Finite Group Databasebeta

← #9493

Subgroups — #9493

Order 256.

229 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 229 conjugacy classes of subgroups — too many to draw. Only its 59 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#2921C211yesmaximal, characteristic
2#2599C211yesmaximal, characteristic
3#1491C212yesmaximal, complemented
4#1464C211yesmaximal, characteristic
5#1288C212yesmaximal, complemented
6C2×C4×Q8C2211yescharacteristic
7C2×#117C2211yescharacteristic
8#433—24no—
9#432C2212yes—
10#423—21no—
11#407—21no—
12C4×M16C2212yes—
13#398C411yescharacteristic
14#397C411yescharacteristic
15#395C411yescharacteristic
16#393C411yescharacteristic
17#388—21no—
18#387—21no—
19#387—21no—
20#385—21no—
21#383C2211yescharacteristic
22Q8⋊C8—24no—
23#324—21no—
24#323—21no—
25C22×Q8C2×C411yescharacteristic
26C23×C4D411yescharacteristic
27C2×M16—22no—
28C4×Q8—22no—
29C4×Q8—22no—
30#117—22no—
31#117—22no—
32C2×C4⋊C4—21no—
33C2×C4⋊C4—21no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4C2×C411yescharacteristic
36C2×C4⋊C4C2×C411yescharacteristic
37C2×C4⋊C4D411yescharacteristic
38C2×C22⋊C4—21no—
39C2×C22⋊C4—21no—
40C2×C22⋊C4C2×C411yescharacteristic
41C2×C22⋊C4D411yescharacteristic
42C2×C42—21no—
43C2×C42D411yescharacteristic
44C2×C42C2311yescharacteristic
45C4⋊C8—24no—
46C4⋊C8—22no—
47C22⋊C8—24no—
48C22⋊C8—22no—
49#97—22no—
50#97—22no—
51C4×C8D414yes—
52#95—21no—
53#95—21no—
54#95—21no—
55#95—21no—
56#95—21no—
57#95—21no—
58#95C2×C411yescharacteristic
59#95C2×C411yescharacteristic
60C24C22⋊C411yescharacteristic
61C2×Q8—22no—
62C2×Q8—42no—
63C22×C4—21no—
64C22×C4—21no—
65C22×C4—21no—
66C22×C4—21no—
67C22×C4—21no—
68C22×C4—21no—
69C22×C4—41no—
70C22×C4—41no—
71C22×C4C22⋊C411yescharacteristic
72C22×C4C22⋊C411yescharacteristic
73C22×C4C22⋊C411yescharacteristic
74C22×C4C22×C411yescharacteristic
75C22×C4C2×D411yescharacteristic
76C22×C4C2×D411yescharacteristic
77M16—42no—
78M16—42no—
79C2×C8—24no—
80C2×C8—42no—
81C4⋊C4—22no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—42no—
85C4⋊C4—42no—
86C4⋊C4—41no—
87C4⋊C4—41no—
88C22⋊C4—22no—
89C22⋊C4—22no—
90C22⋊C4—42no—
91C22⋊C4—42no—
92C42—21no—
93C42—21no—
94C42—42no—
95C42C2×D412yes—
96C42#4112yes—
97C23—21no—
98C23—21no—
99C23—21no—
100C23—41no—
101C23—41no—
102C23C2×C22⋊C411yescharacteristic
103Q8—24no—
104Q8—42no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—22no—
108C2×C4—21no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—42no—
116C2×C4—42no—
117C2×C4—41no—
118C2×C4—41no—
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×C4C4×D412yes—
131C2×C4#12011yescharacteristic
132C2×C4#12112yes—
133C2×C4#12311yescharacteristic
134C8—44no—
135C8—82no—
136C22—21no—
137C22—21no—
138C22—42no—
139C22—41no—
140C22—41no—
141C22—41no—
142C22—81no—
143C22#38611yescharacteristic
144C22#42111yescharacteristic
145C22#42111yescharacteristic
146C4—22no—
147C4—21no—
148C4—21no—
149C4—22no—
150C4—41no—
151C4—42no—
152C4—41no—
153C4—41no—
154C4—81no—
155C4—81no—
156C4—81no—
157C2—21no—
158C2—21no—
159C2—81no—
160C2#189111yescharacteristic
161C2#189711yescharacteristic
162C2#190911yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
prime radicalC24C22⋊C4
LCSG ▷ C22×C4 ▷ 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
3. #1491C2semidirect
5. #1288C2semidirect

Maximal subgroups

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

subgroupindex
#29212
#25992
#14912
#14642
#12882