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8—21no—
74C4×Q8×C11—21no—
75C4×Q8×C11—21no—
76C4×Q8×C11D411yescharacteristic
77C4×Q8×C11C2311yescharacteristic
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11D411yescharacteristic
81C4×D4×C11C2311yescharacteristic
82C11×#117—21no—
83C11×#117—21no—
84C11×#117D411yescharacteristic
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87C2×#4326—21no—
88C2×#4326—21no—
89#66979—21no—
90#66977—21no—
91#66977—21no—
92C22×C11⋊C8—21no—
93C22×C11⋊C8—21no—
94C22×C11⋊C8—21no—
95C22×C11⋊C8D411yescharacteristic
96C22×C11⋊C8D411yescharacteristic
97#66923—21no—
98#66922C2311yescharacteristic
99#66922C2311yescharacteristic
100C4×Dic22—21no—
101C4×Dic22—21no—
102C11×#107—21no—
103C11×#107—21no—
104C11×#106—21no—
105C11×#106—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#103—21no—
110C11×#103—21no—
111C11×#102—21no—
112C11×#102—21no—
113#66899—21no—
114#66899—21no—
115#66899—21no—
116#66899—21no—
117#66896—21no—
118#66896—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66874—21no—
123#66874—21no—
124#66872—21no—
125#66872—21no—
126#66871—21no—
127#66871—21no—
128#66871—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4×C11⋊C8—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8D411yescharacteristic
141C4×C11⋊C8D411yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19126—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41Q1614yescomplemented
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11C2×D411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—42no—
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⋊C4C2×D411yescharacteristic
172C11×C4⋊C4C2×D411yescharacteristic
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—41no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—41no—
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11#4111yescharacteristic
184C42×C11C2411yescharacteristic
185C22⋊Dic11—41no—
186#4326—42no—
187#4326—42no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192Dic11⋊C4—41no—
193Dic11⋊C4—41no—
194C4×Dic11—41no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—41no—
201C2×C11⋊C8—42no—
202C2×C11⋊C8—42no—
203C2×C11⋊C8—42no—
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#3170—111no—
209#3076—111no—
210#3076D1111yescharacteristic
211C8×#41—111no—
212#1684—111no—
213#1684—111no—
214#1683—111no—
215#1683—111no—
216#1676—111no—
217#1675—111no—
218#1670—111no—
219#1669—111no—
220C2×#335—111no—
221#1542—111no—
222#1542—111no—
223C23×C11—21no—
224C23×C11#12111yescharacteristic
225Q8×C11—21no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—81no—
229Q8×C11C2×Q1612yes—
230D4×C11—24no—
231D4×C11—21no—
232D4×C11C2×Q1612yes—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—24no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11C2×Q1612yes—
249C2×C4×C11#13512yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×Dic11—41no—
254C2×Dic11—41no—
255Dic22—41no—
256Dic22—41no—
257Dic22—81no—
258C8×C11—41no—
259C8×C11—41no—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—21no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8#13512yes—
268#533—111no—
269#533C2×D1111yescharacteristic
270C4×#41C2×D1111yescharacteristic
271#500—111no—
272#494—111no—
273#487—111no—
274#487—111no—
275#479—21no—
276#479—221no—
277#478—21no—
278#478—221no—
279#477—111no—
280#477C2×D1111yescharacteristic
281#476—111no—
282#476C2×D1111yescharacteristic
283#475—111no—
284#475C2×D1111yescharacteristic
285#474—111no—
286#474C2×D1111yescharacteristic
287#467—221no—
288#467—221no—
289C8×Q8—111no—
290C8×Q8—111no—
291C4×Q16—221no—
292C4×Q16—221no—
293C8×D4—111no—
294C8×D4—111no—
295C8×D4—221no—
296C8×D4—221no—
297#431—111no—
298#431—221no—
299#427—21no—
300#427—221no—
301C2×C4⋊C8—111no—
302C2×C4⋊C8C2×D1111yescharacteristic
303#416—21no—
304#416—221no—
305C2×C4×C8—111no—
306C2×C4×C8—221no—
307#335—111no—
308#335—111no—
309#335—111no—
310#335—111no—
311#333—111no—
312#333—111no—
313#333—111no—
314#333—111no—
315#332—111no—
316#332—111no—
317#332—111no—
318#332—111no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—22no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11#46712yes—
325C22×C11C2×#12111yescharacteristic
326C4×C11—21no—
327C4×C11—22no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11#46712yes—
335C4×C11C22×Q1611yescharacteristic
336C4×C11C2×#13511yescharacteristic
337C4×C11C2×#13511yescharacteristic
338C4×C11#57511yescharacteristic
339Dic11—81no—
340Dic11—81no—
341C2×#41C22⋊D1111yescharacteristic
342C2×Q16—221no—
343C2×Q16—221no—
344C22×C8—21no—
345C22×C8—111no—
346C22×C8—111no—
347C22×C8—221no—
348C22×C8—221no—
349C22×C8—221no—
350C4⋊Q8—111no—
351C4⋊Q8—111no—
352C4⋊Q8C22×D1111yescharacteristic
353C4⋊Q8C22×D1111yescharacteristic
354#125—21no—
355#125—221no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8—221no—
359C22⋊Q8—221no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—221no—
363C4×Q8—221no—
364C4×Q8C22⋊D1111yescharacteristic
365C4×Q8C22×D1111yescharacteristic
366C4×D4—21no—
367C4×D4—21no—
368C4×D4C22⋊D1111yescharacteristic
369C4×D4C22×D1111yescharacteristic
370#117—21no—
371#117—21no—
372#117—221no—
373#117C22⋊D1111yescharacteristic
374C2×C42—21no—
375C2×C42C22×D1111yescharacteristic
376#107—21no—
377#107—21no—
378#107—221no—
379#107—221no—
380#107—221no—
381#107—221no—
382#106—21no—
383#106—21no—
384#106—221no—
385#106—221no—
386C4⋊C8—21no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8C22×D1111yescharacteristic
395C4⋊C8C22×D1111yescharacteristic
396#103—21no—
397#103—21no—
398#103—221no—
399#103—221no—
400#103—221no—
401#103—221no—
402#103—221no—
403#103—221no—
404#102—21no—
405#102—21no—
406#102—221no—
407#102—221no—
408C22⋊C8—221no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—221no—
416C4×C8—221no—
417C4×C8—221no—
418C2×C11—22no—
419C2×C11—42no—
420C2×C11#303511yescharacteristic
421C2×C11C2×#46711yescharacteristic
422C2×C11#306711yescharacteristic
423#41—22no—
424#41#432614yescomplemented
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—221no—
428C2×Q8—221no—
429C2×Q8C2×C22⋊D1111yescharacteristic
430C2×D4—21no—
431C2×D4C2×C22⋊D1111yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4D4×D1111yescharacteristic
436C22×C4#434111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438Q16—442no—
439Q16—442no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—42no—
443C2×C8—111no—
444C2×C8—111no—
445C2×C8—111no—
446C2×C8—111no—
447C2×C8—222no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—442no—
453C2×C8—441no—
454C2×C8—442no—
455C2×C8—442no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—441no—
469C4⋊C4—441no—
470C4⋊C4C2×C22⋊D1111yescharacteristic
471C4⋊C4C2×C22⋊D1111yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C22⋊C4—441no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—41no—
481C42—441no—
482C42D4×D1111yescharacteristic
483C42#434111yescharacteristic
484C42C2×C22⋊D1111yescharacteristic
485C42C23×D1111yescharacteristic
486C11#1912611yescharacteristic, complemented, Sylow
487C23—21no—
488C23#6699211yescharacteristic
489Q8—21no—
490Q8—41no—
491Q8—41no—
492Q8—81no—
493Q8—441no—
494Q8—441no—
495Q8—881no—
496Q8C2×#432612yes—
497D4—24no—
498D4—21no—
499D4C2×#432612yes—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—24no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4#6699211yescharacteristic
515C2×C4#6699211yescharacteristic
516C2×C4#6699211yescharacteristic
517C2×C4C2×#432612yes—
518C2×C4#6700312yes—
519C2×C4C2×D4×D1111yescharacteristic
520C2×C4C2×#434111yescharacteristic
521C2×C4C22×C22⋊D1111yescharacteristic
522C8—41no—
523C8—41no—
524C8—112no—
525C8—221no—
526C8—221no—
527C8—221no—
528C8—441no—
529C8—441no—
530C8—441no—
531C8—441no—
532C22—21no—
533C22—21no—
534C22—22no—
535C22—41no—
536C22—41no—
537C22#1062266412yes—
538C22C2×#6699211yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—22no—
543C4—41no—
544C4—41no—
545C4—81no—
546C4—81no—
547C4—881no—
548C4—881no—
549C4#1062266412yes—
550C4D11×#13511yescharacteristic
551C4#1062329911yescharacteristic
552C4C22×#432611yescharacteristic
553C4C2×#6700311yescharacteristic
554C2—22no—
555C2—42no—
556C2#1307806711yescharacteristic
557C2C2×#1062266411yescharacteristic
558C2#1307833311yescharacteristic
subgroupG/H
centerC2×C4#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3076C2
socleC22×C11C2×#121
prime radicalC2×C11×#41D4
hypercenter#3076D11
hypocenterC11#19126
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #13079198C2semidirect
4. #13068076C2semidirect
5. #13068072C2semidirect
6. #13068069C2semidirect
7. #13068065C2semidirect
8. #13068018C2semidirect
9. #13068013C2semidirect
10. #13067984C2semidirect
11. #13067979C2semidirect
12. C2×#10622117C2semidirect
13. #13067274C2semidirect
14. #13067273C2semidirect
146. C11×#41Q16semidirect
424. #41#4326semidirect
486. C11#19126semidirect

Maximal subgroups

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

subgroupindex
#130791982
#130784042
#41×C11⋊C82
#130680762
#130680722
#130680692
#130680652
#130680182
#130680132
#130679842
#130679792
C2×#106221172
#130672742
#130672732
C11×#30762
#1912611