Finite Group Databasebeta

← C22×#64162 #11900245

Subgroups — C22×#64162 #11900245

Order 1152.

13632 conjugacy classes of subgroups; only the 1801 normal subgroups are shown.

normal subgroups only

This group has 13632 conjugacy classes of subgroups — too many to draw. Only its 1801 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
1C26×C32C211yesmaximal, characteristic, complemented
2C23×#638C213yesmaximal, complemented
3C2×#64162C2124yesmaximal, direct product factor
4C22×#3757C213yesmaximal, complemented
5C22×#953—34nomaximal
6C25×C32—224no—
7C25×C32C2213yes—
8C25×C32C22112yescomplemented
9C24×C3⋊D3C2211yescharacteristic, complemented
10C22×#638—224no—
11C22×#638C22136yescomplemented
12C23×C3⋊Dic3C2213yescomplemented
13#64162C22164yesdirect product factor
14C2×#3757C22136yescomplemented
15C26×C3D314yescomplemented
16C23×#67—312no—
17C2×#953—396no—
18C22×#217—312no—
19C24×C32—2128no—
20C24×C32—224no—
21C24×C32—2144no—
22C24×C32D4124yescomplemented
23C24×C32C23118yes—
24C24×C32C2311yescharacteristic
25C24×C32C23116yescomplemented
26C23×C3⋊D3—212no—
27C23×C3⋊D3C2316yescomplemented
28C2×#638—2144no—
29C2×#638C23148yescomplemented
30C22×C3⋊Dic3—212no—
31C22×C3⋊Dic3C23118yescomplemented
32#3757C23148yescomplemented
33C22×#120—91noSylow
34C25×C3—296no—
35C25×C3C2×D3112yes—
36C25×C3C2×D3148yescomplemented
37C24×D3—34no—
38C22×#67—3144no—
39C22×#67—696no—
40C23×Dic3—312no—
41#953—3256no—
42C2×#217—3144no—
43C23×C32—2384no—
44C23×C32—296no—
45C23×C32—272no—
46C23×C32—296no—
47C23×C32C2×D4112yes—
48C23×C32C2×D4172yescomplemented
49C23×C32C24112yes—
50C23×C32C2413yes—
51C22×C3⋊D3—236no—
52C22×C3⋊D3—416no—
53C22×C3⋊D3C2414yescomplemented
54#638—296no—
55C2×C3⋊Dic3—236no—
56C2×C3⋊Dic3C24112yescomplemented
57C26C3⋊D311yescharacteristic, complemented
58C23×D4—93no—
59C2×#120—924no—
60C22×C22⋊C4—93no—
61C24×C3—2512no—
62C24×C3—296no—
63C24×C3—2576no—
64C24×C3#67196yescomplemented
65C24×C3C22×D3172yes—
66C24×C3C22×D314yes—
67C24×C3C22×D3164yescomplemented
68C23×D3—324no—
69C23×D3—648no—
70C2×#67—3192no—
71C2×#67—6576no—
72C22×Dic3—372no—
73C22×Dic3—648no—
74#217—3192no—
75C22×C32—2128no—
76C22×C32—2144no—
77C22×C32—224no—
78C22×C32#120116yescomplemented
79C22×C32C22×D4118yes—
80C22×C32C22×D4124yescomplemented
81C22×C32C2511yescharacteristic
82C2×C3⋊D3—212no—
83C2×C3⋊D3—424no—
84C3⋊Dic3—212no—
85C25—224no—
86C25—91no—
87C25C2×C3⋊D313yes—
88C25C2×C3⋊D3112yescomplemented
89C22×D4—936no—
90C22×D4—1824no—
91C23×C4—93no—
92#120—964no—
93C2×C22⋊C4—936no—
94C23×C3—21536no—
95C23×C3—2384no—
96C23×C3—2288no—
97C23×C3—2384no—
98C23×C3C2×#67148yes—
99C23×C3C2×#671288yescomplemented
100C23×C3C23×D3148yes—
101C23×C3C23×D3112yes—
102C22×D3—316no—
103C22×D3—6144no—
104C22×D3—1264no—
105#67—6384no—
106C2×Dic3—348no—
107C2×Dic3—6144no—
108C2×C32—224no—
109C2×C32C2×#120112yescomplemented
110C2×C32C23×D413yes—
111C3⋊D3—44no—
112C24—2128no—
113C24—224no—
114C24—2144no—
115C24—96no—
116C24—1812no—
117C24#638124yescomplemented
118C24C22×C3⋊D3118yes—
119C24C22×C3⋊D311yescharacteristic
120C24C22×C3⋊D3116yescomplemented
121C2×D4—948no—
122C2×D4—18144no—
123C22×C4—918no—
124C22×C4—1812no—
125C22⋊C4—948no—
126C22×C3—2512no—
127C22×C3—296no—
128C22×C3—2576no—
129C22×C3#953164yescomplemented
130C22×C3C22×#67172yes—
131C22×C3C22×#67196yescomplemented
132C22×C3C24×D314yes—
133C2×D3—648no—
134C2×D3—1296no—
135Dic3—648no—
136C32C22×#12011yescharacteristic, complemented, Sylow
137C23—2384no—
138C23—272no—
139C23—296no—
140C23—296no—
141C23—94no—
142C23—1836no—
143C23—3616no—
144C23C2×#638112yes—
145C23C2×#638172yescomplemented
146C23C23×C3⋊D3112yes—
147C23C23×C3⋊D313yes—
148D4—1896no—
149C2×C4—912no—
150C2×C4—1836no—
151C2×C3—296no—
152C2×C3C2×#953148yescomplemented
153C2×C3C23×#67112yes—
154D3—1216no—
155C22—2128no—
156C22—224no—
157C22—2144no—
158C22—1812no—
159C22—3624no—
160C22#64162116yesdirect product factor
161C22C22×#638118yes—
162C22C22×#638124yescomplemented
163C22C24×C3⋊D311yescharacteristic
164C4—1812no—
165C3C22×#95314yescomplemented
166C2—224no—
167C2—364no—
168C2C2×#64162112yesdirect product factor
169C2C23×#63813yes—
subgroupG/H
centerC24C22×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC26×C32C2
socleC24×C32C23
hypercenterC26C3⋊D3
hypocenterC32C22×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C26

Complements

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

NH ≅ G/Ntype
1. C26×C32C2semidirect
2. C23×#638C2semidirect
3. C2×#64162C2direct (N × H)
4. C22×#3757C2semidirect
8. C25×C32C22semidirect
9. C24×C3⋊D3C22semidirect
11. C22×#638C22semidirect
12. C23×C3⋊Dic3C22semidirect
13. #64162C22direct (N × H)
14. C2×#3757C22semidirect
15. C26×C3D3semidirect
22. C24×C32D4semidirect
25. C24×C32C23semidirect
27. C23×C3⋊D3C23semidirect
29. C2×#638C23semidirect
31. C22×C3⋊Dic3C23semidirect
32. #3757C23semidirect
36. C25×C3C2×D3semidirect
48. C23×C32C2×D4semidirect
53. C22×C3⋊D3C24semidirect
56. C2×C3⋊Dic3C24semidirect
57. C26C3⋊D3semidirect
64. C24×C3#67semidirect
67. C24×C3C22×D3semidirect
78. C22×C32#120semidirect
80. C22×C32C22×D4semidirect
88. C25C2×C3⋊D3semidirect
99. C23×C3C2×#67semidirect
109. C2×C32C2×#120semidirect
117. C24#638semidirect
120. C24C22×C3⋊D3semidirect
129. C22×C3#953semidirect
131. C22×C3C22×#67semidirect
136. C32C22×#120semidirect
145. C23C2×#638semidirect
152. C2×C3C2×#953semidirect
160. C22#64162direct (N × H)
162. C22C22×#638semidirect
165. C3C22×#953semidirect
168. C2C2×#64162direct (N × H)

Maximal subgroups

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

subgroupindex
C26×C322
C23×#6382
C2×#641622
C22×#37572
C22×#9533