Finite Group Databasebeta

← #46781918

Subgroups — #46781918

Order 33664.

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

normal subgroups only

This group has 194 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#30682661C211yesmaximal, characteristic
2#30682288C211yesmaximal, characteristic, complemented
3#30682225C211yesmaximal, characteristic
4#30681683C211yesmaximal, characteristic, complemented
5Q8⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic
7#477×C263C211yesmaximal, characteristic, complemented
8#22554470C2211yescharacteristic
9#22554465—22no—
10#22554458—21no—
11#22554446—21no—
12C4×Dic526—21no—
13C4×D1052C2211yescharacteristic
14#22554428—21no—
15#22554401—21no—
16C4⋊(C263⋊C8)C2211yescharacteristic
17#22554394—22no—
18#22554390—21no—
19C4×C263⋊C8C2211yescharacteristic
20C4⋊Q8×C263C2211yescharacteristic
21C4×Q8×C263C2211yescharacteristic
22#107×C263—21no—
23C4⋊C8×C263C2211yescharacteristic
24#103×C263—21no—
25C2×Dic526—21no—
26C2×D1052D411yescharacteristic
27C2×C4×D263—21no—
28C2×C263⋊C8—21no—
29C2×C263⋊C8—21no—
30C4⋊Dic263—21no—
31C4⋊Dic263D412yes—
32C4⋊Dic263D411yescharacteristic
33Dic263⋊C4—22no—
34(C2×D263)⋊C4—22no—
35(C2×D263)⋊C4—22no—
36(C2×D263)⋊C4—21no—
37C4×Dic263—22no—
38C2×Q8×C263—21no—
39C2×Q8×C263D411yescharacteristic
40C2×C8×C263—21no—
41C4⋊C4×C263—21no—
42C4⋊C4×C263—21no—
43C4⋊C4×C263—21no—
44C4⋊C4×C263D411yescharacteristic
45C42×C263—21no—
46C42×C263C2311yescharacteristic
47C22×D263—21no—
48Dic526—41no—
49Dic526—41no—
50D1052—21no—
51D1052—21no—
52C2×Dic263—21no—
53C2×Dic263—22no—
54C4×D263—41no—
55C4×D263—41no—
56C263⋊C8—41no—
57C263⋊C8—41no—
58Q8×C263—21no—
59Q8×C263—21no—
60Q8×C263—42no—
61C2×C4×C263—21no—
62C2×C4×C263—21no—
63C2×C4×C263—41no—
64C2×C4×C263C2×D411yescharacteristic
65C2×C4×C263C2×D411yescharacteristic
66C2×C4×C263C2×D411yescharacteristic
67C8×C263—41no—
68C22×C263#12011yescharacteristic
69C2×D263—41no—
70C2×D263—41no—
71C2×D263—41no—
72C4×C263—21no—
73C4×C263—41no—
74C4×C263—41no—
75C4×C263—81no—
76C4×C263#13511yescharacteristic
77C4×C263#13511yescharacteristic
78C4×C263#13711yescharacteristic
79C4×C263#13711yescharacteristic
80Dic263—41no—
81Dic263—42no—
82C2×C263#45211yescharacteristic
83C2×C263#45211yescharacteristic
84C2×C263#45411yescharacteristic
85D263—81no—
86C263#163811yescharacteristic, complemented, Sylow
87#1638—2631nomaximal, Sylow
88#556—2631no—
89#487—2631no—
90#477D26311yescharacteristic, complemented
91#476—2631no—
92#332—2631no—
93Q8⋊C8—2631no—
94D4⋊C8—2631no—
95C4⋊Q8—2631no—
96C4⋊Q8C2×D26311yescharacteristic
97#126—5262no—
98#124—5261no—
99C22⋊Q8—5261no—
100C4×Q8—5261no—
101C4×Q8C2×D26311yescharacteristic
102C4×D4—2631no—
103#117—5261no—
104#107—21no—
105#106—5261no—
106C4⋊C8—2631no—
107C4⋊C8C2×D26311yescharacteristic
108#103—21no—
109#103—5262no—
110#102—5261no—
111C4×C8—2631no—
112C2×Q8—21no—
113C2×Q8—5261no—
114C2×Q8C22⋊D26311yescharacteristic
115C2×D4—2631no—
116C22×C4—5261no—
117C2×C8—21no—
118C2×C8—5261no—
119C2×C8—5261no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—2632no—
124C4⋊C4—2631no—
125C4⋊C4—5262no—
126C4⋊C4—5261no—
127C4⋊C4C22⋊D26311yescharacteristic
128C22⋊C4—5262no—
129C22⋊C4—5262no—
130C22⋊C4—5261no—
131C42—21no—
132C42—5262no—
133C42C22×D26311yescharacteristic
134C23—5261no—
135Q8—21no—
136Q8—21no—
137Q8—42no—
138Q8—10521no—
139Q8—10521no—
140D4—5261no—
141D4—5261no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—5261no—
146C2×C4—5262no—
147C2×C4—10521no—
148C2×C4—10521no—
149C2×C4D4×D26311yescharacteristic
150C2×C4D4×D26311yescharacteristic
151C2×C4C2×C22⋊D26311yescharacteristic
152C8—41no—
153C8—10521no—
154C8—10521no—
155C22—10521no—
156C22—10521no—
157C22—10521no—
158C22#2255443811yescharacteristic
159C4—21no—
160C4—41no—
161C4—41no—
162C4—81no—
163C4—10521no—
164C4—10522no—
165C4#2255449011yescharacteristic
166C4#2255449311yescharacteristic
167C4#2255450111yescharacteristic
168C4#2255450211yescharacteristic
169C2—21041no—
170C2#3068209811yescharacteristic
171C2#3068209911yescharacteristic
172C2#3068210911yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#477×C263C2
socleC22×C263#120
prime radicalC2×D1052D4
hypercenter#477D263
hypocenterC263#1638
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #30682288C2semidirect
4. #30681683C2semidirect
5. Q8⋊(C263⋊C8)C2semidirect
7. #477×C263C2semidirect
86. C263#1638semidirect
90. #477D263semidirect

Maximal subgroups

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

subgroupindex
#306826612
#306822882
#306822252
#306816832
Q8⋊(C263⋊C8)2
#306816652
#477×C2632
#1638263