Finite Group Databasebeta

← #9385

Subgroups — #9385

Order 256.

274 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 67 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#2973C211yesmaximal, characteristic
2#2564C211yesmaximal, characteristic
3#1799C211yesmaximal, characteristic
4#1520C212yesmaximal, complemented
5#1294C212yesmaximal, complemented
6C2×C22⋊Q8C2211yescharacteristic
7C2×C4×D4C2211yescharacteristic
8#435—24no—
9#432—21no—
10C2×#99—21no—
11#407—21no—
12C2×C22⋊C8C2212yes—
13#400C411yescharacteristic, complemented
14#399C411yescharacteristic, complemented
15#395C411yescharacteristic, complemented
16#393C411yescharacteristic, complemented
17#387—21no—
18#386—21no—
19#385—21no—
20#380—21no—
21#380C2212yes—
22C2×#95C2211yescharacteristic
23#342—21no—
24#328—24no—
25C22×Q8C2×C411yescharacteristic
26C22×D4D411yescharacteristic
27C23×C4—21no—
28C23×C4D411yescharacteristic
29C23×C4C2311yescharacteristic
30C2×M16—22no—
31C22×C8—22no—
32C22⋊Q8—22no—
33C22⋊Q8—22no—
34C4×D4—22no—
35C4×D4—22no—
36C2×C4⋊C4—21no—
37C2×C4⋊C4—21no—
38C2×C4⋊C4—21no—
39C2×C4⋊C4—22no—
40C2×C4⋊C4C2×C411yescharacteristic
41C2×C4⋊C4C2×C411yescharacteristic
42C2×C22⋊C4—21no—
43C2×C22⋊C4—21no—
44C2×C22⋊C4—22no—
45C2×C22⋊C4—21no—
46C2×C22⋊C4C2×C411yescharacteristic
47C2×C22⋊C4D411yescharacteristic
48C2×C42D411yescharacteristic
49C4⋊C8—22no—
50#99—42no—
51C22⋊C8—22no—
52C22⋊C8—22no—
53C22⋊C8D414yes—
54#97—22no—
55#95—21no—
56#95—21no—
57#95—21no—
58#95—21no—
59#95—21no—
60#95—22no—
61#95C2×C411yescharacteristic
62#95C2×C411yescharacteristic
63C24C22⋊C411yescharacteristic
64C24C2×D411yescharacteristic
65C2×Q8—22no—
66C2×Q8—81no—
67C2×D4—22no—
68C2×D4—21no—
69C2×D4—21no—
70C2×D4—22no—
71C22×C4—21no—
72C22×C4—21no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—42no—
78C22×C4—41no—
79C22×C4—41no—
80C22×C4—42no—
81C22×C4—81no—
82C22×C4—81no—
83C22×C4—81no—
84C22×C4C22⋊C411yescharacteristic
85C22×C4C22⋊C411yescharacteristic
86C22×C4C22⋊C411yescharacteristic
87C22×C4C22×C411yescharacteristic
88C22×C4C2×D412yes—
89C22×C4C2×D411yescharacteristic
90C22×C4#4112yes—
91M16—82no—
92C2×C8—24no—
93C2×C8—82no—
94C4⋊C4—22no—
95C4⋊C4—22no—
96C4⋊C4—42no—
97C4⋊C4—41no—
98C4⋊C4—41no—
99C4⋊C4—81no—
100C4⋊C4—82no—
101C22⋊C4—22no—
102C22⋊C4—22no—
103C22⋊C4—42no—
104C22⋊C4—42no—
105C22⋊C4—42no—
106C22⋊C4—42no—
107C22⋊C4—81no—
108C42—21no—
109C42—21no—
110C23—21no—
111C23—21no—
112C23—21no—
113C23—41no—
114C23—41no—
115C23—41no—
116C23—41no—
117C23C2×C22⋊C411yescharacteristic
118C23#12112yes—
119C23AGL(1,ℤ/8)11yescharacteristic
120C23#13711yescharacteristic
121C23#13712yes—
122Q8—82no—
123D4—42no—
124D4—42no—
125C2×C4—22no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—42no—
132C2×C4—42no—
133C2×C4—41no—
134C2×C4—41no—
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—82no—
151C2×C4—82no—
152C2×C4—82no—
153C2×C4—82no—
154C2×C4—82no—
155C2×C4C4×D412yes—
156C2×C4#12011yescharacteristic
157C2×C4#12311yescharacteristic
158C8—44no—
159C22—21no—
160C22—22no—
161C22—21no—
162C22—22no—
163C22—41no—
164C22—41no—
165C22—42no—
166C22—42no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22—81no—
171C22#38611yescharacteristic
172C22#41711yescharacteristic
173C22#41911yescharacteristic
174C22#46812yes—
175C22#47012yes—
176C4—21no—
177C4—21no—
178C4—22no—
179C4—42no—
180C4—41no—
181C4—41no—
182C4—41no—
183C4—81no—
184C4—81no—
185C4—81no—
186C4—162no—
187C2—21no—
188C2—22no—
189C2—21no—
190C2—22no—
191C2—81no—
192C2#188411yescharacteristic
193C2#189411yescharacteristic
194C2#191311yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC22×C4C22×C4
Frattini, cosocleC23×C4C23
prime radicalC22×D4D4
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
4. #1520C2semidirect
5. #1294C2semidirect
13. #400C4semidirect
14. #399C4semidirect
15. #395C4semidirect
16. #393C4semidirect

Maximal subgroups

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

subgroupindex
#29732
#25642
#17992
#15202
#12942