Finite Group Databasebeta

← #46782973

Subgroups — #46782973

Order 33664.

302 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 93 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#30681981C211yesmaximal, characteristic, complemented
2C2×#22554397C211yesmaximal, characteristic
3#30681939C211yesmaximal, characteristic
4#30681807C211yesmaximal, characteristic, complemented
5#30681707C211yesmaximal, characteristic, complemented
6#30681697C211yesmaximal, characteristic, complemented
7#520×C263C211yesmaximal, characteristic
8C2×#16862360C2211yescharacteristic
9C2×#16862360C2211yescharacteristic
10C2×C4⋊Dic263C2211yescharacteristic
11C2×Dic263⋊C4—22no—
12C2×C4×Dic263C2211yescharacteristic
13#22554403—21no—
14#22554401—21no—
15#22554397C414yescomplemented
16#22554394—21no—
17#22554391—21no—
18C2×#41×C263C2211yescharacteristic
19C4×Q8×C263—21no—
20C4×D4×C263—21no—
21C4×D4×C263—22no—
22#117×C263—21no—
23#117×C263C2211yescharacteristic
24C2×C4⋊C4×C263—21no—
25C2×C4⋊C4×C263C2211yescharacteristic
26C22×Dic263—21no—
27C22×Dic263—21no—
28#16862360—21no—
29#16862360—21no—
30#16862360—21no—
31#16862360C2×C412yescomplemented
32C2×C263⋊C8—21no—
33C2×C263⋊C8—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263—21no—
36Dic263⋊C4—44no—
37C4×Dic263—21no—
38C4×Dic263C2×C412yescomplemented
39#41×C263—21no—
40#41×C263—21no—
41#41×C263C2×C412yes—
42#41×C263Q812yes—
43C2×Q8×C263D411yescharacteristic
44C2×D4×C263—21no—
45C2×D4×C263D411yescharacteristic
46C22×C4×C263—21no—
47C22×C4×C263—22no—
48C22×C4×C263D412yes—
49C22×C4×C263C2311yescharacteristic
50C4⋊C4×C263—22no—
51C4⋊C4×C263—21no—
52C4⋊C4×C263—21no—
53C4⋊C4×C263D411yescharacteristic
54C4⋊C4×C263D411yescharacteristic
55C22⋊C4×C263—22no—
56C22⋊C4×C263—21no—
57C42×C263—22no—
58C42×C263—21no—
59C2×Dic263—22no—
60C2×Dic263—22no—
61C2×Dic263—22no—
62C2×Dic263—42no—
63C2×Dic263—41no—
64C263⋊C8—22no—
65C263⋊C8—41no—
66C23×C263—21no—
67C23×C263C2×D411yescharacteristic
68Q8×C263—21no—
69Q8×C263C4⋊C412yescomplemented
70D4×C263—22no—
71D4×C263—22no—
72D4×C263—21no—
73D4×C263C4⋊C412yescomplemented
74C2×C4×C263—21no—
75C2×C4×C263—22no—
76C2×C4×C263—22no—
77C2×C4×C263—21no—
78C2×C4×C263—22no—
79C2×C4×C263—21no—
80C2×C4×C263—42no—
81C2×C4×C263—82no—
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×C263—22no—
91C22×C263—41no—
92C22×C263—41no—
93C22×C263C4×D411yescharacteristic
94C22×C263#12011yescharacteristic
95C22×C263C22⋊Q811yescharacteristic
96C4×C263—22no—
97C4×C263—42no—
98C4×C263—41no—
99C4×C263—41no—
100C4×C263C2×C4⋊C411yescharacteristic
101C4×C263C4×D411yescharacteristic
102C4×C263C22⋊Q811yescharacteristic
103C4×C263#12311yescharacteristic
104Dic263—24no—
105Dic263—81no—
106C2×C263—21no—
107C2×C263—21no—
108C2×C263—42no—
109C2×C263#38511yescharacteristic
110C2×C263#45311yescharacteristic
111C2×C263#45611yescharacteristic
112C263#185911yescharacteristic, complemented, Sylow
113#1859—2631nomaximal, Sylow
114#520D26311yescharacteristic
115#428—2631no—
116C2×#104—2631no—
117#417—2631no—
118#384—2631no—
119#343—2631no—
120#339—2631no—
121C2×#41C2×D26311yescharacteristic
122C2×M16—2631no—
123C2×M16—2631no—
124C4×Q8—21no—
125C4×D4—21no—
126C4×D4—22no—
127#117—21no—
128#117C2×D26311yescharacteristic
129C2×C4⋊C4—21no—
130C2×C4⋊C4—2631no—
131C2×C4⋊C4—5262no—
132C2×C4⋊C4C2×D26311yescharacteristic
133C2×C42—2631no—
134#107—5261no—
135#106—5261no—
136#104—2634no—
137#103—5261no—
138#102—5261no—
139#41—21no—
140#41—21no—
141#41C4×D26312yes—
142#41Dic52612yes—
143C2×Q8C22⋊D26311yescharacteristic
144C2×D4—21no—
145C2×D4C22⋊D26311yescharacteristic
146C22×C4—21no—
147C22×C4—22no—
148C22×C4—5261no—
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—22no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—5261no—
162C4⋊C4—5261no—
163C4⋊C4—10524no—
164C4⋊C4C22⋊D26311yescharacteristic
165C4⋊C4C22⋊D26311yescharacteristic
166C22⋊C4—22no—
167C22⋊C4—21no—
168C42—22no—
169C42—21no—
170C42—2632no—
171C42—5261no—
172C23—21no—
173C23C2×C22⋊D26311yescharacteristic
174Q8—21no—
175Q8Dic263⋊C412yescomplemented
176D4—22no—
177D4—22no—
178D4—21no—
179D4Dic263⋊C412yescomplemented
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—42no—
187C2×C4—82no—
188C2×C4—5262no—
189C2×C4—5262no—
190C2×C4—5262no—
191C2×C4—10522no—
192C2×C4—10521no—
193C2×C4C2×C4×D26311yescharacteristic
194C2×C4C2×C22⋊D26311yescharacteristic
195C2×C4C2×C22⋊D26311yescharacteristic
196C2×C4C2×Dic52611yescharacteristic
197C2×C4#1686237611yescharacteristic
198C2×C4#1686237611yescharacteristic
199C8—5262no—
200C8—10521no—
201C22—21no—
202C22—21no—
203C22—22no—
204C22—41no—
205C22—41no—
206C22C4×C22⋊D26311yescharacteristic
207C22#2255443911yescharacteristic
208C22#2255444911yescharacteristic
209C4—22no—
210C4—41no—
211C4—42no—
212C4—41no—
213C4—5264no—
214C4—21041no—
215C4C2×Dic263⋊C411yescharacteristic
216C4C4×C22⋊D26311yescharacteristic
217C4#2255444911yescharacteristic
218C4#2255445311yescharacteristic
219C2—21no—
220C2—21no—
221C2—42no—
222C2#3068181111yescharacteristic
223C2#3068210611yescharacteristic
224C2#3068212111yescharacteristic
subgroupG/H
centerC22#22554439
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#520×C263C2
socleC22×C263#120
prime radicalC2×#41×C263C22
cosocleC22×C4×C263C23
hypercenter#520D263
hypocenterC263#1859
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #30681981C2semidirect
4. #30681807C2semidirect
5. #30681707C2semidirect
6. #30681697C2semidirect
15. #22554397C4semidirect
31. #16862360C2×C4semidirect
38. C4×Dic263C2×C4semidirect
69. Q8×C263C4⋊C4semidirect
73. D4×C263C4⋊C4semidirect
112. C263#1859semidirect
175. Q8Dic263⋊C4semidirect
179. D4Dic263⋊C4semidirect

Maximal subgroups

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

subgroupindex
#306819812
C2×#225543972
#306819392
#306818072
#306817072
#306816972
#520×C2632
#1859263