Finite Group Databasebeta

← C17×#19411 #16877155

Subgroups — C17×#19411 #16877155

Order 4352.

620 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3209C211yesmaximal, characteristic, complemented
2C17×#3079C211yesmaximal, characteristic
3C17×#3076C211yesmaximal, characteristic
4C17×#2988C211yesmaximal, characteristic
5C17×#1684C212yesmaximal, complemented
6C17×#1683C212yesmaximal, complemented
7C17×#1670C212yesmaximal, complemented
8C17×#1669C212yesmaximal, complemented
9C17×#1571C211yesmaximal, characteristic, complemented
10C17×#1550C211yesmaximal, characteristic, complemented
11C2×C17×#332C211yesmaximal, characteristic, complemented
12C17×#533C2211yescharacteristic
13C2×C17×C4⋊Q8C2211yescharacteristic
14C4×#41×C17C2211yescharacteristic
15C17×#494C2212yes—
16C17×#487C2212yes—
17C17×#479—21no—
18C17×#478—21no—
19C17×#477—21no—
20C17×#477C2211yescharacteristic
21C17×#476—21no—
22C17×#476C2211yescharacteristic
23C17×#475C2211yescharacteristic
24C17×#475C2212yes—
25C17×#474C2211yescharacteristic
26C17×#474C2212yes—
27C17×#462—21no—
28C17×#462—21no—
29C17×#451—22no—
30C8×Q8×C17C2212yes—
31C8×D4×C17—22no—
32C8×D4×C17C2212yes—
33C17×#431—21no—
34C17×#431C2211yescharacteristic
35C17×#428—21no—
36C17×#427—21no—
37C17×#423C2211yescharacteristic
38C2×C17×C4⋊C8—21no—
39C2×C17×C4⋊C8C2211yescharacteristic
40C2×C17×C4⋊C8C2211yescharacteristic
41C17×#417—21no—
42C17×#416—21no—
43C17×#335C2212yes—
44C17×#335C2212yes—
45C17×#333C2212yes—
46C17×#332C2212yes—
47C17×#332C2212yes—
48C17×#332C2212yes—
49C2×#41×C17D411yescharacteristic
50C22×Q8×C17—21no—
51C2×Q16×C17—22no—
52C2×Q16×C17—22no—
53C2×M16×C17—21no—
54C22×C8×C17—21no—
55C22×C8×C17—21no—
56C22×C8×C17—22no—
57C17×C4⋊Q8—21no—
58C17×C4⋊Q8—21no—
59C17×C4⋊Q8—21no—
60C17×C4⋊Q8C2311yescharacteristic
61C17×C4⋊Q8C2312yes—
62C17×C4⋊Q8C2311yescharacteristic
63C17×#125—21no—
64C17×C22⋊Q8—21no—
65C17×C22⋊Q8—21no—
66C4×Q8×C17—21no—
67C4×Q8×C17—21no—
68C4×Q8×C17D411yescharacteristic
69C4×Q8×C17C2311yescharacteristic
70C4×D4×C17—21no—
71C4×D4×C17—21no—
72C4×D4×C17D411yescharacteristic
73C4×D4×C17C2311yescharacteristic
74C17×#117—21no—
75C17×#117—21no—
76C17×#117D411yescharacteristic
77C2×C4⋊C4×C17—21no—
78C2×C4⋊C4×C17—21no—
79C2×C42×C17—21no—
80C2×C42×C17C2311yescharacteristic
81C17×#107—21no—
82C17×#107—21no—
83C17×#107—22no—
84C17×#106—21no—
85C17×#106—21no—
86C17×#106—22no—
87C17×C4⋊C8—22no—
88C17×C4⋊C8—21no—
89C17×C4⋊C8—21no—
90C17×C4⋊C8—21no—
91C17×C4⋊C8D411yescharacteristic
92C17×C4⋊C8D411yescharacteristic
93C17×C4⋊C8C2312yes—
94C17×C4⋊C8C2311yescharacteristic
95C17×C4⋊C8C2311yescharacteristic
96C17×C4⋊C8C2312yes—
97C17×#103—21no—
98C17×#103—21no—
99C17×#103—22no—
100C17×#103—22no—
101C17×#103—22no—
102C17×#102—21no—
103C17×#102—21no—
104C17×#102—22no—
105C17×C22⋊C8—22no—
106C17×C22⋊C8D412yes—
107C4×C8×C17—22no—
108C4×C8×C17C2312yes—
109#41×C17—22no—
110#41×C17Q1614yescomplemented
111C2×Q8×C17—21no—
112C2×Q8×C17—22no—
113C2×Q8×C17—21no—
114C2×Q8×C17—41no—
115C2×Q8×C17—81no—
116C2×Q8×C17—81no—
117C2×Q8×C17C2×D411yescharacteristic
118C2×D4×C17—21no—
119C2×D4×C17C2×D411yescharacteristic
120C22×C4×C17—21no—
121C22×C4×C17—21no—
122C22×C4×C17—21no—
123C22×C4×C17—41no—
124C22×C4×C17C2×D411yescharacteristic
125C22×C4×C17C2×D411yescharacteristic
126C22×C4×C17#4111yescharacteristic
127Q16×C17—82no—
128Q16×C17—82no—
129M16×C17—42no—
130C2×C8×C17—22no—
131C2×C8×C17—21no—
132C2×C8×C17—21no—
133C2×C8×C17—22no—
134C2×C8×C17—42no—
135C2×C8×C17—82no—
136C2×C8×C17—81no—
137C2×C8×C17C2×D412yes—
138C2×C8×C17C2×D412yes—
139C4⋊C4×C17—21no—
140C4⋊C4×C17—21no—
141C4⋊C4×C17—21no—
142C4⋊C4×C17—21no—
143C4⋊C4×C17—21no—
144C4⋊C4×C17—22no—
145C4⋊C4×C17—21no—
146C4⋊C4×C17—22no—
147C4⋊C4×C17—41no—
148C4⋊C4×C17—41no—
149C4⋊C4×C17—41no—
150C4⋊C4×C17—41no—
151C4⋊C4×C17C2×D411yescharacteristic
152C4⋊C4×C17C2×D411yescharacteristic
153C22⋊C4×C17—21no—
154C22⋊C4×C17—21no—
155C22⋊C4×C17—21no—
156C22⋊C4×C17—41no—
157C42×C17—21no—
158C42×C17—21no—
159C42×C17—21no—
160C42×C17—41no—
161C42×C17C2×D411yescharacteristic
162C42×C17C2×D411yescharacteristic
163C42×C17#4111yescharacteristic
164C42×C17C2411yescharacteristic
165#19411C1711yesmaximal, characteristic, direct product factor, Sylow
166C23×C17—21no—
167C23×C17#12111yescharacteristic
168Q8×C17—21no—
169Q8×C17—41no—
170Q8×C17—42no—
171Q8×C17—41no—
172Q8×C17—42no—
173Q8×C17—81no—
174Q8×C17—82no—
175Q8×C17C2×Q1612yes—
176D4×C17—24no—
177D4×C17—21no—
178D4×C17C2×Q1612yes—
179C2×C4×C17—21no—
180C2×C4×C17—21no—
181C2×C4×C17—21no—
182C2×C4×C17—24no—
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—42no—
191C2×C4×C17—81no—
192C2×C4×C17—82no—
193C2×C4×C17#12111yescharacteristic
194C2×C4×C17#12111yescharacteristic
195C2×C4×C17#12111yescharacteristic
196C2×C4×C17C2×Q1612yes—
197C2×C4×C17#13512yes—
198C2×C4×C17C22×D411yescharacteristic
199C2×C4×C17C22×D411yescharacteristic
200C2×C4×C17C2×#4111yescharacteristic
201C8×C17—22no—
202C8×C17—22no—
203C8×C17—41no—
204C8×C17—41no—
205C8×C17—42no—
206C8×C17—42no—
207#3209C2×C1711yescharacteristic, complemented
208#3079C2×C1711yescharacteristic
209#3076C2×C1711yescharacteristic
210#2988C2×C1711yescharacteristic
211#1684C2×C1712yescomplemented
212#1683C2×C1712yescomplemented
213#1670C2×C1712yescomplemented
214#1669C2×C1712yescomplemented
215#1571C2×C1711yescharacteristic, complemented
216#1550C2×C1711yescharacteristic, complemented
217C2×#332C2×C1711yescharacteristic, complemented
218C22×C17—21no—
219C22×C17—21no—
220C22×C17—22no—
221C22×C17—41no—
222C22×C17—41no—
223C22×C17#46712yes—
224C22×C17C2×#12111yescharacteristic
225C4×C17—21no—
226C4×C17—22no—
227C4×C17—21no—
228C4×C17—21no—
229C4×C17—41no—
230C4×C17—41no—
231C4×C17—82no—
232C4×C17—81no—
233C4×C17—81no—
234C4×C17#46712yes—
235C4×C17C22×Q1611yescharacteristic
236C4×C17C2×#13511yescharacteristic
237C4×C17#57611yescharacteristic
238C4×C17#57711yescharacteristic
239#533C22×C1711yescharacteristic
240C2×C4⋊Q8C22×C1711yescharacteristic
241C4×#41C22×C1711yescharacteristic
242#494C22×C1712yes—
243#487C22×C1712yes—
244#479—21no—
245#478—21no—
246#477—21no—
247#477C22×C1711yescharacteristic
248#476—21no—
249#476C22×C1711yescharacteristic
250#475C22×C1711yescharacteristic
251#475C22×C1712yes—
252#474C22×C1711yescharacteristic
253#474C22×C1712yes—
254#462—21no—
255#462—21no—
256#451—22no—
257C8×Q8C22×C1712yes—
258C8×D4—22no—
259C8×D4C22×C1712yes—
260#431—21no—
261#431C22×C1711yescharacteristic
262#428—21no—
263#427—21no—
264#423C22×C1711yescharacteristic
265C2×C4⋊C8—21no—
266C2×C4⋊C8C22×C1711yescharacteristic
267C2×C4⋊C8C22×C1711yescharacteristic
268#417—21no—
269#416—21no—
270#335C22×C1712yes—
271#335C22×C1712yes—
272#333C22×C1712yes—
273#332C22×C1712yes—
274#332C22×C1712yes—
275#332C22×C1712yes—
276C2×C17—22no—
277C2×C17—42no—
278C2×C17#304511yescharacteristic
279C2×C17C2×#46711yescharacteristic
280C2×C17#306911yescharacteristic
281C2×#41D4×C1711yescharacteristic
282C22×Q8—21no—
283C2×Q16—22no—
284C2×Q16—22no—
285C2×M16—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—22no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8C23×C1712yes—
293C4⋊Q8C23×C1711yescharacteristic
294C4⋊Q8C23×C1711yescharacteristic
295#125—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×Q8D4×C1711yescharacteristic
301C4×Q8C23×C1711yescharacteristic
302C4×D4—21no—
303C4×D4—21no—
304C4×D4D4×C1711yescharacteristic
305C4×D4C23×C1711yescharacteristic
306#117—21no—
307#117—21no—
308#117D4×C1711yescharacteristic
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C42—21no—
312C2×C42C23×C1711yescharacteristic
313#107—21no—
314#107—21no—
315#107—22no—
316#106—21no—
317#106—21no—
318#106—22no—
319C4⋊C8—22no—
320C4⋊C8—21no—
321C4⋊C8—21no—
322C4⋊C8—21no—
323C4⋊C8D4×C1711yescharacteristic
324C4⋊C8D4×C1711yescharacteristic
325C4⋊C8C23×C1712yes—
326C4⋊C8C23×C1711yescharacteristic
327C4⋊C8C23×C1711yescharacteristic
328C4⋊C8C23×C1712yes—
329#103—21no—
330#103—21no—
331#103—22no—
332#103—22no—
333#103—22no—
334#102—21no—
335#102—21no—
336#102—22no—
337C22⋊C8—22no—
338C22⋊C8D4×C1712yes—
339C4×C8—22no—
340C4×C8C23×C1712yes—
341C17#1941111yescharacteristic, direct product factor, Sylow
342#41—22no—
343#41Q16×C1714yescomplemented
344C2×Q8—22no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—41no—
348C2×Q8—81no—
349C2×Q8—81no—
350C2×Q8C2×D4×C1711yescharacteristic
351C2×D4—21no—
352C2×D4C2×D4×C1711yescharacteristic
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—41no—
357C22×C4C2×D4×C1711yescharacteristic
358C22×C4C2×D4×C1711yescharacteristic
359C22×C4#41×C1711yescharacteristic
360Q16—82no—
361Q16—82no—
362M16—42no—
363C2×C8—22no—
364C2×C8—21no—
365C2×C8—22no—
366C2×C8—21no—
367C2×C8—42no—
368C2×C8—82no—
369C2×C8—81no—
370C2×C8C2×D4×C1712yes—
371C2×C8C2×D4×C1712yes—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4C2×D4×C1711yescharacteristic
385C4⋊C4C2×D4×C1711yescharacteristic
386C22⋊C4—21no—
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—41no—
390C42—21no—
391C42—21no—
392C42—21no—
393C42—41no—
394C42C2×D4×C1711yescharacteristic
395C42C2×D4×C1711yescharacteristic
396C42#41×C1711yescharacteristic
397C42C24×C1711yescharacteristic
398C23—21no—
399C23C17×#12111yescharacteristic
400Q8—21no—
401Q8—41no—
402Q8—42no—
403Q8—41no—
404Q8—42no—
405Q8—81no—
406Q8—82no—
407Q8C2×Q16×C1712yes—
408D4—24no—
409D4—21no—
410D4C2×Q16×C1712yes—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—24no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—81no—
424C2×C4—82no—
425C2×C4C17×#12111yescharacteristic
426C2×C4C17×#12111yescharacteristic
427C2×C4C17×#12111yescharacteristic
428C2×C4C2×Q16×C1712yes—
429C2×C4C17×#13512yes—
430C2×C4C22×D4×C1711yescharacteristic
431C2×C4C22×D4×C1711yescharacteristic
432C2×C4C2×#41×C1711yescharacteristic
433C8—22no—
434C8—22no—
435C8—41no—
436C8—41no—
437C8—42no—
438C8—42no—
439C22—21no—
440C22—21no—
441C22—22no—
442C22—41no—
443C22—41no—
444C22C17×#46712yes—
445C22C2×C17×#12111yescharacteristic
446C4—21no—
447C4—22no—
448C4—21no—
449C4—21no—
450C4—41no—
451C4—41no—
452C4—82no—
453C4—81no—
454C4—81no—
455C4C17×#46712yes—
456C4C22×Q16×C1711yescharacteristic
457C4C2×C17×#13511yescharacteristic
458C4C17×#57611yescharacteristic
459C4C17×#57711yescharacteristic
460C2—22no—
461C2—42no—
462C2C17×#304511yescharacteristic
463C2C2×C17×#46711yescharacteristic
464C2C17×#306911yescharacteristic
subgroupG/H
center, socleC22×C17C2×#121
commutator, Frattini, cosocleC42C24×C17
prime radicalC2×#41×C17D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#3209C2semidirect
5. C17×#1684C2semidirect
6. C17×#1683C2semidirect
7. C17×#1670C2semidirect
8. C17×#1669C2semidirect
9. C17×#1571C2semidirect
10. C17×#1550C2semidirect
11. C2×C17×#332C2semidirect
110. #41×C17Q16semidirect
165. #19411C17direct (N × H)
207. #3209C2×C17semidirect
211. #1684C2×C17semidirect
212. #1683C2×C17semidirect
213. #1670C2×C17semidirect
214. #1669C2×C17semidirect
215. #1571C2×C17semidirect
216. #1550C2×C17semidirect
217. C2×#332C2×C17semidirect
341. C17#19411direct (N × H)
343. #41Q16×C17semidirect

Maximal subgroups

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

subgroupindex
C17×#32092
C17×#30792
C17×#30762
C17×#29882
C17×#16842
C17×#16832
C17×#16702
C17×#16692
C17×#15712
C17×#15502
C2×C17×#3322
#1941117