Finite Group Databasebeta

← #13074786

Subgroups — #13074786

Order 1408.

424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C4×C11×C22⋊C4C211yesmaximal, characteristic
2#10622825C211yesmaximal, characteristic
3#10622824C211yesmaximal, characteristic
4#10622561C212yesmaximal
5#10622560C212yesmaximal
6#10622546C212yesmaximal, complemented
7#10622542C212yesmaximal, complemented
8#10622273C212yesmaximal, complemented
9#10622269C212yesmaximal, complemented
10C23×C4×C11C2211yescharacteristic
11C22×Dic22C2212yes—
12C2×C11×C22⋊C4C2212yes—
13C2×C42×C11C2212yes—
14C2×C22⋊Dic11C2211yescharacteristic
15C2×C22⋊Dic11C2212yes—
16C2×C22⋊Dic11C2211yescharacteristic
17C2×C4⋊Dic11C2212yes—
18C2×C4⋊Dic11C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C11×#95C2211yescharacteristic
22C11×#95C2211yescharacteristic
23C11⋊#95C2212yes—
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2211yescharacteristic
29C11⋊#95C2212yes—
30C11⋊#95C2211yescharacteristic
31C24×C11C2311yescharacteristic
32C22×C4×C11—42no—
33C22×C4×C11Q814yescomplemented
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C2×Dic22—24no—
43C2×Dic22—42no—
44C2×Dic22—42no—
45C11×C22⋊C4—24no—
46C42×C11—42no—
47C22⋊Dic11—41no—
48C22⋊Dic11—41no—
49C22⋊Dic11—42no—
50C4⋊Dic11—42no—
51C4⋊Dic11—42no—
52Dic11⋊C4—24no—
53Dic11⋊C4—42no—
54#2665—111nomaximal, Sylow
55C23×C11—22no—
56C23×C11—21no—
57C23×C11—22no—
58C23×C11—21no—
59C23×C11C2×Q812yes—
60C23×C11C2411yescharacteristic
61C2×C4×C11—22no—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—44no—
69C2×C4×C11C2×Q812yes—
70C2×C4×C11C2×Q812yes—
71C2×C4×C11#4114yes—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—22no—
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—
84Dic22—48no—
85#400—112no—
86#396—112no—
87#395—112no—
88#393—112no—
89#391—112no—
90#387—112no—
91#381—111no—
92#380—111no—
93C4×C22⋊C4D1111yescharacteristic
94C22×C11—22no—
95C22×C11—22no—
96C22×C11—22no—
97C22×C11—42no—
98C22×C11—42no—
99C22×C11C22×Q811yescharacteristic
100C22×C11C2×#4112yes—
101C22×C11H(5,𝔽2)12yes—
102C22×C11H(5,𝔽2)11yescharacteristic
103C22×C112−1+411yescharacteristic
104C4×C11—24no—
105C4×C11—22no—
106C4×C11—22no—
107C4×C11—42no—
108Dic11—42no—
109Dic11—42no—
110Dic11—42no—
111Dic11—42no—
112C22×Q8—112no—
113C23×C4C2×D1111yescharacteristic
114C2×C4⋊C4—112no—
115C2×C4⋊C4—112no—
116C2×C4⋊C4—112no—
117C2×C4⋊C4—112no—
118C2×C22⋊C4—111no—
119C2×C22⋊C4—111no—
120C2×C22⋊C4—112no—
121C2×C22⋊C4C2×D1112yes—
122C2×C42C2×D1112yes—
123#95—112no—
124#95—111no—
125#95—111no—
126#95—112no—
127#95—112no—
128#95—112no—
129#95—112no—
130#95—112no—
131#95C2×D1111yescharacteristic
132#95C2×D1111yescharacteristic
133C2×C11—42no—
134C2×C11#53311yescharacteristic
135C2×C11#53812yes—
136C2×C11#54212yes—
137C2×C11#54311yescharacteristic
138C2×C11#54411yescharacteristic
139C24C22×D1111yescharacteristic
140C2×Q8—224no—
141C2×Q8—442no—
142C2×Q8—442no—
143C22×C4—42no—
144C22×C4—112no—
145C22×C4—112no—
146C22×C4—112no—
147C22×C4—112no—
148C22×C4Dic2214yescomplemented
149C22×C4C22×D1112yes—
150C22×C4C22×D1111yescharacteristic
151C22×C4C22×D1111yescharacteristic
152C22×C4C22×D1112yes—
153C4⋊C4—224no—
154C4⋊C4—442no—
155C4⋊C4—442no—
156C4⋊C4—442no—
157C22⋊C4—24no—
158C22⋊C4—442no—
159C22⋊C4—441no—
160C22⋊C4—441no—
161C42—42no—
162C11#266511yescharacteristic, complemented, Sylow
163C23—22no—
164C23—22no—
165C23—21no—
166C23—21no—
167C23C2×Dic2212yes—
168C23C23×D1111yescharacteristic
169Q8—448no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—44no—
178C2×C4—222no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4—222no—
182C2×C4—222no—
183C2×C4—222no—
184C2×C4—222no—
185C2×C4—222no—
186C2×C4—222no—
187C2×C4—222no—
188C2×C4—222no—
189C2×C4—222no—
190C2×C4C2×Dic2212yes—
191C2×C4C2×Dic2212yes—
192C2×C4#433914yes—
193C22—22no—
194C22—22no—
195C22—22no—
196C22—42no—
197C22—42no—
198C22C22×Dic2211yescharacteristic
199C22C2×#433912yes—
200C22#6703712yes—
201C22#6704211yescharacteristic
202C22#6704311yescharacteristic
203C4—22no—
204C4—22no—
205C4—24no—
206C4—42no—
207C4—442no—
208C4—442no—
209C4—442no—
210C4—442no—
211C2—42no—
212C2#1062300111yescharacteristic
213C2#1062301411yescharacteristic
214C2#1062305011yescharacteristic
215C2#1062309112yes—
216C2#1062309212yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC4×C11×C22⋊C4C2
prime radicalC24×C11C23
hypercenterC4×C22⋊C4D11
hypocenterC11#2665
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. #10622546C2semidirect
7. #10622542C2semidirect
8. #10622273C2semidirect
9. #10622269C2semidirect
33. C22×C4×C11Q8semidirect
148. C22×C4Dic22semidirect
162. C11#2665semidirect

Maximal subgroups

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

subgroupindex
C4×C11×C22⋊C42
#106228252
#106228242
#106225612
#106225602
#106225462
#106225422
#106222732
#106222692
#266511