Finite Group Databasebeta

← #9292

Subgroups — #9292

Order 256.

213 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 213 conjugacy classes of subgroups — too many to draw. Only its 69 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#3229C211yesmaximal, characteristic
2#2961C211yesmaximal, characteristic
3#1960C211yesmaximal, characteristic
4#1546C211yesmaximal, characteristic
5#1518C211yesmaximal, characteristic
6#1286C211yesmaximal, characteristic
7#1275C211yesmaximal, characteristic
8#533C2211yescharacteristic
9C2×C4⋊Q8C2211yescharacteristic
10#498C412yescomplemented
11#487C412yescomplemented
12#483—22no—
13#475—22no—
14#446—22no—
15#446—22no—
16#431C2211yescharacteristic
17#431C2211yescharacteristic
18#424—21no—
19#423C2211yescharacteristic
20C2×#103—21no—
21C2×#103—21no—
22#405—21no—
23C2×#97C2211yescharacteristic
24#382C2211yescharacteristic
25#332—22no—
26#328—22no—
27C22×Q8—21no—
28C2×M16—21no—
29C22×C8D411yescharacteristic
30C22×C8D411yescharacteristic
31C4⋊Q8—21no—
32C4⋊Q8—21no—
33C4⋊Q8—21no—
34C4⋊Q8C2×C412yes—
35C4⋊Q8C2×C411yescharacteristic
36C4⋊Q8C2×C411yescharacteristic
37#125—21no—
38C22⋊Q8—21no—
39C22⋊Q8D412yes—
40C4×Q8—21no—
41C4×Q8D412yes—
42#117—21no—
43C2×C4⋊C4—21no—
44C2×C4⋊C4—21no—
45C2×C4⋊C4—21no—
46C2×C42C2311yescharacteristic
47#106—24no—
48C4⋊C8—24no—
49C4⋊C8—21no—
50C4⋊C8—21no—
51C4⋊C8—21no—
52C4⋊C8D412yes—
53#103—24no—
54#103—42no—
55#103—42no—
56C22⋊C8—21no—
57C22⋊C8—21no—
58#97—22no—
59#97—21no—
60#97—21no—
61C4×C8—22no—
62C4×C8—21no—
63C4×C8C2×C412yes—
64#95—21no—
65#95—21no—
66C2×Q8—21no—
67C2×Q8—22no—
68C2×Q8—41no—
69C2×Q8—41no—
70C2×Q8—41no—
71C2×Q8—41no—
72C2×Q8—41no—
73C2×Q8C22⋊C412yes—
74C22×C4—41no—
75C22×C4—41no—
76C22×C4C2×D411yescharacteristic
77C22×C4C2×D411yescharacteristic
78C22×C4#4111yescharacteristic
79M16—41no—
80M16—41no—
81C2×C8—21no—
82C2×C8—21no—
83C2×C8—22no—
84C2×C8—22no—
85C2×C8—21no—
86C2×C8—21no—
87C2×C8—21no—
88C2×C8—41no—
89C2×C8SD1612yes—
90C4⋊C4—21no—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—22no—
94C4⋊C4—22no—
95C4⋊C4—22no—
96C4⋊C4—22no—
97C4⋊C4—41no—
98C4⋊C4—41no—
99C4⋊C4—41no—
100C4⋊C4—41no—
101C4⋊C4C22⋊C412yes—
102C22⋊C4—22no—
103C42—22no—
104C42C22×C411yescharacteristic
105C42C2×D411yescharacteristic
106C42C2×D411yescharacteristic
107C42#4111yescharacteristic
108C23#12111yescharacteristic
109Q8—42no—
110Q8—42no—
111Q8—42no—
112Q8—81no—
113Q8—81no—
114Q8—81no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—42no—
120C2×C4—81no—
121C2×C4—81no—
122C2×C4—81no—
123C2×C4—81no—
124C2×C4—81no—
125C2×C4C2×C22⋊C411yescharacteristic
126C2×C4C4×D411yescharacteristic
127C2×C4C4×D411yescharacteristic
128C2×C4#12011yescharacteristic
129C2×C4#12111yescharacteristic
130C2×C4#12311yescharacteristic
131C2×C4C2×SD1611yescharacteristic
132C2×C4#13511yescharacteristic
133C2×C4AGL(1,ℤ/8)11yescharacteristic
134C2×C4#13711yescharacteristic
135C8—22no—
136C8—42no—
137C8—41no—
138C8—42no—
139C8—81no—
140C22—21no—
141C22—21no—
142C22#38611yescharacteristic
143C22#46011yescharacteristic
144C22#46411yescharacteristic
145C4—21no—
146C4—21no—
147C4—21no—
148C4—21no—
149C4—42no—
150C4—42no—
151C4—82no—
152C4—161no—
153C4C4×SD1611yescharacteristic
154C4#44011yescharacteristic
155C4#44811yescharacteristic
156C4#44911yescharacteristic
157C2—21no—
158C2—21no—
159C2#188011yescharacteristic
160C2#190211yescharacteristic
161C2#190911yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC42C22×C4
Frattini, cosocleC2×C42C23
prime radicalC23#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
10. #498C4semidirect
11. #487C4semidirect

Maximal subgroups

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

subgroupindex
#32292
#29612
#19602
#15462
#15182
#12862
#12752