Finite Group Databasebeta

← C17×#18379 #16876123

Subgroups — C17×#18379 #16876123

Order 4352.

980 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3492C211yesmaximal, characteristic
2C17×#3190C212yesmaximal, complemented
3C17×#2583C211yesmaximal, characteristic, complemented
4C17×#1611C211yesmaximal, characteristic, complemented
5C17×#1610C211yesmaximal, characteristic, complemented
6C17×#1609C212yesmaximal, complemented
7C17×#1605C211yesmaximal, characteristic, complemented
8C17×#1604C211yesmaximal, characteristic, complemented
9C17×#1603C212yesmaximal, complemented
10C17×#1501C212yesmaximal, complemented
11C2×C17×#324C211yesmaximal, characteristic, complemented
12C17×#554—22no—
13C17×#553—22no—
14C17×#552—22no—
15C17×#547—22no—
16C17×#544C2211yescharacteristic
17C17×#539—21no—
18C17×#539C2212yes—
19C17×#537C2211yescharacteristic
20C17×#525—21no—
21C17×#525—21no—
22C17×#525C2212yes—
23C2×C17×C22⋊Q8C2211yescharacteristic
24C17×#520—21no—
25C22×C4⋊C4×C17C2211yescharacteristic
26C17×#485—22no—
27C17×#483C2212yes—
28C17×#480C2212yes—
29C17×#467—22no—
30C17×#465—22no—
31C17×#452—22no—
32C17×#451C2212yes—
33C17×#448C2212yes—
34C2×C17×C22⋊C8C2212yes—
35C17×#398C2211yescharacteristic
36C17×#398C2211yescharacteristic
37C17×#395C2211yescharacteristic
38C17×#395C2211yescharacteristic
39C17×#389—21no—
40C17×#389—21no—
41C17×#385—21no—
42C17×#385—21no—
43C4×C22⋊C4×C17C2211yescharacteristic
44C17×#328C2212yes—
45C17×#328C2212yes—
46C17×#327C2212yes—
47C17×#327C2212yes—
48C17×#324C2212yes—
49C17×#324C2211yescharacteristic
50C17×#324C2211yescharacteristic
51C2×#41×C17—21no—
52C2×#41×C17—21no—
53C2×#41×C17D412yes—
54C22×Q8×C17C2311yescharacteristic
55C23×C4×C17D411yescharacteristic
56C23×C4×C17D411yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C2×Q16×C17—22no—
59C2×SD16×C17—22no—
60C22×C8×C17—22no—
61C17×C4⋊Q8—22no—
62C17×#126—22no—
63C17×#126—22no—
64C17×#125—22no—
65C17×#125—22no—
66C17×#125—22no—
67C17×#123—22no—
68C17×#123—22no—
69C17×#123—22no—
70C17×#123—22no—
71C17×#123—22no—
72C17×C22⋊Q8—21no—
73C17×C22⋊Q8—21no—
74C17×C22⋊Q8—21no—
75C17×C22⋊Q8—22no—
76C17×C22⋊Q8—22no—
77C17×C22⋊Q8—21no—
78C17×C22⋊Q8—22no—
79C17×C22⋊Q8—22no—
80C17×C22⋊Q8—22no—
81C17×C22⋊Q8D412yes—
82C17×C22⋊Q8C2312yes—
83C17×#121—21no—
84C17×#121—21no—
85C17×#121—21no—
86C17×#121—22no—
87C17×#121—21no—
88C17×#121D412yes—
89C17×#121C2312yes—
90C17×#120—22no—
91C4×Q8×C17—22no—
92C4×D4×C17—22no—
93C4×D4×C17—22no—
94C4×D4×C17—22no—
95C4×D4×C17—22no—
96C4×D4×C17—22no—
97C4×D4×C17—22no—
98C4×D4×C17—22no—
99C17×#117—22no—
100C17×#117—21no—
101C17×#117—21no—
102C17×#117D412yes—
103C2×C4⋊C4×C17—22no—
104C2×C4⋊C4×C17—22no—
105C2×C4⋊C4×C17—22no—
106C2×C4⋊C4×C17—21no—
107C2×C4⋊C4×C17—21no—
108C2×C4⋊C4×C17—21no—
109C2×C4⋊C4×C17—21no—
110C2×C4⋊C4×C17—21no—
111C2×C4⋊C4×C17D411yescharacteristic
112C2×C4⋊C4×C17D411yescharacteristic
113C2×C4⋊C4×C17C2311yescharacteristic
114C2×C4⋊C4×C17C2311yescharacteristic
115C2×C4⋊C4×C17C2311yescharacteristic
116C2×C22⋊C4×C17—21no—
117C2×C22⋊C4×C17—21no—
118C2×C42×C17—21no—
119C17×#107—22no—
120C17×#106—22no—
121C17×#103—22no—
122C17×#103—22no—
123C17×#103—22no—
124C17×#102—22no—
125C17×C22⋊C8—22no—
126C17×C22⋊C8C2312yes—
127C17×C22⋊C8C2312yes—
128C17×#95—21no—
129C17×#95—21no—
130C17×#95—21no—
131C17×#95—21no—
132C17×#95C2311yescharacteristic
133C17×#95C2311yescharacteristic
134C24×C17C2×D411yescharacteristic
135#41×C17—42no—
136#41×C17—42no—
137#41×C17—82no—
138#41×C17—82no—
139C2×Q8×C17—21no—
140C2×Q8×C17—21no—
141C2×Q8×C17—22no—
142C2×Q8×C17—81no—
143C2×Q8×C17C2×D412yes—
144C2×D4×C17—21no—
145C2×D4×C17—22no—
146C2×D4×C17—22no—
147C2×D4×C17—22no—
148C2×D4×C17—21no—
149C2×D4×C17C2×D412yes—
150C22×C4×C17—22no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—22no—
157C22×C4×C17—21no—
158C22×C4×C17—22no—
159C22×C4×C17—22no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—41no—
163C22×C4×C17—81no—
164C22×C4×C17—81no—
165C22×C4×C17C2×D411yescharacteristic
166C22×C4×C17C2×D411yescharacteristic
167C22×C4×C17C2×D411yescharacteristic
168C22×C4×C17C2×D411yescharacteristic
169C22×C4×C17C2×D411yescharacteristic
170C22×C4×C17C2×D412yes—
171C22×C4×C17C2×D412yes—
172C22×C4×C17C2411yescharacteristic
173Q16×C17—82no—
174SD16×C17—82no—
175C2×C8×C17—22no—
176C2×C8×C17—22no—
177C2×C8×C17—82no—
178C4⋊C4×C17—22no—
179C4⋊C4×C17—21no—
180C4⋊C4×C17—22no—
181C4⋊C4×C17—22no—
182C4⋊C4×C17—22no—
183C4⋊C4×C17—21no—
184C4⋊C4×C17—21no—
185C4⋊C4×C17—21no—
186C4⋊C4×C17—22no—
187C4⋊C4×C17—22no—
188C4⋊C4×C17—22no—
189C4⋊C4×C17—22no—
190C4⋊C4×C17—22no—
191C4⋊C4×C17—22no—
192C4⋊C4×C17—22no—
193C4⋊C4×C17—42no—
194C4⋊C4×C17—42no—
195C4⋊C4×C17—42no—
196C4⋊C4×C17—81no—
197C4⋊C4×C17—81no—
198C4⋊C4×C17C2×D412yes—
199C4⋊C4×C17C2×D412yes—
200C22⋊C4×C17—22no—
201C22⋊C4×C17—22no—
202C22⋊C4×C17—22no—
203C22⋊C4×C17—22no—
204C22⋊C4×C17—24no—
205C22⋊C4×C17—22no—
206C22⋊C4×C17—22no—
207C22⋊C4×C17—22no—
208C22⋊C4×C17—22no—
209C22⋊C4×C17—22no—
210C22⋊C4×C17—41no—
211C22⋊C4×C17—41no—
212C42×C17—22no—
213C42×C17—22no—
214C42×C17—22no—
215C42×C17—81no—
216#18379C1711yesmaximal, characteristic, direct product factor, Sylow
217C23×C17—21no—
218C23×C17—21no—
219C23×C17—22no—
220C23×C17—22no—
221C23×C17—41no—
222C23×C17#12011yescharacteristic
223C23×C17#12011yescharacteristic
224C23×C17C22×D411yescharacteristic
225Q8×C17—42no—
226Q8×C17—42no—
227Q8×C17—42no—
228Q8×C17—42no—
229Q8×C17—81no—
230D4×C17—42no—
231D4×C17—42no—
232D4×C17—44no—
233D4×C17—42no—
234D4×C17—42no—
235D4×C17—44no—
236D4×C17—81no—
237C2×C4×C17—21no—
238C2×C4×C17—21no—
239C2×C4×C17—22no—
240C2×C4×C17—22no—
241C2×C4×C17—22no—
242C2×C4×C17—22no—
243C2×C4×C17—21no—
244C2×C4×C17—22no—
245C2×C4×C17—21no—
246C2×C4×C17—21no—
247C2×C4×C17—21no—
248C2×C4×C17—21no—
249C2×C4×C17—41no—
250C2×C4×C17—42no—
251C2×C4×C17—42no—
252C2×C4×C17—41no—
253C2×C4×C17—42no—
254C2×C4×C17—42no—
255C2×C4×C17—44no—
256C2×C4×C17—41no—
257C2×C4×C17—41no—
258C2×C4×C17—42no—
259C2×C4×C17—41no—
260C2×C4×C17—41no—
261C2×C4×C17—41no—
262C2×C4×C17—41no—
263C2×C4×C17—41no—
264C2×C4×C17—41no—
265C2×C4×C17—41no—
266C2×C4×C17—41no—
267C2×C4×C17—41no—
268C2×C4×C17—41no—
269C2×C4×C17—82no—
270C2×C4×C17—81no—
271C2×C4×C17—82no—
272C2×C4×C17#12012yes—
273C2×C4×C17#13512yes—
274C2×C4×C17C22×D412yes—
275C8×C17—42no—
276C8×C17—42no—
277#3492C2×C1711yescharacteristic
278#3190C2×C1712yescomplemented
279#2583C2×C1711yescharacteristic, complemented
280#1611C2×C1711yescharacteristic, complemented
281#1610C2×C1711yescharacteristic, complemented
282#1609C2×C1712yescomplemented
283#1605C2×C1711yescharacteristic, complemented
284#1604C2×C1711yescharacteristic, complemented
285#1603C2×C1712yescomplemented
286#1501C2×C1712yescomplemented
287C2×#324C2×C1711yescharacteristic, complemented
288C22×C17—21no—
289C22×C17—21no—
290C22×C17—21no—
291C22×C17—21no—
292C22×C17—21no—
293C22×C17—21no—
294C22×C17—21no—
295C22×C17—42no—
296C22×C17—42no—
297C22×C17—42no—
298C22×C17—42no—
299C22×C17—42no—
300C22×C17#45612yes—
301C22×C17C2×#12011yescharacteristic
302C22×C17C2×#13511yescharacteristic
303C22×C17#57511yescharacteristic
304C4×C17—22no—
305C4×C17—22no—
306C4×C17—22no—
307C4×C17—42no—
308C4×C17—42no—
309C4×C17—41no—
310C4×C17—42no—
311C4×C17—42no—
312C4×C17—41no—
313C4×C17—41no—
314C4×C17—42no—
315C4×C17—81no—
316C4×C17—81no—
317#554—22no—
318#553—22no—
319#552—22no—
320#547—22no—
321#544C22×C1711yescharacteristic
322#539—21no—
323#539C22×C1712yes—
324#537C22×C1711yescharacteristic
325#525—21no—
326#525—21no—
327#525C22×C1712yes—
328C2×C22⋊Q8C22×C1711yescharacteristic
329#520—21no—
330C22×C4⋊C4C22×C1711yescharacteristic
331#485—22no—
332#483C22×C1712yes—
333#480C22×C1712yes—
334#467—22no—
335#465—22no—
336#452—22no—
337#451C22×C1712yes—
338#448C22×C1712yes—
339C2×C22⋊C8C22×C1712yes—
340#398C22×C1711yescharacteristic
341#398C22×C1711yescharacteristic
342#395C22×C1711yescharacteristic
343#395C22×C1711yescharacteristic
344#389—21no—
345#389—21no—
346#385—21no—
347#385—21no—
348C4×C22⋊C4C22×C1711yescharacteristic
349#328C22×C1712yes—
350#328C22×C1712yes—
351#327C22×C1712yes—
352#327C22×C1712yes—
353#324C22×C1712yes—
354#324C22×C1711yescharacteristic
355#324C22×C1711yescharacteristic
356C2×C17—21no—
357C2×C17—21no—
358C2×C17—22no—
359C2×C17—41no—
360C2×C17—82no—
361C2×C17#300211yescharacteristic
362C2×C17C2×#45611yescharacteristic
363C2×C17#302611yescharacteristic
364C2×#41—21no—
365C2×#41—21no—
366C2×#41D4×C1712yes—
367C22×Q8C23×C1711yescharacteristic
368C23×C4D4×C1711yescharacteristic
369C23×C4D4×C1711yescharacteristic
370C23×C4C23×C1711yescharacteristic
371C2×Q16—22no—
372C2×SD16—22no—
373C22×C8—22no—
374C4⋊Q8—22no—
375#126—22no—
376#126—22no—
377#125—22no—
378#125—22no—
379#125—22no—
380#123—22no—
381#123—22no—
382#123—22no—
383#123—22no—
384#123—22no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—21no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8D4×C1712yes—
395C22⋊Q8C23×C1712yes—
396#121—21no—
397#121—21no—
398#121—21no—
399#121—22no—
400#121—21no—
401#121D4×C1712yes—
402#121C23×C1712yes—
403#120—22no—
404C4×Q8—22no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—22no—
412#117—22no—
413#117—21no—
414#117—21no—
415#117D4×C1712yes—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4D4×C1711yescharacteristic
425C2×C4⋊C4D4×C1711yescharacteristic
426C2×C4⋊C4C23×C1711yescharacteristic
427C2×C4⋊C4C23×C1711yescharacteristic
428C2×C4⋊C4C23×C1711yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C42—21no—
432#107—22no—
433#106—22no—
434#103—22no—
435#103—22no—
436#103—22no—
437#102—22no—
438C22⋊C8—22no—
439C22⋊C8C23×C1712yes—
440C22⋊C8C23×C1712yes—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95C23×C1711yescharacteristic
446#95C23×C1711yescharacteristic
447C17#1837911yescharacteristic, direct product factor, Sylow
448C24C2×D4×C1711yescharacteristic
449#41—42no—
450#41—42no—
451#41—82no—
452#41—82no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—22no—
456C2×Q8—81no—
457C2×Q8C2×D4×C1712yes—
458C2×D4—21no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4C2×D4×C1712yes—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—41no—
477C22×C4—81no—
478C22×C4—81no—
479C22×C4C2×D4×C1711yescharacteristic
480C22×C4C2×D4×C1711yescharacteristic
481C22×C4C2×D4×C1711yescharacteristic
482C22×C4C2×D4×C1711yescharacteristic
483C22×C4C2×D4×C1712yes—
484C22×C4C2×D4×C1712yes—
485C22×C4C2×D4×C1711yescharacteristic
486C22×C4C24×C1711yescharacteristic
487Q16—82no—
488SD16—82no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—82no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—81no—
511C4⋊C4—81no—
512C4⋊C4C2×D4×C1712yes—
513C4⋊C4C2×D4×C1712yes—
514C22⋊C4—24no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C42—22no—
527C42—22no—
528C42—22no—
529C42—81no—
530C23—21no—
531C23—21no—
532C23—22no—
533C23—22no—
534C23—41no—
535C23C17×#12011yescharacteristic
536C23C17×#12011yescharacteristic
537C23C22×D4×C1711yescharacteristic
538Q8—42no—
539Q8—42no—
540Q8—42no—
541Q8—42no—
542Q8—81no—
543D4—42no—
544D4—42no—
545D4—44no—
546D4—42no—
547D4—42no—
548D4—44no—
549D4—81no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—44no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—82no—
583C2×C4—81no—
584C2×C4—82no—
585C2×C4C17×#12012yes—
586C2×C4C17×#13512yes—
587C2×C4C22×D4×C1712yes—
588C8—42no—
589C8—42no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22C17×#45612yes—
603C22C2×C17×#12011yescharacteristic
604C22C2×C17×#13511yescharacteristic
605C22C17×#57511yescharacteristic
606C4—22no—
607C4—22no—
608C4—22no—
609C4—42no—
610C4—42no—
611C4—41no—
612C4—42no—
613C4—42no—
614C4—41no—
615C4—41no—
616C4—42no—
617C4—81no—
618C4—81no—
619C2—21no—
620C2—21no—
621C2—22no—
622C2—41no—
623C2—82no—
624C2C17×#300211yescharacteristic
625C2C2×C17×#45611yescharacteristic
626C2C17×#302611yescharacteristic
subgroupG/H
center, socleC22×C17C2×#120
commutator, Frattini, cosocleC22×C4C24×C17
prime radicalC17×#3492C2
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. C17×#3190C2semidirect
3. C17×#2583C2semidirect
4. C17×#1611C2semidirect
5. C17×#1610C2semidirect
6. C17×#1609C2semidirect
7. C17×#1605C2semidirect
8. C17×#1604C2semidirect
9. C17×#1603C2semidirect
10. C17×#1501C2semidirect
11. C2×C17×#324C2semidirect
216. #18379C17direct (N × H)
278. #3190C2×C17semidirect
279. #2583C2×C17semidirect
280. #1611C2×C17semidirect
281. #1610C2×C17semidirect
282. #1609C2×C17semidirect
283. #1605C2×C17semidirect
284. #1604C2×C17semidirect
285. #1603C2×C17semidirect
286. #1501C2×C17semidirect
287. C2×#324C2×C17semidirect
447. C17#18379direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#34922
C17×#31902
C17×#25832
C17×#16112
C17×#16102
C17×#16092
C17×#16052
C17×#16042
C17×#16032
C17×#15012
C2×C17×#3242
#1837917