Finite Group Databasebeta

← #11776879

Subgroups — #11776879

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#10590041C214yesmaximal, 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#1566—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×C4SD1614yes—
34C2×C32×C4C2×D411yescharacteristic
35C2×C3⋊Dic3—22no—
36C2×C3⋊Dic3—22no—
37C2×C3⋊Dic3C4⋊C411yescharacteristic
38C2×C3⋊Dic3C4⋊C411yescharacteristic
39C2×C3⋊Dic3C22×C411yescharacteristic
40C2×C3⋊Dic3C2×Q811yescharacteristic
41#622—22no—
42#622M1614yescomplemented
43C3×C3⋊C8—44no—
44#423—92no—
45C2×C4×C8—91no—
46#334—94no—
47C22×C3×C4—22no—
48C22×Dic3—62no—
49C22×Dic3—62no—
50C3×M16—124no—
51C2×C3×C8—64no—
52C4×Dic3—62no—
53C4×Dic3—62no—
54C4×Dic3—62no—
55C4×Dic3—62no—
56#208—44no—
57C2×C3⋊C8—24no—
58C22×C32—21no—
59C22×C32—21no—
60C22×C32#10612yes—
61C22×C32C2×C4⋊C411yescharacteristic
62C32×C4#10612yes—
63C32×C4C2×SD1612yes—
64C3⋊Dic3—21no—
65C3⋊Dic3—21no—
66C3⋊Dic3#10812yes—
67C3⋊Dic3C2×M1612yes—
68C2×M16—62no—
69C22×C8—92no—
70C2×C42—91no—
71C4⋊C8—94no—
72C4⋊C8—182no—
73C4×C8—91no—
74C4×C8—91no—
75C4×C8—92no—
76C23×C3—22no—
77C2×C3×C4—22no—
78C2×C3×C4—22no—
79C2×C3×C4—24no—
80C2×C3×C4—24no—
81C2×Dic3—62no—
82C2×Dic3—62no—
83C2×Dic3—62no—
84C2×Dic3—62no—
85C2×Dic3—124no—
86C2×Dic3—124no—
87C3×C8—124no—
88C3⋊C8—44no—
89C2×C32—22no—
90C2×C32#42311yescharacteristic
91C2×C32C2×#10611yescharacteristic
92C2×C32C2×#10811yescharacteristic
93C22×C4—91no—
94C22×C4—91no—
95C22×C4GO+(4,𝔽2)11yescharacteristic
96M16—124no—
97C2×C8—64no—
98C2×C8—92no—
99C2×C8—92no—
100C2×C8—184no—
101C42—91no—
102C42—91no—
103C42—91no—
104C42—91no—
105C22×C3—22no—
106C22×C3—24no—
107C22×C3—42no—
108C22×C3—42no—
109C3×C4—22no—
110C3×C4—22no—
111C3×C4—24no—
112Dic3—64no—
113Dic3—64no—
114Dic3—122no—
115Dic3—122no—
116C32#156611yescharacteristic, complemented, Sylow
117C23#377311yescharacteristic
118C2×C4—91no—
119C2×C4—91no—
120C2×C4—91no—
121C2×C4—91no—
122C2×C4—182no—
123C2×C4—182no—
124C2×C4#377311yescharacteristic
125C2×C4#377514yes—
126C2×C4C2×GO+(4,𝔽2)11yescharacteristic
127C8—94no—
128C8—124no—
129C8—182no—
130C2×C3—22no—
131C2×C3—22no—
132C2×C3—22no—
133C2×C3—44no—
134C22—21no—
135C22—21no—
136C22#6374212yes—
137C22C2×#377311yescharacteristic
138C4—92no—
139C4—92no—
140C4—181no—
141C4—181no—
142C4#6374212yes—
143C4C2×#377512yes—
144C3—22no—
145C2—22no—
146C2#1059332811yescharacteristic
147C2#1059333111yescharacteristic
148C2C2×#6374211yescharacteristic
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#1566
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. #10590041C2semidirect
42. #622M16semidirect
116. C32#1566semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6222
#105911202
#105900412
#15669