Finite Group Databasebeta

← #44500960

Subgroups — #44500960

Order 30656.

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×#21440161C211yesmaximal, characteristic, complemented
2C22×C22⋊D479C211yesmaximal, characteristic, complemented
3#29506378C212yesmaximal, complemented
4#29506368C212yesmaximal, complemented
5#29506355C212yesmaximal, complemented
6#29506354C212yesmaximal, complemented
7#29506352C211yesmaximal, characteristic, complemented
8#29506351C211yesmaximal, characteristic, complemented
9#29506350C211yesmaximal, characteristic, complemented
10#29506338C211yesmaximal, characteristic, complemented
11#120×C479C211yesmaximal, characteristic, complemented
12C23×D479C2211yescharacteristic
13#21440161—24no—
14C2×Dic958C2211yescharacteristic, complemented
15C2×D1916C2212yescomplemented
16C2×C22⋊D479—24no—
17C2×C22⋊D479C2211yescharacteristic
18C2×C22⋊D479C2212yes—
19C2×C22⋊D479C2212yes—
20C2×C22⋊D479C2211yescharacteristic, complemented
21C2×C22⋊D479C2212yescomplemented
22C2×C22⋊D479C2212yescomplemented
23C22×Dic479C2211yescharacteristic
24C22×Dic479C2211yescharacteristic, complemented
25C2×C4×D479C2211yescharacteristic, complemented
26Dic479⋊C4C2212yescomplemented
27C22⋊Dic479C2211yescharacteristic
28C22⋊Dic479C2212yescomplemented
29(C2×D479)⋊C4C2212yescomplemented
30(C2×D479)⋊C4C2212yescomplemented
31C4×Dic479C2212yescomplemented
32C24×C479C2211yescharacteristic
33C2×D4×C479C2211yescharacteristic
34C2×D4×C479C2212yescomplemented
35C22⋊C4×C479C2211yescharacteristic
36C22⋊C4×C479C2212yescomplemented
37C22×D479—22no—
38C22×D479—42no—
39C22×D479C2312yes—
40C22×D479C2311yescharacteristic
41Dic958—22no—
42D1916—42no—
43C22⋊D479—22no—
44C22⋊D479—24no—
45C22⋊D479—24no—
46C22⋊D479—22no—
47C22⋊D479—42no—
48C22⋊D479—42no—
49C2×Dic479—22no—
50C2×Dic479D414yescomplemented
51C2×Dic479C2312yes—
52C2×Dic479C2311yescharacteristic
53C2×Dic479C2311yescharacteristic
54C2×Dic479C2311yescharacteristic
55C4×D479—22no—
56C23×C479—22no—
57C23×C479—42no—
58C23×C479C2312yes—
59C23×C479C2311yescharacteristic
60C23×C479C2311yescharacteristic
61D4×C479—22no—
62D4×C479—42no—
63C2×C4×C479C2312yes—
64C2×C4×C479C2311yescharacteristic
65C22×C479—22no—
66C22×C479—21no—
67C22×C479—22no—
68C22×C479—22no—
69C22×C479—22no—
70C22×C479—22no—
71C22×C479—44no—
72C22×C479C2×D412yes—
73C22×C479C2411yescharacteristic
74C2×D479—21no—
75C2×D479—22no—
76C2×D479—22no—
77C2×D479—22no—
78C2×D479—22no—
79C2×D479—44no—
80C4×C479—21no—
81C4×C479—22no—
82Dic479—21no—
83Dic479—22no—
84Dic479C2×D412yes—
85Dic479C2×D412yes—
86C2×C479—22no—
87C2×C479—41no—
88C2×C479—42no—
89C2×C479C22×D411yescharacteristic
90C2×C479H(5,𝔽2)12yes—
91D479—41no—
92D479—42no—
93C479#53511yescharacteristic, complemented, Sylow
94#535—4791nomaximal, Sylow
95C2×#41—4791no—
96C22×D4—4791no—
97#127—4792no—
98#124—4792no—
99#121—4792no—
100#121—4792no—
101#120—4791no—
102#120—4791no—
103#120—4791no—
104#120D47911yescharacteristic, complemented
105#117—4791no—
106C24—4791no—
107C24C2×D47911yescharacteristic
108#41—9584no—
109C2×Q8—4791no—
110C2×D4—9584no—
111C2×D4—4792no—
112C2×D4—4792no—
113C2×D4—4791no—
114C2×D4—4792no—
115C2×D4—4792no—
116C2×D4—4791no—
117C2×D4—4792no—
118C2×D4C2×D47911yescharacteristic
119C2×D4C2×D47912yescomplemented
120C22×C4—4791no—
121C22×C4—4791no—
122C22×C4—4791no—
123C4⋊C4—4792no—
124C22⋊C4—4791no—
125C22⋊C4—4792no—
126C22⋊C4—4792no—
127C22⋊C4—4792no—
128C22⋊C4C2×D47911yescharacteristic
129C22⋊C4C2×D47912yescomplemented
130C42—4792no—
131C23—22no—
132C23—42no—
133C23—19162no—
134C23—9582no—
135C23—4792no—
136C23—4791no—
137C23C22×D47912yes—
138C23C22×D47911yescharacteristic
139C23C22×D47911yescharacteristic
140Q8—9582no—
141D4—22no—
142D4—42no—
143D4—19162no—
144D4—19162no—
145D4—19162no—
146D4—9582no—
147D4—9584no—
148D4—9584no—
149D4—9582no—
150C2×C4—9582no—
151C2×C4—9582no—
152C2×C4—4792no—
153C2×C4—4791no—
154C2×C4—4794no—
155C2×C4—4791no—
156C2×C4—4791no—
157C2×C4C22×D47912yes—
158C2×C4C22×D47911yescharacteristic
159C22—22no—
160C22—21no—
161C22—22no—
162C22—22no—
163C22—22no—
164C22—22no—
165C22—44no—
166C22—19164no—
167C22—9581no—
168C22—9582no—
169C22—9582no—
170C22—9582no—
171C22—9582no—
172C22D4×D47912yes—
173C22C23×D47911yescharacteristic
174C4—21no—
175C4—22no—
176C4—9581no—
177C4—9582no—
178C4—4792no—
179C4—4792no—
180C2—22no—
181C2—42no—
182C2—41no—
183C2—19162no—
184C2—19161no—
185C2C2×D4×D47911yescharacteristic
186C2#2950642712yes—
subgroupG/H
center, FrattiniC22C23×D479
commutator, socle, cosocleC22×C479C24
Fitting#120×C479C2
hypercenter#120D479
hypocenterC479#535
LCSG ▷ C22×C479 ▷ C479
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C2×#21440161C2semidirect
2. C22×C22⋊D479C2semidirect
3. #29506378C2semidirect
4. #29506368C2semidirect
5. #29506355C2semidirect
6. #29506354C2semidirect
7. #29506352C2semidirect
8. #29506351C2semidirect
9. #29506350C2semidirect
10. #29506338C2semidirect
11. #120×C479C2semidirect
14. C2×Dic958C22semidirect
15. C2×D1916C22semidirect
20. C2×C22⋊D479C22semidirect
21. C2×C22⋊D479C22semidirect
22. C2×C22⋊D479C22semidirect
24. C22×Dic479C22semidirect
25. C2×C4×D479C22semidirect
26. Dic479⋊C4C22semidirect
28. C22⋊Dic479C22semidirect
29. (C2×D479)⋊C4C22semidirect
30. (C2×D479)⋊C4C22semidirect
31. C4×Dic479C22semidirect
34. C2×D4×C479C22semidirect
36. C22⋊C4×C479C22semidirect
50. C2×Dic479D4semidirect
93. C479#535semidirect
104. #120D479semidirect
119. C2×D4C2×D479semidirect
129. C22⋊C4C2×D479semidirect

Maximal subgroups

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

subgroupindex
C2×#214401612
C22×C22⋊D4792
#295063782
#295063682
#295063552
#295063542
#295063522
#295063512
#295063502
#295063382
#120×C4792
#535479