Finite Group Databasebeta

← #46242

Subgroups — #46242

Order 256.

650 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2864C212yesmaximal
2#2845C211yesmaximal, characteristic
3#2845C211yesmaximal, characteristic
4#2802C214yesmaximal
5#2791C214yesmaximal
6#2791C214yesmaximal
7#2590C214yesmaximal
8#2585C214yesmaximal
9#2507C214yesmaximal
10#2382C212yesmaximal
11C4×#125C211yesmaximal, characteristic
12C2×#125C2211yescharacteristic
13#400C2214yes—
14#400C2214yes—
15#398C2214yes—
16#398C2214yes—
17#398C2214yes—
18#398C2214yes—
19#398C2214yes—
20#398C2214yes—
21#398C2214yes—
22#398C2214yes—
23#398C2214yes—
24#398C2214yes—
25#389C2212yes—
26#389C2214yes—
27#389C2212yes—
28#389C2214yes—
29#389C2214yes—
30#389C2212yes—
31#389C2212yes—
32#389C2212yes—
33#389C2214yes—
34#389C2214yes—
35#389C2214yes—
36#387C2214yes—
37#387C2214yes—
38#387C2214yes—
39#387C2214yes—
40#387C2214yes—
41#387C2214yes—
42#387C2214yes—
43#387C2214yes—
44#387C2214yes—
45#387C2214yes—
46#387C2214yes—
47#387C2214yes—
48#387C2214yes—
49#384C2214yes—
50#382C2211yescharacteristic
51#382C2212yes—
52#382C2212yes—
53C4×C4⋊C4C2214yes—
54C4×C4⋊C4C2212yes—
55C4×C4⋊C4C2214yes—
56C43C2211yescharacteristic
57#125Q818yes—
58C2×C4⋊C4C2314yes—
59C2×C4⋊C4C2312yes—
60C2×C4⋊C4C2314yes—
61C2×C4⋊C4C2314yes—
62C2×C4⋊C4C2312yes—
63C2×C4⋊C4C2312yes—
64C2×C4⋊C4C2312yes—
65C2×C4⋊C4C2312yes—
66C2×C4⋊C4C2314yes—
67C2×C4⋊C4C2314yes—
68C2×C4⋊C4C2314yes—
69C2×C4⋊C4C2314yes—
70C2×C4⋊C4C2314yes—
71C2×C4⋊C4C2314yes—
72C2×C4⋊C4C2314yes—
73C2×C4⋊C4C2314yes—
74C2×C4⋊C4C2314yes—
75C2×C4⋊C4C2314yes—
76C2×C4⋊C4C2312yes—
77C2×C4⋊C4C2314yes—
78C2×C42C2311yescharacteristic
79C2×C42C2312yes—
80C2×C42C2312yes—
81C2×C42C2311yescharacteristic
82C2×C42C2314yes—
83C2×C42C2314yes—
84C2×C42C2314yes—
85C2×C42C2311yescharacteristic
86#95C2314yes—
87#95C2314yes—
88#95C2314yes—
89#95C2314yes—
90#95C2314yes—
91#95C2314yes—
92#95C2314yes—
93#95C2314yes—
94#95C2314yes—
95#95C2314yes—
96#95C2314yes—
97#95C2314yes—
98#95C2314yes—
99#95C2314yes—
100#95C2314yes—
101#95C2314yes—
102#95C2314yes—
103C22×C4C2411yescharacteristic
104C22×C4C2414yes—
105C22×C4C2414yes—
106C22×C4C2412yes—
107C22×C4C2414yes—
108C22×C4C2414yes—
109C22×C4C2414yes—
110C22×C4C2411yescharacteristic
111C22×C4C2414yes—
112C22×C4C2412yes—
113C22×C4C2411yescharacteristic
114C4⋊C4—28no—
115C4⋊C4—44no—
116C4⋊C4—42no—
117C4⋊C4—42no—
118C4⋊C4—44no—
119C4⋊C4—44no—
120C4⋊C4—42no—
121C4⋊C4—42no—
122C4⋊C4—42no—
123C4⋊C4—44no—
124C4⋊C4—44no—
125C4⋊C4—44no—
126C4⋊C4—44no—
127C4⋊C4—44no—
128C4⋊C4—44no—
129C4⋊C4—44no—
130C4⋊C4—44no—
131C4⋊C4—44no—
132C4⋊C4C2×Q818yes—
133C4⋊C4C2×Q8116yes—
134C42—22no—
135C42—44no—
136C42—42no—
137C42—44no—
138C42—41no—
139C42—42no—
140C42—44no—
141C42C2×Q814yes—
142C23C2511yescharacteristic
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—24no—
146C2×C4—21no—
147C2×C4—24no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—24no—
152C2×C4—24no—
153C2×C4—22no—
154C2×C4—24no—
155C2×C4—24no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—24no—
168C2×C4—24no—
169C2×C4—24no—
170C2×C4C22×Q812yes—
171C2×C4C22×Q814yes—
172C2×C4C22×Q818yes—
173C2×C42−1+412yes—
174C22C23×Q811yescharacteristic
175C22C2×2−1+411yescharacteristic
176C22#58511yescharacteristic
177C22#58512yes—
178C22#58512yes—
179C4—22no—
180C4—28no—
181C4—24no—
182C4—22no—
183C4—41no—
184C4—44no—
185C4—44no—
186C4—42no—
187C4—44no—
188C4—44no—
189C4—44no—
190C2#350211yescharacteristic
191C2#350412yes—
192C2#353111yescharacteristic
193C2#355311yescharacteristic
194C2#356712yes—
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC23C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#28642
#28452
#28022
#27912
#25902
#25852
#25072
#23822
C4×#1252