Finite Group Databasebeta

← #94397

Subgroups — #94397

Order 512.

180 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 42 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#13200C211yesmaximal, characteristic
2#11483C211yesmaximal, characteristic
3#11468C211yesmaximal, characteristic
4#2929C2211yescharacteristic
5#2153C411yescharacteristic
6#2117—21no—
7#2115—21no—
8#2112—21no—
9C2×C22⋊C16—21no—
10#2110C411yescharacteristic
11#1328—21no—
12#1323—21no—
13#1320C412yes—
14#1315C412yes—
15C2×#131D411yescharacteristic
16C23×C8D411yescharacteristic
17#525Q811yescharacteristic
18C2×M32—21no—
19C2×M32—21no—
20C2×M32—41no—
21C22×C16—41no—
22#435—41no—
23C8×D4—41no—
24#424D411yescharacteristic
25#408C2×C411yescharacteristic
26#407C2×C411yescharacteristic
27#405C2×C411yescharacteristic
28#364—41no—
29#350—42no—
30#349—22no—
31#349—41no—
32C22⋊C16—22no—
33C22⋊C16—42no—
34C22⋊C16—41no—
35#347—41no—
36C2×#41C4⋊C411yescharacteristic
37C23×C4C4⋊C411yescharacteristic
38#131—41no—
39#131—41no—
40C2×M16—21no—
41C2×M16C4211yescharacteristic
42C2×M16C22⋊C411yescharacteristic
43C22×C8—21no—
44C22×C8—21no—
45C22×C8—21no—
46C22×C8—41no—
47C22×C8—41no—
48C22×C8C22⋊C411yescharacteristic
49C22×C8C22⋊C411yescharacteristic
50#123—21no—
51C22⋊Q8—21no—
52#121—21no—
53#120—21no—
54C4×D4—41no—
55#117C4⋊C411yescharacteristic
56M32—41no—
57M32—41no—
58M32—42no—
59M32—41no—
60M32—41no—
61M32—81no—
62C2×C16—22no—
63C2×C16—42no—
64C2×C16—41no—
65C2×C16—81no—
66C2×C16—81no—
67C2×C16—81no—
68C4⋊C8—41no—
69C22⋊C8—41no—
70C22⋊C8—41no—
71#97—21no—
72C4×C8—21no—
73C24#10811yescharacteristic
74#41—41no—
75#41—41no—
76C2×Q8#10811yescharacteristic
77C2×D4—21no—
78C2×D4—41no—
79C2×D4#10811yescharacteristic
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—41no—
84C22×C4—41no—
85C22×C4#9511yescharacteristic
86C22×C4#10811yescharacteristic
87M16—41no—
88M16—41no—
89M16—81no—
90C2×C8—21no—
91C2×C8—21no—
92C2×C8—21no—
93C2×C8—21no—
94C2×C8—21no—
95C2×C8—41no—
96C2×C8—41no—
97C2×C8—41no—
98C2×C8—41no—
99C2×C8—41no—
100C2×C8—81no—
101C2×C8#9911yescharacteristic
102C2×C8#9911yescharacteristic
103C4⋊C4—21no—
104C4⋊C4—41no—
105C22⋊C4—21no—
106C22⋊C4—41no—
107C22⋊C4—41no—
108C42—21no—
109C16—42no—
110C16—82no—
111C16—82no—
112C16—81no—
113C23—21no—
114C23—21no—
115C23—41no—
116C23—42no—
117C23#34111yescharacteristic
118Q8—41no—
119D4—41no—
120D4—81no—
121D4—82no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—81no—
133C2×C4#34111yescharacteristic
134C2×C4#34211yescharacteristic
135C8—21no—
136C8—41no—
137C8—41no—
138C8—41no—
139C8#35311yescharacteristic
140C8#35411yescharacteristic
141C22—22no—
142C22—21no—
143C22—41no—
144C22—41no—
145C22—42no—
146C22—41no—
147C22—41no—
148C22—81no—
149C22—81no—
150C22#129811yescharacteristic
151C4—21no—
152C4—41no—
153C4—41no—
154C4—81no—
155C4#139211yescharacteristic
156C4#139311yescharacteristic
157C2—21no—
158C2—42no—
159C2—41no—
160C2—81no—
161C2#728711yescharacteristic
subgroupG/H
centerC8#353
commutatorC2×M16C42
Frattini, cosocle#2929C22
socleC2#7287
prime radical#525Q8
LCSG ▷ C2×M16 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C8 ◁ C2×C8 ◁ C22×C8 ◁ #2929 ◁ G
LECSG ▷ #2929 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#132002
#114832
#114682