Finite Group Databasebeta

← #46783190

Subgroups — #46783190

Order 33664.

442 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 101 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
2C2×#22554398C212yesmaximal, complemented
3#30681902C211yesmaximal, characteristic, complemented
4#30681698C212yesmaximal, complemented
5C22×C42×C263C211yesmaximal, characteristic, complemented
6C2×#16862376C2211yescharacteristic
7C2×#16862360C2212yes—
8#22554453—21no—
9#22554449C412yescomplemented
10#22554444C412yescomplemented
11#22554439—21no—
12C4×C22⋊D263—22no—
13#22554429C2211yescharacteristic
14#22554398—24no—
15C22⋊(C263⋊C8)—22no—
16C23×C4×C263—21no—
17C23×C4×C263C2211yescharacteristic
18C2×C42×C263—21no—
19C2×C42×C263—24no—
20C2×C42×C263C2212yes—
21#16862376—22no—
22#16862376—22no—
23C2×Dic526C2×C411yescharacteristic, complemented
24C2×D1052C2×C411yescharacteristic, complemented
25C2×C22⋊D263—22no—
26C2×C22⋊D263—21no—
27C2×C4×D263—21no—
28#16862360—22no—
29#16862360—22no—
30C2×C263⋊C8—22no—
31C4⋊Dic263C2×C412yescomplemented
32Dic263⋊C4—22no—
33C22⋊Dic263—22no—
34C22⋊Dic263—21no—
35(C2×D263)⋊C4—22no—
36C4×Dic263—21no—
37C24×C263D411yescharacteristic
38C22×C4×C263—28no—
39C22×C4×C263—24no—
40C22×C4×C263—22no—
41C22×C4×C263—22no—
42C22×C4×C263—22no—
43C22×C4×C263C2×C412yes—
44C22×C4×C263D411yescharacteristic
45C22×C4×C263D412yes—
46C22×C4×C263C2311yescharacteristic
47C42×C263—24no—
48C42×C263—22no—
49C42×C263D414yescomplemented
50C22×D263—21no—
51Dic526—22no—
52D1052—22no—
53C22⋊D263—44no—
54C22⋊D263—41no—
55C22⋊D263—41no—
56C2×Dic263—22no—
57C2×Dic263—21no—
58C4×D263—42no—
59C263⋊C8—42no—
60C23×C263—24no—
61C23×C263—21no—
62C23×C263—21no—
63C23×C263C22⋊C412yes—
64C23×C263C2×D411yescharacteristic
65C2×C4×C263—216no—
66C2×C4×C263—28no—
67C2×C4×C263—21no—
68C2×C4×C263—24no—
69C2×C4×C263—21no—
70C2×C4×C263—24no—
71C2×C4×C263—24no—
72C2×C4×C263C22⋊C412yes—
73C2×C4×C263C22×C411yescharacteristic
74C2×C4×C263C2×D412yes—
75C2×C4×C263C2×D411yescharacteristic
76C2×C4×C263#4112yes—
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—28no—
89C4×C263—22no—
90C4×C263C4×D412yes—
91C4×C263#12112yes—
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×C42D26311yescharacteristic, complemented
104C2×#104—2632no—
105#407—2631no—
106#339—2632no—
107C2×#41—2631no—
108C23×C4—21no—
109C23×C4C2×D26311yescharacteristic
110C2×M16—2632no—
111#123—5261no—
112C22⋊Q8—2632no—
113#121—2632no—
114#120—5261no—
115C4×D4—5262no—
116#117—2631no—
117C2×C42—21no—
118C2×C42—24no—
119C2×C42C2×D26312yes—
120#104—5264no—
121C22⋊C8—5262no—
122C24C22⋊D26311yescharacteristic
123#41—5262no—
124#41—5262no—
125C2×Q8—2631no—
126C2×D4—2631no—
127C2×D4—5262no—
128C2×D4—5261no—
129C22×C4—24no—
130C22×C4—28no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—5261no—
135C22×C4C4×D26312yes—
136C22×C4C22⋊D26311yescharacteristic
137C22×C4D105212yes—
138C22×C4C22×D26311yescharacteristic
139M16—5262no—
140M16—5262no—
141C2×C8—5262no—
142C4⋊C4—2632no—
143C4⋊C4—5262no—
144C22⋊C4—5262no—
145C22⋊C4—5261no—
146C22⋊C4—5262no—
147C42—24no—
148C42—22no—
149C42—5261no—
150C42C22⋊D26314yescomplemented
151C23—24no—
152C23—21no—
153C23—21no—
154C23—5261no—
155C23(C2×D263)⋊C412yes—
156C23C2×C22⋊D26311yescharacteristic
157Q8—5262no—
158D4—5262no—
159D4—10524no—
160D4—10521no—
161D4—10521no—
162C2×C4—216no—
163C2×C4—28no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—24no—
168C2×C4—24no—
169C2×C4—5262no—
170C2×C4—5261no—
171C2×C4—10522no—
172C2×C4(C2×D263)⋊C412yes—
173C2×C4C2×C4×D26311yescharacteristic
174C2×C4C2×C22⋊D26312yes—
175C2×C4C2×D105211yescharacteristic
176C2×C4#1686237612yes—
177C8—10522no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—10522no—
184C22—10521no—
185C22#2255439814yescomplemented
186C22C2×(C2×D263)⋊C411yescharacteristic
187C22#2255443911yescharacteristic
188C22#2255445311yescharacteristic
189C4—28no—
190C4—22no—
191C4—10522no—
192C4—10521no—
193C4C4×C22⋊D26312yes—
194C4#2255444412yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—21041no—
199C2#3068181711yescharacteristic
200C2C2×#2255439812yes—
subgroupG/H
centerC2×C4C2×D1052
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC22×C42×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682449C2
cosocleC22×C4×C263C23
hypercenterC22×C42D263
hypocenterC263#1896
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C2×#22554398C2semidirect
3. #30681902C2semidirect
4. #30681698C2semidirect
5. C22×C42×C263C2semidirect
9. #22554449C4semidirect
10. #22554444C4semidirect
23. C2×Dic526C2×C4semidirect
24. C2×D1052C2×C4semidirect
31. C4⋊Dic263C2×C4semidirect
49. C42×C263D4semidirect
82. C22×C263#104semidirect
100. C263#1896semidirect
103. C22×C42D263semidirect
150. C42C22⋊D263semidirect
185. C22#22554398semidirect

Maximal subgroups

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

subgroupindex
#306824492
C2×#225543982
#306819022
#306816982
C22×C42×C2632
#1896263