Finite Group Databasebeta

← C3×C7×Dic385 #44568530

Subgroups — C3×C7×Dic385 #44568530

Order 32340.

144 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C2×C3×C5×C72×C11C211yesmaximal, characteristic
2C7×Dic385C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5×C72×C11C411yescharacteristic, complemented, Hall
4C3×C7×Dic77—51nomaximal, Hall
5C2×C5×C72×C11C2×C311yescharacteristic
6C3×Dic385C711yesmaximal, characteristic, direct product factor
7C3×C7×Dic55—71nomaximal
8C2×C3×C72×C11D511yescharacteristic
9C3×C7×Dic35—111nomaximal, Hall
10C5×C72×C11C3×C411yescharacteristic, complemented, Hall
11C2×C3×C5×C7×C11—23no—
12C2×C3×C5×C7×C11D711yescharacteristic
13C2×C3×C5×C7×C11C2×C711yescharacteristic
14C7×Dic77—51noHall
15C3×C72×C11Dic511yescharacteristic, complemented, Hall
16Dic385C3×C711yescharacteristic, direct product factor
17C7×Dic55—71no—
18C2×C3×C5×C72D1111yescharacteristic
19C3×C5×C7×C11—23no—
20C3×C5×C7×C11Dic711yescharacteristic, complemented
21C3×C5×C7×C11C4×C711yescharacteristic, complemented
22C2×C72×C11C3×D511yescharacteristic
23C7×Dic35—111noHall
24C3×Dic77—51no—
25C3×C7×Dic11—351no—
26C2×C5×C7×C11—23no—
27C2×C5×C7×C11C3×D711yescharacteristic
28C2×C5×C7×C11C2×C3×C711yescharacteristic
29C3×C5×C72Dic1111yescharacteristic, complemented, Hall
30C3×Dic55—71noHall
31C3×C7×Dic7—551noHall
32C72×C11C3×Dic511yescharacteristic, complemented, Hall
33C2×C5×C72C3×D1111yescharacteristic
34C2×C3×C7×C11—23no—
35C2×C3×C7×C11C7×D511yescharacteristic
36C2×C3×C7×C11D3511yescharacteristic
37C3×Dic35—111no—
38C3×C7×Dic5—771no—
39C5×C7×C11—23no—
40C5×C7×C11C3×Dic711yescharacteristic, complemented
41C5×C7×C11C3×C4×C711yescharacteristic, complemented
42C2×C3×C5×C11C7×D711yescharacteristic
43Dic77—51no—
44C7×Dic11—351no—
45C2×C3×C72D5511yescharacteristic
46C5×C72C3×Dic1111yescharacteristic, complemented, Hall
47C3×C7×C11—23no—
48C3×C7×C11C7×Dic511yescharacteristic, complemented
49C3×C7×C11Dic3511yescharacteristic, complemented
50Dic55—71noHall
51C2×C3×C5×C7—23no—
52C2×C3×C5×C7C7×D1111yescharacteristic
53C2×C3×C5×C7D7711yescharacteristic
54C7×Dic7—551noHall
55C3×C5×C11C7×Dic711yescharacteristic, complemented, Hall
56C2×C7×C11—23no—
57C2×C7×C11C3×C7×D511yescharacteristic
58C2×C7×C11C3×D3511yescharacteristic
59C3×C72Dic5511yescharacteristic, complemented, Hall
60Dic35—111no—
61C7×Dic5—771no—
62C3×Dic11—351noHall
63C2×C5×C11C3×C7×D711yescharacteristic
64C3×C5×C7—23no—
65C3×C5×C7C7×Dic1111yescharacteristic, complemented
66C3×C5×C7Dic7711yescharacteristic, complemented
67C2×C72C3×D5511yescharacteristic
68C3×C4×C7—3851no—
69C3×Dic7—551no—
70C7×C11—23no—
71C7×C11C3×C7×Dic511yescharacteristic, complemented
72C7×C11C3×Dic3511yescharacteristic, complemented
73C2×C5×C7—23no—
74C2×C5×C7C3×C7×D1111yescharacteristic
75C2×C5×C7C3×D7711yescharacteristic
76C2×C3×C11C7×D3511yescharacteristic
77C3×Dic5—771noHall
78C5×C11C3×C7×Dic711yescharacteristic, complemented, Hall
79C72C3×Dic5511yescharacteristic, complemented, Sylow
80Dic11—351noHall
81C2×C3×C7—23no—
82C2×C3×C7C7×D5511yescharacteristic
83C2×C3×C7D38511yescharacteristic
84C5×C7—23no—
85C5×C7C3×C7×Dic1111yescharacteristic, complemented
86C5×C7C3×Dic7711yescharacteristic, complemented
87C3×C11C7×Dic3511yescharacteristic, complemented, Hall
88C2×C3×C5C7×D7711yescharacteristic
89C4×C7—3851no—
90Dic7—551no—
91C2×C11C3×C7×D3511yescharacteristic
92C3×C7—23no—
93C3×C7C7×Dic5511yescharacteristic, complemented
94C3×C7Dic38511yescharacteristic, direct product factor
95Dic5—771noHall
96C3×C5C7×Dic7711yescharacteristic, complemented, Hall
97C2×C7—23no—
98C2×C7C3×C7×D5511yescharacteristic
99C2×C7C3×D38511yescharacteristic
100C3×C4—3851noHall
101C11C3×C7×Dic3511yescharacteristic, complemented, Sylow
102C2×C5C3×C7×D7711yescharacteristic
103C7—23no—
104C7C3×C7×Dic5511yescharacteristic, complemented
105C7C3×Dic38511yescharacteristic, direct product factor
106C2×C3C7×D38511yescharacteristic
107C5C3×C7×Dic7711yescharacteristic, complemented, Sylow
108C4—3851noSylow
109C3C7×Dic38511yescharacteristic, direct product factor, Sylow
110C2C3×C7×D38511yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C7D385
commutator, hypocenterC5×C7×C11C3×C4×C7
FrattiniC2C3×C7×D385
Fitting, socle, prime radicalC2×C3×C5×C72×C11C2
cosocleC2×C5×C7×C11C2×C3×C7
LCSG ▷ C5×C7×C11
UCSC1 ◁ C2×C3×C7

Complements

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

NH ≅ G/Ntype
2. C7×Dic385C3direct (N × H)
3. C3×C5×C72×C11C4semidirect
6. C3×Dic385C7direct (N × H)
10. C5×C72×C11C3×C4semidirect
15. C3×C72×C11Dic5semidirect
16. Dic385C3×C7direct (N × H)
20. C3×C5×C7×C11Dic7semidirect
21. C3×C5×C7×C11C4×C7semidirect
29. C3×C5×C72Dic11semidirect
32. C72×C11C3×Dic5semidirect
40. C5×C7×C11C3×Dic7semidirect
41. C5×C7×C11C3×C4×C7semidirect
46. C5×C72C3×Dic11semidirect
48. C3×C7×C11C7×Dic5semidirect
49. C3×C7×C11Dic35semidirect
55. C3×C5×C11C7×Dic7semidirect
59. C3×C72Dic55semidirect
65. C3×C5×C7C7×Dic11semidirect
66. C3×C5×C7Dic77semidirect
71. C7×C11C3×C7×Dic5semidirect
72. C7×C11C3×Dic35semidirect
78. C5×C11C3×C7×Dic7semidirect
79. C72C3×Dic55semidirect
85. C5×C7C3×C7×Dic11semidirect
86. C5×C7C3×Dic77semidirect
87. C3×C11C7×Dic35semidirect
93. C3×C7C7×Dic55semidirect
94. C3×C7Dic385direct (N × H)
96. C3×C5C7×Dic77semidirect
101. C11C3×C7×Dic35semidirect
104. C7C3×C7×Dic55semidirect
105. C7C3×Dic385direct (N × H)
107. C5C3×C7×Dic77semidirect
109. C3C7×Dic385direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C72×C112
C7×Dic3853
C3×C7×Dic775
C3×Dic3857
C3×C7×Dic557
C3×C7×Dic3511