Finite Group Databasebeta

← #13069747

Subgroups — #13069747

Order 1408.

430 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 73 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×#66982C212yesmaximal, complemented
2#10623024C211yesmaximal, characteristic
3C11×#381C211yesmaximal, characteristic, complemented
4C2×#66870C212yesmaximal, complemented
5#10622164C211yesmaximal, characteristic, complemented
6C23×C4×C11C2211yescharacteristic
7C22×C22⋊D11C2212yes—
8C2×C11×C22⋊C4C2211yescharacteristic
9C2×C11×C22⋊C4C2211yescharacteristic
10C2×C22⋊Dic11C2212yes—
11#66983—22no—
12#66982—24no—
13#66982—24no—
14C2×(C2×D11)⋊C4—22no—
15C2×Dic11⋊C4—22no—
16#66939—22no—
17#66935—22no—
18C11×#95—22no—
19#66870—24no—
20C24×C11C2311yescharacteristic
21C23×D11D412yes—
22C22×C4×C11—21no—
23C22×C4×C11—22no—
24C22×C4×C11—22no—
25C22×C4×C11—21no—
26C22×C4×C11—21no—
27C22×C4×C11D412yes—
28C22×C4×C11D412yescomplemented
29C2×C22⋊D11—22no—
30C2×C22⋊D11—22no—
31C2×C22⋊D11—22no—
32C2×C22⋊D11—22no—
33C2×C22⋊D11—22no—
34C2×C22⋊D11—22no—
35C22×Dic11—22no—
36C22×Dic11D412yes—
37C2×D44—22no—
38C11×C22⋊C4—22no—
39C11×C22⋊C4—22no—
40C22⋊Dic11—22no—
41C22⋊Dic11D414yescomplemented
42(C2×D11)⋊C4—24no—
43(C2×D11)⋊C4—28no—
44C4⋊Dic11—22no—
45Dic11⋊C4—28no—
46#2022—111nomaximal, Sylow
47C23×C11—42no—
48C23×C11C2×D411yescharacteristic
49C23×C11C2×D412yes—
50C23×C11C2×D412yes—
51C23×C11C2×D411yescharacteristic
52C23×C11#4111yescharacteristic
53C22×D11—22no—
54C22×D11—22no—
55C22×D11—22no—
56C22×D11—44no—
57C2×C4×C11—24no—
58C2×C4×C11—22no—
59C2×C4×C11—22no—
60C2×C4×C11—41no—
61C2×C4×C11—42no—
62C2×C4×C11—41no—
63C2×C4×C11—42no—
64C2×C4×C11—42no—
65C2×C4×C11—41no—
66C22⋊D11—42no—
67C22⋊D11—42no—
68C22⋊D11—42no—
69C22⋊D11—42no—
70C2×Dic11—22no—
71C2×Dic11—24no—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—44no—
75D44—82no—
76#534—111no—
77C2×#123—112no—
78C2×#99—112no—
79#381D1111yescharacteristic, complemented
80#342—111no—
81C22×C11—22no—
82C22×C11—24no—
83C22×C11—41no—
84C22×C11—42no—
85C22×C11—41no—
86C22×C11#12012yes—
87C22×C11#12011yescharacteristic
88C22×C11#12112yes—
89C22×C11#12111yescharacteristic
90C22×C11#12711yescharacteristic
91C2×D11—44no—
92C2×D11—42no—
93C2×D11—44no—
94C2×D11—82no—
95C4×C11—42no—
96C4×C11—42no—
97C4×C11—81no—
98Dic11—44no—
99Dic11—42no—
100C22×D4—112no—
101C23×C4C2×D1111yescharacteristic
102#123—222no—
103#123—224no—
104#123—224no—
105#121—222no—
106#120—222no—
107C2×C4⋊C4—222no—
108C2×C22⋊C4—112no—
109C2×C22⋊C4—222no—
110C2×C22⋊C4C2×D1111yescharacteristic
111C2×C22⋊C4C2×D1111yescharacteristic
112#99—224no—
113#95—22no—
114C2×C11—22no—
115C2×C11—21no—
116C2×C11—22no—
117C2×C11—21no—
118C2×C11#39211yescharacteristic
119C2×C11#45812yes—
120D11—82no—
121C24—112no—
122C24C22×D1111yescharacteristic
123C2×D4—222no—
124C2×D4—222no—
125C2×D4—222no—
126C2×D4—222no—
127C2×D4—222no—
128C2×D4—222no—
129C2×D4—222no—
130C22×C4—21no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—112no—
136C22×C4—222no—
137C22×C4D4412yescomplemented
138C22×C4C22⋊D1112yes—
139C4⋊C4—228no—
140C4⋊C4—222no—
141C22⋊C4—22no—
142C22⋊C4—22no—
143C22⋊C4—114no—
144C22⋊C4—228no—
145C22⋊C4—224no—
146C22⋊C4—222no—
147C11#202211yescharacteristic, complemented, Sylow
148C23—42no—
149C23—222no—
150C23—222no—
151C23—222no—
152C23—444no—
153C23C2×D4411yescharacteristic
154C23#433911yescharacteristic
155C23D4×D1112yes—
156C23D4×D1112yes—
157C23C2×C22⋊D1111yescharacteristic
158D4—442no—
159D4—442no—
160D4—442no—
161D4—442no—
162D4—882no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—224no—
173C2×C4—222no—
174C2×C4—222no—
175C2×C4—222no—
176C2×C4—444no—
177C22—22no—
178C22—24no—
179C22—41no—
180C22—41no—
181C22—42no—
182C22—444no—
183C22—442no—
184C22—444no—
185C22—882no—
186C22#6693512yes—
187C22#6693712yes—
188C22#6698311yescharacteristic
189C22#6699011yescharacteristic
190C22#6699311yescharacteristic
191C4—42no—
192C4—42no—
193C4—81no—
194C4—444no—
195C4—442no—
196C2—21no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—882no—
201C2#1062257311yescharacteristic
202C2#1062266612yes—
subgroupG/H
centerC22#66990
commutator, cosocleC24×C11C23
FrattiniC24C22×D11
FittingC11×#381C2
socleC22×C11#120
prime radical#10623024C2
hypercenter#381D11
hypocenterC11#2022
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C2×#66982C2semidirect
3. C11×#381C2semidirect
4. C2×#66870C2semidirect
5. #10622164C2semidirect
28. C22×C4×C11D4semidirect
41. C22⋊Dic11D4semidirect
79. #381D11semidirect
137. C22×C4D44semidirect
147. C11#2022semidirect

Maximal subgroups

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

subgroupindex
C2×#669822
#106230242
C11×#3812
C2×#668702
#106221642
#202211