Finite Group Databasebeta

← #11879

Subgroups — #11879

Order 256.

220 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 57 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#2536C211yesmaximal, characteristic
2#1801C211yesmaximal, characteristic, complemented
3#1461C211yesmaximal, characteristic, complemented
4#1346C212yesmaximal, complemented
5#1345C212yesmaximal
6C2×C22⋊Q8—21no—
7C2×C4×Q8C2211yescharacteristic
8C2×C4×D4C411yescharacteristic
9#431—21no—
10#423—21no—
11C2×#101—21no—
12#398C411yescharacteristic
13#398C2211yescharacteristic
14#394C411yescharacteristic
15#394C2211yescharacteristic
16#388—21no—
17#388—21no—
18#382C411yescharacteristic
19#380—21no—
20#343C2212yes—
21#324—21no—
22#324C2212yes—
23C22×Q8D411yescharacteristic
24C22×D4C2×C411yescharacteristic
25C23×C4—21no—
26C2×M16—22no—
27C22⋊Q8—42no—
28C22⋊Q8—42no—
29C4×Q8—41no—
30C4×Q8—41no—
31C4×D4—41no—
32C4×D4—41no—
33C2×C4⋊C4—21no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4—21no—
36C2×C4⋊C4C2×C411yescharacteristic
37C2×C4⋊C4C2×C411yescharacteristic
38C2×C4⋊C4D411yescharacteristic
39C2×C4⋊C4C2311yescharacteristic
40C2×C22⋊C4—21no—
41C2×C22⋊C4—21no—
42C2×C22⋊C4—21no—
43C2×C22⋊C4—21no—
44C2×C22⋊C4—21no—
45C2×C42C2×C411yescharacteristic
46C2×C42D411yescharacteristic
47C2×C42D411yescharacteristic
48C4⋊C8—41no—
49C4⋊C8—41no—
50C4⋊C8—41no—
51#101—42no—
52C22⋊C8—22no—
53C4×C8—41no—
54#95—21no—
55#95—21no—
56#95—21no—
57#95C2×C411yescharacteristic
58#95C2×C411yescharacteristic
59C24—21no—
60C2×Q8—41no—
61C2×Q8—41no—
62C2×Q8D812yes—
63C2×Q8SD1612yes—
64C2×D4—41no—
65C2×D4—42no—
66C22×C4—21no—
67C22×C4—21no—
68C22×C4—21no—
69C22×C4—42no—
70C22×C4—42no—
71C22×C4—42no—
72C22×C4C22⋊C411yescharacteristic
73C22×C4C22⋊C411yescharacteristic
74C22×C4C22⋊C411yescharacteristic
75C22×C4C22⋊C411yescharacteristic
76C22×C4C22×C411yescharacteristic
77C22×C4C2×D411yescharacteristic
78C22×C4C2×D411yescharacteristic
79M16—42no—
80M16—42no—
81C2×C8—42no—
82C2×C8—42no—
83C4⋊C4—41no—
84C4⋊C4—41no—
85C4⋊C4—41no—
86C4⋊C4—41no—
87C4⋊C4—42no—
88C4⋊C4—42no—
89C4⋊C4—41no—
90C4⋊C4—41no—
91C22⋊C4—42no—
92C22⋊C4—42no—
93C22⋊C4—41no—
94C22⋊C4—41no—
95C22⋊C4—42no—
96C22⋊C4—41no—
97C22⋊C4—41no—
98C42—21no—
99C42—21no—
100C42—21no—
101C42—21no—
102C42—21no—
103C42—21no—
104C23—22no—
105C23—41no—
106C23—41no—
107C23—41no—
108C23—41no—
109C23—41no—
110C23—41no—
111C23C2×C22⋊C411yescharacteristic
112Q8—42no—
113Q8—42no—
114D4—42no—
115D4—42no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—21no—
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—41no—
137C2×C4—41no—
138C2×C4—84no—
139C2×C4#9911yescharacteristic
140C2×C4#9911yescharacteristic
141C2×C4#10212yes—
142C2×C4#10212yes—
143C2×C4C2×D811yescharacteristic
144C2×C4C2×SD1611yescharacteristic
145C8—82no—
146C8—82no—
147C22—21no—
148C22—21no—
149C22—42no—
150C22—42no—
151C22—42no—
152C22—81no—
153C22—81no—
154C22—81no—
155C22—81no—
156C22C2×#9911yescharacteristic
157C22C2×#10211yescharacteristic
158C22#42111yescharacteristic
159C4—21no—
160C4—21no—
161C4—21no—
162C4—22no—
163C4—22no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—41no—
168C4—81no—
169C4—81no—
170C4—81no—
171C2—21no—
172C2—21no—
173C2—82no—
174C2#151911yescharacteristic
175C2#212011yescharacteristic
176C2#213311yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC22×C4C22×C4
Frattini, cosocleC2×C4⋊C4C23
prime radicalC22×D4C2×C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #1801C2semidirect
3. #1461C2semidirect
4. #1346C2semidirect

Maximal subgroups

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

subgroupindex
#25362
#18012
#14612
#13462
#13452