Finite Group Databasebeta

← #46781747

Subgroups — #46781747

Order 33664.

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

normal subgroups only

This group has 216 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#30682537C211yesmaximal, characteristic
2#30682266C211yesmaximal, characteristic, complemented
3#30682252C211yesmaximal, characteristic
4#30681870C211yesmaximal, characteristic, complemented
5#30681671C211yesmaximal, characteristic
6#30681663C211yesmaximal, characteristic, complemented
7#328×C263C211yesmaximal, characteristic, complemented
8#22554465—21no—
9#22554461—21no—
10#22554455—21no—
11#22554454—21no—
12#22554446—21no—
13#22554444C2211yescharacteristic
14(C22⋊D263)⋊C4—21no—
15C2×C4⋊Dic263—21no—
16C2×C4⋊Dic263C2211yescharacteristic
17C2×Dic263⋊C4C2211yescharacteristic
18#22554404—21no—
19#22554401—21no—
20#22554394—21no—
21#22554392—21no—
22C22⋊(C263⋊C8)C2211yescharacteristic
23C263⋊#95—21no—
24C22⋊Q8×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic
26#95×C263C2211yescharacteristic
27C2×D1052D411yescharacteristic
28C2×C22⋊D263—21no—
29C22×Dic263—21no—
30C22×Dic263D411yescharacteristic
31C22×Dic263D411yescharacteristic
32C2×C4×D263—21no—
33C2×C263⋊C8—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263—21no—
37C4⋊Dic263—21no—
38C4⋊Dic263—42no—
39C4⋊Dic263D411yescharacteristic
40Dic263⋊C4—21no—
41Dic263⋊C4—21no—
42Dic263⋊C4—21no—
43(C2×D263)⋊C4—21no—
44(C2×D263)⋊C4—21no—
45(C2×D263)⋊C4—21no—
46(C2×D263)⋊C4—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—
55C22×D263—21no—
56D1052—41no—
57C22⋊D263—41no—
58C22⋊D263—41no—
59C2×Dic263—21no—
60C2×Dic263—21no—
61C2×Dic263—21no—
62C2×Dic263—21no—
63C2×Dic263—21no—
64C2×Dic263—41no—
65C2×Dic263—41no—
66C2×Dic263—41no—
67C2×Dic263—41no—
68C4×D263—81no—
69C263⋊C8—41no—
70C23×C263C2×D411yescharacteristic
71Q8×C263—41no—
72C2×C4×C263—22no—
73C2×C4×C263—21no—
74C2×C4×C263—21no—
75C2×C4×C263—41no—
76C2×C4×C263—41no—
77C2×C4×C263—41no—
78C2×C4×C263C2×D411yescharacteristic
79C2×C4×C263C2×D411yescharacteristic
80C8×C263—41no—
81C22×C263—21no—
82C22×C263—21no—
83C22×C263#12011yescharacteristic
84C22×C263#13511yescharacteristic
85C22×C263AGL(1,ℤ/8)11yescharacteristic
86C2×D263—41no—
87C2×D263—41no—
88C2×D263—41no—
89C4×C263—21no—
90C4×C263—21no—
91C4×C263—42no—
92C4×C263—41no—
93C4×C263—41no—
94Dic263—41no—
95Dic263—41no—
96Dic263—41no—
97Dic263—81no—
98C2×C263—21no—
99C2×C263—21no—
100C2×C263#44911yescharacteristic
101C2×C263#45611yescharacteristic
102C2×C263#45811yescharacteristic
103D263—81no—
104C263#160911yescharacteristic, complemented, Sylow
105#1609—2631nomaximal, Sylow
106#539—2631no—
107#483—2631no—
108#480—2631no—
109#398—2631no—
110#328D26311yescharacteristic, complemented
111#327—2631no—
112#324—2631no—
113#126—5261no—
114#125—5261no—
115#123—5261no—
116#123—5261no—
117C22⋊Q8—5261no—
118C22⋊Q8C2×D26311yescharacteristic
119#121—2631no—
120C4×D4—5261no—
121C2×C4⋊C4—2631no—
122C2×C4⋊C4—2631no—
123C2×C4⋊C4—5261no—
124#107—5261no—
125#106—5261no—
126#103—5261no—
127#102—5261no—
128C22⋊C8—2631no—
129C22⋊C8C2×D26311yescharacteristic
130#95—5261no—
131#95C2×D26311yescharacteristic
132C2×Q8D105211yescharacteristic
133C2×D4—2631no—
134C2×D4—5261no—
135C22×C4—21no—
136C22×C4—2631no—
137C22×C4—2631no—
138C22×C4—5261no—
139C22×C4—5261no—
140C22×C4C22×D26311yescharacteristic
141C2×C8—21no—
142C2×C8—5261no—
143C4⋊C4—21no—
144C4⋊C4—2631no—
145C4⋊C4—5261no—
146C4⋊C4—5261no—
147C4⋊C4—5261no—
148C4⋊C4—5261no—
149C4⋊C4—5261no—
150C4⋊C4—5261no—
151C4⋊C4—5261no—
152C4⋊C4—10522no—
153C4⋊C4D105211yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—5261no—
156C22⋊C4—5261no—
157C22⋊C4—5261no—
158C22⋊C4—5261no—
159C42—5261no—
160C23—5261no—
161C23D4×D26311yescharacteristic
162Q8—41no—
163D4—10521no—
164D4—10521no—
165D4—10521no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—5261no—
173C2×C4—5261no—
174C2×C4—5261no—
175C2×C4—5261no—
176C2×C4—5261no—
177C2×C4—10521no—
178C2×C4—10521no—
179C2×C4—10521no—
180C2×C4—10521no—
181C2×C4—21041no—
182C2×C4D4×D26311yescharacteristic
183C2×C4C2×D105211yescharacteristic
184C8—41no—
185C8—10521no—
186C22—21no—
187C22—21no—
188C22—10521no—
189C22—10521no—
190C22—10521no—
191C22#2255444011yescharacteristic
192C22#2255449311yescharacteristic
193C22#2255449711yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4—10521no—
200C4—10521no—
201C4—10521no—
202C4—21041no—
203C2—21no—
204C2—21no—
205C2—21041no—
206C2#3068208611yescharacteristic
207C2#3068212211yescharacteristic
208C2#3068212911yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#328×C263C2
socleC22×C263#120
prime radical#22554444C22
hypercenter#328D263
hypocenterC263#1609
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
2. #30682266C2semidirect
4. #30681870C2semidirect
6. #30681663C2semidirect
7. #328×C263C2semidirect
104. C263#1609semidirect
110. #328D263semidirect

Maximal subgroups

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

subgroupindex
#306825372
#306822662
#306822522
#306818702
#306816712
#306816632
#328×C2632
#1609263