Finite Group Databasebeta

← C22×#11745302 #16832763

Subgroups — C22×#11745302 #16832763

Order 3712.

3000 conjugacy classes of subgroups; only the 725 normal subgroups are shown.

normal subgroups only

This group has 3000 conjugacy classes of subgroups — too many to draw. Only its 725 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×D116C211yesmaximal, characteristic, complemented
2C23×C22⋊D29C214yesmaximal, complemented
3C2×#11745302C2124yesmaximal, direct product factor
4C22×C4×Dic29C211yesmaximal, characteristic, complemented
5C23×D4×C29C211yesmaximal, characteristic, complemented
6C25×C29C2212yes—
7C24×D29C2212yes—
8C22×D4×C29—28no—
9C22×D4×C29C22112yescomplemented
10C23×C4×C29C2211yescharacteristic
11C22×C22⋊D29—232no—
12C22×C22⋊D29C22148yescomplemented
13C23×Dic29C2212yes—
14C22×D116—28no—
15C22×D116C22112yescomplemented
16#11745302C22164yesdirect product factor
17C2×C4×Dic29C22112yescomplemented
18C24×C29—216no—
19C24×C29—28no—
20C24×C29C23112yes—
21C24×C29C2311yescharacteristic
22C23×D29—28no—
23C23×D29—216no—
24C23×D29C23112yes—
25C2×D4×C29—248no—
26C2×D4×C29C23116yescomplemented
27C22×C4×C29D418yescomplemented
28C22×C4×C29C2316yes—
29C2×C22⋊D29—2192no—
30C2×C22⋊D29C23164yescomplemented
31C22×Dic29D4116yescomplemented
32C22×Dic29C23112yes—
33C2×D116—248no—
34C2×D116C23116yescomplemented
35C4×Dic29C23116yescomplemented
36C23×C29—248no—
37C23×C29—224no—
38C23×C29—432no—
39C23×C29C2×D418yes—
40C23×C29C2×D414yes—
41C23×C29C2418yes—
42C23×C29C2413yes—
43C22×D29—224no—
44C22×D29—248no—
45C22×D29—432no—
46C22×D29C2418yes—
47D4×C29—232no—
48C2×C4×C29C2×D4124yescomplemented
49C2×C4×C29C2414yes—
50C22⋊D29—2128no—
51C2×Dic29C2×D4148yescomplemented
52C2×Dic29C2418yes—
53D116—232no—
54C22×#127—291nomaximal, Sylow
55C22×C29—216no—
56C22×C29—28no—
57C22×C29—448no—
58C22×C29#127116yescomplemented
59C22×C29C22×D4112yes—
60C22×C29C22×D416yes—
61C22×C29C2511yescharacteristic
62C2×D29—28no—
63C2×D29—216no—
64C2×D29—448no—
65C4×C29C22×D418yescomplemented
66Dic29C22×D4116yescomplemented
67C23×D4—294no—
68C23×D4—291no—
69C23×D4D2911yescharacteristic, complemented
70C2×#127—2924no—
71C22×C42—291no—
72C2×C29—48no—
73C2×C29C2×#127112yescomplemented
74C2×C29C23×D412yes—
75C2×C29C23×D411yescharacteristic
76D29—48no—
77C25—292no—
78C25C2×D2912yes—
79C22×D4—28no—
80C22×D4—2948no—
81C22×D4—2912no—
82C22×D4—5832no—
83C22×D4—588no—
84C22×D4C2×D29112yescomplemented
85C23×C4—292no—
86C23×C4C2×D2911yescharacteristic
87#127—2964no—
88C2×C42—2912no—
89C29C22×#12711yescharacteristic, complemented, Sylow
90C24—216no—
91C24—28no—
92C24—2912no—
93C24—5816no—
94C24—588no—
95C24C22×D29112yes—
96C24C22×D2911yescharacteristic
97C2×D4—248no—
98C2×D4—2964no—
99C2×D4—2916no—
100C2×D4—58192no—
101C2×D4—5848no—
102C2×D4C22×D29116yescomplemented
103C22×C4—2916no—
104C22×C4—2912no—
105C22×C4C22⋊D2918yescomplemented
106C22×C4C22×D2916yes—
107C42—2916no—
108C23—248no—
109C23—224no—
110C23—432no—
111C23—298no—
112C23—5848no—
113C23—5824no—
114C23—11632no—
115C23D4×D2918yes—
116C23C2×C22⋊D2914yes—
117C23C23×D2918yes—
118C23C23×D2913yes—
119D4—232no—
120D4—58128no—
121D4—5832no—
122C2×C4—2948no—
123C2×C4—298no—
124C2×C4C2×C22⋊D29124yescomplemented
125C2×C4C23×D2914yes—
126C22—216no—
127C22—28no—
128C22—448no—
129C22—5816no—
130C22—588no—
131C22—11648no—
132C22#11745302116yesdirect product factor
133C22C2×D4×D29112yes—
134C22C22×C22⋊D2916yes—
135C22C24×D2911yescharacteristic
136C4—2916no—
137C4C22×C22⋊D2918yescomplemented
138C2—48no—
139C2—1168no—
140C2C2×#11745302112yesdirect product factor
141C2C22×D4×D2912yes—
142C2C23×C22⋊D2911yescharacteristic
subgroupG/H
centerC24C22×D29
commutator, cosocleC22×C29C25
FrattiniC22C24×D29
FittingC23×D4×C29C2
socleC24×C29C23
hypercenterC23×D4D29
hypocenterC29C22×#127
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×D116C2semidirect
2. C23×C22⋊D29C2semidirect
3. C2×#11745302C2direct (N × H)
4. C22×C4×Dic29C2semidirect
5. C23×D4×C29C2semidirect
9. C22×D4×C29C22semidirect
12. C22×C22⋊D29C22semidirect
15. C22×D116C22semidirect
16. #11745302C22direct (N × H)
17. C2×C4×Dic29C22semidirect
26. C2×D4×C29C23semidirect
27. C22×C4×C29D4semidirect
30. C2×C22⋊D29C23semidirect
31. C22×Dic29D4semidirect
34. C2×D116C23semidirect
35. C4×Dic29C23semidirect
48. C2×C4×C29C2×D4semidirect
51. C2×Dic29C2×D4semidirect
58. C22×C29#127semidirect
65. C4×C29C22×D4semidirect
66. Dic29C22×D4semidirect
69. C23×D4D29semidirect
73. C2×C29C2×#127semidirect
84. C22×D4C2×D29semidirect
89. C29C22×#127semidirect
102. C2×D4C22×D29semidirect
105. C22×C4C22⋊D29semidirect
124. C2×C4C2×C22⋊D29semidirect
132. C22#11745302direct (N × H)
137. C4C22×C22⋊D29semidirect
140. C2C2×#11745302direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D1162
C23×C22⋊D292
C2×#117453022
C22×C4×Dic292
C23×D4×C292
C22×#12729