Finite Group Databasebeta

← #46782972

Subgroups — #46782972

Order 33664.

302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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#30682419C211yesmaximal, characteristic
2#30681978C211yesmaximal, characteristic, complemented
3C2×#22554398C211yesmaximal, characteristic
4#30681937C211yesmaximal, characteristic
5#30681707C211yesmaximal, characteristic, complemented
6#30681698C211yesmaximal, characteristic, complemented
7#384×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C2×#16862360C2211yescharacteristic
10C2×#16862360C2211yescharacteristic
11#22554435—21no—
12#22554432—21no—
13C4×C22⋊D263—22no—
14#22554429C2211yescharacteristic
15#22554428—21no—
16C4⋊C4×D263—21no—
17#22554403—21no—
18#22554401—21no—
19#22554398C414yescomplemented
20#22554393—21no—
21#22554390—21no—
22C2×C4⋊C4×C263—22no—
23C2×C4⋊C4×C263C2211yescharacteristic
24C2×C4⋊C4×C263C2211yescharacteristic
25C2×C42×C263C2211yescharacteristic
26#16862376—21no—
27#16862376—21no—
28#16862376C2×C412yes—
29#16862376Q812yes—
30C2×Dic526D411yescharacteristic
31C2×D1052D411yescharacteristic
32C2×C22⋊D263—21no—
33C2×C4×D263—22no—
34C2×C4×D263—21no—
35#16862360—21no—
36#16862360—21no—
37#16862360—21no—
38#16862360C2×C412yescomplemented
39C2×C263⋊C8—21no—
40C2×C263⋊C8—21no—
41C4⋊Dic263D411yescharacteristic
42C4⋊Dic263D411yescharacteristic
43Dic263⋊C4—22no—
44C22⋊Dic263—21no—
45(C2×D263)⋊C4—22no—
46C4×Dic263—22no—
47C4×Dic263—21no—
48C22×C4×C263—21no—
49C22×C4×C263—21no—
50C22×C4×C263D412yes—
51C22×C4×C263C2311yescharacteristic
52C4⋊C4×C263—21no—
53C4⋊C4×C263—21no—
54C4⋊C4×C263—21no—
55C4⋊C4×C263—21no—
56C4⋊C4×C263—44no—
57C42×C263—21no—
58C42×C263C2×C412yescomplemented
59C22×D263—21no—
60Dic526—21no—
61Dic526C4⋊C412yescomplemented
62D1052—21no—
63D1052C4⋊C412yescomplemented
64C22⋊D263—22no—
65C22⋊D263—22no—
66C2×Dic263—21no—
67C2×Dic263—21no—
68C2×Dic263—21no—
69C4×D263—22no—
70C4×D263—22no—
71C4×D263—82no—
72C263⋊C8—22no—
73C263⋊C8—41no—
74C23×C263C2×D411yescharacteristic
75C2×C4×C263—22no—
76C2×C4×C263—22no—
77C2×C4×C263—22no—
78C2×C4×C263—22no—
79C2×C4×C263—42no—
80C2×C4×C263—42no—
81C2×C4×C263—41no—
82C2×C4×C263C22×C411yescharacteristic
83C2×C4×C263C2×D411yescharacteristic
84C2×C4×C263C2×D411yescharacteristic
85C2×C4×C263C2×Q811yescharacteristic
86C2×C4×C263#4111yescharacteristic
87C2×C4×C263#4111yescharacteristic
88C22×C263—21no—
89C22×C263—21no—
90C22×C263C4×D411yescharacteristic
91C22×C263#12011yescharacteristic
92C22×C263C22⋊Q811yescharacteristic
93C2×D263—22no—
94C2×D263—41no—
95C2×D263—41no—
96C4×C263—24no—
97C4×C263—42no—
98C4×C263—81no—
99C4×C263C2×C4⋊C411yescharacteristic
100C4×C263C4×D411yescharacteristic
101C4×C263C22⋊Q811yescharacteristic
102C4×C263#12311yescharacteristic
103Dic263—22no—
104Dic263—41no—
105Dic263—41no—
106C2×C263—21no—
107C2×C263—21no—
108C2×C263#38511yescharacteristic
109C2×C263#45311yescharacteristic
110C2×C263#45611yescharacteristic
111D263—42no—
112C263#185911yescharacteristic, complemented, Sylow
113#1859—2631nomaximal, Sylow
114#520—2631no—
115#428—2631no—
116C2×#104—2631no—
117#417—2631no—
118#384D26311yescharacteristic, complemented
119#343—2631no—
120#339—2631no—
121C2×#41—2631no—
122C2×M16—2631no—
123C2×M16—2631no—
124C4×Q8—5261no—
125C4×D4—5261no—
126C4×D4—5262no—
127#117—2631no—
128#117—5261no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—5261no—
131C2×C4⋊C4C2×D26311yescharacteristic
132C2×C4⋊C4C2×D26311yescharacteristic
133C2×C42C2×D26311yescharacteristic
134#107—5261no—
135#106—5261no—
136#104—2634no—
137#103—5261no—
138#102—5261no—
139#41—2632no—
140#41—2632no—
141#41—5261no—
142#41—5261no—
143C2×Q8—2631no—
144C2×D4—2631no—
145C2×D4—5261no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—5262no—
149C22×C4—5261no—
150C22×C4C22⋊D26312yes—
151C22×C4C22×D26311yescharacteristic
152M16—2632no—
153M16—5261no—
154M16—5261no—
155M16—5261no—
156C2×C8—5261no—
157C2×C8—5261no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—44no—
163C4⋊C4—2631no—
164C4⋊C4—2631no—
165C4⋊C4—5262no—
166C22⋊C4—5262no—
167C22⋊C4—5261no—
168C42—21no—
169C42—5262no—
170C42—5261no—
171C42C4×D26312yescomplemented
172C23—5261no—
173C23C2×C22⋊D26311yescharacteristic
174Q8—2632no—
175Q8—5261no—
176D4—2632no—
177D4—5262no—
178D4—5262no—
179D4—5261no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—41no—
187C2×C4—5261no—
188C2×C4—5262no—
189C2×C4—5262no—
190C2×C4—5261no—
191C2×C4—5261no—
192C2×C4—21042no—
193C2×C4C2×C4×D26311yescharacteristic
194C2×C4D4×D26311yescharacteristic
195C2×C4D4×D26311yescharacteristic
196C2×C4Q8×D26311yescharacteristic
197C2×C4#1686237611yescharacteristic
198C2×C4#1686237711yescharacteristic
199C8—5262no—
200C8—10521no—
201C22—21no—
202C22—21no—
203C22—5262no—
204C22—10521no—
205C22—10521no—
206C22C4×C22⋊D26311yescharacteristic
207C22#2255443811yescharacteristic
208C22#2255444611yescharacteristic
209C4—24no—
210C4—42no—
211C4—81no—
212C4—5262no—
213C4—10521no—
214C4—10521no—
215C4C4⋊C4×D26311yescharacteristic
216C4#2255443211yescharacteristic
217C4#2255444811yescharacteristic
218C4#2255445511yescharacteristic
219C2—21no—
220C2—21no—
221C2—10522no—
222C2#3068180911yescharacteristic
223C2#3068210511yescharacteristic
224C2#3068212011yescharacteristic
subgroupG/H
centerC22#22554438
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#384×C263C2
socleC22×C263#120
prime radicalC2×#16862376C22
cosocleC22×C4×C263C23
hypercenter#384D263
hypocenterC263#1859
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. #30681978C2semidirect
5. #30681707C2semidirect
6. #30681698C2semidirect
7. #384×C263C2semidirect
19. #22554398C4semidirect
38. #16862360C2×C4semidirect
58. C42×C263C2×C4semidirect
61. Dic526C4⋊C4semidirect
63. D1052C4⋊C4semidirect
112. C263#1859semidirect
118. #384D263semidirect
171. C42C4×D263semidirect

Maximal subgroups

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

subgroupindex
#306824192
#306819782
C2×#225543982
#306819372
#306817072
#306816982
#384×C2632
#1859263