Finite Group Databasebeta

← #14737205

Subgroups — #14737205

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079791C211yesmaximal, characteristic
2#13079198C211yesmaximal, characteristic, complemented
3#13077592C211yesmaximal, characteristic
4#13068142C211yesmaximal, characteristic, complemented
5#13068137C211yesmaximal, characteristic, complemented
6#13068108C211yesmaximal, characteristic, complemented
7#13068103C211yesmaximal, characteristic, complemented
8#13068076C211yesmaximal, characteristic, complemented
9#13068072C211yesmaximal, characteristic, complemented
10#13068069C211yesmaximal, characteristic, complemented
11#13068065C211yesmaximal, characteristic, complemented
12#13067362C211yesmaximal, characteristic, complemented
13#13067326C211yesmaximal, characteristic, complemented
14#13067324C211yesmaximal, characteristic, complemented
15C11×#3233C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#499—21no—
20C11×#488—21no—
21C11×#485—21no—
22C11×#482—21no—
23C11×#477C2211yescharacteristic
24C11×#476C2211yescharacteristic
25C11×#475C2211yescharacteristic
26C11×#474C2211yescharacteristic
27C11×#431C2211yescharacteristic
28#10622706C2211yescharacteristic
29#10622705C2211yescharacteristic
30#10622694C2211yescharacteristic
31#10622691C2211yescharacteristic
32#10622677—21no—
33#10622669—21no—
34#10622664—21no—
35#10622664—21no—
36#10622658—21no—
37#10622648—21no—
38C4×#4326—21no—
39C4×#4326—21no—
40#10622637C2211yescharacteristic
41Q8×C11⋊C8C2211yescharacteristic
42#10622634C2211yescharacteristic
43#10622633C2211yescharacteristic
44#10622625C2211yescharacteristic
45#10622624—21no—
46D4×C11⋊C8—21no—
47D4×C11⋊C8C2211yescharacteristic
48#10622621C2211yescharacteristic
49#10622620C2211yescharacteristic
50#10622613—21no—
51#10622610—21no—
52#10622539C2211yescharacteristic
53#10622538C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58#10622184C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C11×C4⋊Q8C2311yescharacteristic
68C11×C4⋊Q8C2311yescharacteristic
69C11×#126—21no—
70C11×#125—21no—
71C11×#125D411yescharacteristic
72C11×#124D411yescharacteristic
73C11×#123—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8D411yescharacteristic
77C11×#121D411yescharacteristic
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11C2311yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11C2311yescharacteristic
83C11×#117—21no—
84C11×#117—21no—
85C2×C42×C11C2311yescharacteristic
86C2×#4326—21no—
87C2×#4326—21no—
88#66979—21no—
89#66977—21no—
90#66977—21no—
91C2×#4318—21no—
92C22×C11⋊C8—21no—
93C22×C11⋊C8D411yescharacteristic
94C22×C11⋊C8D411yescharacteristic
95#66923—21no—
96#66922C2311yescharacteristic
97#66922C2311yescharacteristic
98C4×Dic22—21no—
99C4×Dic22—21no—
100C11×#107—21no—
101C11×#107—21no—
102C11×#106—21no—
103C11×#106—21no—
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×#103—21no—
107C11×#103—21no—
108C11×#102—21no—
109C11×#102—21no—
110C11×C22⋊C8—21no—
111C4×C8×C11—21no—
112#66899—21no—
113#66899—21no—
114#66899—21no—
115#66899—21no—
116#66896—21no—
117#66896—21no—
118C22⋊(C11⋊C8)—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)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136#66867—21no—
137#66867—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8D411yescharacteristic
141C4×C11⋊C8D411yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19226—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—41no—
167C11×C4⋊C4—41no—
168C11×C4⋊C4C2×D411yescharacteristic
169C11×C4⋊C4C2×D411yescharacteristic
170C11×C22⋊C4—21no—
171C11×C22⋊C4—21no—
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—41no—
176C42×C11—21no—
177C42×C11—41no—
178C42×C11C2×D411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11#4111yescharacteristic
181C42×C11C2411yescharacteristic
182C22⋊Dic11—41no—
183#4326—42no—
184#4326—42no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189Dic11⋊C4—41no—
190Dic11⋊C4—41no—
191C4×Dic11—41no—
192#4318—42no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—41no—
199C2×C11⋊C8—42no—
200C2×C11⋊C8C2×D411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204#3233—111no—
205#3233D1111yescharacteristic
206#3170—111no—
207#2966—111no—
208#1696—111no—
209#1695—111no—
210#1690—111no—
211#1689—111no—
212#1684—111no—
213#1684—111no—
214#1683—111no—
215#1683—111no—
216#1564—111no—
217#1554—111no—
218#1554—111no—
219C23×C11—21no—
220C23×C11#12111yescharacteristic
221Q8×C11—21no—
222Q8×C11—21no—
223Q8×C11—41no—
224Q8×C11—41no—
225Q8×C11—81no—
226D4×C11—21no—
227D4×C11—21no—
228D4×C11—42no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×Dic11—41no—
248C2×Dic11—41no—
249Dic22—41no—
250Dic22—41no—
251Dic22—81no—
252C8×C11—41no—
253C8×C11—41no—
254C11⋊C8—21no—
255C11⋊C8—21no—
256C11⋊C8—21no—
257C11⋊C8—41no—
258C11⋊C8—41no—
259C11⋊C8—41no—
260C11⋊C8—41no—
261C11⋊C8#13512yes—
262#533—111no—
263#533C2×D1111yescharacteristic
264#529C2×D1111yescharacteristic
265#500—111no—
266#499—21no—
267#499—221no—
268#494—111no—
269#488—21no—
270#488—221no—
271#487—111no—
272#487—111no—
273#485—21no—
274#485—221no—
275#482—21no—
276#482—221no—
277#477—111no—
278#477C2×D1111yescharacteristic
279#476—111no—
280#476C2×D1111yescharacteristic
281#475—111no—
282#475C2×D1111yescharacteristic
283#474—111no—
284#474C2×D1111yescharacteristic
285#467—221no—
286#467—221no—
287#446—111no—
288C8×Q8—111no—
289C4×Q16—221no—
290C4×Q16—221no—
291#436—111no—
292#435—221no—
293C8×D4—111no—
294C8×D4—221no—
295#433—221no—
296#432—111no—
297#431—111no—
298#431C2×D1111yescharacteristic
299#405—221no—
300C2×C4×C8—111no—
301#335—111no—
302#335—111no—
303#334—111no—
304#334—111no—
305#333—111no—
306#333—111no—
307#333—111no—
308#333—111no—
309#332—111no—
310#332—111no—
311#332—111no—
312#332—111no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11C2×#12111yescharacteristic
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—41no—
325C4×C11—41no—
326C4×C11—41no—
327C4×C11—81no—
328C4×C11—81no—
329C4×C11C2×#13511yescharacteristic
330C4×C11#57511yescharacteristic
331C4×C11#57811yescharacteristic
332C4×C11#57811yescharacteristic
333Dic11—81no—
334Dic11—81no—
335C2×Q16—221no—
336C2×Q16—221no—
337C2×M16—221no—
338C22×C8—111no—
339C22×C8—111no—
340C22×C8—221no—
341C4⋊Q8—111no—
342C4⋊Q8—111no—
343C4⋊Q8C22×D1111yescharacteristic
344C4⋊Q8C22×D1111yescharacteristic
345#126—21no—
346#125—21no—
347#125—221no—
348#125C22⋊D1111yescharacteristic
349#124C22⋊D1111yescharacteristic
350#123—21no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—221no—
354C22⋊Q8—221no—
355C22⋊Q8C22⋊D1111yescharacteristic
356#121C22⋊D1111yescharacteristic
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8—221no—
360C4×Q8—221no—
361C4×Q8C22×D1111yescharacteristic
362C4×D4—21no—
363C4×D4C22×D1111yescharacteristic
364#117—21no—
365#117—21no—
366#117—221no—
367C2×C42C22×D1111yescharacteristic
368#107—21no—
369#107—21no—
370#107—221no—
371#107—221no—
372#107—221no—
373#107—221no—
374#106—21no—
375#106—21no—
376#106—221no—
377#106—221no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8C22×D1111yescharacteristic
385C4⋊C8C22×D1111yescharacteristic
386#103—21no—
387#103—21no—
388#103—221no—
389#103—221no—
390#103—221no—
391#103—221no—
392#103—221no—
393#103—221no—
394#102—21no—
395#102—21no—
396#102—221no—
397#102—221no—
398C22⋊C8—21no—
399C22⋊C8—221no—
400C22⋊C8—221no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#97—221no—
404#97—221no—
405C4×C8—21no—
406C4×C8—111no—
407C4×C8—111no—
408C4×C8—111no—
409C4×C8—111no—
410C4×C8—221no—
411C4×C8—221no—
412C2×C11—41no—
413C2×C11—81no—
414C2×C11#303511yescharacteristic
415C2×C11#305911yescharacteristic
416C2×C11#306711yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—221no—
420C2×Q8—221no—
421C2×Q8C2×C22⋊D1111yescharacteristic
422C2×D4—21no—
423C2×D4C2×C22⋊D1111yescharacteristic
424C22×C4—21no—
425C22×C4D4×D1111yescharacteristic
426C22×C4#434111yescharacteristic
427C22×C4C2×C22⋊D1111yescharacteristic
428Q16—442no—
429Q16—442no—
430M16—442no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—111no—
434C2×C8—111no—
435C2×C8—111no—
436C2×C8—111no—
437C2×C8—222no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—441no—
443C2×C8—442no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—441no—
459C4⋊C4—441no—
460C4⋊C4C2×C22⋊D1111yescharacteristic
461C4⋊C4C2×C22⋊D1111yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—41no—
468C22⋊C4—441no—
469C42—21no—
470C42—41no—
471C42—441no—
472C42D4×D1111yescharacteristic
473C42#434111yescharacteristic
474C42C2×C22⋊D1111yescharacteristic
475C42C23×D1111yescharacteristic
476C11#1922611yescharacteristic, complemented, Sylow
477C23—21no—
478C23#6699211yescharacteristic
479Q8—21no—
480Q8—21no—
481Q8—41no—
482Q8—41no—
483Q8—81no—
484Q8—441no—
485Q8—441no—
486Q8—881no—
487D4—21no—
488D4—21no—
489D4—42no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4#6699211yescharacteristic
505C2×C4#6699211yescharacteristic
506C2×C4#6699211yescharacteristic
507C2×C4C2×D4×D1111yescharacteristic
508C2×C4C2×#434111yescharacteristic
509C2×C4C22×C22⋊D1111yescharacteristic
510C8—41no—
511C8—41no—
512C8—112no—
513C8—221no—
514C8—221no—
515C8—221no—
516C8—441no—
517C8—441no—
518C8—441no—
519C8—441no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22C2×#6699211yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—81no—
535C4—81no—
536C4—881no—
537C4—881no—
538C4D11×#13511yescharacteristic
539C4#1062329911yescharacteristic
540C4#1062336911yescharacteristic
541C4#1062336911yescharacteristic
542C2—41no—
543C2—81no—
544C2#1307806711yescharacteristic
545C2#1307826811yescharacteristic
546C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3233C2
socleC22×C11C2×#121
prime radicalC11×#121D4
hypercenter#3233D11
hypocenterC11#19226
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3233

Complements

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

NH ≅ G/Ntype
2. #13079198C2semidirect
4. #13068142C2semidirect
5. #13068137C2semidirect
6. #13068108C2semidirect
7. #13068103C2semidirect
8. #13068076C2semidirect
9. #13068072C2semidirect
10. #13068069C2semidirect
11. #13068065C2semidirect
12. #13067362C2semidirect
13. #13067326C2semidirect
14. #13067324C2semidirect
476. C11#19226semidirect

Maximal subgroups

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

subgroupindex
#130797912
#130791982
#130775922
#130681422
#130681372
#130681082
#130681032
#130680762
#130680722
#130680692
#130680652
#130673622
#130673262
#130673242
C11×#32332
#1922611