Finite Group Databasebeta

← #44501029

Subgroups — #44501029

Order 30656.

428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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×D1916C211yesmaximal, characteristic, complemented
2C2×D4×D479C212yesmaximal, complemented
3C2×D4×D479C211yesmaximal, characteristic, complemented
4#29506378C211yesmaximal, characteristic, complemented
5#29506357C211yesmaximal, characteristic, complemented
6#29506355C212yesmaximal, complemented
7#29506352C212yesmaximal, complemented
8#29506350C212yesmaximal, complemented
9#29506344C211yesmaximal, characteristic, complemented
10C4×C22⋊D479C211yesmaximal, characteristic, complemented
11#121×C479C211yesmaximal, characteristic, complemented
12C23×D479C2212yescomplemented
13C23×D479C2212yescomplemented
14C2×D1916—24no—
15C2×D1916C2211yescharacteristic
16C2×D1916C2212yescomplemented
17C2×D1916C2212yescomplemented
18C2×D1916C2211yescharacteristic, complemented
19C2×C22⋊D479C2211yescharacteristic
20C2×C22⋊D479C2212yescomplemented
21C2×C22⋊D479C2212yescomplemented
22C2×C22⋊D479C2212yescomplemented
23D4×D479—24no—
24D4×D479—28no—
25C2×C4×D479C2211yescharacteristic, complemented
26C2×C4×D479C2212yescomplemented
27Dic479⋊C4C2211yescharacteristic, complemented
28C22⋊Dic479C2211yescharacteristic, complemented
29(C2×D479)⋊C4C2211yescharacteristic, complemented
30(C2×D479)⋊C4C2212yescomplemented
31(C2×D479)⋊C4C2212yescomplemented
32C4×Dic479C2211yescharacteristic, complemented
33C2×D4×C479C2212yescomplemented
34C2×D4×C479C2211yescharacteristic, complemented
35C22×C4×C479C2211yescharacteristic, complemented
36C4⋊C4×C479C2211yescharacteristic, complemented
37C22⋊C4×C479C2212yescomplemented
38C22×D479—24no—
39C22×D479—24no—
40C22×D479—24no—
41C22×D479—24no—
42C22×D479—42no—
43C22×D479—42no—
44C22×D479C2312yes—
45C22×D479C2311yescharacteristic
46C22×D479C2312yes—
47D1916—24no—
48D1916—24no—
49D1916—22no—
50D1916D414yescomplemented
51C22⋊D479—24no—
52C22⋊D479—24no—
53C22⋊D479—42no—
54C22⋊D479D414yescomplemented
55C2×Dic479C2311yescharacteristic
56C2×Dic479C2311yescharacteristic
57C2×Dic479C2311yescharacteristic
58C4×D479—22no—
59C4×D479—24no—
60C23×C479C2312yes—
61C23×C479C2311yescharacteristic
62D4×C479—24no—
63D4×C479—22no—
64C2×C4×C479—22no—
65C2×C4×C479C2311yescharacteristic
66C2×C4×C479C2312yes—
67C2×C4×C479C2311yescharacteristic
68C22×C479—21no—
69C22×C479—21no—
70C22×C479—22no—
71C22×C479—22no—
72C22×C479—22no—
73C22×C479C2×D412yescomplemented
74C22×C479C2411yescharacteristic
75C2×D479—21no—
76C2×D479—22no—
77C2×D479—21no—
78C2×D479—22no—
79C2×D479—22no—
80C2×D479—22no—
81C2×D479—22no—
82C2×D479—48no—
83C2×D479—48no—
84C2×D479C2×D414yescomplemented
85C2×D479C2×D412yescomplemented
86C4×C479—21no—
87C4×C479—22no—
88C4×C479C2×D412yescomplemented
89Dic479—21no—
90Dic479—21no—
91Dic479C2×D412yescomplemented
92C2×C479—22no—
93C2×C479—42no—
94C2×C479C22×D411yescharacteristic
95C2×C479C22×D411yescharacteristic
96C2×C479H(5,𝔽2)11yescharacteristic
97D479—22no—
98D479—24no—
99D479—42no—
100C479D4211yescharacteristic, complemented, Sylow
101D42—4791nomaximal, Sylow
102C22×D4—4791no—
103C22×D4—4792no—
104C22×D4—4791no—
105#127—4791no—
106#121—4791no—
107#121—4792no—
108#121D47911yescharacteristic, complemented
109#120—4792no—
110#120—4792no—
111C4×D4—4791no—
112C4×D4—4791no—
113C24—4792no—
114C24—4792no—
115C2×D4—9584no—
116C2×D4—9588no—
117C2×D4—9584no—
118C2×D4—4792no—
119C2×D4—4792no—
120C2×D4—4792no—
121C2×D4—4791no—
122C2×D4—4792no—
123C2×D4—4792no—
124C2×D4—4791no—
125C2×D4—4791no—
126C2×D4C2×D47912yescomplemented
127C2×D4C2×D47911yescharacteristic, complemented
128C22×C4—4792no—
129C22×C4—4791no—
130C22×C4C2×D47911yescharacteristic, complemented
131C4⋊C4—4791no—
132C4⋊C4C2×D47911yescharacteristic, complemented
133C22⋊C4—4791no—
134C22⋊C4—4792no—
135C22⋊C4—4791no—
136C22⋊C4—4792no—
137C22⋊C4C2×D47912yescomplemented
138C42—4791no—
139C23—19162no—
140C23—19162no—
141C23—9584no—
142C23—9584no—
143C23—9584no—
144C23—9584no—
145C23—4792no—
146C23—4792no—
147C23—4791no—
148C23C22×D47912yes—
149C23C22×D47911yescharacteristic
150D4—24no—
151D4—22no—
152D4—19162no—
153D4—9584no—
154D4—9584no—
155D4—9584no—
156D4—9584no—
157D4—9582no—
158D4—4794no—
159D4—4794no—
160C2×C4—22no—
161C2×C4—9584no—
162C2×C4—9582no—
163C2×C4—4791no—
164C2×C4—4791no—
165C2×C4—4791no—
166C2×C4C22×D47912yes—
167C2×C4C22×D47911yescharacteristic
168C2×C4C22×D47911yescharacteristic
169C22—21no—
170C22—21no—
171C22—22no—
172C22—22no—
173C22—22no—
174C22—19168no—
175C22—19168no—
176C22—9582no—
177C22—9582no—
178C22—9582no—
179C22—9582no—
180C22—9581no—
181C22—9582no—
182C22—9581no—
183C22—4792no—
184C22—4794no—
185C22D4×D47912yescomplemented
186C22C23×D47911yescharacteristic
187C4—21no—
188C4—22no—
189C4—9581no—
190C4—9581no—
191C4—4792no—
192C4D4×D47912yescomplemented
193C2—22no—
194C2—42no—
195C2—19162no—
196C2—9584no—
197C2—9582no—
198C2C2×D4×D47911yescharacteristic
199C2C2×D4×D47911yescharacteristic
200C2#2950642811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D479
commutator, socle, cosocleC22×C479C24
Fitting#121×C479C2
hypercenter#121D479
hypocenterC479D42
LCSG ▷ C22×C479 ▷ C479
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C22×D1916C2semidirect
2. C2×D4×D479C2semidirect
3. C2×D4×D479C2semidirect
4. #29506378C2semidirect
5. #29506357C2semidirect
6. #29506355C2semidirect
7. #29506352C2semidirect
8. #29506350C2semidirect
9. #29506344C2semidirect
10. C4×C22⋊D479C2semidirect
11. #121×C479C2semidirect
12. C23×D479C22semidirect
13. C23×D479C22semidirect
16. C2×D1916C22semidirect
17. C2×D1916C22semidirect
18. C2×D1916C22semidirect
20. C2×C22⋊D479C22semidirect
21. C2×C22⋊D479C22semidirect
22. C2×C22⋊D479C22semidirect
25. C2×C4×D479C22semidirect
26. C2×C4×D479C22semidirect
27. Dic479⋊C4C22semidirect
28. C22⋊Dic479C22semidirect
29. (C2×D479)⋊C4C22semidirect
30. (C2×D479)⋊C4C22semidirect
31. (C2×D479)⋊C4C22semidirect
32. C4×Dic479C22semidirect
33. C2×D4×C479C22semidirect
34. C2×D4×C479C22semidirect
35. C22×C4×C479C22semidirect
36. C4⋊C4×C479C22semidirect
37. C22⋊C4×C479C22semidirect
50. D1916D4semidirect
54. C22⋊D479D4semidirect
73. C22×C479C2×D4semidirect
84. C2×D479C2×D4semidirect
85. C2×D479C2×D4semidirect
88. C4×C479C2×D4semidirect
91. Dic479C2×D4semidirect
100. C479D42semidirect
108. #121D479semidirect
126. C2×D4C2×D479semidirect
127. C2×D4C2×D479semidirect
130. C22×C4C2×D479semidirect
132. C4⋊C4C2×D479semidirect
137. C22⋊C4C2×D479semidirect
185. C22D4×D479semidirect
192. C4D4×D479semidirect

Maximal subgroups

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

subgroupindex
C22×D19162
C2×D4×D4792
#295063782
#295063572
#295063552
#295063522
#295063502
#295063442
C4×C22⋊D4792
#121×C4792
D42479