Finite Group Databasebeta

← #10428

Subgroups — #10428

Order 256.

193 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 193 conjugacy classes of subgroups — too many to draw. Only its 53 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#2822C211yesmaximal, characteristic
2#1992C212yesmaximal
3#1836C211yesmaximal, characteristic
4C2×#330C212yesmaximal
5#1295C211yesmaximal, characteristic
6C2×#125C2212yes—
7C2×#97C2212yes—
8C2×#97C2211yescharacteristic
9#400—22no—
10#398—22no—
11#398—22no—
12#384C2211yescharacteristic
13#382C2211yescharacteristic
14#340—22no—
15#340—22no—
16#340—22no—
17#330—24no—
18C22×C8—22no—
19C22×C8—21no—
20#125—22no—
21#125—22no—
22#125—22no—
23#125—22no—
24C2×C4⋊C4—22no—
25C2×C4⋊C4—22no—
26C2×C4⋊C4—22no—
27C2×C4⋊C4—21no—
28C2×C4⋊C4—22no—
29C2×C4⋊C4D412yes—
30C2×C4⋊C4D412yes—
31C2×C4⋊C4D412yes—
32C2×C42C2311yescharacteristic
33#97—22no—
34#97—21no—
35#97—22no—
36#97D412yes—
37#95—24no—
38#95—22no—
39#95—22no—
40C22×C4—22no—
41C22×C4—22no—
42C22×C4—22no—
43C22×C4—41no—
44C22×C4C2×D412yes—
45C22×C4C2×D411yescharacteristic
46C2×C8—24no—
47C2×C8—22no—
48C2×C8—42no—
49C2×C8—41no—
50C2×C8—41no—
51C2×C8—42no—
52C4⋊C4—22no—
53C4⋊C4—22no—
54C4⋊C4—22no—
55C4⋊C4—22no—
56C4⋊C4—42no—
57C4⋊C4—44no—
58C4⋊C4—42no—
59C4⋊C4—42no—
60C4⋊C4—42no—
61C4⋊C4—42no—
62C4⋊C4—42no—
63C4⋊C4—82no—
64C42C2×D411yescharacteristic
65C42#4111yescharacteristic
66C42#4112yes—
67C23#12011yescharacteristic
68C2×C4—22no—
69C2×C4—21no—
70C2×C4—21no—
71C2×C4—22no—
72C2×C4—42no—
73C2×C4—42no—
74C2×C4—42no—
75C2×C4—42no—
76C2×C4—42no—
77C2×C4—42no—
78C2×C4—42no—
79C2×C4—42no—
80C2×C4—42no—
81C2×C4—81no—
82C2×C4—82no—
83C2×C4#12112yes—
84C2×C4#12111yescharacteristic
85C2×C4#12312yes—
86C2×C4#12411yescharacteristic
87C8—44no—
88C8—42no—
89C22#39411yescharacteristic
90C22#45411yescharacteristic
91C22#45412yes—
92C22#45511yescharacteristic
93C22#45612yes—
94C4—22no—
95C4—22no—
96C4—21no—
97C4—21no—
98C4—82no—
99C4—82no—
100C4—82no—
101C4—161no—
102C2#165811yescharacteristic
103C2#166311yescharacteristic
104C2#166412yes—
105C2#203812yes—
106C2#204011yescharacteristic
subgroupG/H
center, socle, prime radicalC23#120
commutator, Frattini, cosocleC2×C42C23
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#28222
#19922
#18362
C2×#3302
#12952