Finite Group Databasebeta

← #14737070

Subgroups — #14737070

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079564C211yesmaximal, characteristic, complemented
2#13079559C211yesmaximal, characteristic
3C2×#10622701C211yesmaximal, characteristic
4#13077546C211yesmaximal, characteristic, complemented
5#13068187C214yesmaximal, complemented
6#13068063C214yesmaximal, complemented
7#13067362C211yesmaximal, characteristic, complemented
8#13067285C211yesmaximal, characteristic
9C11×#1549C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66927C2211yescharacteristic
12#10623001C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C11×#423C2211yescharacteristic
15#10622841—22no—
16#10622735—21no—
17#10622732—21no—
18#10622705—21no—
19#10622703C2214yescomplemented
20#10622701—21no—
21#10622701—21no—
22#10622701C2212yes—
23#10622701C2212yes—
24#10622694—21no—
25C2×#66873—21no—
26C2×#66873—21no—
27#10622538C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29#10622461C2214yes—
30#10622444—21no—
31#10622444C2212yescomplemented
32#10622443—21no—
33#10622443C2212yescomplemented
34#10622344—22no—
35#10622307—21no—
36#10622306—21no—
37C11×#332C2214yescomplemented
38#10622123C2214yes—
39#10622118C2212yescomplemented
40#10622117C2212yescomplemented
41C22×Q8×C11—21no—
42C22×D44—21no—
43C22×D44—21no—
44C22×D44—21no—
45C2×C11×M16—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8C2312yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4326—24no—
54#66979—21no—
55#66977—21no—
56#66977D412yes—
57C22×C11⋊C8D411yescharacteristic
58C22×C11⋊C8D411yescharacteristic
59C2×#4314—24no—
60#66927—21no—
61#66927—21no—
62#66927—21no—
63#66927C2312yes—
64#66923—21no—
65#66922D411yescharacteristic
66#66922D411yescharacteristic
67C4×Dic22—21no—
68C4×Dic22C2312yes—
69C11×C4⋊C8—21no—
70C11×C4⋊C8C2312yes—
71C11×C4⋊C8C2312yes—
72C11×C22⋊C8—21no—
73C4×C8×C11—21no—
74#66899—24no—
75C22⋊(C11⋊C8)—21no—
76#66885—24no—
77#66879—22no—
78Dic11⋊C8—22no—
79Dic11⋊C8—22no—
80C8×Dic11—22no—
81#66873—22no—
82#66873—22no—
83#66873—22no—
84#66873—22no—
85C4⋊(C11⋊C8)C2312yes—
86C4×C11⋊C8—21no—
87C4×C11⋊C8D411yescharacteristic
88C4×C11⋊C8D411yescharacteristic
89C4×C11⋊C8C2311yescharacteristic
90C4×C11⋊C8C2311yescharacteristic
91#19214—111nomaximal, Sylow
92C23×D11—41no—
93C2×Q8×C11—22no—
94C2×Q8×C11—41no—
95C2×Q8×C11—82no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C2×D44—22no—
101C2×D44—22no—
102C2×D44—22no—
103C2×D44—41no—
104C2×D44—41no—
105C2×D44—41no—
106C2×D44—42no—
107C2×D44—42no—
108C2×D44—82no—
109C2×D44—82no—
110C2×Dic22—21no—
111C2×Dic22C2×D412yes—
112C11×M16—42no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122C42×C11C2411yescharacteristic
123C22⋊Dic11—22no—
124#4326—84no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128C4⋊Dic11C2×D412yes—
129Dic11⋊C4—22no—
130Dic11⋊C4—22no—
131C4×Dic11—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8C2×D411yescharacteristic
136C2×C11⋊C8C2×D411yescharacteristic
137C2×C11⋊C8C2×D411yescharacteristic
138C2×C11⋊C8C2×D411yescharacteristic
139#4314—84no—
140#3209—111no—
141#3208—111no—
142C2×#486—111no—
143#2960—111no—
144#1702—114no—
145#1682—114no—
146#1564—111no—
147#1549D1111yescharacteristic, complemented
148#1545—111no—
149C23×C11#12111yescharacteristic
150C22×D11—42no—
151C22×D11—82no—
152C22×D11—82no—
153C22×D11—82no—
154Q8×C11—44no—
155Q8×C11—82no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—42no—
159C2×C4×C11—82no—
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#13512yes—
164C2×C4×C11#13712yes—
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C2×#4111yescharacteristic
168C2×Dic11—22no—
169C2×Dic11—22no—
170D44—42no—
171D44—42no—
172D44—44no—
173D44—82no—
174D44—82no—
175D44—82no—
176D44—82no—
177Dic22—24no—
178Dic22—42no—
179C8×C11—42no—
180C8×C11—42no—
181C11⋊C8—21no—
182C11⋊C8—21no—
183C11⋊C8—21no—
184C11⋊C8—21no—
185C11⋊C8—42no—
186#533—111no—
187C2×C4⋊Q8C2×D1111yescharacteristic
188C2×#127—111no—
189#494—221no—
190#492—221no—
191#487—221no—
192#486—112no—
193#486—112no—
194#486—221no—
195#486—221no—
196#486—221no—
197#462—114no—
198#460—114no—
199#451—222no—
200#450—222no—
201#446—112no—
202#446—221no—
203C8×Q8—112no—
204C8×Q8—221no—
205#431—111no—
206#431C2×D1111yescharacteristic
207#424—221no—
208#423C2×D1111yescharacteristic
209C2×#102—221no—
210C2×#102—221no—
211#405—221no—
212C2×C4×C8—111no—
213#335—112no—
214#334—112no—
215#332C2×D1114yescomplemented
216#331—114no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11#46412yes—
220C22×C11C2×#12111yescharacteristic
221C2×D11—82no—
222C2×D11—82no—
223C2×D11—82no—
224C2×D11—164no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—82no—
228C4×C11#46412yes—
229C4×C11#47112yes—
230C4×C11C2×#13511yescharacteristic
231C4×C11C2×#13711yescharacteristic
232C4×C11#57612yes—
233Dic11—42no—
234Dic11—42no—
235C22×Q8—21no—
236C22×D4—221no—
237C22×D4—221no—
238C22×D4—221no—
239C2×Q16—224no—
240C2×SD16—224no—
241C2×M16—21no—
242C22×C8—111no—
243C22×C8—111no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—111no—
248C4⋊Q8—111no—
249C4⋊Q8C22×D1112yes—
250#127—112no—
251#127—221no—
252#127—221no—
253#127—221no—
254#125—221no—
255C22⋊Q8—112no—
256C22⋊Q8—221no—
257C4×Q8—112no—
258C4×Q8—221no—
259#117—221no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C42C22×D1111yescharacteristic
263C4⋊C8—21no—
264C4⋊C8—112no—
265C4⋊C8—222no—
266C4⋊C8—222no—
267C4⋊C8C22×D1112yes—
268C4⋊C8C22×D1112yes—
269#103—224no—
270#102—222no—
271#102—222no—
272#102—222no—
273#102—222no—
274#102—224no—
275C22⋊C8—21no—
276C22⋊C8—221no—
277#97—222no—
278C4×C8—21no—
279C4×C8—111no—
280C4×C8—111no—
281C4×C8—111no—
282C4×C8—111no—
283C4×C8—222no—
284C4×C8—221no—
285C2×C11—22no—
286C2×C11C2×#46411yescharacteristic
287C2×C11#305811yescharacteristic
288C2×C11C2×#47111yescharacteristic
289D11—162no—
290C24—441no—
291C2×Q8—22no—
292C2×Q8—41no—
293C2×Q8—82no—
294C2×Q8—112no—
295C2×Q8—221no—
296C2×D4—222no—
297C2×D4—222no—
298C2×D4—222no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—441no—
302C2×D4—442no—
303C2×D4—442no—
304C2×D4—882no—
305C2×D4—882no—
306C22×C4—41no—
307C22×C4#433911yescharacteristic
308C22×C4D4×D1111yescharacteristic
309C22×C4D4×D1111yescharacteristic
310Q16—884no—
311SD16—884no—
312M16—42no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—111no—
316C2×C8—111no—
317C2×C8—111no—
318C2×C8—111no—
319C2×C8—222no—
320C2×C8—222no—
321C2×C8—222no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—112no—
327C4⋊C4—221no—
328C4⋊C4—221no—
329C4⋊C4—222no—
330C4⋊C4—221no—
331C4⋊C4—222no—
332C22⋊C4—222no—
333C42—222no—
334C42#433911yescharacteristic
335C42D4×D1111yescharacteristic
336C42D4×D1111yescharacteristic
337C42C23×D1111yescharacteristic
338C11#1921411yescharacteristic, complemented, Sylow
339C23—442no—
340C23—882no—
341C23—882no—
342C23—882no—
343C23#6693711yescharacteristic
344Q8—44no—
345Q8—82no—
346Q8—224no—
347Q8—442no—
348D4—442no—
349D4—442no—
350D4—444no—
351D4—882no—
352D4—882no—
353D4—882no—
354D4—882no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4#6693711yescharacteristic
362C2×C4#6693711yescharacteristic
363C2×C4#6693711yescharacteristic
364C2×C4#6696912yes—
365C2×C4#6697112yes—
366C2×C4C2×#433911yescharacteristic
367C2×C4C2×D4×D1111yescharacteristic
368C2×C4C2×D4×D1111yescharacteristic
369C8—42no—
370C8—42no—
371C8—221no—
372C8—221no—
373C8—221no—
374C8—221no—
375C8—442no—
376C22—21no—
377C22—21no—
378C22—882no—
379C22—882no—
380C22—882no—
381C22—1764no—
382C22#1062241112yes—
383C22C2×#6693711yescharacteristic
384C4—21no—
385C4—21no—
386C4—82no—
387C4—442no—
388C4—442no—
389C4#1062236712yes—
390C4#1062241112yes—
391C4C2×#6696911yescharacteristic
392C4C2×#6697111yescharacteristic
393C4#1062330512yes—
394C2—22no—
395C2—1762no—
396C2C2×#1062241111yescharacteristic
397C2#1307826311yescharacteristic
398C2C2×#1062236711yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1549C2
socleC22×C11C2×#121
prime radicalC2×#66927C22
hypercenter#1549D11
hypocenterC11#19214
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
1. #13079564C2semidirect
4. #13077546C2semidirect
5. #13068187C2semidirect
6. #13068063C2semidirect
7. #13067362C2semidirect
9. C11×#1549C2semidirect
19. #10622703C22semidirect
31. #10622444C22semidirect
33. #10622443C22semidirect
37. C11×#332C22semidirect
39. #10622118C22semidirect
40. #10622117C22semidirect
147. #1549D11semidirect
215. #332C2×D11semidirect
338. C11#19214semidirect

Maximal subgroups

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

subgroupindex
#130795642
#130795592
C2×#106227012
#130775462
#130681872
#130680632
#130673622
#130672852
C11×#15492
#1921411