Finite Group Databasebeta

← #9342

Subgroups — #9342

Order 256.

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

normal subgroups only

This group has 239 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#3195C211yesmaximal, characteristic
2#2378C211yesmaximal, characteristic
3#1996C211yesmaximal, characteristic
4#1511C211yesmaximal, characteristic
5#1508C211yesmaximal, characteristic
6#1305C211yesmaximal, characteristic
7#1284C211yesmaximal, characteristic
8C2×C22⋊Q8C2211yescharacteristic
9C2×C22⋊Q8C2211yescharacteristic
10#483—21no—
11#483C412yescomplemented
12#470—22no—
13#451—21no—
14#451C412yescomplemented
15#407C2211yescharacteristic
16#407C2211yescharacteristic
17#391—21no—
18#389—21no—
19#388—21no—
20#388—21no—
21#387—21no—
22#387—21no—
23#381C2211yescharacteristic
24#380C2211yescharacteristic
25C4×C22⋊C4C2211yescharacteristic
26#342—21no—
27#342—21no—
28#328—22no—
29#328—21no—
30#328—21no—
31C22×Q8C2×C411yescharacteristic
32C22×Q8D411yescharacteristic
33C23×C4C2311yescharacteristic
34C2×Q16—22no—
35C2×M16—21no—
36C2×M16—21no—
37C22⋊Q8—21no—
38C22⋊Q8—21no—
39C22⋊Q8—21no—
40C22⋊Q8—21no—
41C22⋊Q8—21no—
42C22⋊Q8—21no—
43C22⋊Q8C2×C412yes—
44C22⋊Q8D412yes—
45C2×C4⋊C4—21no—
46C2×C4⋊C4—21no—
47C2×C4⋊C4—21no—
48C2×C4⋊C4—21no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4C2×C411yescharacteristic
51C2×C4⋊C4D411yescharacteristic
52C2×C22⋊C4—21no—
53C2×C22⋊C4—21no—
54C2×C22⋊C4—21no—
55C2×C22⋊C4—21no—
56C2×C22⋊C4D411yescharacteristic
57C2×C22⋊C4D411yescharacteristic
58C2×C42—21no—
59C2×C42—21no—
60C2×C42—21no—
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#95D411yescharacteristic
76#95D411yescharacteristic
77C24C2×D411yescharacteristic
78C2×Q8—21no—
79C2×Q8—21no—
80C2×Q8—21no—
81C2×Q8—81no—
82C2×Q8—81no—
83C2×Q8C22⋊C412yes—
84C22×C4—21no—
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—21no—
92C22×C4—41no—
93C22×C4—81no—
94C22×C4C22×C411yescharacteristic
95C22×C4C2×D411yescharacteristic
96C22×C4C2×D411yescharacteristic
97C22×C4C2×D411yescharacteristic
98C22×C4#4111yescharacteristic
99C22×C4#4111yescharacteristic
100Q16—82no—
101M16—81no—
102M16—81no—
103C2×C8—22no—
104C2×C8—41no—
105C4⋊C4—22no—
106C4⋊C4—22no—
107C4⋊C4—21no—
108C4⋊C4—21no—
109C4⋊C4—21no—
110C4⋊C4—41no—
111C4⋊C4—41no—
112C4⋊C4—81no—
113C4⋊C4—81no—
114C4⋊C4—81no—
115C4⋊C4C22⋊C412yes—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—22no—
119C22⋊C4—41no—
120C22⋊C4—41no—
121C22⋊C4—41no—
122C22⋊C4—41no—
123C22⋊C4—41no—
124C22⋊C4—81no—
125C42—81no—
126C42—81no—
127C42—81no—
128C23—21no—
129C23—21no—
130C23—41no—
131C23—41no—
132C23C4×D411yescharacteristic
133C23#12011yescharacteristic
134C23#12111yescharacteristic
135Q8—42no—
136Q8—42no—
137Q8—81no—
138Q8—81no—
139C2×C4—22no—
140C2×C4—22no—
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—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—42no—
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—81no—
167C2×C4—81no—
168C2×C4—81no—
169C2×C4—81no—
170C2×C4C2×C22⋊C411yescharacteristic
171C2×C4C4×D411yescharacteristic
172C2×C4#12111yescharacteristic
173C2×C4#12311yescharacteristic
174C8—42no—
175C8—81no—
176C22—21no—
177C22—21no—
178C22—21no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—81no—
185C22—81no—
186C22#38611yescharacteristic
187C22#45511yescharacteristic
188C22#45611yescharacteristic
189C4—21no—
190C4—21no—
191C4—21no—
192C4—21no—
193C4—42no—
194C4—42no—
195C4—81no—
196C4—81no—
197C4—81no—
198C4—81no—
199C4—82no—
200C4—81no—
201C4—81no—
202C2—21no—
203C2—21no—
204C2—41no—
205C2—41no—
206C2#188211yescharacteristic
207C2#190511yescharacteristic
208C2#191311yescharacteristic
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. #483C4semidirect
14. #451C4semidirect

Maximal subgroups

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

subgroupindex
#31952
#23782
#19962
#15112
#15082
#13052
#12842