Finite Group Databasebeta

← #38734683

Subgroups — #38734683

Order 24896.

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#27159378C211yesmaximal, characteristic, complemented
2#27159377C211yesmaximal, characteristic, complemented
3#27159373C211yesmaximal, characteristic, complemented
4#27159368C211yesmaximal, characteristic, complemented
5#27159366C211yesmaximal, characteristic, complemented
6#27159360C211yesmaximal, characteristic, complemented
7#27159357C211yesmaximal, characteristic, complemented
8#27159357C211yesmaximal, characteristic, complemented
9#27159356C211yesmaximal, characteristic, complemented
10#27159354C211yesmaximal, characteristic, complemented
11#27159352C211yesmaximal, characteristic, complemented
12C4×D1556C211yesmaximal, characteristic, complemented
13#27159344C211yesmaximal, characteristic, complemented
14C22⋊C4×D389C211yesmaximal, characteristic, complemented
15#124×C389C211yesmaximal, characteristic, complemented
16C23×D389C2211yescharacteristic
17C2×D1556C2211yescharacteristic
18C2×D1556C2211yescharacteristic
19C2×C22⋊D389C2211yescharacteristic
20C2×C22⋊D389C2211yescharacteristic
21C2×C22⋊D389C2211yescharacteristic
22C2×C22⋊D389C2211yescharacteristic, complemented
23C22×Dic389C2211yescharacteristic, complemented
24C2×C4×D389C2211yescharacteristic
25C2×C4×D389C2211yescharacteristic
26C2×C4×D389C2211yescharacteristic, complemented
27C4⋊Dic389C2211yescharacteristic, complemented
28C4⋊Dic389C2211yescharacteristic, complemented
29#20261945C2211yescharacteristic, complemented
30#20261945C2211yescharacteristic, complemented
31#20261945C2211yescharacteristic, complemented
32#20261945C2211yescharacteristic, complemented
33C22⋊Dic389C2211yescharacteristic
34C22⋊Dic389C2211yescharacteristic
35#20261943C2211yescharacteristic
36#20261943C2211yescharacteristic
37#20261943C2211yescharacteristic
38#20261943C2211yescharacteristic
39#20261943C2211yescharacteristic
40#20261943C2211yescharacteristic
41#20261943C2211yescharacteristic, complemented
42#20261943C2211yescharacteristic, complemented
43C4×Dic389C2211yescharacteristic, complemented
44C2×Q8×C389C2211yescharacteristic, complemented
45C2×D4×C389C2211yescharacteristic
46C22⋊C4×C389C2211yescharacteristic
47C22⋊C4×C389C2211yescharacteristic
48C22⋊C4×C389C2211yescharacteristic, complemented
49C22⋊C4×C389C2211yescharacteristic, complemented
50C42×C389C2211yescharacteristic, complemented
51C22×D389—22no—
52C22×D389—41no—
53C22×D389—41no—
54C22×D389C2311yescharacteristic
55C22×D389C2311yescharacteristic
56C22×D389C2311yescharacteristic
57D1556—22no—
58D1556—41no—
59C22⋊D389—22no—
60C22⋊D389—41no—
61C22⋊D389—41no—
62C22⋊D389—41no—
63C2×Dic389—41no—
64C2×Dic389C2311yescharacteristic
65C2×Dic389C2311yescharacteristic
66C2×Dic389C2311yescharacteristic
67C2×Dic389C2311yescharacteristic
68C2×Dic389C2311yescharacteristic
69C4×D389—41no—
70C4×D389—41no—
71C4×D389—41no—
72C23×C389C2311yescharacteristic
73C23×C389C2311yescharacteristic
74Q8×C389—41no—
75D4×C389—41no—
76C2×C4×C389C2311yescharacteristic
77C2×C4×C389C2311yescharacteristic
78C2×C4×C389C2311yescharacteristic
79C2×C4×C389C2311yescharacteristic
80C2×C4×C389C2311yescharacteristic
81C22×C389—21no—
82C22×C389—21no—
83C22×C389—21no—
84C22×C389—21no—
85C22×C389—21no—
86C22×C389—21no—
87C22×C389C2411yescharacteristic
88C2×D389—21no—
89C2×D389—21no—
90C2×D389—21no—
91C2×D389—21no—
92C2×D389—21no—
93C2×D389—21no—
94C2×D389—21no—
95C2×D389—21no—
96C2×D389—44no—
97C2×D389#4112yes—
98C4×C389—21no—
99C4×C389—21no—
100C4×C389—21no—
101C4×C389—21no—
102C4×C389—21no—
103Dic389—21no—
104Dic389—21no—
105Dic389—21no—
106Dic389—21no—
107Dic389—21no—
108C2×C389—41no—
109C2×C389—41no—
110C2×C389C2×#4111yescharacteristic
111C2×C389H(5,𝔽2)11yescharacteristic
112C2×C389H(5,𝔽2)11yescharacteristic
113D389—22no—
114D389—41no—
115D389—41no—
116C389#53811yescharacteristic, complemented, Sylow
117#538—3891nomaximal, Sylow
118#126—3891no—
119#126—3891no—
120#124—3891no—
121#124D38911yescharacteristic, complemented
122#123—3891no—
123#123—3891no—
124C22⋊Q8—3891no—
125#121—3891no—
126#121—3891no—
127#121—3891no—
128#120—3891no—
129#120—3891no—
130C4×D4—3891no—
131C4×D4—3891no—
132C2×C22⋊C4—3891no—
133C24—3891no—
134C2×Q8C2×D38911yescharacteristic, complemented
135C2×D4—3891no—
136C2×D4—3891no—
137C2×D4—3891no—
138C2×D4—3891no—
139C2×D4—3891no—
140C2×D4—3891no—
141C2×D4C2×D38911yescharacteristic
142C22×C4—3891no—
143C22×C4—3891no—
144C22×C4—3891no—
145C22×C4—3891no—
146C4⋊C4—3891no—
147C4⋊C4—3891no—
148C4⋊C4—3891no—
149C4⋊C4—3891no—
150C4⋊C4—3891no—
151C4⋊C4—3891no—
152C22⋊C4—3891no—
153C22⋊C4—3891no—
154C22⋊C4—3891no—
155C22⋊C4—3891no—
156C22⋊C4—3891no—
157C22⋊C4—3891no—
158C22⋊C4—3891no—
159C22⋊C4—3891no—
160C22⋊C4—3891no—
161C22⋊C4—3891no—
162C22⋊C4C2×D38911yescharacteristic
163C22⋊C4C2×D38911yescharacteristic
164C22⋊C4C2×D38911yescharacteristic, complemented
165C22⋊C4C2×D38911yescharacteristic, complemented
166C42—3891no—
167C42C2×D38911yescharacteristic, complemented
168C23—7782no—
169C23—15561no—
170C23—15561no—
171C23—3891no—
172C23—3891no—
173C23—3891no—
174C23C22×D38911yescharacteristic
175C23C22×D38911yescharacteristic
176Q8—41no—
177D4—41no—
178D4—7782no—
179D4—7782no—
180D4—15561no—
181D4—15561no—
182D4—15561no—
183D4—15561no—
184C2×C4—15561no—
185C2×C4—15561no—
186C2×C4—15561no—
187C2×C4—15561no—
188C2×C4—3891no—
189C2×C4—3891no—
190C2×C4—3891no—
191C2×C4—3891no—
192C2×C4—3891no—
193C2×C4C22×D38911yescharacteristic
194C2×C4C22×D38911yescharacteristic
195C2×C4C22×D38911yescharacteristic
196C2×C4C22×D38911yescharacteristic
197C2×C4C22×D38911yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—7781no—
205C22—7781no—
206C22—7781no—
207C22—7781no—
208C22—7781no—
209C22—7781no—
210C22—7781no—
211C22—7781no—
212C22—15564no—
213C22—3892no—
214C22C23×D38911yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—7781no—
221C4—7781no—
222C4—7781no—
223C4—7781no—
224C4—7781no—
225C2—41no—
226C2—41no—
227C2—7782no—
228C2—15561no—
229C2—15561no—
230C2#41×D38911yescharacteristic
231C2#2715942911yescharacteristic
232C2#2715943011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D389
commutator, socle, cosocleC22×C389C24
Fitting#124×C389C2
hypercenter#124D389
hypocenterC389#538
LCSG ▷ C22×C389 ▷ C389
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #27159378C2semidirect
2. #27159377C2semidirect
3. #27159373C2semidirect
4. #27159368C2semidirect
5. #27159366C2semidirect
6. #27159360C2semidirect
7. #27159357C2semidirect
8. #27159357C2semidirect
9. #27159356C2semidirect
10. #27159354C2semidirect
11. #27159352C2semidirect
12. C4×D1556C2semidirect
13. #27159344C2semidirect
14. C22⋊C4×D389C2semidirect
15. #124×C389C2semidirect
22. C2×C22⋊D389C22semidirect
23. C22×Dic389C22semidirect
26. C2×C4×D389C22semidirect
27. C4⋊Dic389C22semidirect
28. C4⋊Dic389C22semidirect
29. #20261945C22semidirect
30. #20261945C22semidirect
31. #20261945C22semidirect
32. #20261945C22semidirect
41. #20261943C22semidirect
42. #20261943C22semidirect
43. C4×Dic389C22semidirect
44. C2×Q8×C389C22semidirect
48. C22⋊C4×C389C22semidirect
49. C22⋊C4×C389C22semidirect
50. C42×C389C22semidirect
116. C389#538semidirect
121. #124D389semidirect
134. C2×Q8C2×D389semidirect
164. C22⋊C4C2×D389semidirect
165. C22⋊C4C2×D389semidirect
167. C42C2×D389semidirect

Maximal subgroups

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

subgroupindex
#271593782
#271593772
#271593732
#271593682
#271593662
#271593602
#271593572
#271593562
#271593542
#271593522
C4×D15562
#271593442
C22⋊C4×D3892
#124×C3892
#538389