Finite Group Databasebeta

← #11770823

Subgroups — #11770823

Order 1152.

270 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 56 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
1#10593801C211yesmaximal, characteristic
2C2×#63777C211yesmaximal, characteristic
3#10592417C211yesmaximal, characteristic
4C22×#622C412yes—
5C2×C4×C3⋊Dic3C2211yescharacteristic
6C22⋊#622C412yes—
7#63779—21no—
8#63777—21no—
9#63777—21no—
10C4×#622—21no—
11C32×C22⋊C8C411yescharacteristic
12#63657C411yescharacteristic
13#63641—21no—
14C8×C3⋊Dic3—21no—
15#4718—62no—
16C22×C32×C4C2×C411yescharacteristic
17C22×C3⋊Dic3C2×C411yescharacteristic
18C22×C3⋊Dic3C2×C411yescharacteristic
19C2×#622—22no—
20C2×#622—22no—
21C2×#622—22no—
22C2×#622C814yescomplemented
23C2×C32×C8—21no—
24C4×C3⋊Dic3D411yescharacteristic
25C4×C3⋊Dic3D411yescharacteristic
26C4×C3⋊Dic3D411yescharacteristic
27C4×C3⋊Dic3Q811yescharacteristic
28C2×C3⋊(C3⋊C8)—21no—
29#1281—91nomaximal, Sylow
30C2×C4×Dic3—62no—
31C3×C22⋊C8—22no—
32#830—62no—
33Dic3⋊C8—64no—
34C8×Dic3—64no—
35C23×C32C4211yescharacteristic
36C2×C32×C4—41no—
37C2×C32×C4C22⋊C411yescharacteristic
38C2×C32×C4C4⋊C411yescharacteristic
39C2×C3⋊Dic3—41no—
40C2×C3⋊Dic3C22⋊C411yescharacteristic
41C2×C3⋊Dic3C22⋊C411yescharacteristic
42C2×C3⋊Dic3C4⋊C411yescharacteristic
43C2×C3⋊Dic3C4⋊C411yescharacteristic
44C2×C3⋊Dic3C2×C812yes—
45C2×C3⋊Dic3M1612yes—
46#622—24no—
47#622—42no—
48C32×C8—41no—
49C3⋊(C3⋊C8)—41no—
50#431—91no—
51#431—91no—
52C2×#97—91no—
53C22×C3×C4—22no—
54C22×Dic3—62no—
55C22×Dic3—62no—
56C2×C3×C8—24no—
57C4×Dic3—62no—
58C4×Dic3—62no—
59C4×Dic3—62no—
60C4×Dic3—62no—
61C2×C3⋊C8—64no—
62C22×C32—21no—
63C22×C32—21no—
64C22×C32#9511yescharacteristic
65C22×C32C4×C811yescharacteristic
66C22×C32#9711yescharacteristic
67C32×C4—21no—
68C32×C4—21no—
69C3⋊Dic3—21no—
70C3⋊Dic3—21no—
71C3⋊Dic3C22⋊C812yes—
72C3⋊Dic3C4⋊C812yes—
73C22×C8—92no—
74C2×C42—91no—
75C4⋊C8—181no—
76C4⋊C8—181no—
77C22⋊C8—92no—
78C22⋊C8—91no—
79C22⋊C8#15711yescharacteristic
80#97—181no—
81#97—181no—
82C4×C8—181no—
83C4×C8—181no—
84C23×C3—22no—
85C2×C3×C4—22no—
86C2×C3×C4—22no—
87C2×C3×C4—44no—
88C2×Dic3—62no—
89C2×Dic3—62no—
90C2×Dic3—62no—
91C2×Dic3—64no—
92C2×Dic3—64no—
93C2×Dic3—62no—
94C2×Dic3—124no—
95C3×C8—44no—
96C3⋊C8—124no—
97C2×C32—21no—
98C2×C32—21no—
99C2×C32#33611yescharacteristic
100C2×C32#34411yescharacteristic
101C2×C32#34411yescharacteristic
102C22×C4—91no—
103C22×C4—91no—
104C22×C4C2×#15711yescharacteristic
105C2×C8—21no—
106C2×C8—94no—
107C2×C8—182no—
108C2×C8—182no—
109C2×C8—182no—
110C2×C8—181no—
111C42—91no—
112C42—91no—
113C42—91no—
114C42—91no—
115C22×C3—22no—
116C22×C3—22no—
117C22×C3—22no—
118C22×C3—42no—
119C22×C3—42no—
120C3×C4—24no—
121C3×C4—42no—
122Dic3—64no—
123Dic3—64no—
124Dic3—64no—
125Dic3—122no—
126C32#128111yescharacteristic, complemented, Sylow
127C23C4×#15711yescharacteristic
128C2×C4—41no—
129C2×C4—92no—
130C2×C4—92no—
131C2×C4—91no—
132C2×C4—91no—
133C2×C4—91no—
134C2×C4—91no—
135C2×C4—361no—
136C2×C4C4⋊#15711yescharacteristic
137C2×C4C22⋊#15711yescharacteristic
138C8—41no—
139C8—184no—
140C8—361no—
141C8—362no—
142C2×C3—22no—
143C2×C3—22no—
144C2×C3—22no—
145C2×C3—42no—
146C2×C3—42no—
147C22—21no—
148C22—21no—
149C22C8×#15711yescharacteristic
150C22#6376711yescharacteristic
151C22#6378111yescharacteristic
152C4—21no—
153C4—21no—
154C4—92no—
155C4—92no—
156C4—181no—
157C4—181no—
158C3—22no—
159C2—21no—
160C2—21no—
161C2#1059015611yescharacteristic
162C2#1059018111yescharacteristic
163C2#1059019111yescharacteristic
subgroupG/H
centerC22#63781
commutatorC22×C32C4×C8
FrattiniC22×C4C2×#157
FittingC32×C22⋊C8C4
socleC22×C32#95
prime radicalC23×C32C42
cosocleC2×C4×C3⋊Dic3C22
hypercenterC22⋊C8#157
hypocenterC32#1281
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
22. C2×#622C8semidirect
126. C32#1281semidirect

Maximal subgroups

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

subgroupindex
#105938012
C2×#637772
#105924172
#12819