Finite Group Databasebeta

← #8912

Subgroups — #8912

Order 256.

206 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 67 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#2382C211yesmaximal, characteristic
2#1992C211yesmaximal, characteristic
3#1847C211yesmaximal, characteristic
4#1836C211yesmaximal, characteristic
5C2×#330C211yesmaximal, characteristic
6#1295C211yesmaximal, characteristic
7#1295C211yesmaximal, characteristic
8C2×#125C2211yescharacteristic
9C2×#107—21no—
10C2×#106—21no—
11C2×#97C2211yescharacteristic
12C2×#97C2211yescharacteristic
13C2×#97C2211yescharacteristic
14#389—21no—
15#389—21no—
16#387—21no—
17#387—21no—
18#387—21no—
19#387—21no—
20#384C2211yescharacteristic
21#382C2211yescharacteristic
22#382C2211yescharacteristic
23#340—21no—
24#340—21no—
25#340—21no—
26#340—21no—
27#330C414yescomplemented
28C22×C8—21no—
29C22×C8—21no—
30C22×C8—21no—
31#125—21no—
32#125—21no—
33#125C2×C412yes—
34#125Q812yes—
35C2×C4⋊C4—21no—
36C2×C4⋊C4—21no—
37C2×C4⋊C4—21no—
38C2×C4⋊C4—21no—
39C2×C4⋊C4—21no—
40C2×C4⋊C4—21no—
41C2×C4⋊C4—21no—
42C2×C4⋊C4D411yescharacteristic
43C2×C4⋊C4D411yescharacteristic
44C2×C4⋊C4D411yescharacteristic
45C2×C4⋊C4D411yescharacteristic
46C2×C4⋊C4D411yescharacteristic
47C2×C4⋊C4D411yescharacteristic
48C2×C42—21no—
49C2×C42—21no—
50C2×C42C2311yescharacteristic
51#107—42no—
52#106—42no—
53#97—21no—
54#97—21no—
55#97—21no—
56#97—21no—
57#97C2×C412yes—
58#97C2×C412yes—
59#95—21no—
60#95—21no—
61#95—21no—
62#95—21no—
63#95—21no—
64#95—21no—
65#95—21no—
66#95—21no—
67C22×C4—21no—
68C22×C4—21no—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4—21no—
72C22×C4—21no—
73C22×C4—41no—
74C22×C4C2×D411yescharacteristic
75C22×C4C2×D411yescharacteristic
76C22×C4C2×D411yescharacteristic
77C2×C8—22no—
78C2×C8—22no—
79C2×C8—22no—
80C2×C8—22no—
81C2×C8—22no—
82C2×C8—41no—
83C2×C8—41no—
84C2×C8—41no—
85C2×C8—41no—
86C4⋊C4—22no—
87C4⋊C4—22no—
88C4⋊C4—22no—
89C4⋊C4—22no—
90C4⋊C4—21no—
91C4⋊C4—21no—
92C4⋊C4—41no—
93C4⋊C4—41no—
94C4⋊C4—41no—
95C4⋊C4—41no—
96C4⋊C4—41no—
97C4⋊C4—41no—
98C4⋊C4—42no—
99C4⋊C4—42no—
100C4⋊C4—81no—
101C4⋊C4—81no—
102C4⋊C4C4⋊C412yes—
103C4⋊C4C4⋊C412yes—
104C42—81no—
105C42—81no—
106C42C22×C411yescharacteristic
107C42C2×Q811yescharacteristic
108C42#4111yescharacteristic
109C42#4111yescharacteristic
110C23#12011yescharacteristic
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—22no—
118C2×C4—22no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—81no—
136C2×C4—81no—
137C2×C4—81no—
138C2×C4C2×C4⋊C411yescharacteristic
139C2×C4C4×D411yescharacteristic
140C2×C4C4×D411yescharacteristic
141C2×C4C22⋊Q811yescharacteristic
142C2×C4C22⋊Q811yescharacteristic
143C2×C4#12311yescharacteristic
144C8—24no—
145C8—42no—
146C8—42no—
147C22#38511yescharacteristic
148C22#45311yescharacteristic
149C22#45411yescharacteristic
150C22#45411yescharacteristic
151C22#45511yescharacteristic
152C22#45611yescharacteristic
153C22#45611yescharacteristic
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—21no—
160C4—42no—
161C4—42no—
162C4—81no—
163C4—81no—
164C4—81no—
165C4—81no—
166C4—161no—
167C2#165711yescharacteristic
168C2#166111yescharacteristic
169C2#166311yescharacteristic
170C2#166411yescharacteristic
171C2#185711yescharacteristic
172C2#185911yescharacteristic
173C2#186011yescharacteristic
subgroupG/H
center, socle, prime radicalC23#120
commutatorC42C22×C4
Frattini, cosocleC2×C42C23
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
27. #330C4semidirect

Maximal subgroups

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

subgroupindex
#23822
#19922
#18472
#18362
C2×#3302
#12952