Finite Group Databasebeta

← #14910141

Subgroups — #14910141

Order 2816.

484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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#13079197C212yesmaximal
2#13070757C212yesmaximal, complemented
3#13070756C212yesmaximal, complemented
4#13070724C211yesmaximal, characteristic
5#13070722C212yesmaximal
6#13070665C212yesmaximal, complemented
7#13070664C212yesmaximal, complemented
8#13070371C211yesmaximal, characteristic
9C11×#2219C211yesmaximal, characteristic
10#10623153—22no—
11C2×C11×Q32C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13C11×#467C2212yes—
14Q16×Dic11C2212yes—
15#10622794C2212yes—
16C2×#66893C2212yes—
17#10622729C2212yes—
18C2×C8×Dic11C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20#10622664—22no—
21C2×Dic88C2211yescharacteristic
22#10622487C2212yes—
23#10622486C2212yes—
24#10622405—22no—
25#10622403—22no—
26C11×#367C2211yescharacteristic
27C11×#358C2212yes—
28#10622202C2212yes—
29#10622143C2211yescharacteristic
30#10622141C2212yes—
31Dic11⋊C16C2212yes—
32Dic11⋊C16C2212yes—
33#10622130C2212yes—
34#10622128C2212yes—
35C2×C11×Q16C2312yes—
36C22×C8×C11C2311yescharacteristic
37C11×C22⋊Q8—22no—
38Q8×Dic11—22no—
39#66997—22no—
40C2×#4326—22no—
41#66977—22no—
42C2×C4×Dic11D411yescharacteristic
43C22×C11⋊C8D411yescharacteristic
44C2×Dic44C2312yes—
45#66942—42no—
46#66941—22no—
47#66940—22no—
48#66940—42no—
49#66931—42no—
50#66930—42no—
51C11×Q32—41no—
52C11×M32—41no—
53C2×C11×C16C2311yescharacteristic
54C2×C11×C16C2311yescharacteristic
55C11×#107C2312yes—
56C11×#103—22no—
57#66899—22no—
58#66893—42no—
59#66882C2312yes—
60#66880—22no—
61C8×Dic11D412yes—
62C8×Dic11C2312yes—
63#66876—41no—
64C2×C11⋊C16C2312yes—
65#66874—22no—
66#66871—22no—
67Dic88—41no—
68#33821—111nomaximal, Sylow
69C2×Q8×C11—22no—
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11D812yes—
72C2×Dic22—22no—
73C2×Dic22—42no—
74C11×Q16—22no—
75C11×Q16—22no—
76C2×C8×C11—21no—
77C2×C8×C11—21no—
78C2×C8×C11C2×D411yescharacteristic
79C2×C8×C11C2411yescharacteristic
80C11×C4⋊C4—22no—
81C11×C4⋊C4—42no—
82C11×C22⋊C4—42no—
83C22⋊Dic11—42no—
84#4326—44no—
85C4⋊Dic11—22no—
86C4⋊Dic11—42no—
87Dic11⋊C4—42no—
88Dic11⋊C4—42no—
89Dic11⋊C4—42no—
90Dic11⋊C4—42no—
91Dic11⋊C4—42no—
92C4×Dic11—42no—
93C4×Dic11—42no—
94C4×Dic11D811yescharacteristic
95C4×Dic11D811yescharacteristic
96C4×Dic11C2×D412yes—
97C2×C11⋊C8—41no—
98C2×C11⋊C8C2×D412yes—
99Dic44—22no—
100Dic44—22no—
101C11×C16—21no—
102C11×C16—21no—
103C11⋊C16—22no—
104#3170—112no—
105#2225—112no—
106#2225—112no—
107#2219—111no—
108#2219—112no—
109#2219D1111yescharacteristic
110#2209—112no—
111#2209—112no—
112#2150—111no—
113C23×C11C2×D811yescharacteristic
114Q8×C11—42no—
115Q8×C11—42no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11C2×D811yescharacteristic
121C2×C4×C11C22×D411yescharacteristic
122C2×Dic11—24no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11C2×D812yes—
126C2×Dic11C2×D812yes—
127Dic22—42no—
128Dic22—42no—
129Dic22—84no—
130C8×C11—21no—
131C8×C11H(5,𝔽2)11yescharacteristic
132C8×C112−1+411yescharacteristic
133C11⋊C8—22no—
134#533—222no—
135C2×Q32—112no—
136C2×Q32—111no—
137C2×Q32C2×D1111yescharacteristic
138C2×M32—111no—
139C2×M32C2×D1111yescharacteristic
140#500—112no—
141#494—112no—
142#487—222no—
143#467—112no—
144#467—222no—
145#467C2×D1112yes—
146C4×Q16—112no—
147C4×Q16—112no—
148C4×Q16—222no—
149C2×C4×C8—111no—
150#367—111no—
151#367—112no—
152#367C2×D1111yescharacteristic
153C4⋊C16—112no—
154C4⋊C16—112no—
155#358—112no—
156#358—112no—
157#358—112no—
158#358C2×D1112yes—
159C22×C11—22no—
160C22×C11—21no—
161C22×C11C22×D811yescharacteristic
162C4×C11—21no—
163C4×C11—82no—
164C4×C11—82no—
165C4×C11#53711yescharacteristic
166C4×C11#57511yescharacteristic
167Dic11—22no—
168Dic11—82no—
169Dic11—82no—
170Dic11#51014yes—
171C2×Q16—112no—
172C2×Q16—222no—
173C2×Q16C22×D1112yes—
174C22×C8—111no—
175C22×C8C22×D1111yescharacteristic
176C4⋊Q8—222no—
177C4⋊Q8—222no—
178#125—442no—
179C22⋊Q8—22no—
180C22⋊Q8—222no—
181C22⋊Q8—442no—
182C4×Q8—222no—
183C4×Q8—222no—
184C4×Q8—442no—
185#117—442no—
186C2×C42—111no—
187Q32—41no—
188Q32—441no—
189Q32—442no—
190M32—41no—
191M32—441no—
192C2×C16—112no—
193C2×C16C22×D1111yescharacteristic
194C2×C16C22×D1111yescharacteristic
195#107—112no—
196#107—222no—
197#107C22×D1112yes—
198#103—22no—
199#103—222no—
200#103—222no—
201#103—222no—
202C4×C8—112no—
203C4×C8—112no—
204C2×C11—41no—
205C2×C11#324511yescharacteristic
206C2×C11C2×#51012yes—
207C2×Q8—22no—
208C2×Q8—222no—
209C2×Q8—442no—
210C22×C4—112no—
211C22×C4D4×D1111yescharacteristic
212Q16—22no—
213Q16—22no—
214Q16—222no—
215Q16—222no—
216Q16—444no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—112no—
220C2×C8—441no—
221C2×C8D4×D1111yescharacteristic
222C2×C8C23×D1111yescharacteristic
223C4⋊C4—22no—
224C4⋊C4—42no—
225C4⋊C4—222no—
226C4⋊C4—442no—
227C4⋊C4—442no—
228C4⋊C4—442no—
229C4⋊C4—442no—
230C4⋊C4—442no—
231C4⋊C4—442no—
232C22⋊C4—42no—
233C22⋊C4—442no—
234C42—111no—
235C42—111no—
236C42—112no—
237C42—442no—
238C42—442no—
239C16—21no—
240C16—21no—
241C16—222no—
242C11#3382111yescharacteristic, complemented, Sylow
243C23D8×D1111yescharacteristic
244Q8—42no—
245Q8—42no—
246Q8—442no—
247Q8—442no—
248Q8—884no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—112no—
254C2×C4—112no—
255C2×C4—224no—
256C2×C4—442no—
257C2×C4—442no—
258C2×C4D8×D1111yescharacteristic
259C2×C4C2×D4×D1111yescharacteristic
260C8—21no—
261C8—222no—
262C8#6703711yescharacteristic
263C8#6704311yescharacteristic
264C22—21no—
265C22—22no—
266C22C2×D8×D1111yescharacteristic
267C4—21no—
268C4—82no—
269C4—82no—
270C4—114no—
271C4—222no—
272C4—882no—
273C4—882no—
274C4#1062312811yescharacteristic
275C4#1062329911yescharacteristic
276C2—41no—
277C2#1307992211yescharacteristic
278C2D11×#51012yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2219C2
socleC22×C11C22×D8
prime radicalC23×C11C2×D8
hypercenter#2219D11
hypocenterC11#33821
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
2. #13070757C2semidirect
3. #13070756C2semidirect
6. #13070665C2semidirect
7. #13070664C2semidirect
242. C11#33821semidirect

Maximal subgroups

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

subgroupindex
#130791972
#130707572
#130707562
#130707242
#130707222
#130706652
#130706642
#130703712
C11×#22192
#3382111