Finite Group Databasebeta

← #17010442

Subgroups — #17010442

Order 4352.

982 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 163 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
1C2×#11763545C211yesmaximal, characteristic
2#14538910C212yesmaximal, complemented
3#14527967C218yesmaximal, complemented
4#14527498C211yesmaximal, characteristic
5#14527232C212yesmaximal, complemented
6C17×#3138C211yesmaximal, characteristic
7#11763545—24no—
8#11763545—22no—
9#11763545C2214yes—
10C2×#10587622—22no—
11C2×#10587621—22no—
12C2×C4×Dic34C2212yes—
13C2×D4×Dic17—22no—
14#11763137—22no—
15#11763091C2214yescomplemented
16#11763016C2214yescomplemented
17#11762964—22no—
18#11762914—24no—
19#11762866C2212yes—
20#11762553C2214yes—
21#11762541C2218yescomplemented
22C17×#533C2211yescharacteristic
23C2×C17×#127C2211yescharacteristic
24C17×#490—22no—
25C17×#486C2214yes—
26C17×#418—22no—
27C4×M16×C17C2211yescharacteristic
28C22×D4×C17—22no—
29C22×D4×C17D412yes—
30C23×Dic17—22no—
31C22×Dic34D412yes—
32C2×M16×C17—21no—
33C17×C4⋊Q8C2312yes—
34C17×#127—22no—
35C17×#127D412yes—
36C17×#127C2312yes—
37C17×#125—21no—
38C17×C22⋊Q8—22no—
39C4×Q8×C17—22no—
40C17×#117—21no—
41C2×C42×C17C2311yescharacteristic
42C2×C22⋊Dic17—24no—
43C2×C22⋊Dic17—22no—
44C2×#63231—24no—
45#10587622—28no—
46#10587622—28no—
47#10587621—28no—
48#10587621—28no—
49D4×Dic17—28no—
50D4×Dic17—28no—
51C2×C4⋊Dic17D412yes—
52C2×#63225—22no—
53C2×C4×Dic17—22no—
54C4×Dic34—22no—
55C4×Dic34—22no—
56C4×Dic34D414yes—
57C4×Dic34C2314yes—
58C17×#102—28no—
59C17×#97—21no—
60C4×C8×C17C2312yes—
61#10587506—24no—
62C22⋊#3622—22no—
63#10587481—24no—
64#10587479—24no—
65C4⋊#3622C2314yes—
66#10587474—22no—
67C24×C17—22no—
68C2×Q8×C17—22no—
69C2×D4×C17—24no—
70C2×D4×C17—22no—
71C2×D4×C17—24no—
72C2×D4×C17—48no—
73C2×D4×C17—44no—
74C2×D4×C17C2×D414yes—
75C22×C4×C17C2×D412yes—
76C22×C4×C17C2×D411yescharacteristic
77C22×Dic17—22no—
78C22×Dic17—22no—
79C22×Dic17—28no—
80C22×Dic17—84no—
81C2×Dic34—22no—
82C2×Dic34—44no—
83C2×Dic34C2×D414yes—
84M16×C17—42no—
85C2×C8×C17—22no—
86C4⋊C4×C17—22no—
87C4⋊C4×C17—22no—
88C4⋊C4×C17—42no—
89C22⋊C4×C17—41no—
90C42×C17—41no—
91C42×C17C2×D412yes—
92C42×C17C2×D411yescharacteristic
93C42×C17C2411yescharacteristic
94C22⋊Dic17—216no—
95C22⋊Dic17—28no—
96#63231—48no—
97C4⋊Dic17—22no—
98C4⋊Dic17C2×D414yes—
99#63225—24no—
100#63225—24no—
101C4×Dic17—24no—
102C4×Dic17—24no—
103C2×#3622—24no—
104#18531—171nomaximal, Sylow
105C23×C17—24no—
106C23×C17—48no—
107C23×C17—44no—
108C23×C17#12011yescharacteristic
109Q8×C17—44no—
110D4×C17—44no—
111D4×C17—48no—
112D4×C17—48no—
113D4×C17—82no—
114C2×C4×C17—22no—
115C2×C4×C17—24no—
116C2×C4×C17—42no—
117C2×C4×C17#12011yescharacteristic
118C2×C4×C17#12012yes—
119C2×C4×C17C22×D412yes—
120C2×C4×C17C22×D411yescharacteristic
121C2×Dic17—24no—
122C2×Dic17—24no—
123C2×Dic17—44no—
124C2×Dic17—44no—
125C2×Dic17—88no—
126Dic34—24no—
127Dic34—24no—
128Dic34—44no—
129C8×C17—42no—
130#3622—44no—
131C2×#559—171no—
132#3138D1711yescharacteristic
133#3113—172no—
134#1640—178no—
135#1555—171no—
136#1491—172no—
137C22×C17—22no—
138C22×C17—48no—
139C22×C17—44no—
140C22×C17—88no—
141C22×C17#45512yes—
142C22×C17C2×#12011yescharacteristic
143C4×C17—22no—
144C4×C17—21no—
145C4×C17—21no—
146C4×C17—82no—
147C4×C17#57514yes—
148Dic17—44no—
149Dic17—44no—
150#559—174no—
151#559—344no—
152#559—342no—
153#533C2×D1711yescharacteristic
154C2×#127C2×D1711yescharacteristic
155C2×#124—342no—
156C2×#123—342no—
157C2×C4×Q8—172no—
158C2×C4×D4—342no—
159#490—22no—
160#486C2×D1714yes—
161#483—342no—
162#475—174no—
163#462—174no—
164#451—342no—
165#441—344no—
166#432—172no—
167#418—22no—
168C4×M16C2×D1711yescharacteristic
169#331—174no—
170Q8⋊C8—178no—
171C2×C17—22no—
172C2×C17—84no—
173C2×C17#300512yes—
174C2×C17C2×#45511yescharacteristic
175C22×Q8—172no—
176C22×D4—22no—
177C22×D4C22⋊D1712yes—
178C23×C4—342no—
179C2×Q16—344no—
180C2×M16—21no—
181C4⋊Q8C22×D1712yes—
182#127—22no—
183#127C22⋊D1712yes—
184#127C22×D1712yes—
185#125—21no—
186#124—348no—
187#124—348no—
188#123—348no—
189#123—348no—
190C22⋊Q8—22no—
191C4×Q8—22no—
192C4×Q8—174no—
193C4×Q8—174no—
194C4×Q8—342no—
195C4×Q8—342no—
196C4×D4—348no—
197C4×D4—348no—
198#117—21no—
199C2×C4⋊C4—172no—
200C2×C4⋊C4—342no—
201C2×C22⋊C4—344no—
202C2×C22⋊C4—342no—
203C2×C42—342no—
204C2×C42C22×D1711yescharacteristic
205#106—344no—
206C4⋊C8—174no—
207#103—344no—
208#103—344no—
209#102—28no—
210C22⋊C8—342no—
211#97—21no—
212#97—342no—
213C4×C8C22×D1712yes—
214C17#1853111yescharacteristic, complemented, Sylow
215C24—22no—
216C2×Q8—22no—
217C2×Q8—174no—
218C2×Q8—342no—
219C2×Q8—684no—
220C2×D4—24no—
221C2×D4—24no—
222C2×D4—22no—
223C2×D4—48no—
224C2×D4—44no—
225C2×D4C2×C22⋊D1714yes—
226C22×C4—342no—
227C22×C4—342no—
228C22×C4—348no—
229C22×C4—1364no—
230C22×C4D4×D1712yes—
231C22×C4C2×C22⋊D1711yescharacteristic
232Q16—688no—
233M16—42no—
234C2×C8—22no—
235C2×C8—344no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—42no—
239C4⋊C4—174no—
240C4⋊C4—344no—
241C4⋊C4—342no—
242C4⋊C4—344no—
243C22⋊C4—41no—
244C22⋊C4—3416no—
245C22⋊C4—348no—
246C42—41no—
247C42—344no—
248C42—344no—
249C42D4×D1712yes—
250C42C2×C22⋊D1711yescharacteristic
251C42C23×D1711yescharacteristic
252C23—24no—
253C23—48no—
254C23—44no—
255C23#1058762311yescharacteristic
256Q8—44no—
257Q8—344no—
258Q8—344no—
259Q8—684no—
260D4—44no—
261D4—48no—
262D4—48no—
263D4—82no—
264C2×C4—22no—
265C2×C4—24no—
266C2×C4—42no—
267C2×C4—344no—
268C2×C4—344no—
269C2×C4—684no—
270C2×C4—684no—
271C2×C4—1368no—
272C2×C4#1058762311yescharacteristic
273C2×C4#1058762312yes—
274C2×C4C2×D4×D1712yes—
275C2×C4C22×C22⋊D1711yescharacteristic
276C8—42no—
277C8—684no—
278C22—22no—
279C22—48no—
280C22—44no—
281C22—88no—
282C22#1176298612yes—
283C22C2×#1058762311yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—82no—
288C4—684no—
289C4—684no—
290C4#1176360514yes—
291C2—22no—
292C2—84no—
293C2#1453802312yes—
294C2C2×#1176298611yescharacteristic
subgroupG/H
centerC22C2×#10587623
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
FittingC17×#3138C2
socleC22×C17C2×#120
prime radicalC2×C17×#127C22
hypercenter#3138D17
hypocenterC17#18531
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3138

Complements

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

NH ≅ G/Ntype
2. #14538910C2semidirect
3. #14527967C2semidirect
5. #14527232C2semidirect
15. #11763091C22semidirect
16. #11763016C22semidirect
21. #11762541C22semidirect
214. C17#18531semidirect

Maximal subgroups

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

subgroupindex
C2×#117635452
#145389102
#145279672
#145274982
#145272322
C17×#31382
#1853117