Finite Group Databasebeta

← C17×#11576 #16869320

Subgroups — C17×#11576 #16869320

Order 4352.

426 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2487C211yesmaximal, characteristic
2C17×#1466C211yesmaximal, characteristic
3C17×#1459C211yesmaximal, characteristic
4C17×#1326C214yesmaximal, complemented
5C2×C4×D4×C17C2211yescharacteristic
6C22×C4⋊C4×C17C411yescharacteristic
7C17×#432—21no—
8C2×C17×C22⋊C8—21no—
9C17×#400—21no—
10C17×#399—21no—
11C17×#389—21no—
12C17×#386C412yes—
13C17×#385C2212yes—
14C17×#380—21no—
15C17×#380C411yescharacteristic
16C17×#324—21no—
17C17×#323—21no—
18C17×#323C2212yes—
19C17×#323C2212yes—
20C22×D4×C17C2×C411yescharacteristic
21C23×C4×C17C2×C411yescharacteristic
22C23×C4×C17C2×C412yes—
23C23×C4×C17D411yescharacteristic
24C22×C8×C17—41no—
25C4×D4×C17—41no—
26C4×D4×C17—41no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—22no—
31C2×C4⋊C4×C17—41no—
32C2×C4⋊C4×C17—41no—
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C22⋊C4×C17—22no—
35C2×C22⋊C4×C17C2×C412yes—
36C2×C22⋊C4×C17D411yescharacteristic
37C2×C22⋊C4×C17C2311yescharacteristic
38C2×C42×C17D411yescharacteristic
39C17×C4⋊C8—41no—
40C17×C22⋊C8—22no—
41C17×C22⋊C8—22no—
42C17×C22⋊C8—41no—
43C17×#97—41no—
44C17×#95—21no—
45C17×#95—22no—
46C17×#95—22no—
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—22no—
57C22×C4×C17—22no—
58C22×C4×C17—42no—
59C22×C4×C17—42no—
60C22×C4×C17—42no—
61C22×C4×C17—82no—
62C22×C4×C17C22⋊C411yescharacteristic
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17C2×D411yescharacteristic
66C22×C4×C17C2×D411yescharacteristic
67C2×C8×C17—42no—
68C2×C8×C17—42no—
69C2×C8×C17—82no—
70C4⋊C4×C17—41no—
71C4⋊C4×C17—42no—
72C4⋊C4×C17—42no—
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—82no—
76C22⋊C4×C17—24no—
77C22⋊C4×C17—41no—
78C22⋊C4×C17—41no—
79C22⋊C4×C17—82no—
80C42×C17—21no—
81C42×C17—21no—
82#11576C1711yesmaximal, characteristic, direct product factor, Sylow
83C23×C17—21no—
84C23×C17—21no—
85C23×C17—21no—
86C23×C17—21no—
87C23×C17—41no—
88C23×C17—41no—
89C23×C17—41no—
90C23×C17—41no—
91C23×C17#10112yes—
92C23×C17C2×C22⋊C411yescharacteristic
93C23×C17#13112yes—
94D4×C17—44no—
95C2×C4×C17—22no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—42no—
103C2×C4×C17—42no—
104C2×C4×C17—42no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—42no—
109C2×C4×C17—42no—
110C2×C4×C17—42no—
111C2×C4×C17—42no—
112C2×C4×C17—42no—
113C2×C4×C17—42no—
114C2×C4×C17—81no—
115C2×C4×C17—84no—
116C2×C4×C17#9911yescharacteristic
117C2×C4×C17#9911yescharacteristic
118C8×C17—82no—
119C8×C17—82no—
120#2487C2×C1711yescharacteristic
121#1466C2×C1711yescharacteristic
122#1459C2×C1711yescharacteristic
123#1326C2×C1714yescomplemented
124C22×C17—21no—
125C22×C17—21no—
126C22×C17—22no—
127C22×C17—22no—
128C22×C17—42no—
129C22×C17—42no—
130C22×C17—42no—
131C22×C17—41no—
132C22×C17—41no—
133C22×C17—41no—
134C22×C17—41no—
135C22×C17—81no—
136C22×C17#40811yescharacteristic
137C22×C17C2×#9911yescharacteristic
138C22×C17C2×#10111yescharacteristic
139C4×C17—21no—
140C4×C17—41no—
141C4×C17—41no—
142C4×C17—41no—
143C4×C17—41no—
144C4×C17—82no—
145C4×C17—82no—
146C4×C17#35212yes—
147C2×C4×D4C22×C1711yescharacteristic
148C22×C4⋊C4C4×C1711yescharacteristic
149#432—21no—
150C2×C22⋊C8—21no—
151#400—21no—
152#399—21no—
153#389—21no—
154#386C4×C1712yes—
155#385C22×C1712yes—
156#380—21no—
157#380C4×C1711yescharacteristic
158#324—21no—
159#323—21no—
160#323C22×C1712yes—
161#323C22×C1712yes—
162C2×C17—21no—
163C2×C17—21no—
164C2×C17—42no—
165C2×C17—42no—
166C2×C17#147211yescharacteristic
167C2×C17C2×#35211yescharacteristic
168C2×C17#212211yescharacteristic
169C22×D4C2×C4×C1711yescharacteristic
170C23×C4C2×C4×C1711yescharacteristic
171C23×C4C2×C4×C1712yes—
172C23×C4D4×C1711yescharacteristic
173C22×C8—41no—
174C4×D4—41no—
175C4×D4—41no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4D4×C1711yescharacteristic
183C2×C22⋊C4—22no—
184C2×C22⋊C4C2×C4×C1712yes—
185C2×C22⋊C4D4×C1711yescharacteristic
186C2×C22⋊C4C23×C1711yescharacteristic
187C2×C42D4×C1711yescharacteristic
188C4⋊C8—41no—
189C22⋊C8—22no—
190C22⋊C8—22no—
191C22⋊C8—41no—
192#97—41no—
193#95—21no—
194#95—22no—
195#95—22no—
196C17#1157611yescharacteristic, direct product factor, Sylow
197C24C22⋊C4×C1711yescharacteristic
198C24C22×C4×C1711yescharacteristic
199C2×D4—22no—
200C2×D4—22no—
201C2×D4—41no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—82no—
212C22×C4C22⋊C4×C1711yescharacteristic
213C22×C4C22⋊C4×C1711yescharacteristic
214C22×C4C22⋊C4×C1711yescharacteristic
215C22×C4C2×D4×C1711yescharacteristic
216C22×C4C2×D4×C1711yescharacteristic
217C2×C8—42no—
218C2×C8—42no—
219C2×C8—82no—
220C4⋊C4—41no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—82no—
226C22⋊C4—24no—
227C22⋊C4—41no—
228C22⋊C4—41no—
229C22⋊C4—82no—
230C42—21no—
231C42—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—41no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23C17×#10112yes—
241C23C2×C22⋊C4×C1711yescharacteristic
242C23C17×#13112yes—
243D4—44no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—81no—
264C2×C4—84no—
265C2×C4C17×#9911yescharacteristic
266C2×C4C17×#9911yescharacteristic
267C8—82no—
268C8—82no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—81no—
281C22C17×#40811yescharacteristic
282C22C2×C17×#9911yescharacteristic
283C22C2×C17×#10111yescharacteristic
284C4—21no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—41no—
289C4—82no—
290C4—82no—
291C4C17×#35212yes—
292C2—21no—
293C2—21no—
294C2—42no—
295C2—42no—
296C2C17×#147211yescharacteristic
297C2C2×C17×#35211yescharacteristic
298C2C17×#212211yescharacteristic
subgroupG/H
center, socleC22×C17C2×#99
commutatorC24C22×C4×C17
Frattini, cosocleC2×C22⋊C4C23×C17
prime radicalC22×D4×C17C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C4×D4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
4. C17×#1326C2semidirect
82. #11576C17direct (N × H)
123. #1326C2×C17semidirect
196. C17#11576direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#24872
C17×#14662
C17×#14592
C17×#13262
#1157617