Finite Group Databasebeta

← #9886

Subgroups — #9886

Order 256.

283 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 283 conjugacy classes of subgroups — too many to draw. Only its 79 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#2851C211yesmaximal, characteristic
2C4×C22⋊C8C211yesmaximal, characteristic
3#1434C211yesmaximal, characteristic
4#1294C212yesmaximal
5#1294C212yesmaximal
6C2×#125C411yescharacteristic, complemented
7C22×C42C2211yescharacteristic
8C2×C22⋊C8C2212yes—
9C2×C4×C8—21no—
10#389C411yescharacteristic, complemented
11#389C411yescharacteristic, complemented
12#387—21no—
13#387—21no—
14#385—21no—
15#385—21no—
16#382C411yescharacteristic, complemented
17#380C2211yescharacteristic
18#380C2211yescharacteristic
19C2×#95—21no—
20C2×#95—21no—
21C2×#95C2212yes—
22#336—21no—
23C23×C4—22no—
24C23×C4D411yescharacteristic
25C23×C4D411yescharacteristic
26C23×C4C2311yescharacteristic
27C22×C8—22no—
28#125—42no—
29C2×C4⋊C4—21no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4—21no—
32C2×C4⋊C4—21no—
33C2×C4⋊C4C2×C411yescharacteristic
34C2×C4⋊C4C2×C411yescharacteristic
35C2×C4⋊C4C2×C411yescharacteristic
36C2×C4⋊C4C2×C411yescharacteristic
37C2×C22⋊C4—21no—
38C2×C22⋊C4—21no—
39C2×C42—42no—
40C2×C42C2×C411yescharacteristic
41C2×C42C2×C411yescharacteristic
42C2×C42D411yescharacteristic
43C2×C42D411yescharacteristic
44C22⋊C8—22no—
45C22⋊C8Q814yes—
46C4×C8—42no—
47#95—24no—
48#95—21no—
49#95—21no—
50#95—21no—
51#95—21no—
52#95—21no—
53#95—21no—
54#95—24no—
55#95—42no—
56C24C2×D411yescharacteristic
57C22×C4—22no—
58C22×C4—22no—
59C22×C4—22no—
60C22×C4—22no—
61C22×C4—24no—
62C22×C4—21no—
63C22×C4—21no—
64C22×C4—21no—
65C22×C4—21no—
66C22×C4—41no—
67C22×C4—41no—
68C22×C4—41no—
69C22×C4—41no—
70C22×C4—42no—
71C22×C4—42no—
72C22×C4—42no—
73C22×C4—42no—
74C22×C4—42no—
75C22×C4—42no—
76C22×C4C22⋊C411yescharacteristic
77C22×C4C22⋊C411yescharacteristic
78C22×C4C22⋊C411yescharacteristic
79C22×C4C22⋊C411yescharacteristic
80C22×C4C22×C411yescharacteristic
81C22×C4C2×D411yescharacteristic
82C22×C4C2×Q812yes—
83C22×C4#4112yes—
84C2×C8—24no—
85C2×C8—42no—
86C2×C8—42no—
87C4⋊C4—41no—
88C4⋊C4—41no—
89C4⋊C4—41no—
90C4⋊C4—41no—
91C4⋊C4—42no—
92C4⋊C4—42no—
93C4⋊C4—42no—
94C4⋊C4—42no—
95C22⋊C4—42no—
96C22⋊C4—42no—
97C42—22no—
98C42—22no—
99C42—41no—
100C42—41no—
101C23—21no—
102C23—21no—
103C23—21no—
104C23—21no—
105C23C2×C22⋊C411yescharacteristic
106C23#12411yescharacteristic
107C23C4⋊Q811yescharacteristic
108C23#13512yes—
109C23#13512yes—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—42no—
125C2×C4—42no—
126C2×C4—44no—
127C2×C4—44no—
128C2×C4—44no—
129C2×C4—44no—
130C2×C4—44no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—82no—
144C2×C4—82no—
145C2×C4—82no—
146C2×C4—82no—
147C2×C4#9912yes—
148C2×C4#10412yes—
149C2×C4C4×Q812yes—
150C2×C4C22⋊Q812yes—
151C8—44no—
152C22—21no—
153C22—21no—
154C22—21no—
155C22—21no—
156C22—22no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22#39111yescharacteristic
161C22C2×#9911yescharacteristic
162C22#41011yescharacteristic
163C22#41611yescharacteristic
164C22#41611yescharacteristic
165C22C2×#10411yescharacteristic
166C22#42111yescharacteristic
167C22#48812yes—
168C22#49912yes—
169C4—22no—
170C4—22no—
171C4—22no—
172C4—22no—
173C4—41no—
174C4—41no—
175C4—84no—
176C4—81no—
177C4—81no—
178C4—81no—
179C4—81no—
180C2—22no—
181C2—22no—
182C2#150011yescharacteristic
183C2#150111yescharacteristic
184C2#151611yescharacteristic
185C2#152111yescharacteristic
186C2#198611yescharacteristic
187C2#199111yescharacteristic
188C2#199611yescharacteristic
subgroupG/H
center, socleC23C2×C22⋊C4
commutatorC22×C4C22×C4
Frattini, cosocleC23×C4C23
prime radicalC24C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
6. C2×#125C4semidirect
10. #389C4semidirect
11. #389C4semidirect
16. #382C4semidirect

Maximal subgroups

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

subgroupindex
#28512
C4×C22⋊C82
#14342
#12942