Finite Group Databasebeta

← C22×#13093986 #20256558

Subgroups — C22×#13093986 #20256558

Order 6016.

2528 conjugacy classes of subgroups; only the 941 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 941 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
1C23×D188C211yesmaximal, characteristic
2C23×C4×D47C212yesmaximal, complemented
3C2×#13093986C2124yesmaximal, direct product factor
4C22×(C2×D47)⋊C4C212yesmaximal, complemented
5C22×C4×Dic47C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×C47C211yesmaximal, characteristic, complemented
7C24×D47C2212yes—
8C22×D188C4116yescomplemented
9C22×D188C22112yes—
10C23×Dic47C2211yescharacteristic
11C23×Dic47C2211yescharacteristic
12C22×C4×D47—216no—
13C22×C4×D47C22124yescomplemented
14#13093986C22164yesdirect product factor
15C2×(C2×D47)⋊C4C22124yescomplemented
16C2×C4×Dic47C22112yescomplemented
17C23×C4×C47C2212yes—
18C23×C4×C47C2211yescharacteristic
19C2×C4⋊C4×C47C22112yescomplemented
20C24×C47C2311yescharacteristic
21C23×D47—28no—
22C23×D47—28no—
23C23×D47C2×C4116yescomplemented
24C23×D47C23112yes—
25C22×C4×C47—28no—
26C22×C4×C47C2×C418yescomplemented
27C22×C4×C47C23112yes—
28C22×C4×C47C2316yes—
29C22×Dic47—24no—
30C22×Dic47D418yescomplemented
31C22×Dic47C2316yes—
32C22×Dic47C2316yes—
33C2×D188C2×C4196yescomplemented
34C2×D188C23116yes—
35C2×C4×D47—296no—
36C2×C4×D47C23132yescomplemented
37C4⋊C4×C47C23116yescomplemented
38(C2×D47)⋊C4C23132yescomplemented
39C4×Dic47C23116yescomplemented
40C23×C47C22×C414yes—
41C23×C47C2×D414yes—
42C23×C47#4114yes—
43C23×C47C2413yes—
44C22×D47—264no—
45C22×D47—224no—
46C22×D47—224no—
47C22×D47C22×C4148yescomplemented
48C22×D47C2418yes—
49C2×C4×C47—224no—
50C2×C4×C47C22×C4124yescomplemented
51C2×C4×C47C2418yes—
52C2×C4×C47C2414yes—
53C2×Dic47—212no—
54C2×Dic47C2×D4124yescomplemented
55C2×Dic47C2414yes—
56C2×Dic47C2414yes—
57D188C22×C4164yescomplemented
58C4×D47—264no—
59C22×C47C4×D4116yescomplemented
60C22×C47C23×C416yes—
61C22×C47C22×D416yes—
62C22×C47C2×#4116yes—
63C22×C47C2511yescharacteristic
64C2×D47—296no—
65C2×D47—28no—
66C2×D47—28no—
67C2×D47C23×C4116yescomplemented
68C4×C47—28no—
69C4×C47C23×C418yescomplemented
70Dic47—24no—
71Dic47C22×D418yescomplemented
72C22×C4×D4—471nomaximal, Sylow
73C2×C47C2×C4×D4112yescomplemented
74C2×C47C24×C411yescharacteristic
75C2×C47C23×D411yescharacteristic
76C2×C47C22×#4111yescharacteristic
77D47—216no—
78C23×D4—471no—
79C24×C4—472no—
80C2×C4×D4—4724no—
81C22×C4⋊C4D4711yescharacteristic, complemented
82C22×C22⋊C4—472no—
83C22×C42—471no—
84C47C22×C4×D411yescharacteristic, complemented, Sylow
85C25—472no—
86C22×D4—4716no—
87C22×D4—4712no—
88C23×C4—471no—
89C23×C4—471no—
90C23×C4—4724no—
91C23×C4—9416no—
92C23×C4C2×D4712yes—
93C23×C4C2×D4711yescharacteristic
94C4×D4—4764no—
95C2×C4⋊C4C2×D47112yescomplemented
96C2×C22⋊C4—4724no—
97C2×C42—4712no—
98C24—4716no—
99C24—4712no—
100C24—948no—
101C24—948no—
102C24C22×D4711yescharacteristic
103C2×D4—4796no—
104C2×D4—4716no—
105C22×C4—28no—
106C22×C4—478no—
107C22×C4—476no—
108C22×C4—476no—
109C22×C4—4732no—
110C22×C4—9496no—
111C22×C4—944no—
112C22×C4C4×D4718yescomplemented
113C22×C4C22×D47112yes—
114C22×C4C22×D4716yes—
115C4⋊C4C22×D47116yescomplemented
116C22⋊C4—4732no—
117C42—4716no—
118C23—4748no—
119C23—478no—
120C23—9464no—
121C23—9424no—
122C23—9424no—
123C23C2×C4×D4714yes—
124C23D4×D4714yes—
125C23#1062535414yes—
126C23C23×D4713yes—
127D4—4764no—
128C2×C4—224no—
129C2×C4—4724no—
130C2×C4—474no—
131C2×C4—474no—
132C2×C4—9464no—
133C2×C4—9412no—
134C2×C4C2×C4×D47124yescomplemented
135C2×C4C23×D4718yes—
136C2×C4C23×D4714yes—
137C22—4716no—
138C22—9496no—
139C22—948no—
140C22—948no—
141C22#13093986116yesdirect product factor
142C22C22×C4×D4716yes—
143C22C2×D4×D4716yes—
144C22C2×#1062535416yes—
145C22C24×D4711yescharacteristic
146C4—28no—
147C4—478no—
148C4—944no—
149C4C22×C4×D4718yescomplemented
150C2—9416no—
151C2C2×#13093986112yesdirect product factor
152C2C23×C4×D4711yescharacteristic
153C2C22×D4×D4711yescharacteristic
154C2C22×#1062535411yescharacteristic
subgroupG/H
centerC24C22×D47
commutatorC2×C47C24×C4
FrattiniC22C24×D47
FittingC22×C4⋊C4×C47C2
socleC24×C47C23
hypercenterC22×C4⋊C4D47
hypocenterC47C22×C4×D4
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×C4×D47C2semidirect
3. C2×#13093986C2direct (N × H)
4. C22×(C2×D47)⋊C4C2semidirect
5. C22×C4×Dic47C2semidirect
6. C22×C4⋊C4×C47C2semidirect
8. C22×D188C4semidirect
13. C22×C4×D47C22semidirect
14. #13093986C22direct (N × H)
15. C2×(C2×D47)⋊C4C22semidirect
16. C2×C4×Dic47C22semidirect
19. C2×C4⋊C4×C47C22semidirect
23. C23×D47C2×C4semidirect
26. C22×C4×C47C2×C4semidirect
30. C22×Dic47D4semidirect
33. C2×D188C2×C4semidirect
36. C2×C4×D47C23semidirect
37. C4⋊C4×C47C23semidirect
38. (C2×D47)⋊C4C23semidirect
39. C4×Dic47C23semidirect
47. C22×D47C22×C4semidirect
50. C2×C4×C47C22×C4semidirect
54. C2×Dic47C2×D4semidirect
57. D188C22×C4semidirect
59. C22×C47C4×D4semidirect
67. C2×D47C23×C4semidirect
69. C4×C47C23×C4semidirect
71. Dic47C22×D4semidirect
73. C2×C47C2×C4×D4semidirect
81. C22×C4⋊C4D47semidirect
84. C47C22×C4×D4semidirect
95. C2×C4⋊C4C2×D47semidirect
112. C22×C4C4×D47semidirect
115. C4⋊C4C22×D47semidirect
134. C2×C4C2×C4×D47semidirect
141. C22#13093986direct (N × H)
149. C4C22×C4×D47semidirect
151. C2C2×#13093986direct (N × H)