Finite Group Databasebeta

← C2×#3861⋊(C37⋊C3) #45657486

Subgroups — C2×#3861⋊(C37⋊C3) #45657486

Order 32634.

112 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 32 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
1#3861⋊(C37⋊C3)C211yesmaximal, characteristic, direct product factor, Hall
2C2×C37×#3861C311yesmaximal, characteristic, complemented
3C2×C7×#11715912C311yesmaximal, characteristic, complemented
4C2×C7×#11715913C311yesmaximal, characteristic, complemented
5C2×C37⋊#3862C311yesmaximal, characteristic, complemented
6C37⋊#3862C2×C311yescharacteristic, complemented
7C37×#3861C2×C311yescharacteristic, complemented
8C7×#11715912C2×C311yescharacteristic, complemented
9C7×#11715913C2×C311yescharacteristic, complemented
10C2×ΓL(1,𝔽8)×C37⋊C3—71nomaximal
11C2×ΓL(1,𝔽8)×C37⋊C3—71nomaximal
12C2×C72×C37C3211yescharacteristic, complemented, Hall
13ΓL(1,𝔽8)×C37⋊C3—71no—
14ΓL(1,𝔽8)×C37⋊C3—71no—
15C72×C37C2×C3211yescharacteristic, complemented, Hall
16C2×#11715912—71no—
17C2×#11715912ΓL(1,𝔽8)11yescharacteristic, complemented
18C2×#11715913—71no—
19C2×#11715913ΓL(1,𝔽8)11yescharacteristic, complemented
20C2×ΓL(1,𝔽8)×C37—71no—
21C2×ΓL(1,𝔽8)×C37—71no—
22C2×ΓL(1,𝔽8)×C37—212no—
23C2×C7×C37⋊C3—71no—
24C2×C7×C37⋊C3—71no—
25C2×ΓL(1,𝔽8)2—371nomaximal, Hall
26#11715913—71no—
27#11715913C2×ΓL(1,𝔽8)11yescharacteristic, complemented
28#11715912—71no—
29#11715912C2×ΓL(1,𝔽8)11yescharacteristic, complemented
30C7×C37⋊C3—71no—
31C7×C37⋊C3—71no—
32ΓL(1,𝔽8)×C37—71no—
33ΓL(1,𝔽8)×C37—71no—
34ΓL(1,𝔽8)×C37—212no—
35C2×C3×C37⋊C3—491noHall
36C2×C7×C37—32no—
37C2×C7×C37C3×ΓL(1,𝔽8)11yescharacteristic, complemented
38C2×C7×C37C3×ΓL(1,𝔽8)11yescharacteristic, complemented
39ΓL(1,𝔽8)2—371noHall
40C3×C37⋊C3—491noHall
41C2×#3862—371no—
42C2×#3861C37⋊C311yescharacteristic, complemented
43C2×C7×ΓL(1,𝔽8)—371no—
44C2×C7×ΓL(1,𝔽8)—371no—
45C7×C37—32no—
46C7×C37C2×C3×ΓL(1,𝔽8)11yescharacteristic, complemented
47C7×C37C2×C3×ΓL(1,𝔽8)11yescharacteristic, complemented
48C2×C3×C37—491no—
49C2×C37⋊C3—71no—
50C2×C37⋊C3—71no—
51C2×C37⋊C3—491no—
52#3862—371no—
53#3861C2×C37⋊C311yescharacteristic, complemented
54C7×ΓL(1,𝔽8)—371no—
55C7×ΓL(1,𝔽8)—371no—
56C2×C3×ΓL(1,𝔽8)—2591no—
57C2×C3×ΓL(1,𝔽8)—2591no—
58C3×C37—491no—
59C37⋊C3—71no—
60C37⋊C3—71no—
61C37⋊C3—491no—
62C2×C72C3×C37⋊C311yescharacteristic, complemented, Hall
63C2×C37ΓL(1,𝔽8)211yescharacteristic, complemented, Hall
64C3×ΓL(1,𝔽8)—2591no—
65C3×ΓL(1,𝔽8)—2591no—
66C72C2×C3×C37⋊C311yescharacteristic, complemented, Sylow
67C2×C3×C7—2591no—
68C2×C3×C7—2591no—
69C2×ΓL(1,𝔽8)—2591no—
70C2×ΓL(1,𝔽8)—2591no—
71C2×ΓL(1,𝔽8)—71no—
72C2×ΓL(1,𝔽8)—71no—
73C2×ΓL(1,𝔽8)—212no—
74C2×ΓL(1,𝔽8)—371no—
75C2×ΓL(1,𝔽8)—371no—
76C37C2×ΓL(1,𝔽8)211yescharacteristic, complemented, Sylow
77C3×C7—2591no—
78C3×C7—2591no—
79ΓL(1,𝔽8)—2591no—
80ΓL(1,𝔽8)—2591no—
81ΓL(1,𝔽8)—71no—
82ΓL(1,𝔽8)—71no—
83ΓL(1,𝔽8)—212no—
84ΓL(1,𝔽8)—371no—
85ΓL(1,𝔽8)—371no—
86C2×C32—18131noHall
87C2×C7—32no—
88C2×C7ΓL(1,𝔽8)×C37⋊C311yescharacteristic, complemented
89C2×C7ΓL(1,𝔽8)×C37⋊C311yescharacteristic, complemented
90C32—18131noSylow
91C7—32no—
92C7C2×ΓL(1,𝔽8)×C37⋊C311yescharacteristic, complemented
93C7C2×ΓL(1,𝔽8)×C37⋊C311yescharacteristic, complemented
94C2×C3—2591no—
95C2×C3—2591no—
96C2×C3—18131no—
97C2×C3—491no—
98C3—2591no—
99C3—2591no—
100C3—18131no—
101C3—491no—
102C2#3861⋊(C37⋊C3)11yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2#3861⋊(C37⋊C3)
commutator, cosocle, hypocenterC72×C37C2×C32
FrattiniC1G
Fitting, socleC2×C72×C37C32
LCSG ▷ C72×C37
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #3861⋊(C37⋊C3)C2direct (N × H)
2. C2×C37×#3861C3semidirect
3. C2×C7×#11715912C3semidirect
4. C2×C7×#11715913C3semidirect
5. C2×C37⋊#3862C3semidirect
6. C37⋊#3862C2×C3semidirect
7. C37×#3861C2×C3semidirect
8. C7×#11715912C2×C3semidirect
9. C7×#11715913C2×C3semidirect
12. C2×C72×C37C32semidirect
15. C72×C37C2×C32semidirect
17. C2×#11715912ΓL(1,𝔽8)semidirect
19. C2×#11715913ΓL(1,𝔽8)semidirect
27. #11715913C2×ΓL(1,𝔽8)semidirect
29. #11715912C2×ΓL(1,𝔽8)semidirect
37. C2×C7×C37C3×ΓL(1,𝔽8)semidirect
38. C2×C7×C37C3×ΓL(1,𝔽8)semidirect
42. C2×#3861C37⋊C3semidirect
46. C7×C37C2×C3×ΓL(1,𝔽8)semidirect
47. C7×C37C2×C3×ΓL(1,𝔽8)semidirect
53. #3861C2×C37⋊C3semidirect
62. C2×C72C3×C37⋊C3semidirect
63. C2×C37ΓL(1,𝔽8)2semidirect
66. C72C2×C3×C37⋊C3semidirect
76. C37C2×ΓL(1,𝔽8)2semidirect
88. C2×C7ΓL(1,𝔽8)×C37⋊C3semidirect
89. C2×C7ΓL(1,𝔽8)×C37⋊C3semidirect
92. C7C2×ΓL(1,𝔽8)×C37⋊C3semidirect
93. C7C2×ΓL(1,𝔽8)×C37⋊C3semidirect
102. C2#3861⋊(C37⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
#3861⋊(C37⋊C3)2
C2×C37×#38613
C2×C7×#117159123
C2×C7×#117159133
C2×C37⋊#38623
C2×ΓL(1,𝔽8)×C37⋊C37
C2×ΓL(1,𝔽8)237