Finite Group Databasebeta

← #46781791

Subgroups — #46781791

Order 33664.

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

normal subgroups only

This group has 202 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#30682569C211yesmaximal, characteristic
2#30682274C212yesmaximal
3#30681877C211yesmaximal, characteristic
4#30681676C212yesmaximal
5#324×C263C211yesmaximal, characteristic
6#22554469—22no—
7#22554461—22no—
8#22554449—21no—
9#22554449C2212yes—
10#22554429—21no—
11C2×C4⋊Dic263C2211yescharacteristic
12#22554404—22no—
13#22554395—22no—
14C263⋊#95—21no—
15C263⋊#95—21no—
16C263⋊#95C2211yescharacteristic
17C2×C4⋊C4×C263C2211yescharacteristic
18C22⋊C8×C263C2212yes—
19C2×Dic526—21no—
20C2×Dic526D412yes—
21C22×Dic263—21no—
22C22×Dic263—21no—
23C4⋊Dic263—21no—
24C4⋊Dic263—21no—
25C4⋊Dic263—21no—
26C4⋊Dic263—22no—
27C4⋊Dic263D412yes—
28Dic263⋊C4—22no—
29Dic263⋊C4—22no—
30C22⋊Dic263—22no—
31C4×Dic263—22no—
32C22×C4×C263D411yescharacteristic
33C22×C4×C263D411yescharacteristic
34C22×C4×C263C2311yescharacteristic
35C2×C8×C263—22no—
36C4⋊C4×C263—22no—
37Dic526—42no—
38Dic526—81no—
39C2×Dic263—22no—
40C2×Dic263—22no—
41C2×Dic263—41no—
42C2×Dic263—41no—
43C2×Dic263—42no—
44C2×Dic263—41no—
45C2×Dic263—41no—
46C23×C263C2×D411yescharacteristic
47C2×C4×C263—21no—
48C2×C4×C263—21no—
49C2×C4×C263—21no—
50C2×C4×C263—41no—
51C2×C4×C263—41no—
52C2×C4×C263Q1612yes—
53C2×C4×C263C2×D412yes—
54C8×C263—42no—
55C22×C263—21no—
56C22×C263—21no—
57C22×C263#12011yescharacteristic
58C22×C263C2×Q1611yescharacteristic
59C22×C263#13711yescharacteristic
60C4×C263—22no—
61C4×C263—22no—
62C4×C263—41no—
63Dic263—42no—
64Dic263—42no—
65Dic263—81no—
66Dic263—81no—
67C2×C263—21no—
68C2×C263—21no—
69C2×C263#45111yescharacteristic
70C2×C263#45411yescharacteristic
71C2×C263#45811yescharacteristic
72C263#161711yescharacteristic, complemented, Sylow
73#1617—2631nomaximal, Sylow
74#544—2631no—
75#484—2632no—
76#400—2631no—
77#328—2632no—
78#324D26311yescharacteristic
79C4⋊Q8—5262no—
80#125—5262no—
81C22⋊Q8—2632no—
82C22⋊Q8—5261no—
83#117—5261no—
84C2×C4⋊C4—2631no—
85C2×C4⋊C4C2×D26311yescharacteristic
86#107—5262no—
87#103—5262no—
88C22⋊C8C2×D26312yes—
89#95—2631no—
90#95—5261no—
91#95—5261no—
92C2×Q8—2632no—
93C2×Q8—5261no—
94C22×C4—5261no—
95C22×C4—5261no—
96C22×C4D105211yescharacteristic
97C22×C4D105211yescharacteristic
98C22×C4C22×D26311yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—2632no—
102C4⋊C4—5261no—
103C4⋊C4—5261no—
104C4⋊C4—5261no—
105C4⋊C4—5262no—
106C4⋊C4—5262no—
107C4⋊C4—5262no—
108C22⋊C4—5262no—
109C42—5262no—
110C23C2×D105211yescharacteristic
111Q8—10522no—
112Q8—21041no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—5262no—
119C2×C4—5262no—
120C2×C4—10521no—
121C2×C4—10521no—
122C2×C4—10522no—
123C2×C4—10521no—
124C2×C4—10521no—
125C2×C4Dic105212yes—
126C2×C4D4×D26312yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#2255444011yescharacteristic
131C22C2×Dic105211yescharacteristic
132C22#2255450311yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—10522no—
137C4—10522no—
138C4—21041no—
139C4—21041no—
140C2—21no—
141C2—21no—
142C2#3068209611yescharacteristic
143C2#3068211311yescharacteristic
144C2#3068212911yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#324×C263C2
socleC22×C263#120
prime radicalC23×C263C2×D4
hypercenter#324D263
hypocenterC263#1617
LCSG ▷ C22×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
72. C263#1617semidirect

Maximal subgroups

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

subgroupindex
#306825692
#306822742
#306818772
#306816762
#324×C2632
#1617263