Finite Group Databasebeta

← C17×#11544 #16869288

Subgroups — C17×#11544 #16869288

Order 4352.

380 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2484C211yesmaximal, characteristic
2C17×#1464C211yesmaximal, characteristic
3C17×#1458C211yesmaximal, characteristic
4C17×#1326C212yesmaximal
5C17×#1317C212yesmaximal
6C2×C17×#117C2211yescharacteristic
7C22×C4⋊C4×C17C411yescharacteristic
8C17×#432—21no—
9C17×#431—21no—
10C17×#400—21no—
11C17×#398—21no—
12C17×#387—21no—
13C17×#387—21no—
14C17×#385C411yescharacteristic
15C17×#385C2211yescharacteristic
16C17×#381C411yescharacteristic
17C17×#381C411yescharacteristic
18C17×#381C2211yescharacteristic
19C17×#324—21no—
20C17×#324—21no—
21C17×#323C2212yes—
22C17×#323C2212yes—
23C23×C4×C17C2×C411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C17×#117—41no—
27C17×#117—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—41no—
33C2×C4⋊C4×C17—41no—
34C2×C4⋊C4×C17D411yescharacteristic
35C2×C4⋊C4×C17D411yescharacteristic
36C2×C22⋊C4×C17C2×C411yescharacteristic
37C2×C22⋊C4×C17C2×C411yescharacteristic
38C2×C22⋊C4×C17C2×C411yescharacteristic
39C2×C22⋊C4×C17C2311yescharacteristic
40C2×C42×C17D411yescharacteristic
41C2×C42×C17D411yescharacteristic
42C17×C4⋊C8—41no—
43C17×C4⋊C8—41no—
44C17×C22⋊C8—22no—
45C17×C22⋊C8—22no—
46C17×#97—41no—
47C4×C8×C17—41no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95—21no—
51C17×#95—21no—
52C17×#95—21no—
53C17×#95—21no—
54C17×#95—21no—
55C17×#95—21no—
56C24×C17C22×C411yescharacteristic
57C22×C4×C17—21no—
58C22×C4×C17—22no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—22no—
65C22×C4×C17—41no—
66C22×C4×C17—42no—
67C22×C4×C17—41no—
68C22×C4×C17—41no—
69C22×C4×C17—41no—
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C22⋊C411yescharacteristic
74C22×C4×C17C2×D411yescharacteristic
75C22×C4×C17C2×D411yescharacteristic
76C2×C8×C17—42no—
77C2×C8×C17—42no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—42no—
81C4⋊C4×C17—42no—
82C4⋊C4×C17—42no—
83C4⋊C4×C17—41no—
84C4⋊C4×C17—41no—
85C22⋊C4×C17—22no—
86C22⋊C4×C17—41no—
87C22⋊C4×C17—41no—
88C22⋊C4×C17—41no—
89C42×C17—21no—
90C42×C17—21no—
91C42×C17—21no—
92C42×C17—21no—
93#11544C1711yesmaximal, characteristic, direct product factor, Sylow
94C23×C17—21no—
95C23×C17—21no—
96C23×C17—41no—
97C23×C17—41no—
98C23×C17C2×C22⋊C411yescharacteristic
99C23×C17#13112yes—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—22no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—42no—
111C2×C4×C17—42no—
112C2×C4×C17—41no—
113C2×C4×C17—42no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17—41no—
119C2×C4×C17—42no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—82no—
130C2×C4×C17#9911yescharacteristic
131C2×C4×C17#9911yescharacteristic
132C8×C17—82no—
133C8×C17—82no—
134#2484C2×C1711yescharacteristic
135#1464C2×C1711yescharacteristic
136#1458C2×C1711yescharacteristic
137#1326C2×C1712yes—
138#1317C2×C1712yes—
139C22×C17—21no—
140C22×C17—21no—
141C22×C17—22no—
142C22×C17—42no—
143C22×C17—42no—
144C22×C17—41no—
145C22×C17—41no—
146C22×C17#40811yescharacteristic
147C22×C17C2×#9911yescharacteristic
148C22×C17#41311yescharacteristic
149C4×C17—21no—
150C4×C17—21no—
151C4×C17—41no—
152C4×C17—41no—
153C4×C17—42no—
154C4×C17—41no—
155C4×C17—41no—
156C4×C17—41no—
157C4×C17—81no—
158C4×C17—81no—
159C4×C17—81no—
160C2×#117C22×C1711yescharacteristic
161C22×C4⋊C4C4×C1711yescharacteristic
162#432—21no—
163#431—21no—
164#400—21no—
165#398—21no—
166#387—21no—
167#387—21no—
168#385C4×C1711yescharacteristic
169#385C22×C1711yescharacteristic
170#381C4×C1711yescharacteristic
171#381C4×C1711yescharacteristic
172#381C22×C1711yescharacteristic
173#324—21no—
174#324—21no—
175#323C22×C1712yes—
176#323C22×C1712yes—
177C2×C17—21no—
178C2×C17—21no—
179C2×C17—42no—
180C2×C17#146811yescharacteristic
181C2×C17#212011yescharacteristic
182C2×C17#212311yescharacteristic
183C23×C4C2×C4×C1711yescharacteristic
184C23×C4C2×C4×C1711yescharacteristic
185C23×C4C2×C4×C1711yescharacteristic
186#117—41no—
187#117—41no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—41no—
193C2×C4⋊C4—41no—
194C2×C4⋊C4D4×C1711yescharacteristic
195C2×C4⋊C4D4×C1711yescharacteristic
196C2×C22⋊C4C2×C4×C1711yescharacteristic
197C2×C22⋊C4C2×C4×C1711yescharacteristic
198C2×C22⋊C4C2×C4×C1711yescharacteristic
199C2×C22⋊C4C23×C1711yescharacteristic
200C2×C42D4×C1711yescharacteristic
201C2×C42D4×C1711yescharacteristic
202C4⋊C8—41no—
203C4⋊C8—41no—
204C22⋊C8—22no—
205C22⋊C8—22no—
206#97—41no—
207C4×C8—41no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216C17#1154411yescharacteristic, direct product factor, Sylow
217C24C22×C4×C1711yescharacteristic
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—41no—
227C22×C4—42no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4C22⋊C4×C1711yescharacteristic
232C22×C4C22⋊C4×C1711yescharacteristic
233C22×C4C22⋊C4×C1711yescharacteristic
234C22×C4C22⋊C4×C1711yescharacteristic
235C22×C4C2×D4×C1711yescharacteristic
236C22×C4C2×D4×C1711yescharacteristic
237C2×C8—42no—
238C2×C8—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C22⋊C4—22no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×C22⋊C4×C1711yescharacteristic
259C23C17×#13112yes—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—82no—
290C2×C4C17×#9911yescharacteristic
291C2×C4C17×#9911yescharacteristic
292C8—82no—
293C8—82no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22C17×#40811yescharacteristic
302C22C2×C17×#9911yescharacteristic
303C22C17×#41311yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—42no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4—81no—
314C4—81no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2C17×#146811yescharacteristic
319C2C17×#212011yescharacteristic
320C2C17×#212311yescharacteristic
subgroupG/H
center, socleC22×C17C2×#99
commutatorC24C22×C4×C17
Frattini, cosocleC2×C22⋊C4C23×C17
prime radicalC24×C17C22×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C17×#117 ◁ G

Complements

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

NH ≅ G/Ntype
93. #11544C17direct (N × H)
216. C17#11544direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#24842
C17×#14642
C17×#14582
C17×#13262
C17×#13172
#1154417