Finite Group Databasebeta

← #13076524

Subgroups — #13076524

Order 1408.

420 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 119 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×#399C211yesmaximal, characteristic, complemented
2#10622603C213yesmaximal, complemented
3#10622585C213yesmaximal, complemented
4#10622572C213yesmaximal
5#10622557C213yesmaximal, complemented
6#10622289C211yesmaximal, characteristic, complemented
7C11⋊#401C211yesmaximal, characteristic, complemented
8C22×C22⋊D11C2211yescharacteristic
9C2×C11×C4⋊C4C2213yes—
10C2×C11×C22⋊C4C2213yes—
11C2×C22⋊Dic11C2213yes—
12C2×(C2×D11)⋊C4C2213yes—
13C2×(C2×D11)⋊C4C2213yes—
14C2×Dic11⋊C4C2213yes—
15C2×Dic11⋊C4C2213yes—
16C2×C4×Dic11C2213yes—
17C11×#95C2211yescharacteristic
18C11⋊#95C2213yes—
19C11⋊#95C2213yes—
20C11⋊#95C2213yes—
21C24×C11C2311yescharacteristic
22C23×D11C2311yescharacteristic
23C22×C4×C11C2313yes—
24C22×C4×C11C2313yes—
25C2×C22⋊D11—43no—
26C22×Dic11C2313yes—
27C22×Dic11C2311yescharacteristic
28C22×Dic11C2313yes—
29C11×C4⋊C4—43no—
30C11×C22⋊C4—43no—
31C22⋊Dic11—26no—
32(C2×D11)⋊C4—26no—
33(C2×D11)⋊C4—43no—
34Dic11⋊C4—26no—
35Dic11⋊C4—43no—
36C4×Dic11—43no—
37#2801—111nomaximal, Sylow
38C23×C11—23no—
39C23×C11—23no—
40C23×C11—21no—
41C23×C11C2411yescharacteristic
42C22×D11—23no—
43C22×D11—23no—
44C22×D11—21no—
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#4116yes—
59#401—111no—
60#399D1111yescharacteristic, complemented
61#396—111no—
62#394—113no—
63#389—113no—
64#388—113no—
65#388—113no—
66C22×C11—43no—
67C22×C11—43no—
68C22×C11—41no—
69C22×C11C2×#4113yes—
70C22×C11H(5,𝔽2)13yes—
71C22×C112−1+411yescharacteristic
72C2×D11—43no—
73C2×D11—43no—
74C2×D11—41no—
75C4×C11—43no—
76C4×C11—43no—
77Dic11—26no—
78Dic11—43no—
79Dic11—41no—
80C22×D4—111no—
81C2×C4⋊C4—113no—
82C2×C4⋊C4—113no—
83C2×C4⋊C4C2×D1113yes—
84C2×C22⋊C4—113no—
85C2×C22⋊C4—113no—
86C2×C22⋊C4—113no—
87C2×C22⋊C4C2×D1113yes—
88C2×C42—113no—
89#95—113no—
90#95—113no—
91#95—113no—
92#95C2×D1111yescharacteristic
93C2×C11—81no—
94C2×C11#54213yes—
95C2×C11#55313yes—
96C2×C11#56011yescharacteristic
97D11—81no—
98C24—111no—
99C24C22×D1111yescharacteristic
100C2×D4—443no—
101C22×C4—113no—
102C22×C4—113no—
103C22×C4—111no—
104C22×C4C22×D1113yes—
105C22×C4C22×D1113yes—
106C4⋊C4—43no—
107C4⋊C4—226no—
108C4⋊C4—443no—
109C22⋊C4—43no—
110C22⋊C4—226no—
111C22⋊C4—226no—
112C22⋊C4—443no—
113C42—443no—
114C11#280111yescharacteristic, complemented, Sylow
115C23—23no—
116C23—21no—
117C23—23no—
118C23—223no—
119C23—221no—
120C23—223no—
121C23C23×D1111yescharacteristic
122D4—444no—
123C2×C4—23no—
124C2×C4—23no—
125C2×C4—23no—
126C2×C4—23no—
127C2×C4—23no—
128C2×C4—23no—
129C2×C4—116no—
130C2×C4—223no—
131C2×C4—223no—
132C2×C4—223no—
133C2×C4—223no—
134C2×C4—223no—
135C2×C4—223no—
136C22—41no—
137C22—43no—
138C22—43no—
139C22—441no—
140C22—443no—
141C22—443no—
142C22#6703713yes—
143C22#6704011yescharacteristic
144C22#41×D1113yes—
145C4—43no—
146C4—43no—
147C4—226no—
148C4—441no—
149C4—443no—
150C2—81no—
151C2—881no—
152C2#1062317113yes—
153C2#1062319213yes—
154C2#1062325111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#399C2
prime radicalC22×C22⋊D11C22
hypercenter#399D11
hypocenterC11#2801
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C11×#399C2semidirect
2. #10622603C2semidirect
3. #10622585C2semidirect
5. #10622557C2semidirect
6. #10622289C2semidirect
7. C11⋊#401C2semidirect
60. #399D11semidirect
114. C11#2801semidirect

Maximal subgroups

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

subgroupindex
C11×#3992
#106226032
#106225852
#106225722
#106225572
#106222892
C11⋊#4012
#280111