Finite Group Databasebeta

← #13076981

Subgroups — #13076981

Order 1408.

516 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 149 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×#126C211yesmaximal, characteristic, complemented
2C2×#66929C211yesmaximal, characteristic, complemented
3#10622603C213yesmaximal, complemented
4#10622585C213yesmaximal, complemented
5#10622570C213yesmaximal
6#10622558C213yesmaximal, complemented
7C42×Dic11C211yesmaximal, characteristic, complemented
8C22×C22⋊D11C2211yescharacteristic
9C11×#126—24no—
10C2×C11×C4⋊C4C2213yes—
11C2×C11×C22⋊C4C2213yes—
12C2×C42×C11C2211yescharacteristic
13C2×C22⋊Dic11C2213yes—
14C2×(C2×D11)⋊C4C2213yes—
15C2×(C2×D11)⋊C4C2213yes—
16C2×Dic11⋊C4C2213yes—
17C2×Dic11⋊C4C2213yes—
18C2×C4×Dic11C2213yes—
19C2×C4×Dic11C2213yes—
20#66929—24no—
21C11⋊#95C2216yes—
22C24×C11C2311yescharacteristic
23C23×D11C2311yescharacteristic
24C22×C4×C11C2313yes—
25C22×C4×C11C2313yes—
26C2×C22⋊D11—26no—
27C22×Dic11C2313yes—
28C22×Dic11C2313yes—
29C22×Dic11C2311yescharacteristic
30C11×C4⋊C4—26no—
31C11×C22⋊C4—26no—
32C42×C11D414yescomplemented
33C22⋊Dic11—26no—
34(C2×D11)⋊C4—26no—
35(C2×D11)⋊C4—26no—
36Dic11⋊C4—26no—
37Dic11⋊C4—26no—
38C4×Dic11—26no—
39C4×Dic11—26no—
40#2860—111nomaximal, Sylow
41C23×C11—21no—
42C23×C11—23no—
43C23×C11—23no—
44C23×C11C2411yescharacteristic
45C22×D11—21no—
46C22×D11—23no—
47C22×D11—23no—
48C2×C4×C11—23no—
49C2×C4×C11—23no—
50C2×C4×C11—23no—
51C2×C4×C11—23no—
52C2×C4×C11—23no—
53C2×C4×C11C2×D416yes—
54C22⋊D11—44no—
55C2×Dic11—23no—
56C2×Dic11—23no—
57C2×Dic11—23no—
58C2×Dic11—23no—
59C2×Dic11—23no—
60C2×Dic11#4116yes—
61C2×Dic11#4116yes—
62C2×#126—111no—
63C2×#126D1111yescharacteristic, complemented
64#390—113no—
65#389—113no—
66#388—113no—
67#388—113no—
68C43—111no—
69C22×C11—41no—
70C22×C11—43no—
71C22×C11—43no—
72C22×C11C22×D411yescharacteristic
73C22×C11C2×#4113yes—
74C22×C11C2×#4113yes—
75C2×D11—41no—
76C2×D11—43no—
77C2×D11—43no—
78C4×C11—26no—
79C4×C11—43no—
80Dic11—26no—
81Dic11—43no—
82Dic11#12614yescomplemented
83C22×D4—111no—
84#126—24no—
85#126—224no—
86C2×C4⋊C4—113no—
87C2×C4⋊C4—113no—
88C2×C4⋊C4C2×D1113yes—
89C2×C22⋊C4—113no—
90C2×C22⋊C4—113no—
91C2×C22⋊C4—113no—
92C2×C22⋊C4C2×D1113yes—
93C2×C42—113no—
94C2×C42—113no—
95C2×C42C2×D1111yescharacteristic
96#95—116no—
97C2×C11—81no—
98C2×C11C2×#12611yescharacteristic
99C2×C11#52913yes—
100C2×C11#53213yes—
101D11—81no—
102C24—111no—
103C24C22×D1111yescharacteristic
104C2×D4—226no—
105C22×C4—111no—
106C22×C4—113no—
107C22×C4—113no—
108C22×C4C22×D1113yes—
109C22×C4C22×D1113yes—
110C4⋊C4—26no—
111C4⋊C4—226no—
112C4⋊C4—226no—
113C22⋊C4—26no—
114C22⋊C4—226no—
115C22⋊C4—226no—
116C22⋊C4—226no—
117C42—226no—
118C42—226no—
119C42C22⋊D1114yescomplemented
120C11#286011yescharacteristic, complemented, Sylow
121C23—23no—
122C23—23no—
123C23—21no—
124C23—223no—
125C23—223no—
126C23—221no—
127C23C23×D1111yescharacteristic
128D4—444no—
129C2×C4—23no—
130C2×C4—23no—
131C2×C4—23no—
132C2×C4—23no—
133C2×C4—23no—
134C2×C4—116no—
135C2×C4—116no—
136C2×C4—223no—
137C2×C4—223no—
138C2×C4—223no—
139C2×C4—223no—
140C2×C4—223no—
141C2×C4C2×C22⋊D1116yes—
142C22—41no—
143C22—43no—
144C22—43no—
145C22—441no—
146C22—443no—
147C22—443no—
148C22#41×D1113yes—
149C22#41×D1113yes—
150C22C22×C22⋊D1111yescharacteristic
151C4—26no—
152C4—43no—
153C4—114no—
154C4—226no—
155C4—443no—
156C2—81no—
157C2—881no—
158C2D11×#12611yescharacteristic
159C2#1062323713yes—
160C2#1062336313yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#126C2
prime radicalC22×C22⋊D11C22
hypercenterC2×#126D11
hypocenterC11#2860
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×C11×#126C2semidirect
2. C2×#66929C2semidirect
3. #10622603C2semidirect
4. #10622585C2semidirect
6. #10622558C2semidirect
7. C42×Dic11C2semidirect
32. C42×C11D4semidirect
63. C2×#126D11semidirect
82. Dic11#126semidirect
119. C42C22⋊D11semidirect
120. C11#2860semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1262
C2×#669292
#106226032
#106225852
#106225702
#106225582
C42×Dic112
#286011