Finite Group Databasebeta

← #46782074

Subgroups — #46782074

Order 33664.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C263⋊#564C211yesmaximal, characteristic
2#30682344C211yesmaximal, characteristic
3#30682306C211yesmaximal, characteristic
4#30681680C211yesmaximal, characteristic
5#30681679C211yesmaximal, characteristic
6#30681679C211yesmaximal, characteristic
7#501×C263C211yesmaximal, characteristic
8#22554462C2211yescharacteristic
9#22554462C2211yescharacteristic
10#22554461—21no—
11#22554461—21no—
12#22554460—21no—
13#22554460—21no—
14#22554460—21no—
15#22554460—21no—
16#22554403—21no—
17#22554401—21no—
18#22554394—21no—
19#22554394—21no—
20#22554381C2211yescharacteristic
21#22554381C2211yescharacteristic
22C4⋊Q8×C263C2211yescharacteristic
23#125×C263C2211yescharacteristic
24#107×C263—21no—
25#106×C263—21no—
26#97×C263C2211yescharacteristic
27C2×C263⋊C8—21no—
28C2×C263⋊C8—21no—
29C4⋊Dic263—21no—
30C4⋊Dic263—21no—
31C4⋊Dic263D411yescharacteristic
32C4⋊Dic263D411yescharacteristic
33C4⋊Dic263D411yescharacteristic
34C4⋊Dic263D411yescharacteristic
35Dic263⋊C4—21no—
36Dic263⋊C4—21no—
37Dic263⋊C4—21no—
38Dic263⋊C4—21no—
39Dic263⋊C4—21no—
40Dic263⋊C4—21no—
41Dic263⋊C4—21no—
42Dic263⋊C4—21no—
43C4×Dic263—21no—
44C4×Dic263—21no—
45C2×Q8×C263—21no—
46C2×C8×C263—21no—
47C4⋊C4×C263—21no—
48C4⋊C4×C263—21no—
49C4⋊C4×C263—21no—
50C4⋊C4×C263—21no—
51C4⋊C4×C263D411yescharacteristic
52C4⋊C4×C263D411yescharacteristic
53C42×C263C2311yescharacteristic
54C2×Dic263—21no—
55C2×Dic263—21no—
56C2×Dic263—21no—
57C2×Dic263—21no—
58C263⋊C8—22no—
59C263⋊C8—41no—
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—22no—
68C22×C263#12011yescharacteristic
69C4×C263—21no—
70C4×C263—21no—
71C4×C263—21no—
72C4×C263—41no—
73C4×C263—41no—
74C4×C263—81no—
75Dic263—41no—
76Dic263—41no—
77Dic263—41no—
78Dic263—41no—
79C2×C263#45411yescharacteristic
80C2×C263#45611yescharacteristic
81C2×C263#45611yescharacteristic
82C263#166311yescharacteristic, complemented, Sylow
83#1663—2631nomaximal, Sylow
84#564—2631no—
85#501—2631no—
86#501D26311yescharacteristic
87#491—2631no—
88#330—2631no—
89#330—2631no—
90#330—2631no—
91C4⋊Q8C2×D26311yescharacteristic
92#125—2631no—
93#125—2631no—
94#125—5261no—
95#125—5261no—
96#125—5261no—
97#125—5261no—
98#125—5261no—
99#125—5261no—
100#125C2×D26311yescharacteristic
101#107—21no—
102#107—5261no—
103#106—21no—
104#106—5261no—
105#103—5261no—
106#103—5261no—
107#97—2631no—
108#97—2631no—
109#97C2×D26311yescharacteristic
110C2×Q8—21no—
111C2×C8—21no—
112C2×C8—5261no—
113C2×C8—5261no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—2631no—
119C4⋊C4—2631no—
120C4⋊C4—2631no—
121C4⋊C4—2631no—
122C4⋊C4—5261no—
123C4⋊C4—5261no—
124C4⋊C4—5261no—
125C4⋊C4—5261no—
126C4⋊C4—5261no—
127C4⋊C4—5261no—
128C4⋊C4—5261no—
129C4⋊C4—5261no—
130C4⋊C4—5261no—
131C4⋊C4—5261no—
132C4⋊C4C22⋊D26311yescharacteristic
133C4⋊C4C22⋊D26311yescharacteristic
134C42—5261no—
135C42—5261no—
136C42C22×D26311yescharacteristic
137Q8—42no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—5261no—
142C2×C4—5261no—
143C2×C4—5261no—
144C2×C4—5261no—
145C2×C4D4×D26311yescharacteristic
146C2×C4D4×D26311yescharacteristic
147C2×C4C2×C22⋊D26311yescharacteristic
148C8—22no—
149C8—5262no—
150C8—10521no—
151C22#2255443811yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—81no—
158C4—10521no—
159C4—10521no—
160C4—10521no—
161C4—10521no—
162C2#3068210911yescharacteristic
163C2#3068211911yescharacteristic
164C2#3068212011yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#501×C263C2
socle, prime radicalC22×C263#120
hypercenter#501D263
hypocenterC263#1663
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
82. C263#1663semidirect

Maximal subgroups

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

subgroupindex
C263⋊#5642
#306823442
#306823062
#306816802
#306816792
#501×C2632
#1663263