Finite Group Databasebeta

← #9186

Subgroups — #9186

Order 256.

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

normal subgroups only

This group has 290 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#2975C211yesmaximal, characteristic, complemented
2#2635C211yesmaximal, characteristic
3C4×#99C211yesmaximal, characteristic, complemented
4#1507C212yesmaximal, complemented
5#1284C212yesmaximal, complemented
6C2×#121C2211yescharacteristic
7C2×C4×D4C2211yescharacteristic
8#436—24no—
9#431—21no—
10C2×#99—21no—
11#407—21no—
12#407C2212yes—
13#400C411yescharacteristic, complemented
14#399C411yescharacteristic, complemented
15#394—21no—
16#394C411yescharacteristic, complemented
17#392—21no—
18#392C411yescharacteristic, complemented
19#388—21no—
20#386—21no—
21#381C2211yescharacteristic
22C4×C22⋊C4C2212yes—
23#342—21no—
24#327—24no—
25C22×D4—21no—
26C22×D4—21no—
27C22×D4C2×C411yescharacteristic
28C22×D4D411yescharacteristic
29C23×C4D411yescharacteristic
30C23×C4C2311yescharacteristic
31C2×M16—22no—
32C2×M16—22no—
33#121—22no—
34#121—22no—
35C4×D4—22no—
36C4×D4—22no—
37C2×C4⋊C4—21no—
38C2×C4⋊C4C2×C411yescharacteristic
39C2×C4⋊C4C2×C411yescharacteristic
40C2×C22⋊C4—22no—
41C2×C22⋊C4—21no—
42C2×C22⋊C4—21no—
43C2×C22⋊C4—21no—
44C2×C22⋊C4—21no—
45C2×C22⋊C4—21no—
46C2×C22⋊C4—21no—
47C2×C22⋊C4C2×C411yescharacteristic
48C2×C22⋊C4D411yescharacteristic
49C2×C42—22no—
50C2×C42D411yescharacteristic
51C4⋊C8—22no—
52#99—24no—
53C22⋊C8—22no—
54C22⋊C8—22no—
55C22⋊C8D414yescomplemented
56C4×C8—22no—
57#95—21no—
58#95—21no—
59#95—21no—
60#95—22no—
61#95C2×C411yescharacteristic
62#95C2×C411yescharacteristic
63C24—21no—
64C24C22⋊C411yescharacteristic
65C24C2×D411yescharacteristic
66C2×D4—22no—
67C2×D4—22no—
68C2×D4—22no—
69C2×D4—41no—
70C2×D4—42no—
71C2×D4—42no—
72C2×D4—81no—
73C2×D4—81no—
74C2×D4—81no—
75C2×D4—81no—
76C2×D4—81no—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—42no—
83C22×C4—81no—
84C22×C4—81no—
85C22×C4C22⋊C411yescharacteristic
86C22×C4C22⋊C411yescharacteristic
87C22×C4C22⋊C411yescharacteristic
88C22×C4C22×C411yescharacteristic
89C22×C4C2×D412yes—
90C22×C4C2×D411yescharacteristic
91C22×C4#4112yes—
92M16—82no—
93M16—82no—
94C2×C8—24no—
95C4⋊C4—22no—
96C4⋊C4—22no—
97C4⋊C4—81no—
98C22⋊C4—22no—
99C22⋊C4—22no—
100C22⋊C4—24no—
101C22⋊C4—42no—
102C22⋊C4—42no—
103C22⋊C4—41no—
104C22⋊C4—41no—
105C22⋊C4—81no—
106C22⋊C4—81no—
107C22⋊C4—81no—
108C22⋊C4—81no—
109C42—21no—
110C42—21no—
111C42—82no—
112C23—21no—
113C23—21no—
114C23—21no—
115C23—21no—
116C23—21no—
117C23—41no—
118C23—41no—
119C23—41no—
120C23—41no—
121C23—41no—
122C23—41no—
123C23—41no—
124C23—41no—
125C23—41no—
126C23—41no—
127C23—41no—
128C23C2×C22⋊C411yescharacteristic
129C23#12112yes—
130D4—44no—
131D4—82no—
132D4—84no—
133D4—84no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—42no—
139C2×C4—42no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—42no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—44no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—81no—
156C2×C4—82no—
157C2×C4—82no—
158C2×C4#10412yes—
159C2×C4C4×D412yes—
160C2×C4#12011yescharacteristic
161C2×C4#12311yescharacteristic
162C8—44no—
163C22—21no—
164C22—21no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—81no—
180C22—81no—
181C22—81no—
182C22#38611yescharacteristic
183C22C2×#10411yescharacteristic
184C22#42111yescharacteristic
185C4—22no—
186C4—21no—
187C4—21no—
188C4—22no—
189C4—41no—
190C4—41no—
191C4—81no—
192C4—81no—
193C4—84no—
194C4—81no—
195C2—21no—
196C2—21no—
197C2—42no—
198C2—81no—
199C2—161no—
200C2#187111yescharacteristic
201C2#191011yescharacteristic
202C2#191311yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC22×C4C22×C4
Frattini, cosocleC23×C4C23
prime radical#2635C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #2975C2semidirect
3. C4×#99C2semidirect
4. #1507C2semidirect
5. #1284C2semidirect
13. #400C4semidirect
14. #399C4semidirect
16. #394C4semidirect
18. #392C4semidirect
55. C22⋊C8D4semidirect

Maximal subgroups

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

subgroupindex
#29752
#26352
C4×#992
#15072
#12842