Finite Group Databasebeta

← #9650

Subgroups — #9650

Order 256.

328 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C2×#389C211yesmaximal, characteristic
2#1797C211yesmaximal, characteristic
3C4×C22⋊C8C211yesmaximal, characteristic
4C2×#324C214yesmaximal
5C22×C4⋊C4C411yescharacteristic
6C22×C4⋊C4C411yescharacteristic
7C22×C4⋊C4C2212yes—
8C22×C42C2211yescharacteristic
9C2×C4⋊C8—21no—
10C2×C22⋊C8C2212yes—
11C2×C22⋊C8C2212yes—
12C2×C4×C8—21no—
13#389—21no—
14#389—21no—
15#389—21no—
16#389—21no—
17C2×#95C412yes—
18#336—21no—
19#336—21no—
20#324—28no—
21C23×C4C2×C412yes—
22C23×C4C2×C411yescharacteristic
23C23×C4C2×C411yescharacteristic
24C23×C4C2×C412yes—
25C23×C4C2311yescharacteristic
26C22×C8—22no—
27C22×C8—22no—
28C2×C4⋊C4—21no—
29C2×C4⋊C4—21no—
30C2×C4⋊C4—22no—
31C2×C4⋊C4—21no—
32C2×C4⋊C4—21no—
33C2×C4⋊C4—24no—
34C2×C4⋊C4—22no—
35C2×C4⋊C4—22no—
36C2×C4⋊C4—24no—
37C2×C4⋊C4—42no—
38C2×C4⋊C4C814yescomplemented
39C2×C42—42no—
40C2×C42D411yescharacteristic
41C2×C42D411yescharacteristic
42C2×C42D411yescharacteristic
43C2×C42D411yescharacteristic
44C4⋊C8—42no—
45C22⋊C8—22no—
46C22⋊C8—24no—
47C22⋊C8D414yes—
48C4×C8—42no—
49#95—22no—
50#95—22no—
51C24C22×C411yescharacteristic
52C22×C4—22no—
53C22×C4—22no—
54C22×C4—22no—
55C22×C4—24no—
56C22×C4—22no—
57C22×C4—22no—
58C22×C4—24no—
59C22×C4—22no—
60C22×C4—22no—
61C22×C4—24no—
62C22×C4—41no—
63C22×C4—41no—
64C22×C4—41no—
65C22×C4—42no—
66C22×C4—42no—
67C22×C4C22⋊C411yescharacteristic
68C22×C4C22⋊C411yescharacteristic
69C22×C4C22⋊C411yescharacteristic
70C22×C4C22⋊C411yescharacteristic
71C22×C4C2×C814yes—
72C22×C4C2×C812yes—
73C22×C4M1612yes—
74C22×C4C2×D411yescharacteristic
75C22×C4C2×D411yescharacteristic
76C22×C4C2×D412yes—
77C22×C4#4112yes—
78C2×C8—24no—
79C2×C8—42no—
80C2×C8—42no—
81C2×C8—42no—
82C2×C8—42no—
83C2×C8—42no—
84C4⋊C4—24no—
85C4⋊C4—24no—
86C4⋊C4—42no—
87C4⋊C4—42no—
88C4⋊C4—44no—
89C4⋊C4—42no—
90C4⋊C4—42no—
91C42—22no—
92C42—22no—
93C42—41no—
94C42—41no—
95C23—21no—
96C23—21no—
97C23—21no—
98C23—21no—
99C23C2×C22⋊C411yescharacteristic
100C23C4×D412yes—
101C23C22×C811yescharacteristic
102C23C2×M1611yescharacteristic
103C23#13112yes—
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—24no—
113C2×C4—24no—
114C2×C4—24no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—28no—
119C2×C4—42no—
120C2×C4—42no—
121C2×C4—44no—
122C2×C4—42no—
123C2×C4—42no—
124C2×C4—44no—
125C2×C4—42no—
126C2×C4—42no—
127C2×C4—42no—
128C2×C4—84no—
129C2×C4C22⋊C812yes—
130C2×C4C22⋊C812yes—
131C2×C4#9912yes—
132C2×C4#10112yes—
133C2×C4#10112yes—
134C2×C4#12112yes—
135C2×C4#12411yescharacteristic
136C2×C4#12711yescharacteristic
137C8—44no—
138C8—82no—
139C22—22no—
140C22—22no—
141C22—21no—
142C22—21no—
143C22—21no—
144C22—21no—
145C22—22no—
146C22—22no—
147C22#39011yescharacteristic
148C22C2×C22⋊C811yescharacteristic
149C22#40811yescharacteristic
150C22C2×#9911yescharacteristic
151C22#41011yescharacteristic
152C22C2×#10111yescharacteristic
153C22C2×#10111yescharacteristic
154C22C8×D412yes—
155C22#43612yes—
156C4—22no—
157C4—21no—
158C4—21no—
159C4—22no—
160C4—22no—
161C4—44no—
162C4—41no—
163C4—82no—
164C4#32414yescomplemented
165C2—22no—
166C2—22no—
167C2C2×#32411yescharacteristic
168C2#146111yescharacteristic
169C2#147011yescharacteristic
170C2#147211yescharacteristic
171C2#195411yescharacteristic
172C2#196411yescharacteristic
173C2#196611yescharacteristic
subgroupG/H
center, socleC23C2×C22⋊C4
commutatorC23C22×C8
Frattini, cosocleC23×C4C23
prime radicalC24C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
38. C2×C4⋊C4C8semidirect
164. C4#324semidirect

Maximal subgroups

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

subgroupindex
C2×#3892
#17972
C4×C22⋊C82
C2×#3242