Finite Group Databasebeta

← C22×#11758461 #16858932

Subgroups — C22×#11758461 #16858932

Order 3968.

2528 conjugacy classes of subgroups; only the 645 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 645 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⋊D31C211yesmaximal, characteristic, complemented
3C23×C22⋊D31C211yesmaximal, characteristic, complemented
4C23×C4×D31C211yesmaximal, characteristic, complemented
5C2×#11758461C2124yesmaximal, direct product factor
6C22×Dic31⋊C4C211yesmaximal, characteristic, complemented
7C22×(C2×D31)⋊C4C211yesmaximal, characteristic, complemented
8C22×C22⋊C4×C31C211yesmaximal, characteristic, complemented
9C25×C31C2211yescharacteristic
10C24×D31C2211yescharacteristic
11C24×D31C2211yescharacteristic
12C23×C4×C31C2211yescharacteristic
13C23×C4×C31C2211yescharacteristic
14C22×C22⋊D31—28no—
15C22×C22⋊D31—28no—
16C22×C22⋊D31C22112yescomplemented
17C22×C22⋊D31C22112yescomplemented
18C23×Dic31C2211yescharacteristic
19C23×Dic31C2211yescharacteristic
20C22×D124—28no—
21C22×D124C22112yescomplemented
22C22×C4×D31—28no—
23C22×C4×D31C22112yescomplemented
24C2×C22⋊C4×C31C22112yescomplemented
25C2×(C2×D31)⋊C4C22112yescomplemented
26C2×Dic31⋊C4C22112yescomplemented
27#11758461C22164yesdirect product factor
28C24×C31—24no—
29C24×C31—24no—
30C24×C31—24no—
31C24×C31C2316yes—
32C24×C31C2311yescharacteristic
33C23×D31—24no—
34C23×D31—24no—
35C23×D31—24no—
36C23×D31—24no—
37C23×D31—24no—
38C23×D31D418yescomplemented
39C23×D31C2316yes—
40C23×D31C2316yes—
41C22×C4×C31—24no—
42C22×C4×C31—24no—
43C22×C4×C31C2316yes—
44C22×C4×C31C2316yes—
45C2×C22⋊D31—248no—
46C2×C22⋊D31—248no—
47C2×C22⋊D31C23116yescomplemented
48C2×C22⋊D31C23116yescomplemented
49C22×Dic31—24no—
50C22×Dic31D418yescomplemented
51C22×Dic31C2316yes—
52C22×Dic31C2316yes—
53C2×D124—248no—
54C2×D124C23116yescomplemented
55C2×C4×D31—248no—
56C2×C4×D31C23116yescomplemented
57C22⋊C4×C31C23116yescomplemented
58(C2×D31)⋊C4C23116yescomplemented
59Dic31⋊C4C23116yescomplemented
60C23×C31—212no—
61C23×C31—212no—
62C23×C31—212no—
63C23×C31—416no—
64C23×C31C2×D414yes—
65C23×C31C2×D414yes—
66C23×C31#4114yes—
67C23×C31C2414yes—
68C23×C31C2413yes—
69C22×D31—232no—
70C22×D31—212no—
71C22×D31—212no—
72C22×D31—212no—
73C22×D31—212no—
74C22×D31—212no—
75C22×D31—416no—
76C22×D31C2×D4124yescomplemented
77C22×D31C2414yes—
78C22×D31C2414yes—
79C2×C4×C31—212no—
80C2×C4×C31—212no—
81C2×C4×C31C2414yes—
82C2×C4×C31C2414yes—
83C22⋊D31—232no—
84C22⋊D31—232no—
85C2×Dic31—212no—
86C2×Dic31C2×D4124yescomplemented
87C2×Dic31C2414yes—
88C2×Dic31C2414yes—
89D124—232no—
90C4×D31—232no—
91C22×#121—311nomaximal, Sylow
92C22×C31—24no—
93C22×C31—24no—
94C22×C31—24no—
95C22×C31—424no—
96C22×C31#121116yescomplemented
97C22×C31C22×D416yes—
98C22×C31C22×D416yes—
99C22×C31C2×#4116yes—
100C22×C31C2511yescharacteristic
101C2×D31—248no—
102C2×D31—24no—
103C2×D31—24no—
104C2×D31—24no—
105C2×D31—24no—
106C2×D31—24no—
107C2×D31—424no—
108C2×D31C22×D418yescomplemented
109C4×C31—24no—
110C4×C31—24no—
111Dic31—24no—
112Dic31C22×D418yescomplemented
113C23×D4—311no—
114C23×D4—311no—
115C23×D4—311no—
116C24×C4—311no—
117C2×#121—3124no—
118C22×C4⋊C4—311no—
119C22×C22⋊C4—311no—
120C22×C22⋊C4D3111yescharacteristic, complemented
121C2×C31—44no—
122C2×C31C2×#121112yescomplemented
123C2×C31C23×D411yescharacteristic
124C2×C31C23×D411yescharacteristic
125C2×C31C22×#4111yescharacteristic
126D31—28no—
127D31—44no—
128C25—311no—
129C25—311no—
130C25C2×D3111yescharacteristic
131C22×D4—3112no—
132C22×D4—3112no—
133C22×D4—3112no—
134C22×D4—628no—
135C22×D4—628no—
136C22×D4—628no—
137C23×C4—311no—
138C23×C4—311no—
139C23×C4—3112no—
140C23×C4—628no—
141C23×C4C2×D3111yescharacteristic
142C23×C4C2×D3111yescharacteristic
143#121—3164no—
144C2×C4⋊C4—3112no—
145C2×C22⋊C4—3112no—
146C2×C22⋊C4C2×D31112yescomplemented
147C31C22×#12111yescharacteristic, complemented, Sylow
148C24—24no—
149C24—24no—
150C24—24no—
151C24—318no—
152C24—316no—
153C24—316no—
154C24—624no—
155C24—624no—
156C24—624no—
157C24—624no—
158C24—624no—
159C24C22×D3116yes—
160C24C22×D3111yescharacteristic
161C2×D4—3116no—
162C2×D4—3116no—
163C2×D4—3116no—
164C2×D4—6248no—
165C2×D4—6248no—
166C2×D4—6248no—
167C22×C4—24no—
168C22×C4—24no—
169C22×C4—318no—
170C22×C4—316no—
171C22×C4—316no—
172C22×C4—3116no—
173C22×C4—6248no—
174C22×C4—624no—
175C22×C4C22×D3116yes—
176C22×C4C22×D3116yes—
177C4⋊C4—3116no—
178C22⋊C4—3116no—
179C22⋊C4C22×D31116yescomplemented
180C23—212no—
181C23—212no—
182C23—212no—
183C23—416no—
184C23—3124no—
185C23—314no—
186C23—314no—
187C23—6232no—
188C23—6212no—
189C23—6212no—
190C23—6212no—
191C23—6212no—
192C23—6212no—
193C23—12416no—
194C23#9249514yes—
195C23D4×D3114yes—
196C23D4×D3114yes—
197C23C23×D3114yes—
198C23C23×D3113yes—
199D4—6232no—
200D4—6232no—
201D4—6232no—
202C2×C4—212no—
203C2×C4—212no—
204C2×C4—3124no—
205C2×C4—314no—
206C2×C4—314no—
207C2×C4—6232no—
208C2×C4—6212no—
209C2×C4C23×D3114yes—
210C2×C4C23×D3114yes—
211C22—24no—
212C22—24no—
213C22—24no—
214C22—424no—
215C22—318no—
216C22—624no—
217C22—624no—
218C22—6248no—
219C22—624no—
220C22—624no—
221C22—624no—
222C22—12424no—
223C22#11758461116yesdirect product factor
224C22C2×#9249516yes—
225C22C2×D4×D3116yes—
226C22C2×D4×D3116yes—
227C22C24×D3111yescharacteristic
228C4—24no—
229C4—24no—
230C4—318no—
231C4—624no—
232C2—44no—
233C2—628no—
234C2—1244no—
235C2C2×#11758461112yesdirect product factor
236C2C22×D4×D3111yescharacteristic
237C2C22×D4×D3111yescharacteristic
238C2C22×#9249511yescharacteristic
subgroupG/H
centerC24C22×D31
commutator, cosocleC22×C31C25
FrattiniC22C24×D31
FittingC22×C22⋊C4×C31C2
socleC24×C31C23
hypercenterC22×C22⋊C4D31
hypocenterC31C22×#121
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×D124C2semidirect
2. C23×C22⋊D31C2semidirect
3. C23×C22⋊D31C2semidirect
4. C23×C4×D31C2semidirect
5. C2×#11758461C2direct (N × H)
6. C22×Dic31⋊C4C2semidirect
7. C22×(C2×D31)⋊C4C2semidirect
8. C22×C22⋊C4×C31C2semidirect
16. C22×C22⋊D31C22semidirect
17. C22×C22⋊D31C22semidirect
21. C22×D124C22semidirect
23. C22×C4×D31C22semidirect
24. C2×C22⋊C4×C31C22semidirect
25. C2×(C2×D31)⋊C4C22semidirect
26. C2×Dic31⋊C4C22semidirect
27. #11758461C22direct (N × H)
38. C23×D31D4semidirect
47. C2×C22⋊D31C23semidirect
48. C2×C22⋊D31C23semidirect
50. C22×Dic31D4semidirect
54. C2×D124C23semidirect
56. C2×C4×D31C23semidirect
57. C22⋊C4×C31C23semidirect
58. (C2×D31)⋊C4C23semidirect
59. Dic31⋊C4C23semidirect
76. C22×D31C2×D4semidirect
86. C2×Dic31C2×D4semidirect
96. C22×C31#121semidirect
108. C2×D31C22×D4semidirect
112. Dic31C22×D4semidirect
120. C22×C22⋊C4D31semidirect
122. C2×C31C2×#121semidirect
146. C2×C22⋊C4C2×D31semidirect
147. C31C22×#121semidirect
179. C22⋊C4C22×D31semidirect
223. C22#11758461direct (N × H)
235. C2C2×#11758461direct (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
C23×C4×D312
C2×#117584612
C22×Dic31⋊C42
C22×(C2×D31)⋊C42
C22×C22⋊C4×C312
C22×#12131