Finite Group Databasebeta

← #16943972

Subgroups — #16943972

Order 4352.

424 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 87 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#14533957C211yesmaximal, characteristic
2#14527102C211yesmaximal, characteristic
3#14526727C214yesmaximal, complemented
4C17×#1465C211yesmaximal, characteristic
5C2×#10587555C411yescharacteristic
6C2×C22⋊#3622—21no—
7#11762721—21no—
8#11762721—21no—
9#11762712C412yes—
10#11762674C2212yes—
11#11762669—21no—
12#11762669—21no—
13C4×C4⋊Dic17C411yescharacteristic
14#11762535C2212yes—
15#11762533—21no—
16C2×C4×D4×C17C2211yescharacteristic
17C17×#407—21no—
18C17×#324C2212yes—
19C17×#323—21no—
20C22×D4×C17C2×C411yescharacteristic
21C23×C4×C17D411yescharacteristic
22C23×C4×C17D411yescharacteristic
23C22×Dic34—21no—
24C2×M16×C17—41no—
25C4×D4×C17—41no—
26C4×D4×C17—41no—
27C2×C4⋊C4×C17C2311yescharacteristic
28C2×C22⋊C4×C17D411yescharacteristic
29C2×C22⋊C4×C17D411yescharacteristic
30C2×C42×C17C2×C411yescharacteristic
31C2×C22⋊Dic17—22no—
32C2×C22⋊Dic17—22no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17C2×C412yes—
36C2×C4×Dic17C2×C412yes—
37C22×#3622—41no—
38#10587555—41no—
39#10587555—41no—
40C17×C22⋊C8—22no—
41C17×C22⋊C8—41no—
42#10587502—21no—
43#10587502—22no—
44#10587502—22no—
45C22⋊#3622—22no—
46C22⋊#3622—41no—
47C24×C17C22⋊C411yescharacteristic
48C24×C17C22⋊C411yescharacteristic
49C2×D4×C17—22no—
50C2×D4×C17—22no—
51C2×D4×C17—41no—
52C22×C4×C17—21no—
53C22×C4×C17—21no—
54C22×C4×C17—21no—
55C22×C4×C17—21no—
56C22×C4×C17—42no—
57C22×C4×C17—42no—
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22×C411yescharacteristic
61C22×C4×C17C2×D411yescharacteristic
62C22×C4×C17C2×D411yescharacteristic
63C22×Dic17—22no—
64C22×Dic17—22no—
65C2×Dic34—42no—
66C2×Dic34—82no—
67M16×C17—82no—
68C2×C8×C17—42no—
69C4⋊C4×C17—41no—
70C22⋊C4×C17—41no—
71C22⋊C4×C17—41no—
72C42×C17—21no—
73C42×C17—21no—
74C22⋊Dic17—82no—
75C22⋊Dic17—82no—
76C4⋊Dic17—42no—
77C4⋊Dic17—41no—
78C4⋊Dic17—41no—
79C4⋊Dic17—42no—
80C4×Dic17—24no—
81C2×#3622—42no—
82C2×#3622—82no—
83#11569—171nomaximal, Sylow
84C23×C17—21no—
85C23×C17—21no—
86C23×C17—21no—
87C23×C17—21no—
88C23×C17—21no—
89C23×C17—41no—
90C23×C17—41no—
91C23×C17—41no—
92C23×C17—41no—
93C23×C17#10112yes—
94C23×C17C2×C22⋊C411yescharacteristic
95D4×C17—44no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—22no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—42no—
103C2×C4×C17—42no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—81no—
108C2×C4×C17—81no—
109C2×C4×C17#9911yescharacteristic
110C2×C4×C17#9911yescharacteristic
111C2×C4×C17#13112yes—
112C2×Dic17—42no—
113C2×Dic17—42no—
114C2×Dic17—42no—
115C2×Dic17—42no—
116C2×Dic17—42no—
117C2×Dic17—42no—
118Dic34—84no—
119C8×C17—82no—
120#3622—82no—
121#2563—171no—
122#1465D1711yescharacteristic
123#1459—171no—
124#1324—174no—
125C22×C17—21no—
126C22×C17—21no—
127C22×C17—22no—
128C22×C17—42no—
129C22×C17—42no—
130C22×C17—41no—
131C22×C17—41no—
132C22×C17—41no—
133C22×C17—41no—
134C22×C17—41no—
135C22×C17—81no—
136C22×C17—81no—
137C22×C17#40811yescharacteristic
138C22×C17C2×#9911yescharacteristic
139C22×C17C2×#10111yescharacteristic
140C4×C17—21no—
141C4×C17—22no—
142C4×C17—41no—
143C4×C17—41no—
144C4×C17—41no—
145C4×C17#35412yes—
146Dic17—82no—
147Dic17—82no—
148C2×C4⋊Q8—171no—
149C2×C4×D4C2×D1711yescharacteristic
150#407—21no—
151C2×C22⋊C8—341no—
152#393—341no—
153#393—341no—
154#390—172no—
155#382—172no—
156#380—341no—
157#380—341no—
158C4×C4⋊C4—171no—
159#324—172no—
160#324C2×D1712yes—
161#323—21no—
162#323—341no—
163C2×C17—21no—
164C2×C17—21no—
165C2×C17—42no—
166C2×C17—81no—
167C2×C17#147211yescharacteristic
168C2×C17C2×#35411yescharacteristic
169C2×C17#213411yescharacteristic
170C22×Q8—341no—
171C22×D4C4×D1711yescharacteristic
172C23×C4D6811yescharacteristic
173C23×C4C22⋊D1711yescharacteristic
174C2×M16—41no—
175C22×C8—681no—
176C4⋊Q8—681no—
177C4⋊Q8—681no—
178C4×D4—41no—
179C4×D4—41no—
180C2×C4⋊C4—172no—
181C2×C4⋊C4—341no—
182C2×C4⋊C4—341no—
183C2×C4⋊C4C22×D1711yescharacteristic
184C2×C22⋊C4—342no—
185C2×C22⋊C4—342no—
186C2×C22⋊C4D6811yescharacteristic
187C2×C22⋊C4C22⋊D1711yescharacteristic
188C2×C42—172no—
189C2×C42C4×D1711yescharacteristic
190C22⋊C8—22no—
191C22⋊C8—41no—
192C22⋊C8—342no—
193C22⋊C8—681no—
194#95—342no—
195#95—342no—
196#95—341no—
197C17#1156911yescharacteristic, complemented, Sylow
198C24#6322711yescharacteristic
199C24#6322711yescharacteristic
200C2×Q8—682no—
201C2×Q8—1362no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—41no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—342no—
212C22×C4—342no—
213C22×C4#6322711yescharacteristic
214C22×C4#6322711yescharacteristic
215C22×C4C2×C4×D1711yescharacteristic
216C22×C4C2×D6811yescharacteristic
217C22×C4C2×C22⋊D1711yescharacteristic
218M16—82no—
219C2×C8—42no—
220C2×C8—682no—
221C2×C8—1362no—
222C4⋊C4—41no—
223C4⋊C4—682no—
224C4⋊C4—682no—
225C4⋊C4—681no—
226C4⋊C4—681no—
227C22⋊C4—41no—
228C22⋊C4—41no—
229C22⋊C4—1362no—
230C22⋊C4—1362no—
231C42—21no—
232C42—21no—
233C42—344no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23#1058749512yes—
244C23C2×#6322711yescharacteristic
245Q8—1364no—
246D4—44no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—682no—
261C2×C4—682no—
262C2×C4—682no—
263C2×C4—682no—
264C2×C4—682no—
265C2×C4—682no—
266C2×C4#1058747711yescharacteristic
267C2×C4#1058747711yescharacteristic
268C2×C4#1058759312yes—
269C8—82no—
270C8—1362no—
271C22—21no—
272C22—21no—
273C22—22no—
274C22—42no—
275C22—42no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—81no—
282C22—81no—
283C22#1176277711yescharacteristic
284C22C2×#1058747711yescharacteristic
285C22C2×#1058749511yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—1362no—
292C4—1362no—
293C4#1176260312yes—
294C2—21no—
295C2—21no—
296C2—42no—
297C2—81no—
298C2#1452714911yescharacteristic
299C2C2×#1176260311yescharacteristic
300C2#1453047511yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#1465C2
socleC22×C17C2×#99
prime radicalC22×D4×C17C2×C4
cosocleC2×C4⋊C4×C17C23
hypercenter#1465D17
hypocenterC17#11569
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #14526727C2semidirect
197. C17#11569semidirect

Maximal subgroups

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

subgroupindex
#145339572
#145271022
#145267272
C17×#14652
#1156917