Finite Group Databasebeta

← C17×#60218 #16917962

Subgroups — C17×#60218 #16917962

Order 4352.

1950 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3480C211yesmaximal, characteristic
2C17×#2971C212yesmaximal, complemented
3C17×#2969C216yesmaximal, complemented
4C17×#2966C216yesmaximal, complemented
5C8×#41×C17C212yesmaximal, complemented
6Q8×M16×C17C211yesmaximal, characteristic, complemented
7C2×C8×Q8×C17C211yesmaximal, characteristic, complemented
8C17×#2935C213yesmaximal, complemented
9C17×#2931C213yesmaximal, complemented
10C17×#2925C213yesmaximal, complemented
11C4×C17×#131C213yesmaximal, complemented
12C2×C17×#131C2213yes—
13C2×C17×#131C2213yes—
14C17×#559C413yes—
15C17×#557C411yescharacteristic
16C17×#556C413yes—
17C17×#553C416yes—
18C17×#550C411yescharacteristic
19C17×#548C412yes—
20C17×#532C2213yes—
21C17×#529C2216yes—
22C4×#41×C17C2212yes—
23C4×#41×C17C2213yes—
24C2×C4×Q8×C17C2211yescharacteristic
25C17×#446C2216yes—
26C8×Q8×C17C2211yescharacteristic
27C8×Q8×C17C2213yes—
28C8×Q8×C17C2213yes—
29C8×Q8×C17C2211yescharacteristic
30C8×Q8×C17C2212yes—
31C17×#436C2216yes—
32C17×#436C2216yes—
33C17×#436C2216yes—
34C17×#435C22112yes—
35C8×D4×C17C2216yes—
36C8×D4×C17C2216yes—
37C8×D4×C17C2216yes—
38C17×#433C22112yes—
39C17×#432C2216yes—
40C17×#431C2216yes—
41C17×#423C2213yes—
42C2×C17×C4⋊C8C2213yes—
43C17×#408C2216yes—
44C17×#405C2216yes—
45C17×#405C2216yes—
46C17×#405C2211yescharacteristic
47C17×#405C2213yes—
48C4×M16×C17C2213yes—
49C4×M16×C17C2216yes—
50C2×C4×C8×C17C2213yes—
51C2×C4×C8×C17C2216yes—
52C2×#41×C17C2×C412yes—
53C2×#41×C17C2313yes—
54C22×Q8×C17C2×C411yescharacteristic
55C17×#131—212no—
56C17×#131—212no—
57C2×M16×C17C2313yes—
58C2×M16×C17C2316yes—
59C2×M16×C17C2316yes—
60C2×M16×C17C2311yescharacteristic
61C22×C8×C17C2313yes—
62C22×C8×C17C2316yes—
63C22×C8×C17C2316yes—
64C22×C8×C17C2311yescharacteristic
65C17×C4⋊Q8C2×C413yes—
66C17×#127C2×C413yes—
67C17×#126C2×C4112yes—
68C17×#125C2×C416yes—
69C17×#124C2×C416yes—
70C17×#124C2×C416yes—
71C17×#123C2×C4112yes—
72C17×C22⋊Q8C2×C416yes—
73C17×#121C2×C416yes—
74C17×#121C2×C416yes—
75C17×#121C2×C416yes—
76C4×Q8×C17C2×C411yescharacteristic
77C4×Q8×C17C2×C413yes—
78C4×Q8×C17C2×C412yes—
79C4×Q8×C17C2×C413yes—
80C4×Q8×C17C2×C413yes—
81C4×Q8×C17C2311yescharacteristic
82C4×Q8×C17C2313yes—
83C4×D4×C17C2×C416yes—
84C4×D4×C17C2×C413yes—
85C4×D4×C17C2×C416yes—
86C4×D4×C17C2×C416yes—
87C4×D4×C17C2×C413yes—
88C4×D4×C17C2316yes—
89C4×D4×C17C2316yes—
90C17×#117C2×C416yes—
91C17×#117C2311yescharacteristic
92C17×#117C2316yes—
93C2×C4⋊C4×C17C2×C413yes—
94C2×C42×C17C2313yes—
95C2×C42×C17C2316yes—
96C17×C4⋊C8C2313yes—
97C17×C4⋊C8C2313yes—
98C17×C4⋊C8C2316yes—
99C17×C4⋊C8C2316yes—
100C17×C4⋊C8C2316yes—
101C17×C22⋊C8C23112yes—
102C17×C22⋊C8C23112yes—
103C17×#97C2312yes—
104C17×#97C2316yes—
105C17×#97C2316yes—
106C4×C8×C17C2316yes—
107C4×C8×C17C2313yes—
108C4×C8×C17C2316yes—
109C4×C8×C17C2313yes—
110C4×C8×C17C2312yes—
111C4×C8×C17C2313yes—
112C4×C8×C17C2313yes—
113#41×C17—28no—
114#41×C17—26no—
115#41×C17—26no—
116C2×Q8×C17—24no—
117C2×Q8×C17C22×C413yes—
118C2×Q8×C17C22×C413yes—
119C2×Q8×C17C22×C411yescharacteristic
120C2×D4×C17C22×C413yes—
121C2×D4×C17C22×C416yes—
122C2×D4×C17C22×C416yes—
123C2×D4×C17C22×C416yes—
124C22×C4×C17C22×C416yes—
125C22×C4×C17C22×C413yes—
126C22×C4×C17C22×C416yes—
127C22×C4×C17C22×C413yes—
128C22×C4×C17C2416yes—
129C22×C4×C17C2411yescharacteristic
130M16×C17—26no—
131M16×C17—212no—
132M16×C17—212no—
133M16×C17#4114yescomplemented
134C2×C8×C17—26no—
135C2×C8×C17—212no—
136C2×C8×C17—212no—
137C2×C8×C17#4114yescomplemented
138C2×C8×C17C2413yes—
139C2×C8×C17C2413yes—
140C2×C8×C17C2416yes—
141C2×C8×C17C2412yes—
142C2×C8×C17C2411yescharacteristic
143C2×C8×C17C2411yescharacteristic
144C4⋊C4×C17C22×C416yes—
145C4⋊C4×C17C22×C416yes—
146C4⋊C4×C17C22×C416yes—
147C4⋊C4×C17C22×C416yes—
148C4⋊C4×C17C22×C416yes—
149C4⋊C4×C17C22×C413yes—
150C4⋊C4×C17C22×C413yes—
151C4⋊C4×C17C22×C411yescharacteristic
152C4⋊C4×C17C22×C411yescharacteristic
153C22⋊C4×C17C22×C4112yes—
154C22⋊C4×C17C22×C416yes—
155C22⋊C4×C17C22×C4112yes—
156C22⋊C4×C17C22×C416yes—
157C22⋊C4×C17C22×C412yes—
158C42×C17C22×C413yes—
159C42×C17C22×C416yes—
160C42×C17C22×C416yes—
161C42×C17C22×C413yes—
162C42×C17C2412yes—
163C42×C17C2413yes—
164C42×C17C2413yes—
165#60218C1711yesmaximal, characteristic, direct product factor, Sylow
166C23×C17C23×C416yes—
167C23×C17C23×C411yescharacteristic
168Q8×C17—26no—
169Q8×C17—26no—
170Q8×C17#13114yescomplemented
171D4×C17—212no—
172D4×C17—26no—
173D4×C17—212no—
174D4×C17—46no—
175C2×C4×C17—26no—
176C2×C4×C17—212no—
177C2×C4×C17—26no—
178C2×C4×C17—26no—
179C2×C4×C17—46no—
180C2×C4×C17—43no—
181C2×C4×C17C23×C412yes—
182C2×C4×C17C23×C413yes—
183C2×C4×C17C23×C412yes—
184C2×C4×C17C23×C416yes—
185C2×C4×C17C23×C413yes—
186C2×C4×C17C23×C413yes—
187C2×C4×C17C23×C411yescharacteristic
188C2×C4×C17C23×C413yes—
189C2×C4×C17C2×#4112yes—
190C2×C4×C17C2×#4112yes—
191C2×C4×C17C2511yescharacteristic
192C8×C17—23no—
193C8×C17—23no—
194C8×C17—26no—
195C8×C17C2×#4112yes—
196C8×C17C2×#4114yes—
197C8×C17C2×#4112yes—
198#3480C2×C1711yescharacteristic
199#2971C2×C1712yescomplemented
200#2969C2×C1716yescomplemented
201#2966C2×C1716yescomplemented
202C8×#41C2×C1712yescomplemented
203Q8×M16C2×C1711yescharacteristic, complemented
204C2×C8×Q8C2×C1711yescharacteristic, complemented
205#2935C2×C1713yescomplemented
206#2931C2×C1713yescomplemented
207#2925C2×C1713yescomplemented
208C4×#131C2×C1713yescomplemented
209C22×C17—21no—
210C22×C17—21no—
211C22×C17—26no—
212C22×C17—26no—
213C22×C17—26no—
214C22×C17C4×#4112yes—
215C22×C17C24×C411yescharacteristic
216C4×C17—26no—
217C4×C17—22no—
218C4×C17—23no—
219C4×C17—22no—
220C4×C17—23no—
221C4×C17—23no—
222C4×C17C4×#4112yes—
223C4×C17C2×#13116yes—
224C4×C17C22×#4111yescharacteristic
225C4×C17C22×#4111yescharacteristic
226C2×#131C22×C1713yes—
227C2×#131C22×C1713yes—
228#559C4×C1713yes—
229#557C4×C1711yescharacteristic
230#556C4×C1713yes—
231#553C4×C1716yes—
232#550C4×C1711yescharacteristic
233#548C4×C1712yes—
234#532C22×C1713yes—
235#529C22×C1716yes—
236C4×#41C22×C1712yes—
237C4×#41C22×C1713yes—
238C2×C4×Q8C22×C1711yescharacteristic
239#446C22×C1716yes—
240C8×Q8C22×C1711yescharacteristic
241C8×Q8C22×C1713yes—
242C8×Q8C22×C1713yes—
243C8×Q8C22×C1711yescharacteristic
244C8×Q8C22×C1712yes—
245#436C22×C1716yes—
246#436C22×C1716yes—
247#436C22×C1716yes—
248#435C22×C17112yes—
249C8×D4C22×C1716yes—
250C8×D4C22×C1716yes—
251C8×D4C22×C1716yes—
252#433C22×C17112yes—
253#432C22×C1716yes—
254#431C22×C1716yes—
255#423C22×C1713yes—
256C2×C4⋊C8C22×C1713yes—
257#408C22×C1716yes—
258#405C22×C1711yescharacteristic
259#405C22×C1713yes—
260#405C22×C1716yes—
261#405C22×C1716yes—
262C4×M16C22×C1713yes—
263C4×M16C22×C1716yes—
264C2×C4×C8C22×C1713yes—
265C2×C4×C8C22×C1716yes—
266C2×C17—22no—
267C2×C17—46no—
268C2×C17C2×C4×#4111yescharacteristic
269C2×C17C22×#13111yescharacteristic
270C2×C17#357311yescharacteristic
271C2×#41C2×C4×C1712yes—
272C2×#41C23×C1713yes—
273C22×Q8C2×C4×C1711yescharacteristic
274#131—212no—
275#131—212no—
276C2×M16C23×C1713yes—
277C2×M16C23×C1716yes—
278C2×M16C23×C1716yes—
279C2×M16C23×C1711yescharacteristic
280C22×C8C23×C1713yes—
281C22×C8C23×C1716yes—
282C22×C8C23×C1716yes—
283C22×C8C23×C1711yescharacteristic
284C4⋊Q8C2×C4×C1713yes—
285#127C2×C4×C1713yes—
286#126C2×C4×C17112yes—
287#125C2×C4×C1716yes—
288#124C2×C4×C1716yes—
289#124C2×C4×C1716yes—
290#123C2×C4×C17112yes—
291C22⋊Q8C2×C4×C1716yes—
292#121C2×C4×C1716yes—
293#121C2×C4×C1716yes—
294#121C2×C4×C1716yes—
295C4×Q8C2×C4×C1711yescharacteristic
296C4×Q8C2×C4×C1713yes—
297C4×Q8C2×C4×C1712yes—
298C4×Q8C2×C4×C1713yes—
299C4×Q8C2×C4×C1713yes—
300C4×Q8C23×C1711yescharacteristic
301C4×Q8C23×C1713yes—
302C4×D4C2×C4×C1716yes—
303C4×D4C2×C4×C1713yes—
304C4×D4C2×C4×C1716yes—
305C4×D4C2×C4×C1716yes—
306C4×D4C2×C4×C1713yes—
307C4×D4C23×C1716yes—
308C4×D4C23×C1716yes—
309#117C2×C4×C1716yes—
310#117C23×C1711yescharacteristic
311#117C23×C1716yes—
312C2×C4⋊C4C2×C4×C1713yes—
313C2×C42C23×C1713yes—
314C2×C42C23×C1716yes—
315C4⋊C8C23×C1713yes—
316C4⋊C8C23×C1713yes—
317C4⋊C8C23×C1716yes—
318C4⋊C8C23×C1716yes—
319C4⋊C8C23×C1716yes—
320C22⋊C8C23×C17112yes—
321C22⋊C8C23×C17112yes—
322#97C23×C1712yes—
323#97C23×C1716yes—
324#97C23×C1716yes—
325C4×C8C23×C1712yes—
326C4×C8C23×C1713yes—
327C4×C8C23×C1716yes—
328C4×C8C23×C1713yes—
329C4×C8C23×C1716yes—
330C4×C8C23×C1713yes—
331C4×C8C23×C1713yes—
332C17#6021811yescharacteristic, direct product factor, Sylow
333#41—28no—
334#41—26no—
335#41—26no—
336C2×Q8—24no—
337C2×Q8C22×C4×C1713yes—
338C2×Q8C22×C4×C1713yes—
339C2×Q8C22×C4×C1711yescharacteristic
340C2×D4C22×C4×C1716yes—
341C2×D4C22×C4×C1713yes—
342C2×D4C22×C4×C1716yes—
343C2×D4C22×C4×C1716yes—
344C22×C4C22×C4×C1713yes—
345C22×C4C22×C4×C1716yes—
346C22×C4C22×C4×C1713yes—
347C22×C4C22×C4×C1716yes—
348C22×C4C24×C1716yes—
349C22×C4C24×C1711yescharacteristic
350M16—26no—
351M16—212no—
352M16—212no—
353M16#41×C1714yescomplemented
354C2×C8—26no—
355C2×C8—212no—
356C2×C8—212no—
357C2×C8#41×C1714yescomplemented
358C2×C8C24×C1713yes—
359C2×C8C24×C1716yes—
360C2×C8C24×C1713yes—
361C2×C8C24×C1711yescharacteristic
362C2×C8C24×C1712yes—
363C2×C8C24×C1711yescharacteristic
364C4⋊C4C22×C4×C1713yes—
365C4⋊C4C22×C4×C1713yes—
366C4⋊C4C22×C4×C1716yes—
367C4⋊C4C22×C4×C1716yes—
368C4⋊C4C22×C4×C1711yescharacteristic
369C4⋊C4C22×C4×C1711yescharacteristic
370C4⋊C4C22×C4×C1716yes—
371C4⋊C4C22×C4×C1716yes—
372C4⋊C4C22×C4×C1716yes—
373C22⋊C4C22×C4×C17112yes—
374C22⋊C4C22×C4×C1712yes—
375C22⋊C4C22×C4×C1716yes—
376C22⋊C4C22×C4×C1716yes—
377C22⋊C4C22×C4×C17112yes—
378C42C22×C4×C1716yes—
379C42C22×C4×C1716yes—
380C42C22×C4×C1713yes—
381C42C22×C4×C1713yes—
382C42C24×C1712yes—
383C42C24×C1713yes—
384C42C24×C1713yes—
385C23C23×C4×C1716yes—
386C23C23×C4×C1711yescharacteristic
387Q8—26no—
388Q8—26no—
389Q8C17×#13114yescomplemented
390D4—212no—
391D4—26no—
392D4—212no—
393D4—46no—
394C2×C4—26no—
395C2×C4—212no—
396C2×C4—26no—
397C2×C4—26no—
398C2×C4—46no—
399C2×C4—43no—
400C2×C4C23×C4×C1712yes—
401C2×C4C23×C4×C1713yes—
402C2×C4C23×C4×C1712yes—
403C2×C4C23×C4×C1716yes—
404C2×C4C23×C4×C1713yes—
405C2×C4C23×C4×C1713yes—
406C2×C4C23×C4×C1711yescharacteristic
407C2×C4C23×C4×C1713yes—
408C2×C4C2×#41×C1712yes—
409C2×C4C2×#41×C1712yes—
410C2×C4C25×C1711yescharacteristic
411C8—23no—
412C8—23no—
413C8—26no—
414C8C2×#41×C1712yes—
415C8C2×#41×C1714yes—
416C8C2×#41×C1712yes—
417C22—21no—
418C22—21no—
419C22—26no—
420C22—26no—
421C22—26no—
422C22C4×#41×C1712yes—
423C22C24×C4×C1711yescharacteristic
424C4—22no—
425C4—23no—
426C4—22no—
427C4—23no—
428C4—23no—
429C4—26no—
430C4C4×#41×C1712yes—
431C4C2×C17×#13116yes—
432C4C22×#41×C1711yescharacteristic
433C4C22×#41×C1711yescharacteristic
434C2—22no—
435C2—46no—
436C2C2×C4×#41×C1711yescharacteristic
437C2C22×C17×#13111yescharacteristic
438C2C17×#357311yescharacteristic
subgroupG/H
centerC2×C8×C17C24
commutatorC22C24×C4×C17
Frattini, cosocleC2×C4C25×C17
socleC22×C17C24×C4
prime radicalC17×#3480C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C8×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#2971C2semidirect
3. C17×#2969C2semidirect
4. C17×#2966C2semidirect
5. C8×#41×C17C2semidirect
6. Q8×M16×C17C2semidirect
7. C2×C8×Q8×C17C2semidirect
8. C17×#2935C2semidirect
9. C17×#2931C2semidirect
10. C17×#2925C2semidirect
11. C4×C17×#131C2semidirect
133. M16×C17#41semidirect
137. C2×C8×C17#41semidirect
165. #60218C17direct (N × H)
170. Q8×C17#131semidirect
199. #2971C2×C17semidirect
200. #2969C2×C17semidirect
201. #2966C2×C17semidirect
202. C8×#41C2×C17semidirect
203. Q8×M16C2×C17semidirect
204. C2×C8×Q8C2×C17semidirect
205. #2935C2×C17semidirect
206. #2931C2×C17semidirect
207. #2925C2×C17semidirect
208. C4×#131C2×C17semidirect
332. C17#60218direct (N × H)
353. M16#41×C17semidirect
357. C2×C8#41×C17semidirect
389. Q8C17×#131semidirect

Maximal subgroups

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

subgroupindex
C17×#34802
C17×#29712
C17×#29692
C17×#29662
C8×#41×C172
Q8×M16×C172
C2×C8×Q8×C172
C17×#29352
C17×#29312
C17×#29252
C4×C17×#1312
#6021817