Finite Group Databasebeta

← #11770908

Subgroups — #11770908

Order 1152.

218 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 43 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
1C4×C4⋊#157C211yesmaximal, characteristic
2#10593731C211yesmaximal, characteristic
3#10593730C211yesmaximal, characteristic
4C2×C4⋊#157—21no—
5C2×C4×#157C412yes—
6C42×C3⋊D3C2211yescharacteristic
7#63781—21no—
8#63779—21no—
9#63778—21no—
10#63778—21no—
11#63777—21no—
12#63777C412yescomplemented
13C4⋊#622C412yescomplemented
14C22×#157—22no—
15C2×C4×C3⋊D3C2×C411yescharacteristic
16C2×C4×C3⋊D3D411yescharacteristic
17C2×C4×C3⋊D3D411yescharacteristic
18C2×#622—22no—
19C2×#622—22no—
20C4⋊#157—24no—
21C4×#157—42no—
22C32×C42Q811yescharacteristic
23C4×C3⋊Dic3C2×C411yescharacteristic
24C4×C3⋊Dic3C2×C411yescharacteristic
25C4×C3⋊Dic3D411yescharacteristic
26#1285—91nomaximal, Sylow
27C42×D3—121no—
28C22×C3⋊D3C22⋊C411yescharacteristic
29C2×#157—24no—
30C2×#157—42no—
31C2×#157—42no—
32C2×C32×C4C4⋊C411yescharacteristic
33C2×C32×C4C4⋊C411yescharacteristic
34C2×C32×C4C4⋊C411yescharacteristic
35C2×C3⋊Dic3C4211yescharacteristic
36C2×C3⋊Dic3C22⋊C411yescharacteristic
37C2×C3⋊Dic3C22⋊C411yescharacteristic
38C4×C3⋊D3—21no—
39C4×C3⋊D3—21no—
40C4×C3⋊D3—22no—
41C4×C3⋊D3—41no—
42#622—42no—
43#622—42no—
44#432—91no—
45#432—91no—
46C4×C4⋊C4—91no—
47C2×C4×D3—121no—
48C2×C4×D3—121no—
49C2×C4×D3—121no—
50C3×C42—41no—
51C4×Dic3—121no—
52C4×Dic3—121no—
53C4×Dic3—121no—
54C22×C32#9511yescharacteristic
55C2×C3⋊D3—21no—
56C2×C3⋊D3—21no—
57C2×C3⋊D3#10011yescharacteristic
58C2×C3⋊D3#10111yescharacteristic
59#157—44no—
60C32×C4—21no—
61C32×C4—21no—
62C32×C4—21no—
63C3⋊Dic3—21no—
64C3⋊Dic3—21no—
65C3⋊Dic3#10412yes—
66C2×C4⋊C4—181no—
67C2×C42—91no—
68C2×C42—92no—
69C4⋊C8—92no—
70C4⋊C8—181no—
71C22⋊C8—181no—
72C22⋊C8—181no—
73#97—92no—
74#97—181no—
75#95—181no—
76C22×D3—121no—
77C2×C3×C4—41no—
78C2×C3×C4—41no—
79C2×C3×C4—41no—
80C2×Dic3—121no—
81C2×Dic3—121no—
82C2×Dic3—121no—
83C4×D3—124no—
84C4×D3—122no—
85C4×D3—122no—
86C4×D3—124no—
87C2×C32H(3,ℤ/4)11yescharacteristic
88C2×C32#33911yescharacteristic
89C2×C32#34311yescharacteristic
90C3⋊D3—21no—
91C3⋊D3—21no—
92C22×C4—91no—
93C22×C4—91no—
94C22×C4—91no—
95C22×C4—182no—
96C2×C8—182no—
97C2×C8—182no—
98C4⋊C4—184no—
99C42—91no—
100C42—91no—
101C42—91no—
102C42—362no—
103C42PSU(3,𝔽2)11yescharacteristic
104C22×C3—41no—
105C2×D3—121no—
106C2×D3—121no—
107C2×D3—122no—
108C2×D3—122no—
109C3×C4—42no—
110C3×C4—42no—
111C3×C4—42no—
112Dic3—122no—
113Dic3—122no—
114Dic3—122no—
115C32#128511yescharacteristic, complemented, Sylow
116C23—91no—
117C2×C4—91no—
118C2×C4—91no—
119C2×C4—91no—
120C2×C4—182no—
121C2×C4—181no—
122C2×C4—181no—
123C2×C4—184no—
124C2×C4—361no—
125C2×C4—362no—
126C2×C4—362no—
127C2×C4#377711yescharacteristic
128C2×C4#377711yescharacteristic
129C2×C4#377711yescharacteristic
130C8—362no—
131C8—362no—
132C2×C3—41no—
133C2×C3—41no—
134C2×C3—41no—
135D3—122no—
136D3—122no—
137C22—91no—
138C22—91no—
139C22—181no—
140C22—181no—
141C22#6374711yescharacteristic
142C4—21no—
143C4—21no—
144C4—21no—
145C4—92no—
146C4—181no—
147C4—181no—
148C4—364no—
149C3—41no—
150C2—181no—
151C2—181no—
152C2#1059009111yescharacteristic
153C2#1059009211yescharacteristic
154C2#1059009411yescharacteristic
subgroupG/H
centerC22#63747
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC42PSU(3,𝔽2)
FittingC32×C42Q8
socleC22×C32#95
prime radicalC22×C3⋊D3C22⋊C4
cosocleC42×C3⋊D3C22
hypocenterC32#1285
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
12. #63777C4semidirect
13. C4⋊#622C4semidirect
115. C32#1285semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#1572
#105937312
#105937302
#12859