Finite Group Databasebeta

← C17×#3241 #14526247

Subgroups — C17×#3241 #14526247

Order 2176.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#544C211yesmaximal, characteristic, complemented
2C17×#540C211yesmaximal, characteristic
3C17×#501C211yesmaximal, characteristic, complemented
4C17×#499C211yesmaximal, characteristic, complemented
5C17×#490C211yesmaximal, characteristic, complemented
6C17×#486C211yesmaximal, characteristic, complemented
7C17×#482C211yesmaximal, characteristic, complemented
8C17×#482C211yesmaximal, characteristic, complemented
9C17×#481C211yesmaximal, characteristic, complemented
10C17×#480C211yesmaximal, characteristic, complemented
11C17×#478C211yesmaximal, characteristic, complemented
12C17×#478C211yesmaximal, characteristic, complemented
13C17×#476C211yesmaximal, characteristic, complemented
14C17×#474C211yesmaximal, characteristic, complemented
15C17×#433C211yesmaximal, characteristic, complemented
16C17×C4⋊Q8—21no—
17C17×C4⋊Q8C2211yescharacteristic
18C17×C4⋊Q8C2211yescharacteristic
19C17×#127C2211yescharacteristic
20C17×#125—21no—
21C17×#125C2211yescharacteristic
22C17×#125C2211yescharacteristic
23C17×#125C2211yescharacteristic
24C17×#123—21no—
25C17×#123—21no—
26C17×C22⋊Q8—21no—
27C17×C22⋊Q8—21no—
28C17×#121—21no—
29C17×#121—21no—
30C17×#121C2211yescharacteristic
31C17×#121C2211yescharacteristic
32C4×D4×C17C2211yescharacteristic
33C4×D4×C17C2211yescharacteristic
34C17×#117C2211yescharacteristic
35C17×#117C2211yescharacteristic
36C2×C4⋊C4×C17C2211yescharacteristic
37C17×#107C2211yescharacteristic
38C17×#107C2211yescharacteristic
39C17×#107C2211yescharacteristic
40C17×#107C2211yescharacteristic
41C17×#106C2211yescharacteristic
42C17×#106C2211yescharacteristic
43C17×#106C2211yescharacteristic
44C17×#106C2211yescharacteristic
45C17×C4⋊C8C2211yescharacteristic
46C17×C4⋊C8C2211yescharacteristic
47C17×#102C2211yescharacteristic
48C17×#102C2211yescharacteristic
49C17×#102C2211yescharacteristic
50C17×#102C2211yescharacteristic
51C17×#102C2211yescharacteristic
52C17×#102C2211yescharacteristic
53C17×#102C2211yescharacteristic
54C17×#102C2211yescharacteristic
55C17×C22⋊C8C2211yescharacteristic
56C17×C22⋊C8C2211yescharacteristic
57C17×#97C2211yescharacteristic
58C4×C8×C17C2211yescharacteristic
59C2×Q8×C17—21no—
60C2×Q8×C17—21no—
61C2×D4×C17—21no—
62C2×D4×C17—21no—
63C2×D4×C17—21no—
64C2×D4×C17—21no—
65C2×D4×C17C2311yescharacteristic
66C2×D4×C17C2311yescharacteristic
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17C2311yescharacteristic
71C2×C8×C17C2311yescharacteristic
72C2×C8×C17C2311yescharacteristic
73C2×C8×C17C2311yescharacteristic
74C2×C8×C17C2311yescharacteristic
75C4⋊C4×C17—21no—
76C4⋊C4×C17—21no—
77C4⋊C4×C17—21no—
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×C17D411yescharacteristic
85C4⋊C4×C17D411yescharacteristic
86C4⋊C4×C17C2311yescharacteristic
87C4⋊C4×C17C2311yescharacteristic
88C4⋊C4×C17C2311yescharacteristic
89C4⋊C4×C17C2311yescharacteristic
90C4⋊C4×C17C2311yescharacteristic
91C4⋊C4×C17C2311yescharacteristic
92C22⋊C4×C17—21no—
93C22⋊C4×C17—21no—
94C22⋊C4×C17—21no—
95C22⋊C4×C17—21no—
96C22⋊C4×C17—21no—
97C22⋊C4×C17D411yescharacteristic
98C22⋊C4×C17D411yescharacteristic
99C42×C17—21no—
100C42×C17C2311yescharacteristic
101C42×C17C2311yescharacteristic
102C23×C17—21no—
103C23×C17—21no—
104C23×C17C2×D411yescharacteristic
105Q8×C17—81no—
106Q8×C17—81no—
107D4×C17—21no—
108D4×C17—21no—
109D4×C17—21no—
110D4×C17—21no—
111D4×C17—81no—
112D4×C17—81no—
113D4×C17—81no—
114D4×C17—81no—
115C2×C4×C17—21no—
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—81no—
124C2×C4×C17—81no—
125C2×C4×C17—81no—
126C2×C4×C17C2×D411yescharacteristic
127C2×C4×C17C2×D411yescharacteristic
128C2×C4×C17C2×D411yescharacteristic
129C2×C4×C17C2×D411yescharacteristic
130C2×C4×C17C2×D411yescharacteristic
131C2×C4×C17C2411yescharacteristic
132C8×C17—21no—
133C8×C17—21no—
134C8×C17—21no—
135C8×C17—21no—
136#3241C1711yesmaximal, characteristic, direct product factor, Sylow
137C22×C17—21no—
138C22×C17—21no—
139C22×C17—21no—
140C22×C17—41no—
141C22×C17—41no—
142C22×C17—41no—
143C22×C17—41no—
144C22×C17—41no—
145C22×C17—41no—
146C22×C17C22×D411yescharacteristic
147C4×C17—21no—
148C4×C17—21no—
149C4×C17—21no—
150C4×C17—21no—
151C4×C17—21no—
152C4×C17—41no—
153C4×C17—41no—
154C4×C17—41no—
155C4×C17—41no—
156C4×C17—41no—
157C4×C17—41no—
158C4×C172−1+411yescharacteristic
159C4×C172−1+411yescharacteristic
160#544C2×C1711yescharacteristic, complemented
161#540C2×C1711yescharacteristic
162#501C2×C1711yescharacteristic, complemented
163#499C2×C1711yescharacteristic, complemented
164#490C2×C1711yescharacteristic, complemented
165#486C2×C1711yescharacteristic, complemented
166#482C2×C1711yescharacteristic, complemented
167#482C2×C1711yescharacteristic, complemented
168#481C2×C1711yescharacteristic, complemented
169#480C2×C1711yescharacteristic, complemented
170#478C2×C1711yescharacteristic, complemented
171#478C2×C1711yescharacteristic, complemented
172#476C2×C1711yescharacteristic, complemented
173#474C2×C1711yescharacteristic, complemented
174#433C2×C1711yescharacteristic, complemented
175C2×C17—41no—
176C2×C17—81no—
177C2×C17—81no—
178C2×C17#53611yescharacteristic
179C2×C17#57611yescharacteristic
180C2×C17#57711yescharacteristic
181C4⋊Q8—21no—
182C4⋊Q8C22×C1711yescharacteristic
183C4⋊Q8C22×C1711yescharacteristic
184#127C22×C1711yescharacteristic
185#125—21no—
186#125C22×C1711yescharacteristic
187#125C22×C1711yescharacteristic
188#125C22×C1711yescharacteristic
189#123—21no—
190#123—21no—
191C22⋊Q8—21no—
192C22⋊Q8—21no—
193#121—21no—
194#121—21no—
195#121C22×C1711yescharacteristic
196#121C22×C1711yescharacteristic
197C4×D4C22×C1711yescharacteristic
198C4×D4C22×C1711yescharacteristic
199#117C22×C1711yescharacteristic
200#117C22×C1711yescharacteristic
201C2×C4⋊C4C22×C1711yescharacteristic
202#107C22×C1711yescharacteristic
203#107C22×C1711yescharacteristic
204#107C22×C1711yescharacteristic
205#107C22×C1711yescharacteristic
206#106C22×C1711yescharacteristic
207#106C22×C1711yescharacteristic
208#106C22×C1711yescharacteristic
209#106C22×C1711yescharacteristic
210C4⋊C8C22×C1711yescharacteristic
211C4⋊C8C22×C1711yescharacteristic
212#102C22×C1711yescharacteristic
213#102C22×C1711yescharacteristic
214#102C22×C1711yescharacteristic
215#102C22×C1711yescharacteristic
216#102C22×C1711yescharacteristic
217#102C22×C1711yescharacteristic
218#102C22×C1711yescharacteristic
219#102C22×C1711yescharacteristic
220C22⋊C8C22×C1711yescharacteristic
221C22⋊C8C22×C1711yescharacteristic
222#97C22×C1711yescharacteristic
223C4×C8C22×C1711yescharacteristic
224C17#324111yescharacteristic, direct product factor, Sylow
225C2×Q8—21no—
226C2×Q8—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4C23×C1711yescharacteristic
232C2×D4C23×C1711yescharacteristic
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4C23×C1711yescharacteristic
237C2×C8C23×C1711yescharacteristic
238C2×C8C23×C1711yescharacteristic
239C2×C8C23×C1711yescharacteristic
240C2×C8C23×C1711yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4D4×C1711yescharacteristic
251C4⋊C4D4×C1711yescharacteristic
252C4⋊C4C23×C1711yescharacteristic
253C4⋊C4C23×C1711yescharacteristic
254C4⋊C4C23×C1711yescharacteristic
255C4⋊C4C23×C1711yescharacteristic
256C4⋊C4C23×C1711yescharacteristic
257C4⋊C4C23×C1711yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4D4×C1711yescharacteristic
264C22⋊C4D4×C1711yescharacteristic
265C42—21no—
266C42C23×C1711yescharacteristic
267C42C23×C1711yescharacteristic
268C23—21no—
269C23—21no—
270C23C2×D4×C1711yescharacteristic
271Q8—81no—
272Q8—81no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—81no—
280D4—81no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4C2×D4×C1711yescharacteristic
293C2×C4C2×D4×C1711yescharacteristic
294C2×C4C2×D4×C1711yescharacteristic
295C2×C4C2×D4×C1711yescharacteristic
296C2×C4C2×D4×C1711yescharacteristic
297C2×C4C24×C1711yescharacteristic
298C8—21no—
299C8—21no—
300C8—21no—
301C8—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22C22×D4×C1711yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4C17×2−1+411yescharacteristic
324C4C17×2−1+411yescharacteristic
325C2—41no—
326C2—81no—
327C2—81no—
328C2C17×#53611yescharacteristic
329C2C17×#57611yescharacteristic
330C2C17×#57711yescharacteristic
subgroupG/H
center, socleC22×C17C22×D4
commutator, Frattini, cosocleC2×C4C24×C17
prime radicalC17×#540C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C17×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#544C2semidirect
3. C17×#501C2semidirect
4. C17×#499C2semidirect
5. C17×#490C2semidirect
6. C17×#486C2semidirect
7. C17×#482C2semidirect
8. C17×#482C2semidirect
9. C17×#481C2semidirect
10. C17×#480C2semidirect
11. C17×#478C2semidirect
12. C17×#478C2semidirect
13. C17×#476C2semidirect
14. C17×#474C2semidirect
15. C17×#433C2semidirect
136. #3241C17direct (N × H)
160. #544C2×C17semidirect
162. #501C2×C17semidirect
163. #499C2×C17semidirect
164. #490C2×C17semidirect
165. #486C2×C17semidirect
166. #482C2×C17semidirect
167. #482C2×C17semidirect
168. #481C2×C17semidirect
169. #480C2×C17semidirect
170. #478C2×C17semidirect
171. #478C2×C17semidirect
172. #476C2×C17semidirect
173. #474C2×C17semidirect
174. #433C2×C17semidirect
224. C17#3241direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#5442
C17×#5402
C17×#5012
C17×#4992
C17×#4902
C17×#4862
C17×#4822
C17×#4812
C17×#4802
C17×#4782
C17×#4762
C17×#4742
C17×#4332
#324117