Finite Group Databasebeta

← C17×#61908 #16919652

Subgroups — C17×#61908 #16919652

Order 4352.

1734 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3507C211yesmaximal, characteristic, complemented
2C17×#3480C211yesmaximal, characteristic, complemented
3C17×#3402C212yesmaximal, complemented
4C17×#3401C212yesmaximal, complemented
5C17×#3400C211yesmaximal, characteristic, complemented
6C17×#3399C211yesmaximal, characteristic, complemented
7C17×#3396C211yesmaximal, characteristic, complemented
8C17×#3394C211yesmaximal, characteristic, complemented
9C17×#3376C212yesmaximal, complemented
10C17×#3374C211yesmaximal, characteristic, complemented
11C17×#3370C212yesmaximal, complemented
12C17×#3368C211yesmaximal, characteristic, complemented
13C17×#3365C211yesmaximal, characteristic, complemented
14C17×#3364C211yesmaximal, characteristic, complemented
15C17×#3219C212yesmaximal, complemented
16C17×#3216C211yesmaximal, characteristic, complemented
17C17×#3212C212yesmaximal, complemented
18C17×#3207C211yesmaximal, characteristic, complemented
19C17×#3115C211yesmaximal, characteristic, complemented
20C17×#3111C212yesmaximal, complemented
21C17×#3107C211yesmaximal, characteristic, complemented
22C17×#3102C212yesmaximal, complemented
23C17×#2984C211yesmaximal, characteristic, complemented
24C17×#559C2211yescharacteristic
25C17×#559C2212yes—
26C17×#559C2211yescharacteristic
27C17×#559C2211yescharacteristic
28C17×#557C2211yescharacteristic
29C17×#557C2211yescharacteristic
30C17×#557C2211yescharacteristic
31C17×#556—21no—
32C17×#556—21no—
33C17×#556C2211yescharacteristic
34C17×#556C2212yes—
35C17×#556C2212yes—
36C17×#554C2212yes—
37C17×#553—21no—
38C17×#553—22no—
39C17×#552—22no—
40C17×#550C2211yescharacteristic
41C17×#548—21no—
42C17×#539—22no—
43C17×#536—21no—
44C17×#533C2211yescharacteristic
45C17×#532C2211yescharacteristic
46C17×#532C2211yescharacteristic
47C17×#532C2212yes—
48C17×#529—22no—
49C17×#529—21no—
50C17×#529C2212yes—
51C17×#529C2212yes—
52C17×#520—21no—
53C4×#41×C17—21no—
54C4×#41×C17C2212yes—
55C4×#41×C17C2211yescharacteristic
56C2×C4×Q8×C17C2211yescharacteristic
57C17×#497C2212yes—
58C17×#497C2212yes—
59C17×#496C2212yes—
60C17×#495C2212yes—
61C17×#495C2212yes—
62C17×#493C2211yescharacteristic
63C17×#492C2211yescharacteristic
64C17×#491C2212yes—
65C17×#490C2212yes—
66C17×#489C2212yes—
67C17×#488C2212yes—
68C17×#488C2212yes—
69C17×#487C2211yescharacteristic
70C17×#486C2211yescharacteristic
71C17×#485C2211yescharacteristic
72C17×#485C2211yescharacteristic
73C17×#482C2212yes—
74C17×#479C2212yes—
75C17×#479C2212yes—
76C17×#478C2212yes—
77C17×#478C2212yes—
78C17×#475C2211yescharacteristic
79C17×#475C2211yescharacteristic
80C17×#474C2211yescharacteristic
81C17×#474C2211yescharacteristic
82C17×#464C2212yes—
83C17×#464C2212yes—
84C17×#464C2212yes—
85C17×#464C2212yes—
86C17×#463C2212yes—
87C17×#463C2212yes—
88C17×#463C2212yes—
89C17×#463C2212yes—
90C17×#463C2212yes—
91C17×#463C2212yes—
92C17×#462C2212yes—
93C17×#462C2211yescharacteristic
94C17×#462C2211yescharacteristic
95C17×#462C2211yescharacteristic
96C17×#461C2212yes—
97C17×#461C2211yescharacteristic
98C17×#460C2212yes—
99C17×#460C2211yescharacteristic
100C17×#460C2211yescharacteristic
101C17×#460C2211yescharacteristic
102C17×#459C2212yes—
103C17×#459C2211yescharacteristic
104C17×#452C2211yescharacteristic
105C17×#452C2212yes—
106C17×#452C2212yes—
107C17×#452C2211yescharacteristic
108C17×#449C2212yes—
109C17×#449C2212yes—
110C17×#449C2212yes—
111C17×#446C2211yescharacteristic
112C17×#446C2212yes—
113C17×#446C2211yescharacteristic
114C17×#446C2212yes—
115C8×Q8×C17C2211yescharacteristic
116C8×Q8×C17C2211yescharacteristic
117C17×#442C2212yes—
118C17×#442C2212yes—
119C17×#441C2212yes—
120C17×#440C2212yes—
121C17×#440C2212yes—
122C17×#440C2212yes—
123C4×Q16×C17C2212yes—
124C4×Q16×C17C2211yescharacteristic
125C4×Q16×C17C2211yescharacteristic
126C4×SD16×C17C2212yes—
127C4×SD16×C17C2212yes—
128C4×SD16×C17C2211yescharacteristic
129C4×SD16×C17C2211yescharacteristic
130C4×D8×C17C2212yes—
131C17×#432C2211yescharacteristic
132C17×#432C2212yes—
133C17×#431C2211yescharacteristic
134C17×#431C2212yes—
135C2×#41×C17—21no—
136C2×#41×C17—21no—
137C2×#41×C17C2312yes—
138C2×#41×C17C2311yescharacteristic
139C22×Q8×C17D411yescharacteristic
140C2×Q16×C17C2311yescharacteristic
141C2×Q16×C17C2312yes—
142C2×Q16×C17C2312yes—
143C2×Q16×C17C2311yescharacteristic
144C2×SD16×C17C2312yes—
145C2×SD16×C17C2312yes—
146C2×SD16×C17C2311yescharacteristic
147C2×SD16×C17C2312yes—
148C2×SD16×C17C2312yes—
149C2×SD16×C17C2311yescharacteristic
150C2×SD16×C17C2312yes—
151C2×D8×C17C2312yes—
152C2×D8×C17C2312yes—
153C2×D8×C17C2312yes—
154C17×C4⋊Q8—21no—
155C17×C4⋊Q8—21no—
156C17×C4⋊Q8C2312yes—
157C17×C4⋊Q8C2311yescharacteristic
158C17×C4⋊Q8C2311yescharacteristic
159C17×C4⋊Q8C2311yescharacteristic
160C17×C4⋊Q8C2311yescharacteristic
161C17×#127C2311yescharacteristic
162C17×#127C2311yescharacteristic
163C17×#127C2312yes—
164C17×#126—22no—
165C17×#126—22no—
166C17×#126—22no—
167C17×#126—22no—
168C17×#126—22no—
169C17×#126—22no—
170C17×#126—22no—
171C17×#125—22no—
172C17×#125—21no—
173C17×#125—22no—
174C17×#125—22no—
175C17×#125—21no—
176C17×#125C2312yes—
177C17×#125C2312yes—
178C17×#124—21no—
179C17×#124—22no—
180C17×#124—21no—
181C17×#124—21no—
182C17×#124—21no—
183C17×#124C2312yes—
184C17×#124C2312yes—
185C17×#124C2312yes—
186C17×#124C2312yes—
187C17×#124C2312yes—
188C17×#123—22no—
189C17×#123—22no—
190C17×#123—22no—
191C17×#123—22no—
192C17×#123—22no—
193C17×#123—22no—
194C17×#123—22no—
195C17×C22⋊Q8—21no—
196C17×C22⋊Q8—22no—
197C17×C22⋊Q8—22no—
198C17×C22⋊Q8—22no—
199C17×C22⋊Q8—21no—
200C17×C22⋊Q8—22no—
201C17×C22⋊Q8—22no—
202C17×C22⋊Q8C2311yescharacteristic
203C17×C22⋊Q8C2311yescharacteristic
204C17×#121—21no—
205C17×#121—21no—
206C17×#121—22no—
207C17×#121—21no—
208C17×#121—22no—
209C17×#121—22no—
210C17×#121—21no—
211C17×#121C2312yes—
212C4×Q8×C17—21no—
213C4×Q8×C17—21no—
214C4×Q8×C17—21no—
215C4×Q8×C17—21no—
216C4×Q8×C17D411yescharacteristic
217C4×Q8×C17D412yes—
218C4×Q8×C17D411yescharacteristic
219C4×Q8×C17C2312yes—
220C4×Q8×C17C2311yescharacteristic
221C4×Q8×C17C2311yescharacteristic
222C4×Q8×C17C2312yes—
223C4×Q8×C17C2312yes—
224C4×Q8×C17C2312yes—
225C4×Q8×C17C2311yescharacteristic
226C4×Q8×C17C2311yescharacteristic
227C4×Q8×C17C2311yescharacteristic
228C4×Q8×C17C2312yes—
229C4×Q8×C17C2311yescharacteristic
230C4×D4×C17—21no—
231C4×D4×C17—22no—
232C4×D4×C17—21no—
233C4×D4×C17—22no—
234C4×D4×C17—22no—
235C4×D4×C17—22no—
236C4×D4×C17—22no—
237C4×D4×C17—21no—
238C4×D4×C17—21no—
239C4×D4×C17—21no—
240C4×D4×C17—21no—
241C4×D4×C17—22no—
242C4×D4×C17—21no—
243C4×D4×C17—22no—
244C4×D4×C17—21no—
245C4×D4×C17C2311yescharacteristic
246C4×D4×C17C2312yes—
247C4×D4×C17C2312yes—
248C4×D4×C17C2311yescharacteristic
249C4×D4×C17C2312yes—
250C4×D4×C17C2312yes—
251C4×D4×C17C2312yes—
252C17×#117—21no—
253C17×#117—22no—
254C17×#117—21no—
255C17×#117—22no—
256C17×#117—21no—
257C17×#117—22no—
258C17×#117—22no—
259C17×#117—22no—
260C17×#117C2311yescharacteristic
261C2×C4⋊C4×C17—22no—
262C2×C4⋊C4×C17D411yescharacteristic
263C2×C4⋊C4×C17D412yes—
264C2×C42×C17—21no—
265C2×C42×C17—22no—
266C2×C42×C17C2312yes—
267C2×C42×C17C2311yescharacteristic
268C17×#107C2311yescharacteristic
269C17×#107C2311yescharacteristic
270C17×#107C2312yes—
271C17×#106C2311yescharacteristic
272C17×#106C2312yes—
273C17×#106C2311yescharacteristic
274C17×C4⋊C8C2312yes—
275C17×C4⋊C8C2312yes—
276C17×C4⋊C8C2311yescharacteristic
277C17×C4⋊C8C2311yescharacteristic
278C17×C4⋊C8C2311yescharacteristic
279C17×C4⋊C8C2311yescharacteristic
280C17×C4⋊C8C2312yes—
281C17×C4⋊C8C2312yes—
282C17×#103C2311yescharacteristic
283C17×#103C2312yes—
284C17×#103C2312yes—
285C17×#103C2312yes—
286C17×#103C2311yescharacteristic
287C17×#103C2311yescharacteristic
288C17×#103C2311yescharacteristic
289C17×#103C2311yescharacteristic
290C17×#103C2312yes—
291C17×#103C2311yescharacteristic
292C17×#103C2312yes—
293C17×#102C2312yes—
294C17×#102C2312yes—
295C17×#102C2312yes—
296C17×#102C2312yes—
297C17×#102C2311yescharacteristic
298C17×#102C2311yescharacteristic
299C17×#102C2312yes—
300C17×#102C2312yes—
301C17×#102C2312yes—
302C17×C22⋊C8C2311yescharacteristic
303C17×C22⋊C8C2311yescharacteristic
304C17×C22⋊C8C2312yes—
305C17×#97C2312yes—
306C17×#97C2312yes—
307C17×#97C2312yes—
308C4×C8×C17C2311yescharacteristic
309C4×C8×C17C2311yescharacteristic
310C4×C8×C17C2312yes—
311C4×C8×C17C2312yes—
312#41×C17—41no—
313#41×C17—42no—
314#41×C17—42no—
315#41×C17—41no—
316#41×C17—44no—
317#41×C17—44no—
318C2×Q8×C17—21no—
319C2×Q8×C17—21no—
320C2×Q8×C17—42no—
321C2×Q8×C17C2×D411yescharacteristic
322C2×Q8×C17C2×D411yescharacteristic
323C2×Q8×C17C2×D412yes—
324C2×Q8×C17C2411yescharacteristic
325C2×Q8×C17C2411yescharacteristic
326C2×Q8×C17C2411yescharacteristic
327C2×Q8×C17C2412yes—
328C2×D4×C17—22no—
329C2×D4×C17—22no—
330C2×D4×C17—21no—
331C2×D4×C17—21no—
332C2×D4×C17—22no—
333C2×D4×C17—21no—
334C2×D4×C17—21no—
335C2×D4×C17—22no—
336C2×D4×C17—21no—
337C2×D4×C17C2411yescharacteristic
338C2×D4×C17C2412yes—
339C2×D4×C17C2412yes—
340C22×C4×C17—22no—
341C22×C4×C17—22no—
342C22×C4×C17—21no—
343C22×C4×C17—22no—
344C22×C4×C17—21no—
345C22×C4×C17—22no—
346C22×C4×C17—22no—
347C22×C4×C17—22no—
348C22×C4×C17—21no—
349C22×C4×C17C2×D411yescharacteristic
350C22×C4×C17C2×D411yescharacteristic
351C22×C4×C17C2×D412yes—
352C22×C4×C17C2×D412yes—
353C22×C4×C17C2411yescharacteristic
354Q16×C17—41no—
355Q16×C17—42no—
356Q16×C17—41no—
357Q16×C17—42no—
358SD16×C17—41no—
359SD16×C17—42no—
360SD16×C17—42no—
361SD16×C17—41no—
362SD16×C17—42no—
363SD16×C17—42no—
364SD16×C17—42no—
365D8×C17—42no—
366D8×C17—42no—
367D8×C17—42no—
368C2×C8×C17C2411yescharacteristic
369C2×C8×C17C2411yescharacteristic
370C2×C8×C17C2412yes—
371C2×C8×C17C2411yescharacteristic
372C2×C8×C17C2411yescharacteristic
373C2×C8×C17C2412yes—
374C4⋊C4×C17—22no—
375C4⋊C4×C17—22no—
376C4⋊C4×C17—21no—
377C4⋊C4×C17—21no—
378C4⋊C4×C17—22no—
379C4⋊C4×C17—21no—
380C4⋊C4×C17—21no—
381C4⋊C4×C17—21no—
382C4⋊C4×C17—22no—
383C4⋊C4×C17—22no—
384C4⋊C4×C17—22no—
385C4⋊C4×C17—22no—
386C4⋊C4×C17—22no—
387C4⋊C4×C17—21no—
388C4⋊C4×C17—21no—
389C4⋊C4×C17—21no—
390C4⋊C4×C17—21no—
391C4⋊C4×C17—22no—
392C4⋊C4×C17—21no—
393C4⋊C4×C17—21no—
394C4⋊C4×C17—22no—
395C4⋊C4×C17—21no—
396C4⋊C4×C17C2×D412yes—
397C4⋊C4×C17C2×D412yes—
398C4⋊C4×C17C2×D412yes—
399C4⋊C4×C17C2×D412yes—
400C4⋊C4×C17C2×D412yes—
401C4⋊C4×C17C2×D411yescharacteristic
402C4⋊C4×C17C2×D411yescharacteristic
403C4⋊C4×C17C2411yescharacteristic
404C4⋊C4×C17C2411yescharacteristic
405C4⋊C4×C17C2412yes—
406C4⋊C4×C17C2411yescharacteristic
407C4⋊C4×C17C2411yescharacteristic
408C22⋊C4×C17—21no—
409C22⋊C4×C17—21no—
410C22⋊C4×C17—21no—
411C22⋊C4×C17—22no—
412C22⋊C4×C17—22no—
413C22⋊C4×C17—22no—
414C22⋊C4×C17—22no—
415C22⋊C4×C17—22no—
416C22⋊C4×C17—22no—
417C22⋊C4×C17—22no—
418C22⋊C4×C17—22no—
419C22⋊C4×C17—22no—
420C22⋊C4×C17—21no—
421C22⋊C4×C17—22no—
422C22⋊C4×C17—22no—
423C22⋊C4×C17—22no—
424C22⋊C4×C17—22no—
425C22⋊C4×C17—22no—
426C22⋊C4×C17—22no—
427C22⋊C4×C17—22no—
428C22⋊C4×C17—21no—
429C42×C17—22no—
430C42×C17—21no—
431C42×C17—21no—
432C42×C17—21no—
433C42×C17—22no—
434C42×C17—22no—
435C42×C17—22no—
436C42×C17—21no—
437C42×C17—21no—
438C42×C17C2×D411yescharacteristic
439C42×C17C2×D411yescharacteristic
440C42×C17C2×D412yes—
441C42×C17C2×D412yes—
442C42×C17C2412yes—
443C42×C17C2411yescharacteristic
444C42×C17C2412yes—
445C42×C17C2411yescharacteristic
446#61908C1711yesmaximal, characteristic, direct product factor, Sylow
447C23×C17—22no—
448C23×C17—21no—
449C23×C17—22no—
450C23×C17C22×D411yescharacteristic
451Q8×C17—22no—
452Q8×C17—22no—
453Q8×C17—21no—
454Q8×C17—21no—
455Q8×C17—21no—
456Q8×C17—21no—
457Q8×C17—22no—
458Q8×C17—22no—
459Q8×C17—21no—
460Q8×C17—21no—
461Q8×C17—42no—
462Q8×C17—42no—
463Q8×C17—81no—
464D4×C17—22no—
465D4×C17—21no—
466D4×C17—22no—
467D4×C17—22no—
468D4×C17—22no—
469D4×C17—21no—
470D4×C17—44no—
471D4×C17—42no—
472D4×C17—44no—
473D4×C17—44no—
474D4×C17—42no—
475D4×C17—42no—
476D4×C17—82no—
477D4×C17—81no—
478D4×C17—81no—
479C2×C4×C17—22no—
480C2×C4×C17—21no—
481C2×C4×C17—21no—
482C2×C4×C17—21no—
483C2×C4×C17—21no—
484C2×C4×C17—21no—
485C2×C4×C17—21no—
486C2×C4×C17—21no—
487C2×C4×C17—22no—
488C2×C4×C17—22no—
489C2×C4×C17—21no—
490C2×C4×C17—21no—
491C2×C4×C17—42no—
492C2×C4×C17—41no—
493C2×C4×C17—42no—
494C2×C4×C17—42no—
495C2×C4×C17—44no—
496C2×C4×C17—44no—
497C2×C4×C17—44no—
498C2×C4×C17—42no—
499C2×C4×C17—82no—
500C2×C4×C17—82no—
501C2×C4×C17—82no—
502C2×C4×C17—81no—
503C2×C4×C17C22×D412yes—
504C2×C4×C17C22×D411yescharacteristic
505C2×C4×C17C22×D411yescharacteristic
506C2×C4×C17C22×D412yes—
507C2×C4×C17C22×D412yes—
508C2×C4×C17C22×D412yes—
509C2×C4×C17C22×D411yescharacteristic
510C2×C4×C17C22×D411yescharacteristic
511C2×C4×C17C22×D411yescharacteristic
512C2×C4×C17C2511yescharacteristic
513C8×C17—21no—
514C8×C17—21no—
515C8×C17—22no—
516C8×C17—21no—
517C8×C17—22no—
518C8×C17—21no—
519#3507C2×C1711yescharacteristic, complemented
520#3480C2×C1711yescharacteristic, complemented
521#3402C2×C1712yescomplemented
522#3401C2×C1712yescomplemented
523#3400C2×C1711yescharacteristic, complemented
524#3399C2×C1711yescharacteristic, complemented
525#3396C2×C1711yescharacteristic, complemented
526#3394C2×C1711yescharacteristic, complemented
527#3376C2×C1712yescomplemented
528#3374C2×C1711yescharacteristic, complemented
529#3370C2×C1712yescomplemented
530#3368C2×C1711yescharacteristic, complemented
531#3365C2×C1711yescharacteristic, complemented
532#3364C2×C1711yescharacteristic, complemented
533#3219C2×C1712yescomplemented
534#3216C2×C1711yescharacteristic, complemented
535#3212C2×C1712yescomplemented
536#3207C2×C1711yescharacteristic, complemented
537#3115C2×C1711yescharacteristic, complemented
538#3111C2×C1712yescomplemented
539#3107C2×C1711yescharacteristic, complemented
540#3102C2×C1712yescomplemented
541#2984C2×C1711yescharacteristic, complemented
542C22×C17—21no—
543C22×C17—21no—
544C22×C17—21no—
545C22×C17—42no—
546C22×C17—42no—
547C22×C17—41no—
548C22×C17—41no—
549C22×C17—42no—
550C22×C17—42no—
551C22×C17—42no—
552C22×C17—42no—
553C22×C17—41no—
554C22×C17C23×D411yescharacteristic
555C4×C17—22no—
556C4×C17—22no—
557C4×C17—21no—
558C4×C17—21no—
559C4×C17—21no—
560C4×C17—21no—
561C4×C17—22no—
562C4×C17—22no—
563C4×C17—41no—
564C4×C17—41no—
565C4×C17—41no—
566C4×C17—41no—
567C4×C17—42no—
568C4×C17—41no—
569C4×C17—41no—
570C4×C17—41no—
571C4×C17—42no—
572C4×C17#57512yes—
573C4×C17#58511yescharacteristic
574C4×C17#58511yescharacteristic
575#559C22×C1711yescharacteristic
576#559C22×C1712yes—
577#559C22×C1711yescharacteristic
578#559C22×C1711yescharacteristic
579#557C22×C1711yescharacteristic
580#557C22×C1711yescharacteristic
581#557C22×C1711yescharacteristic
582#556—21no—
583#556—21no—
584#556C22×C1711yescharacteristic
585#556C22×C1712yes—
586#556C22×C1712yes—
587#554C22×C1712yes—
588#553—21no—
589#553—22no—
590#552—22no—
591#550C22×C1711yescharacteristic
592#548—21no—
593#539—22no—
594#536—21no—
595#533C22×C1711yescharacteristic
596#532C22×C1711yescharacteristic
597#532C22×C1712yes—
598#532C22×C1711yescharacteristic
599#529—22no—
600#529—21no—
601#529C22×C1712yes—
602#529C22×C1712yes—
603#520—21no—
604C4×#41—21no—
605C4×#41C22×C1712yes—
606C4×#41C22×C1711yescharacteristic
607C2×C4×Q8C22×C1711yescharacteristic
608#497C22×C1712yes—
609#497C22×C1712yes—
610#496C22×C1712yes—
611#495C22×C1712yes—
612#495C22×C1712yes—
613#493C22×C1711yescharacteristic
614#492C22×C1711yescharacteristic
615#491C22×C1712yes—
616#490C22×C1712yes—
617#489C22×C1712yes—
618#488C22×C1712yes—
619#488C22×C1712yes—
620#487C22×C1711yescharacteristic
621#486C22×C1711yescharacteristic
622#485C22×C1711yescharacteristic
623#485C22×C1711yescharacteristic
624#482C22×C1712yes—
625#479C22×C1712yes—
626#479C22×C1712yes—
627#478C22×C1712yes—
628#478C22×C1712yes—
629#475C22×C1711yescharacteristic
630#475C22×C1711yescharacteristic
631#474C22×C1711yescharacteristic
632#474C22×C1711yescharacteristic
633#464C22×C1712yes—
634#464C22×C1712yes—
635#464C22×C1712yes—
636#464C22×C1712yes—
637#463C22×C1712yes—
638#463C22×C1712yes—
639#463C22×C1712yes—
640#463C22×C1712yes—
641#463C22×C1712yes—
642#463C22×C1712yes—
643#462C22×C1711yescharacteristic
644#462C22×C1711yescharacteristic
645#462C22×C1711yescharacteristic
646#462C22×C1712yes—
647#461C22×C1711yescharacteristic
648#461C22×C1712yes—
649#460C22×C1711yescharacteristic
650#460C22×C1711yescharacteristic
651#460C22×C1712yes—
652#460C22×C1711yescharacteristic
653#459C22×C1712yes—
654#459C22×C1711yescharacteristic
655#452C22×C1712yes—
656#452C22×C1711yescharacteristic
657#452C22×C1711yescharacteristic
658#452C22×C1712yes—
659#449C22×C1712yes—
660#449C22×C1712yes—
661#449C22×C1712yes—
662#446C22×C1711yescharacteristic
663#446C22×C1712yes—
664#446C22×C1711yescharacteristic
665#446C22×C1712yes—
666C8×Q8C22×C1711yescharacteristic
667C8×Q8C22×C1711yescharacteristic
668#442C22×C1712yes—
669#442C22×C1712yes—
670#441C22×C1712yes—
671#440C22×C1712yes—
672#440C22×C1712yes—
673#440C22×C1712yes—
674C4×Q16C22×C1712yes—
675C4×Q16C22×C1711yescharacteristic
676C4×Q16C22×C1711yescharacteristic
677C4×SD16C22×C1712yes—
678C4×SD16C22×C1712yes—
679C4×SD16C22×C1711yescharacteristic
680C4×SD16C22×C1711yescharacteristic
681C4×D8C22×C1712yes—
682#432C22×C1712yes—
683#432C22×C1711yescharacteristic
684#431C22×C1712yes—
685#431C22×C1711yescharacteristic
686C2×C17—41no—
687C2×C17—82no—
688C2×C17—81no—
689C2×C17—82no—
690C2×C17#348711yescharacteristic
691C2×C17C2×#57511yescharacteristic
692C2×C17#358411yescharacteristic
693C2×#41—21no—
694C2×#41—21no—
695C2×#41C23×C1712yes—
696C2×#41C23×C1711yescharacteristic
697C22×Q8D4×C1711yescharacteristic
698C2×Q16C23×C1711yescharacteristic
699C2×Q16C23×C1712yes—
700C2×Q16C23×C1711yescharacteristic
701C2×Q16C23×C1712yes—
702C2×SD16C23×C1712yes—
703C2×SD16C23×C1711yescharacteristic
704C2×SD16C23×C1712yes—
705C2×SD16C23×C1711yescharacteristic
706C2×SD16C23×C1712yes—
707C2×SD16C23×C1712yes—
708C2×SD16C23×C1712yes—
709C2×D8C23×C1712yes—
710C2×D8C23×C1712yes—
711C2×D8C23×C1712yes—
712C4⋊Q8—21no—
713C4⋊Q8—21no—
714C4⋊Q8C23×C1712yes—
715C4⋊Q8C23×C1711yescharacteristic
716C4⋊Q8C23×C1711yescharacteristic
717C4⋊Q8C23×C1711yescharacteristic
718C4⋊Q8C23×C1711yescharacteristic
719#127C23×C1712yes—
720#127C23×C1711yescharacteristic
721#127C23×C1711yescharacteristic
722#126—22no—
723#126—22no—
724#126—22no—
725#126—22no—
726#126—22no—
727#126—22no—
728#126—22no—
729#125—21no—
730#125—22no—
731#125—22no—
732#125—22no—
733#125—21no—
734#125C23×C1712yes—
735#125C23×C1712yes—
736#124—21no—
737#124—22no—
738#124—21no—
739#124—21no—
740#124—21no—
741#124C23×C1712yes—
742#124C23×C1712yes—
743#124C23×C1712yes—
744#124C23×C1712yes—
745#124C23×C1712yes—
746#123—22no—
747#123—22no—
748#123—22no—
749#123—22no—
750#123—22no—
751#123—22no—
752#123—22no—
753C22⋊Q8—21no—
754C22⋊Q8—22no—
755C22⋊Q8—22no—
756C22⋊Q8—22no—
757C22⋊Q8—21no—
758C22⋊Q8—22no—
759C22⋊Q8—22no—
760C22⋊Q8C23×C1711yescharacteristic
761C22⋊Q8C23×C1711yescharacteristic
762#121—21no—
763#121—21no—
764#121—22no—
765#121—22no—
766#121—21no—
767#121—21no—
768#121—22no—
769#121C23×C1712yes—
770C4×Q8—21no—
771C4×Q8—21no—
772C4×Q8—21no—
773C4×Q8—21no—
774C4×Q8D4×C1711yescharacteristic
775C4×Q8D4×C1712yes—
776C4×Q8D4×C1711yescharacteristic
777C4×Q8C23×C1712yes—
778C4×Q8C23×C1711yescharacteristic
779C4×Q8C23×C1711yescharacteristic
780C4×Q8C23×C1712yes—
781C4×Q8C23×C1712yes—
782C4×Q8C23×C1712yes—
783C4×Q8C23×C1711yescharacteristic
784C4×Q8C23×C1711yescharacteristic
785C4×Q8C23×C1711yescharacteristic
786C4×Q8C23×C1712yes—
787C4×Q8C23×C1711yescharacteristic
788C4×D4—21no—
789C4×D4—22no—
790C4×D4—22no—
791C4×D4—21no—
792C4×D4—22no—
793C4×D4—22no—
794C4×D4—21no—
795C4×D4—22no—
796C4×D4—21no—
797C4×D4—21no—
798C4×D4—22no—
799C4×D4—21no—
800C4×D4—22no—
801C4×D4—21no—
802C4×D4—21no—
803C4×D4C23×C1711yescharacteristic
804C4×D4C23×C1712yes—
805C4×D4C23×C1712yes—
806C4×D4C23×C1711yescharacteristic
807C4×D4C23×C1712yes—
808C4×D4C23×C1712yes—
809C4×D4C23×C1712yes—
810#117—21no—
811#117—21no—
812#117—22no—
813#117—22no—
814#117—22no—
815#117—21no—
816#117—22no—
817#117—22no—
818#117C23×C1711yescharacteristic
819C2×C4⋊C4—22no—
820C2×C4⋊C4D4×C1711yescharacteristic
821C2×C4⋊C4D4×C1712yes—
822C2×C42—22no—
823C2×C42—21no—
824C2×C42C23×C1712yes—
825C2×C42C23×C1711yescharacteristic
826#107C23×C1711yescharacteristic
827#107C23×C1711yescharacteristic
828#107C23×C1712yes—
829#106C23×C1711yescharacteristic
830#106C23×C1712yes—
831#106C23×C1711yescharacteristic
832C4⋊C8C23×C1712yes—
833C4⋊C8C23×C1712yes—
834C4⋊C8C23×C1711yescharacteristic
835C4⋊C8C23×C1711yescharacteristic
836C4⋊C8C23×C1711yescharacteristic
837C4⋊C8C23×C1711yescharacteristic
838C4⋊C8C23×C1712yes—
839C4⋊C8C23×C1712yes—
840#103C23×C1711yescharacteristic
841#103C23×C1711yescharacteristic
842#103C23×C1711yescharacteristic
843#103C23×C1712yes—
844#103C23×C1711yescharacteristic
845#103C23×C1712yes—
846#103C23×C1711yescharacteristic
847#103C23×C1711yescharacteristic
848#103C23×C1712yes—
849#103C23×C1712yes—
850#103C23×C1712yes—
851#102C23×C1712yes—
852#102C23×C1712yes—
853#102C23×C1712yes—
854#102C23×C1712yes—
855#102C23×C1711yescharacteristic
856#102C23×C1711yescharacteristic
857#102C23×C1712yes—
858#102C23×C1712yes—
859#102C23×C1712yes—
860C22⋊C8C23×C1711yescharacteristic
861C22⋊C8C23×C1711yescharacteristic
862C22⋊C8C23×C1712yes—
863#97C23×C1712yes—
864#97C23×C1712yes—
865#97C23×C1712yes—
866C4×C8C23×C1712yes—
867C4×C8C23×C1712yes—
868C4×C8C23×C1711yescharacteristic
869C4×C8C23×C1711yescharacteristic
870C17#6190811yescharacteristic, direct product factor, Sylow
871#41—41no—
872#41—42no—
873#41—42no—
874#41—41no—
875#41—44no—
876#41—44no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—42no—
880C2×Q8C2×D4×C1711yescharacteristic
881C2×Q8C2×D4×C1711yescharacteristic
882C2×Q8C2×D4×C1712yes—
883C2×Q8C24×C1711yescharacteristic
884C2×Q8C24×C1712yes—
885C2×Q8C24×C1711yescharacteristic
886C2×Q8C24×C1711yescharacteristic
887C2×D4—21no—
888C2×D4—22no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—22no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4C24×C1711yescharacteristic
897C2×D4C24×C1712yes—
898C2×D4C24×C1712yes—
899C22×C4—22no—
900C22×C4—21no—
901C22×C4—22no—
902C22×C4—21no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—21no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4C2×D4×C1711yescharacteristic
909C22×C4C2×D4×C1712yes—
910C22×C4C2×D4×C1711yescharacteristic
911C22×C4C2×D4×C1712yes—
912C22×C4C24×C1711yescharacteristic
913Q16—41no—
914Q16—42no—
915Q16—41no—
916Q16—42no—
917SD16—41no—
918SD16—42no—
919SD16—42no—
920SD16—41no—
921SD16—42no—
922SD16—42no—
923SD16—42no—
924D8—42no—
925D8—42no—
926D8—42no—
927C2×C8C24×C1711yescharacteristic
928C2×C8C24×C1711yescharacteristic
929C2×C8C24×C1712yes—
930C2×C8C24×C1711yescharacteristic
931C2×C8C24×C1712yes—
932C2×C8C24×C1711yescharacteristic
933C4⋊C4—21no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—22no—
940C4⋊C4—21no—
941C4⋊C4—22no—
942C4⋊C4—21no—
943C4⋊C4—22no—
944C4⋊C4—21no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—21no—
948C4⋊C4—22no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4C2×D4×C1712yes—
956C4⋊C4C2×D4×C1711yescharacteristic
957C4⋊C4C2×D4×C1712yes—
958C4⋊C4C2×D4×C1711yescharacteristic
959C4⋊C4C2×D4×C1712yes—
960C4⋊C4C2×D4×C1712yes—
961C4⋊C4C2×D4×C1712yes—
962C4⋊C4C24×C1711yescharacteristic
963C4⋊C4C24×C1711yescharacteristic
964C4⋊C4C24×C1712yes—
965C4⋊C4C24×C1711yescharacteristic
966C4⋊C4C24×C1711yescharacteristic
967C22⋊C4—21no—
968C22⋊C4—21no—
969C22⋊C4—21no—
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—21no—
978C22⋊C4—22no—
979C22⋊C4—21no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C42—21no—
989C42—22no—
990C42—21no—
991C42—22no—
992C42—21no—
993C42—22no—
994C42—22no—
995C42—21no—
996C42—21no—
997C42C2×D4×C1712yes—
998C42C2×D4×C1711yescharacteristic
999C42C2×D4×C1712yes—
1000C42C2×D4×C1711yescharacteristic
1001C42C24×C1712yes—
1002C42C24×C1711yescharacteristic
1003C42C24×C1711yescharacteristic
1004C42C24×C1712yes—
1005C23—22no—
1006C23—21no—
1007C23—22no—
1008C23C22×D4×C1711yescharacteristic
1009Q8—22no—
1010Q8—22no—
1011Q8—21no—
1012Q8—21no—
1013Q8—21no—
1014Q8—21no—
1015Q8—22no—
1016Q8—22no—
1017Q8—21no—
1018Q8—21no—
1019Q8—42no—
1020Q8—42no—
1021Q8—81no—
1022D4—22no—
1023D4—21no—
1024D4—22no—
1025D4—22no—
1026D4—22no—
1027D4—21no—
1028D4—44no—
1029D4—42no—
1030D4—44no—
1031D4—44no—
1032D4—42no—
1033D4—42no—
1034D4—82no—
1035D4—81no—
1036D4—81no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—42no—
1050C2×C4—42no—
1051C2×C4—41no—
1052C2×C4—42no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—42no—
1057C2×C4—82no—
1058C2×C4—82no—
1059C2×C4—82no—
1060C2×C4—81no—
1061C2×C4C22×D4×C1712yes—
1062C2×C4C22×D4×C1711yescharacteristic
1063C2×C4C22×D4×C1711yescharacteristic
1064C2×C4C22×D4×C1712yes—
1065C2×C4C22×D4×C1712yes—
1066C2×C4C22×D4×C1712yes—
1067C2×C4C22×D4×C1711yescharacteristic
1068C2×C4C22×D4×C1711yescharacteristic
1069C2×C4C22×D4×C1711yescharacteristic
1070C2×C4C25×C1711yescharacteristic
1071C8—21no—
1072C8—21no—
1073C8—22no—
1074C8—21no—
1075C8—22no—
1076C8—21no—
1077C22—21no—
1078C22—21no—
1079C22—21no—
1080C22—41no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—41no—
1086C22—42no—
1087C22—42no—
1088C22—41no—
1089C22C23×D4×C1711yescharacteristic
1090C4—21no—
1091C4—21no—
1092C4—22no—
1093C4—22no—
1094C4—22no—
1095C4—22no—
1096C4—21no—
1097C4—21no—
1098C4—41no—
1099C4—42no—
1100C4—41no—
1101C4—41no—
1102C4—41no—
1103C4—42no—
1104C4—41no—
1105C4—41no—
1106C4—41no—
1107C4C17×#57512yes—
1108C4C17×#58511yescharacteristic
1109C4C17×#58511yescharacteristic
1110C2—41no—
1111C2—81no—
1112C2—82no—
1113C2—82no—
1114C2C17×#348711yescharacteristic
1115C2C2×C17×#57511yescharacteristic
1116C2C17×#358411yescharacteristic
subgroupG/H
center, socleC22×C17C23×D4
commutator, Frattini, cosocleC2×C4C25×C17
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C2×C4×Q8×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#3507C2semidirect
2. C17×#3480C2semidirect
3. C17×#3402C2semidirect
4. C17×#3401C2semidirect
5. C17×#3400C2semidirect
6. C17×#3399C2semidirect
7. C17×#3396C2semidirect
8. C17×#3394C2semidirect
9. C17×#3376C2semidirect
10. C17×#3374C2semidirect
11. C17×#3370C2semidirect
12. C17×#3368C2semidirect
13. C17×#3365C2semidirect
14. C17×#3364C2semidirect
15. C17×#3219C2semidirect
16. C17×#3216C2semidirect
17. C17×#3212C2semidirect
18. C17×#3207C2semidirect
19. C17×#3115C2semidirect
20. C17×#3111C2semidirect
21. C17×#3107C2semidirect
22. C17×#3102C2semidirect
23. C17×#2984C2semidirect
446. #61908C17direct (N × H)
519. #3507C2×C17semidirect
520. #3480C2×C17semidirect
521. #3402C2×C17semidirect
522. #3401C2×C17semidirect
523. #3400C2×C17semidirect
524. #3399C2×C17semidirect
525. #3396C2×C17semidirect
526. #3394C2×C17semidirect
527. #3376C2×C17semidirect
528. #3374C2×C17semidirect
529. #3370C2×C17semidirect
530. #3368C2×C17semidirect
531. #3365C2×C17semidirect
532. #3364C2×C17semidirect
533. #3219C2×C17semidirect
534. #3216C2×C17semidirect
535. #3212C2×C17semidirect
536. #3207C2×C17semidirect
537. #3115C2×C17semidirect
538. #3111C2×C17semidirect
539. #3107C2×C17semidirect
540. #3102C2×C17semidirect
541. #2984C2×C17semidirect
870. C17#61908direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#35072
C17×#34802
C17×#34022
C17×#34012
C17×#34002
C17×#33992
C17×#33962
C17×#33942
C17×#33762
C17×#33742
C17×#33702
C17×#33682
C17×#33652
C17×#33642
C17×#32192
C17×#32162
C17×#32122
C17×#32072
C17×#31152
C17×#31112
C17×#31072
C17×#31022
C17×#29842
#6190817