Finite Group Databasebeta

← C22×A4×Dic7 #13062180

Subgroups — C22×A4×Dic7 #13062180

Order 1344.

634 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 129 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×C7×A4C211yesmaximal, characteristic
2C2×A4×Dic7C216yesmaximal, direct product factor
3C24×Dic7C311yesmaximal, characteristic, complemented, Hall
4C22×C7×A4C414yescomplemented
5C22×C7×A4C2213yes—
6C22×C3×Dic7—41nomaximal
7A4×Dic7C2214yesdirect product factor
8C25×C7C2×C311yescharacteristic
9C23×Dic7—31no—
10C23×Dic7—31no—
11C23×Dic7—36no—
12C23×Dic7C2×C316yescomplemented
13C22×C4×A4—71nomaximal, Hall
14C23×C3×C7—41no—
15C2×C7×A4C2×C416yescomplemented
16C2×C7×A4C2311yescharacteristic
17C2×C3×Dic7—46no—
18C24×C7—31no—
19C24×C7—33no—
20C24×C7—34no—
21C24×C7C3×C414yescomplemented
22C24×C7C22×C313yes—
23C22×Dic7—36no—
24C22×Dic7—38no—
25C22×Dic7—31no—
26C22×Dic7—36no—
27C22×Dic7—36no—
28C22×Dic7—36no—
29C22×Dic7—312no—
30C22×Dic7A411yescharacteristic, direct product factor
31C22×Dic7C22×C314yescomplemented
32C23×A4D711yescharacteristic
33C2×C4×A4—76no—
34C22×C3×C7—44no—
35C22×C3×C7—43no—
36C7×A4C22×C411yescharacteristic, complemented
37C3×Dic7—44no—
38C24×C4—71noSylow
39C23×C7—33no—
40C23×C7—312no—
41C23×C7—36no—
42C23×C7—32no—
43C23×C7—312no—
44C23×C7—34no—
45C23×C7—34no—
46C23×C7—33no—
47C23×C7—33no—
48C23×C7C2×C3×C416yescomplemented
49C23×C7C2×A411yescharacteristic
50C23×C7C23×C311yescharacteristic
51C2×Dic7—312no—
52C2×Dic7—36no—
53C2×Dic7—312no—
54C2×Dic7—34no—
55C2×Dic7—34no—
56C2×Dic7C2×A416yesdirect product factor
57C22×A4Dic714yesdirect product factor
58C22×A4C2×D713yes—
59C22×C3×C4—281no—
60C4×A4—74no—
61C2×C3×C7—46no—
62C2×C3×C7—41no—
63C25C3×D711yescharacteristic
64C23×C4—76no—
65C23×C4—211no—
66C23×C4—216no—
67C23×C4—211no—
68C22×C7—36no—
69C22×C7—31no—
70C22×C7—36no—
71C22×C7—38no—
72C22×C7—312no—
73C22×C7—36no—
74C22×C7—36no—
75C22×C7—33no—
76C22×C7—31no—
77C22×C7C4×A414yescomplemented
78C22×C7C22×C3×C411yescharacteristic, complemented
79C22×C7C22×A413yes—
80Dic7—34no—
81Dic7C22×A414yesdirect product factor
82C23×C3—41no—
83C2×A4C2×Dic716yesdirect product factor
84C2×A4C22×D711yescharacteristic
85C2×C3×C4—286no—
86C3×C7—41noHall
87C24—33no—
88C24—34no—
89C24—31no—
90C24C3×Dic714yescomplemented
91C24C2×C3×D713yes—
92C22×C4—71no—
93C22×C4—74no—
94C22×C4—216no—
95C22×C4—216no—
96C22×C4—218no—
97C22×C4—216no—
98C22×C4—211no—
99C22×C4—2112no—
100C22×C4—216no—
101C2×C7—36no—
102C2×C7—31no—
103C2×C7—31no—
104C2×C7C2×C4×A416yescomplemented
105C2×C7C23×A411yescharacteristic
106C22×C3—44no—
107C22×C3—43no—
108A4C22×Dic711yescharacteristic, direct product factor
109C3×C4—284no—
110C23—33no—
111C23—312no—
112C23—36no—
113C23—32no—
114C23—312no—
115C23—34no—
116C23—34no—
117C23—33no—
118C23—33no—
119C23C2×C3×Dic716yescomplemented
120C23A4×D711yescharacteristic
121C23C22×C3×D711yescharacteristic
122C2×C4—76no—
123C2×C4—214no—
124C2×C4—2112no—
125C2×C4—2112no—
126C2×C4—216no—
127C2×C4—214no—
128C7C22×C4×A411yescharacteristic, complemented, Sylow
129C2×C3—46no—
130C2×C3—41no—
131C22—36no—
132C22—31no—
133C22—36no—
134C22—38no—
135C22—36no—
136C22—312no—
137C22—36no—
138C22—31no—
139C22—33no—
140C22A4×Dic714yesdirect product factor
141C22C22×C3×Dic711yescharacteristic, complemented
142C22C2×A4×D713yes—
143C4—74no—
144C4—214no—
145C3—41noSylow
146C2—31no—
147C2—36no—
148C2—31no—
149C2C2×A4×Dic716yesdirect product factor
150C2C22×A4×D711yescharacteristic
subgroupG/H
center, hypercenterC23A4×D7
commutator, hypocenterC22×C7C22×C3×C4
FrattiniC2C22×A4×D7
Fitting, socleC25×C7C2×C3
prime radicalC23×C7×A4C2
cosocleC23×C7C23×C3
LCSG ▷ C22×C7
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×A4×Dic7C2direct (N × H)
3. C24×Dic7C3semidirect
4. C22×C7×A4C4semidirect
7. A4×Dic7C22direct (N × H)
12. C23×Dic7C2×C3semidirect
15. C2×C7×A4C2×C4semidirect
21. C24×C7C3×C4semidirect
30. C22×Dic7A4direct (N × H)
31. C22×Dic7C22×C3semidirect
36. C7×A4C22×C4semidirect
48. C23×C7C2×C3×C4semidirect
56. C2×Dic7C2×A4direct (N × H)
57. C22×A4Dic7direct (N × H)
77. C22×C7C4×A4semidirect
78. C22×C7C22×C3×C4semidirect
81. Dic7C22×A4direct (N × H)
83. C2×A4C2×Dic7direct (N × H)
90. C24C3×Dic7semidirect
104. C2×C7C2×C4×A4semidirect
108. A4C22×Dic7direct (N × H)
119. C23C2×C3×Dic7semidirect
128. C7C22×C4×A4semidirect
140. C22A4×Dic7direct (N × H)
141. C22C22×C3×Dic7semidirect
149. C2C2×A4×Dic7direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C7×A42
C2×A4×Dic72
C24×Dic73
C22×C3×Dic74
C22×C4×A47