Finite Group Databasebeta

← #17045654

Subgroups — #17045654

Order 4352.

1024 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531479C211yesmaximal, characteristic, complemented
2#14531376C211yesmaximal, characteristic, complemented
3#14529667C211yesmaximal, characteristic, complemented
4#14529651C211yesmaximal, characteristic, complemented
5#14529483C211yesmaximal, characteristic, complemented
6#14529462C211yesmaximal, characteristic, complemented
7#14529427C211yesmaximal, characteristic, complemented
8#14529406C211yesmaximal, characteristic, complemented
9#14529134C211yesmaximal, characteristic, complemented
10#14529120C211yesmaximal, characteristic, complemented
11#14529102C211yesmaximal, characteristic, complemented
12#14528974C211yesmaximal, characteristic, complemented
13#14528724C211yesmaximal, characteristic, complemented
14#14528552C211yesmaximal, characteristic, complemented
15C2×C17×#449C211yesmaximal, characteristic
16C2×D4×Dic17C2211yescharacteristic
17C2×#10587612C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C2×#10587489C2211yescharacteristic
20C2×#10587489C2211yescharacteristic
21C2×#10587506C2211yescharacteristic
22C2×#10587506C2211yescharacteristic
23C2×#10587503C2211yescharacteristic
24C2×#10587503C2211yescharacteristic
25C2×#10587503C2211yescharacteristic
26C2×#10587503C2211yescharacteristic
27C2×C22⋊#3622C2211yescharacteristic
28C2×#10587486C2211yescharacteristic
29C2×C8×Dic17C2211yescharacteristic
30#11762716C2211yescharacteristic
31#11762716C2211yescharacteristic
32#11762712—21no—
33#11762712C2211yescharacteristic
34#11762712C2211yescharacteristic
35#11762712C2211yescharacteristic
36#11762708C2211yescharacteristic
37#11762702—21no—
38#11762689—21no—
39#11762689—21no—
40#11762689—21no—
41#11762684—21no—
42#11762669—21no—
43#11762669—21no—
44#11762669C2211yescharacteristic
45C4⋊C4×Dic17C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762563C2211yescharacteristic
51#11762563C2211yescharacteristic
52C22×#41×C17C2211yescharacteristic
53C22×SD16×C17C2211yescharacteristic
54C22×D8×C17C2211yescharacteristic
55C2×C17×#121C2211yescharacteristic
56C17×#449C418yescomplemented
57C2×C17×#103C2211yescharacteristic
58C2×C17×#102C2211yescharacteristic
59C2×C17×C22⋊C8C2211yescharacteristic
60C2×#41×C17—22no—
61C2×#41×C17—41no—
62C2×#41×C17—41no—
63C2×#41×C17—41no—
64C2×#41×C17—41no—
65C2×#41×C17C2×C414yescomplemented
66C22×Q8×C17C2311yescharacteristic
67C22×D4×C17—21no—
68C22×D4×C17—21no—
69C22×D4×C17C2311yescharacteristic
70C22×D4×C17C2311yescharacteristic
71C23×C4×C17—21no—
72C23×C4×C17C2311yescharacteristic
73C23×Dic17—21no—
74C23×Dic17—21no—
75C2×SD16×C17—41no—
76C2×SD16×C17—41no—
77C2×SD16×C17C2×C414yescomplemented
78C2×D8×C17—41no—
79C2×D8×C17—41no—
80C2×D8×C17C2×C414yescomplemented
81C22×C8×C17C2311yescharacteristic
82C22×C8×C17C2311yescharacteristic
83C17×#121—22no—
84C17×#121C2×C414yes—
85C2×C4⋊C4×C17C2311yescharacteristic
86C2×C22⋊C4×C17—21no—
87C2×C22⋊Dic17—21no—
88C2×C22⋊Dic17—21no—
89C2×C22⋊Dic17—21no—
90C2×C22⋊Dic17—21no—
91C2×C22⋊Dic17—21no—
92C2×C22⋊Dic17—21no—
93C2×C22⋊Dic17—21no—
94C2×C22⋊Dic17—21no—
95C2×C22⋊Dic17D411yescharacteristic
96C2×C22⋊Dic17D411yescharacteristic
97D4×Dic17—41no—
98D4×Dic17—41no—
99#10587612—41no—
100#10587612—41no—
101C2×C4⋊Dic17—21no—
102C2×C4⋊Dic17—21no—
103C2×C4⋊Dic17—41no—
104C2×C4⋊Dic17—41no—
105C2×C4⋊Dic17D411yescharacteristic
106C2×C4⋊Dic17D411yescharacteristic
107C2×C4⋊Dic17C2311yescharacteristic
108C2×C4⋊Dic17C2311yescharacteristic
109C2×C4⋊Dic17C2311yescharacteristic
110C2×C4⋊Dic17C2311yescharacteristic
111C2×C4×Dic17—21no—
112C2×C4×Dic17C2311yescharacteristic
113C2×C4×Dic17C2311yescharacteristic
114C22×#3622C2311yescharacteristic
115C22×#3622C2311yescharacteristic
116C17×#103C2×C414yescomplemented
117C17×#102C2×C414yescomplemented
118C17×C22⋊C8C2×C414yescomplemented
119#10587506—41no—
120#10587506—41no—
121#10587503—41no—
122#10587503—41no—
123#10587503—41no—
124#10587503—41no—
125#10587502—21no—
126#10587502—21no—
127#10587502—21no—
128#10587502—21no—
129#10587502—21no—
130#10587502—21no—
131#10587502—21no—
132C22⋊#3622—22no—
133#10587489—41no—
134#10587489—41no—
135#10587486—41no—
136C8×Dic17—41no—
137C24×C17—21no—
138C24×C17—21no—
139C24×C17C2×D411yescharacteristic
140#41×C17—44no—
141#41×C17—44no—
142#41×C17—44no—
143#41×C17—44no—
144C2×Q8×C17—21no—
145C2×Q8×C17—21no—
146C2×Q8×C17—21no—
147C2×Q8×C17—21no—
148C2×Q8×C17—21no—
149C2×Q8×C17C22×C412yes—
150C2×D4×C17—24no—
151C2×D4×C17—24no—
152C2×D4×C17—21no—
153C2×D4×C17—21no—
154C2×D4×C17—21no—
155C2×D4×C17—21no—
156C2×D4×C17—21no—
157C2×D4×C17—21no—
158C2×D4×C17—21no—
159C2×D4×C17—21no—
160C2×D4×C17—21no—
161C2×D4×C17—21no—
162C2×D4×C17—42no—
163C2×D4×C17—42no—
164C2×D4×C17—81no—
165C2×D4×C17—81no—
166C2×D4×C17C22×C412yes—
167C2×D4×C17C22×C412yes—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—24no—
175C22×C4×C17—42no—
176C22×C4×C17—42no—
177C22×C4×C17C22×C412yes—
178C22×C4×C17C2×D411yescharacteristic
179C22×C4×C17#4112yes—
180C22×C4×C17C2411yescharacteristic
181C22×Dic17—21no—
182C22×Dic17—21no—
183C22×Dic17—21no—
184C22×Dic17—21no—
185C22×Dic17—42no—
186C22×Dic17—42no—
187C22×Dic17—81no—
188C22×Dic17—81no—
189C22×Dic17—81no—
190C22×Dic17—81no—
191C22×Dic17C2×D411yescharacteristic
192C22×Dic17C2×D411yescharacteristic
193C22×Dic17C2×D411yescharacteristic
194C22×Dic17C2×D411yescharacteristic
195SD16×C17—44no—
196D8×C17—44no—
197C2×C8×C17—21no—
198C2×C8×C17—21no—
199C2×C8×C17—21no—
200C2×C8×C17—21no—
201C2×C8×C17C22×C412yes—
202C2×C8×C17C22×C412yes—
203C4⋊C4×C17—21no—
204C4⋊C4×C17C22×C412yes—
205C22⋊C4×C17—24no—
206C22⋊Dic17—41no—
207C22⋊Dic17—41no—
208C22⋊Dic17—42no—
209C22⋊Dic17—81no—
210C22⋊Dic17—81no—
211C22⋊Dic17—81no—
212C22⋊Dic17—81no—
213C22⋊Dic17—81no—
214C22⋊Dic17—81no—
215C22⋊Dic17—81no—
216C4⋊Dic17—21no—
217C4⋊Dic17—21no—
218C4⋊Dic17—21no—
219C4⋊Dic17—21no—
220C4⋊Dic17—21no—
221C4⋊Dic17—21no—
222C4⋊Dic17—21no—
223C4⋊Dic17—21no—
224C4⋊Dic17—41no—
225C4⋊Dic17—41no—
226C4⋊Dic17—42no—
227C4⋊Dic17—81no—
228C4×Dic17—21no—
229C4×Dic17—21no—
230C4×Dic17—21no—
231C4×Dic17—21no—
232C4×Dic17—81no—
233C2×#3622—21no—
234C2×#3622—21no—
235C2×#3622—21no—
236C2×#3622—21no—
237C2×#3622—21no—
238C2×#3622—21no—
239#22055—171nomaximal, Sylow
240C23×C17—21no—
241C23×C17—21no—
242C23×C17—21no—
243C23×C17—21no—
244C23×C17—21no—
245C23×C17—21no—
246C23×C17—22no—
247C23×C17—22no—
248C23×C17—41no—
249C23×C17—41no—
250C23×C17—41no—
251C23×C17—41no—
252C23×C17—41no—
253C23×C17—41no—
254C23×C17—41no—
255C23×C17—41no—
256C23×C17—41no—
257C23×C17—41no—
258C23×C17—41no—
259C23×C17—41no—
260C23×C17C4×D412yes—
261C23×C17C22×D411yescharacteristic
262Q8×C17—22no—
263Q8×C17—22no—
264Q8×C17—41no—
265Q8×C17—41no—
266D4×C17—22no—
267D4×C17—22no—
268D4×C17—22no—
269D4×C17—22no—
270D4×C17—48no—
271D4×C17—41no—
272D4×C17—41no—
273D4×C17—41no—
274D4×C17—41no—
275D4×C17—84no—
276C2×C4×C17—21no—
277C2×C4×C17—21no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—48no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—41no—
288C2×C4×C17—41no—
289C2×C4×C17C4×D412yes—
290C2×C4×C17C23×C411yescharacteristic
291C2×C4×C17C2×#4111yescharacteristic
292C2×C4×C17H(5,𝔽2)11yescharacteristic
293C2×C4×C17H(5,𝔽2)11yescharacteristic
294C2×C4×C17H(5,𝔽2)11yescharacteristic
295C2×C4×C17H(5,𝔽2)11yescharacteristic
296C2×Dic17—21no—
297C2×Dic17—21no—
298C2×Dic17—21no—
299C2×Dic17—21no—
300C2×Dic17—21no—
301C2×Dic17—21no—
302C2×Dic17—21no—
303C2×Dic17—21no—
304C2×Dic17—21no—
305C2×Dic17—21no—
306C2×Dic17—21no—
307C2×Dic17—21no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17—41no—
312C2×Dic17—41no—
313C2×Dic17—41no—
314C2×Dic17—41no—
315C2×Dic17—41no—
316C2×Dic17—41no—
317C2×Dic17—41no—
318C2×Dic17—41no—
319C2×Dic17—41no—
320C2×Dic17—84no—
321C2×Dic17—84no—
322C8×C17—22no—
323C8×C17—22no—
324#3622—41no—
325#3622—41no—
326C2×#449D1711yescharacteristic
327#2324—171no—
328#2311—171no—
329#1973—171no—
330#1970—171no—
331#1936—171no—
332#1933—171no—
333#1928—171no—
334#1925—171no—
335#1879—171no—
336#1877—171no—
337#1874—171no—
338#1852—171no—
339#1788—171no—
340#1750—171no—
341C22×C17—22no—
342C22×C17—22no—
343C22×C17—22no—
344C22×C17—41no—
345C22×C17—41no—
346C22×C17—41no—
347C22×C17—41no—
348C22×C17—42no—
349C22×C17—42no—
350C22×C17—42no—
351C22×C17—42no—
352C22×C17—42no—
353C22×C17—42no—
354C22×C17—81no—
355C22×C17—81no—
356C22×C17—81no—
357C22×C17—81no—
358C22×C17—81no—
359C22×C17—81no—
360C22×C17—81no—
361C22×C17—81no—
362C22×C17C2×C4×D411yescharacteristic
363C22×C17#53411yescharacteristic
364C22×C17#53511yescharacteristic
365C22×C17#57611yescharacteristic
366C22×C17#57611yescharacteristic
367C22×C17#57711yescharacteristic
368C22×C17#57811yescharacteristic
369C4×C17—22no—
370C4×C17—42no—
371C4×C17—42no—
372C4×C17#51811yescharacteristic
373C4×C17#51811yescharacteristic
374C4×C17#53811yescharacteristic
375C4×C17#53811yescharacteristic
376Dic17—41no—
377Dic17—41no—
378Dic17—41no—
379Dic17—41no—
380Dic17—81no—
381Dic17—81no—
382Dic17—81no—
383Dic17—81no—
384C22×#41C2×D1711yescharacteristic
385C22×SD16C2×D1711yescharacteristic
386C22×D8C2×D1711yescharacteristic
387C2×#121C2×D1711yescharacteristic
388C2×C4×D4—171no—
389C2×#117—171no—
390C22×C4⋊C4—171no—
391#449Dic1718yescomplemented
392C2×#107—171no—
393C2×#107—171no—
394C2×#103—171no—
395C2×#103—171no—
396C2×#103C2×D1711yescharacteristic
397C2×#102—171no—
398C2×#102—171no—
399C2×#102—171no—
400C2×#102—171no—
401C2×#102C2×D1711yescharacteristic
402C2×C22⋊C8—171no—
403C2×C22⋊C8C2×D1711yescharacteristic
404C2×#97—171no—
405C2×C4×C8—171no—
406#391—171no—
407#391—171no—
408#390—171no—
409#390—171no—
410#390—171no—
411#390—341no—
412#389—171no—
413#388—341no—
414#386—341no—
415#386—341no—
416#386—341no—
417#385—341no—
418#380—171no—
419#380—341no—
420#380—341no—
421C4×C4⋊C4—171no—
422#340—171no—
423#340—171no—
424#340—171no—
425#340—171no—
426#336—171no—
427#336—171no—
428C2×C17—42no—
429C2×C17—82no—
430C2×C17—82no—
431C2×C17#232111yescharacteristic
432C2×C17#294611yescharacteristic
433C2×C17#295111yescharacteristic
434C2×C17#319811yescharacteristic
435C2×C17#320311yescharacteristic
436C2×C17#322011yescharacteristic
437C2×C17#322511yescharacteristic
438C2×#41—22no—
439C2×#41—41no—
440C2×#41—41no—
441C2×#41—41no—
442C2×#41—41no—
443C2×#41C2×Dic1714yescomplemented
444C22×Q8C22×D1711yescharacteristic
445C22×D4—21no—
446C22×D4—21no—
447C22×D4C22×D1711yescharacteristic
448C22×D4C22×D1711yescharacteristic
449C23×C4—21no—
450C23×C4—341no—
451C23×C4—341no—
452C23×C4C22×D1711yescharacteristic
453C2×SD16—41no—
454C2×SD16—41no—
455C2×SD16C2×Dic1714yescomplemented
456C2×D8—41no—
457C2×D8—41no—
458C2×D8C2×Dic1714yescomplemented
459C22×C8—171no—
460C22×C8—171no—
461C22×C8C22×D1711yescharacteristic
462C22×C8C22×D1711yescharacteristic
463#121—22no—
464#121C2×Dic1714yes—
465C4×D4—681no—
466C4×D4—681no—
467#117—681no—
468#117—681no—
469C2×C4⋊C4—171no—
470C2×C4⋊C4—171no—
471C2×C4⋊C4—171no—
472C2×C4⋊C4—171no—
473C2×C4⋊C4—171no—
474C2×C4⋊C4—171no—
475C2×C4⋊C4—341no—
476C2×C4⋊C4—341no—
477C2×C4⋊C4—681no—
478C2×C4⋊C4—681no—
479C2×C4⋊C4C22×D1711yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—171no—
482C2×C22⋊C4—171no—
483C2×C22⋊C4—341no—
484C2×C22⋊C4—341no—
485C2×C22⋊C4—341no—
486C2×C22⋊C4—341no—
487C2×C22⋊C4—341no—
488C2×C22⋊C4—341no—
489C2×C22⋊C4—341no—
490C2×C22⋊C4—341no—
491C2×C42—171no—
492C2×C42—171no—
493C2×C42—341no—
494#107—681no—
495#107—681no—
496#103—681no—
497#103—681no—
498#103C2×Dic1714yescomplemented
499#102—681no—
500#102—681no—
501#102—681no—
502#102—681no—
503#102C2×Dic1714yescomplemented
504C22⋊C8—342no—
505C22⋊C8C2×Dic1714yescomplemented
506#97—681no—
507C4×C8—681no—
508#95—341no—
509#95—341no—
510#95—341no—
511#95—341no—
512#95—341no—
513#95—341no—
514#95—341no—
515C17#2205511yescharacteristic, complemented, Sylow
516C24—21no—
517C24—21no—
518C24D4×D1711yescharacteristic
519#41—44no—
520#41—44no—
521#41—44no—
522#41—44no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8C22×Dic1712yes—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—81no—
544C2×D4—81no—
545C2×D4C22×Dic1712yes—
546C2×D4C22×Dic1712yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—171no—
557C22×C4—171no—
558C22×C4—171no—
559C22×C4—171no—
560C22×C4—341no—
561C22×C4—341no—
562C22×C4—341no—
563C22×C4—341no—
564C22×C4—682no—
565C22×C4—682no—
566C22×C4—1361no—
567C22×C4—1361no—
568C22×C4—1361no—
569C22×C4—1361no—
570C22×C4D4×D1711yescharacteristic
571C22×C4#6325412yes—
572C22×C4C22×Dic1712yes—
573C22×C4C23×D1711yescharacteristic
574SD16—44no—
575D8—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—341no—
581C2×C8—341no—
582C2×C8—341no—
583C2×C8—341no—
584C2×C8—341no—
585C2×C8—341no—
586C2×C8C22×Dic1712yes—
587C2×C8C22×Dic1712yes—
588C4⋊C4—21no—
589C4⋊C4—341no—
590C4⋊C4—341no—
591C4⋊C4—341no—
592C4⋊C4—341no—
593C4⋊C4—341no—
594C4⋊C4—341no—
595C4⋊C4—341no—
596C4⋊C4—341no—
597C4⋊C4—681no—
598C4⋊C4—681no—
599C4⋊C4—682no—
600C4⋊C4—1361no—
601C4⋊C4C22×Dic1712yes—
602C22⋊C4—24no—
603C22⋊C4—681no—
604C22⋊C4—681no—
605C22⋊C4—682no—
606C22⋊C4—1361no—
607C22⋊C4—1361no—
608C22⋊C4—1361no—
609C22⋊C4—1361no—
610C22⋊C4—1361no—
611C22⋊C4—1361no—
612C22⋊C4—1361no—
613C42—341no—
614C42—341no—
615C42—341no—
616C42—341no—
617C42—1361no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23D4×Dic1712yes—
639C23C2×D4×D1711yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—41no—
643Q8—41no—
644D4—22no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—48no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—84no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—48no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—341no—
668C2×C4—341no—
669C2×C4—341no—
670C2×C4—341no—
671C2×C4—341no—
672C2×C4—341no—
673C2×C4—341no—
674C2×C4—341no—
675C2×C4—341no—
676C2×C4—341no—
677C2×C4—341no—
678C2×C4—341no—
679C2×C4—681no—
680C2×C4—681no—
681C2×C4—681no—
682C2×C4—681no—
683C2×C4—681no—
684C2×C4—681no—
685C2×C4—681no—
686C2×C4—681no—
687C2×C4—681no—
688C2×C4—681no—
689C2×C4—681no—
690C2×C4—681no—
691C2×C4—1364no—
692C2×C4—1364no—
693C2×C4D4×Dic1712yes—
694C2×C4C2×#6325411yescharacteristic
695C2×C4#1058769111yescharacteristic
696C2×C4#1058769111yescharacteristic
697C2×C4#1058769111yescharacteristic
698C2×C4#1058769111yescharacteristic
699C2×C4C23×Dic1711yescharacteristic
700C8—22no—
701C8—22no—
702C8—681no—
703C8—681no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22C2×D4×Dic1711yescharacteristic
726C22#1176336911yescharacteristic
727C22#1176337411yescharacteristic
728C22#1176361111yescharacteristic
729C22#1176361311yescharacteristic
730C22#1176361911yescharacteristic
731C22#1176362311yescharacteristic
732C4—22no—
733C4—42no—
734C4—42no—
735C4—681no—
736C4—681no—
737C4—681no—
738C4—681no—
739C4—1361no—
740C4—1361no—
741C4—1361no—
742C4—1361no—
743C4#1176328411yescharacteristic
744C4#1176328411yescharacteristic
745C4#1176339411yescharacteristic
746C4#1176339411yescharacteristic
747C2—42no—
748C2—82no—
749C2—82no—
750C2#1453144511yescharacteristic
751C2#1453761711yescharacteristic
752C2#1453766011yescharacteristic
753C2#1453963311yescharacteristic
754C2#1453968311yescharacteristic
755C2#1453983211yescharacteristic
756C2#1453988911yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
Fitting, prime radicalC2×C17×#449C2
socleC23×C17C22×D4
cosocleC22×C4×C17C24
hypercenterC2×#449D17
hypocenterC17#22055
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. #14531479C2semidirect
2. #14531376C2semidirect
3. #14529667C2semidirect
4. #14529651C2semidirect
5. #14529483C2semidirect
6. #14529462C2semidirect
7. #14529427C2semidirect
8. #14529406C2semidirect
9. #14529134C2semidirect
10. #14529120C2semidirect
11. #14529102C2semidirect
12. #14528974C2semidirect
13. #14528724C2semidirect
14. #14528552C2semidirect
56. C17×#449C4semidirect
65. C2×#41×C17C2×C4semidirect
77. C2×SD16×C17C2×C4semidirect
80. C2×D8×C17C2×C4semidirect
116. C17×#103C2×C4semidirect
117. C17×#102C2×C4semidirect
118. C17×C22⋊C8C2×C4semidirect
391. #449Dic17semidirect
443. C2×#41C2×Dic17semidirect
455. C2×SD16C2×Dic17semidirect
458. C2×D8C2×Dic17semidirect
498. #103C2×Dic17semidirect
503. #102C2×Dic17semidirect
505. C22⋊C8C2×Dic17semidirect
515. C17#22055semidirect

Maximal subgroups

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

subgroupindex
#145314792
#145313762
#145296672
#145296512
#145294832
#145294622
#145294272
#145294062
#145291342
#145291202
#145291022
#145289742
#145287242
#145285522
C2×C17×#4492
#2205517