Finite Group Databasebeta

← D17×#1863 #17035249

Subgroups — D17×#1863 #17035249

Order 4352.

1542 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D17C211yesmaximal, characteristic
2C2×#107×D17C211yesmaximal, characteristic
3C2×#103×D17C211yesmaximal, characteristic
4C2×#103×D17C211yesmaximal, characteristic
5D17×#389C211yesmaximal, characteristic
6#14529041C211yesmaximal, characteristic, complemented
7#14529040C211yesmaximal, characteristic, complemented
8#14529039C211yesmaximal, characteristic, complemented
9#14529038C211yesmaximal, characteristic, complemented
10#14529037C211yesmaximal, characteristic, complemented
11#14529036C211yesmaximal, characteristic, complemented
12#14529035C211yesmaximal, characteristic, complemented
13D17×#340C211yesmaximal, characteristic
14D17×#336C211yesmaximal, characteristic
15C17×#1863C211yesmaximal, characteristic, complemented
16C22×Q8×D17C2211yescharacteristic
17C22×C8×D17C2211yescharacteristic
18C22×C8×D17C2211yescharacteristic
19C2×Q8×Dic17C2211yescharacteristic
20C2×C4×Dic34—21no—
21C2×C4×Dic34C2211yescharacteristic
22C2×#10587573—21no—
23C2×#10587573C2211yescharacteristic
24C4×Q8×D17—24no—
25C4×Q8×D17—24no—
26C2×C4⋊C4×D17—21no—
27C2×C4⋊C4×D17—21no—
28C2×C4⋊C4×D17C2211yescharacteristic
29C2×C4⋊C4×D17C2211yescharacteristic
30C2×C4⋊C4×D17C2211yescharacteristic
31C2×C42×D17—21no—
32C2×C42×D17C2211yescharacteristic
33C2×#10587489C2211yescharacteristic
34C2×#10587478C2211yescharacteristic
35C2×#10587478C2211yescharacteristic
36#107×D17—24no—
37C2×#10587487C2211yescharacteristic
38C2×#10587487C2211yescharacteristic
39C2×#10587506C2211yescharacteristic
40C2×#10587506C2211yescharacteristic
41C2×#10587481C2211yescharacteristic
42C2×#10587481C2211yescharacteristic
43#103×D17—24no—
44#103×D17C418yescomplemented
45#11762708C2211yescharacteristic
46#11762707C2211yescharacteristic
47#11762706—21no—
48#11762705C2211yescharacteristic
49#11762704—21no—
50#95×D17—21no—
51#11762572C2211yescharacteristic
52#11762571C2211yescharacteristic
53#11762571C2211yescharacteristic
54#11762564C2211yescharacteristic
55#11762563C2211yescharacteristic
56#11762563C2211yescharacteristic
57C2×C4×Q8×C17C2211yescharacteristic
58C2×C17×#107C2211yescharacteristic
59C2×C17×#103C2211yescharacteristic
60C2×C17×#103C2211yescharacteristic
61C17×#389C2211yescharacteristic
62C17×#340C2211yescharacteristic
63C17×#336C2211yescharacteristic
64C22×Q8×C17C2311yescharacteristic
65C2×Q8×D17—22no—
66C2×Q8×D17—22no—
67C2×Q8×D17—22no—
68C2×Q8×D17C2×C414yes—
69C2×Q8×D17D414yes—
70C2×Q8×D17Q814yes—
71C22×C4×D17—21no—
72C22×C4×D17—21no—
73C22×C4×D17—21no—
74C22×C4×D17—21no—
75C22×C4×D17D411yescharacteristic
76C22×C4×D17D411yescharacteristic
77C22×C4×D17C2311yescharacteristic
78C22×Dic34—21no—
79C22×Dic34C2311yescharacteristic
80C22×C8×C17C2311yescharacteristic
81C22×C8×C17C2311yescharacteristic
82C4×Q8×C17—22no—
83C4×Q8×C17—22no—
84C2×C4⋊C4×C17—21no—
85C2×C4⋊C4×C17—21no—
86C2×C4⋊C4×C17C2311yescharacteristic
87C2×C4⋊C4×C17C2311yescharacteristic
88C2×C4⋊C4×C17C2311yescharacteristic
89C2×C42×C17—21no—
90C2×C42×C17C2311yescharacteristic
91Q8×Dic17—22no—
92Q8×Dic17—22no—
93C2×C4⋊Dic17—21no—
94C2×C4⋊Dic17—21no—
95C2×C4⋊Dic17C2311yescharacteristic
96C2×C4⋊Dic17C2311yescharacteristic
97C2×C4⋊Dic17C2311yescharacteristic
98C2×#63225—21no—
99C2×#63225—21no—
100C2×#63225—21no—
101C2×#63225—21no—
102C2×#63225—21no—
103C2×#63225—21no—
104C2×#63225—21no—
105C2×C4×Dic17—21no—
106C2×C4×Dic17—21no—
107C2×C4×Dic17—21no—
108C2×C4×Dic17D411yescharacteristic
109C2×C4×Dic17D411yescharacteristic
110C2×C4×Dic17C2311yescharacteristic
111C22×#3622C2311yescharacteristic
112C22×#3622C2311yescharacteristic
113C2×C8×D17—22no—
114C2×C8×D17—22no—
115C2×C8×D17—22no—
116C2×C8×D17—22no—
117C2×C8×D17—22no—
118C2×C8×D17C2×C414yes—
119C4⋊C4×D17—28no—
120C4⋊C4×D17—22no—
121C4⋊C4×D17—22no—
122C4⋊C4×D17—22no—
123C4⋊C4×D17—22no—
124C4⋊C4×D17—44no—
125C4⋊C4×D17C2×C414yes—
126C4⋊C4×D17D414yes—
127#10587573—28no—
128#10587573—22no—
129#10587573—22no—
130C42×D17—28no—
131C42×D17—22no—
132C42×D17—22no—
133C4×Dic34—28no—
134C4×Dic34—22no—
135C4×Dic34—22no—
136C17×#107—22no—
137C17×#103—22no—
138C17×#103C2×C414yescomplemented
139C17×#95—21no—
140#10587506—22no—
141#10587506C2×C414yescomplemented
142#10587502—21no—
143#10587502—21no—
144#10587502—21no—
145#10587489—22no—
146#10587487—22no—
147#10587487C2×C414yescomplemented
148#10587481—22no—
149#10587481C2×C414yescomplemented
150#10587478—22no—
151#10587478—22no—
152C23×D17C2×D411yescharacteristic
153C2×Q8×C17—21no—
154C2×Q8×C17—21no—
155C2×Q8×C17—21no—
156C2×Q8×C17C22×C412yes—
157C2×Q8×C17C2×D412yes—
158C2×Q8×C17C2×Q812yes—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17C2×D411yescharacteristic
164C22×C4×C17C2×D411yescharacteristic
165C22×C4×C17C2411yescharacteristic
166C22×Dic17—21no—
167C22×Dic17—21no—
168C22×Dic17—21no—
169C22×Dic17—21no—
170C22×Dic17C2×D411yescharacteristic
171C22×Dic17C2×D411yescharacteristic
172C22×Dic17C2×D411yescharacteristic
173Q8×D17—28no—
174Q8×D17—28no—
175Q8×D17—28no—
176Q8×D17C4⋊C4116yescomplemented
177C2×C4×D17—24no—
178C2×C4×D17—24no—
179C2×C4×D17—22no—
180C2×C4×D17—24no—
181C2×C4×D17—22no—
182C2×C4×D17—24no—
183C2×C4×D17—24no—
184C2×C4×D17—22no—
185C2×C4×D17—22no—
186C2×C4×D17—22no—
187C2×C4×D17—42no—
188C2×C4×D17—42no—
189C2×C4×D17—42no—
190C2×C4×D17—42no—
191C2×C4×D17—42no—
192C2×C4×D17—42no—
193C2×C4×D17—42no—
194C2×C4×D17Q1614yes—
195C2×C4×D17C22×C412yes—
196C2×C4×D17C2×D412yes—
197C2×C4×D17C2×D412yes—
198C2×C4×D17C2×Q812yes—
199C2×C4×D17#4112yes—
200C2×C4×D17#4112yes—
201C2×Dic34—21no—
202C2×Dic34—21no—
203C2×Dic34—21no—
204C2×Dic34—24no—
205C2×Dic34—24no—
206C2×Dic34—24no—
207C2×Dic34C22×C412yes—
208C2×Dic34C2×D412yes—
209C2×Dic34C2×Q812yes—
210C2×C8×C17—21no—
211C2×C8×C17—21no—
212C2×C8×C17—21no—
213C2×C8×C17—21no—
214C2×C8×C17—21no—
215C2×C8×C17C22×C412yes—
216C4⋊C4×C17—24no—
217C4⋊C4×C17—21no—
218C4⋊C4×C17—21no—
219C4⋊C4×C17—21no—
220C4⋊C4×C17—21no—
221C4⋊C4×C17—42no—
222C4⋊C4×C17C22×C412yes—
223C4⋊C4×C17C2×D412yes—
224C42×C17—24no—
225C42×C17—21no—
226C42×C17—21no—
227C4⋊Dic17—24no—
228C4⋊Dic17—21no—
229C4⋊Dic17—21no—
230C4⋊Dic17—21no—
231C4⋊Dic17—21no—
232C4⋊Dic17—42no—
233C4⋊Dic17C22×C412yes—
234C4⋊Dic17C2×D412yes—
235#63225—24no—
236#63225—24no—
237#63225—24no—
238#63225—24no—
239#63225—42no—
240#63225—42no—
241#63225—42no—
242C4×Dic17—24no—
243C4×Dic17—24no—
244C4×Dic17—24no—
245C4×Dic17—21no—
246C4×Dic17—21no—
247C4×Dic17—22no—
248C4×Dic17—22no—
249C2×#3622—21no—
250C2×#3622—21no—
251C2×#3622—21no—
252C2×#3622—21no—
253C2×#3622—21no—
254C2×#3622C22×C412yes—
255C8×D17—28no—
256C8×D17—44no—
257C2×#1863—171nomaximal, Sylow
258C23×C17C22×D411yescharacteristic
259C22×D17C4×D412yes—
260C22×D17#12012yes—
261C22×D17C22⋊Q812yes—
262C22×D17C2×Q1612yes—
263C22×D17#13512yes—
264C22×D17AGL(1,ℤ/8)12yes—
265C22×D17#13712yes—
266Q8×C17—22no—
267Q8×C17—22no—
268Q8×C17—22no—
269Q8×C17C2×C4⋊C414yescomplemented
270C2×C4×C17—22no—
271C2×C4×C17—21no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—21no—
275C2×C4×C17—22no—
276C2×C4×C17—21no—
277C2×C4×C17—22no—
278C2×C4×C17—21no—
279C2×C4×C17—21no—
280C2×C4×C17—41no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—41no—
284C2×C4×C17—41no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17C2×Q1612yes—
288C2×C4×C17C23×C411yescharacteristic
289C2×C4×C17C22×D411yescharacteristic
290C2×C4×C17C22×D411yescharacteristic
291C2×C4×C17C22×Q811yescharacteristic
292C2×C4×C17C2×#4111yescharacteristic
293C2×C4×C17C2×#4111yescharacteristic
294C2×Dic17—22no—
295C2×Dic17—22no—
296C2×Dic17—21no—
297C2×Dic17—22no—
298C2×Dic17—21no—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17—21no—
302C2×Dic17—21no—
303C2×Dic17—21no—
304C2×Dic17—41no—
305C2×Dic17—41no—
306C2×Dic17—41no—
307C2×Dic17—41no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17C4×D412yes—
312C2×Dic17#12012yes—
313C2×Dic17C22⋊Q812yes—
314C2×Dic17C2×Q1612yes—
315C4×D17—216no—
316C4×D17—28no—
317C4×D17—48no—
318C4×D17—44no—
319C4×D17—48no—
320C4×D17—84no—
321C4×D17C2×C4⋊C414yes—
322C4×D17C4×D414yes—
323C4×D17C22⋊Q814yes—
324C4×D17#12314yes—
325Dic34—22no—
326Dic34—22no—
327Dic34—22no—
328Dic34—216no—
329Dic34C2×C4⋊C414yescomplemented
330C8×C17—22no—
331C8×C17—41no—
332#3622—22no—
333#3622—41no—
334C22×C4×Q8—171no—
335C22×#107—171no—
336C22×#103—171no—
337C22×#103—171no—
338C2×#389—171no—
339#1863—171no—
340#1863—171no—
341#1863—171no—
342#1863—171no—
343#1863—171no—
344#1863—171no—
345#1863—171no—
346#1863D1711yescharacteristic, direct product factor
347C2×#340—171no—
348C2×#336—171no—
349C22×C17C2×C4×D411yescharacteristic
350C22×C17C2×#12011yescharacteristic
351C22×C17C2×C22⋊Q811yescharacteristic
352C22×C17C22×Q1611yescharacteristic
353C22×C17C2×#13511yescharacteristic
354C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C17C2×#13711yescharacteristic
356C2×D17#38514yes—
357C2×D17C4×Q1614yes—
358C2×D17#44014yes—
359C2×D17#44914yes—
360C2×D17#45114yes—
361C2×D17#47714yes—
362C2×D17#47914yes—
363C4×C17—22no—
364C4×C17—24no—
365C4×C17—42no—
366C4×C17—41no—
367C4×C17—42no—
368C4×C17—81no—
369C4×C17C22×C4⋊C411yescharacteristic
370C4×C17C2×C4×D411yescharacteristic
371C4×C17C2×C22⋊Q811yescharacteristic
372C4×C17C2×#12311yescharacteristic
373Dic17—22no—
374Dic17—24no—
375Dic17—42no—
376Dic17—41no—
377Dic17—42no—
378Dic17—81no—
379Dic17#38514yes—
380C23×Q8—171no—
381C23×C8—171no—
382C23×C8—171no—
383C2×C4×Q8—171no—
384C2×C4×Q8—171no—
385C2×C4×Q8—171no—
386C2×C4×Q8—341no—
387C2×C4×Q8—341no—
388C2×C4×Q8—344no—
389C2×C4×Q8—344no—
390C2×C4×Q8C2×D1711yescharacteristic
391C22×C4⋊C4—171no—
392C22×C4⋊C4—171no—
393C22×C4⋊C4—171no—
394C22×C4⋊C4—341no—
395C22×C4⋊C4—341no—
396C22×C42—171no—
397C22×C42—341no—
398C2×#107—171no—
399C2×#107—171no—
400C2×#107—171no—
401C2×#107—344no—
402C2×#107C2×D1711yescharacteristic
403C2×#103—171no—
404C2×#103—171no—
405C2×#103—171no—
406C2×#103—178no—
407C2×#103—171no—
408C2×#103—171no—
409C2×#103—171no—
410C2×#103—344no—
411C2×#103C2×D1711yescharacteristic
412C2×#103C2×D1711yescharacteristic
413#389—171no—
414#389—171no—
415#389—171no—
416#389—341no—
417#389—341no—
418#389C2×D1711yescharacteristic
419C2×#95—341no—
420#340—171no—
421#340—171no—
422#340—171no—
423#340C2×D1711yescharacteristic
424#336—171no—
425#336—171no—
426#336—171no—
427#336C2×D1711yescharacteristic
428C2×C17C2×#38511yescharacteristic
429C2×C17C2×C4×Q1611yescharacteristic
430C2×C17C2×#44011yescharacteristic
431C2×C17C2×#45111yescharacteristic
432C2×C17C2×#44911yescharacteristic
433C2×C17C2×#47711yescharacteristic
434C2×C17C2×#47911yescharacteristic
435D17#186318yesdirect product factor
436C22×Q8—174no—
437C22×Q8—174no—
438C22×Q8—174no—
439C22×Q8—171no—
440C22×Q8—341no—
441C22×Q8—342no—
442C22×Q8—342no—
443C22×Q8—342no—
444C22×Q8C22×D1711yescharacteristic
445C23×C4—171no—
446C23×C4—171no—
447C23×C4—171no—
448C23×C4—341no—
449C23×C4—341no—
450C23×C4—341no—
451C23×C4—341no—
452C22×C8—171no—
453C22×C8—174no—
454C22×C8—171no—
455C22×C8—342no—
456C22×C8—342no—
457C22×C8—342no—
458C22×C8—342no—
459C22×C8—342no—
460C22×C8C22×D1711yescharacteristic
461C22×C8C22×D1711yescharacteristic
462C4×Q8—22no—
463C4×Q8—22no—
464C4×Q8—342no—
465C4×Q8—342no—
466C4×Q8—348no—
467C4×Q8—342no—
468C4×Q8—348no—
469C4×Q8—342no—
470C4×Q8—342no—
471C4×Q8—342no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—171no—
475C2×C4⋊C4—171no—
476C2×C4⋊C4—174no—
477C2×C4⋊C4—174no—
478C2×C4⋊C4—171no—
479C2×C4⋊C4—342no—
480C2×C4⋊C4—342no—
481C2×C4⋊C4—348no—
482C2×C4⋊C4—342no—
483C2×C4⋊C4—342no—
484C2×C4⋊C4—341no—
485C2×C4⋊C4—341no—
486C2×C4⋊C4—341no—
487C2×C4⋊C4—341no—
488C2×C4⋊C4—341no—
489C2×C4⋊C4—341no—
490C2×C4⋊C4—341no—
491C2×C4⋊C4—341no—
492C2×C4⋊C4—341no—
493C2×C4⋊C4—684no—
494C2×C4⋊C4C22×D1711yescharacteristic
495C2×C4⋊C4C22×D1711yescharacteristic
496C2×C4⋊C4C22×D1711yescharacteristic
497C2×C42—21no—
498C2×C42—171no—
499C2×C42—171no—
500C2×C42—171no—
501C2×C42—342no—
502C2×C42—342no—
503C2×C42—348no—
504C2×C42—341no—
505C2×C42—341no—
506C2×C42—341no—
507C2×C42C22×D1711yescharacteristic
508#107—22no—
509#107—342no—
510#107—342no—
511#107—342no—
512#103—22no—
513#103—174no—
514#103—174no—
515#103—174no—
516#103—342no—
517#103—342no—
518#103—342no—
519#103C4×D1714yescomplemented
520#95—21no—
521#95—341no—
522#95—341no—
523#95—341no—
524C17C2×#186311yescharacteristic, complemented, Sylow
525C24—171no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—1716no—
530C2×Q8—172no—
531C2×Q8—172no—
532C2×Q8—172no—
533C2×Q8—344no—
534C2×Q8—344no—
535C2×Q8—344no—
536C2×Q8—348no—
537C2×Q8—348no—
538C2×Q8—348no—
539C2×Q8—341no—
540C2×Q8—341no—
541C2×Q8—341no—
542C2×Q8C2×C4×D1712yes—
543C2×Q8D4×D1712yes—
544C2×Q8Q8×D1712yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—171no—
550C22×C4—172no—
551C22×C4—172no—
552C22×C4—172no—
553C22×C4—172no—
554C22×C4—172no—
555C22×C4—172no—
556C22×C4—171no—
557C22×C4—174no—
558C22×C4—171no—
559C22×C4—342no—
560C22×C4—344no—
561C22×C4—342no—
562C22×C4—344no—
563C22×C4—344no—
564C22×C4—344no—
565C22×C4—342no—
566C22×C4—344no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4—341no—
570C22×C4—341no—
571C22×C4—341no—
572C22×C4—341no—
573C22×C4—682no—
574C22×C4—682no—
575C22×C4—682no—
576C22×C4—682no—
577C22×C4—682no—
578C22×C4—682no—
579C22×C4—682no—
580C22×C4D4×D1711yescharacteristic
581C22×C4D4×D1711yescharacteristic
582C22×C4C23×D1711yescharacteristic
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—172no—
589C2×C8—348no—
590C2×C8—341no—
591C2×C8—341no—
592C2×C8—341no—
593C2×C8—341no—
594C2×C8—341no—
595C2×C8—684no—
596C2×C8C2×C4×D1712yes—
597C4⋊C4—24no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—172no—
604C4⋊C4—172no—
605C4⋊C4—344no—
606C4⋊C4—344no—
607C4⋊C4—344no—
608C4⋊C4—344no—
609C4⋊C4—344no—
610C4⋊C4—341no—
611C4⋊C4—341no—
612C4⋊C4—341no—
613C4⋊C4—341no—
614C4⋊C4—682no—
615C4⋊C4—682no—
616C4⋊C4—682no—
617C4⋊C4—682no—
618C4⋊C4C2×C4×D1712yes—
619C4⋊C4D4×D1712yes—
620C42—24no—
621C42—21no—
622C42—21no—
623C42—342no—
624C42—342no—
625C42—344no—
626C42—344no—
627C42—344no—
628C42—341no—
629C42—341no—
630C23—172no—
631C23—172no—
632C23—172no—
633C23—172no—
634C23—172no—
635C23—172no—
636C23—172no—
637C23C2×D4×D1711yescharacteristic
638Q8—22no—
639Q8—22no—
640Q8—22no—
641Q8—174no—
642Q8—3416no—
643Q8—342no—
644Q8—342no—
645Q8—342no—
646Q8C4⋊C4×D1714yescomplemented
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—172no—
665C2×C4—172no—
666C2×C4—172no—
667C2×C4—174no—
668C2×C4—174no—
669C2×C4—174no—
670C2×C4—174no—
671C2×C4—172no—
672C2×C4—348no—
673C2×C4—3416no—
674C2×C4—342no—
675C2×C4—341no—
676C2×C4—342no—
677C2×C4—342no—
678C2×C4—341no—
679C2×C4—342no—
680C2×C4—342no—
681C2×C4—341no—
682C2×C4—341no—
683C2×C4—341no—
684C2×C4—684no—
685C2×C4—688no—
686C2×C4—688no—
687C2×C4—681no—
688C2×C4—681no—
689C2×C4—681no—
690C2×C4—681no—
691C2×C4—681no—
692C2×C4—681no—
693C2×C4—681no—
694C2×C4—1364no—
695C2×C4Q16×D1712yes—
696C2×C4C22×C4×D1711yescharacteristic
697C2×C4C2×D4×D1711yescharacteristic
698C2×C4C2×D4×D1711yescharacteristic
699C2×C4C2×Q8×D1711yescharacteristic
700C2×C4#41×D1711yescharacteristic
701C2×C4#41×D1711yescharacteristic
702C8—22no—
703C8—41no—
704C8—342no—
705C8—681no—
706C22—174no—
707C22—174no—
708C22—174no—
709C22—174no—
710C22—174no—
711C22—174no—
712C22—174no—
713C22C4×D4×D1711yescharacteristic
714C22#120×D1711yescharacteristic
715C22C22⋊Q8×D1711yescharacteristic
716C22C2×Q16×D1711yescharacteristic
717C22#135×D1711yescharacteristic
718C22AGL(1,ℤ/8)×D1711yescharacteristic
719C22#137×D1711yescharacteristic
720C4—24no—
721C4—22no—
722C4—42no—
723C4—41no—
724C4—42no—
725C4—81no—
726C4—174no—
727C4—344no—
728C4—342no—
729C4—682no—
730C4—681no—
731C4—682no—
732C4—1361no—
733C4C2×C4⋊C4×D1711yescharacteristic
734C4C4×D4×D1711yescharacteristic
735C4C22⋊Q8×D1711yescharacteristic
736C4#123×D1711yescharacteristic
737C2—178no—
738C2D17×#38511yescharacteristic
739C2C4×Q16×D1711yescharacteristic
740C2D17×#44011yescharacteristic
741C2D17×#45111yescharacteristic
742C2D17×#44911yescharacteristic
743C2D17×#47711yescharacteristic
744C2D17×#47911yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1863C2
socleC23×C17C22×D4
prime radicalC23×D17C2×D4
cosocleC22×C4×C17C24
hypercenter#1863D17
hypocenterC17C2×#1863
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
6. #14529041C2semidirect
7. #14529040C2semidirect
8. #14529039C2semidirect
9. #14529038C2semidirect
10. #14529037C2semidirect
11. #14529036C2semidirect
12. #14529035C2semidirect
15. C17×#1863C2semidirect
44. #103×D17C4semidirect
138. C17×#103C2×C4semidirect
141. #10587506C2×C4semidirect
147. #10587487C2×C4semidirect
149. #10587481C2×C4semidirect
176. Q8×D17C4⋊C4semidirect
269. Q8×C17C2×C4⋊C4semidirect
329. Dic34C2×C4⋊C4semidirect
346. #1863D17direct (N × H)
435. D17#1863direct (N × H)
519. #103C4×D17semidirect
524. C17C2×#1863semidirect
646. Q8C4⋊C4×D17semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D172
C2×#107×D172
C2×#103×D172
D17×#3892
#145290412
#145290402
#145290392
#145290382
#145290372
#145290362
#145290352
D17×#3402
D17×#3362
C17×#18632
C2×#186317