Finite Group Databasebeta

← #14909594

Subgroups — #14909594

Order 2816.

592 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078199C212yesmaximal, complemented
2#13070822C212yesmaximal, complemented
3#13070809C212yesmaximal, complemented
4#13070731C212yesmaximal, complemented
5#13070719C211yesmaximal, characteristic, complemented
6#13070555C212yesmaximal, complemented
7#13070542C212yesmaximal, complemented
8#13070226C211yesmaximal, characteristic, complemented
9C11×#2219C211yesmaximal, characteristic, complemented
10C2×#66972C2212yes—
11C22×C8×D11C2211yescharacteristic
12#10623158—22no—
13C2×C11×Q32C2211yescharacteristic, complemented
14C2×C11×M32C2211yescharacteristic
15C11×#467C2212yes—
16#10622801C2212yes—
17C2×#66892C2212yescomplemented
18#10622728C2212yes—
19C2×#66876C2211yescharacteristic
20#10622661—22no—
21C2×D176C2211yescharacteristic, complemented
22#10622496C2212yes—
23#10622493C2212yes—
24#10622420—22no—
25#10622417—22no—
26C11×#367C2211yescharacteristic, complemented
27C11×#358C2212yescomplemented
28#10622202C2212yescomplemented
29#10622147C2212yescomplemented
30(C2×D11)⋊C16C2212yes—
31(C2×D11)⋊C16C2212yes—
32#10622143C2211yescharacteristic, complemented
33#10622129C2212yescomplemented
34#10622127C2212yescomplemented
35C2×#4343—22no—
36C22×C4×D11D411yescharacteristic
37C2×C11×Q16C2312yes—
38C22×C8×C11C2311yescharacteristic
39C11×C22⋊Q8—22no—
40#66999—22no—
41C2×#4325—22no—
42#66983—22no—
43C22×C11⋊C8D411yescharacteristic
44#66972—42no—
45#66972—42no—
46C2×D88C2312yes—
47C2×C8×D11—41no—
48C2×C8×D11—41no—
49C2×C8×D11D412yes—
50C2×C8×D11C2312yes—
51#66948—22no—
52#66947—42no—
53#66946—42no—
54#66945—22no—
55#66935—42no—
56(C22⋊D11)⋊C4—42no—
57C11×Q32—41no—
58C11×M32—41no—
59C2×C11×C16C2311yescharacteristic
60C2×C11×C16C2311yescharacteristic
61C11×#107C2312yes—
62C11×#103—22no—
63#66899—22no—
64#66892—42no—
65#66885—22no—
66#66882C2312yes—
67#66876—41no—
68C2×C11⋊C16C2312yes—
69#66873—22no—
70#66872—22no—
71D176—41no—
72#33763—111nomaximal, Sylow
73C23×D11D811yescharacteristic
74C2×Q8×C11—22no—
75C22×C4×C11C2×D411yescharacteristic
76C2×C22⋊D11—42no—
77C22×Dic11D811yescharacteristic
78#4343—44no—
79#4343—44no—
80C2×D44—22no—
81C2×D44—42no—
82C2×D44—42no—
83C2×C4×D11—41no—
84C2×C4×D11—41no—
85C2×C4×D11—42no—
86C2×C4×D11D812yes—
87C2×C4×D11C2×D412yes—
88C11×Q16—22no—
89C11×Q16—22no—
90C2×C8×C11—21no—
91C2×C8×C11—21no—
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2411yescharacteristic
94C11×C4⋊C4—22no—
95C11×C4⋊C4—42no—
96C11×C22⋊C4—42no—
97#4325—44no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102C4⋊Dic11—22no—
103Dic11⋊C4—42no—
104C4×Dic11—42no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8C2×D412yes—
107D88—22no—
108D88—22no—
109C8×D11—22no—
110C8×D11—22no—
111C8×D11—42no—
112C11×C16—21no—
113C11×C16—21no—
114C11⋊C16—22no—
115#3050—112no—
116#2237—112no—
117#2234—112no—
118#2220—112no—
119#2219D1111yescharacteristic, complemented
120#2218—111no—
121#2189—112no—
122#2186—112no—
123#2112—111no—
124C23×C11C2×D811yescharacteristic
125C22×D11—41no—
126C22×D11—42no—
127C22×D11—42no—
128C22×D11C2×D812yes—
129Q8×C11—42no—
130Q8×C11—42no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11C2×D811yescharacteristic
136C2×C4×C11C22×D411yescharacteristic
137C22⋊D11—84no—
138C2×Dic11—41no—
139C2×Dic11—42no—
140C2×Dic11C2×D812yes—
141D44—42no—
142D44—42no—
143D44—84no—
144D44—84no—
145C4×D11—22no—
146C4×D11—22no—
147C4×D11—42no—
148C4×D11—84no—
149C8×C11—21no—
150C8×C11H(5,𝔽2)11yescharacteristic
151C8×C11H(5,𝔽2)11yescharacteristic
152C11⋊C8—22no—
153C2×#135—112no—
154C23×C8—111no—
155#525—222no—
156C2×Q32C2×D1111yescharacteristic, complemented
157C2×SD32—112no—
158C2×D16—111no—
159C2×M32—111no—
160C2×M32C2×D1111yescharacteristic
161#467—112no—
162#467C2×D1112yes—
163#466—112no—
164#466—112no—
165#465—222no—
166#465—222no—
167#427—112no—
168#416—222no—
169#367—111no—
170#367C2×D1111yescharacteristic, complemented
171#366—112no—
172#358—112no—
173#358C2×D1112yescomplemented
174#357—112no—
175#357—112no—
176C22⋊C16—112no—
177C22⋊C16—112no—
178C22×C11—22no—
179C22×C11—21no—
180C22×C11C22×D811yescharacteristic
181C2×D11—22no—
182C2×D11—22no—
183C2×D11—22no—
184C2×D11—44no—
185C2×D11—82no—
186C2×D11—82no—
187C2×D11—82no—
188C4×C11—21no—
189C4×C11—82no—
190C4×C11—82no—
191C4×C11#53411yescharacteristic
192C4×C11#57511yescharacteristic
193Dic11—22no—
194Dic11—82no—
195C2×#41—222no—
196C23×C4—111no—
197#135—442no—
198#135—442no—
199C2×Q16C22×D1112yes—
200C2×SD16—222no—
201C2×D8—112no—
202C22×C8—111no—
203C22×C8—112no—
204C22×C8—112no—
205C22×C8—441no—
206C22×C8—441no—
207C22×C8C22×D1111yescharacteristic
208#123—442no—
209C22⋊Q8—22no—
210C22⋊Q8—222no—
211#121—222no—
212#121—222no—
213#120—442no—
214C4×D4—442no—
215C4×D4—442no—
216#117—222no—
217Q32—41no—
218SD32—442no—
219D16—441no—
220M32—41no—
221M32—441no—
222C2×C16—112no—
223C2×C16C22×D1111yescharacteristic
224C2×C16C22×D1111yescharacteristic
225#107—112no—
226#107C22×D1112yes—
227#106—222no—
228#103—22no—
229#103—222no—
230#102—222no—
231#102—222no—
232C2×C11—41no—
233C2×C11#318611yescharacteristic
234C2×C11#341412yes—
235D11—42no—
236D11—162no—
237C24—111no—
238#41—444no—
239#41—444no—
240C2×Q8—22no—
241C2×D4—222no—
242C2×D4—442no—
243C2×D4—442no—
244C2×D4—442no—
245C22×C4—111no—
246C22×C4—112no—
247C22×C4—112no—
248C22×C4—441no—
249C22×C4—441no—
250C22×C4—442no—
251C22×C4D4×D1111yescharacteristic
252Q16—22no—
253Q16—22no—
254SD16—444no—
255D8—222no—
256D8—222no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—112no—
260C2×C8—222no—
261C2×C8—222no—
262C2×C8—442no—
263C2×C8—441no—
264C2×C8D4×D1111yescharacteristic
265C2×C8C23×D1111yescharacteristic
266C4⋊C4—22no—
267C4⋊C4—42no—
268C4⋊C4—222no—
269C4⋊C4—442no—
270C22⋊C4—42no—
271C22⋊C4—442no—
272C22⋊C4—442no—
273C22⋊C4—442no—
274C22⋊C4—442no—
275C42—442no—
276C16—21no—
277C16—21no—
278C16—222no—
279C11#3376311yescharacteristic, complemented, Sylow
280C23—112no—
281C23—441no—
282C23—442no—
283C23—442no—
284C23D8×D1111yescharacteristic
285Q8—42no—
286Q8—42no—
287D4—442no—
288D4—442no—
289D4—884no—
290D4—884no—
291D4—884no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—112no—
297C2×C4—222no—
298C2×C4—222no—
299C2×C4—442no—
300C2×C4—441no—
301C2×C4—442no—
302C2×C4—884no—
303C2×C4D8×D1111yescharacteristic
304C2×C4C2×D4×D1111yescharacteristic
305C8—21no—
306C8—222no—
307C8#6703711yescharacteristic
308C8#6704211yescharacteristic
309C22—21no—
310C22—22no—
311C22—222no—
312C22—222no—
313C22—222no—
314C22—444no—
315C22—882no—
316C22—882no—
317C22—882no—
318C22C2×D8×D1111yescharacteristic
319C4—21no—
320C4—82no—
321C4—82no—
322C4—222no—
323C4—882no—
324C4#1062313611yescharacteristic
325C4#1062329911yescharacteristic
326C2—41no—
327C2—442no—
328C2—1762no—
329C2#1307936311yescharacteristic
330C2#1308175112yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2219C2
socleC22×C11C22×D8
hypercenter#2219D11
hypocenterC11#33763
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2219

Complements

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

NH ≅ G/Ntype
1. #13078199C2semidirect
2. #13070822C2semidirect
3. #13070809C2semidirect
4. #13070731C2semidirect
5. #13070719C2semidirect
6. #13070555C2semidirect
7. #13070542C2semidirect
8. #13070226C2semidirect
9. C11×#2219C2semidirect
13. C2×C11×Q32C22semidirect
17. C2×#66892C22semidirect
21. C2×D176C22semidirect
26. C11×#367C22semidirect
27. C11×#358C22semidirect
28. #10622202C22semidirect
29. #10622147C22semidirect
32. #10622143C22semidirect
33. #10622129C22semidirect
34. #10622127C22semidirect
119. #2219D11semidirect
156. C2×Q32C2×D11semidirect
170. #367C2×D11semidirect
173. #358C2×D11semidirect
279. C11#33763semidirect

Maximal subgroups

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

subgroupindex
#130781992
#130708222
#130708092
#130707312
#130707192
#130705552
#130705422
#130702262
C11×#22192
#3376311