Finite Group Databasebeta

← #11772339

Subgroups — #11772339

Order 1152.

222 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 51 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#10593765C211yesmaximal, characteristic
2C2×#63544C211yesmaximal, characteristic
3#10590625C211yesmaximal, characteristic
4#64286C411yescharacteristic
5#64283C411yescharacteristic
6C2×C8×C3⋊D3C2211yescharacteristic
7#63767—21no—
8C8×#157—21no—
9C3×#812—21no—
10C2×C3×C3⋊C16—21no—
11#63544—21no—
12#63544—21no—
13#63544C412yescomplemented
14#63542C412yescomplemented
15D3×M32—61no—
16C2×#798—61no—
17C2×C4×C3⋊D3C2×C411yescharacteristic
18C22⋊#157C812yes—
19#3792—21no—
20C4⋊#157—21no—
21C4×#157—21no—
22#3788C812yes—
23#3787—21no—
24C2×C32×C8D411yescharacteristic
25C2×C3⋊(C3⋊C8)Q811yescharacteristic
26C8×C3⋊D3C2×C411yescharacteristic
27C8×C3⋊D3C2×C411yescharacteristic
28C8×C3⋊D3D411yescharacteristic
29C8×C3⋊D3D411yescharacteristic
30C3×C3⋊C16—22no—
31C3×C3⋊C16—22no—
32#1378—91nomaximal, Sylow
33C2×D3×C8—61no—
34C2×D3×C8—61no—
35C3×M32—61no—
36C2×C3×C16—61no—
37#812—21no—
38C2×C3⋊C16—21no—
39#798—62no—
40#798—62no—
41#798—62no—
42D3×C16—62no—
43C22×C3⋊D3C2×C811yescharacteristic
44C2×#157—22no—
45C2×C32×C4C4⋊C411yescharacteristic
46C2×C3⋊Dic3M1611yescharacteristic
47C4×C3⋊D3C4211yescharacteristic
48C4×C3⋊D3C22⋊C411yescharacteristic
49C4×C3⋊D3C2×C811yescharacteristic
50C4×C3⋊D3M1611yescharacteristic
51#622—22no—
52C32×C8C22⋊C411yescharacteristic
53C32×C8C22⋊C411yescharacteristic
54C3⋊(C3⋊C8)C4⋊C411yescharacteristic
55C3⋊(C3⋊C8)C4⋊C411yescharacteristic
56C2×M32—91no—
57C2×M32—91no—
58#405—91no—
59C2×C4×D3—61no—
60C2×C4×D3—61no—
61C2×C3×C8—21no—
62C2×C3×C8—21no—
63C2×C3⋊C8—61no—
64C2×C3⋊C8—61no—
65D3×C8—61no—
66D3×C8—61no—
67D3×C8—61no—
68D3×C8—61no—
69D3×C8—61no—
70D3×C8—61no—
71D3×C8—61no—
72D3×C8—61no—
73C3×C16—62no—
74C3×C16—62no—
75C3⋊C16—22no—
76C3⋊C16—22no—
77C22×C32C4⋊C811yescharacteristic
78C2×C3⋊D3—41no—
79C2×C3⋊D3C4×C811yescharacteristic
80C2×C3⋊D3C22⋊C811yescharacteristic
81#157—42no—
82C32×C4#9511yescharacteristic
83C32×C4C4⋊C811yescharacteristic
84C3⋊Dic3#9711yescharacteristic
85C3⋊Dic3C22⋊C811yescharacteristic
86C2×M16—91no—
87C22×C8—91no—
88#117—91no—
89M32—61no—
90M32—92no—
91M32—181no—
92M32—181no—
93C2×C16—61no—
94C2×C16—92no—
95#97—181no—
96C4×C8—181no—
97C22×D3—61no—
98C22×D3—61no—
99C2×C3×C4—21no—
100C2×C3×C4—21no—
101C2×Dic3—61no—
102C2×Dic3—61no—
103C4×D3—61no—
104C4×D3—61no—
105C4×D3—61no—
106C4×D3—61no—
107C4×D3—61no—
108C4×D3—61no—
109C4×D3—61no—
110C4×D3—61no—
111C3×C8—21no—
112C3×C8—21no—
113C3×C8—21no—
114C3×C8—21no—
115C3⋊C8—61no—
116C3⋊C8—61no—
117C3⋊C8—61no—
118C3⋊C8—61no—
119C2×C32—21no—
120C2×C32#33611yescharacteristic
121C3⋊D3—21no—
122C3⋊D3—21no—
123C22×C4—91no—
124M16—92no—
125M16—181no—
126C2×C8—91no—
127C2×C8—91no—
128C2×C8—91no—
129C2×C8—91no—
130C2×C8—91no—
131C2×C8—181no—
132C2×C8GO+(4,𝔽2)11yescharacteristic
133C4⋊C4—181no—
134C22⋊C4—92no—
135C42—181no—
136C16—62no—
137C16—62no—
138C22×C3—21no—
139C22×C3—21no—
140C2×D3—61no—
141C2×D3—61no—
142C2×D3—61no—
143C2×D3—61no—
144C2×D3—122no—
145C2×D3—122no—
146C3×C4—21no—
147C3×C4—21no—
148C3×C4—21no—
149C3×C4—21no—
150Dic3—61no—
151Dic3—61no—
152Dic3—61no—
153Dic3—61no—
154C32#137811yescharacteristic, complemented, Sylow
155C23—91no—
156C2×C4—91no—
157C2×C4—91no—
158C2×C4—91no—
159C2×C4—91no—
160C2×C4—91no—
161C2×C4—182no—
162C2×C4#377311yescharacteristic
163C8—91no—
164C8—91no—
165C8—182no—
166C8D32⋊C411yescharacteristic
167C8D32⋊C411yescharacteristic
168C2×C3—22no—
169C2×C3—21no—
170C2×C3—21no—
171C2×C3—41no—
172D3—62no—
173D3—121no—
174D3—121no—
175D3—121no—
176C22—91no—
177C22—91no—
178C22—361no—
179C22#6373211yescharacteristic
180C4—91no—
181C4—91no—
182C4—362no—
183C4#6373211yescharacteristic
184C4#6373711yescharacteristic
185C3—21no—
186C3—21no—
187C2—21no—
188C2—181no—
189C2—181no—
190C2#1059004411yescharacteristic
subgroupG/H
centerC8D32⋊C4
commutatorC2×C3⋊D3C4×C8
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#336
prime radicalC22×C3⋊D3C2×C8
cosocleC2×C8×C3⋊D3C22
hypocenterC32#1378
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
13. #63544C4semidirect
14. #63542C4semidirect
154. C32#1378semidirect

Maximal subgroups

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

subgroupindex
#105937652
C2×#635442
#105906252
#13789