Finite Group Databasebeta

← #16943607

Subgroups — #16943607

Order 4352.

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

normal subgroups only

This group has 524 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#14531508C211yesmaximal, characteristic
2#14527101C212yesmaximal, complemented
3#14526727C212yesmaximal, complemented
4#14526716C211yesmaximal, characteristic, complemented
5C17×#1318C211yesmaximal, characteristic, complemented
6C2×#10587626C411yescharacteristic
7C2×D4×Dic17C411yescharacteristic
8C2×#10587579C2211yescharacteristic
9C22⋊C8×D17—22no—
10#11762711C411yescharacteristic
11#11762686—22no—
12#11762685—22no—
13#11762674C2211yescharacteristic
14#11762655C411yescharacteristic
15#11762535C2212yes—
16#11762532—22no—
17C17×#390C2211yescharacteristic
18C17×#324C2212yes—
19C22×D4×C17C2×C411yescharacteristic
20C22×C22⋊D17—22no—
21C23×Dic17—21no—
22C22×D68C2×C411yescharacteristic
23C22×C4×D17D412yes—
24C2×C4⋊C4×C17C2311yescharacteristic
25C2×C22⋊C4×C17—22no—
26C2×C42×C17C2×C411yescharacteristic
27C2×C22⋊Dic17—21no—
28#10587626—22no—
29#10587626C814yescomplemented
30D4×Dic17—42no—
31C2×#63227—22no—
32C2×#63227D412yes—
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×C4×Dic17C2×C411yescharacteristic
35C2×C4×Dic17C2×C411yescharacteristic
36C2×C8×D17—42no—
37#10587579—42no—
38C17×C22⋊C8—22no—
39#10587502—22no—
40#10587502—21no—
41#10587502—21no—
42C22⋊#3622—22no—
43#10587491—42no—
44C24×C17—21no—
45C23×D17C22⋊C412yes—
46C2×D4×C17—21no—
47C2×D4×C17—41no—
48C2×D4×C17—41no—
49C2×D4×C17C2×C812yescomplemented
50C22×C4×C17—21no—
51C22×C4×C17C22×C411yescharacteristic
52C22×C4×C17C2×D412yes—
53C2×C22⋊D17—28no—
54C2×C22⋊D17—82no—
55C2×C22⋊D17—82no—
56C22×Dic17—21no—
57C22×Dic17—21no—
58C22×Dic17—42no—
59C22×Dic17—82no—
60C22×Dic17C22⋊C411yescharacteristic
61C22×Dic17C22⋊C411yescharacteristic
62C2×D68—41no—
63C2×D68—41no—
64C2×D68C2×C812yes—
65C2×D68M1612yes—
66C2×C4×D17—22no—
67C2×C4×D17—22no—
68C2×C4×D17—82no—
69C2×C8×C17—42no—
70C4⋊C4×C17—41no—
71C22⋊C4×C17—82no—
72C42×C17—41no—
73C22⋊Dic17—42no—
74#63227—42no—
75#63227—82no—
76C4⋊Dic17—41no—
77C4×Dic17—21no—
78C4×Dic17—22no—
79C4×Dic17C2×C812yescomplemented
80C2×#3622—42no—
81C8×D17—84no—
82#11479—171nomaximal, Sylow
83C23×C17—22no—
84C23×C17—42no—
85C23×C17—42no—
86C23×C17—41no—
87C23×C17—41no—
88C23×C17C2×C22⋊C411yescharacteristic
89C22×D17—22no—
90C22×D17—22no—
91C22×D17—42no—
92C22×D17—42no—
93C22×D17C22⋊C814yes—
94D4×C17—42no—
95D4×C17—42no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—22no—
99C2×C4×C17—42no—
100C2×C4×C17—41no—
101C2×C4×C17—41no—
102C2×C4×C17—41no—
103C2×C4×C17C22×C811yescharacteristic
104C2×C4×C17C2×M1611yescharacteristic
105C22⋊D17—88no—
106C2×Dic17—22no—
107C2×Dic17—21no—
108C2×Dic17—41no—
109C2×Dic17—41no—
110C2×Dic17—41no—
111C2×Dic17—41no—
112C2×Dic17—42no—
113C2×Dic17—41no—
114C2×Dic17—84no—
115C2×Dic17#9912yes—
116D68—42no—
117D68—42no—
118C4×D17—44no—
119C4×D17—82no—
120C8×C17—82no—
121#3622—82no—
122#2328—171no—
123#1459—172no—
124#1324—172no—
125#1318—171no—
126#1318D1711yescharacteristic, complemented
127C22×C17—21no—
128C22×C17—21no—
129C22×C17—44no—
130C22×C17—42no—
131C22×C17—82no—
132C22×C17—81no—
133C22×C17—81no—
134C22×C17C2×C22⋊C811yescharacteristic
135C22×C17C2×#9911yescharacteristic
136C22×C17#41311yescharacteristic
137C2×D17—24no—
138C2×D17—42no—
139C2×D17—42no—
140C2×D17—44no—
141C2×D17—82no—
142C4×C17—21no—
143C4×C17—21no—
144C4×C17—42no—
145C4×C17—81no—
146Dic17—22no—
147Dic17—42no—
148Dic17—41no—
149Dic17—81no—
150C2×#127—171no—
151C2×C4×D4—171no—
152C2×C4×D4—171no—
153C2×C22⋊C8—342no—
154#390—171no—
155#390C2×D1711yescharacteristic
156#386—342no—
157#386—342no—
158#382—171no—
159#376—171no—
160#324—172no—
161#324C2×D1712yes—
162#323—342no—
163C2×C17—21no—
164C2×C17—21no—
165C2×C17—82no—
166C2×C17#145911yescharacteristic
167C2×C17#212711yescharacteristic
168C2×C17#213411yescharacteristic
169D17—44no—
170C22×D4—171no—
171C22×D4—342no—
172C22×D4C4×D1711yescharacteristic
173C23×C4—172no—
174C23×C4—341no—
175C22×C8—682no—
176#127—174no—
177#127—342no—
178C4×D4—682no—
179C4×D4—682no—
180C2×C4⋊C4—171no—
181C2×C4⋊C4C22×D1711yescharacteristic
182C2×C22⋊C4—22no—
183C2×C22⋊C4—172no—
184C2×C22⋊C4—341no—
185C2×C22⋊C4—342no—
186C2×C42—171no—
187C2×C42—171no—
188C2×C42C4×D1711yescharacteristic
189C22⋊C8—22no—
190C22⋊C8—342no—
191C22⋊C8—682no—
192#95—341no—
193#95—341no—
194#95—342no—
195C17#1147911yescharacteristic, complemented, Sylow
196C24—21no—
197C24—172no—
198C2×D4—21no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4—172no—
202C2×D4—172no—
203C2×D4—348no—
204C2×D4—681no—
205C2×D4—681no—
206C2×D4—1362no—
207C2×D4—1362no—
208C2×D4C8×D1712yescomplemented
209C22×C4—21no—
210C22×C4—171no—
211C22×C4—171no—
212C22×C4—342no—
213C22×C4—342no—
214C22×C4—341no—
215C22×C4—341no—
216C22×C4—682no—
217C22×C4—1362no—
218C22×C4—1362no—
219C22×C4C2×C4×D1711yescharacteristic
220C22×C4D4×D1712yes—
221C2×C8—42no—
222C2×C8—682no—
223C2×C8—1364no—
224C4⋊C4—41no—
225C4⋊C4—681no—
226C22⋊C4—82no—
227C22⋊C4—682no—
228C22⋊C4—682no—
229C22⋊C4—1362no—
230C42—41no—
231C42—172no—
232C42—342no—
233C42—341no—
234C23—22no—
235C23—42no—
236C23—42no—
237C23—41no—
238C23—41no—
239C23—174no—
240C23—342no—
241C23—342no—
242C23—682no—
243C23—682no—
244C23C22⋊C4×D1711yescharacteristic
245D4—42no—
246D4—42no—
247D4—682no—
248D4—682no—
249D4—1368no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—172no—
258C2×C4—342no—
259C2×C4—341no—
260C2×C4—684no—
261C2×C4—681no—
262C2×C4—681no—
263C2×C4—681no—
264C2×C4—681no—
265C2×C4—682no—
266C2×C4—681no—
267C2×C4—1362no—
268C2×C4—1364no—
269C2×C4C2×C8×D1711yescharacteristic
270C2×C4M16×D1711yescharacteristic
271C8—82no—
272C8—1362no—
273C22—21no—
274C22—21no—
275C22—44no—
276C22—42no—
277C22—82no—
278C22—81no—
279C22—81no—
280C22—344no—
281C22—684no—
282C22—682no—
283C22—682no—
284C22—1362no—
285C22C22⋊C8×D1711yescharacteristic
286C22#99×D1711yescharacteristic
287C22#1176279011yescharacteristic
288C4—21no—
289C4—21no—
290C4—42no—
291C4—81no—
292C4—342no—
293C4—682no—
294C4—681no—
295C4—1361no—
296C2—21no—
297C2—21no—
298C2—82no—
299C2—684no—
300C2#1452709911yescharacteristic
301C2#1453045011yescharacteristic
302C2#1453047411yescharacteristic
subgroupG/H
centerC22#99×D17
commutatorC2×C4×C17C22×C8
FrattiniC2×C4⋊C4C22×D17
FittingC17×#1318C2
socleC22×C17C2×#99
prime radicalC2×#10587626C4
cosocleC2×C4⋊C4×C17C23
hypercenter#1318D17
hypocenterC17#11479
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #14527101C2semidirect
3. #14526727C2semidirect
4. #14526716C2semidirect
5. C17×#1318C2semidirect
29. #10587626C8semidirect
49. C2×D4×C17C2×C8semidirect
79. C4×Dic17C2×C8semidirect
126. #1318D17semidirect
195. C17#11479semidirect
208. C2×D4C8×D17semidirect

Maximal subgroups

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

subgroupindex
#145315082
#145271012
#145267272
#145267162
C17×#13182
#1147917