Finite Group Databasebeta

← C22×#14519739 #21458989

Subgroups — C22×#14519739 #21458989

Order 7808.

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×D244C211yesmaximal, characteristic
2C23×C4×D61C212yesmaximal, complemented
3C2×#14519739C2124yesmaximal, direct product factor
4C22×#11758198C212yesmaximal, complemented
5C22×C4×Dic61C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×C61C211yesmaximal, characteristic, complemented
7C24×D61C2212yes—
8C22×D244C4116yescomplemented
9C22×D244C22112yes—
10C23×Dic61C2211yescharacteristic
11C23×Dic61C2211yescharacteristic
12C22×C4×D61—216no—
13C22×C4×D61C22124yescomplemented
14#14519739C22164yesdirect product factor
15C2×#11758198C22124yescomplemented
16C2×C4×Dic61C22112yescomplemented
17C23×C4×C61C2212yes—
18C23×C4×C61C2211yescharacteristic
19C2×C4⋊C4×C61C22112yescomplemented
20C24×C61C2311yescharacteristic
21C23×D61—28no—
22C23×D61—28no—
23C23×D61C2×C4116yescomplemented
24C23×D61C23112yes—
25C22×C4×C61—28no—
26C22×C4×C61C2×C418yescomplemented
27C22×C4×C61C23112yes—
28C22×C4×C61C2316yes—
29C22×Dic61—24no—
30C22×Dic61D418yescomplemented
31C22×Dic61C2316yes—
32C22×Dic61C2316yes—
33C2×D244C2×C4196yescomplemented
34C2×D244C23116yes—
35C2×C4×D61—296no—
36C2×C4×D61C23132yescomplemented
37C4⋊C4×C61C23116yescomplemented
38#11758198C23132yescomplemented
39C4×Dic61C23116yescomplemented
40C23×C61C22×C414yes—
41C23×C61C2×D414yes—
42C23×C61#4114yes—
43C23×C61C2413yes—
44C22×D61—264no—
45C22×D61—224no—
46C22×D61—224no—
47C22×D61C22×C4148yescomplemented
48C22×D61C2418yes—
49C2×C4×C61—224no—
50C2×C4×C61C22×C4124yescomplemented
51C2×C4×C61C2418yes—
52C2×C4×C61C2414yes—
53C2×Dic61—212no—
54C2×Dic61C2×D4124yescomplemented
55C2×Dic61C2414yes—
56C2×Dic61C2414yes—
57D244C22×C4164yescomplemented
58C4×D61—264no—
59C22×C61C4×D4116yescomplemented
60C22×C61C23×C416yes—
61C22×C61C22×D416yes—
62C22×C61C2×#4116yes—
63C22×C61C2511yescharacteristic
64C2×D61—296no—
65C2×D61—28no—
66C2×D61—28no—
67C2×D61C23×C4116yescomplemented
68C4×C61—28no—
69C4×C61C23×C418yescomplemented
70Dic61—24no—
71Dic61C22×D418yescomplemented
72C22×C4×D4—611nomaximal, Sylow
73C2×C61C2×C4×D4112yescomplemented
74C2×C61C24×C411yescharacteristic
75C2×C61C23×D411yescharacteristic
76C2×C61C22×#4111yescharacteristic
77D61—216no—
78C23×D4—611no—
79C24×C4—612no—
80C2×C4×D4—6124no—
81C22×C4⋊C4D6111yescharacteristic, complemented
82C22×C22⋊C4—612no—
83C22×C42—611no—
84C61C22×C4×D411yescharacteristic, complemented, Sylow
85C25—612no—
86C22×D4—6116no—
87C22×D4—6112no—
88C23×C4—611no—
89C23×C4—611no—
90C23×C4—6124no—
91C23×C4—12216no—
92C23×C4C2×D6112yes—
93C23×C4C2×D6111yescharacteristic
94C4×D4—6164no—
95C2×C4⋊C4C2×D61112yescomplemented
96C2×C22⋊C4—6124no—
97C2×C42—6112no—
98C24—6116no—
99C24—6112no—
100C24—1228no—
101C24—1228no—
102C24C22×D6111yescharacteristic
103C2×D4—6196no—
104C2×D4—6116no—
105C22×C4—28no—
106C22×C4—618no—
107C22×C4—616no—
108C22×C4—616no—
109C22×C4—6132no—
110C22×C4—12296no—
111C22×C4—1224no—
112C22×C4C4×D6118yescomplemented
113C22×C4C22×D61112yes—
114C22×C4C22×D6116yes—
115C4⋊C4C22×D61116yescomplemented
116C22⋊C4—6132no—
117C42—6116no—
118C23—6148no—
119C23—618no—
120C23—12224no—
121C23—12224no—
122C23—12264no—
123C23C2×C4×D6114yes—
124C23D4×D6114yes—
125C23#1175822614yes—
126C23C23×D6113yes—
127D4—6164no—
128C2×C4—224no—
129C2×C4—6124no—
130C2×C4—614no—
131C2×C4—614no—
132C2×C4—12264no—
133C2×C4—12212no—
134C2×C4C2×C4×D61124yescomplemented
135C2×C4C23×D6118yes—
136C2×C4C23×D6114yes—
137C22—6116no—
138C22—12296no—
139C22—1228no—
140C22—1228no—
141C22#14519739116yesdirect product factor
142C22C22×C4×D6116yes—
143C22C2×D4×D6116yes—
144C22C2×#1175822616yes—
145C22C24×D6111yescharacteristic
146C4—28no—
147C4—618no—
148C4—1224no—
149C4C22×C4×D6118yescomplemented
150C2—12216no—
151C2C2×#14519739112yesdirect product factor
152C2C23×C4×D6111yescharacteristic
153C2C22×D4×D6111yescharacteristic
154C2C22×#1175822611yescharacteristic
subgroupG/H
centerC24C22×D61
commutatorC2×C61C24×C4
FrattiniC22C24×D61
FittingC22×C4⋊C4×C61C2
socleC24×C61C23
hypercenterC22×C4⋊C4D61
hypocenterC61C22×C4×D4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×C4×D61C2semidirect
3. C2×#14519739C2direct (N × H)
4. C22×#11758198C2semidirect
5. C22×C4×Dic61C2semidirect
6. C22×C4⋊C4×C61C2semidirect
8. C22×D244C4semidirect
13. C22×C4×D61C22semidirect
14. #14519739C22direct (N × H)
15. C2×#11758198C22semidirect
16. C2×C4×Dic61C22semidirect
19. C2×C4⋊C4×C61C22semidirect
23. C23×D61C2×C4semidirect
26. C22×C4×C61C2×C4semidirect
30. C22×Dic61D4semidirect
33. C2×D244C2×C4semidirect
36. C2×C4×D61C23semidirect
37. C4⋊C4×C61C23semidirect
38. #11758198C23semidirect
39. C4×Dic61C23semidirect
47. C22×D61C22×C4semidirect
50. C2×C4×C61C22×C4semidirect
54. C2×Dic61C2×D4semidirect
57. D244C22×C4semidirect
59. C22×C61C4×D4semidirect
67. C2×D61C23×C4semidirect
69. C4×C61C23×C4semidirect
71. Dic61C22×D4semidirect
73. C2×C61C2×C4×D4semidirect
81. C22×C4⋊C4D61semidirect
84. C61C22×C4×D4semidirect
95. C2×C4⋊C4C2×D61semidirect
112. C22×C4C4×D61semidirect
115. C4⋊C4C22×D61semidirect
134. C2×C4C2×C4×D61semidirect
141. C22#14519739direct (N × H)
149. C4C22×C4×D61semidirect
151. C2C2×#14519739direct (N × H)