Finite Group Databasebeta

← #11772824

Subgroups — #11772824

Order 1152.

192 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 19 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#10591629C211yesmaximal, characteristic
2#10590217C211yesmaximal, characteristic
3#10589183C211yesmaximal, characteristic
4#64156C2211yescharacteristic
5C2×C3×#216—21no—
6#63873C411yescharacteristic, complemented
7C2×#3717—21no—
8#63774—21no—
9C3×#836—21no—
10#63555C411yescharacteristic, complemented
11#5190—61no—
12#4477—61no—
13C2×C32×Q8D411yescharacteristic
14C2×C4⋊(C3⋊D3)D411yescharacteristic
15C2×C3×Dic6—21no—
16C22⋊#157—41no—
17#3752—41no—
18C4×C3⋊Dic3C2×C411yescharacteristic
19C3×#216—42no—
20C3×#208—41no—
21C2×C3×C3⋊C8—21no—
22#3724—41no—
23#3717—42no—
24#1407—91nomaximal, Sylow
25C2×C3×Q16—61no—
26#947—61no—
27#947—61no—
28#944—61no—
29C2×#216—21no—
30C2×#215—61no—
31C2×#204—61no—
32C3×#101—61no—
33#836—21no—
34#815—61no—
35C22×C3⋊D3—21no—
36C2×#157—81no—
37C32×Q8—41no—
38C2×C32×C4—21no—
39C2×C32×C4C22⋊C411yescharacteristic
40C2×C3⋊Dic3—21no—
41C4⋊(C3⋊D3)—41no—
42C2×C3×Dic3—41no—
43C3×Dic6—41no—
44C3×Dic6—41no—
45C3×C3⋊C8—22no—
46C3×C3⋊C8—81no—
47#497—91no—
48#355—91no—
49#354—91no—
50C2×C3×Q8—21no—
51C2×C3×Q8—21no—
52C2×C3×Q8—61no—
53C2×D12—61no—
54C2×D12—61no—
55C2×Dic6—21no—
56C3×Q16—122no—
57C3×M16—121no—
58C2×C3×C8—61no—
59#216—42no—
60#215—122no—
61(C2×D3)⋊C4—122no—
62(C2×D3)⋊C4—121no—
63(C2×D3)⋊C4—121no—
64Dic3⋊C4—122no—
65C4×Dic3—61no—
66C4×Dic3—61no—
67#208—41no—
68C2×C3⋊C8—21no—
69#204—122no—
70C22×C32#9911yescharacteristic
71C2×C3⋊D3—41no—
72C2×C3⋊D3—81no—
73#157—161no—
74C32×C4—21no—
75C32×C4—41no—
76C3⋊Dic3—41no—
77C3×Dic3—81no—
78C2×Q16—61no—
79C2×SD16—181no—
80C4⋊Q8—91no—
81#124—91no—
82#101—61no—
83#99—181no—
84#97—91no—
85C22×D3—121no—
86C22×D3—121no—
87C3×Q8—41no—
88C3×Q8—41no—
89C3×Q8—81no—
90C3×Q8—121no—
91C3×Q8—121no—
92C2×C3×C4—21no—
93C2×C3×C4—21no—
94C2×C3×C4—21no—
95C2×C3×C4—21no—
96C2×C3×C4—41no—
97C2×C3×C4—121no—
98C2×Dic3—41no—
99C2×Dic3—62no—
100C2×Dic3—121no—
101D12—121no—
102D12—121no—
103D12—241no—
104Dic6—41no—
105Dic6—41no—
106C3×C8—62no—
107C3×C8—241no—
108C3⋊C8—22no—
109C3⋊C8—81no—
110C2×C32—21no—
111C2×C32#35311yescharacteristic
112C3⋊D3—81no—
113C2×Q8—61no—
114C2×Q8GO+(4,𝔽2)11yescharacteristic
115C2×D4—91no—
116Q16—122no—
117SD16—362no—
118M16—121no—
119C2×C8—61no—
120C4⋊C4—361no—
121C22⋊C4—361no—
122C22⋊C4—361no—
123C42—91no—
124C22×C3—21no—
125C22×C3—21no—
126C2×D3—241no—
127C2×D3—241no—
128C2×D3—242no—
129C2×D3—242no—
130C3×C4—21no—
131C3×C4—21no—
132C3×C4—41no—
133C3×C4—41no—
134C3×C4—41no—
135C3×C4—81no—
136C3×C4—241no—
137Dic3—81no—
138Dic3—122no—
139Dic3—241no—
140C32#140711yescharacteristic, complemented, Sylow
141C23—181no—
142Q8—41no—
143Q8—121no—
144Q8—121no—
145D4—361no—
146C2×C4—21no—
147C2×C4—121no—
148C2×C4—181no—
149C2×C4—721no—
150C2×C4D32⋊C411yescharacteristic
151C8—62no—
152C8—241no—
153C2×C3—22no—
154C2×C3—21no—
155C2×C3—21no—
156C2×C3—41no—
157D3—481no—
158D3—481no—
159C22—361no—
160C22—721no—
161C22#6373811yescharacteristic
162C4—21no—
163C4—41no—
164C4—241no—
165C4—361no—
166C4—1441no—
167C3—21no—
168C3—21no—
169C2—21no—
170C2—721no—
171C2#1059008011yescharacteristic
subgroupG/H
centerC2#10590080
commutatorC4×C3⋊Dic3C2×C4
Frattini, hypercenterC2×Q8GO+(4,𝔽2)
FittingC2×C32×Q8D4
socleC2×C32#353
prime radicalC2×C4⋊(C3⋊D3)D4
cosocle#64156C22
hypocenterC32#1407
LCSG ▷ C4×C3⋊Dic3 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
6. #63873C4semidirect
10. #63555C4semidirect
140. C32#1407semidirect

Maximal subgroups

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

subgroupindex
#105916292
#105902172
#105891832
#14079