Finite Group Databasebeta

← C22×#63515 #11900244

Subgroups — C22×#63515 #11900244

Order 1152.

6816 conjugacy classes of subgroups; only the 1054 normal subgroups are shown.

normal subgroups only

This group has 6816 conjugacy classes of subgroups — too many to draw. Only its 1054 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×C9C211yesmaximal, characteristic, complemented
2C23×#611C213yesmaximal, complemented
3C2×#63515C2124yesmaximal, direct product factor
4C22×#3676C213yesmaximal, complemented
5C22×#953—31nomaximal
6C25×C9—224no—
7C25×C9C2213yes—
8C25×C9C22112yescomplemented
9C24×D9C2211yescharacteristic, complemented
10C22×#611—224no—
11C22×#611C22136yescomplemented
12C23×Dic9C2213yescomplemented
13#63515C22164yesdirect product factor
14C2×#3676C22136yescomplemented
15C26×C3D311yescharacteristic
16C23×#67—33no—
17C2×#953—324no—
18C22×#217—33no—
19C24×C9—2128no—
20C24×C9—224no—
21C24×C9—2144no—
22C24×C9D4124yescomplemented
23C24×C9C23118yes—
24C24×C9C2311yescharacteristic
25C24×C9C23116yescomplemented
26C23×D9—212no—
27C23×D9C2316yescomplemented
28C2×#611—2144no—
29C2×#611C23148yescomplemented
30C22×Dic9—212no—
31C22×Dic9C23118yescomplemented
32#3676C23148yescomplemented
33C22×#120—91noSylow
34C25×C3—224no—
35C25×C3C2×D313yes—
36C25×C3C2×D3112yes—
37C24×D3—31no—
38C22×#67—336no—
39C22×#67—624no—
40C23×Dic3—33no—
41#953—364no—
42C2×#217—336no—
43C23×C9—2384no—
44C23×C9—296no—
45C23×C9—272no—
46C23×C9—296no—
47C23×C9C2×D4112yes—
48C23×C9C2×D4172yescomplemented
49C23×C9C24112yes—
50C23×C9C2413yes—
51C22×D9—236no—
52C22×D9—416no—
53C22×D9C2414yescomplemented
54#611—296no—
55C2×Dic9—236no—
56C2×Dic9C24112yescomplemented
57C26D911yescharacteristic, complemented
58C23×D4—93no—
59C2×#120—924no—
60C22×C22⋊C4—93no—
61C24×C3—2128no—
62C24×C3—224no—
63C24×C3—2144no—
64C24×C3#67124yes—
65C24×C3C22×D3118yes—
66C24×C3C22×D311yescharacteristic
67C24×C3C22×D3116yes—
68C23×D3—36no—
69C23×D3—612no—
70C2×#67—348no—
71C2×#67—6144no—
72C22×Dic3—318no—
73C22×Dic3—612no—
74#217—348no—
75C22×C9—2128no—
76C22×C9—2144no—
77C22×C9—224no—
78C22×C9#120116yescomplemented
79C22×C9C22×D4118yes—
80C22×C9C22×D4124yescomplemented
81C22×C9C2511yescharacteristic
82C2×D9—212no—
83C2×D9—424no—
84Dic9—212no—
85C25—224no—
86C25—91no—
87C25C2×D913yes—
88C25C2×D9112yescomplemented
89C22×D4—936no—
90C22×D4—1824no—
91C23×C4—93no—
92#120—964no—
93C2×C22⋊C4—936no—
94C23×C3—2384no—
95C23×C3—296no—
96C23×C3—272no—
97C23×C3—296no—
98C23×C3C2×#67112yes—
99C23×C3C2×#67172yes—
100C23×C3C23×D3112yes—
101C23×C3C23×D313yes—
102C22×D3—34no—
103C22×D3—636no—
104C22×D3—1216no—
105#67—696no—
106C2×Dic3—312no—
107C2×Dic3—636no—
108C2×C9—224no—
109C2×C9C2×#120112yescomplemented
110C2×C9C23×D413yes—
111D9—44no—
112C24—2128no—
113C24—224no—
114C24—2144no—
115C24—96no—
116C24—1812no—
117C24#611124yescomplemented
118C24C22×D9118yes—
119C24C22×D911yescharacteristic
120C24C22×D9116yescomplemented
121C2×D4—948no—
122C2×D4—18144no—
123C22×C4—918no—
124C22×C4—1812no—
125C22⋊C4—948no—
126C22×C3—2128no—
127C22×C3—224no—
128C22×C3—2144no—
129C22×C3#953116yes—
130C22×C3C22×#67118yes—
131C22×C3C22×#67124yes—
132C22×C3C24×D311yescharacteristic
133C2×D3—612no—
134C2×D3—1224no—
135Dic3—612no—
136C9C22×#12011yescharacteristic, complemented, Sylow
137C23—2384no—
138C23—296no—
139C23—272no—
140C23—296no—
141C23—94no—
142C23—1836no—
143C23—3616no—
144C23C2×#611112yes—
145C23C2×#611172yescomplemented
146C23C23×D9112yes—
147C23C23×D913yes—
148D4—1896no—
149C2×C4—912no—
150C2×C4—1836no—
151C2×C3—224no—
152C2×C3C2×#953112yes—
153C2×C3C23×#6713yes—
154D3—124no—
155C22—2128no—
156C22—224no—
157C22—2144no—
158C22—1812no—
159C22—3624no—
160C22#63515116yesdirect product factor
161C22C22×#611118yes—
162C22C22×#611124yescomplemented
163C22C24×D911yescharacteristic
164C4—1812no—
165C3C22×#95311yescharacteristic
166C2—224no—
167C2—364no—
168C2C2×#63515112yesdirect product factor
169C2C23×#61113yes—
subgroupG/H
centerC24C22×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC26×C9C2
socleC24×C3C22×D3
hypercenterC26D9
hypocenterC9C22×#120
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C24 ◁ C26

Complements

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

NH ≅ G/Ntype
1. C26×C9C2semidirect
2. C23×#611C2semidirect
3. C2×#63515C2direct (N × H)
4. C22×#3676C2semidirect
8. C25×C9C22semidirect
9. C24×D9C22semidirect
11. C22×#611C22semidirect
12. C23×Dic9C22semidirect
13. #63515C22direct (N × H)
14. C2×#3676C22semidirect
22. C24×C9D4semidirect
25. C24×C9C23semidirect
27. C23×D9C23semidirect
29. C2×#611C23semidirect
31. C22×Dic9C23semidirect
32. #3676C23semidirect
48. C23×C9C2×D4semidirect
53. C22×D9C24semidirect
56. C2×Dic9C24semidirect
57. C26D9semidirect
78. C22×C9#120semidirect
80. C22×C9C22×D4semidirect
88. C25C2×D9semidirect
109. C2×C9C2×#120semidirect
117. C24#611semidirect
120. C24C22×D9semidirect
136. C9C22×#120semidirect
145. C23C2×#611semidirect
160. C22#63515direct (N × H)
162. C22C22×#611semidirect
168. C2C2×#63515direct (N × H)

Maximal subgroups

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

subgroupindex
C26×C92
C23×#6112
C2×#635152
C22×#36762
C22×#9533