Finite Group Databasebeta

← #93058

Subgroups — #93058

Order 512.

245 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 245 conjugacy classes of subgroups — too many to draw. Only its 62 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#8001C211yesmaximal, characteristic
4C2×#431C2211yescharacteristic
5C2×#423—21no—
6#2163—21no—
7#1797—21no—
8C2×#335C411yescharacteristic
9C2×#334C411yescharacteristic
10#1322—21no—
11#1314C412yes—
12#1292—21no—
13#1292C412yes—
14#1277—21no—
15C22×M16—41no—
16C22×C42D411yescharacteristic
17#431—41no—
18#431—41no—
19#423—22no—
20#423—22no—
21#423—41no—
22#423—41no—
23C2×C4⋊C8—22no—
24C2×C4⋊C8—21no—
25C2×C4⋊C8—21no—
26C2×C4⋊C8—41no—
27C2×C4⋊C8C2×C411yescharacteristic
28C2×C4⋊C8D411yescharacteristic
29C2×C22⋊C8—41no—
30C2×C22⋊C8C2×C411yescharacteristic
31C2×C22⋊C8Q811yescharacteristic
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×C4C4⋊C411yescharacteristic
41C23×C4SD1611yescharacteristic
42C23×C4SD1611yescharacteristic
43C2×M16—42no—
44C2×M16—42no—
45C2×M16—82no—
46C2×M16—82no—
47C22×C8—42no—
48C22×C8—41no—
49C22×C8—41no—
50C22×C8C4211yescharacteristic
51C22×C8C22⋊C411yescharacteristic
52C22×C8C4⋊C411yescharacteristic
53C22×C8C4⋊C411yescharacteristic
54C2×C42—21no—
55C2×C42—21no—
56C2×C42—21no—
57C2×C42—21no—
58C2×C42C22⋊C411yescharacteristic
59C2×C42C22⋊C411yescharacteristic
60C2×C42D811yescharacteristic
61C2×C42Q1611yescharacteristic
62C2×C16—42no—
63C4⋊C8—24no—
64C4⋊C8—41no—
65C4⋊C8—41no—
66C4⋊C8—42no—
67C4⋊C8—42no—
68C4⋊C8—42no—
69C4⋊C8—41no—
70C4⋊C8—41no—
71C4⋊C8—41no—
72C4⋊C8—41no—
73C22⋊C8—41no—
74C22⋊C8—41no—
75C22⋊C8—82no—
76C4×C8—21no—
77C4×C8—21no—
78C4×C8—21no—
79C4×C8—21no—
80C24#10611yescharacteristic
81C22×C4—22no—
82C22×C4—21no—
83C22×C4—21no—
84C22×C4—21no—
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—41no—
91C22×C4—41no—
92C22×C4—41no—
93C22×C4—41no—
94C22×C4#9511yescharacteristic
95C22×C4#10211yescharacteristic
96C22×C4#10211yescharacteristic
97C22×C4#10311yescharacteristic
98C22×C4#10311yescharacteristic
99C22×C4#10711yescharacteristic
100M16—84no—
101M16—82no—
102M16—82no—
103C2×C8—21no—
104C2×C8—21no—
105C2×C8—21no—
106C2×C8—21no—
107C2×C8—41no—
108C2×C8—41no—
109C2×C8—41no—
110C2×C8—41no—
111C2×C8—44no—
112C2×C8—84no—
113C2×C8—81no—
114C2×C8—81no—
115C2×C8—81no—
116C2×C8—81no—
117C2×C8—81no—
118C2×C8—81no—
119C42—21no—
120C42—21no—
121C42—21no—
122C42—21no—
123C42—21no—
124C42—21no—
125C42#9911yescharacteristic
126C42#9911yescharacteristic
127C42#10411yescharacteristic
128C42#10411yescharacteristic
129C16—82no—
130C23—21no—
131C23—21no—
132C23—41no—
133C23—41no—
134C23#34011yescharacteristic
135C23#36512yes—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4#32711yescharacteristic
159C2×C4#32711yescharacteristic
160C2×C4#32811yescharacteristic
161C2×C4#32811yescharacteristic
162C2×C4#33911yescharacteristic
163C2×C4#34211yescharacteristic
164C2×C4#36111yescharacteristic
165C2×C4#36211yescharacteristic
166C8—41no—
167C8—41no—
168C8—41no—
169C8—41no—
170C8—84no—
171C8—161no—
172C8—161no—
173C22—21no—
174C22—21no—
175C22—22no—
176C22—42no—
177C22—41no—
178C22—41no—
179C22—81no—
180C22#129411yescharacteristic
181C22#138311yescharacteristic
182C22#138711yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4#134111yescharacteristic
192C4#134211yescharacteristic
193C4#139211yescharacteristic
194C4#139511yescharacteristic
195C2—21no—
196C2—21no—
197C2—42no—
198C2#725311yescharacteristic
199C2#725511yescharacteristic
200C2#726411yescharacteristic
subgroupG/H
center, socleC22#1294
commutatorC22×C8C42
Frattini, cosocleC2×#431C22
prime radicalC24#106
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
#80012