Finite Group Databasebeta

← C17×#18204 #16875948

Subgroups — C17×#18204 #16875948

Order 4352.

1002 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3501C211yesmaximal, characteristic
2C2×C17×#483C212yesmaximal, complemented
3C17×#2486C211yesmaximal, characteristic
4C17×#1611C214yesmaximal, complemented
5C17×#1608C214yesmaximal, complemented
6C17×#1520C212yesmaximal, complemented
7C17×#1459C211yesmaximal, characteristic
8C17×#554—22no—
9C17×#554—24no—
10D4×Q8×C17—22no—
11C17×#544C2212yes—
12C17×#543—21no—
13C17×#543C2212yes—
14C17×#533—21no—
15C2×C17×#123—21no—
16C2×C17×C22⋊Q8—21no—
17C2×C17×C22⋊Q8C2212yes—
18C17×#518—21no—
19C2×C4×D4×C17C2211yescharacteristic
20C22×C4⋊C4×C17C2211yescharacteristic
21C17×#483—24no—
22C17×#483C2218yes—
23C2×C17×#106—22no—
24C2×C17×#103—22no—
25C2×C17×C22⋊C8C2212yes—
26C17×#398C2212yes—
27C17×#397C2212yes—
28C17×#389—21no—
29C17×#381—21no—
30C17×#380—21no—
31C17×#380C2211yescharacteristic
32C17×#328C2218yes—
33C17×#324C2212yes—
34C17×#323C2212yes—
35C22×Q8×C17—21no—
36C22×Q8×C17D412yes—
37C22×D4×C17D411yescharacteristic
38C23×C4×C17—21no—
39C23×C4×C17D411yescharacteristic
40C23×C4×C17C2311yescharacteristic
41C22×C8×C17—22no—
42C17×C4⋊Q8—21no—
43C17×C4⋊Q8—21no—
44C17×C4⋊Q8—24no—
45C17×#125—22no—
46C17×#125—24no—
47C17×#123—44no—
48C17×C22⋊Q8—22no—
49C17×C22⋊Q8—22no—
50C17×C22⋊Q8—24no—
51C17×C22⋊Q8—24no—
52C17×C22⋊Q8—24no—
53C17×C22⋊Q8—22no—
54C17×C22⋊Q8—22no—
55C17×C22⋊Q8—22no—
56C17×C22⋊Q8—22no—
57C17×C22⋊Q8—24no—
58C17×C22⋊Q8D414yes—
59C17×C22⋊Q8C2314yes—
60C4×Q8×C17—22no—
61C4×Q8×C17—22no—
62C4×D4×C17—24no—
63C4×D4×C17—24no—
64C4×D4×C17—22no—
65C4×D4×C17—22no—
66C17×#117—22no—
67C2×C4⋊C4×C17—21no—
68C2×C4⋊C4×C17—22no—
69C2×C4⋊C4×C17—22no—
70C2×C4⋊C4×C17—22no—
71C2×C4⋊C4×C17—22no—
72C2×C4⋊C4×C17—21no—
73C2×C4⋊C4×C17—22no—
74C2×C4⋊C4×C17—21no—
75C2×C4⋊C4×C17D412yes—
76C2×C4⋊C4×C17C2312yes—
77C2×C4⋊C4×C17C2311yescharacteristic
78C2×C22⋊C4×C17—22no—
79C2×C22⋊C4×C17—22no—
80C2×C22⋊C4×C17—22no—
81C2×C22⋊C4×C17—21no—
82C2×C22⋊C4×C17D411yescharacteristic
83C2×C22⋊C4×C17C2311yescharacteristic
84C2×C42×C17D411yescharacteristic
85C17×#106—28no—
86C17×#103—28no—
87C17×C22⋊C8—22no—
88C17×C22⋊C8C2314yes—
89C17×#95—22no—
90C17×#95—22no—
91C17×#95C2312yes—
92C24×C17C2×D411yescharacteristic
93C24×C17C2×D411yescharacteristic
94C2×Q8×C17—22no—
95C2×Q8×C17—22no—
96C2×Q8×C17—22no—
97C2×Q8×C17—44no—
98C2×Q8×C17—82no—
99C2×Q8×C17C2×D414yes—
100C2×D4×C17—22no—
101C2×D4×C17—22no—
102C2×D4×C17SD1614yes—
103C22×C4×C17—22no—
104C22×C4×C17—22no—
105C22×C4×C17—22no—
106C22×C4×C17—22no—
107C22×C4×C17—21no—
108C22×C4×C17—21no—
109C22×C4×C17—22no—
110C22×C4×C17—22no—
111C22×C4×C17—42no—
112C22×C4×C17—42no—
113C22×C4×C17—42no—
114C22×C4×C17—42no—
115C22×C4×C17—42no—
116C22×C4×C17C2×D411yescharacteristic
117C22×C4×C17C2×D412yes—
118C22×C4×C17C2×D411yescharacteristic
119C22×C4×C17C2×D411yescharacteristic
120C22×C4×C17C2×D411yescharacteristic
121C22×C4×C17C2×D412yes—
122C22×C4×C17C2411yescharacteristic
123C2×C8×C17—24no—
124C2×C8×C17—44no—
125C4⋊C4×C17—24no—
126C4⋊C4×C17—22no—
127C4⋊C4×C17—22no—
128C4⋊C4×C17—24no—
129C4⋊C4×C17—22no—
130C4⋊C4×C17—22no—
131C4⋊C4×C17—22no—
132C4⋊C4×C17—24no—
133C4⋊C4×C17—24no—
134C4⋊C4×C17—22no—
135C4⋊C4×C17—24no—
136C4⋊C4×C17—42no—
137C4⋊C4×C17—41no—
138C4⋊C4×C17—41no—
139C4⋊C4×C17—44no—
140C4⋊C4×C17C2×D414yes—
141C22⋊C4×C17—24no—
142C22⋊C4×C17—22no—
143C22⋊C4×C17—24no—
144C22⋊C4×C17—24no—
145C22⋊C4×C17—22no—
146C22⋊C4×C17—42no—
147C22⋊C4×C17—44no—
148C42×C17—24no—
149C42×C17—21no—
150C42×C17—21no—
151#18204C1711yesmaximal, characteristic, direct product factor, Sylow
152C23×C17—21no—
153C23×C17—21no—
154C23×C17—41no—
155C23×C17—41no—
156C23×C17—41no—
157C23×C17—41no—
158C23×C17#12012yes—
159C23×C17C2×SD1612yes—
160C23×C17C2×SD1612yes—
161C23×C17#13712yes—
162C23×C17C22×D411yescharacteristic
163Q8×C17—44no—
164Q8×C17—44no—
165Q8×C17—82no—
166Q8×C17—82no—
167D4×C17—28no—
168C2×C4×C17—21no—
169C2×C4×C17—21no—
170C2×C4×C17—22no—
171C2×C4×C17—24no—
172C2×C4×C17—21no—
173C2×C4×C17—24no—
174C2×C4×C17—24no—
175C2×C4×C17—21no—
176C2×C4×C17—42no—
177C2×C4×C17—41no—
178C2×C4×C17—42no—
179C2×C4×C17—41no—
180C2×C4×C17—41no—
181C2×C4×C17—42no—
182C2×C4×C17—42no—
183C2×C4×C17—42no—
184C2×C4×C17—42no—
185C2×C4×C17—42no—
186C2×C4×C17—42no—
187C2×C4×C17—81no—
188C2×C4×C17—82no—
189C2×C4×C17—82no—
190C2×C4×C17—82no—
191C2×C4×C17—82no—
192C2×C4×C17—84no—
193C2×C4×C17#12011yescharacteristic
194C2×C4×C17#12011yescharacteristic
195C2×C4×C17C2×SD1612yes—
196C2×C4×C17C22×D412yes—
197C8×C17—44no—
198#3501C2×C1711yescharacteristic
199C2×#483C2×C1712yescomplemented
200#2486C2×C1711yescharacteristic
201#1611C2×C1714yescomplemented
202#1608C2×C1714yescomplemented
203#1520C2×C1712yescomplemented
204#1459C2×C1711yescharacteristic
205C22×C17—21no—
206C22×C17—22no—
207C22×C17—21no—
208C22×C17—22no—
209C22×C17—22no—
210C22×C17—42no—
211C22×C17—42no—
212C22×C17—42no—
213C22×C17—41no—
214C22×C17—41no—
215C22×C17—81no—
216C22×C17#44814yes—
217C22×C17C2×#12011yescharacteristic
218C22×C17C22×SD1611yescharacteristic
219C22×C17C2×#13711yescharacteristic
220C4×C17—22no—
221C4×C17—22no—
222C4×C17—21no—
223C4×C17—41no—
224C4×C17—44no—
225C4×C17—41no—
226C4×C17—44no—
227C4×C17—82no—
228C4×C17—82no—
229C4×C17#45812yes—
230#554—24no—
231#554—22no—
232D4×Q8—22no—
233#544C22×C1712yes—
234#543—21no—
235#543C22×C1712yes—
236#533—21no—
237C2×#123—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8C22×C1712yes—
240#518—21no—
241C2×C4×D4C22×C1711yescharacteristic
242C22×C4⋊C4C22×C1711yescharacteristic
243#483—24no—
244#483C22×C1718yes—
245C2×#106—22no—
246C2×#103—22no—
247C2×C22⋊C8C22×C1712yes—
248#398C22×C1712yes—
249#397C22×C1712yes—
250#389—21no—
251#381—21no—
252#380—21no—
253#380C22×C1711yescharacteristic
254#328C22×C1718yes—
255#324C22×C1712yes—
256#323C22×C1712yes—
257C2×C17—21no—
258C2×C17—21no—
259C2×C17—24no—
260C2×C17—42no—
261C2×C17C2×#44811yescharacteristic
262C2×C17#302211yescharacteristic
263C2×C17C2×#45811yescharacteristic
264C22×Q8—21no—
265C22×Q8D4×C1712yes—
266C22×D4D4×C1711yescharacteristic
267C23×C4—21no—
268C23×C4D4×C1711yescharacteristic
269C23×C4C23×C1711yescharacteristic
270C22×C8—22no—
271C4⋊Q8—21no—
272C4⋊Q8—21no—
273C4⋊Q8—24no—
274#125—22no—
275#125—24no—
276#123—44no—
277C22⋊Q8—22no—
278C22⋊Q8—22no—
279C22⋊Q8—24no—
280C22⋊Q8—24no—
281C22⋊Q8—24no—
282C22⋊Q8—22no—
283C22⋊Q8—22no—
284C22⋊Q8—22no—
285C22⋊Q8—22no—
286C22⋊Q8—24no—
287C22⋊Q8D4×C1714yes—
288C22⋊Q8C23×C1714yes—
289C4×Q8—22no—
290C4×Q8—22no—
291C4×D4—24no—
292C4×D4—24no—
293C4×D4—22no—
294C4×D4—22no—
295#117—22no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4D4×C1712yes—
305C2×C4⋊C4C23×C1712yes—
306C2×C4⋊C4C23×C1711yescharacteristic
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4D4×C1711yescharacteristic
312C2×C22⋊C4C23×C1711yescharacteristic
313C2×C42D4×C1711yescharacteristic
314#106—28no—
315#103—28no—
316C22⋊C8—22no—
317C22⋊C8C23×C1714yes—
318#95—22no—
319#95—22no—
320#95C23×C1712yes—
321C17#1820411yescharacteristic, direct product factor, Sylow
322C24C2×D4×C1711yescharacteristic
323C24C2×D4×C1711yescharacteristic
324C2×Q8—22no—
325C2×Q8—22no—
326C2×Q8—22no—
327C2×Q8—44no—
328C2×Q8—82no—
329C2×Q8C2×D4×C1714yes—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4SD16×C1714yes—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4C2×D4×C1711yescharacteristic
347C22×C4C2×D4×C1712yes—
348C22×C4C2×D4×C1711yescharacteristic
349C22×C4C2×D4×C1711yescharacteristic
350C22×C4C2×D4×C1711yescharacteristic
351C22×C4C2×D4×C1712yes—
352C22×C4C24×C1711yescharacteristic
353C2×C8—24no—
354C2×C8—44no—
355C4⋊C4—22no—
356C4⋊C4—24no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—24no—
360C4⋊C4—22no—
361C4⋊C4—24no—
362C4⋊C4—22no—
363C4⋊C4—24no—
364C4⋊C4—22no—
365C4⋊C4—24no—
366C4⋊C4—42no—
367C4⋊C4—44no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4C2×D4×C1714yes—
371C22⋊C4—24no—
372C22⋊C4—24no—
373C22⋊C4—24no—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—42no—
377C22⋊C4—44no—
378C42—24no—
379C42—21no—
380C42—21no—
381C23—21no—
382C23—21no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23C17×#12012yes—
388C23C2×SD16×C1712yes—
389C23C2×SD16×C1712yes—
390C23C17×#13712yes—
391C23C22×D4×C1711yescharacteristic
392Q8—44no—
393Q8—44no—
394Q8—82no—
395Q8—82no—
396D4—28no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—21no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—21no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—81no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—84no—
422C2×C4C17×#12011yescharacteristic
423C2×C4C17×#12011yescharacteristic
424C2×C4C2×SD16×C1712yes—
425C2×C4C22×D4×C1712yes—
426C8—44no—
427C22—21no—
428C22—22no—
429C22—21no—
430C22—22no—
431C22—22no—
432C22—42no—
433C22—42no—
434C22—42no—
435C22—41no—
436C22—41no—
437C22—81no—
438C22C17×#44814yes—
439C22C2×C17×#12011yescharacteristic
440C22C22×SD16×C1711yescharacteristic
441C22C2×C17×#13711yescharacteristic
442C4—22no—
443C4—22no—
444C4—21no—
445C4—41no—
446C4—44no—
447C4—41no—
448C4—44no—
449C4—82no—
450C4—82no—
451C4C17×#45812yes—
452C2—21no—
453C2—21no—
454C2—24no—
455C2—42no—
456C2C2×C17×#44811yescharacteristic
457C2C17×#302211yescharacteristic
458C2C2×C17×#45811yescharacteristic
subgroupG/H
center, socleC22×C17C2×#120
commutator, Frattini, cosocleC22×C4C24×C17
prime radicalC22×D4×C17D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C17×#483C2semidirect
4. C17×#1611C2semidirect
5. C17×#1608C2semidirect
6. C17×#1520C2semidirect
151. #18204C17direct (N × H)
199. C2×#483C2×C17semidirect
201. #1611C2×C17semidirect
202. #1608C2×C17semidirect
203. #1520C2×C17semidirect
321. C17#18204direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#35012
C2×C17×#4832
C17×#24862
C17×#16112
C17×#16082
C17×#15202
C17×#14592
#1820417