Finite Group Databasebeta

← C17×#19417 #16877161

Subgroups — C17×#19417 #16877161

Order 4352.

608 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3230C211yesmaximal, characteristic, complemented
2C17×#3079C211yesmaximal, characteristic
3C17×#3076C211yesmaximal, characteristic
4C17×#2988C211yesmaximal, characteristic
5C17×#1684C212yesmaximal, complemented
6C17×#1683C212yesmaximal, complemented
7C17×#1676C212yesmaximal, complemented
8C17×#1675C212yesmaximal, complemented
9C17×#1571C211yesmaximal, characteristic, complemented
10C17×#1550C211yesmaximal, characteristic, complemented
11C2×C17×#333C211yesmaximal, characteristic, complemented
12C17×#533C2211yescharacteristic
13C2×C17×C4⋊Q8C2211yescharacteristic
14C4×#41×C17C2211yescharacteristic
15C17×#500C2212yes—
16C17×#487C2212yes—
17C17×#484—22no—
18C17×#479—21no—
19C17×#478—21no—
20C17×#477—21no—
21C17×#477—21no—
22C17×#477C2211yescharacteristic
23C17×#477C2212yes—
24C17×#476C2211yescharacteristic
25C17×#476C2212yes—
26C17×#475—21no—
27C17×#475C2211yescharacteristic
28C17×#474—21no—
29C17×#474C2211yescharacteristic
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×#333C2212yes—
47C17×#333C2212yes—
48C17×#332C2212yes—
49C2×#41×C17D411yescharacteristic
50C22×Q8×C17—21no—
51C2×M16×C17—21no—
52C22×C8×C17—21no—
53C22×C8×C17—21no—
54C22×C8×C17—22no—
55C17×C4⋊Q8—21no—
56C17×C4⋊Q8—21no—
57C17×C4⋊Q8—21no—
58C17×C4⋊Q8C2311yescharacteristic
59C17×C4⋊Q8C2312yes—
60C17×C4⋊Q8C2311yescharacteristic
61C17×#125—21no—
62C17×C22⋊Q8—21no—
63C17×C22⋊Q8—21no—
64C4×Q8×C17—21no—
65C4×Q8×C17—21no—
66C4×Q8×C17D411yescharacteristic
67C4×Q8×C17C2311yescharacteristic
68C4×D4×C17—21no—
69C4×D4×C17—21no—
70C4×D4×C17D411yescharacteristic
71C4×D4×C17C2311yescharacteristic
72C17×#117—21no—
73C17×#117—21no—
74C17×#117D411yescharacteristic
75C2×C4⋊C4×C17—21no—
76C2×C4⋊C4×C17—21no—
77C2×C42×C17—21no—
78C2×C42×C17C2311yescharacteristic
79C17×#107—22no—
80C17×#107—22no—
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⋊C8C2312yes—
95C17×C4⋊C8C2311yescharacteristic
96C17×C4⋊C8C2311yescharacteristic
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×C17Q1614yes—
111C2×Q8×C17—21no—
112C2×Q8×C17—21no—
113C2×Q8×C17—22no—
114C2×Q8×C17—41no—
115C2×Q8×C17—82no—
116C2×Q8×C17C2×D411yescharacteristic
117C2×D4×C17—21no—
118C2×D4×C17C2×D411yescharacteristic
119C22×C4×C17—21no—
120C22×C4×C17—21no—
121C22×C4×C17—21no—
122C22×C4×C17—41no—
123C22×C4×C17C2×D411yescharacteristic
124C22×C4×C17C2×D411yescharacteristic
125C22×C4×C17#4111yescharacteristic
126M16×C17—42no—
127C2×C8×C17—22no—
128C2×C8×C17—21no—
129C2×C8×C17—21no—
130C2×C8×C17—22no—
131C2×C8×C17—42no—
132C2×C8×C17—82no—
133C2×C8×C17—81no—
134C2×C8×C17C2×D412yes—
135C2×C8×C17C2×D412yes—
136C4⋊C4×C17—21no—
137C4⋊C4×C17—21no—
138C4⋊C4×C17—21no—
139C4⋊C4×C17—21no—
140C4⋊C4×C17—21no—
141C4⋊C4×C17—22no—
142C4⋊C4×C17—22no—
143C4⋊C4×C17—21no—
144C4⋊C4×C17—41no—
145C4⋊C4×C17—41no—
146C4⋊C4×C17—41no—
147C4⋊C4×C17—41no—
148C4⋊C4×C17C2×D411yescharacteristic
149C4⋊C4×C17C2×D411yescharacteristic
150C22⋊C4×C17—21no—
151C22⋊C4×C17—21no—
152C22⋊C4×C17—21no—
153C22⋊C4×C17—41no—
154C42×C17—21no—
155C42×C17—21no—
156C42×C17—21no—
157C42×C17—41no—
158C42×C17C2×D411yescharacteristic
159C42×C17C2×D411yescharacteristic
160C42×C17#4111yescharacteristic
161C42×C17C2411yescharacteristic
162#19417C1711yesmaximal, characteristic, direct product factor, Sylow
163C23×C17—21no—
164C23×C17#12111yescharacteristic
165Q8×C17—21no—
166Q8×C17—41no—
167Q8×C17—41no—
168Q8×C17—81no—
169Q8×C17—82no—
170Q8×C17—82no—
171Q8×C17C2×Q1612yes—
172D4×C17—24no—
173D4×C17—21no—
174D4×C17C2×Q1612yes—
175C2×C4×C17—21no—
176C2×C4×C17—21no—
177C2×C4×C17—21no—
178C2×C4×C17—24no—
179C2×C4×C17—21no—
180C2×C4×C17—21no—
181C2×C4×C17—41no—
182C2×C4×C17—41no—
183C2×C4×C17—41no—
184C2×C4×C17—41no—
185C2×C4×C17—41no—
186C2×C4×C17—42no—
187C2×C4×C17—81no—
188C2×C4×C17—82no—
189C2×C4×C17#12111yescharacteristic
190C2×C4×C17#12111yescharacteristic
191C2×C4×C17#12111yescharacteristic
192C2×C4×C17C2×Q1612yes—
193C2×C4×C17#13512yes—
194C2×C4×C17C22×D411yescharacteristic
195C2×C4×C17C22×D411yescharacteristic
196C2×C4×C17C2×#4111yescharacteristic
197C8×C17—22no—
198C8×C17—22no—
199C8×C17—41no—
200C8×C17—41no—
201C8×C17—42no—
202C8×C17—42no—
203#3230C2×C1711yescharacteristic, complemented
204#3079C2×C1711yescharacteristic
205#3076C2×C1711yescharacteristic
206#2988C2×C1711yescharacteristic
207#1684C2×C1712yescomplemented
208#1683C2×C1712yescomplemented
209#1676C2×C1712yescomplemented
210#1675C2×C1712yescomplemented
211#1571C2×C1711yescharacteristic, complemented
212#1550C2×C1711yescharacteristic, complemented
213C2×#333C2×C1711yescharacteristic, complemented
214C22×C17—21no—
215C22×C17—21no—
216C22×C17—22no—
217C22×C17—41no—
218C22×C17—41no—
219C22×C17#46712yes—
220C22×C17C2×#12111yescharacteristic
221C4×C17—21no—
222C4×C17—22no—
223C4×C17—21no—
224C4×C17—21no—
225C4×C17—41no—
226C4×C17—41no—
227C4×C17—81no—
228C4×C17—82no—
229C4×C17—81no—
230C4×C17#46712yes—
231C4×C17C22×Q1611yescharacteristic
232C4×C17C2×#13511yescharacteristic
233C4×C17#57711yescharacteristic
234C4×C17#57811yescharacteristic
235#533C22×C1711yescharacteristic
236C2×C4⋊Q8C22×C1711yescharacteristic
237C4×#41C22×C1711yescharacteristic
238#500C22×C1712yes—
239#487C22×C1712yes—
240#484—22no—
241#479—21no—
242#478—21no—
243#477—21no—
244#477—21no—
245#477C22×C1711yescharacteristic
246#477C22×C1712yes—
247#476C22×C1711yescharacteristic
248#476C22×C1712yes—
249#475—21no—
250#475C22×C1711yescharacteristic
251#474—21no—
252#474C22×C1711yescharacteristic
253C8×Q8C22×C1712yes—
254C8×D4—22no—
255C8×D4C22×C1712yes—
256#431—21no—
257#431C22×C1711yescharacteristic
258#428—21no—
259#427—21no—
260#423C22×C1711yescharacteristic
261C2×C4⋊C8—21no—
262C2×C4⋊C8C22×C1711yescharacteristic
263C2×C4⋊C8C22×C1711yescharacteristic
264#417—21no—
265#416—21no—
266#335C22×C1712yes—
267#335C22×C1712yes—
268#333C22×C1712yes—
269#333C22×C1712yes—
270#333C22×C1712yes—
271#332C22×C1712yes—
272C2×C17—22no—
273C2×C17—42no—
274C2×C17#304611yescharacteristic
275C2×C17C2×#46711yescharacteristic
276C2×C17#306811yescharacteristic
277C2×#41D4×C1711yescharacteristic
278C22×Q8—21no—
279C2×M16—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—22no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8C23×C1712yes—
287C4⋊Q8C23×C1711yescharacteristic
288C4⋊Q8C23×C1711yescharacteristic
289#125—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×Q8D4×C1711yescharacteristic
295C4×Q8C23×C1711yescharacteristic
296C4×D4—21no—
297C4×D4—21no—
298C4×D4D4×C1711yescharacteristic
299C4×D4C23×C1711yescharacteristic
300#117—21no—
301#117—21no—
302#117D4×C1711yescharacteristic
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C42—21no—
306C2×C42C23×C1711yescharacteristic
307#107—22no—
308#107—22no—
309#107—21no—
310#107—21no—
311#107—22no—
312#106—21no—
313#106—21no—
314#106—22no—
315C4⋊C8—22no—
316C4⋊C8—21no—
317C4⋊C8—21no—
318C4⋊C8—21no—
319C4⋊C8D4×C1711yescharacteristic
320C4⋊C8D4×C1711yescharacteristic
321C4⋊C8C23×C1712yes—
322C4⋊C8C23×C1712yes—
323C4⋊C8C23×C1711yescharacteristic
324C4⋊C8C23×C1711yescharacteristic
325#103—21no—
326#103—21no—
327#103—22no—
328#103—22no—
329#103—22no—
330#102—21no—
331#102—21no—
332#102—22no—
333C22⋊C8—22no—
334C22⋊C8D4×C1712yes—
335C4×C8—22no—
336C4×C8C23×C1712yes—
337C17#1941711yescharacteristic, direct product factor, Sylow
338#41—22no—
339#41Q16×C1714yes—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—22no—
343C2×Q8—41no—
344C2×Q8—82no—
345C2×Q8C2×D4×C1711yescharacteristic
346C2×D4—21no—
347C2×D4C2×D4×C1711yescharacteristic
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—41no—
352C22×C4C2×D4×C1711yescharacteristic
353C22×C4C2×D4×C1711yescharacteristic
354C22×C4#41×C1711yescharacteristic
355M16—42no—
356C2×C8—22no—
357C2×C8—21no—
358C2×C8—22no—
359C2×C8—21no—
360C2×C8—42no—
361C2×C8—82no—
362C2×C8—81no—
363C2×C8C2×D4×C1712yes—
364C2×C8C2×D4×C1712yes—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4C2×D4×C1711yescharacteristic
378C4⋊C4C2×D4×C1711yescharacteristic
379C22⋊C4—21no—
380C22⋊C4—21no—
381C22⋊C4—21no—
382C22⋊C4—41no—
383C42—21no—
384C42—21no—
385C42—21no—
386C42—41no—
387C42C2×D4×C1711yescharacteristic
388C42C2×D4×C1711yescharacteristic
389C42#41×C1711yescharacteristic
390C42C24×C1711yescharacteristic
391C23—21no—
392C23C17×#12111yescharacteristic
393Q8—21no—
394Q8—41no—
395Q8—41no—
396Q8—82no—
397Q8—81no—
398Q8—82no—
399Q8C2×Q16×C1712yes—
400D4—24no—
401D4—21no—
402D4C2×Q16×C1712yes—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—24no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—81no—
416C2×C4—82no—
417C2×C4C17×#12111yescharacteristic
418C2×C4C17×#12111yescharacteristic
419C2×C4C17×#12111yescharacteristic
420C2×C4C2×Q16×C1712yes—
421C2×C4C17×#13512yes—
422C2×C4C22×D4×C1711yescharacteristic
423C2×C4C22×D4×C1711yescharacteristic
424C2×C4C2×#41×C1711yescharacteristic
425C8—22no—
426C8—22no—
427C8—41no—
428C8—41no—
429C8—42no—
430C8—42no—
431C22—21no—
432C22—21no—
433C22—22no—
434C22—41no—
435C22—41no—
436C22C17×#46712yes—
437C22C2×C17×#12111yescharacteristic
438C4—21no—
439C4—22no—
440C4—21no—
441C4—21no—
442C4—41no—
443C4—41no—
444C4—81no—
445C4—82no—
446C4—81no—
447C4C17×#46712yes—
448C4C22×Q16×C1711yescharacteristic
449C4C2×C17×#13511yescharacteristic
450C4C17×#57711yescharacteristic
451C4C17×#57811yescharacteristic
452C2—22no—
453C2—42no—
454C2C17×#304611yescharacteristic
455C2C2×C17×#46711yescharacteristic
456C2C17×#306811yescharacteristic
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×#3230C2semidirect
5. C17×#1684C2semidirect
6. C17×#1683C2semidirect
7. C17×#1676C2semidirect
8. C17×#1675C2semidirect
9. C17×#1571C2semidirect
10. C17×#1550C2semidirect
11. C2×C17×#333C2semidirect
162. #19417C17direct (N × H)
203. #3230C2×C17semidirect
207. #1684C2×C17semidirect
208. #1683C2×C17semidirect
209. #1676C2×C17semidirect
210. #1675C2×C17semidirect
211. #1571C2×C17semidirect
212. #1550C2×C17semidirect
213. C2×#333C2×C17semidirect
337. C17#19417direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#32302
C17×#30792
C17×#30762
C17×#29882
C17×#16842
C17×#16832
C17×#16762
C17×#16752
C17×#15712
C17×#15502
C2×C17×#3332
#1941717