Finite Group Databasebeta

← #17051639

Subgroups — #17051639

Order 4352.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762814C211yesmaximal, characteristic
2#14531667C211yesmaximal, characteristic, complemented
3#14529484C211yesmaximal, characteristic, complemented
4#14529470C211yesmaximal, characteristic, complemented
5#14529408C211yesmaximal, characteristic, complemented
6#14529401C211yesmaximal, characteristic, complemented
7#14529045C211yesmaximal, characteristic, complemented
8#14529031C211yesmaximal, characteristic, complemented
9#14528876C211yesmaximal, characteristic, complemented
10#14528815C211yesmaximal, characteristic, complemented
11#14528715C211yesmaximal, characteristic
12#14528609C211yesmaximal, characteristic, complemented
13C4×#10587503C211yesmaximal, characteristic, complemented
14#14528568C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C17C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic
17C2×#10587612C2211yescharacteristic
18C2×#10587478C2211yescharacteristic, complemented
19C2×#10587479C2211yescharacteristic, complemented
20#11762814C418yescomplemented
21C2×#10587503C2211yescharacteristic
22C2×#10587503C2211yescharacteristic
23C2×#10587503C2211yescharacteristic
24C2×#10587503C2211yescharacteristic
25C2×#10587503C2211yescharacteristic
26C2×#10587503C2211yescharacteristic
27C2×#10587503C2211yescharacteristic
28C2×#10587503C2211yescharacteristic
29C2×C22⋊#3622C2211yescharacteristic
30C2×#10587474C2211yescharacteristic, complemented
31C2×C4×#3622C2211yescharacteristic, complemented
32#11762707C2211yescharacteristic, complemented
33#11762707C2211yescharacteristic, complemented
34#11762697—21no—
35#11762697—21no—
36#11762673—21no—
37#11762669C2211yescharacteristic
38C4×C4⋊Dic17C2211yescharacteristic, complemented
39C4×C4⋊Dic17C2211yescharacteristic, complemented
40#11762654—21no—
41#11762571C2211yescharacteristic, complemented
42#11762571C2211yescharacteristic, complemented
43#11762571C2211yescharacteristic, complemented
44#11762571C2211yescharacteristic, complemented
45#11762571C2211yescharacteristic, complemented
46#11762571C2211yescharacteristic, complemented
47#11762564C2211yescharacteristic, complemented
48#11762564C2211yescharacteristic, complemented
49C23×D4×C17C2211yescharacteristic
50C2×C4×D4×C17C2211yescharacteristic
51C2×C4×D4×C17C2211yescharacteristic
52C22×C22⋊C4×C17—21no—
53C17×#390C2211yescharacteristic
54C17×#390C2211yescharacteristic
55C17×#386—21no—
56C17×#386—21no—
57C17×#380C2211yescharacteristic
58C17×#379—21no—
59C4×C22⋊C4×C17C2211yescharacteristic
60C25×C17—21no—
61C22×D4×C17—22no—
62C22×D4×C17—22no—
63C22×D4×C17—21no—
64C22×D4×C17—22no—
65C22×D4×C17—41no—
66C22×D4×C17—41no—
67C22×D4×C17C2×C414yes—
68C22×D4×C17C2311yescharacteristic
69C22×D4×C17C2311yescharacteristic
70C23×C4×C17—21no—
71C23×C4×C17—21no—
72C23×C4×C17C2311yescharacteristic
73C4×D4×C17—22no—
74C4×D4×C17—22no—
75C4×D4×C17—41no—
76C4×D4×C17—41no—
77C2×C4⋊C4×C17C2311yescharacteristic
78C2×C4⋊C4×C17C2311yescharacteristic
79C2×C22⋊C4×C17—21no—
80C2×C22⋊C4×C17—21no—
81C2×C22⋊C4×C17—21no—
82C2×C22⋊C4×C17—21no—
83C2×C22⋊C4×C17—21no—
84C2×C22⋊C4×C17—21no—
85C2×C22⋊C4×C17—21no—
86C2×C22⋊C4×C17—44no—
87C2×C22⋊C4×C17D411yescharacteristic
88C2×C22⋊C4×C17D411yescharacteristic
89C2×C42×C17C2311yescharacteristic
90C2×C42×C17C2311yescharacteristic
91C2×C22⋊Dic17—21no—
92C2×C22⋊Dic17—21no—
93#10587612—22no—
94#10587612C2×C414yescomplemented
95C2×C4⋊Dic17C2311yescharacteristic
96C2×C4⋊Dic17C2311yescharacteristic
97C2×C4⋊Dic17C2311yescharacteristic
98C2×C4⋊Dic17C2311yescharacteristic
99C2×#63225—21no—
100C2×#63225—21no—
101C2×C4×Dic17—21no—
102C2×C4×Dic17—21no—
103C2×C4×Dic17—21no—
104C2×#63223—41no—
105C2×#63223—41no—
106C2×#63223C2×C414yescomplemented
107C22×#3622C2311yescharacteristic
108C22×#3622C2311yescharacteristic
109C22×#3622C2311yescharacteristic
110C22×#3622C2311yescharacteristic
111C17×#95—21no—
112C17×#95D411yescharacteristic
113C17×#95D411yescharacteristic
114#10587503—22no—
115#10587503—22no—
116#10587503—41no—
117#10587503—41no—
118#10587503C2×C414yes—
119#10587503C2×C414yes—
120#10587503C2×C414yescomplemented
121#10587503C2×C414yescomplemented
122#10587502—21no—
123#10587502—21no—
124#10587502—21no—
125#10587502—21no—
126#10587502—21no—
127C22⋊#3622—22no—
128#10587479—41no—
129#10587478—41no—
130#10587474—41no—
131C4×#3622—41no—
132C24×C17—21no—
133C24×C17—21no—
134C24×C17—24no—
135C24×C17—42no—
136C24×C17—42no—
137C24×C17—42no—
138C24×C17—42no—
139C24×C17—81no—
140C24×C17—81no—
141C24×C17C2×D411yescharacteristic
142C2×D4×C17—28no—
143C2×D4×C17—24no—
144C2×D4×C17—21no—
145C2×D4×C17—21no—
146C2×D4×C17—21no—
147C2×D4×C17—21no—
148C2×D4×C17—21no—
149C2×D4×C17—21no—
150C2×D4×C17—21no—
151C2×D4×C17—21no—
152C2×D4×C17—44no—
153C2×D4×C17—44no—
154C2×D4×C17—44no—
155C2×D4×C17—42no—
156C2×D4×C17—42no—
157C2×D4×C17C22×C412yes—
158C2×D4×C17C22×C412yes—
159C2×D4×C17#4112yes—
160C2×D4×C17#4112yes—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—42no—
168C22×C4×C17—42no—
169C22×C4×C17—42no—
170C22×C4×C17—42no—
171C22×C4×C17—81no—
172C22×C4×C17—81no—
173C22×C4×C17C22×C412yes—
174C22×C4×C17C2×D411yescharacteristic
175C22×C4×C17C2×D411yescharacteristic
176C22×C4×C17C2×D411yescharacteristic
177C22×C4×C17C2×D411yescharacteristic
178C22×C4×C17C2×D411yescharacteristic
179C22×C4×C17#4112yes—
180C22×C4×C17C2411yescharacteristic
181C22×Dic17—21no—
182C22×Dic17—21no—
183C22×Dic17—21no—
184C22×Dic17—21no—
185C4⋊C4×C17—21no—
186C4⋊C4×C17—21no—
187C4⋊C4×C17—21no—
188C4⋊C4×C17—21no—
189C22⋊C4×C17—22no—
190C22⋊C4×C17—41no—
191C22⋊C4×C17—42no—
192C22⋊C4×C17—42no—
193C22⋊C4×C17—42no—
194C22⋊C4×C17—42no—
195C22⋊C4×C17—42no—
196C22⋊C4×C17—81no—
197C22⋊C4×C17—81no—
198C42×C17—21no—
199C42×C17—21no—
200C42×C17—21no—
201C42×C17—21no—
202C22⋊Dic17—24no—
203C22⋊Dic17—81no—
204C4⋊Dic17—21no—
205C4⋊Dic17—21no—
206C4⋊Dic17—21no—
207C4⋊Dic17—21no—
208C4⋊Dic17—21no—
209C4⋊Dic17—21no—
210C4⋊Dic17C22×C412yes—
211C4⋊Dic17C22×C412yes—
212#63225—81no—
213#63225—81no—
214C4×Dic17—24no—
215C4×Dic17—42no—
216C4×Dic17—42no—
217#63223—44no—
218C2×#3622—21no—
219C2×#3622—21no—
220C2×#3622—21no—
221C2×#3622—21no—
222C2×#3622—21no—
223C2×#3622—21no—
224C2×#3622—21no—
225C2×#3622—21no—
226C2×#3622—21no—
227C2×#3622—21no—
228C2×#3622C22×C412yes—
229C2×#3622C22×C412yes—
230#22584—171nomaximal, Sylow
231C23×C17—22no—
232C23×C17—22no—
233C23×C17—22no—
234C23×C17—21no—
235C23×C17—21no—
236C23×C17—21no—
237C23×C17—21no—
238C23×C17—21no—
239C23×C17—21no—
240C23×C17—22no—
241C23×C17—48no—
242C23×C17—48no—
243C23×C17—41no—
244C23×C17—41no—
245C23×C17—41no—
246C23×C17—41no—
247C23×C17—41no—
248C23×C17—41no—
249C23×C17—41no—
250C23×C17—41no—
251C23×C17—41no—
252C23×C17—41no—
253C23×C17—84no—
254C23×C17—84no—
255C23×C17—84no—
256C23×C17—84no—
257C23×C17—84no—
258C23×C17C4×D412yes—
259C23×C17C22×D411yescharacteristic
260D4×C17—22no—
261D4×C17—22no—
262D4×C17—22no—
263D4×C17—22no—
264D4×C17—22no—
265D4×C17—48no—
266D4×C17—41no—
267D4×C17—41no—
268D4×C17#11714yes—
269C2×C4×C17—21no—
270C2×C4×C17—21no—
271C2×C4×C17—21no—
272C2×C4×C17—21no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—21no—
278C2×C4×C17—21no—
279C2×C4×C17—21no—
280C2×C4×C17—21no—
281C2×C4×C17—21no—
282C2×C4×C17—21no—
283C2×C4×C17—21no—
284C2×C4×C17—21no—
285C2×C4×C17—21no—
286C2×C4×C17—41no—
287C2×C4×C17—41no—
288C2×C4×C17—41no—
289C2×C4×C17—41no—
290C2×C4×C17—41no—
291C2×C4×C17—41no—
292C2×C4×C17—84no—
293C2×C4×C17—84no—
294C2×C4×C17C4×D412yes—
295C2×C4×C17AGL(1,ℤ/8)12yes—
296C2×C4×C17C23×C411yescharacteristic
297C2×C4×C17C2×#4111yescharacteristic
298C2×C4×C17C2×#4111yescharacteristic
299C2×C4×C17C2×#4111yescharacteristic
300C2×C4×C17H(5,𝔽2)11yescharacteristic
301C2×C4×C17H(5,𝔽2)11yescharacteristic
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—41no—
305C2×Dic17—41no—
306C2×Dic17—41no—
307C2×Dic17—41no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17—41no—
312C2×Dic17—41no—
313C2×Dic17—41no—
314#3622—22no—
315#3622—22no—
316#3622—41no—
317#3622—41no—
318C2×#418—171no—
319#2346—171no—
320D4×C22⋊C4D1711yescharacteristic
321#1936—171no—
322#1934—171no—
323#1926—171no—
324#1925—171no—
325#1864—171no—
326#1862—171no—
327#1825—171no—
328#1809—171no—
329#1786—171no—
330#1762—171no—
331C4×#102—171no—
332#1753—171no—
333C22×C17—22no—
334C22×C17—24no—
335C22×C17—22no—
336C22×C17—22no—
337C22×C17—42no—
338C22×C17—42no—
339C22×C17—42no—
340C22×C17—41no—
341C22×C17—41no—
342C22×C17—42no—
343C22×C17—41no—
344C22×C17—42no—
345C22×C17—42no—
346C22×C17—41no—
347C22×C17—42no—
348C22×C17—42no—
349C22×C17—42no—
350C22×C17—816no—
351C22×C17—81no—
352C22×C17—81no—
353C22×C17—81no—
354C22×C17—81no—
355C22×C17C2×C4×D411yescharacteristic
356C22×C17#54611yescharacteristic
357C22×C17#54611yescharacteristic
358C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
359C22×C17#57511yescharacteristic
360C22×C17#57611yescharacteristic
361C22×C17#57711yescharacteristic
362C4×C17—22no—
363C4×C17—22no—
364C4×C17—41no—
365C4×C17—41no—
366C4×C17—41no—
367C4×C17—81no—
368C4×C17—81no—
369C4×C17C2×#11711yescharacteristic
370C4×C17#51811yescharacteristic
371C4×C17#55111yescharacteristic
372C4×C17#55111yescharacteristic
373Dic17—42no—
374Dic17—42no—
375Dic17—81no—
376Dic17—81no—
377C23×D4C2×D1711yescharacteristic
378C22×M16—171no—
379C2×C4×D4C2×D1711yescharacteristic
380C2×C4×D4C2×D1711yescharacteristic
381C2×#117—171no—
382C22×C22⋊C4—21no—
383C2×#107—171no—
384C2×#106—171no—
385#418—178no—
386C2×#102—171no—
387C2×#102—171no—
388C2×#102—171no—
389C2×#102—171no—
390C2×#102—171no—
391C2×#102—171no—
392C2×#102—171no—
393C2×#102—171no—
394C2×C22⋊C8—171no—
395C2×#97—171no—
396C2×C4×C8—171no—
397#390C2×D1711yescharacteristic
398#390C2×D1711yescharacteristic
399#389—171no—
400#389—171no—
401#388—341no—
402#388—341no—
403#386—21no—
404#386—21no—
405#382—341no—
406#380—171no—
407#380C2×D1711yescharacteristic
408#379—21no—
409C4×C4⋊C4—171no—
410C4×C4⋊C4—171no—
411C4×C22⋊C4C2×D1711yescharacteristic
412#376—341no—
413#340—171no—
414#340—171no—
415#340—171no—
416#340—171no—
417#340—171no—
418#340—171no—
419#336—171no—
420#336—171no—
421C2×C17—42no—
422C2×C17—44no—
423C2×C17—82no—
424C2×C17#234211yescharacteristic
425C2×C17C4×AGL(1,ℤ/8)11yescharacteristic
426C2×C17#294611yescharacteristic
427C2×C17#331011yescharacteristic
428C2×C17#331911yescharacteristic
429C2×C17#332311yescharacteristic
430C2×C17#332511yescharacteristic
431C25—21no—
432C22×D4—22no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—21no—
436C22×D4—41no—
437C22×D4—41no—
438C22×D4C4×D1714yes—
439C22×D4C22×D1711yescharacteristic
440C22×D4C22×D1711yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4C22×D1711yescharacteristic
444C2×M16—174no—
445C2×M16—681no—
446C2×M16—681no—
447C22×C8—171no—
448C22×C8—171no—
449C22×C8—171no—
450C22×C8—171no—
451C4×D4—22no—
452C4×D4—22no—
453C4×D4—41no—
454C4×D4—41no—
455#117—174no—
456#117—342no—
457C2×C4⋊C4—171no—
458C2×C4⋊C4—171no—
459C2×C4⋊C4—171no—
460C2×C4⋊C4—171no—
461C2×C4⋊C4—341no—
462C2×C4⋊C4—341no—
463C2×C4⋊C4C22×D1711yescharacteristic
464C2×C4⋊C4C22×D1711yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—44no—
473C2×C22⋊C4—341no—
474C2×C22⋊C4—341no—
475C2×C22⋊C4C22⋊D1711yescharacteristic
476C2×C22⋊C4C22⋊D1711yescharacteristic
477C2×C42—341no—
478C2×C42—341no—
479C2×C42—341no—
480C2×C42C22×D1711yescharacteristic
481C2×C42C22×D1711yescharacteristic
482#107—681no—
483#106—681no—
484#102—174no—
485#102—174no—
486#102—174no—
487#102—174no—
488#102—342no—
489#102—342no—
490#102—681no—
491#102—681no—
492C22⋊C8—342no—
493#97—681no—
494C4×C8—681no—
495#95—21no—
496#95—341no—
497#95—341no—
498#95—341no—
499#95—341no—
500#95—341no—
501#95C22⋊D1711yescharacteristic
502#95C22⋊D1711yescharacteristic
503C17#2258411yescharacteristic, complemented, Sylow
504C24—21no—
505C24—21no—
506C24—24no—
507C24—42no—
508C24—42no—
509C24—42no—
510C24—42no—
511C24—81no—
512C24—81no—
513C24C2×C22⋊D1711yescharacteristic
514C2×D4—28no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—24no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4C2×C4×D1712yes—
530C2×D4C2×C4×D1712yes—
531C2×D4#6325412yes—
532C2×D4#6325412yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—341no—
546C22×C4—341no—
547C22×C4—341no—
548C22×C4—341no—
549C22×C4C2×C4×D1712yes—
550C22×C4#6325212yes—
551C22×C4C2×C22⋊D1711yescharacteristic
552C22×C4C2×C22⋊D1711yescharacteristic
553C22×C4C2×C22⋊D1711yescharacteristic
554C22×C4C2×C22⋊D1711yescharacteristic
555C22×C4C2×C22⋊D1711yescharacteristic
556C22×C4C23×D1711yescharacteristic
557M16—684no—
558C2×C8—172no—
559C2×C8—172no—
560C2×C8—341no—
561C2×C8—341no—
562C2×C8—341no—
563C2×C8—341no—
564C2×C8—341no—
565C2×C8—341no—
566C2×C8—341no—
567C2×C8—341no—
568C2×C8—341no—
569C2×C8—341no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—172no—
575C4⋊C4—172no—
576C4⋊C4—341no—
577C4⋊C4—341no—
578C4⋊C4—341no—
579C4⋊C4—341no—
580C4⋊C4—341no—
581C4⋊C4—341no—
582C4⋊C4—1361no—
583C4⋊C4—1361no—
584C22⋊C4—22no—
585C22⋊C4—41no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—81no—
592C22⋊C4—81no—
593C22⋊C4—344no—
594C22⋊C4—1361no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—344no—
600C42—682no—
601C42—682no—
602C23—22no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—22no—
608C23—22no—
609C23—21no—
610C23—21no—
611C23—22no—
612C23—48no—
613C23—48no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—84no—
625C23—84no—
626C23—84no—
627C23—84no—
628C23—84no—
629C23C4×C22⋊D1712yes—
630C23C22×C22⋊D1711yescharacteristic
631D4—22no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639D4#1058756314yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
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—84no—
664C2×C4—84no—
665C2×C4—342no—
666C2×C4—342no—
667C2×C4—681no—
668C2×C4—681no—
669C2×C4—681no—
670C2×C4—681no—
671C2×C4—681no—
672C2×C4—681no—
673C2×C4—681no—
674C2×C4—681no—
675C2×C4—681no—
676C2×C4—681no—
677C2×C4C4×C22⋊D1712yes—
678C2×C4#1058761812yes—
679C2×C4C22×C4×D1711yescharacteristic
680C2×C4C2×#6325211yescharacteristic
681C2×C4C2×#6325411yescharacteristic
682C2×C4C2×#6325411yescharacteristic
683C2×C4#1058769111yescharacteristic
684C2×C4#1058769111yescharacteristic
685C8—342no—
686C8—342no—
687C8—681no—
688C8—681no—
689C22—22no—
690C22—24no—
691C22—22no—
692C22—22no—
693C22—42no—
694C22—41no—
695C22—42no—
696C22—41no—
697C22—42no—
698C22—42no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—41no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—816no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22C2×C4×C22⋊D1711yescharacteristic
712C22#1176345311yescharacteristic
713C22#1176345311yescharacteristic
714C22C2×#1058761811yescharacteristic
715C22#1176360711yescharacteristic
716C22#1176361211yescharacteristic
717C22#1176362011yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—81no—
724C4—81no—
725C4—682no—
726C4—682no—
727C4—1361no—
728C4—1361no—
729C4C2×#1058756311yescharacteristic
730C4#1176328211yescharacteristic
731C4#1176348511yescharacteristic
732C4#1176348511yescharacteristic
733C2—42no—
734C2—44no—
735C2—82no—
736C2#1453162911yescharacteristic
737C2C4×#1058761811yescharacteristic
738C2#1453761611yescharacteristic
739C2#1454080511yescharacteristic
740C2#1454094011yescharacteristic
741C2#1454100011yescharacteristic
742C2#1454102611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingD4×C22⋊C4×C17C2
socleC23×C17C22×D4
prime radicalC23×D4×C17C22
cosocleC22×C4×C17C24
hypercenterD4×C22⋊C4D17
hypocenterC17#22584
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #14531667C2semidirect
3. #14529484C2semidirect
4. #14529470C2semidirect
5. #14529408C2semidirect
6. #14529401C2semidirect
7. #14529045C2semidirect
8. #14529031C2semidirect
9. #14528876C2semidirect
10. #14528815C2semidirect
12. #14528609C2semidirect
13. C4×#10587503C2semidirect
14. #14528568C2semidirect
18. C2×#10587478C22semidirect
19. C2×#10587479C22semidirect
20. #11762814C4semidirect
30. C2×#10587474C22semidirect
31. C2×C4×#3622C22semidirect
32. #11762707C22semidirect
33. #11762707C22semidirect
38. C4×C4⋊Dic17C22semidirect
39. C4×C4⋊Dic17C22semidirect
41. #11762571C22semidirect
42. #11762571C22semidirect
43. #11762571C22semidirect
44. #11762571C22semidirect
45. #11762571C22semidirect
46. #11762571C22semidirect
47. #11762564C22semidirect
48. #11762564C22semidirect
94. #10587612C2×C4semidirect
106. C2×#63223C2×C4semidirect
120. #10587503C2×C4semidirect
121. #10587503C2×C4semidirect
503. C17#22584semidirect

Maximal subgroups

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

subgroupindex
C2×#117628142
#145316672
#145294842
#145294702
#145294082
#145294012
#145290452
#145290312
#145288762
#145288152
#145287152
#145286092
C4×#105875032
#145285682
D4×C22⋊C4×C172
#2258417