Finite Group Databasebeta

← #16943808

Subgroups — #16943808

Order 4352.

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

normal subgroups only

This group has 504 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
1#14527122C212yesmaximal, complemented
2#14526728C212yesmaximal, complemented
3#14526716C212yesmaximal, complemented
4C17×#2328C211yesmaximal, characteristic
5#11762773—22no—
6#11762535C2214yes—
7#11762533—22no—
8C2×C17×#127C411yescharacteristic
9C2×C4×D4×C17C411yescharacteristic
10C2×C4×D4×C17C2211yescharacteristic
11C17×#390C411yescharacteristic
12C17×#390C2211yescharacteristic
13C17×#386—22no—
14C17×#386—22no—
15C17×#382C2211yescharacteristic
16C17×#376C411yescharacteristic
17C22×D4×C17—22no—
18C22×D4×C17C2×C411yescharacteristic
19C22×D4×C17C2×C411yescharacteristic
20C23×C4×C17—21no—
21C23×C4×C17D412yes—
22C17×#127—22no—
23C17×#127—22no—
24C4×D4×C17—42no—
25C4×D4×C17—42no—
26C2×C4⋊C4×C17C2×C411yescharacteristic
27C2×C4⋊C4×C17C2311yescharacteristic
28C2×C22⋊C4×C17—21no—
29C2×C22⋊C4×C17—22no—
30C2×C22⋊C4×C17—22no—
31C2×C22⋊C4×C17D412yes—
32C2×C42×C17C2×C411yescharacteristic
33C2×C42×C17C2×C411yescharacteristic
34C2×C42×C17C2×C411yescharacteristic
35C2×#63223—42no—
36C17×#95—21no—
37C17×#95—21no—
38C17×#95—22no—
39C22⋊#3622—24no—
40C22⋊#3622—42no—
41C24×C17—21no—
42C24×C17C22⋊C412yes—
43C2×D4×C17—28no—
44C2×D4×C17—21no—
45C2×D4×C17—21no—
46C2×D4×C17—21no—
47C2×D4×C17—41no—
48C2×D4×C17—41no—
49C2×D4×C17—41no—
50C2×D4×C17—41no—
51C2×D4×C17—82no—
52C2×D4×C17—82no—
53C2×D4×C17M1612yescomplemented
54C22×C4×C17—21no—
55C22×C4×C17—22no—
56C22×C4×C17—22no—
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17—42no—
60C22×C4×C17—82no—
61C22×C4×C17—82no—
62C22×C4×C17C22⋊C411yescharacteristic
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22×C411yescharacteristic
65C22×C4×C17C2×D412yes—
66C4⋊C4×C17—41no—
67C4⋊C4×C17—41no—
68C22⋊C4×C17—42no—
69C22⋊C4×C17—42no—
70C22⋊C4×C17—82no—
71C22⋊C4×C17—82no—
72C42×C17—22no—
73C42×C17—21no—
74C42×C17—41no—
75C42×C17M1612yescomplemented
76#63223—84no—
77C2×#3622—44no—
78#11533—171nomaximal, Sylow
79C23×C17—22no—
80C23×C17—22no—
81C23×C17—22no—
82C23×C17—22no—
83C23×C17—42no—
84C23×C17—42no—
85C23×C17—42no—
86C23×C17—42no—
87C23×C17—41no—
88C23×C17—41no—
89C23×C17C2×C22⋊C411yescharacteristic
90D4×C17—42no—
91D4×C17—42no—
92D4×C17—42no—
93D4×C17—42no—
94D4×C17—88no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—22no—
98C2×C4×C17—21no—
99C2×C4×C17—22no—
100C2×C4×C17—41no—
101C2×C4×C17—44no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17—42no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—42no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—82no—
112C2×C4×C17—84no—
113C2×C4×C17#9912yes—
114C2×C4×C17C2×M1611yescharacteristic
115C2×C4×C17C2×M1611yescharacteristic
116#3622—84no—
117#2328D1711yescharacteristic
118#1465—172no—
119#1324—172no—
120#1318—172no—
121C22×C17—21no—
122C22×C17—21no—
123C22×C17—44no—
124C22×C17—44no—
125C22×C17—42no—
126C22×C17—42no—
127C22×C17—42no—
128C22×C17—42no—
129C22×C17—82no—
130C22×C17—82no—
131C22×C17—81no—
132C22×C17—81no—
133C22×C17#40711yescharacteristic
134C22×C17C2×#9911yescharacteristic
135C22×C17#41311yescharacteristic
136C4×C17—22no—
137C4×C17—21no—
138C4×C17—21no—
139C4×C17—42no—
140C4×C17—42no—
141C4×C17—41no—
142C4×C17—81no—
143C4×C17—81no—
144C2×#127Dic1711yescharacteristic
145C2×C4×D4Dic1711yescharacteristic
146C2×C4×D4C2×D1711yescharacteristic
147#407—342no—
148#390Dic1711yescharacteristic
149#390C2×D1711yescharacteristic
150#386—22no—
151#386—22no—
152#382C2×D1711yescharacteristic
153#376Dic1711yescharacteristic
154#324—174no—
155#323—342no—
156C2×C17—21no—
157C2×C17—21no—
158C2×C17—82no—
159C2×C17—82no—
160C2×C17#146511yescharacteristic
161C2×C17#212711yescharacteristic
162C2×C17#213411yescharacteristic
163C22×D4—22no—
164C22×D4C2×Dic1711yescharacteristic
165C22×D4C2×Dic1711yescharacteristic
166C23×C4—21no—
167C23×C4C22⋊D1712yes—
168C2×M16—682no—
169#127—22no—
170#127—22no—
171C4×D4—42no—
172C4×D4—42no—
173C2×C4⋊C4C2×Dic1711yescharacteristic
174C2×C4⋊C4C22×D1711yescharacteristic
175C2×C22⋊C4—21no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4C22⋊D1712yes—
179C2×C42C2×Dic1711yescharacteristic
180C2×C42C2×Dic1711yescharacteristic
181C2×C42C2×Dic1711yescharacteristic
182C22⋊C8—344no—
183C22⋊C8—682no—
184#95—21no—
185#95—21no—
186#95—22no—
187C17#1153311yescharacteristic, complemented, Sylow
188C24—21no—
189C24C22⋊Dic1712yes—
190C2×D4—28no—
191C2×D4—21no—
192C2×D4—21no—
193C2×D4—21no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4—41no—
197C2×D4—41no—
198C2×D4—82no—
199C2×D4—82no—
200C2×D4#6322312yescomplemented
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—42no—
207C22×C4—82no—
208C22×C4—82no—
209C22×C4C22⋊Dic1711yescharacteristic
210C22×C4C22⋊Dic1711yescharacteristic
211C22×C4C22×Dic1711yescharacteristic
212C22×C4C2×C22⋊D1712yes—
213M16—1364no—
214C2×C8—684no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C22⋊C4—42no—
218C22⋊C4—42no—
219C22⋊C4—82no—
220C22⋊C4—82no—
221C42—22no—
222C42—21no—
223C42—41no—
224C42#6322312yescomplemented
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—42no—
233C23—41no—
234C23—41no—
235C23C2×C22⋊Dic1711yescharacteristic
236D4—42no—
237D4—42no—
238D4—42no—
239D4—42no—
240D4—88no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—44no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—82no—
258C2×C4—84no—
259C2×C4#1058750512yes—
260C2×C4C2×#6322311yescharacteristic
261C2×C4C2×#6322311yescharacteristic
262C8—1364no—
263C22—21no—
264C22—21no—
265C22—44no—
266C22—44no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—82no—
272C22—82no—
273C22—81no—
274C22—81no—
275C22#1176277311yescharacteristic
276C22C2×#1058750511yescharacteristic
277C22#1176279311yescharacteristic
278C4—21no—
279C4—21no—
280C4—22no—
281C4—42no—
282C4—42no—
283C4—41no—
284C4—81no—
285C4—81no—
286C2—21no—
287C2—21no—
288C2—82no—
289C2—82no—
290C2#1452712211yescharacteristic
291C2#1453045311yescharacteristic
292C2#1453047611yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2328C2
socleC22×C17C2×#99
prime radicalC2×C17×#127C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2328D17
hypocenterC17#11533
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2328

Complements

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

NH ≅ G/Ntype
1. #14527122C2semidirect
2. #14526728C2semidirect
3. #14526716C2semidirect
53. C2×D4×C17M16semidirect
75. C42×C17M16semidirect
187. C17#11533semidirect
200. C2×D4#63223semidirect
224. C42#63223semidirect

Maximal subgroups

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

subgroupindex
#145271222
#145267282
#145267162
C17×#23282
#1153317