Finite Group Databasebeta

← #11771252

Subgroups — #11771252

Order 1152.

382 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 41 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#10593811C211yesmaximal, characteristic
2#10591159C212yesmaximal
3C22×C4×C3⋊D3C2211yescharacteristic
4C2×C22⋊#157C412yes—
5C2×#3712—22no—
6#63781—22no—
7C3×#830—22no—
8#63557C414yescomplemented
9#4726—62no—
10C23×C3⋊D3C2×C411yescharacteristic
11C22×#157—22no—
12C22×C32×C4D411yescharacteristic
13C22×C3⋊Dic3Q811yescharacteristic
14C2×C4×C3⋊D3—42no—
15C2×C4×C3⋊D3C2×C412yes—
16C2×C4×C3⋊D3D412yes—
17C22⋊#157—42no—
18C2×C3×C3⋊C8—24no—
19#3712—44no—
20#1306—91nomaximal, Sylow
21C22×C4×D3—62no—
22C2×ΓL(1,𝔽25)—64no—
23C3×C22⋊C8—62no—
24#830—22no—
25(C2×D3)⋊C8—64no—
26C23×C32C4⋊C411yescharacteristic
27C22×C3⋊D3—22no—
28C22×C3⋊D3—42no—
29C22×C3⋊D3C4211yescharacteristic
30C22×C3⋊D3C22⋊C411yescharacteristic
31C2×#157—44no—
32C2×#157—42no—
33C2×C32×C4—41no—
34C2×C32×C4C22⋊C412yes—
35C2×C3⋊Dic3—41no—
36C2×C3⋊Dic3C4⋊C412yes—
37C4×C3⋊D3—24no—
38C4×C3⋊D3—42no—
39C3×C3⋊C8—44no—
40#407—92no—
41#381—91no—
42C23×D3—62no—
43C22×C3×C4—22no—
44C22×Dic3—62no—
45C2×C4×D3—62no—
46C2×C4×D3—62no—
47C2×C4×D3—62no—
48C2×C4×D3—62no—
49C2×C4×D3—128no—
50C2×C3×C8—64no—
51C2×C3⋊C8—24no—
52ΓL(1,𝔽25)—128no—
53C22×C32—22no—
54C22×C32—21no—
55C22×C32#9511yescharacteristic
56C2×C3⋊D3—22no—
57C2×C3⋊D3—22no—
58C2×C3⋊D3—21no—
59C2×C3⋊D3—44no—
60C2×C3⋊D3#9912yes—
61#157—82no—
62C32×C4—22no—
63C3⋊Dic3—22no—
64C23×C4—91no—
65C2×M16—182no—
66C2×C22⋊C4—92no—
67C22⋊C8—62no—
68C22⋊C8—94no—
69#95—182no—
70C23×C3—22no—
71C22×D3—62no—
72C22×D3—62no—
73C22×D3—124no—
74C22×D3—124no—
75C22×D3—124no—
76C2×C3×C4—22no—
77C2×C3×C4—22no—
78C2×C3×C4—44no—
79C2×Dic3—62no—
80C2×Dic3—62no—
81C2×Dic3—124no—
82C4×D3—68no—
83C4×D3—124no—
84C4×D3—124no—
85C4×D3—124no—
86C3×C8—124no—
87C3⋊C8—44no—
88C2×C32—41no—
89C2×C32#34211yescharacteristic
90C2×C32#34412yes—
91C3⋊D3—22no—
92C3⋊D3—41no—
93C24—91no—
94C22×C4—91no—
95C22×C4—92no—
96C22×C4—92no—
97C22×C4—182no—
98C22×C4—362no—
99C22×C4GO+(4,𝔽2)11yescharacteristic
100M16—364no—
101C2×C8—64no—
102C22⋊C4—362no—
103C22×C3—24no—
104C22×C3—22no—
105C22×C3—42no—
106C22×C3—42no—
107C2×D3—64no—
108C2×D3—64no—
109C2×D3—122no—
110C2×D3—122no—
111C2×D3—122no—
112C2×D3—122no—
113C2×D3—1216no—
114C3×C4—24no—
115C3×C4—42no—
116Dic3—64no—
117Dic3—122no—
118C32#130611yescharacteristic, complemented, Sylow
119C23—91no—
120C23—91no—
121C23—182no—
122C23—362no—
123C23#377311yescharacteristic
124C2×C4—41no—
125C2×C4—92no—
126C2×C4—184no—
127C2×C4—362no—
128C2×C4—361no—
129C2×C4—362no—
130C2×C4—364no—
131C2×C4D32⋊C412yes—
132C8—124no—
133C2×C3—22no—
134C2×C3—22no—
135C2×C3—22no—
136C2×C3—44no—
137D3—124no—
138D3—124no—
139C22—22no—
140C22—21no—
141C22—92no—
142C22—182no—
143C22—182no—
144C22—181no—
145C22—364no—
146C22#6373711yescharacteristic
147C4—22no—
148C4—182no—
149C4—722no—
150C3—22no—
151C2—41no—
152C2—182no—
153C2—361no—
154C2#1059005512yes—
155C2#1059007711yescharacteristic
subgroupG/H
centerC22#63737
commutatorC22×C3⋊D3C42
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#95
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C4×C3⋊D3C22
hypocenterC32#1306
LCSG ▷ C22×C3⋊D3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. #63557C4semidirect
118. C32#1306semidirect

Maximal subgroups

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

subgroupindex
#105938112
#105911592
#13069