Finite Group Databasebeta

← #46781870

Subgroups — #46781870

Order 33664.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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#30682673C211yesmaximal, characteristic
2#30682311C211yesmaximal, characteristic
3#30682234C211yesmaximal, characteristic, complemented
4#30682233C211yesmaximal, characteristic, complemented
5#30681681C211yesmaximal, characteristic
6#30681670C211yesmaximal, characteristic, complemented
7Q8⋊C8×C263C211yesmaximal, characteristic, complemented
8C2×#16862365—22no—
9#22554470C2211yescharacteristic
10#22554467C2211yescharacteristic
11#22554459—21no—
12#22554458—21no—
13#22554455—22no—
14C4×Dic526C2211yescharacteristic
15C4×D1052—21no—
16#22554432—21no—
17#22554404—21no—
18#22554403—21no—
19C4⋊(C263⋊C8)C2211yescharacteristic
20#22554395—21no—
21#22554394—21no—
22C4×Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4×C8×C263C2211yescharacteristic
25C2×Dic526—21no—
26C2×Dic526D411yescharacteristic
27C2×D1052—21no—
28C2×D1052—21no—
29C2×D1052D412yes—
30C2×C4×D263—22no—
31#16862365—44no—
32C2×C263⋊C8—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263D411yescharacteristic
36Dic263⋊C4—21no—
37(C2×D263)⋊C4—22no—
38(C2×D263)⋊C4—22no—
39(C2×D263)⋊C4—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
48C22×D263—22no—
49Dic526—21no—
50Dic526—21no—
51Dic526—42no—
52D1052—42no—
53D1052—41no—
54D1052—41no—
55D1052—41no—
56D1052—41no—
57C2×Dic263—21no—
58C2×Dic263—21no—
59C2×Dic263—41no—
60C4×D263—82no—
61C263⋊C8—41no—
62Q8×C263—21no—
63Q8×C263—21no—
64C2×C4×C263—21no—
65C2×C4×C263—21no—
66C2×C4×C263C2×D411yescharacteristic
67C2×C4×C263C2×D411yescharacteristic
68C2×C4×C263C2×D411yescharacteristic
69C8×C263—22no—
70C8×C263—41no—
71C22×C263#12011yescharacteristic
72C2×D263—42no—
73C2×D263—42no—
74C2×D263—42no—
75C4×C263—21no—
76C4×C263—41no—
77C4×C263—41no—
78C4×C263#13511yescharacteristic
79C4×C263#13511yescharacteristic
80C4×C263#13711yescharacteristic
81C4×C263#13711yescharacteristic
82Dic263—41no—
83Dic263—41no—
84Dic263—81no—
85C2×C263#45211yescharacteristic
86C2×C263#45211yescharacteristic
87C2×C263#45311yescharacteristic
88D263—82no—
89C263#163011yescharacteristic, complemented, Sylow
90#1630—2631nomaximal, Sylow
91#559—2631no—
92#492—2631no—
93#477—2631no—
94#477—2631no—
95#331—2631no—
96Q8⋊C8—2631no—
97Q8⋊C8D26311yescharacteristic, complemented
98C2×SD16—5262no—
99C4⋊Q8—2631no—
100#127—2631no—
101#124—5261no—
102#124—5261no—
103#123—5262no—
104C4×Q8—2631no—
105C4×Q8C2×D26311yescharacteristic
106C4×D4—5261no—
107C4×D4—5261no—
108#107—5261no—
109#107—5261no—
110C4⋊C8—2631no—
111C4⋊C8C2×D26311yescharacteristic
112#103—5261no—
113#103—5261no—
114C4×C8C2×D26311yescharacteristic
115C2×Q8—2631no—
116C2×Q8—5261no—
117C2×Q8D105211yescharacteristic
118C2×D4—2632no—
119C2×D4—5261no—
120C2×D4—5261no—
121C22×C4—5262no—
122SD16—10524no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—5261no—
126C4⋊C4—21no—
127C4⋊C4—2631no—
128C4⋊C4—5261no—
129C4⋊C4—5261no—
130C4⋊C4—5261no—
131C4⋊C4D105211yescharacteristic
132C22⋊C4—5262no—
133C22⋊C4—5262no—
134C22⋊C4—5262no—
135C42—21no—
136C42—5261no—
137C42C22×D26311yescharacteristic
138C23—5262no—
139Q8—21no—
140Q8—21no—
141Q8—5261no—
142Q8—5261no—
143Q8—10522no—
144D4—10522no—
145D4—10521no—
146D4—10521no—
147D4—10521no—
148D4—10521no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—5261no—
152C2×C4—5261no—
153C2×C4—10521no—
154C2×C4—21042no—
155C2×C4D4×D26311yescharacteristic
156C2×C4D4×D26311yescharacteristic
157C2×C4C2×D105211yescharacteristic
158C8—22no—
159C8—41no—
160C8—10521no—
161C22—10522no—
162C22—10522no—
163C22—10522no—
164C22#2255444011yescharacteristic
165C4—21no—
166C4—41no—
167C4—41no—
168C4—10521no—
169C4—10521no—
170C4—21041no—
171C4#2255449111yescharacteristic
172C4#2255449211yescharacteristic
173C4#2255450211yescharacteristic
174C4#2255450311yescharacteristic
175C2—21042no—
176C2#3068210211yescharacteristic
177C2#3068210311yescharacteristic
178C2#3068210711yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
FittingQ8⋊C8×C263C2
socleC22×C263#120
prime radical#22554467C22
hypercenterQ8⋊C8D263
hypocenterC263#1630
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
3. #30682234C2semidirect
4. #30682233C2semidirect
6. #30681670C2semidirect
7. Q8⋊C8×C263C2semidirect
89. C263#1630semidirect
97. Q8⋊C8D263semidirect

Maximal subgroups

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

subgroupindex
#306826732
#306823112
#306822342
#306822332
#306816812
#306816702
Q8⋊C8×C2632
#1630263