Finite Group Databasebeta

← #93022

Subgroups — #93022

Order 512.

224 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 52 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#12977C211yesmaximal, characteristic
2#8620C211yesmaximal, characteristic
3#8611C211yesmaximal, characteristic
4C22×M32C411yescharacteristic
5C2×C8×D4C2211yescharacteristic
6C2×C22⋊C16—21no—
7C2×C22⋊C16C411yescharacteristic
8#1810—21no—
9#1568—21no—
10#1466—21no—
11#1465—21no—
12#1374—21no—
13#1293C412yes—
14#1290C412yes—
15C23×C8C2×C411yescharacteristic
16C23×C8D411yescharacteristic
17C2×C4×D4D411yescharacteristic
18C2×M32—42no—
19C2×M32—41no—
20C22×C16—21no—
21C22×C16—21no—
22C8×D4—41no—
23C8×D4—41no—
24#432—22no—
25C2×#108—41no—
26C2×C4⋊C8C2×C411yescharacteristic
27#407—22no—
28C2×C22⋊C8C2×C411yescharacteristic
29C2×C22⋊C8Q811yescharacteristic
30C2×C4×C8D411yescharacteristic
31C22⋊C16—42no—
32C22⋊C16—41no—
33#341—41no—
34#335—41no—
35#334—41no—
36#324—41no—
37#323—41no—
38#323—41no—
39#323—41no—
40C22×D4Q1611yescharacteristic
41C23×C4C22⋊C411yescharacteristic
42C23×C4C4⋊C411yescharacteristic
43C2×M16—42no—
44C22×C8—21no—
45C22×C8—21no—
46C22×C8—21no—
47C22×C8—21no—
48C22×C8—41no—
49C22×C8—41no—
50C22×C8—41no—
51C22×C8—41no—
52C22×C8C4211yescharacteristic
53C22×C8C22⋊C411yescharacteristic
54C22×C8C4⋊C411yescharacteristic
55C22×C8C4⋊C411yescharacteristic
56C4×D4—41no—
57C4×D4—41no—
58C2×C4⋊C4SD1611yescharacteristic
59C2×C22⋊C4D811yescharacteristic
60C2×C22⋊C4SD1611yescharacteristic
61C2×C42C22⋊C411yescharacteristic
62M32—42no—
63M32—42no—
64C2×C16—22no—
65C2×C16—41no—
66C2×C16—41no—
67C2×C16—41no—
68C2×C16—41no—
69C2×C16—41no—
70#108—81no—
71#108—81no—
72C4⋊C8—41no—
73C4⋊C8—42no—
74C22⋊C8—41no—
75C22⋊C8—41no—
76C22⋊C8—42no—
77C22⋊C8—42no—
78C22⋊C8—42no—
79#97—42no—
80C4×C8—21no—
81C4×C8—21no—
82C24#10311yescharacteristic
83C24#10711yescharacteristic
84C2×D4—41no—
85C2×D4—41no—
86C2×D4—41no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—41no—
92C22×C4—41no—
93C22×C4—41no—
94C22×C4—41no—
95C22×C4#9511yescharacteristic
96C22×C4#10211yescharacteristic
97C22×C4#10211yescharacteristic
98C22×C4#10311yescharacteristic
99C22×C4#10611yescharacteristic
100M16—82no—
101M16—82no—
102C2×C8—21no—
103C2×C8—21no—
104C2×C8—21no—
105C2×C8—21no—
106C2×C8—21no—
107C2×C8—42no—
108C2×C8—41no—
109C2×C8—41no—
110C2×C8—41no—
111C2×C8—41no—
112C2×C8—41no—
113C2×C8—41no—
114C2×C8—41no—
115C2×C8—81no—
116C2×C8—82no—
117C2×C8—82no—
118C2×C8#9911yescharacteristic
119C2×C8#9911yescharacteristic
120C4⋊C4—41no—
121C22⋊C4—41no—
122C22⋊C4—41no—
123C42—21no—
124C42—21no—
125C16—42no—
126C16—81no—
127C23—21no—
128C23—21no—
129C23—21no—
130C23—21no—
131C23—21no—
132C23—21no—
133C23—41no—
134C23—41no—
135C23—41no—
136C23—41no—
137C23#34011yescharacteristic
138D4—44no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—81no—
156C2×C4H(3,ℤ/4)11yescharacteristic
157C2×C4#34211yescharacteristic
158C8—21no—
159C8—41no—
160C8—41no—
161C8—41no—
162C8—162no—
163C8—162no—
164C8AΣL(1,𝔽16)11yescharacteristic
165C8#35211yescharacteristic
166C22—21no—
167C22—21no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—41no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22#128911yescharacteristic
179C22#138811yescharacteristic
180C22#138811yescharacteristic
181C4—21no—
182C4—41no—
183C4—41no—
184C4—41no—
185C4—41no—
186C4#139011yescharacteristic
187C4#139511yescharacteristic
188C2—21no—
189C2—21no—
190C2—81no—
191C2—81no—
192C2#722711yescharacteristic
193C2#723411yescharacteristic
194C2#723611yescharacteristic
subgroupG/H
center, socleC22#1289
commutatorC22×C8C42
Frattini, cosocleC2×C8×D4C22
prime radicalC22×D4Q16
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C8×D4 ◁ G
LECSG ▷ C2×C8×D4 ▷ C22×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#129772
#86202
#86112