Finite Group Databasebeta

← #38734665

Subgroups — #38734665

Order 24896.

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

normal subgroups only

This group has 334 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×#20261966C211yesmaximal, characteristic, complemented
2C2×D4×D389C211yesmaximal, characteristic, complemented
3#27159380C212yesmaximal, complemented
4#27159370C212yesmaximal, complemented
5#27159359C211yesmaximal, characteristic, complemented
6#27159358C211yesmaximal, characteristic, complemented
7#27159355C211yesmaximal, characteristic, complemented
8#27159354C212yesmaximal, complemented
9#27159352C212yesmaximal, complemented
10#27159342C211yesmaximal, characteristic, complemented
11#121×C389C211yesmaximal, characteristic, complemented
12C23×D389C2212yes—
13#20261966—24no—
14C2×Dic778C2211yescharacteristic, complemented
15C2×D1556C2211yescharacteristic
16C2×D1556C2211yescharacteristic
17C2×D1556C2212yescomplemented
18C2×C22⋊D389C2211yescharacteristic
19C2×C22⋊D389C2212yes—
20C2×C22⋊D389C2211yescharacteristic, complemented
21C2×C22⋊D389C2212yescomplemented
22C2×C22⋊D389C2212yescomplemented
23D4×D389—24no—
24C2×C4×D389C2211yescharacteristic
25C2×C4×D389C2211yescharacteristic, complemented
26C4⋊Dic389C2211yescharacteristic, complemented
27C22⋊Dic389C2212yescomplemented
28#20261943C2212yes—
29#20261943C2212yescomplemented
30#20261943C2212yescomplemented
31C4×Dic389C2212yescomplemented
32C2×D4×C389C2211yescharacteristic
33C2×D4×C389C2212yescomplemented
34C22×C4×C389C2211yescharacteristic, complemented
35C4⋊C4×C389C2211yescharacteristic, complemented
36C22⋊C4×C389C2212yescomplemented
37C22×D389—24no—
38C22×D389—42no—
39C22×D389—42no—
40C22×D389C2312yes—
41C22×D389C2311yescharacteristic
42C22×D389C2311yescharacteristic
43Dic778—22no—
44D1556—22no—
45D1556—22no—
46D1556—42no—
47C22⋊D389—22no—
48C22⋊D389—24no—
49C22⋊D389—22no—
50C22⋊D389—42no—
51C22⋊D389—42no—
52C2×Dic389C2312yes—
53C2×Dic389C2311yescharacteristic
54C2×Dic389C2311yescharacteristic
55C4×D389—22no—
56C4×D389D414yescomplemented
57C23×C389C2312yes—
58C23×C389C2311yescharacteristic
59D4×C389—22no—
60D4×C389—42no—
61C2×C4×C389—22no—
62C2×C4×C389C2311yescharacteristic
63C2×C4×C389C2312yes—
64C2×C4×C389C2311yescharacteristic
65C22×C389—21no—
66C22×C389—22no—
67C22×C389—21no—
68C22×C389—22no—
69C22×C389—22no—
70C22×C389—21no—
71C22×C389C2411yescharacteristic
72C2×D389—21no—
73C2×D389—21no—
74C2×D389—22no—
75C2×D389—21no—
76C2×D389—21no—
77C2×D389—22no—
78C2×D389—21no—
79C2×D389—22no—
80C2×D389—48no—
81C2×D389C2×D412yes—
82C4×C389—21no—
83C4×C389—22no—
84C4×C389C2×D412yes—
85Dic389—21no—
86Dic389—22no—
87Dic389C2×D412yes—
88C2×C389—42no—
89C2×C389—41no—
90C2×C389C22×D411yescharacteristic
91C2×C389H(5,𝔽2)11yescharacteristic
92C2×C389H(5,𝔽2)11yescharacteristic
93D389—22no—
94D389—41no—
95D389—42no—
96C389#53511yescharacteristic, complemented, Sylow
97#535—3891nomaximal, Sylow
98C2×#41—3891no—
99C22×D4—3891no—
100#127—3892no—
101#124—3892no—
102#121—3891no—
103#121—3891no—
104#121—3891no—
105#121D38911yescharacteristic, complemented
106#120—3892no—
107#120—3892no—
108#117—3891no—
109C24—3892no—
110#41—7784no—
111C2×Q8—3891no—
112C2×D4—7784no—
113C2×D4—3891no—
114C2×D4—3892no—
115C2×D4—3891no—
116C2×D4—3892no—
117C2×D4—3892no—
118C2×D4—3891no—
119C2×D4—3891no—
120C2×D4—3892no—
121C2×D4C2×D38911yescharacteristic
122C2×D4C2×D38912yescomplemented
123C22×C4—3891no—
124C22×C4—3891no—
125C22×C4C2×D38911yescharacteristic, complemented
126C4⋊C4—3891no—
127C4⋊C4C2×D38911yescharacteristic, complemented
128C22⋊C4—3892no—
129C22⋊C4—3892no—
130C22⋊C4—3892no—
131C22⋊C4—3892no—
132C22⋊C4C2×D38912yescomplemented
133C42—3892no—
134C23—7784no—
135C23—15562no—
136C23—15562no—
137C23—3892no—
138C23—3891no—
139C23—3891no—
140C23C22×D38912yes—
141C23C22×D38911yescharacteristic
142Q8—7782no—
143D4—22no—
144D4—42no—
145D4—7782no—
146D4—7782no—
147D4—7784no—
148D4—7782no—
149D4—7782no—
150D4—15562no—
151D4—15562no—
152D4—15562no—
153C2×C4—22no—
154C2×C4—7782no—
155C2×C4—3892no—
156C2×C4—3891no—
157C2×C4—3891no—
158C2×C4—3894no—
159C2×C4C22×D38912yes—
160C2×C4C22×D38911yescharacteristic
161C2×C4C22×D38911yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—7781no—
169C22—7781no—
170C22—7781no—
171C22—7782no—
172C22—7781no—
173C22—7782no—
174C22—7781no—
175C22—7782no—
176C22—15568no—
177C22—3892no—
178C22C23×D38911yescharacteristic
179C4—21no—
180C4—22no—
181C4—7781no—
182C4—7782no—
183C4—3892no—
184C4D4×D38912yes—
185C2—42no—
186C2—41no—
187C2—7782no—
188C2—15562no—
189C2—15561no—
190C2C2×D4×D38911yescharacteristic
191C2#2715942911yescharacteristic
192C2#2715943011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D389
commutator, socle, cosocleC22×C389C24
Fitting#121×C389C2
hypercenter#121D389
hypocenterC389#535
LCSG ▷ C22×C389 ▷ C389
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#20261966C2semidirect
2. C2×D4×D389C2semidirect
3. #27159380C2semidirect
4. #27159370C2semidirect
5. #27159359C2semidirect
6. #27159358C2semidirect
7. #27159355C2semidirect
8. #27159354C2semidirect
9. #27159352C2semidirect
10. #27159342C2semidirect
11. #121×C389C2semidirect
14. C2×Dic778C22semidirect
17. C2×D1556C22semidirect
20. C2×C22⋊D389C22semidirect
21. C2×C22⋊D389C22semidirect
22. C2×C22⋊D389C22semidirect
25. C2×C4×D389C22semidirect
26. C4⋊Dic389C22semidirect
27. C22⋊Dic389C22semidirect
29. #20261943C22semidirect
30. #20261943C22semidirect
31. C4×Dic389C22semidirect
33. C2×D4×C389C22semidirect
34. C22×C4×C389C22semidirect
35. C4⋊C4×C389C22semidirect
36. C22⋊C4×C389C22semidirect
56. C4×D389D4semidirect
96. C389#535semidirect
105. #121D389semidirect
122. C2×D4C2×D389semidirect
125. C22×C4C2×D389semidirect
127. C4⋊C4C2×D389semidirect
132. C22⋊C4C2×D389semidirect

Maximal subgroups

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

subgroupindex
C2×#202619662
C2×D4×D3892
#271593802
#271593702
#271593592
#271593582
#271593552
#271593542
#271593522
#271593422
#121×C3892
#535389