Finite Group Databasebeta

← #13066735

Subgroups — #13066735

Order 1408.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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×#100C211yesmaximal, characteristic
2#10622833C211yesmaximal, characteristic
3C2×#66898C211yesmaximal, characteristic
4C22×D4×C11C2211yescharacteristic
5C23×Dic11C411yescharacteristic, complemented
6C2×C11×M16—21no—
7C2×C22⋊Dic11—21no—
8C2×C22⋊Dic11—21no—
9C2×C22⋊Dic11C411yescharacteristic, complemented
10C11×#100—21no—
11C11×#100C412yescomplemented
12#66898—21no—
13#66898C412yescomplemented
14C11⋊#95—21no—
15C24×C11C2×C411yescharacteristic
16C24×C11D411yescharacteristic
17C2×D4×C11—41no—
18C2×D4×C11—41no—
19C2×D4×C11C2×C411yescharacteristic
20C2×D4×C11C2×C411yescharacteristic
21C2×D4×C11D411yescharacteristic
22C2×D4×C11Q811yescharacteristic
23C22×C4×C11D411yescharacteristic
24C22×Dic11—21no—
25C22×Dic11—21no—
26C22×Dic11—41no—
27C22×Dic11—41no—
28C22×Dic11—42no—
29C11×M16—22no—
30C11×M16—41no—
31C2×C8×C11—41no—
32C22⋊Dic11—22no—
33C22⋊Dic11—41no—
34C22⋊Dic11—41no—
35C22⋊Dic11—42no—
36#1390—111nomaximal, Sylow
37C23×C11—21no—
38C23×C11—21no—
39C23×C11—21no—
40C23×C11—21no—
41C23×C11—41no—
42C23×C11—41no—
43C23×C11—41no—
44C23×C11—41no—
45C23×C11C4211yescharacteristic
46C23×C11C22⋊C411yescharacteristic
47C23×C11C22⋊C411yescharacteristic
48C23×C11C4⋊C411yescharacteristic
49C23×C11C4⋊C411yescharacteristic
50D4×C11—41no—
51D4×C11—41no—
52D4×C11—41no—
53D4×C11—41no—
54C2×C4×C11—21no—
55C2×C4×C11—21no—
56C2×C4×C11C22⋊C411yescharacteristic
57C2×C4×C11C4⋊C411yescharacteristic
58C2×Dic11—22no—
59C2×Dic11—41no—
60C2×Dic11—42no—
61C2×Dic11—41no—
62C2×Dic11—42no—
63C2×Dic11—42no—
64C2×Dic11—41no—
65C2×Dic11—41no—
66C2×Dic11—41no—
67C2×Dic11—81no—
68C2×Dic11—81no—
69C8×C11—42no—
70C2×#100D1111yescharacteristic
71C2×#99—111no—
72#386—111no—
73C22×C11—21no—
74C22×C11—21no—
75C22×C11—21no—
76C22×C11—21no—
77C22×C11—21no—
78C22×C11—21no—
79C22×C11—41no—
80C22×C11—41no—
81C22×C11—41no—
82C22×C11—41no—
83C22×C11—42no—
84C22×C11—41no—
85C22×C11—41no—
86C22×C11—41no—
87C22×C11—41no—
88C22×C11—81no—
89C22×C11#9511yescharacteristic
90C22×C11#9911yescharacteristic
91C22×C11#9911yescharacteristic
92C4×C11—21no—
93C4×C11—21no—
94Dic11—42no—
95Dic11—81no—
96Dic11—82no—
97C22×D4C2×D1111yescharacteristic
98C23×C4—111no—
99C2×M16—21no—
100C2×C22⋊C4—111no—
101C2×C22⋊C4—221no—
102C2×C22⋊C4—221no—
103#100—21no—
104#100Dic1112yescomplemented
105#99—112no—
106#99—221no—
107#95—221no—
108C2×C11—21no—
109C2×C11—21no—
110C2×C11—41no—
111C2×C11—41no—
112C2×C11—41no—
113C2×C11—41no—
114C2×C11#34211yescharacteristic
115C2×C11AΣL(1,𝔽16)11yescharacteristic
116C2×C11#35211yescharacteristic
117C24C4×D1111yescharacteristic
118C24D4411yescharacteristic
119C2×D4—41no—
120C2×D4—41no—
121C2×D4Dic2211yescharacteristic
122C2×D4C4×D1111yescharacteristic
123C2×D4C2×Dic1111yescharacteristic
124C2×D4C22⋊D1111yescharacteristic
125C22×C4—221no—
126C22×C4—221no—
127C22×C4—442no—
128C22×C4—441no—
129C22×C4—441no—
130C22×C4C22⋊D1111yescharacteristic
131M16—22no—
132M16—41no—
133C2×C8—41no—
134C22⋊C4—222no—
135C22⋊C4—442no—
136C22⋊C4—441no—
137C22⋊C4—441no—
138C11#139011yescharacteristic, complemented, Sylow
139C23—21no—
140C23—21no—
141C23—21no—
142C23—21no—
143C23—41no—
144C23—41no—
145C23—41no—
146C23—41no—
147C23C4×Dic1111yescharacteristic
148C23Dic11⋊C411yescharacteristic
149C23C4⋊Dic1111yescharacteristic
150C23(C2×D11)⋊C411yescharacteristic
151C23(C2×D11)⋊C411yescharacteristic
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—222no—
159C2×C4—441no—
160C2×C4—442no—
161C2×C4—441no—
162C2×C4—442no—
163C2×C4—442no—
164C2×C4—441no—
165C2×C4—441no—
166C2×C4—441no—
167C2×C4—881no—
168C2×C4—881no—
169C2×C4Dic11⋊C411yescharacteristic
170C2×C4C22⋊Dic1111yescharacteristic
171C8—42no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—42no—
183C22—41no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22—81no—
188C22#6687011yescharacteristic
189C22#6687011yescharacteristic
190C22C11⋊#9511yescharacteristic
191C4—21no—
192C4—21no—
193C4—442no—
194C4—881no—
195C4—882no—
196C2—21no—
197C2—21no—
198C2—41no—
199C2—41no—
200C2—41no—
201C2—41no—
202C2#1062211311yescharacteristic
203C2#1062211411yescharacteristic
204C2#1062216511yescharacteristic
subgroupG/H
centerC22#66870
commutatorC23×C11C42
FrattiniC22×D4C2×D11
FittingC2×C11×#100C2
socleC22×C11#99
prime radical, cosocleC22×D4×C11C22
hypercenterC2×#100D11
hypocenterC11#1390
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
5. C23×Dic11C4semidirect
9. C2×C22⋊Dic11C4semidirect
11. C11×#100C4semidirect
13. #66898C4semidirect
104. #100Dic11semidirect
138. C11#1390semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1002
#106228332
C2×#668982
#139011