Finite Group Databasebeta

← #44500903

Subgroups — #44500903

Order 30656.

330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 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×C4×D479C211yesmaximal, characteristic, complemented
3#29506365C211yesmaximal, characteristic, complemented
4#29506360C212yesmaximal, complemented
5#29506355C212yesmaximal, complemented
6#29506352C211yesmaximal, characteristic, complemented
7#29506350C211yesmaximal, characteristic, complemented
8#29506344C212yesmaximal, complemented
9(C22⋊D479)⋊C4C212yesmaximal, complemented
10#29506338C211yesmaximal, characteristic, complemented
11#123×C479C211yesmaximal, characteristic, complemented
12C23×D479C2211yescharacteristic
13#21440161—24no—
14C2×Dic958C2211yescharacteristic, complemented
15C2×D1916C2212yes—
16C2×C22⋊D479C2212yes—
17C2×C22⋊D479C2211yescharacteristic
18C2×C22⋊D479C2211yescharacteristic, complemented
19C22×Dic479C2211yescharacteristic
20C22×Dic479C2211yescharacteristic, complemented
21C2×C4×D479—24no—
22C2×C4×D479C2212yes—
23C2×C4×D479C2212yes—
24C2×C4×D479C2211yescharacteristic, complemented
25Dic479⋊C4C2212yescomplemented
26Dic479⋊C4C2212yescomplemented
27C22⋊Dic479C2211yescharacteristic
28(C2×D479)⋊C4C2212yes—
29(C2×D479)⋊C4C2212yes—
30(C2×D479)⋊C4C2212yescomplemented
31C4×Dic479C2212yescomplemented
32C2×D4×C479C2211yescharacteristic
33C22×C4×C479C2211yescharacteristic
34C4⋊C4×C479C2212yescomplemented
35C22⋊C4×C479C2211yescharacteristic
36C22⋊C4×C479C2212yescomplemented
37C22×D479—22no—
38C22×D479—24no—
39C22×D479C2311yescharacteristic
40C22×D479C2312yes—
41Dic958—22no—
42D1916—24no—
43C22⋊D479—22no—
44C22⋊D479—24no—
45C22⋊D479—22no—
46C2×Dic479—22no—
47C2×Dic479D414yescomplemented
48C2×Dic479C2312yes—
49C2×Dic479C2311yescharacteristic
50C2×Dic479C2311yescharacteristic
51C2×Dic479C2311yescharacteristic
52C4×D479—24no—
53C4×D479—24no—
54C4×D479—22no—
55C23×C479C2311yescharacteristic
56C23×C479C2311yescharacteristic
57D4×C479—22no—
58C2×C4×C479—22no—
59C2×C4×C479C2312yes—
60C2×C4×C479C2312yes—
61C2×C4×C479C2311yescharacteristic
62C22×C479—22no—
63C22×C479—21no—
64C22×C479—22no—
65C22×C479C2×D412yes—
66C22×C479C2411yescharacteristic
67C2×D479—28no—
68C2×D479—22no—
69C2×D479—22no—
70C2×D479—21no—
71C2×D479—22no—
72C2×D479#4114yescomplemented
73C4×C479—22no—
74C4×C479—21no—
75C4×C479—22no—
76Dic479—21no—
77Dic479—22no—
78Dic479C2×D412yes—
79Dic479C2×D412yes—
80C2×C479—22no—
81C2×C479—41no—
82C2×C479C22×D411yescharacteristic
83C2×C479C2×#4112yes—
84D479—24no—
85D479—41no—
86C479#52511yescharacteristic, complemented, Sylow
87#525—4791nomaximal, Sylow
88C2×#41—4791no—
89C23×C4—4791no—
90#123—4791no—
91#123D47911yescharacteristic, complemented
92C22⋊Q8—4792no—
93#121—4792no—
94#120—4791no—
95#120—4791no—
96C4×D4—4792no—
97C4×D4—4792no—
98#117—4791no—
99C24—4791no—
100#41—9584no—
101C2×Q8—4791no—
102C2×D4—4792no—
103C2×D4—4791no—
104C2×D4—4791no—
105C2×D4—4792no—
106C2×D4C2×D47911yescharacteristic
107C22×C4—9584no—
108C22×C4—4791no—
109C22×C4—4792no—
110C22×C4—4791no—
111C22×C4—4792no—
112C22×C4—4791no—
113C22×C4C2×D47911yescharacteristic
114C4⋊C4—4792no—
115C4⋊C4—4792no—
116C4⋊C4C2×D47912yescomplemented
117C22⋊C4—4791no—
118C22⋊C4—4792no—
119C22⋊C4—4792no—
120C22⋊C4—4792no—
121C22⋊C4C2×D47911yescharacteristic
122C22⋊C4C2×D47912yescomplemented
123C42—4792no—
124C23—9584no—
125C23—9582no—
126C23—4791no—
127C23—4792no—
128C23C22×D47911yescharacteristic
129C23C22×D47911yescharacteristic
130Q8—9582no—
131D4—22no—
132D4—9584no—
133D4—9584no—
134D4—9582no—
135D4—9582no—
136C2×C4—22no—
137C2×C4—9584no—
138C2×C4—9584no—
139C2×C4—9582no—
140C2×C4—9582no—
141C2×C4—4792no—
142C2×C4—4791no—
143C2×C4—4794no—
144C2×C4—4791no—
145C2×C4—4791no—
146C2×C4C22×D47912yes—
147C2×C4C22×D47911yescharacteristic
148C2×C4C22×D47912yes—
149C22—22no—
150C22—21no—
151C22—22no—
152C22—9588no—
153C22—9581no—
154C22—9582no—
155C22—9582no—
156C22—9582no—
157C22—4794no—
158C22D4×D47912yes—
159C22C23×D47911yescharacteristic
160C4—22no—
161C4—21no—
162C4—22no—
163C4—9581no—
164C4—9582no—
165C4—4792no—
166C4—4792no—
167C2—22no—
168C2—41no—
169C2—19161no—
170C2—9584no—
171C2C2×D4×D47911yescharacteristic
172C2#41×D47912yes—
subgroupG/H
center, FrattiniC22C23×D479
commutator, socle, cosocleC22×C479C24
Fitting#123×C479C2
hypercenter#123D479
hypocenterC479#525
LCSG ▷ C22×C479 ▷ C479
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#21440161C2semidirect
2. C22×C4×D479C2semidirect
3. #29506365C2semidirect
4. #29506360C2semidirect
5. #29506355C2semidirect
6. #29506352C2semidirect
7. #29506350C2semidirect
8. #29506344C2semidirect
9. (C22⋊D479)⋊C4C2semidirect
10. #29506338C2semidirect
11. #123×C479C2semidirect
14. C2×Dic958C22semidirect
18. C2×C22⋊D479C22semidirect
20. C22×Dic479C22semidirect
24. C2×C4×D479C22semidirect
25. Dic479⋊C4C22semidirect
26. Dic479⋊C4C22semidirect
30. (C2×D479)⋊C4C22semidirect
31. C4×Dic479C22semidirect
34. C4⋊C4×C479C22semidirect
36. C22⋊C4×C479C22semidirect
47. C2×Dic479D4semidirect
72. C2×D479#41semidirect
86. C479#525semidirect
91. #123D479semidirect
116. C4⋊C4C2×D479semidirect
122. 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×C4×D4792
#295063652
#295063602
#295063552
#295063522
#295063502
#295063442
(C22⋊D479)⋊C42
#295063382
#123×C4792
#525479