Finite Group Databasebeta

← #10585

Subgroups — #10585

Order 256.

191 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 191 conjugacy classes of subgroups — too many to draw. Only its 57 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#2845C211yesmaximal, characteristic
2#1847C212yesmaximal
3#1836C211yesmaximal, characteristic
4#1295C211yesmaximal, characteristic
5#1295C212yesmaximal
6C2×#107—22no—
7C2×#106—22no—
8C2×#97C2211yescharacteristic
9C2×#97C2212yes—
10#398—22no—
11#398—22no—
12#398—22no—
13#384C2211yescharacteristic
14#382C2211yescharacteristic
15#382C2212yes—
16#340—22no—
17C22×C8—22no—
18C22×C8—21no—
19C2×C4⋊C4—21no—
20C2×C4⋊C4—22no—
21C2×C4⋊C4—22no—
22C2×C4⋊C4—22no—
23C2×C4⋊C4—22no—
24C2×C4⋊C4D412yes—
25C2×C4⋊C4D412yes—
26C2×C4⋊C4D412yes—
27C2×C42C2311yescharacteristic
28#107—44no—
29#106—44no—
30#97—22no—
31#97—21no—
32#97Q814yes—
33#97Q812yes—
34#95—22no—
35#95—22no—
36#95—22no—
37#95—22no—
38C22×C4—22no—
39C22×C4—22no—
40C22×C4—22no—
41C22×C4—41no—
42C22×C4C2×D412yes—
43C22×C4C2×D411yescharacteristic
44C2×C8—24no—
45C2×C8—24no—
46C2×C8—24no—
47C2×C8—22no—
48C2×C8—41no—
49C2×C8—41no—
50C4⋊C4—42no—
51C4⋊C4—42no—
52C4⋊C4—42no—
53C4⋊C4—42no—
54C4⋊C4—42no—
55C4⋊C4—42no—
56C4⋊C4—82no—
57C4⋊C4—82no—
58C4⋊C4—82no—
59C42C2×Q812yes—
60C42C2×Q811yescharacteristic
61C42#4111yescharacteristic
62C23#12011yescharacteristic
63C2×C4—22no—
64C2×C4—21no—
65C2×C4—21no—
66C2×C4—22no—
67C2×C4—42no—
68C2×C4—42no—
69C2×C4—42no—
70C2×C4—42no—
71C2×C4—42no—
72C2×C4—42no—
73C2×C4—42no—
74C2×C4—42no—
75C2×C4—42no—
76C2×C4—82no—
77C2×C4—81no—
78C2×C4C22⋊Q812yes—
79C2×C4C22⋊Q811yescharacteristic
80C2×C4C4⋊Q812yes—
81C2×C4C4⋊Q811yescharacteristic
82C8—28no—
83C8—42no—
84C22#39511yescharacteristic
85C22#45312yes—
86C22#45411yescharacteristic
87C22#45511yescharacteristic
88C22#45612yes—
89C4—22no—
90C4—22no—
91C4—21no—
92C4—21no—
93C4—82no—
94C4—82no—
95C4—82no—
96C4—161no—
97C2#165611yescharacteristic
98C2#166112yes—
99C2#166311yescharacteristic
100C2#206012yes—
101C2#206111yescharacteristic
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
#28452
#18472
#18362
#12952