Finite Group Databasebeta

← #46781366

Subgroups — #46781366

Order 33664.

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

normal subgroups only

This group has 218 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#30682473C211yesmaximal, characteristic
2#30681993C211yesmaximal, characteristic, complemented
3#97×D263C211yesmaximal, characteristic, complemented
4#30681680C211yesmaximal, characteristic, complemented
5#30681677C211yesmaximal, characteristic, complemented
6#30681677C211yesmaximal, characteristic, complemented
7#330×C263C211yesmaximal, characteristic, complemented
8C2×C8×D263—21no—
9#22554465—21no—
10#22554458C2211yescharacteristic
11#22554455—21no—
12#22554450C411yescharacteristic
13#22554445C411yescharacteristic
14#22554435C411yescharacteristic
15#22554432—21no—
16#22554432C411yescharacteristic
17#22554428—21no—
18C42×D263C2211yescharacteristic
19Dic263⋊C8—21no—
20(C2×D263)⋊C8—21no—
21#22554381C2211yescharacteristic
22#22554381C2211yescharacteristic
23#22554380—21no—
24#125×C263C2211yescharacteristic
25#97×C263C2211yescharacteristic
26#97×C263C2211yescharacteristic
27C2×Dic526C2×C411yescharacteristic
28C2×D1052—21no—
29C2×D1052C2×C411yescharacteristic
30C2×C4×D263—21no—
31C2×C4×D263C2×C411yescharacteristic
32C2×C4×D263D411yescharacteristic
33C2×C4×D263D411yescharacteristic
34C2×C263⋊C8—21no—
35C2×C263⋊C8—21no—
36C8×D263—24no—
37C4⋊Dic263—21no—
38Dic263⋊C4—21no—
39(C2×D263)⋊C4—21no—
40(C2×D263)⋊C4—21no—
41(C2×D263)⋊C4—21no—
42(C2×D263)⋊C4—21no—
43(C2×D263)⋊C4—21no—
44C4×Dic263—21no—
45C4×Dic263C2×C411yescharacteristic
46C4×Dic263D411yescharacteristic
47C4×Dic263D411yescharacteristic
48C2×C8×C263—21no—
49C2×C8×C263—21no—
50C4⋊C4×C263—21no—
51C4⋊C4×C263—21no—
52C4⋊C4×C263C2×C411yescharacteristic
53C4⋊C4×C263C2×C411yescharacteristic
54C42×C263C2311yescharacteristic
55C22×D263—21no—
56C22×D263C22⋊C411yescharacteristic
57Dic526—41no—
58D1052—41no—
59D1052—42no—
60C2×Dic263—21no—
61C2×Dic263C22⋊C411yescharacteristic
62C2×Dic263C22⋊C411yescharacteristic
63C2×Dic263C22⋊C411yescharacteristic
64C4×D263—22no—
65C4×D263—41no—
66C4×D263—41no—
67C4×D263—42no—
68C263⋊C8—22no—
69C263⋊C8—41no—
70C2×C4×C263—21no—
71C2×C4×C263—21no—
72C2×C4×C263C22×C411yescharacteristic
73C2×C4×C263C2×D411yescharacteristic
74C2×C4×C263C2×D411yescharacteristic
75C8×C263—22no—
76C8×C263—41no—
77C22×C263C2×C22⋊C411yescharacteristic
78C2×D263—21no—
79C2×D263—21no—
80C2×D263—41no—
81C2×D263—41no—
82C2×D263—41no—
83C2×D263#10412yes—
84C4×C263—21no—
85C4×C263—21no—
86C4×C263—21no—
87C4×C263—41no—
88C4×C263—41no—
89Dic263—21no—
90Dic263—21no—
91Dic263—21no—
92Dic263—41no—
93C2×C263#41311yescharacteristic
94C2×C263C2×#10411yescharacteristic
95C2×C263#42111yescharacteristic
96D263—22no—
97D263—81no—
98C263#153211yescharacteristic, complemented, Sylow
99#1532—2631nomaximal, Sylow
100#529—2631no—
101#432—2631no—
102C2×#97—2631no—
103#330—2631no—
104#330D26311yescharacteristic, complemented
105#329—2631no—
106#329—2631no—
107C22×C8—5261no—
108#126—5261no—
109#125C2×D26311yescharacteristic
110#124—2631no—
111#123—5261no—
112C22⋊Q8—2631no—
113#121—2631no—
114C4×Q8—2631no—
115C4×D4—2631no—
116C4×D4—5261no—
117#117—5261no—
118C2×C42—2631no—
119C4⋊C8—5261no—
120C22⋊C8—5261no—
121#97—2631no—
122#97—2631no—
123#97—5261no—
124#97C2×D26311yescharacteristic
125#97C2×D26311yescharacteristic
126C2×Q8—2631no—
127C2×D4—2631no—
128C2×D4—5261no—
129C22×C4—2631no—
130C22×C4—2631no—
131C22×C4—2631no—
132C22×C4—5261no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—5264no—
136C2×C8—5261no—
137C2×C8—5261no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—5261no—
141C4⋊C4—5261no—
142C4⋊C4C4×D26311yescharacteristic
143C4⋊C4C4×D26311yescharacteristic
144C22⋊C4—5261no—
145C22⋊C4—5261no—
146C22⋊C4—5261no—
147C22⋊C4—5261no—
148C22⋊C4—5261no—
149C42—2631no—
150C42—2631no—
151C42—2631no—
152C42—5261no—
153C42C22×D26311yescharacteristic
154C23—2631no—
155C23—5261no—
156Q8—10521no—
157D4—10521no—
158D4—10522no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—2631no—
162C2×C4—2631no—
163C2×C4—2631no—
164C2×C4—5262no—
165C2×C4—5261no—
166C2×C4—10521no—
167C2×C4—10521no—
168C2×C4—10522no—
169C2×C4C2×C4×D26311yescharacteristic
170C2×C4D4×D26311yescharacteristic
171C2×C4D4×D26311yescharacteristic
172C8—22no—
173C8—41no—
174C8—5262no—
175C8—10521no—
176C22—2632no—
177C22—5261no—
178C22—5261no—
179C22—10521no—
180C22—10521no—
181C22—10521no—
182C22C22⋊C4×D26311yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—5261no—
189C4—5261no—
190C4—5261no—
191C4—10521no—
192C2—5262no—
193C2—21041no—
194C2#3068192111yescharacteristic
195C2#104×D26311yescharacteristic
196C2#3068195311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
Fitting#330×C263C2
socleC22×C263C2×C22⋊C4
prime radical#22554445C4
cosocleC42×C263C23
hypercenter#330D263
hypocenterC263#1532
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #30681993C2semidirect
3. #97×D263C2semidirect
4. #30681680C2semidirect
5. #30681677C2semidirect
6. #30681677C2semidirect
7. #330×C263C2semidirect
98. C263#1532semidirect
104. #330D263semidirect

Maximal subgroups

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

subgroupindex
#306824732
#306819932
#97×D2632
#306816802
#306816772
#330×C2632
#1532263