Finite Group Databasebeta

← #10499

Subgroups — #10499

Order 256.

163 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 163 conjugacy classes of subgroups — too many to draw. Only its 45 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#1998C211yesmaximal, characteristic
3#1569C211yesmaximal, characteristic
4#1559C211yesmaximal, characteristic
5#1528C211yesmaximal, characteristic
6#1526C211yesmaximal, characteristic
7#1291C211yesmaximal, 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#423C2211yescharacteristic
19C4×M16C2211yescharacteristic
20C4×M16C2211yescharacteristic
21#343—21no—
22#343—21no—
23#335—21no—
24#334—21no—
25#333—21no—
26#332—21no—
27#330—21no—
28#330—21no—
29#330—21no—
30#330—21no—
31C2×M16—21no—
32C2×M16—21no—
33C2×M16—21no—
34C4⋊Q8D411yescharacteristic
35C4⋊Q8D411yescharacteristic
36#125—21no—
37#125—21no—
38#125—21no—
39#125—21no—
40#125—21no—
41C22⋊Q8—21no—
42C22⋊Q8—21no—
43C4×Q8—21no—
44C4×Q8—21no—
45#117—21no—
46C2×C4⋊C4—21no—
47C2×C4⋊C4—21no—
48C2×C4⋊C4D411yescharacteristic
49C2×C4⋊C4D411yescharacteristic
50C2×C42C2311yescharacteristic
51#107—21no—
52#107—21no—
53#106—21no—
54#106—21no—
55C4⋊C8—21no—
56C4⋊C8—21no—
57C4⋊C8—21no—
58C4⋊C8D411yescharacteristic
59C4⋊C8D411yescharacteristic
60#103—21no—
61#103—21no—
62#103—21no—
63#103—21no—
64C22⋊C8—21no—
65C22⋊C8—21no—
66#97—21no—
67#97—21no—
68#97—21no—
69#97D411yescharacteristic
70#97D411yescharacteristic
71C4×C8—21no—
72C4×C8—21no—
73C2×Q8—21no—
74C2×Q8—21no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4C2×D411yescharacteristic
78C22×C4#4111yescharacteristic
79C22×C4#4111yescharacteristic
80M16—22no—
81M16—42no—
82M16—41no—
83M16—42no—
84C2×C8—21no—
85C2×C8—21no—
86C2×C8—21no—
87C2×C8—21no—
88C2×C8—41no—
89C2×C8—41no—
90C2×C8—41no—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—21no—
97C4⋊C4—21no—
98C4⋊C4—21no—
99C4⋊C4—41no—
100C4⋊C4—41no—
101C4⋊C4—41no—
102C4⋊C4—41no—
103C4⋊C4—41no—
104C4⋊C4—41no—
105C22⋊C4—41no—
106C42—41no—
107C42C2×D411yescharacteristic
108C42C2×D411yescharacteristic
109C42C2×D411yescharacteristic
110C42#4111yescharacteristic
111C23#12311yescharacteristic
112Q8—41no—
113Q8—41no—
114Q8—81no—
115C2×C4—21no—
116C2×C4—21no—
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#12011yescharacteristic
126C2×C4#12111yescharacteristic
127C2×C4#12111yescharacteristic
128C2×C4#12111yescharacteristic
129C2×C4#12311yescharacteristic
130C2×C4#12411yescharacteristic
131C8—22no—
132C8—41no—
133C8—42no—
134C8—41no—
135C8—41no—
136C8—81no—
137C8—81no—
138C22—21no—
139C22—21no—
140C22—21no—
141C22#39411yescharacteristic
142C4—21no—
143C4—21no—
144C4—21no—
145C4—21no—
146C4—21no—
147C4—81no—
148C4—81no—
149C4—81no—
150C4—81no—
151C4#45411yescharacteristic
152C4#45611yescharacteristic
153C2—41no—
154C2#203811yescharacteristic
155C2#204911yescharacteristic
156C2#205011yescharacteristic
subgroupG/H
center, socleC22#394
commutator, Frattini, cosocleC2×C42C23
prime radicalC23#123
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
#19982
#15692
#15592
#15282
#15262
#12912