Finite Group Databasebeta

← #9246

Subgroups — #9246

Order 256.

203 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 203 conjugacy classes of subgroups — too many to draw. Only its 63 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×#479C211yesmaximal, characteristic
2#2984C211yesmaximal, characteristic
3#1528C211yesmaximal, characteristic
4#1491C211yesmaximal, characteristic
5#1470C211yesmaximal, characteristic
6#1290C211yesmaximal, characteristic
7#1283C211yesmaximal, characteristic
8C2×#125C2211yescharacteristic
9C2×C4×Q8C2211yescharacteristic
10#479—21no—
11#479—21no—
12#479—21no—
13#479—21no—
14#446—21no—
15#446—22no—
16C8×Q8—21no—
17#432—21no—
18#432C2211yescharacteristic
19#432C2211yescharacteristic
20#431—21no—
21#431C2211yescharacteristic
22C2×#107C411yescharacteristic
23C2×#106C411yescharacteristic
24C2×C4⋊C8C2211yescharacteristic
25C2×#103C411yescharacteristic
26C2×#103C411yescharacteristic
27C4×M16C2211yescharacteristic
28#330—22no—
29Q8⋊C8—21no—
30Q8⋊C8—21no—
31#324—21no—
32#324—21no—
33C22×Q8C2×C411yescharacteristic
34C2×M16—21no—
35C22×C8C2×C411yescharacteristic
36C22×C8C2×C411yescharacteristic
37#125—21no—
38#125—21no—
39#125—21no—
40#125—21no—
41C4×Q8—21no—
42C4×Q8—21no—
43C4×Q8D411yescharacteristic
44C4×Q8D411yescharacteristic
45C4×Q8D411yescharacteristic
46C4×Q8D411yescharacteristic
47C2×C4⋊C4—21no—
48C2×C4⋊C4—21no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4C2×C411yescharacteristic
51C2×C4⋊C4C2×C411yescharacteristic
52C2×C4⋊C4C2×C411yescharacteristic
53C2×C42—21no—
54C2×C42C2311yescharacteristic
55#107—21no—
56#107—21no—
57#106—21no—
58#106—21no—
59C4⋊C8—22no—
60C4⋊C8—22no—
61C4⋊C8—21no—
62C4⋊C8—21no—
63C4⋊C8—21no—
64C4⋊C8—21no—
65C4⋊C8—21no—
66#103—21no—
67#103—21no—
68#103—21no—
69#103—21no—
70C22⋊C8—21no—
71C22⋊C8—21no—
72C22⋊C8D411yescharacteristic
73C22⋊C8D411yescharacteristic
74#97—22no—
75#97—21no—
76#97—21no—
77#97D412yes—
78C4×C8—22no—
79C4×C8—21no—
80C4×C8—21no—
81C2×Q8—21no—
82C2×Q8—22no—
83C2×Q8—41no—
84C2×Q8C22⋊C411yescharacteristic
85C2×Q8C22⋊C411yescharacteristic
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4C22×C411yescharacteristic
91C22×C4C2×D411yescharacteristic
92C22×C4#4111yescharacteristic
93M16—22no—
94M16—41no—
95C2×C8—21no—
96C2×C8—21no—
97C2×C8—21no—
98C2×C8—21no—
99C2×C8—22no—
100C2×C8—41no—
101C2×C8—41no—
102C2×C8—41no—
103C2×C8—41no—
104C4⋊C4—21no—
105C4⋊C4—21no—
106C4⋊C4—21no—
107C4⋊C4—21no—
108C4⋊C4—21no—
109C4⋊C4—21no—
110C4⋊C4—21no—
111C4⋊C4—21no—
112C4⋊C4—21no—
113C4⋊C4—41no—
114C4⋊C4—41no—
115C4⋊C4—41no—
116C4⋊C4—41no—
117C4⋊C4C22⋊C411yescharacteristic
118C4⋊C4C22⋊C411yescharacteristic
119C42—21no—
120C42—21no—
121C42—21no—
122C42—21no—
123C42C2×D411yescharacteristic
124C42C2×D411yescharacteristic
125C42C2×D411yescharacteristic
126C42#4111yescharacteristic
127C23C4×D411yescharacteristic
128Q8—21no—
129Q8—21no—
130Q8—21no—
131Q8—42no—
132Q8#10112yes—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—41no—
142C2×C4—42no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—81no—
150C2×C4C2×C22⋊C411yescharacteristic
151C2×C4C4×D411yescharacteristic
152C2×C4#12011yescharacteristic
153C2×C4#12111yescharacteristic
154C2×C4#12111yescharacteristic
155C2×C4#12311yescharacteristic
156C8—41no—
157C8—41no—
158C8—42no—
159C8—42no—
160C8—41no—
161C8—41no—
162C8—81no—
163C22—21no—
164C22—21no—
165C22#38611yescharacteristic
166C22#44311yescharacteristic
167C22#44411yescharacteristic
168C4—21no—
169C4—21no—
170C4—21no—
171C4—22no—
172C4—21no—
173C4—21no—
174C4—41no—
175C4—41no—
176C4—41no—
177C4—81no—
178C4—81no—
179C4C2×#10111yescharacteristic
180C4#41311yescharacteristic
181C2—21no—
182C2—21no—
183C2#187611yescharacteristic
184C2#190111yescharacteristic
185C2#190511yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
prime radicalC23C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#4792
#29842
#15282
#14912
#14702
#12902
#12832