Finite Group Databasebeta

← #10511

Subgroups — #10511

Order 256.

169 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 169 conjugacy classes of subgroups — too many to draw. Only its 47 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#3236C211yesmaximal, characteristic
2#1989C211yesmaximal, characteristic
3#1573C211yesmaximal, characteristic
4#1552C211yesmaximal, characteristic
5#1503C211yesmaximal, characteristic
6#1470C211yesmaximal, characteristic
7#1285C211yesmaximal, characteristic
8#533C2211yescharacteristic
9C2×#125C2211yescharacteristic
10#501—21no—
11#491—21no—
12#484—21no—
13#483—21no—
14#479—21no—
15#479—21no—
16#432C2211yescharacteristic
17#432C2211yescharacteristic
18#431C2211yescharacteristic
19C2×C4⋊C8C2211yescharacteristic
20C4×C4⋊C4C2211yescharacteristic
21#340—21no—
22#340—21no—
23#335—21no—
24#334—21no—
25#332—21no—
26#332—21no—
27#328—22no—
28#324—22no—
29C22×C8—21no—
30C4⋊Q8D411yescharacteristic
31C4⋊Q8D411yescharacteristic
32#125—21no—
33#125—21no—
34#125—21no—
35#125—21no—
36#125—21no—
37C22⋊Q8—21no—
38C22⋊Q8—21no—
39C4×Q8—21no—
40C4×Q8—21no—
41#117—21no—
42C2×C4⋊C4—21no—
43C2×C4⋊C4—21no—
44C2×C4⋊C4—21no—
45C2×C4⋊C4D411yescharacteristic
46C2×C4⋊C4D411yescharacteristic
47C2×C42—21no—
48C2×C42C2311yescharacteristic
49#107—21no—
50#107—21no—
51#106—21no—
52#106—21no—
53C4⋊C8—21no—
54C4⋊C8—21no—
55C4⋊C8—21no—
56C4⋊C8—21no—
57C4⋊C8D411yescharacteristic
58C4⋊C8D411yescharacteristic
59#103—21no—
60#103—21no—
61#103—21no—
62#103—21no—
63C22⋊C8—21no—
64C22⋊C8—21no—
65C22⋊C8D412yes—
66#97—21no—
67#97—21no—
68C4×C8—21no—
69#95—21no—
70C2×Q8—21no—
71C2×Q8—21no—
72C22×C4—21no—
73C22×C4—21no—
74C22×C4—41no—
75C22×C4C2×D411yescharacteristic
76C22×C4C2×D411yescharacteristic
77C22×C4#4111yescharacteristic
78C2×C8—21no—
79C2×C8—21no—
80C2×C8—22no—
81C2×C8—42no—
82C2×C8—41no—
83C2×C8—41no—
84C4⋊C4—22no—
85C4⋊C4—21no—
86C4⋊C4—21no—
87C4⋊C4—21no—
88C4⋊C4—21no—
89C4⋊C4—21no—
90C4⋊C4—21no—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—41no—
94C4⋊C4—41no—
95C4⋊C4—41no—
96C4⋊C4—41no—
97C4⋊C4—41no—
98C4⋊C4—41no—
99C4⋊C4—41no—
100C22⋊C4—41no—
101C42—41no—
102C42—81no—
103C42C2×D411yescharacteristic
104C42C2×D411yescharacteristic
105C42#4111yescharacteristic
106C42#4111yescharacteristic
107C23#12111yescharacteristic
108Q8—41no—
109Q8—41no—
110Q8—81no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—42no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—81no—
124C2×C4—81no—
125C2×C4—81no—
126C2×C4#12011yescharacteristic
127C2×C4#12111yescharacteristic
128C2×C4#12111yescharacteristic
129C2×C4#12311yescharacteristic
130C2×C4#12311yescharacteristic
131C2×C4#12411yescharacteristic
132C8—42no—
133C8—41no—
134C8—41no—
135C8—81no—
136C8—81no—
137C22—21no—
138C22—21no—
139C22#39411yescharacteristic
140C22#47111yescharacteristic
141C22#47311yescharacteristic
142C4—21no—
143C4—21no—
144C4—21no—
145C4—21no—
146C4—21no—
147C4—82no—
148C4—81no—
149C4—81no—
150C4—81no—
151C4—81no—
152C4#45411yescharacteristic
153C4#45611yescharacteristic
154C2—21no—
155C2—21no—
156C2#203811yescharacteristic
157C2#205211yescharacteristic
158C2#205311yescharacteristic
subgroupG/H
center, socleC22#394
commutator, Frattini, cosocleC2×C42C23
prime radicalC23#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ 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
#32362
#19892
#15732
#15522
#15032
#14702
#12852