Finite Group Databasebeta

← #13294

Subgroups — #13294

Order 256.

242 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 61 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#2579C211yesmaximal, characteristic
2#1799C211yesmaximal, characteristic
3C4×#100C211yesmaximal, characteristic
4#1390C212yesmaximal
5#1390C212yesmaximal
6C2×C4×D4C2211yescharacteristic
7C22×C4⋊C4C411yescharacteristic, complemented
8C2×#100C2212yes—
9C2×#99C2212yes—
10C4×M16—21no—
11#398—21no—
12#396—21no—
13#387—21no—
14#386C2211yescharacteristic
15#386C2211yescharacteristic
16#385—21no—
17#385C411yescharacteristic, complemented
18#385C411yescharacteristic, complemented
19#380—21no—
20#380C411yescharacteristic, complemented
21#343—21no—
22#342—21no—
23C22×D4C2311yescharacteristic
24C23×C4C2×C411yescharacteristic
25C23×C4C2×C411yescharacteristic
26C23×C4C2×C411yescharacteristic
27C23×C4D411yescharacteristic
28C2×M16—22no—
29C4×D4—41no—
30C4×D4—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⋊C4—41no—
39C2×C4⋊C4D411yescharacteristic
40C2×C22⋊C4—21no—
41C2×C22⋊C4—22no—
42C2×C22⋊C4—21no—
43C2×C22⋊C4C2×C411yescharacteristic
44C2×C22⋊C4C2×C411yescharacteristic
45C2×C22⋊C4C2×C411yescharacteristic
46C2×C22⋊C4D411yescharacteristic
47C2×C42D411yescharacteristic
48#100—22no—
49#100Q814yes—
50#99—24no—
51#97—41no—
52C4×C8—41no—
53#95—21no—
54#95—21no—
55#95—21no—
56#95—21no—
57#95—21no—
58#95—41no—
59C24C22×C411yescharacteristic
60C24C2×D411yescharacteristic
61C2×D4—41no—
62C2×D4—41no—
63C2×D4C2×Q812yes—
64C2×D4#4112yes—
65C22×C4—21no—
66C22×C4—21no—
67C22×C4—21no—
68C22×C4—21no—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4—21no—
72C22×C4—21no—
73C22×C4—42no—
74C22×C4—41no—
75C22×C4—41no—
76C22×C4—42no—
77C22×C4—81no—
78C22×C4—81no—
79C22×C4—81no—
80C22×C4C22⋊C411yescharacteristic
81C22×C4C22⋊C411yescharacteristic
82C22×C4C22⋊C411yescharacteristic
83C22×C4C22⋊C411yescharacteristic
84C22×C4C2×D411yescharacteristic
85M16—24no—
86M16—42no—
87C2×C8—42no—
88C4⋊C4—41no—
89C4⋊C4—42no—
90C4⋊C4—42no—
91C4⋊C4—41no—
92C4⋊C4—41no—
93C4⋊C4—81no—
94C4⋊C4—81no—
95C4⋊C4—82no—
96C22⋊C4—41no—
97C22⋊C4—41no—
98C22⋊C4—42no—
99C22⋊C4—41no—
100C22⋊C4—41no—
101C22⋊C4—42no—
102C22⋊C4—42no—
103C22⋊C4—81no—
104C42—21no—
105C42—21no—
106C23—21no—
107C23—21no—
108C23—21no—
109C23—21no—
110C23—41no—
111C23—41no—
112C23—41no—
113C23—41no—
114C23C2×C22⋊C411yescharacteristic
115C23C4×Q812yes—
116C23#12411yescharacteristic
117C23C4⋊Q811yescharacteristic
118D4—42no—
119D4—42no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—22no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—41no—
127C2×C4—42no—
128C2×C4—41no—
129C2×C4—42no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—42no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—81no—
145C2×C4—81no—
146C2×C4—81no—
147C2×C4—82no—
148C2×C4—82no—
149C2×C4—82no—
150C2×C4—82no—
151C2×C4#9911yescharacteristic
152C2×C4#9911yescharacteristic
153C2×C4C22⋊Q812yes—
154C8—44no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—22no—
159C22—21no—
160C22—42no—
161C22—41no—
162C22—41no—
163C22—42no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22—81no—
169C22#39111yescharacteristic
170C22C2×#9911yescharacteristic
171C22#41011yescharacteristic
172C4—21no—
173C4—21no—
174C4—22no—
175C4—41no—
176C4—42no—
177C4—41no—
178C4—41no—
179C4—81no—
180C4—81no—
181C4—81no—
182C4—162no—
183C2—21no—
184C2—21no—
185C2—41no—
186C2—42no—
187C2—41no—
188C2#199611yescharacteristic
189C2#212011yescharacteristic
190C2#212111yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC24C22×C4
Frattini, prime radical, cosocleC22×D4C23
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ G
LECSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
7. C22×C4⋊C4C4semidirect
17. #385C4semidirect
18. #385C4semidirect
20. #380C4semidirect

Maximal subgroups

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

subgroupindex
#25792
#17992
C4×#1002
#13902