Finite Group Databasebeta

← #13074573

Subgroups — #13074573

Order 1408.

462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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#10622602C213yesmaximal, complemented
3#10622595C213yesmaximal, complemented
4#10622569C213yesmaximal
5#10622565C213yesmaximal, complemented
6D11×#95C211yesmaximal, characteristic, complemented
7C11⋊#401C211yesmaximal, characteristic, complemented
8C22×C22⋊D11C2211yescharacteristic
9C22×C4×D11C2213yes—
10C2×C11×C4⋊C4C2213yes—
11C2×C11×C22⋊C4C2213yes—
12C2×C22⋊Dic11C2213yes—
13C2×(C2×D11)⋊C4C2213yes—
14C2×Dic11⋊C4C2213yes—
15C11×#95C2211yescharacteristic
16C11⋊#95C2213yes—
17C11⋊#95C2213yes—
18C11⋊#95C2213yes—
19C11⋊#95C2213yes—
20C11⋊#95C2213yes—
21C24×C11C2311yescharacteristic
22C23×D11C2311yescharacteristic
23C22×C4×C11C2313yes—
24C22×C4×C11C2313yes—
25C2×C22⋊D11—26no—
26C22×Dic11C2311yescharacteristic
27C22×Dic11C2313yes—
28C22×Dic11C2313yes—
29C2×C4×D11—26no—
30C2×C4×D11—43no—
31C2×C4×D11—43no—
32C11×C4⋊C4—43no—
33C11×C22⋊C4—43no—
34C22⋊Dic11—43no—
35(C2×D11)⋊C4—26no—
36Dic11⋊C4—43no—
37#2643—111nomaximal, Sylow
38C23×C11—23no—
39C23×C11—23no—
40C23×C11—21no—
41C23×C11C2411yescharacteristic
42C22×D11—23no—
43C22×D11—21no—
44C22×D11#4116yes—
45C2×C4×C11—23no—
46C2×C4×C11—23no—
47C2×C4×C11—23no—
48C2×C4×C11—23no—
49C2×C4×C11—23no—
50C2×C4×C11—23no—
51C22⋊D11—44no—
52C2×Dic11—23no—
53C2×Dic11—23no—
54C2×Dic11—23no—
55C2×Dic11—23no—
56C2×Dic11—23no—
57C2×Dic11—23no—
58C2×Dic11—23no—
59C4×D11—412no—
60#401—111no—
61#400—113no—
62#397—113no—
63#396D1111yescharacteristic, complemented
64#386—113no—
65#385—113no—
66C2×#95—111no—
67C22×C11—41no—
68C22×C11—43no—
69C22×C11—43no—
70C22×C11C2×#4113yes—
71C22×C11H(5,𝔽2)13yes—
72C22×C112−1+411yescharacteristic
73C2×D11—26no—
74C2×D11—26no—
75C2×D11#12614yes—
76C4×C11—43no—
77C4×C11—43no—
78Dic11—41no—
79Dic11—43no—
80Dic11—43no—
81C22×D4—111no—
82C23×C4—113no—
83C2×C4⋊C4—113no—
84C2×C4⋊C4C2×D1113yes—
85C2×C22⋊C4—113no—
86C2×C22⋊C4—113no—
87C2×C22⋊C4C2×D1113yes—
88#95—113no—
89#95—113no—
90#95—113no—
91#95—113no—
92#95—113no—
93#95C2×D1111yescharacteristic
94C2×C11—81no—
95C2×C11C2×#12611yescharacteristic
96C2×C11#53813yes—
97C2×C11#53913yes—
98D11—24no—
99C24—111no—
100C24C22×D1111yescharacteristic
101C2×D4—226no—
102C22×C4—111no—
103C22×C4—113no—
104C22×C4—113no—
105C22×C4—226no—
106C22×C4—443no—
107C22×C4—443no—
108C22×C4C22×D1113yes—
109C22×C4C22×D1113yes—
110C4⋊C4—43no—
111C4⋊C4—443no—
112C22⋊C4—43no—
113C22⋊C4—226no—
114C22⋊C4—443no—
115C11#264311yescharacteristic, complemented, Sylow
116C23—23no—
117C23—21no—
118C23—23no—
119C23—116no—
120C23—223no—
121C23—221no—
122C23C23×D1111yescharacteristic
123D4—444no—
124C2×C4—23no—
125C2×C4—23no—
126C2×C4—23no—
127C2×C4—23no—
128C2×C4—23no—
129C2×C4—23no—
130C2×C4—223no—
131C2×C4—223no—
132C2×C4—223no—
133C2×C4—223no—
134C2×C4—223no—
135C2×C4—223no—
136C2×C4—223no—
137C2×C4—4412no—
138C22—41no—
139C22—43no—
140C22—43no—
141C22—114no—
142C22—226no—
143C22—226no—
144C22#6703713yes—
145C22#6704011yescharacteristic
146C22#41×D1113yes—
147C4—43no—
148C4—43no—
149C4—441no—
150C4—443no—
151C4—443no—
152C2—81no—
153C2—224no—
154C2#1062314413yes—
155C2#1062316913yes—
156C2D11×#12611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#396C2
prime radicalC22×C22⋊D11C22
hypercenter#396D11
hypocenterC11#2643
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. #10622602C2semidirect
3. #10622595C2semidirect
5. #10622565C2semidirect
6. D11×#95C2semidirect
7. C11⋊#401C2semidirect
63. #396D11semidirect
115. C11#2643semidirect

Maximal subgroups

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

subgroupindex
C11×#3962
#106226022
#106225952
#106225692
#106225652
D11×#952
C11⋊#4012
#264311