Finite Group Databasebeta

← #11773834

Subgroups — #11773834

Order 1152.

546 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 84 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×#64096C211yesmaximal, characteristic
2#10593795C212yesmaximal
3#10590203C214yesmaximal
4C22×#634C411yescharacteristic
5C2×C32×C4⋊C4C411yescharacteristic
6C2×#3750C2212yes—
7C2×C4×C3⋊Dic3C412yes—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9#64096—22no—
10#64096—22no—
11C22⋊#622C2214yes—
12C4⋊#622—22no—
13C4×#622—22no—
14C2×#887—62no—
15C22×C32×C4C2×C412yes—
16C22×C32×C4C2×C411yescharacteristic
17C22×C3⋊Dic3C2×C411yescharacteristic
18C22×C3⋊Dic3C2×C412yes—
19C22×C3⋊Dic3C2311yescharacteristic
20C2×#634—22no—
21C2×#634—22no—
22C2×#634C814yescomplemented
23C2×#622—24no—
24C32×C4⋊C4—22no—
25#3750—24no—
26C4×C3⋊Dic3—22no—
27C4×C3⋊Dic3—22no—
28C4×C3⋊Dic3D412yes—
29C4×C3⋊Dic3D412yes—
30#1461—91nomaximal, Sylow
31C22×Dic6—62no—
32C2×C3×C4⋊C4—22no—
33C2×Dic3⋊C4—64no—
34C2×C4×Dic3—64no—
35C2×C4×Dic3—62no—
36#887—68no—
37#887—68no—
38C23×C32C22×C411yescharacteristic
39C2×C32×C4—22no—
40C2×C32×C4—42no—
41C2×C32×C4C22⋊C412yes—
42C2×C32×C4C2×C812yes—
43C2×C32×C4M1612yes—
44C2×C3⋊Dic3—22no—
45C2×C3⋊Dic3—22no—
46C2×C3⋊Dic3—22no—
47C2×C3⋊Dic3—41no—
48C2×C3⋊Dic3C22⋊C411yescharacteristic
49C2×C3⋊Dic3C22⋊C411yescharacteristic
50C2×C3⋊Dic3C2×C814yes—
51C2×C3⋊Dic3C2×D412yes—
52#634—28no—
53#622—44no—
54C2×C4×Q8—91no—
55#431—92no—
56#324—94no—
57C22×C3×C4—24no—
58C22×C3×C4—22no—
59C22×Dic3—62no—
60C22×Dic3—64no—
61C22×Dic3—62no—
62C2×Dic6—68no—
63C2×Dic6—68no—
64C2×Dic6—68no—
65C3×C4⋊C4—28no—
66Dic3⋊C4—616no—
67C4×Dic3—64no—
68C4×Dic3—64no—
69C4×Dic3—68no—
70C4×Dic3—68no—
71C22×C32—21no—
72C22×C32—21no—
73C22×C32C2×C22⋊C411yescharacteristic
74C22×C32C22×C811yescharacteristic
75C22×C32C2×M1611yescharacteristic
76C32×C4—42no—
77C32×C4C22⋊C814yes—
78C3⋊Dic3—24no—
79C3⋊Dic3—21no—
80C3⋊Dic3—22no—
81C3⋊Dic3#10112yes—
82C22×Q8—91no—
83C4×Q8—182no—
84C4×Q8—182no—
85C2×C4⋊C4—92no—
86C2×C4⋊C4#15711yescharacteristic
87C2×C42—91no—
88C2×C42—92no—
89C4⋊C8—182no—
90C22⋊C8—94no—
91C4×C8—182no—
92C23×C3—22no—
93C2×C3×C4—28no—
94C2×C3×C4—24no—
95C2×C3×C4—24no—
96C2×C3×C4—24no—
97C2×C3×C4—48no—
98C2×Dic3—62no—
99C2×Dic3—62no—
100C2×Dic3—68no—
101C2×Dic3—64no—
102C2×Dic3—68no—
103C2×Dic3—68no—
104C2×Dic3—68no—
105C2×Dic3—124no—
106Dic6—632no—
107C2×C32—21no—
108C2×C32—21no—
109C2×C32C2×C22⋊C811yescharacteristic
110C2×C32#41011yescharacteristic
111C2×C32C2×#10111yescharacteristic
112C2×Q8—94no—
113C2×Q8—182no—
114C2×Q8—182no—
115C22×C4—91no—
116C22×C4—92no—
117C22×C4—91no—
118C22×C4C2×#15712yes—
119C22×C4C2×#15711yescharacteristic
120C2×C8—184no—
121C4⋊C4—22no—
122C4⋊C4—184no—
123C42—92no—
124C42—92no—
125C42—182no—
126C42—182no—
127C22×C3—24no—
128C22×C3—24no—
129C22×C3—22no—
130C22×C3—22no—
131C22×C3—22no—
132C3×C4—28no—
133C3×C4—48no—
134Dic3—64no—
135Dic3—616no—
136Dic3—64no—
137Dic3—124no—
138C32#146111yescharacteristic, complemented, Sylow
139C23C22×#15711yescharacteristic
140Q8—188no—
141C2×C4—22no—
142C2×C4—42no—
143C2×C4—91no—
144C2×C4—94no—
145C2×C4—91no—
146C2×C4—92no—
147C2×C4—182no—
148C2×C4—182no—
149C2×C4—182no—
150C2×C4—361no—
151C2×C4#378712yes—
152C2×C4#378812yes—
153C2×C4C22⋊#15712yes—
154C8—364no—
155C2×C3—24no—
156C2×C3—24no—
157C2×C3—22no—
158C2×C3—22no—
159C2×C3—22no—
160C22—21no—
161C22—21no—
162C22C2×#378711yescharacteristic
163C22C2×#378811yescharacteristic
164C22C2×C22⋊#15711yescharacteristic
165C4—42no—
166C4—92no—
167C4—184no—
168C4—182no—
169C4—181no—
170C4#6377814yes—
171C3—22no—
172C2—21no—
173C2—21no—
174C2C2×#6377811yescharacteristic
175C2#1059381811yescharacteristic
176C2#1059383611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC22×C32C22×C8
FrattiniC23C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1461
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
22. C2×#634C8semidirect
138. C32#1461semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
#105937952
#105902032
#14619