Finite Group Databasebeta

← #11819

Subgroups — #11819

Order 256.

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

normal subgroups only

This group has 184 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#2628C211yesmaximal, characteristic
2#1822C211yesmaximal, characteristic
3#1464C211yesmaximal, characteristic
4#1354C214yesmaximal, complemented
5C2×C4⋊Q8C411yescharacteristic
6C2×#117C2211yescharacteristic
7#432—21no—
8#407—21no—
9#400—21no—
10#399—21no—
11#395C2212yes—
12#393C412yes—
13#389—21no—
14#382C411yescharacteristic
15#380—21no—
16#343—21no—
17#343C2212yes—
18#324C2212yes—
19#323—21no—
20C22×Q8C2×C412yes—
21C23×C4D411yescharacteristic
22C2×M16—22no—
23C4⋊Q8—41no—
24C4⋊Q8—41no—
25#117—41no—
26#117—41no—
27C2×C4⋊C4—21no—
28C2×C4⋊C4—21no—
29C2×C4⋊C4—21no—
30C2×C4⋊C4—22no—
31C2×C4⋊C4D411yescharacteristic
32C2×C4⋊C4C2311yescharacteristic
33C2×C22⋊C4—22no—
34C2×C22⋊C4C2×C411yescharacteristic
35C2×C22⋊C4D411yescharacteristic
36C2×C42C2×C411yescharacteristic
37C2×C42D411yescharacteristic
38C4⋊C8—41no—
39C22⋊C8—22no—
40C22⋊C8—41no—
41C22⋊C8—41no—
42#97—41no—
43#95—21no—
44#95—22no—
45#95—22no—
46#95C2×C412yes—
47C24C22⋊C411yescharacteristic
48C2×Q8—42no—
49C2×Q8—82no—
50C22×C4—21no—
51C22×C4—21no—
52C22×C4—22no—
53C22×C4—22no—
54C22×C4—22no—
55C22×C4—41no—
56C22×C4C22⋊C411yescharacteristic
57C22×C4C22⋊C411yescharacteristic
58C22×C4C22⋊C411yescharacteristic
59C22×C4C22×C411yescharacteristic
60C22×C4C2×D411yescharacteristic
61C22×C4C2×D411yescharacteristic
62M16—42no—
63M16—42no—
64C2×C8—42no—
65C2×C8—42no—
66C4⋊C4—41no—
67C4⋊C4—41no—
68C4⋊C4—42no—
69C4⋊C4—42no—
70C4⋊C4—41no—
71C4⋊C4—41no—
72C4⋊C4—82no—
73C22⋊C4—41no—
74C22⋊C4—41no—
75C22⋊C4—82no—
76C42—21no—
77C42—21no—
78C42—21no—
79C42—21no—
80C23—21no—
81C23—21no—
82C23—21no—
83C23—41no—
84C23—41no—
85C23C2×C22⋊C411yescharacteristic
86Q8—84no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—42no—
96C2×C4—42no—
97C2×C4—41no—
98C2×C4—41no—
99C2×C4—41no—
100C2×C4—41no—
101C2×C4—42no—
102C2×C4—42no—
103C2×C4—42no—
104C2×C4—42no—
105C2×C4—42no—
106C2×C4—42no—
107C2×C4#9911yescharacteristic
108C2×C4#9911yescharacteristic
109C2×C4#13712yes—
110C8—82no—
111C8—82no—
112C22—21no—
113C22—21no—
114C22—42no—
115C22—41no—
116C22—41no—
117C22—41no—
118C22—81no—
119C22C2×#9911yescharacteristic
120C22#41911yescharacteristic
121C22#42111yescharacteristic
122C4—22no—
123C4—21no—
124C4—21no—
125C4—41no—
126C4—41no—
127C4—41no—
128C4—41no—
129C4—82no—
130C4—82no—
131C2—21no—
132C2—21no—
133C2—81no—
134C2#151111yescharacteristic
135C2#212211yescharacteristic
136C2#213511yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC22×C4C22×C4
Frattini, cosocleC2×C4⋊C4C23
prime radicalC24C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #1354C2semidirect

Maximal subgroups

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

subgroupindex
#26282
#18222
#14642
#13542