Finite Group Databasebeta

← #93055

Subgroups — #93055

Order 512.

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

normal subgroups only

This group has 265 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#7981C211yesmaximal, characteristic
4C2×#431C2211yescharacteristic
5#2285—21no—
6#2163—21no—
7#1797—21no—
8C2×#335C411yescharacteristic, complemented
9C2×#334C411yescharacteristic, complemented
10#1322C412yescomplemented
11#1314—21no—
12#1289—21no—
13#1289C412yes—
14#1277—21no—
15C2×#117—41no—
16C22×C42D411yescharacteristic
17#431—41no—
18#431—41no—
19C2×C4⋊C8—21no—
20C2×C4⋊C8—21no—
21C2×C4⋊C8C2×C411yescharacteristic
22C2×C4⋊C8Q811yescharacteristic
23C2×C22⋊C8—41no—
24C2×C22⋊C8C2×C411yescharacteristic
25C2×C22⋊C8D411yescharacteristic
26C2×C4×C8C2×C411yescharacteristic
27C2×C4×C8D411yescharacteristic
28#384—41no—
29#382—22no—
30#380—22no—
31#380—41no—
32C4×C4⋊C4—22no—
33C4×C4⋊C4—41no—
34C4⋊C16—41no—
35C22⋊C16—22no—
36#346—41no—
37#336—41no—
38#335—41no—
39#334—41no—
40C23×C4C22⋊C411yescharacteristic
41C23×C4D811yescharacteristic
42C23×C4SD1611yescharacteristic
43C22×C8—41no—
44C22×C8—41no—
45C22×C8C4211yescharacteristic
46C22×C8C22⋊C411yescharacteristic
47C22×C8C4⋊C411yescharacteristic
48C22×C8C4⋊C411yescharacteristic
49#117—82no—
50#117—82no—
51C2×C4⋊C4—42no—
52C2×C4⋊C4—42no—
53C2×C4⋊C4—42no—
54C2×C22⋊C4—42no—
55C2×C42—21no—
56C2×C42—21no—
57C2×C42—21no—
58C2×C42—21no—
59C2×C42—42no—
60C2×C42C22⋊C411yescharacteristic
61C2×C42C4⋊C411yescharacteristic
62C2×C42SD1611yescharacteristic
63C2×C42Q1611yescharacteristic
64C2×C16—42no—
65C4⋊C8—41no—
66C4⋊C8—41no—
67C4⋊C8—41no—
68C4⋊C8—41no—
69C4⋊C8—41no—
70C4⋊C8—41no—
71C22⋊C8—41no—
72C22⋊C8—41no—
73C22⋊C8—82no—
74C4×C8—21no—
75C4×C8—21no—
76C4×C8—21no—
77C4×C8—21no—
78#95—24no—
79#95—42no—
80C24#10211yescharacteristic
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—21no—
84C22×C4—21no—
85C22×C4—22no—
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—44no—
95C22×C4#9511yescharacteristic
96C22×C4#10211yescharacteristic
97C22×C4#10311yescharacteristic
98C22×C4#10311yescharacteristic
99C22×C4#10611yescharacteristic
100C22×C4#10711yescharacteristic
101C2×C8—21no—
102C2×C8—21no—
103C2×C8—21no—
104C2×C8—21no—
105C2×C8—41no—
106C2×C8—41no—
107C2×C8—41no—
108C2×C8—41no—
109C2×C8—81no—
110C2×C8—81no—
111C2×C8—81no—
112C2×C8—81no—
113C2×C8—81no—
114C2×C8—81no—
115C4⋊C4—84no—
116C4⋊C4—82no—
117C4⋊C4—82no—
118C4⋊C4—82no—
119C4⋊C4—82no—
120C22⋊C4—82no—
121C22⋊C4—82no—
122C42—21no—
123C42—21no—
124C42—21no—
125C42—21no—
126C42—21no—
127C42—21no—
128C42—84no—
129C42#9911yescharacteristic
130C42#9911yescharacteristic
131C42#10411yescharacteristic
132C42#10411yescharacteristic
133C16—82no—
134C23—21no—
135C23—21no—
136C23—41no—
137C23—41no—
138C23#34011yescharacteristic
139C23#36111yescharacteristic
140C23#36211yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—81no—
162C2×C4—81no—
163C2×C4—84no—
164C2×C4—84no—
165C2×C4—84no—
166C2×C4#32711yescharacteristic
167C2×C4#32711yescharacteristic
168C2×C4#32811yescharacteristic
169C2×C4#32811yescharacteristic
170C2×C4#33911yescharacteristic
171C2×C4#34211yescharacteristic
172C2×C4#36512yes—
173C8—41no—
174C8—41no—
175C8—41no—
176C8—41no—
177C8—161no—
178C8—161no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—41no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22—81no—
188C22#129411yescharacteristic
189C22#138311yescharacteristic
190C22#138711yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—22no—
196C4—41no—
197C4—41no—
198C4—164no—
199C4#133911yescharacteristic
200C4#134011yescharacteristic
201C4#139111yescharacteristic
202C4#139511yescharacteristic
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2#725211yescharacteristic
208C2#725411yescharacteristic
209C2#726411yescharacteristic
subgroupG/H
center, socleC22#1294
commutatorC22×C8C42
Frattini, cosocleC2×#431C22
prime radicalC24#102
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#431 ◁ G
LECSG ▷ C2×#431 ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
8. C2×#335C4semidirect
9. C2×#334C4semidirect
10. #1322C4semidirect

Maximal subgroups

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

subgroupindex
#114602
#86002
#79812