Finite Group Databasebeta

← C17×#13082 #16870826

Subgroups — C17×#13082 #16870826

Order 4352.

1088 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C17×#100C211yesmaximal, characteristic, complemented
2C17×#2403C211yesmaximal, characteristic
3C2×C17×AΣL(1,𝔽16)C212yesmaximal, complemented
4C17×#1781C211yesmaximal, characteristic, complemented
5C17×#1390C212yesmaximal, complemented
6C23×D4×C17C411yescharacteristic, complemented
7C23×D4×C17C2211yescharacteristic
8C22×M16×C17—21no—
9C2×C17×#120—21no—
10C2×C17×#120C411yescharacteristic, complemented
11C2×C17×#120C2211yescharacteristic
12C2×C17×#100—24no—
13C2×C17×#100—21no—
14C2×C17×#100C2212yes—
15C2×C17×#99—21no—
16C2×C17×#99C2212yes—
17C17×#392—21no—
18C17×#392—21no—
19C17×#386—21no—
20C17×#386C411yescharacteristic, complemented
21C17×#386C2211yescharacteristic
22C17×#379—21no—
23C17×#379C411yescharacteristic, complemented
24C17×AΣL(1,𝔽16)—24no—
25C25×C17C2×C411yescharacteristic
26C25×C17C2×C411yescharacteristic
27C25×C17D411yescharacteristic
28C22×D4×C17—21no—
29C22×D4×C17—22no—
30C22×D4×C17—22no—
31C22×D4×C17—21no—
32C22×D4×C17—21no—
33C22×D4×C17—21no—
34C22×D4×C17—42no—
35C22×D4×C17—41no—
36C22×D4×C17—41no—
37C22×D4×C17—44no—
38C22×D4×C17—41no—
39C22×D4×C17—41no—
40C22×D4×C17C2×C411yescharacteristic
41C22×D4×C17D411yescharacteristic
42C22×D4×C17D411yescharacteristic
43C22×D4×C17C2311yescharacteristic
44C23×C4×C17C2×C411yescharacteristic
45C23×C4×C17D411yescharacteristic
46C2×M16×C17—24no—
47C2×M16×C17—22no—
48C2×M16×C17—41no—
49C2×M16×C17—42no—
50C22×C8×C17—41no—
51C17×#120—22no—
52C17×#120—22no—
53C17×#120—44no—
54C17×#120—42no—
55C2×C22⋊C4×C17—21no—
56C2×C22⋊C4×C17—21no—
57C2×C22⋊C4×C17—21no—
58C2×C22⋊C4×C17—21no—
59C2×C22⋊C4×C17—21no—
60C2×C22⋊C4×C17—22no—
61C2×C22⋊C4×C17—21no—
62C2×C22⋊C4×C17—41no—
63C2×C22⋊C4×C17—41no—
64C2×C22⋊C4×C17C2×C411yescharacteristic
65C2×C22⋊C4×C17C2×C411yescharacteristic
66C17×#100—24no—
67C17×#100—22no—
68C17×#100D414yescomplemented
69C17×#99—22no—
70C17×#99—22no—
71C17×#99—42no—
72C17×#95—21no—
73C17×#95—21no—
74C24×C17—21no—
75C24×C17—21no—
76C24×C17—21no—
77C24×C17—21no—
78C24×C17—21no—
79C24×C17—22no—
80C24×C17—22no—
81C24×C17—22no—
82C24×C17—41no—
83C24×C17—41no—
84C24×C17—42no—
85C24×C17—41no—
86C24×C17—42no—
87C24×C17—42no—
88C24×C17—41no—
89C24×C17—81no—
90C24×C17—81no—
91C24×C17—81no—
92C24×C17C22⋊C411yescharacteristic
93C24×C17C22⋊C411yescharacteristic
94C24×C17C22⋊C411yescharacteristic
95C24×C17C22×C411yescharacteristic
96C24×C17C2×D411yescharacteristic
97C2×D4×C17—24no—
98C2×D4×C17—22no—
99C2×D4×C17—22no—
100C2×D4×C17—22no—
101C2×D4×C17—22no—
102C2×D4×C17—21no—
103C2×D4×C17—21no—
104C2×D4×C17—41no—
105C2×D4×C17—41no—
106C2×D4×C17—41no—
107C2×D4×C17—41no—
108C2×D4×C17—41no—
109C2×D4×C17—41no—
110C2×D4×C17—44no—
111C2×D4×C17—44no—
112C2×D4×C17—44no—
113C2×D4×C17—44no—
114C2×D4×C17—42no—
115C2×D4×C17—42no—
116C2×D4×C17—42no—
117C2×D4×C17—42no—
118C2×D4×C17—44no—
119C2×D4×C17—44no—
120C2×D4×C17—44no—
121C2×D4×C17—41no—
122C2×D4×C17—41no—
123C2×D4×C17—44no—
124C2×D4×C17—42no—
125C2×D4×C17—42no—
126C2×D4×C17—42no—
127C2×D4×C17—42no—
128C2×D4×C17—81no—
129C2×D4×C17—81no—
130C2×D4×C17C2×D412yes—
131C2×D4×C17#4112yes—
132C22×C4×C17—21no—
133C22×C4×C17—21no—
134C22×C4×C17—22no—
135C22×C4×C17—21no—
136C22×C4×C17—21no—
137C22×C4×C17—21no—
138C22×C4×C17—21no—
139C22×C4×C17—21no—
140C22×C4×C17—42no—
141C22×C4×C17—41no—
142C22×C4×C17—42no—
143C22×C4×C17C22⋊C411yescharacteristic
144C22×C4×C17C2×D411yescharacteristic
145M16×C17—24no—
146M16×C17—44no—
147M16×C17—42no—
148C2×C8×C17—44no—
149C2×C8×C17—42no—
150C22⋊C4×C17—22no—
151C22⋊C4×C17—42no—
152C22⋊C4×C17—42no—
153C22⋊C4×C17—42no—
154C22⋊C4×C17—42no—
155C22⋊C4×C17—41no—
156C22⋊C4×C17—41no—
157C22⋊C4×C17—41no—
158C22⋊C4×C17—42no—
159C22⋊C4×C17—42no—
160C22⋊C4×C17—81no—
161C22⋊C4×C17—82no—
162C22⋊C4×C17—82no—
163#13082C1711yesmaximal, characteristic, direct product factor, Sylow
164C23×C17—22no—
165C23×C17—21no—
166C23×C17—21no—
167C23×C17—21no—
168C23×C17—21no—
169C23×C17—21no—
170C23×C17—21no—
171C23×C17—22no—
172C23×C17—21no—
173C23×C17—21no—
174C23×C17—21no—
175C23×C17—21no—
176C23×C17—21no—
177C23×C17—21no—
178C23×C17—41no—
179C23×C17—42no—
180C23×C17—42no—
181C23×C17—42no—
182C23×C17—42no—
183C23×C17—41no—
184C23×C17—41no—
185C23×C17—41no—
186C23×C17—41no—
187C23×C17—41no—
188C23×C17—41no—
189C23×C17—42no—
190C23×C17—41no—
191C23×C17—42no—
192C23×C17—41no—
193C23×C17—41no—
194C23×C17—41no—
195C23×C17—41no—
196C23×C17—42no—
197C23×C17—42no—
198C23×C17—42no—
199C23×C17—42no—
200C23×C17—41no—
201C23×C17—41no—
202C23×C17—41no—
203C23×C17—81no—
204C23×C17—81no—
205C23×C17—81no—
206C23×C17—81no—
207C23×C17—82no—
208C23×C17—84no—
209C23×C17—84no—
210C23×C17—84no—
211C23×C17—84no—
212C23×C17—84no—
213C23×C17—84no—
214C23×C17—82no—
215C23×C17#9911yescharacteristic
216C23×C17#9911yescharacteristic
217C23×C17C2×C22⋊C411yescharacteristic
218C23×C17C4×D412yes—
219C23×C17#12112yes—
220D4×C17—42no—
221D4×C17—42no—
222D4×C17—44no—
223D4×C17—44no—
224D4×C17—42no—
225D4×C17—42no—
226D4×C17—44no—
227D4×C17—48no—
228D4×C17—44no—
229D4×C17—84no—
230D4×C17—84no—
231C2×C4×C17—22no—
232C2×C4×C17—22no—
233C2×C4×C17—22no—
234C2×C4×C17—22no—
235C2×C4×C17—21no—
236C2×C4×C17—21no—
237C2×C4×C17—21no—
238C2×C4×C17—21no—
239C2×C4×C17—22no—
240C2×C4×C17—41no—
241C2×C4×C17—42no—
242C2×C4×C17—41no—
243C2×C4×C17—42no—
244C2×C4×C17—41no—
245C2×C4×C17—41no—
246C2×C4×C17—41no—
247C2×C4×C17—41no—
248C2×C4×C17—41no—
249C2×C4×C17—41no—
250C2×C4×C17—82no—
251C2×C4×C17—82no—
252C2×C4×C17—82no—
253C2×C4×C17#9912yes—
254C2×C4×C17#12011yescharacteristic
255C2×C4×C17#12311yescharacteristic
256C8×C17—44no—
257C22×#100C2×C1711yescharacteristic, complemented
258#2403C2×C1711yescharacteristic
259C2×AΣL(1,𝔽16)C2×C1712yescomplemented
260#1781C2×C1711yescharacteristic, complemented
261#1390C2×C1712yescomplemented
262C22×C17—21no—
263C22×C17—21no—
264C22×C17—21no—
265C22×C17—21no—
266C22×C17—21no—
267C22×C17—21no—
268C22×C17—21no—
269C22×C17—22no—
270C22×C17—22no—
271C22×C17—42no—
272C22×C17—42no—
273C22×C17—42no—
274C22×C17—42no—
275C22×C17—42no—
276C22×C17—42no—
277C22×C17—42no—
278C22×C17—42no—
279C22×C17—41no—
280C22×C17—41no—
281C22×C17—41no—
282C22×C17—41no—
283C22×C17—42no—
284C22×C17—41no—
285C22×C17—41no—
286C22×C17—41no—
287C22×C17—41no—
288C22×C17—41no—
289C22×C17—41no—
290C22×C17—81no—
291C22×C17—84no—
292C22×C17—84no—
293C22×C17—81no—
294C22×C17—81no—
295C22×C17—81no—
296C22×C17—81no—
297C22×C17—81no—
298C22×C17—84no—
299C22×C17—84no—
300C22×C17—84no—
301C22×C17—84no—
302C22×C17—81no—
303C22×C17—81no—
304C22×C17AΣL(1,𝔽16)12yescomplemented
305C22×C17#38611yescharacteristic
306C22×C17C2×#9911yescharacteristic
307C22×C17C2×#9911yescharacteristic
308C4×C17—21no—
309C4×C17—22no—
310C4×C17—21no—
311C4×C17—42no—
312C4×C17—81no—
313C4×C17—81no—
314C4×C17—162no—
315C23×D4C4×C1711yescharacteristic, complemented
316C23×D4C22×C1711yescharacteristic
317C22×M16—21no—
318C2×#120—21no—
319C2×#120C4×C1711yescharacteristic, complemented
320C2×#120C22×C1711yescharacteristic
321C2×#100—21no—
322C2×#100—24no—
323C2×#100C22×C1712yes—
324C2×#99—21no—
325C2×#99C22×C1712yes—
326#392—21no—
327#392—21no—
328#386—21no—
329#386C4×C1711yescharacteristic, complemented
330#386C22×C1711yescharacteristic
331#379—21no—
332#379C4×C1711yescharacteristic, complemented
333AΣL(1,𝔽16)—24no—
334C2×C17—21no—
335C2×C17—21no—
336C2×C17—22no—
337C2×C17—42no—
338C2×C17—41no—
339C2×C17—42no—
340C2×C17—81no—
341C2×C17—82no—
342C2×C17—81no—
343C2×C17#189811yescharacteristic
344C2×C17C2×AΣL(1,𝔽16)11yescharacteristic
345C2×C17#212111yescharacteristic
346C25C2×C4×C1711yescharacteristic
347C25C2×C4×C1711yescharacteristic
348C25D4×C1711yescharacteristic
349C22×D4—21no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—42no—
356C22×D4—41no—
357C22×D4—41no—
358C22×D4—44no—
359C22×D4—41no—
360C22×D4—41no—
361C22×D4C2×C4×C1711yescharacteristic
362C22×D4D4×C1711yescharacteristic
363C22×D4D4×C1711yescharacteristic
364C22×D4C23×C1711yescharacteristic
365C23×C4C2×C4×C1711yescharacteristic
366C23×C4D4×C1711yescharacteristic
367C2×M16—24no—
368C2×M16—22no—
369C2×M16—41no—
370C2×M16—42no—
371C22×C8—41no—
372#120—22no—
373#120—22no—
374#120—44no—
375#120—42no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4C2×C4×C1711yescharacteristic
386C2×C22⋊C4C2×C4×C1711yescharacteristic
387#100—24no—
388#100—22no—
389#100D4×C1714yescomplemented
390#99—22no—
391#99—22no—
392#99—42no—
393#95—21no—
394#95—21no—
395C17#1308211yescharacteristic, direct product factor, Sylow
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—41no—
405C24—41no—
406C24—42no—
407C24—41no—
408C24—42no—
409C24—42no—
410C24—41no—
411C24—81no—
412C24—81no—
413C24—81no—
414C24C22⋊C4×C1711yescharacteristic
415C24C22⋊C4×C1711yescharacteristic
416C24C22⋊C4×C1711yescharacteristic
417C24C22×C4×C1711yescharacteristic
418C24C2×D4×C1711yescharacteristic
419C2×D4—24no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—21no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—44no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—81no—
451C2×D4—81no—
452C2×D4C2×D4×C1712yes—
453C2×D4#41×C1712yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—42no—
463C22×C4—41no—
464C22×C4—42no—
465C22×C4C22⋊C4×C1711yescharacteristic
466C22×C4C2×D4×C1711yescharacteristic
467M16—24no—
468M16—44no—
469M16—42no—
470C2×C8—44no—
471C2×C8—42no—
472C22⋊C4—22no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—41no—
477C22⋊C4—42no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—81no—
483C22⋊C4—82no—
484C22⋊C4—82no—
485C23—22no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—22no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—41no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—41no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—81no—
525C23—81no—
526C23—81no—
527C23—81no—
528C23—82no—
529C23—84no—
530C23—84no—
531C23—84no—
532C23—84no—
533C23—84no—
534C23—84no—
535C23—82no—
536C23C17×#9911yescharacteristic
537C23C17×#9911yescharacteristic
538C23C2×C22⋊C4×C1711yescharacteristic
539C23C4×D4×C1712yes—
540C23C17×#12112yes—
541D4—42no—
542D4—42no—
543D4—44no—
544D4—44no—
545D4—42no—
546D4—42no—
547D4—44no—
548D4—48no—
549D4—44no—
550D4—84no—
551D4—84no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4C17×#9912yes—
575C2×C4C17×#12011yescharacteristic
576C2×C4C17×#12311yescharacteristic
577C8—44no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—22no—
586C22—22no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—81no—
607C22—84no—
608C22—84no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—84no—
615C22—84no—
616C22—84no—
617C22—84no—
618C22—81no—
619C22—81no—
620C22C17×AΣL(1,𝔽16)12yescomplemented
621C22C17×#38611yescharacteristic
622C22C2×C17×#9911yescharacteristic
623C22C2×C17×#9911yescharacteristic
624C4—21no—
625C4—21no—
626C4—22no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—162no—
631C2—21no—
632C2—21no—
633C2—22no—
634C2—42no—
635C2—41no—
636C2—42no—
637C2—81no—
638C2—82no—
639C2—81no—
640C2C17×#189811yescharacteristic
641C2C2×C17×AΣL(1,𝔽16)11yescharacteristic
642C2C17×#212111yescharacteristic
subgroupG/H
center, socleC22×C17C2×#99
commutatorC24C22×C4×C17
Frattini, cosocleC22×D4C23×C17
prime radicalC17×#2403C2
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
1. C22×C17×#100C2semidirect
3. C2×C17×AΣL(1,𝔽16)C2semidirect
4. C17×#1781C2semidirect
5. C17×#1390C2semidirect
6. C23×D4×C17C4semidirect
10. C2×C17×#120C4semidirect
20. C17×#386C4semidirect
23. C17×#379C4semidirect
68. C17×#100D4semidirect
163. #13082C17direct (N × H)
257. C22×#100C2×C17semidirect
259. C2×AΣL(1,𝔽16)C2×C17semidirect
260. #1781C2×C17semidirect
261. #1390C2×C17semidirect
304. C22×C17AΣL(1,𝔽16)semidirect
315. C23×D4C4×C17semidirect
319. C2×#120C4×C17semidirect
329. #386C4×C17semidirect
332. #379C4×C17semidirect
389. #100D4×C17semidirect
395. C17#13082direct (N × H)
620. C22C17×AΣL(1,𝔽16)semidirect

Maximal subgroups

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

subgroupindex
C22×C17×#1002
C17×#24032
C2×C17×AΣL(1,𝔽16)2
C17×#17812
C17×#13902
#1308217