Finite Group Databasebeta

← C17×#8991 #16866735

Subgroups — C17×#8991 #16866735

Order 4352.

578 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3100C211yesmaximal, characteristic
2D4×M16×C17C211yesmaximal, characteristic, complemented
3C17×#1980C211yesmaximal, characteristic, complemented
4C4×C17×#102C211yesmaximal, characteristic, complemented
5C17×#1492C211yesmaximal, characteristic, complemented
6C17×#1303C211yesmaximal, characteristic, complemented
7C17×#1278C211yesmaximal, characteristic, complemented
8C22×M16×C17—21no—
9C17×#532C2211yescharacteristic
10C2×C4×D4×C17C2211yescharacteristic
11C17×#480—21no—
12C17×#474C411yescharacteristic, complemented
13C17×#474C411yescharacteristic, complemented
14C17×#459C411yescharacteristic, complemented
15C17×#459C411yescharacteristic, complemented
16C17×#447—21no—
17C4×D8×C17—21no—
18C4×D8×C17—21no—
19C17×#436—21no—
20C17×#435—22no—
21C8×D4×C17—21no—
22C17×#431C2211yescharacteristic
23C17×#423C2211yescharacteristic
24C2×C17×#104—21no—
25C2×C17×#104—21no—
26C2×C17×#102—21no—
27C17×#407—21no—
28C4×M16×C17C2211yescharacteristic
29C2×C4×C8×C17C2211yescharacteristic
30C4×C4⋊C4×C17C2211yescharacteristic
31C17×#340—21no—
32C17×D4⋊C8—22no—
33C2×#41×C17—21no—
34C22×D4×C17D411yescharacteristic
35C23×C4×C17—21no—
36C2×D8×C17—21no—
37C2×D8×C17—21no—
38C2×M16×C17—22no—
39C2×M16×C17—21no—
40C2×M16×C17—42no—
41C2×M16×C17—42no—
42C2×M16×C17D411yescharacteristic
43C2×M16×C17D411yescharacteristic
44C22×C8×C17—22no—
45C22×C8×C17—21no—
46C17×C4⋊Q8C2×C411yescharacteristic
47C17×#127C2×C411yescharacteristic
48C17×#124—21no—
49C17×#121—21no—
50C17×#121—21no—
51C4×D4×C17—21no—
52C4×D4×C17—21no—
53C4×D4×C17—21no—
54C4×D4×C17—21no—
55C4×D4×C17C2×C411yescharacteristic
56C4×D4×C17C2×C411yescharacteristic
57C4×D4×C17D411yescharacteristic
58C4×D4×C17D411yescharacteristic
59C2×C4⋊C4×C17—21no—
60C2×C4⋊C4×C17D411yescharacteristic
61C2×C22⋊C4×C17—21no—
62C2×C42×C17—21no—
63C2×C42×C17C2311yescharacteristic
64C17×#107—21no—
65C17×#107—21no—
66C17×C4⋊C8—21no—
67C17×C4⋊C8C2×C411yescharacteristic
68C17×C4⋊C8C2×C411yescharacteristic
69C17×C4⋊C8D412yes—
70C17×#104—42no—
71C17×#104—42no—
72C17×#102—24no—
73C17×#102—21no—
74C17×#102—21no—
75C17×#102—21no—
76C17×#102—21no—
77C17×C22⋊C8—22no—
78C17×C22⋊C8—22no—
79C17×C22⋊C8—21no—
80C17×#97—21no—
81C4×C8×C17—21no—
82C4×C8×C17—21no—
83C4×C8×C17—21no—
84C4×C8×C17—21no—
85C17×#95—21no—
86C24×C17—21no—
87#41×C17—41no—
88#41×C17—41no—
89#41×C17—41no—
90#41×C17—41no—
91C2×Q8×C17—21no—
92C2×D4×C17—22no—
93C2×D4×C17—21no—
94C2×D4×C17—21no—
95C2×D4×C17—21no—
96C2×D4×C17—21no—
97C2×D4×C17—41no—
98C2×D4×C17—41no—
99C2×D4×C17C22⋊C411yescharacteristic
100C2×D4×C17C22⋊C411yescharacteristic
101C22×C4×C17—21no—
102C22×C4×C17—21no—
103C22×C4×C17—21no—
104C22×C4×C17—21no—
105C22×C4×C17—21no—
106C22×C4×C17—41no—
107C22×C4×C17—41no—
108C22×C4×C17—41no—
109C22×C4×C17—41no—
110C22×C4×C17—41no—
111C22×C4×C17—41no—
112C22×C4×C17C2×D411yescharacteristic
113C22×C4×C17C2×D411yescharacteristic
114C22×C4×C17#4111yescharacteristic
115D8×C17—42no—
116D8×C17—42no—
117M16×C17—21no—
118M16×C17—21no—
119M16×C17—21no—
120M16×C17—44no—
121M16×C17—41no—
122M16×C17—41no—
123M16×C17D812yescomplemented
124C2×C8×C17—21no—
125C2×C8×C17—22no—
126C2×C8×C17—21no—
127C2×C8×C17—21no—
128C2×C8×C17—22no—
129C2×C8×C17—21no—
130C2×C8×C17—44no—
131C2×C8×C17—41no—
132C2×C8×C17—41no—
133C4⋊C4×C17—21no—
134C4⋊C4×C17—22no—
135C4⋊C4×C17—21no—
136C4⋊C4×C17—21no—
137C4⋊C4×C17—41no—
138C4⋊C4×C17C22⋊C411yescharacteristic
139C4⋊C4×C17C22⋊C411yescharacteristic
140C22⋊C4×C17—21no—
141C22⋊C4×C17—21no—
142C22⋊C4×C17—21no—
143C22⋊C4×C17—21no—
144C22⋊C4×C17—41no—
145C22⋊C4×C17—41no—
146C42×C17—41no—
147C42×C17—41no—
148C42×C17C22×C411yescharacteristic
149C42×C17C2×D411yescharacteristic
150C42×C17C2×D411yescharacteristic
151C42×C17#4111yescharacteristic
152#8991C1711yesmaximal, characteristic, direct product factor, Sylow
153C23×C17—21no—
154C23×C17—21no—
155C23×C17—42no—
156C23×C17—41no—
157C23×C17—41no—
158C23×C17—41no—
159C23×C17—81no—
160C23×C17#12111yescharacteristic
161Q8×C17—41no—
162Q8×C17—41no—
163D4×C17—21no—
164D4×C17—21no—
165D4×C17—21no—
166D4×C17—42no—
167D4×C17—42no—
168D4×C17—41no—
169D4×C17—41no—
170D4×C17—41no—
171D4×C17—41no—
172D4×C17—81no—
173D4×C17—81no—
174D4×C17#10412yescomplemented
175C2×C4×C17—21no—
176C2×C4×C17—21no—
177C2×C4×C17—21no—
178C2×C4×C17—21no—
179C2×C4×C17—41no—
180C2×C4×C17—41no—
181C2×C4×C17—41no—
182C2×C4×C17—41no—
183C2×C4×C17—41no—
184C2×C4×C17—41no—
185C2×C4×C17—41no—
186C2×C4×C17—41no—
187C2×C4×C17—41no—
188C2×C4×C17—41no—
189C2×C4×C17—41no—
190C2×C4×C17—42no—
191C2×C4×C17—41no—
192C2×C4×C17—81no—
193C2×C4×C17—81no—
194C2×C4×C17—81no—
195C2×C4×C17—81no—
196C2×C4×C17C2×C22⋊C411yescharacteristic
197C2×C4×C17C4×D411yescharacteristic
198C2×C4×C17C4×D411yescharacteristic
199C2×C4×C17#12011yescharacteristic
200C2×C4×C17#12111yescharacteristic
201C2×C4×C17#12311yescharacteristic
202C2×C4×C17C2×D811yescharacteristic
203C2×C4×C17#13511yescharacteristic
204C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
205C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
206C8×C17—22no—
207C8×C17—42no—
208C8×C17—41no—
209C8×C17—41no—
210C8×C17—42no—
211C8×C17—41no—
212#3100C2×C1711yescharacteristic
213D4×M16C2×C1711yescharacteristic, complemented
214#1980C2×C1711yescharacteristic, complemented
215C4×#102C2×C1711yescharacteristic, complemented
216#1492C2×C1711yescharacteristic, complemented
217#1303C2×C1711yescharacteristic, complemented
218#1278C2×C1711yescharacteristic, complemented
219C22×C17—21no—
220C22×C17—21no—
221C22×C17—22no—
222C22×C17—41no—
223C22×C17—41no—
224C22×C17—41no—
225C22×C17—41no—
226C22×C17—41no—
227C22×C17—82no—
228C22×C17—82no—
229C22×C17—81no—
230C22×C17—81no—
231C22×C17—81no—
232C22×C17#38611yescharacteristic
233C22×C17#45911yescharacteristic
234C22×C17#46311yescharacteristic
235C4×C17—21no—
236C4×C17—21no—
237C4×C17—21no—
238C4×C17—41no—
239C4×C17—41no—
240C4×C17—82no—
241C4×C17—81no—
242C4×C17C2×#10411yescharacteristic
243C4×C17#42111yescharacteristic
244C4×C17C4×D811yescharacteristic
245C4×C17#44211yescharacteristic
246C4×C17#44711yescharacteristic
247C4×C17#44911yescharacteristic
248C22×M16—21no—
249#532C22×C1711yescharacteristic
250C2×C4×D4C22×C1711yescharacteristic
251#480—21no—
252#474C4×C1711yescharacteristic, complemented
253#474C4×C1711yescharacteristic, complemented
254#459C4×C1711yescharacteristic, complemented
255#459C4×C1711yescharacteristic, complemented
256#447—21no—
257C4×D8—21no—
258C4×D8—21no—
259#436—21no—
260#435—22no—
261C8×D4—21no—
262#431C22×C1711yescharacteristic
263#423C22×C1711yescharacteristic
264C2×#104—21no—
265C2×#104—21no—
266C2×#102—21no—
267#407—21no—
268C4×M16C22×C1711yescharacteristic
269C2×C4×C8C22×C1711yescharacteristic
270C4×C4⋊C4C22×C1711yescharacteristic
271#340—21no—
272D4⋊C8—22no—
273C2×C17—21no—
274C2×C17—21no—
275C2×C17—42no—
276C2×C17—81no—
277C2×C17—161no—
278C2×C17#187111yescharacteristic
279C2×C17#187911yescharacteristic
280C2×C17#188111yescharacteristic
281C2×#41—21no—
282C22×D4D4×C1711yescharacteristic
283C23×C4—21no—
284C2×D8—21no—
285C2×D8—21no—
286C2×M16—22no—
287C2×M16—21no—
288C2×M16—42no—
289C2×M16—42no—
290C2×M16D4×C1711yescharacteristic
291C2×M16D4×C1711yescharacteristic
292C22×C8—22no—
293C22×C8—21no—
294C4⋊Q8C2×C4×C1711yescharacteristic
295#127C2×C4×C1711yescharacteristic
296#124—21no—
297#121—21no—
298#121—21no—
299C4×D4—21no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4C2×C4×C1711yescharacteristic
304C4×D4C2×C4×C1711yescharacteristic
305C4×D4D4×C1711yescharacteristic
306C4×D4D4×C1711yescharacteristic
307C2×C4⋊C4—21no—
308C2×C4⋊C4D4×C1711yescharacteristic
309C2×C22⋊C4—21no—
310C2×C42—21no—
311C2×C42C23×C1711yescharacteristic
312#107—21no—
313#107—21no—
314C4⋊C8—21no—
315C4⋊C8C2×C4×C1711yescharacteristic
316C4⋊C8C2×C4×C1711yescharacteristic
317C4⋊C8D4×C1712yes—
318#104—42no—
319#104—42no—
320#102—24no—
321#102—21no—
322#102—21no—
323#102—21no—
324#102—21no—
325C22⋊C8—22no—
326C22⋊C8—22no—
327C22⋊C8—21no—
328#97—21no—
329C4×C8—21no—
330C4×C8—21no—
331C4×C8—21no—
332C4×C8—21no—
333#95—21no—
334C17#899111yescharacteristic, direct product factor, Sylow
335C24—21no—
336#41—41no—
337#41—41no—
338#41—41no—
339#41—41no—
340C2×Q8—21no—
341C2×D4—22no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4C22⋊C4×C1711yescharacteristic
349C2×D4C22⋊C4×C1711yescharacteristic
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4C2×D4×C1711yescharacteristic
362C22×C4C2×D4×C1711yescharacteristic
363C22×C4#41×C1711yescharacteristic
364D8—42no—
365D8—42no—
366M16—21no—
367M16—21no—
368M16—21no—
369M16—44no—
370M16—41no—
371M16—41no—
372M16D8×C1712yescomplemented
373C2×C8—21no—
374C2×C8—22no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—22no—
379C2×C8—44no—
380C2×C8—41no—
381C2×C8—41no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—41no—
387C4⋊C4C22⋊C4×C1711yescharacteristic
388C4⋊C4C22⋊C4×C1711yescharacteristic
389C22⋊C4—21no—
390C22⋊C4—21no—
391C22⋊C4—21no—
392C22⋊C4—21no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C42—41no—
396C42—41no—
397C42C22×C4×C1711yescharacteristic
398C42C2×D4×C1711yescharacteristic
399C42C2×D4×C1711yescharacteristic
400C42#41×C1711yescharacteristic
401C23—21no—
402C23—21no—
403C23—42no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—81no—
408C23C17×#12111yescharacteristic
409Q8—41no—
410Q8—41no—
411D4—21no—
412D4—21no—
413D4—21no—
414D4—42no—
415D4—42no—
416D4—41no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—81no—
421D4—81no—
422D4C17×#10412yescomplemented
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4C2×C22⋊C4×C1711yescharacteristic
445C2×C4C4×D4×C1711yescharacteristic
446C2×C4C4×D4×C1711yescharacteristic
447C2×C4C17×#12011yescharacteristic
448C2×C4C17×#12111yescharacteristic
449C2×C4C17×#12311yescharacteristic
450C2×C4C2×D8×C1711yescharacteristic
451C2×C4C17×#13511yescharacteristic
452C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
453C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
454C8—22no—
455C8—42no—
456C8—41no—
457C8—41no—
458C8—42no—
459C8—41no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—82no—
469C22—82no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22C17×#38611yescharacteristic
474C22C17×#45911yescharacteristic
475C22C17×#46311yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—41no—
480C4—41no—
481C4—82no—
482C4—81no—
483C4C2×C17×#10411yescharacteristic
484C4C17×#42111yescharacteristic
485C4C4×D8×C1711yescharacteristic
486C4C17×#44211yescharacteristic
487C4C17×#44711yescharacteristic
488C4C17×#44911yescharacteristic
489C2—21no—
490C2—21no—
491C2—42no—
492C2—81no—
493C2—161no—
494C2C17×#187111yescharacteristic
495C2C17×#187911yescharacteristic
496C2C17×#188111yescharacteristic
subgroupG/H
centerC2×C4×C17#120
commutatorC42C22×C4×C17
Frattini, cosocleC2×C42C23×C17
socleC22×C17#386
prime radicalC17×#3100C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. D4×M16×C17C2semidirect
3. C17×#1980C2semidirect
4. C4×C17×#102C2semidirect
5. C17×#1492C2semidirect
6. C17×#1303C2semidirect
7. C17×#1278C2semidirect
12. C17×#474C4semidirect
13. C17×#474C4semidirect
14. C17×#459C4semidirect
15. C17×#459C4semidirect
123. M16×C17D8semidirect
152. #8991C17direct (N × H)
174. D4×C17#104semidirect
213. D4×M16C2×C17semidirect
214. #1980C2×C17semidirect
215. C4×#102C2×C17semidirect
216. #1492C2×C17semidirect
217. #1303C2×C17semidirect
218. #1278C2×C17semidirect
252. #474C4×C17semidirect
253. #474C4×C17semidirect
254. #459C4×C17semidirect
255. #459C4×C17semidirect
334. C17#8991direct (N × H)
372. M16D8×C17semidirect
422. D4C17×#104semidirect

Maximal subgroups

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

subgroupindex
C17×#31002
D4×M16×C172
C17×#19802
C4×C17×#1022
C17×#14922
C17×#13032
C17×#12782
#899117