Finite Group Databasebeta

← #11577

Subgroups — #11577

Order 256.

212 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 51 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#2579C211yesmaximal, characteristic
2#1465C211yesmaximal, characteristic
3#1460C211yesmaximal, characteristic
4#1326C212yesmaximal, complemented
5#1326C212yesmaximal, complemented
6C2×C4×D4C2211yescharacteristic
7C22×C4⋊C4C411yescharacteristic
8#431—21no—
9#407—21no—
10#398—21no—
11#396—21no—
12#387—21no—
13#386C411yescharacteristic
14#386C411yescharacteristic
15#385—21no—
16#385C2211yescharacteristic
17#385C2211yescharacteristic
18#380C411yescharacteristic
19#324—21no—
20#323—21no—
21#323C2212yes—
22#323C2212yes—
23C22×D4C2×C411yescharacteristic
24C23×C4C2×C411yescharacteristic
25C23×C4C2×C411yescharacteristic
26C23×C4C2×C411yescharacteristic
27C23×C4D411yescharacteristic
28C2×M16—41no—
29C4×D4—41no—
30C4×D4—41no—
31C2×C4⋊C4—21no—
32C2×C4⋊C4—21no—
33C2×C4⋊C4—21no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4—21no—
36C2×C4⋊C4—41no—
37C2×C4⋊C4—41no—
38C2×C4⋊C4D411yescharacteristic
39C2×C22⋊C4—21no—
40C2×C22⋊C4—21no—
41C2×C22⋊C4C2×C411yescharacteristic
42C2×C22⋊C4C2×C411yescharacteristic
43C2×C22⋊C4D411yescharacteristic
44C2×C22⋊C4C2311yescharacteristic
45C2×C42D411yescharacteristic
46C4⋊C8—41no—
47C22⋊C8—22no—
48C22⋊C8—22no—
49C22⋊C8—41no—
50C4×C8—41no—
51#95—21no—
52#95—21no—
53#95—21no—
54#95—21no—
55#95—21no—
56C24C22⋊C411yescharacteristic
57C24C22×C411yescharacteristic
58C2×D4—22no—
59C2×D4—22no—
60C2×D4—41no—
61C22×C4—21no—
62C22×C4—21no—
63C22×C4—21no—
64C22×C4—21no—
65C22×C4—21no—
66C22×C4—21no—
67C22×C4—21no—
68C22×C4—21no—
69C22×C4—42no—
70C22×C4—41no—
71C22×C4—41no—
72C22×C4—81no—
73C22×C4—81no—
74C22×C4—81no—
75C22×C4C22⋊C411yescharacteristic
76C22×C4C22⋊C411yescharacteristic
77C22×C4C22⋊C411yescharacteristic
78C22×C4C2×D411yescharacteristic
79C22×C4C2×D411yescharacteristic
80M16—82no—
81C2×C8—42no—
82C2×C8—42no—
83C4⋊C4—41no—
84C4⋊C4—42no—
85C4⋊C4—42no—
86C4⋊C4—41no—
87C4⋊C4—41no—
88C4⋊C4—81no—
89C4⋊C4—81no—
90C22⋊C4—22no—
91C22⋊C4—22no—
92C22⋊C4—41no—
93C22⋊C4—41no—
94C22⋊C4—42no—
95C22⋊C4—81no—
96C42—21no—
97C42—21no—
98C23—21no—
99C23—21no—
100C23—21no—
101C23—21no—
102C23—21no—
103C23—41no—
104C23—41no—
105C23—41no—
106C23—41no—
107C23C2×C22⋊C411yescharacteristic
108C23#13112yes—
109D4—44no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—22no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—42no—
118C2×C4—41no—
119C2×C4—42no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—42no—
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—81no—
135C2×C4—81no—
136C2×C4—81no—
137C2×C4—82no—
138C2×C4#9911yescharacteristic
139C2×C4#9911yescharacteristic
140C2×C4#10112yes—
141C8—82no—
142C8—82no—
143C22—21no—
144C22—21no—
145C22—22no—
146C22—42no—
147C22—42no—
148C22—42no—
149C22—41no—
150C22—41no—
151C22—41no—
152C22—41no—
153C22—41no—
154C22—81no—
155C22#40811yescharacteristic
156C22C2×#9911yescharacteristic
157C22C2×#10111yescharacteristic
158C4—21no—
159C4—21no—
160C4—22no—
161C4—41no—
162C4—42no—
163C4—41no—
164C4—41no—
165C4—81no—
166C4—81no—
167C4—81no—
168C2—21no—
169C2—21no—
170C2—42no—
171C2—81no—
172C2#147211yescharacteristic
173C2#212011yescharacteristic
174C2#212111yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC24C22×C4
Frattini, cosocleC2×C22⋊C4C23
prime radicalC22×D4C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #1326C2semidirect
5. #1326C2semidirect

Maximal subgroups

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

subgroupindex
#25792
#14652
#14602
#13262