Finite Group Databasebeta

← #44417452

Subgroups — #44417452

Order 29248.

248 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 95 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#28410545C211yesmaximal, characteristic, complemented
2#28410538C211yesmaximal, characteristic, complemented
3#28410537C211yesmaximal, characteristic, complemented
4#28410537C211yesmaximal, characteristic, complemented
5#28410534C211yesmaximal, characteristic, complemented
6#28410532C211yesmaximal, characteristic, complemented
7#28410530C211yesmaximal, characteristic, complemented
8#28410522C211yesmaximal, characteristic
9C4×D1828C211yesmaximal, characteristic, complemented
10#28410514C211yesmaximal, characteristic, complemented
11#28410510C211yesmaximal, characteristic, complemented
12#28410509C211yesmaximal, characteristic, complemented
13C22⋊C4×D457C211yesmaximal, characteristic, complemented
14C22⋊C4×D457C211yesmaximal, characteristic, complemented
15#126×C457C211yesmaximal, characteristic, complemented
16C23×D457C2211yescharacteristic
17C2×Dic914C2211yescharacteristic, complemented
18C2×D1828C2211yescharacteristic
19C2×D1828C2211yescharacteristic
20C2×C22⋊D457C2211yescharacteristic
21C2×C4×D457C2211yescharacteristic
22C2×C4×D457C2211yescharacteristic
23C2×C4×D457C2211yescharacteristic
24C2×C4×D457C2211yescharacteristic
25C2×C4×D457C2211yescharacteristic, complemented
26C4⋊Dic457C2211yescharacteristic, complemented
27C4⋊Dic457C2211yescharacteristic, complemented
28#20300720C2211yescharacteristic, complemented
29#20300720C2211yescharacteristic, complemented
30#20300720C2211yescharacteristic, complemented
31C22⋊Dic457C2211yescharacteristic
32C22⋊Dic457C2211yescharacteristic
33#20300718C2211yescharacteristic
34#20300718C2211yescharacteristic
35#20300718C2211yescharacteristic
36#20300718C2211yescharacteristic
37#20300718C2211yescharacteristic
38#20300718C2211yescharacteristic
39#20300718C2211yescharacteristic, complemented
40#20300718C2211yescharacteristic, complemented
41#20300718C2211yescharacteristic, complemented
42C4×Dic457C2211yescharacteristic, complemented
43C4×Dic457C2211yescharacteristic, complemented
44C4⋊C4×C457C2211yescharacteristic, complemented
45C4⋊C4×C457C2211yescharacteristic, complemented
46C4⋊C4×C457C2211yescharacteristic, complemented
47C22⋊C4×C457C2211yescharacteristic
48C22⋊C4×C457C2211yescharacteristic
49C22⋊C4×C457C2211yescharacteristic
50C42×C457C2211yescharacteristic, complemented
51C22×D457—22no—
52C22×D457—22no—
53C22×D457—41no—
54C22×D457C2311yescharacteristic
55C22×D457C2311yescharacteristic
56C22×D457C2311yescharacteristic
57Dic914—41no—
58D1828—22no—
59D1828—22no—
60C22⋊D457—41no—
61C2×Dic457C2311yescharacteristic
62C2×Dic457C2311yescharacteristic
63C2×Dic457C2311yescharacteristic
64C2×Dic457C2311yescharacteristic
65C2×Dic457C2311yescharacteristic
66C4×D457—22no—
67C4×D457—22no—
68C4×D457—41no—
69C4×D457—41no—
70C4×D457—41no—
71C23×C457C2311yescharacteristic
72C2×C4×C457C2311yescharacteristic
73C2×C4×C457C2311yescharacteristic
74C2×C4×C457C2311yescharacteristic
75C2×C4×C457C2311yescharacteristic
76C2×C4×C457C2311yescharacteristic
77C2×C4×C457C2311yescharacteristic
78C22×C457—21no—
79C22×C457—21no—
80C22×C457—21no—
81C22×C457C2411yescharacteristic
82C2×D457—21no—
83C2×D457—21no—
84C2×D457—21no—
85C2×D457—21no—
86C2×D457—21no—
87C2×D457—21no—
88C2×D457—21no—
89C2×D457—44no—
90C2×D457#4112yes—
91C2×D457#4112yes—
92C4×C457—21no—
93C4×C457—21no—
94C4×C457—21no—
95C4×C457—21no—
96C4×C457—21no—
97C4×C457—21no—
98Dic457—21no—
99Dic457—21no—
100Dic457—21no—
101Dic457—21no—
102Dic457—21no—
103C2×C457—41no—
104C2×C457C2×#4111yescharacteristic
105C2×C457C2×#4111yescharacteristic
106C2×C457H(5,𝔽2)11yescharacteristic
107D457—22no—
108D457—22no—
109D457—41no—
110C457#55111yescharacteristic, complemented, Sylow
111#551—4571nomaximal, Sylow
112#126—4571no—
113#126D45711yescharacteristic, complemented
114#124—4571no—
115#123—4571no—
116#123—4571no—
117#123—4571no—
118C22⋊Q8—4571no—
119C22⋊Q8—4571no—
120#120—4571no—
121C4×D4—4571no—
122C4×D4—4571no—
123#117—4571no—
124#117—4571no—
125C2×C22⋊C4—4571no—
126C2×C22⋊C4—4571no—
127C24—4571no—
128C2×Q8—4571no—
129C2×D4—4571no—
130C2×D4—4571no—
131C2×D4—4571no—
132C22×C4—4571no—
133C22×C4—4571no—
134C22×C4—4571no—
135C22×C4—4571no—
136C22×C4—4571no—
137C4⋊C4—4571no—
138C4⋊C4—4571no—
139C4⋊C4—4571no—
140C4⋊C4—4571no—
141C4⋊C4—4571no—
142C4⋊C4C2×D45711yescharacteristic, complemented
143C4⋊C4C2×D45711yescharacteristic, complemented
144C4⋊C4C2×D45711yescharacteristic, complemented
145C22⋊C4—4571no—
146C22⋊C4—4571no—
147C22⋊C4—4571no—
148C22⋊C4—4571no—
149C22⋊C4—4571no—
150C22⋊C4—4571no—
151C22⋊C4—4571no—
152C22⋊C4—4571no—
153C22⋊C4—4571no—
154C22⋊C4—4571no—
155C22⋊C4—4571no—
156C22⋊C4C2×D45711yescharacteristic
157C22⋊C4C2×D45711yescharacteristic
158C22⋊C4C2×D45711yescharacteristic
159C42—4571no—
160C42—4571no—
161C42C2×D45711yescharacteristic, complemented
162C23—18281no—
163C23—9142no—
164C23—9142no—
165C23—4571no—
166C23—4571no—
167C23—4571no—
168C23C22×D45711yescharacteristic
169Q8—18281no—
170D4—18281no—
171D4—9142no—
172D4—9142no—
173C2×C4—18281no—
174C2×C4—18281no—
175C2×C4—18281no—
176C2×C4—9142no—
177C2×C4—9142no—
178C2×C4—4571no—
179C2×C4—4571no—
180C2×C4—4571no—
181C2×C4—4571no—
182C2×C4—4571no—
183C2×C4C22×D45711yescharacteristic
184C2×C4C22×D45711yescharacteristic
185C2×C4C22×D45711yescharacteristic
186C2×C4C22×D45711yescharacteristic
187C2×C4C22×D45711yescharacteristic
188C2×C4C22×D45711yescharacteristic
189C22—21no—
190C22—21no—
191C22—21no—
192C22—18284no—
193C22—9141no—
194C22—9141no—
195C22—9141no—
196C22—9141no—
197C22—9141no—
198C22—9141no—
199C22—9141no—
200C22—4572no—
201C22—4572no—
202C22C23×D45711yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—9141no—
210C4—9141no—
211C4—9141no—
212C4—9141no—
213C4—9141no—
214C2—41no—
215C2—18281no—
216C2—9142no—
217C2—9142no—
218C2#41×D45711yescharacteristic
219C2#41×D45711yescharacteristic
220C2#2841059811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D457
commutator, socle, cosocleC22×C457C24
Fitting#126×C457C2
prime radical#28410522C2
hypercenter#126D457
hypocenterC457#551
LCSG ▷ C22×C457 ▷ C457
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #28410545C2semidirect
2. #28410538C2semidirect
3. #28410537C2semidirect
4. #28410537C2semidirect
5. #28410534C2semidirect
6. #28410532C2semidirect
7. #28410530C2semidirect
9. C4×D1828C2semidirect
10. #28410514C2semidirect
11. #28410510C2semidirect
12. #28410509C2semidirect
13. C22⋊C4×D457C2semidirect
14. C22⋊C4×D457C2semidirect
15. #126×C457C2semidirect
17. C2×Dic914C22semidirect
25. C2×C4×D457C22semidirect
26. C4⋊Dic457C22semidirect
27. C4⋊Dic457C22semidirect
28. #20300720C22semidirect
29. #20300720C22semidirect
30. #20300720C22semidirect
39. #20300718C22semidirect
40. #20300718C22semidirect
41. #20300718C22semidirect
42. C4×Dic457C22semidirect
43. C4×Dic457C22semidirect
44. C4⋊C4×C457C22semidirect
45. C4⋊C4×C457C22semidirect
46. C4⋊C4×C457C22semidirect
50. C42×C457C22semidirect
110. C457#551semidirect
113. #126D457semidirect
142. C4⋊C4C2×D457semidirect
143. C4⋊C4C2×D457semidirect
144. C4⋊C4C2×D457semidirect
161. C42C2×D457semidirect

Maximal subgroups

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

subgroupindex
#284105452
#284105382
#284105372
#284105342
#284105322
#284105302
#284105222
C4×D18282
#284105142
#284105102
#284105092
C22⋊C4×D4572
#126×C4572
#551457