Finite Group Databasebeta

← #9125

Subgroups — #9125

Order 256.

265 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 265 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C2×#432C211yesmaximal, characteristic
2#2851C211yesmaximal, characteristic
3#1749C211yesmaximal, characteristic
4C2×#330C212yesmaximal, complemented
5#1295C212yesmaximal, complemented
6C2×#125C2211yescharacteristic
7C22×C42C2211yescharacteristic
8#432—24no—
9C2×C4⋊C8—21no—
10C2×C22⋊C8—21no—
11C2×C22⋊C8—21no—
12C2×#97C2212yes—
13C2×#97C2212yes—
14#389C411yescharacteristic
15#389C411yescharacteristic
16#387—21no—
17#387—21no—
18#385—21no—
19#385—21no—
20#382C2211yescharacteristic
21#380C411yescharacteristic
22#380C411yescharacteristic
23#336—21no—
24#330—24no—
25C23×C4C2×C411yescharacteristic
26C23×C4D411yescharacteristic
27C23×C4D411yescharacteristic
28C22×C8—22no—
29C22×C8—22no—
30#125—22no—
31#125—22no—
32C2×C4⋊C4—21no—
33C2×C4⋊C4—21no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4—21no—
36C2×C4⋊C4C2×C411yescharacteristic
37C2×C4⋊C4C2×C411yescharacteristic
38C2×C4⋊C4C2×C411yescharacteristic
39C2×C4⋊C4C2×C411yescharacteristic
40C2×C22⋊C4—21no—
41C2×C22⋊C4—21no—
42C2×C42—22no—
43C2×C42—22no—
44C2×C42C2×C411yescharacteristic
45C2×C42D411yescharacteristic
46C2×C42D411yescharacteristic
47C2×C42C2311yescharacteristic
48C4⋊C8—24no—
49C22⋊C8—24no—
50C22⋊C8—24no—
51#97—22no—
52#97—22no—
53#97—22no—
54#97D414yes—
55#95—21no—
56#95—21no—
57#95—21no—
58#95—21no—
59#95—21no—
60#95—21no—
61C24C22⋊C411yescharacteristic
62C22×C4—22no—
63C22×C4—22no—
64C22×C4—22no—
65C22×C4—21no—
66C22×C4—22no—
67C22×C4—21no—
68C22×C4—21no—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4—21no—
72C22×C4—41no—
73C22×C4—41no—
74C22×C4—41no—
75C22×C4—41no—
76C22×C4C22⋊C411yescharacteristic
77C22×C4C22⋊C411yescharacteristic
78C22×C4C22⋊C411yescharacteristic
79C22×C4C22×C411yescharacteristic
80C22×C4C2×D411yescharacteristic
81C22×C4C2×D411yescharacteristic
82C2×C8—24no—
83C2×C8—24no—
84C2×C8—42no—
85C2×C8—42no—
86C2×C8—42no—
87C2×C8—42no—
88C4⋊C4—22no—
89C4⋊C4—22no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C4⋊C4—42no—
93C4⋊C4—42no—
94C4⋊C4—41no—
95C4⋊C4—42no—
96C4⋊C4—41no—
97C22⋊C4—42no—
98C22⋊C4—42no—
99C42—22no—
100C42—21no—
101C42—22no—
102C42—21no—
103C42C2×D412yes—
104C42#4112yes—
105C23—21no—
106C23—21no—
107C23—21no—
108C23—21no—
109C23—21no—
110C23—21no—
111C23#10412yes—
112C23C2×C22⋊C411yescharacteristic
113C2×C4—21no—
114C2×C4—21no—
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—21no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—44no—
128C2×C4—44no—
129C2×C4—42no—
130C2×C4—42no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
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#10112yes—
144C2×C4C4×D412yes—
145C2×C4#12011yescharacteristic
146C2×C4#12112yes—
147C2×C4#12311yescharacteristic
148C8—44no—
149C8—44no—
150C22—22no—
151C22—22no—
152C22—22no—
153C22—41no—
154C22—41no—
155C22—41no—
156C22—41no—
157C22#38611yescharacteristic
158C22C2×#10111yescharacteristic
159C22#41311yescharacteristic
160C22C2×#10411yescharacteristic
161C22#42111yescharacteristic
162C22#42111yescharacteristic
163C22#42111yescharacteristic
164C4—22no—
165C4—21no—
166C4—21no—
167C4—22no—
168C4—22no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—81no—
173C4—81no—
174C4—81no—
175C2—42no—
176C2#152811yescharacteristic
177C2#153211yescharacteristic
178C2#153511yescharacteristic
179C2#153711yescharacteristic
180C2#187111yescharacteristic
181C2#189711yescharacteristic
182C2#190111yescharacteristic
subgroupG/H
center, socleC23C2×C22⋊C4
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
prime radicalC24C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#330C2semidirect
5. #1295C2semidirect

Maximal subgroups

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

subgroupindex
C2×#4322
#28512
#17492
C2×#3302
#12952