Finite Group Databasebeta

← #13076580

Subgroups — #13076580

Order 1408.

392 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C11×#391C211yesmaximal, characteristic
2#10622843C212yesmaximal
3#10622597C212yesmaximal
4#10622542C211yesmaximal, characteristic
5#10622541C211yesmaximal, characteristic
6#10622274C212yesmaximal
7#10622269C212yesmaximal
8#10622267C212yesmaximal
9#10622260C212yesmaximal
10C22×Q8×C11C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C42×C11C2211yescharacteristic
14C2×C4⋊Dic11C2211yescharacteristic
15C2×C4⋊Dic11C2212yes—
16C2×C4⋊Dic11C2212yes—
17C2×C4⋊Dic11C2211yescharacteristic
18C2×C4⋊Dic11C2211yescharacteristic
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×C4×Dic11C2212yes—
23C11×#95C2212yes—
24C11×#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C2×Q8×C11—41no—
32C2×Q8×C11—41no—
33C2×Q8×C11Q814yescomplemented
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2311yescharacteristic
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C2×Dic22—22no—
44C2×Dic22—41no—
45C2×Dic22—41no—
46C11×C4⋊C4—41no—
47C42×C11—41no—
48C4⋊Dic11—41no—
49C4⋊Dic11—41no—
50C4⋊Dic11—42no—
51C4⋊Dic11—42no—
52C4⋊Dic11Q814yescomplemented
53Dic11⋊C4—24no—
54Dic11⋊C4—42no—
55Dic11⋊C4—42no—
56C4×Dic11—42no—
57#2806—111nomaximal, Sylow
58C23×C11C2411yescharacteristic
59Q8×C11—44no—
60C2×C4×C11—22no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—22no—
64C2×C4×C11—21no—
65C2×C4×C11—21no—
66C2×C4×C11—21no—
67C2×C4×C11—21no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11C2×Q812yes—
72C2×C4×C11C2×Q814yes—
73C2×C4×C11C2×Q812yes—
74C2×C4×C11#4112yes—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11C2×Q814yes—
87Dic22—44no—
88#398—112no—
89#398—112no—
90#395—112no—
91#391—112no—
92#391—111no—
93#391D1111yescharacteristic
94#389—111no—
95#389—112no—
96#387—112no—
97C22×C11C22×Q811yescharacteristic
98C22×C11C22×Q811yescharacteristic
99C22×C11C2×#4111yescharacteristic
100C22×C11H(5,𝔽2)11yescharacteristic
101C22×C11H(5,𝔽2)11yescharacteristic
102C22×C11H(5,𝔽2)11yescharacteristic
103C22×C112−1+411yescharacteristic
104C4×C11—22no—
105C4×C11—24no—
106C4×C11—22no—
107C4×C11—22no—
108C4×C11—42no—
109Dic11—24no—
110Dic11—42no—
111Dic11—42no—
112Dic11—42no—
113C22×Q8—111no—
114C22×Q8C2×D1111yescharacteristic
115C2×C4⋊C4—111no—
116C2×C4⋊C4—112no—
117C2×C4⋊C4—112no—
118C2×C4⋊C4—111no—
119C2×C4⋊C4—112no—
120C2×C4⋊C4—111no—
121C2×C4⋊C4—112no—
122C2×C4⋊C4—112no—
123C2×C4⋊C4C2×D1111yescharacteristic
124C2×C42—112no—
125C2×C42C2×D1111yescharacteristic
126#95—112no—
127#95—112no—
128#95—112no—
129#95—112no—
130#95—112no—
131#95—112no—
132#95C2×D1112yes—
133#95C2×D1112yes—
134C2×C11#53811yescharacteristic
135C2×C11#54311yescharacteristic
136C2×C11#54411yescharacteristic
137C2×C11#55411yescharacteristic
138C2×C11#55711yescharacteristic
139C2×C11Q8211yescharacteristic
140C2×C11#56211yescharacteristic
141C2×Q8—41no—
142C2×Q8—41no—
143C2×Q8—222no—
144C2×Q8—441no—
145C2×Q8—441no—
146C2×Q8Dic2214yescomplemented
147C22×C4—112no—
148C22×C4—112no—
149C22×C4—112no—
150C22×C4—112no—
151C22×C4C22×D1112yes—
152C22×C4C22×D1111yescharacteristic
153C22×C4C22×D1112yes—
154C22×C4C22×D1111yescharacteristic
155C22×C4C22×D1111yescharacteristic
156C4⋊C4—41no—
157C4⋊C4—114no—
158C4⋊C4—224no—
159C4⋊C4—442no—
160C4⋊C4—442no—
161C4⋊C4—441no—
162C4⋊C4—442no—
163C4⋊C4—441no—
164C4⋊C4—442no—
165C42—41no—
166C42—442no—
167C11#280611yescharacteristic, complemented, Sylow
168C23C23×D1111yescharacteristic
169Q8—44no—
170Q8—444no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—114no—
183C2×C4—222no—
184C2×C4—222no—
185C2×C4—222no—
186C2×C4—222no—
187C2×C4—222no—
188C2×C4—222no—
189C2×C4—222no—
190C2×C4—222no—
191C2×C4—222no—
192C2×C4—222no—
193C2×C4—222no—
194C2×C4C2×Dic2212yes—
195C2×C4C2×Dic2214yes—
196C2×C4Q8×D1112yes—
197C2×C4#434312yes—
198C22C22×Dic2211yescharacteristic
199C22#6703711yescharacteristic
200C22#6703711yescharacteristic
201C22C2×Q8×D1111yescharacteristic
202C22C2×#434311yescharacteristic
203C22#6704211yescharacteristic
204C22#6704311yescharacteristic
205C4—22no—
206C4—24no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—224no—
211C4—442no—
212C4—442no—
213C4—442no—
214C2#1062301411yescharacteristic
215C2Q8×Dic2211yescharacteristic
216C2#1062310111yescharacteristic
217C2#1062315411yescharacteristic
218C2#1062317511yescharacteristic
219C2#1062321511yescharacteristic
220C2#1062326111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#391C2
hypercenter#391D11
hypocenterC11#2806
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
33. C2×Q8×C11Q8semidirect
52. C4⋊Dic11Q8semidirect
146. C2×Q8Dic22semidirect
167. C11#2806semidirect

Maximal subgroups

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

subgroupindex
C11×#3912
#106228432
#106225972
#106225422
#106225412
#106222742
#106222692
#106222672
#106222602
#280611