Finite Group Databasebeta

← #11771247

Subgroups — #11771247

Order 1152.

410 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 44 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#10593845C212yesmaximal
2#10592642C211yesmaximal, characteristic
3C23×C3⋊Dic3C2211yescharacteristic
4C2×#3792—22no—
5C2×C32×C22⋊C4C411yescharacteristic
6C2×#3757C411yescharacteristic
7C22⋊#622—22no—
8C22⋊#622C414yescomplemented
9#63658—22no—
10#4943—62no—
11C24×C32C2×C411yescharacteristic
12C22×C32×C4—21no—
13C22×C3⋊Dic3—21no—
14C22×C3⋊Dic3—41no—
15C22×C3⋊Dic3—41no—
16C22×C3⋊Dic3C2×C412yes—
17C22×C3⋊Dic3D412yes—
18C22×C3⋊Dic3D411yescharacteristic
19C22×C3⋊Dic3Q811yescharacteristic
20#3792—42no—
21#3792—42no—
22C2×#622—24no—
23C32×C22⋊C4—41no—
24#3757—41no—
25#1306—91nomaximal, Sylow
26C23×Dic3—62no—
27C2×C3×C22⋊C4—22no—
28C2×#217—62no—
29C3⋊#95—68no—
30C23×C32—21no—
31C23×C32—21no—
32C23×C32—42no—
33C23×C32C4211yescharacteristic
34C23×C32C22⋊C411yescharacteristic
35C23×C32C4⋊C411yescharacteristic
36C2×C32×C4—42no—
37C2×C32×C4—41no—
38C2×C3⋊Dic3—22no—
39C2×C3⋊Dic3—22no—
40C2×C3⋊Dic3—42no—
41C2×C3⋊Dic3—41no—
42C2×C3⋊Dic3—41no—
43C2×C3⋊Dic3—42no—
44C2×C3⋊Dic3—41no—
45C2×C3⋊Dic3C22⋊C412yes—
46C2×C3⋊Dic3C4⋊C412yes—
47#622—44no—
48#407—92no—
49#381—91no—
50C24×C3—22no—
51C22×C3×C4—24no—
52C22×Dic3—64no—
53C22×Dic3—64no—
54C22×Dic3—62no—
55C22×Dic3—62no—
56C22×Dic3—64no—
57C22×Dic3—124no—
58C22×Dic3—124no—
59C3×C22⋊C4—44no—
60#217—124no—
61C22×C32—22no—
62C22×C32—21no—
63C22×C32—21no—
64C22×C32—22no—
65C22×C32—22no—
66C22×C32—42no—
67C22×C32—42no—
68C22×C32#9511yescharacteristic
69C22×C32#9911yescharacteristic
70C22×C32#9911yescharacteristic
71C32×C4—81no—
72C3⋊Dic3—22no—
73C3⋊Dic3—22no—
74C3⋊Dic3—81no—
75C23×C4—91no—
76C2×M16—182no—
77C2×C22⋊C4—91no—
78C2×C22⋊C4#15711yescharacteristic
79C22⋊C8—94no—
80C22⋊C8—182no—
81#95—182no—
82C23×C3—24no—
83C23×C3—24no—
84C23×C3—22no—
85C23×C3—22no—
86C23×C3—22no—
87C23×C3—48no—
88C2×C3×C4—44no—
89C2×C3×C4—48no—
90C2×Dic3—64no—
91C2×Dic3—64no—
92C2×Dic3—124no—
93C2×Dic3—124no—
94C2×Dic3—128no—
95C2×Dic3—124no—
96C2×Dic3—124no—
97C2×Dic3—124no—
98C2×Dic3—128no—
99C2×C32—21no—
100C2×C32—21no—
101C2×C32—41no—
102C2×C32—41no—
103C2×C32#34211yescharacteristic
104C2×C32#34412yes—
105C24C2×#15711yescharacteristic
106C22×C4—21no—
107C22×C4—92no—
108C22×C4—92no—
109C22×C4—91no—
110C22×C4—91no—
111C22×C4—181no—
112C22×C4—361no—
113C22×C4—361no—
114M16—362no—
115M16—362no—
116C2×C8—184no—
117C22⋊C4—41no—
118C22⋊C4—361no—
119C22×C3—28no—
120C22×C3—24no—
121C22×C3—24no—
122C22×C3—22no—
123C22×C3—22no—
124C22×C3—22no—
125C22×C3—44no—
126C22×C3—44no—
127C22×C3—48no—
128C22×C3—48no—
129C3×C4—84no—
130Dic3—124no—
131Dic3—124no—
132Dic3—244no—
133C32#130611yescharacteristic, complemented, Sylow
134C23—21no—
135C23—21no—
136C23—42no—
137C23C4×#15711yescharacteristic
138C23C4⋊#15711yescharacteristic
139C23C22⋊#15711yescharacteristic
140C2×C4—42no—
141C2×C4—41no—
142C2×C4—92no—
143C2×C4—92no—
144C2×C4—182no—
145C2×C4—182no—
146C2×C4—361no—
147C2×C4—362no—
148C2×C4—361no—
149C2×C4—362no—
150C2×C4—361no—
151C8—364no—
152C2×C3—24no—
153C2×C3—24no—
154C2×C3—24no—
155C2×C3—22no—
156C2×C3—44no—
157C2×C3—44no—
158C22—22no—
159C22—22no—
160C22—22no—
161C22—21no—
162C22—21no—
163C22—42no—
164C22—42no—
165C22#6377411yescharacteristic
166C22#6378111yescharacteristic
167C22#6378611yescharacteristic
168C4—81no—
169C4—182no—
170C4—182no—
171C4—721no—
172C3—22no—
173C2—21no—
174C2—21no—
175C2—41no—
176C2—41no—
177C2#1059015612yes—
178C2#1059020611yescharacteristic
subgroupG/H
centerC22#63781
commutatorC23×C32C42
FrattiniC24C2×#157
FittingC2×C32×C22⋊C4C4
socleC22×C32#95
prime radicalC24×C32C2×C4
cosocleC23×C3⋊Dic3C22
hypercenterC2×C22⋊C4#157
hypocenterC32#1306
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C22⋊#622C4semidirect
133. C32#1306semidirect

Maximal subgroups

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

subgroupindex
#105938452
#105926422
#13069