Finite Group Databasebeta

← #16943980

Subgroups — #16943980

Order 4352.

350 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 91 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
2#14527108C211yesmaximal, characteristic
3#14526730C212yesmaximal
4#14526728C212yesmaximal
5C17×#2565C211yesmaximal, characteristic
6#11762866—21no—
7#11762862—21no—
8#11762535—21no—
9#11762535—21no—
10#11762535C2212yes—
11#11762535C2212yes—
12C2×C17×#125C411yescharacteristic
13C2×C4×Q8×C17C2211yescharacteristic
14C17×#398—21no—
15C17×#398—21no—
16C17×#391C411yescharacteristic
17C17×#391C411yescharacteristic
18C17×#387—21no—
19C17×#387—21no—
20C17×#384C2211yescharacteristic
21C17×#382C2211yescharacteristic
22C4×C4⋊C4×C17C411yescharacteristic
23C22×Q8×C17C2×C411yescharacteristic
24C17×#125—41no—
25C17×#125—41no—
26C4×Q8×C17—41no—
27C4×Q8×C17—41no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17C2×C411yescharacteristic
34C2×C4⋊C4×C17C2×C411yescharacteristic
35C2×C4⋊C4×C17D411yescharacteristic
36C2×C4⋊C4×C17D411yescharacteristic
37C2×C4⋊C4×C17C2311yescharacteristic
38C2×C42×C17C2×C411yescharacteristic
39C2×C42×C17C2×C411yescharacteristic
40C2×C42×C17C2×C411yescharacteristic
41C2×C42×C17D411yescharacteristic
42C2×C42×C17D411yescharacteristic
43C17×#95—21no—
44C17×#95—21no—
45C17×#95—21no—
46C17×#95—21no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95—21no—
50C22⋊#3622—22no—
51C22⋊#3622—22no—
52C4⋊#3622—41no—
53C4⋊#3622—41no—
54#10587474—41no—
55C4×#3622—41no—
56C2×Q8×C17—22no—
57C2×Q8×C17—22no—
58C2×Q8×C17—41no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17C22⋊C411yescharacteristic
66C22×C4×C17C22⋊C411yescharacteristic
67C22×C4×C17C22×C411yescharacteristic
68C22×C4×C17C2×D411yescharacteristic
69C22×C4×C17C2×D411yescharacteristic
70C4⋊C4×C17—41no—
71C4⋊C4×C17—41no—
72C4⋊C4×C17—41no—
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—42no—
76C4⋊C4×C17—42no—
77C4⋊C4×C17—42no—
78C4⋊C4×C17—42no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C42×C17—21no—
82C42×C17—21no—
83C42×C17—21no—
84C42×C17—21no—
85C42×C17—21no—
86C42×C17—21no—
87C42×C17—22no—
88C42×C17—22no—
89C2×#3622—42no—
90C2×#3622—42no—
91#11571—171nomaximal, Sylow
92C23×C17C2×C22⋊C411yescharacteristic
93Q8×C17—44no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
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—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—42no—
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17—41no—
119C2×C4×C17#9911yescharacteristic
120C2×C4×C17#9911yescharacteristic
121C2×C4×C17#10112yes—
122C2×C4×C17#13112yes—
123#3622—82no—
124#3622—82no—
125#2565D1711yescharacteristic
126#1467—171no—
127#1461—171no—
128#1325—172no—
129#1324—172no—
130C22×C17—21no—
131C22×C17—21no—
132C22×C17#40811yescharacteristic
133C22×C17C2×#9911yescharacteristic
134C22×C17C2×#10111yescharacteristic
135C4×C17—21no—
136C4×C17—21no—
137C4×C17—22no—
138C4×C17—22no—
139C4×C17—42no—
140C4×C17—41no—
141C4×C17—41no—
142C4×C17—41no—
143C4×C17—41no—
144C4×C17—81no—
145C4×C17—81no—
146C4×C17—81no—
147C2×#125Dic1711yescharacteristic
148C2×C4×Q8C2×D1711yescharacteristic
149#432—341no—
150#431—341no—
151#398—21no—
152#398—21no—
153#391Dic1711yescharacteristic
154#391Dic1711yescharacteristic
155#387—21no—
156#387—21no—
157#384C2×D1711yescharacteristic
158#382C2×D1711yescharacteristic
159C4×C4⋊C4Dic1711yescharacteristic
160#324—172no—
161#324—172no—
162#324—341no—
163#324—341no—
164C2×C17—21no—
165C2×C17—21no—
166C2×C17#147211yescharacteristic
167C2×C17#212611yescharacteristic
168C2×C17#213311yescharacteristic
169C22×Q8C2×Dic1711yescharacteristic
170#125—41no—
171#125—41no—
172C4×Q8—41no—
173C4×Q8—41no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4C2×Dic1711yescharacteristic
180C2×C4⋊C4C2×Dic1711yescharacteristic
181C2×C4⋊C4C22⋊D1711yescharacteristic
182C2×C4⋊C4C22⋊D1711yescharacteristic
183C2×C4⋊C4C22×D1711yescharacteristic
184C2×C42C2×Dic1711yescharacteristic
185C2×C42C2×Dic1711yescharacteristic
186C2×C42C2×Dic1711yescharacteristic
187C2×C42C22⋊D1711yescharacteristic
188C2×C42C22⋊D1711yescharacteristic
189C4⋊C8—681no—
190C4⋊C8—681no—
191C22⋊C8—342no—
192C22⋊C8—342no—
193#97—681no—
194C4×C8—681no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202C17#1157111yescharacteristic, complemented, Sylow
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—41no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4C22⋊Dic1711yescharacteristic
211C22×C4C22⋊Dic1711yescharacteristic
212C22×C4C22⋊Dic1711yescharacteristic
213C22×C4C22⋊Dic1711yescharacteristic
214C22×C4C22×Dic1711yescharacteristic
215C22×C4C2×C22⋊D1711yescharacteristic
216C22×C4C2×C22⋊D1711yescharacteristic
217C2×C8—682no—
218C2×C8—682no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—22no—
237C42—22no—
238C23C2×C22⋊Dic1711yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4#1058750511yescharacteristic
266C2×C4#1058750511yescharacteristic
267C2×C4#1058750712yes—
268C2×C4#1058763412yes—
269C8—1362no—
270C8—1362no—
271C22—21no—
272C22—21no—
273C22#1176277611yescharacteristic
274C22C2×#1058750511yescharacteristic
275C22C2×#1058750711yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—42no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—41no—
285C4—81no—
286C4—81no—
287C4—81no—
288C2—21no—
289C2—21no—
290C2#1452714811yescharacteristic
291C2#1453044911yescharacteristic
292C2#1453047311yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2565C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2565D17
hypocenterC17#11571
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2565

Complements

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

NH ≅ G/Ntype
202. C17#11571semidirect

Maximal subgroups

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

subgroupindex
#145271282
#145271082
#145267302
#145267282
C17×#25652
#1157117