Finite Group Databasebeta

← #9029

Subgroups — #9029

Order 256.

267 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 267 conjugacy classes of subgroups — too many to draw. Only its 63 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#2973C211yesmaximal, characteristic
2#2398C211yesmaximal, characteristic
3C4×#100C211yesmaximal, characteristic
4#1491C212yesmaximal, complemented
5#1300C212yesmaximal, complemented
6C2×C4×Q8C2211yescharacteristic
7C2×C4×D4C2211yescharacteristic
8#435—24no—
9#432C2212yes—
10C2×#100—21no—
11#407—21no—
12C2×C22⋊C8—21no—
13C4×M16C2212yes—
14#400—21no—
15#397C411yescharacteristic
16#397C411yescharacteristic
17#394—21no—
18#393C411yescharacteristic
19#393C411yescharacteristic
20C4×C22⋊C4—21no—
21C4×C22⋊C4—21no—
22#376C2211yescharacteristic
23#343—21no—
24Q8⋊C8—24no—
25C22×Q8C2×C411yescharacteristic
26C22×D4D411yescharacteristic
27C23×C4D411yescharacteristic
28C23×C4D411yescharacteristic
29C2×M16—22no—
30C2×M16—22no—
31C22×C8—22no—
32C4×Q8—22no—
33C4×Q8—22no—
34C4×D4—22no—
35C4×D4—22no—
36C2×C4⋊C4—21no—
37C2×C4⋊C4C2×C411yescharacteristic
38C2×C4⋊C4D411yescharacteristic
39C2×C22⋊C4—21no—
40C2×C22⋊C4—21no—
41C2×C22⋊C4—21no—
42C2×C22⋊C4—21no—
43C2×C22⋊C4C2×C411yescharacteristic
44C2×C22⋊C4C2×C411yescharacteristic
45C2×C42—21no—
46C2×C42—21no—
47C2×C42C2311yescharacteristic
48C4⋊C8D414yes—
49#100—24no—
50C22⋊C8—22no—
51C22⋊C8—22no—
52C22⋊C8—22no—
53#97—22no—
54#97—22no—
55C4×C8—22no—
56#95—21no—
57#95—21no—
58#95—21no—
59#95—21no—
60#95—21no—
61#95C2×C411yescharacteristic
62#95C2×C411yescharacteristic
63C24C22⋊C411yescharacteristic
64C24C22⋊C411yescharacteristic
65C2×Q8—22no—
66C2×Q8—42no—
67C2×D4—22no—
68C2×D4—22no—
69C2×D4—41no—
70C22×C4—21no—
71C22×C4—21no—
72C22×C4—21no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—42no—
79C22×C4—42no—
80C22×C4C22⋊C411yescharacteristic
81C22×C4C22⋊C411yescharacteristic
82C22×C4C22×C411yescharacteristic
83C22×C4C2×D411yescharacteristic
84C22×C4C2×D411yescharacteristic
85M16—24no—
86M16—42no—
87M16—82no—
88C2×C8—24no—
89C2×C8—42no—
90C2×C8—82no—
91C4⋊C4—22no—
92C4⋊C4—22no—
93C4⋊C4—42no—
94C22⋊C4—22no—
95C22⋊C4—22no—
96C22⋊C4—42no—
97C22⋊C4—42no—
98C22⋊C4—42no—
99C22⋊C4—42no—
100C42—42no—
101C42—41no—
102C42—41no—
103C42C2×D412yes—
104C42#4112yes—
105C23—21no—
106C23—21no—
107C23—21no—
108C23—21no—
109C23—21no—
110C23—41no—
111C23—41no—
112C23—41no—
113C23—41no—
114C23#10412yes—
115C23C2×C22⋊C411yescharacteristic
116Q8—24no—
117Q8—42no—
118D4—44no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—22no—
122C2×C4—22no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—42no—
129C2×C4—42no—
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—41no—
141C2×C4—81no—
142C2×C4—81no—
143C2×C4C4×D412yes—
144C2×C4#12011yescharacteristic
145C2×C4#12112yes—
146C2×C4#12311yescharacteristic
147C8—44no—
148C8—44no—
149C22—21no—
150C22—21no—
151C22—22no—
152C22—42no—
153C22—42no—
154C22—41no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22—41no—
159C22—81no—
160C22—81no—
161C22#38611yescharacteristic
162C22C2×#10411yescharacteristic
163C22#42111yescharacteristic
164C4—22no—
165C4—21no—
166C4—22no—
167C4—41no—
168C4—41no—
169C4—42no—
170C4—81no—
171C4—81no—
172C4—81no—
173C4#45512yes—
174C2—21no—
175C2—21no—
176C2—42no—
177C2—81no—
178C2#187111yescharacteristic
179C2#188511yescharacteristic
180C2#189111yescharacteristic
subgroupG/H
centerC2×C4#120
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
socleC22#386
prime radicalC22×D4D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #1491C2semidirect
5. #1300C2semidirect

Maximal subgroups

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

subgroupindex
#29732
#23982
C4×#1002
#14912
#13002