Finite Group Databasebeta

← C17×#33910 #16891654

Subgroups — C17×#33910 #16891654

Order 4352.

504 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3336C211yesmaximal, characteristic, complemented
2C17×#3334C211yesmaximal, characteristic
3C17×#2255C211yesmaximal, characteristic, complemented
4C17×#2236C211yesmaximal, characteristic, complemented
5C17×#2235C211yesmaximal, characteristic, complemented
6C17×#2234C211yesmaximal, characteristic, complemented
7C17×#2232C211yesmaximal, characteristic, complemented
8C17×#2228C211yesmaximal, characteristic, complemented
9C17×#2227C211yesmaximal, characteristic, complemented
10C17×#2220C211yesmaximal, characteristic, complemented
11C17×#2217C211yesmaximal, characteristic, complemented
12C17×#2175C211yesmaximal, characteristic, complemented
13C17×#2168C211yesmaximal, characteristic, complemented
14C17×#2159C211yesmaximal, characteristic, complemented
15C2×C17×#366C211yesmaximal, characteristic, complemented
16C17×#552—21no—
17C17×#547—21no—
18C2×C17×SD32C2211yescharacteristic
19C2×C17×M32C2211yescharacteristic
20C22×C16×C17C2211yescharacteristic
21C17×#500C2211yescharacteristic
22C17×#499C2211yescharacteristic
23C17×#485—21no—
24C17×#483—21no—
25C17×#480—21no—
26C17×#480—21no—
27C17×#479—21no—
28C17×#474—21no—
29C17×#467C2211yescharacteristic
30C17×#467C2211yescharacteristic
31C17×#466C2211yescharacteristic
32C17×#466C2211yescharacteristic
33C4×Q16×C17C2211yescharacteristic
34C4×D8×C17C2211yescharacteristic
35C8×D4×C17C2211yescharacteristic
36C17×#427C2211yescharacteristic
37C2×C17×#107C2211yescharacteristic
38C2×C17×#107C2211yescharacteristic
39C2×C17×#107C2211yescharacteristic
40C17×#367C2211yescharacteristic
41C17×#367C2211yescharacteristic
42C17×#367C2211yescharacteristic
43C17×#366C2211yescharacteristic
44C17×#366C2211yescharacteristic
45C17×#366C2211yescharacteristic
46C17×#366C2211yescharacteristic
47C17×#366C2211yescharacteristic
48C17×#366C2211yescharacteristic
49C17×C4⋊C16C2211yescharacteristic
50C17×#358C2211yescharacteristic
51C17×#358C2211yescharacteristic
52C17×#358C2211yescharacteristic
53C17×#357C2211yescharacteristic
54C17×#357C2211yescharacteristic
55C17×#357C2211yescharacteristic
56C17×C22⋊C16C2211yescharacteristic
57C17×C22⋊C16C2211yescharacteristic
58C17×#346C2211yescharacteristic
59C2×#41×C17—41no—
60C2×Q16×C17C2311yescharacteristic
61C2×D8×C17C2311yescharacteristic
62C22×C8×C17C2311yescharacteristic
63C22×C8×C17C2311yescharacteristic
64C17×C4⋊Q8—21no—
65C17×#126—41no—
66C17×#125—21no—
67C17×#125—41no—
68C17×#123—41no—
69C17×#123—41no—
70C17×#123—41no—
71C17×C22⋊Q8—21no—
72C17×C22⋊Q8—21no—
73C17×C22⋊Q8—41no—
74C17×#121—21no—
75C17×#121—21no—
76C4×Q8×C17—21no—
77C4×D4×C17—21no—
78C4×D4×C17D411yescharacteristic
79C17×#117—21no—
80C17×#117—41no—
81C2×C4⋊C4×C17—21no—
82C2×C4⋊C4×C17—21no—
83C2×C4⋊C4×C17—21no—
84C17×SD32—22no—
85C17×M32—22no—
86C2×C16×C17—22no—
87C2×C16×C17C2311yescharacteristic
88C2×C16×C17C2311yescharacteristic
89C2×C16×C17C2311yescharacteristic
90C2×C16×C17C2311yescharacteristic
91C17×#107—21no—
92C17×#107—21no—
93C17×#107—21no—
94C17×#107—21no—
95C17×#107C2311yescharacteristic
96C17×#107C2311yescharacteristic
97C17×#107C2311yescharacteristic
98C17×#107C2311yescharacteristic
99C17×#107C2311yescharacteristic
100C17×#107C2311yescharacteristic
101C17×#106—21no—
102C17×#106—21no—
103C17×C4⋊C8D411yescharacteristic
104C17×#103—21no—
105C17×#103—21no—
106C17×#103—21no—
107C17×#102—21no—
108C17×#102—21no—
109C17×#102—21no—
110C17×C22⋊C8D411yescharacteristic
111C17×C22⋊C8D411yescharacteristic
112C4×C8×C17C2311yescharacteristic
113#41×C17—84no—
114C2×Q8×C17—21no—
115C2×Q8×C17—41no—
116C2×D4×C17—21no—
117C2×D4×C17—41no—
118C2×D4×C17—41no—
119C2×D4×C17D811yescharacteristic
120C22×C4×C17—41no—
121C22×C4×C17—41no—
122C22×C4×C17—41no—
123C22×C4×C17—41no—
124C22×C4×C17C2×D411yescharacteristic
125C22×C4×C17C2×D411yescharacteristic
126Q16×C17—21no—
127Q16×C17—21no—
128D8×C17—21no—
129D8×C17—21no—
130C2×C8×C17—21no—
131C2×C8×C17—21no—
132C2×C8×C17—21no—
133C2×C8×C17—21no—
134C2×C8×C17C2×D411yescharacteristic
135C2×C8×C17C2×D411yescharacteristic
136C2×C8×C17C2×D411yescharacteristic
137C2×C8×C17C2411yescharacteristic
138C4⋊C4×C17—21no—
139C4⋊C4×C17—21no—
140C4⋊C4×C17—21no—
141C4⋊C4×C17—21no—
142C4⋊C4×C17—21no—
143C4⋊C4×C17—21no—
144C4⋊C4×C17—41no—
145C4⋊C4×C17—41no—
146C4⋊C4×C17—41no—
147C4⋊C4×C17—41no—
148C4⋊C4×C17—41no—
149C4⋊C4×C17—41no—
150C4⋊C4×C17—41no—
151C4⋊C4×C17—41no—
152C4⋊C4×C17—41no—
153C4⋊C4×C17D811yescharacteristic
154C22⋊C4×C17—41no—
155C22⋊C4×C17—41no—
156C22⋊C4×C17—41no—
157C22⋊C4×C17—41no—
158C22⋊C4×C17—41no—
159C22⋊C4×C17—41no—
160C22⋊C4×C17D811yescharacteristic
161C22⋊C4×C17D811yescharacteristic
162C42×C17—41no—
163C42×C17—41no—
164C42×C17C2×D411yescharacteristic
165C16×C17—21no—
166C16×C17—21no—
167C16×C17—21no—
168C16×C17#4112yescomplemented
169#33910C1711yesmaximal, characteristic, direct product factor, Sylow
170C23×C17—41no—
171C23×C17C2×D811yescharacteristic
172C23×C17C2×D811yescharacteristic
173Q8×C17—41no—
174Q8×C17—41no—
175Q8×C17—82no—
176D4×C17—22no—
177D4×C17—41no—
178D4×C17—41no—
179D4×C17—82no—
180D4×C17—82no—
181C2×C4×C17—21no—
182C2×C4×C17—21no—
183C2×C4×C17—21no—
184C2×C4×C17—21no—
185C2×C4×C17—41no—
186C2×C4×C17—41no—
187C2×C4×C17—41no—
188C2×C4×C17—41no—
189C2×C4×C17—41no—
190C2×C4×C17—41no—
191C2×C4×C17—41no—
192C2×C4×C17—82no—
193C2×C4×C17—82no—
194C2×C4×C17—82no—
195C2×C4×C17—82no—
196C2×C4×C17C2×D811yescharacteristic
197C2×C4×C17C2×D811yescharacteristic
198C2×C4×C17C2×D811yescharacteristic
199C2×C4×C17C2×D811yescharacteristic
200C2×C4×C17C22×D411yescharacteristic
201C8×C17—21no—
202C8×C17—21no—
203C8×C17—21no—
204C8×C17C2×#4111yescharacteristic
205C8×C172−1+411yescharacteristic
206#3336C2×C1711yescharacteristic, complemented
207#3334C2×C1711yescharacteristic
208#2255C2×C1711yescharacteristic, complemented
209#2236C2×C1711yescharacteristic, complemented
210#2235C2×C1711yescharacteristic, complemented
211#2234C2×C1711yescharacteristic, complemented
212#2232C2×C1711yescharacteristic, complemented
213#2228C2×C1711yescharacteristic, complemented
214#2227C2×C1711yescharacteristic, complemented
215#2220C2×C1711yescharacteristic, complemented
216#2217C2×C1711yescharacteristic, complemented
217#2175C2×C1711yescharacteristic, complemented
218#2168C2×C1711yescharacteristic, complemented
219#2159C2×C1711yescharacteristic, complemented
220C2×#366C2×C1711yescharacteristic, complemented
221C22×C17—21no—
222C22×C17—21no—
223C22×C17—21no—
224C22×C17—21no—
225C22×C17—21no—
226C22×C17—81no—
227C22×C17—81no—
228C22×C17—81no—
229C22×C17#50912yes—
230C22×C17C22×D811yescharacteristic
231C4×C17—21no—
232C4×C17—21no—
233C4×C17—21no—
234C4×C17—21no—
235C4×C17—81no—
236C4×C17—81no—
237C4×C17—81no—
238C4×C17—81no—
239C4×C17—81no—
240C4×C17—81no—
241C4×C17—81no—
242C4×C17#54711yescharacteristic
243C4×C17#57811yescharacteristic
244#552—21no—
245#547—21no—
246C2×SD32C22×C1711yescharacteristic
247C2×M32C22×C1711yescharacteristic
248C22×C16C22×C1711yescharacteristic
249#500C22×C1711yescharacteristic
250#499C22×C1711yescharacteristic
251#485—21no—
252#483—21no—
253#480—21no—
254#480—21no—
255#479—21no—
256#474—21no—
257#467C22×C1711yescharacteristic
258#467C22×C1711yescharacteristic
259#466C22×C1711yescharacteristic
260#466C22×C1711yescharacteristic
261C4×Q16C22×C1711yescharacteristic
262C4×D8C22×C1711yescharacteristic
263C8×D4C22×C1711yescharacteristic
264#427C22×C1711yescharacteristic
265C2×#107C22×C1711yescharacteristic
266C2×#107C22×C1711yescharacteristic
267C2×#107C22×C1711yescharacteristic
268#367C22×C1711yescharacteristic
269#367C22×C1711yescharacteristic
270#367C22×C1711yescharacteristic
271#366C22×C1711yescharacteristic
272#366C22×C1711yescharacteristic
273#366C22×C1711yescharacteristic
274#366C22×C1711yescharacteristic
275#366C22×C1711yescharacteristic
276#366C22×C1711yescharacteristic
277C4⋊C16C22×C1711yescharacteristic
278#358C22×C1711yescharacteristic
279#358C22×C1711yescharacteristic
280#358C22×C1711yescharacteristic
281#357C22×C1711yescharacteristic
282#357C22×C1711yescharacteristic
283#357C22×C1711yescharacteristic
284C22⋊C16C22×C1711yescharacteristic
285C22⋊C16C22×C1711yescharacteristic
286#346C22×C1711yescharacteristic
287C2×C17—22no—
288C2×C17—41no—
289C2×C17—161no—
290C2×C17#333411yescharacteristic
291C2×C17C2×#50911yescharacteristic
292C2×C17#341711yescharacteristic
293C2×#41—41no—
294C2×Q16C23×C1711yescharacteristic
295C2×D8C23×C1711yescharacteristic
296C22×C8C23×C1711yescharacteristic
297C22×C8C23×C1711yescharacteristic
298C4⋊Q8—21no—
299#126—41no—
300#125—21no—
301#125—41no—
302#123—41no—
303#123—41no—
304#123—41no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—41no—
308#121—21no—
309#121—21no—
310C4×Q8—21no—
311C4×D4—21no—
312C4×D4D4×C1711yescharacteristic
313#117—21no—
314#117—41no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318SD32—22no—
319M32—22no—
320C2×C16—22no—
321C2×C16C23×C1711yescharacteristic
322C2×C16C23×C1711yescharacteristic
323C2×C16C23×C1711yescharacteristic
324C2×C16C23×C1711yescharacteristic
325#107—21no—
326#107—21no—
327#107—21no—
328#107—21no—
329#107C23×C1711yescharacteristic
330#107C23×C1711yescharacteristic
331#107C23×C1711yescharacteristic
332#107C23×C1711yescharacteristic
333#107C23×C1711yescharacteristic
334#107C23×C1711yescharacteristic
335#106—21no—
336#106—21no—
337C4⋊C8D4×C1711yescharacteristic
338#103—21no—
339#103—21no—
340#103—21no—
341#102—21no—
342#102—21no—
343#102—21no—
344C22⋊C8D4×C1711yescharacteristic
345C22⋊C8D4×C1711yescharacteristic
346C4×C8C23×C1711yescharacteristic
347C17#3391011yescharacteristic, direct product factor, Sylow
348#41—84no—
349C2×Q8—21no—
350C2×Q8—41no—
351C2×D4—21no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4D8×C1711yescharacteristic
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4C2×D4×C1711yescharacteristic
360C22×C4C2×D4×C1711yescharacteristic
361Q16—21no—
362Q16—21no—
363D8—21no—
364D8—21no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8C2×D4×C1711yescharacteristic
370C2×C8C2×D4×C1711yescharacteristic
371C2×C8C2×D4×C1711yescharacteristic
372C2×C8C24×C1711yescharacteristic
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4D8×C1711yescharacteristic
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4D8×C1711yescharacteristic
396C22⋊C4D8×C1711yescharacteristic
397C42—41no—
398C42—41no—
399C42C2×D4×C1711yescharacteristic
400C16—21no—
401C16—21no—
402C16—21no—
403C16#41×C1712yescomplemented
404C23—41no—
405C23C2×D8×C1711yescharacteristic
406C23C2×D8×C1711yescharacteristic
407Q8—41no—
408Q8—41no—
409Q8—82no—
410D4—22no—
411D4—41no—
412D4—41no—
413D4—82no—
414D4—82no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4C2×D8×C1711yescharacteristic
431C2×C4C2×D8×C1711yescharacteristic
432C2×C4C2×D8×C1711yescharacteristic
433C2×C4C2×D8×C1711yescharacteristic
434C2×C4C22×D4×C1711yescharacteristic
435C8—21no—
436C8—21no—
437C8—21no—
438C8C2×#41×C1711yescharacteristic
439C8C17×2−1+411yescharacteristic
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22C17×#50912yes—
449C22C22×D8×C1711yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—81no—
455C4—81no—
456C4—81no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4C17×#54711yescharacteristic
462C4C17×#57811yescharacteristic
463C2—22no—
464C2—41no—
465C2—161no—
466C2C17×#333411yescharacteristic
467C2C2×C17×#50911yescharacteristic
468C2C17×#341711yescharacteristic
subgroupG/H
center, socleC22×C17C22×D8
commutator, Frattini, cosocleC2×C8C24×C17
prime radicalC17×#3334C2
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×#2255C2semidirect
4. C17×#2236C2semidirect
5. C17×#2235C2semidirect
6. C17×#2234C2semidirect
7. C17×#2232C2semidirect
8. C17×#2228C2semidirect
9. C17×#2227C2semidirect
10. C17×#2220C2semidirect
11. C17×#2217C2semidirect
12. C17×#2175C2semidirect
13. C17×#2168C2semidirect
14. C17×#2159C2semidirect
15. C2×C17×#366C2semidirect
168. C16×C17#41semidirect
169. #33910C17direct (N × H)
206. #3336C2×C17semidirect
208. #2255C2×C17semidirect
209. #2236C2×C17semidirect
210. #2235C2×C17semidirect
211. #2234C2×C17semidirect
212. #2232C2×C17semidirect
213. #2228C2×C17semidirect
214. #2227C2×C17semidirect
215. #2220C2×C17semidirect
216. #2217C2×C17semidirect
217. #2175C2×C17semidirect
218. #2168C2×C17semidirect
219. #2159C2×C17semidirect
220. C2×#366C2×C17semidirect
347. C17#33910direct (N × H)
403. C16#41×C17semidirect

Maximal subgroups

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

subgroupindex
C17×#33362
C17×#33342
C17×#22552
C17×#22362
C17×#22352
C17×#22342
C17×#22322
C17×#22282
C17×#22272
C17×#22202
C17×#22172
C17×#21752
C17×#21682
C17×#21592
C2×C17×#3662
#3391017