Finite Group Databasebeta

← #9887

Subgroups — #9887

Order 256.

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

normal subgroups only

This group has 299 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
2#1749C211yesmaximal, characteristic
3C4⋊#95C211yesmaximal, characteristic
4#1294C212yesmaximal
5#1294C212yesmaximal
6C2×#125C411yescharacteristic, complemented
7C22×C4⋊C4—21no—
8C22×C42C2211yescharacteristic
9C2×C22⋊C8C2212yes—
10C2×#97—21no—
11#389C411yescharacteristic, complemented
12#389C411yescharacteristic, complemented
13#387—21no—
14#387—21no—
15#385—21no—
16#385—21no—
17#382C411yescharacteristic, complemented
18#380C2211yescharacteristic
19#380C2211yescharacteristic
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—24no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4—21no—
32C2×C4⋊C4—21no—
33C2×C4⋊C4—21no—
34C2×C4⋊C4—42no—
35C2×C4⋊C4—42no—
36C2×C4⋊C4C2×C411yescharacteristic
37C2×C4⋊C4C2×C411yescharacteristic
38C2×C4⋊C4C2×C411yescharacteristic
39C2×C4⋊C4C2×C411yescharacteristic
40C2×C22⋊C4—21no—
41C2×C22⋊C4—21no—
42C2×C42—42no—
43C2×C42C2×C411yescharacteristic
44C2×C42C2×C411yescharacteristic
45C2×C42D411yescharacteristic
46C2×C42D411yescharacteristic
47C22⋊C8—22no—
48C22⋊C8Q814yes—
49#97—42no—
50#95—21no—
51#95—21no—
52#95—21no—
53#95—21no—
54#95—21no—
55#95—21no—
56#95—24no—
57#95—42no—
58C24C2×D411yescharacteristic
59C22×C4—21no—
60C22×C4—21no—
61C22×C4—22no—
62C22×C4—22no—
63C22×C4—21no—
64C22×C4—21no—
65C22×C4—24no—
66C22×C4—21no—
67C22×C4—21no—
68C22×C4—21no—
69C22×C4—21no—
70C22×C4—41no—
71C22×C4—41no—
72C22×C4—41no—
73C22×C4—41no—
74C22×C4—42no—
75C22×C4—42no—
76C22×C4—42no—
77C22×C4—42no—
78C22×C4—42no—
79C22×C4—42no—
80C22×C4C22⋊C411yescharacteristic
81C22×C4C22⋊C411yescharacteristic
82C22×C4C22⋊C411yescharacteristic
83C22×C4C22⋊C411yescharacteristic
84C22×C4C22×C411yescharacteristic
85C22×C4C2×D411yescharacteristic
86C22×C4C2×Q812yes—
87C22×C4#4112yes—
88C2×C8—24no—
89C2×C8—42no—
90C2×C8—42no—
91C4⋊C4—41no—
92C4⋊C4—41no—
93C4⋊C4—41no—
94C4⋊C4—41no—
95C4⋊C4—42no—
96C4⋊C4—48no—
97C4⋊C4—42no—
98C4⋊C4—42no—
99C4⋊C4—42no—
100C22⋊C4—41no—
101C22⋊C4—41no—
102C22⋊C4—41no—
103C22⋊C4—41no—
104C42—22no—
105C42—22no—
106C42—41no—
107C42—41no—
108C23—21no—
109C23—21no—
110C23—21no—
111C23—21no—
112C23C2×C22⋊C411yescharacteristic
113C23#12411yescharacteristic
114C23C4⋊Q811yescharacteristic
115C23AGL(1,ℤ/8)11yescharacteristic
116C23AGL(1,ℤ/8)11yescharacteristic
117C23#13711yescharacteristic
118C23#13711yescharacteristic
119C2×C4—24no—
120C2×C4—24no—
121C2×C4—21no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—42no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—42no—
139C2×C4—44no—
140C2×C4—44no—
141C2×C4—44no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—82no—
155C2×C4—82no—
156C2×C4—82no—
157C2×C4—82no—
158C2×C4#9912yes—
159C2×C4#10412yes—
160C2×C4C4×Q812yes—
161C2×C4C22⋊Q812yes—
162C8—44no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22#39111yescharacteristic
176C22C2×#9911yescharacteristic
177C22#41011yescharacteristic
178C22#41711yescharacteristic
179C22#41711yescharacteristic
180C22C2×#10411yescharacteristic
181C22#42111yescharacteristic
182C22#49011yescharacteristic
183C22#49111yescharacteristic
184C22#50111yescharacteristic
185C22#50111yescharacteristic
186C4—22no—
187C4—22no—
188C4—22no—
189C4—22no—
190C4—41no—
191C4—41no—
192C4—84no—
193C4—81no—
194C4—81no—
195C4—81no—
196C4—81no—
197C2—21no—
198C2—21no—
199C2—21no—
200C2—21no—
201C2#150411yescharacteristic
202C2#150911yescharacteristic
203C2#151211yescharacteristic
204C2#151311yescharacteristic
205C2#198611yescharacteristic
206C2#199211yescharacteristic
207C2#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
11. #389C4semidirect
12. #389C4semidirect
17. #382C4semidirect

Maximal subgroups

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

subgroupindex
#28512
#17492
C4⋊#952
#12942