Finite Group Databasebeta

← #38734733

Subgroups — #38734733

Order 24896.

428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C22×D1556C211yesmaximal, characteristic, complemented
2C2×D4×D389C212yesmaximal, complemented
3C2×D4×D389C211yesmaximal, characteristic, complemented
4#27159380C211yesmaximal, characteristic, complemented
5#27159359C211yesmaximal, characteristic, complemented
6#27159357C212yesmaximal, complemented
7#27159354C212yesmaximal, complemented
8#27159352C212yesmaximal, complemented
9#27159346C211yesmaximal, characteristic, complemented
10C4×C22⋊D389C211yesmaximal, characteristic, complemented
11#121×C389C211yesmaximal, characteristic, complemented
12C23×D389C2212yescomplemented
13C23×D389C2212yescomplemented
14C2×D1556—24no—
15C2×D1556C2211yescharacteristic
16C2×D1556C2212yescomplemented
17C2×D1556C2212yescomplemented
18C2×D1556C2211yescharacteristic, complemented
19C2×C22⋊D389C2211yescharacteristic
20C2×C22⋊D389C2212yescomplemented
21C2×C22⋊D389C2212yescomplemented
22C2×C22⋊D389C2212yescomplemented
23D4×D389—24no—
24D4×D389—28no—
25C2×C4×D389C2211yescharacteristic, complemented
26C2×C4×D389C2212yescomplemented
27#20261945C2211yescharacteristic, complemented
28C22⋊Dic389C2211yescharacteristic, complemented
29#20261943C2211yescharacteristic, complemented
30#20261943C2212yescomplemented
31#20261943C2212yescomplemented
32C4×Dic389C2211yescharacteristic, complemented
33C2×D4×C389C2212yescomplemented
34C2×D4×C389C2211yescharacteristic, complemented
35C22×C4×C389C2211yescharacteristic, complemented
36C4⋊C4×C389C2211yescharacteristic, complemented
37C22⋊C4×C389C2212yescomplemented
38C22×D389—24no—
39C22×D389—24no—
40C22×D389—24no—
41C22×D389—24no—
42C22×D389—42no—
43C22×D389—42no—
44C22×D389C2312yes—
45C22×D389C2311yescharacteristic
46C22×D389C2312yes—
47D1556—24no—
48D1556—24no—
49D1556—22no—
50D1556D414yescomplemented
51C22⋊D389—24no—
52C22⋊D389—24no—
53C22⋊D389—42no—
54C22⋊D389D414yescomplemented
55C2×Dic389C2311yescharacteristic
56C2×Dic389C2311yescharacteristic
57C2×Dic389C2311yescharacteristic
58C4×D389—22no—
59C4×D389—24no—
60C23×C389C2312yes—
61C23×C389C2311yescharacteristic
62D4×C389—24no—
63D4×C389—22no—
64C2×C4×C389—22no—
65C2×C4×C389C2311yescharacteristic
66C2×C4×C389C2312yes—
67C2×C4×C389C2311yescharacteristic
68C22×C389—21no—
69C22×C389—21no—
70C22×C389—22no—
71C22×C389—22no—
72C22×C389—22no—
73C22×C389C2×D412yescomplemented
74C22×C389C2411yescharacteristic
75C2×D389—21no—
76C2×D389—22no—
77C2×D389—21no—
78C2×D389—22no—
79C2×D389—22no—
80C2×D389—22no—
81C2×D389—22no—
82C2×D389—48no—
83C2×D389—48no—
84C2×D389C2×D414yescomplemented
85C2×D389C2×D412yescomplemented
86C4×C389—21no—
87C4×C389—22no—
88C4×C389C2×D412yescomplemented
89Dic389—21no—
90Dic389—21no—
91Dic389C2×D412yescomplemented
92C2×C389—22no—
93C2×C389—42no—
94C2×C389C22×D411yescharacteristic
95C2×C389C22×D411yescharacteristic
96C2×C389H(5,𝔽2)11yescharacteristic
97D389—22no—
98D389—24no—
99D389—42no—
100C389D4211yescharacteristic, complemented, Sylow
101D42—3891nomaximal, Sylow
102C22×D4—3891no—
103C22×D4—3892no—
104C22×D4—3891no—
105#127—3891no—
106#121—3891no—
107#121—3892no—
108#121D38911yescharacteristic, complemented
109#120—3892no—
110#120—3892no—
111C4×D4—3891no—
112C4×D4—3891no—
113C24—3892no—
114C24—3892no—
115C2×D4—7784no—
116C2×D4—7788no—
117C2×D4—7784no—
118C2×D4—3892no—
119C2×D4—3892no—
120C2×D4—3892no—
121C2×D4—3891no—
122C2×D4—3892no—
123C2×D4—3892no—
124C2×D4—3891no—
125C2×D4—3891no—
126C2×D4C2×D38912yescomplemented
127C2×D4C2×D38911yescharacteristic, complemented
128C22×C4—3892no—
129C22×C4—3891no—
130C22×C4C2×D38911yescharacteristic, complemented
131C4⋊C4—3891no—
132C4⋊C4C2×D38911yescharacteristic, complemented
133C22⋊C4—3891no—
134C22⋊C4—3892no—
135C22⋊C4—3891no—
136C22⋊C4—3892no—
137C22⋊C4C2×D38912yescomplemented
138C42—3891no—
139C23—7784no—
140C23—7784no—
141C23—7784no—
142C23—7784no—
143C23—15562no—
144C23—15562no—
145C23—3892no—
146C23—3891no—
147C23—3892no—
148C23C22×D38912yes—
149C23C22×D38911yescharacteristic
150D4—24no—
151D4—22no—
152D4—7784no—
153D4—7784no—
154D4—7784no—
155D4—7784no—
156D4—7782no—
157D4—15562no—
158D4—3894no—
159D4—3894no—
160C2×C4—22no—
161C2×C4—7784no—
162C2×C4—7782no—
163C2×C4—3891no—
164C2×C4—3891no—
165C2×C4—3891no—
166C2×C4C22×D38912yes—
167C2×C4C22×D38911yescharacteristic
168C2×C4C22×D38911yescharacteristic
169C22—21no—
170C22—21no—
171C22—22no—
172C22—22no—
173C22—22no—
174C22—7782no—
175C22—7781no—
176C22—7782no—
177C22—7781no—
178C22—7782no—
179C22—7782no—
180C22—7782no—
181C22—15568no—
182C22—15568no—
183C22—3892no—
184C22—3894no—
185C22D4×D38912yescomplemented
186C22C23×D38911yescharacteristic
187C4—21no—
188C4—22no—
189C4—7781no—
190C4—7781no—
191C4—3892no—
192C4D4×D38912yescomplemented
193C2—22no—
194C2—42no—
195C2—7784no—
196C2—7782no—
197C2—15562no—
198C2C2×D4×D38911yescharacteristic
199C2C2×D4×D38911yescharacteristic
200C2#2715943011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D389
commutator, socle, cosocleC22×C389C24
Fitting#121×C389C2
hypercenter#121D389
hypocenterC389D42
LCSG ▷ C22×C389 ▷ C389
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C22×D1556C2semidirect
2. C2×D4×D389C2semidirect
3. C2×D4×D389C2semidirect
4. #27159380C2semidirect
5. #27159359C2semidirect
6. #27159357C2semidirect
7. #27159354C2semidirect
8. #27159352C2semidirect
9. #27159346C2semidirect
10. C4×C22⋊D389C2semidirect
11. #121×C389C2semidirect
12. C23×D389C22semidirect
13. C23×D389C22semidirect
16. C2×D1556C22semidirect
17. C2×D1556C22semidirect
18. C2×D1556C22semidirect
20. C2×C22⋊D389C22semidirect
21. C2×C22⋊D389C22semidirect
22. C2×C22⋊D389C22semidirect
25. C2×C4×D389C22semidirect
26. C2×C4×D389C22semidirect
27. #20261945C22semidirect
28. C22⋊Dic389C22semidirect
29. #20261943C22semidirect
30. #20261943C22semidirect
31. #20261943C22semidirect
32. C4×Dic389C22semidirect
33. C2×D4×C389C22semidirect
34. C2×D4×C389C22semidirect
35. C22×C4×C389C22semidirect
36. C4⋊C4×C389C22semidirect
37. C22⋊C4×C389C22semidirect
50. D1556D4semidirect
54. C22⋊D389D4semidirect
73. C22×C389C2×D4semidirect
84. C2×D389C2×D4semidirect
85. C2×D389C2×D4semidirect
88. C4×C389C2×D4semidirect
91. Dic389C2×D4semidirect
100. C389D42semidirect
108. #121D389semidirect
126. C2×D4C2×D389semidirect
127. C2×D4C2×D389semidirect
130. C22×C4C2×D389semidirect
132. C4⋊C4C2×D389semidirect
137. C22⋊C4C2×D389semidirect
185. C22D4×D389semidirect
192. C4D4×D389semidirect

Maximal subgroups

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

subgroupindex
C22×D15562
C2×D4×D3892
#271593802
#271593592
#271593572
#271593542
#271593522
#271593462
C4×C22⋊D3892
#121×C3892
D42389