Finite Group Databasebeta

← #46783188

Subgroups — #46783188

Order 33664.

442 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 97 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#30682449C211yesmaximal, characteristic
2C22×C4×Dic263C211yesmaximal, characteristic, complemented
3C2×#22554396C212yesmaximal, complemented
4#30681699C212yesmaximal, complemented
5#407×C263C211yesmaximal, characteristic, complemented
6C2×#16862376C2211yescharacteristic
7C23×Dic263—21no—
8#22554453—21no—
9#22554449C412yescomplemented
10#22554444C412yescomplemented
11#22554439—21no—
12C4×C22⋊D263—22no—
13#22554429C2211yescharacteristic
14C2×C4×Dic263—24no—
15C2×C4×Dic263—21no—
16C2×C4×Dic263C2212yes—
17#22554396—24no—
18C23×C4×C263C2211yescharacteristic
19C2×M16×C263C2212yes—
20C22⋊C8×C263—22no—
21#16862376—22no—
22#16862376—22no—
23C2×Dic526C2×C411yescharacteristic, complemented
24C2×D1052C2×C411yescharacteristic, complemented
25C2×C22⋊D263—22no—
26C2×C22⋊D263—21no—
27C22×Dic263—24no—
28C22×Dic263—28no—
29C22×Dic263—22no—
30C2×C4×D263—21no—
31C4⋊Dic263C2×C412yescomplemented
32Dic263⋊C4—22no—
33C22⋊Dic263—22no—
34C22⋊Dic263—21no—
35(C2×D263)⋊C4—22no—
36C4×Dic263—24no—
37C4×Dic263—22no—
38C4×Dic263—21no—
39C4×Dic263D414yescomplemented
40C24×C263D411yescharacteristic
41C22×C4×C263—22no—
42C22×C4×C263—22no—
43C22×C4×C263C2×C412yes—
44C22×C4×C263D412yes—
45C22×C4×C263D411yescharacteristic
46C22×C4×C263C2311yescharacteristic
47M16×C263—22no—
48M16×C263—22no—
49C2×C8×C263—22no—
50C22×D263—21no—
51Dic526—22no—
52D1052—22no—
53C22⋊D263—44no—
54C22⋊D263—41no—
55C22⋊D263—41no—
56C2×Dic263—216no—
57C2×Dic263—28no—
58C2×Dic263—24no—
59C2×Dic263—22no—
60C2×Dic263—21no—
61C4×D263—42no—
62C23×C263—24no—
63C23×C263—21no—
64C23×C263—21no—
65C23×C263C22⋊C412yes—
66C23×C263C2×D411yescharacteristic
67C2×C4×C263—21no—
68C2×C4×C263—21no—
69C2×C4×C263—24no—
70C2×C4×C263—24no—
71C2×C4×C263C22⋊C412yes—
72C2×C4×C263C22×C411yescharacteristic
73C2×C4×C263C2×D412yes—
74C2×C4×C263C2×D411yescharacteristic
75C2×C4×C263#4112yes—
76C8×C263—42no—
77C22×C263—24no—
78C22×C263—24no—
79C22×C263—22no—
80C22×C263—22no—
81C22×C263—22no—
82C22×C263#10414yescomplemented
83C22×C263C2×C22⋊C411yescharacteristic
84C22×C263#12011yescharacteristic
85C22×C263#12311yescharacteristic
86C2×D263—41no—
87C2×D263—42no—
88C4×C263—22no—
89C4×C263C4×D412yes—
90C4×C263#12112yes—
91Dic263—28no—
92Dic263—41no—
93Dic263—42no—
94C2×C263—21no—
95C2×C263—24no—
96C2×C263—21no—
97C2×C263#38611yescharacteristic
98C2×C263C2×#10412yes—
99D263—81no—
100C263#189611yescharacteristic, complemented, Sylow
101#1896—2631nomaximal, Sylow
102#525—2631no—
103C22×C42—2631no—
104C2×#104—2632no—
105#407D26311yescharacteristic, complemented
106#339—2632no—
107C2×#41—2631no—
108C23×C4—5261no—
109C23×C4C2×D26311yescharacteristic
110C2×M16C2×D26312yes—
111#123—5261no—
112C22⋊Q8—2632no—
113#121—2632no—
114#120—5261no—
115C4×D4—5262no—
116#117—2631no—
117C2×C42—2632no—
118C2×C42—5264no—
119C2×C42—5261no—
120#104—5264no—
121C22⋊C8—22no—
122C24D105211yescharacteristic
123#41—5262no—
124#41—5262no—
125C2×Q8—2631no—
126C2×D4—2631no—
127C2×D4—5262no—
128C2×D4—5261no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—5264no—
132C22×C4—5268no—
133C22×C4—5262no—
134C22×C4—5261no—
135C22×C4C4×D26312yes—
136C22×C4C22⋊D26312yes—
137C22×C4D105211yescharacteristic
138C22×C4C22×D26311yescharacteristic
139M16—22no—
140M16—22no—
141C2×C8—22no—
142C4⋊C4—2632no—
143C4⋊C4—5262no—
144C22⋊C4—5262no—
145C22⋊C4—5261no—
146C22⋊C4—5262no—
147C42—2634no—
148C42—5264no—
149C42—5262no—
150C42—5261no—
151C23—24no—
152C23—21no—
153C23—21no—
154C23—5261no—
155C23(C2×D263)⋊C412yes—
156C23C2×D105211yescharacteristic
157Q8—5262no—
158D4—5262no—
159D4—10524no—
160D4—10521no—
161D4—10521no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—52616no—
167C2×C4—5268no—
168C2×C4—5264no—
169C2×C4—5262no—
170C2×C4—5261no—
171C2×C4—10522no—
172C2×C4(C2×D263)⋊C412yes—
173C2×C4C2×C4×D26311yescharacteristic
174C2×C4D4×D26312yes—
175C2×C4C2×C22⋊D26311yescharacteristic
176C2×C4#1686237512yes—
177C8—42no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—10522no—
184C22—10521no—
185C22#2255439614yescomplemented
186C22C2×(C2×D263)⋊C411yescharacteristic
187C22#2255444011yescharacteristic
188C22#2255445411yescharacteristic
189C4—22no—
190C4—5268no—
191C4—10522no—
192C4—10521no—
193C4(C22⋊D263)⋊C412yes—
194C4#2255444212yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—21041no—
199C2#3068181511yescharacteristic
200C2C2×#2255439612yes—
subgroupG/H
centerC2×C4C2×C22⋊D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#407×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682449C2
cosocleC22×C4×C263C23
hypercenter#407D263
hypocenterC263#1896
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic263C2semidirect
3. C2×#22554396C2semidirect
4. #30681699C2semidirect
5. #407×C263C2semidirect
9. #22554449C4semidirect
10. #22554444C4semidirect
23. C2×Dic526C2×C4semidirect
24. C2×D1052C2×C4semidirect
31. C4⋊Dic263C2×C4semidirect
39. C4×Dic263D4semidirect
82. C22×C263#104semidirect
100. C263#1896semidirect
105. #407D263semidirect
185. C22#22554396semidirect

Maximal subgroups

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

subgroupindex
#306824492
C22×C4×Dic2632
C2×#225543962
#306816992
#407×C2632
#1896263