Finite Group Databasebeta

← #9526

Subgroups — #9526

Order 256.

241 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 241 conjugacy classes of subgroups — too many to draw. Only its 59 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#3095C211yesmaximal, characteristic
2#2332C211yesmaximal, characteristic
3#1826C211yesmaximal, characteristic
4#1820C211yesmaximal, characteristic
5#1511C211yesmaximal, characteristic
6#1306C211yesmaximal, characteristic
7#1284C211yesmaximal, characteristic
8C2×C22⋊Q8C2211yescharacteristic
9C2×#117C2211yescharacteristic
10#485—22no—
11#484C412yescomplemented
12#483C412yescomplemented
13#428—21no—
14#419—21no—
15#407C2211yescharacteristic
16#407C2211yescharacteristic
17#391—21no—
18#388—21no—
19#388—21no—
20#387—21no—
21#387—21no—
22#381C2211yescharacteristic
23#381C2211yescharacteristic
24C4×C4⋊C4—21no—
25C4×C22⋊C4C2211yescharacteristic
26#342—21no—
27#342—21no—
28#339—21no—
29#339—21no—
30#328—22no—
31C22×Q8D411yescharacteristic
32C23×C4C2311yescharacteristic
33C2×M16—21no—
34C2×M16—21no—
35C22⋊Q8—21no—
36C22⋊Q8—21no—
37C22⋊Q8C2×C412yes—
38C22⋊Q8D412yes—
39#117—21no—
40#117—21no—
41#117—21no—
42#117—21no—
43C2×C4⋊C4—21no—
44C2×C4⋊C4—21no—
45C2×C4⋊C4—21no—
46C2×C4⋊C4C2×C411yescharacteristic
47C2×C4⋊C4C2×C411yescharacteristic
48C2×C4⋊C4D411yescharacteristic
49C2×C22⋊C4—21no—
50C2×C22⋊C4—21no—
51C2×C22⋊C4—21no—
52C2×C22⋊C4—21no—
53C2×C22⋊C4D411yescharacteristic
54C2×C22⋊C4D411yescharacteristic
55C2×C42—21no—
56C2×C42—21no—
57C2×C42—21no—
58C2×C42D411yescharacteristic
59C2×C42D411yescharacteristic
60#107—22no—
61#106—22no—
62#103—22no—
63#103—22no—
64C22⋊C8—21no—
65C22⋊C8—21no—
66C22⋊C8—21no—
67C22⋊C8C2×C412yes—
68#95—21no—
69#95—21no—
70#95—21no—
71#95—21no—
72#95—21no—
73#95—21no—
74#95—21no—
75#95—21no—
76#95—21no—
77C24C2×D411yescharacteristic
78C2×Q8—21no—
79C2×Q8—41no—
80C2×Q8—41no—
81C2×Q8C22⋊C412yes—
82C22×C4—21no—
83C22×C4—21no—
84C22×C4—21no—
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—41no—
91C22×C4—41no—
92C22×C4—41no—
93C22×C4C22×C411yescharacteristic
94C22×C4C2×D411yescharacteristic
95C22×C4C2×D411yescharacteristic
96C22×C4C2×D411yescharacteristic
97C22×C4#4111yescharacteristic
98C22×C4#4111yescharacteristic
99M16—41no—
100M16—41no—
101M16—41no—
102M16—41no—
103C2×C8—22no—
104C2×C8—41no—
105C4⋊C4—22no—
106C4⋊C4—22no—
107C4⋊C4—21no—
108C4⋊C4—21no—
109C4⋊C4—21no—
110C4⋊C4—21no—
111C4⋊C4—21no—
112C4⋊C4—42no—
113C4⋊C4—81no—
114C4⋊C4C22⋊C412yes—
115C22⋊C4—22no—
116C22⋊C4—22no—
117C22⋊C4—42no—
118C22⋊C4—41no—
119C22⋊C4—41no—
120C22⋊C4—41no—
121C22⋊C4—41no—
122C22⋊C4—41no—
123C22⋊C4—41no—
124C42—41no—
125C42—41no—
126C42—42no—
127C42—41no—
128C42—41no—
129C42—81no—
130C23—21no—
131C23—21no—
132C23—41no—
133C23—41no—
134C23C4×D411yescharacteristic
135C23#12011yescharacteristic
136C23#12111yescharacteristic
137Q8—42no—
138Q8—81no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
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—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—81no—
168C2×C4—81no—
169C2×C4—81no—
170C2×C4—81no—
171C2×C4—81no—
172C2×C4C2×C22⋊C411yescharacteristic
173C2×C4C4×D411yescharacteristic
174C2×C4#12111yescharacteristic
175C2×C4#12311yescharacteristic
176C8—42no—
177C8—81no—
178C22—21no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—81no—
187C22—81no—
188C22#38611yescharacteristic
189C22#45811yescharacteristic
190C22#45811yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—42no—
196C4—42no—
197C4—42no—
198C4—81no—
199C4—81no—
200C4—81no—
201C4—81no—
202C4—81no—
203C4—161no—
204C2—21no—
205C2—21no—
206C2—41no—
207C2—41no—
208C2#189011yescharacteristic
209C2#190511yescharacteristic
210C2#190611yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC22×C4C22×C4
Frattini, cosocleC23×C4C23
prime radicalC24C2×D4
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
11. #484C4semidirect
12. #483C4semidirect

Maximal subgroups

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

subgroupindex
#30952
#23322
#18262
#18202
#15112
#13062
#12842