Finite Group Databasebeta

← #46781369

Subgroups — #46781369

Order 33664.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D263C211yesmaximal, characteristic
2#30681993C212yesmaximal, complemented
3#30681678C211yesmaximal, characteristic, complemented
4#30681677C212yesmaximal, complemented
5#329×C263C211yesmaximal, characteristic, complemented
6C2×Q8×D263C411yescharacteristic
7C2×D4×D263C411yescharacteristic
8#22554459C411yescharacteristic
9#22554458C2211yescharacteristic
10#22554457C411yescharacteristic
11#22554456—22no—
12C22⋊C4×D263—22no—
13C42×D263C2211yescharacteristic
14Dic263⋊C8—22no—
15(C2×D263)⋊C8—22no—
16#22554381C2212yescomplemented
17#124×C263C2211yescharacteristic
18#97×C263C2212yescomplemented
19C23×D263—21no—
20C2×Dic526—21no—
21C2×Dic526C2×C411yescharacteristic
22Q8×D263—42no—
23C2×D1052C2×C411yescharacteristic
24C2×C22⋊D263—21no—
25D4×D263—42no—
26C2×C4×D263—21no—
27C2×C4×D263C2×C411yescharacteristic
28C2×C4×D263D412yes—
29C2×C263⋊C8—22no—
30C22⋊Dic263—22no—
31(C2×D263)⋊C4—22no—
32(C2×D263)⋊C4—22no—
33C4×Dic263C2×C411yescharacteristic
34C4×Dic263D412yes—
35C2×Q8×C263C2×C411yescharacteristic
36C2×D4×C263C2×C411yescharacteristic
37C2×C8×C263—22no—
38C22⋊C4×C263—22no—
39C42×C263C2311yescharacteristic
40C22×D263—21no—
41C22×D263—44no—
42C22×D263—42no—
43C22×D263C22⋊C411yescharacteristic
44Dic526—42no—
45Dic526—41no—
46D1052—41no—
47C22⋊D263—42no—
48C2×Dic263—21no—
49C2×Dic263C22⋊C412yes—
50C2×Dic263C22⋊C411yescharacteristic
51C4×D263—22no—
52C4×D263—42no—
53C4×D263—42no—
54C263⋊C8—42no—
55C23×C263—21no—
56Q8×C263—41no—
57D4×C263—41no—
58C2×C4×C263—21no—
59C2×C4×C263C22×C411yescharacteristic
60C2×C4×C263C2×D412yes—
61C8×C263—42no—
62C22×C263—41no—
63C22×C263—42no—
64C22×C263C2×C22⋊C411yescharacteristic
65C2×D263—22no—
66C2×D263—41no—
67C2×D263—42no—
68C2×D263—84no—
69C2×D263#10012yes—
70C4×C263—21no—
71C4×C263—22no—
72C4×C263—41no—
73Dic263—21no—
74Dic263—22no—
75Dic263—41no—
76C2×C263—81no—
77C2×C263C2×#10011yescharacteristic
78C2×C263#42112yes—
79D263—22no—
80D263—81no—
81C263#153311yescharacteristic, complemented, Sylow
82#1533—2631nomaximal, Sylow
83C2×#124—2631no—
84#432—2632no—
85#329—2631no—
86#329—2632no—
87#329D26311yescharacteristic, complemented
88C22×Q8—2631no—
89C22×D4—2631no—
90#124—2631no—
91#124—2631no—
92#124—2631no—
93#124—5262no—
94#124C2×D26311yescharacteristic
95C2×C22⋊C4—5262no—
96C2×C42—2631no—
97C4⋊C8—5262no—
98C22⋊C8—5262no—
99#97—2632no—
100#97C2×D26312yescomplemented
101C24—5261no—
102C2×Q8—2631no—
103C2×Q8—5261no—
104C2×Q8—10522no—
105C2×Q8C4×D26311yescharacteristic
106C2×D4—2631no—
107C2×D4—5261no—
108C2×D4—10522no—
109C2×D4C4×D26311yescharacteristic
110C22×C4—2631no—
111C22×C4—2632no—
112C22×C4—5261no—
113C2×C8—22no—
114C2×C8—5262no—
115C22⋊C4—22no—
116C22⋊C4—5262no—
117C22⋊C4—5262no—
118C22⋊C4—5262no—
119C42—2631no—
120C42—2632no—
121C42C22×D26311yescharacteristic
122C23—21no—
123C23—2631no—
124C23—5261no—
125C23—10522no—
126C23—10524no—
127Q8—41no—
128Q8—10521no—
129Q8—10522no—
130D4—41no—
131D4—10521no—
132D4—10522no—
133C2×C4—21no—
134C2×C4—2632no—
135C2×C4—2631no—
136C2×C4—5262no—
137C2×C4—5261no—
138C2×C4—10522no—
139C2×C4—10522no—
140C2×C4C2×C4×D26311yescharacteristic
141C2×C4D4×D26312yes—
142C8—42no—
143C8—10522no—
144C22—41no—
145C22—42no—
146C22—2632no—
147C22—5262no—
148C22—10521no—
149C22—10522no—
150C22—21044no—
151C22C22⋊C4×D26311yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—5261no—
156C4—5262no—
157C4—10521no—
158C2—81no—
159C2—5262no—
160C2—21041no—
161C2#100×D26311yescharacteristic
162C2#3068195312yes—
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
Fitting#329×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC2×D4×D263C4
cosocleC42×C263C23
hypercenter#329D263
hypocenterC263#1533
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #30681993C2semidirect
3. #30681678C2semidirect
4. #30681677C2semidirect
5. #329×C263C2semidirect
16. #22554381C22semidirect
18. #97×C263C22semidirect
81. C263#1533semidirect
87. #329D263semidirect
100. #97C2×D263semidirect

Maximal subgroups

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

subgroupindex
#124×D2632
#306819932
#306816782
#306816772
#329×C2632
#1533263