Finite Group Databasebeta

← #17958391

Subgroups — #17958391

Order 4352.

662 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 76 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#14544035C212yesmaximal, complemented
2#14543711C212yesmaximal, complemented
3#14543709C212yesmaximal
4#14531163C211yesmaximal, characteristic
5#11763829—22no—
6#11763654—22no—
7#11763652C2214yes—
8C23×C4×D17C411yescharacteristic
9C2×#10587612C2211yescharacteristic
10#11762670C411yescharacteristic
11#11762670C2211yescharacteristic
12#11762666—22no—
13#11762664C411yescharacteristic
14#11762664C2211yescharacteristic
15C4×#63227—22no—
16C2×C17×#117C411yescharacteristic
17C24×D17C2×C411yescharacteristic
18C23×C4×C17C2×C411yescharacteristic
19C23×Dic17C2×C411yescharacteristic
20C22×C4×D17—22no—
21C22×C4×D17—21no—
22C22×C4×D17—21no—
23C22×C4×D17—22no—
24C22×C4×D17—42no—
25C22×C4×D17—42no—
26C17×#117—42no—
27C2×C4⋊C4×C17—21no—
28C2×C22⋊C4×C17C2×C411yescharacteristic
29C2×C22⋊C4×C17C2×C411yescharacteristic
30C2×C42×C17—21no—
31C2×C22⋊Dic17C2×C411yescharacteristic
32C2×C22⋊Dic17C2311yescharacteristic
33C2×#63227—22no—
34C2×#63227—22no—
35#10587612—42no—
36C2×C4⋊Dic17D412yes—
37C2×C4×Dic17D412yes—
38C22⋊#3624—24no—
39#10587544—42no—
40#10587542—42no—
41#10587502—22no—
42#10587502—22no—
43C24×C17C22×C411yescharacteristic
44C23×D17—21no—
45C23×D17—21no—
46C23×D17—44no—
47C23×D17—41no—
48C23×D17—41no—
49C23×D17M1612yes—
50C22×C4×C17—21no—
51C22×C4×C17—21no—
52C22×C4×C17—22no—
53C22×C4×C17—22no—
54C22×C4×C17—21no—
55C22×C4×C17—21no—
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22⋊C411yescharacteristic
58C22×Dic17—21no—
59C22×Dic17—21no—
60C22×Dic17—41no—
61C22×Dic17—41no—
62C22×Dic17C22⋊C412yes—
63C22×Dic17M1612yes—
64C22×Dic17C2×D412yes—
65C2×C4×D17—24no—
66C2×C4×D17—24no—
67C2×C4×D17—48no—
68C2×C4×D17—42no—
69C2×C4×D17—42no—
70C2×C4×D17—48no—
71C2×C4×D17—42no—
72C2×C4×D17—42no—
73C2×#3624—44no—
74C4⋊C4×C17—42no—
75C22⋊C4×C17—41no—
76C22⋊C4×C17—41no—
77C42×C17—42no—
78C22⋊Dic17—41no—
79C22⋊Dic17—41no—
80#63227—44no—
81#63227—44no—
82C4⋊Dic17—42no—
83C4×Dic17—22no—
84C4×Dic17—22no—
85#11501—171nomaximal, Sylow
86C23×C17—21no—
87C23×C17—21no—
88C23×C17—42no—
89C23×C17C2×C22⋊C411yescharacteristic
90C23×C17C2×M1611yescharacteristic
91C23×C17C2×M1611yescharacteristic
92C22×D17—24no—
93C22×D17—22no—
94C22×D17—44no—
95C22×D17—44no—
96C22×D17—42no—
97C22×D17—42no—
98C22×D17—48no—
99C22×D17—44no—
100C22×D17—41no—
101C22×D17—41no—
102C22×D17—42no—
103C22×D17—44no—
104C2×C4×C17—24no—
105C2×C4×C17—24no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—42no—
111C2×C4×C17—42no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17#9912yes—
115C2×C4×C17#10012yes—
116C2×Dic17—22no—
117C2×Dic17—22no—
118C2×Dic17—22no—
119C2×Dic17—42no—
120C2×Dic17—41no—
121C2×Dic17—41no—
122C2×Dic17—42no—
123C2×Dic17—42no—
124C2×Dic17—42no—
125C4×D17—48no—
126C4×D17—48no—
127#3624—84no—
128#2280—171no—
129#1464—172no—
130#1317—172no—
131#1316—172no—
132C22×C17—22no—
133C22×C17—21no—
134C22×C17—21no—
135C22×C17—41no—
136C22×C17—41no—
137C22×C17—42no—
138C22×C17—42no—
139C22×C17#40711yescharacteristic
140C22×C17C2×#9911yescharacteristic
141C22×C17C2×#10011yescharacteristic
142C2×D17—24no—
143C2×D17—44no—
144C2×D17—42no—
145C2×D17—48no—
146C2×D17—44no—
147C2×D17—44no—
148C2×D17—42no—
149C2×D17—44no—
150C4×C17—22no—
151C4×C17—22no—
152C4×C17—81no—
153C4×C17—81no—
154Dic17—42no—
155Dic17—42no—
156Dic17—42no—
157C24×C4—171no—
158C2×#117—171no—
159C2×#117#59511yescharacteristic
160#432—342no—
161#381—171no—
162#381—171no—
163#380—342no—
164#379—171no—
165#379—171no—
166C4×C22⋊C4—342no—
167#324—342no—
168#323—174no—
169C2×C17—21no—
170C2×C17—21no—
171C2×C17—41no—
172C2×C17—41no—
173C2×C17#146211yescharacteristic
174C2×C17#212012yes—
175D17—44no—
176C25—171no—
177C23×C4—171no—
178C23×C4—342no—
179C23×C4—342no—
180C23×C4—341no—
181C23×C4—341no—
182C23×C4—682no—
183C23×C4—682no—
184C23×C4C2×#59511yescharacteristic
185#117—42no—
186#117—682no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—172no—
189C2×C22⋊C4—171no—
190C2×C22⋊C4—171no—
191C2×C22⋊C4—342no—
192C2×C22⋊C4—342no—
193C2×C22⋊C4C2×#59511yescharacteristic
194C2×C22⋊C4C2×#59511yescharacteristic
195C2×C42—21no—
196C2×C42—172no—
197C4⋊C8—682no—
198C22⋊C8—344no—
199#97—682no—
200#95—342no—
201#95—342no—
202C17#1150111yescharacteristic, complemented, Sylow
203C24—172no—
204C24—341no—
205C24—341no—
206C24—681no—
207C24—681no—
208C24—684no—
209C24C22×#59511yescharacteristic
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—172no—
217C22×C4—172no—
218C22×C4—172no—
219C22×C4—344no—
220C22×C4—344no—
221C22×C4—341no—
222C22×C4—341no—
223C22×C4—688no—
224C22×C4—688no—
225C22×C4—682no—
226C22×C4—682no—
227C22×C4—682no—
228C22×C4—682no—
229C22×C4—681no—
230C22×C4—681no—
231C22×C4C22⋊#59511yescharacteristic
232C22×C4C22⋊#59511yescharacteristic
233C2×C8—684no—
234C4⋊C4—42no—
235C4⋊C4—682no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—684no—
239C22⋊C4—684no—
240C22⋊C4—681no—
241C22⋊C4—681no—
242C42—42no—
243C42—342no—
244C42—342no—
245C23—21no—
246C23—21no—
247C23—42no—
248C23—344no—
249C23—342no—
250C23—682no—
251C23—682no—
252C23—682no—
253C23—684no—
254C23—684no—
255C23—684no—
256C23—688no—
257C23—684no—
258C23—681no—
259C23—681no—
260C23D17⋊M1611yescharacteristic
261C23D17⋊M1611yescharacteristic
262C23C2×C22⋊#59511yescharacteristic
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—342no—
274C2×C4—342no—
275C2×C4—342no—
276C2×C4—688no—
277C2×C4—688no—
278C2×C4—682no—
279C2×C4—681no—
280C2×C4—681no—
281C2×C4—682no—
282C2×C4—682no—
283C2×C4—682no—
284C2×C4#1058753912yes—
285C2×C4#1058755312yes—
286C8—1364no—
287C22—22no—
288C22—21no—
289C22—21no—
290C22—41no—
291C22—41no—
292C22—42no—
293C22—42no—
294C22—344no—
295C22—684no—
296C22—682no—
297C22—684no—
298C22—684no—
299C22—688no—
300C22—684no—
301C22—682no—
302C22#1176378111yescharacteristic
303C22C2×#1058753911yescharacteristic
304C22C2×#1058755311yescharacteristic
305C4—22no—
306C4—22no—
307C4—81no—
308C4—81no—
309C4—682no—
310C4—682no—
311C4—682no—
312C2—21no—
313C2—21no—
314C2—41no—
315C2—41no—
316C2—684no—
317C2#1454403111yescharacteristic
318C2#1454503712yes—
subgroupG/H
centerC22C2×#10587539
commutatorC24×C17C22×C4
FrattiniC24C22×#595
FittingC2×C17×#117C4
socleC22×C17C2×#99
prime radicalC24×D17C2×C4
cosocleC2×C22⋊Dic17C23
hypercenterC2×#117#595
hypocenterC17#11501
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #14544035C2semidirect
2. #14543711C2semidirect
202. C17#11501semidirect

Maximal subgroups

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

subgroupindex
#145440352
#145437112
#145437092
#145311632
#1150117