Finite Group Databasebeta

← C17×#33889 #16891633

Subgroups — C17×#33889 #16891633

Order 4352.

574 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3339C211yesmaximal, characteristic, complemented
2C17×#3280C211yesmaximal, characteristic, complemented
3C17×#2242C211yesmaximal, characteristic, complemented
4C17×#2237C211yesmaximal, characteristic, complemented
5C17×#2232C211yesmaximal, characteristic, complemented
6C17×#2228C211yesmaximal, characteristic, complemented
7C17×#2220C211yesmaximal, characteristic, complemented
8C17×#2218C211yesmaximal, characteristic, complemented
9C17×#2210C211yesmaximal, characteristic, complemented
10C17×#2186C211yesmaximal, characteristic, complemented
11C17×#2184C211yesmaximal, characteristic, complemented
12C4×C17×D16C211yesmaximal, characteristic, complemented
13C17×#2169C211yesmaximal, characteristic, complemented
14C17×#2140C211yesmaximal, characteristic, complemented
15C17×#2139C211yesmaximal, characteristic, complemented
16C2×C17×#135C2211yescharacteristic
17C22×D8×C17C2211yescharacteristic
18C17×#553—21no—
19C17×#546—21no—
20C2×C17×SD32C2211yescharacteristic, complemented
21C2×C17×D16C2211yescharacteristic
22C2×C17×D16C2211yescharacteristic
23C2×C17×M32C2211yescharacteristic
24C2×C17×M32C2211yescharacteristic, complemented
25C17×#499C2211yescharacteristic, complemented
26C17×#495C2211yescharacteristic
27C17×#482—21no—
28C17×#481—21no—
29C17×#478—21no—
30C17×#467C2211yescharacteristic
31C17×#466C2211yescharacteristic
32C17×#466C2211yescharacteristic
33C17×#466C2211yescharacteristic, complemented
34C17×#463—21no—
35C17×#450—21no—
36C17×#449—21no—
37C4×D8×C17C2211yescharacteristic
38C4×D8×C17C2211yescharacteristic, complemented
39C8×D4×C17C2211yescharacteristic
40C17×#427C2211yescharacteristic
41C2×C17×#107C2211yescharacteristic, complemented
42C17×#367C2211yescharacteristic, complemented
43C17×#366C2211yescharacteristic, complemented
44C17×#366C2211yescharacteristic, complemented
45C17×C4⋊C16C2211yescharacteristic, complemented
46C17×#358C2211yescharacteristic, complemented
47C17×#358C2211yescharacteristic, complemented
48C17×#358C2211yescharacteristic, complemented
49C17×#357C2211yescharacteristic
50C17×#357C2211yescharacteristic
51C17×#357C2211yescharacteristic
52C17×#357C2211yescharacteristic
53C17×#357C2211yescharacteristic
54C17×#357C2211yescharacteristic
55C17×#357C2211yescharacteristic, complemented
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×SD16×C17—21no—
65C2×SD16×C17—21no—
66C2×D8×C17—22no—
67C2×D8×C17—21no—
68C2×D8×C17—41no—
69C2×D8×C17C2311yescharacteristic
70C2×D8×C17C2311yescharacteristic
71C2×D8×C17C2311yescharacteristic
72C22×C8×C17C2311yescharacteristic
73C22×C8×C17C2311yescharacteristic
74C17×#126—41no—
75C17×#125—21no—
76C17×#124—21no—
77C17×#123—41no—
78C17×#123—41no—
79C17×C22⋊Q8—21no—
80C17×#121—21no—
81C17×#121—21no—
82C17×#121—21no—
83C17×#121—41no—
84C17×#121—41no—
85C17×#120—41no—
86C4×D4×C17—21no—
87C4×D4×C17—21no—
88C4×D4×C17—41no—
89C4×D4×C17D411yescharacteristic
90C17×#117—21no—
91C2×C4⋊C4×C17—21no—
92C2×C22⋊C4×C17—41no—
93C17×SD32—41no—
94C17×D16—22no—
95C17×D16—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×#102—21no—
112C17×#102—21no—
113C17×#102—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×D4×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—41no—
131C2×D4×C17—41no—
132C2×D4×C17—81no—
133C2×D4×C17D811yescharacteristic
134C22×C4×C17—41no—
135C22×C4×C17—41no—
136C22×C4×C17—41no—
137C22×C4×C17—41no—
138C22×C4×C17C2×D411yescharacteristic
139C22×C4×C17C2×D411yescharacteristic
140Q16×C17—21no—
141Q16×C17—21no—
142SD16×C17—42no—
143SD16×C17—81no—
144D8×C17—21no—
145D8×C17—21no—
146D8×C17—21no—
147D8×C17—21no—
148D8×C17—21no—
149D8×C17—42no—
150D8×C17#4112yes—
151C2×C8×C17—21no—
152C2×C8×C17—21no—
153C2×C8×C17—21no—
154C2×C8×C17—21no—
155C2×C8×C17C2×D411yescharacteristic
156C2×C8×C17C2×D411yescharacteristic
157C2×C8×C17C2×D411yescharacteristic
158C2×C8×C17C2411yescharacteristic
159C4⋊C4×C17—21no—
160C4⋊C4×C17—21no—
161C4⋊C4×C17—21no—
162C4⋊C4×C17—21no—
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×C17—41no—
177C22⋊C4×C17D811yescharacteristic
178C22⋊C4×C17D811yescharacteristic
179C42×C17—41no—
180C42×C17C2×D411yescharacteristic
181C16×C17—21no—
182C16×C17—21no—
183C16×C17—21no—
184C16×C17—21no—
185#33889C1711yesmaximal, characteristic, direct product factor, Sylow
186C23×C17—41no—
187C23×C17—41no—
188C23×C17—41no—
189C23×C17—82no—
190C23×C17—82no—
191C23×C17—161no—
192C23×C17C2×D811yescharacteristic
193C23×C17C2×D811yescharacteristic
194Q8×C17—41no—
195Q8×C17—41no—
196D4×C17—22no—
197D4×C17—41no—
198D4×C17—41no—
199D4×C17—41no—
200D4×C17—41no—
201D4×C17—41no—
202D4×C17—41no—
203D4×C17—82no—
204D4×C17—82no—
205D4×C17—82no—
206D4×C17—161no—
207D4×C17—161no—
208C2×C4×C17—21no—
209C2×C4×C17—21no—
210C2×C4×C17—21no—
211C2×C4×C17—21no—
212C2×C4×C17—41no—
213C2×C4×C17—41no—
214C2×C4×C17—41no—
215C2×C4×C17—41no—
216C2×C4×C17—41no—
217C2×C4×C17—82no—
218C2×C4×C17—161no—
219C2×C4×C17—161no—
220C2×C4×C17—161no—
221C2×C4×C17C2×D811yescharacteristic
222C2×C4×C17C2×D811yescharacteristic
223C2×C4×C17C2×D811yescharacteristic
224C2×C4×C17C2×D811yescharacteristic
225C2×C4×C17C22×D411yescharacteristic
226C8×C17—21no—
227C8×C17—21no—
228C8×C17—21no—
229C8×C17C2×#4111yescharacteristic
230C8×C17H(5,𝔽2)11yescharacteristic
231#3339C2×C1711yescharacteristic, complemented
232#3280C2×C1711yescharacteristic, complemented
233#2242C2×C1711yescharacteristic, complemented
234#2237C2×C1711yescharacteristic, complemented
235#2232C2×C1711yescharacteristic, complemented
236#2228C2×C1711yescharacteristic, complemented
237#2220C2×C1711yescharacteristic, complemented
238#2218C2×C1711yescharacteristic, complemented
239#2210C2×C1711yescharacteristic, complemented
240#2186C2×C1711yescharacteristic, complemented
241#2184C2×C1711yescharacteristic, complemented
242C4×D16C2×C1711yescharacteristic, complemented
243#2169C2×C1711yescharacteristic, complemented
244#2140C2×C1711yescharacteristic, complemented
245#2139C2×C1711yescharacteristic, complemented
246C22×C17—21no—
247C22×C17—21no—
248C22×C17—21no—
249C22×C17—21no—
250C22×C17—21no—
251C22×C17—21no—
252C22×C17—42no—
253C22×C17—81no—
254C22×C17—81no—
255C22×C17—81no—
256C22×C17—81no—
257C22×C17—81no—
258C22×C17—81no—
259C22×C17—81no—
260C22×C17—81no—
261C22×C17—164no—
262C22×C17C22×D811yescharacteristic
263C4×C17—21no—
264C4×C17—21no—
265C4×C17—21no—
266C4×C17—21no—
267C4×C17—81no—
268C4×C17—81no—
269C4×C17—81no—
270C4×C17—81no—
271C4×C17—81no—
272C4×C17#54611yescharacteristic
273C4×C17#57711yescharacteristic
274C2×#135C22×C1711yescharacteristic
275C22×D8C22×C1711yescharacteristic
276#553—21no—
277#546—21no—
278C2×SD32C22×C1711yescharacteristic, complemented
279C2×D16C22×C1711yescharacteristic
280C2×D16C22×C1711yescharacteristic
281C2×M32C22×C1711yescharacteristic
282C2×M32C22×C1711yescharacteristic, complemented
283#499C22×C1711yescharacteristic, complemented
284#495C22×C1711yescharacteristic
285#482—21no—
286#481—21no—
287#478—21no—
288#467C22×C1711yescharacteristic
289#466C22×C1711yescharacteristic
290#466C22×C1711yescharacteristic
291#466C22×C1711yescharacteristic, complemented
292#463—21no—
293#450—21no—
294#449—21no—
295C4×D8C22×C1711yescharacteristic
296C4×D8C22×C1711yescharacteristic, complemented
297C8×D4C22×C1711yescharacteristic
298#427C22×C1711yescharacteristic
299C2×#107C22×C1711yescharacteristic, complemented
300#367C22×C1711yescharacteristic, complemented
301#366C22×C1711yescharacteristic, complemented
302#366C22×C1711yescharacteristic, complemented
303C4⋊C16C22×C1711yescharacteristic, complemented
304#358C22×C1711yescharacteristic, complemented
305#358C22×C1711yescharacteristic, complemented
306#358C22×C1711yescharacteristic, complemented
307#357C22×C1711yescharacteristic
308#357C22×C1711yescharacteristic
309#357C22×C1711yescharacteristic
310#357C22×C1711yescharacteristic
311#357C22×C1711yescharacteristic
312#357C22×C1711yescharacteristic
313#357C22×C1711yescharacteristic, complemented
314C22⋊C16C22×C1711yescharacteristic
315C22⋊C16C22×C1711yescharacteristic, complemented
316C4×C16C22×C1711yescharacteristic, complemented
317C2×C17—41no—
318C2×C17—41no—
319C2×C17—82no—
320C2×C17—161no—
321C2×C17—161no—
322C2×C17#329411yescharacteristic
323C2×C17#341411yescharacteristic
324C2×C17#341511yescharacteristic
325C2×#41—21no—
326C22×D4—21no—
327#135—22no—
328#135—41no—
329C2×Q16C23×C1711yescharacteristic
330C2×SD16—21no—
331C2×SD16—21no—
332C2×D8—22no—
333C2×D8—21no—
334C2×D8—41no—
335C2×D8C23×C1711yescharacteristic
336C2×D8C23×C1711yescharacteristic
337C2×D8C23×C1711yescharacteristic
338C22×C8C23×C1711yescharacteristic
339C22×C8C23×C1711yescharacteristic
340#126—41no—
341#125—21no—
342#124—21no—
343#123—41no—
344#123—41no—
345C22⋊Q8—21no—
346#121—21no—
347#121—21no—
348#121—21no—
349#121—41no—
350#121—41no—
351#120—41no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—41no—
355C4×D4D4×C1711yescharacteristic
356#117—21no—
357C2×C4⋊C4—21no—
358C2×C22⋊C4—41no—
359SD32—41no—
360D16—22no—
361D16—41no—
362M32—41no—
363M32—41no—
364C2×C16C23×C1711yescharacteristic
365C2×C16C23×C1711yescharacteristic
366C2×C16C23×C1711yescharacteristic
367C2×C16C23×C1711yescharacteristic
368#107—21no—
369#107C23×C1711yescharacteristic
370#107C23×C1711yescharacteristic
371#107C23×C1711yescharacteristic
372#107C23×C1711yescharacteristic
373#106—21no—
374#106—21no—
375C4⋊C8D4×C1711yescharacteristic
376#103—21no—
377#102—21no—
378#102—21no—
379#102—21no—
380#102—21no—
381#102—21no—
382C22⋊C8D4×C1711yescharacteristic
383C22⋊C8D4×C1711yescharacteristic
384C4×C8C23×C1711yescharacteristic
385C17#3388911yescharacteristic, direct product factor, Sylow
386C24—41no—
387#41—42no—
388#41—81no—
389C2×Q8—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—42no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—81no—
400C2×D4D8×C1711yescharacteristic
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4C2×D4×C1711yescharacteristic
406C22×C4C2×D4×C1711yescharacteristic
407Q16—21no—
408Q16—21no—
409SD16—42no—
410SD16—81no—
411D8—21no—
412D8—21no—
413D8—21no—
414D8—21no—
415D8—21no—
416D8—42no—
417D8#41×C1712yes—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8C2×D4×C1711yescharacteristic
423C2×C8C2×D4×C1711yescharacteristic
424C2×C8C2×D4×C1711yescharacteristic
425C2×C8C24×C1711yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C4⋊C4D8×C1711yescharacteristic
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4D8×C1711yescharacteristic
445C22⋊C4D8×C1711yescharacteristic
446C42—41no—
447C42C2×D4×C1711yescharacteristic
448C16—21no—
449C16—21no—
450C16—21no—
451C16—21no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—82no—
456C23—82no—
457C23—161no—
458C23C2×D8×C1711yescharacteristic
459C23C2×D8×C1711yescharacteristic
460Q8—41no—
461Q8—41no—
462D4—22no—
463D4—41no—
464D4—41no—
465D4—41no—
466D4—41no—
467D4—41no—
468D4—41no—
469D4—82no—
470D4—82no—
471D4—82no—
472D4—161no—
473D4—161no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—82no—
484C2×C4—161no—
485C2×C4—161no—
486C2×C4—161no—
487C2×C4C2×D8×C1711yescharacteristic
488C2×C4C2×D8×C1711yescharacteristic
489C2×C4C2×D8×C1711yescharacteristic
490C2×C4C2×D8×C1711yescharacteristic
491C2×C4C22×D4×C1711yescharacteristic
492C8—21no—
493C8—21no—
494C8—21no—
495C8C2×#41×C1711yescharacteristic
496C8C17×H(5,𝔽2)11yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—42no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—164no—
513C22C22×D8×C1711yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—81no—
519C4—81no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4C17×#54611yescharacteristic
524C4C17×#57711yescharacteristic
525C2—41no—
526C2—41no—
527C2—82no—
528C2—161no—
529C2—161no—
530C2C17×#329411yescharacteristic
531C2C17×#341411yescharacteristic
532C2C17×#341511yescharacteristic
subgroupG/H
center, socleC22×C17C22×D8
commutator, Frattini, cosocleC2×C8C24×C17
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×#3339C2semidirect
2. C17×#3280C2semidirect
3. C17×#2242C2semidirect
4. C17×#2237C2semidirect
5. C17×#2232C2semidirect
6. C17×#2228C2semidirect
7. C17×#2220C2semidirect
8. C17×#2218C2semidirect
9. C17×#2210C2semidirect
10. C17×#2186C2semidirect
11. C17×#2184C2semidirect
12. C4×C17×D16C2semidirect
13. C17×#2169C2semidirect
14. C17×#2140C2semidirect
15. C17×#2139C2semidirect
20. C2×C17×SD32C22semidirect
24. C2×C17×M32C22semidirect
25. C17×#499C22semidirect
33. C17×#466C22semidirect
38. C4×D8×C17C22semidirect
41. C2×C17×#107C22semidirect
42. C17×#367C22semidirect
43. C17×#366C22semidirect
44. C17×#366C22semidirect
45. C17×C4⋊C16C22semidirect
46. C17×#358C22semidirect
47. C17×#358C22semidirect
48. C17×#358C22semidirect
55. C17×#357C22semidirect
57. C17×C22⋊C16C22semidirect
58. C4×C16×C17C22semidirect
185. #33889C17direct (N × H)
231. #3339C2×C17semidirect
232. #3280C2×C17semidirect
233. #2242C2×C17semidirect
234. #2237C2×C17semidirect
235. #2232C2×C17semidirect
236. #2228C2×C17semidirect
237. #2220C2×C17semidirect
238. #2218C2×C17semidirect
239. #2210C2×C17semidirect
240. #2186C2×C17semidirect
241. #2184C2×C17semidirect
242. C4×D16C2×C17semidirect
243. #2169C2×C17semidirect
244. #2140C2×C17semidirect
245. #2139C2×C17semidirect
278. C2×SD32C22×C17semidirect
282. C2×M32C22×C17semidirect
283. #499C22×C17semidirect
291. #466C22×C17semidirect
296. C4×D8C22×C17semidirect
299. C2×#107C22×C17semidirect
300. #367C22×C17semidirect
301. #366C22×C17semidirect
302. #366C22×C17semidirect
303. C4⋊C16C22×C17semidirect
304. #358C22×C17semidirect
305. #358C22×C17semidirect
306. #358C22×C17semidirect
313. #357C22×C17semidirect
315. C22⋊C16C22×C17semidirect
316. C4×C16C22×C17semidirect
385. C17#33889direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#33392
C17×#32802
C17×#22422
C17×#22372
C17×#22322
C17×#22282
C17×#22202
C17×#22182
C17×#22102
C17×#21862
C17×#21842
C4×C17×D162
C17×#21692
C17×#21402
C17×#21392
#3388917