Finite Group Databasebeta

← #44500908

Subgroups — #44500908

Order 30656.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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×#21440163C211yesmaximal, characteristic, complemented
2C22×C4×D479C211yesmaximal, characteristic, complemented
3#29506367C212yesmaximal, complemented
4#29506358C211yesmaximal, characteristic, complemented
5#29506357C211yesmaximal, characteristic, complemented
6#29506356C211yesmaximal, characteristic, complemented
7#29506352C212yesmaximal, complemented
8#29506344C212yesmaximal, complemented
9(C22⋊D479)⋊C4C212yesmaximal, complemented
10#29506340C211yesmaximal, characteristic, complemented
11C22⋊Q8×C479C211yesmaximal, characteristic, complemented
12C23×D479C2211yescharacteristic
13#21440163—24no—
14C2×D1916C2212yes—
15C2×D1916C2212yes—
16C2×D1916C2211yescharacteristic, complemented
17C2×C22⋊D479C2212yes—
18C22×Dic479C2211yescharacteristic
19C2×C4×D479—24no—
20C2×C4×D479C2211yescharacteristic
21C2×C4×D479C2211yescharacteristic
22C2×C4×D479C2211yescharacteristic
23C2×C4×D479C2211yescharacteristic
24C2×C4×D479C2212yescomplemented
25C4⋊Dic479C2211yescharacteristic, complemented
26Dic479⋊C4C2212yescomplemented
27(C2×D479)⋊C4C2212yes—
28(C2×D479)⋊C4C2212yes—
29(C2×D479)⋊C4C2212yescomplemented
30(C2×D479)⋊C4C2212yescomplemented
31C4×Dic479C2212yescomplemented
32C2×Q8×C479C2211yescharacteristic, complemented
33C22×C4×C479C2211yescharacteristic
34C4⋊C4×C479C2211yescharacteristic, complemented
35C4⋊C4×C479C2212yescomplemented
36C22⋊C4×C479C2212yes—
37C22×D479—22no—
38C22×D479—22no—
39C22×D479—22no—
40C22×D479C2312yes—
41C22×D479C2311yescharacteristic
42C22×D479C2311yescharacteristic
43D1916—24no—
44D1916—24no—
45D1916—22no—
46C22⋊D479—24no—
47C2×Dic479—22no—
48C2×Dic479C2312yes—
49C2×Dic479C2311yescharacteristic
50C2×Dic479C2311yescharacteristic
51C4×D479—22no—
52C4×D479—22no—
53C4×D479—22no—
54C4×D479—24no—
55C4×D479D414yescomplemented
56C23×C479C2311yescharacteristic
57Q8×C479—22no—
58C2×C4×C479—22no—
59C2×C4×C479C2312yes—
60C2×C4×C479C2312yes—
61C2×C4×C479C2311yescharacteristic
62C2×C4×C479C2311yescharacteristic
63C22×C479—21no—
64C22×C479—21no—
65C22×C479#4112yescomplemented
66C22×C479C2411yescharacteristic
67C2×D479—28no—
68C2×D479—21no—
69C2×D479—21no—
70C2×D479—21no—
71C2×D479—21no—
72C2×D479—22no—
73C2×D479—22no—
74C2×D479—22no—
75C2×D479C2×D412yes—
76C2×D479#4112yescomplemented
77C4×C479—21no—
78C4×C479—22no—
79C4×C479—22no—
80C4×C479C2×D412yes—
81Dic479—21no—
82Dic479—22no—
83Dic479C2×D412yes—
84C2×C479—22no—
85C2×C479C22×D411yescharacteristic
86C2×C479C2×#4111yescharacteristic
87C2×C479C2×#4111yescharacteristic
88D479—22no—
89D479—22no—
90D479—42no—
91C479#52511yescharacteristic, complemented, Sylow
92#525—4791nomaximal, Sylow
93C2×#41—4791no—
94C23×C4—4791no—
95#123—4792no—
96C22⋊Q8—4791no—
97C22⋊Q8D47911yescharacteristic, complemented
98#121—4791no—
99#121—4791no—
100#120—4792no—
101C4×D4—4792no—
102C4×D4—4792no—
103#117—4791no—
104C24—4791no—
105#41—9584no—
106C2×Q8C2×D47911yescharacteristic, complemented
107C2×D4—4792no—
108C2×D4—4792no—
109C2×D4—4792no—
110C2×D4—4791no—
111C22×C4—9584no—
112C22×C4—4791no—
113C22×C4—4791no—
114C22×C4—4792no—
115C22×C4—4791no—
116C22×C4—4791no—
117C22×C4—4791no—
118C22×C4C2×D47911yescharacteristic
119C4⋊C4—4791no—
120C4⋊C4—4792no—
121C4⋊C4C2×D47911yescharacteristic, complemented
122C4⋊C4C2×D47912yescomplemented
123C22⋊C4—4792no—
124C22⋊C4—4792no—
125C22⋊C4—4792no—
126C22⋊C4—4792no—
127C22⋊C4C2×D47912yes—
128C42—4792no—
129C23—9582no—
130C23—9582no—
131C23—9582no—
132C23—4792no—
133C23—4791no—
134C23—4791no—
135C23C22×D47911yescharacteristic
136Q8—22no—
137D4—9584no—
138D4—9584no—
139D4—9584no—
140D4—9582no—
141C2×C4—22no—
142C2×C4—9582no—
143C2×C4—9582no—
144C2×C4—9584no—
145C2×C4—9582no—
146C2×C4—9582no—
147C2×C4—4792no—
148C2×C4—4791no—
149C2×C4—4791no—
150C2×C4—4794no—
151C2×C4C22×D47912yes—
152C2×C4C22×D47911yescharacteristic
153C2×C4C22×D47912yes—
154C2×C4C22×D47911yescharacteristic
155C22—21no—
156C22—21no—
157C22—9588no—
158C22—9582no—
159C22—9582no—
160C22—9582no—
161C22—9581no—
162C22—9581no—
163C22—9581no—
164C22—9581no—
165C22—4792no—
166C22—4792no—
167C22#2144016312yescomplemented
168C22C23×D47911yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—9581no—
173C4—9582no—
174C4—4792no—
175C4D4×D47912yes—
176C2—22no—
177C2—19162no—
178C2—9582no—
179C2—9582no—
180C2C2×D4×D47911yescharacteristic
181C2#41×D47911yescharacteristic
182C2C2×#2144016311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D479
commutator, socle, cosocleC22×C479C24
FittingC22⋊Q8×C479C2
hypercenterC22⋊Q8D479
hypocenterC479#525
LCSG ▷ C22×C479 ▷ C479
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#21440163C2semidirect
2. C22×C4×D479C2semidirect
3. #29506367C2semidirect
4. #29506358C2semidirect
5. #29506357C2semidirect
6. #29506356C2semidirect
7. #29506352C2semidirect
8. #29506344C2semidirect
9. (C22⋊D479)⋊C4C2semidirect
10. #29506340C2semidirect
11. C22⋊Q8×C479C2semidirect
16. C2×D1916C22semidirect
24. C2×C4×D479C22semidirect
25. C4⋊Dic479C22semidirect
26. Dic479⋊C4C22semidirect
29. (C2×D479)⋊C4C22semidirect
30. (C2×D479)⋊C4C22semidirect
31. C4×Dic479C22semidirect
32. C2×Q8×C479C22semidirect
34. C4⋊C4×C479C22semidirect
35. C4⋊C4×C479C22semidirect
55. C4×D479D4semidirect
65. C22×C479#41semidirect
76. C2×D479#41semidirect
91. C479#525semidirect
97. C22⋊Q8D479semidirect
106. C2×Q8C2×D479semidirect
121. C4⋊C4C2×D479semidirect
122. C4⋊C4C2×D479semidirect
167. C22#21440163semidirect

Maximal subgroups

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

subgroupindex
C2×#214401632
C22×C4×D4792
#295063672
#295063582
#295063572
#295063562
#295063522
#295063442
(C22⋊D479)⋊C42
#295063402
C22⋊Q8×C4792
#525479