Finite Group Databasebeta

← #45688170

Subgroups — #45688170

Order 33344.

252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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#30659704C211yesmaximal, characteristic, complemented
2#30659703C211yesmaximal, characteristic, complemented
3#30659701C211yesmaximal, characteristic, complemented
4#30659693C211yesmaximal, characteristic, complemented
5#30659692C211yesmaximal, characteristic, complemented
6#30659691C211yesmaximal, characteristic, complemented
7#30659682C211yesmaximal, characteristic, complemented
8#30659681C211yesmaximal, characteristic, complemented
9#30659680C211yesmaximal, characteristic, complemented
10#30659680C211yesmaximal, characteristic, complemented
11#30659679C211yesmaximal, characteristic, complemented
12#30659678C211yesmaximal, characteristic, complemented
13#30659676C211yesmaximal, characteristic, complemented
14#30659676C211yesmaximal, characteristic, complemented
15#121×C521C211yesmaximal, characteristic, complemented
16C23×D521C2211yescharacteristic
17C2×D2084C2211yescharacteristic
18C2×D2084C2211yescharacteristic
19C2×C22⋊D521C2211yescharacteristic
20C2×C22⋊D521C2211yescharacteristic
21C2×C22⋊D521C2211yescharacteristic
22C2×C22⋊D521C2211yescharacteristic
23C2×C22⋊D521C2211yescharacteristic
24C2×C22⋊D521C2211yescharacteristic, complemented
25C2×C22⋊D521C2211yescharacteristic, complemented
26C22×Dic521C2211yescharacteristic, complemented
27C2×C4×D521C2211yescharacteristic, complemented
28C4⋊Dic521C2211yescharacteristic, complemented
29C4⋊Dic521C2211yescharacteristic, complemented
30#22552343C2211yescharacteristic, complemented
31#22552343C2211yescharacteristic, complemented
32#22552343C2211yescharacteristic, complemented
33C22⋊Dic521C2211yescharacteristic
34C22⋊Dic521C2211yescharacteristic
35C22⋊Dic521C2211yescharacteristic, complemented
36#22552341C2211yescharacteristic
37#22552341C2211yescharacteristic
38#22552341C2211yescharacteristic
39#22552341C2211yescharacteristic
40#22552341C2211yescharacteristic
41#22552341C2211yescharacteristic
42#22552341C2211yescharacteristic, complemented
43C4×Dic521C2211yescharacteristic, complemented
44C2×D4×C521C2211yescharacteristic
45C2×D4×C521C2211yescharacteristic
46C2×D4×C521C2211yescharacteristic, complemented
47C22×C4×C521C2211yescharacteristic, complemented
48C4⋊C4×C521C2211yescharacteristic, complemented
49C22⋊C4×C521C2211yescharacteristic
50C22⋊C4×C521C2211yescharacteristic, complemented
51C22×D521—41no—
52C22×D521—41no—
53C22×D521—41no—
54C22×D521C2311yescharacteristic
55C22×D521C2311yescharacteristic
56C22×D521C2311yescharacteristic
57D2084—41no—
58D2084—41no—
59C22⋊D521—41no—
60C22⋊D521—41no—
61C22⋊D521—41no—
62C22⋊D521—41no—
63C22⋊D521—41no—
64C22⋊D521—41no—
65C22⋊D521—41no—
66C2×Dic521—41no—
67C2×Dic521C2311yescharacteristic
68C2×Dic521C2311yescharacteristic
69C2×Dic521C2311yescharacteristic
70C2×Dic521C2311yescharacteristic
71C2×Dic521C2311yescharacteristic
72C4×D521—41no—
73C23×C521C2311yescharacteristic
74C23×C521C2311yescharacteristic
75C23×C521C2311yescharacteristic
76D4×C521—41no—
77D4×C521—41no—
78D4×C521—41no—
79C2×C4×C521—41no—
80C2×C4×C521C2311yescharacteristic
81C2×C4×C521C2311yescharacteristic
82C2×C4×C521C2311yescharacteristic
83C2×C4×C521C2311yescharacteristic
84C22×C521—21no—
85C22×C521—21no—
86C22×C521—21no—
87C22×C521—21no—
88C22×C521—21no—
89C22×C521—21no—
90C22×C521—21no—
91C22×C521—21no—
92C22×C521—21no—
93C22×C521C2411yescharacteristic
94C2×D521—21no—
95C2×D521—21no—
96C2×D521—21no—
97C2×D521—21no—
98C2×D521—21no—
99C2×D521—21no—
100C2×D521—21no—
101C2×D521—21no—
102C2×D521—21no—
103C2×D521—44no—
104C4×C521—21no—
105C4×C521—21no—
106C4×C521—21no—
107C4×C521—21no—
108Dic521—21no—
109Dic521—21no—
110Dic521—21no—
111Dic521—21no—
112Dic521—21no—
113C2×C521—41no—
114C2×C521—41no—
115C2×C521—41no—
116C2×C521H(5,𝔽2)11yescharacteristic
117C2×C521H(5,𝔽2)11yescharacteristic
118C2×C521H(5,𝔽2)11yescharacteristic
119D521—41no—
120D521—41no—
121D521—41no—
122C521#56011yescharacteristic, complemented, Sylow
123#560—5211nomaximal, Sylow
124#127—5211no—
125#126—5211no—
126#126—5211no—
127#123—5211no—
128#123—5211no—
129#123—5211no—
130#121—5211no—
131#121—5211no—
132#121—5211no—
133#121—5211no—
134#121—5211no—
135#121D52111yescharacteristic, complemented
136#120—5211no—
137#120—5211no—
138#120—5211no—
139C24—5211no—
140C2×D4—5211no—
141C2×D4—5211no—
142C2×D4—5211no—
143C2×D4—5211no—
144C2×D4—5211no—
145C2×D4—5211no—
146C2×D4—5211no—
147C2×D4—5211no—
148C2×D4—5211no—
149C2×D4C2×D52111yescharacteristic
150C2×D4C2×D52111yescharacteristic
151C2×D4C2×D52111yescharacteristic, complemented
152C22×C4—5211no—
153C22×C4—5211no—
154C22×C4C2×D52111yescharacteristic, complemented
155C4⋊C4—5211no—
156C4⋊C4—5211no—
157C4⋊C4—5211no—
158C4⋊C4—5211no—
159C4⋊C4—5211no—
160C4⋊C4C2×D52111yescharacteristic, complemented
161C22⋊C4—5211no—
162C22⋊C4—5211no—
163C22⋊C4—5211no—
164C22⋊C4—5211no—
165C22⋊C4—5211no—
166C22⋊C4—5211no—
167C22⋊C4—5211no—
168C22⋊C4—5211no—
169C22⋊C4—5211no—
170C22⋊C4—5211no—
171C22⋊C4C2×D52111yescharacteristic
172C22⋊C4C2×D52111yescharacteristic, complemented
173C42—5211no—
174C23—5211no—
175C23—5211no—
176C23—5211no—
177C23—20841no—
178C23—20841no—
179C23—20841no—
180C23C22×D52111yescharacteristic
181C23C22×D52111yescharacteristic
182C23C22×D52111yescharacteristic
183D4—41no—
184D4—41no—
185D4—41no—
186D4—20841no—
187D4—20841no—
188D4—20841no—
189D4—20841no—
190D4—20841no—
191D4—20841no—
192D4—20841no—
193D4—20841no—
194D4—20841no—
195C2×C4—41no—
196C2×C4—5211no—
197C2×C4—5211no—
198C2×C4—5211no—
199C2×C4—5211no—
200C2×C4—5211no—
201C2×C4—20841no—
202C2×C4—20841no—
203C2×C4C22×D52111yescharacteristic
204C2×C4C22×D52111yescharacteristic
205C2×C4C22×D52111yescharacteristic
206C2×C4C22×D52111yescharacteristic
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—10421no—
217C22—10421no—
218C22—10421no—
219C22—10421no—
220C22—10421no—
221C22—10421no—
222C22—10421no—
223C22—10421no—
224C22—10421no—
225C22—20844no—
226C22C23×D52111yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—10421no—
232C4—10421no—
233C4—10421no—
234C4—10421no—
235C4—10421no—
236C2—41no—
237C2—41no—
238C2—41no—
239C2—20841no—
240C2—20841no—
241C2—20841no—
242C2#3065975311yescharacteristic
243C2#3065975311yescharacteristic
244C2#3065975411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D521
commutator, socle, cosocleC22×C521C24
Fitting#121×C521C2
hypercenter#121D521
hypocenterC521#560
LCSG ▷ C22×C521 ▷ C521
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #30659704C2semidirect
2. #30659703C2semidirect
3. #30659701C2semidirect
4. #30659693C2semidirect
5. #30659692C2semidirect
6. #30659691C2semidirect
7. #30659682C2semidirect
8. #30659681C2semidirect
9. #30659680C2semidirect
10. #30659680C2semidirect
11. #30659679C2semidirect
12. #30659678C2semidirect
13. #30659676C2semidirect
14. #30659676C2semidirect
15. #121×C521C2semidirect
24. C2×C22⋊D521C22semidirect
25. C2×C22⋊D521C22semidirect
26. C22×Dic521C22semidirect
27. C2×C4×D521C22semidirect
28. C4⋊Dic521C22semidirect
29. C4⋊Dic521C22semidirect
30. #22552343C22semidirect
31. #22552343C22semidirect
32. #22552343C22semidirect
35. C22⋊Dic521C22semidirect
42. #22552341C22semidirect
43. C4×Dic521C22semidirect
46. C2×D4×C521C22semidirect
47. C22×C4×C521C22semidirect
48. C4⋊C4×C521C22semidirect
50. C22⋊C4×C521C22semidirect
122. C521#560semidirect
135. #121D521semidirect
151. C2×D4C2×D521semidirect
154. C22×C4C2×D521semidirect
160. C4⋊C4C2×D521semidirect
172. C22⋊C4C2×D521semidirect

Maximal subgroups

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

subgroupindex
#306597042
#306597032
#306597012
#306596932
#306596922
#306596912
#306596822
#306596812
#306596802
#306596792
#306596782
#306596762
#121×C5212
#560521