Finite Group Databasebeta

← C11×D7×#3874 #37528489

Subgroups — C11×D7×#3874 #37528489

Order 23100.

120 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 26 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
1C11×D7×C52⋊C3C211yesmaximal, characteristic, complemented
2C11×C7⋊#3874C211yesmaximal, characteristic, complemented
3C7×C11×#3874C211yesmaximal, characteristic, complemented
4C5×D5×C11×D7—31nomaximal, Hall
5C7×C11×C52⋊C3C2211yescharacteristic, complemented, Hall
6C5×C11×D35—31no—
7C5×C7×D5×C11—31no—
8C52×C11×D7D311yescharacteristic, complemented
9C2×C11×#3874—71nomaximal, Hall
10D7×#3874C1111yesmaximal, characteristic, direct product factor, Hall
11C52×C7×C11C2×D311yescharacteristic, complemented, Hall
12C2×C11×C52⋊C3—71no—
13C11×#3874—71no—
14C11×#3874D711yescharacteristic, direct product factor
15C2×C5×C11×D7—151no—
16D5×C11×D7—31no—
17C2×C5×D5×C11—211noHall
18D7×C52⋊C3C2×C1111yescharacteristic, complemented
19C7⋊#3874C2×C1111yescharacteristic, complemented
20C7×#3874C2×C1111yescharacteristic, complemented
21D3×C11×D7—251nomaximal, Hall
22C11×C52⋊C3C2×D711yescharacteristic, complemented, Hall
23C2×C5×C7×C11—151no—
24C11×D35—31no—
25C7×D5×C11—31no—
26C5×C11×D7—31no—
27C5×C11×D7—31no—
28C5×C11×D7—151no—
29C5×D5×D7—31noHall
30C2×C52×C11—71no—
31C5×D5×C11—31no—
32C5×D5×C11—211no—
33C7×C52⋊C3C22×C1111yescharacteristic, complemented, Hall
34C11×D21—251no—
35D3×C7×C11—251no—
36C3×C11×D7—251no—
37C5×C7×C11—31no—
38C5×C7×C11—31no—
39C5×D35—31no—
40C5×C7×D5—31no—
41C52×D7D3×C1111yescharacteristic, complemented
42C2×C11×D7—151noHall
43C2×#3874—71noHall
44C52×C11D3×D711yescharacteristic, complemented, Hall
45C3×C7×C11—251noHall
46C22×C5×C11—1051no—
47C2×D5×C11—211no—
48C52×C7C2×D3×C1111yescharacteristic, complemented, Hall
49C2×C7×C11—151no—
50C11×D7—151no—
51C11×D7#387411yescharacteristic, direct product factor
52C2×C52⋊C3—71no—
53#3874—71no—
54#3874C11×D711yescharacteristic, direct product factor
55C2×C5×D7—151no—
56D5×D7—31no—
57C2×D3×C11—1751noHall
58C2×C5×C11—151no—
59C2×C5×C11—211no—
60C2×C5×C11—211no—
61C2×C5×C11—1051no—
62D5×C11—31no—
63D5×C11—211no—
64C2×C5×D5—211noHall
65D3×D7—251noHall
66C7×C11C2×#387411yescharacteristic, complemented, Hall
67C52⋊C3C2×C11×D711yescharacteristic, complemented, Hall
68C2×C5×C7—151no—
69D35—31no—
70C5×D7—31no—
71C5×D7—31no—
72C5×D7—151no—
73C7×D5—31no—
74C2×C3×C11—1751no—
75D3×C11—251no—
76D3×C11—1751no—
77C5×C11—31no—
78C5×C11—31no—
79C2×C52—71no—
80C5×D5—31no—
81C5×D5—211no—
82C22×C11—1051noHall
83D21—251no—
84C3×D7—251no—
85D3×C7—251no—
86C5×C7—31no—
87C5×C7—31no—
88C3×C11—251noHall
89C2×D7—151noHall
90C52D3×C11×D711yescharacteristic, complemented, Sylow
91C2×C11—71no—
92C2×C11—151no—
93C2×C11—1051no—
94C3×C7—251noHall
95C22×C5—1051no—
96C2×D5—211no—
97C2×C7—151no—
98D7—151no—
99D7C11×#387411yescharacteristic, direct product factor
100C2×D3—1751noHall
101C11D7×#387411yescharacteristic, direct product factor, Sylow
102C2×C5—151no—
103C2×C5—211no—
104C2×C5—211no—
105C2×C5—1051no—
106D5—31no—
107D5—211no—
108C7C2×C11×#387411yescharacteristic, complemented, Sylow
109C2×C3—1751no—
110D3—251no—
111D3—1751no—
112C5—31no—
113C5—31no—
114C22—1051noSylow
115C3—251noSylow
116C2—71no—
117C2—151no—
118C2—1051no—
subgroupG/H
center, hypercenterC11D7×#3874
commutator, cosocle, hypocenterC7×C52⋊C3C22×C11
FrattiniC1G
Fitting, socleC52×C7×C11C2×D3
LCSG ▷ C7×C52⋊C3
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×D7×C52⋊C3C2semidirect
2. C11×C7⋊#3874C2semidirect
3. C7×C11×#3874C2semidirect
5. C7×C11×C52⋊C3C22semidirect
8. C52×C11×D7D3semidirect
10. D7×#3874C11direct (N × H)
11. C52×C7×C11C2×D3semidirect
14. C11×#3874D7direct (N × H)
18. D7×C52⋊C3C2×C11semidirect
19. C7⋊#3874C2×C11semidirect
20. C7×#3874C2×C11semidirect
22. C11×C52⋊C3C2×D7semidirect
33. C7×C52⋊C3C22×C11semidirect
41. C52×D7D3×C11semidirect
44. C52×C11D3×D7semidirect
48. C52×C7C2×D3×C11semidirect
51. C11×D7#3874direct (N × H)
54. #3874C11×D7direct (N × H)
66. C7×C11C2×#3874semidirect
67. C52⋊C3C2×C11×D7semidirect
90. C52D3×C11×D7semidirect
99. D7C11×#3874direct (N × H)
101. C11D7×#3874direct (N × H)
108. C7C2×C11×#3874semidirect

Maximal subgroups

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

subgroupindex
C11×D7×C52⋊C32
C11×C7⋊#38742
C7×C11×#38742
C5×D5×C11×D73
C2×C11×#38747
D7×#387411
D3×C11×D725