Finite Group Databasebeta

← #11776902

Subgroups — #11776902

Order 1152.

310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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×C4×#622C211yesmaximal, characteristic
2#10591120C212yesmaximal
3#10590042C214yesmaximal, complemented
4C22×#622C412yes—
5C2×C4×C3⋊Dic3C2211yescharacteristic
6C2×C3×#208—22no—
7C4×#622C411yescharacteristic
8C4×#622C411yescharacteristic
9C4×#622C2212yes—
10#63572—22no—
11#63572C2214yes—
12#5118—62no—
13C22×C32×C4D411yescharacteristic
14C22×C3⋊Dic3C2×C411yescharacteristic
15C22×C3⋊Dic3Q811yescharacteristic
16C2×#622—24no—
17C2×#622C2×C412yes—
18C2×#622C2×C412yes—
19C4×C3⋊Dic3C2×C411yescharacteristic
20C4×C3⋊Dic3D411yescharacteristic
21C4×C3⋊Dic3Q811yescharacteristic
22C4×C3⋊Dic3C2311yescharacteristic
23C3×#208—44no—
24C2×C3×C3⋊C8—24no—
25#1567—91nomaximal, Sylow
26C2×C3×M16—62no—
27C2×C4×Dic3—62no—
28C2×#208—22no—
29Dic3⋊C8—64no—
30Dic3⋊C8—64no—
31C23×C32C4⋊C411yescharacteristic
32C2×C32×C4C4⋊C411yescharacteristic
33C2×C32×C4D812yes—
34C2×C32×C4Q1612yes—
35C2×C32×C4C2×D411yescharacteristic
36C2×C3⋊Dic3—22no—
37C2×C3⋊Dic3—22no—
38C2×C3⋊Dic3C4⋊C411yescharacteristic
39C2×C3⋊Dic3C4⋊C411yescharacteristic
40C2×C3⋊Dic3C22×C411yescharacteristic
41C2×C3⋊Dic3C2×Q811yescharacteristic
42#622—22no—
43#622M1614yescomplemented
44C3×C3⋊C8—44no—
45#423—92no—
46C2×C4×C8—91no—
47#335—94no—
48C22×C3×C4—22no—
49C22×Dic3—62no—
50C22×Dic3—62no—
51C3×M16—124no—
52C2×C3×C8—64no—
53C4×Dic3—62no—
54C4×Dic3—62no—
55C4×Dic3—62no—
56C4×Dic3—62no—
57#208—44no—
58C2×C3⋊C8—24no—
59C22×C32—21no—
60C22×C32—21no—
61C22×C32#10712yes—
62C22×C32C2×C4⋊C411yescharacteristic
63C32×C4#10712yes—
64C32×C4C2×D811yescharacteristic
65C32×C4C2×Q1611yescharacteristic
66C3⋊Dic3—21no—
67C3⋊Dic3—21no—
68C3⋊Dic3#10812yes—
69C3⋊Dic3C2×M1612yes—
70C2×M16—62no—
71C22×C8—92no—
72C2×C42—91no—
73C4⋊C8—94no—
74C4⋊C8—182no—
75C4×C8—91no—
76C4×C8—91no—
77C4×C8—92no—
78C23×C3—22no—
79C2×C3×C4—22no—
80C2×C3×C4—22no—
81C2×C3×C4—24no—
82C2×C3×C4—24no—
83C2×Dic3—62no—
84C2×Dic3—62no—
85C2×Dic3—62no—
86C2×Dic3—62no—
87C2×Dic3—124no—
88C2×Dic3—124no—
89C3×C8—124no—
90C3⋊C8—44no—
91C2×C32—22no—
92C2×C32#42311yescharacteristic
93C2×C32C2×#10711yescharacteristic
94C2×C32C2×#10811yescharacteristic
95C22×C4—91no—
96C22×C4—91no—
97C22×C4GO+(4,𝔽2)11yescharacteristic
98M16—124no—
99C2×C8—64no—
100C2×C8—92no—
101C2×C8—92no—
102C2×C8—184no—
103C42—91no—
104C42—91no—
105C42—91no—
106C42—91no—
107C22×C3—22no—
108C22×C3—24no—
109C22×C3—42no—
110C22×C3—42no—
111C3×C4—22no—
112C3×C4—22no—
113C3×C4—24no—
114Dic3—64no—
115Dic3—64no—
116Dic3—122no—
117Dic3—122no—
118C32#156711yescharacteristic, complemented, Sylow
119C23#377311yescharacteristic
120C2×C4—91no—
121C2×C4—91no—
122C2×C4—91no—
123C2×C4—91no—
124C2×C4—182no—
125C2×C4—182no—
126C2×C4#377311yescharacteristic
127C2×C4#377412yes—
128C2×C4#377612yes—
129C2×C4C2×GO+(4,𝔽2)11yescharacteristic
130C8—94no—
131C8—124no—
132C8—182no—
133C2×C3—22no—
134C2×C3—22no—
135C2×C3—22no—
136C2×C3—44no—
137C22—21no—
138C22—21no—
139C22#6374312yes—
140C22C2×#377311yescharacteristic
141C4—92no—
142C4—92no—
143C4—181no—
144C4—181no—
145C4#6374312yes—
146C4C2×#377411yescharacteristic
147C4C2×#377611yescharacteristic
148C3—22no—
149C2—22no—
150C2#1059332811yescharacteristic
151C2#1059333111yescharacteristic
152C2C2×#6374311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC22×C32C2×C4⋊C4
prime radicalC23×C32C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1567
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #10590042C2semidirect
43. #622M16semidirect
118. C32#1567semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6222
#105911202
#105900422
#15679