Finite Group Databasebeta

← D17×#1872 #17035514

Subgroups — D17×#1872 #17035514

Order 4352.

2270 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D17C211yesmaximal, characteristic
2C22×C4⋊C4×D17C211yesmaximal, characteristic
3C2×#103×D17C212yesmaximal, complemented
4C2×C22⋊C8×D17C211yesmaximal, characteristic
5#14529092C211yesmaximal, characteristic, complemented
6#14529091C211yesmaximal, characteristic, complemented
7#14529090C212yesmaximal, complemented
8#14529089C211yesmaximal, characteristic, complemented
9#14529088C212yesmaximal, complemented
10D17×#340C212yesmaximal, complemented
11C17×#1872C211yesmaximal, characteristic, complemented
12C22×Q8×D17C2211yescharacteristic
13C23×C4×D17—21no—
14C23×C4×D17C2211yescharacteristic
15C22×C8×D17C2212yes—
16C2×#10587583C2211yescharacteristic
17C2×#10587610C2211yescharacteristic
18C2×#10587582—21no—
19C2×#10587564—21no—
20C2×#10587632C2211yescharacteristic
21C22⋊Q8×D17—24no—
22C22⋊Q8×D17C418yescomplemented
23C22×C4⋊Dic17C2211yescharacteristic
24C22×#63225—21no—
25C2×C4⋊C4×D17—28no—
26C2×C4⋊C4×D17—21no—
27C2×C4⋊C4×D17—21no—
28C2×C4⋊C4×D17—21no—
29C2×C4⋊C4×D17C2212yes—
30C2×C4⋊C4×D17C2211yescharacteristic
31C2×C4⋊C4×D17C2212yes—
32C2×C22⋊C4×D17—21no—
33C2×#10587487C2212yescomplemented
34C2×#10587506C2212yescomplemented
35C2×#10587481C2212yescomplemented
36#103×D17—28no—
37C2×C22⋊#3622C2211yescharacteristic
38C2×#10587491C2212yes—
39C22⋊C8×D17—24no—
40#11762572C2212yescomplemented
41#11762571C2212yescomplemented
42#11762571C2212yescomplemented
43C2×C17×C22⋊Q8C2211yescharacteristic
44C22×C4⋊C4×C17C2211yescharacteristic
45C2×C17×#103C2212yescomplemented
46C2×C17×C22⋊C8C2211yescharacteristic
47C17×#340C2212yescomplemented
48C24×D17D411yescharacteristic
49C22×Q8×C17C2311yescharacteristic
50C23×C4×C17—21no—
51C23×C4×C17C2311yescharacteristic
52C23×Dic17—21no—
53C23×Dic17D411yescharacteristic
54C2×Q8×D17—22no—
55C2×Q8×D17—24no—
56C2×Q8×D17—24no—
57C2×Q8×D17C2×C414yescomplemented
58C22×C4×D17—24no—
59C22×C4×D17—24no—
60C22×C4×D17—28no—
61C22×C4×D17—21no—
62C22×C4×D17—21no—
63C22×C4×D17—22no—
64C22×C4×D17—22no—
65C22×C4×D17—44no—
66C22×C4×D17—44no—
67C22×C4×D17C2×C414yes—
68C22×C4×D17D411yescharacteristic
69C22×C4×D17D411yescharacteristic
70C22×C4×D17D414yes—
71C22×C4×D17C2311yescharacteristic
72C22×C4×D17C2311yescharacteristic
73C22×Dic34—21no—
74C22×Dic34C2311yescharacteristic
75C22×C8×C17C2312yes—
76C17×C22⋊Q8—22no—
77C17×C22⋊Q8C2×C414yescomplemented
78C2×C4⋊C4×C17—21no—
79C2×C4⋊C4×C17—21no—
80C2×C4⋊C4×C17—24no—
81C2×C4⋊C4×C17C2311yescharacteristic
82C2×C4⋊C4×C17C2312yes—
83C2×C22⋊C4×C17—21no—
84C2×C22⋊Dic17—21no—
85#10587632—22no—
86#10587632C2×C414yescomplemented
87C2×#63227—21no—
88C2×#63227—21no—
89C2×C4⋊Dic17—24no—
90C2×C4⋊Dic17—21no—
91C2×C4⋊Dic17—21no—
92C2×C4⋊Dic17C2311yescharacteristic
93C2×C4⋊Dic17C2312yes—
94#10587610—22no—
95#10587610C2×C414yescomplemented
96C2×#63225—28no—
97C2×#63225—21no—
98C2×#63225—22no—
99C2×#63225—22no—
100C2×#63225—21no—
101C2×#63225—21no—
102C22×#3622C2312yes—
103C2×C8×D17—24no—
104C2×C8×D17—24no—
105C2×C8×D17—24no—
106#10587583—22no—
107#10587583C2×C414yescomplemented
108#10587582—28no—
109C4⋊C4×D17—28no—
110C4⋊C4×D17—28no—
111C4⋊C4×D17—24no—
112C4⋊C4×D17—28no—
113C4⋊C4×D17—24no—
114C4⋊C4×D17—22no—
115C4⋊C4×D17—24no—
116C4⋊C4×D17C2×C414yescomplemented
117C4⋊C4×D17D418yes—
118C22⋊C4×D17—28no—
119#10587564—28no—
120C17×#103—24no—
121C17×C22⋊C8—22no—
122#10587506—24no—
123C22⋊#3622—22no—
124#10587491—24no—
125#10587487—24no—
126#10587481—24no—
127C24×C17C2×D411yescharacteristic
128C23×D17—22no—
129C23×D17—22no—
130C23×D17—22no—
131C23×D17—22no—
132C23×D17C22⋊C414yes—
133C23×D17SD1614yes—
134C23×D17Q1614yes—
135C23×D17C2×D411yescharacteristic
136C23×D17C2×D411yescharacteristic
137C2×Q8×C17—21no—
138C2×Q8×C17—22no—
139C2×Q8×C17—22no—
140C2×Q8×C17C22×C412yescomplemented
141C22×C4×C17—22no—
142C22×C4×C17—22no—
143C22×C4×C17—24no—
144C22×C4×C17—21no—
145C22×C4×C17—22no—
146C22×C4×C17—21no—
147C22×C4×C17—42no—
148C22×C4×C17—42no—
149C22×C4×C17C22×C412yes—
150C22×C4×C17C2×D411yescharacteristic
151C22×C4×C17C2×D412yes—
152C22×C4×C17C2411yescharacteristic
153C22×Dic17—22no—
154C22×Dic17—22no—
155C22×Dic17—24no—
156C22×Dic17—21no—
157C22×Dic17—22no—
158C22×Dic17—21no—
159C22×Dic17—42no—
160C22×Dic17—42no—
161C22×Dic17C22⋊C414yes—
162C22×Dic17C2×D411yescharacteristic
163C22×Dic17C2×D411yescharacteristic
164Q8×D17—216no—
165Q8×D17—48no—
166C2×C4×D17—22no—
167C2×C4×D17—22no—
168C2×C4×D17—22no—
169C2×C4×D17—22no—
170C2×C4×D17—22no—
171C2×C4×D17—22no—
172C2×C4×D17—216no—
173C2×C4×D17—216no—
174C2×C4×D17—28no—
175C2×C4×D17—24no—
176C2×C4×D17—24no—
177C2×C4×D17—28no—
178C2×C4×D17—44no—
179C2×C4×D17—432no—
180C2×C4×D17—42no—
181C2×C4×D17—42no—
182C2×C4×D17—44no—
183C2×C4×D17—44no—
184C2×C4×D17—42no—
185C2×C4×D17—44no—
186C2×C4×D17—42no—
187C2×C4×D17C22⋊C414yes—
188C2×C4×D17C22⋊C414yes—
189C2×C4×D17C22×C412yes—
190C2×C4×D17C22×C412yes—
191C2×C4×D17C2×D412yes—
192C2×C4×D17C2×D414yes—
193C2×C4×D17C2×D412yes—
194C2×C4×D17#4114yes—
195C2×Dic34—22no—
196C2×Dic34—22no—
197C2×Dic34—21no—
198C2×Dic34—24no—
199C2×Dic34—42no—
200C2×Dic34—42no—
201C2×Dic34C22×C412yescomplemented
202C2×C8×C17—22no—
203C2×C8×C17—22no—
204C2×C8×C17—22no—
205C4⋊C4×C17—24no—
206C4⋊C4×C17—24no—
207C4⋊C4×C17—21no—
208C4⋊C4×C17—22no—
209C4⋊C4×C17C22×C412yescomplemented
210C4⋊C4×C17C2×D414yes—
211C22⋊C4×C17—24no—
212C22⋊Dic17—24no—
213#63227—24no—
214#63227—24no—
215C4⋊Dic17—24no—
216C4⋊Dic17—22no—
217C4⋊Dic17—21no—
218C4⋊Dic17—24no—
219C4⋊Dic17C22×C412yescomplemented
220C4⋊Dic17C2×D414yes—
221#63225—28no—
222#63225—24no—
223#63225—24no—
224#63225—24no—
225#63225—28no—
226C2×#3622—22no—
227C2×#3622—22no—
228C2×#3622—22no—
229C8×D17—48no—
230C2×#1872—171nomaximal, Sylow
231C23×C17—21no—
232C23×C17—21no—
233C23×C17—21no—
234C23×C17—21no—
235C23×C17C2×C22⋊C412yes—
236C23×C17C2×SD1612yes—
237C23×C17C2×Q1612yes—
238C23×C17C22×D411yescharacteristic
239C22×D17—21no—
240C22×D17—21no—
241C22×D17—21no—
242C22×D17—21no—
243C22×D17—28no—
244C22×D17—28no—
245C22×D17—28no—
246C22×D17—28no—
247C22×D17—28no—
248C22×D17—28no—
249C22×D17#103116yescomplemented
250C22×D17C2×C22⋊C412yes—
251C22×D17C2×C22⋊C412yes—
252C22×D17#12012yes—
253C22×D17#12312yes—
254C22×D17C2×SD1612yes—
255C22×D17C2×SD1612yes—
256C22×D17C2×Q1612yes—
257C22×D17C2×Q1612yes—
258C22×D17AGL(1,ℤ/8)12yes—
259C22×D17#13712yes—
260Q8×C17—24no—
261Q8×C17—42no—
262C2×C4×C17—21no—
263C2×C4×C17—21no—
264C2×C4×C17—24no—
265C2×C4×C17—24no—
266C2×C4×C17—22no—
267C2×C4×C17—22no—
268C2×C4×C17—24no—
269C2×C4×C17—48no—
270C2×C4×C17—41no—
271C2×C4×C17—41no—
272C2×C4×C17—42no—
273C2×C4×C17—42no—
274C2×C4×C17—41no—
275C2×C4×C17—41no—
276C2×C4×C17C2×C22⋊C412yes—
277C2×C4×C17C23×C411yescharacteristic
278C2×C4×C17C22×D412yes—
279C2×C4×C17C22×D411yescharacteristic
280C2×C4×C17C2×#4112yes—
281C2×Dic17—21no—
282C2×Dic17—21no—
283C2×Dic17—28no—
284C2×Dic17—22no—
285C2×Dic17—22no—
286C2×Dic17—24no—
287C2×Dic17—48no—
288C2×Dic17—41no—
289C2×Dic17—41no—
290C2×Dic17—42no—
291C2×Dic17—42no—
292C2×Dic17—41no—
293C2×Dic17—41no—
294C2×Dic17C2×C22⋊C412yes—
295C2×Dic17C2×C22⋊C412yes—
296C2×Dic17#12012yes—
297C2×Dic17#12312yes—
298C4×D17—28no—
299C4×D17—24no—
300C4×D17—24no—
301C4×D17—28no—
302C4×D17—416no—
303C4×D17—48no—
304C4×D17—48no—
305C4×D17—416no—
306C4×D17C4×D418yes—
307C4×D17#12118yes—
308Dic34—24no—
309Dic34—42no—
310Dic34—48no—
311C8×C17—42no—
312#3622—42no—
313C22×C22⋊Q8—171no—
314C23×C4⋊C4—171no—
315C22×#103—172no—
316C22×C22⋊C8—171no—
317#1872—172no—
318#1872—171no—
319#1872—172no—
320#1872—171no—
321#1872—171no—
322#1872D1711yescharacteristic, direct product factor
323C2×#340—172no—
324C22×C17—22no—
325C22×C17—22no—
326C22×C17—22no—
327C22×C17—22no—
328C22×C17—22no—
329C22×C17—22no—
330C22×C17C2×#10314yescomplemented
331C22×C17C22×C22⋊C411yescharacteristic
332C22×C17C2×#12011yescharacteristic
333C22×C17C2×#12311yescharacteristic
334C22×C17C22×SD1611yescharacteristic
335C22×C17C22×Q1611yescharacteristic
336C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
337C22×C17C2×#13711yescharacteristic
338C2×D17—22no—
339C2×D17—22no—
340C2×D17—22no—
341C2×D17—22no—
342C2×D17—22no—
343C2×D17—22no—
344C2×D17—232no—
345C2×D17#38614yes—
346C2×D17C2×#10314yes—
347C2×D17C2×#10314yescomplemented
348C2×D17#41714yes—
349C2×D17#45014yes—
350C2×D17#45114yes—
351C2×D17#48314yes—
352C2×D17#48414yes—
353C4×C17—22no—
354C4×C17—42no—
355C4×C17—44no—
356C4×C17—42no—
357C4×C17C2×C4×D412yes—
358C4×C17C2×#12112yes—
359Dic17—22no—
360Dic17—42no—
361Dic17—44no—
362Dic17—42no—
363Dic17#38614yes—
364C23×Q8—171no—
365C24×C4—171no—
366C24×C4—341no—
367C23×C8—172no—
368C2×C22⋊Q8—171no—
369C2×C22⋊Q8—171no—
370C2×C22⋊Q8—178no—
371C2×C22⋊Q8—171no—
372C2×C22⋊Q8—341no—
373C2×C22⋊Q8—341no—
374C2×C22⋊Q8—344no—
375C2×C22⋊Q8C2×D1711yescharacteristic
376C22×C4⋊C4—172no—
377C22×C4⋊C4—171no—
378C22×C4⋊C4—171no—
379C22×C4⋊C4—172no—
380C22×C4⋊C4—348no—
381C22×C4⋊C4—341no—
382C22×C4⋊C4—341no—
383C22×C4⋊C4—341no—
384C22×C4⋊C4—341no—
385C22×C4⋊C4C2×D1711yescharacteristic
386C22×C22⋊C4—341no—
387C2×#103—172no—
388C2×#103—172no—
389C2×#103—172no—
390C2×#103—348no—
391C2×#103C2×D1712yescomplemented
392C2×C22⋊C8—171no—
393C2×C22⋊C8—172no—
394C2×C22⋊C8—344no—
395C2×C22⋊C8C2×D1711yescharacteristic
396#340—172no—
397#340—172no—
398#340—172no—
399#340C2×D1712yescomplemented
400C2×C17—24no—
401C2×C17C2×#38611yescharacteristic
402C2×C17C22×#10311yescharacteristic
403C2×C17C2×#41711yescharacteristic
404C2×C17C2×#45011yescharacteristic
405C2×C17C2×#45111yescharacteristic
406C2×C17C2×#48311yescharacteristic
407C2×C17C2×#48411yescharacteristic
408D17—24no—
409D17#187218yesdirect product factor
410C25—171no—
411C22×Q8—174no—
412C22×Q8—171no—
413C22×Q8—341no—
414C22×Q8—342no—
415C22×Q8—344no—
416C22×Q8—344no—
417C22×Q8C22×D1711yescharacteristic
418C23×C4—21no—
419C23×C4—171no—
420C23×C4—171no—
421C23×C4—174no—
422C23×C4—171no—
423C23×C4—171no—
424C23×C4—174no—
425C23×C4—171no—
426C23×C4—344no—
427C23×C4—344no—
428C23×C4—341no—
429C23×C4—341no—
430C23×C4—342no—
431C23×C4—342no—
432C23×C4—348no—
433C23×C4—341no—
434C23×C4—684no—
435C23×C4—684no—
436C23×C4C22×D1711yescharacteristic
437C22×C8—172no—
438C22×C8—344no—
439C22×C8—344no—
440C22×C8—344no—
441C22×C8C22×D1712yes—
442C22⋊Q8—22no—
443C22⋊Q8—174no—
444C22⋊Q8—174no—
445C22⋊Q8—174no—
446C22⋊Q8—348no—
447C22⋊Q8—348no—
448C22⋊Q8—342no—
449C22⋊Q8—342no—
450C22⋊Q8—342no—
451C22⋊Q8C4×D1714yescomplemented
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—172no—
456C2×C4⋊C4—171no—
457C2×C4⋊C4—174no—
458C2×C4⋊C4—178no—
459C2×C4⋊C4—344no—
460C2×C4⋊C4—344no—
461C2×C4⋊C4—342no—
462C2×C4⋊C4—348no—
463C2×C4⋊C4—348no—
464C2×C4⋊C4—348no—
465C2×C4⋊C4—344no—
466C2×C4⋊C4—342no—
467C2×C4⋊C4—342no—
468C2×C4⋊C4—341no—
469C2×C4⋊C4—341no—
470C2×C4⋊C4—341no—
471C2×C4⋊C4—348no—
472C2×C4⋊C4—341no—
473C2×C4⋊C4—341no—
474C2×C4⋊C4—344no—
475C2×C4⋊C4C22×D1711yescharacteristic
476C2×C4⋊C4C22×D1712yes—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—348no—
479C2×C22⋊C4—341no—
480C2×C22⋊C4—341no—
481C2×C22⋊C4—341no—
482#103—24no—
483#103—344no—
484#103—344no—
485#103—344no—
486C22⋊C8—22no—
487C22⋊C8—344no—
488C22⋊C8—342no—
489C17C2×#187211yescharacteristic, complemented, Sylow
490C24—171no—
491C24—171no—
492C24—174no—
493C24—174no—
494C24—174no—
495C24—342no—
496C24—342no—
497C24—342no—
498C24—342no—
499C24D4×D1711yescharacteristic
500C2×Q8—21no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—172no—
504C2×Q8—344no—
505C2×Q8—3416no—
506C2×Q8—341no—
507C2×Q8—342no—
508C2×Q8—342no—
509C2×Q8—682no—
510C2×Q8—682no—
511C2×Q8—688no—
512C2×Q8C2×C4×D1712yescomplemented
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—171no—
522C22×C4—172no—
523C22×C4—174no—
524C22×C4—172no—
525C22×C4—174no—
526C22×C4—171no—
527C22×C4—174no—
528C22×C4—172no—
529C22×C4—172no—
530C22×C4—174no—
531C22×C4—174no—
532C22×C4—342no—
533C22×C4—342no—
534C22×C4—3416no—
535C22×C4—3416no—
536C22×C4—342no—
537C22×C4—342no—
538C22×C4—344no—
539C22×C4—344no—
540C22×C4—348no—
541C22×C4—348no—
542C22×C4—342no—
543C22×C4—342no—
544C22×C4—342no—
545C22×C4—342no—
546C22×C4—344no—
547C22×C4—341no—
548C22×C4—341no—
549C22×C4—342no—
550C22×C4—682no—
551C22×C4—682no—
552C22×C4—684no—
553C22×C4—684no—
554C22×C4—684no—
555C22×C4—682no—
556C22×C4—682no—
557C22×C4—6832no—
558C22×C4—684no—
559C22×C4—682no—
560C22×C4—682no—
561C22×C4C2×C4×D1712yes—
562C22×C4D4×D1712yes—
563C22×C4D4×D1711yescharacteristic
564C22×C4C23×D1711yescharacteristic
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—342no—
569C2×C8—342no—
570C2×C8—342no—
571C2×C8—688no—
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—24no—
576C4⋊C4—172no—
577C4⋊C4—174no—
578C4⋊C4—348no—
579C4⋊C4—344no—
580C4⋊C4—344no—
581C4⋊C4—344no—
582C4⋊C4—348no—
583C4⋊C4—344no—
584C4⋊C4—342no—
585C4⋊C4—341no—
586C4⋊C4—344no—
587C4⋊C4C2×C4×D1712yescomplemented
588C4⋊C4D4×D1714yes—
589C22⋊C4—24no—
590C22⋊C4—344no—
591C22⋊C4—344no—
592C22⋊C4—344no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—172no—
598C23—172no—
599C23—172no—
600C23—172no—
601C23—172no—
602C23—172no—
603C23—172no—
604C23—172no—
605C23—1716no—
606C23—172no—
607C23—172no—
608C23—348no—
609C23—348no—
610C23—348no—
611C23—348no—
612C23—348no—
613C23—348no—
614C23—341no—
615C23—341no—
616C23—341no—
617C23—341no—
618C23C22⋊C4×D1712yes—
619C23SD16×D1712yes—
620C23Q16×D1712yes—
621C23C2×D4×D1711yescharacteristic
622Q8—24no—
623Q8—42no—
624Q8—344no—
625Q8—688no—
626Q8—682no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—48no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—172no—
642C2×C4—172no—
643C2×C4—172no—
644C2×C4—178no—
645C2×C4—178no—
646C2×C4—172no—
647C2×C4—348no—
648C2×C4—348no—
649C2×C4—348no—
650C2×C4—341no—
651C2×C4—341no—
652C2×C4—344no—
653C2×C4—344no—
654C2×C4—342no—
655C2×C4—342no—
656C2×C4—344no—
657C2×C4—6816no—
658C2×C4—688no—
659C2×C4—688no—
660C2×C4—6816no—
661C2×C4—688no—
662C2×C4—681no—
663C2×C4—681no—
664C2×C4—682no—
665C2×C4—682no—
666C2×C4—681no—
667C2×C4—681no—
668C2×C4C22⋊C4×D1712yes—
669C2×C4C22×C4×D1711yescharacteristic
670C2×C4C2×D4×D1712yes—
671C2×C4C2×D4×D1711yescharacteristic
672C2×C4#41×D1712yes—
673C8—42no—
674C8—682no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—174no—
682C22—174no—
683C22—174no—
684C22—174no—
685C22—174no—
686C22—174no—
687C22—174no—
688C22—174no—
689C22—3432no—
690C22—342no—
691C22—342no—
692C22—342no—
693C22—342no—
694C22—342no—
695C22—342no—
696C22#103×D1714yescomplemented
697C22C2×C22⋊C4×D1711yescharacteristic
698C22#120×D1711yescharacteristic
699C22#123×D1711yescharacteristic
700C22C2×SD16×D1711yescharacteristic
701C22C2×Q16×D1711yescharacteristic
702C22AGL(1,ℤ/8)×D1711yescharacteristic
703C22#137×D1711yescharacteristic
704C4—22no—
705C4—42no—
706C4—42no—
707C4—44no—
708C4—174no—
709C4—342no—
710C4—682no—
711C4—682no—
712C4—684no—
713C4C4×D4×D1712yes—
714C4#121×D1712yes—
715C2—24no—
716C2—178no—
717C2—344no—
718C2D17×#38611yescharacteristic
719C2C2×#103×D1711yescharacteristic
720C2D17×#41711yescharacteristic
721C2D17×#45011yescharacteristic
722C2D17×#45111yescharacteristic
723C2D17×#48311yescharacteristic
724C2D17×#48411yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1872C2
socleC23×C17C22×D4
prime radicalC24×D17D4
cosocleC22×C4×C17C24
hypercenter#1872D17
hypocenterC17C2×#1872
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
3. C2×#103×D17C2semidirect
5. #14529092C2semidirect
6. #14529091C2semidirect
7. #14529090C2semidirect
8. #14529089C2semidirect
9. #14529088C2semidirect
10. D17×#340C2semidirect
11. C17×#1872C2semidirect
22. C22⋊Q8×D17C4semidirect
33. C2×#10587487C22semidirect
34. C2×#10587506C22semidirect
35. C2×#10587481C22semidirect
40. #11762572C22semidirect
41. #11762571C22semidirect
42. #11762571C22semidirect
45. C2×C17×#103C22semidirect
47. C17×#340C22semidirect
57. C2×Q8×D17C2×C4semidirect
77. C17×C22⋊Q8C2×C4semidirect
86. #10587632C2×C4semidirect
95. #10587610C2×C4semidirect
107. #10587583C2×C4semidirect
116. C4⋊C4×D17C2×C4semidirect
140. C2×Q8×C17C22×C4semidirect
201. C2×Dic34C22×C4semidirect
209. C4⋊C4×C17C22×C4semidirect
219. C4⋊Dic17C22×C4semidirect
249. C22×D17#103semidirect
322. #1872D17direct (N × H)
330. C22×C17C2×#103semidirect
347. C2×D17C2×#103semidirect
391. C2×#103C2×D17semidirect
399. #340C2×D17semidirect
409. D17#1872direct (N × H)
451. C22⋊Q8C4×D17semidirect
489. C17C2×#1872semidirect
512. C2×Q8C2×C4×D17semidirect
587. C4⋊C4C2×C4×D17semidirect
696. C22#103×D17semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D172
C22×C4⋊C4×D172
C2×#103×D172
C2×C22⋊C8×D172
#145290922
#145290912
#145290902
#145290892
#145290882
D17×#3402
C17×#18722
C2×#187217