Finite Group Databasebeta

← C17×#61902 #16919646

Subgroups — C17×#61902 #16919646

Order 4352.

1734 conjugacy classes of subgroups.

The subgroup lattice has 1128 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×#3403C212yesmaximal, complemented
4C17×#3401C212yesmaximal, complemented
5C17×#3398C211yesmaximal, characteristic, complemented
6C17×#3397C211yesmaximal, characteristic, complemented
7C17×#3394C211yesmaximal, characteristic, complemented
8C17×#3393C211yesmaximal, characteristic, complemented
9C17×#3377C212yesmaximal, complemented
10C17×#3372C211yesmaximal, characteristic, complemented
11C17×#3371C212yesmaximal, complemented
12C17×#3366C211yesmaximal, characteristic, complemented
13C17×#3361C211yesmaximal, characteristic, complemented
14C17×#3360C211yesmaximal, characteristic, complemented
15C17×#3219C212yesmaximal, complemented
16C17×#3214C211yesmaximal, characteristic, complemented
17C17×#3212C212yesmaximal, complemented
18C17×#3210C211yesmaximal, characteristic, complemented
19C17×#3116C211yesmaximal, characteristic, complemented
20C17×#3111C212yesmaximal, complemented
21C17×#3106C211yesmaximal, characteristic, complemented
22C17×#3102C212yesmaximal, complemented
23C17×#2984C211yesmaximal, characteristic, complemented
24C17×#559C2211yescharacteristic
25C17×#559C2212yes—
26C17×#559C2212yes—
27C17×#557C2211yescharacteristic
28C17×#557C2212yes—
29C17×#556—22no—
30C17×#556C2211yescharacteristic
31C17×#556C2212yes—
32C17×#556C2211yescharacteristic
33C17×#556C2211yescharacteristic
34C17×#554C2211yescharacteristic
35C17×#554C2211yescharacteristic
36C17×#553—21no—
37C17×#553—22no—
38C17×#552—21no—
39C17×#552—21no—
40C17×#550C2211yescharacteristic
41C17×#548—21no—
42C17×#539—22no—
43C17×#536—21no—
44C17×#533C2211yescharacteristic
45C17×#532C2211yescharacteristic
46C17×#532C2211yescharacteristic
47C17×#532C2212yes—
48C17×#529—21no—
49C17×#529—22no—
50C17×#529C2212yes—
51C17×#529C2212yes—
52C17×#520—21no—
53C4×#41×C17—21no—
54C4×#41×C17C2212yes—
55C4×#41×C17C2211yescharacteristic
56C2×C4×Q8×C17C2211yescharacteristic
57C17×#497C2212yes—
58C17×#496C2212yes—
59C17×#496C2212yes—
60C17×#495C2212yes—
61C17×#495C2212yes—
62C17×#494C2211yescharacteristic
63C17×#492C2211yescharacteristic
64C17×#491C2212yes—
65C17×#490C2212yes—
66C17×#489C2212yes—
67C17×#488C2212yes—
68C17×#488C2212yes—
69C17×#487C2211yescharacteristic
70C17×#486C2211yescharacteristic
71C17×#485C2212yes—
72C17×#482C2211yescharacteristic
73C17×#482C2211yescharacteristic
74C17×#479C2212yes—
75C17×#479C2212yes—
76C17×#478C2212yes—
77C17×#478C2212yes—
78C17×#477C2211yescharacteristic
79C17×#477C2211yescharacteristic
80C17×#476C2211yescharacteristic
81C17×#476C2211yescharacteristic
82C17×#464C2212yes—
83C17×#464C2212yes—
84C17×#464C2212yes—
85C17×#464C2212yes—
86C17×#464C2212yes—
87C17×#464C2212yes—
88C17×#463C2212yes—
89C17×#463C2212yes—
90C17×#463C2212yes—
91C17×#463C2212yes—
92C17×#462C2212yes—
93C17×#462C2211yescharacteristic
94C17×#461C2212yes—
95C17×#461C2211yescharacteristic
96C17×#461C2211yescharacteristic
97C17×#461C2211yescharacteristic
98C17×#460C2212yes—
99C17×#460C2211yescharacteristic
100C17×#459C2212yes—
101C17×#459C2211yescharacteristic
102C17×#459C2211yescharacteristic
103C17×#459C2211yescharacteristic
104C17×#452C2212yes—
105C17×#452C2212yes—
106C17×#452C2212yes—
107C17×#449C2211yescharacteristic
108C17×#449C2212yes—
109C17×#449C2212yes—
110C17×#449C2211yescharacteristic
111C17×#446C2211yescharacteristic
112C17×#446C2212yes—
113C17×#446C2211yescharacteristic
114C17×#446C2212yes—
115C8×Q8×C17C2211yescharacteristic
116C8×Q8×C17C2211yescharacteristic
117C17×#442C2212yes—
118C17×#441C2212yes—
119C17×#441C2212yes—
120C17×#440C2212yes—
121C17×#440C2212yes—
122C17×#440C2212yes—
123C4×Q16×C17C2212yes—
124C4×SD16×C17C2212yes—
125C4×SD16×C17C2212yes—
126C4×SD16×C17C2211yescharacteristic
127C4×SD16×C17C2211yescharacteristic
128C4×D8×C17C2212yes—
129C4×D8×C17C2211yescharacteristic
130C4×D8×C17C2211yescharacteristic
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×C17C2312yes—
141C2×Q16×C17C2312yes—
142C2×Q16×C17C2312yes—
143C2×SD16×C17C2312yes—
144C2×SD16×C17C2312yes—
145C2×SD16×C17C2311yescharacteristic
146C2×SD16×C17C2312yes—
147C2×SD16×C17C2312yes—
148C2×SD16×C17C2312yes—
149C2×SD16×C17C2311yescharacteristic
150C2×D8×C17C2311yescharacteristic
151C2×D8×C17C2312yes—
152C2×D8×C17C2312yes—
153C2×D8×C17C2311yescharacteristic
154C17×C4⋊Q8—22no—
155C17×C4⋊Q8C2312yes—
156C17×C4⋊Q8C2311yescharacteristic
157C17×C4⋊Q8C2311yescharacteristic
158C17×C4⋊Q8C2311yescharacteristic
159C17×C4⋊Q8C2311yescharacteristic
160C17×#127C2311yescharacteristic
161C17×#127C2311yescharacteristic
162C17×#127C2312yes—
163C17×#126—22no—
164C17×#126—22no—
165C17×#126—22no—
166C17×#126—22no—
167C17×#126—22no—
168C17×#126—22no—
169C17×#126—22no—
170C17×#125—22no—
171C17×#125—21no—
172C17×#125—22no—
173C17×#125—22no—
174C17×#125—21no—
175C17×#125C2312yes—
176C17×#125C2312yes—
177C17×#124—21no—
178C17×#124—22no—
179C17×#124—22no—
180C17×#124—21no—
181C17×#124C2312yes—
182C17×#124C2312yes—
183C17×#124C2312yes—
184C17×#124C2312yes—
185C17×#124C2312yes—
186C17×#123—22no—
187C17×#123—22no—
188C17×#123—22no—
189C17×#123—22no—
190C17×#123—22no—
191C17×#123—22no—
192C17×#123—22no—
193C17×C22⋊Q8—21no—
194C17×C22⋊Q8—22no—
195C17×C22⋊Q8—21no—
196C17×C22⋊Q8—21no—
197C17×C22⋊Q8—21no—
198C17×C22⋊Q8—21no—
199C17×C22⋊Q8—21no—
200C17×C22⋊Q8—22no—
201C17×C22⋊Q8—22no—
202C17×C22⋊Q8C2312yes—
203C17×#121—21no—
204C17×#121—21no—
205C17×#121—22no—
206C17×#121—21no—
207C17×#121—22no—
208C17×#121—22no—
209C17×#121—21no—
210C17×#121C2311yescharacteristic
211C17×#121C2311yescharacteristic
212C4×Q8×C17—21no—
213C4×Q8×C17—22no—
214C4×Q8×C17—21no—
215C4×Q8×C17D411yescharacteristic
216C4×Q8×C17D411yescharacteristic
217C4×Q8×C17D412yes—
218C4×Q8×C17C2312yes—
219C4×Q8×C17C2311yescharacteristic
220C4×Q8×C17C2311yescharacteristic
221C4×Q8×C17C2312yes—
222C4×Q8×C17C2312yes—
223C4×Q8×C17C2312yes—
224C4×Q8×C17C2312yes—
225C4×Q8×C17C2311yescharacteristic
226C4×Q8×C17C2311yescharacteristic
227C4×Q8×C17C2312yes—
228C4×D4×C17—21no—
229C4×D4×C17—22no—
230C4×D4×C17—21no—
231C4×D4×C17—22no—
232C4×D4×C17—22no—
233C4×D4×C17—22no—
234C4×D4×C17—22no—
235C4×D4×C17—21no—
236C4×D4×C17—22no—
237C4×D4×C17—21no—
238C4×D4×C17—22no—
239C4×D4×C17—21no—
240C4×D4×C17—22no—
241C4×D4×C17—21no—
242C4×D4×C17C2311yescharacteristic
243C4×D4×C17C2312yes—
244C4×D4×C17C2312yes—
245C4×D4×C17C2311yescharacteristic
246C4×D4×C17C2312yes—
247C4×D4×C17C2312yes—
248C4×D4×C17C2311yescharacteristic
249C4×D4×C17C2311yescharacteristic
250C17×#117—21no—
251C17×#117—22no—
252C17×#117—21no—
253C17×#117—21no—
254C17×#117—21no—
255C17×#117—21no—
256C17×#117—22no—
257C17×#117—22no—
258C17×#117—22no—
259C17×#117C2311yescharacteristic
260C2×C4⋊C4×C17—21no—
261C2×C4⋊C4×C17—21no—
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×#107C2312yes—
270C17×#107C2311yescharacteristic
271C17×#106C2311yescharacteristic
272C17×#106C2311yescharacteristic
273C17×#106C2312yes—
274C17×C4⋊C8C2312yes—
275C17×C4⋊C8C2311yescharacteristic
276C17×C4⋊C8C2312yes—
277C17×C4⋊C8C2311yescharacteristic
278C17×C4⋊C8C2311yescharacteristic
279C17×C4⋊C8C2311yescharacteristic
280C17×C4⋊C8C2312yes—
281C17×C4⋊C8C2312yes—
282C17×#103C2311yescharacteristic
283C17×#103C2312yes—
284C17×#103C2312yes—
285C17×#103C2312yes—
286C17×#103C2312yes—
287C17×#103C2311yescharacteristic
288C17×#103C2312yes—
289C17×#103C2312yes—
290C17×#103C2312yes—
291C17×#102C2311yescharacteristic
292C17×#102C2311yescharacteristic
293C17×#102C2311yescharacteristic
294C17×#102C2311yescharacteristic
295C17×#102C2311yescharacteristic
296C17×#102C2312yes—
297C17×#102C2311yescharacteristic
298C17×#102C2312yes—
299C17×#102C2312yes—
300C17×#102C2312yes—
301C17×#102C2312yes—
302C17×C22⋊C8C2311yescharacteristic
303C17×C22⋊C8C2312yes—
304C17×C22⋊C8C2311yescharacteristic
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×C17C2412yes—
325C2×Q8×C17C2411yescharacteristic
326C2×Q8×C17C2412yes—
327C2×D4×C17—21no—
328C2×D4×C17—21no—
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×C17C2411yescharacteristic
340C2×D4×C17C2411yescharacteristic
341C22×C4×C17—21no—
342C22×C4×C17—21no—
343C22×C4×C17—22no—
344C22×C4×C17—21no—
345C22×C4×C17—22no—
346C22×C4×C17—21no—
347C22×C4×C17—22no—
348C22×C4×C17—22no—
349C22×C4×C17—22no—
350C22×C4×C17—21no—
351C22×C4×C17C2×D411yescharacteristic
352C22×C4×C17C2×D411yescharacteristic
353C22×C4×C17C2×D412yes—
354C22×C4×C17C2×D412yes—
355C22×C4×C17C2411yescharacteristic
356Q16×C17—42no—
357Q16×C17—42no—
358Q16×C17—42no—
359SD16×C17—42no—
360SD16×C17—42no—
361SD16×C17—42no—
362SD16×C17—42no—
363SD16×C17—42no—
364SD16×C17—41no—
365SD16×C17—41no—
366D8×C17—42no—
367D8×C17—41no—
368D8×C17—42no—
369D8×C17—41no—
370C2×C8×C17C2411yescharacteristic
371C2×C8×C17C2412yes—
372C2×C8×C17C2412yes—
373C2×C8×C17C2411yescharacteristic
374C2×C8×C17C2411yescharacteristic
375C2×C8×C17C2411yescharacteristic
376C4⋊C4×C17—22no—
377C4⋊C4×C17—22no—
378C4⋊C4×C17—21no—
379C4⋊C4×C17—21no—
380C4⋊C4×C17—21no—
381C4⋊C4×C17—22no—
382C4⋊C4×C17—22no—
383C4⋊C4×C17—22no—
384C4⋊C4×C17—22no—
385C4⋊C4×C17—22no—
386C4⋊C4×C17—22no—
387C4⋊C4×C17—22no—
388C4⋊C4×C17—21no—
389C4⋊C4×C17—21no—
390C4⋊C4×C17—22no—
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×C17C2412yes—
404C4⋊C4×C17C2411yescharacteristic
405C4⋊C4×C17C2411yescharacteristic
406C4⋊C4×C17C2411yescharacteristic
407C4⋊C4×C17C2411yescharacteristic
408C22⋊C4×C17—22no—
409C22⋊C4×C17—21no—
410C22⋊C4×C17—22no—
411C22⋊C4×C17—22no—
412C22⋊C4×C17—21no—
413C22⋊C4×C17—21no—
414C22⋊C4×C17—22no—
415C22⋊C4×C17—22no—
416C22⋊C4×C17—22no—
417C22⋊C4×C17—22no—
418C22⋊C4×C17—22no—
419C22⋊C4×C17—21no—
420C22⋊C4×C17—22no—
421C22⋊C4×C17—22no—
422C22⋊C4×C17—22no—
423C22⋊C4×C17—22no—
424C22⋊C4×C17—22no—
425C22⋊C4×C17—22no—
426C22⋊C4×C17—21no—
427C22⋊C4×C17—21no—
428C22⋊C4×C17—22no—
429C22⋊C4×C17—21no—
430C42×C17—22no—
431C42×C17—21no—
432C42×C17—22no—
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#61902C1711yesmaximal, characteristic, direct product factor, Sylow
447C23×C17—21no—
448C23×C17—21no—
449C23×C17—21no—
450C23×C17—22no—
451C23×C17C22×D411yescharacteristic
452Q8×C17—22no—
453Q8×C17—22no—
454Q8×C17—22no—
455Q8×C17—21no—
456Q8×C17—22no—
457Q8×C17—22no—
458Q8×C17—22no—
459Q8×C17—21no—
460Q8×C17—42no—
461Q8×C17—42no—
462Q8×C17—81no—
463D4×C17—21no—
464D4×C17—21no—
465D4×C17—21no—
466D4×C17—21no—
467D4×C17—22no—
468D4×C17—22no—
469D4×C17—21no—
470D4×C17—21no—
471D4×C17—42no—
472D4×C17—44no—
473D4×C17—42no—
474D4×C17—44no—
475D4×C17—42no—
476D4×C17—42no—
477D4×C17—42no—
478D4×C17—81no—
479D4×C17—82no—
480D4×C17—81no—
481C2×C4×C17—22no—
482C2×C4×C17—21no—
483C2×C4×C17—21no—
484C2×C4×C17—21no—
485C2×C4×C17—21no—
486C2×C4×C17—22no—
487C2×C4×C17—21no—
488C2×C4×C17—22no—
489C2×C4×C17—21no—
490C2×C4×C17—21no—
491C2×C4×C17—22no—
492C2×C4×C17—42no—
493C2×C4×C17—41no—
494C2×C4×C17—42no—
495C2×C4×C17—42no—
496C2×C4×C17—44no—
497C2×C4×C17—44no—
498C2×C4×C17—42no—
499C2×C4×C17—42no—
500C2×C4×C17—42no—
501C2×C4×C17—82no—
502C2×C4×C17—82no—
503C2×C4×C17—81no—
504C2×C4×C17—82no—
505C2×C4×C17C22×D412yes—
506C2×C4×C17C22×D411yescharacteristic
507C2×C4×C17C22×D411yescharacteristic
508C2×C4×C17C22×D412yes—
509C2×C4×C17C22×D411yescharacteristic
510C2×C4×C17C22×D412yes—
511C2×C4×C17C22×D412yes—
512C2×C4×C17C22×D411yescharacteristic
513C2×C4×C17C22×D411yescharacteristic
514C2×C4×C17C2511yescharacteristic
515C8×C17—22no—
516C8×C17—21no—
517C8×C17—22no—
518C8×C17—21no—
519C8×C17—21no—
520C8×C17—21no—
521#3507C2×C1711yescharacteristic, complemented
522#3480C2×C1711yescharacteristic, complemented
523#3403C2×C1712yescomplemented
524#3401C2×C1712yescomplemented
525#3398C2×C1711yescharacteristic, complemented
526#3397C2×C1711yescharacteristic, complemented
527#3394C2×C1711yescharacteristic, complemented
528#3393C2×C1711yescharacteristic, complemented
529#3377C2×C1712yescomplemented
530#3372C2×C1711yescharacteristic, complemented
531#3371C2×C1712yescomplemented
532#3366C2×C1711yescharacteristic, complemented
533#3361C2×C1711yescharacteristic, complemented
534#3360C2×C1711yescharacteristic, complemented
535#3219C2×C1712yescomplemented
536#3214C2×C1711yescharacteristic, complemented
537#3212C2×C1712yescomplemented
538#3210C2×C1711yescharacteristic, complemented
539#3116C2×C1711yescharacteristic, complemented
540#3111C2×C1712yescomplemented
541#3106C2×C1711yescharacteristic, complemented
542#3102C2×C1712yescomplemented
543#2984C2×C1711yescharacteristic, complemented
544C22×C17—21no—
545C22×C17—21no—
546C22×C17—21no—
547C22×C17—41no—
548C22×C17—41no—
549C22×C17—42no—
550C22×C17—41no—
551C22×C17—41no—
552C22×C17—42no—
553C22×C17—41no—
554C22×C17—41no—
555C22×C17—42no—
556C22×C17—41no—
557C22×C17—41no—
558C22×C17—41no—
559C22×C17C23×D411yescharacteristic
560C4×C17—22no—
561C4×C17—22no—
562C4×C17—21no—
563C4×C17—21no—
564C4×C17—21no—
565C4×C17—21no—
566C4×C17—22no—
567C4×C17—22no—
568C4×C17—41no—
569C4×C17—42no—
570C4×C17—41no—
571C4×C17—42no—
572C4×C17—42no—
573C4×C17—41no—
574C4×C17—41no—
575C4×C17—41no—
576C4×C17#57512yes—
577C4×C17#58511yescharacteristic
578C4×C17#58511yescharacteristic
579#559C22×C1711yescharacteristic
580#559C22×C1712yes—
581#559C22×C1712yes—
582#557C22×C1711yescharacteristic
583#557C22×C1712yes—
584#556—22no—
585#556C22×C1711yescharacteristic
586#556C22×C1712yes—
587#556C22×C1711yescharacteristic
588#556C22×C1711yescharacteristic
589#554C22×C1711yescharacteristic
590#554C22×C1711yescharacteristic
591#553—21no—
592#553—22no—
593#552—21no—
594#552—21no—
595#550C22×C1711yescharacteristic
596#548—21no—
597#539—22no—
598#536—21no—
599#533C22×C1711yescharacteristic
600#532C22×C1711yescharacteristic
601#532C22×C1712yes—
602#532C22×C1711yescharacteristic
603#529—21no—
604#529—22no—
605#529C22×C1712yes—
606#529C22×C1712yes—
607#520—21no—
608C4×#41—21no—
609C4×#41C22×C1712yes—
610C4×#41C22×C1711yescharacteristic
611C2×C4×Q8C22×C1711yescharacteristic
612#497C22×C1712yes—
613#496C22×C1712yes—
614#496C22×C1712yes—
615#495C22×C1712yes—
616#495C22×C1712yes—
617#494C22×C1711yescharacteristic
618#492C22×C1711yescharacteristic
619#491C22×C1712yes—
620#490C22×C1712yes—
621#489C22×C1712yes—
622#488C22×C1712yes—
623#488C22×C1712yes—
624#487C22×C1711yescharacteristic
625#486C22×C1711yescharacteristic
626#485C22×C1712yes—
627#482C22×C1711yescharacteristic
628#482C22×C1711yescharacteristic
629#479C22×C1712yes—
630#479C22×C1712yes—
631#478C22×C1712yes—
632#478C22×C1712yes—
633#477C22×C1711yescharacteristic
634#477C22×C1711yescharacteristic
635#476C22×C1711yescharacteristic
636#476C22×C1711yescharacteristic
637#464C22×C1712yes—
638#464C22×C1712yes—
639#464C22×C1712yes—
640#464C22×C1712yes—
641#464C22×C1712yes—
642#464C22×C1712yes—
643#463C22×C1712yes—
644#463C22×C1712yes—
645#463C22×C1712yes—
646#463C22×C1712yes—
647#462C22×C1711yescharacteristic
648#462C22×C1712yes—
649#461C22×C1711yescharacteristic
650#461C22×C1711yescharacteristic
651#461C22×C1711yescharacteristic
652#461C22×C1712yes—
653#460C22×C1711yescharacteristic
654#460C22×C1712yes—
655#459C22×C1711yescharacteristic
656#459C22×C1711yescharacteristic
657#459C22×C1711yescharacteristic
658#459C22×C1712yes—
659#452C22×C1712yes—
660#452C22×C1712yes—
661#452C22×C1712yes—
662#449C22×C1712yes—
663#449C22×C1711yescharacteristic
664#449C22×C1711yescharacteristic
665#449C22×C1712yes—
666#446C22×C1711yescharacteristic
667#446C22×C1712yes—
668#446C22×C1711yescharacteristic
669#446C22×C1712yes—
670C8×Q8C22×C1711yescharacteristic
671C8×Q8C22×C1711yescharacteristic
672#442C22×C1712yes—
673#441C22×C1712yes—
674#441C22×C1712yes—
675#440C22×C1712yes—
676#440C22×C1712yes—
677#440C22×C1712yes—
678C4×Q16C22×C1712yes—
679C4×SD16C22×C1712yes—
680C4×SD16C22×C1712yes—
681C4×SD16C22×C1711yescharacteristic
682C4×SD16C22×C1711yescharacteristic
683C4×D8C22×C1712yes—
684C4×D8C22×C1711yescharacteristic
685C4×D8C22×C1711yescharacteristic
686#432C22×C1712yes—
687#432C22×C1711yescharacteristic
688#431C22×C1712yes—
689#431C22×C1711yescharacteristic
690C2×C17—41no—
691C2×C17—81no—
692C2×C17—81no—
693C2×C17—81no—
694C2×C17—82no—
695C2×C17#348711yescharacteristic
696C2×C17C2×#57511yescharacteristic
697C2×C17#358411yescharacteristic
698C2×#41—21no—
699C2×#41—21no—
700C2×#41C23×C1712yes—
701C2×#41C23×C1711yescharacteristic
702C22×Q8D4×C1711yescharacteristic
703C2×Q16C23×C1712yes—
704C2×Q16C23×C1712yes—
705C2×Q16C23×C1712yes—
706C2×SD16C23×C1711yescharacteristic
707C2×SD16C23×C1711yescharacteristic
708C2×SD16C23×C1712yes—
709C2×SD16C23×C1712yes—
710C2×SD16C23×C1712yes—
711C2×SD16C23×C1712yes—
712C2×SD16C23×C1712yes—
713C2×D8C23×C1711yescharacteristic
714C2×D8C23×C1712yes—
715C2×D8C23×C1711yescharacteristic
716C2×D8C23×C1712yes—
717C4⋊Q8—22no—
718C4⋊Q8C23×C1711yescharacteristic
719C4⋊Q8C23×C1712yes—
720C4⋊Q8C23×C1711yescharacteristic
721C4⋊Q8C23×C1711yescharacteristic
722C4⋊Q8C23×C1711yescharacteristic
723#127C23×C1711yescharacteristic
724#127C23×C1712yes—
725#127C23×C1711yescharacteristic
726#126—22no—
727#126—22no—
728#126—22no—
729#126—22no—
730#126—22no—
731#126—22no—
732#126—22no—
733#125—21no—
734#125—22no—
735#125—22no—
736#125—22no—
737#125—21no—
738#125C23×C1712yes—
739#125C23×C1712yes—
740#124—21no—
741#124—22no—
742#124—22no—
743#124—21no—
744#124C23×C1712yes—
745#124C23×C1712yes—
746#124C23×C1712yes—
747#124C23×C1712yes—
748#124C23×C1712yes—
749#123—22no—
750#123—22no—
751#123—22no—
752#123—22no—
753#123—22no—
754#123—22no—
755#123—22no—
756C22⋊Q8—21no—
757C22⋊Q8—22no—
758C22⋊Q8—21no—
759C22⋊Q8—21no—
760C22⋊Q8—21no—
761C22⋊Q8—21no—
762C22⋊Q8—21no—
763C22⋊Q8—22no—
764C22⋊Q8—22no—
765C22⋊Q8C23×C1712yes—
766#121—21no—
767#121—21no—
768#121—22no—
769#121—22no—
770#121—21no—
771#121—21no—
772#121—22no—
773#121C23×C1711yescharacteristic
774#121C23×C1711yescharacteristic
775C4×Q8—21no—
776C4×Q8—22no—
777C4×Q8—21no—
778C4×Q8D4×C1711yescharacteristic
779C4×Q8D4×C1711yescharacteristic
780C4×Q8D4×C1712yes—
781C4×Q8C23×C1712yes—
782C4×Q8C23×C1711yescharacteristic
783C4×Q8C23×C1711yescharacteristic
784C4×Q8C23×C1712yes—
785C4×Q8C23×C1712yes—
786C4×Q8C23×C1712yes—
787C4×Q8C23×C1712yes—
788C4×Q8C23×C1711yescharacteristic
789C4×Q8C23×C1711yescharacteristic
790C4×Q8C23×C1712yes—
791C4×D4—21no—
792C4×D4—22no—
793C4×D4—22no—
794C4×D4—21no—
795C4×D4—22no—
796C4×D4—22no—
797C4×D4—21no—
798C4×D4—22no—
799C4×D4—22no—
800C4×D4—22no—
801C4×D4—21no—
802C4×D4—22no—
803C4×D4—21no—
804C4×D4—21no—
805C4×D4C23×C1711yescharacteristic
806C4×D4C23×C1712yes—
807C4×D4C23×C1712yes—
808C4×D4C23×C1711yescharacteristic
809C4×D4C23×C1712yes—
810C4×D4C23×C1712yes—
811C4×D4C23×C1711yescharacteristic
812C4×D4C23×C1711yescharacteristic
813#117—21no—
814#117—21no—
815#117—22no—
816#117—21no—
817#117—21no—
818#117—22no—
819#117—21no—
820#117—22no—
821#117—22no—
822#117C23×C1711yescharacteristic
823C2×C4⋊C4—21no—
824C2×C4⋊C4—21no—
825C2×C4⋊C4D4×C1711yescharacteristic
826C2×C4⋊C4D4×C1712yes—
827C2×C42—22no—
828C2×C42—21no—
829C2×C42C23×C1712yes—
830C2×C42C23×C1711yescharacteristic
831#107C23×C1711yescharacteristic
832#107C23×C1712yes—
833#107C23×C1711yescharacteristic
834#106C23×C1711yescharacteristic
835#106C23×C1711yescharacteristic
836#106C23×C1712yes—
837C4⋊C8C23×C1712yes—
838C4⋊C8C23×C1711yescharacteristic
839C4⋊C8C23×C1712yes—
840C4⋊C8C23×C1711yescharacteristic
841C4⋊C8C23×C1711yescharacteristic
842C4⋊C8C23×C1711yescharacteristic
843C4⋊C8C23×C1712yes—
844C4⋊C8C23×C1712yes—
845#103C23×C1712yes—
846#103C23×C1711yescharacteristic
847#103C23×C1711yescharacteristic
848#103C23×C1712yes—
849#103C23×C1712yes—
850#103C23×C1712yes—
851#103C23×C1712yes—
852#103C23×C1712yes—
853#103C23×C1712yes—
854#102C23×C1711yescharacteristic
855#102C23×C1711yescharacteristic
856#102C23×C1711yescharacteristic
857#102C23×C1711yescharacteristic
858#102C23×C1711yescharacteristic
859#102C23×C1712yes—
860#102C23×C1711yescharacteristic
861#102C23×C1712yes—
862#102C23×C1712yes—
863#102C23×C1712yes—
864#102C23×C1712yes—
865C22⋊C8C23×C1711yescharacteristic
866C22⋊C8C23×C1712yes—
867C22⋊C8C23×C1711yescharacteristic
868#97C23×C1712yes—
869#97C23×C1712yes—
870#97C23×C1712yes—
871C4×C8C23×C1711yescharacteristic
872C4×C8C23×C1711yescharacteristic
873C4×C8C23×C1712yes—
874C4×C8C23×C1712yes—
875C17#6190211yescharacteristic, direct product factor, Sylow
876#41—41no—
877#41—42no—
878#41—42no—
879#41—41no—
880#41—44no—
881#41—44no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—42no—
885C2×Q8C2×D4×C1711yescharacteristic
886C2×Q8C2×D4×C1711yescharacteristic
887C2×Q8C2×D4×C1712yes—
888C2×Q8C24×C1711yescharacteristic
889C2×Q8C24×C1712yes—
890C2×Q8C24×C1712yes—
891C2×D4—21no—
892C2×D4—22no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—22no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—22no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4C24×C1711yescharacteristic
902C2×D4C24×C1712yes—
903C2×D4C24×C1711yescharacteristic
904C2×D4C24×C1711yescharacteristic
905C22×C4—22no—
906C22×C4—21no—
907C22×C4—22no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—22no—
912C22×C4—21no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4C2×D4×C1711yescharacteristic
916C22×C4C2×D4×C1712yes—
917C22×C4C2×D4×C1711yescharacteristic
918C22×C4C2×D4×C1712yes—
919C22×C4C24×C1711yescharacteristic
920Q16—42no—
921Q16—42no—
922Q16—42no—
923SD16—42no—
924SD16—42no—
925SD16—42no—
926SD16—42no—
927SD16—42no—
928SD16—41no—
929SD16—41no—
930D8—42no—
931D8—41no—
932D8—42no—
933D8—41no—
934C2×C8C24×C1711yescharacteristic
935C2×C8C24×C1711yescharacteristic
936C2×C8C24×C1711yescharacteristic
937C2×C8C24×C1712yes—
938C2×C8C24×C1711yescharacteristic
939C2×C8C24×C1712yes—
940C4⋊C4—21no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—21no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—21no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—21no—
954C4⋊C4—22no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4C2×D4×C1711yescharacteristic
961C4⋊C4C2×D4×C1711yescharacteristic
962C4⋊C4C2×D4×C1712yes—
963C4⋊C4C2×D4×C1712yes—
964C4⋊C4C2×D4×C1712yes—
965C4⋊C4C2×D4×C1712yes—
966C4⋊C4C2×D4×C1712yes—
967C4⋊C4C24×C1712yes—
968C4⋊C4C24×C1711yescharacteristic
969C4⋊C4C24×C1711yescharacteristic
970C4⋊C4C24×C1711yescharacteristic
971C4⋊C4C24×C1711yescharacteristic
972C22⋊C4—22no—
973C22⋊C4—21no—
974C22⋊C4—21no—
975C22⋊C4—21no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—21no—
983C22⋊C4—21no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—21no—
991C22⋊C4—21no—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C42—21no—
995C42—22no—
996C42—21no—
997C42—22no—
998C42—21no—
999C42—22no—
1000C42—22no—
1001C42—22no—
1002C42C2×D4×C1712yes—
1003C42C2×D4×C1711yescharacteristic
1004C42C2×D4×C1712yes—
1005C42C2×D4×C1711yescharacteristic
1006C42C24×C1711yescharacteristic
1007C42C24×C1712yes—
1008C42C24×C1712yes—
1009C42C24×C1711yescharacteristic
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—22no—
1014C23C22×D4×C1711yescharacteristic
1015Q8—22no—
1016Q8—22no—
1017Q8—22no—
1018Q8—21no—
1019Q8—22no—
1020Q8—22no—
1021Q8—22no—
1022Q8—21no—
1023Q8—42no—
1024Q8—42no—
1025Q8—81no—
1026D4—21no—
1027D4—21no—
1028D4—21no—
1029D4—21no—
1030D4—22no—
1031D4—22no—
1032D4—21no—
1033D4—21no—
1034D4—42no—
1035D4—44no—
1036D4—42no—
1037D4—44no—
1038D4—42no—
1039D4—42no—
1040D4—42no—
1041D4—81no—
1042D4—82no—
1043D4—81no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—42no—
1056C2×C4—42no—
1057C2×C4—41no—
1058C2×C4—42no—
1059C2×C4—44no—
1060C2×C4—44no—
1061C2×C4—42no—
1062C2×C4—42no—
1063C2×C4—42no—
1064C2×C4—82no—
1065C2×C4—82no—
1066C2×C4—81no—
1067C2×C4—82no—
1068C2×C4C22×D4×C1712yes—
1069C2×C4C22×D4×C1711yescharacteristic
1070C2×C4C22×D4×C1711yescharacteristic
1071C2×C4C22×D4×C1711yescharacteristic
1072C2×C4C22×D4×C1712yes—
1073C2×C4C22×D4×C1712yes—
1074C2×C4C22×D4×C1712yes—
1075C2×C4C22×D4×C1711yescharacteristic
1076C2×C4C22×D4×C1711yescharacteristic
1077C2×C4C25×C1711yescharacteristic
1078C8—22no—
1079C8—21no—
1080C8—22no—
1081C8—21no—
1082C8—21no—
1083C8—21no—
1084C22—21no—
1085C22—21no—
1086C22—21no—
1087C22—41no—
1088C22—42no—
1089C22—41no—
1090C22—41no—
1091C22—42no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—41no—
1097C22—42no—
1098C22—41no—
1099C22C23×D4×C1711yescharacteristic
1100C4—21no—
1101C4—21no—
1102C4—22no—
1103C4—22no—
1104C4—22no—
1105C4—22no—
1106C4—21no—
1107C4—21no—
1108C4—41no—
1109C4—42no—
1110C4—42no—
1111C4—41no—
1112C4—41no—
1113C4—41no—
1114C4—41no—
1115C4—42no—
1116C4C17×#57512yes—
1117C4C17×#58511yescharacteristic
1118C4C17×#58511yescharacteristic
1119C2—41no—
1120C2—81no—
1121C2—82no—
1122C2—81no—
1123C2—81no—
1124C2C17×#348711yescharacteristic
1125C2C2×C17×#57511yescharacteristic
1126C2C17×#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×#3403C2semidirect
4. C17×#3401C2semidirect
5. C17×#3398C2semidirect
6. C17×#3397C2semidirect
7. C17×#3394C2semidirect
8. C17×#3393C2semidirect
9. C17×#3377C2semidirect
10. C17×#3372C2semidirect
11. C17×#3371C2semidirect
12. C17×#3366C2semidirect
13. C17×#3361C2semidirect
14. C17×#3360C2semidirect
15. C17×#3219C2semidirect
16. C17×#3214C2semidirect
17. C17×#3212C2semidirect
18. C17×#3210C2semidirect
19. C17×#3116C2semidirect
20. C17×#3111C2semidirect
21. C17×#3106C2semidirect
22. C17×#3102C2semidirect
23. C17×#2984C2semidirect
446. #61902C17direct (N × H)
521. #3507C2×C17semidirect
522. #3480C2×C17semidirect
523. #3403C2×C17semidirect
524. #3401C2×C17semidirect
525. #3398C2×C17semidirect
526. #3397C2×C17semidirect
527. #3394C2×C17semidirect
528. #3393C2×C17semidirect
529. #3377C2×C17semidirect
530. #3372C2×C17semidirect
531. #3371C2×C17semidirect
532. #3366C2×C17semidirect
533. #3361C2×C17semidirect
534. #3360C2×C17semidirect
535. #3219C2×C17semidirect
536. #3214C2×C17semidirect
537. #3212C2×C17semidirect
538. #3210C2×C17semidirect
539. #3116C2×C17semidirect
540. #3111C2×C17semidirect
541. #3106C2×C17semidirect
542. #3102C2×C17semidirect
543. #2984C2×C17semidirect
875. C17#61902direct (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×#34032
C17×#34012
C17×#33982
C17×#33972
C17×#33942
C17×#33932
C17×#33772
C17×#33722
C17×#33712
C17×#33662
C17×#33612
C17×#33602
C17×#32192
C17×#32142
C17×#32122
C17×#32102
C17×#31162
C17×#31112
C17×#31062
C17×#31022
C17×#29842
#6190217