Finite Group Databasebeta

← #38734657

Subgroups — #38734657

Order 24896.

346 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C2×D4×D389C212yesmaximal, complemented
2#27159369C212yesmaximal, complemented
3#27159366C212yesmaximal, complemented
4#27159358C211yesmaximal, characteristic, complemented
5#27159356C212yesmaximal, complemented
6#27159354C212yesmaximal, complemented
7#27159352C212yesmaximal, complemented
8C2×#20261943C211yesmaximal, characteristic, complemented
9#121×C389C211yesmaximal, characteristic, complemented
10C23×D389C2211yescharacteristic
11C23×D389C2212yescomplemented
12C2×D1556C2212yes—
13C2×D1556C2211yescharacteristic, complemented
14C2×C22⋊D389C2212yes—
15C2×C22⋊D389C2212yescomplemented
16C2×C22⋊D389C2212yescomplemented
17D4×D389—28no—
18C22×Dic389C2211yescharacteristic, complemented
19C2×C4×D389C2212yescomplemented
20C4⋊Dic389C2211yescharacteristic, complemented
21#20261945C2212yescomplemented
22C22⋊Dic389C2212yescomplemented
23#20261943C2212yescomplemented
24#20261943C2212yescomplemented
25#20261943C2212yescomplemented
26#20261943C2212yescomplemented
27C2×D4×C389C2212yescomplemented
28C2×D4×C389C2211yescharacteristic, complemented
29C22×C4×C389C2211yescharacteristic, complemented
30C4⋊C4×C389C2211yescharacteristic, complemented
31C22⋊C4×C389C2212yescomplemented
32C22×D389—24no—
33C22×D389—41no—
34C22×D389—41no—
35C22×D389—42no—
36C22×D389—42no—
37C22×D389D414yescomplemented
38C22×D389C2312yes—
39C22×D389C2312yes—
40D1556—24no—
41D1556—41no—
42C22⋊D389—24no—
43C22⋊D389—24no—
44C22⋊D389—42no—
45C2×Dic389—41no—
46C2×Dic389C2312yes—
47C2×Dic389C2312yes—
48C4×D389—24no—
49C23×C389C2312yes—
50C23×C389C2311yescharacteristic
51D4×C389—24no—
52D4×C389—41no—
53C2×C4×C389—41no—
54C2×C4×C389C2311yescharacteristic
55C2×C4×C389C2312yes—
56C2×C4×C389C2311yescharacteristic
57C22×C389—21no—
58C22×C389—21no—
59C22×C389—22no—
60C22×C389—22no—
61C22×C389—22no—
62C22×C389C2×D412yes—
63C22×C389C2411yescharacteristic
64C2×D389—22no—
65C2×D389—22no—
66C2×D389—22no—
67C2×D389—22no—
68C2×D389—22no—
69C2×D389—44no—
70C2×D389—48no—
71C2×D389C2×D414yes—
72C4×C389—22no—
73C4×C389—21no—
74C4×C389—21no—
75Dic389—22no—
76Dic389—22no—
77C2×C389—22no—
78C2×C389—42no—
79C2×C389C22×D411yescharacteristic
80C2×C389H(5,𝔽2)11yescharacteristic
81C2×C389H(5,𝔽2)11yescharacteristic
82D389—24no—
83D389—42no—
84C389#53411yescharacteristic, complemented, Sylow
85#534—3891nomaximal, Sylow
86C22×D4—3892no—
87#123—3892no—
88#123—3892no—
89#121—3892no—
90#121—3891no—
91#121D38911yescharacteristic, complemented
92#120—3892no—
93#120—3892no—
94C2×C22⋊C4—3891no—
95C24—3892no—
96C24—3891no—
97C2×D4—7788no—
98C2×D4—3892no—
99C2×D4—3892no—
100C2×D4—3892no—
101C2×D4—3892no—
102C2×D4—3891no—
103C2×D4C2×D38912yescomplemented
104C2×D4C2×D38911yescharacteristic, complemented
105C22×C4—3892no—
106C22×C4—3891no—
107C22×C4C2×D38911yescharacteristic, complemented
108C4⋊C4—3892no—
109C4⋊C4—3891no—
110C4⋊C4C2×D38911yescharacteristic, complemented
111C22⋊C4—3892no—
112C22⋊C4—3892no—
113C22⋊C4—3892no—
114C22⋊C4—3892no—
115C22⋊C4—3892no—
116C22⋊C4C2×D38912yescomplemented
117C23—7784no—
118C23—15561no—
119C23—15561no—
120C23—15562no—
121C23—15562no—
122C23—3892no—
123C23—3892no—
124C23—3894no—
125C23C22×D38912yes—
126C23C22×D38911yescharacteristic
127D4—24no—
128D4—41no—
129D4—7784no—
130D4—7784no—
131D4—7784no—
132D4—15561no—
133D4—15562no—
134C2×C4—41no—
135C2×C4—7784no—
136C2×C4—15561no—
137C2×C4—3892no—
138C2×C4—3892no—
139C2×C4C22×D38911yescharacteristic
140C2×C4C22×D38911yescharacteristic
141C2×C4C22×D38912yes—
142C22—21no—
143C22—21no—
144C22—22no—
145C22—22no—
146C22—22no—
147C22—7782no—
148C22—7782no—
149C22—7782no—
150C22—7782no—
151C22—7782no—
152C22—15564no—
153C22—15568no—
154C22—3894no—
155C22D4×D38912yes—
156C22C23×D38911yescharacteristic
157C4—22no—
158C4—21no—
159C4—21no—
160C4—7782no—
161C4—7782no—
162C2—22no—
163C2—42no—
164C2—7784no—
165C2—15562no—
166C2C2×D4×D38911yescharacteristic
167C2#2715942911yescharacteristic
168C2#2715943011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D389
commutator, socle, cosocleC22×C389C24
Fitting#121×C389C2
hypercenter#121D389
hypocenterC389#534
LCSG ▷ C22×C389 ▷ C389
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D389C2semidirect
2. #27159369C2semidirect
3. #27159366C2semidirect
4. #27159358C2semidirect
5. #27159356C2semidirect
6. #27159354C2semidirect
7. #27159352C2semidirect
8. C2×#20261943C2semidirect
9. #121×C389C2semidirect
11. C23×D389C22semidirect
13. C2×D1556C22semidirect
15. C2×C22⋊D389C22semidirect
16. C2×C22⋊D389C22semidirect
18. C22×Dic389C22semidirect
19. C2×C4×D389C22semidirect
20. C4⋊Dic389C22semidirect
21. #20261945C22semidirect
22. C22⋊Dic389C22semidirect
23. #20261943C22semidirect
24. #20261943C22semidirect
25. #20261943C22semidirect
26. #20261943C22semidirect
27. C2×D4×C389C22semidirect
28. C2×D4×C389C22semidirect
29. C22×C4×C389C22semidirect
30. C4⋊C4×C389C22semidirect
31. C22⋊C4×C389C22semidirect
37. C22×D389D4semidirect
84. C389#534semidirect
91. #121D389semidirect
103. C2×D4C2×D389semidirect
104. C2×D4C2×D389semidirect
107. C22×C4C2×D389semidirect
110. C4⋊C4C2×D389semidirect
116. C22⋊C4C2×D389semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D3892
#271593692
#271593662
#271593582
#271593562
#271593542
#271593522
C2×#202619432
#121×C3892
#534389