Finite Group Databasebeta

← #46781992

Subgroups — #46781992

Order 33664.

194 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 57 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#30682667C211yesmaximal, characteristic
2#30682343C211yesmaximal, characteristic
3#30682223C211yesmaximal, characteristic
4#30682149C211yesmaximal, characteristic
5#30681685C211yesmaximal, characteristic
6#30681670C211yesmaximal, characteristic
7Q8⋊C8×C263C211yesmaximal, characteristic
8C2×Dic1052—21no—
9#22554470—21no—
10#22554470C2211yescharacteristic
11#22554470C2211yescharacteristic
12#22554461—22no—
13#22554461—21no—
14Q8×Dic263—21no—
15C4×Dic526—21no—
16C4×Dic526C2211yescharacteristic
17#22554404—22no—
18#22554401—21no—
19C4⋊(C263⋊C8)C2211yescharacteristic
20#22554395—21no—
21#22554394—21no—
22C4×Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4×C8×C263C2211yescharacteristic
25C2×Dic526—21no—
26C2×Dic526—21no—
27C2×Dic526D411yescharacteristic
28Dic1052—42no—
29C2×C263⋊C8—21no—
30C4⋊Dic263—22no—
31C4⋊Dic263—22no—
32C4⋊Dic263—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263D411yescharacteristic
36C4⋊Dic263D412yes—
37Dic263⋊C4—22no—
38Dic263⋊C4—21no—
39C4×Dic263—22no—
40C4×Dic263—21no—
41C2×Q8×C263D411yescharacteristic
42C2×C8×C263—21no—
43C2×C8×C263—21no—
44C4⋊C4×C263—21no—
45C4⋊C4×C263D411yescharacteristic
46C42×C263—21no—
47C42×C263C2311yescharacteristic
48Dic526—21no—
49Dic526—21no—
50Dic526—41no—
51Dic526—41no—
52Dic526—41no—
53Dic526—41no—
54C2×Dic263—21no—
55C2×Dic263—21no—
56C2×Dic263—22no—
57C2×Dic263—41no—
58C263⋊C8—41no—
59Q8×C263—21no—
60Q8×C263Q1612yescomplemented
61C2×C4×C263—21no—
62C2×C4×C263—21no—
63C2×C4×C263C2×D411yescharacteristic
64C2×C4×C263C2×D411yescharacteristic
65C2×C4×C263C2×D411yescharacteristic
66C8×C263—22no—
67C8×C263—41no—
68C22×C263#12011yescharacteristic
69C4×C263—22no—
70C4×C263—21no—
71C4×C263—41no—
72C4×C263C2×Q1611yescharacteristic
73C4×C263#13511yescharacteristic
74C4×C263AGL(1,ℤ/8)11yescharacteristic
75C4×C263#13711yescharacteristic
76Dic263—41no—
77Dic263—42no—
78Dic263—41no—
79Dic263—81no—
80C2×C263#44911yescharacteristic
81C2×C263#45111yescharacteristic
82C2×C263#45611yescharacteristic
83C263#164811yescharacteristic, complemented, Sylow
84#1648—2631nomaximal, Sylow
85#557—2631no—
86#500—2631no—
87#475—2631no—
88#462—2631no—
89#332—2631no—
90Q8⋊C8—2631no—
91Q8⋊C8D26311yescharacteristic
92C2×Q16—5261no—
93C4⋊Q8—2631no—
94C4⋊Q8—2631no—
95C4⋊Q8—5261no—
96#125—5262no—
97#125—5261no—
98C4×Q8—2631no—
99C4×Q8—5261no—
100C4×Q8—5261no—
101C4×Q8C2×D26311yescharacteristic
102#107—5262no—
103#106—5261no—
104C4⋊C8—2631no—
105C4⋊C8C2×D26311yescharacteristic
106#103—5261no—
107#103—5261no—
108C4×C8C2×D26311yescharacteristic
109C2×Q8—2631no—
110C2×Q8—5261no—
111C2×Q8—5261no—
112C2×Q8D105211yescharacteristic
113Q16—10522no—
114C2×C8—21no—
115C2×C8—21no—
116C2×C8—5261no—
117C4⋊C4—21no—
118C4⋊C4—2631no—
119C4⋊C4—2632no—
120C4⋊C4—5262no—
121C4⋊C4—5262no—
122C4⋊C4—5262no—
123C4⋊C4—5261no—
124C4⋊C4—5261no—
125C4⋊C4—5261no—
126C4⋊C4—5261no—
127C4⋊C4D105211yescharacteristic
128C42—21no—
129C42—5262no—
130C42—5261no—
131C42C22×D26311yescharacteristic
132Q8—21no—
133Q8—5261no—
134Q8—5261no—
135Q8—10521no—
136Q8—10521no—
137Q8—10521no—
138Q8—10521no—
139Q8Dic105212yescomplemented
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—5261no—
143C2×C4—5262no—
144C2×C4—5261no—
145C2×C4—10521no—
146C2×C4D4×D26311yescharacteristic
147C2×C4D4×D26311yescharacteristic
148C2×C4C2×D105211yescharacteristic
149C8—22no—
150C8—41no—
151C8—10521no—
152C22#2255444011yescharacteristic
153C4—21no—
154C4—22no—
155C4—41no—
156C4—10521no—
157C4—10521no—
158C4—10522no—
159C4—21041no—
160C4C2×Dic105211yescharacteristic
161C4#2255449311yescharacteristic
162C4#2255449711yescharacteristic
163C4#2255450311yescharacteristic
164C2#3068208611yescharacteristic
165C2#3068209611yescharacteristic
166C2#3068212211yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
FittingQ8⋊C8×C263C2
socle, prime radicalC22×C263#120
hypercenterQ8⋊C8D263
hypocenterC263#1648
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
60. Q8×C263Q16semidirect
83. C263#1648semidirect
139. Q8Dic1052semidirect

Maximal subgroups

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

subgroupindex
#306826672
#306823432
#306822232
#306821492
#306816852
#306816702
Q8⋊C8×C2632
#1648263