Finite Group Databasebeta

← C17×#33890 #16891634

Subgroups — C17×#33890 #16891634

Order 4352.

562 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3336C211yesmaximal, characteristic, complemented
2C17×#3280C211yesmaximal, characteristic
3C17×#2242C211yesmaximal, characteristic, complemented
4C17×#2237C211yesmaximal, characteristic, complemented
5C17×#2233C211yesmaximal, characteristic, complemented
6C17×#2228C211yesmaximal, characteristic, complemented
7C17×#2220C211yesmaximal, characteristic, complemented
8C17×#2219C211yesmaximal, characteristic, complemented
9C17×#2211C211yesmaximal, characteristic, complemented
10C17×#2189C211yesmaximal, characteristic, complemented
11C17×#2187C211yesmaximal, characteristic, complemented
12C4×C17×SD32C211yesmaximal, characteristic, complemented
13C17×#2169C211yesmaximal, characteristic, complemented
14C17×#2140C211yesmaximal, characteristic, complemented
15C17×#2139C211yesmaximal, characteristic, complemented
16C2×C17×#135C2211yescharacteristic
17C22×D8×C17C2211yescharacteristic
18C17×#552—21no—
19C17×#546—21no—
20C2×C17×Q32C2211yescharacteristic, complemented
21C2×C17×SD32C2211yescharacteristic
22C2×C17×SD32C2211yescharacteristic
23C2×C17×M32C2211yescharacteristic
24C2×C17×M32C2211yescharacteristic, complemented
25C17×#499C2211yescharacteristic, complemented
26C17×#495C2211yescharacteristic
27C17×#485—21no—
28C17×#483—21no—
29C17×#479—21no—
30C17×#467C2211yescharacteristic
31C17×#467C2211yescharacteristic
32C17×#467C2211yescharacteristic, complemented
33C17×#466C2211yescharacteristic
34C17×#463—21no—
35C17×#450—21no—
36C17×#449—21no—
37C4×Q16×C17C2211yescharacteristic, complemented
38C4×D8×C17C2211yescharacteristic
39C8×D4×C17C2211yescharacteristic
40C17×#427C2211yescharacteristic
41C2×C17×#107C2211yescharacteristic, complemented
42C17×#367C2211yescharacteristic, complemented
43C17×#367C2211yescharacteristic, complemented
44C17×#366C2211yescharacteristic, complemented
45C17×C4⋊C16C2211yescharacteristic, complemented
46C17×#358C2211yescharacteristic, complemented
47C17×#358C2211yescharacteristic, complemented
48C17×#358C2211yescharacteristic, complemented
49C17×#358C2211yescharacteristic, complemented
50C17×#357C2211yescharacteristic
51C17×#357C2211yescharacteristic
52C17×#357C2211yescharacteristic
53C17×#357C2211yescharacteristic
54C17×#357C2211yescharacteristic
55C17×#357C2211yescharacteristic
56C17×C22⋊C16C2211yescharacteristic
57C17×C22⋊C16C2211yescharacteristic, complemented
58C4×C16×C17C2211yescharacteristic, complemented
59C2×#41×C17—21no—
60C22×D4×C17—21no—
61C17×#135—22no—
62C17×#135—41no—
63C2×Q16×C17C2311yescharacteristic
64C2×Q16×C17C2311yescharacteristic
65C2×SD16×C17—21no—
66C2×SD16×C17—21no—
67C2×D8×C17—22no—
68C2×D8×C17—21no—
69C2×D8×C17—41no—
70C2×D8×C17C2311yescharacteristic
71C2×D8×C17C2311yescharacteristic
72C22×C8×C17C2311yescharacteristic
73C22×C8×C17C2311yescharacteristic
74C17×#126—41no—
75C17×#125—21no—
76C17×#125—41no—
77C17×#124—21no—
78C17×#123—41no—
79C17×#123—41no—
80C17×C22⋊Q8—21no—
81C17×C22⋊Q8—21no—
82C17×C22⋊Q8—21no—
83C17×#121—21no—
84C17×#121—41no—
85C17×#120—41no—
86C4×Q8×C17—21no—
87C4×D4×C17—21no—
88C4×D4×C17D411yescharacteristic
89C17×#117—21no—
90C17×#117—41no—
91C2×C4⋊C4×C17—21no—
92C2×C22⋊C4×C17—41no—
93C17×Q32—41no—
94C17×SD32—22no—
95C17×SD32—41no—
96C17×M32—41no—
97C17×M32—41no—
98C2×C16×C17C2311yescharacteristic
99C2×C16×C17C2311yescharacteristic
100C2×C16×C17C2311yescharacteristic
101C2×C16×C17C2311yescharacteristic
102C17×#107—21no—
103C17×#107C2311yescharacteristic
104C17×#107C2311yescharacteristic
105C17×#107C2311yescharacteristic
106C17×#107C2311yescharacteristic
107C17×#106—21no—
108C17×#106—21no—
109C17×C4⋊C8D411yescharacteristic
110C17×#103—21no—
111C17×#103—21no—
112C17×#103—21no—
113C17×#103—21no—
114C17×#102—21no—
115C17×#102—21no—
116C17×C22⋊C8D411yescharacteristic
117C17×C22⋊C8D411yescharacteristic
118C4×C8×C17C2311yescharacteristic
119C24×C17—41no—
120#41×C17—42no—
121#41×C17—81no—
122C2×Q8×C17—21no—
123C2×Q8×C17—21no—
124C2×D4×C17—21no—
125C2×D4×C17—21no—
126C2×D4×C17—42no—
127C2×D4×C17—41no—
128C2×D4×C17—41no—
129C2×D4×C17—41no—
130C2×D4×C17—81no—
131C2×D4×C17D811yescharacteristic
132C22×C4×C17—41no—
133C22×C4×C17—41no—
134C22×C4×C17—41no—
135C22×C4×C17C2×D411yescharacteristic
136C22×C4×C17C2×D411yescharacteristic
137Q16×C17—21no—
138Q16×C17—21no—
139Q16×C17—21no—
140Q16×C17—21no—
141SD16×C17—42no—
142SD16×C17—81no—
143D8×C17—21no—
144D8×C17—21no—
145D8×C17—21no—
146D8×C17—42no—
147D8×C17#4112yes—
148C2×C8×C17—21no—
149C2×C8×C17—21no—
150C2×C8×C17—21no—
151C2×C8×C17—21no—
152C2×C8×C17C2×D411yescharacteristic
153C2×C8×C17C2×D411yescharacteristic
154C2×C8×C17C2×D411yescharacteristic
155C2×C8×C17C2411yescharacteristic
156C4⋊C4×C17—21no—
157C4⋊C4×C17—21no—
158C4⋊C4×C17—21no—
159C4⋊C4×C17—21no—
160C4⋊C4×C17—41no—
161C4⋊C4×C17—41no—
162C4⋊C4×C17—41no—
163C4⋊C4×C17—41no—
164C4⋊C4×C17—41no—
165C4⋊C4×C17—41no—
166C4⋊C4×C17—41no—
167C4⋊C4×C17D811yescharacteristic
168C22⋊C4×C17—41no—
169C22⋊C4×C17—41no—
170C22⋊C4×C17—41no—
171C22⋊C4×C17—41no—
172C22⋊C4×C17—41no—
173C22⋊C4×C17—41no—
174C22⋊C4×C17—41no—
175C22⋊C4×C17—41no—
176C22⋊C4×C17D811yescharacteristic
177C22⋊C4×C17D811yescharacteristic
178C42×C17—41no—
179C42×C17—41no—
180C42×C17C2×D411yescharacteristic
181C16×C17—21no—
182C16×C17—21no—
183C16×C17—21no—
184C16×C17—21no—
185#33890C1711yesmaximal, characteristic, direct product factor, Sylow
186C23×C17—41no—
187C23×C17—41no—
188C23×C17—82no—
189C23×C17—82no—
190C23×C17—161no—
191C23×C17C2×D811yescharacteristic
192C23×C17C2×D811yescharacteristic
193Q8×C17—41no—
194Q8×C17—41no—
195Q8×C17—41no—
196Q8×C17—41no—
197D4×C17—22no—
198D4×C17—41no—
199D4×C17—41no—
200D4×C17—41no—
201D4×C17—41no—
202D4×C17—82no—
203D4×C17—82no—
204D4×C17—161no—
205C2×C4×C17—21no—
206C2×C4×C17—21no—
207C2×C4×C17—21no—
208C2×C4×C17—21no—
209C2×C4×C17—41no—
210C2×C4×C17—41no—
211C2×C4×C17—41no—
212C2×C4×C17—41no—
213C2×C4×C17—41no—
214C2×C4×C17—41no—
215C2×C4×C17—82no—
216C2×C4×C17—82no—
217C2×C4×C17—161no—
218C2×C4×C17C2×D811yescharacteristic
219C2×C4×C17C2×D811yescharacteristic
220C2×C4×C17C2×D811yescharacteristic
221C2×C4×C17C2×D811yescharacteristic
222C2×C4×C17C22×D411yescharacteristic
223C8×C17—21no—
224C8×C17—21no—
225C8×C17—21no—
226C8×C17C2×#4111yescharacteristic
227C8×C17H(5,𝔽2)11yescharacteristic
228#3336C2×C1711yescharacteristic, complemented
229#3280C2×C1711yescharacteristic
230#2242C2×C1711yescharacteristic, complemented
231#2237C2×C1711yescharacteristic, complemented
232#2233C2×C1711yescharacteristic, complemented
233#2228C2×C1711yescharacteristic, complemented
234#2220C2×C1711yescharacteristic, complemented
235#2219C2×C1711yescharacteristic, complemented
236#2211C2×C1711yescharacteristic, complemented
237#2189C2×C1711yescharacteristic, complemented
238#2187C2×C1711yescharacteristic, complemented
239C4×SD32C2×C1711yescharacteristic, complemented
240#2169C2×C1711yescharacteristic, complemented
241#2140C2×C1711yescharacteristic, complemented
242#2139C2×C1711yescharacteristic, complemented
243C22×C17—21no—
244C22×C17—21no—
245C22×C17—21no—
246C22×C17—21no—
247C22×C17—21no—
248C22×C17—21no—
249C22×C17—42no—
250C22×C17—81no—
251C22×C17—81no—
252C22×C17—81no—
253C22×C17—81no—
254C22×C17—81no—
255C22×C17—164no—
256C22×C17C22×D811yescharacteristic
257C4×C17—21no—
258C4×C17—21no—
259C4×C17—21no—
260C4×C17—21no—
261C4×C17—81no—
262C4×C17—81no—
263C4×C17—81no—
264C4×C17—81no—
265C4×C17—81no—
266C4×C17—81no—
267C4×C17#54611yescharacteristic
268C4×C17#57711yescharacteristic
269C2×#135C22×C1711yescharacteristic
270C22×D8C22×C1711yescharacteristic
271#552—21no—
272#546—21no—
273C2×Q32C22×C1711yescharacteristic, complemented
274C2×SD32C22×C1711yescharacteristic
275C2×SD32C22×C1711yescharacteristic
276C2×M32C22×C1711yescharacteristic
277C2×M32C22×C1711yescharacteristic, complemented
278#499C22×C1711yescharacteristic, complemented
279#495C22×C1711yescharacteristic
280#485—21no—
281#483—21no—
282#479—21no—
283#467C22×C1711yescharacteristic
284#467C22×C1711yescharacteristic
285#467C22×C1711yescharacteristic, complemented
286#466C22×C1711yescharacteristic
287#463—21no—
288#450—21no—
289#449—21no—
290C4×Q16C22×C1711yescharacteristic, complemented
291C4×D8C22×C1711yescharacteristic
292C8×D4C22×C1711yescharacteristic
293#427C22×C1711yescharacteristic
294C2×#107C22×C1711yescharacteristic, complemented
295#367C22×C1711yescharacteristic, complemented
296#367C22×C1711yescharacteristic, complemented
297#366C22×C1711yescharacteristic, complemented
298C4⋊C16C22×C1711yescharacteristic, complemented
299#358C22×C1711yescharacteristic, complemented
300#358C22×C1711yescharacteristic, complemented
301#358C22×C1711yescharacteristic, complemented
302#358C22×C1711yescharacteristic, complemented
303#357C22×C1711yescharacteristic
304#357C22×C1711yescharacteristic
305#357C22×C1711yescharacteristic
306#357C22×C1711yescharacteristic
307#357C22×C1711yescharacteristic
308#357C22×C1711yescharacteristic
309C22⋊C16C22×C1711yescharacteristic
310C22⋊C16C22×C1711yescharacteristic, complemented
311C4×C16C22×C1711yescharacteristic, complemented
312C2×C17—41no—
313C2×C17—41no—
314C2×C17—82no—
315C2×C17—161no—
316C2×C17#329411yescharacteristic
317C2×C17#341411yescharacteristic
318C2×C17#341611yescharacteristic
319C2×#41—21no—
320C22×D4—21no—
321#135—22no—
322#135—41no—
323C2×Q16C23×C1711yescharacteristic
324C2×Q16C23×C1711yescharacteristic
325C2×SD16—21no—
326C2×SD16—21no—
327C2×D8—22no—
328C2×D8—21no—
329C2×D8—41no—
330C2×D8C23×C1711yescharacteristic
331C2×D8C23×C1711yescharacteristic
332C22×C8C23×C1711yescharacteristic
333C22×C8C23×C1711yescharacteristic
334#126—41no—
335#125—21no—
336#125—41no—
337#124—21no—
338#123—41no—
339#123—41no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342C22⋊Q8—21no—
343#121—21no—
344#121—41no—
345#120—41no—
346C4×Q8—21no—
347C4×D4—21no—
348C4×D4D4×C1711yescharacteristic
349#117—21no—
350#117—41no—
351C2×C4⋊C4—21no—
352C2×C22⋊C4—41no—
353Q32—41no—
354SD32—22no—
355SD32—41no—
356M32—41no—
357M32—41no—
358C2×C16C23×C1711yescharacteristic
359C2×C16C23×C1711yescharacteristic
360C2×C16C23×C1711yescharacteristic
361C2×C16C23×C1711yescharacteristic
362#107—21no—
363#107C23×C1711yescharacteristic
364#107C23×C1711yescharacteristic
365#107C23×C1711yescharacteristic
366#107C23×C1711yescharacteristic
367#106—21no—
368#106—21no—
369C4⋊C8D4×C1711yescharacteristic
370#103—21no—
371#103—21no—
372#103—21no—
373#103—21no—
374#102—21no—
375#102—21no—
376C22⋊C8D4×C1711yescharacteristic
377C22⋊C8D4×C1711yescharacteristic
378C4×C8C23×C1711yescharacteristic
379C17#3389011yescharacteristic, direct product factor, Sylow
380C24—41no—
381#41—42no—
382#41—81no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—42no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—81no—
392C2×D4D8×C1711yescharacteristic
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4C2×D4×C1711yescharacteristic
397C22×C4C2×D4×C1711yescharacteristic
398Q16—21no—
399Q16—21no—
400Q16—21no—
401Q16—21no—
402SD16—42no—
403SD16—81no—
404D8—21no—
405D8—21no—
406D8—21no—
407D8—42no—
408D8#41×C1712yes—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8C2×D4×C1711yescharacteristic
414C2×C8C2×D4×C1711yescharacteristic
415C2×C8C2×D4×C1711yescharacteristic
416C2×C8C24×C1711yescharacteristic
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4D8×C1711yescharacteristic
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4D8×C1711yescharacteristic
438C22⋊C4D8×C1711yescharacteristic
439C42—41no—
440C42—41no—
441C42C2×D4×C1711yescharacteristic
442C16—21no—
443C16—21no—
444C16—21no—
445C16—21no—
446C23—41no—
447C23—41no—
448C23—82no—
449C23—82no—
450C23—161no—
451C23C2×D8×C1711yescharacteristic
452C23C2×D8×C1711yescharacteristic
453Q8—41no—
454Q8—41no—
455Q8—41no—
456Q8—41no—
457D4—22no—
458D4—41no—
459D4—41no—
460D4—41no—
461D4—41no—
462D4—82no—
463D4—82no—
464D4—161no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4—161no—
478C2×C4C2×D8×C1711yescharacteristic
479C2×C4C2×D8×C1711yescharacteristic
480C2×C4C2×D8×C1711yescharacteristic
481C2×C4C2×D8×C1711yescharacteristic
482C2×C4C22×D4×C1711yescharacteristic
483C8—21no—
484C8—21no—
485C8—21no—
486C8C2×#41×C1711yescharacteristic
487C8C17×H(5,𝔽2)11yescharacteristic
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—42no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—164no—
501C22C22×D8×C1711yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—81no—
507C4—81no—
508C4—81no—
509C4—81no—
510C4—81no—
511C4—81no—
512C4C17×#54611yescharacteristic
513C4C17×#57711yescharacteristic
514C2—41no—
515C2—41no—
516C2—82no—
517C2—161no—
518C2C17×#329411yescharacteristic
519C2C17×#341411yescharacteristic
520C2C17×#341611yescharacteristic
subgroupG/H
center, socleC22×C17C22×D8
commutator, Frattini, cosocleC2×C8C24×C17
prime radicalC17×#3280C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C4×D4×C17 ◁ C8×D4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#3336C2semidirect
3. C17×#2242C2semidirect
4. C17×#2237C2semidirect
5. C17×#2233C2semidirect
6. C17×#2228C2semidirect
7. C17×#2220C2semidirect
8. C17×#2219C2semidirect
9. C17×#2211C2semidirect
10. C17×#2189C2semidirect
11. C17×#2187C2semidirect
12. C4×C17×SD32C2semidirect
13. C17×#2169C2semidirect
14. C17×#2140C2semidirect
15. C17×#2139C2semidirect
20. C2×C17×Q32C22semidirect
24. C2×C17×M32C22semidirect
25. C17×#499C22semidirect
32. C17×#467C22semidirect
37. C4×Q16×C17C22semidirect
41. C2×C17×#107C22semidirect
42. C17×#367C22semidirect
43. C17×#367C22semidirect
44. C17×#366C22semidirect
45. C17×C4⋊C16C22semidirect
46. C17×#358C22semidirect
47. C17×#358C22semidirect
48. C17×#358C22semidirect
49. C17×#358C22semidirect
57. C17×C22⋊C16C22semidirect
58. C4×C16×C17C22semidirect
185. #33890C17direct (N × H)
228. #3336C2×C17semidirect
230. #2242C2×C17semidirect
231. #2237C2×C17semidirect
232. #2233C2×C17semidirect
233. #2228C2×C17semidirect
234. #2220C2×C17semidirect
235. #2219C2×C17semidirect
236. #2211C2×C17semidirect
237. #2189C2×C17semidirect
238. #2187C2×C17semidirect
239. C4×SD32C2×C17semidirect
240. #2169C2×C17semidirect
241. #2140C2×C17semidirect
242. #2139C2×C17semidirect
273. C2×Q32C22×C17semidirect
277. C2×M32C22×C17semidirect
278. #499C22×C17semidirect
285. #467C22×C17semidirect
290. C4×Q16C22×C17semidirect
294. C2×#107C22×C17semidirect
295. #367C22×C17semidirect
296. #367C22×C17semidirect
297. #366C22×C17semidirect
298. C4⋊C16C22×C17semidirect
299. #358C22×C17semidirect
300. #358C22×C17semidirect
301. #358C22×C17semidirect
302. #358C22×C17semidirect
310. C22⋊C16C22×C17semidirect
311. C4×C16C22×C17semidirect
379. C17#33890direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#33362
C17×#32802
C17×#22422
C17×#22372
C17×#22332
C17×#22282
C17×#22202
C17×#22192
C17×#22112
C17×#21892
C17×#21872
C4×C17×SD322
C17×#21692
C17×#21402
C17×#21392
#3389017