Finite Group Databasebeta

← C22×#11758517 #16858982

Subgroups — C22×#11758517 #16858982

Order 3968.

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×D124C211yesmaximal, characteristic, complemented
2C23×C22⋊D31C214yesmaximal, complemented
3C2×#11758517C2124yesmaximal, direct product factor
4C22×C4×Dic31C211yesmaximal, characteristic, complemented
5C23×D4×C31C211yesmaximal, characteristic, complemented
6C25×C31C2212yes—
7C24×D31C2212yes—
8C22×D4×C31—28no—
9C22×D4×C31C22112yescomplemented
10C23×C4×C31C2211yescharacteristic
11C22×C22⋊D31—232no—
12C22×C22⋊D31C22148yescomplemented
13C23×Dic31C2212yes—
14C22×D124—28no—
15C22×D124C22112yescomplemented
16#11758517C22164yesdirect product factor
17C2×C4×Dic31C22112yescomplemented
18C24×C31—216no—
19C24×C31—28no—
20C24×C31C23112yes—
21C24×C31C2311yescharacteristic
22C23×D31—28no—
23C23×D31—216no—
24C23×D31C23112yes—
25C2×D4×C31—248no—
26C2×D4×C31C23116yescomplemented
27C22×C4×C31D418yescomplemented
28C22×C4×C31C2316yes—
29C2×C22⋊D31—2192no—
30C2×C22⋊D31C23164yescomplemented
31C22×Dic31D4116yescomplemented
32C22×Dic31C23112yes—
33C2×D124—248no—
34C2×D124C23116yescomplemented
35C4×Dic31C23116yescomplemented
36C23×C31—248no—
37C23×C31—224no—
38C23×C31—432no—
39C23×C31C2×D418yes—
40C23×C31C2×D414yes—
41C23×C31C2418yes—
42C23×C31C2413yes—
43C22×D31—224no—
44C22×D31—248no—
45C22×D31—432no—
46C22×D31C2418yes—
47D4×C31—232no—
48C2×C4×C31C2×D4124yescomplemented
49C2×C4×C31C2414yes—
50C22⋊D31—2128no—
51C2×Dic31C2×D4148yescomplemented
52C2×Dic31C2418yes—
53D124—232no—
54C22×#127—311nomaximal, Sylow
55C22×C31—216no—
56C22×C31—28no—
57C22×C31—448no—
58C22×C31#127116yescomplemented
59C22×C31C22×D4112yes—
60C22×C31C22×D416yes—
61C22×C31C2511yescharacteristic
62C2×D31—28no—
63C2×D31—216no—
64C2×D31—448no—
65C4×C31C22×D418yescomplemented
66Dic31C22×D4116yescomplemented
67C23×D4—314no—
68C23×D4—311no—
69C23×D4D3111yescharacteristic, complemented
70C2×#127—3124no—
71C22×C42—311no—
72C2×C31—48no—
73C2×C31C2×#127112yescomplemented
74C2×C31C23×D412yes—
75C2×C31C23×D411yescharacteristic
76D31—48no—
77C25—312no—
78C25C2×D3112yes—
79C22×D4—28no—
80C22×D4—3148no—
81C22×D4—3112no—
82C22×D4—6232no—
83C22×D4—628no—
84C22×D4C2×D31112yescomplemented
85C23×C4—312no—
86C23×C4C2×D3111yescharacteristic
87#127—3164no—
88C2×C42—3112no—
89C31C22×#12711yescharacteristic, complemented, Sylow
90C24—216no—
91C24—28no—
92C24—3112no—
93C24—6216no—
94C24—628no—
95C24C22×D31112yes—
96C24C22×D3111yescharacteristic
97C2×D4—248no—
98C2×D4—3164no—
99C2×D4—3116no—
100C2×D4—62192no—
101C2×D4—6248no—
102C2×D4C22×D31116yescomplemented
103C22×C4—3116no—
104C22×C4—3112no—
105C22×C4C22⋊D3118yescomplemented
106C22×C4C22×D3116yes—
107C42—3116no—
108C23—248no—
109C23—224no—
110C23—432no—
111C23—318no—
112C23—6248no—
113C23—6224no—
114C23—12432no—
115C23D4×D3118yes—
116C23C2×C22⋊D3114yes—
117C23C23×D3118yes—
118C23C23×D3113yes—
119D4—232no—
120D4—62128no—
121D4—6232no—
122C2×C4—3148no—
123C2×C4—318no—
124C2×C4C2×C22⋊D31124yescomplemented
125C2×C4C23×D3114yes—
126C22—216no—
127C22—28no—
128C22—448no—
129C22—6216no—
130C22—628no—
131C22—12448no—
132C22#11758517116yesdirect product factor
133C22C2×D4×D31112yes—
134C22C22×C22⋊D3116yes—
135C22C24×D3111yescharacteristic
136C4—3116no—
137C4C22×C22⋊D3118yescomplemented
138C2—48no—
139C2—1248no—
140C2C2×#11758517112yesdirect product factor
141C2C22×D4×D3112yes—
142C2C23×C22⋊D3111yescharacteristic
subgroupG/H
centerC24C22×D31
commutator, cosocleC22×C31C25
FrattiniC22C24×D31
FittingC23×D4×C31C2
socleC24×C31C23
hypercenterC23×D4D31
hypocenterC31C22×#127
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×D124C2semidirect
2. C23×C22⋊D31C2semidirect
3. C2×#11758517C2direct (N × H)
4. C22×C4×Dic31C2semidirect
5. C23×D4×C31C2semidirect
9. C22×D4×C31C22semidirect
12. C22×C22⋊D31C22semidirect
15. C22×D124C22semidirect
16. #11758517C22direct (N × H)
17. C2×C4×Dic31C22semidirect
26. C2×D4×C31C23semidirect
27. C22×C4×C31D4semidirect
30. C2×C22⋊D31C23semidirect
31. C22×Dic31D4semidirect
34. C2×D124C23semidirect
35. C4×Dic31C23semidirect
48. C2×C4×C31C2×D4semidirect
51. C2×Dic31C2×D4semidirect
58. C22×C31#127semidirect
65. C4×C31C22×D4semidirect
66. Dic31C22×D4semidirect
69. C23×D4D31semidirect
73. C2×C31C2×#127semidirect
84. C22×D4C2×D31semidirect
89. C31C22×#127semidirect
102. C2×D4C22×D31semidirect
105. C22×C4C22⋊D31semidirect
124. C2×C4C2×C22⋊D31semidirect
132. C22#11758517direct (N × H)
137. C4C22×C22⋊D31semidirect
140. C2C2×#11758517direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D1242
C23×C22⋊D312
C2×#117585172
C22×C4×Dic312
C23×D4×C312
C22×#12731