Finite Group Databasebeta

← #120×D293 #34036613

Subgroups — #120×D293 #34036613

Order 18752.

662 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C24×D293C211yesmaximal, characteristic, complemented
2C2×D4×D293C213yesmaximal, complemented
3#22627594C213yesmaximal, complemented
4#22627593C211yesmaximal, characteristic, complemented
5#22627592C213yesmaximal, complemented
6C22⋊C4×D293C213yesmaximal, complemented
7#120×C293C211yesmaximal, characteristic, complemented
8C23×D293—212no—
9C23×D293C2213yes—
10C23×D293C2213yescomplemented
11C23×D293C2211yescharacteristic, complemented
12C2×D1172C2213yescomplemented
13C2×C22⋊D293C2213yescomplemented
14C2×C22⋊D293C2213yescomplemented
15D4×D293—212no—
16C2×C4×D293C2213yescomplemented
17C22⋊Dic293C2213yescomplemented
18#17989779C2216yescomplemented
19C24×C293C2211yescharacteristic, complemented
20C2×D4×C293C2213yescomplemented
21C22⋊C4×C293C2213yescomplemented
22C22×D293—232no—
23C22×D293—26no—
24C22×D293—212no—
25C22×D293—212no—
26C22×D293—26no—
27C22×D293D4112yescomplemented
28C22×D293C2313yes—
29C22×D293C2311yescharacteristic
30C22×D293C2311yescharacteristic, complemented
31D1172—26no—
32C22⋊D293—26no—
33C22⋊D293—26no—
34C2×Dic293C2313yescomplemented
35C4×D293—26no—
36C23×C293—26no—
37C23×C293C2313yes—
38C23×C293C2311yescharacteristic, complemented
39D4×C293—26no—
40C2×C4×C293C2313yescomplemented
41C22×C293—28no—
42C22×C293—26no—
43C22×C293—23no—
44C22×C293C2×D416yescomplemented
45C22×C293C2411yescharacteristic
46C2×D293—224no—
47C2×D293—26no—
48C2×D293—224no—
49C2×D293—23no—
50C2×D293—44no—
51C2×D293C2×D416yes—
52C2×D293C2×D416yescomplemented
53C4×C293—23no—
54Dic293—23no—
55C2×C293—26no—
56C2×C293—41no—
57C2×C293C22×D413yes—
58D293—26no—
59D293—41no—
60D293#12014yesdirect product factor
61C293C2×#12011yescharacteristic, complemented, Sylow
62C2×#120—2931nomaximal, Sylow
63C25—2931no—
64C22×D4—2933no—
65#120—2931no—
66#120—2933no—
67#120—2933no—
68#120D29311yescharacteristic, direct product factor
69C2×C22⋊C4—2933no—
70C24—2933no—
71C24—2933no—
72C24—2931no—
73C24—58612no—
74C24C2×D29311yescharacteristic, complemented
75C2×D4—2933no—
76C2×D4—2933no—
77C2×D4—2933no—
78C2×D4—58612no—
79C2×D4C2×D29313yescomplemented
80C22×C4—2933no—
81C22⋊C4—2933no—
82C22⋊C4—2936no—
83C22⋊C4C2×D29313yescomplemented
84C23—26no—
85C23—2931no—
86C23—29312no—
87C23—2933no—
88C23—2931no—
89C23—58612no—
90C23—58612no—
91C23—5866no—
92C23—58632no—
93C23—5866no—
94C23C22×D29313yes—
95C23C22×D29311yescharacteristic, complemented
96D4—26no—
97D4—5866no—
98D4—5866no—
99D4—5866no—
100C2×C4—2933no—
101C2×C4—5866no—
102C2×C4C22×D29313yescomplemented
103C22—28no—
104C22—26no—
105C22—23no—
106C22—2936no—
107C22—2936no—
108C22—58624no—
109C22—58624no—
110C22—5866no—
111C22—5863no—
112C22—11724no—
113C22D4×D29316yescomplemented
114C22C23×D29311yescharacteristic
115C4—23no—
116C4—5863no—
117C2—26no—
118C2—41no—
119C2—2934no—
120C2—5866no—
121C2—11721no—
122C2C2×D4×D29313yes—
subgroupG/H
center, FrattiniC22C23×D293
commutator, socle, cosocleC22×C293C24
Fitting#120×C293C2
hypercenter#120D293
hypocenterC293C2×#120
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C24×D293C2semidirect
2. C2×D4×D293C2semidirect
3. #22627594C2semidirect
4. #22627593C2semidirect
5. #22627592C2semidirect
6. C22⋊C4×D293C2semidirect
7. #120×C293C2semidirect
10. C23×D293C22semidirect
11. C23×D293C22semidirect
12. C2×D1172C22semidirect
13. C2×C22⋊D293C22semidirect
14. C2×C22⋊D293C22semidirect
16. C2×C4×D293C22semidirect
17. C22⋊Dic293C22semidirect
18. #17989779C22semidirect
19. C24×C293C22semidirect
20. C2×D4×C293C22semidirect
21. C22⋊C4×C293C22semidirect
27. C22×D293D4semidirect
30. C22×D293C23semidirect
34. C2×Dic293C23semidirect
38. C23×C293C23semidirect
40. C2×C4×C293C23semidirect
44. C22×C293C2×D4semidirect
52. C2×D293C2×D4semidirect
60. D293#120direct (N × H)
61. C293C2×#120semidirect
68. #120D293direct (N × H)
74. C24C2×D293semidirect
79. C2×D4C2×D293semidirect
83. C22⋊C4C2×D293semidirect
95. C23C22×D293semidirect
102. C2×C4C22×D293semidirect
113. C22D4×D293semidirect

Maximal subgroups

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

subgroupindex
C24×D2932
C2×D4×D2932
#226275942
#226275932
#226275922
C22⋊C4×D2932
#120×C2932
C2×#120293