Finite Group Databasebeta

← #9032

Subgroups — #9032

Order 256.

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

normal subgroups only

This group has 258 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#2983C211yesmaximal, characteristic, complemented
2#2398C211yesmaximal, characteristic
3C4×#101C211yesmaximal, characteristic, complemented
4#1490C212yesmaximal
5#1300C212yesmaximal, complemented
6C2×C4×Q8C2211yescharacteristic
7C2×C4×D4C2211yescharacteristic
8#446—24no—
9#432—21no—
10#432C2212yes—
11#431—21no—
12C2×#101—21no—
13C4×M16C2212yes—
14#400C411yescharacteristic
15#400C411yescharacteristic
16#397—21no—
17#394C411yescharacteristic
18#394C411yescharacteristic
19#393—21no—
20C4×C22⋊C4—21no—
21C4×C22⋊C4—21no—
22#376C2211yescharacteristic
23#343—21no—
24D4⋊C8—24no—
25C22×Q8D411yescharacteristic
26C22×D4C2×C411yescharacteristic
27C23×C4—21no—
28C2×M16—22no—
29C4×Q8—22no—
30C4×Q8—22no—
31C4×D4—22no—
32C4×D4—22no—
33C2×C4⋊C4C2×C411yescharacteristic
34C2×C4⋊C4C2×C411yescharacteristic
35C2×C4⋊C4C2×C411yescharacteristic
36C2×C4⋊C4D411yescharacteristic
37C2×C22⋊C4—21no—
38C2×C22⋊C4—21no—
39C2×C22⋊C4—21no—
40C2×C22⋊C4—21no—
41C2×C22⋊C4—21no—
42C2×C42—21no—
43C2×C42D411yescharacteristic
44C2×C42D411yescharacteristic
45C2×C42C2311yescharacteristic
46C4⋊C8—22no—
47C4⋊C8—22no—
48C4⋊C8D414yes—
49#101—24no—
50C22⋊C8—22no—
51#97—22no—
52#97—22no—
53#97—22no—
54C4×C8—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
63C24—21no—
64C2×Q8—22no—
65C2×Q8—22no—
66C2×Q8—41no—
67C2×D4—22no—
68C2×D4—42no—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4—21no—
72C22×C4—42no—
73C22×C4—42no—
74C22×C4—41no—
75C22×C4—41no—
76C22×C4C22⋊C411yescharacteristic
77C22×C4C22⋊C411yescharacteristic
78C22×C4C22⋊C411yescharacteristic
79C22×C4C22⋊C411yescharacteristic
80C22×C4C22×C411yescharacteristic
81C22×C4C2×D411yescharacteristic
82C22×C4C2×D411yescharacteristic
83M16—24no—
84M16—42no—
85C2×C8—24no—
86C2×C8—42no—
87C4⋊C4—22no—
88C4⋊C4—22no—
89C4⋊C4—22no—
90C4⋊C4—22no—
91C22⋊C4—42no—
92C22⋊C4—42no—
93C22⋊C4—42no—
94C22⋊C4—42no—
95C22⋊C4—42no—
96C42—21no—
97C42—21no—
98C42—21no—
99C42—21no—
100C42—42no—
101C42C2×D412yes—
102C42#4112yes—
103C23—22no—
104C23—41no—
105C23—41no—
106C23—41no—
107C23—41no—
108C23—41no—
109C23—41no—
110C23C2×C22⋊C411yescharacteristic
111Q8—44no—
112D4—24no—
113D4—42no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
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—82no—
137C2×C4—82no—
138C2×C4#10412yes—
139C2×C4C4×D412yes—
140C2×C4#12011yescharacteristic
141C2×C4#12112yes—
142C2×C4#12311yescharacteristic
143C8—44no—
144C8—44no—
145C22—21no—
146C22—21no—
147C22—42no—
148C22—42no—
149C22—42no—
150C22—81no—
151C22—81no—
152C22—81no—
153C22—81no—
154C22#38611yescharacteristic
155C22C2×#10411yescharacteristic
156C22#42111yescharacteristic
157C4—22no—
158C4—22no—
159C4—21no—
160C4—22no—
161C4—41no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—81no—
166C4—81no—
167C4#45412yes—
168C2—21no—
169C2—21no—
170C2—82no—
171C2#187111yescharacteristic
172C2#188811yescharacteristic
173C2#189111yescharacteristic
subgroupG/H
centerC2×C4#120
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
socleC22#386
prime radicalC22×D4C2×C4
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
1. #2983C2semidirect
3. C4×#101C2semidirect
5. #1300C2semidirect

Maximal subgroups

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

subgroupindex
#29832
#23982
C4×#1012
#14902
#13002