Finite Group Databasebeta

← #9941

Subgroups — #9941

Order 256.

300 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 51 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#3094C211yesmaximal, characteristic
2#2591C211yesmaximal, characteristic
3#2484C211yesmaximal, characteristic, complemented
4#1826C211yesmaximal, characteristic, complemented
5#1510C211yesmaximal, characteristic
6#1463C211yesmaximal, characteristic, complemented
7#1284C211yesmaximal, characteristic, complemented
8C2×#121C2211yescharacteristic
9C2×#117C2211yescharacteristic
10C22×C4⋊C4C2211yescharacteristic
11#482—22no—
12#481—21no—
13#480—21no—
14#428—21no—
15#418—21no—
16#407C2211yescharacteristic
17#407C2211yescharacteristic
18#400—21no—
19#400—21no—
20#398—21no—
21#394—21no—
22#388—22no—
23#387—22no—
24#386—21no—
25#386—21no—
26#385—21no—
27#381—21no—
28#381C2211yescharacteristic
29C4×C22⋊C4C2211yescharacteristic
30#339—22no—
31#327—22no—
32#324—22no—
33C22×D4—21no—
34C22×D4D411yescharacteristic
35C23×C4D411yescharacteristic
36C23×C4D411yescharacteristic
37C23×C4C2311yescharacteristic
38C2×M16—21no—
39C2×M16—21no—
40#121—21no—
41#121—21no—
42#121—21no—
43#121—21no—
44#117—21no—
45#117—21no—
46#117—21no—
47#117—21no—
48C2×C4⋊C4—22no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4—21no—
51C2×C4⋊C4—21no—
52C2×C4⋊C4—21no—
53C2×C4⋊C4—21no—
54C2×C4⋊C4—21no—
55C2×C4⋊C4D411yescharacteristic
56C2×C4⋊C4D411yescharacteristic
57C2×C4⋊C4D411yescharacteristic
58C2×C22⋊C4—22no—
59C2×C22⋊C4—21no—
60C2×C22⋊C4—21no—
61C2×C22⋊C4—21no—
62C2×C22⋊C4—21no—
63C2×C22⋊C4—22no—
64C2×C42—21no—
65C2×C42D412yes—
66#107—22no—
67#106—22no—
68#102—22no—
69#102—22no—
70C22⋊C8—21no—
71C22⋊C8—21no—
72C22⋊C8—21no—
73C22⋊C8D412yes—
74#95—22no—
75#95—22no—
76#95—22no—
77#95—22no—
78#95—22no—
79#95—21no—
80#95—21no—
81#95D412yes—
82C24—21no—
83C24C2×D411yescharacteristic
84C2×D4—21no—
85C2×D4—21no—
86C2×D4—42no—
87C2×D4—44no—
88C2×D4—41no—
89C2×D4—41no—
90C22×C4—21no—
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—22no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—21no—
97C22×C4—22no—
98C22×C4—21no—
99C22×C4—21no—
100C22×C4—21no—
101C22×C4—42no—
102C22×C4—42no—
103C22×C4—42no—
104C22×C4C2×D411yescharacteristic
105C22×C4C2×D411yescharacteristic
106C22×C4C2×D411yescharacteristic
107C22×C4C2×D411yescharacteristic
108C22×C4C2×D411yescharacteristic
109C22×C4#4111yescharacteristic
110M16—42no—
111M16—42no—
112C2×C8—22no—
113C2×C8—41no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—44no—
121C4⋊C4—41no—
122C4⋊C4—41no—
123C4⋊C4—41no—
124C4⋊C4—41no—
125C22⋊C4—44no—
126C22⋊C4—42no—
127C22⋊C4—42no—
128C22⋊C4—41no—
129C22⋊C4—41no—
130C22⋊C4—41no—
131C22⋊C4—41no—
132C22⋊C4—82no—
133C42—42no—
134C42—41no—
135C42—41no—
136C23—22no—
137C23—22no—
138C23—41no—
139C23—42no—
140C23—42no—
141C23—41no—
142C23—42no—
143C23#12011yescharacteristic
144C23#12011yescharacteristic
145C23#12111yescharacteristic
146D4—42no—
147D4—81no—
148D4—82no—
149D4—82no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
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—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—81no—
179C2×C4#12011yescharacteristic
180C2×C4#12111yescharacteristic
181C2×C4#12111yescharacteristic
182C2×C4#12711yescharacteristic
183C8—42no—
184C8—81no—
185C22—21no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—44no—
193C22—84no—
194C22—81no—
195C22—81no—
196C22—81no—
197C22#39211yescharacteristic
198C22#45412yes—
199C22#45812yes—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—21no—
204C4—42no—
205C4—82no—
206C4—82no—
207C4—81no—
208C4—81no—
209C4—81no—
210C4—81no—
211C2—22no—
212C2—22no—
213C2—41no—
214C2—161no—
215C2#200311yescharacteristic
216C2#201011yescharacteristic
217C2#202211yescharacteristic
subgroupG/H
center, socleC22#392
commutator, Frattini, cosocleC23×C4C23
prime radicalC2×#121C22
LCSG ▷ C23×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
3. #2484C2semidirect
4. #1826C2semidirect
6. #1463C2semidirect
7. #1284C2semidirect

Maximal subgroups

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

subgroupindex
#30942
#25912
#24842
#18262
#15102
#14632
#12842