Finite Group Databasebeta

← #11847

Subgroups — #11847

Order 256.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#2598C211yesmaximal, characteristic
2#1822C211yesmaximal, characteristic, complemented
3#1458C211yesmaximal, characteristic, complemented
4#1353C212yesmaximal, complemented
5#1345C212yesmaximal, complemented
6C2×C4×D4C411yescharacteristic
7C2×#117C2211yescharacteristic
8#431—21no—
9#407—21no—
10#400C2211yescharacteristic
11#399C411yescharacteristic
12#394C2211yescharacteristic
13#392C411yescharacteristic
14#388—21no—
15#386—21no—
16#386—21no—
17#385—21no—
18#383C411yescharacteristic
19#343—21no—
20#343C2212yes—
21#324C2212yes—
22#323—21no—
23C22×D4—21no—
24C22×D4C2×C411yescharacteristic
25C23×C4—21no—
26C23×C4D411yescharacteristic
27C2×M16—22no—
28C4×D4—41no—
29C4×D4—41no—
30#117—41no—
31#117—41no—
32C2×C4⋊C4—21no—
33C2×C4⋊C4C2×C411yescharacteristic
34C2×C4⋊C4D411yescharacteristic
35C2×C4⋊C4C2311yescharacteristic
36C2×C22⋊C4—21no—
37C2×C22⋊C4—21no—
38C2×C22⋊C4—21no—
39C2×C22⋊C4—21no—
40C2×C22⋊C4—21no—
41C2×C22⋊C4C2×C411yescharacteristic
42C2×C22⋊C4D411yescharacteristic
43C2×C42C2×C411yescharacteristic
44C2×C42D411yescharacteristic
45C4⋊C8—41no—
46C22⋊C8—22no—
47C22⋊C8—41no—
48C22⋊C8—41no—
49C4×C8—41no—
50#95—21no—
51#95—21no—
52#95—21no—
53#95—21no—
54#95C2×C411yescharacteristic
55#95C2×C411yescharacteristic
56C24—21no—
57C24C22⋊C411yescharacteristic
58C2×D4—41no—
59C2×D4—42no—
60C2×D4—42no—
61C2×D4—42no—
62C2×D4—81no—
63C22×C4—21no—
64C22×C4—21no—
65C22×C4—22no—
66C22×C4—21no—
67C22×C4—21no—
68C22×C4—21no—
69C22×C4—41no—
70C22×C4—42no—
71C22×C4—81no—
72C22×C4—81no—
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—81no—
87C22⋊C4—41no—
88C22⋊C4—41no—
89C22⋊C4—42no—
90C22⋊C4—41no—
91C22⋊C4—41no—
92C22⋊C4—42no—
93C22⋊C4—81no—
94C22⋊C4—81no—
95C42—21no—
96C42—21no—
97C42—21no—
98C42—21no—
99C23—22no—
100C23—21no—
101C23—21no—
102C23—21no—
103C23—41no—
104C23—41no—
105C23—41no—
106C23—41no—
107C23—41no—
108C23—41no—
109C23—41no—
110C23—41no—
111C23C2×C22⋊C411yescharacteristic
112D4—42no—
113D4—42no—
114D4—84no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—21no—
123C2×C4—42no—
124C2×C4—42no—
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#13512yes—
142C8—82no—
143C8—82no—
144C22—21no—
145C22—21no—
146C22—42no—
147C22—42no—
148C22—42no—
149C22—42no—
150C22—41no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22—81no—
155C22—81no—
156C22—81no—
157C22—81no—
158C22C2×#9911yescharacteristic
159C22#41611yescharacteristic
160C22#42111yescharacteristic
161C4—22no—
162C4—21no—
163C4—21no—
164C4—41no—
165C4—41no—
166C4—41no—
167C4—41no—
168C4—81no—
169C4—81no—
170C4—81no—
171C2—21no—
172C2—21no—
173C2—81no—
174C2—82no—
175C2#151611yescharacteristic
176C2#212011yescharacteristic
177C2#213411yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC22×C4C22×C4
Frattini, cosocleC2×C4⋊C4C23
prime radical#392C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #1822C2semidirect
3. #1458C2semidirect
4. #1353C2semidirect
5. #1345C2semidirect

Maximal subgroups

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

subgroupindex
#25982
#18222
#14582
#13532
#13452