Finite Group Databasebeta

← #7613

Subgroups — #7613

Order 256.

258 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 69 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#2296C211yesmaximal, characteristic
2#1797C211yesmaximal, characteristic
3#1749C211yesmaximal, characteristic
4#1271C212yesmaximal, complemented
5#1271C212yesmaximal, complemented
6C2×#117C411yescharacteristic
7C2×#117C411yescharacteristic
8C22×C42C2211yescharacteristic
9C2×C4⋊C8—21no—
10C2×C22⋊C8—21no—
11C2×C22⋊C8—21no—
12C2×#97—21no—
13#389C411yescharacteristic
14#389C411yescharacteristic
15#389C2211yescharacteristic
16#389C2211yescharacteristic
17#385—21no—
18#385—21no—
19C4×C4⋊C4—21no—
20C4×C4⋊C4—21no—
21#336C2212yes—
22#336C2212yes—
23C23×C4C2×C411yescharacteristic
24C23×C4D411yescharacteristic
25C23×C4D411yescharacteristic
26C22×C8—22no—
27C22×C8—22no—
28#117—22no—
29#117—22no—
30#117—42no—
31C2×C4⋊C4—21no—
32C2×C4⋊C4—21no—
33C2×C4⋊C4—21no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4C2×C411yescharacteristic
36C2×C4⋊C4C2×C411yescharacteristic
37C2×C4⋊C4C2×C411yescharacteristic
38C2×C4⋊C4C2×C411yescharacteristic
39C2×C22⋊C4—21no—
40C2×C22⋊C4—21no—
41C2×C42—21no—
42C2×C42—21no—
43C2×C42—42no—
44C2×C42C2×C411yescharacteristic
45C2×C42D411yescharacteristic
46C2×C42D411yescharacteristic
47C2×C42C2311yescharacteristic
48C4⋊C8—42no—
49C22⋊C8—24no—
50C22⋊C8—42no—
51#97—42no—
52#95—21no—
53#95—21no—
54#95—21no—
55#95—21no—
56C24C22⋊C411yescharacteristic
57C22×C4—22no—
58C22×C4—22no—
59C22×C4—21no—
60C22×C4—21no—
61C22×C4—21no—
62C22×C4—21no—
63C22×C4—22no—
64C22×C4—22no—
65C22×C4—21no—
66C22×C4—21no—
67C22×C4—21no—
68C22×C4—21no—
69C22×C4—41no—
70C22×C4—41no—
71C22×C4—41no—
72C22×C4C22⋊C411yescharacteristic
73C22×C4C22⋊C411yescharacteristic
74C22×C4C22⋊C411yescharacteristic
75C22×C4C22×C411yescharacteristic
76C22×C4C2×D411yescharacteristic
77C22×C4C2×D411yescharacteristic
78C2×C8—24no—
79C2×C8—42no—
80C2×C8—42no—
81C2×C8—42no—
82C2×C8—42no—
83C2×C8—42no—
84C4⋊C4—21no—
85C4⋊C4—21no—
86C4⋊C4—41no—
87C4⋊C4—41no—
88C4⋊C4—42no—
89C4⋊C4—42no—
90C4⋊C4—42no—
91C4⋊C4—41no—
92C4⋊C4—41no—
93C4⋊C4M1612yes—
94C4⋊C4M1612yes—
95C22⋊C4—24no—
96C22⋊C4—42no—
97C42—24no—
98C42—22no—
99C42—22no—
100C42—41no—
101C42—41no—
102C42—42no—
103C23—21no—
104C23—21no—
105C23—21no—
106C23—21no—
107C23—21no—
108C23—21no—
109C23#10112yes—
110C23C2×C22⋊C411yescharacteristic
111C2×C4—24no—
112C2×C4—24no—
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—22no—
124C2×C4—22no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—44no—
129C2×C4—42no—
130C2×C4—42no—
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#9912yes—
142C2×C4#10412yes—
143C2×C4C2×M1611yescharacteristic
144C2×C4C2×M1611yescharacteristic
145C2×C4#13512yes—
146C2×C4AGL(1,ℤ/8)11yescharacteristic
147C2×C4#13711yescharacteristic
148C8—44no—
149C8—82no—
150C22—22no—
151C22—22no—
152C22—22no—
153C22—41no—
154C22—41no—
155C22—41no—
156C22—41no—
157C22#40711yescharacteristic
158C22C2×#9911yescharacteristic
159C22C2×#10111yescharacteristic
160C22#41611yescharacteristic
161C22#41711yescharacteristic
162C22C2×#10411yescharacteristic
163C22#42111yescharacteristic
164C4—22no—
165C4—21no—
166C4—21no—
167C4—22no—
168C4—22no—
169C4—21no—
170C4—21no—
171C4—42no—
172C4—42no—
173C4—41no—
174C4—81no—
175C4—81no—
176C2—42no—
177C2#146311yescharacteristic
178C2#148811yescharacteristic
179C2#148911yescharacteristic
180C2#150111yescharacteristic
181C2#151311yescharacteristic
182C2#153111yescharacteristic
183C2#155211yescharacteristic
subgroupG/H
center, socleC23C2×C22⋊C4
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
prime radicalC24C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #1271C2semidirect
5. #1271C2semidirect

Maximal subgroups

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

subgroupindex
#22962
#17972
#17492
#12712