Finite Group Databasebeta

← C17×#61444 #16919188

Subgroups — C17×#61444 #16919188

Order 4352.

1978 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3481C212yesmaximal, complemented
2C17×#3403C211yesmaximal, characteristic, complemented
3C17×#3389C211yesmaximal, characteristic, complemented
4C17×#3370C212yesmaximal, complemented
5C17×#3355C211yesmaximal, characteristic, complemented
6C17×#3346C212yesmaximal, complemented
7C17×#3322C212yesmaximal, complemented
8C17×#3318C212yesmaximal, complemented
9C17×#3314C212yesmaximal, complemented
10C17×#3273C211yesmaximal, characteristic, complemented
11C17×#3264C212yesmaximal, complemented
12C17×#3171C212yesmaximal, complemented
13C17×#3168C211yesmaximal, characteristic, complemented
14C17×#3105C212yesmaximal, complemented
15C17×#3102C212yesmaximal, complemented
16C17×#3100C212yesmaximal, complemented
17C17×#2965C211yesmaximal, characteristic, complemented
18C4×C17×AGL(1,ℤ/8)C212yesmaximal, complemented
19C2×C4×D8×C17C211yesmaximal, characteristic, complemented
20C2×C17×AGL(1,ℤ/8)C2212yes—
21C22×D8×C17C2211yescharacteristic
22C17×#559C2212yescomplemented
23C17×#554C2212yescomplemented
24C17×#554C2212yescomplemented
25C17×#553—22no—
26C17×#553C2212yes—
27C17×#553C2212yescomplemented
28C17×#551—22no—
29C17×#551—22no—
30C17×#546—22no—
31C17×#546C2212yes—
32C17×#546C2212yescomplemented
33D42×C17C2212yescomplemented
34C17×#532C2212yescomplemented
35C17×#529—22no—
36C17×#529C2212yescomplemented
37C17×#529C2212yescomplemented
38C17×#525—22no—
39C17×#525—22no—
40C4×#41×C17C2211yescharacteristic
41C4×#41×C17C2212yescomplemented
42C2×C4×D4×C17—22no—
43C2×C4×D4×C17C2212yescomplemented
44C2×C4×D4×C17C2212yescomplemented
45C17×#501C2212yescomplemented
46C17×#499C2211yescharacteristic, complemented
47C17×#496C2212yescomplemented
48C17×#495C2211yescharacteristic, complemented
49C17×#490C2212yescomplemented
50C17×#489C2212yescomplemented
51C17×#488C2212yescomplemented
52C17×#485C2212yescomplemented
53C17×#484C2212yescomplemented
54C17×#482C2212yescomplemented
55C17×#481C2212yescomplemented
56C17×#480C2212yescomplemented
57C17×#480C2212yescomplemented
58C17×#479C2212yescomplemented
59C17×#478C2212yescomplemented
60C17×#478C2212yescomplemented
61C17×#478C2212yescomplemented
62C17×#474C2212yescomplemented
63C17×#474C2212yescomplemented
64C17×#469C2212yescomplemented
65C17×#469C2212yescomplemented
66C17×#468C2212yescomplemented
67C17×#468C2212yescomplemented
68C17×#467C2211yescharacteristic, complemented
69C17×#466C2211yescharacteristic
70C17×#465C2212yescomplemented
71C17×#464C2212yescomplemented
72C17×#463C2212yescomplemented
73C17×#463C2212yescomplemented
74C17×#463C2212yescomplemented
75C17×#459C2212yes—
76C17×#459C2212yescomplemented
77C17×#452C2212yescomplemented
78C17×#450C2212yescomplemented
79C17×#449C2212yes—
80C17×#447C2212yes—
81C17×#447C2212yescomplemented
82C17×#447C2212yescomplemented
83C17×#446C2211yescharacteristic, complemented
84C17×#446C2211yescharacteristic, complemented
85C17×#442C2212yes—
86C17×#442C2212yescomplemented
87C17×#440C2212yescomplemented
88C17×#440C2212yescomplemented
89C4×Q16×C17C2211yescharacteristic, complemented
90C4×SD16×C17C2212yescomplemented
91C4×SD16×C17C2212yescomplemented
92C4×SD16×C17C2212yescomplemented
93C4×D8×C17C2211yescharacteristic
94C4×D8×C17C2211yescharacteristic
95C4×D8×C17C2212yescomplemented
96C4×D8×C17C2211yescharacteristic, complemented
97C4×D8×C17C2211yescharacteristic, complemented
98C4×D8×C17C2212yescomplemented
99C4×D8×C17C2212yescomplemented
100C4×D8×C17C2212yescomplemented
101C4×D8×C17C2211yescharacteristic, complemented
102C17×#436C2211yescharacteristic, complemented
103C17×#436C2211yescharacteristic, complemented
104C17×#435C2212yescomplemented
105C17×#435C2212yescomplemented
106C17×#431C2212yescomplemented
107C17×#431C2211yescharacteristic, complemented
108C17×#428C2212yescomplemented
109C2×C17×#107C2211yescharacteristic, complemented
110C17×#418C2212yescomplemented
111C17×#417C2212yescomplemented
112C2×C17×#102C2212yescomplemented
113C4×M16×C17C2212yescomplemented
114C2×C4×C8×C17C2211yescharacteristic, complemented
115C2×#41×C17—22no—
116C2×#41×C17D411yescharacteristic
117C2×#41×C17C2312yes—
118C22×D4×C17—22no—
119C22×D4×C17C2312yes—
120C22×D4×C17C2312yes—
121C23×C4×C17—22no—
122C23×C4×C17—22no—
123C17×AGL(1,ℤ/8)—28no—
124C2×Q16×C17C2311yescharacteristic
125C2×SD16×C17C2312yes—
126C2×SD16×C17C2312yes—
127C2×SD16×C17C2312yes—
128C2×D8×C17—24no—
129C2×D8×C17C2311yescharacteristic
130C2×D8×C17C2312yes—
131C2×D8×C17C2312yes—
132C2×D8×C17C2311yescharacteristic
133C2×D8×C17C2312yes—
134C2×D8×C17C2311yescharacteristic
135C2×M16×C17C2312yes—
136C2×M16×C17C2312yes—
137C22×C8×C17C2311yescharacteristic
138C22×C8×C17C2311yescharacteristic
139C17×C4⋊Q8C2312yes—
140C17×#127C2312yes—
141C17×#126—22no—
142C17×#126—22no—
143C17×#126—22no—
144C17×#126—22no—
145C17×#125—22no—
146C17×#125C2312yes—
147C17×#125C2312yes—
148C17×#124—22no—
149C17×#124—22no—
150C17×#124C2312yes—
151C17×#124C2312yes—
152C17×#123—22no—
153C17×#123—22no—
154C17×#123—22no—
155C17×#123—22no—
156C17×#123—22no—
157C17×#123—22no—
158C17×#123—22no—
159C17×#123—22no—
160C17×C22⋊Q8—22no—
161C17×C22⋊Q8—22no—
162C17×C22⋊Q8—22no—
163C17×C22⋊Q8—22no—
164C17×C22⋊Q8—22no—
165C17×C22⋊Q8C2312yes—
166C17×C22⋊Q8C2312yes—
167C17×#121—22no—
168C17×#121—22no—
169C17×#121—22no—
170C17×#121—22no—
171C17×#121—22no—
172C17×#121—22no—
173C17×#121C2312yes—
174C17×#121C2312yes—
175C17×#121C2312yes—
176C17×#121C2312yes—
177C17×#120—22no—
178C17×#120—22no—
179C17×#120—22no—
180C17×#120—22no—
181C4×Q8×C17D411yescharacteristic
182C4×Q8×C17C2312yes—
183C4×Q8×C17C2312yes—
184C4×Q8×C17C2311yescharacteristic
185C4×D4×C17—22no—
186C4×D4×C17—22no—
187C4×D4×C17—22no—
188C4×D4×C17—22no—
189C4×D4×C17—22no—
190C4×D4×C17—22no—
191C4×D4×C17—22no—
192C4×D4×C17—22no—
193C4×D4×C17—22no—
194C4×D4×C17—22no—
195C4×D4×C17—22no—
196C4×D4×C17—22no—
197C4×D4×C17—22no—
198C4×D4×C17D412yes—
199C4×D4×C17D411yescharacteristic
200C4×D4×C17C2312yes—
201C4×D4×C17C2312yes—
202C4×D4×C17C2312yes—
203C4×D4×C17C2312yes—
204C4×D4×C17C2312yes—
205C4×D4×C17C2312yes—
206C4×D4×C17C2312yes—
207C4×D4×C17C2312yes—
208C4×D4×C17C2312yes—
209C4×D4×C17C2311yescharacteristic
210C17×#117—22no—
211C17×#117—22no—
212C17×#117—22no—
213C17×#117D411yescharacteristic
214C17×#117D412yes—
215C17×#117C2312yes—
216C2×C4⋊C4×C17—22no—
217C2×C4⋊C4×C17C2312yes—
218C2×C4⋊C4×C17C2312yes—
219C2×C22⋊C4×C17—22no—
220C2×C22⋊C4×C17—22no—
221C2×C22⋊C4×C17—22no—
222C2×C22⋊C4×C17—22no—
223C2×C42×C17—22no—
224C2×C42×C17C2311yescharacteristic
225C2×C42×C17C2312yes—
226C17×#107C2311yescharacteristic
227C17×#107C2311yescharacteristic
228C17×#107C2311yescharacteristic
229C17×#107C2312yes—
230C17×#107C2311yescharacteristic
231C17×#107C2312yes—
232C17×#107C2312yes—
233C17×#106C2312yes—
234C17×#106C2312yes—
235C17×#106C2312yes—
236C17×C4⋊C8C2312yes—
237C17×C4⋊C8C2312yes—
238C17×C4⋊C8C2311yescharacteristic
239C17×C4⋊C8C2311yescharacteristic
240C17×#103C2312yes—
241C17×#103C2312yes—
242C17×#103C2312yes—
243C17×#103C2312yes—
244C17×#102C2312yes—
245C17×#102C2312yes—
246C17×#102C2312yes—
247C17×#102C2312yes—
248C17×#102C2312yes—
249C17×#102C2312yes—
250C17×#102C2312yes—
251C17×#102C2312yes—
252C17×#102C2312yes—
253C17×#102C2312yes—
254C17×#102C2312yes—
255C17×#102C2312yes—
256C17×C22⋊C8C2312yes—
257C17×C22⋊C8C2312yes—
258C17×C22⋊C8C2312yes—
259C17×#97C2312yes—
260C17×#97C2312yes—
261C4×C8×C17C2311yescharacteristic
262C4×C8×C17C2311yescharacteristic
263C4×C8×C17C2311yescharacteristic
264C4×C8×C17C2311yescharacteristic
265C4×C8×C17C2312yes—
266C24×C17—22no—
267C24×C17—22no—
268#41×C17—24no—
269#41×C17—42no—
270#41×C17—42no—
271#41×C17—84no—
272C2×Q8×C17—22no—
273C2×Q8×C17C2×D411yescharacteristic
274C2×Q8×C17C2412yes—
275C2×D4×C17—24no—
276C2×D4×C17—24no—
277C2×D4×C17—22no—
278C2×D4×C17—22no—
279C2×D4×C17—22no—
280C2×D4×C17—22no—
281C2×D4×C17—22no—
282C2×D4×C17—22no—
283C2×D4×C17—22no—
284C2×D4×C17—22no—
285C2×D4×C17—22no—
286C2×D4×C17—42no—
287C2×D4×C17—42no—
288C2×D4×C17—48no—
289C2×D4×C17C2×D412yes—
290C2×D4×C17C2×D411yescharacteristic
291C2×D4×C17C2412yes—
292C2×D4×C17C2412yes—
293C2×D4×C17C2412yes—
294C22×C4×C17—22no—
295C22×C4×C17—22no—
296C22×C4×C17—22no—
297C22×C4×C17—22no—
298C22×C4×C17—22no—
299C22×C4×C17—22no—
300C22×C4×C17—22no—
301C22×C4×C17—22no—
302C22×C4×C17—22no—
303C22×C4×C17—22no—
304C22×C4×C17—22no—
305C22×C4×C17—84no—
306C22×C4×C17—84no—
307C22×C4×C17C2×D411yescharacteristic
308C22×C4×C17C2×D411yescharacteristic
309C22×C4×C17C2×D412yes—
310C22×C4×C17C2×D412yes—
311C22×C4×C17C2411yescharacteristic
312C22×C4×C17C2412yes—
313Q16×C17—41no—
314SD16×C17—24no—
315SD16×C17—24no—
316SD16×C17—42no—
317D8×C17—24no—
318D8×C17—24no—
319D8×C17—22no—
320D8×C17—41no—
321D8×C17—42no—
322D8×C17#4114yescomplemented
323M16×C17—24no—
324M16×C17—42no—
325C2×C8×C17—22no—
326C2×C8×C17—41no—
327C2×C8×C17C2411yescharacteristic
328C2×C8×C17C2411yescharacteristic
329C2×C8×C17C2411yescharacteristic
330C2×C8×C17C2412yes—
331C2×C8×C17C2412yes—
332C2×C8×C17C2411yescharacteristic
333C4⋊C4×C17—22no—
334C4⋊C4×C17—22no—
335C4⋊C4×C17—22no—
336C4⋊C4×C17—22no—
337C4⋊C4×C17—22no—
338C4⋊C4×C17—22no—
339C4⋊C4×C17—22no—
340C4⋊C4×C17—22no—
341C4⋊C4×C17—22no—
342C4⋊C4×C17—22no—
343C4⋊C4×C17—22no—
344C4⋊C4×C17C2×D411yescharacteristic
345C4⋊C4×C17C2×D412yes—
346C4⋊C4×C17C2×D411yescharacteristic
347C4⋊C4×C17C2×D412yes—
348C4⋊C4×C17C2412yes—
349C4⋊C4×C17C2412yes—
350C4⋊C4×C17C2412yes—
351C4⋊C4×C17C2412yes—
352C22⋊C4×C17—22no—
353C22⋊C4×C17—22no—
354C22⋊C4×C17—22no—
355C22⋊C4×C17—22no—
356C22⋊C4×C17—22no—
357C22⋊C4×C17—22no—
358C22⋊C4×C17—22no—
359C22⋊C4×C17—22no—
360C22⋊C4×C17—22no—
361C22⋊C4×C17—22no—
362C22⋊C4×C17—22no—
363C22⋊C4×C17—22no—
364C22⋊C4×C17—22no—
365C22⋊C4×C17—22no—
366C22⋊C4×C17—22no—
367C22⋊C4×C17—22no—
368C22⋊C4×C17—22no—
369C22⋊C4×C17—22no—
370C22⋊C4×C17—22no—
371C22⋊C4×C17C2×D412yes—
372C22⋊C4×C17C2×D412yes—
373C22⋊C4×C17C2×D412yes—
374C42×C17—22no—
375C42×C17—22no—
376C42×C17—22no—
377C42×C17C2×D412yes—
378C42×C17C2×D411yescharacteristic
379C42×C17C2×D412yes—
380C42×C17C2×D411yescharacteristic
381C42×C17C2411yescharacteristic
382C42×C17C2412yes—
383C42×C17C2411yescharacteristic
384#61444C1711yesmaximal, characteristic, direct product factor, Sylow
385C23×C17—22no—
386C23×C17—22no—
387C23×C17—22no—
388C23×C17—44no—
389C23×C17—44no—
390C23×C17—44no—
391C23×C17—44no—
392C23×C17—82no—
393C23×C17—82no—
394C23×C17C22×D412yes—
395C23×C17C22×D411yescharacteristic
396Q8×C17—22no—
397Q8×C17—22no—
398Q8×C17—41no—
399Q8×C17—82no—
400D4×C17—24no—
401D4×C17—22no—
402D4×C17—22no—
403D4×C17—22no—
404D4×C17—22no—
405D4×C17—22no—
406D4×C17—41no—
407D4×C17—44no—
408D4×C17—44no—
409D4×C17—44no—
410D4×C17—44no—
411D4×C17—44no—
412D4×C17—44no—
413D4×C17—82no—
414D4×C17—82no—
415D4×C17—82no—
416D4×C17C2×#4114yes—
417C2×C4×C17—22no—
418C2×C4×C17—22no—
419C2×C4×C17—24no—
420C2×C4×C17—21no—
421C2×C4×C17—22no—
422C2×C4×C17—21no—
423C2×C4×C17—22no—
424C2×C4×C17—22no—
425C2×C4×C17—22no—
426C2×C4×C17—22no—
427C2×C4×C17—22no—
428C2×C4×C17—22no—
429C2×C4×C17—42no—
430C2×C4×C17—44no—
431C2×C4×C17—44no—
432C2×C4×C17—44no—
433C2×C4×C17—44no—
434C2×C4×C17—44no—
435C2×C4×C17—82no—
436C2×C4×C17—82no—
437C2×C4×C17—82no—
438C2×C4×C17—82no—
439C2×C4×C17—82no—
440C2×C4×C17—82no—
441C2×C4×C17C22×D412yes—
442C2×C4×C17C22×D412yes—
443C2×C4×C17C22×D411yescharacteristic
444C2×C4×C17C22×D411yescharacteristic
445C2×C4×C17C22×D411yescharacteristic
446C2×C4×C17C22×D411yescharacteristic
447C2×C4×C17C22×D412yes—
448C2×C4×C17C22×D411yescharacteristic
449C2×C4×C17C2511yescharacteristic
450C8×C17—21no—
451C8×C17—22no—
452C8×C17—21no—
453C8×C17—21no—
454C8×C17—22no—
455C8×C17C2×#4112yes—
456#3481C2×C1712yescomplemented
457#3403C2×C1711yescharacteristic, complemented
458#3389C2×C1711yescharacteristic, complemented
459#3370C2×C1712yescomplemented
460#3355C2×C1711yescharacteristic, complemented
461#3346C2×C1712yescomplemented
462#3322C2×C1712yescomplemented
463#3318C2×C1712yescomplemented
464#3314C2×C1712yescomplemented
465#3273C2×C1711yescharacteristic, complemented
466#3264C2×C1712yescomplemented
467#3171C2×C1712yescomplemented
468#3168C2×C1711yescharacteristic, complemented
469#3105C2×C1712yescomplemented
470#3102C2×C1712yescomplemented
471#3100C2×C1712yescomplemented
472#2965C2×C1711yescharacteristic, complemented
473C4×AGL(1,ℤ/8)C2×C1712yescomplemented
474C2×C4×D8C2×C1711yescharacteristic, complemented
475C22×C17—21no—
476C22×C17—21no—
477C22×C17—22no—
478C22×C17—24no—
479C22×C17—22no—
480C22×C17—22no—
481C22×C17—42no—
482C22×C17—42no—
483C22×C17—42no—
484C22×C17—42no—
485C22×C17—42no—
486C22×C17—42no—
487C22×C17—42no—
488C22×C17—42no—
489C22×C17—88no—
490C22×C17—88no—
491C22×C17#57512yes—
492C22×C17C23×D411yescharacteristic
493C4×C17—22no—
494C4×C17—21no—
495C4×C17—21no—
496C4×C17—21no—
497C4×C17—22no—
498C4×C17—21no—
499C4×C17—22no—
500C4×C17—42no—
501C4×C17—42no—
502C4×C17—42no—
503C4×C17—42no—
504C4×C17—42no—
505C4×C17#57612yes—
506C4×C17C22×#4111yescharacteristic
507C4×C17#58511yescharacteristic
508C2×AGL(1,ℤ/8)C22×C1712yes—
509C22×D8C22×C1711yescharacteristic
510#559C22×C1712yescomplemented
511#554C22×C1712yescomplemented
512#554C22×C1712yescomplemented
513#553—22no—
514#553C22×C1712yes—
515#553C22×C1712yescomplemented
516#551—22no—
517#551—22no—
518#546—22no—
519#546C22×C1712yes—
520#546C22×C1712yescomplemented
521D42C22×C1712yescomplemented
522#532C22×C1712yescomplemented
523#529—22no—
524#529C22×C1712yescomplemented
525#529C22×C1712yescomplemented
526#525—22no—
527#525—22no—
528C4×#41C22×C1711yescharacteristic
529C4×#41C22×C1712yescomplemented
530C2×C4×D4—22no—
531C2×C4×D4C22×C1712yescomplemented
532C2×C4×D4C22×C1712yescomplemented
533#501C22×C1712yescomplemented
534#499C22×C1711yescharacteristic, complemented
535#496C22×C1712yescomplemented
536#495C22×C1711yescharacteristic, complemented
537#490C22×C1712yescomplemented
538#489C22×C1712yescomplemented
539#488C22×C1712yescomplemented
540#485C22×C1712yescomplemented
541#484C22×C1712yescomplemented
542#482C22×C1712yescomplemented
543#481C22×C1712yescomplemented
544#480C22×C1712yescomplemented
545#480C22×C1712yescomplemented
546#479C22×C1712yescomplemented
547#478C22×C1712yescomplemented
548#478C22×C1712yescomplemented
549#478C22×C1712yescomplemented
550#474C22×C1712yescomplemented
551#474C22×C1712yescomplemented
552#469C22×C1712yescomplemented
553#469C22×C1712yescomplemented
554#468C22×C1712yescomplemented
555#468C22×C1712yescomplemented
556#467C22×C1711yescharacteristic, complemented
557#466C22×C1711yescharacteristic
558#465C22×C1712yescomplemented
559#464C22×C1712yescomplemented
560#463C22×C1712yescomplemented
561#463C22×C1712yescomplemented
562#463C22×C1712yescomplemented
563#459C22×C1712yes—
564#459C22×C1712yescomplemented
565#452C22×C1712yescomplemented
566#450C22×C1712yescomplemented
567#449C22×C1712yes—
568#447C22×C1712yes—
569#447C22×C1712yescomplemented
570#447C22×C1712yescomplemented
571#446C22×C1711yescharacteristic, complemented
572#446C22×C1711yescharacteristic, complemented
573#442C22×C1712yes—
574#442C22×C1712yescomplemented
575#440C22×C1712yescomplemented
576#440C22×C1712yescomplemented
577C4×Q16C22×C1711yescharacteristic, complemented
578C4×SD16C22×C1712yescomplemented
579C4×SD16C22×C1712yescomplemented
580C4×SD16C22×C1712yescomplemented
581C4×D8C22×C1711yescharacteristic
582C4×D8C22×C1711yescharacteristic
583C4×D8C22×C1711yescharacteristic, complemented
584C4×D8C22×C1711yescharacteristic, complemented
585C4×D8C22×C1712yescomplemented
586C4×D8C22×C1712yescomplemented
587C4×D8C22×C1712yescomplemented
588C4×D8C22×C1712yescomplemented
589C4×D8C22×C1711yescharacteristic, complemented
590#436C22×C1711yescharacteristic, complemented
591#436C22×C1711yescharacteristic, complemented
592#435C22×C1712yescomplemented
593#435C22×C1712yescomplemented
594#431C22×C1712yescomplemented
595#431C22×C1711yescharacteristic, complemented
596#428C22×C1712yescomplemented
597C2×#107C22×C1711yescharacteristic, complemented
598#418C22×C1712yescomplemented
599#417C22×C1712yescomplemented
600C2×#102C22×C1712yescomplemented
601C4×M16C22×C1712yescomplemented
602C2×C4×C8C22×C1711yescharacteristic, complemented
603C2×C17—22no—
604C2×C17—42no—
605C2×C17—44no—
606C2×C17—82no—
607C2×C17—82no—
608C2×C17D4×#4111yescharacteristic
609C2×C17C2×#57511yescharacteristic
610C2×C17C2×#57611yescharacteristic
611C2×#41—22no—
612C2×#41D4×C1711yescharacteristic
613C2×#41C23×C1712yes—
614C22×D4—22no—
615C22×D4C23×C1712yes—
616C22×D4C23×C1712yes—
617C23×C4—22no—
618C23×C4—22no—
619AGL(1,ℤ/8)—28no—
620C2×Q16C23×C1711yescharacteristic
621C2×SD16C23×C1712yes—
622C2×SD16C23×C1712yes—
623C2×SD16C23×C1712yes—
624C2×D8—24no—
625C2×D8C23×C1712yes—
626C2×D8C23×C1711yescharacteristic
627C2×D8C23×C1712yes—
628C2×D8C23×C1712yes—
629C2×D8C23×C1711yescharacteristic
630C2×D8C23×C1711yescharacteristic
631C2×M16C23×C1712yes—
632C2×M16C23×C1712yes—
633C22×C8C23×C1711yescharacteristic
634C22×C8C23×C1711yescharacteristic
635C4⋊Q8C23×C1712yes—
636#127C23×C1712yes—
637#126—22no—
638#126—22no—
639#126—22no—
640#126—22no—
641#125—22no—
642#125C23×C1712yes—
643#125C23×C1712yes—
644#124—22no—
645#124—22no—
646#124C23×C1712yes—
647#124C23×C1712yes—
648#123—22no—
649#123—22no—
650#123—22no—
651#123—22no—
652#123—22no—
653#123—22no—
654#123—22no—
655#123—22no—
656C22⋊Q8—22no—
657C22⋊Q8—22no—
658C22⋊Q8—22no—
659C22⋊Q8—22no—
660C22⋊Q8—22no—
661C22⋊Q8C23×C1712yes—
662C22⋊Q8C23×C1712yes—
663#121—22no—
664#121—22no—
665#121—22no—
666#121—22no—
667#121—22no—
668#121—22no—
669#121C23×C1712yes—
670#121C23×C1712yes—
671#121C23×C1712yes—
672#121C23×C1712yes—
673#120—22no—
674#120—22no—
675#120—22no—
676#120—22no—
677C4×Q8D4×C1711yescharacteristic
678C4×Q8C23×C1712yes—
679C4×Q8C23×C1712yes—
680C4×Q8C23×C1711yescharacteristic
681C4×D4—22no—
682C4×D4—22no—
683C4×D4—22no—
684C4×D4—22no—
685C4×D4—22no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—22no—
689C4×D4—22no—
690C4×D4—22no—
691C4×D4—22no—
692C4×D4—22no—
693C4×D4—22no—
694C4×D4D4×C1712yes—
695C4×D4D4×C1711yescharacteristic
696C4×D4C23×C1712yes—
697C4×D4C23×C1712yes—
698C4×D4C23×C1712yes—
699C4×D4C23×C1712yes—
700C4×D4C23×C1712yes—
701C4×D4C23×C1712yes—
702C4×D4C23×C1712yes—
703C4×D4C23×C1712yes—
704C4×D4C23×C1712yes—
705C4×D4C23×C1711yescharacteristic
706#117—22no—
707#117—22no—
708#117—22no—
709#117D4×C1711yescharacteristic
710#117D4×C1712yes—
711#117C23×C1712yes—
712C2×C4⋊C4—22no—
713C2×C4⋊C4C23×C1712yes—
714C2×C4⋊C4C23×C1712yes—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C42—22no—
720C2×C42C23×C1711yescharacteristic
721C2×C42C23×C1712yes—
722#107C23×C1711yescharacteristic
723#107C23×C1711yescharacteristic
724#107C23×C1712yes—
725#107C23×C1712yes—
726#107C23×C1711yescharacteristic
727#107C23×C1712yes—
728#107C23×C1711yescharacteristic
729#106C23×C1712yes—
730#106C23×C1712yes—
731#106C23×C1712yes—
732C4⋊C8C23×C1712yes—
733C4⋊C8C23×C1712yes—
734C4⋊C8C23×C1711yescharacteristic
735C4⋊C8C23×C1711yescharacteristic
736#103C23×C1712yes—
737#103C23×C1712yes—
738#103C23×C1712yes—
739#103C23×C1712yes—
740#102C23×C1712yes—
741#102C23×C1712yes—
742#102C23×C1712yes—
743#102C23×C1712yes—
744#102C23×C1712yes—
745#102C23×C1712yes—
746#102C23×C1712yes—
747#102C23×C1712yes—
748#102C23×C1712yes—
749#102C23×C1712yes—
750#102C23×C1712yes—
751#102C23×C1712yes—
752C22⋊C8C23×C1712yes—
753C22⋊C8C23×C1712yes—
754C22⋊C8C23×C1712yes—
755#97C23×C1712yes—
756#97C23×C1712yes—
757C4×C8C23×C1711yescharacteristic
758C4×C8C23×C1711yescharacteristic
759C4×C8C23×C1711yescharacteristic
760C4×C8C23×C1711yescharacteristic
761C4×C8C23×C1712yes—
762C17#6144411yescharacteristic, direct product factor, Sylow
763C24—22no—
764C24—22no—
765#41—24no—
766#41—42no—
767#41—42no—
768#41—84no—
769C2×Q8—22no—
770C2×Q8C2×D4×C1711yescharacteristic
771C2×Q8C24×C1712yes—
772C2×D4—24no—
773C2×D4—24no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—22no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—48no—
786C2×D4C2×D4×C1712yes—
787C2×D4C2×D4×C1711yescharacteristic
788C2×D4C24×C1712yes—
789C2×D4C24×C1712yes—
790C2×D4C24×C1712yes—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—84no—
803C22×C4—84no—
804C22×C4C2×D4×C1711yescharacteristic
805C22×C4C2×D4×C1711yescharacteristic
806C22×C4C2×D4×C1712yes—
807C22×C4C2×D4×C1712yes—
808C22×C4C24×C1711yescharacteristic
809C22×C4C24×C1712yes—
810Q16—41no—
811SD16—24no—
812SD16—24no—
813SD16—42no—
814D8—24no—
815D8—24no—
816D8—22no—
817D8—41no—
818D8—42no—
819D8#41×C1714yescomplemented
820M16—24no—
821M16—42no—
822C2×C8—22no—
823C2×C8—41no—
824C2×C8C24×C1711yescharacteristic
825C2×C8C24×C1711yescharacteristic
826C2×C8C24×C1711yescharacteristic
827C2×C8C24×C1712yes—
828C2×C8C24×C1712yes—
829C2×C8C24×C1711yescharacteristic
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4C2×D4×C1712yes—
842C4⋊C4C2×D4×C1711yescharacteristic
843C4⋊C4C2×D4×C1712yes—
844C4⋊C4C2×D4×C1711yescharacteristic
845C4⋊C4C24×C1712yes—
846C4⋊C4C24×C1712yes—
847C4⋊C4C24×C1712yes—
848C4⋊C4C24×C1712yes—
849C22⋊C4—22no—
850C22⋊C4—22no—
851C22⋊C4—22no—
852C22⋊C4—22no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—22no—
856C22⋊C4—22no—
857C22⋊C4—22no—
858C22⋊C4—22no—
859C22⋊C4—22no—
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—22no—
863C22⋊C4—22no—
864C22⋊C4—22no—
865C22⋊C4—22no—
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4C2×D4×C1712yes—
869C22⋊C4C2×D4×C1712yes—
870C22⋊C4C2×D4×C1712yes—
871C42—22no—
872C42—22no—
873C42—22no—
874C42C2×D4×C1712yes—
875C42C2×D4×C1711yescharacteristic
876C42C2×D4×C1712yes—
877C42C2×D4×C1711yescharacteristic
878C42C24×C1711yescharacteristic
879C42C24×C1711yescharacteristic
880C42C24×C1712yes—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—44no—
885C23—44no—
886C23—44no—
887C23—44no—
888C23—82no—
889C23—82no—
890C23C22×D4×C1712yes—
891C23C22×D4×C1711yescharacteristic
892Q8—22no—
893Q8—22no—
894Q8—41no—
895Q8—82no—
896D4—24no—
897D4—22no—
898D4—22no—
899D4—22no—
900D4—22no—
901D4—22no—
902D4—41no—
903D4—44no—
904D4—44no—
905D4—44no—
906D4—44no—
907D4—44no—
908D4—44no—
909D4—82no—
910D4—82no—
911D4—82no—
912D4C2×#41×C1714yes—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—24no—
916C2×C4—21no—
917C2×C4—22no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—42no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—82no—
932C2×C4—82no—
933C2×C4—82no—
934C2×C4—82no—
935C2×C4—82no—
936C2×C4—82no—
937C2×C4C22×D4×C1712yes—
938C2×C4C22×D4×C1712yes—
939C2×C4C22×D4×C1711yescharacteristic
940C2×C4C22×D4×C1711yescharacteristic
941C2×C4C22×D4×C1711yescharacteristic
942C2×C4C22×D4×C1711yescharacteristic
943C2×C4C22×D4×C1712yes—
944C2×C4C22×D4×C1711yescharacteristic
945C2×C4C25×C1711yescharacteristic
946C8—21no—
947C8—22no—
948C8—21no—
949C8—21no—
950C8—22no—
951C8C2×#41×C1712yes—
952C22—21no—
953C22—21no—
954C22—22no—
955C22—24no—
956C22—22no—
957C22—22no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—88no—
967C22—88no—
968C22C17×#57512yes—
969C22C23×D4×C1711yescharacteristic
970C4—22no—
971C4—21no—
972C4—21no—
973C4—21no—
974C4—22no—
975C4—21no—
976C4—22no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4C17×#57612yes—
983C4C22×#41×C1711yescharacteristic
984C4C17×#58511yescharacteristic
985C2—22no—
986C2—42no—
987C2—44no—
988C2—82no—
989C2—82no—
990C2D4×#41×C1711yescharacteristic
991C2C2×C17×#57511yescharacteristic
992C2C2×C17×#57611yescharacteristic
subgroupG/H
centerC2×C4×C17C22×D4
commutator, Frattini, cosocleC2×C4C25×C17
socleC22×C17C23×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C17 ◁ C4×#41×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#3481C2semidirect
2. C17×#3403C2semidirect
3. C17×#3389C2semidirect
4. C17×#3370C2semidirect
5. C17×#3355C2semidirect
6. C17×#3346C2semidirect
7. C17×#3322C2semidirect
8. C17×#3318C2semidirect
9. C17×#3314C2semidirect
10. C17×#3273C2semidirect
11. C17×#3264C2semidirect
12. C17×#3171C2semidirect
13. C17×#3168C2semidirect
14. C17×#3105C2semidirect
15. C17×#3102C2semidirect
16. C17×#3100C2semidirect
17. C17×#2965C2semidirect
18. C4×C17×AGL(1,ℤ/8)C2semidirect
19. C2×C4×D8×C17C2semidirect
22. C17×#559C22semidirect
23. C17×#554C22semidirect
24. C17×#554C22semidirect
27. C17×#553C22semidirect
32. C17×#546C22semidirect
33. D42×C17C22semidirect
34. C17×#532C22semidirect
36. C17×#529C22semidirect
37. C17×#529C22semidirect
41. C4×#41×C17C22semidirect
43. C2×C4×D4×C17C22semidirect
44. C2×C4×D4×C17C22semidirect
45. C17×#501C22semidirect
46. C17×#499C22semidirect
47. C17×#496C22semidirect
48. C17×#495C22semidirect
49. C17×#490C22semidirect
50. C17×#489C22semidirect
51. C17×#488C22semidirect
52. C17×#485C22semidirect
53. C17×#484C22semidirect
54. C17×#482C22semidirect
55. C17×#481C22semidirect
56. C17×#480C22semidirect
57. C17×#480C22semidirect
58. C17×#479C22semidirect
59. C17×#478C22semidirect
60. C17×#478C22semidirect
61. C17×#478C22semidirect
62. C17×#474C22semidirect
63. C17×#474C22semidirect
64. C17×#469C22semidirect
65. C17×#469C22semidirect
66. C17×#468C22semidirect
67. C17×#468C22semidirect
68. C17×#467C22semidirect
70. C17×#465C22semidirect
71. C17×#464C22semidirect
72. C17×#463C22semidirect
73. C17×#463C22semidirect
74. C17×#463C22semidirect
76. C17×#459C22semidirect
77. C17×#452C22semidirect
78. C17×#450C22semidirect
81. C17×#447C22semidirect
82. C17×#447C22semidirect
83. C17×#446C22semidirect
84. C17×#446C22semidirect
86. C17×#442C22semidirect
87. C17×#440C22semidirect
88. C17×#440C22semidirect
89. C4×Q16×C17C22semidirect
90. C4×SD16×C17C22semidirect
91. C4×SD16×C17C22semidirect
92. C4×SD16×C17C22semidirect
95. C4×D8×C17C22semidirect
96. C4×D8×C17C22semidirect
97. C4×D8×C17C22semidirect
98. C4×D8×C17C22semidirect
99. C4×D8×C17C22semidirect
100. C4×D8×C17C22semidirect
101. C4×D8×C17C22semidirect
102. C17×#436C22semidirect
103. C17×#436C22semidirect
104. C17×#435C22semidirect
105. C17×#435C22semidirect
106. C17×#431C22semidirect
107. C17×#431C22semidirect
108. C17×#428C22semidirect
109. C2×C17×#107C22semidirect
110. C17×#418C22semidirect
111. C17×#417C22semidirect
112. C2×C17×#102C22semidirect
113. C4×M16×C17C22semidirect
114. C2×C4×C8×C17C22semidirect
322. D8×C17#41semidirect
384. #61444C17direct (N × H)
456. #3481C2×C17semidirect
457. #3403C2×C17semidirect
458. #3389C2×C17semidirect
459. #3370C2×C17semidirect
460. #3355C2×C17semidirect
461. #3346C2×C17semidirect
462. #3322C2×C17semidirect
463. #3318C2×C17semidirect
464. #3314C2×C17semidirect
465. #3273C2×C17semidirect
466. #3264C2×C17semidirect
467. #3171C2×C17semidirect
468. #3168C2×C17semidirect
469. #3105C2×C17semidirect
470. #3102C2×C17semidirect
471. #3100C2×C17semidirect
472. #2965C2×C17semidirect
473. C4×AGL(1,ℤ/8)C2×C17semidirect
474. C2×C4×D8C2×C17semidirect
510. #559C22×C17semidirect
511. #554C22×C17semidirect
512. #554C22×C17semidirect
515. #553C22×C17semidirect
520. #546C22×C17semidirect
521. D42C22×C17semidirect
522. #532C22×C17semidirect
524. #529C22×C17semidirect
525. #529C22×C17semidirect
529. C4×#41C22×C17semidirect
531. C2×C4×D4C22×C17semidirect
532. C2×C4×D4C22×C17semidirect
533. #501C22×C17semidirect
534. #499C22×C17semidirect
535. #496C22×C17semidirect
536. #495C22×C17semidirect
537. #490C22×C17semidirect
538. #489C22×C17semidirect
539. #488C22×C17semidirect
540. #485C22×C17semidirect
541. #484C22×C17semidirect
542. #482C22×C17semidirect
543. #481C22×C17semidirect
544. #480C22×C17semidirect
545. #480C22×C17semidirect
546. #479C22×C17semidirect
547. #478C22×C17semidirect
548. #478C22×C17semidirect
549. #478C22×C17semidirect
550. #474C22×C17semidirect
551. #474C22×C17semidirect
552. #469C22×C17semidirect
553. #469C22×C17semidirect
554. #468C22×C17semidirect
555. #468C22×C17semidirect
556. #467C22×C17semidirect
558. #465C22×C17semidirect
559. #464C22×C17semidirect
560. #463C22×C17semidirect
561. #463C22×C17semidirect
562. #463C22×C17semidirect
564. #459C22×C17semidirect
565. #452C22×C17semidirect
566. #450C22×C17semidirect
569. #447C22×C17semidirect
570. #447C22×C17semidirect
571. #446C22×C17semidirect
572. #446C22×C17semidirect
574. #442C22×C17semidirect
575. #440C22×C17semidirect
576. #440C22×C17semidirect
577. C4×Q16C22×C17semidirect
578. C4×SD16C22×C17semidirect
579. C4×SD16C22×C17semidirect
580. C4×SD16C22×C17semidirect
583. C4×D8C22×C17semidirect
584. C4×D8C22×C17semidirect
585. C4×D8C22×C17semidirect
586. C4×D8C22×C17semidirect
587. C4×D8C22×C17semidirect
588. C4×D8C22×C17semidirect
589. C4×D8C22×C17semidirect
590. #436C22×C17semidirect
591. #436C22×C17semidirect
592. #435C22×C17semidirect
593. #435C22×C17semidirect
594. #431C22×C17semidirect
595. #431C22×C17semidirect
596. #428C22×C17semidirect
597. C2×#107C22×C17semidirect
598. #418C22×C17semidirect
599. #417C22×C17semidirect
600. C2×#102C22×C17semidirect
601. C4×M16C22×C17semidirect
602. C2×C4×C8C22×C17semidirect
762. C17#61444direct (N × H)
819. D8#41×C17semidirect

Maximal subgroups

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

subgroupindex
C17×#34812
C17×#34032
C17×#33892
C17×#33702
C17×#33552
C17×#33462
C17×#33222
C17×#33182
C17×#33142
C17×#32732
C17×#32642
C17×#31712
C17×#31682
C17×#31052
C17×#31022
C17×#31002
C17×#29652
C4×C17×AGL(1,ℤ/8)2
C2×C4×D8×C172
#6144417