Finite Group Databasebeta

← C22×C4×D124 #16858883

Subgroups — C22×C4×D124 #16858883

Order 3968.

2528 conjugacy classes of subgroups; only the 981 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 981 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×D124C211yesmaximal, characteristic
2C23×C4×D31C212yesmaximal, complemented
3C2×C4×D124C2124yesmaximal, direct product factor
4C22×C4⋊Dic31C211yesmaximal, characteristic, complemented
5C22×(C2×D31)⋊C4C212yesmaximal, complemented
6C22×C42×C31C211yesmaximal, characteristic, complemented
7C24×D31C2212yes—
8C23×C4×C31C2211yescharacteristic
9C23×C4×C31C2211yescharacteristic
10C23×C4×C31C2211yescharacteristic
11C23×Dic31C2212yes—
12C22×D124C4116yesdirect product factor
13C22×D124C22112yes—
14C22×C4×D31—216no—
15C22×C4×D31C22124yescomplemented
16C2×C42×C31C22112yescomplemented
17C2×(C2×D31)⋊C4C22124yescomplemented
18C2×C4⋊Dic31C22112yescomplemented
19C4×D124C22164yesdirect product factor
20C24×C31C2311yescharacteristic
21C23×D31—28no—
22C23×D31—28no—
23C23×D31C2×C4116yescomplemented
24C23×D31C23112yes—
25C22×C4×C31—24no—
26C22×C4×C31C2×C418yescomplemented
27C22×C4×C31D418yescomplemented
28C22×C4×C31C2316yes—
29C22×C4×C31C2316yes—
30C22×C4×C31C2316yes—
31C22×Dic31—28no—
32C22×Dic31C23112yes—
33C2×D124C2×C4196yesdirect product factor
34C2×D124C23116yes—
35C2×C4×D31—296no—
36C2×C4×D31C23132yescomplemented
37C42×C31C23116yescomplemented
38(C2×D31)⋊C4C23132yescomplemented
39C4⋊Dic31C23116yescomplemented
40C23×C31C22×C414yes—
41C23×C31C2×D414yes—
42C23×C31#4114yes—
43C23×C31C2413yes—
44C22×D31—264no—
45C22×D31—224no—
46C22×D31—224no—
47C22×D31C22×C4148yescomplemented
48C22×D31C2418yes—
49C2×C4×C31—212no—
50C2×C4×C31C22×C4124yescomplemented
51C2×C4×C31C2×D4124yescomplemented
52C2×C4×C31C2414yes—
53C2×C4×C31C2414yes—
54C2×C4×C31C2414yes—
55C2×Dic31—224no—
56C2×Dic31C2418yes—
57D124C22×C4164yesdirect product factor
58C4×D31—264no—
59C22×C4×D4—311nomaximal, Sylow
60C22×C31C4×D4116yescomplemented
61C22×C31C23×C416yes—
62C22×C31C22×D416yes—
63C22×C31C2×#4116yes—
64C22×C31C2511yescharacteristic
65C2×D31—296no—
66C2×D31—28no—
67C2×D31—28no—
68C2×D31C23×C4116yescomplemented
69C4×C31—24no—
70C4×C31C23×C418yescomplemented
71C4×C31C22×D418yescomplemented
72Dic31—28no—
73C23×D4—311no—
74C24×C4—312no—
75C2×C4×D4—3124no—
76C22×C4⋊C4—311no—
77C22×C22⋊C4—312no—
78C22×C42D3111yescharacteristic, complemented
79C2×C31C2×C4×D4112yescomplemented
80C2×C31C24×C411yescharacteristic
81C2×C31C23×D411yescharacteristic
82C2×C31C22×#4111yescharacteristic
83D31—216no—
84C25—312no—
85C22×D4—3116no—
86C22×D4—3112no—
87C23×C4—312no—
88C23×C4—3124no—
89C23×C4—6216no—
90C23×C4C2×D3111yescharacteristic
91C23×C4C2×D3111yescharacteristic
92C23×C4C2×D3111yescharacteristic
93C4×D4—3164no—
94C2×C4⋊C4—3112no—
95C2×C22⋊C4—3124no—
96C2×C42C2×D31112yescomplemented
97C31C22×C4×D411yescharacteristic, complemented, Sylow
98C24—3116no—
99C24—3112no—
100C24—628no—
101C24—628no—
102C24C22×D3111yescharacteristic
103C2×D4—3196no—
104C2×D4—3116no—
105C22×C4—24no—
106C22×C4—3112no—
107C22×C4—3132no—
108C22×C4—628no—
109C22×C4—6296no—
110C22×C4C4×D3118yescomplemented
111C22×C4D12418yesdirect product factor
112C22×C4C22×D3116yes—
113C22×C4C22×D3116yes—
114C22×C4C22×D3116yes—
115C4⋊C4—3116no—
116C22⋊C4—3132no—
117C42C22×D31116yescomplemented
118C23—3148no—
119C23—318no—
120C23—6264no—
121C23—6224no—
122C23—6224no—
123C23C2×C4×D3114yes—
124C23C2×D12414yes—
125C23#9249514yes—
126C23C23×D3113yes—
127D4—3164no—
128C2×C4—212no—
129C2×C4—318no—
130C2×C4—6224no—
131C2×C4—6264no—
132C2×C4C2×C4×D31124yescomplemented
133C2×C4C2×D124124yesdirect product factor
134C2×C4C23×D3114yes—
135C2×C4C23×D3114yes—
136C2×C4C23×D3114yes—
137C22—3116no—
138C22—628no—
139C22—628no—
140C22—6296no—
141C22C4×D124116yesdirect product factor
142C22C22×C4×D3116yes—
143C22C22×D12416yes—
144C22C2×#9249516yes—
145C22C24×D3111yescharacteristic
146C4—24no—
147C4—628no—
148C4C22×C4×D3118yescomplemented
149C4C22×D12418yesdirect product factor
150C2—6216no—
151C2C2×C4×D124112yesdirect product factor
152C2C23×C4×D3111yescharacteristic
153C2C23×D12411yescharacteristic
154C2C22×#9249511yescharacteristic
subgroupG/H
centerC23×C4C2×D31
commutatorC2×C31C24×C4
FrattiniC22C24×D31
FittingC22×C42×C31C2
socleC24×C31C23
prime radicalC23×D124C2
cosocleC22×C31C25
hypercenterC22×C42D31
hypocenterC31C22×C4×D4
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C23×C4×D31C2semidirect
3. C2×C4×D124C2direct (N × H)
4. C22×C4⋊Dic31C2semidirect
5. C22×(C2×D31)⋊C4C2semidirect
6. C22×C42×C31C2semidirect
12. C22×D124C4direct (N × H)
15. C22×C4×D31C22semidirect
16. C2×C42×C31C22semidirect
17. C2×(C2×D31)⋊C4C22semidirect
18. C2×C4⋊Dic31C22semidirect
19. C4×D124C22direct (N × H)
23. C23×D31C2×C4semidirect
26. C22×C4×C31C2×C4semidirect
27. C22×C4×C31D4semidirect
33. C2×D124C2×C4direct (N × H)
36. C2×C4×D31C23semidirect
37. C42×C31C23semidirect
38. (C2×D31)⋊C4C23semidirect
39. C4⋊Dic31C23semidirect
47. C22×D31C22×C4semidirect
50. C2×C4×C31C22×C4semidirect
51. C2×C4×C31C2×D4semidirect
57. D124C22×C4direct (N × H)
60. C22×C31C4×D4semidirect
68. C2×D31C23×C4semidirect
70. C4×C31C23×C4semidirect
71. C4×C31C22×D4semidirect
78. C22×C42D31semidirect
79. C2×C31C2×C4×D4semidirect
96. C2×C42C2×D31semidirect
97. C31C22×C4×D4semidirect
110. C22×C4C4×D31semidirect
111. C22×C4D124direct (N × H)
117. C42C22×D31semidirect
132. C2×C4C2×C4×D31semidirect
133. C2×C4C2×D124direct (N × H)
141. C22C4×D124direct (N × H)
148. C4C22×C4×D31semidirect
149. C4C22×D124direct (N × H)
151. C2C2×C4×D124direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D1242
C23×C4×D312
C2×C4×D1242
C22×C4⋊Dic312
C22×(C2×D31)⋊C42
C22×C42×C312
C22×C4×D431