Finite Group Databasebeta

← #16944898

Subgroups — #16944898

Order 4352.

480 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C4×#10587505C211yesmaximal, characteristic
2#14527122C211yesmaximal, characteristic
3#14526784C214yesmaximal, complemented
4C17×#2547C211yesmaximal, characteristic
5C2×#10587505—21no—
6#11762773—21no—
7C4×C22⋊Dic17—21no—
8#11762576C2212yes—
9#11762535—21no—
10#11762533C2212yes—
11C2×C17×C4⋊Q8C411yescharacteristic, complemented
12C2×C17×#124—21no—
13C2×C4×D4×C17C2211yescharacteristic
14C17×#397C412yescomplemented
15C17×#397C2212yes—
16C17×#391—21no—
17C17×#380—21no—
18C17×#380—21no—
19C4×C4⋊C4×C17C411yescharacteristic, complemented
20C22×Q8×C17—21no—
21C22×D4×C17D411yescharacteristic
22C23×C4×C17D411yescharacteristic
23C23×C4×C17D411yescharacteristic
24C17×C4⋊Q8—41no—
25C17×C4⋊Q8—41no—
26C17×#124—44no—
27C4×D4×C17—41no—
28C4×D4×C17—41no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17C2×C412yes—
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C22⋊C4×C17—22no—
34C2×C22⋊C4×C17—22no—
35C2×C22⋊C4×C17C2×C411yescharacteristic
36C2×C22⋊C4×C17C2311yescharacteristic
37C2×C42×C17—21no—
38C2×C42×C17C2×C411yescharacteristic
39C2×C22⋊Dic17—22no—
40C2×C4×Dic17—41no—
41C2×#63223—41no—
42C17×#95—22no—
43C17×#95—22no—
44C17×#95C2×C412yes—
45#10587505—24no—
46#10587502—41no—
47C22⋊#3622—22no—
48C22⋊#3622—41no—
49C24×C17C22⋊C411yescharacteristic
50C24×C17C2×D411yescharacteristic
51C2×Q8×C17—42no—
52C2×Q8×C17—42no—
53C2×Q8×C17—42no—
54C2×D4×C17—22no—
55C2×D4×C17—22no—
56C2×D4×C17—41no—
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—22no—
62C22×C4×C17—22no—
63C22×C4×C17—42no—
64C22×C4×C17—42no—
65C22×C4×C17C22⋊C411yescharacteristic
66C22×C4×C17C22⋊C411yescharacteristic
67C22×C4×C17C22⋊C411yescharacteristic
68C22×C4×C17C22×C411yescharacteristic
69C22×C4×C17C2×D411yescharacteristic
70C22×Dic17—42no—
71C4⋊C4×C17—41no—
72C4⋊C4×C17—42no—
73C4⋊C4×C17—42no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C22⋊C4×C17—41no—
77C22⋊C4×C17—41no—
78C22⋊C4×C17—44no—
79C22⋊C4×C17—44no—
80C42×C17—21no—
81C42×C17—21no—
82C42×C17—42no—
83C22⋊Dic17—24no—
84C22⋊Dic17—42no—
85C4×Dic17—82no—
86#63223—82no—
87C2×#3622—42no—
88#11777—171nomaximal, Sylow
89C23×C17—21no—
90C23×C17—21no—
91C23×C17—21no—
92C23×C17—21no—
93C23×C17—21no—
94C23×C17—41no—
95C23×C17—41no—
96C23×C17—41no—
97C23×C17—41no—
98C23×C17C2×C22⋊C411yescharacteristic
99C23×C17AGL(1,ℤ/8)12yes—
100Q8×C17—84no—
101D4×C17—44no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—22no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—42no—
109C2×C4×C17—42no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—42no—
114C2×C4×C17—42no—
115C2×C4×C17—42no—
116C2×C4×C17—42no—
117C2×C4×C17—42no—
118C2×C4×C17—42no—
119C2×C4×C17—81no—
120C2×C4×C17—81no—
121C2×C4×C17#9911yescharacteristic
122C2×C4×C17#9911yescharacteristic
123C2×C4×C17#10412yes—
124C2×Dic17—44no—
125C2×Dic17—82no—
126C2×Dic17—82no—
127#3622—82no—
128#2547D1711yescharacteristic
129C4×#99—171no—
130#1465—171no—
131#1344—174no—
132C22×C17—21no—
133C22×C17—21no—
134C22×C17—22no—
135C22×C17—42no—
136C22×C17—42no—
137C22×C17—41no—
138C22×C17—41no—
139C22×C17—41no—
140C22×C17—41no—
141C22×C17—41no—
142C22×C17—81no—
143C22×C17—81no—
144C22×C17C2×#9911yescharacteristic
145C22×C17#41811yescharacteristic
146C22×C17C2×#10411yescharacteristic
147C4×C17—21no—
148C4×C17—22no—
149C4×C17—41no—
150C4×C17—41no—
151C4×C17—41no—
152C4×C17—82no—
153C4×C17—82no—
154C4×C17#35412yes—
155Dic17—84no—
156C2×C4⋊Q8Dic1711yescharacteristic, complemented
157C2×#124—21no—
158C2×C4×D4C2×D1711yescharacteristic
159C2×#99—341no—
160#407—341no—
161#397Dic1712yescomplemented
162#397C2×D1712yes—
163#391—21no—
164#380—21no—
165#380—21no—
166C4×C4⋊C4Dic1711yescharacteristic, complemented
167C4×C22⋊C4—341no—
168#342—172no—
169#324—341no—
170#323—172no—
171C2×C17—21no—
172C2×C17—21no—
173C2×C17—42no—
174C2×C17—81no—
175C2×C17#150711yescharacteristic
176C2×C17#212311yescharacteristic
177C2×C17C2×#35411yescharacteristic
178C22×Q8—21no—
179C22×D4C22⋊D1711yescharacteristic
180C23×C4C22⋊D1711yescharacteristic
181C23×C4C22⋊D1711yescharacteristic
182C2×M16—681no—
183C4⋊Q8—41no—
184C4⋊Q8—41no—
185#124—44no—
186C4×D4—41no—
187C4×D4—41no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C2×Dic1712yes—
191C2×C4⋊C4C22⋊D1711yescharacteristic
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—342no—
195C2×C22⋊C4C2×Dic1711yescharacteristic
196C2×C22⋊C4C22×D1711yescharacteristic
197C2×C42—21no—
198C2×C42—681no—
199C2×C42C2×Dic1711yescharacteristic
200#99—344no—
201C22⋊C8—342no—
202C22⋊C8—681no—
203#95—22no—
204#95—22no—
205#95—681no—
206#95C2×Dic1712yes—
207C17#1177711yescharacteristic, complemented, Sylow
208C24C22⋊Dic1711yescharacteristic
209C24C2×C22⋊D1711yescharacteristic
210C2×Q8—42no—
211C2×Q8—42no—
212C2×Q8—42no—
213C2×D4—22no—
214C2×D4—22no—
215C2×D4—41no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—682no—
225C22×C4C22⋊Dic1711yescharacteristic
226C22×C4C22⋊Dic1711yescharacteristic
227C22×C4C22⋊Dic1711yescharacteristic
228C22×C4C22×Dic1711yescharacteristic
229C22×C4C2×C22⋊D1711yescharacteristic
230M16—1362no—
231C2×C8—682no—
232C4⋊C4—41no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—44no—
240C22⋊C4—44no—
241C22⋊C4—344no—
242C22⋊C4—682no—
243C42—21no—
244C42—21no—
245C42—42no—
246C42—1362no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23#1058761812yes—
257C23C2×C22⋊Dic1711yescharacteristic
258Q8—84no—
259D4—44no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—684no—
280C2×C4—1362no—
281C2×C4—1362no—
282C2×C4#1058750511yescharacteristic
283C2×C4#1058750511yescharacteristic
284C2×C4#1058750812yes—
285C8—1362no—
286C22—21no—
287C22—21no—
288C22—22no—
289C22—42no—
290C22—42no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—81no—
297C22—81no—
298C22C2×#1058750511yescharacteristic
299C22#1176281411yescharacteristic
300C22C2×#1058750811yescharacteristic
301C4—22no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—82no—
307C4—82no—
308C4—1364no—
309C4#1176260412yes—
310C2—21no—
311C2—21no—
312C2—42no—
313C2—81no—
314C2#1452730011yescharacteristic
315C2#1453043811yescharacteristic
316C2C2×#1176260411yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#2547C2
socleC22×C17C2×#99
prime radicalC22×D4×C17D4
cosocleC2×C22⋊C4×C17C23
hypercenter#2547D17
hypocenterC17#11777
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2547

Complements

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

NH ≅ G/Ntype
3. #14526784C2semidirect
11. C2×C17×C4⋊Q8C4semidirect
14. C17×#397C4semidirect
19. C4×C4⋊C4×C17C4semidirect
156. C2×C4⋊Q8Dic17semidirect
161. #397Dic17semidirect
166. C4×C4⋊C4Dic17semidirect
207. C17#11777semidirect

Maximal subgroups

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

subgroupindex
C4×#105875052
#145271222
#145267842
C17×#25472
#1177717