Finite Group Databasebeta

← #13076879

Subgroups — #13076879

Order 1408.

548 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 125 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×#396C211yesmaximal, characteristic, complemented
2#10622607C213yesmaximal, complemented
3#10622605C213yesmaximal, complemented
4#10622568C213yesmaximal
5#10622561C213yesmaximal, complemented
6#10622290C211yesmaximal, characteristic, complemented
7#10622289C211yesmaximal, characteristic, complemented
8C24×D11C2211yescharacteristic
9C2×C11×C4⋊C4C2213yescomplemented
10C2×C11×C22⋊C4C2213yes—
11C2×C22⋊Dic11C2213yes—
12C2×(C2×D11)⋊C4C2213yes—
13C2×(C2×D11)⋊C4C2213yes—
14C2×(C2×D11)⋊C4C2213yes—
15C2×(C2×D11)⋊C4C2213yes—
16C2×C4⋊Dic11C2213yescomplemented
17C2×Dic11⋊C4C2213yescomplemented
18C2×Dic11⋊C4C2213yescomplemented
19C11×#95C2211yescharacteristic, complemented
20C11⋊#95C2213yescomplemented
21C24×C11C2311yescharacteristic
22C23×D11—43no—
23C23×D11—43no—
24C23×D11Q814yes—
25C23×D11C2311yescharacteristic
26C23×D11C2311yescharacteristic
27C22×C4×C11C2313yes—
28C22×C4×C11C2313yes—
29C22×Dic11C2313yes—
30C22×Dic11C2313yes—
31C11×C4⋊C4—43no—
32C11×C22⋊C4—43no—
33C22⋊Dic11—43no—
34(C2×D11)⋊C4—43no—
35(C2×D11)⋊C4—43no—
36(C2×D11)⋊C4—43no—
37(C2×D11)⋊C4—43no—
38C4⋊Dic11—43no—
39Dic11⋊C4—43no—
40Dic11⋊C4—43no—
41#2842—111nomaximal, Sylow
42C23×C11—23no—
43C23×C11—23no—
44C23×C11C2×Q812yes—
45C23×C11C2411yescharacteristic
46C22×D11—23no—
47C22×D11—23no—
48C22×D11—23no—
49C22×D11—23no—
50C22×D11—412no—
51C22×D11—44no—
52C22×D11—412no—
53C22×D11C2×Q812yes—
54C22×D11C2×Q812yes—
55C2×C4×C11—23no—
56C2×C4×C11—23no—
57C2×C4×C11—23no—
58C2×C4×C11—23no—
59C2×C4×C11—23no—
60C2×C4×C11—23no—
61C2×Dic11—23no—
62C2×Dic11—23no—
63C2×Dic11—23no—
64C2×Dic11—23no—
65C2×Dic11—23no—
66C2×Dic11—23no—
67#399—113no—
68#399—111no—
69#396—113no—
70#396—113no—
71#396—111no—
72#396D1111yescharacteristic, complemented
73#379—113no—
74C22×C11—26no—
75C22×C11—41no—
76C22×C11—43no—
77C22×C11C22×Q811yescharacteristic
78C22×C11H(5,𝔽2)13yes—
79C22×C11H(5,𝔽2)13yes—
80C2×D11—26no—
81C2×D11—26no—
82C2×D11—416no—
83C2×D11—41no—
84C2×D11—41no—
85C2×D11—43no—
86C2×D11—43no—
87C4×C11—43no—
88C4×C11—43no—
89Dic11—43no—
90Dic11—43no—
91C25—111no—
92C2×C4⋊C4—113no—
93C2×C4⋊C4—113no—
94C2×C4⋊C4—113no—
95C2×C4⋊C4C2×D1113yescomplemented
96C2×C22⋊C4—113no—
97C2×C22⋊C4—113no—
98C2×C22⋊C4—113no—
99C2×C22⋊C4—113no—
100C2×C22⋊C4—113no—
101C2×C22⋊C4C2×D1113yes—
102#95—113no—
103#95C2×D1111yescharacteristic, complemented
104C2×C11—42no—
105C2×C11#54313yes—
106C2×C11#56011yescharacteristic
107C2×C11#56013yes—
108D11—42no—
109D11—42no—
110C24—111no—
111C24—111no—
112C24—114no—
113C24—443no—
114C24—443no—
115C24C22×D1111yescharacteristic
116C22×C4—113no—
117C22×C4—113no—
118C22×C4C22×D1113yes—
119C22×C4C22×D1113yes—
120C4⋊C4—43no—
121C4⋊C4—443no—
122C4⋊C4—443no—
123C4⋊C4—443no—
124C22⋊C4—43no—
125C22⋊C4—443no—
126C22⋊C4—443no—
127C22⋊C4—443no—
128C22⋊C4—443no—
129C22⋊C4—443no—
130C11#284211yescharacteristic, complemented, Sylow
131C23—23no—
132C23—23no—
133C23—112no—
134C23—112no—
135C23—223no—
136C23—223no—
137C23—223no—
138C23—223no—
139C23—4412no—
140C23—444no—
141C23—4412no—
142C23Q8×D1112yes—
143C23C23×D1111yescharacteristic
144C2×C4—23no—
145C2×C4—23no—
146C2×C4—23no—
147C2×C4—23no—
148C2×C4—23no—
149C2×C4—23no—
150C2×C4—223no—
151C2×C4—223no—
152C2×C4—223no—
153C2×C4—223no—
154C2×C4—223no—
155C2×C4—223no—
156C22—26no—
157C22—41no—
158C22—43no—
159C22—226no—
160C22—226no—
161C22—4416no—
162C22—441no—
163C22—441no—
164C22—443no—
165C22—443no—
166C22#6703713yes—
167C22C2×Q8×D1111yescharacteristic
168C22#6704213yes—
169C4—43no—
170C4—43no—
171C4—443no—
172C4—443no—
173C2—42no—
174C2—442no—
175C2—442no—
176C2#1062315113yes—
177C2#1062316513yes—
178C2#1062324211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#396C2
prime radicalC24×D11C22
hypercenter#396D11
hypocenterC11#2842
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C11×#396C2semidirect
2. #10622607C2semidirect
3. #10622605C2semidirect
5. #10622561C2semidirect
6. #10622290C2semidirect
7. #10622289C2semidirect
9. C2×C11×C4⋊C4C22semidirect
16. C2×C4⋊Dic11C22semidirect
17. C2×Dic11⋊C4C22semidirect
18. C2×Dic11⋊C4C22semidirect
19. C11×#95C22semidirect
20. C11⋊#95C22semidirect
72. #396D11semidirect
95. C2×C4⋊C4C2×D11semidirect
103. #95C2×D11semidirect
130. C11#2842semidirect

Maximal subgroups

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

subgroupindex
C11×#3962
#106226072
#106226052
#106225682
#106225612
#106222902
#106222892
#284211