Finite Group Databasebeta

← #93056

Subgroups — #93056

Order 512.

222 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 58 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#11460C211yesmaximal, characteristic
2#8600C211yesmaximal, characteristic
3#8007C211yesmaximal, characteristic
4#2920—21no—
5C2×#431C2211yescharacteristic
6#2163—21no—
7#1797—21no—
8C2×#335C411yescharacteristic
9C2×#334C411yescharacteristic
10#1322C412yes—
11#1314—21no—
12#1293—21no—
13#1293C412yes—
14#1277—21no—
15C22×C42D411yescharacteristic
16#432—22no—
17#432—41no—
18#431—22no—
19#431—41no—
20#431—41no—
21#431—41no—
22#423—41no—
23C2×C4⋊C8—21no—
24C2×C4⋊C8—21no—
25C2×C4⋊C8C2×C411yescharacteristic
26C2×C4⋊C8Q811yescharacteristic
27#407—22no—
28C2×C22⋊C8—41no—
29C2×C22⋊C8C2×C411yescharacteristic
30C2×C22⋊C8D411yescharacteristic
31C4×M16—41no—
32C2×C4×C8C2×C411yescharacteristic
33C2×C4×C8D411yescharacteristic
34C4⋊C16—41no—
35C22⋊C16—22no—
36#346—41no—
37#336—41no—
38#335—41no—
39#334—41no—
40C23×C4C22⋊C411yescharacteristic
41C23×C4SD1611yescharacteristic
42C23×C4Q1611yescharacteristic
43C2×M16—42no—
44C22×C8—41no—
45C22×C8—41no—
46C22×C8C4211yescharacteristic
47C22×C8C22⋊C411yescharacteristic
48C22×C8C4⋊C411yescharacteristic
49C22×C8C4⋊C411yescharacteristic
50C2×C42—21no—
51C2×C42—21no—
52C2×C42—21no—
53C2×C42—21no—
54C2×C42C22⋊C411yescharacteristic
55C2×C42C4⋊C411yescharacteristic
56C2×C42D811yescharacteristic
57C2×C42SD1611yescharacteristic
58C2×C16—42no—
59C4⋊C8—41no—
60C4⋊C8—41no—
61C4⋊C8—42no—
62C4⋊C8—42no—
63C4⋊C8—41no—
64C4⋊C8—41no—
65C4⋊C8—41no—
66C4⋊C8—41no—
67C22⋊C8—24no—
68C22⋊C8—41no—
69C22⋊C8—41no—
70C22⋊C8—42no—
71C22⋊C8—82no—
72#97—42no—
73C4×C8—21no—
74C4×C8—21no—
75C4×C8—21no—
76C4×C8—21no—
77C4×C8—42no—
78C24#10311yescharacteristic
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—21no—
84C22×C4—21no—
85C22×C4—41no—
86C22×C4—41no—
87C22×C4—41no—
88C22×C4—41no—
89C22×C4—41no—
90C22×C4—41no—
91C22×C4#9511yescharacteristic
92C22×C4#10211yescharacteristic
93C22×C4#10211yescharacteristic
94C22×C4#10311yescharacteristic
95C22×C4#10611yescharacteristic
96C22×C4#10711yescharacteristic
97M16—82no—
98M16—82no—
99C2×C8—21no—
100C2×C8—21no—
101C2×C8—21no—
102C2×C8—21no—
103C2×C8—41no—
104C2×C8—41no—
105C2×C8—41no—
106C2×C8—41no—
107C2×C8—44no—
108C2×C8—81no—
109C2×C8—81no—
110C2×C8—81no—
111C2×C8—81no—
112C2×C8—81no—
113C2×C8—81no—
114C42—21no—
115C42—21no—
116C42—21no—
117C42—21no—
118C42—21no—
119C42—21no—
120C42#9911yescharacteristic
121C42#9911yescharacteristic
122C42#10411yescharacteristic
123C42#10411yescharacteristic
124C16—82no—
125C23—21no—
126C23—21no—
127C23—21no—
128C23—41no—
129C23—41no—
130C23#34011yescharacteristic
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—81no—
151C2×C4—81no—
152C2×C4#32711yescharacteristic
153C2×C4#32711yescharacteristic
154C2×C4#32811yescharacteristic
155C2×C4#32811yescharacteristic
156C2×C4#33911yescharacteristic
157C2×C4#34211yescharacteristic
158C8—41no—
159C8—41no—
160C8—41no—
161C8—41no—
162C8—84no—
163C8—161no—
164C8—161no—
165C22—21no—
166C22—21no—
167C22—42no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22—81no—
172C22#129411yescharacteristic
173C22#138511yescharacteristic
174C22#138811yescharacteristic
175C4—21no—
176C4—21no—
177C4—21no—
178C4—21no—
179C4—41no—
180C4—41no—
181C4—41no—
182C4#134111yescharacteristic
183C4#134211yescharacteristic
184C4#139111yescharacteristic
185C4#139511yescharacteristic
186C2—21no—
187C2—21no—
188C2—81no—
189C2#725211yescharacteristic
190C2#725511yescharacteristic
191C2#726511yescharacteristic
subgroupG/H
center, socleC22#1294
commutatorC22×C8C42
Frattini, cosocleC2×#431C22
prime radicalC24#103
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#431 ◁ G
LECSG ▷ C2×#431 ▷ C22×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#114602
#86002
#80072