Finite Group Databasebeta

← #38734737

Subgroups — #38734737

Order 24896.

334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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×D389C211yesmaximal, characteristic, complemented
2#27159373C211yesmaximal, characteristic, complemented
3#27159367C212yesmaximal, complemented
4#27159360C211yesmaximal, characteristic, complemented
5#27159358C211yesmaximal, characteristic, complemented
6#27159356C212yesmaximal, complemented
7#27159352C212yesmaximal, complemented
8D4×Dic389C211yesmaximal, characteristic, complemented
9C4×C22⋊D389C211yesmaximal, characteristic, complemented
10C2×#20261943C212yesmaximal, complemented
11C2×#41×C389C211yesmaximal, characteristic, complemented
12C23×D389C2212yes—
13C2×D1556C2211yescharacteristic
14C2×C22⋊D389C2211yescharacteristic
15C2×C22⋊D389C2212yes—
16C2×C22⋊D389C2212yescomplemented
17D4×D389—24no—
18C22×Dic389C2212yescomplemented
19C2×C4×D389C2211yescharacteristic
20C4⋊Dic389C2211yescharacteristic, complemented
21#20261945C2211yescharacteristic, complemented
22#20261945C2212yescomplemented
23C22⋊Dic389C2211yescharacteristic, complemented
24C22⋊Dic389C2212yescomplemented
25#20261943C2211yescharacteristic
26#20261943C2212yes—
27#20261943C2212yescomplemented
28#20261943C2212yescomplemented
29#20261943C2212yescomplemented
30C4×Dic389C2211yescharacteristic, complemented
31#41×C389—24no—
32C2×Q8×C389C2211yescharacteristic, complemented
33C2×D4×C389C2211yescharacteristic
34C2×D4×C389C2212yescomplemented
35C22×C4×C389C2212yescomplemented
36C22×C4×C389C2211yescharacteristic, complemented
37C22×D389—24no—
38C22×D389—24no—
39C22×D389—42no—
40C22×D389C2312yes—
41C22×D389C2311yescharacteristic
42D1556—22no—
43C22⋊D389—24no—
44C22⋊D389—22no—
45C22⋊D389—42no—
46C2×Dic389—42no—
47C2×Dic389C2311yescharacteristic
48C2×Dic389C2311yescharacteristic
49C2×Dic389C2312yes—
50C2×Dic389C2311yescharacteristic
51C4×D389—22no—
52C23×C389C2311yescharacteristic
53C23×C389C2312yes—
54Q8×C389—22no—
55D4×C389—24no—
56D4×C389D414yescomplemented
57C2×C4×C389—24no—
58C2×C4×C389—22no—
59C2×C4×C389C2311yescharacteristic
60C2×C4×C389C2312yes—
61C2×C4×C389C2311yescharacteristic
62C22×C389—22no—
63C22×C389—22no—
64C22×C389—21no—
65C22×C389—21no—
66C22×C389—21no—
67C22×C389C2×D414yes—
68C22×C389C2411yescharacteristic
69C2×D389—21no—
70C2×D389—21no—
71C2×D389—22no—
72C2×D389—22no—
73C2×D389—22no—
74C2×D389—48no—
75C2×D389#4112yescomplemented
76C4×C389—21no—
77C4×C389—22no—
78C4×C389C2×D412yes—
79Dic389—21no—
80Dic389—21no—
81Dic389—22no—
82Dic389—21no—
83C2×C389—24no—
84C2×C389—41no—
85C2×C389C22×D411yescharacteristic
86C2×C389C2×#4111yescharacteristic
87C2×C389H(5,𝔽2)11yescharacteristic
88D389—22no—
89D389—42no—
90C389#54611yescharacteristic, complemented, Sylow
91#546—3891nomaximal, Sylow
92C2×#41D38911yescharacteristic, complemented
93C22×D4—3891no—
94#124—3891no—
95#123—3892no—
96C22⋊Q8—3891no—
97#121—3892no—
98#121—3891no—
99#120—3892no—
100C4×D4—3891no—
101C4×D4—3891no—
102C2×C22⋊C4—3892no—
103C24—3892no—
104#41—24no—
105C2×Q8C2×D38911yescharacteristic, complemented
106C2×D4—7784no—
107C2×D4—3891no—
108C2×D4—3892no—
109C2×D4—3892no—
110C2×D4—3891no—
111C2×D4C2×D38911yescharacteristic
112C2×D4C2×D38912yescomplemented
113C22×C4—3891no—
114C22×C4—3892no—
115C22×C4C2×D38912yescomplemented
116C22×C4C2×D38911yescharacteristic, complemented
117C4⋊C4—3891no—
118C4⋊C4—3892no—
119C4⋊C4—3891no—
120C22⋊C4—3892no—
121C22⋊C4—3891no—
122C22⋊C4—3891no—
123C22⋊C4—3892no—
124C22⋊C4—3892no—
125C22⋊C4—3892no—
126C22⋊C4—3892no—
127C42—3891no—
128C23—7784no—
129C23—7784no—
130C23—15562no—
131C23—3892no—
132C23—3891no—
133C23C22×D38911yescharacteristic
134C23C22×D38912yes—
135Q8—22no—
136D4—24no—
137D4—7782no—
138D4—7784no—
139D4—7782no—
140D4—15562no—
141D4C22⋊D38914yescomplemented
142C2×C4—24no—
143C2×C4—22no—
144C2×C4—7782no—
145C2×C4—15562no—
146C2×C4—3891no—
147C2×C4—3891no—
148C2×C4—3892no—
149C2×C4—3891no—
150C2×C4C22×D38911yescharacteristic
151C2×C4C22×D38912yes—
152C2×C4C22×D38911yescharacteristic
153C22—22no—
154C22—22no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—7781no—
159C22—7781no—
160C22—7782no—
161C22—7782no—
162C22—7782no—
163C22—15568no—
164C22—3892no—
165C22C2×C22⋊D38914yes—
166C22C23×D38911yescharacteristic
167C4—21no—
168C4—22no—
169C4—7781no—
170C4—7781no—
171C4—7781no—
172C4—7782no—
173C4C2×C22⋊D38912yes—
174C2—24no—
175C2—41no—
176C2—7782no—
177C2—15562no—
178C2C22×C22⋊D38911yescharacteristic
179C2#41×D38911yescharacteristic
180C2#2715943011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D389
commutator, socle, cosocleC22×C389C24
FittingC2×#41×C389C2
hypercenterC2×#41D389
hypocenterC389#546
LCSG ▷ C22×C389 ▷ C389
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×D4×D389C2semidirect
2. #27159373C2semidirect
3. #27159367C2semidirect
4. #27159360C2semidirect
5. #27159358C2semidirect
6. #27159356C2semidirect
7. #27159352C2semidirect
8. D4×Dic389C2semidirect
9. C4×C22⋊D389C2semidirect
10. C2×#20261943C2semidirect
11. C2×#41×C389C2semidirect
16. C2×C22⋊D389C22semidirect
18. C22×Dic389C22semidirect
20. C4⋊Dic389C22semidirect
21. #20261945C22semidirect
22. #20261945C22semidirect
23. C22⋊Dic389C22semidirect
24. C22⋊Dic389C22semidirect
27. #20261943C22semidirect
28. #20261943C22semidirect
29. #20261943C22semidirect
30. C4×Dic389C22semidirect
32. C2×Q8×C389C22semidirect
34. C2×D4×C389C22semidirect
35. C22×C4×C389C22semidirect
36. C22×C4×C389C22semidirect
56. D4×C389D4semidirect
75. C2×D389#41semidirect
90. C389#546semidirect
92. C2×#41D389semidirect
105. C2×Q8C2×D389semidirect
112. C2×D4C2×D389semidirect
115. C22×C4C2×D389semidirect
116. C22×C4C2×D389semidirect
141. D4C22⋊D389semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D3892
#271593732
#271593672
#271593602
#271593582
#271593562
#271593522
D4×Dic3892
C4×C22⋊D3892
C2×#202619432
C2×#41×C3892
#546389