Finite Group Databasebeta

← #43244190

Subgroups — #43244190

Order 28096.

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

normal subgroups only

This group has 250 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#28380738C211yesmaximal, characteristic, complemented
2#28380736C211yesmaximal, characteristic, complemented
3#28380729C211yesmaximal, characteristic, complemented
4#28380729C211yesmaximal, characteristic, complemented
5#28380728C211yesmaximal, characteristic, complemented
6#28380723C211yesmaximal, characteristic, complemented
7#28380717C211yesmaximal, characteristic, complemented
8#28380716C211yesmaximal, characteristic, complemented
9#28380714C211yesmaximal, characteristic, complemented
10#28380713C211yesmaximal, characteristic, complemented
11#28380711C211yesmaximal, characteristic, complemented
12#28380705C211yesmaximal, characteristic, complemented
13C4×C22⋊D439C211yesmaximal, characteristic, complemented
14C22⋊C4×D439C211yesmaximal, characteristic, complemented
15#123×C439C211yesmaximal, characteristic, complemented
16C23×D439C2211yescharacteristic
17C2×Dic878C2211yescharacteristic, complemented
18C2×D1756C2211yescharacteristic
19C2×D1756C2211yescharacteristic
20C2×C22⋊D439C2211yescharacteristic
21C2×C22⋊D439C2211yescharacteristic
22C2×C22⋊D439C2211yescharacteristic
23C2×C22⋊D439C2211yescharacteristic, complemented
24C2×C4×D439C2211yescharacteristic
25C2×C4×D439C2211yescharacteristic
26C2×C4×D439C2211yescharacteristic, complemented
27C4⋊Dic439C2211yescharacteristic, complemented
28C4⋊Dic439C2211yescharacteristic, complemented
29Dic439⋊C4C2211yescharacteristic, complemented
30Dic439⋊C4C2211yescharacteristic, complemented
31C22⋊Dic439C2211yescharacteristic
32C22⋊Dic439C2211yescharacteristic
33C22⋊Dic439C2211yescharacteristic, complemented
34(C2×D439)⋊C4C2211yescharacteristic
35(C2×D439)⋊C4C2211yescharacteristic
36(C2×D439)⋊C4C2211yescharacteristic
37(C2×D439)⋊C4C2211yescharacteristic
38(C2×D439)⋊C4C2211yescharacteristic
39(C2×D439)⋊C4C2211yescharacteristic
40(C2×D439)⋊C4C2211yescharacteristic, complemented
41(C2×D439)⋊C4C2211yescharacteristic, complemented
42C4×Dic439C2211yescharacteristic, complemented
43C4×Dic439C2211yescharacteristic, complemented
44C2×D4×C439C2211yescharacteristic
45C22×C4×C439C2211yescharacteristic, complemented
46C4⋊C4×C439C2211yescharacteristic, complemented
47C4⋊C4×C439C2211yescharacteristic, complemented
48C22⋊C4×C439C2211yescharacteristic
49C22⋊C4×C439C2211yescharacteristic
50C22⋊C4×C439C2211yescharacteristic, complemented
51C22×D439—22no—
52C22×D439—41no—
53C22×D439—41no—
54C22×D439C2311yescharacteristic
55C22×D439C2311yescharacteristic
56C22×D439C2311yescharacteristic
57Dic878—41no—
58D1756—22no—
59D1756—41no—
60C22⋊D439—22no—
61C22⋊D439—41no—
62C22⋊D439—41no—
63C22⋊D439—41no—
64C2×Dic439C2311yescharacteristic
65C2×Dic439C2311yescharacteristic
66C2×Dic439C2311yescharacteristic
67C2×Dic439C2311yescharacteristic
68C2×Dic439C2311yescharacteristic
69C4×D439—41no—
70C4×D439—41no—
71C4×D439—41no—
72C23×C439C2311yescharacteristic
73C23×C439C2311yescharacteristic
74D4×C439—41no—
75C2×C4×C439—41no—
76C2×C4×C439C2311yescharacteristic
77C2×C4×C439C2311yescharacteristic
78C2×C4×C439C2311yescharacteristic
79C2×C4×C439C2311yescharacteristic
80C2×C4×C439C2311yescharacteristic
81C22×C439—21no—
82C22×C439—21no—
83C22×C439—21no—
84C22×C439—21no—
85C22×C439—21no—
86C22×C439—21no—
87C22×C439C2411yescharacteristic
88C2×D439—21no—
89C2×D439—21no—
90C2×D439—21no—
91C2×D439—21no—
92C2×D439—21no—
93C2×D439—21no—
94C2×D439—21no—
95C2×D439—21no—
96C2×D439—44no—
97C2×D439#4112yes—
98C4×C439—21no—
99C4×C439—21no—
100C4×C439—21no—
101C4×C439—21no—
102C4×C439—21no—
103Dic439—21no—
104Dic439—21no—
105Dic439—21no—
106Dic439—21no—
107Dic439—21no—
108C2×C439—41no—
109C2×C439—41no—
110C2×C439C2×#4111yescharacteristic
111C2×C439H(5,𝔽2)11yescharacteristic
112C2×C439H(5,𝔽2)11yescharacteristic
113D439—22no—
114D439—41no—
115D439—41no—
116C439#53811yescharacteristic, complemented, Sylow
117#538—4391nomaximal, Sylow
118#126—4391no—
119#126—4391no—
120#124—4391no—
121#124—4391no—
122#123—4391no—
123#123D43911yescharacteristic, complemented
124C22⋊Q8—4391no—
125#121—4391no—
126#121—4391no—
127#121—4391no—
128#120—4391no—
129#120—4391no—
130C4×D4—4391no—
131C4×D4—4391no—
132C2×C22⋊C4—4391no—
133C24—4391no—
134C2×Q8—4391no—
135C2×D4—4391no—
136C2×D4—4391no—
137C2×D4—4391no—
138C2×D4—4391no—
139C2×D4—4391no—
140C2×D4—4391no—
141C2×D4C2×D43911yescharacteristic
142C22×C4—4391no—
143C22×C4—4391no—
144C22×C4—4391no—
145C22×C4C2×D43911yescharacteristic, complemented
146C4⋊C4—4391no—
147C4⋊C4—4391no—
148C4⋊C4—4391no—
149C4⋊C4—4391no—
150C4⋊C4C2×D43911yescharacteristic, complemented
151C4⋊C4C2×D43911yescharacteristic, complemented
152C22⋊C4—4391no—
153C22⋊C4—4391no—
154C22⋊C4—4391no—
155C22⋊C4—4391no—
156C22⋊C4—4391no—
157C22⋊C4—4391no—
158C22⋊C4—4391no—
159C22⋊C4—4391no—
160C22⋊C4—4391no—
161C22⋊C4—4391no—
162C22⋊C4—4391no—
163C22⋊C4C2×D43911yescharacteristic
164C22⋊C4C2×D43911yescharacteristic
165C22⋊C4C2×D43911yescharacteristic, complemented
166C42—4391no—
167C42—4391no—
168C23—8782no—
169C23—4391no—
170C23—4391no—
171C23—4391no—
172C23—17561no—
173C23—17561no—
174C23C22×D43911yescharacteristic
175C23C22×D43911yescharacteristic
176Q8—17561no—
177D4—41no—
178D4—8782no—
179D4—8782no—
180D4—17561no—
181D4—17561no—
182D4—17561no—
183D4—17561no—
184C2×C4—41no—
185C2×C4—4391no—
186C2×C4—4391no—
187C2×C4—4391no—
188C2×C4—4391no—
189C2×C4—4391no—
190C2×C4—17561no—
191C2×C4—17561no—
192C2×C4—17561no—
193C2×C4C22×D43911yescharacteristic
194C2×C4C22×D43911yescharacteristic
195C2×C4C22×D43911yescharacteristic
196C2×C4C22×D43911yescharacteristic
197C2×C4C22×D43911yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—8781no—
205C22—8781no—
206C22—8781no—
207C22—8781no—
208C22—8781no—
209C22—8781no—
210C22—8781no—
211C22—8781no—
212C22—4392no—
213C22—17564no—
214C22C23×D43911yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—8781no—
221C4—8781no—
222C4—8781no—
223C4—8781no—
224C4—8781no—
225C2—41no—
226C2—41no—
227C2—8782no—
228C2—17561no—
229C2—17561no—
230C2#41×D43911yescharacteristic
231C2#2838078811yescharacteristic
232C2#2838078911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D439
commutator, socle, cosocleC22×C439C24
Fitting#123×C439C2
hypercenter#123D439
hypocenterC439#538
LCSG ▷ C22×C439 ▷ C439
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #28380738C2semidirect
2. #28380736C2semidirect
3. #28380729C2semidirect
4. #28380729C2semidirect
5. #28380728C2semidirect
6. #28380723C2semidirect
7. #28380717C2semidirect
8. #28380716C2semidirect
9. #28380714C2semidirect
10. #28380713C2semidirect
11. #28380711C2semidirect
12. #28380705C2semidirect
13. C4×C22⋊D439C2semidirect
14. C22⋊C4×D439C2semidirect
15. #123×C439C2semidirect
17. C2×Dic878C22semidirect
23. C2×C22⋊D439C22semidirect
26. C2×C4×D439C22semidirect
27. C4⋊Dic439C22semidirect
28. C4⋊Dic439C22semidirect
29. Dic439⋊C4C22semidirect
30. Dic439⋊C4C22semidirect
33. C22⋊Dic439C22semidirect
40. (C2×D439)⋊C4C22semidirect
41. (C2×D439)⋊C4C22semidirect
42. C4×Dic439C22semidirect
43. C4×Dic439C22semidirect
45. C22×C4×C439C22semidirect
46. C4⋊C4×C439C22semidirect
47. C4⋊C4×C439C22semidirect
50. C22⋊C4×C439C22semidirect
116. C439#538semidirect
123. #123D439semidirect
145. C22×C4C2×D439semidirect
150. C4⋊C4C2×D439semidirect
151. C4⋊C4C2×D439semidirect
165. C22⋊C4C2×D439semidirect

Maximal subgroups

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

subgroupindex
#283807382
#283807362
#283807292
#283807282
#283807232
#283807172
#283807162
#283807142
#283807132
#283807112
#283807052
C4×C22⋊D4392
C22⋊C4×D4392
#123×C4392
#538439