Finite Group Databasebeta

← #9380

Subgroups — #9380

Order 256.

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

normal subgroups only

This group has 212 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#3236C211yesmaximal, characteristic
2#2336C211yesmaximal, characteristic
3#1986C211yesmaximal, characteristic
4#1528C211yesmaximal, characteristic
5#1515C211yesmaximal, characteristic
6#1288C211yesmaximal, characteristic
7#1285C211yesmaximal, characteristic
8#533C2211yescharacteristic
9C2×#125C2211yescharacteristic
10#501C412yescomplemented
11#491C412yescomplemented
12#484—21no—
13#483—21no—
14#479—22no—
15#432C2211yescharacteristic
16#432C2211yescharacteristic
17C4×M16C2211yescharacteristic
18#389—21no—
19#387—21no—
20#387—21no—
21#387—21no—
22#387—21no—
23#383C2211yescharacteristic
24C4×C4⋊C4—21no—
25C4×C4⋊C4C2211yescharacteristic
26#339—21no—
27#339—21no—
28#330—22no—
29#328—21no—
30#328—21no—
31C2×M16—21no—
32C4⋊Q8C2×C411yescharacteristic
33C4⋊Q8C2×C411yescharacteristic
34#125—21no—
35#125—21no—
36#125—21no—
37#125C2×C412yes—
38#125D412yes—
39C22⋊Q8—21no—
40C22⋊Q8—21no—
41C4×Q8—21no—
42C4×Q8—21no—
43#117—21no—
44C2×C4⋊C4—21no—
45C2×C4⋊C4—21no—
46C2×C4⋊C4—21no—
47C2×C4⋊C4—21no—
48C2×C4⋊C4—21no—
49C2×C4⋊C4D411yescharacteristic
50C2×C4⋊C4D411yescharacteristic
51C2×C42—21no—
52C2×C42—21no—
53C2×C42D411yescharacteristic
54C2×C42D411yescharacteristic
55C2×C42C2311yescharacteristic
56#107—22no—
57#106—22no—
58C4⋊C8—21no—
59C4⋊C8—21no—
60#103—22no—
61#103—22no—
62C22⋊C8—21no—
63C22⋊C8—21no—
64#97—21no—
65#97—21no—
66#97C2×C412yes—
67C4×C8—21no—
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
77C2×Q8—21no—
78C2×Q8—21no—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—21no—
84C22×C4—21no—
85C22×C4C2×D411yescharacteristic
86C22×C4C2×D411yescharacteristic
87C22×C4C2×D411yescharacteristic
88M16—22no—
89M16—41no—
90C2×C8—22no—
91C2×C8—41no—
92C2×C8—41no—
93C4⋊C4—22no—
94C4⋊C4—22no—
95C4⋊C4—22no—
96C4⋊C4—22no—
97C4⋊C4—21no—
98C4⋊C4—21no—
99C4⋊C4—21no—
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4—42no—
104C4⋊C4—42no—
105C4⋊C4—41no—
106C4⋊C4—41no—
107C4⋊C4—81no—
108C4⋊C4C22⋊C412yes—
109C4⋊C4C22⋊C412yes—
110C22⋊C4—41no—
111C42—41no—
112C42—41no—
113C42—42no—
114C42—41no—
115C42—81no—
116C42C22×C411yescharacteristic
117C42C2×D411yescharacteristic
118C42#4111yescharacteristic
119C42#4111yescharacteristic
120C23#12011yescharacteristic
121Q8—42no—
122Q8—81no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—22no—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—41no—
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—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4C2×C22⋊C411yescharacteristic
148C2×C4C4×D411yescharacteristic
149C2×C4C4×D411yescharacteristic
150C2×C4#12111yescharacteristic
151C2×C4#12111yescharacteristic
152C2×C4#12311yescharacteristic
153C8—42no—
154C8—42no—
155C8—81no—
156C22—21no—
157C22—21no—
158C22#38611yescharacteristic
159C22#45511yescharacteristic
160C22#45611yescharacteristic
161C4—21no—
162C4—21no—
163C4—21no—
164C4—21no—
165C4—21no—
166C4—21no—
167C4—42no—
168C4—42no—
169C4—42no—
170C4—81no—
171C4—81no—
172C4—81no—
173C4—81no—
174C4—81no—
175C2—21no—
176C2—21no—
177C2#188211yescharacteristic
178C2#190611yescharacteristic
179C2#191211yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC42C22×C4
Frattini, cosocleC2×C42C23
prime radicalC23#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
10. #501C4semidirect
11. #491C4semidirect

Maximal subgroups

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

subgroupindex
#32362
#23362
#19862
#15282
#15152
#12882
#12852