Finite Group Databasebeta

← #93302

Subgroups — #93302

Order 512.

382 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 74 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#12846C212yesmaximal
2#10693C211yesmaximal, characteristic
3C22×#97C411yescharacteristic
4C22×#97C2211yescharacteristic
5C2×C43C411yescharacteristic
6#2112—22no—
7C2×#336—22no—
8#1377—22no—
9#1377C414yescomplemented
10C23×C8—21no—
11C23×C8D412yes—
12C22×C42—21no—
13C22×C42—21no—
14C22×C42C812yes—
15C22×C42C2×C411yescharacteristic
16C2×M32—24no—
17C2×#97—21no—
18C2×#97—41no—
19C2×#97—41no—
20C2×#97—41no—
21C2×#97—41no—
22C2×#97C812yes—
23C2×#97C2×C412yes—
24C2×#97D411yescharacteristic
25C2×#97Q811yescharacteristic
26C43—41no—
27C43—41no—
28C22⋊C16—42no—
29C22⋊C16—42no—
30#336—28no—
31C23×C4—22no—
32C23×C4C22⋊C411yescharacteristic
33C23×C4C2×C811yescharacteristic
34C23×C4M1611yescharacteristic
35C22×C8—24no—
36C22×C8—22no—
37C22×C8—22no—
38C22×C8—22no—
39C22×C8—24no—
40C22×C8—42no—
41C22×C8—42no—
42C22×C8—41no—
43C22×C8—41no—
44C22×C8C22⋊C412yes—
45C22×C8C4⋊C412yes—
46C2×C42—21no—
47C2×C42—21no—
48C2×C42—21no—
49C2×C42—21no—
50C2×C42—24no—
51C2×C42—42no—
52C2×C42—42no—
53C2×C42—42no—
54C2×C42—44no—
55C2×C42—41no—
56C2×C42—41no—
57C2×C42—44no—
58C2×C42C4211yescharacteristic
59C2×C42C4⋊C411yescharacteristic
60C2×C42C2×C811yescharacteristic
61C2×C42M1611yescharacteristic
62M32—44no—
63M32—44no—
64C2×C16—44no—
65#97—42no—
66#97—41no—
67#97—41no—
68#97—42no—
69#97—42no—
70C24C22⋊C811yescharacteristic
71C22×C4—22no—
72C22×C4—22no—
73C22×C4—24no—
74C22×C4—24no—
75C22×C4—24no—
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—21no—
80C22×C4—42no—
81C22×C4—42no—
82C22×C4—42no—
83C22×C4—42no—
84C22×C4—42no—
85C22×C4—42no—
86C22×C4#9511yescharacteristic
87C22×C4C4×C811yescharacteristic
88C22×C4#9711yescharacteristic
89C22×C4C22⋊C811yescharacteristic
90C22×C4#9911yescharacteristic
91C22×C4#9911yescharacteristic
92C22×C4#10011yescharacteristic
93C22×C4#10111yescharacteristic
94C22×C4C4⋊C811yescharacteristic
95C22×C4C4⋊C811yescharacteristic
96C2×C8—22no—
97C2×C8—22no—
98C2×C8—24no—
99C2×C8—22no—
100C2×C8—22no—
101C2×C8—22no—
102C2×C8—44no—
103C2×C8—44no—
104C2×C8—42no—
105C2×C8—44no—
106C2×C8—44no—
107C2×C8—42no—
108C2×C8#10414yes—
109C42—21no—
110C42—21no—
111C42—21no—
112C42—21no—
113C42—21no—
114C42—21no—
115C42—21no—
116C42—21no—
117C42—44no—
118C42—44no—
119C42—44no—
120C42—48no—
121C42—44no—
122C16—84no—
123C23—22no—
124C23—22no—
125C23—21no—
126C23—21no—
127C23#32311yescharacteristic
128C23#32411yescharacteristic
129C23#33611yescharacteristic
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—28no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—44no—
142C2×C4—44no—
143C2×C4—42no—
144C2×C4—44no—
145C2×C4—44no—
146C2×C4—44no—
147C2×C4—42no—
148C2×C4—42no—
149C2×C4—44no—
150C2×C4—42no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4#32311yescharacteristic
156C2×C4#32411yescharacteristic
157C2×C4H(3,ℤ/4)12yes—
158C2×C4#33912yes—
159C2×C4#34211yescharacteristic
160C2×C4#34311yescharacteristic
161C8—24no—
162C8—44no—
163C8—42no—
164C22—22no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—21no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22—21no—
174C22#127411yescharacteristic
175C22#127611yescharacteristic
176C22#128011yescharacteristic
177C22#132012yes—
178C22#132712yes—
179C4—21no—
180C4—21no—
181C4—48no—
182C4—41no—
183C4—41no—
184C4—41no—
185C4—41no—
186C4#128412yes—
187C4#128512yes—
188C2—22no—
189C2—22no—
190C2—21no—
191C2—21no—
192C2#701711yescharacteristic
193C2#719111yescharacteristic
194C2#719311yescharacteristic
subgroupG/H
centerC2×C4#342
commutatorC22×C4C4×C8
Frattini, cosocleC22×#97C22
socleC22#1280
prime radicalC24C22⋊C8
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#97 ◁ G
LECSG ▷ C22×#97 ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
9. #1377C4semidirect

Maximal subgroups

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

subgroupindex
#128462
#106932