Finite Group Databasebeta

← C22×#15668008 #26033523

Subgroups — C22×#15668008 #26033523

Order 11392.

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×D356C211yesmaximal, characteristic, complemented
2C23×C22⋊D89C214yesmaximal, complemented
3C2×#15668008C2124yesmaximal, direct product factor
4C22×C4×Dic89C211yesmaximal, characteristic, complemented
5C23×D4×C89C211yesmaximal, characteristic, complemented
6C24×D89C2212yes—
7C22×D356—28no—
8C22×D356C22112yescomplemented
9C22×C22⋊D89—232no—
10C22×C22⋊D89C22148yescomplemented
11C23×Dic89C2212yes—
12#15668008C22164yesdirect product factor
13C2×C4×Dic89C22112yescomplemented
14C25×C89C2212yes—
15C22×D4×C89—28no—
16C22×D4×C89C22112yescomplemented
17C23×C4×C89C2211yescharacteristic
18C23×D89—216no—
19C23×D89—28no—
20C23×D89C23112yes—
21C2×D356—248no—
22C2×D356C23116yescomplemented
23C2×C22⋊D89—2192no—
24C2×C22⋊D89C23164yescomplemented
25C22×Dic89D4116yescomplemented
26C22×Dic89C23112yes—
27C4×Dic89C23116yescomplemented
28C24×C89—216no—
29C24×C89—28no—
30C24×C89C23112yes—
31C24×C89C2311yescharacteristic
32C2×D4×C89—248no—
33C2×D4×C89C23116yescomplemented
34C22×C4×C89D418yescomplemented
35C22×C4×C89C2316yes—
36C23×C89—224no—
37C23×C89—248no—
38C23×C89—432no—
39C23×C89C2×D418yes—
40C23×C89C2×D414yes—
41C23×C89C2418yes—
42C23×C89C2413yes—
43C22×D89—248no—
44C22×D89—224no—
45C22×D89—432no—
46C22×D89C2418yes—
47D4×C89—232no—
48C2×C4×C89C2×D4124yescomplemented
49C2×C4×C89C2414yes—
50C22⋊D89—2128no—
51C2×Dic89C2×D4148yescomplemented
52C2×Dic89C2418yes—
53D356—232no—
54C22×C89—216no—
55C22×C89—28no—
56C22×C89—448no—
57C22×C89#127116yescomplemented
58C22×C89C22×D4112yes—
59C22×C89C22×D416yes—
60C22×C89C2511yescharacteristic
61C2×D89—28no—
62C2×D89—216no—
63C2×D89—448no—
64C4×C89C22×D418yescomplemented
65Dic89C22×D4116yescomplemented
66C2×C89—48no—
67C2×C89C2×#127112yescomplemented
68C2×C89C23×D412yes—
69C2×C89C23×D411yescharacteristic
70D89—48no—
71C22×#127—891nomaximal, Sylow
72C89C22×#12711yescharacteristic, complemented, Sylow
73C23×D4—894no—
74C23×D4—891no—
75C23×D4D8911yescharacteristic, complemented
76C2×#127—8924no—
77C22×C42—891no—
78C25—892no—
79C25C2×D8912yes—
80C22×D4—28no—
81C22×D4—8948no—
82C22×D4—8912no—
83C22×D4—17832no—
84C22×D4—1788no—
85C22×D4C2×D89112yescomplemented
86C23×C4—892no—
87C23×C4C2×D8911yescharacteristic
88#127—8964no—
89C2×C42—8912no—
90C24—216no—
91C24—28no—
92C24—8912no—
93C24—17816no—
94C24—1788no—
95C24C22×D89112yes—
96C24C22×D8911yescharacteristic
97C2×D4—248no—
98C2×D4—8964no—
99C2×D4—8916no—
100C2×D4—178192no—
101C2×D4—17848no—
102C2×D4C22×D89116yescomplemented
103C22×C4—8916no—
104C22×C4—8912no—
105C22×C4C22⋊D8918yescomplemented
106C22×C4C22×D8916yes—
107C42—8916no—
108C23—248no—
109C23—224no—
110C23—432no—
111C23—898no—
112C23—35632no—
113C23—17848no—
114C23—17824no—
115C23D4×D8918yes—
116C23C2×C22⋊D8914yes—
117C23C23×D8918yes—
118C23C23×D8913yes—
119D4—232no—
120D4—178128no—
121D4—17832no—
122C2×C4—8948no—
123C2×C4—898no—
124C2×C4C2×C22⋊D89124yescomplemented
125C2×C4C23×D8914yes—
126C22—216no—
127C22—28no—
128C22—448no—
129C22—35648no—
130C22—17816no—
131C22—1788no—
132C22#15668008116yesdirect product factor
133C22C2×D4×D89112yes—
134C22C22×C22⋊D8916yes—
135C22C24×D8911yescharacteristic
136C4—8916no—
137C4C22×C22⋊D8918yescomplemented
138C2—48no—
139C2—3568no—
140C2C2×#15668008112yesdirect product factor
141C2C22×D4×D8912yes—
142C2C23×C22⋊D8911yescharacteristic
subgroupG/H
centerC24C22×D89
commutator, cosocleC22×C89C25
FrattiniC22C24×D89
FittingC23×D4×C89C2
socleC24×C89C23
hypercenterC23×D4D89
hypocenterC89C22×#127
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×D356C2semidirect
2. C23×C22⋊D89C2semidirect
3. C2×#15668008C2direct (N × H)
4. C22×C4×Dic89C2semidirect
5. C23×D4×C89C2semidirect
8. C22×D356C22semidirect
10. C22×C22⋊D89C22semidirect
12. #15668008C22direct (N × H)
13. C2×C4×Dic89C22semidirect
16. C22×D4×C89C22semidirect
22. C2×D356C23semidirect
24. C2×C22⋊D89C23semidirect
25. C22×Dic89D4semidirect
27. C4×Dic89C23semidirect
33. C2×D4×C89C23semidirect
34. C22×C4×C89D4semidirect
48. C2×C4×C89C2×D4semidirect
51. C2×Dic89C2×D4semidirect
57. C22×C89#127semidirect
64. C4×C89C22×D4semidirect
65. Dic89C22×D4semidirect
67. C2×C89C2×#127semidirect
72. C89C22×#127semidirect
75. C23×D4D89semidirect
85. C22×D4C2×D89semidirect
102. C2×D4C22×D89semidirect
105. C22×C4C22⋊D89semidirect
124. C2×C4C2×C22⋊D89semidirect
132. C22#15668008direct (N × H)
137. C4C22×C22⋊D89semidirect
140. C2C2×#15668008direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3562
C23×C22⋊D892
C2×#156680082
C22×C4×Dic892
C23×D4×C892
C22×#12789