Finite Group Databasebeta

← #9985

Subgroups — #9985

Order 256.

251 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 251 conjugacy classes of subgroups — too many to draw. Only its 49 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#3095C212yesmaximal
2#2817C211yesmaximal, characteristic
3#1820C211yesmaximal, characteristic
4#1511C212yesmaximal
5#1306C211yesmaximal, characteristic
6C2×C22⋊Q8C2212yes—
7C2×#117C2211yescharacteristic
8#485—24no—
9#484—22no—
10#483—22no—
11#428—22no—
12#419—22no—
13#407C2212yes—
14#400—22no—
15#397—22no—
16#395—22no—
17#381C2211yescharacteristic
18#381C2211yescharacteristic
19#342—22no—
20#328—24no—
21C22×Q8D412yes—
22C23×C4C2311yescharacteristic
23C2×M16—22no—
24C22⋊Q8—22no—
25C22⋊Q8—22no—
26C22⋊Q8—22no—
27C22⋊Q8—22no—
28#117—22no—
29#117—22no—
30C2×C4⋊C4—22no—
31C2×C4⋊C4—22no—
32C2×C4⋊C4D412yes—
33C2×C4⋊C4D412yes—
34C2×C22⋊C4—21no—
35C2×C22⋊C4—22no—
36C2×C22⋊C4—21no—
37C2×C22⋊C4D412yes—
38C2×C42—21no—
39#107—24no—
40#106—24no—
41#103—24no—
42#103—24no—
43C22⋊C8—22no—
44C22⋊C8D414yes—
45#95—24no—
46#95—22no—
47#95—22no—
48#95—22no—
49C24C2×D411yescharacteristic
50C2×Q8—22no—
51C2×Q8—22no—
52C2×Q8—44no—
53C22×C4—22no—
54C22×C4—22no—
55C22×C4—22no—
56C22×C4—22no—
57C22×C4—42no—
58C22×C4—41no—
59C22×C4C2×D412yes—
60C22×C4C2×D411yescharacteristic
61C22×C4C2×D412yes—
62C22×C4#4111yescharacteristic
63M16—44no—
64C2×C8—24no—
65C4⋊C4—22no—
66C4⋊C4—22no—
67C4⋊C4—22no—
68C4⋊C4—22no—
69C4⋊C4—42no—
70C4⋊C4—42no—
71C4⋊C4—82no—
72C22⋊C4—41no—
73C22⋊C4—42no—
74C22⋊C4—41no—
75C22⋊C4—42no—
76C22⋊C4—42no—
77C22⋊C4—42no—
78C42—42no—
79C23—22no—
80C23—42no—
81C23#12011yescharacteristic
82C23#12111yescharacteristic
83C23#12711yescharacteristic
84Q8—44no—
85Q8—82no—
86C2×C4—24no—
87C2×C4—41no—
88C2×C4—42no—
89C2×C4—41no—
90C2×C4—44no—
91C2×C4—44no—
92C2×C4—42no—
93C2×C4—42no—
94C2×C4—42no—
95C2×C4—42no—
96C2×C4—44no—
97C2×C4—82no—
98C2×C4—81no—
99C2×C4—82no—
100C2×C4#12012yes—
101C2×C4#12112yes—
102C8—44no—
103C22—22no—
104C22—22no—
105C22—22no—
106C22—21no—
107C22—21no—
108C22—82no—
109C22#39211yescharacteristic
110C22#45812yes—
111C4—22no—
112C4—22no—
113C4—82no—
114C4—82no—
115C4—82no—
116C4—82no—
117C4—161no—
118C2—22no—
119C2—41no—
120C2—41no—
121C2#200912yes—
122C2#202211yescharacteristic
subgroupG/H
center, socleC22#392
commutator, Frattini, cosocleC23×C4C23
prime radicalC24C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#30952
#28172
#18202
#15112
#13062