Finite Group Databasebeta

← C22×#22627593 #49172001

Subgroups — C22×#22627593 #49172001

Order 37504.

4544 conjugacy classes of subgroups; only the 805 normal subgroups are shown.

normal subgroups only

This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 805 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
1C23×C22⋊D293C213yesmaximal, complemented
2C2×#22627593C2124yesmaximal, direct product factor
3C22×C22⋊Dic293C213yesmaximal, complemented
4C26×C293C211yesmaximal, characteristic, complemented
5C24×D293C2211yescharacteristic, complemented
6C22×C22⋊D293—224no—
7C22×C22⋊D293C22136yescomplemented
8C23×Dic293C2213yescomplemented
9#22627593C22164yesdirect product factor
10C2×C22⋊Dic293C22136yescomplemented
11C25×C293—224no—
12C25×C293C2213yes—
13C25×C293C22112yescomplemented
14C23×D293—212no—
15C23×D293C2316yescomplemented
16C2×C22⋊D293—2144no—
17C2×C22⋊D293C23148yescomplemented
18C22×Dic293—212no—
19C22×Dic293C23118yescomplemented
20C22⋊Dic293C23148yescomplemented
21C24×C293—2128no—
22C24×C293—224no—
23C24×C293—2144no—
24C24×C293D4124yescomplemented
25C24×C293C23118yes—
26C24×C293C2311yescharacteristic
27C24×C293C23116yescomplemented
28C22×D293—236no—
29C22×D293—416no—
30C22×D293C2414yescomplemented
31C22⋊D293—296no—
32C2×Dic293—236no—
33C2×Dic293C24112yescomplemented
34C23×C293—2384no—
35C23×C293—296no—
36C23×C293—272no—
37C23×C293—296no—
38C23×C293C2×D4112yes—
39C23×C293C2×D4172yescomplemented
40C23×C293C24112yes—
41C23×C293C2413yes—
42C22×C293—2128no—
43C22×C293—2144no—
44C22×C293—224no—
45C22×C293#120116yescomplemented
46C22×C293C22×D4118yes—
47C22×C293C22×D4124yescomplemented
48C22×C293C2511yescharacteristic
49C2×D293—212no—
50C2×D293—424no—
51Dic293—212no—
52C2×C293—224no—
53C2×C293C2×#120112yescomplemented
54C2×C293C23×D413yes—
55D293—44no—
56C293C22×#12011yescharacteristic, complemented, Sylow
57C22×#120—2931nomaximal, Sylow
58C26D29311yescharacteristic, complemented
59C23×D4—2933no—
60C2×#120—29324no—
61C22×C22⋊C4—2933no—
62C25—224no—
63C25—2931no—
64C25C2×D29313yes—
65C25C2×D293112yescomplemented
66C22×D4—29336no—
67C22×D4—58624no—
68C23×C4—2933no—
69#120—29364no—
70C2×C22⋊C4—29336no—
71C24—2128no—
72C24—224no—
73C24—2144no—
74C24—2936no—
75C24—58612no—
76C24C22⋊D293124yescomplemented
77C24C22×D293118yes—
78C24C22×D29311yescharacteristic
79C24C22×D293116yescomplemented
80C2×D4—29348no—
81C2×D4—586144no—
82C22×C4—29318no—
83C22×C4—58612no—
84C22⋊C4—29348no—
85C23—2384no—
86C23—296no—
87C23—272no—
88C23—296no—
89C23—2934no—
90C23—58636no—
91C23—117216no—
92C23C2×C22⋊D293112yes—
93C23C2×C22⋊D293172yescomplemented
94C23C23×D293112yes—
95C23C23×D29313yes—
96D4—58696no—
97C2×C4—29312no—
98C2×C4—58636no—
99C22—2128no—
100C22—2144no—
101C22—224no—
102C22—58612no—
103C22—117224no—
104C22#22627593116yesdirect product factor
105C22C22×C22⋊D293118yes—
106C22C22×C22⋊D293124yescomplemented
107C22C24×D29311yescharacteristic
108C4—58612no—
109C2—224no—
110C2—11724no—
111C2C2×#22627593112yesdirect product factor
112C2C23×C22⋊D29313yes—
subgroupG/H
centerC24C22×D293
commutator, cosocleC22×C293C25
FrattiniC22C24×D293
FittingC26×C293C2
socleC24×C293C23
hypercenterC26D293
hypocenterC293C22×#120
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C24 ◁ C26

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D293C2semidirect
2. C2×#22627593C2direct (N × H)
3. C22×C22⋊Dic293C2semidirect
4. C26×C293C2semidirect
5. C24×D293C22semidirect
7. C22×C22⋊D293C22semidirect
8. C23×Dic293C22semidirect
9. #22627593C22direct (N × H)
10. C2×C22⋊Dic293C22semidirect
13. C25×C293C22semidirect
15. C23×D293C23semidirect
17. C2×C22⋊D293C23semidirect
19. C22×Dic293C23semidirect
20. C22⋊Dic293C23semidirect
24. C24×C293D4semidirect
27. C24×C293C23semidirect
30. C22×D293C24semidirect
33. C2×Dic293C24semidirect
39. C23×C293C2×D4semidirect
45. C22×C293#120semidirect
47. C22×C293C22×D4semidirect
53. C2×C293C2×#120semidirect
56. C293C22×#120semidirect
58. C26D293semidirect
65. C25C2×D293semidirect
76. C24C22⋊D293semidirect
79. C24C22×D293semidirect
93. C23C2×C22⋊D293semidirect
104. C22#22627593direct (N × H)
106. C22C22×C22⋊D293semidirect
111. C2C2×#22627593direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D2932
C2×#226275932
C22×C22⋊Dic2932
C26×C2932
C22×#120293