Finite Group Databasebeta

← #46781101

Subgroups — #46781101

Order 33664.

204 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#22554460C211yesmaximal, characteristic
2#30681992C211yesmaximal, characteristic
3#30681988C211yesmaximal, characteristic
4#30681664C211yesmaximal, characteristic
5#30681663C211yesmaximal, characteristic
6#30681663C211yesmaximal, characteristic
7#324×C263C211yesmaximal, characteristic
8#22554460—21no—
9#22554460—21no—
10#22554460—21no—
11#22554460—21no—
12C2×C4⋊Dic263C411yescharacteristic
13C2×Dic263⋊C4C411yescharacteristic
14C2×Dic263⋊C4C411yescharacteristic
15C2×Dic263⋊C4C411yescharacteristic
16C2×Dic263⋊C4C2211yescharacteristic
17C2×C4×Dic263C2211yescharacteristic
18Dic263⋊C8—21no—
19Dic263⋊C8—21no—
20C22⋊(C263⋊C8)C2211yescharacteristic
21C22⋊(C263⋊C8)C2211yescharacteristic
22#22554380—21no—
23C8×Dic263—21no—
24C2×C4⋊C4×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic
26C22⋊C8×C263C2211yescharacteristic
27C22×Dic263C2×C411yescharacteristic
28C22×Dic263C2×C411yescharacteristic
29C22×Dic263C2×C411yescharacteristic
30C22×Dic263C2×C411yescharacteristic
31C2×C263⋊C8—21no—
32C2×C263⋊C8—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263—21no—
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×Dic263D411yescharacteristic
44C4×Dic263D411yescharacteristic
45C4×Dic263D411yescharacteristic
46C4×Dic263D411yescharacteristic
47C22×C4×C263C2×C411yescharacteristic
48C22×C4×C263C2×C411yescharacteristic
49C22×C4×C263C2311yescharacteristic
50C2×C8×C263—21no—
51C2×C8×C263—21no—
52C4⋊C4×C263—21no—
53C4⋊C4×C263—21no—
54C2×Dic263—21no—
55C2×Dic263—21no—
56C2×Dic263—22no—
57C2×Dic263—21no—
58C2×Dic263—21no—
59C2×Dic263—21no—
60C2×Dic263—21no—
61C2×Dic263—41no—
62C2×Dic263C22⋊C411yescharacteristic
63C2×Dic263C22⋊C411yescharacteristic
64C2×Dic263C22⋊C411yescharacteristic
65C2×Dic263C22⋊C411yescharacteristic
66C263⋊C8—41no—
67C263⋊C8—41no—
68C23×C263C22×C411yescharacteristic
69C2×C4×C263—21no—
70C2×C4×C263—21no—
71C2×C4×C263—21no—
72C2×C4×C263—21no—
73C2×C4×C263—41no—
74C2×C4×C263—41no—
75C2×C4×C263C2×D411yescharacteristic
76C2×C4×C263C2×D411yescharacteristic
77C8×C263—41no—
78C8×C263—41no—
79C22×C263—21no—
80C22×C263—21no—
81C22×C263C2×C22⋊C411yescharacteristic
82C22×C263#13111yescharacteristic
83C22×C263#13111yescharacteristic
84C4×C263—21no—
85C4×C263—21no—
86C4×C263—41no—
87C4×C263—41no—
88Dic263—21no—
89Dic263—21no—
90Dic263—21no—
91Dic263—41no—
92Dic263—41no—
93Dic263#10112yes—
94C2×C263—21no—
95C2×C263—21no—
96C2×C263#40811yescharacteristic
97C2×C263#41011yescharacteristic
98C2×C263C2×#10111yescharacteristic
99C263#147011yescharacteristic, complemented, Sylow
100#1470—2631nomaximal, Sylow
101C2×#125—2631no—
102#432—2631no—
103#431—2631no—
104#324—2631no—
105#324—2631no—
106#324—2631no—
107#324D26311yescharacteristic
108#125—5261no—
109#125—5261no—
110#125—5261no—
111#125—5261no—
112C2×C4⋊C4—2631no—
113C2×C4⋊C4—2631no—
114C2×C4⋊C4—2631no—
115C2×C4⋊C4—2631no—
116C2×C4⋊C4—2631no—
117C2×C4⋊C4C2×D26311yescharacteristic
118C2×C42—2631no—
119C4⋊C8—5261no—
120C4⋊C8—5261no—
121C22⋊C8—2631no—
122C22⋊C8—2631no—
123C22⋊C8C2×D26311yescharacteristic
124C22⋊C8C2×D26311yescharacteristic
125#97—5261no—
126C4×C8—5261no—
127C22×C4—2631no—
128C22×C4—2631no—
129C22×C4—2631no—
130C22×C4—2631no—
131C22×C4C4×D26311yescharacteristic
132C22×C4C4×D26311yescharacteristic
133C22×C4C22×D26311yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—5261no—
137C2×C8—5261no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—5261no—
141C4⋊C4—5261no—
142C4⋊C4—5261no—
143C4⋊C4—5261no—
144C4⋊C4—5261no—
145C4⋊C4—5261no—
146C4⋊C4—5261no—
147C4⋊C4—5261no—
148C4⋊C4—5261no—
149C4⋊C4—5261no—
150C42—2631no—
151C42—2631no—
152C42—2631no—
153C42—2631no—
154C23C2×C4×D26311yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—2631no—
162C2×C4—2631no—
163C2×C4—2631no—
164C2×C4—2631no—
165C2×C4—5262no—
166C2×C4—5261no—
167C2×C4—5261no—
168C2×C4—5261no—
169C2×C4—5261no—
170C2×C4—5261no—
171C2×C4—5261no—
172C2×C4—10521no—
173C2×C4D4×D26311yescharacteristic
174C2×C4D4×D26311yescharacteristic
175C8—41no—
176C8—41no—
177C8—10521no—
178C8—10521no—
179C22—21no—
180C22—21no—
181C22C22⋊C4×D26311yescharacteristic
182C22#2255447611yescharacteristic
183C22#2255447811yescharacteristic
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—2632no—
189C4—5261no—
190C4—5261no—
191C4—5261no—
192C4—10521no—
193C4—10521no—
194C2—21no—
195C2—21no—
196C2#3068190311yescharacteristic
197C2#3068191011yescharacteristic
198C2#101×D26311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutator, prime radicalC23×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#324×C263C2
socleC22×C263C2×C22⋊C4
cosocleC22×C4×C263C23
hypercenter#324D263
hypocenterC263#1470
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
99. C263#1470semidirect

Maximal subgroups

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

subgroupindex
C2×#225544602
#306819922
#306819882
#306816642
#306816632
#324×C2632
#1470263