Finite Group Databasebeta

← #16944749

Subgroups — #16944749

Order 4352.

352 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14530587C211yesmaximal, characteristic, complemented
2C4×#10587489C211yesmaximal, characteristic, complemented
3#14526796C212yesmaximal, complemented
4#14526793C212yesmaximal
5C17×#3168C211yesmaximal, characteristic
6C2×#10587489—21no—
7C4×C4⋊Dic17—21no—
8C4⋊#63214—21no—
9C22⋊#63214C2212yes—
10#11762585—21no—
11#11762572C2212yes—
12C17×#529—21no—
13C17×#499C411yescharacteristic, complemented
14C17×#495C411yescharacteristic, complemented
15C17×#488—21no—
16C17×#467C2211yescharacteristic
17C17×#466C2211yescharacteristic
18C17×#465—21no—
19C4×Q16×C17C411yescharacteristic, complemented
20C4×SD16×C17—21no—
21C4×D8×C17C411yescharacteristic, complemented
22C2×C4×C8×C17C2211yescharacteristic
23C2×Q16×C17C2×C411yescharacteristic
24C2×SD16×C17—21no—
25C2×D8×C17C2×C411yescharacteristic
26C22×C8×C17D411yescharacteristic
27C22×C8×C17C2311yescharacteristic
28C17×#126—41no—
29C17×#125—21no—
30C17×#124—21no—
31C17×#123—41no—
32C17×C22⋊Q8—21no—
33C17×#121—21no—
34C4×Q8×C17—21no—
35C4×D4×C17—21no—
36C4×D4×C17—41no—
37C17×#117—41no—
38C2×C42×C17D411yescharacteristic
39C2×C4⋊Dic17—22no—
40C2×C4×Dic17—41no—
41C17×#107C2×C411yescharacteristic
42C17×#107C2×C411yescharacteristic
43C17×#106—21no—
44C17×#103—21no—
45C17×#103—21no—
46C17×#102—21no—
47C17×#102—21no—
48C4×C8×C17C2×C411yescharacteristic
49C4×C8×C17C2×C411yescharacteristic
50C4×C8×C17D411yescharacteristic
51C4×C8×C17D411yescharacteristic
52#10587502—41no—
53#10587489—24no—
54C2×#63214—22no—
55C2×Q8×C17—21no—
56C2×D4×C17—21no—
57C2×D4×C17—41no—
58C22×C4×C17—41no—
59C22×C4×C17D811yescharacteristic
60C22×C4×C17D811yescharacteristic
61C22×C4×C17C2×D411yescharacteristic
62C22×Dic17—42no—
63Q16×C17—41no—
64SD16×C17—42no—
65D8×C17—41no—
66C2×C8×C17—22no—
67C2×C8×C17—41no—
68C2×C8×C17C22⋊C411yescharacteristic
69C2×C8×C17C22⋊C411yescharacteristic
70C2×C8×C17C22×C411yescharacteristic
71C2×C8×C17C2×D411yescharacteristic
72C4⋊C4×C17—21no—
73C4⋊C4×C17—21no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—41no—
78C22⋊C4×C17—41no—
79C22⋊C4×C17—41no—
80C22⋊C4×C17—41no—
81C22⋊C4×C17—41no—
82C22⋊C4×C17—41no—
83C42×C17—41no—
84C42×C17C22⋊C411yescharacteristic
85C42×C17C22⋊C411yescharacteristic
86C42×C17SD1611yescharacteristic
87C42×C17SD1611yescharacteristic
88C4⋊Dic17—24no—
89C4⋊Dic17—42no—
90C4×Dic17—82no—
91#63214—42no—
92#11746—171nomaximal, Sylow
93C23×C17—41no—
94C23×C17C2×D811yescharacteristic
95Q8×C17—41no—
96Q8×C17—41no—
97D4×C17—41no—
98D4×C17—41no—
99D4×C17—81no—
100D4×C17—81no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17—82no—
110C2×C4×C17#10211yescharacteristic
111C2×C4×C17#10211yescharacteristic
112C2×C4×C17#10211yescharacteristic
113C2×C4×C17#10211yescharacteristic
114C2×C4×C17C2×C22⋊C411yescharacteristic
115C2×C4×C17C2×SD1611yescharacteristic
116C2×Dic17—44no—
117C2×Dic17—82no—
118C2×Dic17—82no—
119C8×C17—21no—
120C8×C17—21no—
121C8×C17—21no—
122C8×C17#10412yes—
123#3168D1711yescharacteristic
124#2163—171no—
125C4×#107—171no—
126#1348—172no—
127#1347—172no—
128C22×C17—21no—
129C22×C17—21no—
130C22×C17—81no—
131C22×C17—81no—
132C22×C17—81no—
133C22×C17C2×#10211yescharacteristic
134C22×C17#50911yescharacteristic
135C22×C17#51011yescharacteristic
136C4×C17—21no—
137C4×C17—21no—
138C4×C17—21no—
139C4×C17—21no—
140C4×C17—21no—
141C4×C17—81no—
142C4×C17—81no—
143C4×C17—81no—
144C4×C17#41011yescharacteristic
145C4×C17C2×#10411yescharacteristic
146Dic17—84no—
147#529—21no—
148#499Dic1711yescharacteristic, complemented
149#495Dic1711yescharacteristic, complemented
150#488—21no—
151#467C2×D1711yescharacteristic
152#466C2×D1711yescharacteristic
153#465—21no—
154C4×Q16Dic1711yescharacteristic, complemented
155C4×SD16—21no—
156C4×D8Dic1711yescharacteristic, complemented
157C2×#107—341no—
158C2×C4×C8C2×D1711yescharacteristic
159C4×C4⋊C4—341no—
160C4⋊C16—341no—
161C22⋊C16—172no—
162#346—341no—
163#340—172no—
164C2×C17—21no—
165C2×C17—21no—
166C2×C17—161no—
167C2×C17#150211yescharacteristic
168C2×C17#213911yescharacteristic
169C2×C17#214511yescharacteristic
170C2×Q16C2×Dic1711yescharacteristic
171C2×SD16—21no—
172C2×D8C2×Dic1711yescharacteristic
173C22×C8C22⋊D1711yescharacteristic
174C22×C8C22×D1711yescharacteristic
175#126—41no—
176#125—21no—
177#124—21no—
178#123—41no—
179C22⋊Q8—21no—
180#121—21no—
181C4×Q8—21no—
182C4×D4—21no—
183C4×D4—41no—
184#117—41no—
185C2×C4⋊C4—342no—
186C2×C42—681no—
187C2×C42C22⋊D1711yescharacteristic
188C2×C16—342no—
189#107—344no—
190#107C2×Dic1711yescharacteristic
191#107C2×Dic1711yescharacteristic
192#106—21no—
193#103—21no—
194#103—21no—
195#102—21no—
196#102—21no—
197C4×C8C2×Dic1711yescharacteristic
198C4×C8C2×Dic1711yescharacteristic
199C4×C8C22⋊D1711yescharacteristic
200C4×C8C22⋊D1711yescharacteristic
201#95—681no—
202C17#1174611yescharacteristic, complemented, Sylow
203C2×Q8—21no—
204C2×D4—21no—
205C2×D4—41no—
206C22×C4—41no—
207C22×C4—682no—
208C22×C4#6322811yescharacteristic
209C22×C4#6322811yescharacteristic
210C22×C4C2×C22⋊D1711yescharacteristic
211Q16—41no—
212SD16—42no—
213D8—41no—
214C2×C8—22no—
215C2×C8—41no—
216C2×C8C22⋊Dic1711yescharacteristic
217C2×C8C22⋊Dic1711yescharacteristic
218C2×C8C22×Dic1711yescharacteristic
219C2×C8C2×C22⋊D1711yescharacteristic
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—344no—
227C4⋊C4—682no—
228C22⋊C4—41no—
229C22⋊C4—41no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C42—41no—
234C42—1362no—
235C42#6322911yescharacteristic
236C42#6322911yescharacteristic
237C42C22⋊Dic1711yescharacteristic
238C42C22⋊Dic1711yescharacteristic
239C16—682no—
240C23—41no—
241C23C2×#6322811yescharacteristic
242Q8—41no—
243Q8—41no—
244D4—41no—
245D4—41no—
246D4—81no—
247D4—81no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—82no—
257C2×C4—684no—
258C2×C4—1362no—
259C2×C4—1362no—
260C2×C4#1058750311yescharacteristic
261C2×C4#1058750311yescharacteristic
262C2×C4#1058750311yescharacteristic
263C2×C4#1058750311yescharacteristic
264C2×C4C2×#6322911yescharacteristic
265C2×C4C2×C22⋊Dic1711yescharacteristic
266C8—21no—
267C8—21no—
268C8—21no—
269C8#1058750812yes—
270C22—21no—
271C22—21no—
272C22—81no—
273C22—81no—
274C22—81no—
275C22C2×#1058750311yescharacteristic
276C22#1176324411yescharacteristic
277C22#1176324911yescharacteristic
278C4—21no—
279C4—21no—
280C4—21no—
281C4—21no—
282C4—21no—
283C4—81no—
284C4—81no—
285C4—81no—
286C4—1364no—
287C4#1176278311yescharacteristic
288C4C2×#1058750811yescharacteristic
289C2—21no—
290C2—21no—
291C2—161no—
292C2#1452727911yescharacteristic
293C2#1453049611yescharacteristic
294C2#1453052011yescharacteristic
subgroupG/H
centerC22C2×#10587503
commutatorC2×C8×C17C22×C4
FrattiniC22×C8C22×D17
FittingC17×#3168C2
socleC22×C17C2×#102
prime radicalC17×#466C22
cosocleC22×C8×C17C23
hypercenter#3168D17
hypocenterC17#11746
LCSG ▷ C2×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #14530587C2semidirect
2. C4×#10587489C2semidirect
3. #14526796C2semidirect
13. C17×#499C4semidirect
14. C17×#495C4semidirect
19. C4×Q16×C17C4semidirect
21. C4×D8×C17C4semidirect
148. #499Dic17semidirect
149. #495Dic17semidirect
154. C4×Q16Dic17semidirect
156. C4×D8Dic17semidirect
202. C17#11746semidirect

Maximal subgroups

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

subgroupindex
#145305872
C4×#105874892
#145267962
#145267932
C17×#31682
#1174617