Finite Group Databasebeta

← #14738890

Subgroups — #14738890

Order 2816.

572 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#13079989C211yesmaximal, characteristic
2#13079843C211yesmaximal, characteristic
3#13078997C211yesmaximal, characteristic, complemented
4#13068198C211yesmaximal, characteristic, complemented
5#13068191C211yesmaximal, characteristic, complemented
6#13068170C211yesmaximal, characteristic, complemented
7#13068163C211yesmaximal, characteristic, complemented
8#13068074C211yesmaximal, characteristic, complemented
9#13068067C211yesmaximal, characteristic, complemented
10#13068046C211yesmaximal, characteristic, complemented
11#13068039C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067324C211yesmaximal, characteristic, complemented
14#13067300C211yesmaximal, characteristic, complemented
15C11×#2969C211yesmaximal, characteristic
16C11×#529C2211yescharacteristic
17#10623001C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C11×#436—21no—
22C11×#436C2211yescharacteristic
23C11×#435—21no—
24C8×D4×C11C2211yescharacteristic
25C11×#433—21no—
26C11×#431C2211yescharacteristic
27C11×#405—21no—
28C4×C11×M16C2211yescharacteristic
29#10622733—21no—
30#10622733—21no—
31#10622678—21no—
32#10622676—21no—
33#10622668—21no—
34#10622667—21no—
35#10622665—21no—
36#10622657—21no—
37#10622655—21no—
38#10622647—21no—
39#10622644C2211yescharacteristic
40#10622634C2211yescharacteristic
41#10622633C2211yescharacteristic
42#10622633C2211yescharacteristic
43#10622632C2211yescharacteristic
44#10622621C2211yescharacteristic
45#10622620C2211yescharacteristic
46#10622620C2211yescharacteristic
47#10622539C2211yescharacteristic
48#10622537C2211yescharacteristic
49#10622316—21no—
50#10622316—21no—
51#10622294C2211yescharacteristic
52#10622294C2211yescharacteristic
53#10622294C2211yescharacteristic
54#10622294C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622120C2211yescharacteristic
58#10622120C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C22×Dic22—21no—
68C2×C11×M16—21no—
69C2×C11×M16D411yescharacteristic
70C2×C11×M16D411yescharacteristic
71C22×C8×C11—21no—
72C11×#126—21no—
73C11×#125D411yescharacteristic
74C11×#124D411yescharacteristic
75C11×#123—21no—
76C11×C22⋊Q8D411yescharacteristic
77C11×#121D411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11C2311yescharacteristic
81C11×#117—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4326—21no—
84C2×#4324—21no—
85#66979—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88#66977—21no—
89#66977—21no—
90C2×#4318—21no—
91#66923—21no—
92#66922—21no—
93#66922—21no—
94#66922—21no—
95#66922C2311yescharacteristic
96#66922C2311yescharacteristic
97#66922C2311yescharacteristic
98#66922C2311yescharacteristic
99C4×Dic22—21no—
100C4×Dic22—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C22⋊C8—21no—
106C11×C22⋊C8—21no—
107C11×C22⋊C8—21no—
108C11×#97—21no—
109C11×#97D411yescharacteristic
110C11×#97D411yescharacteristic
111C4×C8×C11—21no—
112C4×C8×C11—21no—
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115#66899—21no—
116#66899—21no—
117#66899—21no—
118#66896—21no—
119#66896—21no—
120#66896—21no—
121C22⋊(C11⋊C8)—21no—
122#66880—21no—
123#66880—21no—
124#66880—21no—
125#66880—21no—
126#66880—21no—
127#66880—21no—
128#66880—21no—
129#66880—21no—
130#66874—21no—
131#66874—21no—
132#66872—21no—
133#66872—21no—
134#66872—21no—
135#66871—21no—
136#66871—21no—
137#66871—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143#66867—21no—
144#19381—111nomaximal, Sylow
145C2×Q8×C11C2×D411yescharacteristic
146C2×D4×C11—21no—
147C2×D4×C11C2×D411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C22×Dic11—41no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—42no—
158C2×Dic22—42no—
159C2×Dic22—41no—
160C11×M16—41no—
161C11×M16—41no—
162C11×M16—42no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—42no—
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4C2×D411yescharacteristic
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C42×C11—21no—
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11#4111yescharacteristic
185C42×C11C2411yescharacteristic
186C22⋊Dic11—41no—
187#4326—81no—
188#4324—81no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—41no—
198C4⋊Dic11—41no—
199Dic11⋊C4—41no—
200Dic11⋊C4—41no—
201C4×Dic11—41no—
202#4318—81no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207#3252—111no—
208#3239—111no—
209#3139—111no—
210#2969D1111yescharacteristic
211#1704—111no—
212#1703—111no—
213#1700—111no—
214#1699—111no—
215#1684—111no—
216#1683—111no—
217#1680—111no—
218#1679—111no—
219#1569—111no—
220#1554—111no—
221#1549—111no—
222C23×C11—21no—
223C23×C11#12111yescharacteristic
224Q8×C11—21no—
225Q8×C11—21no—
226D4×C11—21no—
227D4×C11—21no—
228D4×C11—81no—
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#12111yescharacteristic
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—82no—
250Dic22—41no—
251Dic22—41no—
252Dic22—41no—
253Dic22—41no—
254Dic22—41no—
255Dic22—41no—
256Dic22—82no—
257Dic22—81no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—41no—
263C8×C11—41no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268#533—111no—
269C2×C4⋊Q8—111no—
270#529C2×D1111yescharacteristic
271#501—221no—
272#491—221no—
273#491—221no—
274#489—221no—
275#487—111no—
276#487—111no—
277#487—111no—
278#487—111no—
279#484—221no—
280#481—221no—
281#479—221no—
282#477—111no—
283#476—111no—
284#475—111no—
285#475—111no—
286#474—111no—
287#474—111no—
288#470—221no—
289#468—221no—
290#464—221no—
291#462—111no—
292#461—111no—
293#446C2×D1111yescharacteristic
294C8×Q8C2×D1111yescharacteristic
295#436—21no—
296#436C2×D1111yescharacteristic
297#435—21no—
298C8×D4C2×D1111yescharacteristic
299#433—21no—
300#432—111no—
301#431C2×D1111yescharacteristic
302#423—111no—
303#419—221no—
304#419—221no—
305#405—21no—
306C4×M16C2×D1111yescharacteristic
307#335—111no—
308#335—111no—
309#334—111no—
310#334—111no—
311#333—111no—
312#333—111no—
313#332—111no—
314#332—111no—
315#332—111no—
316#332—111no—
317#332—111no—
318#332—111no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11C2×#12111yescharacteristic
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11#57511yescharacteristic
334C4×C11#57511yescharacteristic
335C4×C11#57711yescharacteristic
336C4×C11#57811yescharacteristic
337Dic11—81no—
338Dic11—81no—
339Dic11—81no—
340Dic11—81no—
341C22×Q8—221no—
342C2×Q16—221no—
343C2×SD16—221no—
344C2×M16—21no—
345C2×M16—221no—
346C2×M16C22⋊D1111yescharacteristic
347C2×M16C22⋊D1111yescharacteristic
348C22×C8—21no—
349C4⋊Q8—111no—
350C4⋊Q8—111no—
351C4⋊Q8—111no—
352C4⋊Q8—111no—
353C4⋊Q8—221no—
354C4⋊Q8—221no—
355C4⋊Q8—221no—
356#126—21no—
357#125—221no—
358#125D4411yescharacteristic
359#124D4411yescharacteristic
360#123—21no—
361C22⋊Q8—221no—
362C22⋊Q8—221no—
363C22⋊Q8D4411yescharacteristic
364#121D4411yescharacteristic
365C4×Q8—221no—
366C4×Q8—221no—
367C4×Q8C22×D1111yescharacteristic
368C4×D4—21no—
369C4×D4C22×D1111yescharacteristic
370#117—21no—
371#117—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C42C22×D1111yescharacteristic
375#107—221no—
376#107—221no—
377#107—221no—
378#106—221no—
379#106—221no—
380#106—221no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—111no—
384C4⋊C8—111no—
385C4⋊C8—111no—
386C4⋊C8—111no—
387C4⋊C8—221no—
388C4⋊C8C22×D1111yescharacteristic
389C4⋊C8C22×D1111yescharacteristic
390#103—221no—
391#103—221no—
392#103—221no—
393#103—221no—
394#103—221no—
395#103—221no—
396#103—221no—
397#103—221no—
398#103—221no—
399#103—221no—
400#103—221no—
401#103—221no—
402#103—221no—
403#102—221no—
404#102—221no—
405#102—221no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8—221no—
410#97—21no—
411#97—221no—
412#97C22⋊D1111yescharacteristic
413#97C22⋊D1111yescharacteristic
414C4×C8—21no—
415C4×C8—21no—
416C4×C8C22×D1111yescharacteristic
417C4×C8C22×D1111yescharacteristic
418C2×C11—41no—
419C2×C11—81no—
420C2×C11#304011yescharacteristic
421C2×C11#306311yescharacteristic
422C2×C11#306911yescharacteristic
423C2×Q8—221no—
424C2×Q8—221no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×Q8—442no—
428C2×Q8—442no—
429C2×Q8—441no—
430C2×Q8C2×D4411yescharacteristic
431C2×D4—21no—
432C2×D4C2×D4411yescharacteristic
433C22×C4—21no—
434C22×C4—441no—
435C22×C4C2×D4411yescharacteristic
436C22×C4#433911yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438Q16—881no—
439SD16—881no—
440M16—41no—
441M16—41no—
442M16—42no—
443M16—881no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—42no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8C2×C22⋊D1111yescharacteristic
452C2×C8C2×C22⋊D1111yescharacteristic
453C2×C8C2×C22⋊D1111yescharacteristic
454C2×C8C2×C22⋊D1111yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
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⋊C4C2×D4411yescharacteristic
472C4⋊C4C2×D4411yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—441no—
479C42—21no—
480C42—441no—
481C42C2×D4411yescharacteristic
482C42#433911yescharacteristic
483C42C2×C22⋊D1111yescharacteristic
484C42C23×D1111yescharacteristic
485C11#1938111yescharacteristic, complemented, Sylow
486C23—21no—
487C23#6698311yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—441no—
491Q8—441no—
492Q8—441no—
493Q8—441no—
494Q8—441no—
495Q8—441no—
496Q8—881no—
497Q8—882no—
498D4—21no—
499D4—21no—
500D4—81no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—882no—
516C2×C4#6698311yescharacteristic
517C2×C4#6698311yescharacteristic
518C2×C4#6698311yescharacteristic
519C2×C4C22×D4411yescharacteristic
520C2×C4C2×#433911yescharacteristic
521C2×C4C22×C22⋊D1111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—441no—
529C8—441no—
530C8—441no—
531C8—441no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22C2×#6698311yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—881no—
547C4—881no—
548C4—881no—
549C4—881no—
550C4#1062328211yescharacteristic
551C4#1062328411yescharacteristic
552C4#1062335311yescharacteristic
553C4#1062335311yescharacteristic
554C2—41no—
555C2—81no—
556C2#1307811011yescharacteristic
557C2#1307830711yescharacteristic
558C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2969C2
socleC22×C11C2×#121
prime radicalC11×#121D4
hypercenter#2969D11
hypocenterC11#19381
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2969

Complements

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

NH ≅ G/Ntype
3. #13078997C2semidirect
4. #13068198C2semidirect
5. #13068191C2semidirect
6. #13068170C2semidirect
7. #13068163C2semidirect
8. #13068074C2semidirect
9. #13068067C2semidirect
10. #13068046C2semidirect
11. #13068039C2semidirect
12. #13067383C2semidirect
13. #13067324C2semidirect
14. #13067300C2semidirect
485. C11#19381semidirect

Maximal subgroups

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

subgroupindex
#130799892
#130798432
#130789972
#130681982
#130681912
#130681702
#130681632
#130680742
#130680672
#130680462
#130680392
#130673832
#130673242
#130673002
C11×#29692
#1938111