Finite Group Databasebeta

← C17×#3346 #14526352

Subgroups — C17×#3346 #14526352

Order 2176.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#554C211yesmaximal, characteristic, complemented
2C17×#553C211yesmaximal, characteristic
3C17×#501C211yesmaximal, characteristic, complemented
4C17×#485C211yesmaximal, characteristic, complemented
5C17×#484C211yesmaximal, characteristic, complemented
6C17×#481C211yesmaximal, characteristic, complemented
7C17×#480C211yesmaximal, characteristic, complemented
8C17×#479C211yesmaximal, characteristic, complemented
9C17×#474C211yesmaximal, characteristic, complemented
10C17×#468C211yesmaximal, characteristic, complemented
11C17×#465C211yesmaximal, characteristic, complemented
12C17×#440C211yesmaximal, characteristic, complemented
13C17×#435C211yesmaximal, characteristic, complemented
14C17×#428C211yesmaximal, characteristic, complemented
15C2×C17×#107C211yesmaximal, characteristic, complemented
16C2×SD16×C17C2211yescharacteristic
17C2×M16×C17C2211yescharacteristic
18C22×C8×C17C2211yescharacteristic
19C17×C4⋊Q8C2211yescharacteristic
20C17×#126—21no—
21C17×#125—21no—
22C17×#125C2211yescharacteristic
23C17×#123—21no—
24C17×C22⋊Q8—21no—
25C17×C22⋊Q8—21no—
26C17×C22⋊Q8C2211yescharacteristic
27C17×C22⋊Q8C2211yescharacteristic
28C17×#121—21no—
29C17×#121C2211yescharacteristic
30C17×#121C2211yescharacteristic
31C4×Q8×C17C2211yescharacteristic
32C4×D4×C17—21no—
33C4×D4×C17—21no—
34C4×D4×C17C2211yescharacteristic
35C4×D4×C17C2211yescharacteristic
36C17×#117C2211yescharacteristic
37C2×C4⋊C4×C17C2211yescharacteristic
38C2×C4⋊C4×C17C2211yescharacteristic
39C2×C4⋊C4×C17C2211yescharacteristic
40C17×#107C2211yescharacteristic
41C17×#107C2211yescharacteristic
42C17×#107C2211yescharacteristic
43C17×#107C2211yescharacteristic
44C17×#107C2211yescharacteristic
45C17×#107C2211yescharacteristic
46C17×#106C2211yescharacteristic
47C17×#106C2211yescharacteristic
48C17×#106C2211yescharacteristic
49C17×C4⋊C8C2211yescharacteristic
50C17×#103C2211yescharacteristic
51C17×#103C2211yescharacteristic
52C17×#103C2211yescharacteristic
53C17×#102C2211yescharacteristic
54C17×#102C2211yescharacteristic
55C17×#102C2211yescharacteristic
56C17×C22⋊C8C2211yescharacteristic
57C17×C22⋊C8C2211yescharacteristic
58C17×#97C2211yescharacteristic
59C2×Q8×C17—21no—
60C2×Q8×C17C2311yescharacteristic
61C2×D4×C17—21no—
62C2×D4×C17—21no—
63C2×D4×C17D411yescharacteristic
64C2×D4×C17C2311yescharacteristic
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17C2311yescharacteristic
70C22×C4×C17C2311yescharacteristic
71SD16×C17—22no—
72M16×C17—22no—
73C2×C8×C17—22no—
74C2×C8×C17C2311yescharacteristic
75C2×C8×C17C2311yescharacteristic
76C2×C8×C17C2311yescharacteristic
77C2×C8×C17C2311yescharacteristic
78C4⋊C4×C17—21no—
79C4⋊C4×C17—21no—
80C4⋊C4×C17—21no—
81C4⋊C4×C17—21no—
82C4⋊C4×C17—21no—
83C4⋊C4×C17—21no—
84C4⋊C4×C17—21no—
85C4⋊C4×C17—21no—
86C4⋊C4×C17—21no—
87C4⋊C4×C17D411yescharacteristic
88C4⋊C4×C17C2311yescharacteristic
89C4⋊C4×C17C2311yescharacteristic
90C4⋊C4×C17C2311yescharacteristic
91C4⋊C4×C17C2311yescharacteristic
92C4⋊C4×C17C2311yescharacteristic
93C4⋊C4×C17C2311yescharacteristic
94C22⋊C4×C17—21no—
95C22⋊C4×C17—21no—
96C22⋊C4×C17—21no—
97C22⋊C4×C17—21no—
98C22⋊C4×C17—21no—
99C22⋊C4×C17—21no—
100C22⋊C4×C17D411yescharacteristic
101C22⋊C4×C17D411yescharacteristic
102C42×C17—21no—
103C42×C17—21no—
104C42×C17C2311yescharacteristic
105C23×C17—21no—
106C23×C17C2×D411yescharacteristic
107C23×C17C2×D411yescharacteristic
108Q8×C17—21no—
109Q8×C17—21no—
110Q8×C17—81no—
111D4×C17—22no—
112D4×C17—21no—
113D4×C17—21no—
114D4×C17—42no—
115D4×C17—81no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
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—21no—
127C2×C4×C17—81no—
128C2×C4×C17—81no—
129C2×C4×C17—81no—
130C2×C4×C17—81no—
131C2×C4×C17C2×D411yescharacteristic
132C2×C4×C17C2×D411yescharacteristic
133C2×C4×C17C2×D411yescharacteristic
134C2×C4×C17C2×D411yescharacteristic
135C2×C4×C17C2411yescharacteristic
136C8×C17—21no—
137C8×C17—21no—
138C8×C17—21no—
139C8×C17#4112yes—
140#3346C1711yesmaximal, characteristic, direct product factor, Sylow
141C22×C17—21no—
142C22×C17—21no—
143C22×C17—21no—
144C22×C17—21no—
145C22×C17—21no—
146C22×C17—41no—
147C22×C17—41no—
148C22×C17—41no—
149C22×C17#13712yes—
150C22×C17C22×D411yescharacteristic
151C4×C17—21no—
152C4×C17—21no—
153C4×C17—21no—
154C4×C17—21no—
155C4×C17—41no—
156C4×C17—41no—
157C4×C17—41no—
158C4×C17—41no—
159C4×C17—41no—
160C4×C17—41no—
161C4×C17—41no—
162C4×C17C2×#4111yescharacteristic
163C4×C172−1+411yescharacteristic
164#554C2×C1711yescharacteristic, complemented
165#553C2×C1711yescharacteristic
166#501C2×C1711yescharacteristic, complemented
167#485C2×C1711yescharacteristic, complemented
168#484C2×C1711yescharacteristic, complemented
169#481C2×C1711yescharacteristic, complemented
170#480C2×C1711yescharacteristic, complemented
171#479C2×C1711yescharacteristic, complemented
172#474C2×C1711yescharacteristic, complemented
173#468C2×C1711yescharacteristic, complemented
174#465C2×C1711yescharacteristic, complemented
175#440C2×C1711yescharacteristic, complemented
176#435C2×C1711yescharacteristic, complemented
177#428C2×C1711yescharacteristic, complemented
178C2×#107C2×C1711yescharacteristic, complemented
179C2×C17—22no—
180C2×C17—41no—
181C2×C17—81no—
182C2×C17#54711yescharacteristic
183C2×C17C2×#13711yescharacteristic
184C2×C17#57611yescharacteristic
185C2×SD16C22×C1711yescharacteristic
186C2×M16C22×C1711yescharacteristic
187C22×C8C22×C1711yescharacteristic
188C4⋊Q8C22×C1711yescharacteristic
189#126—21no—
190#125—21no—
191#125C22×C1711yescharacteristic
192#123—21no—
193C22⋊Q8—21no—
194C22⋊Q8—21no—
195C22⋊Q8C22×C1711yescharacteristic
196C22⋊Q8C22×C1711yescharacteristic
197#121—21no—
198#121C22×C1711yescharacteristic
199#121C22×C1711yescharacteristic
200C4×Q8C22×C1711yescharacteristic
201C4×D4—21no—
202C4×D4—21no—
203C4×D4C22×C1711yescharacteristic
204C4×D4C22×C1711yescharacteristic
205#117C22×C1711yescharacteristic
206C2×C4⋊C4C22×C1711yescharacteristic
207C2×C4⋊C4C22×C1711yescharacteristic
208C2×C4⋊C4C22×C1711yescharacteristic
209#107C22×C1711yescharacteristic
210#107C22×C1711yescharacteristic
211#107C22×C1711yescharacteristic
212#107C22×C1711yescharacteristic
213#107C22×C1711yescharacteristic
214#107C22×C1711yescharacteristic
215#106C22×C1711yescharacteristic
216#106C22×C1711yescharacteristic
217#106C22×C1711yescharacteristic
218C4⋊C8C22×C1711yescharacteristic
219#103C22×C1711yescharacteristic
220#103C22×C1711yescharacteristic
221#103C22×C1711yescharacteristic
222#102C22×C1711yescharacteristic
223#102C22×C1711yescharacteristic
224#102C22×C1711yescharacteristic
225C22⋊C8C22×C1711yescharacteristic
226C22⋊C8C22×C1711yescharacteristic
227#97C22×C1711yescharacteristic
228C17#334611yescharacteristic, direct product factor, Sylow
229C2×Q8—21no—
230C2×Q8C23×C1711yescharacteristic
231C2×D4—21no—
232C2×D4—21no—
233C2×D4D4×C1711yescharacteristic
234C2×D4C23×C1711yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4C23×C1711yescharacteristic
240C22×C4C23×C1711yescharacteristic
241SD16—22no—
242M16—22no—
243C2×C8—22no—
244C2×C8C23×C1711yescharacteristic
245C2×C8C23×C1711yescharacteristic
246C2×C8C23×C1711yescharacteristic
247C2×C8C23×C1711yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4D4×C1711yescharacteristic
258C4⋊C4C23×C1711yescharacteristic
259C4⋊C4C23×C1711yescharacteristic
260C4⋊C4C23×C1711yescharacteristic
261C4⋊C4C23×C1711yescharacteristic
262C4⋊C4C23×C1711yescharacteristic
263C4⋊C4C23×C1711yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4D4×C1711yescharacteristic
271C22⋊C4D4×C1711yescharacteristic
272C42—21no—
273C42—21no—
274C42C23×C1711yescharacteristic
275C23—21no—
276C23C2×D4×C1711yescharacteristic
277C23C2×D4×C1711yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—81no—
281D4—22no—
282D4—21no—
283D4—21no—
284D4—42no—
285D4—81no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4C2×D4×C1711yescharacteristic
302C2×C4C2×D4×C1711yescharacteristic
303C2×C4C2×D4×C1711yescharacteristic
304C2×C4C2×D4×C1711yescharacteristic
305C2×C4C24×C1711yescharacteristic
306C8—21no—
307C8—21no—
308C8—21no—
309C8#41×C1712yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22C17×#13712yes—
319C22C22×D4×C1711yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4C2×#41×C1711yescharacteristic
332C4C17×2−1+411yescharacteristic
333C2—22no—
334C2—41no—
335C2—81no—
336C2C17×#54711yescharacteristic
337C2C2×C17×#13711yescharacteristic
338C2C17×#57611yescharacteristic
subgroupG/H
center, socleC22×C17C22×D4
commutator, Frattini, cosocleC2×C4C24×C17
prime radicalC17×#553C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C4×D4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#554C2semidirect
3. C17×#501C2semidirect
4. C17×#485C2semidirect
5. C17×#484C2semidirect
6. C17×#481C2semidirect
7. C17×#480C2semidirect
8. C17×#479C2semidirect
9. C17×#474C2semidirect
10. C17×#468C2semidirect
11. C17×#465C2semidirect
12. C17×#440C2semidirect
13. C17×#435C2semidirect
14. C17×#428C2semidirect
15. C2×C17×#107C2semidirect
140. #3346C17direct (N × H)
164. #554C2×C17semidirect
166. #501C2×C17semidirect
167. #485C2×C17semidirect
168. #484C2×C17semidirect
169. #481C2×C17semidirect
170. #480C2×C17semidirect
171. #479C2×C17semidirect
172. #474C2×C17semidirect
173. #468C2×C17semidirect
174. #465C2×C17semidirect
175. #440C2×C17semidirect
176. #435C2×C17semidirect
177. #428C2×C17semidirect
178. C2×#107C2×C17semidirect
228. C17#3346direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#5542
C17×#5532
C17×#5012
C17×#4852
C17×#4842
C17×#4812
C17×#4802
C17×#4792
C17×#4742
C17×#4682
C17×#4652
C17×#4402
C17×#4352
C17×#4282
C2×C17×#1072
#334617