Finite Group Databasebeta

← C17×#61860 #16919604

Subgroups — C17×#61860 #16919604

Order 4352.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3554C211yesmaximal, characteristic, complemented
2C17×#3503C211yesmaximal, characteristic, complemented
3C17×#3388C212yesmaximal, complemented
4C17×#3387C211yesmaximal, characteristic, complemented
5C17×#3384C211yesmaximal, characteristic, complemented
6C17×#3384C212yesmaximal, complemented
7C17×#3381C211yesmaximal, characteristic, complemented
8Q8×SD16×C17C211yesmaximal, characteristic, complemented
9C17×#3375C211yesmaximal, characteristic, complemented
10C17×#3373C212yesmaximal, complemented
11C17×#3371C212yesmaximal, complemented
12C17×#3366C211yesmaximal, characteristic, complemented
13C17×#3362C211yesmaximal, characteristic, complemented
14C17×#3361C211yesmaximal, characteristic, complemented
15C17×#3244C212yesmaximal, complemented
16C17×#3241C212yesmaximal, complemented
17C17×#3238C211yesmaximal, characteristic, complemented
18C17×#3227C211yesmaximal, characteristic, complemented
19C17×#3125C212yesmaximal, complemented
20C17×#3119C212yesmaximal, complemented
21C17×#3115C211yesmaximal, characteristic, complemented
22C17×#3102C211yesmaximal, characteristic, complemented
23C17×#2985C211yesmaximal, characteristic, complemented
24C17×#562—22no—
25C17×#559C2211yescharacteristic
26C17×#559C2212yes—
27Q82×C17C2211yescharacteristic
28Q82×C17C2211yescharacteristic
29C17×#557C2212yes—
30C17×#557C2211yescharacteristic
31C17×#554—21no—
32C17×#554—21no—
33C17×#554C2211yescharacteristic
34C17×#554C2211yescharacteristic
35C17×#554C2212yes—
36C17×#550C2211yescharacteristic
37D4×Q8×C17—22no—
38D4×Q8×C17C2212yes—
39D4×Q8×C17C2211yescharacteristic
40C17×#548—21no—
41C17×#547—21no—
42C17×#544—22no—
43C17×#544C2212yes—
44C17×#542—21no—
45C17×#542C2212yes—
46C17×#540C2212yes—
47C17×#539—22no—
48C17×#536—21no—
49C17×#533—21no—
50C17×#533C2211yescharacteristic
51C17×#532C2211yescharacteristic
52C2×C17×C4⋊Q8—21no—
53C2×C17×C4⋊Q8C2211yescharacteristic
54C17×#529C2211yescharacteristic
55C17×#520C2212yes—
56C4×#41×C17C2211yescharacteristic
57C17×#501C2212yes—
58C17×#501C2212yes—
59C17×#501C2212yes—
60C17×#499C2212yes—
61C17×#498C2211yescharacteristic
62C17×#498C2211yescharacteristic
63C17×#498C2212yes—
64C17×#490C2212yes—
65C17×#489C2212yes—
66C17×#489C2212yes—
67C17×#488C2212yes—
68C17×#486C2211yescharacteristic
69C17×#486C2211yescharacteristic
70C17×#486C2212yes—
71C17×#485C2211yescharacteristic
72C17×#483C2212yes—
73C17×#482C2211yescharacteristic
74C17×#482C2212yes—
75C17×#481C2212yes—
76C17×#481C2212yes—
77C17×#480C2212yes—
78C17×#479C2212yes—
79C17×#479C2211yescharacteristic
80C17×#479C2212yes—
81C17×#478C2212yes—
82C17×#478C2212yes—
83C17×#478C2212yes—
84C17×#478C2211yescharacteristic
85C17×#478C2212yes—
86C17×#477C2211yescharacteristic
87C17×#477C2211yescharacteristic
88C17×#476C2212yes—
89C17×#476C2212yes—
90C17×#476C2211yescharacteristic
91C17×#476C2211yescharacteristic
92C17×#476C2212yes—
93C17×#476C2212yes—
94C17×#476C2212yes—
95C17×#475C2212yes—
96C17×#475C2211yescharacteristic
97C17×#475C2212yes—
98C17×#474C2212yes—
99C17×#474C2211yescharacteristic
100C17×#464C2211yescharacteristic
101C17×#464C2212yes—
102C17×#463C2211yescharacteristic
103C17×#463C2212yes—
104C17×#460C2211yescharacteristic
105C17×#460C2212yes—
106C17×#459C2211yescharacteristic
107C17×#459C2212yes—
108C17×#452C2211yescharacteristic
109C17×#449C2211yescharacteristic
110C17×#449C2212yes—
111C17×#446C2211yescharacteristic
112C17×#446C2212yes—
113C17×#446C2212yes—
114C17×#446C2211yescharacteristic
115C8×Q8×C17C2211yescharacteristic
116C8×Q8×C17C2211yescharacteristic
117C17×#442C2212yes—
118C17×#442C2212yes—
119C17×#442C2212yes—
120C17×#441C2212yes—
121C17×#440C2212yes—
122C17×#440C2212yes—
123C4×Q16×C17C2211yescharacteristic
124C4×SD16×C17C2211yescharacteristic
125C4×SD16×C17C2211yescharacteristic
126C4×SD16×C17C2212yes—
127C4×SD16×C17C2212yes—
128C4×SD16×C17C2212yes—
129C4×D8×C17C2211yescharacteristic
130C4×D8×C17C2212yes—
131C17×#433C2212yes—
132C17×#433C2212yes—
133C17×#432C2211yescharacteristic
134C17×#431C2211yescharacteristic
135C2×#41×C17—21no—
136C2×#41×C17—21no—
137C2×#41×C17C2311yescharacteristic
138C22×Q8×C17—22no—
139C22×Q8×C17—21no—
140C22×Q8×C17—21no—
141C2×Q16×C17C2311yescharacteristic
142C2×SD16×C17C2311yescharacteristic
143C2×SD16×C17C2311yescharacteristic
144C2×SD16×C17C2312yes—
145C2×D8×C17C2311yescharacteristic
146C2×D8×C17C2312yes—
147C17×C4⋊Q8—22no—
148C17×C4⋊Q8—21no—
149C17×C4⋊Q8—22no—
150C17×C4⋊Q8—21no—
151C17×C4⋊Q8—21no—
152C17×C4⋊Q8—22no—
153C17×C4⋊Q8—22no—
154C17×C4⋊Q8—21no—
155C17×C4⋊Q8—21no—
156C17×C4⋊Q8D411yescharacteristic
157C17×C4⋊Q8D411yescharacteristic
158C17×C4⋊Q8C2311yescharacteristic
159C17×C4⋊Q8C2312yes—
160C17×C4⋊Q8C2311yescharacteristic
161C17×C4⋊Q8C2311yescharacteristic
162C17×C4⋊Q8C2312yes—
163C17×C4⋊Q8C2312yes—
164C17×C4⋊Q8C2312yes—
165C17×#127C2311yescharacteristic
166C17×#127C2312yes—
167C17×#126—22no—
168C17×#126—21no—
169C17×#125—22no—
170C17×#125—22no—
171C17×#125—22no—
172C17×#125—22no—
173C17×#125D412yes—
174C17×#125C2312yes—
175C17×#125C2312yes—
176C17×#125C2311yescharacteristic
177C17×#125C2312yes—
178C17×#124—21no—
179C17×#124—22no—
180C17×#124—22no—
181C17×#124—21no—
182C17×#124C2311yescharacteristic
183C17×#124C2312yes—
184C17×#123—21no—
185C17×#123—22no—
186C17×#123—22no—
187C17×#123—22no—
188C17×#123—22no—
189C17×#123—22no—
190C17×#123—22no—
191C17×C22⋊Q8—21no—
192C17×C22⋊Q8—21no—
193C17×C22⋊Q8—22no—
194C17×C22⋊Q8—22no—
195C17×C22⋊Q8—22no—
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⋊Q8—22no—
203C17×C22⋊Q8—22no—
204C17×C22⋊Q8—22no—
205C17×C22⋊Q8—22no—
206C17×C22⋊Q8D411yescharacteristic
207C17×C22⋊Q8D411yescharacteristic
208C17×C22⋊Q8D412yes—
209C17×C22⋊Q8C2311yescharacteristic
210C17×#121—21no—
211C17×#121—22no—
212C17×#121—21no—
213C17×#121—22no—
214C17×#121—22no—
215C17×#121C2311yescharacteristic
216C17×#121C2312yes—
217C4×Q8×C17—21no—
218C4×Q8×C17—21no—
219C4×Q8×C17—22no—
220C4×Q8×C17—21no—
221C4×Q8×C17C2311yescharacteristic
222C4×Q8×C17C2311yescharacteristic
223C4×Q8×C17C2312yes—
224C4×Q8×C17C2312yes—
225C4×Q8×C17C2311yescharacteristic
226C4×Q8×C17C2312yes—
227C4×Q8×C17C2312yes—
228C4×Q8×C17C2311yescharacteristic
229C4×Q8×C17C2311yescharacteristic
230C4×D4×C17—21no—
231C4×D4×C17—21no—
232C4×D4×C17—21no—
233C4×D4×C17—22no—
234C4×D4×C17—21no—
235C4×D4×C17—22no—
236C4×D4×C17—22no—
237C4×D4×C17—21no—
238C4×D4×C17C2311yescharacteristic
239C4×D4×C17C2311yescharacteristic
240C4×D4×C17C2312yes—
241C4×D4×C17C2312yes—
242C4×D4×C17C2311yescharacteristic
243C4×D4×C17C2312yes—
244C4×D4×C17C2312yes—
245C4×D4×C17C2312yes—
246C4×D4×C17C2312yes—
247C17×#117—22no—
248C17×#117—21no—
249C17×#117—21no—
250C17×#117C2311yescharacteristic
251C17×#117C2312yes—
252C2×C4⋊C4×C17—21no—
253C2×C4⋊C4×C17—22no—
254C2×C4⋊C4×C17—21no—
255C2×C4⋊C4×C17—21no—
256C2×C4⋊C4×C17—22no—
257C2×C4⋊C4×C17C2312yes—
258C2×C42×C17—21no—
259C2×C42×C17C2311yescharacteristic
260C17×#107C2312yes—
261C17×#107C2312yes—
262C17×#107C2312yes—
263C17×#107C2311yescharacteristic
264C17×#107C2311yescharacteristic
265C17×#106C2311yescharacteristic
266C17×#106C2312yes—
267C17×#106C2312yes—
268C17×#106C2312yes—
269C17×#106C2312yes—
270C17×#106C2312yes—
271C17×#106C2312yes—
272C17×#106C2311yescharacteristic
273C17×#106C2312yes—
274C17×C4⋊C8C2311yescharacteristic
275C17×C4⋊C8C2311yescharacteristic
276C17×C4⋊C8C2311yescharacteristic
277C17×C4⋊C8C2311yescharacteristic
278C17×C4⋊C8C2312yes—
279C17×C4⋊C8C2312yes—
280C17×C4⋊C8C2312yes—
281C17×C4⋊C8C2312yes—
282C17×#103C2311yescharacteristic
283C17×#103C2312yes—
284C17×#103C2312yes—
285C17×#103C2311yescharacteristic
286C17×#103C2311yescharacteristic
287C17×#103C2311yescharacteristic
288C17×#103C2312yes—
289C17×#102C2311yescharacteristic
290C17×#102C2311yescharacteristic
291C17×#102C2312yes—
292C17×#102C2311yescharacteristic
293C17×#102C2312yes—
294C17×#102C2312yes—
295C17×#102C2311yescharacteristic
296C17×#102C2312yes—
297C17×#102C2312yes—
298C17×#102C2312yes—
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—22no—
313#41×C17—22no—
314#41×C17—82no—
315#41×C17—82no—
316C2×Q8×C17—21no—
317C2×Q8×C17—22no—
318C2×Q8×C17—22no—
319C2×Q8×C17—22no—
320C2×Q8×C17—22no—
321C2×Q8×C17—21no—
322C2×Q8×C17—21no—
323C2×Q8×C17—82no—
324C2×Q8×C17—82no—
325C2×Q8×C17—84no—
326C2×Q8×C17C2×D411yescharacteristic
327C2×Q8×C17C2×D411yescharacteristic
328C2×Q8×C17C2×D412yes—
329C2×Q8×C17C2411yescharacteristic
330C2×Q8×C17C2411yescharacteristic
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×C17—22no—
338C2×D4×C17C2411yescharacteristic
339C2×D4×C17C2412yes—
340C2×D4×C17C2411yescharacteristic
341C22×C4×C17—21no—
342C22×C4×C17—22no—
343C22×C4×C17—21no—
344C22×C4×C17—21no—
345C22×C4×C17—21no—
346C22×C4×C17—22no—
347C22×C4×C17—22no—
348C22×C4×C17—22no—
349C22×C4×C17—22no—
350C22×C4×C17—22no—
351C22×C4×C17—22no—
352C22×C4×C17C2×D411yescharacteristic
353C22×C4×C17C2×D411yescharacteristic
354C22×C4×C17C2411yescharacteristic
355Q16×C17—22no—
356SD16×C17—22no—
357SD16×C17—24no—
358SD16×C17—22no—
359D8×C17—22no—
360D8×C17—24no—
361C2×C8×C17C2411yescharacteristic
362C2×C8×C17C2412yes—
363C2×C8×C17C2411yescharacteristic
364C2×C8×C17C2411yescharacteristic
365C2×C8×C17C2412yes—
366C2×C8×C17C2411yescharacteristic
367C4⋊C4×C17—21no—
368C4⋊C4×C17—22no—
369C4⋊C4×C17—22no—
370C4⋊C4×C17—22no—
371C4⋊C4×C17—22no—
372C4⋊C4×C17—22no—
373C4⋊C4×C17—21no—
374C4⋊C4×C17—22no—
375C4⋊C4×C17—22no—
376C4⋊C4×C17—21no—
377C4⋊C4×C17—22no—
378C4⋊C4×C17—22no—
379C4⋊C4×C17—21no—
380C4⋊C4×C17—22no—
381C4⋊C4×C17—22no—
382C4⋊C4×C17—21no—
383C4⋊C4×C17—21no—
384C4⋊C4×C17—21no—
385C4⋊C4×C17—21no—
386C4⋊C4×C17—22no—
387C4⋊C4×C17—22no—
388C4⋊C4×C17—22no—
389C4⋊C4×C17—21no—
390C4⋊C4×C17C2×D412yes—
391C4⋊C4×C17C2×D412yes—
392C4⋊C4×C17C2×D412yes—
393C4⋊C4×C17C2×D412yes—
394C4⋊C4×C17C2×D412yes—
395C4⋊C4×C17C2×D411yescharacteristic
396C4⋊C4×C17C2×D412yes—
397C4⋊C4×C17C2×D411yescharacteristic
398C4⋊C4×C17C2×D412yes—
399C4⋊C4×C17C2411yescharacteristic
400C4⋊C4×C17C2411yescharacteristic
401C4⋊C4×C17C2411yescharacteristic
402C4⋊C4×C17C2412yes—
403C4⋊C4×C17C2412yes—
404C4⋊C4×C17C2412yes—
405C4⋊C4×C17C2411yescharacteristic
406C22⋊C4×C17—21no—
407C22⋊C4×C17—21no—
408C22⋊C4×C17—21no—
409C22⋊C4×C17—21no—
410C22⋊C4×C17—22no—
411C22⋊C4×C17—22no—
412C22⋊C4×C17—22no—
413C22⋊C4×C17—22no—
414C22⋊C4×C17—22no—
415C22⋊C4×C17—21no—
416C22⋊C4×C17—22no—
417C22⋊C4×C17—22no—
418C22⋊C4×C17—22no—
419C22⋊C4×C17—21no—
420C22⋊C4×C17—21no—
421C22⋊C4×C17—22no—
422C22⋊C4×C17—21no—
423C22⋊C4×C17C2×D412yes—
424C22⋊C4×C17C2×D412yes—
425C42×C17—22no—
426C42×C17—21no—
427C42×C17—21no—
428C42×C17—22no—
429C42×C17—22no—
430C42×C17—21no—
431C42×C17—21no—
432C42×C17C2×D411yescharacteristic
433C42×C17C2×D411yescharacteristic
434C42×C17C2412yes—
435C42×C17C2411yescharacteristic
436C42×C17C2412yes—
437C42×C17C2411yescharacteristic
438#61860C1711yesmaximal, characteristic, direct product factor, Sylow
439C23×C17—21no—
440C23×C17—22no—
441C23×C17—21no—
442C23×C17C22×D411yescharacteristic
443Q8×C17—22no—
444Q8×C17—22no—
445Q8×C17—21no—
446Q8×C17—21no—
447Q8×C17—21no—
448Q8×C17—42no—
449Q8×C17—44no—
450Q8×C17—42no—
451Q8×C17—81no—
452Q8×C17—81no—
453Q8×C17—82no—
454Q8×C17—82no—
455Q8×C17—82no—
456Q8×C172−1+412yes—
457D4×C17—24no—
458D4×C17—21no—
459D4×C17—21no—
460D4×C17—22no—
461D4×C17—21no—
462D4×C17—22no—
463D4×C17—42no—
464D4×C17—81no—
465D4×C17—82no—
466D4×C17—82no—
467D4×C17—81no—
468D4×C17—82no—
469D4×C172−1+412yes—
470C2×C4×C17—24no—
471C2×C4×C17—21no—
472C2×C4×C17—22no—
473C2×C4×C17—21no—
474C2×C4×C17—21no—
475C2×C4×C17—21no—
476C2×C4×C17—21no—
477C2×C4×C17—21no—
478C2×C4×C17—21no—
479C2×C4×C17—22no—
480C2×C4×C17—22no—
481C2×C4×C17—22no—
482C2×C4×C17—21no—
483C2×C4×C17—41no—
484C2×C4×C17—42no—
485C2×C4×C17—42no—
486C2×C4×C17—42no—
487C2×C4×C17—82no—
488C2×C4×C17—82no—
489C2×C4×C17—82no—
490C2×C4×C17—82no—
491C2×C4×C17—82no—
492C2×C4×C17—82no—
493C2×C4×C17—82no—
494C2×C4×C17C22×D411yescharacteristic
495C2×C4×C17C22×D411yescharacteristic
496C2×C4×C17C22×D412yes—
497C2×C4×C17C22×D412yes—
498C2×C4×C17C22×D412yes—
499C2×C4×C17C22×D411yescharacteristic
500C2×C4×C17C22×D411yescharacteristic
501C2×C4×C17C22×D412yes—
502C2×C4×C17C22×D411yescharacteristic
503C2×C4×C17C2511yescharacteristic
504C8×C17—21no—
505C8×C17—22no—
506C8×C17—21no—
507C8×C17—22no—
508C8×C17—21no—
509C8×C17—21no—
510#3554C2×C1711yescharacteristic, complemented
511#3503C2×C1711yescharacteristic, complemented
512#3388C2×C1712yescomplemented
513#3387C2×C1711yescharacteristic, complemented
514#3384C2×C1712yescomplemented
515#3384C2×C1711yescharacteristic, complemented
516#3381C2×C1711yescharacteristic, complemented
517Q8×SD16C2×C1711yescharacteristic, complemented
518#3375C2×C1711yescharacteristic, complemented
519#3373C2×C1712yescomplemented
520#3371C2×C1712yescomplemented
521#3366C2×C1711yescharacteristic, complemented
522#3362C2×C1711yescharacteristic, complemented
523#3361C2×C1711yescharacteristic, complemented
524#3244C2×C1712yescomplemented
525#3241C2×C1712yescomplemented
526#3238C2×C1711yescharacteristic, complemented
527#3227C2×C1711yescharacteristic, complemented
528#3125C2×C1712yescomplemented
529#3119C2×C1712yescomplemented
530#3115C2×C1711yescharacteristic, complemented
531#3102C2×C1711yescharacteristic, complemented
532#2985C2×C1711yescharacteristic, complemented
533C22×C17—21no—
534C22×C17—21no—
535C22×C17—22no—
536C22×C17—21no—
537C22×C17—41no—
538C22×C17—41no—
539C22×C17—42no—
540C22×C17—41no—
541C22×C17—42no—
542C22×C17—41no—
543C22×C17—41no—
544C22×C17—42no—
545C22×C17C23×D411yescharacteristic
546C4×C17—21no—
547C4×C17—21no—
548C4×C17—22no—
549C4×C17—22no—
550C4×C17—21no—
551C4×C17—22no—
552C4×C17—21no—
553C4×C17—22no—
554C4×C17—22no—
555C4×C17—41no—
556C4×C17—41no—
557C4×C17—42no—
558C4×C17—42no—
559C4×C17—41no—
560C4×C17—41no—
561C4×C17—41no—
562C4×C17—42no—
563C4×C17#57712yes—
564C4×C17C2×2−1+411yescharacteristic
565C4×C17C2×2−1+411yescharacteristic
566#562—22no—
567#559C22×C1711yescharacteristic
568#559C22×C1712yes—
569Q82C22×C1711yescharacteristic
570Q82C22×C1711yescharacteristic
571#557C22×C1712yes—
572#557C22×C1711yescharacteristic
573#554—21no—
574#554—21no—
575#554C22×C1711yescharacteristic
576#554C22×C1711yescharacteristic
577#554C22×C1712yes—
578#550C22×C1711yescharacteristic
579D4×Q8—22no—
580D4×Q8C22×C1712yes—
581D4×Q8C22×C1711yescharacteristic
582#548—21no—
583#547—21no—
584#544—22no—
585#544C22×C1712yes—
586#542—21no—
587#542C22×C1712yes—
588#540C22×C1712yes—
589#539—22no—
590#536—21no—
591#533—21no—
592#533C22×C1711yescharacteristic
593#532C22×C1711yescharacteristic
594C2×C4⋊Q8—21no—
595C2×C4⋊Q8C22×C1711yescharacteristic
596#529C22×C1711yescharacteristic
597#520C22×C1712yes—
598C4×#41C22×C1711yescharacteristic
599#501C22×C1712yes—
600#501C22×C1712yes—
601#501C22×C1712yes—
602#499C22×C1712yes—
603#498C22×C1711yescharacteristic
604#498C22×C1712yes—
605#498C22×C1711yescharacteristic
606#490C22×C1712yes—
607#489C22×C1712yes—
608#489C22×C1712yes—
609#488C22×C1712yes—
610#486C22×C1711yescharacteristic
611#486C22×C1712yes—
612#486C22×C1711yescharacteristic
613#485C22×C1711yescharacteristic
614#483C22×C1712yes—
615#482C22×C1711yescharacteristic
616#482C22×C1712yes—
617#481C22×C1712yes—
618#481C22×C1712yes—
619#480C22×C1712yes—
620#479C22×C1711yescharacteristic
621#479C22×C1712yes—
622#479C22×C1712yes—
623#478C22×C1711yescharacteristic
624#478C22×C1712yes—
625#478C22×C1712yes—
626#478C22×C1712yes—
627#478C22×C1712yes—
628#477C22×C1711yescharacteristic
629#477C22×C1711yescharacteristic
630#476C22×C1711yescharacteristic
631#476C22×C1712yes—
632#476C22×C1711yescharacteristic
633#476C22×C1712yes—
634#476C22×C1712yes—
635#476C22×C1712yes—
636#476C22×C1712yes—
637#475C22×C1711yescharacteristic
638#475C22×C1712yes—
639#475C22×C1712yes—
640#474C22×C1711yescharacteristic
641#474C22×C1712yes—
642#464C22×C1711yescharacteristic
643#464C22×C1712yes—
644#463C22×C1711yescharacteristic
645#463C22×C1712yes—
646#460C22×C1711yescharacteristic
647#460C22×C1712yes—
648#459C22×C1711yescharacteristic
649#459C22×C1712yes—
650#452C22×C1711yescharacteristic
651#449C22×C1711yescharacteristic
652#449C22×C1712yes—
653#446C22×C1711yescharacteristic
654#446C22×C1712yes—
655#446C22×C1712yes—
656#446C22×C1711yescharacteristic
657C8×Q8C22×C1711yescharacteristic
658C8×Q8C22×C1711yescharacteristic
659#442C22×C1712yes—
660#442C22×C1712yes—
661#442C22×C1712yes—
662#441C22×C1712yes—
663#440C22×C1712yes—
664#440C22×C1712yes—
665C4×Q16C22×C1711yescharacteristic
666C4×SD16C22×C1711yescharacteristic
667C4×SD16C22×C1711yescharacteristic
668C4×SD16C22×C1712yes—
669C4×SD16C22×C1712yes—
670C4×SD16C22×C1712yes—
671C4×D8C22×C1711yescharacteristic
672C4×D8C22×C1712yes—
673#433C22×C1712yes—
674#433C22×C1712yes—
675#432C22×C1711yescharacteristic
676#431C22×C1711yescharacteristic
677C2×C17—41no—
678C2×C17—42no—
679C2×C17—82no—
680C2×C17—81no—
681C2×C17#348611yescharacteristic
682C2×C17C2×#57711yescharacteristic
683C2×C17#358511yescharacteristic
684C2×#41—21no—
685C2×#41—21no—
686C2×#41C23×C1711yescharacteristic
687C22×Q8—22no—
688C22×Q8—21no—
689C22×Q8—21no—
690C2×Q16C23×C1711yescharacteristic
691C2×SD16C23×C1711yescharacteristic
692C2×SD16C23×C1711yescharacteristic
693C2×SD16C23×C1712yes—
694C2×D8C23×C1711yescharacteristic
695C2×D8C23×C1712yes—
696C4⋊Q8—22no—
697C4⋊Q8—21no—
698C4⋊Q8—22no—
699C4⋊Q8—21no—
700C4⋊Q8—21no—
701C4⋊Q8—22no—
702C4⋊Q8—22no—
703C4⋊Q8—21no—
704C4⋊Q8—21no—
705C4⋊Q8D4×C1711yescharacteristic
706C4⋊Q8D4×C1711yescharacteristic
707C4⋊Q8C23×C1712yes—
708C4⋊Q8C23×C1711yescharacteristic
709C4⋊Q8C23×C1711yescharacteristic
710C4⋊Q8C23×C1711yescharacteristic
711C4⋊Q8C23×C1712yes—
712C4⋊Q8C23×C1712yes—
713C4⋊Q8C23×C1712yes—
714#127C23×C1711yescharacteristic
715#127C23×C1712yes—
716#126—22no—
717#126—21no—
718#125—22no—
719#125—22no—
720#125—22no—
721#125—22no—
722#125D4×C1712yes—
723#125C23×C1711yescharacteristic
724#125C23×C1712yes—
725#125C23×C1712yes—
726#125C23×C1712yes—
727#124—21no—
728#124—22no—
729#124—22no—
730#124—21no—
731#124C23×C1711yescharacteristic
732#124C23×C1712yes—
733#123—21no—
734#123—22no—
735#123—22no—
736#123—22no—
737#123—22no—
738#123—22no—
739#123—22no—
740C22⋊Q8—21no—
741C22⋊Q8—21no—
742C22⋊Q8—22no—
743C22⋊Q8—22no—
744C22⋊Q8—22no—
745C22⋊Q8—22no—
746C22⋊Q8—22no—
747C22⋊Q8—22no—
748C22⋊Q8—21no—
749C22⋊Q8—22no—
750C22⋊Q8—22no—
751C22⋊Q8—22no—
752C22⋊Q8—22no—
753C22⋊Q8—22no—
754C22⋊Q8—22no—
755C22⋊Q8D4×C1711yescharacteristic
756C22⋊Q8D4×C1711yescharacteristic
757C22⋊Q8D4×C1712yes—
758C22⋊Q8C23×C1711yescharacteristic
759#121—21no—
760#121—22no—
761#121—21no—
762#121—22no—
763#121—22no—
764#121C23×C1711yescharacteristic
765#121C23×C1712yes—
766C4×Q8—21no—
767C4×Q8—21no—
768C4×Q8—22no—
769C4×Q8—21no—
770C4×Q8C23×C1711yescharacteristic
771C4×Q8C23×C1711yescharacteristic
772C4×Q8C23×C1712yes—
773C4×Q8C23×C1712yes—
774C4×Q8C23×C1711yescharacteristic
775C4×Q8C23×C1712yes—
776C4×Q8C23×C1712yes—
777C4×Q8C23×C1711yescharacteristic
778C4×Q8C23×C1711yescharacteristic
779C4×D4—21no—
780C4×D4—21no—
781C4×D4—21no—
782C4×D4—22no—
783C4×D4—21no—
784C4×D4—22no—
785C4×D4—22no—
786C4×D4—21no—
787C4×D4C23×C1711yescharacteristic
788C4×D4C23×C1711yescharacteristic
789C4×D4C23×C1712yes—
790C4×D4C23×C1712yes—
791C4×D4C23×C1711yescharacteristic
792C4×D4C23×C1712yes—
793C4×D4C23×C1712yes—
794C4×D4C23×C1712yes—
795C4×D4C23×C1712yes—
796#117—22no—
797#117—21no—
798#117—21no—
799#117C23×C1711yescharacteristic
800#117C23×C1712yes—
801C2×C4⋊C4—21no—
802C2×C4⋊C4—22no—
803C2×C4⋊C4—21no—
804C2×C4⋊C4—21no—
805C2×C4⋊C4—22no—
806C2×C4⋊C4C23×C1712yes—
807C2×C42—21no—
808C2×C42C23×C1711yescharacteristic
809#107C23×C1712yes—
810#107C23×C1711yescharacteristic
811#107C23×C1711yescharacteristic
812#107C23×C1712yes—
813#107C23×C1712yes—
814#106C23×C1712yes—
815#106C23×C1712yes—
816#106C23×C1711yescharacteristic
817#106C23×C1712yes—
818#106C23×C1711yescharacteristic
819#106C23×C1712yes—
820#106C23×C1712yes—
821#106C23×C1712yes—
822#106C23×C1712yes—
823C4⋊C8C23×C1711yescharacteristic
824C4⋊C8C23×C1711yescharacteristic
825C4⋊C8C23×C1711yescharacteristic
826C4⋊C8C23×C1711yescharacteristic
827C4⋊C8C23×C1712yes—
828C4⋊C8C23×C1712yes—
829C4⋊C8C23×C1712yes—
830C4⋊C8C23×C1712yes—
831#103C23×C1711yescharacteristic
832#103C23×C1712yes—
833#103C23×C1712yes—
834#103C23×C1711yescharacteristic
835#103C23×C1711yescharacteristic
836#103C23×C1711yescharacteristic
837#103C23×C1712yes—
838#102C23×C1711yescharacteristic
839#102C23×C1711yescharacteristic
840#102C23×C1712yes—
841#102C23×C1711yescharacteristic
842#102C23×C1712yes—
843#102C23×C1712yes—
844#102C23×C1711yescharacteristic
845#102C23×C1712yes—
846#102C23×C1712yes—
847#102C23×C1712yes—
848#102C23×C1712yes—
849#102C23×C1712yes—
850#102C23×C1712yes—
851C22⋊C8C23×C1711yescharacteristic
852C22⋊C8C23×C1711yescharacteristic
853C22⋊C8C23×C1712yes—
854#97C23×C1712yes—
855#97C23×C1712yes—
856#97C23×C1712yes—
857C4×C8C23×C1711yescharacteristic
858C4×C8C23×C1711yescharacteristic
859C4×C8C23×C1712yes—
860C4×C8C23×C1712yes—
861C17#6186011yescharacteristic, direct product factor, Sylow
862#41—22no—
863#41—22no—
864#41—82no—
865#41—82no—
866C2×Q8—21no—
867C2×Q8—22no—
868C2×Q8—22no—
869C2×Q8—22no—
870C2×Q8—22no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—82no—
874C2×Q8—82no—
875C2×Q8—84no—
876C2×Q8C2×D4×C1711yescharacteristic
877C2×Q8C2×D4×C1711yescharacteristic
878C2×Q8C2×D4×C1712yes—
879C2×Q8C24×C1711yescharacteristic
880C2×Q8C24×C1711yescharacteristic
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—22no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—22no—
887C2×D4—22no—
888C2×D4C24×C1712yes—
889C2×D4C24×C1711yescharacteristic
890C2×D4C24×C1711yescharacteristic
891C22×C4—21no—
892C22×C4—22no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4C2×D4×C1711yescharacteristic
903C22×C4C2×D4×C1711yescharacteristic
904C22×C4C24×C1711yescharacteristic
905Q16—22no—
906SD16—22no—
907SD16—24no—
908SD16—22no—
909D8—22no—
910D8—24no—
911C2×C8C24×C1711yescharacteristic
912C2×C8C24×C1711yescharacteristic
913C2×C8C24×C1711yescharacteristic
914C2×C8C24×C1712yes—
915C2×C8C24×C1711yescharacteristic
916C2×C8C24×C1712yes—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—22no—
927C4⋊C4—22no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—21no—
940C4⋊C4C2×D4×C1712yes—
941C4⋊C4C2×D4×C1711yescharacteristic
942C4⋊C4C2×D4×C1711yescharacteristic
943C4⋊C4C2×D4×C1712yes—
944C4⋊C4C2×D4×C1712yes—
945C4⋊C4C2×D4×C1712yes—
946C4⋊C4C2×D4×C1712yes—
947C4⋊C4C2×D4×C1712yes—
948C4⋊C4C2×D4×C1712yes—
949C4⋊C4C24×C1712yes—
950C4⋊C4C24×C1712yes—
951C4⋊C4C24×C1711yescharacteristic
952C4⋊C4C24×C1711yescharacteristic
953C4⋊C4C24×C1711yescharacteristic
954C4⋊C4C24×C1712yes—
955C4⋊C4C24×C1711yescharacteristic
956C22⋊C4—21no—
957C22⋊C4—21no—
958C22⋊C4—21no—
959C22⋊C4—21no—
960C22⋊C4—22no—
961C22⋊C4—22no—
962C22⋊C4—21no—
963C22⋊C4—21no—
964C22⋊C4—21no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—21no—
969C22⋊C4—22no—
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4C2×D4×C1712yes—
974C22⋊C4C2×D4×C1712yes—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—22no—
980C42—22no—
981C42—22no—
982C42C2×D4×C1711yescharacteristic
983C42C2×D4×C1711yescharacteristic
984C42C24×C1711yescharacteristic
985C42C24×C1712yes—
986C42C24×C1712yes—
987C42C24×C1711yescharacteristic
988C23—21no—
989C23—21no—
990C23—22no—
991C23C22×D4×C1711yescharacteristic
992Q8—22no—
993Q8—22no—
994Q8—21no—
995Q8—21no—
996Q8—21no—
997Q8—42no—
998Q8—44no—
999Q8—42no—
1000Q8—82no—
1001Q8—81no—
1002Q8—81no—
1003Q8—82no—
1004Q8—82no—
1005Q8C17×2−1+412yes—
1006D4—24no—
1007D4—21no—
1008D4—22no—
1009D4—21no—
1010D4—21no—
1011D4—22no—
1012D4—42no—
1013D4—82no—
1014D4—81no—
1015D4—82no—
1016D4—82no—
1017D4—81no—
1018D4C17×2−1+412yes—
1019C2×C4—24no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—41no—
1033C2×C4—42no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—82no—
1037C2×C4—82no—
1038C2×C4—82no—
1039C2×C4—82no—
1040C2×C4—82no—
1041C2×C4—82no—
1042C2×C4—82no—
1043C2×C4C22×D4×C1711yescharacteristic
1044C2×C4C22×D4×C1711yescharacteristic
1045C2×C4C22×D4×C1712yes—
1046C2×C4C22×D4×C1712yes—
1047C2×C4C22×D4×C1712yes—
1048C2×C4C22×D4×C1711yescharacteristic
1049C2×C4C22×D4×C1711yescharacteristic
1050C2×C4C22×D4×C1712yes—
1051C2×C4C22×D4×C1711yescharacteristic
1052C2×C4C25×C1711yescharacteristic
1053C8—21no—
1054C8—22no—
1055C8—21no—
1056C8—22no—
1057C8—21no—
1058C8—21no—
1059C22—21no—
1060C22—22no—
1061C22—21no—
1062C22—21no—
1063C22—41no—
1064C22—41no—
1065C22—41no—
1066C22—42no—
1067C22—41no—
1068C22—42no—
1069C22—42no—
1070C22—41no—
1071C22C23×D4×C1711yescharacteristic
1072C4—21no—
1073C4—22no—
1074C4—21no—
1075C4—22no—
1076C4—22no—
1077C4—21no—
1078C4—21no—
1079C4—22no—
1080C4—22no—
1081C4—41no—
1082C4—41no—
1083C4—41no—
1084C4—42no—
1085C4—41no—
1086C4—41no—
1087C4—42no—
1088C4—42no—
1089C4C17×#57712yes—
1090C4C2×C17×2−1+411yescharacteristic
1091C4C2×C17×2−1+411yescharacteristic
1092C2—41no—
1093C2—42no—
1094C2—81no—
1095C2—82no—
1096C2C17×#348611yescharacteristic
1097C2C2×C17×#57711yescharacteristic
1098C2C17×#358511yescharacteristic
subgroupG/H
center, socleC22×C17C23×D4
commutator, Frattini, cosocleC2×C4C25×C17
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C17×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#3554C2semidirect
2. C17×#3503C2semidirect
3. C17×#3388C2semidirect
4. C17×#3387C2semidirect
5. C17×#3384C2semidirect
6. C17×#3384C2semidirect
7. C17×#3381C2semidirect
8. Q8×SD16×C17C2semidirect
9. C17×#3375C2semidirect
10. C17×#3373C2semidirect
11. C17×#3371C2semidirect
12. C17×#3366C2semidirect
13. C17×#3362C2semidirect
14. C17×#3361C2semidirect
15. C17×#3244C2semidirect
16. C17×#3241C2semidirect
17. C17×#3238C2semidirect
18. C17×#3227C2semidirect
19. C17×#3125C2semidirect
20. C17×#3119C2semidirect
21. C17×#3115C2semidirect
22. C17×#3102C2semidirect
23. C17×#2985C2semidirect
438. #61860C17direct (N × H)
510. #3554C2×C17semidirect
511. #3503C2×C17semidirect
512. #3388C2×C17semidirect
513. #3387C2×C17semidirect
514. #3384C2×C17semidirect
515. #3384C2×C17semidirect
516. #3381C2×C17semidirect
517. Q8×SD16C2×C17semidirect
518. #3375C2×C17semidirect
519. #3373C2×C17semidirect
520. #3371C2×C17semidirect
521. #3366C2×C17semidirect
522. #3362C2×C17semidirect
523. #3361C2×C17semidirect
524. #3244C2×C17semidirect
525. #3241C2×C17semidirect
526. #3238C2×C17semidirect
527. #3227C2×C17semidirect
528. #3125C2×C17semidirect
529. #3119C2×C17semidirect
530. #3115C2×C17semidirect
531. #3102C2×C17semidirect
532. #2985C2×C17semidirect
861. C17#61860direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#35542
C17×#35032
C17×#33882
C17×#33872
C17×#33842
C17×#33812
Q8×SD16×C172
C17×#33752
C17×#33732
C17×#33712
C17×#33662
C17×#33622
C17×#33612
C17×#32442
C17×#32412
C17×#32382
C17×#32272
C17×#31252
C17×#31192
C17×#31152
C17×#31022
C17×#29852
#6186017