Finite Group Databasebeta

← C17×#13084 #16870828

Subgroups — C17×#13084 #16870828

Order 4352.

894 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C17×#99C211yesmaximal, characteristic
2C17×#2405C211yesmaximal, characteristic
3C2×C17×#352C212yesmaximal, complemented
4C17×#1783C211yesmaximal, characteristic
5C17×#1390C212yesmaximal, complemented
6C23×D4×C17C2211yescharacteristic
7C2×C17×#123C411yescharacteristic, complemented
8C2×C17×#123C2211yescharacteristic
9C22×C22⋊C4×C17—21no—
10C22×C22⋊C4×C17C411yescharacteristic, complemented
11C2×C17×#100—21no—
12C2×C17×#100C2212yes—
13C2×C17×#99—24no—
14C2×C17×#99—21no—
15C2×C17×#99C2212yes—
16C17×#407—21no—
17C17×#394—21no—
18C17×#394—21no—
19C17×#386C411yescharacteristic, complemented
20C17×#386C2211yescharacteristic
21C17×#385—21no—
22C17×#379—21no—
23C17×#379C411yescharacteristic, complemented
24C17×#352—24no—
25C25×C17C2×C411yescharacteristic
26C25×C17D411yescharacteristic
27C22×D4×C17—22no—
28C22×D4×C17—22no—
29C22×D4×C17—41no—
30C22×D4×C17—41no—
31C22×D4×C17—42no—
32C22×D4×C17C2×C411yescharacteristic
33C22×D4×C17D411yescharacteristic
34C22×D4×C17D411yescharacteristic
35C22×D4×C17C2311yescharacteristic
36C23×C4×C17—41no—
37C23×C4×C17C2×C411yescharacteristic, complemented
38C23×C4×C17C2×C411yescharacteristic, complemented
39C23×C4×C17D411yescharacteristic
40C2×M16×C17—22no—
41C17×#123—22no—
42C17×#123—22no—
43C17×#123—42no—
44C2×C4⋊C4×C17—21no—
45C2×C4⋊C4×C17—21no—
46C2×C22⋊C4×C17—24no—
47C2×C22⋊C4×C17—22no—
48C2×C22⋊C4×C17—21no—
49C2×C22⋊C4×C17—21no—
50C2×C22⋊C4×C17—21no—
51C2×C22⋊C4×C17—21no—
52C2×C22⋊C4×C17—21no—
53C2×C22⋊C4×C17—21no—
54C2×C22⋊C4×C17—21no—
55C2×C22⋊C4×C17—21no—
56C2×C22⋊C4×C17—41no—
57C2×C22⋊C4×C17—42no—
58C2×C22⋊C4×C17—41no—
59C2×C22⋊C4×C17—41no—
60C2×C22⋊C4×C17C2×C411yescharacteristic, complemented
61C2×C22⋊C4×C17C2×C411yescharacteristic, complemented
62C17×#100—22no—
63C17×#100—22no—
64C17×#100—42no—
65C17×#99—24no—
66C17×#99—22no—
67C17×#99D414yes—
68C17×C22⋊C8—41no—
69C17×C22⋊C8—41no—
70C17×#95—21no—
71C17×#95—21no—
72C24×C17—21no—
73C24×C17—22no—
74C24×C17—21no—
75C24×C17—21no—
76C24×C17—21no—
77C24×C17—21no—
78C24×C17—21no—
79C24×C17—22no—
80C24×C17—41no—
81C24×C17—42no—
82C24×C17—42no—
83C24×C17—81no—
84C24×C17—81no—
85C24×C17C22⋊C411yescharacteristic
86C24×C17C22⋊C411yescharacteristic
87C24×C17C22⋊C411yescharacteristic
88C24×C17C22×C411yescharacteristic
89C24×C17C2×D411yescharacteristic
90C2×D4×C17—22no—
91C2×D4×C17—22no—
92C2×D4×C17—22no—
93C2×D4×C17—21no—
94C2×D4×C17—21no—
95C2×D4×C17—22no—
96C2×D4×C17—41no—
97C2×D4×C17—41no—
98C2×D4×C17—41no—
99C2×D4×C17—41no—
100C2×D4×C17—41no—
101C2×D4×C17—41no—
102C2×D4×C17—44no—
103C2×D4×C17—44no—
104C2×D4×C17—44no—
105C2×D4×C17—44no—
106C2×D4×C17C2×D412yes—
107C2×D4×C17#4112yes—
108C22×C4×C17—21no—
109C22×C4×C17—21no—
110C22×C4×C17—22no—
111C22×C4×C17—21no—
112C22×C4×C17—21no—
113C22×C4×C17—21no—
114C22×C4×C17—21no—
115C22×C4×C17—22no—
116C22×C4×C17—41no—
117C22×C4×C17—44no—
118C22×C4×C17—42no—
119C22×C4×C17—41no—
120C22×C4×C17—41no—
121C22×C4×C17—41no—
122C22×C4×C17—81no—
123C22×C4×C17—82no—
124C22×C4×C17—82no—
125C22×C4×C17C22⋊C411yescharacteristic
126C22×C4×C17C2×D411yescharacteristic
127M16×C17—42no—
128M16×C17—42no—
129C2×C8×C17—42no—
130C4⋊C4×C17—42no—
131C4⋊C4×C17—42no—
132C22⋊C4×C17—22no—
133C22⋊C4×C17—24no—
134C22⋊C4×C17—42no—
135C22⋊C4×C17—44no—
136C22⋊C4×C17—42no—
137C22⋊C4×C17—42no—
138C22⋊C4×C17—42no—
139C22⋊C4×C17—41no—
140C22⋊C4×C17—41no—
141C22⋊C4×C17—41no—
142C22⋊C4×C17—41no—
143C22⋊C4×C17—41no—
144C22⋊C4×C17—81no—
145C22⋊C4×C17—81no—
146C22⋊C4×C17—81no—
147#13084C1711yesmaximal, characteristic, direct product factor, Sylow
148C23×C17—22no—
149C23×C17—22no—
150C23×C17—22no—
151C23×C17—22no—
152C23×C17—22no—
153C23×C17—21no—
154C23×C17—21no—
155C23×C17—21no—
156C23×C17—21no—
157C23×C17—21no—
158C23×C17—21no—
159C23×C17—21no—
160C23×C17—21no—
161C23×C17—21no—
162C23×C17—21no—
163C23×C17—21no—
164C23×C17—41no—
165C23×C17—42no—
166C23×C17—42no—
167C23×C17—41no—
168C23×C17—41no—
169C23×C17—42no—
170C23×C17—41no—
171C23×C17—41no—
172C23×C17—41no—
173C23×C17—41no—
174C23×C17—42no—
175C23×C17—41no—
176C23×C17—41no—
177C23×C17—42no—
178C23×C17—42no—
179C23×C17—81no—
180C23×C17—81no—
181C23×C17—81no—
182C23×C17—81no—
183C23×C17—84no—
184C23×C17—82no—
185C23×C17—82no—
186C23×C17—84no—
187C23×C17—84no—
188C23×C17#9911yescharacteristic
189C23×C17#9911yescharacteristic
190C23×C17#9912yes—
191C23×C17C2×C22⋊C411yescharacteristic
192C23×C17C4×D412yes—
193C23×C17#12011yescharacteristic
194C23×C17#12311yescharacteristic
195D4×C17—42no—
196D4×C17—42no—
197D4×C17—44no—
198D4×C17—44no—
199D4×C17—42no—
200D4×C17—42no—
201C2×C4×C17—21no—
202C2×C4×C17—21no—
203C2×C4×C17—21no—
204C2×C4×C17—21no—
205C2×C4×C17—21no—
206C2×C4×C17—42no—
207C2×C4×C17—42no—
208C2×C4×C17—44no—
209C2×C4×C17—41no—
210C2×C4×C17—41no—
211C2×C4×C17—41no—
212C2×C4×C17—41no—
213C2×C4×C17—41no—
214C2×C4×C17—41no—
215C2×C4×C17—41no—
216C2×C4×C17—41no—
217C2×C4×C17—41no—
218C2×C4×C17—41no—
219C2×C4×C17—41no—
220C2×C4×C17—41no—
221C2×C4×C17—88no—
222C2×C4×C17—82no—
223C2×C4×C17—82no—
224C2×C4×C17—82no—
225C2×C4×C17—82no—
226C2×C4×C17#12112yes—
227C8×C17—82no—
228C22×#99C2×C1711yescharacteristic
229#2405C2×C1711yescharacteristic
230C2×#352C2×C1712yescomplemented
231#1783C2×C1711yescharacteristic
232#1390C2×C1712yescomplemented
233C22×C17—21no—
234C22×C17—21no—
235C22×C17—21no—
236C22×C17—21no—
237C22×C17—21no—
238C22×C17—21no—
239C22×C17—21no—
240C22×C17—21no—
241C22×C17—22no—
242C22×C17—22no—
243C22×C17—21no—
244C22×C17—42no—
245C22×C17—42no—
246C22×C17—42no—
247C22×C17—42no—
248C22×C17—41no—
249C22×C17—41no—
250C22×C17—44no—
251C22×C17—42no—
252C22×C17—44no—
253C22×C17—41no—
254C22×C17—41no—
255C22×C17—41no—
256C22×C17—41no—
257C22×C17—41no—
258C22×C17—41no—
259C22×C17—41no—
260C22×C17—41no—
261C22×C17—41no—
262C22×C17—81no—
263C22×C17—81no—
264C22×C17—84no—
265C22×C17—81no—
266C22×C17—81no—
267C22×C17—82no—
268C22×C17—82no—
269C22×C17—84no—
270C22×C17#35212yescomplemented
271C22×C17#38611yescharacteristic
272C22×C17C2×#9911yescharacteristic
273C22×C17C2×#9911yescharacteristic
274C4×C17—22no—
275C4×C17—41no—
276C4×C17—81no—
277C4×C17—81no—
278C4×C17—84no—
279C4×C17—81no—
280C4×C17—81no—
281C23×D4C22×C1711yescharacteristic
282C2×#123C4×C1711yescharacteristic, complemented
283C2×#123C22×C1711yescharacteristic
284C22×C22⋊C4—21no—
285C22×C22⋊C4C4×C1711yescharacteristic, complemented
286C2×#100—21no—
287C2×#100C22×C1712yes—
288C2×#99—21no—
289C2×#99—24no—
290C2×#99C22×C1712yes—
291#407—21no—
292#394—21no—
293#394—21no—
294#386C4×C1711yescharacteristic, complemented
295#386C22×C1711yescharacteristic
296#385—21no—
297#379—21no—
298#379C4×C1711yescharacteristic, complemented
299#352—24no—
300C2×C17—21no—
301C2×C17—21no—
302C2×C17—22no—
303C2×C17—41no—
304C2×C17—41no—
305C2×C17—42no—
306C2×C17—41no—
307C2×C17—42no—
308C2×C17—81no—
309C2×C17#189811yescharacteristic
310C2×C17C2×#35211yescharacteristic
311C2×C17#212111yescharacteristic
312C25C2×C4×C1711yescharacteristic
313C25D4×C1711yescharacteristic
314C22×D4—22no—
315C22×D4—22no—
316C22×D4—41no—
317C22×D4—41no—
318C22×D4—42no—
319C22×D4C2×C4×C1711yescharacteristic
320C22×D4D4×C1711yescharacteristic
321C22×D4D4×C1711yescharacteristic
322C22×D4C23×C1711yescharacteristic
323C23×C4—41no—
324C23×C4C2×C4×C1711yescharacteristic, complemented
325C23×C4C2×C4×C1711yescharacteristic, complemented
326C23×C4D4×C1711yescharacteristic
327C2×M16—22no—
328#123—22no—
329#123—22no—
330#123—42no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—41no—
346C2×C22⋊C4—41no—
347C2×C22⋊C4C2×C4×C1711yescharacteristic, complemented
348C2×C22⋊C4C2×C4×C1711yescharacteristic, complemented
349#100—22no—
350#100—22no—
351#100—42no—
352#99—24no—
353#99—22no—
354#99D4×C1714yes—
355C22⋊C8—41no—
356C22⋊C8—41no—
357#95—21no—
358#95—21no—
359C17#1308411yescharacteristic, direct product factor, Sylow
360C24—21no—
361C24—21no—
362C24—22no—
363C24—21no—
364C24—21no—
365C24—21no—
366C24—21no—
367C24—22no—
368C24—41no—
369C24—42no—
370C24—42no—
371C24—81no—
372C24—81no—
373C24C22⋊C4×C1711yescharacteristic
374C24C22⋊C4×C1711yescharacteristic
375C24C22⋊C4×C1711yescharacteristic
376C24C22×C4×C1711yescharacteristic
377C24C2×D4×C1711yescharacteristic
378C2×D4—21no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—44no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4C2×D4×C1712yes—
395C2×D4#41×C1712yes—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—41no—
405C22×C4—44no—
406C22×C4—42no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—81no—
411C22×C4—82no—
412C22×C4—82no—
413C22×C4C22⋊C4×C1711yescharacteristic
414C22×C4C2×D4×C1711yescharacteristic
415M16—42no—
416M16—42no—
417C2×C8—42no—
418C4⋊C4—42no—
419C4⋊C4—42no—
420C22⋊C4—22no—
421C22⋊C4—24no—
422C22⋊C4—42no—
423C22⋊C4—44no—
424C22⋊C4—42no—
425C22⋊C4—42no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—42no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—81no—
433C22⋊C4—81no—
434C22⋊C4—81no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—22no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—41no—
452C23—42no—
453C23—42no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—42no—
462C23—41no—
463C23—41no—
464C23—42no—
465C23—42no—
466C23—81no—
467C23—81no—
468C23—81no—
469C23—81no—
470C23—82no—
471C23—84no—
472C23—82no—
473C23—84no—
474C23—84no—
475C23C17×#9911yescharacteristic
476C23C17×#9911yescharacteristic
477C23C17×#9912yes—
478C23C2×C22⋊C4×C1711yescharacteristic
479C23C4×D4×C1712yes—
480C23C17×#12011yescharacteristic
481C23C17×#12311yescharacteristic
482D4—42no—
483D4—42no—
484D4—44no—
485D4—44no—
486D4—42no—
487D4—42no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—44no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—88no—
509C2×C4—82no—
510C2×C4—82no—
511C2×C4—82no—
512C2×C4—82no—
513C2×C4C17×#12112yes—
514C8—82no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—22no—
524C22—21no—
525C22—22no—
526C22—42no—
527C22—42no—
528C22—41no—
529C22—42no—
530C22—42no—
531C22—41no—
532C22—44no—
533C22—42no—
534C22—44no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—81no—
545C22—81no—
546C22—84no—
547C22—81no—
548C22—81no—
549C22—82no—
550C22—82no—
551C22—84no—
552C22C17×#35212yescomplemented
553C22C17×#38611yescharacteristic
554C22C2×C17×#9911yescharacteristic
555C22C2×C17×#9911yescharacteristic
556C4—22no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—84no—
561C4—81no—
562C4—81no—
563C2—21no—
564C2—21no—
565C2—22no—
566C2—41no—
567C2—41no—
568C2—41no—
569C2—42no—
570C2—42no—
571C2—81no—
572C2C17×#189811yescharacteristic
573C2C2×C17×#35211yescharacteristic
574C2C17×#212111yescharacteristic
subgroupG/H
center, socleC22×C17C2×#99
commutatorC24C22×C4×C17
Frattini, cosocleC22×D4C23×C17
prime radicalC23×D4×C17C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C24×C17 ◁ C23×D4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C17×#352C2semidirect
5. C17×#1390C2semidirect
7. C2×C17×#123C4semidirect
10. C22×C22⋊C4×C17C4semidirect
19. C17×#386C4semidirect
23. C17×#379C4semidirect
37. C23×C4×C17C2×C4semidirect
38. C23×C4×C17C2×C4semidirect
60. C2×C22⋊C4×C17C2×C4semidirect
61. C2×C22⋊C4×C17C2×C4semidirect
147. #13084C17direct (N × H)
230. C2×#352C2×C17semidirect
232. #1390C2×C17semidirect
270. C22×C17#352semidirect
282. C2×#123C4×C17semidirect
285. C22×C22⋊C4C4×C17semidirect
294. #386C4×C17semidirect
298. #379C4×C17semidirect
324. C23×C4C2×C4×C17semidirect
325. C23×C4C2×C4×C17semidirect
347. C2×C22⋊C4C2×C4×C17semidirect
348. C2×C22⋊C4C2×C4×C17semidirect
359. C17#13084direct (N × H)
552. C22C17×#352semidirect

Maximal subgroups

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

subgroupindex
C22×C17×#992
C17×#24052
C2×C17×#3522
C17×#17832
C17×#13902
#1308417