Finite Group Databasebeta

← #44501033

Subgroups — #44501033

Order 30656.

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×D479C211yesmaximal, characteristic, complemented
2#29506371C211yesmaximal, characteristic, complemented
3#29506365C212yesmaximal, complemented
4#29506358C211yesmaximal, characteristic, complemented
5#29506356C211yesmaximal, characteristic, complemented
6#29506354C212yesmaximal, complemented
7#29506350C212yesmaximal, complemented
8D4×Dic479C211yesmaximal, characteristic, complemented
9C4×C22⋊D479C211yesmaximal, characteristic, complemented
10C2×(C2×D479)⋊C4C212yesmaximal, complemented
11C2×#41×C479C211yesmaximal, characteristic, complemented
12C23×D479C2212yes—
13C2×D1916C2211yescharacteristic
14C2×C22⋊D479C2211yescharacteristic
15C2×C22⋊D479C2212yes—
16C2×C22⋊D479C2212yescomplemented
17D4×D479—24no—
18C22×Dic479C2212yescomplemented
19C2×C4×D479C2211yescharacteristic
20C4⋊Dic479C2211yescharacteristic, complemented
21Dic479⋊C4C2211yescharacteristic, complemented
22Dic479⋊C4C2212yescomplemented
23C22⋊Dic479C2211yescharacteristic, complemented
24C22⋊Dic479C2212yescomplemented
25(C2×D479)⋊C4C2211yescharacteristic
26(C2×D479)⋊C4C2212yes—
27(C2×D479)⋊C4C2212yescomplemented
28(C2×D479)⋊C4C2212yescomplemented
29(C2×D479)⋊C4C2212yescomplemented
30C4×Dic479C2211yescharacteristic, complemented
31#41×C479—24no—
32C2×Q8×C479C2211yescharacteristic, complemented
33C2×D4×C479C2211yescharacteristic
34C2×D4×C479C2212yescomplemented
35C22×C4×C479C2212yescomplemented
36C22×C4×C479C2211yescharacteristic, complemented
37C22×D479—24no—
38C22×D479—24no—
39C22×D479—42no—
40C22×D479C2312yes—
41C22×D479C2311yescharacteristic
42D1916—22no—
43C22⋊D479—24no—
44C22⋊D479—22no—
45C22⋊D479—42no—
46C2×Dic479—42no—
47C2×Dic479C2311yescharacteristic
48C2×Dic479C2311yescharacteristic
49C2×Dic479C2312yes—
50C2×Dic479C2311yescharacteristic
51C4×D479—22no—
52C23×C479C2311yescharacteristic
53C23×C479C2312yes—
54Q8×C479—22no—
55D4×C479—24no—
56D4×C479D414yescomplemented
57C2×C4×C479—24no—
58C2×C4×C479—22no—
59C2×C4×C479C2311yescharacteristic
60C2×C4×C479C2312yes—
61C2×C4×C479C2311yescharacteristic
62C22×C479—22no—
63C22×C479—22no—
64C22×C479—21no—
65C22×C479—21no—
66C22×C479—21no—
67C22×C479C2×D414yes—
68C22×C479C2411yescharacteristic
69C2×D479—21no—
70C2×D479—21no—
71C2×D479—22no—
72C2×D479—22no—
73C2×D479—22no—
74C2×D479—48no—
75C2×D479#4112yescomplemented
76C4×C479—21no—
77C4×C479—22no—
78C4×C479C2×D412yes—
79Dic479—21no—
80Dic479—21no—
81Dic479—21no—
82Dic479—22no—
83C2×C479—24no—
84C2×C479—41no—
85C2×C479C22×D411yescharacteristic
86C2×C479C2×#4111yescharacteristic
87C2×C479H(5,𝔽2)11yescharacteristic
88D479—22no—
89D479—42no—
90C479#54611yescharacteristic, complemented, Sylow
91#546—4791nomaximal, Sylow
92C2×#41D47911yescharacteristic, complemented
93C22×D4—4791no—
94#124—4791no—
95#123—4792no—
96C22⋊Q8—4791no—
97#121—4792no—
98#121—4791no—
99#120—4792no—
100C4×D4—4791no—
101C4×D4—4791no—
102C2×C22⋊C4—4792no—
103C24—4792no—
104#41—24no—
105C2×Q8C2×D47911yescharacteristic, complemented
106C2×D4—9584no—
107C2×D4—4792no—
108C2×D4—4791no—
109C2×D4—4792no—
110C2×D4—4791no—
111C2×D4C2×D47911yescharacteristic
112C2×D4C2×D47912yescomplemented
113C22×C4—4792no—
114C22×C4—4791no—
115C22×C4C2×D47912yescomplemented
116C22×C4C2×D47911yescharacteristic, complemented
117C4⋊C4—4791no—
118C4⋊C4—4791no—
119C4⋊C4—4792no—
120C22⋊C4—4792no—
121C22⋊C4—4791no—
122C22⋊C4—4791no—
123C22⋊C4—4792no—
124C22⋊C4—4792no—
125C22⋊C4—4792no—
126C22⋊C4—4792no—
127C42—4791no—
128C23—19162no—
129C23—9584no—
130C23—9584no—
131C23—4792no—
132C23—4791no—
133C23C22×D47911yescharacteristic
134C23C22×D47912yes—
135Q8—22no—
136D4—24no—
137D4—19162no—
138D4—9582no—
139D4—9584no—
140D4—9582no—
141D4C22⋊D47914yescomplemented
142C2×C4—24no—
143C2×C4—22no—
144C2×C4—19162no—
145C2×C4—9582no—
146C2×C4—4791no—
147C2×C4—4791no—
148C2×C4—4792no—
149C2×C4—4791no—
150C2×C4C22×D47911yescharacteristic
151C2×C4C22×D47912yes—
152C2×C4C22×D47911yescharacteristic
153C22—22no—
154C22—22no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—19168no—
159C22—9582no—
160C22—9582no—
161C22—9582no—
162C22—9581no—
163C22—9581no—
164C22—4792no—
165C22C2×C22⋊D47914yes—
166C22C23×D47911yescharacteristic
167C4—21no—
168C4—22no—
169C4—9581no—
170C4—9581no—
171C4—9581no—
172C4—9582no—
173C4C2×C22⋊D47912yes—
174C2—24no—
175C2—41no—
176C2—19162no—
177C2—9582no—
178C2C22×C22⋊D47911yescharacteristic
179C2#41×D47911yescharacteristic
180C2#2950642811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D479
commutator, socle, cosocleC22×C479C24
FittingC2×#41×C479C2
hypercenterC2×#41D479
hypocenterC479#546
LCSG ▷ C22×C479 ▷ C479
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×D4×D479C2semidirect
2. #29506371C2semidirect
3. #29506365C2semidirect
4. #29506358C2semidirect
5. #29506356C2semidirect
6. #29506354C2semidirect
7. #29506350C2semidirect
8. D4×Dic479C2semidirect
9. C4×C22⋊D479C2semidirect
10. C2×(C2×D479)⋊C4C2semidirect
11. C2×#41×C479C2semidirect
16. C2×C22⋊D479C22semidirect
18. C22×Dic479C22semidirect
20. C4⋊Dic479C22semidirect
21. Dic479⋊C4C22semidirect
22. Dic479⋊C4C22semidirect
23. C22⋊Dic479C22semidirect
24. C22⋊Dic479C22semidirect
27. (C2×D479)⋊C4C22semidirect
28. (C2×D479)⋊C4C22semidirect
29. (C2×D479)⋊C4C22semidirect
30. C4×Dic479C22semidirect
32. C2×Q8×C479C22semidirect
34. C2×D4×C479C22semidirect
35. C22×C4×C479C22semidirect
36. C22×C4×C479C22semidirect
56. D4×C479D4semidirect
75. C2×D479#41semidirect
90. C479#546semidirect
92. C2×#41D479semidirect
105. C2×Q8C2×D479semidirect
112. C2×D4C2×D479semidirect
115. C22×C4C2×D479semidirect
116. C22×C4C2×D479semidirect
141. D4C22⋊D479semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D4792
#295063712
#295063652
#295063582
#295063562
#295063542
#295063502
D4×Dic4792
C4×C22⋊D4792
C2×(C2×D479)⋊C42
C2×#41×C4792
#546479