Finite Group Databasebeta

← #13079437

Subgroups — #13079437

Order 1408.

410 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 125 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×#66977C211yesmaximal, characteristic
3#10622841C212yesmaximal, complemented
4#10622820C211yesmaximal, characteristic
5#10622665C214yesmaximal, complemented
6#10622663C212yesmaximal, complemented
7#10622656C212yesmaximal, complemented
8#10622584C212yesmaximal, complemented
9C22×Q8×C11C2211yescharacteristic
10C23×C4×C11C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C11×C22⋊Q8—21no—
13C11×C22⋊Q8—21no—
14C11×C22⋊Q8C2212yes—
15C11×C22⋊Q8C2212yes—
16C2×C11×C4⋊C4—21no—
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4—21no—
19C2×C22⋊Dic11—21no—
20C2×#4326C2214yescomplemented
21C2×C4⋊Dic11C2211yescharacteristic
22#66977—21no—
23#66977—21no—
24#66977C2212yes—
25#66977C2212yes—
26C2×Dic11⋊C4—21no—
27C2×#4318C2212yes—
28#66899C2214yescomplemented
29C22⋊(C11⋊C8)C2212yes—
30C22⋊(C11⋊C8)C2212yes—
31#66874C2214yescomplemented
32#66872C2214yescomplemented
33C24×C11D411yescharacteristic
34C2×Q8×C11—21no—
35C2×Q8×C11—42no—
36C2×Q8×C11C2312yes—
37C22×C4×C11—21no—
38C22×C4×C11—21no—
39C22×C4×C11—42no—
40C22×C4×C11D411yescharacteristic
41C22×C4×C11D411yescharacteristic
42C22×C4×C11D411yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C22×Dic11—21no—
47C22×Dic11—21no—
48C2×Dic22—21no—
49C2×Dic22—42no—
50C2×Dic22C2312yes—
51C11×C4⋊C4—22no—
52C11×C4⋊C4—22no—
53C11×C4⋊C4—21no—
54C11×C4⋊C4C2312yes—
55C11×C22⋊C4—22no—
56C11×C22⋊C4—22no—
57C22⋊Dic11—22no—
58C22⋊Dic11—22no—
59#4326—44no—
60C4⋊Dic11—21no—
61C4⋊Dic11C2312yes—
62Dic11⋊C4—22no—
63Dic11⋊C4—22no—
64#4318—42no—
65C2×C11⋊C8C2314yes—
66#3195—111nomaximal, Sylow
67C23×C11—22no—
68C23×C11—22no—
69C23×C11—41no—
70C23×C11C2×D411yescharacteristic
71C23×C11C2×D411yescharacteristic
72C23×C11C2×D411yescharacteristic
73Q8×C11—24no—
74Q8×C11—42no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—41no—
81C2×C4×C11—41no—
82C2×C4×C11—41no—
83C2×C4×C11—42no—
84C2×C4×C11—42no—
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2411yescharacteristic
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—42no—
92C2×Dic11—42no—
93Dic22—24no—
94Dic22—42no—
95C11⋊C8—24no—
96C2×C22⋊Q8—111no—
97C2×C22⋊Q8D1111yescharacteristic
98#483—112no—
99#483—112no—
100#470—114no—
101#451—112no—
102#451—112no—
103#407—111no—
104C22×C11—21no—
105C22×C11—21no—
106C22×C11—21no—
107C22×C11—21no—
108C22×C11—21no—
109C22×C11—21no—
110C22×C11—21no—
111C22×C11—44no—
112C22×C11#13712yes—
113C22×C11#13712yes—
114C22×C11C22×D411yescharacteristic
115C4×C11—21no—
116C4×C11—21no—
117C4×C11—21no—
118C4×C11—42no—
119C4×C11—42no—
120C4×C11H(5,𝔽2)12yes—
121Dic11—42no—
122Dic11—42no—
123C22×Q8—111no—
124C22×Q8C2×D1111yescharacteristic
125C23×C4C2×D1111yescharacteristic
126C2×Q16—114no—
127C2×M16—112no—
128C22⋊Q8—21no—
129C22⋊Q8—21no—
130C22⋊Q8—112no—
131C22⋊Q8—112no—
132C22⋊Q8—221no—
133C22⋊Q8—221no—
134C22⋊Q8C2×D1112yes—
135C22⋊Q8C2×D1112yes—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—111no—
138C2×C4⋊C4—221no—
139C2×C4⋊C4C2×D1111yescharacteristic
140C2×C22⋊C4—21no—
141C2×C22⋊C4—221no—
142#106—114no—
143#103—114no—
144#103—114no—
145C22⋊C8—112no—
146C22⋊C8—112no—
147C2×C11—22no—
148C2×C11—22no—
149C2×C11—41no—
150C2×C11#53411yescharacteristic
151C2×C11C2×#13711yescharacteristic
152C2×C11C2×#13711yescharacteristic
153C24C22⋊D1111yescharacteristic
154C2×Q8—21no—
155C2×Q8—42no—
156C2×Q8—112no—
157C2×Q8—221no—
158C2×Q8—442no—
159C2×Q8C22×D1112yes—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—42no—
163C22×C4—221no—
164C22×C4—221no—
165C22×C4C22⋊D1111yescharacteristic
166C22×C4C22⋊D1111yescharacteristic
167C22×C4C22⋊D1111yescharacteristic
168C22×C4C22×D1111yescharacteristic
169C22×C4C22×D1111yescharacteristic
170C22×C4C22×D1111yescharacteristic
171Q16—444no—
172M16—442no—
173C2×C8—114no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—21no—
177C4⋊C4—112no—
178C4⋊C4—221no—
179C4⋊C4—222no—
180C4⋊C4—222no—
181C4⋊C4C22×D1112yes—
182C22⋊C4—22no—
183C22⋊C4—22no—
184C22⋊C4—222no—
185C22⋊C4—222no—
186C11#319511yescharacteristic, complemented, Sylow
187C23—22no—
188C23—22no—
189C23—41no—
190C23C2×C22⋊D1111yescharacteristic
191C23C2×C22⋊D1111yescharacteristic
192C23C2×C22⋊D1111yescharacteristic
193Q8—24no—
194Q8—42no—
195Q8—224no—
196Q8—442no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—222no—
208C2×C4—222no—
209C2×C4—442no—
210C2×C4—442no—
211C2×C4C2×C22⋊D1111yescharacteristic
212C2×C4C2×C22⋊D1111yescharacteristic
213C2×C4C2×C22⋊D1111yescharacteristic
214C2×C4C23×D1111yescharacteristic
215C8—224no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—21no—
223C22—44no—
224C22#6699512yes—
225C22#6700412yes—
226C22C22×C22⋊D1111yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—42no—
231C4—42no—
232C4—442no—
233C4—442no—
234C4#6703712yes—
235C2—22no—
236C2—22no—
237C2—41no—
238C2#1062333511yescharacteristic
239C2C2×#6699511yescharacteristic
240C2C2×#6700411yescharacteristic
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#3195
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. #10622841C2semidirect
5. #10622665C2semidirect
6. #10622663C2semidirect
7. #10622656C2semidirect
8. #10622584C2semidirect
20. C2×#4326C22semidirect
28. #66899C22semidirect
31. #66874C22semidirect
32. #66872C22semidirect
186. C11#3195semidirect

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×#669772
#106228412
#106228202
#106226652
#106226632
#106226562
#106225842
#319511