Finite Group Databasebeta

← #11793

Subgroups — #11793

Order 256.

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

normal subgroups only

This group has 222 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#2564C211yesmaximal, characteristic
2C4×#100C211yesmaximal, characteristic
3#1465C211yesmaximal, characteristic
4#1354C212yesmaximal, complemented
5#1353C212yesmaximal, complemented
6C2×C22⋊Q8C411yescharacteristic
7C2×C4×D4C2211yescharacteristic
8C2×#100—21no—
9#407—21no—
10C4×M16—21no—
11#400C2211yescharacteristic
12#399C411yescharacteristic
13#395C2211yescharacteristic
14#393C411yescharacteristic
15#387—21no—
16#386—21no—
17#385—21no—
18#380—21no—
19C2×#95C411yescharacteristic
20#343C2212yes—
21#324C2212yes—
22#323—21no—
23C22×Q8C2×C411yescharacteristic
24C22×D4D411yescharacteristic
25C23×C4—21no—
26C23×C4C2×C411yescharacteristic
27C23×C4D411yescharacteristic
28C2×M16—22no—
29C2×M16—41no—
30C22⋊Q8—41no—
31C22⋊Q8—41no—
32C4×D4—41no—
33C4×D4—41no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4—21no—
36C2×C4⋊C4—21no—
37C2×C4⋊C4C2×C411yescharacteristic
38C2×C4⋊C4C2311yescharacteristic
39C2×C22⋊C4—21no—
40C2×C22⋊C4—21no—
41C2×C22⋊C4—21no—
42C2×C22⋊C4C2×C411yescharacteristic
43C2×C22⋊C4D411yescharacteristic
44C2×C42D411yescharacteristic
45#100—24no—
46C22⋊C8—22no—
47C22⋊C8—41no—
48#97—41no—
49C4×C8—41no—
50#95—21no—
51#95—21no—
52#95—21no—
53#95—21no—
54#95—21no—
55#95C2×C411yescharacteristic
56#95C2×C411yescharacteristic
57C24C22⋊C411yescharacteristic
58C24C22⋊C411yescharacteristic
59C2×Q8—41no—
60C2×Q8—81no—
61C2×D4—22no—
62C2×D4—22no—
63C2×D4—41no—
64C22×C4—21no—
65C22×C4—21no—
66C22×C4—21no—
67C22×C4—21no—
68C22×C4—21no—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4—21no—
72C22×C4—42no—
73C22×C4—42no—
74C22×C4—81no—
75C22×C4—81no—
76C22×C4—81no—
77C22×C4C22⋊C411yescharacteristic
78C22×C4C22⋊C411yescharacteristic
79C22×C4C22×C411yescharacteristic
80C22×C4C2×D411yescharacteristic
81C22×C4C2×D411yescharacteristic
82M16—24no—
83M16—42no—
84M16—82no—
85C2×C8—42no—
86C2×C8—42no—
87C4⋊C4—41no—
88C4⋊C4—41no—
89C4⋊C4—42no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C4⋊C4—81no—
93C22⋊C4—41no—
94C22⋊C4—41no—
95C22⋊C4—42no—
96C22⋊C4—42no—
97C22⋊C4—81no—
98C42—21no—
99C42—21no—
100C23—21no—
101C23—21no—
102C23—21no—
103C23—21no—
104C23—21no—
105C23—41no—
106C23—41no—
107C23—41no—
108C23—41no—
109C23#10412yes—
110C23C2×C22⋊C411yescharacteristic
111Q8—82no—
112D4—44no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—22no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
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—81no—
136C2×C4—81no—
137C2×C4—81no—
138C2×C4—84no—
139C2×C4#9911yescharacteristic
140C2×C4#9911yescharacteristic
141C2×C4#13712yes—
142C8—44no—
143C8—82no—
144C22—21no—
145C22—21no—
146C22—22no—
147C22—42no—
148C22—42no—
149C22—42no—
150C22—41no—
151C22—41no—
152C22—41no—
153C22—41no—
154C22—41no—
155C22—81no—
156C22C2×#9911yescharacteristic
157C22#41911yescharacteristic
158C22C2×#10411yescharacteristic
159C4—21no—
160C4—21no—
161C4—22no—
162C4—42no—
163C4—41no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—81no—
168C4—81no—
169C2—21no—
170C2—21no—
171C2—42no—
172C2—81no—
173C2#150811yescharacteristic
174C2#212111yescharacteristic
175C2#213211yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC22×C4C22×C4
Frattini, cosocleC2×C4⋊C4C23
prime radicalC22×D4D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #1354C2semidirect
5. #1353C2semidirect

Maximal subgroups

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

subgroupindex
#25642
C4×#1002
#14652
#13542
#13532