Finite Group Databasebeta

← #93238

Subgroups — #93238

Order 512.

228 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 28 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#10345C211yesmaximal, characteristic
2#7308C211yesmaximal, characteristic
3#7131C211yesmaximal, characteristic
4#2646C411yescharacteristic
5#1787—21no—
6#1784—21no—
7#1446C2211yescharacteristic
8#1294—21no—
9#1280—21no—
10#1280C411yescharacteristic
11C23×Q8D411yescharacteristic
12C2×#103—41no—
13C2×#103—41no—
14C2×#101—22no—
15C2×#101—41no—
16#407—41no—
17C2×C22⋊C8—21no—
18C2×C22⋊C8—41no—
19#400—41no—
20#398—41no—
21#385—41no—
22#380—21no—
23C2×#95—41no—
24C2×#95C2×C411yescharacteristic
25C2×#95D411yescharacteristic
26C22×Q8—21no—
27C22×Q8—41no—
28C22×Q8—41no—
29C22×Q8—82no—
30C22×Q8SD1611yescharacteristic
31C22×Q8Q1611yescharacteristic
32C23×C4—21no—
33C23×C4—21no—
34C23×C4—21no—
35C23×C4C22⋊C411yescharacteristic
36C2×M16—42no—
37C22×C8—41no—
38C22×C8—81no—
39C2×C4⋊C4—21no—
40C2×C4⋊C4—21no—
41C2×C4⋊C4—41no—
42C2×C4⋊C4—41no—
43C2×C22⋊C4—41no—
44#103—82no—
45#103—82no—
46#101—82no—
47#101—82no—
48C22⋊C8—41no—
49C22⋊C8—42no—
50C22⋊C8—41no—
51C22⋊C8—81no—
52C22⋊C8—81no—
53C22⋊C8—81no—
54#95—41no—
55#95—41no—
56#95—41no—
57#95—41no—
58#95—41no—
59#95—82no—
60C24#9911yescharacteristic
61C2×Q8—42no—
62C2×Q8—42no—
63C2×Q8—41no—
64C2×Q8—41no—
65C2×Q8—42no—
66C2×Q8—42no—
67C2×Q8—81no—
68C2×Q8—81no—
69C2×Q8—81no—
70C2×Q8—81no—
71C2×Q8—81no—
72C2×Q8—82no—
73C2×Q8—82no—
74C22×C4—21no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—21no—
80C22×C4—42no—
81C22×C4—41no—
82C22×C4—41no—
83C22×C4—41no—
84C22×C4—41no—
85C22×C4—41no—
86C22×C4—41no—
87C22×C4—41no—
88C22×C4—41no—
89C22×C4—41no—
90C22×C4—81no—
91C22×C4—81no—
92C22×C4—81no—
93C22×C4—81no—
94C22×C4—81no—
95C22×C4—81no—
96C22×C4#10311yescharacteristic
97C22×C4#10411yescharacteristic
98M16—82no—
99M16—82no—
100C2×C8—81no—
101C2×C8—82no—
102C2×C8—82no—
103C2×C8—81no—
104C2×C8—81no—
105C2×C8—161no—
106C2×C8—161no—
107C4⋊C4—81no—
108C4⋊C4—81no—
109C4⋊C4—161no—
110C4⋊C4—161no—
111C22⋊C4—81no—
112C22⋊C4—81no—
113C23—21no—
114C23—21no—
115C23—21no—
116C23—21no—
117C23—41no—
118C23#32811yescharacteristic
119C23AΣL(1,𝔽16)11yescharacteristic
120C23#35411yescharacteristic
121Q8—42no—
122Q8—42no—
123Q8—81no—
124Q8—82no—
125Q8—82no—
126Q8—81no—
127C2×C4—22no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—81no—
142C2×C4—82no—
143C2×C4—82no—
144C2×C4—81no—
145C2×C4—81no—
146C2×C4—81no—
147C2×C4—81no—
148C2×C4—81no—
149C2×C4—81no—
150C2×C4—81no—
151C2×C4—81no—
152C2×C4—81no—
153C2×C4—81no—
154C2×C4—82no—
155C2×C4—81no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4—161no—
159C2×C4—161no—
160C8—161no—
161C8—162no—
162C8—162no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22#135111yescharacteristic
175C22#140311yescharacteristic
176C22#140511yescharacteristic
177C22#141311yescharacteristic
178C22#141411yescharacteristic
179C4—41no—
180C4—42no—
181C4—41no—
182C4—81no—
183C4—81no—
184C4—81no—
185C4—161no—
186C4—161no—
187C4—161no—
188C2—21no—
189C2—21no—
190C2—21no—
191C2—21no—
192C2—41no—
193C2#742611yescharacteristic
194C2#742911yescharacteristic
195C2#743111yescharacteristic
subgroupG/H
center, socleC22#1351
commutatorC2×#95C2×C4
Frattini, cosocle#1446C22
prime radicalC24#99
LCSG ▷ C2×#95 ▷ C23×C4 ▷ C23 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ #1446 ◁ G
LECSG ▷ #1446 ▷ C23×C4 ▷ C23 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#103452
#73082
#71312