Finite Group Databasebeta

← C3⋊D21×D91 #37525639

Subgroups — C3⋊D21×D91 #37525639

Order 22932.

312 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C32×C7×D91C211yesmaximal, characteristic, complemented
2C7×C13×C3⋊D21C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊(C7⋊D91))C211yesmaximal, characteristic, complemented
4D21×D91—34nomaximal
5C32×C72×C13C2211yescharacteristic, complemented, Hall
6C3⋊(C7⋊D91)—34no—
7C7×C13×D21—34no—
8C3×C7×D91D314yescomplemented
9C3⋊D3×D91—71nomaximal
10D13×C3⋊D21—71nomaximal
11D7×D91—91noHall
12C3×C72×C13C2×D314yescomplemented
13D7×C3⋊D21—131nomaximal, Hall
14C3⋊D273—71no—
15C3⋊D273—71no—
16C3⋊D273—143no—
17C13×C3⋊D21D711yescharacteristic, complemented
18C7×C13×C3⋊D3—71no—
19C32×D91D711yescharacteristic, complemented
20C32×C7×D13—71no—
21C7⋊D91—91no—
22C7×D91C3⋊D311yescharacteristic, complemented
23C7×C13×D7—91no—
24D3×D91—214no—
25D13×D21—214no—
26C3⋊(C3⋊(C7⋊D7))—131no—
27C7×C3⋊D21D1311yescharacteristic, complemented
28C32×C7×D7—131no—
29C32×C7×C13—23no—
30C32×C7×C13C2×D711yescharacteristic, complemented
31C32×C7×C13C2×D711yescharacteristic, complemented
32C72×C13C2×C3⋊D311yescharacteristic, complemented, Hall
33D7×D21—394no—
34D273—214no—
35D273—214no—
36D273—4212no—
37C13×D21—34no—
38D3×C7×C13—214no—
39C3×D91D2114yescomplemented
40C3×C7×D13—74no—
41C3⋊D3×D13—491noHall
42C32×C72C2×D1311yescharacteristic, complemented, Hall
43C2×D91—631no—
44D7×D13—631no—
45C3⋊(C7⋊D7)—394no—
46C7×D21—34no—
47C3×C7×D7—134no—
48C3×C7×C13—212no—
49C3×C7×C13D3×D714yescomplemented
50C3×C7×C13C2×D2114yescomplemented
51C2×C3⋊D21—911no—
52D7×C3⋊D3—911no—
53C3⋊D39—491no—
54C13×C3⋊D3—71no—
55C32×D13—71no—
56D72—1171noHall
57C2×C7×C13—631no—
58D91—631no—
59D91—631no—
60D91—1263no—
61D91C3⋊D2111yescharacteristic, direct product factor
62C7×D13—71no—
63C13×D7—91no—
64D3×D13—1474no—
65C3×C72D3×D1314yescomplemented
66C2×C32×C7—911no—
67C3⋊D21—911no—
68C3⋊D21—911no—
69C3⋊D21—1823no—
70C3⋊D21D9111yescharacteristic, direct product factor
71C7×C3⋊D3—71no—
72C32×D7—131no—
73C32×C13D7211yescharacteristic, complemented, Hall
74C7⋊D7—1171no—
75C7×D7—91no—
76C7×D7—131no—
77C7×C13—23no—
78C7×C13D7×C3⋊D311yescharacteristic, complemented
79C7×C13C2×C3⋊D2111yescharacteristic, complemented
80C2×D21—2734no—
81D3×D7—2734no—
82D39—1474no—
83C3×D13—74no—
84D3×C13—214no—
85C32×C7—23no—
86C32×C7D7×D1311yescharacteristic, complemented
87C32×C7C2×D9111yescharacteristic, complemented
88C2×D13—4411noHall
89C72C3⋊D3×D1311yescharacteristic, complemented, Sylow
90C2×C3×C7—914no—
91D21—34no—
92D21—2734no—
93D21—2734no—
94D21—54612no—
95C3×D7—134no—
96D3×C7—214no—
97C3×C13D7×D2114yescomplemented
98C2×C3⋊D3—6371noHall
99C2×D7—8191no—
100C2×D7—8191no—
101C2×C13—631no—
102D13—71no—
103D13—4411no—
104C3×C7—212no—
105C3×C7D13×D2114yescomplemented
106C3×C7D3×D9114yescomplemented
107C2×C32—911no—
108C3⋊D3—71no—
109C3⋊D3—6371no—
110C2×C7—631no—
111C2×C7—911no—
112D7—91no—
113D7—131no—
114D7—8191no—
115D7—8191no—
116D7—16383no—
117C13D7×C3⋊D2111yescharacteristic, complemented, Sylow
118C2×D3—19114no—
119C32D7×D9111yescharacteristic, complemented, Sylow
120C7—23no—
121C7D13×C3⋊D2111yescharacteristic, complemented
122C7C3⋊D3×D9111yescharacteristic, complemented
123C2×C3—914no—
124D3—214no—
125D3—19114no—
126C22—57331noSylow
127C3D21×D9114yescomplemented
128C2—631no—
129C2—911no—
130C2—57331no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C72×C13C22
LCSG ▷ C32×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C7×D91C2semidirect
2. C7×C13×C3⋊D21C2semidirect
3. C3⋊(C3⋊(C7⋊D91))C2semidirect
5. C32×C72×C13C22semidirect
8. C3×C7×D91D3semidirect
12. C3×C72×C13C2×D3semidirect
17. C13×C3⋊D21D7semidirect
19. C32×D91D7semidirect
22. C7×D91C3⋊D3semidirect
27. C7×C3⋊D21D13semidirect
30. C32×C7×C13C2×D7semidirect
31. C32×C7×C13C2×D7semidirect
32. C72×C13C2×C3⋊D3semidirect
39. C3×D91D21semidirect
42. C32×C72C2×D13semidirect
49. C3×C7×C13D3×D7semidirect
50. C3×C7×C13C2×D21semidirect
61. D91C3⋊D21direct (N × H)
65. C3×C72D3×D13semidirect
70. C3⋊D21D91direct (N × H)
73. C32×C13D72semidirect
78. C7×C13D7×C3⋊D3semidirect
79. C7×C13C2×C3⋊D21semidirect
86. C32×C7D7×D13semidirect
87. C32×C7C2×D91semidirect
89. C72C3⋊D3×D13semidirect
97. C3×C13D7×D21semidirect
105. C3×C7D13×D21semidirect
106. C3×C7D3×D91semidirect
117. C13D7×C3⋊D21semidirect
119. C32D7×D91semidirect
121. C7D13×C3⋊D21semidirect
122. C7C3⋊D3×D91semidirect
127. C3D21×D91semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D912
C7×C13×C3⋊D212
C3⋊(C3⋊(C7⋊D91))2
D21×D913
C3⋊D3×D917
D13×C3⋊D217
D7×C3⋊D2113