Finite Group Databasebeta

← #93495

Subgroups — #93495

Order 512.

264 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 78 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#12844C211yesmaximal, characteristic
2#12783C211yesmaximal, characteristic
3#8145C211yesmaximal, characteristic
4C22×C4×C8C2211yescharacteristic
5C2×C4⋊C16—21no—
6C2×C22⋊C16C412yes—
7C2×C22⋊C16C412yes—
8C4×C22⋊C8C411yescharacteristic
9C4×C22⋊C8C411yescharacteristic
10C2×#322—21no—
11#1374—21no—
12#1374—21no—
13#1374—21no—
14#1273—21no—
15C23×C8C2×C411yescharacteristic
16C23×C8C2×C411yescharacteristic
17C22×C42C2×C411yescharacteristic
18C22×C16—22no—
19C22×C16—22no—
20C2×C22⋊C8—21no—
21C2×C22⋊C8—21no—
22C2×C4×C8—21no—
23C2×C4×C8—21no—
24C2×C4×C8—42no—
25C2×C4×C8D411yescharacteristic
26C2×C4×C8D411yescharacteristic
27C2×C4×C8D411yescharacteristic
28C2×C4×C8Q811yescharacteristic
29C4⋊C16—42no—
30C22⋊C16—42no—
31C22⋊C16—42no—
32#336C812yes—
33#336C812yes—
34#322—42no—
35C23×C4C4211yescharacteristic
36C23×C4M1611yescharacteristic
37C23×C4M1611yescharacteristic
38C22×C8—22no—
39C22×C8—22no—
40C22×C8—21no—
41C22×C8—21no—
42C22×C8—22no—
43C22×C8—41no—
44C22×C8—41no—
45C22×C8—41no—
46C22×C8—41no—
47C22×C8C22⋊C411yescharacteristic
48C22×C8C22⋊C411yescharacteristic
49C22×C8C4⋊C411yescharacteristic
50C22×C8C4⋊C411yescharacteristic
51C2×C42—41no—
52C2×C42—41no—
53C2×C42C22⋊C411yescharacteristic
54C2×C42C4⋊C411yescharacteristic
55C2×C42C2×C811yescharacteristic
56C2×C42C2×C811yescharacteristic
57C2×C16—42no—
58C2×C16—42no—
59C2×C16—42no—
60C2×C16—42no—
61C2×C16—42no—
62C2×C16—42no—
63C22⋊C8—24no—
64C22⋊C8—42no—
65C4×C8—22no—
66C4×C8—22no—
67C4×C8—41no—
68C4×C8—41no—
69C4×C8—41no—
70C4×C8—41no—
71C4×C8—41no—
72C4×C8—41no—
73C24#9711yescharacteristic
74C22×C4—22no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—22no—
82C22×C4—22no—
83C22×C4—22no—
84C22×C4—41no—
85C22×C4—41no—
86C22×C4#9511yescharacteristic
87C22×C4C4×C811yescharacteristic
88C22×C4C22⋊C811yescharacteristic
89C22×C4C22⋊C811yescharacteristic
90C22×C4C4⋊C811yescharacteristic
91C22×C4C4⋊C811yescharacteristic
92C2×C8—21no—
93C2×C8—21no—
94C2×C8—21no—
95C2×C8—21no—
96C2×C8—24no—
97C2×C8—21no—
98C2×C8—21no—
99C2×C8—21no—
100C2×C8—21no—
101C2×C8—21no—
102C2×C8—21no—
103C2×C8—42no—
104C2×C8—42no—
105C2×C8—44no—
106C2×C8—42no—
107C2×C8—42no—
108C2×C8—42no—
109C2×C8—42no—
110C2×C8—42no—
111C2×C8#9912yes—
112C2×C8#10011yescharacteristic
113C2×C8#10111yescharacteristic
114C42—21no—
115C42—21no—
116C42—21no—
117C42—21no—
118C42—41no—
119C42—41no—
120C16—82no—
121C16—82no—
122C23—21no—
123C23—21no—
124C23—21no—
125C23—21no—
126C23—21no—
127C23—21no—
128C23#33611yescharacteristic
129C23#34712yes—
130C2×C4—21no—
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—44no—
143C2×C4—44no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4#34211yescharacteristic
149C2×C4#34311yescharacteristic
150C2×C4#34411yescharacteristic
151C2×C4#34411yescharacteristic
152C2×C4#34411yescharacteristic
153C2×C4#34411yescharacteristic
154C2×C4#35012yes—
155C2×C4#35012yes—
156C2×C4#36412yes—
157C8—21no—
158C8—21no—
159C8—22no—
160C8—44no—
161C8—41no—
162C8—41no—
163C8—82no—
164C22—22no—
165C22—22no—
166C22—22no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22#128111yescharacteristic
172C22#128211yescharacteristic
173C22#128311yescharacteristic
174C22#137511yescharacteristic
175C22#137611yescharacteristic
176C22#137911yescharacteristic
177C22#137911yescharacteristic
178C4—22no—
179C4—22no—
180C4—22no—
181C4—41no—
182C4—41no—
183C4#130511yescharacteristic
184C4#130611yescharacteristic
185C4#130711yescharacteristic
186C4#130811yescharacteristic
187C2—42no—
188C2#703311yescharacteristic
189C2#719611yescharacteristic
190C2#719811yescharacteristic
191C2#720011yescharacteristic
192C2#720211yescharacteristic
193C2#721011yescharacteristic
194C2#721211yescharacteristic
subgroupG/H
centerC22×C4#95
commutatorC22×C4C4×C8
Frattini, cosocleC22×C4×C8C22
socleC23#336
prime radicalC24#97
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C4×C8 ◁ G
LECSG ▷ C22×C4×C8 ▷ C22×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#128442
#127832
#81452