Finite Group Databasebeta

← C17×#11508 #16869252

Subgroups — C17×#11508 #16869252

Order 4352.

574 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C17×#2311C211yesmaximal, characteristic
2C17×#1463C212yesmaximal, complemented
3C17×#1319C212yesmaximal, complemented
4C17×#1318C212yesmaximal, complemented
5C22×#41×C17C411yescharacteristic
6C2×C17×#117C411yescharacteristic
7C22×C4⋊C4×C17C2211yescharacteristic
8C17×#407—22no—
9C17×#391C411yescharacteristic
10C17×#391C2211yescharacteristic
11C17×#390C411yescharacteristic
12C17×#390C2211yescharacteristic
13C17×#386—22no—
14C17×#380—22no—
15C17×#324—22no—
16C17×#324C2214yes—
17C2×#41×C17—22no—
18C2×#41×C17—22no—
19C2×#41×C17—42no—
20C2×#41×C17—42no—
21C22×Q8×C17C2×C411yescharacteristic
22C22×D4×C17—21no—
23C22×D4×C17C2×C411yescharacteristic
24C23×C4×C17—21no—
25C23×C4×C17C2×C411yescharacteristic
26C23×C4×C17D412yes—
27C2×M16×C17—42no—
28C17×#117—42no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—42no—
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C4⋊C4×C17D412yes—
33C2×C4⋊C4×C17C2311yescharacteristic
34C2×C22⋊C4×C17—21no—
35C2×C22⋊C4×C17—22no—
36C2×C22⋊C4×C17—22no—
37C2×C42×C17C2×C411yescharacteristic
38C2×C42×C17C2×C411yescharacteristic
39C17×C22⋊C8—24no—
40C17×C22⋊C8—42no—
41C17×#95—22no—
42C17×#95—22no—
43C24×C17—21no—
44C24×C17C22⋊C411yescharacteristic
45#41×C17—48no—
46#41×C17—48no—
47C2×Q8×C17—21no—
48C2×Q8×C17—41no—
49C2×Q8×C17—41no—
50C2×Q8×C17M1612yescomplemented
51C2×D4×C17—24no—
52C2×D4×C17—21no—
53C2×D4×C17—41no—
54C2×D4×C17—41no—
55C2×D4×C17—42no—
56C2×D4×C17—42no—
57C2×D4×C17M1612yescomplemented
58C22×C4×C17—22no—
59C22×C4×C17—22no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—24no—
63C22×C4×C17—22no—
64C22×C4×C17—21no—
65C22×C4×C17—22no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—42no—
69C22×C4×C17—42no—
70C22×C4×C17—82no—
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17C22⋊C412yes—
73C22×C4×C17C22×C411yescharacteristic
74C22×C4×C17C2×D412yes—
75M16×C17—84no—
76C2×C8×C17—44no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—42no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—42no—
81C22⋊C4×C17—42no—
82C22⋊C4×C17—82no—
83C22⋊C4×C17—82no—
84C42×C17—41no—
85C42×C17—41no—
86#11508C1711yesmaximal, characteristic, direct product factor, Sylow
87C23×C17—21no—
88C23×C17—21no—
89C23×C17—22no—
90C23×C17—41no—
91C23×C17—41no—
92C23×C17—42no—
93C23×C17—42no—
94C23×C17—41no—
95C23×C17—41no—
96C23×C17#9912yes—
97C23×C17C2×C22⋊C411yescharacteristic
98Q8×C17—42no—
99Q8×C17—42no—
100D4×C17—42no—
101D4×C17—42no—
102D4×C17—48no—
103C2×C4×C17—24no—
104C2×C4×C17—24no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—22no—
110C2×C4×C17—22no—
111C2×C4×C17—22no—
112C2×C4×C17—48no—
113C2×C4×C17—44no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—42no—
117C2×C4×C17—42no—
118C2×C4×C17—41no—
119C2×C4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—82no—
125C2×C4×C17#10012yes—
126C2×C4×C17C2×M1611yescharacteristic
127C2×C4×C17C2×M1611yescharacteristic
128C8×C17—84no—
129#2311C2×C1711yescharacteristic
130#1463C2×C1712yescomplemented
131#1319C2×C1712yescomplemented
132#1318C2×C1712yescomplemented
133C22×C17—21no—
134C22×C17—21no—
135C22×C17—22no—
136C22×C17—22no—
137C22×C17—22no—
138C22×C17—42no—
139C22×C17—42no—
140C22×C17—44no—
141C22×C17—42no—
142C22×C17—82no—
143C22×C17—81no—
144C22×C17—81no—
145C22×C17#40711yescharacteristic
146C22×C17C2×#9911yescharacteristic
147C22×C17C2×#10011yescharacteristic
148C4×C17—22no—
149C4×C17—21no—
150C4×C17—21no—
151C4×C17—42no—
152C4×C17—42no—
153C4×C17—42no—
154C4×C17—81no—
155C4×C17—81no—
156C22×#41C4×C1711yescharacteristic
157C2×#117C4×C1711yescharacteristic
158C22×C4⋊C4C22×C1711yescharacteristic
159#407—22no—
160#391C4×C1711yescharacteristic
161#391C22×C1711yescharacteristic
162#390C4×C1711yescharacteristic
163#390C22×C1711yescharacteristic
164#386—22no—
165#380—22no—
166#324—22no—
167#324C22×C1714yes—
168C2×C17—21no—
169C2×C17—21no—
170C2×C17—42no—
171C2×C17—82no—
172C2×C17#146211yescharacteristic
173C2×C17#212711yescharacteristic
174C2×C17#213311yescharacteristic
175C2×#41—22no—
176C2×#41—22no—
177C2×#41—42no—
178C2×#41—42no—
179C22×Q8C2×C4×C1711yescharacteristic
180C22×D4—21no—
181C22×D4C2×C4×C1711yescharacteristic
182C23×C4—21no—
183C23×C4C2×C4×C1711yescharacteristic
184C23×C4D4×C1712yes—
185C2×M16—42no—
186#117—42no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—42no—
189C2×C4⋊C4C2×C4×C1711yescharacteristic
190C2×C4⋊C4D4×C1712yes—
191C2×C4⋊C4C23×C1711yescharacteristic
192C2×C22⋊C4—21no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C42C2×C4×C1711yescharacteristic
196C2×C42C2×C4×C1711yescharacteristic
197C22⋊C8—24no—
198C22⋊C8—42no—
199#95—22no—
200#95—22no—
201C17#1150811yescharacteristic, direct product factor, Sylow
202C24—21no—
203C24C22⋊C4×C1711yescharacteristic
204#41—48no—
205#41—48no—
206C2×Q8—21no—
207C2×Q8—41no—
208C2×Q8—41no—
209C2×Q8M16×C1712yescomplemented
210C2×D4—24no—
211C2×D4—21no—
212C2×D4—41no—
213C2×D4—41no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4M16×C1712yescomplemented
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—24no—
222C22×C4—22no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—82no—
230C22×C4C22⋊C4×C1711yescharacteristic
231C22×C4C22⋊C4×C1712yes—
232C22×C4C22×C4×C1711yescharacteristic
233C22×C4C2×D4×C1712yes—
234M16—84no—
235C2×C8—44no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—41no—
239C4⋊C4—42no—
240C22⋊C4—42no—
241C22⋊C4—82no—
242C22⋊C4—82no—
243C42—41no—
244C42—41no—
245C23—21no—
246C23—21no—
247C23—22no—
248C23—41no—
249C23—41no—
250C23—42no—
251C23—42no—
252C23—41no—
253C23—41no—
254C23C17×#9912yes—
255C23C2×C22⋊C4×C1711yescharacteristic
256Q8—42no—
257Q8—42no—
258D4—42no—
259D4—42no—
260D4—48no—
261C2×C4—24no—
262C2×C4—24no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—48no—
271C2×C4—44no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—82no—
283C2×C4C17×#10012yes—
284C2×C4C2×M16×C1711yescharacteristic
285C2×C4C2×M16×C1711yescharacteristic
286C8—84no—
287C22—21no—
288C22—21no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—44no—
295C22—42no—
296C22—82no—
297C22—81no—
298C22—81no—
299C22C17×#40711yescharacteristic
300C22C2×C17×#9911yescharacteristic
301C22C2×C17×#10011yescharacteristic
302C4—22no—
303C4—21no—
304C4—21no—
305C4—42no—
306C4—42no—
307C4—42no—
308C4—81no—
309C4—81no—
310C2—21no—
311C2—21no—
312C2—42no—
313C2—82no—
314C2C17×#146211yescharacteristic
315C2C17×#212711yescharacteristic
316C2C17×#213311yescharacteristic
subgroupG/H
center, socleC22×C17C2×#99
commutatorC22×C4C22×C4×C17
Frattini, cosocleC2×C4⋊C4C23×C17
prime radicalC22×#41×C17C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C24×C17 ◁ C22×C4⋊C4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#1463C2semidirect
3. C17×#1319C2semidirect
4. C17×#1318C2semidirect
50. C2×Q8×C17M16semidirect
57. C2×D4×C17M16semidirect
86. #11508C17direct (N × H)
130. #1463C2×C17semidirect
131. #1319C2×C17semidirect
132. #1318C2×C17semidirect
201. C17#11508direct (N × H)
209. C2×Q8M16×C17semidirect
216. C2×D4M16×C17semidirect

Maximal subgroups

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

subgroupindex
C17×#23112
C17×#14632
C17×#13192
C17×#13182
#1150817