Finite Group Databasebeta

← #46781756

Subgroups — #46781756

Order 33664.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#30682567C211yesmaximal, characteristic
2#30682269C211yesmaximal, characteristic
3#30682266C211yesmaximal, characteristic
4#30681870C211yesmaximal, characteristic
5#30681674C211yesmaximal, characteristic
6#30681663C211yesmaximal, characteristic
7#328×C263C211yesmaximal, characteristic
8#22554469—21no—
9#22554468—21no—
10#22554460—21no—
11#22554460—21no—
12#22554449C2211yescharacteristic
13#22554447—21no—
14#22554426—21no—
15C2×C4⋊Dic263—21no—
16C2×C4⋊Dic263C2211yescharacteristic
17C2×Dic263⋊C4C2211yescharacteristic
18#22554402—21no—
19#22554401—21no—
20#22554395—21no—
21#22554394—21no—
22C22⋊(C263⋊C8)C2211yescharacteristic
23C263⋊#95—21no—
24C22⋊Q8×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic
26#95×C263C2211yescharacteristic
27C2×Dic526—21no—
28C2×Dic526D411yescharacteristic
29C22×Dic263—21no—
30C22×Dic263D411yescharacteristic
31C22×Dic263D411yescharacteristic
32C2×C263⋊C8—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263—42no—
37C4⋊Dic263D411yescharacteristic
38Dic263⋊C4—21no—
39Dic263⋊C4—21no—
40Dic263⋊C4—21no—
41Dic263⋊C4—21no—
42Dic263⋊C4—21no—
43Dic263⋊C4—21no—
44Dic263⋊C4—21no—
45C22⋊Dic263—21no—
46C4×Dic263—21no—
47C4×Dic263—21no—
48C2×Q8×C263D411yescharacteristic
49C22×C4×C263—21no—
50C22×C4×C263C2311yescharacteristic
51C2×C8×C263—21no—
52C4⋊C4×C263—21no—
53C4⋊C4×C263D411yescharacteristic
54C22⋊C4×C263—21no—
55Dic526—41no—
56Dic526—81no—
57C2×Dic263—21no—
58C2×Dic263—21no—
59C2×Dic263—21no—
60C2×Dic263—21no—
61C2×Dic263—21no—
62C2×Dic263—41no—
63C2×Dic263—41no—
64C2×Dic263—41no—
65C2×Dic263—41no—
66C2×Dic263SD1612yes—
67C263⋊C8—41no—
68C23×C263C2×D411yescharacteristic
69Q8×C263—41no—
70C2×C4×C263—22no—
71C2×C4×C263—21no—
72C2×C4×C263—21no—
73C2×C4×C263—41no—
74C2×C4×C263—41no—
75C2×C4×C263—41no—
76C2×C4×C263C2×D411yescharacteristic
77C2×C4×C263C2×D411yescharacteristic
78C8×C263—41no—
79C22×C263—21no—
80C22×C263—21no—
81C22×C263#12011yescharacteristic
82C22×C263C2×SD1611yescharacteristic
83C22×C263#13711yescharacteristic
84C4×C263—21no—
85C4×C263—21no—
86C4×C263—42no—
87C4×C263—41no—
88C4×C263—41no—
89Dic263—22no—
90Dic263—41no—
91Dic263—41no—
92Dic263—41no—
93Dic263—81no—
94C2×C263—21no—
95C2×C263—21no—
96C2×C263#44811yescharacteristic
97C2×C263#45611yescharacteristic
98C2×C263#45811yescharacteristic
99C263#161111yescharacteristic, complemented, Sylow
100#1611—2631nomaximal, Sylow
101#544—2631no—
102#483—2631no—
103#483—2631no—
104#398—2631no—
105#328—2631no—
106#328D26311yescharacteristic
107#324—2631no—
108C4⋊Q8—5261no—
109C4⋊Q8—5261no—
110#125—5261no—
111#125—5261no—
112C22⋊Q8—2631no—
113C22⋊Q8—5261no—
114C22⋊Q8C2×D26311yescharacteristic
115#117—5261no—
116C2×C4⋊C4—2631no—
117C2×C4⋊C4—2631no—
118C2×C4⋊C4—5261no—
119#106—5261no—
120#106—5261no—
121#103—5261no—
122#103—5261no—
123C22⋊C8—2631no—
124C22⋊C8C2×D26311yescharacteristic
125#95—5261no—
126#95C2×D26311yescharacteristic
127C2×Q8—2631no—
128C2×Q8—5261no—
129C2×Q8D105211yescharacteristic
130C22×C4—21no—
131C22×C4—2631no—
132C22×C4—2631no—
133C22×C4—5261no—
134C22×C4C22×D26311yescharacteristic
135C2×C8—21no—
136C2×C8—5261no—
137C4⋊C4—21no—
138C4⋊C4—2631no—
139C4⋊C4—5261no—
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—10522no—
150C4⋊C4D105211yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—5261no—
153C42—5261no—
154C42—5261no—
155C23D4×D26311yescharacteristic
156Q8—41no—
157Q8—10521no—
158Q8—21041no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—2632no—
166C2×C4—5261no—
167C2×C4—5261no—
168C2×C4—5261no—
169C2×C4—5261no—
170C2×C4—5261no—
171C2×C4—10521no—
172C2×C4—10521no—
173C2×C4—10521no—
174C2×C4—10521no—
175C2×C4D4×D26311yescharacteristic
176C2×C4C2×D105211yescharacteristic
177C8—41no—
178C8—10521no—
179C22—21no—
180C22—21no—
181C22#2255444011yescharacteristic
182C22SD16×D26311yescharacteristic
183C22#2255450211yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—5262no—
190C4—10521no—
191C4—10521no—
192C4—10521no—
193C4—21041no—
194C2—21no—
195C2—21no—
196C2#3068207811yescharacteristic
197C2#3068212211yescharacteristic
198C2#3068212911yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#328×C263C2
socleC22×C263#120
prime radicalC23×C263C2×D4
hypercenter#328D263
hypocenterC263#1611
LCSG ▷ C22×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
99. C263#1611semidirect

Maximal subgroups

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

subgroupindex
#306825672
#306822692
#306822662
#306818702
#306816742
#306816632
#328×C2632
#1611263