Finite Group Databasebeta

← D4×C22⋊D389 #38734732

Subgroups — D4×C22⋊D389 #38734732

Order 24896.

428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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×C22⋊D389C212yesmaximal, complemented
2C2×D4×D389C211yesmaximal, characteristic, complemented
3#27159380C211yesmaximal, characteristic, complemented
4#27159358C211yesmaximal, characteristic, complemented
5#27159356C212yesmaximal, complemented
6#27159355C211yesmaximal, characteristic, complemented
7#27159353C212yesmaximal, complemented
8#27159352C212yesmaximal, complemented
9D4×Dic389C211yesmaximal, characteristic, complemented
10C4×C22⋊D389C211yesmaximal, characteristic, complemented
11C22×D4×C389C211yesmaximal, characteristic, complemented
12C23×D389C2212yescomplemented
13C2×D1556C2211yescharacteristic, complemented
14C2×C22⋊D389—28no—
15C2×C22⋊D389C2211yescharacteristic
16C2×C22⋊D389C2212yescomplemented
17C2×C22⋊D389C2212yescomplemented
18C2×C22⋊D389C2212yescomplemented
19C2×C22⋊D389C2212yescomplemented
20C2×C22⋊D389C2212yescomplemented
21D4×D389—24no—
22C22×Dic389C2212yescomplemented
23C2×C4×D389C2211yescharacteristic, complemented
24C4⋊Dic389C2211yescharacteristic, complemented
25#20261945C2211yescharacteristic, complemented
26C22⋊Dic389C2211yescharacteristic, complemented
27C22⋊Dic389C2212yescomplemented
28C22⋊Dic389C2212yescomplemented
29#20261943C2211yescharacteristic, complemented
30#20261943C2212yescomplemented
31C4×Dic389C2211yescharacteristic, complemented
32C24×C389C2212yescomplemented
33C2×D4×C389—24no—
34C2×D4×C389C2211yescharacteristic
35C2×D4×C389C2212yescomplemented
36C2×D4×C389C2211yescharacteristic, complemented
37C22×C4×C389C2211yescharacteristic, complemented
38C22×D389—24no—
39C22×D389—24no—
40C22×D389—42no—
41C22×D389C2312yes—
42C22×D389C2311yescharacteristic
43D1556—22no—
44C22⋊D389—24no—
45C22⋊D389—24no—
46C22⋊D389—24no—
47C22⋊D389—24no—
48C22⋊D389—42no—
49C22⋊D389D414yesdirect product factor
50C2×Dic389—24no—
51C2×Dic389C2311yescharacteristic
52C2×Dic389C2312yes—
53C2×Dic389C2311yescharacteristic
54C2×Dic389C2311yescharacteristic
55C4×D389—22no—
56C23×C389—24no—
57C23×C389—24no—
58C23×C389—42no—
59C23×C389C2312yes—
60C23×C389C2311yescharacteristic
61C23×C389C2312yes—
62D4×C389—24no—
63D4×C389—22no—
64D4×C389D414yescomplemented
65C2×C4×C389—22no—
66C2×C4×C389C2311yescharacteristic
67C2×C4×C389C2311yescharacteristic
68C22×C389—22no—
69C22×C389—21no—
70C22×C389—22no—
71C22×C389—21no—
72C22×C389—22no—
73C22×C389—22no—
74C22×C389—22no—
75C22×C389—48no—
76C22×C389C2×D412yescomplemented
77C22×C389C2×D414yescomplemented
78C22×C389C2411yescharacteristic
79C2×D389—21no—
80C2×D389—21no—
81C2×D389—22no—
82C2×D389—22no—
83C2×D389—22no—
84C2×D389—48no—
85C2×D389C2×D412yescomplemented
86C4×C389—21no—
87C4×C389C2×D412yescomplemented
88Dic389—21no—
89Dic389—22no—
90Dic389—21no—
91Dic389C2×D412yescomplemented
92C2×C389—24no—
93C2×C389—22no—
94C2×C389—42no—
95C2×C389C22×D411yescharacteristic
96C2×C389C22×D411yescharacteristic
97C2×C389H(5,𝔽2)11yescharacteristic
98D389—22no—
99D389—42no—
100C389D4211yescharacteristic, complemented, Sylow
101D42—3891nomaximal, Sylow
102C22×D4—3892no—
103C22×D4—3891no—
104C22×D4D38911yescharacteristic, complemented
105#127—3891no—
106#121—3891no—
107#121—3892no—
108#121—3891no—
109#120—3892no—
110#120—3892no—
111C4×D4—3891no—
112C4×D4—3891no—
113C24—3892no—
114C24C2×D38912yescomplemented
115C2×D4—24no—
116C2×D4—7788no—
117C2×D4—7784no—
118C2×D4—3892no—
119C2×D4—3892no—
120C2×D4—3892no—
121C2×D4—3892no—
122C2×D4—3892no—
123C2×D4—3891no—
124C2×D4—3891no—
125C2×D4C2×D38911yescharacteristic
126C2×D4C2×D38912yescomplemented
127C2×D4C2×D38911yescharacteristic, complemented
128C22×C4—3892no—
129C22×C4—3891no—
130C22×C4C2×D38911yescharacteristic, complemented
131C4⋊C4—3891no—
132C4⋊C4—3891no—
133C22⋊C4—3891no—
134C22⋊C4—3892no—
135C22⋊C4—3892no—
136C22⋊C4—3891no—
137C22⋊C4—3892no—
138C42—3891no—
139C23—24no—
140C23—24no—
141C23—42no—
142C23—7784no—
143C23—7784no—
144C23—15562no—
145C23—3892no—
146C23—3891no—
147C23C22×D38912yes—
148C23C22×D38911yescharacteristic
149C23C22×D38912yes—
150D4—24no—
151D4—22no—
152D4—7784no—
153D4—7784no—
154D4—7784no—
155D4—7784no—
156D4—7782no—
157D4—15562no—
158D4—3894no—
159D4C22⋊D38914yesdirect product factor
160C2×C4—22no—
161C2×C4—7784no—
162C2×C4—7782no—
163C2×C4—3891no—
164C2×C4—3892no—
165C2×C4—3891no—
166C2×C4—3891no—
167C2×C4C22×D38911yescharacteristic
168C2×C4C22×D38911yescharacteristic
169C22—22no—
170C22—21no—
171C22—21no—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—48no—
177C22—7781no—
178C22—7781no—
179C22—7782no—
180C22—7782no—
181C22—7782no—
182C22—15568no—
183C22—3892no—
184C22D4×D38912yescomplemented
185C22C2×C22⋊D38914yescomplemented
186C22C23×D38911yescharacteristic
187C4—21no—
188C4—7782no—
189C4—7781no—
190C4—7781no—
191C4—3892no—
192C4C2×C22⋊D38912yescomplemented
193C2—22no—
194C2—24no—
195C2—42no—
196C2—7782no—
197C2—15562no—
198C2C2×D4×D38911yescharacteristic
199C2C22×C22⋊D38911yescharacteristic
200C2#2715942911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D389
commutator, socle, cosocleC22×C389C24
FittingC22×D4×C389C2
hypercenterC22×D4D389
hypocenterC389D42
LCSG ▷ C22×C389 ▷ C389
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D389C2semidirect
2. C2×D4×D389C2semidirect
3. #27159380C2semidirect
4. #27159358C2semidirect
5. #27159356C2semidirect
6. #27159355C2semidirect
7. #27159353C2semidirect
8. #27159352C2semidirect
9. D4×Dic389C2semidirect
10. C4×C22⋊D389C2semidirect
11. C22×D4×C389C2semidirect
12. C23×D389C22semidirect
13. C2×D1556C22semidirect
16. C2×C22⋊D389C22semidirect
17. C2×C22⋊D389C22semidirect
18. C2×C22⋊D389C22semidirect
19. C2×C22⋊D389C22semidirect
20. C2×C22⋊D389C22semidirect
22. C22×Dic389C22semidirect
23. C2×C4×D389C22semidirect
24. C4⋊Dic389C22semidirect
25. #20261945C22semidirect
26. C22⋊Dic389C22semidirect
27. C22⋊Dic389C22semidirect
28. C22⋊Dic389C22semidirect
29. #20261943C22semidirect
30. #20261943C22semidirect
31. C4×Dic389C22semidirect
32. C24×C389C22semidirect
35. C2×D4×C389C22semidirect
36. C2×D4×C389C22semidirect
37. C22×C4×C389C22semidirect
49. C22⋊D389D4direct (N × H)
64. D4×C389D4semidirect
76. C22×C389C2×D4semidirect
77. C22×C389C2×D4semidirect
85. C2×D389C2×D4semidirect
87. C4×C389C2×D4semidirect
91. Dic389C2×D4semidirect
100. C389D42semidirect
104. C22×D4D389semidirect
114. C24C2×D389semidirect
126. C2×D4C2×D389semidirect
127. C2×D4C2×D389semidirect
130. C22×C4C2×D389semidirect
159. D4C22⋊D389direct (N × H)
184. C22D4×D389semidirect
185. C22C2×C22⋊D389semidirect
192. C4C2×C22⋊D389semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D3892
C2×D4×D3892
#271593802
#271593582
#271593562
#271593552
#271593532
#271593522
D4×Dic3892
C4×C22⋊D3892
C22×D4×C3892
D42389