Finite Group Databasebeta

← #44537463

Subgroups — #44537463

Order 31424.

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#30628333C211yesmaximal, characteristic, complemented
2#30628332C211yesmaximal, characteristic, complemented
3#30628330C211yesmaximal, characteristic, complemented
4#30628322C211yesmaximal, characteristic, complemented
5#30628321C211yesmaximal, characteristic, complemented
6#30628320C211yesmaximal, characteristic, complemented
7#30628311C211yesmaximal, characteristic, complemented
8#30628310C211yesmaximal, characteristic, complemented
9#30628309C211yesmaximal, characteristic, complemented
10#30628309C211yesmaximal, characteristic, complemented
11#30628308C211yesmaximal, characteristic, complemented
12#30628307C211yesmaximal, characteristic, complemented
13#30628305C211yesmaximal, characteristic, complemented
14#30628305C211yesmaximal, characteristic, complemented
15#121×C491C211yesmaximal, characteristic, complemented
16C23×D491C2211yescharacteristic
17C2×D1964C2211yescharacteristic
18C2×D1964C2211yescharacteristic
19C2×C22⋊D491C2211yescharacteristic
20C2×C22⋊D491C2211yescharacteristic
21C2×C22⋊D491C2211yescharacteristic
22C2×C22⋊D491C2211yescharacteristic
23C2×C22⋊D491C2211yescharacteristic
24C2×C22⋊D491C2211yescharacteristic, complemented
25C2×C22⋊D491C2211yescharacteristic, complemented
26C22×Dic491C2211yescharacteristic, complemented
27C2×C4×D491C2211yescharacteristic, complemented
28C4⋊Dic491C2211yescharacteristic, complemented
29C4⋊Dic491C2211yescharacteristic, complemented
30Dic491⋊C4C2211yescharacteristic, complemented
31Dic491⋊C4C2211yescharacteristic, complemented
32Dic491⋊C4C2211yescharacteristic, complemented
33C22⋊Dic491C2211yescharacteristic
34C22⋊Dic491C2211yescharacteristic
35C22⋊Dic491C2211yescharacteristic, complemented
36(C2×D491)⋊C4C2211yescharacteristic
37(C2×D491)⋊C4C2211yescharacteristic
38(C2×D491)⋊C4C2211yescharacteristic
39(C2×D491)⋊C4C2211yescharacteristic
40(C2×D491)⋊C4C2211yescharacteristic
41(C2×D491)⋊C4C2211yescharacteristic
42(C2×D491)⋊C4C2211yescharacteristic, complemented
43C4×Dic491C2211yescharacteristic, complemented
44C2×D4×C491C2211yescharacteristic
45C2×D4×C491C2211yescharacteristic
46C2×D4×C491C2211yescharacteristic, complemented
47C22×C4×C491C2211yescharacteristic, complemented
48C4⋊C4×C491C2211yescharacteristic, complemented
49C22⋊C4×C491C2211yescharacteristic
50C22⋊C4×C491C2211yescharacteristic, complemented
51C22×D491—41no—
52C22×D491—41no—
53C22×D491—41no—
54C22×D491C2311yescharacteristic
55C22×D491C2311yescharacteristic
56C22×D491C2311yescharacteristic
57D1964—41no—
58D1964—41no—
59C22⋊D491—41no—
60C22⋊D491—41no—
61C22⋊D491—41no—
62C22⋊D491—41no—
63C22⋊D491—41no—
64C22⋊D491—41no—
65C22⋊D491—41no—
66C2×Dic491—41no—
67C2×Dic491C2311yescharacteristic
68C2×Dic491C2311yescharacteristic
69C2×Dic491C2311yescharacteristic
70C2×Dic491C2311yescharacteristic
71C2×Dic491C2311yescharacteristic
72C4×D491—41no—
73C23×C491C2311yescharacteristic
74C23×C491C2311yescharacteristic
75C23×C491C2311yescharacteristic
76D4×C491—41no—
77D4×C491—41no—
78D4×C491—41no—
79C2×C4×C491—41no—
80C2×C4×C491C2311yescharacteristic
81C2×C4×C491C2311yescharacteristic
82C2×C4×C491C2311yescharacteristic
83C2×C4×C491C2311yescharacteristic
84C22×C491—21no—
85C22×C491—21no—
86C22×C491—21no—
87C22×C491—21no—
88C22×C491—21no—
89C22×C491—21no—
90C22×C491—21no—
91C22×C491—21no—
92C22×C491—21no—
93C22×C491C2411yescharacteristic
94C2×D491—21no—
95C2×D491—21no—
96C2×D491—21no—
97C2×D491—21no—
98C2×D491—21no—
99C2×D491—21no—
100C2×D491—21no—
101C2×D491—21no—
102C2×D491—21no—
103C2×D491—44no—
104C4×C491—21no—
105C4×C491—21no—
106C4×C491—21no—
107C4×C491—21no—
108Dic491—21no—
109Dic491—21no—
110Dic491—21no—
111Dic491—21no—
112Dic491—21no—
113C2×C491—41no—
114C2×C491—41no—
115C2×C491—41no—
116C2×C491H(5,𝔽2)11yescharacteristic
117C2×C491H(5,𝔽2)11yescharacteristic
118C2×C491H(5,𝔽2)11yescharacteristic
119D491—41no—
120D491—41no—
121D491—41no—
122C491#56011yescharacteristic, complemented, Sylow
123#560—4911nomaximal, Sylow
124#127—4911no—
125#126—4911no—
126#126—4911no—
127#123—4911no—
128#123—4911no—
129#123—4911no—
130#121—4911no—
131#121—4911no—
132#121—4911no—
133#121—4911no—
134#121—4911no—
135#121D49111yescharacteristic, complemented
136#120—4911no—
137#120—4911no—
138#120—4911no—
139C24—4911no—
140C2×D4—4911no—
141C2×D4—4911no—
142C2×D4—4911no—
143C2×D4—4911no—
144C2×D4—4911no—
145C2×D4—4911no—
146C2×D4—4911no—
147C2×D4—4911no—
148C2×D4—4911no—
149C2×D4C2×D49111yescharacteristic
150C2×D4C2×D49111yescharacteristic
151C2×D4C2×D49111yescharacteristic, complemented
152C22×C4—4911no—
153C22×C4—4911no—
154C22×C4C2×D49111yescharacteristic, complemented
155C4⋊C4—4911no—
156C4⋊C4—4911no—
157C4⋊C4—4911no—
158C4⋊C4—4911no—
159C4⋊C4—4911no—
160C4⋊C4C2×D49111yescharacteristic, complemented
161C22⋊C4—4911no—
162C22⋊C4—4911no—
163C22⋊C4—4911no—
164C22⋊C4—4911no—
165C22⋊C4—4911no—
166C22⋊C4—4911no—
167C22⋊C4—4911no—
168C22⋊C4—4911no—
169C22⋊C4—4911no—
170C22⋊C4—4911no—
171C22⋊C4C2×D49111yescharacteristic
172C22⋊C4C2×D49111yescharacteristic, complemented
173C42—4911no—
174C23—19641no—
175C23—19641no—
176C23—19641no—
177C23—4911no—
178C23—4911no—
179C23—4911no—
180C23C22×D49111yescharacteristic
181C23C22×D49111yescharacteristic
182C23C22×D49111yescharacteristic
183D4—41no—
184D4—41no—
185D4—41no—
186D4—19641no—
187D4—19641no—
188D4—19641no—
189D4—19641no—
190D4—19641no—
191D4—19641no—
192D4—19641no—
193D4—19641no—
194D4—19641no—
195C2×C4—41no—
196C2×C4—19641no—
197C2×C4—19641no—
198C2×C4—4911no—
199C2×C4—4911no—
200C2×C4—4911no—
201C2×C4—4911no—
202C2×C4—4911no—
203C2×C4C22×D49111yescharacteristic
204C2×C4C22×D49111yescharacteristic
205C2×C4C22×D49111yescharacteristic
206C2×C4C22×D49111yescharacteristic
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—19644no—
217C22—9821no—
218C22—9821no—
219C22—9821no—
220C22—9821no—
221C22—9821no—
222C22—9821no—
223C22—9821no—
224C22—9821no—
225C22—9821no—
226C22C23×D49111yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—9821no—
232C4—9821no—
233C4—9821no—
234C4—9821no—
235C4—9821no—
236C2—41no—
237C2—41no—
238C2—41no—
239C2—19641no—
240C2—19641no—
241C2—19641no—
242C2#3062838211yescharacteristic
243C2#3062838211yescharacteristic
244C2#3062838311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D491
commutator, socle, cosocleC22×C491C24
Fitting#121×C491C2
hypercenter#121D491
hypocenterC491#560
LCSG ▷ C22×C491 ▷ C491
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #30628333C2semidirect
2. #30628332C2semidirect
3. #30628330C2semidirect
4. #30628322C2semidirect
5. #30628321C2semidirect
6. #30628320C2semidirect
7. #30628311C2semidirect
8. #30628310C2semidirect
9. #30628309C2semidirect
10. #30628309C2semidirect
11. #30628308C2semidirect
12. #30628307C2semidirect
13. #30628305C2semidirect
14. #30628305C2semidirect
15. #121×C491C2semidirect
24. C2×C22⋊D491C22semidirect
25. C2×C22⋊D491C22semidirect
26. C22×Dic491C22semidirect
27. C2×C4×D491C22semidirect
28. C4⋊Dic491C22semidirect
29. C4⋊Dic491C22semidirect
30. Dic491⋊C4C22semidirect
31. Dic491⋊C4C22semidirect
32. Dic491⋊C4C22semidirect
35. C22⋊Dic491C22semidirect
42. (C2×D491)⋊C4C22semidirect
43. C4×Dic491C22semidirect
46. C2×D4×C491C22semidirect
47. C22×C4×C491C22semidirect
48. C4⋊C4×C491C22semidirect
50. C22⋊C4×C491C22semidirect
122. C491#560semidirect
135. #121D491semidirect
151. C2×D4C2×D491semidirect
154. C22×C4C2×D491semidirect
160. C4⋊C4C2×D491semidirect
172. C22⋊C4C2×D491semidirect

Maximal subgroups

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

subgroupindex
#306283332
#306283322
#306283302
#306283222
#306283212
#306283202
#306283112
#306283102
#306283092
#306283082
#306283072
#306283052
#121×C4912
#560491