Finite Group Databasebeta

← #13078560

Subgroups — #13078560

Order 1408.

410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×C11×C22⋊Q8C211yesmaximal, characteristic
2C2×#66979C211yesmaximal, characteristic
3#10622838C212yesmaximal, complemented
4#10622820C211yesmaximal, characteristic
5#10622658C214yesmaximal, complemented
6#10622657C212yesmaximal, complemented
7#10622656C212yesmaximal, complemented
8#10622577C212yesmaximal, complemented
9C22×Q8×C11C2211yescharacteristic
10C23×C4×C11C2211yescharacteristic
11C11×C22⋊Q8—21no—
12C11×C22⋊Q8—21no—
13C11×C22⋊Q8C2212yes—
14C11×C22⋊Q8C2212yes—
15C2×C11×C4⋊C4—21no—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4—21no—
18C2×C22⋊Dic11—21no—
19#66979—21no—
20#66979—21no—
21#66979C2212yes—
22#66979C2212yes—
23C2×C4⋊Dic11C2211yescharacteristic
24C2×C4⋊Dic11C2211yescharacteristic
25C2×C4×Dic11—21no—
26C2×#4318C2212yes—
27#66899C2214yescomplemented
28#66899C2214yescomplemented
29C22⋊(C11⋊C8)C2212yes—
30C22⋊(C11⋊C8)C2212yes—
31#66872C2214yescomplemented
32#66871C2214yescomplemented
33C24×C11D411yescharacteristic
34C2×Q8×C11—21no—
35C2×Q8×C11—24no—
36C2×Q8×C11C2312yes—
37C22×C4×C11—24no—
38C22×C4×C11—21no—
39C22×C4×C11—21no—
40C22×C4×C11D411yescharacteristic
41C22×C4×C11D411yescharacteristic
42C22×C4×C11D411yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C22×Dic11—21no—
47C22×Dic11—21no—
48C11×C4⋊C4—22no—
49C11×C4⋊C4—22no—
50C11×C4⋊C4—21no—
51C11×C4⋊C4C2312yes—
52C11×C22⋊C4—22no—
53C11×C22⋊C4—22no—
54C22⋊Dic11—22no—
55C22⋊Dic11—22no—
56C4⋊Dic11—21no—
57C4⋊Dic11—21no—
58C4⋊Dic11C2312yes—
59C4⋊Dic11C2312yes—
60C4×Dic11—22no—
61C4×Dic11—22no—
62#4318—24no—
63C2×C11⋊C8C2314yes—
64#3095—111nomaximal, Sylow
65C23×C11—22no—
66C23×C11—22no—
67C23×C11—41no—
68C23×C11C2×D411yescharacteristic
69C23×C11C2×D411yescharacteristic
70C23×C11C2×D411yescharacteristic
71Q8×C11—24no—
72Q8×C11—42no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—42no—
81C2×C4×C11—42no—
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11#4114yes—
86C2×C4×C11C2411yescharacteristic
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—42no—
90C2×Dic11—42no—
91C11⋊C8—24no—
92C2×C22⋊Q8D1111yescharacteristic
93C2×#117—111no—
94#485—114no—
95#484—112no—
96#483—112no—
97#428—112no—
98#419—112no—
99#407—111no—
100C22×C11—21no—
101C22×C11—21no—
102C22×C11—21no—
103C22×C11—21no—
104C22×C11—21no—
105C22×C11—21no—
106C22×C11—21no—
107C22×C11—44no—
108C22×C11#12312yes—
109C22×C11#13712yes—
110C22×C11C22×D411yescharacteristic
111C4×C11—21no—
112C4×C11—21no—
113C4×C11—42no—
114C4×C11—42no—
115C4×C11#12312yes—
116C4×C11C2×#4112yes—
117Dic11—42no—
118Dic11—42no—
119C22×Q8C2×D1111yescharacteristic
120C23×C4C2×D1111yescharacteristic
121C2×M16—112no—
122C22⋊Q8—21no—
123C22⋊Q8—21no—
124C22⋊Q8C2×D1112yes—
125C22⋊Q8C2×D1112yes—
126#117—112no—
127#117—112no—
128#117—221no—
129#117—221no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—111no—
132C2×C4⋊C4—111no—
133C2×C4⋊C4C2×D1111yescharacteristic
134C2×C22⋊C4—21no—
135C2×C22⋊C4—221no—
136C2×C42—221no—
137#107—114no—
138#106—114no—
139#103—114no—
140#103—114no—
141C22⋊C8—112no—
142C22⋊C8—112no—
143C2×C11—22no—
144C2×C11—22no—
145C2×C11—41no—
146C2×C11C2×#12311yescharacteristic
147C2×C11C2×#13711yescharacteristic
148C2×C11#57511yescharacteristic
149C24C22⋊D1111yescharacteristic
150C2×Q8—21no—
151C2×Q8—24no—
152C2×Q8C22×D1112yes—
153C22×C4—24no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—221no—
157C22×C4—221no—
158C22×C4C22⋊D1111yescharacteristic
159C22×C4C22⋊D1111yescharacteristic
160C22×C4C22⋊D1111yescharacteristic
161C22×C4C22×D1111yescharacteristic
162C22×C4C22×D1111yescharacteristic
163C22×C4C22×D1111yescharacteristic
164M16—224no—
165C2×C8—114no—
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—21no—
169C4⋊C4—112no—
170C4⋊C4—112no—
171C4⋊C4—221no—
172C4⋊C4—221no—
173C4⋊C4C22×D1112yes—
174C22⋊C4—22no—
175C22⋊C4—22no—
176C22⋊C4—222no—
177C22⋊C4—222no—
178C42—222no—
179C42—222no—
180C11#309511yescharacteristic, complemented, Sylow
181C23—22no—
182C23—22no—
183C23—41no—
184C23C2×C22⋊D1111yescharacteristic
185C23C2×C22⋊D1111yescharacteristic
186C23C2×C22⋊D1111yescharacteristic
187Q8—24no—
188Q8—42no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—222no—
199C2×C4—222no—
200C2×C4—442no—
201C2×C4—442no—
202C2×C4#434114yes—
203C2×C4C2×C22⋊D1111yescharacteristic
204C2×C4C2×C22⋊D1111yescharacteristic
205C2×C4C2×C22⋊D1111yescharacteristic
206C2×C4C23×D1111yescharacteristic
207C8—224no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—44no—
216C22#6698812yes—
217C22#6699512yes—
218C22C22×C22⋊D1111yescharacteristic
219C4—21no—
220C4—21no—
221C4—42no—
222C4—42no—
223C4—442no—
224C4—442no—
225C4#6698812yes—
226C4C2×#434112yes—
227C2—22no—
228C2—22no—
229C2—41no—
230C2C2×#6698811yescharacteristic
231C2C2×#6699511yescharacteristic
232C2#1062335311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×C22⋊Q8C2
socleC22×C11C22×D4
prime radicalC24×C11D4
hypercenterC2×C22⋊Q8D11
hypocenterC11#3095
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10622838C2semidirect
5. #10622658C2semidirect
6. #10622657C2semidirect
7. #10622656C2semidirect
8. #10622577C2semidirect
27. #66899C22semidirect
28. #66899C22semidirect
31. #66872C22semidirect
32. #66871C22semidirect
180. C11#3095semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C2×#669792
#106228382
#106228202
#106226582
#106226572
#106226562
#106225772
#309511