Finite Group Databasebeta

← #16943963

Subgroups — #16943963

Order 4352.

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

normal subgroups only

This group has 462 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#14527128C211yesmaximal, characteristic, complemented
2#14527108C211yesmaximal, characteristic, complemented
3#14526716C214yesmaximal, complemented
4C17×#2548C211yesmaximal, characteristic
5#11762866—21no—
6#11762862—21no—
7#11762535—21no—
8#11762535—21no—
9#11762535C2212yes—
10#11762535C2212yes—
11C2×C17×#127C411yescharacteristic
12C2×C17×#124C412yes—
13C2×C4×Q8×C17C2211yescharacteristic
14C17×#394—21no—
15C17×#394—21no—
16C17×#390—21no—
17C17×#390—21no—
18C17×#390C2212yes—
19C4×C4⋊C4×C17C411yescharacteristic
20C22×Q8×C17C2×C411yescharacteristic
21C22×D4×C17—21no—
22C22×D4×C17—21no—
23C22×D4×C17C2×C412yes—
24C17×#127—41no—
25C17×#127—41no—
26C17×#124—44no—
27C4×Q8×C17—41no—
28C4×Q8×C17—41no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C4⋊C4×C17D411yescharacteristic
32C2×C4⋊C4×C17C2311yescharacteristic
33C2×C22⋊C4×C17—22no—
34C2×C22⋊C4×C17—22no—
35C2×C22⋊C4×C17—22no—
36C2×C22⋊C4×C17—22no—
37C2×C42×C17C2×C411yescharacteristic
38C2×C42×C17C2×C412yes—
39C2×C42×C17D411yescharacteristic
40C2×C42×C17D411yescharacteristic
41C17×#95—21no—
42C22⋊#3622—22no—
43C22⋊#3622—22no—
44C4⋊#3622—41no—
45C4⋊#3622—41no—
46#10587474—41no—
47C4×#3622—41no—
48C24×C17—22no—
49C2×Q8×C17—22no—
50C2×Q8×C17—22no—
51C2×Q8×C17—41no—
52C2×D4×C17—24no—
53C2×D4×C17—42no—
54C2×D4×C17—42no—
55C2×D4×C17—42no—
56C2×D4×C17—42no—
57C2×D4×C17—42no—
58C2×D4×C17—41no—
59C2×D4×C17—41no—
60C2×D4×C17—82no—
61C22×C4×C17—22no—
62C22×C4×C17C22⋊C411yescharacteristic
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17C22⋊C411yescharacteristic
66C22×C4×C17C22×C411yescharacteristic
67C22×C4×C17C2×D411yescharacteristic
68C22×C4×C17C2×D411yescharacteristic
69C4⋊C4×C17—41no—
70C4⋊C4×C17—41no—
71C4⋊C4×C17—41no—
72C4⋊C4×C17—42no—
73C22⋊C4×C17—44no—
74C22⋊C4×C17—44no—
75C22⋊C4×C17—82no—
76C22⋊C4×C17—82no—
77C42×C17—21no—
78C42×C17—21no—
79C42×C17—21no—
80C42×C17—21no—
81C42×C17—21no—
82C42×C17—21no—
83C42×C17—42no—
84C2×#3622—42no—
85C2×#3622—42no—
86#11567—171nomaximal, Sylow
87C23×C17—42no—
88C23×C17—42no—
89C23×C17—42no—
90C23×C17—42no—
91C23×C17—42no—
92C23×C17—42no—
93C23×C17—42no—
94C23×C17C2×C22⋊C411yescharacteristic
95Q8×C17—44no—
96D4×C17—84no—
97D4×C17—82no—
98D4×C17—84no—
99D4×C17—82no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
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—21no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—42no—
115C2×C4×C17—42no—
116C2×C4×C17—42no—
117C2×C4×C17#9911yescharacteristic
118C2×C4×C17#9911yescharacteristic
119C2×C4×C17#10012yes—
120C2×C4×C17#13112yes—
121#3622—82no—
122#3622—82no—
123#2548D1711yescharacteristic
124#1467—171no—
125#1461—171no—
126#1318—174no—
127C22×C17—21no—
128C22×C17—21no—
129C22×C17—82no—
130C22×C17—82no—
131C22×C17—82no—
132C22×C17—82no—
133C22×C17—82no—
134C22×C17—82no—
135C22×C17—82no—
136C22×C17#40811yescharacteristic
137C22×C17C2×#9911yescharacteristic
138C22×C17C2×#10011yescharacteristic
139C4×C17—21no—
140C4×C17—22no—
141C4×C17—22no—
142C4×C17—41no—
143C4×C17—41no—
144C4×C17—41no—
145C4×C17—41no—
146C4×C17—82no—
147C4×C17#35512yes—
148C2×#127Dic1711yescharacteristic
149C2×#124Dic1712yes—
150C2×C4×Q8C2×D1711yescharacteristic
151#432—341no—
152#431—341no—
153#394—21no—
154#394—21no—
155#390—21no—
156#390—21no—
157#390C2×D1712yes—
158C4×C4⋊C4Dic1711yescharacteristic
159#324—172no—
160#324—172no—
161#324—341no—
162#324—341no—
163C2×C17—21no—
164C2×C17—21no—
165C2×C17—162no—
166C2×C17#147111yescharacteristic
167C2×C17#212811yescharacteristic
168C2×C17C2×#35511yescharacteristic
169C22×Q8C2×Dic1711yescharacteristic
170C22×D4—21no—
171C22×D4—21no—
172C22×D4C2×Dic1712yes—
173#127—41no—
174#127—41no—
175#124—44no—
176C4×Q8—41no—
177C4×Q8—41no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4C22⋊D1711yescharacteristic
180C2×C4⋊C4C22⋊D1711yescharacteristic
181C2×C4⋊C4C22×D1711yescharacteristic
182C2×C22⋊C4—22no—
183C2×C22⋊C4—22no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C42C2×Dic1711yescharacteristic
187C2×C42C2×Dic1712yes—
188C2×C42C22⋊D1711yescharacteristic
189C2×C42C22⋊D1711yescharacteristic
190C4⋊C8—681no—
191C4⋊C8—681no—
192C22⋊C8—342no—
193C22⋊C8—342no—
194#97—681no—
195C4×C8—681no—
196#95—21no—
197C17#1156711yescharacteristic, complemented, Sylow
198C24—22no—
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—41no—
202C2×D4—24no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—82no—
211C22×C4—22no—
212C22×C4C22⋊Dic1711yescharacteristic
213C22×C4C22⋊Dic1711yescharacteristic
214C22×C4C22⋊Dic1711yescharacteristic
215C22×C4C22⋊Dic1711yescharacteristic
216C22×C4C22×Dic1711yescharacteristic
217C22×C4C2×C22⋊D1711yescharacteristic
218C22×C4C2×C22⋊D1711yescharacteristic
219C2×C8—682no—
220C2×C8—682no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—42no—
225C22⋊C4—44no—
226C22⋊C4—44no—
227C22⋊C4—82no—
228C22⋊C4—82no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—42no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23—42no—
240C23—42no—
241C23—42no—
242C23—42no—
243C23C2×C22⋊Dic1711yescharacteristic
244Q8—44no—
245D4—84no—
246D4—82no—
247D4—84no—
248D4—82no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4#1058750412yes—
267C2×C4#1058750511yescharacteristic
268C2×C4#1058750511yescharacteristic
269C2×C4#1058763412yes—
270C8—1362no—
271C8—1362no—
272C22—21no—
273C22—21no—
274C22—82no—
275C22—82no—
276C22—82no—
277C22—82no—
278C22—82no—
279C22—82no—
280C22—82no—
281C22#1176277611yescharacteristic
282C22C2×#1058750511yescharacteristic
283C22C2×#1058750411yescharacteristic
284C4—21no—
285C4—22no—
286C4—22no—
287C4—41no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—82no—
292C4#1176260612yes—
293C2—21no—
294C2—21no—
295C2—162no—
296C2#1452714411yescharacteristic
297C2#1453045611yescharacteristic
298C2C2×#1176260611yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2548C2
socleC22×C17C2×#99
prime radicalC2×C17×#127C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2548D17
hypocenterC17#11567
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2548

Complements

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

NH ≅ G/Ntype
1. #14527128C2semidirect
2. #14527108C2semidirect
3. #14526716C2semidirect
197. C17#11567semidirect

Maximal subgroups

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

subgroupindex
#145271282
#145271082
#145267162
C17×#25482
#1156717