Finite Group Databasebeta

← D4×C22⋊D491 #44537358

Subgroups — D4×C22⋊D491 #44537358

Order 31424.

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⋊D491C212yesmaximal, complemented
2C2×D4×D491C211yesmaximal, characteristic, complemented
3#30628333C211yesmaximal, characteristic, complemented
4#30628311C211yesmaximal, characteristic, complemented
5#30628309C212yesmaximal, complemented
6#30628308C211yesmaximal, characteristic, complemented
7#30628306C212yesmaximal, complemented
8#30628305C212yesmaximal, complemented
9D4×Dic491C211yesmaximal, characteristic, complemented
10C4×C22⋊D491C211yesmaximal, characteristic, complemented
11C22×D4×C491C211yesmaximal, characteristic, complemented
12C23×D491C2212yescomplemented
13C2×D1964C2211yescharacteristic, complemented
14C2×C22⋊D491—28no—
15C2×C22⋊D491C2211yescharacteristic
16C2×C22⋊D491C2212yescomplemented
17C2×C22⋊D491C2212yescomplemented
18C2×C22⋊D491C2212yescomplemented
19C2×C22⋊D491C2212yescomplemented
20C2×C22⋊D491C2212yescomplemented
21D4×D491—24no—
22C22×Dic491C2212yescomplemented
23C2×C4×D491C2211yescharacteristic, complemented
24C4⋊Dic491C2211yescharacteristic, complemented
25Dic491⋊C4C2211yescharacteristic, complemented
26C22⋊Dic491C2211yescharacteristic, complemented
27C22⋊Dic491C2212yescomplemented
28C22⋊Dic491C2212yescomplemented
29(C2×D491)⋊C4C2211yescharacteristic, complemented
30(C2×D491)⋊C4C2212yescomplemented
31C4×Dic491C2211yescharacteristic, complemented
32C24×C491C2212yescomplemented
33C2×D4×C491—24no—
34C2×D4×C491C2211yescharacteristic
35C2×D4×C491C2212yescomplemented
36C2×D4×C491C2211yescharacteristic, complemented
37C22×C4×C491C2211yescharacteristic, complemented
38C22×D491—24no—
39C22×D491—24no—
40C22×D491—42no—
41C22×D491C2312yes—
42C22×D491C2311yescharacteristic
43D1964—22no—
44C22⋊D491—24no—
45C22⋊D491—24no—
46C22⋊D491—24no—
47C22⋊D491—24no—
48C22⋊D491—42no—
49C22⋊D491D414yesdirect product factor
50C2×Dic491—24no—
51C2×Dic491C2311yescharacteristic
52C2×Dic491C2312yes—
53C2×Dic491C2311yescharacteristic
54C2×Dic491C2311yescharacteristic
55C4×D491—22no—
56C23×C491—24no—
57C23×C491—24no—
58C23×C491—42no—
59C23×C491C2312yes—
60C23×C491C2311yescharacteristic
61C23×C491C2312yes—
62D4×C491—24no—
63D4×C491—22no—
64D4×C491D414yescomplemented
65C2×C4×C491—22no—
66C2×C4×C491C2311yescharacteristic
67C2×C4×C491C2311yescharacteristic
68C22×C491—21no—
69C22×C491—22no—
70C22×C491—21no—
71C22×C491—22no—
72C22×C491—22no—
73C22×C491—22no—
74C22×C491—22no—
75C22×C491—48no—
76C22×C491C2×D412yescomplemented
77C22×C491C2×D414yescomplemented
78C22×C491C2411yescharacteristic
79C2×D491—21no—
80C2×D491—21no—
81C2×D491—22no—
82C2×D491—22no—
83C2×D491—22no—
84C2×D491—48no—
85C2×D491C2×D412yescomplemented
86C4×C491—21no—
87C4×C491C2×D412yescomplemented
88Dic491—21no—
89Dic491—22no—
90Dic491—21no—
91Dic491C2×D412yescomplemented
92C2×C491—24no—
93C2×C491—22no—
94C2×C491—42no—
95C2×C491C22×D411yescharacteristic
96C2×C491C22×D411yescharacteristic
97C2×C491H(5,𝔽2)11yescharacteristic
98D491—22no—
99D491—42no—
100C491D4211yescharacteristic, complemented, Sylow
101D42—4911nomaximal, Sylow
102C22×D4—4912no—
103C22×D4—4911no—
104C22×D4D49111yescharacteristic, complemented
105#127—4911no—
106#121—4911no—
107#121—4912no—
108#121—4911no—
109#120—4912no—
110#120—4912no—
111C4×D4—4911no—
112C4×D4—4911no—
113C24—4912no—
114C24C2×D49112yescomplemented
115C2×D4—24no—
116C2×D4—9828no—
117C2×D4—9824no—
118C2×D4—4912no—
119C2×D4—4912no—
120C2×D4—4912no—
121C2×D4—4912no—
122C2×D4—4912no—
123C2×D4—4911no—
124C2×D4—4911no—
125C2×D4C2×D49111yescharacteristic
126C2×D4C2×D49112yescomplemented
127C2×D4C2×D49111yescharacteristic, complemented
128C22×C4—4912no—
129C22×C4—4911no—
130C22×C4C2×D49111yescharacteristic, complemented
131C4⋊C4—4911no—
132C4⋊C4—4911no—
133C22⋊C4—4911no—
134C22⋊C4—4912no—
135C22⋊C4—4912no—
136C22⋊C4—4911no—
137C22⋊C4—4912no—
138C42—4911no—
139C23—24no—
140C23—24no—
141C23—42no—
142C23—19642no—
143C23—9824no—
144C23—9824no—
145C23—4912no—
146C23—4911no—
147C23C22×D49112yes—
148C23C22×D49111yescharacteristic
149C23C22×D49112yes—
150D4—24no—
151D4—22no—
152D4—19642no—
153D4—9824no—
154D4—9824no—
155D4—9824no—
156D4—9824no—
157D4—9822no—
158D4—4914no—
159D4C22⋊D49114yesdirect product factor
160C2×C4—22no—
161C2×C4—9824no—
162C2×C4—9822no—
163C2×C4—4911no—
164C2×C4—4912no—
165C2×C4—4911no—
166C2×C4—4911no—
167C2×C4C22×D49111yescharacteristic
168C2×C4C22×D49111yescharacteristic
169C22—22no—
170C22—21no—
171C22—21no—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—48no—
177C22—19648no—
178C22—9822no—
179C22—9822no—
180C22—9822no—
181C22—9821no—
182C22—9821no—
183C22—4912no—
184C22D4×D49112yescomplemented
185C22C2×C22⋊D49114yescomplemented
186C22C23×D49111yescharacteristic
187C4—21no—
188C4—9822no—
189C4—9821no—
190C4—9821no—
191C4—4912no—
192C4C2×C22⋊D49112yescomplemented
193C2—22no—
194C2—24no—
195C2—42no—
196C2—19642no—
197C2—9822no—
198C2C2×D4×D49111yescharacteristic
199C2C22×C22⋊D49111yescharacteristic
200C2#3062838211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D491
commutator, socle, cosocleC22×C491C24
FittingC22×D4×C491C2
hypercenterC22×D4D491
hypocenterC491D42
LCSG ▷ C22×C491 ▷ C491
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D491C2semidirect
2. C2×D4×D491C2semidirect
3. #30628333C2semidirect
4. #30628311C2semidirect
5. #30628309C2semidirect
6. #30628308C2semidirect
7. #30628306C2semidirect
8. #30628305C2semidirect
9. D4×Dic491C2semidirect
10. C4×C22⋊D491C2semidirect
11. C22×D4×C491C2semidirect
12. C23×D491C22semidirect
13. C2×D1964C22semidirect
16. C2×C22⋊D491C22semidirect
17. C2×C22⋊D491C22semidirect
18. C2×C22⋊D491C22semidirect
19. C2×C22⋊D491C22semidirect
20. C2×C22⋊D491C22semidirect
22. C22×Dic491C22semidirect
23. C2×C4×D491C22semidirect
24. C4⋊Dic491C22semidirect
25. Dic491⋊C4C22semidirect
26. C22⋊Dic491C22semidirect
27. C22⋊Dic491C22semidirect
28. C22⋊Dic491C22semidirect
29. (C2×D491)⋊C4C22semidirect
30. (C2×D491)⋊C4C22semidirect
31. C4×Dic491C22semidirect
32. C24×C491C22semidirect
35. C2×D4×C491C22semidirect
36. C2×D4×C491C22semidirect
37. C22×C4×C491C22semidirect
49. C22⋊D491D4direct (N × H)
64. D4×C491D4semidirect
76. C22×C491C2×D4semidirect
77. C22×C491C2×D4semidirect
85. C2×D491C2×D4semidirect
87. C4×C491C2×D4semidirect
91. Dic491C2×D4semidirect
100. C491D42semidirect
104. C22×D4D491semidirect
114. C24C2×D491semidirect
126. C2×D4C2×D491semidirect
127. C2×D4C2×D491semidirect
130. C22×C4C2×D491semidirect
159. D4C22⋊D491direct (N × H)
184. C22D4×D491semidirect
185. C22C2×C22⋊D491semidirect
192. C4C2×C22⋊D491semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D4912
C2×D4×D4912
#306283332
#306283112
#306283092
#306283082
#306283062
#306283052
D4×Dic4912
C4×C22⋊D4912
C22×D4×C4912
D42491