Finite Group Databasebeta

← #11555

Subgroups — #11555

Order 256.

207 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 207 conjugacy classes of subgroups — too many to draw. Only its 51 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#2502C211yesmaximal, characteristic
2#1463C211yesmaximal, characteristic
3C2×#324C211yesmaximal, characteristic
4#1325C212yesmaximal, complemented
5#1319C212yesmaximal, complemented
6C2×C22⋊Q8C411yescharacteristic
7C22×C4⋊C4C2211yescharacteristic
8#407—21no—
9C2×C22⋊C8—21no—
10#398—21no—
11#398—21no—
12#391C411yescharacteristic
13#391C2211yescharacteristic
14#385—21no—
15#385—21no—
16#384C411yescharacteristic
17#384C2211yescharacteristic
18C4×C22⋊C4C411yescharacteristic
19#324—21no—
20#324—21no—
21#324C2212yes—
22#324C2212yes—
23C22×Q8C2×C411yescharacteristic
24C23×C4C2×C411yescharacteristic
25C23×C4D411yescharacteristic
26C23×C4D411yescharacteristic
27C2×M16—41no—
28C22×C8—41no—
29C22⋊Q8—41no—
30C22⋊Q8—41no—
31C2×C4⋊C4—21no—
32C2×C4⋊C4—21no—
33C2×C4⋊C4—21no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4—21no—
36C2×C4⋊C4—41no—
37C2×C4⋊C4—41no—
38C2×C4⋊C4C2×C411yescharacteristic
39C2×C4⋊C4C2×C411yescharacteristic
40C2×C4⋊C4D411yescharacteristic
41C2×C4⋊C4D411yescharacteristic
42C2×C4⋊C4C2311yescharacteristic
43C2×C22⋊C4—21no—
44C2×C22⋊C4—21no—
45C2×C42C2×C411yescharacteristic
46C2×C42C2×C411yescharacteristic
47C22⋊C8—22no—
48C22⋊C8—22no—
49C22⋊C8—41no—
50C22⋊C8—41no—
51#95—21no—
52#95—21no—
53#95—21no—
54#95—21no—
55#95—21no—
56C24C22⋊C411yescharacteristic
57C2×Q8—22no—
58C2×Q8—41no—
59C2×Q8—41no—
60C22×C4—21no—
61C22×C4—21no—
62C22×C4—21no—
63C22×C4—21no—
64C22×C4—21no—
65C22×C4—21no—
66C22×C4—21no—
67C22×C4—21no—
68C22×C4—22no—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4—41no—
72C22×C4—81no—
73C22×C4—81no—
74C22×C4C22⋊C411yescharacteristic
75C22×C4C22⋊C411yescharacteristic
76C22×C4C22⋊C411yescharacteristic
77C22×C4C22×C411yescharacteristic
78C22×C4C2×D411yescharacteristic
79C22×C4C2×D411yescharacteristic
80M16—82no—
81C2×C8—42no—
82C2×C8—42no—
83C2×C8—82no—
84C4⋊C4—41no—
85C4⋊C4—41no—
86C4⋊C4—41no—
87C4⋊C4—41no—
88C4⋊C4—41no—
89C4⋊C4—42no—
90C4⋊C4—81no—
91C4⋊C4—81no—
92C4⋊C4—81no—
93C4⋊C4—81no—
94C22⋊C4—24no—
95C22⋊C4—41no—
96C22⋊C4—41no—
97C42—22no—
98C42—41no—
99C23—22no—
100C23—21no—
101C23—21no—
102C23—41no—
103C23#9911yescharacteristic
104C23#9911yescharacteristic
105C23C2×C22⋊C411yescharacteristic
106Q8—82no—
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—22no—
110C2×C4—22no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—42no—
119C2×C4—42no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—42no—
123C2×C4—42no—
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—81no—
137C2×C4—81no—
138C2×C4#13112yes—
139C8—82no—
140C8—82no—
141C22—21no—
142C22—21no—
143C22—21no—
144C22—21no—
145C22—21no—
146C22—21no—
147C22—21no—
148C22—42no—
149C22—42no—
150C22#35612yes—
151C22#40811yescharacteristic
152C22C2×#9911yescharacteristic
153C22#41311yescharacteristic
154C4—22no—
155C4—42no—
156C4—42no—
157C4—41no—
158C4—41no—
159C4—41no—
160C4—41no—
161C4—41no—
162C4—81no—
163C4—81no—
164C2—21no—
165C2—21no—
166C2—22no—
167C2—41no—
168C2#146811yescharacteristic
169C2#212711yescharacteristic
170C2C2×#35611yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC22×C4C22×C4
Frattini, cosocleC2×C4⋊C4C23
prime radicalC24C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #1325C2semidirect
5. #1319C2semidirect

Maximal subgroups

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

subgroupindex
#25022
#14632
C2×#3242
#13252
#13192