Finite Group Databasebeta

← #9448

Subgroups — #9448

Order 256.

243 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 243 conjugacy classes of subgroups — too many to draw. Only its 61 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#2983C211yesmaximal, characteristic, complemented
2#2545C211yesmaximal, characteristic
3#1533C212yesmaximal
4#1467C211yesmaximal, characteristic, complemented
5#1285C212yesmaximal, complemented
6C2×C4⋊Q8C411yescharacteristic
7C2×#124C411yescharacteristic
8C2×#124C2211yescharacteristic
9C2×C4×Q8C2211yescharacteristic
10#446—24no—
11#432—21no—
12#432C2212yes—
13#432C2212yes—
14#431—21no—
15#396—21no—
16#396—21no—
17#391C411yescharacteristic
18#390C411yescharacteristic
19#388—21no—
20#388—21no—
21C4×C4⋊C4C2211yescharacteristic
22#329—24no—
23#324—21no—
24#324—21no—
25C22×Q8C2×C411yescharacteristic
26C22×Q8C2×C411yescharacteristic
27C22×D4C2×C411yescharacteristic
28C4⋊Q8—42no—
29#124—22no—
30#124—22no—
31#124—42no—
32C4×Q8—22no—
33C4×Q8—22no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4—21no—
36C2×C4⋊C4—21no—
37C2×C4⋊C4C2×C411yescharacteristic
38C2×C4⋊C4D411yescharacteristic
39C2×C4⋊C4D411yescharacteristic
40C2×C22⋊C4—21no—
41C2×C22⋊C4—21no—
42C2×C22⋊C4—21no—
43C2×C22⋊C4—21no—
44C2×C22⋊C4—21no—
45C2×C22⋊C4—21no—
46C2×C42C2×C411yescharacteristic
47C2×C42C2×C411yescharacteristic
48C2×C42D411yescharacteristic
49C2×C42D411yescharacteristic
50C2×C42C2311yescharacteristic
51C4⋊C8—22no—
52C4⋊C8—22no—
53C4⋊C8—22no—
54C4⋊C8—22no—
55C22⋊C8—22no—
56C22⋊C8—22no—
57#97—22no—
58#97—22no—
59#97D414yes—
60C4×C8—22no—
61#95—21no—
62#95—21no—
63#95—21no—
64C24—21no—
65C2×Q8—22no—
66C2×Q8—22no—
67C2×Q8—22no—
68C2×Q8—41no—
69C2×Q8—41no—
70C2×Q8—41no—
71C2×D4—22no—
72C2×D4—41no—
73C2×D4—41no—
74C22×C4—21no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4C22⋊C411yescharacteristic
78C22×C4C22⋊C411yescharacteristic
79C22×C4C22⋊C411yescharacteristic
80C22×C4C22⋊C411yescharacteristic
81C22×C4C22×C411yescharacteristic
82C22×C4C2×D411yescharacteristic
83C22×C4C2×D411yescharacteristic
84C2×C8—24no—
85C2×C8—42no—
86C4⋊C4—22no—
87C4⋊C4—22no—
88C4⋊C4—22no—
89C4⋊C4—42no—
90C4⋊C4—42no—
91C4⋊C4—42no—
92C22⋊C4—42no—
93C22⋊C4—42no—
94C22⋊C4—42no—
95C22⋊C4—42no—
96C22⋊C4—41no—
97C22⋊C4—42no—
98C22⋊C4—41no—
99C42—21no—
100C42—21no—
101C42—21no—
102C42—21no—
103C42—41no—
104C42—41no—
105C42C2×D412yes—
106C42#4112yes—
107C23—41no—
108C23—41no—
109C23—41no—
110C23—41no—
111C23—41no—
112C23—41no—
113C23—41no—
114C23C2×C22⋊C411yescharacteristic
115Q8—44no—
116Q8—82no—
117D4—82no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—22no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—41no—
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#10012yes—
141C2×C4C4×D412yes—
142C2×C4#12011yescharacteristic
143C2×C4#12112yes—
144C2×C4#12311yescharacteristic
145C8—44no—
146C8—82no—
147C22—21no—
148C22—21no—
149C22—81no—
150C22—81no—
151C22—81no—
152C22—81no—
153C22—81no—
154C22—81no—
155C22—81no—
156C22#38611yescharacteristic
157C22C2×#10011yescharacteristic
158C22#41311yescharacteristic
159C4—22no—
160C4—22no—
161C4—22no—
162C4—21no—
163C4—21no—
164C4—42no—
165C4—41no—
166C4—41no—
167C4—41no—
168C4—81no—
169C4—81no—
170C2—21no—
171C2—21no—
172C2—161no—
173C2#188411yescharacteristic
174C2#190011yescharacteristic
175C2#191211yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
prime radicalC22×D4C2×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
1. #2983C2semidirect
4. #1467C2semidirect
5. #1285C2semidirect

Maximal subgroups

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

subgroupindex
#29832
#25452
#15332
#14672
#12852