Finite Group Databasebeta

← #11766

Subgroups — #11766

Order 256.

244 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 53 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#2591C211yesmaximal, characteristic
2C2×#343C211yesmaximal, characteristic, complemented
3#1463C211yesmaximal, characteristic, complemented
4#1353C212yesmaximal, complemented
5#1345C212yesmaximal, complemented
6C22×M16—21no—
7C2×#121C411yescharacteristic
8C22×C4⋊C4C2211yescharacteristic
9#407—21no—
10#400C411yescharacteristic
11#400C2211yescharacteristic
12#394C411yescharacteristic
13#394C2211yescharacteristic
14#388—21no—
15#388—21no—
16#386—21no—
17#386—21no—
18C4×C22⋊C4C411yescharacteristic
19#343—21no—
20#343C2212yes—
21#324—21no—
22#324C2212yes—
23C22×D4—21no—
24C22×D4C2×C411yescharacteristic
25C23×C4C2×C411yescharacteristic
26C23×C4D411yescharacteristic
27C23×C4D411yescharacteristic
28C2×M16—24no—
29C2×M16—22no—
30C2×M16—41no—
31C2×M16—42no—
32C2×M16—41no—
33C22×C8—41no—
34#121—41no—
35#121—41no—
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×C22⋊C4—21no—
46C2×C22⋊C4—21no—
47C2×C22⋊C4—21no—
48C2×C22⋊C4—21no—
49C2×C42—21no—
50C22⋊C8—22no—
51C22⋊C8—41no—
52#95—21no—
53#95—21no—
54#95—21no—
55#95—21no—
56#95C2×C411yescharacteristic
57#95C2×C411yescharacteristic
58C24—21no—
59C24C22⋊C411yescharacteristic
60C2×D4—41no—
61C2×D4—42no—
62C2×D4—42no—
63C2×D4—41no—
64C2×D4—41no—
65C2×D4—81no—
66C22×C4—21no—
67C22×C4—21no—
68C22×C4—22no—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4—21no—
72C22×C4—21no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—81no—
79C22×C4—81no—
80C22×C4C22⋊C411yescharacteristic
81C22×C4C22⋊C411yescharacteristic
82C22×C4C22⋊C411yescharacteristic
83C22×C4C22×C411yescharacteristic
84C22×C4C2×D411yescharacteristic
85C22×C4C2×D411yescharacteristic
86M16—24no—
87M16—44no—
88M16—42no—
89M16—82no—
90C2×C8—44no—
91C2×C8—42no—
92C2×C8—42no—
93C4⋊C4—41no—
94C4⋊C4—41no—
95C4⋊C4—41no—
96C4⋊C4—41no—
97C4⋊C4—41no—
98C22⋊C4—42no—
99C22⋊C4—42no—
100C22⋊C4—42no—
101C22⋊C4—41no—
102C22⋊C4—41no—
103C22⋊C4—81no—
104C22⋊C4—81no—
105C42—81no—
106C23—22no—
107C23—21no—
108C23—21no—
109C23—41no—
110C23—41no—
111C23—41no—
112C23—41no—
113C23—41no—
114C23—41no—
115C23—41no—
116C23—41no—
117C23#9911yescharacteristic
118C23#9911yescharacteristic
119C23C2×C22⋊C411yescharacteristic
120D4—82no—
121D4—82no—
122D4—82no—
123C2×C4—22no—
124C2×C4—22no—
125C2×C4—22no—
126C2×C4—22no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—42no—
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—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—81no—
150C2×C4—81no—
151C2×C4—81no—
152C2×C4#10412yes—
153C2×C4AGL(1,ℤ/8)11yescharacteristic
154C2×C4#13711yescharacteristic
155C8—44no—
156C8—82no—
157C22—21no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—21no—
164C22—42no—
165C22—42no—
166C22—81no—
167C22—81no—
168C22—81no—
169C22—81no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22#35512yes—
174C22C2×#9911yescharacteristic
175C22#41711yescharacteristic
176C22C2×#10411yescharacteristic
177C4—21no—
178C4—22no—
179C4—21no—
180C4—41no—
181C4—41no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—81no—
186C4—81no—
187C2—21no—
188C2—21no—
189C2—22no—
190C2—41no—
191C2—161no—
192C2#150411yescharacteristic
193C2#212111yescharacteristic
194C2C2×#35511yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC22×C4C22×C4
Frattini, cosocleC2×C4⋊C4C23
prime radicalC2×#121C4
LCSG ▷ C22×C4 ▷ C23 ▷ 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
2. C2×#343C2semidirect
3. #1463C2semidirect
4. #1353C2semidirect
5. #1345C2semidirect

Maximal subgroups

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

subgroupindex
#25912
C2×#3432
#14632
#13532
#13452