Finite Group Databasebeta

← C22×#11758515 #16858930

Subgroups — C22×#11758515 #16858930

Order 3968.

2528 conjugacy classes of subgroups; only the 685 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 685 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×C22⋊D31C212yesmaximal, complemented
2C23×C4×D31C211yesmaximal, characteristic, complemented
3C2×#11758515C2124yesmaximal, direct product factor
4C22×C4⋊Dic31C211yesmaximal, characteristic, complemented
5C22×C22⋊Dic31C212yesmaximal, complemented
6C23×D4×C31C211yesmaximal, characteristic, complemented
7C25×C31C2212yes—
8C24×D31C2211yescharacteristic
9C22×D4×C31—28no—
10C22×D4×C31C22112yescomplemented
11C23×C4×C31C2211yescharacteristic
12C22×C22⋊D31—216no—
13C22×C22⋊D31C22124yescomplemented
14C23×Dic31C2211yescharacteristic
15C23×Dic31C2212yes—
16C22×C4×D31—28no—
17C22×C4×D31C22112yescomplemented
18C2×C22⋊Dic31C22124yescomplemented
19#11758515C22164yesdirect product factor
20C2×C4⋊Dic31C22112yescomplemented
21C24×C31—28no—
22C24×C31—28no—
23C24×C31—28no—
24C24×C31C23112yes—
25C24×C31C2311yescharacteristic
26C23×D31—24no—
27C23×D31—24no—
28C23×D31D418yescomplemented
29C23×D31C2316yes—
30C2×D4×C31—248no—
31C2×D4×C31C23116yescomplemented
32C22×C4×C31D418yescomplemented
33C22×C4×C31C2316yes—
34C2×C22⋊D31—296no—
35C2×C22⋊D31C23132yescomplemented
36C22×Dic31—24no—
37C22×Dic31—28no—
38C22×Dic31C23112yes—
39C22×Dic31C2316yes—
40C2×C4×D31—248no—
41C2×C4×D31C23116yescomplemented
42C22⋊Dic31C23132yescomplemented
43C4⋊Dic31C23116yescomplemented
44C23×C31—224no—
45C23×C31—224no—
46C23×C31—224no—
47C23×C31—432no—
48C23×C31C2×D414yes—
49C23×C31C2×D414yes—
50C23×C31#4114yes—
51C23×C31C2418yes—
52C23×C31C2413yes—
53C22×D31—232no—
54C22×D31—212no—
55C22×D31—212no—
56C22×D31C2×D4124yescomplemented
57C22×D31C2414yes—
58D4×C31—232no—
59C2×C4×C31C2×D4124yescomplemented
60C2×C4×C31C2414yes—
61C22⋊D31—264no—
62C2×Dic31—212no—
63C2×Dic31—224no—
64C2×Dic31C2418yes—
65C2×Dic31C2414yes—
66C4×D31—232no—
67C22×#121—311nomaximal, Sylow
68C22×C31—28no—
69C22×C31—28no—
70C22×C31—28no—
71C22×C31—448no—
72C22×C31#121116yescomplemented
73C22×C31C22×D416yes—
74C22×C31C22×D416yes—
75C22×C31C2×#4116yes—
76C22×C31C2511yescharacteristic
77C2×D31—248no—
78C2×D31—24no—
79C2×D31—24no—
80C2×D31C22×D418yescomplemented
81C4×C31C22×D418yescomplemented
82Dic31—24no—
83Dic31—28no—
84C23×D4—312no—
85C23×D4D3111yescharacteristic, complemented
86C24×C4—311no—
87C2×#121—3124no—
88C22×C4⋊C4—311no—
89C22×C22⋊C4—312no—
90C2×C31—48no—
91C2×C31C2×#121112yescomplemented
92C2×C31C23×D411yescharacteristic
93C2×C31C23×D411yescharacteristic
94C2×C31C22×#4111yescharacteristic
95D31—28no—
96C25—311no—
97C25C2×D3112yes—
98C22×D4—28no—
99C22×D4—3124no—
100C22×D4—6216no—
101C22×D4C2×D31112yescomplemented
102C23×C4—311no—
103C23×C4—312no—
104C23×C4—3112no—
105C23×C4—628no—
106C23×C4C2×D3111yescharacteristic
107#121—3164no—
108C2×C4⋊C4—3112no—
109C2×C22⋊C4—3124no—
110C31C22×#12111yescharacteristic, complemented, Sylow
111C24—28no—
112C24—28no—
113C24—28no—
114C24—318no—
115C24—316no—
116C24—624no—
117C24—624no—
118C24C22×D31112yes—
119C24C22×D3111yescharacteristic
120C2×D4—248no—
121C2×D4—3132no—
122C2×D4—6296no—
123C2×D4C22×D31116yescomplemented
124C22×C4—316no—
125C22×C4—3112no—
126C22×C4—3116no—
127C22×C4—628no—
128C22×C4—624no—
129C22×C4—6248no—
130C22×C4C22⋊D3118yescomplemented
131C22×C4C22×D3116yes—
132C4⋊C4—3116no—
133C22⋊C4—3132no—
134C23—224no—
135C23—224no—
136C23—224no—
137C23—432no—
138C23—3124no—
139C23—314no—
140C23—6232no—
141C23—6212no—
142C23—6212no—
143C23D4×D3114yes—
144C23#9249714yes—
145C23C2×C22⋊D3114yes—
146C23C23×D3118yes—
147C23C23×D3113yes—
148D4—232no—
149D4—6264no—
150C2×C4—314no—
151C2×C4—318no—
152C2×C4—6224no—
153C2×C4—6212no—
154C2×C4—6232no—
155C2×C4C2×C22⋊D31124yescomplemented
156C2×C4C23×D3114yes—
157C22—28no—
158C22—28no—
159C22—28no—
160C22—448no—
161C22—318no—
162C22—624no—
163C22—624no—
164C22—6248no—
165C22#11758515116yesdirect product factor
166C22C2×D4×D3116yes—
167C22C2×#9249716yes—
168C22C22×C22⋊D3116yes—
169C22C24×D3111yescharacteristic
170C4—628no—
171C4—624no—
172C4C22×C22⋊D3118yescomplemented
173C2—48no—
174C2—628no—
175C2C2×#11758515112yesdirect product factor
176C2C22×D4×D3111yescharacteristic
177C2C23×C22⋊D3111yescharacteristic
178C2C22×#9249711yescharacteristic
subgroupG/H
centerC24C22×D31
commutator, cosocleC22×C31C25
FrattiniC22C24×D31
FittingC23×D4×C31C2
socleC24×C31C23
hypercenterC23×D4D31
hypocenterC31C22×#121
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D31C2semidirect
2. C23×C4×D31C2semidirect
3. C2×#11758515C2direct (N × H)
4. C22×C4⋊Dic31C2semidirect
5. C22×C22⋊Dic31C2semidirect
6. C23×D4×C31C2semidirect
10. C22×D4×C31C22semidirect
13. C22×C22⋊D31C22semidirect
17. C22×C4×D31C22semidirect
18. C2×C22⋊Dic31C22semidirect
19. #11758515C22direct (N × H)
20. C2×C4⋊Dic31C22semidirect
28. C23×D31D4semidirect
31. C2×D4×C31C23semidirect
32. C22×C4×C31D4semidirect
35. C2×C22⋊D31C23semidirect
41. C2×C4×D31C23semidirect
42. C22⋊Dic31C23semidirect
43. C4⋊Dic31C23semidirect
56. C22×D31C2×D4semidirect
59. C2×C4×C31C2×D4semidirect
72. C22×C31#121semidirect
80. C2×D31C22×D4semidirect
81. C4×C31C22×D4semidirect
85. C23×D4D31semidirect
91. C2×C31C2×#121semidirect
101. C22×D4C2×D31semidirect
110. C31C22×#121semidirect
123. C2×D4C22×D31semidirect
130. C22×C4C22⋊D31semidirect
155. C2×C4C2×C22⋊D31semidirect
165. C22#11758515direct (N × H)
172. C4C22×C22⋊D31semidirect
175. C2C2×#11758515direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D312
C23×C4×D312
C2×#117585152
C22×C4⋊Dic312
C22×C22⋊Dic312
C23×D4×C312
C22×#12131