Finite Group Databasebeta

← C22×#10587625 #14542004

Subgroups — C22×#10587625 #14542004

Order 2176.

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⋊D17C211yesmaximal, characteristic, complemented
2C23×C22⋊D17C211yesmaximal, characteristic, complemented
3C24×Dic17C211yesmaximal, characteristic, complemented
4C2×#10587625C2124yesmaximal, direct product factor
5C22×#63225C211yesmaximal, characteristic, complemented
6C22×C22⋊Dic17C211yesmaximal, characteristic, complemented
7C22×#63227C211yesmaximal, characteristic, complemented
8C23×D4×C17C211yesmaximal, characteristic, complemented
9C25×C17C2211yescharacteristic
10C25×C17C2211yescharacteristic
11C24×D17C2211yescharacteristic
12C22×D4×C17—28no—
13C22×D4×C17C22112yescomplemented
14C23×C4×C17C2211yescharacteristic
15C22×C22⋊D17—28no—
16C22×C22⋊D17—28no—
17C22×C22⋊D17C22112yescomplemented
18C22×C22⋊D17C22112yescomplemented
19C23×Dic17—28no—
20C23×Dic17C2211yescharacteristic
21C23×Dic17C2211yescharacteristic
22C23×Dic17C2211yescharacteristic
23C23×Dic17C22112yescomplemented
24C2×C22⋊Dic17C22112yescomplemented
25#10587625C22164yesdirect product factor
26C2×#63227C22112yescomplemented
27C2×#63225C22112yescomplemented
28C24×C17—24no—
29C24×C17—24no—
30C24×C17—24no—
31C24×C17—24no—
32C24×C17—24no—
33C24×C17D418yescomplemented
34C24×C17C2316yes—
35C24×C17C2316yes—
36C24×C17C2311yescharacteristic
37C23×D17—24no—
38C23×D17—24no—
39C23×D17—24no—
40C23×D17C2316yes—
41C2×D4×C17—248no—
42C2×D4×C17C23116yescomplemented
43C22×C4×C17—24no—
44C22×C4×C17C2316yes—
45C2×C22⋊D17—248no—
46C2×C22⋊D17—248no—
47C2×C22⋊D17C23116yescomplemented
48C2×C22⋊D17C23116yescomplemented
49C22×Dic17—24no—
50C22×Dic17—24no—
51C22×Dic17—248no—
52C22×Dic17D418yescomplemented
53C22×Dic17C2316yes—
54C22×Dic17C2316yes—
55C22×Dic17C2316yes—
56C22×Dic17C23116yescomplemented
57C22⋊Dic17C23116yescomplemented
58#63227C23116yescomplemented
59#63225C23116yescomplemented
60C23×C17—232no—
61C23×C17—212no—
62C23×C17—212no—
63C23×C17—212no—
64C23×C17—212no—
65C23×C17—212no—
66C23×C17—416no—
67C23×C17C2×D414yes—
68C23×C17C2×D414yes—
69C23×C17C2×D4124yescomplemented
70C23×C17#4114yes—
71C23×C17C2414yes—
72C23×C17C2414yes—
73C23×C17C2413yes—
74C22×D17—212no—
75C22×D17—212no—
76C22×D17—212no—
77C22×D17—416no—
78C22×D17C2414yes—
79D4×C17—232no—
80C2×C4×C17—212no—
81C2×C4×C17C2414yes—
82C22⋊D17—232no—
83C22⋊D17—232no—
84C2×Dic17—212no—
85C2×Dic17—212no—
86C2×Dic17—232no—
87C2×Dic17C2×D4124yescomplemented
88C2×Dic17C2414yes—
89C2×Dic17C2414yes—
90C2×Dic17C2414yes—
91C22×#121—171nomaximal, Sylow
92C22×C17—248no—
93C22×C17—24no—
94C22×C17—24no—
95C22×C17—24no—
96C22×C17—24no—
97C22×C17—24no—
98C22×C17—424no—
99C22×C17#121116yescomplemented
100C22×C17C22×D416yes—
101C22×C17C22×D416yes—
102C22×C17C22×D418yescomplemented
103C22×C17C2×#4116yes—
104C22×C17C2511yescharacteristic
105C2×D17—24no—
106C2×D17—24no—
107C2×D17—24no—
108C2×D17—424no—
109C4×C17—24no—
110Dic17—24no—
111Dic17—24no—
112Dic17C22×D418yescomplemented
113C23×D4—171no—
114C23×D4—171no—
115C23×D4D1711yescharacteristic, complemented
116C24×C4—171no—
117C2×#121—1724no—
118C22×C4⋊C4—171no—
119C22×C22⋊C4—171no—
120C22×C22⋊C4—171no—
121C2×C17—28no—
122C2×C17—44no—
123C2×C17C2×#121112yescomplemented
124C2×C17C23×D411yescharacteristic
125C2×C17C23×D411yescharacteristic
126C2×C17C22×#4111yescharacteristic
127D17—44no—
128C25—171no—
129C25C2×D1711yescharacteristic
130C25C2×D1711yescharacteristic
131C22×D4—28no—
132C22×D4—1712no—
133C22×D4—1712no—
134C22×D4—348no—
135C22×D4—348no—
136C22×D4C2×D17112yescomplemented
137C23×C4—171no—
138C23×C4—1712no—
139C23×C4—171no—
140C23×C4—171no—
141C23×C4—348no—
142C23×C4C2×D1711yescharacteristic
143#121—1764no—
144C2×C4⋊C4—1712no—
145C2×C22⋊C4—1712no—
146C2×C22⋊C4—1712no—
147C17C22×#12111yescharacteristic, complemented, Sylow
148C24—24no—
149C24—24no—
150C24—24no—
151C24—24no—
152C24—24no—
153C24—176no—
154C24—344no—
155C24—344no—
156C24—344no—
157C24C22⋊D1718yescomplemented
158C24C22×D1716yes—
159C24C22×D1716yes—
160C24C22×D1711yescharacteristic
161C2×D4—248no—
162C2×D4—1716no—
163C2×D4—1716no—
164C2×D4—3448no—
165C2×D4—3448no—
166C2×D4C22×D17116yescomplemented
167C22×C4—24no—
168C22×C4—178no—
169C22×C4—176no—
170C22×C4—176no—
171C22×C4—176no—
172C22×C4—1716no—
173C22×C4—3448no—
174C22×C4—344no—
175C22×C4—344no—
176C22×C4C22×D1716yes—
177C4⋊C4—1716no—
178C22⋊C4—1716no—
179C22⋊C4—1716no—
180C23—212no—
181C23—212no—
182C23—232no—
183C23—212no—
184C23—212no—
185C23—212no—
186C23—416no—
187C23—174no—
188C23—3412no—
189C23—3412no—
190C23—3412no—
191C23—6816no—
192C23D4×D1714yes—
193C23#6325414yes—
194C23C2×C22⋊D1714yes—
195C23C2×C22⋊D17124yescomplemented
196C23C23×D1714yes—
197C23C23×D1714yes—
198C23C23×D1713yes—
199D4—232no—
200D4—3432no—
201D4—3432no—
202C2×C4—212no—
203C2×C4—1724no—
204C2×C4—174no—
205C2×C4—174no—
206C2×C4—174no—
207C2×C4—3432no—
208C2×C4—3412no—
209C2×C4—3412no—
210C2×C4C23×D1714yes—
211C22—248no—
212C22—24no—
213C22—24no—
214C22—24no—
215C22—24no—
216C22—24no—
217C22—424no—
218C22—344no—
219C22—344no—
220C22—344no—
221C22—6824no—
222C22#10587625116yesdirect product factor
223C22C2×D4×D1716yes—
224C22C2×#6325416yes—
225C22C22×C22⋊D1716yes—
226C22C22×C22⋊D1718yescomplemented
227C22C24×D1711yescharacteristic
228C4—24no—
229C4—178no—
230C4—344no—
231C4—344no—
232C2—28no—
233C2—44no—
234C2—684no—
235C2C2×#10587625112yesdirect product factor
236C2C22×D4×D1711yescharacteristic
237C2C23×C22⋊D1711yescharacteristic
238C2C22×#6325411yescharacteristic
subgroupG/H
centerC24C22×D17
commutator, cosocleC22×C17C25
FrattiniC22C24×D17
FittingC23×D4×C17C2
socleC24×C17C23
hypercenterC23×D4D17
hypocenterC17C22×#121
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D17C2semidirect
2. C23×C22⋊D17C2semidirect
3. C24×Dic17C2semidirect
4. C2×#10587625C2direct (N × H)
5. C22×#63225C2semidirect
6. C22×C22⋊Dic17C2semidirect
7. C22×#63227C2semidirect
8. C23×D4×C17C2semidirect
13. C22×D4×C17C22semidirect
17. C22×C22⋊D17C22semidirect
18. C22×C22⋊D17C22semidirect
23. C23×Dic17C22semidirect
24. C2×C22⋊Dic17C22semidirect
25. #10587625C22direct (N × H)
26. C2×#63227C22semidirect
27. C2×#63225C22semidirect
33. C24×C17D4semidirect
42. C2×D4×C17C23semidirect
47. C2×C22⋊D17C23semidirect
48. C2×C22⋊D17C23semidirect
52. C22×Dic17D4semidirect
56. C22×Dic17C23semidirect
57. C22⋊Dic17C23semidirect
58. #63227C23semidirect
59. #63225C23semidirect
69. C23×C17C2×D4semidirect
87. C2×Dic17C2×D4semidirect
99. C22×C17#121semidirect
102. C22×C17C22×D4semidirect
112. Dic17C22×D4semidirect
115. C23×D4D17semidirect
123. C2×C17C2×#121semidirect
136. C22×D4C2×D17semidirect
147. C17C22×#121semidirect
157. C24C22⋊D17semidirect
166. C2×D4C22×D17semidirect
195. C23C2×C22⋊D17semidirect
222. C22#10587625direct (N × H)
226. C22C22×C22⋊D17semidirect
235. C2C2×#10587625direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D172
C24×Dic172
C2×#105876252
C22×#632252
C22×C22⋊Dic172
C22×#632272
C23×D4×C172
C22×#12117