Finite Group Databasebeta

← #13071213

Subgroups — #13071213

Order 1408.

672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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×(C2×D11)⋊C4C211yesmaximal, characteristic
2C11×#380C211yesmaximal, characteristic, complemented
3#10622825C211yesmaximal, characteristic, complemented
4#10622603C214yesmaximal, complemented
5#10622568C212yesmaximal
6C22⋊C4×Dic11C212yesmaximal, complemented
7#10622283C214yesmaximal, complemented
8C24×D11C2211yescharacteristic
9C23×C4×C11C2211yescharacteristic
10C23×Dic11C2211yescharacteristic
11C2×C11×C4⋊C4C2212yescomplemented
12C2×C11×C22⋊C4C2212yes—
13C2×C22⋊Dic11C2212yes—
14C2×(C2×D11)⋊C4C418yescomplemented
15C2×(C2×D11)⋊C4C2214yes—
16C2×(C2×D11)⋊C4C2214yes—
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×C4⋊Dic11C2212yescomplemented
20C2×C4×Dic11C2214yescomplemented
21C11×#95C2212yescomplemented
22C11⋊#95C2214yescomplemented
23C11⋊#95C2212yescomplemented
24C24×C11C2311yescharacteristic
25C23×D11—22no—
26C23×D11—22no—
27C23×D11—42no—
28C23×D11—42no—
29C23×D11C2×C414yes—
30C23×D11C2312yes—
31C22×C4×C11—42no—
32C22×C4×C11C2×C414yes—
33C22×C4×C11C2314yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×Dic11—42no—
37C22×Dic11C2×C414yes—
38C22×Dic11C2314yes—
39C22×Dic11C2312yes—
40C11×C4⋊C4—42no—
41C11×C22⋊C4—24no—
42C22⋊Dic11—24no—
43(C2×D11)⋊C4—44no—
44(C2×D11)⋊C4—44no—
45(C2×D11)⋊C4C2×C418yes—
46(C2×D11)⋊C4C2×C418yes—
47C4⋊Dic11—42no—
48C4×Dic11—44no—
49#2312—111nomaximal, Sylow
50C23×C11—22no—
51C23×C11—22no—
52C23×C11C22×C412yes—
53C23×C11#4112yes—
54C23×C11#4112yes—
55C23×C11C2411yescharacteristic
56C22×D11—28no—
57C22×D11—22no—
58C22×D11—22no—
59C22×D11—24no—
60C22×D11—24no—
61C22×D11—44no—
62C22×D11—44no—
63C22×D11—48no—
64C22×D11—48no—
65C22×D11C22×C414yes—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—24no—
69C2×C4×C11—24no—
70C2×C4×C11—24no—
71C2×C4×C11—44no—
72C2×C4×C11C22×C412yes—
73C2×C4×C11C22×C412yes—
74C2×Dic11—24no—
75C2×Dic11—24no—
76C2×Dic11—24no—
77C2×Dic11—24no—
78C2×Dic11—44no—
79C2×Dic11C22×C414yes—
80C22×C22⋊C4—111no—
81#388—114no—
82#388—114no—
83#380—111no—
84#380D1111yescharacteristic, complemented
85#379—112no—
86C4×C22⋊C4—112no—
87C22×C11—22no—
88C22×C11—22no—
89C22×C11—24no—
90C22×C11—24no—
91C22×C11#11714yes—
92C22×C11C23×C411yescharacteristic
93C22×C11C2×#4111yescharacteristic
94C22×C11C2×#4111yescharacteristic
95C22×C11H(5,𝔽2)12yes—
96C22×C11H(5,𝔽2)12yes—
97C2×D11—24no—
98C2×D11—24no—
99C2×D11—24no—
100C2×D11—416no—
101C2×D11—44no—
102C2×D11—44no—
103C4×C11—22no—
104C4×C11—22no—
105C4×C11—44no—
106Dic11—24no—
107Dic11—44no—
108C25—111no—
109C23×C4—111no—
110C23×C4C2×D1111yescharacteristic
111C2×C4⋊C4—112no—
112C2×C4⋊C4C2×D1112yescomplemented
113C2×C22⋊C4—112no—
114C2×C22⋊C4—112no—
115C2×C22⋊C4—118no—
116C2×C22⋊C4—112no—
117C2×C22⋊C4—114no—
118C2×C22⋊C4—114no—
119C2×C22⋊C4C2×D1112yes—
120C2×C42—114no—
121#95—114no—
122#95—112no—
123#95C2×D1112yescomplemented
124C2×C11—24no—
125C2×C11C2×#11711yescharacteristic
126C2×C11#51811yescharacteristic
127C2×C11#51811yescharacteristic
128C2×C11#53812yes—
129C2×C11#53812yes—
130D11—44no—
131C24—112no—
132C24—114no—
133C24—222no—
134C24—222no—
135C24—442no—
136C24—442no—
137C24C22×D1111yescharacteristic
138C22×C4—42no—
139C22×C4—112no—
140C22×C4—114no—
141C22×C4—114no—
142C22×C4—442no—
143C22×C4C4×D1114yes—
144C22×C4C22×D1114yes—
145C22×C4C22×D1111yescharacteristic
146C22×C4C22×D1111yescharacteristic
147C4⋊C4—42no—
148C4⋊C4—442no—
149C22⋊C4—24no—
150C22⋊C4—118no—
151C22⋊C4—118no—
152C22⋊C4—224no—
153C22⋊C4—444no—
154C22⋊C4—444no—
155C42—444no—
156C11#231211yescharacteristic, complemented, Sylow
157C23—22no—
158C23—22no—
159C23—114no—
160C23—228no—
161C23—222no—
162C23—224no—
163C23—222no—
164C23—224no—
165C23—444no—
166C23—444no—
167C23—448no—
168C23—448no—
169C23C2×C4×D1112yes—
170C23#434112yes—
171C23#434312yes—
172C23C23×D1111yescharacteristic
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—44no—
179C2×C4—114no—
180C2×C4—224no—
181C2×C4—224no—
182C2×C4—224no—
183C2×C4—224no—
184C2×C4—444no—
185C2×C4C2×C4×D1112yes—
186C2×C4C2×C4×D1112yes—
187C22—22no—
188C22—22no—
189C22—24no—
190C22—24no—
191C22—224no—
192C22—224no—
193C22—224no—
194C22—4416no—
195C22—444no—
196C22—444no—
197C22#6694514yes—
198C22C22×C4×D1111yescharacteristic
199C22C2×#434111yescharacteristic
200C22#6703712yes—
201C22C2×#434311yescharacteristic
202C22#6704212yes—
203C4—22no—
204C4—22no—
205C4—44no—
206C4—224no—
207C4—444no—
208C2—24no—
209C2—444no—
210C2#1062301711yescharacteristic
211C2C2×#6694511yescharacteristic
212C2#1062305211yescharacteristic
213C2#1062314812yes—
214C2#1062317512yes—
subgroupG/H
center, FrattiniC23C23×D11
commutatorC22×C11C23×C4
FittingC11×#380C2
socle, cosocleC23×C11C24
prime radicalC24×D11C22
hypercenter#380D11
hypocenterC11#2312
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C11×#380C2semidirect
3. #10622825C2semidirect
4. #10622603C2semidirect
6. C22⋊C4×Dic11C2semidirect
7. #10622283C2semidirect
11. C2×C11×C4⋊C4C22semidirect
14. C2×(C2×D11)⋊C4C4semidirect
19. C2×C4⋊Dic11C22semidirect
20. C2×C4×Dic11C22semidirect
21. C11×#95C22semidirect
22. C11⋊#95C22semidirect
23. C11⋊#95C22semidirect
84. #380D11semidirect
112. C2×C4⋊C4C2×D11semidirect
123. #95C2×D11semidirect
156. C11#2312semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D11)⋊C42
C11×#3802
#106228252
#106226032
#106225682
C22⋊C4×Dic112
#106222832
#231211