Finite Group Databasebeta

← C2×#10622783 #13077802

Subgroups — C2×#10622783 #13077802

Order 1408.

792 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C22×Q8×D11C211yesmaximal, characteristic, complemented
2C22×C11×SD16C211yesmaximal, characteristic, complemented
3C2×#66991C211yesmaximal, characteristic
4C22×#4324C211yesmaximal, characteristic, complemented
5C2×#66899C211yesmaximal, characteristic, complemented
6#10622783C218yesmaximal, direct product factor
7C2×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
8C2×#66880C211yesmaximal, characteristic, complemented
9C22×Q8×C11C2211yescharacteristic
10C22×D4×C11C2211yescharacteristic
11C22×C22⋊D11—21no—
12C2×Q8×D11—24no—
13C2×Q8×D11—22no—
14C2×Q8×D11—24no—
15C2×Q8×D11C2214yescomplemented
16C22×C4×D11—21no—
17C22×C4×D11C2211yescharacteristic
18C22×Dic22—21no—
19C22×Dic22C2211yescharacteristic
20C2×C11×SD16—24no—
21C2×C11×SD16C2214yescomplemented
22C22×C8×C11C2211yescharacteristic
23C2×C22⋊Dic11—21no—
24#66991—22no—
25#66991C2214yes—
26C2×#4324—24no—
27C2×#4324C2214yescomplemented
28C2×C4⋊Dic11C2211yescharacteristic
29C22×C11⋊C8C2211yescharacteristic
30#66899C2214yescomplemented
31(C2×D11)⋊C8C2214yescomplemented
32#66880C2214yescomplemented
33C24×C11—21no—
34C23×D11D411yescharacteristic
35C2×Q8×C11—22no—
36C2×Q8×C11—21no—
37C2×Q8×C11D414yescomplemented
38C2×Q8×C11C2312yes—
39C2×D4×C11—22no—
40C2×D4×C11—22no—
41C2×D4×C11—21no—
42C2×D4×C11C2312yes—
43C22×C4×C11—21no—
44C22×C4×C11C2311yescharacteristic
45C2×C22⋊D11—24no—
46C2×C22⋊D11—44no—
47C22×Dic11—21no—
48C22×Dic11—21no—
49C22×Dic11D411yescharacteristic
50Q8×D11—216no—
51Q8×D11—28no—
52Q8×D11—28no—
53C2×C4×D11—28no—
54C2×C4×D11—24no—
55C2×C4×D11—22no—
56C2×C4×D11—22no—
57C2×C4×D11D412yes—
58C2×C4×D11C2312yes—
59C2×Dic22—28no—
60C2×Dic22—24no—
61C2×Dic22—21no—
62C2×Dic22—22no—
63C2×Dic22D414yescomplemented
64C2×Dic22C2312yes—
65C11×SD16—28no—
66C2×C8×C11—22no—
67C2×C8×C11C2312yes—
68C22⋊Dic11—24no—
69#4324—28no—
70C4⋊Dic11—21no—
71C4⋊Dic11C2312yes—
72C2×C11⋊C8—22no—
73C2×C11⋊C8C2312yes—
74C2×#448—111nomaximal, Sylow
75C23×C11—22no—
76C23×C11—42no—
77C23×C11—42no—
78C23×C11—42no—
79C23×C11C2×D411yescharacteristic
80C22×D11—22no—
81C22×D11—22no—
82C22×D11SD1614yescomplemented
83C22×D11C2×D412yes—
84Q8×C11—24no—
85Q8×C11—22no—
86Q8×C11C2×D414yescomplemented
87D4×C11—22no—
88D4×C11—22no—
89D4×C11—42no—
90C2×C4×C11—24no—
91C2×C4×C11—22no—
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D412yes—
94C2×C4×C11C2×D412yes—
95C2×C4×C11C2411yescharacteristic
96C22⋊D11—48no—
97C2×Dic11—22no—
98C2×Dic11—24no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—42no—
102C2×Dic11C2×D412yes—
103C4×D11—216no—
104C4×D11—24no—
105C4×D11—22no—
106C4×D11—22no—
107Dic22—216no—
108Dic22—24no—
109Dic22—22no—
110Dic22C2×D414yescomplemented
111C8×C11—22no—
112C11⋊C8—22no—
113C23×Q8—111no—
114C22×SD16—111no—
115C22×SD16D1111yescharacteristic, complemented
116C2×#121—111no—
117#448—118no—
118C2×#103—111no—
119C2×#103—111no—
120C2×C22⋊C8—111no—
121C22×C11—42no—
122C22×C11—42no—
123C22×C11—42no—
124C22×C11—84no—
125C22×C11#12012yes—
126C22×C11C2×SD1612yes—
127C22×C11#13712yes—
128C22×C11C22×D411yescharacteristic
129C2×D11—22no—
130C2×D11—22no—
131C2×D11—28no—
132C2×D11C2×SD1614yescomplemented
133C4×C11—24no—
134C4×C11#12012yes—
135C4×C11C22×D411yescharacteristic
136C4×C11C22×D411yescharacteristic
137Dic11—22no—
138Dic11—24no—
139Dic11—42no—
140C22×Q8—114no—
141C22×Q8—111no—
142C22×Q8—221no—
143C22×Q8—222no—
144C22×Q8—224no—
145C22×Q8—224no—
146C22×Q8C2×D1111yescharacteristic
147C22×D4—221no—
148C22×D4C2×D1111yescharacteristic
149C23×C4—111no—
150C23×C4—221no—
151C2×SD16—24no—
152C2×SD16—114no—
153C2×SD16—224no—
154C2×SD16C2×D1114yescomplemented
155C22×C8—111no—
156C22×C8C2×D1111yescharacteristic
157#121—114no—
158#121—222no—
159C2×C4⋊C4—111no—
160C2×C22⋊C4—221no—
161#103—114no—
162#103—114no—
163C22⋊C8—114no—
164C2×C11—82no—
165C2×C11#44814yescomplemented
166C2×C11C2×#12011yescharacteristic
167C2×C11C22×SD1611yescharacteristic
168C2×C11C2×#13711yescharacteristic
169D11—24no—
170C24—21no—
171C24—111no—
172C2×Q8—22no—
173C2×Q8—21no—
174C2×Q8—114no—
175C2×Q8—112no—
176C2×Q8—224no—
177C2×Q8—228no—
178C2×Q8—228no—
179C2×Q8—2216no—
180C2×Q8—228no—
181C2×Q8—221no—
182C2×Q8—222no—
183C2×Q8C22⋊D1114yescomplemented
184C2×Q8C22×D1112yes—
185C2×D4—22no—
186C2×D4—21no—
187C2×D4—22no—
188C2×D4—224no—
189C2×D4—444no—
190C2×D4C22×D1112yes—
191C22×C4—21no—
192C22×C4—111no—
193C22×C4—112no—
194C22×C4—112no—
195C22×C4—224no—
196C22×C4—228no—
197C22×C4—221no—
198C22×C4—222no—
199C22×C4—222no—
200C22×C4—221no—
201C22×C4C22×D1111yescharacteristic
202SD16—28no—
203SD16—228no—
204C2×C8—22no—
205C2×C8—112no—
206C2×C8—222no—
207C2×C8C22×D1112yes—
208C4⋊C4—112no—
209C4⋊C4—221no—
210C22⋊C4—224no—
211C11C2×#44811yescharacteristic, complemented, Sylow
212C23—22no—
213C23—42no—
214C23—42no—
215C23—42no—
216C23—114no—
217C23—112no—
218C23—222no—
219C23—222no—
220C23D4×D1111yescharacteristic
221Q8—24no—
222Q8—22no—
223Q8—114no—
224Q8—2216no—
225Q8—224no—
226Q8—222no—
227Q8C2×C22⋊D1114yescomplemented
228D4—22no—
229D4—22no—
230D4—42no—
231D4—448no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—112no—
235C2×C4—2216no—
236C2×C4—222no—
237C2×C4—224no—
238C2×C4—222no—
239C2×C4—224no—
240C2×C4—222no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—442no—
244C2×C4D4×D1111yescharacteristic
245C2×C4D4×D1112yes—
246C2×C4C2×C22⋊D1112yes—
247C2×C4C23×D1111yescharacteristic
248C8—22no—
249C8—222no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—84no—
254C22—114no—
255C22—222no—
256C22—228no—
257C22—222no—
258C22SD16×D1112yes—
259C22#6696812yes—
260C22#6699012yes—
261C22C2×D4×D1111yescharacteristic
262C4—24no—
263C4—222no—
264C4—224no—
265C4—442no—
266C4#6699012yes—
267C4C2×D4×D1111yescharacteristic
268C4C22×C22⋊D1111yescharacteristic
269C2—82no—
270C2—224no—
271C2#1062278314yesdirect product factor
272C2C2×SD16×D1111yescharacteristic
273C2C2×#6696811yescharacteristic
274C2C2×#6699011yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC22×C11×SD16C2
socleC23×C11C2×D4
prime radicalC2×#66991C2
hypercenterC22×SD16D11
hypocenterC11C2×#448
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D11C2semidirect
2. C22×C11×SD16C2semidirect
4. C22×#4324C2semidirect
5. C2×#66899C2semidirect
6. #10622783C2direct (N × H)
7. C2×(C2×D11)⋊C8C2semidirect
8. C2×#66880C2semidirect
15. C2×Q8×D11C22semidirect
21. C2×C11×SD16C22semidirect
27. C2×#4324C22semidirect
30. #66899C22semidirect
31. (C2×D11)⋊C8C22semidirect
32. #66880C22semidirect
37. C2×Q8×C11D4semidirect
63. C2×Dic22D4semidirect
82. C22×D11SD16semidirect
86. Q8×C11C2×D4semidirect
110. Dic22C2×D4semidirect
115. C22×SD16D11semidirect
132. C2×D11C2×SD16semidirect
154. C2×SD16C2×D11semidirect
165. C2×C11#448semidirect
183. C2×Q8C22⋊D11semidirect
211. C11C2×#448semidirect
227. Q8C2×C22⋊D11semidirect
271. C2#10622783direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D112
C22×C11×SD162
C2×#669912
C22×#43242
C2×#668992
#106227832
C2×(C2×D11)⋊C82
C2×#668802
C2×#44811