Finite Group Databasebeta

← C22×C13×#543 #15749009

Subgroups — C22×C13×#543 #15749009

Order 3328.

9310 conjugacy classes of subgroups; only the 6366 normal subgroups are shown.

normal subgroups only

This group has 9310 conjugacy classes of subgroups — too many to draw. Only its 6366 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×C13×#543C2148yesmaximal, direct product factor
2C22×C13×C22⋊Q8C2112yesmaximal, complemented
3C23×C13×C22⋊C4C213yesmaximal
4C26×C13C2211yescharacteristic
5C23×Q8×C13C2214yescomplemented
6C24×C4×C13C2216yes—
7C13×#543C221256yesdirect product factor
8C2×C13×C22⋊Q8C221288yescomplemented
9C22×C13×C4⋊C4C22112yescomplemented
10C22×C13×C22⋊C4C22112yes—
11C22×C13×C22⋊C4C22172yes—
12C25×C13—48no—
13C25×C13Q8116yescomplemented
14C25×C13C2313yes—
15C25×C13C23112yes—
16C22×Q8×C13—416no—
17C22×Q8×C13C23148yescomplemented
18C23×C4×C13—424no—
19C23×C4×C13C23112yes—
20C23×C4×C13C23172yes—
21C13×C22⋊Q8C231768yescomplemented
22C2×C13×C4⋊C4C231144yescomplemented
23C2×C13×C22⋊C4C231144yes—
24C2×C13×C22⋊C4C231192yes—
25C22×#543C1311yesmaximal, characteristic, direct product factor, Sylow
26C24×C13—224no—
27C24×C13—464no—
28C24×C13—448no—
29C24×C13C2×Q8124yes—
30C24×C13C2×Q8196yescomplemented
31C24×C13C24118yes—
32C24×C13C24116yes—
33C24×C13C2411yescharacteristic
34C2×Q8×C13—496no—
35C2×Q8×C13C24164yescomplemented
36C22×C4×C13—248no—
37C22×C4×C13—4144no—
38C22×C4×C13C24172yes—
39C22×C4×C13C24196yes—
40C13×C4⋊C4C241192yescomplemented
41C13×C22⋊C4C241192yes—
42C2×#543C2×C13148yesdirect product factor
43C22×C22⋊Q8C2×C13112yescomplemented
44C23×C22⋊C4C2×C1313yes—
45C23×C13—296no—
46C23×C13—272no—
47C23×C13—4192no—
48C23×C13—432no—
49C23×C13C22×Q8172yes—
50C23×C13C22×Q814yes—
51C23×C13C22×Q8164yescomplemented
52C23×C13H(5,𝔽2)18yes—
53C23×C13C25112yes—
54C23×C13C2513yes—
55Q8×C13—464no—
56C2×C4×C13—2144no—
57C2×C4×C13—496no—
58C2×C4×C13C25148yes—
59C26C22×C1311yescharacteristic
60C23×Q8C22×C1314yescomplemented
61C24×C4C22×C1316yes—
62#543C22×C131256yesdirect product factor
63C2×C22⋊Q8C22×C131288yescomplemented
64C22×C4⋊C4C22×C13112yescomplemented
65C22×C22⋊C4C22×C13112yes—
66C22×C22⋊C4C22×C13172yes—
67C22×C13—224no—
68C22×C13—2144no—
69C22×C13—464no—
70C22×C13#543116yesdirect product factor
71C22×C13C23×Q8124yes—
72C22×C13C23×Q816yes—
73C22×C13C2×H(5,𝔽2)112yes—
74C22×C13C2611yescharacteristic
75C4×C13—248no—
76C25—48no—
77C25Q8×C13116yescomplemented
78C25C23×C1313yes—
79C25C23×C13112yes—
80C22×Q8—416no—
81C22×Q8C23×C13148yescomplemented
82C23×C4—424no—
83C23×C4C23×C13112yes—
84C23×C4C23×C13172yes—
85C22⋊Q8C23×C131768yescomplemented
86C2×C4⋊C4C23×C131144yescomplemented
87C2×C22⋊C4C23×C131144yes—
88C2×C22⋊C4C23×C131192yes—
89C2×C13—224no—
90C2×C13C2×#543112yesdirect product factor
91C2×C13C24×Q811yescharacteristic
92C2×C13C22×H(5,𝔽2)12yes—
93C24—224no—
94C24—464no—
95C24—448no—
96C24C2×Q8×C13124yes—
97C24C2×Q8×C13196yescomplemented
98C24C24×C13118yes—
99C24C24×C13116yes—
100C24C24×C1311yescharacteristic
101C2×Q8—496no—
102C2×Q8C24×C13164yescomplemented
103C22×C4—248no—
104C22×C4—4144no—
105C22×C4C24×C13172yes—
106C22×C4C24×C13196yes—
107C4⋊C4C24×C131192yescomplemented
108C22⋊C4C24×C131192yes—
109C13C22×#54311yescharacteristic, direct product factor, Sylow
110C23—296no—
111C23—272no—
112C23—4192no—
113C23—432no—
114C23C22×Q8×C13172yes—
115C23C22×Q8×C1314yes—
116C23C22×Q8×C13164yescomplemented
117C23C13×H(5,𝔽2)18yes—
118C23C25×C13112yes—
119C23C25×C1313yes—
120Q8—464no—
121C2×C4—2144no—
122C2×C4—496no—
123C2×C4C25×C13148yes—
124C22—224no—
125C22—2144no—
126C22—464no—
127C22C13×#543116yesdirect product factor
128C22C23×Q8×C13124yes—
129C22C23×Q8×C1316yes—
130C22C2×C13×H(5,𝔽2)112yes—
131C22C26×C1311yescharacteristic
132C4—248no—
133C2—224no—
134C2C2×C13×#543112yesdirect product factor
135C2C24×Q8×C1311yescharacteristic
136C2C22×C13×H(5,𝔽2)12yes—
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC22C26×C13
prime radicalC26×C13C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#543C2direct (N × H)
2. C22×C13×C22⋊Q8C2semidirect
5. C23×Q8×C13C22semidirect
7. C13×#543C22direct (N × H)
8. C2×C13×C22⋊Q8C22semidirect
9. C22×C13×C4⋊C4C22semidirect
13. C25×C13Q8semidirect
17. C22×Q8×C13C23semidirect
21. C13×C22⋊Q8C23semidirect
22. C2×C13×C4⋊C4C23semidirect
25. C22×#543C13direct (N × H)
30. C24×C13C2×Q8semidirect
35. C2×Q8×C13C24semidirect
40. C13×C4⋊C4C24semidirect
42. C2×#543C2×C13direct (N × H)
43. C22×C22⋊Q8C2×C13semidirect
51. C23×C13C22×Q8semidirect
60. C23×Q8C22×C13semidirect
62. #543C22×C13direct (N × H)
63. C2×C22⋊Q8C22×C13semidirect
64. C22×C4⋊C4C22×C13semidirect
70. C22×C13#543direct (N × H)
77. C25Q8×C13semidirect
81. C22×Q8C23×C13semidirect
85. C22⋊Q8C23×C13semidirect
86. C2×C4⋊C4C23×C13semidirect
90. C2×C13C2×#543direct (N × H)
97. C24C2×Q8×C13semidirect
102. C2×Q8C24×C13semidirect
107. C4⋊C4C24×C13semidirect
109. C13C22×#543direct (N × H)
116. C23C22×Q8×C13semidirect
127. C22C13×#543direct (N × H)
134. C2C2×C13×#543direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5432
C22×C13×C22⋊Q82
C23×C13×C22⋊C42
C22×#54313