Finite Group Databasebeta

← C17×#11890 #16869634

Subgroups — C17×#11890 #16869634

Order 4352.

416 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3050C211yesmaximal, characteristic
2C17×#2112C211yesmaximal, characteristic, complemented
3C17×#1808C211yesmaximal, characteristic, complemented
4C17×#1348C212yesmaximal, complemented
5C17×#1347C212yesmaximal, complemented
6C2×C17×#135C411yescharacteristic, complemented
7C23×C8×C17C2211yescharacteristic
8C17×#525—21no—
9C2×C17×M32—21no—
10C17×#467C411yescharacteristic, complemented
11C17×#467C2211yescharacteristic
12C17×#466C411yescharacteristic, complemented
13C17×#466C2211yescharacteristic
14C17×#465—21no—
15C17×#465—21no—
16C17×#427C411yescharacteristic, complemented
17C2×C17×#107—21no—
18C17×#416—21no—
19C17×#380—21no—
20C17×C22⋊C16—21no—
21C17×C22⋊C16C2212yes—
22C17×#340C2212yes—
23C2×#41×C17—21no—
24C23×C4×C17D411yescharacteristic
25C17×#135—42no—
26C2×Q16×C17C2×C411yescharacteristic
27C2×SD16×C17—21no—
28C2×D8×C17C2×C411yescharacteristic
29C22×C8×C17—42no—
30C22×C8×C17C2×C411yescharacteristic
31C22×C8×C17C2×C411yescharacteristic
32C22×C8×C17D411yescharacteristic
33C22×C8×C17D411yescharacteristic
34C22×C8×C17D411yescharacteristic
35C22×C8×C17C2311yescharacteristic
36C17×#123—41no—
37C17×C22⋊Q8—21no—
38C17×C22⋊Q8—21no—
39C17×#121—21no—
40C17×#121—21no—
41C17×#120—41no—
42C4×D4×C17—41no—
43C4×D4×C17—41no—
44C17×#117—21no—
45C2×C4⋊C4×C17—22no—
46C2×C22⋊C4×C17—41no—
47C17×M32—42no—
48C2×C16×C17—22no—
49C17×#107—42no—
50C17×#107C2×C411yescharacteristic
51C17×#107C2×C411yescharacteristic
52C17×#106—21no—
53C17×#103—21no—
54C17×#103—21no—
55C17×#102—21no—
56C17×#102—21no—
57C17×#95—41no—
58C24×C17D811yescharacteristic
59#41×C17—42no—
60#41×C17—42no—
61C2×Q8×C17—21no—
62C2×D4×C17—21no—
63C2×D4×C17—41no—
64C2×D4×C17—41no—
65C2×D4×C17—41no—
66C22×C4×C17—41no—
67C22×C4×C17—41no—
68C22×C4×C17—41no—
69C22×C4×C17—42no—
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17D811yescharacteristic
73C22×C4×C17SD1611yescharacteristic
74C22×C4×C17SD1611yescharacteristic
75C22×C4×C17C2×D411yescharacteristic
76Q16×C17—41no—
77SD16×C17—42no—
78D8×C17—41no—
79C2×C8×C17—22no—
80C2×C8×C17—22no—
81C2×C8×C17—22no—
82C2×C8×C17—41no—
83C2×C8×C17—41no—
84C2×C8×C17—41no—
85C2×C8×C17C22⋊C411yescharacteristic
86C2×C8×C17C22⋊C411yescharacteristic
87C2×C8×C17C22×C411yescharacteristic
88C2×C8×C17C2×D411yescharacteristic
89C4⋊C4×C17—21no—
90C4⋊C4×C17—21no—
91C4⋊C4×C17—42no—
92C4⋊C4×C17—42no—
93C4⋊C4×C17—41no—
94C4⋊C4×C17—41no—
95C22⋊C4×C17—41no—
96C22⋊C4×C17—41no—
97C22⋊C4×C17—41no—
98C22⋊C4×C17—41no—
99C22⋊C4×C17—41no—
100C22⋊C4×C17—82no—
101C42×C17—41no—
102C16×C17—42no—
103#11890C1711yesmaximal, characteristic, direct product factor, Sylow
104C23×C17—21no—
105C23×C17—21no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17—41no—
109C23×C17#10211yescharacteristic
110C23×C17#10211yescharacteristic
111C23×C17C2×D811yescharacteristic
112Q8×C17—41no—
113Q8×C17—41no—
114D4×C17—41no—
115D4×C17—41no—
116D4×C17—82no—
117D4×C17—82no—
118D4×C17—81no—
119D4×C17—81no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17—82no—
133C2×C4×C17—82no—
134C2×C4×C17—82no—
135C2×C4×C17—82no—
136C2×C4×C17#10211yescharacteristic
137C2×C4×C17#10211yescharacteristic
138C2×C4×C17C2×C22⋊C411yescharacteristic
139C2×C4×C17C2×SD1611yescharacteristic
140C8×C17—21no—
141C8×C17—21no—
142C8×C17—21no—
143C8×C17#9912yes—
144#3050C2×C1711yescharacteristic
145#2112C2×C1711yescharacteristic, complemented
146#1808C2×C1711yescharacteristic, complemented
147#1348C2×C1712yescomplemented
148#1347C2×C1712yescomplemented
149C22×C17—21no—
150C22×C17—21no—
151C22×C17—21no—
152C22×C17—21no—
153C22×C17—21no—
154C22×C17—21no—
155C22×C17—21no—
156C22×C17—21no—
157C22×C17—42no—
158C22×C17—42no—
159C22×C17—81no—
160C22×C17—81no—
161C22×C17—81no—
162C22×C17C2×#10211yescharacteristic
163C22×C17#50911yescharacteristic
164C22×C17#51011yescharacteristic
165C4×C17—21no—
166C4×C17—21no—
167C4×C17—21no—
168C4×C17—81no—
169C4×C17—81no—
170C4×C17—81no—
171C4×C17—162no—
172C4×C17C2×#9911yescharacteristic
173C4×C17#42111yescharacteristic
174C2×#135C4×C1711yescharacteristic, complemented
175C23×C8C22×C1711yescharacteristic
176#525—21no—
177C2×M32—21no—
178#467C4×C1711yescharacteristic, complemented
179#467C22×C1711yescharacteristic
180#466C4×C1711yescharacteristic, complemented
181#466C22×C1711yescharacteristic
182#465—21no—
183#465—21no—
184#427C4×C1711yescharacteristic, complemented
185C2×#107—21no—
186#416—21no—
187#380—21no—
188C22⋊C16—21no—
189C22⋊C16C22×C1712yes—
190#340C22×C1712yes—
191C2×C17—21no—
192C2×C17—21no—
193C2×C17—41no—
194C2×C17—41no—
195C2×C17—161no—
196C2×C17#151911yescharacteristic
197C2×C17#213911yescharacteristic
198C2×C17#214511yescharacteristic
199C2×#41—21no—
200C23×C4D4×C1711yescharacteristic
201#135—42no—
202C2×Q16C2×C4×C1711yescharacteristic
203C2×SD16—21no—
204C2×D8C2×C4×C1711yescharacteristic
205C22×C8—42no—
206C22×C8C2×C4×C1711yescharacteristic
207C22×C8C2×C4×C1711yescharacteristic
208C22×C8D4×C1711yescharacteristic
209C22×C8D4×C1711yescharacteristic
210C22×C8D4×C1711yescharacteristic
211C22×C8C23×C1711yescharacteristic
212#123—41no—
213C22⋊Q8—21no—
214C22⋊Q8—21no—
215#121—21no—
216#121—21no—
217#120—41no—
218C4×D4—41no—
219C4×D4—41no—
220#117—21no—
221C2×C4⋊C4—22no—
222C2×C22⋊C4—41no—
223M32—42no—
224C2×C16—22no—
225#107—42no—
226#107C2×C4×C1711yescharacteristic
227#107C2×C4×C1711yescharacteristic
228#106—21no—
229#103—21no—
230#103—21no—
231#102—21no—
232#102—21no—
233#95—41no—
234C17#1189011yescharacteristic, direct product factor, Sylow
235C24D8×C1711yescharacteristic
236#41—42no—
237#41—42no—
238C2×Q8—21no—
239C2×D4—21no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—42no—
247C22×C4C22⋊C4×C1711yescharacteristic
248C22×C4C22⋊C4×C1711yescharacteristic
249C22×C4D8×C1711yescharacteristic
250C22×C4SD16×C1711yescharacteristic
251C22×C4SD16×C1711yescharacteristic
252C22×C4C2×D4×C1711yescharacteristic
253Q16—41no—
254SD16—42no—
255D8—41no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8C22⋊C4×C1711yescharacteristic
263C2×C8C22⋊C4×C1711yescharacteristic
264C2×C8C22×C4×C1711yescharacteristic
265C2×C8C2×D4×C1711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—82no—
278C42—41no—
279C16—42no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23C17×#10211yescharacteristic
286C23C17×#10211yescharacteristic
287C23C2×D8×C1711yescharacteristic
288Q8—41no—
289Q8—41no—
290D4—41no—
291D4—41no—
292D4—82no—
293D4—82no—
294D4—81no—
295D4—81no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4C17×#10211yescharacteristic
313C2×C4C17×#10211yescharacteristic
314C2×C4C2×C22⋊C4×C1711yescharacteristic
315C2×C4C2×SD16×C1711yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8C17×#9912yes—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—42no—
329C22—42no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22C2×C17×#10211yescharacteristic
334C22C17×#50911yescharacteristic
335C22C17×#51011yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4—162no—
343C4C2×C17×#9911yescharacteristic
344C4C17×#42111yescharacteristic
345C2—21no—
346C2—21no—
347C2—41no—
348C2—41no—
349C2—161no—
350C2C17×#151911yescharacteristic
351C2C17×#213911yescharacteristic
352C2C17×#214511yescharacteristic
subgroupG/H
center, socleC22×C17C2×#102
commutatorC2×C8C22×C4×C17
Frattini, cosocleC22×C8C23×C17
prime radicalC17×#3050C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C23×C4×C17 ◁ C23×C8×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#2112C2semidirect
3. C17×#1808C2semidirect
4. C17×#1348C2semidirect
5. C17×#1347C2semidirect
6. C2×C17×#135C4semidirect
10. C17×#467C4semidirect
12. C17×#466C4semidirect
16. C17×#427C4semidirect
103. #11890C17direct (N × H)
145. #2112C2×C17semidirect
146. #1808C2×C17semidirect
147. #1348C2×C17semidirect
148. #1347C2×C17semidirect
174. C2×#135C4×C17semidirect
178. #467C4×C17semidirect
180. #466C4×C17semidirect
184. #427C4×C17semidirect
234. C17#11890direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#30502
C17×#21122
C17×#18082
C17×#13482
C17×#13472
#1189017