Finite Group Databasebeta

← D17×#2842 #17240733

Subgroups — D17×#2842 #17240733

Order 4352.

3294 conjugacy classes of subgroups; only the 579 normal subgroups are shown.

normal subgroups only

This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 579 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
1#14537049C214yesmaximal, complemented
2#14537048C213yesmaximal, complemented
3#14537047C218yesmaximal, complemented
4D17×#399C214yesmaximal, complemented
5D17×#396C218yesmaximal, complemented
6D17×#379C213yesmaximal
7C17×#2842C211yesmaximal, characteristic, complemented
8C25×D17C2211yescharacteristic
9C2×C4⋊C4×D17C22112yescomplemented
10C2×C22⋊C4×D17C22112yes—
11C2×C22⋊C4×D17C2216yes—
12#11762746C2214yescomplemented
13#11762745C22112yescomplemented
14#11762744C22112yescomplemented
15#11762733C2218yescomplemented
16#11762732C22124yescomplemented
17#11762731C22124yescomplemented
18#11762665C2213yes—
19#11762664C22112yes—
20#11762664C2216yes—
21#95×D17C2214yescomplemented
22C17×#399C2214yescomplemented
23C17×#396C2218yescomplemented
24C17×#379C2213yes—
25C25×C17C2311yescharacteristic
26C24×D17—412no—
27C24×D17Q818yes—
28C24×D17C2312yes—
29C24×D17C2311yescharacteristic
30C24×D17C2312yes—
31C24×D17C2311yescharacteristic
32C22×C4×D17C23112yes—
33C2×C4⋊C4×C17C23112yescomplemented
34C2×C22⋊C4×C17C23112yes—
35C2×C22⋊C4×C17C2316yes—
36C2×C22⋊Dic17C23112yes—
37C2×C22⋊Dic17C2316yes—
38C2×#63227C23124yes—
39C2×#63227C23112yes—
40C2×C4⋊Dic17C23112yescomplemented
41C2×#63225C23124yescomplemented
42C4⋊C4×D17—424no—
43C22⋊C4×D17—424no—
44C22⋊C4×D17—412no—
45C17×#95C2314yescomplemented
46#10587502C23112yescomplemented
47C24×C17—46no—
48C24×C17C2×Q814yes—
49C24×C17C2412yes—
50C24×C17C2411yescharacteristic
51C23×D17—224no—
52C23×D17—212no—
53C23×D17—448no—
54C23×D17—412no—
55C23×D17—46no—
56C23×D17—464no—
57C23×D17C2×Q818yes—
58C23×D17C2×Q814yes—
59C23×D17C2×Q818yes—
60C23×D17C2×Q814yes—
61C23×D17C2412yes—
62C23×D17C2411yescharacteristic
63C23×D17C2411yescharacteristic
64C22×C4×C17C24112yes—
65C22×Dic17C24112yes—
66C2×C4×D17—224no—
67C2×C4×D17—248no—
68C4⋊C4×C17—412no—
69C22⋊C4×C17—412no—
70C22⋊C4×C17—46no—
71C22⋊Dic17—46no—
72C22⋊Dic17—412no—
73#63227—412no—
74#63227—424no—
75C4⋊Dic17—412no—
76#63225—424no—
77C2×#2842—171nomaximal, Sylow
78C23×C17—26no—
79C23×C17—212no—
80C23×C17—412no—
81C23×C17—416no—
82C23×C17C22×Q814yes—
83C23×C17C22×Q812yes—
84C23×C17C2511yescharacteristic
85C22×D17—212no—
86C22×D17—26no—
87C22×D17—248no—
88C22×D17—224no—
89C22×D17—424no—
90C22×D17—412no—
91C22×D17—432no—
92C22×D17—416no—
93C22×D17—4128no—
94C22×D17—432no—
95C22×D17—416no—
96C22×D17C22×Q814yes—
97C22×D17C22×Q812yes—
98C22×D17C22×Q812yes—
99C22×D17H(5,𝔽2)112yes—
100C2×C4×C17—224no—
101C2×C4×C17—212no—
102C2×Dic17—212no—
103C2×Dic17—224no—
104C4×D17—448no—
105#2842—174no—
106#2842—178no—
107#2842—173no—
108#2842D1711yescharacteristic, direct product factor
109C2×#399—174no—
110C2×#396—178no—
111C2×#379—173no—
112C22×C17—26no—
113C22×C17—212no—
114C22×C17—416no—
115C22×C17—44no—
116C22×C17—48no—
117C22×C17C23×Q811yescharacteristic
118C22×C17C2×H(5,𝔽2)16yes—
119C2×D17—212no—
120C2×D17—26no—
121C2×D17—432no—
122C2×D17—416no—
123C2×D17—48no—
124C2×D17—44no—
125C2×D17—432no—
126C2×D17—416no—
127C2×D17#543112yes—
128C2×D17#560116yes—
129C4×C17—412no—
130Dic17—412no—
131C26—171no—
132C22×C4⋊C4—1712no—
133C22×C22⋊C4—1712no—
134C22×C22⋊C4—176no—
135#399—1712no—
136#399—1712no—
137#399—174no—
138#399C2×D1714yescomplemented
139#396—1724no—
140#396—1724no—
141#396—178no—
142#396C2×D1718yescomplemented
143#379—173no—
144#379—1712no—
145#379—176no—
146#379C2×D1713yes—
147C2×#95—174no—
148C2×C17—42no—
149C2×C17—44no—
150C2×C17C2×#54313yes—
151C2×C17C2×#56014yes—
152D17—44no—
153D17—42no—
154D17#284218yesdirect product factor
155C25—172no—
156C25—171no—
157C25—178no—
158C25—171no—
159C25—172no—
160C25—6812no—
161C25C22×D1711yescharacteristic
162C23×C4—1712no—
163C2×C4⋊C4—1724no—
164C2×C4⋊C4—1712no—
165C2×C4⋊C4—6824no—
166C2×C4⋊C4C22×D17112yescomplemented
167C2×C22⋊C4—1712no—
168C2×C22⋊C4—176no—
169C2×C22⋊C4—1724no—
170C2×C22⋊C4—1712no—
171C2×C22⋊C4—6824no—
172C2×C22⋊C4—6812no—
173C2×C22⋊C4C22×D17112yes—
174C2×C22⋊C4C22×D1716yes—
175#95—1712no—
176#95C22×D1714yescomplemented
177C17C2×#284211yescharacteristic, complemented, Sylow
178C24—46no—
179C24—171no—
180C24—178no—
181C24—174no—
182C24—172no—
183C24—171no—
184C24—174no—
185C24—178no—
186C24—3424no—
187C24—3412no—
188C24—6812no—
189C24—686no—
190C24—6848no—
191C24—6864no—
192C24Q8×D1714yes—
193C24C23×D1712yes—
194C24C23×D1711yescharacteristic
195C22×C4—1712no—
196C22×C4—3448no—
197C22×C4—3424no—
198C22×C4C23×D17112yes—
199C4⋊C4—412no—
200C4⋊C4—6824no—
201C4⋊C4—6812no—
202C22⋊C4—412no—
203C22⋊C4—46no—
204C22⋊C4—6824no—
205C22⋊C4—6812no—
206C22⋊C4—6812no—
207C22⋊C4—686no—
208C23—212no—
209C23—26no—
210C23—412no—
211C23—416no—
212C23—172no—
213C23—1712no—
214C23—174no—
215C23—172no—
216C23—3448no—
217C23—3424no—
218C23—3412no—
219C23—346no—
220C23—6824no—
221C23—6812no—
222C23—6832no—
223C23—6816no—
224C23—68128no—
225C23—6832no—
226C23—6816no—
227C23C2×Q8×D1714yes—
228C23C2×Q8×D1712yes—
229C23C24×D1711yescharacteristic
230C2×C4—224no—
231C2×C4—212no—
232C2×C4—3412no—
233C2×C4—3424no—
234C2×C4—6848no—
235C22—212no—
236C22—26no—
237C22—416no—
238C22—48no—
239C22—44no—
240C22—1716no—
241C22—1712no—
242C22—3412no—
243C22—346no—
244C22—6832no—
245C22—6816no—
246C22—6832no—
247C22—6816no—
248C22—688no—
249C22—684no—
250C22C22×Q8×D1711yescharacteristic
251C22H(5,𝔽2)×D1716yes—
252C4—412no—
253C4—6812no—
254C2—44no—
255C2—42no—
256C2—178no—
257C2—684no—
258C2—682no—
259C2D17×#54313yes—
260C2D17×#56014yes—
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2842C2
prime radicalC25×D17C22
hypercenter#2842D17
hypocenterC17C2×#2842
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2842

Complements

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

NH ≅ G/Ntype
1. #14537049C2semidirect
2. #14537048C2semidirect
3. #14537047C2semidirect
4. D17×#399C2semidirect
5. D17×#396C2semidirect
7. C17×#2842C2semidirect
9. C2×C4⋊C4×D17C22semidirect
12. #11762746C22semidirect
13. #11762745C22semidirect
14. #11762744C22semidirect
15. #11762733C22semidirect
16. #11762732C22semidirect
17. #11762731C22semidirect
21. #95×D17C22semidirect
22. C17×#399C22semidirect
23. C17×#396C22semidirect
33. C2×C4⋊C4×C17C23semidirect
40. C2×C4⋊Dic17C23semidirect
41. C2×#63225C23semidirect
45. C17×#95C23semidirect
46. #10587502C23semidirect
108. #2842D17direct (N × H)
138. #399C2×D17semidirect
142. #396C2×D17semidirect
154. D17#2842direct (N × H)
166. C2×C4⋊C4C22×D17semidirect
176. #95C22×D17semidirect
177. C17C2×#2842semidirect

Maximal subgroups

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

subgroupindex
#145370492
#145370482
#145370472
D17×#3992
D17×#3962
D17×#3792
C17×#28422
C2×#284217