Finite Group Databasebeta

← #38734681

Subgroups — #38734681

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#27159379C211yesmaximal, characteristic, complemented
2#27159377C211yesmaximal, characteristic, complemented
3#27159371C211yesmaximal, characteristic, complemented
4#27159370C211yesmaximal, characteristic, complemented
5#27159367C211yesmaximal, characteristic, complemented
6#27159365C211yesmaximal, characteristic, complemented
7#27159362C211yesmaximal, characteristic, complemented
8#27159356C211yesmaximal, characteristic, complemented
9#27159355C211yesmaximal, characteristic, complemented
10#27159352C211yesmaximal, characteristic, complemented
11#27159352C211yesmaximal, characteristic, complemented
12C4×C22⋊D389C211yesmaximal, characteristic, complemented
13#27159344C211yesmaximal, characteristic, complemented
14C22⋊C4×D389C211yesmaximal, characteristic, complemented
15#121×C389C211yesmaximal, characteristic, complemented
16C23×D389C2211yescharacteristic
17C2×Dic778C2211yescharacteristic, complemented
18C2×C22⋊D389C2211yescharacteristic
19C2×C22⋊D389C2211yescharacteristic
20C2×C22⋊D389C2211yescharacteristic
21C2×C22⋊D389C2211yescharacteristic
22C22×Dic389C2211yescharacteristic, complemented
23C2×C4×D389C2211yescharacteristic
24C2×C4×D389C2211yescharacteristic
25C4⋊Dic389C2211yescharacteristic, complemented
26#20261945C2211yescharacteristic, complemented
27#20261945C2211yescharacteristic, complemented
28#20261945C2211yescharacteristic, complemented
29#20261945C2211yescharacteristic, complemented
30C22⋊Dic389C2211yescharacteristic
31C22⋊Dic389C2211yescharacteristic
32C22⋊Dic389C2211yescharacteristic
33C22⋊Dic389C2211yescharacteristic, complemented
34C22⋊Dic389C2211yescharacteristic, complemented
35C22⋊Dic389C2211yescharacteristic, complemented
36#20261943C2211yescharacteristic
37#20261943C2211yescharacteristic
38#20261943C2211yescharacteristic
39#20261943C2211yescharacteristic
40#20261943C2211yescharacteristic
41#20261943C2211yescharacteristic
42C4×Dic389C2211yescharacteristic, complemented
43C4×Dic389C2211yescharacteristic, complemented
44C2×D4×C389C2211yescharacteristic
45C2×D4×C389C2211yescharacteristic
46C2×D4×C389C2211yescharacteristic, complemented
47C22×C4×C389C2211yescharacteristic, complemented
48C4⋊C4×C389C2211yescharacteristic, complemented
49C22⋊C4×C389C2211yescharacteristic
50C22⋊C4×C389C2211yescharacteristic, complemented
51C22×D389—22no—
52C22×D389—41no—
53C22×D389—41no—
54C22×D389C2311yescharacteristic
55C22×D389C2311yescharacteristic
56Dic778—41no—
57C22⋊D389—22no—
58C22⋊D389—22no—
59C22⋊D389—41no—
60C22⋊D389—41no—
61C2×Dic389—41no—
62C2×Dic389C2311yescharacteristic
63C2×Dic389C2311yescharacteristic
64C2×Dic389C2311yescharacteristic
65C2×Dic389C2311yescharacteristic
66C2×Dic389C2311yescharacteristic
67C2×Dic389C2311yescharacteristic
68C4×D389—41no—
69C4×D389—41no—
70C23×C389C2311yescharacteristic
71C23×C389C2311yescharacteristic
72C23×C389C2311yescharacteristic
73D4×C389—41no—
74D4×C389—41no—
75D4×C389—41no—
76C2×C4×C389—41no—
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×C389—21no—
88C22×C389—21no—
89C22×C389—21no—
90C22×C389C2411yescharacteristic
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—
102Dic389—21no—
103Dic389—21no—
104Dic389—21no—
105Dic389—21no—
106Dic389—21no—
107Dic389—21no—
108C2×C389—41no—
109C2×C389—41no—
110C2×C389—41no—
111C2×C389C2×#4111yescharacteristic
112C2×C389H(5,𝔽2)11yescharacteristic
113C2×C389H(5,𝔽2)11yescharacteristic
114D389—22no—
115D389—41no—
116C389#53811yescharacteristic, complemented, Sylow
117#538—3891nomaximal, Sylow
118#126—3891no—
119#126—3891no—
120#124—3891no—
121#124—3891no—
122#123—3891no—
123#123—3891no—
124C22⋊Q8—3891no—
125#121—3891no—
126#121—3891no—
127#121D38911yescharacteristic, complemented
128#120—3891no—
129#120—3891no—
130C4×D4—3891no—
131C4×D4—3891no—
132C2×C22⋊C4—3891no—
133C24—3891no—
134C2×Q8—3891no—
135C2×D4—3891no—
136C2×D4—3891no—
137C2×D4—3891no—
138C2×D4—3891no—
139C2×D4C2×D38911yescharacteristic
140C2×D4C2×D38911yescharacteristic
141C2×D4C2×D38911yescharacteristic, complemented
142C22×C4—3891no—
143C22×C4—3891no—
144C22×C4—3891no—
145C22×C4C2×D38911yescharacteristic, complemented
146C4⋊C4—3891no—
147C4⋊C4—3891no—
148C4⋊C4—3891no—
149C4⋊C4—3891no—
150C4⋊C4—3891no—
151C4⋊C4C2×D38911yescharacteristic, complemented
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⋊C4—3891no—
163C22⋊C4—3891no—
164C22⋊C4C2×D38911yescharacteristic
165C22⋊C4C2×D38911yescharacteristic, complemented
166C42—3891no—
167C42—3891no—
168C23—7782no—
169C23—15561no—
170C23—15561no—
171C23—3891no—
172C23—3891no—
173C23C22×D38911yescharacteristic
174C23C22×D38911yescharacteristic
175C23C22×D38911yescharacteristic
176Q8—15561no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—7782no—
181D4—7782no—
182D4—15561no—
183D4—15561no—
184C2×C4—41no—
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×C4—3891no—
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—21no—
205C22—21no—
206C22—21no—
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—7781no—
220C4—7781no—
221C4—7781no—
222C4—7781no—
223C4—7781no—
224C4—7781no—
225C2—41no—
226C2—41no—
227C2—41no—
228C2—7782no—
229C2—15561no—
230C2#41×D38911yescharacteristic
231C2#2715942911yescharacteristic
232C2#2715942911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D389
commutator, socle, cosocleC22×C389C24
Fitting#121×C389C2
hypercenter#121D389
hypocenterC389#538
LCSG ▷ C22×C389 ▷ C389
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #27159379C2semidirect
2. #27159377C2semidirect
3. #27159371C2semidirect
4. #27159370C2semidirect
5. #27159367C2semidirect
6. #27159365C2semidirect
7. #27159362C2semidirect
8. #27159356C2semidirect
9. #27159355C2semidirect
10. #27159352C2semidirect
11. #27159352C2semidirect
12. C4×C22⋊D389C2semidirect
13. #27159344C2semidirect
14. C22⋊C4×D389C2semidirect
15. #121×C389C2semidirect
17. C2×Dic778C22semidirect
22. C22×Dic389C22semidirect
25. C4⋊Dic389C22semidirect
26. #20261945C22semidirect
27. #20261945C22semidirect
28. #20261945C22semidirect
29. #20261945C22semidirect
33. C22⋊Dic389C22semidirect
34. C22⋊Dic389C22semidirect
35. C22⋊Dic389C22semidirect
42. C4×Dic389C22semidirect
43. C4×Dic389C22semidirect
46. C2×D4×C389C22semidirect
47. C22×C4×C389C22semidirect
48. C4⋊C4×C389C22semidirect
50. C22⋊C4×C389C22semidirect
116. C389#538semidirect
127. #121D389semidirect
141. C2×D4C2×D389semidirect
145. C22×C4C2×D389semidirect
151. C4⋊C4C2×D389semidirect
165. C22⋊C4C2×D389semidirect

Maximal subgroups

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

subgroupindex
#271593792
#271593772
#271593712
#271593702
#271593672
#271593652
#271593622
#271593562
#271593552
#271593522
C4×C22⋊D3892
#271593442
C22⋊C4×D3892
#121×C3892
#538389