Finite Group Databasebeta

← #46781776

Subgroups — #46781776

Order 33664.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#30682535C211yesmaximal, characteristic
2#30682273C211yesmaximal, characteristic, complemented
3#30682256C211yesmaximal, characteristic
4#30681674C211yesmaximal, characteristic, complemented
5#30681671C211yesmaximal, characteristic
6#30681664C211yesmaximal, characteristic, complemented
7#400×C263C211yesmaximal, characteristic, complemented
8#22554465—21no—
9#22554460—21no—
10#22554455—21no—
11#22554453—21no—
12#22554449C2211yescharacteristic
13#22554448—21no—
14#22554444C2211yescharacteristic
15C4×C22⋊D263—21no—
16#22554403—21no—
17#22554401—21no—
18#22554393—21no—
19#22554390—21no—
20C22⋊(C263⋊C8)C2211yescharacteristic
21C22⋊(C263⋊C8)C2211yescharacteristic
22C2×C4⋊C4×C263C2211yescharacteristic
23C2×C4⋊C4×C263C2211yescharacteristic
24#95×C263—21no—
25#95×C263—21no—
26#95×C263C2211yescharacteristic
27C2×Dic526D411yescharacteristic
28C2×D1052D411yescharacteristic
29C2×C22⋊D263—21no—
30C2×C4×D263—21no—
31C2×C263⋊C8—21no—
32C2×C263⋊C8—21no—
33C4⋊Dic263D411yescharacteristic
34C4⋊Dic263D411yescharacteristic
35Dic263⋊C4—21no—
36Dic263⋊C4—21no—
37Dic263⋊C4—21no—
38Dic263⋊C4—21no—
39C22⋊Dic263—21no—
40(C2×D263)⋊C4—21no—
41(C2×D263)⋊C4—21no—
42(C2×D263)⋊C4—21no—
43(C2×D263)⋊C4—21no—
44C4×Dic263—21no—
45C22×C4×C263—21no—
46C22×C4×C263—21no—
47C22×C4×C263D411yescharacteristic
48C22×C4×C263D411yescharacteristic
49C22×C4×C263C2311yescharacteristic
50C4⋊C4×C263—21no—
51C4⋊C4×C263—21no—
52C4⋊C4×C263—21no—
53C4⋊C4×C263—21no—
54C22×D263—21no—
55Dic526—41no—
56D1052—41no—
57C22⋊D263—41no—
58C22⋊D263—41no—
59C2×Dic263—21no—
60C2×Dic263—21no—
61C2×Dic263—21no—
62C4×D263—81no—
63C263⋊C8—41no—
64C263⋊C8—41no—
65C23×C263C2×D411yescharacteristic
66C2×C4×C263—21no—
67C2×C4×C263—21no—
68C2×C4×C263—21no—
69C2×C4×C263—21no—
70C2×C4×C263—41no—
71C2×C4×C263—41no—
72C2×C4×C263—41no—
73C2×C4×C263—41no—
74C2×C4×C263—42no—
75C2×C4×C263—41no—
76C2×C4×C263—41no—
77C2×C4×C263C2×D411yescharacteristic
78C2×C4×C263C2×D411yescharacteristic
79C22×C263—21no—
80C22×C263—21no—
81C22×C263#12011yescharacteristic
82C22×C263#13511yescharacteristic
83C22×C263#13711yescharacteristic
84C2×D263—41no—
85C2×D263—41no—
86C2×D263—41no—
87C4×C263—21no—
88C4×C263—21no—
89C4×C263—41no—
90C4×C263—41no—
91C4×C263—81no—
92C4×C263—81no—
93Dic263—41no—
94Dic263—41no—
95Dic263—41no—
96C2×C263—21no—
97C2×C263—21no—
98C2×C263#45211yescharacteristic
99C2×C263#45411yescharacteristic
100C2×C263#45811yescharacteristic
101D263—81no—
102C263#161511yescharacteristic, complemented, Sylow
103#1615—2631nomaximal, Sylow
104#539—2631no—
105#484—2631no—
106#481—2631no—
107#400D26311yescharacteristic, complemented
108#328—2631no—
109#327—2631no—
110#324—2631no—
111#126—5261no—
112#125—5261no—
113#123—5261no—
114#123—5261no—
115C22⋊Q8—2631no—
116C22⋊Q8—5261no—
117#121—2631no—
118C4×D4—5261no—
119C2×C4⋊C4C2×D26311yescharacteristic
120C2×C4⋊C4C2×D26311yescharacteristic
121#107—5261no—
122#106—5261no—
123#103—5261no—
124#102—5261no—
125C22⋊C8—2631no—
126C22⋊C8—2631no—
127#95—21no—
128#95—21no—
129#95C2×D26311yescharacteristic
130C2×Q8—2631no—
131C2×D4—2631no—
132C2×D4—5261no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—5261no—
136C22×C4C22⋊D26311yescharacteristic
137C22×C4C22⋊D26311yescharacteristic
138C22×C4C22×D26311yescharacteristic
139C2×C8—5261no—
140C2×C8—5261no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—2631no—
146C4⋊C4—2631no—
147C4⋊C4—5261no—
148C4⋊C4—5261no—
149C4⋊C4—5261no—
150C4⋊C4—5261no—
151C22⋊C4—5261no—
152C22⋊C4—5261no—
153C22⋊C4—5261no—
154C22⋊C4—5261no—
155C22⋊C4—5261no—
156C42—5261no—
157C23—5261no—
158C23C2×C22⋊D26311yescharacteristic
159Q8—10521no—
160D4—10521no—
161D4—10521no—
162D4—10521no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—5261no—
175C2×C4—5261no—
176C2×C4—5261no—
177C2×C4—21041no—
178C2×C4D4×D26311yescharacteristic
179C2×C4D4×D26311yescharacteristic
180C8—10521no—
181C8—10521no—
182C22—21no—
183C22—21no—
184C22—10521no—
185C22—10521no—
186C22—10521no—
187C22#2255443811yescharacteristic
188C22#2255449011yescharacteristic
189C22#2255450111yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—81no—
196C4—10521no—
197C4—10521no—
198C4—10521no—
199C2—21no—
200C2—21no—
201C2—21041no—
202C2#3068209811yescharacteristic
203C2#3068211011yescharacteristic
204C2#3068212711yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#400×C263C2
socleC22×C263#120
prime radical#22554444C22
hypercenter#400D263
hypocenterC263#1615
LCSG ▷ C22×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #30682273C2semidirect
4. #30681674C2semidirect
6. #30681664C2semidirect
7. #400×C263C2semidirect
102. C263#1615semidirect
107. #400D263semidirect

Maximal subgroups

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

subgroupindex
#306825352
#306822732
#306822562
#306816742
#306816712
#306816642
#400×C2632
#1615263