Finite Group Databasebeta

← #17958390

Subgroups — #17958390

Order 4352.

662 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 74 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#14544036C212yesmaximal, complemented
2#14543711C212yesmaximal, complemented
3#14543708C212yesmaximal
4#14531162C211yesmaximal, characteristic
5#11763830—22no—
6#11763655—22no—
7#11763652C2214yes—
8C24×Dic17C411yescharacteristic
9C2×#10587563C411yescharacteristic
10C2×#10587563C2211yescharacteristic
11#11762670C411yescharacteristic
12#11762670C2211yescharacteristic
13#11762667—22no—
14#11762665C2211yescharacteristic
15C22⋊C4×Dic17—22no—
16C17×#379C411yescharacteristic
17C25×C17C2×C411yescharacteristic
18C23×Dic17—22no—
19C23×Dic17—21no—
20C23×Dic17—21no—
21C23×Dic17—22no—
22C23×Dic17—42no—
23C23×Dic17—42no—
24C23×Dic17C2×C411yescharacteristic
25C23×Dic17C2×C411yescharacteristic
26C2×C22⋊C4×C17—22no—
27C2×C22⋊C4×C17C2×C411yescharacteristic
28C2×C22⋊C4×C17C2×C411yescharacteristic
29C2×C22⋊Dic17—22no—
30C2×C22⋊Dic17C2×C411yescharacteristic
31C2×C22⋊Dic17C2311yescharacteristic
32C2×#63225—21no—
33C2×#63225D412yes—
34C2×C4×Dic17—21no—
35C2×C4×Dic17D412yes—
36#10587563—42no—
37#10587563—42no—
38C22⋊#3624—24no—
39#10587542—42no—
40C4⋊#3624—42no—
41#10587502—22no—
42#10587502—22no—
43C24×C17—21no—
44C24×C17—21no—
45C24×C17—41no—
46C24×C17—41no—
47C24×C17—44no—
48C24×C17M1612yes—
49C24×C17C22×C411yescharacteristic
50C22×C4×C17—21no—
51C22×C4×C17C22⋊C412yes—
52C22×Dic17—21no—
53C22×Dic17—21no—
54C22×Dic17—22no—
55C22×Dic17—22no—
56C22×Dic17—24no—
57C22×Dic17—24no—
58C22×Dic17—21no—
59C22×Dic17—21no—
60C22×Dic17—21no—
61C22×Dic17—48no—
62C22×Dic17—48no—
63C22×Dic17—42no—
64C22×Dic17—42no—
65C22×Dic17—42no—
66C22×Dic17—42no—
67C22×Dic17—41no—
68C22×Dic17—41no—
69C22×Dic17C22⋊C411yescharacteristic
70C22×Dic17C22⋊C411yescharacteristic
71C22×Dic17M1612yes—
72C22×Dic17C2×D412yes—
73C2×#3624—44no—
74C22⋊C4×C17—41no—
75C22⋊C4×C17—44no—
76C22⋊C4×C17—41no—
77C22⋊Dic17—41no—
78C22⋊Dic17—44no—
79C22⋊Dic17—41no—
80#63225—42no—
81#63225—42no—
82C4×Dic17—22no—
83C4×Dic17—22no—
84C4×Dic17—42no—
85#11501—171nomaximal, Sylow
86C23×C17—24no—
87C23×C17—22no—
88C23×C17—21no—
89C23×C17—21no—
90C23×C17—42no—
91C23×C17—44no—
92C23×C17—42no—
93C23×C17—42no—
94C23×C17—42no—
95C23×C17—44no—
96C23×C17—44no—
97C23×C17—48no—
98C23×C17—44no—
99C23×C17—41no—
100C23×C17—41no—
101C23×C17C2×C22⋊C411yescharacteristic
102C23×C17C2×M1611yescharacteristic
103C23×C17C2×M1611yescharacteristic
104C2×C4×C17—22no—
105C2×C4×C17—42no—
106C2×C4×C17—42no—
107C2×C4×C17—41no—
108C2×Dic17—24no—
109C2×Dic17—24no—
110C2×Dic17—21no—
111C2×Dic17—21no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—22no—
115C2×Dic17—22no—
116C2×Dic17—48no—
117C2×Dic17—48no—
118C2×Dic17—42no—
119C2×Dic17—41no—
120C2×Dic17—41no—
121C2×Dic17—42no—
122C2×Dic17—42no—
123C2×Dic17—42no—
124C2×Dic17—41no—
125C2×Dic17#9912yes—
126C2×Dic17#10012yes—
127#3624—84no—
128#2280—171no—
129#1464—172no—
130#1317—172no—
131#1316—172no—
132C22×C17—22no—
133C22×C17—24no—
134C22×C17—21no—
135C22×C17—21no—
136C22×C17—41no—
137C22×C17—41no—
138C22×C17—44no—
139C22×C17—42no—
140C22×C17—42no—
141C22×C17—44no—
142C22×C17—44no—
143C22×C17—48no—
144C22×C17—44no—
145C22×C17—42no—
146C22×C17—42no—
147C22×C17#40711yescharacteristic
148C22×C17C2×#9911yescharacteristic
149C22×C17C2×#10011yescharacteristic
150C4×C17—42no—
151C4×C17—81no—
152Dic17—22no—
153Dic17—22no—
154Dic17—42no—
155Dic17—42no—
156Dic17—81no—
157C24×C4—171no—
158C2×#117—171no—
159C2×#117—171no—
160#432—342no—
161#381—171no—
162#381—171no—
163#380—342no—
164#379—171no—
165#379#59511yescharacteristic
166C4×C22⋊C4—342no—
167#324—342no—
168#323—174no—
169C2×C17—21no—
170C2×C17—21no—
171C2×C17—44no—
172C2×C17—41no—
173C2×C17—41no—
174C2×C17#146211yescharacteristic
175C2×C17#212012yes—
176C25C2×#59511yescharacteristic
177C23×C4—171no—
178C23×C4—171no—
179C23×C4—342no—
180C23×C4—341no—
181C23×C4—341no—
182C23×C4—342no—
183C23×C4—682no—
184C23×C4—682no—
185#117—682no—
186#117—682no—
187C2×C4⋊C4—172no—
188C2×C4⋊C4—341no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—171no—
191C2×C22⋊C4—171no—
192C2×C22⋊C4—342no—
193C2×C22⋊C4C2×#59511yescharacteristic
194C2×C22⋊C4C2×#59511yescharacteristic
195C2×C42—172no—
196C2×C42—341no—
197C4⋊C8—682no—
198C22⋊C8—344no—
199#97—682no—
200#95—342no—
201#95—342no—
202C17#1150111yescharacteristic, complemented, Sylow
203C24—21no—
204C24—21no—
205C24—41no—
206C24—41no—
207C24—44no—
208C24#6324312yes—
209C24C22×#59511yescharacteristic
210C22×C4—21no—
211C22×C4—171no—
212C22×C4—171no—
213C22×C4—172no—
214C22×C4—172no—
215C22×C4—342no—
216C22×C4—342no—
217C22×C4—341no—
218C22×C4—341no—
219C22×C4—344no—
220C22×C4—344no—
221C22×C4—341no—
222C22×C4—341no—
223C22×C4—341no—
224C22×C4—682no—
225C22×C4—682no—
226C22×C4—688no—
227C22×C4—688no—
228C22×C4—682no—
229C22×C4—682no—
230C22×C4—681no—
231C22×C4—681no—
232C22×C4C22⋊#59512yes—
233C2×C8—684no—
234C4⋊C4—682no—
235C4⋊C4—682no—
236C22⋊C4—41no—
237C22⋊C4—44no—
238C22⋊C4—41no—
239C22⋊C4—681no—
240C22⋊C4—684no—
241C22⋊C4—681no—
242C42—342no—
243C42—342no—
244C42—682no—
245C23—24no—
246C23—22no—
247C23—21no—
248C23—21no—
249C23—42no—
250C23—44no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—44no—
255C23—44no—
256C23—48no—
257C23—44no—
258C23—41no—
259C23—41no—
260C23C2×#6324311yescharacteristic
261C23D17⋊M1611yescharacteristic
262C23C2×C22⋊#59511yescharacteristic
263C2×C4—22no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—172no—
268C2×C4—172no—
269C2×C4—344no—
270C2×C4—344no—
271C2×C4—341no—
272C2×C4—341no—
273C2×C4—341no—
274C2×C4—341no—
275C2×C4—342no—
276C2×C4—342no—
277C2×C4—688no—
278C2×C4—688no—
279C2×C4—682no—
280C2×C4—681no—
281C2×C4—681no—
282C2×C4—682no—
283C2×C4—682no—
284C2×C4—682no—
285C2×C4—681no—
286C8—1364no—
287C22—22no—
288C22—24no—
289C22—21no—
290C22—21no—
291C22—41no—
292C22—41no—
293C22—44no—
294C22—42no—
295C22—42no—
296C22—44no—
297C22—44no—
298C22—48no—
299C22—44no—
300C22—42no—
301C22—42no—
302C22#1176378011yescharacteristic
303C22D17⋊#9911yescharacteristic
304C22D17⋊#10011yescharacteristic
305C4—42no—
306C4—81no—
307C4—342no—
308C4—342no—
309C4—682no—
310C4—682no—
311C4—1361no—
312C2—21no—
313C2—21no—
314C2—44no—
315C2—41no—
316C2—41no—
317C2#1454403011yescharacteristic
318C2#1454503612yes—
subgroupG/H
centerC22D17⋊#99
commutatorC24×C17C22×C4
FrattiniC24C22×#595
FittingC17×#379C4
socleC22×C17C2×#99
prime radicalC25×C17C2×C4
cosocleC2×C22⋊Dic17C23
hypercenter#379#595
hypocenterC17#11501
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #14544036C2semidirect
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
#145440362
#145437112
#145437082
#145311622
#1150117