Finite Group Databasebeta

← C2×#14536781 #17240442

Subgroups — C2×#14536781 #17240442

Order 4352.

4438 conjugacy classes of subgroups; only the 667 normal subgroups are shown.

normal subgroups only

This group has 4438 conjugacy classes of subgroups — too many to draw. Only its 667 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
1C22×#10587639C212yesmaximal, complemented
2#14536781C2116yesmaximal, direct product factor
3C2×#11762734C213yesmaximal, complemented
4C2×#11762725C216yesmaximal, complemented
5C2×#11762718C213yesmaximal, complemented
6C2×C17×#379C211yesmaximal, characteristic, complemented
7C23×D68C2211yescharacteristic, complemented
8C23×C22⋊D17C2216yes—
9C2×#10587639—216no—
10C2×#10587639C22116yescomplemented
11C22×C4⋊Dic17C2213yescomplemented
12C22×C22⋊Dic17C2216yes—
13C22×#63227C2216yescomplemented
14#11762734C22124yescomplemented
15#11762725C22148yescomplemented
16#11762718C22124yescomplemented
17C2×#10587502C2213yescomplemented
18C2×#10587502C2213yescomplemented
19C26×C17C2211yescharacteristic
20C22×C22⋊C4×C17C2213yes—
21C22×C22⋊C4×C17C2213yes—
22C17×#379C2218yescomplemented
23C25×C17—46no—
24C25×C17—46no—
25C25×C17D418yescomplemented
26C25×C17C2313yes—
27C25×C17C2314yes—
28C24×D17C2312yes—
29C23×C4×C17C2313yes—
30C23×C4×C17C2311yescharacteristic
31C22×C22⋊D17—224no—
32C22×C22⋊D17—412no—
33C22×C22⋊D17—412no—
34C22×C22⋊D17C23124yes—
35C23×Dic17C2316yes—
36C22×D68—46no—
37C22×D68C2314yescomplemented
38C2×C22⋊C4×C17—46no—
39C2×C22⋊C4×C17—46no—
40C2×C22⋊C4×C17C23112yes—
41C2×C22⋊C4×C17C23112yes—
42#10587639—264no—
43C2×C22⋊Dic17—224no—
44C2×C22⋊Dic17C23124yes—
45C2×#63227—412no—
46C2×#63227C23124yescomplemented
47C2×C4⋊Dic17—46no—
48C2×C4⋊Dic17C23112yescomplemented
49#10587502C23112yescomplemented
50#10587502C23112yescomplemented
51C24×C17—212no—
52C24×C17—212no—
53C24×C17—26no—
54C24×C17—26no—
55C24×C17—448no—
56C24×C17—412no—
57C24×C17—412no—
58C24×C17—448no—
59C24×C17—416no—
60C24×C17C2×D4112yes—
61C24×C17C2×D4116yescomplemented
62C24×C17C2416yes—
63C24×C17C2411yescharacteristic
64C23×D17—24no—
65C23×D17—212no—
66C23×D17—212no—
67C23×D17C2414yes—
68C22×C4×C17—26no—
69C22×C4×C17—26no—
70C22×C4×C17—212no—
71C22×C4×C17C2412yes—
72C22×C4×C17C2416yes—
73C2×C22⋊D17—248no—
74C2×C22⋊D17—424no—
75C2×C22⋊D17—424no—
76C2×C22⋊D17—496no—
77C22×Dic17—212no—
78C22×Dic17—212no—
79C22×Dic17—212no—
80C22×Dic17C24112yes—
81C2×D68—412no—
82C2×D68—416no—
83C22⋊C4×C17—412no—
84C22⋊C4×C17—412no—
85C22⋊Dic17—248no—
86#63227—424no—
87C4⋊Dic17—412no—
88C2×#2812—171nomaximal, Sylow
89C23×C17—248no—
90C23×C17—224no—
91C23×C17—26no—
92C23×C17—26no—
93C23×C17—212no—
94C23×C17—212no—
95C23×C17—448no—
96C23×C17—448no—
97C23×C17—416no—
98C23×C17—4128no—
99C23×C17—412no—
100C23×C17—424no—
101C23×C17—412no—
102C23×C17C22×D4112yes—
103C23×C17C22×D412yes—
104C23×C17H(5,𝔽2)16yes—
105C23×C17H(5,𝔽2)16yes—
106C23×C17C2511yescharacteristic
107C22×D17—24no—
108C22×D17—212no—
109C22×D17—212no—
110C22×D17—424no—
111C22×D17—424no—
112C22×D17—48no—
113C2×C4×C17—26no—
114C2×C4×C17—26no—
115C2×C4×C17—212no—
116C2×C4×C17—412no—
117C2×C4×C17—44no—
118C22⋊D17—496no—
119C2×Dic17—212no—
120C2×Dic17—212no—
121C2×Dic17—212no—
122C2×Dic17—424no—
123D68—416no—
124C22×#120—172no—
125#2812—1716no—
126C2×#397—173no—
127C2×#394—176no—
128C2×#392—173no—
129C2×#379D1711yescharacteristic, complemented
130C22×C17—224no—
131C22×C17—212no—
132C22×C17—464no—
133C22×C17—412no—
134C22×C17—46no—
135C22×C17—46no—
136C22×C17—448no—
137C22×C17#534112yes—
138C22×C17#560112yes—
139C22×C17H(3,𝔽4)14yes—
140C22×C17C23×D411yescharacteristic
141C22×C17C2×H(5,𝔽2)13yes—
142C22×C17C2×H(5,𝔽2)13yes—
143C2×D17—412no—
144C2×D17—412no—
145C2×D17—44no—
146C2×D17—816no—
147C4×C17—46no—
148C4×C17—42no—
149Dic17—412no—
150C26C2×D1711yescharacteristic
151C23×D4—176no—
152C23×D4—171no—
153C2×#120—1716no—
154C2×#120—3416no—
155C22×C4⋊C4—173no—
156C22×C22⋊C4—176no—
157C22×C22⋊C4—176no—
158C22×C22⋊C4C2×D1713yes—
159C22×C22⋊C4C2×D1713yes—
160#397—1724no—
161#394—1748no—
162#392—1724no—
163#379C2×D1718yescomplemented
164C2×#95—173no—
165C2×#95—173no—
166C2×C17—412no—
167C2×C17#281218yescomplemented
168C2×C17C2×#53413yes—
169C2×C17C2×#56013yes—
170C2×C17C2×H(3,𝔽4)11yescharacteristic
171D17—84no—
172C25—46no—
173C25—46no—
174C25—172no—
175C25D6818yescomplemented
176C25C22×D1713yes—
177C25C22×D1714yes—
178C22×D4—1724no—
179C22×D4—174no—
180C22×D4—3424no—
181C22×D4—686no—
182C22×D4—6812no—
183C22×D4—6812no—
184C23×C4—176no—
185C23×C4C22×D1713yes—
186C23×C4C22×D1711yescharacteristic
187#120—3464no—
188C2×C4⋊C4—1712no—
189C2×C4⋊C4—686no—
190C2×C22⋊C4—46no—
191C2×C22⋊C4—46no—
192C2×C22⋊C4—1724no—
193C2×C22⋊C4—1724no—
194C2×C22⋊C4—3424no—
195C2×C22⋊C4—6812no—
196C2×C22⋊C4C22×D17112yes—
197C2×C22⋊C4C22×D17112yes—
198#95—1712no—
199#95—1712no—
200C17C2×#281211yescharacteristic, complemented, Sylow
201C24—26no—
202C24—26no—
203C24—212no—
204C24—212no—
205C24—448no—
206C24—412no—
207C24—412no—
208C24—448no—
209C24—416no—
210C24—174no—
211C24—344no—
212C24—3412no—
213C24—3412no—
214C24C2×D68112yes—
215C24C2×D68116yescomplemented
216C24C23×D1716yes—
217C24C23×D1711yescharacteristic
218C2×D4—3448no—
219C2×D4—6812no—
220C2×D4—6816no—
221C2×D4—6824no—
222C2×D4—6824no—
223C2×D4—6896no—
224C22×C4—212no—
225C22×C4—26no—
226C22×C4—26no—
227C22×C4—1712no—
228C22×C4—3412no—
229C22×C4—3412no—
230C22×C4—3412no—
231C22×C4C23×D1712yes—
232C22×C4C23×D1716yes—
233C4⋊C4—6812no—
234C22⋊C4—412no—
235C22⋊C4—412no—
236C22⋊C4—3448no—
237C22⋊C4—6824no—
238C23—248no—
239C23—224no—
240C23—26no—
241C23—26no—
242C23—212no—
243C23—212no—
244C23—448no—
245C23—448no—
246C23—416no—
247C23—4128no—
248C23—424no—
249C23—412no—
250C23—412no—
251C23—344no—
252C23—3412no—
253C23—3412no—
254C23—6824no—
255C23—688no—
256C23—6824no—
257C23C22×D68112yes—
258C23C22×D6812yes—
259C23#1058769116yes—
260C23#1058769116yes—
261C23C24×D1711yescharacteristic
262D4—6816no—
263D4—6896no—
264C2×C4—212no—
265C2×C4—26no—
266C2×C4—26no—
267C2×C4—412no—
268C2×C4—44no—
269C2×C4—3412no—
270C2×C4—3412no—
271C2×C4—3412no—
272C2×C4—6824no—
273C22—224no—
274C22—212no—
275C22—464no—
276C22—412no—
277C22—46no—
278C22—46no—
279C22—448no—
280C22—6812no—
281C22—6812no—
282C22—684no—
283C22—13616no—
284C22#11763371112yes—
285C22#11763548112yes—
286C22#1176355214yes—
287C22C23×D6811yescharacteristic
288C22C2×#1058769113yes—
289C22C2×#1058769113yes—
290C4—46no—
291C4—42no—
292C4—6812no—
293C2—412no—
294C2—1364no—
295C2#1453678118yesdirect product factor
296C2C2×#1176337113yes—
297C2C2×#1176354813yes—
298C2C2×#1176355211yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#379C2
socleC24×C17C24
hypercenterC2×#379D17
hypocenterC17C2×#2812
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C22×#10587639C2semidirect
2. #14536781C2direct (N × H)
3. C2×#11762734C2semidirect
4. C2×#11762725C2semidirect
5. C2×#11762718C2semidirect
6. C2×C17×#379C2semidirect
7. C23×D68C22semidirect
10. C2×#10587639C22semidirect
11. C22×C4⋊Dic17C22semidirect
13. C22×#63227C22semidirect
14. #11762734C22semidirect
15. #11762725C22semidirect
16. #11762718C22semidirect
17. C2×#10587502C22semidirect
18. C2×#10587502C22semidirect
22. C17×#379C22semidirect
25. C25×C17D4semidirect
37. C22×D68C23semidirect
46. C2×#63227C23semidirect
48. C2×C4⋊Dic17C23semidirect
49. #10587502C23semidirect
50. #10587502C23semidirect
61. C24×C17C2×D4semidirect
129. C2×#379D17semidirect
163. #379C2×D17semidirect
167. C2×C17#2812semidirect
175. C25D68semidirect
200. C17C2×#2812semidirect
215. C24C2×D68semidirect
295. C2#14536781direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876392
#145367812
C2×#117627342
C2×#117627252
C2×#117627182
C2×C17×#3792
C2×#281217