Finite Group Databasebeta

← #13074578

Subgroups — #13074578

Order 1408.

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

normal subgroups only

This group has 420 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#10622606C213yesmaximal, complemented
3#10622585C213yesmaximal, complemented
4#10622570C213yesmaximal
5#10622565C213yesmaximal, complemented
6#10622289C211yesmaximal, characteristic, complemented
7#10622261C211yesmaximal, 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⋊#95C2216yes—
20C24×C11C2311yescharacteristic
21C23×D11C2311yescharacteristic
22C22×C4×C11C2313yes—
23C22×C4×C11C2313yes—
24C2×C22⋊D11—26no—
25C22×Dic11C2313yes—
26C22×Dic11C2313yes—
27C22×Dic11C2311yescharacteristic
28C11×C4⋊C4—43no—
29C11×C22⋊C4—43no—
30C22⋊Dic11—43no—
31(C2×D11)⋊C4—43no—
32(C2×D11)⋊C4—43no—
33Dic11⋊C4—26no—
34Dic11⋊C4—43no—
35C4×Dic11—26no—
36#2644—111nomaximal, Sylow
37C23×C11—23no—
38C23×C11—23no—
39C23×C11—21no—
40C23×C11C2411yescharacteristic
41C22×D11—23no—
42C22×D11—23no—
43C22×D11—21no—
44C2×C4×C11—23no—
45C2×C4×C11—23no—
46C2×C4×C11—23no—
47C2×C4×C11—23no—
48C2×C4×C11—23no—
49C2×C4×C11—23no—
50C22⋊D11—44no—
51C2×Dic11—23no—
52C2×Dic11—23no—
53C2×Dic11—23no—
54C2×Dic11—23no—
55C2×Dic11—23no—
56C2×Dic11—23no—
57C2×Dic11#4116yes—
58#397—113no—
59#397—113no—
60#396—111no—
61#396D1111yescharacteristic, complemented
62#390—113no—
63#389—113no—
64#376—111no—
65C22×C11—41no—
66C22×C11—43no—
67C22×C11—43no—
68C22×C11C2×#4113yes—
69C22×C11H(5,𝔽2)13yes—
70C22×C112−1+411yescharacteristic
71C2×D11—41no—
72C2×D11—43no—
73C2×D11—43no—
74C4×C11—43no—
75C4×C11—43no—
76Dic11—43no—
77Dic11—43no—
78Dic11#12614yes—
79C22×D4—111no—
80C2×C4⋊C4—113no—
81C2×C4⋊C4—113no—
82C2×C4⋊C4C2×D1113yes—
83C2×C22⋊C4—113no—
84C2×C22⋊C4—113no—
85C2×C22⋊C4—113no—
86C2×C22⋊C4C2×D1113yes—
87C2×C42—113no—
88#95—113no—
89#95—116no—
90#95C2×D1111yescharacteristic
91C2×C11—81no—
92C2×C11C2×#12611yescharacteristic
93C2×C11#54013yes—
94C2×C11#54213yes—
95D11—81no—
96C24—111no—
97C24C22×D1111yescharacteristic
98C2×D4—226no—
99C22×C4—111no—
100C22×C4—113no—
101C22×C4—113no—
102C22×C4C22×D1113yes—
103C22×C4C22×D1113yes—
104C4⋊C4—43no—
105C4⋊C4—226no—
106C4⋊C4—443no—
107C22⋊C4—43no—
108C22⋊C4—443no—
109C22⋊C4—443no—
110C22⋊C4—443no—
111C42—226no—
112C11#264411yescharacteristic, complemented, Sylow
113C23—23no—
114C23—21no—
115C23—23no—
116C23—223no—
117C23—221no—
118C23—223no—
119C23C23×D1111yescharacteristic
120D4—444no—
121C2×C4—23no—
122C2×C4—23no—
123C2×C4—23no—
124C2×C4—23no—
125C2×C4—23no—
126C2×C4—23no—
127C2×C4—116no—
128C2×C4—223no—
129C2×C4—223no—
130C2×C4—223no—
131C2×C4—223no—
132C2×C4—223no—
133C2×C4—223no—
134C22—41no—
135C22—43no—
136C22—43no—
137C22—441no—
138C22—443no—
139C22—443no—
140C22#6703713yes—
141C22#6704011yescharacteristic
142C22#41×D1113yes—
143C4—43no—
144C4—43no—
145C4—114no—
146C4—443no—
147C4—443no—
148C2—81no—
149C2—881no—
150C2#1062314613yes—
151C2#1062317113yes—
152C2D11×#12611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#396C2
prime radicalC22×C22⋊D11C22
hypercenter#396D11
hypocenterC11#2644
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. #10622606C2semidirect
3. #10622585C2semidirect
5. #10622565C2semidirect
6. #10622289C2semidirect
7. #10622261C2semidirect
61. #396D11semidirect
112. C11#2644semidirect

Maximal subgroups

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

subgroupindex
C11×#3962
#106226062
#106225852
#106225702
#106225652
#106222892
#106222612
#264411