Finite Group Databasebeta

← C17×#33618 #16891362

Subgroups — C17×#33618 #16891362

Order 4352.

656 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#509C211yesmaximal, characteristic, complemented
2C17×#3407C211yesmaximal, characteristic, complemented
3C17×#3067C211yesmaximal, characteristic, complemented
4C2×C17×#472C211yesmaximal, characteristic, complemented
5C17×#2223C214yesmaximal, complemented
6C17×#2221C214yesmaximal, complemented
7C17×#2161C211yesmaximal, characteristic, complemented
8C17×#2148C211yesmaximal, characteristic, complemented
9C2×C17×#361C211yesmaximal, characteristic, complemented
10C17×#575—21no—
11C2×C17×AGL(1,ℤ/8)—21no—
12C2×C17×#135C2211yescharacteristic
13C22×D8×C17C2211yescharacteristic
14C2×C17×#131C2211yescharacteristic
15C17×#509—22no—
16C17×#509—22no—
17C2×C17×SD32C2212yescomplemented
18C2×C17×D16C2212yescomplemented
19C17×#504—22no—
20C17×#504C2214yescomplemented
21C2×C17×M32—22no—
22C2×C17×M32C2211yescharacteristic
23C2×C17×M32C2211yescharacteristic
24C17×#473C2212yescomplemented
25C17×#472—22no—
26C17×#472C2214yes—
27C17×#472C2212yescomplemented
28C17×#471—22no—
29C2×C17×#108C2211yescharacteristic
30C2×C17×#108C2211yescharacteristic
31C17×#413—21no—
32C2×C17×#100—21no—
33C17×#368C2214yescomplemented
34C17×#362C2212yescomplemented
35C17×#361C2212yescomplemented
36C17×#361C2214yescomplemented
37C2×#41×C17—21no—
38C2×#41×C17D411yescharacteristic
39C22×D4×C17—21no—
40C17×#137—22no—
41C17×#137—41no—
42C17×AGL(1,ℤ/8)—24no—
43C17×AGL(1,ℤ/8)—22no—
44C17×AGL(1,ℤ/8)—42no—
45C17×AGL(1,ℤ/8)—41no—
46C17×#135—21no—
47C17×#135—21no—
48C17×#135—21no—
49C17×#135—21no—
50C17×#135—42no—
51C2×Q16×C17C2311yescharacteristic
52C2×SD16×C17—21no—
53C2×SD16×C17—41no—
54C2×D8×C17—21no—
55C2×D8×C17—21no—
56C2×D8×C17—21no—
57C2×D8×C17—21no—
58C2×D8×C17—21no—
59C2×D8×C17—41no—
60C2×D8×C17C2311yescharacteristic
61C2×D8×C17C2312yes—
62C17×#131—21no—
63C17×#131—21no—
64C17×#131D412yes—
65C17×#131C2312yes—
66C2×M16×C17—21no—
67C2×M16×C17—21no—
68C2×M16×C17—21no—
69C2×M16×C17D411yescharacteristic
70C22×C8×C17—21no—
71C22×C8×C17C2311yescharacteristic
72C17×SD32—24no—
73C17×D16—24no—
74C17×M32—24no—
75C17×M32—21no—
76C17×M32D412yes—
77C17×M32D412yes—
78C17×M32C2312yes—
79C2×C16×C17—24no—
80C2×C16×C17—21no—
81C2×C16×C17C2312yes—
82C17×#108—21no—
83C17×#108—21no—
84C17×#108C2312yes—
85C17×#108C2312yes—
86C17×#101—22no—
87C17×#100—24no—
88C17×#100—22no—
89C24×C17—41no—
90#41×C17—21no—
91#41×C17—21no—
92#41×C17—41no—
93#41×C17—41no—
94#41×C17—41no—
95#41×C17—41no—
96#41×C17D812yes—
97#41×C17C2×D412yes—
98C2×Q8×C17—21no—
99C2×Q8×C17D811yescharacteristic
100C2×D4×C17—21no—
101C2×D4×C17—22no—
102C2×D4×C17—21no—
103C2×D4×C17—41no—
104C2×D4×C17—41no—
105C2×D4×C17—41no—
106C2×D4×C17—41no—
107C2×D4×C17—41no—
108C2×D4×C17—41no—
109C2×D4×C17D811yescharacteristic
110C22×C4×C17—21no—
111C22×C4×C17—41no—
112C22×C4×C17C2×D411yescharacteristic
113Q16×C17—21no—
114Q16×C17—21no—
115Q16×C17—42no—
116SD16×C17—44no—
117SD16×C17—42no—
118SD16×C17—42no—
119SD16×C17—41no—
120SD16×C17—41no—
121D8×C17—22no—
122D8×C17—21no—
123D8×C17—22no—
124D8×C17—21no—
125D8×C17—44no—
126D8×C17—42no—
127D8×C17—41no—
128D8×C17—41no—
129M16×C17—21no—
130M16×C17—22no—
131M16×C17—22no—
132M16×C17—22no—
133M16×C17—22no—
134M16×C17—41no—
135M16×C17—41no—
136M16×C17C2×D412yes—
137C2×C8×C17—21no—
138C2×C8×C17—22no—
139C2×C8×C17—22no—
140C2×C8×C17—41no—
141C2×C8×C17—41no—
142C2×C8×C17C2×D411yescharacteristic
143C2×C8×C17C2×D411yescharacteristic
144C2×C8×C17C2×D411yescharacteristic
145C2×C8×C17#4111yescharacteristic
146C2×C8×C17#4111yescharacteristic
147C2×C8×C17C2411yescharacteristic
148C16×C17—22no—
149C16×C17C2×D414yes—
150#33618C1711yesmaximal, characteristic, direct product factor, Sylow
151C23×C17—21no—
152C23×C17—41no—
153C23×C17—42no—
154C23×C17—81no—
155C23×C17—81no—
156C23×C17—162no—
157C23×C17#13511yescharacteristic
158Q8×C17—21no—
159Q8×C17—41no—
160Q8×C17—41no—
161Q8×C17C2×D812yes—
162D4×C17—22no—
163D4×C17—22no—
164D4×C17—21no—
165D4×C17—42no—
166D4×C17—41no—
167D4×C17—42no—
168D4×C17—41no—
169D4×C17—81no—
170D4×C17—81no—
171D4×C17—81no—
172D4×C17—81no—
173D4×C17C2×D812yes—
174C2×C4×C17—21no—
175C2×C4×C17—22no—
176C2×C4×C17—22no—
177C2×C4×C17—41no—
178C2×C4×C17—81no—
179C2×C4×C17—81no—
180C2×C4×C17#12111yescharacteristic
181C2×C4×C17#12111yescharacteristic
182C2×C4×C17C2×D811yescharacteristic
183C2×C4×C17C2×D811yescharacteristic
184C2×C4×C17#13511yescharacteristic
185C2×C4×C17C22×D411yescharacteristic
186C8×C17—22no—
187C8×C17—42no—
188C8×C17—42no—
189C8×C17#12111yescharacteristic
190C8×C17#12111yescharacteristic
191C8×C17C22×D411yescharacteristic
192C8×C17C2×#4111yescharacteristic
193C2×#509C2×C1711yescharacteristic, complemented
194#3407C2×C1711yescharacteristic, complemented
195#3067C2×C1711yescharacteristic, complemented
196C2×#472C2×C1711yescharacteristic, complemented
197#2223C2×C1714yescomplemented
198#2221C2×C1714yescomplemented
199#2161C2×C1711yescharacteristic, complemented
200#2148C2×C1711yescharacteristic, complemented
201C2×#361C2×C1711yescharacteristic, complemented
202C22×C17—22no—
203C22×C17—41no—
204C22×C17—81no—
205C22×C17—81no—
206C22×C17—82no—
207C22×C17—161no—
208C22×C17—162no—
209C22×C17—162no—
210C22×C17—162no—
211C22×C17#46611yescharacteristic
212C22×C17#46611yescharacteristic
213C22×C17C2×#13511yescharacteristic
214C4×C17—22no—
215C4×C17—81no—
216C4×C17#46611yescharacteristic
217C4×C17#46611yescharacteristic
218C4×C17C2×#12111yescharacteristic
219C4×C17C22×D811yescharacteristic
220#575—21no—
221C2×AGL(1,ℤ/8)—21no—
222C2×#135C22×C1711yescharacteristic
223C22×D8C22×C1711yescharacteristic
224C2×#131C22×C1711yescharacteristic
225#509—22no—
226#509—22no—
227C2×SD32C22×C1712yescomplemented
228C2×D16C22×C1712yescomplemented
229#504—22no—
230#504C22×C1714yescomplemented
231C2×M32—22no—
232C2×M32C22×C1711yescharacteristic
233C2×M32C22×C1711yescharacteristic
234#473C22×C1712yescomplemented
235#472—22no—
236#472C22×C1714yes—
237#472C22×C1712yescomplemented
238#471—22no—
239C2×#108C22×C1711yescharacteristic
240C2×#108C22×C1711yescharacteristic
241#413—21no—
242C2×#100—21no—
243#368C22×C1714yescomplemented
244#362C22×C1712yescomplemented
245#361C22×C1714yescomplemented
246#361C22×C1712yescomplemented
247C2×C17—21no—
248C2×C17—21no—
249C2×C17—21no—
250C2×C17—42no—
251C2×C17—161no—
252C2×C17—162no—
253C2×C17C2×#46611yescharacteristic
254C2×#41—21no—
255C2×#41D4×C1711yescharacteristic
256C22×D4—21no—
257#137—22no—
258#137—41no—
259AGL(1,ℤ/8)—24no—
260AGL(1,ℤ/8)—22no—
261AGL(1,ℤ/8)—42no—
262AGL(1,ℤ/8)—41no—
263#135—21no—
264#135—21no—
265#135—21no—
266#135—21no—
267#135—42no—
268C2×Q16C23×C1711yescharacteristic
269C2×SD16—21no—
270C2×SD16—41no—
271C2×D8—21no—
272C2×D8—21no—
273C2×D8—21no—
274C2×D8—21no—
275C2×D8—21no—
276C2×D8—41no—
277C2×D8C23×C1712yes—
278C2×D8C23×C1711yescharacteristic
279#131—21no—
280#131—21no—
281#131D4×C1712yes—
282#131C23×C1712yes—
283C2×M16—21no—
284C2×M16—21no—
285C2×M16—21no—
286C2×M16D4×C1711yescharacteristic
287C22×C8—21no—
288C22×C8C23×C1711yescharacteristic
289SD32—24no—
290D16—24no—
291M32—21no—
292M32—24no—
293M32D4×C1712yes—
294M32D4×C1712yes—
295M32C23×C1712yes—
296C2×C16—21no—
297C2×C16—24no—
298C2×C16C23×C1712yes—
299#108—21no—
300#108—21no—
301#108C23×C1712yes—
302#108C23×C1712yes—
303#101—22no—
304#100—24no—
305#100—22no—
306C17#3361811yescharacteristic, direct product factor, Sylow
307C24—41no—
308#41—21no—
309#41—21no—
310#41—41no—
311#41—41no—
312#41—41no—
313#41—41no—
314#41D8×C1712yes—
315#41C2×D4×C1712yes—
316C2×Q8—21no—
317C2×Q8D8×C1711yescharacteristic
318C2×D4—21no—
319C2×D4—22no—
320C2×D4—21no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4D8×C1711yescharacteristic
328C22×C4—21no—
329C22×C4—41no—
330C22×C4C2×D4×C1711yescharacteristic
331Q16—21no—
332Q16—21no—
333Q16—42no—
334SD16—44no—
335SD16—42no—
336SD16—42no—
337SD16—41no—
338SD16—41no—
339D8—21no—
340D8—22no—
341D8—22no—
342D8—21no—
343D8—44no—
344D8—42no—
345D8—41no—
346D8—41no—
347M16—21no—
348M16—22no—
349M16—22no—
350M16—22no—
351M16—22no—
352M16—41no—
353M16—41no—
354M16C2×D4×C1712yes—
355C2×C8—21no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—41no—
359C2×C8—41no—
360C2×C8C2×D4×C1711yescharacteristic
361C2×C8C2×D4×C1711yescharacteristic
362C2×C8C2×D4×C1711yescharacteristic
363C2×C8#41×C1711yescharacteristic
364C2×C8#41×C1711yescharacteristic
365C2×C8C24×C1711yescharacteristic
366C16—22no—
367C16C2×D4×C1714yes—
368C23—21no—
369C23—41no—
370C23—42no—
371C23—81no—
372C23—81no—
373C23—162no—
374C23C17×#13511yescharacteristic
375Q8—21no—
376Q8—41no—
377Q8—41no—
378Q8C2×D8×C1712yes—
379D4—22no—
380D4—22no—
381D4—21no—
382D4—42no—
383D4—41no—
384D4—42no—
385D4—41no—
386D4—81no—
387D4—81no—
388D4—81no—
389D4—81no—
390D4C2×D8×C1712yes—
391C2×C4—21no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4C17×#12111yescharacteristic
398C2×C4C17×#12111yescharacteristic
399C2×C4C2×D8×C1711yescharacteristic
400C2×C4C2×D8×C1711yescharacteristic
401C2×C4C17×#13511yescharacteristic
402C2×C4C22×D4×C1711yescharacteristic
403C8—22no—
404C8—42no—
405C8—42no—
406C8C17×#12111yescharacteristic
407C8C17×#12111yescharacteristic
408C8C22×D4×C1711yescharacteristic
409C8C2×#41×C1711yescharacteristic
410C22—22no—
411C22—41no—
412C22—81no—
413C22—81no—
414C22—82no—
415C22—162no—
416C22—161no—
417C22—162no—
418C22—162no—
419C22C17×#46611yescharacteristic
420C22C17×#46611yescharacteristic
421C22C2×C17×#13511yescharacteristic
422C4—22no—
423C4—81no—
424C4C17×#46611yescharacteristic
425C4C17×#46611yescharacteristic
426C4C2×C17×#12111yescharacteristic
427C4C22×D8×C1711yescharacteristic
428C2—21no—
429C2—21no—
430C2—21no—
431C2—42no—
432C2—162no—
433C2—161no—
434C2C2×C17×#46611yescharacteristic
subgroupG/H
center, socleC2×C17C2×#466
commutator, Frattini, cosocleC2×C8C24×C17
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C17×#509C2semidirect
2. C17×#3407C2semidirect
3. C17×#3067C2semidirect
4. C2×C17×#472C2semidirect
5. C17×#2223C2semidirect
6. C17×#2221C2semidirect
7. C17×#2161C2semidirect
8. C17×#2148C2semidirect
9. C2×C17×#361C2semidirect
17. C2×C17×SD32C22semidirect
18. C2×C17×D16C22semidirect
20. C17×#504C22semidirect
24. C17×#473C22semidirect
27. C17×#472C22semidirect
33. C17×#368C22semidirect
34. C17×#362C22semidirect
35. C17×#361C22semidirect
36. C17×#361C22semidirect
150. #33618C17direct (N × H)
193. C2×#509C2×C17semidirect
194. #3407C2×C17semidirect
195. #3067C2×C17semidirect
196. C2×#472C2×C17semidirect
197. #2223C2×C17semidirect
198. #2221C2×C17semidirect
199. #2161C2×C17semidirect
200. #2148C2×C17semidirect
201. C2×#361C2×C17semidirect
227. C2×SD32C22×C17semidirect
228. C2×D16C22×C17semidirect
230. #504C22×C17semidirect
234. #473C22×C17semidirect
237. #472C22×C17semidirect
243. #368C22×C17semidirect
244. #362C22×C17semidirect
245. #361C22×C17semidirect
246. #361C22×C17semidirect
306. C17#33618direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#5092
C17×#34072
C17×#30672
C2×C17×#4722
C17×#22232
C17×#22212
C17×#21612
C17×#21482
C2×C17×#3612
#3361817