Finite Group Databasebeta

← #46783602

Subgroups — #46783602

Order 33664.

348 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C22×#16862364C211yesmaximal, characteristic
2C2×#22554401C211yesmaximal, characteristic, complemented
3C2×#22554395C211yesmaximal, characteristic, complemented
4C2×C8×Dic263C211yesmaximal, characteristic, complemented
5#30681843C211yesmaximal, characteristic, complemented
6#30681841C211yesmaximal, characteristic
7C2×#102×C263C211yesmaximal, characteristic
8C22×Dic526C2211yescharacteristic
9C2×#16862364—22no—
10C2×#16862364—22no—
11C2×#16862364C414yescomplemented
12C22×C263⋊C8C2211yescharacteristic
13C2×C4⋊Dic263C2211yescharacteristic
14C2×C22⋊Dic263—22no—
15C2×C4×Dic263C2211yescharacteristic
16#22554401—22no—
17#22554395—22no—
18C8×Dic263—22no—
19C263⋊#95—22no—
20C22×D4×C263C2211yescharacteristic
21C22×C8×C263C2211yescharacteristic
22C2×C4⋊C4×C263C2211yescharacteristic
23#102×C263—22no—
24C2×Dic526—21no—
25C2×Dic526—21no—
26C2×Dic526—21no—
27C2×Dic526—21no—
28C2×Dic526—21no—
29C2×Dic526C2×C412yes—
30C22×Dic263—21no—
31C22×Dic263—21no—
32C22×Dic263D412yes—
33#16862364—28no—
34C2×C263⋊C8C2×C412yes—
35C2×C263⋊C8D412yes—
36C2×C263⋊C8D412yes—
37C4⋊Dic263—21no—
38C4⋊Dic263—21no—
39C22⋊Dic263—44no—
40C4×Dic263—21no—
41C4×Dic263—21no—
42C24×C263—21no—
43C2×D4×C263—21no—
44C2×D4×C263—21no—
45C2×D4×C263—21no—
46C2×D4×C263—21no—
47C2×D4×C263—21no—
48C2×D4×C263C2×C412yes—
49C22×C4×C263—21no—
50C22×C4×C263C2311yescharacteristic
51C2×C8×C263—21no—
52C2×C8×C263—21no—
53C2×C8×C263D412yes—
54C4⋊C4×C263—21no—
55C4⋊C4×C263—21no—
56Dic526—22no—
57Dic526—22no—
58Dic526—41no—
59Dic526—41no—
60C2×Dic263—22no—
61C2×Dic263—22no—
62C2×Dic263—22no—
63C2×Dic263—41no—
64C2×Dic263—41no—
65C2×Dic263—41no—
66C2×Dic263—42no—
67C2×Dic263SD1614yescomplemented
68C263⋊C8C22⋊C414yescomplemented
69C23×C263—22no—
70C23×C263—41no—
71C23×C263—41no—
72C23×C263—42no—
73C23×C263—42no—
74C23×C263C2×D411yescharacteristic
75D4×C263—22no—
76D4×C263—22no—
77D4×C263—41no—
78D4×C263—41no—
79C2×C4×C263—41no—
80C2×C4×C263—42no—
81C2×C4×C263C22×C411yescharacteristic
82C2×C4×C263C2×D411yescharacteristic
83C2×C4×C263C2×D411yescharacteristic
84C2×C4×C263C2×D411yescharacteristic
85C2×C4×C263#4111yescharacteristic
86C2×C4×C263#4111yescharacteristic
87C8×C263—22no—
88C22×C263—42no—
89C22×C263—44no—
90C22×C263—82no—
91C22×C263—81no—
92C22×C263—81no—
93C22×C263C4×D411yescharacteristic
94C22×C263#12111yescharacteristic
95C22×C263#12711yescharacteristic
96C22×C263C2×SD1612yes—
97C22×C263#13512yes—
98C4×C263—81no—
99C4×C263C2×C22⋊C411yescharacteristic
100C4×C263C4×D411yescharacteristic
101C4×C263#12111yescharacteristic
102C4×C263#12411yescharacteristic
103Dic263—24no—
104Dic263—42no—
105Dic263—81no—
106C2×C263—82no—
107C2×C263#39011yescharacteristic
108C2×C263C4×SD1612yes—
109C2×C263#46512yes—
110C2×C263#49211yescharacteristic
111C2×C263#49511yescharacteristic
112C263#196811yescharacteristic, complemented, Sylow
113#1968—2631nomaximal, Sylow
114C22×SD16—2631no—
115C2×#106—2631no—
116C2×#103—2631no—
117C2×#102D26311yescharacteristic
118C2×C4×C8—2631no—
119#391—2631no—
120#390—2631no—
121C22×Q8—2631no—
122C22×D4C2×D26311yescharacteristic
123C2×SD16—2634no—
124C2×SD16—5262no—
125C2×SD16—5262no—
126C22×C8—2631no—
127C22×C8C2×D26311yescharacteristic
128C2×C4⋊C4—2631no—
129C2×C4⋊C4C2×D26311yescharacteristic
130C2×C22⋊C4—5262no—
131C2×C42—2631no—
132#106—5262no—
133#103—5262no—
134#102—22no—
135C4×C8—5262no—
136#95—5262no—
137C24—21no—
138C2×Q8—2632no—
139C2×Q8—5261no—
140C2×Q8—5261no—
141C2×Q8—5261no—
142C2×Q8—5261no—
143C2×Q8—5261no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4C4×D26312yes—
150C22×C4—21no—
151C22×C4—2632no—
152C22×C4—5261no—
153C22×C4—5261no—
154C22×C4C22×D26311yescharacteristic
155SD16—5268no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—2632no—
159C2×C8—2632no—
160C2×C8—2632no—
161C2×C8C22⋊D26312yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—5261no—
165C4⋊C4—5261no—
166C22⋊C4—10524no—
167C42—5261no—
168C42—5261no—
169C23—22no—
170C23—41no—
171C23—41no—
172C23—42no—
173C23—42no—
174C23D4×D26311yescharacteristic
175Q8—5262no—
176Q8—5262no—
177Q8—10521no—
178Q8—10521no—
179D4—22no—
180D4—22no—
181D4—41no—
182D4—41no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—2634no—
186C2×C4—5262no—
187C2×C4—5262no—
188C2×C4—5262no—
189C2×C4—10521no—
190C2×C4—10521no—
191C2×C4—10521no—
192C2×C4—10522no—
193C2×C4C2×C4×D26311yescharacteristic
194C2×C4D4×D26311yescharacteristic
195C2×C4D4×D26311yescharacteristic
196C2×C4C2×C22⋊D26311yescharacteristic
197C2×C4#1686237511yescharacteristic
198C2×C4#1686237611yescharacteristic
199C8—22no—
200C8—2634no—
201C22—44no—
202C22—42no—
203C22—82no—
204C22—81no—
205C22—81no—
206C22(C22⋊D263)⋊C411yescharacteristic
207C22#2255444311yescharacteristic
208C22#2255446611yescharacteristic
209C22SD16×D26312yes—
210C22#2255448912yes—
211C4—81no—
212C4—5264no—
213C4—10522no—
214C4—21041no—
215C4C22⋊C4×D26311yescharacteristic
216C4C4×C22⋊D26311yescharacteristic
217C4#2255444211yescharacteristic
218C4#2255445611yescharacteristic
219C2—82no—
220C2#3068183811yescharacteristic
221C2#3068202912yes—
222C2#3068216612yes—
223C2#3068230911yescharacteristic
224C2#3068232111yescharacteristic
subgroupG/H
centerC23D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×#102×C263C2
socleC23×C263C2×D4
prime radicalC22×D4×C263C22
cosocleC22×C4×C263C23
hypercenterC2×#102D263
hypocenterC263#1968
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#22554401C2semidirect
3. C2×#22554395C2semidirect
4. C2×C8×Dic263C2semidirect
5. #30681843C2semidirect
11. C2×#16862364C4semidirect
67. C2×Dic263SD16semidirect
68. C263⋊C8C22⋊C4semidirect
112. C263#1968semidirect

Maximal subgroups

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

subgroupindex
C22×#168623642
C2×#225544012
C2×#225543952
C2×C8×Dic2632
#306818432
#306818412
C2×#102×C2632
#1968263