Finite Group Databasebeta

← #17045644

Subgroups — #17045644

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
1C2×#11762952C211yesmaximal, characteristic
2#14531372C211yesmaximal, characteristic, complemented
3#14529664C211yesmaximal, characteristic, complemented
4#14529649C211yesmaximal, characteristic, complemented
5#14529480C211yesmaximal, characteristic, complemented
6#14529459C211yesmaximal, characteristic, complemented
7#14529425C211yesmaximal, characteristic, complemented
8#14529404C211yesmaximal, characteristic, complemented
9#14529132C211yesmaximal, characteristic, complemented
10#14529118C211yesmaximal, characteristic, complemented
11#14529102C211yesmaximal, characteristic, complemented
12#14528971C211yesmaximal, characteristic, complemented
13#14528722C211yesmaximal, characteristic, complemented
14#14528550C211yesmaximal, characteristic, complemented
15C17×#2324C211yesmaximal, characteristic, complemented
16C22×#63252C2211yescharacteristic
17C22×#63229C2211yescharacteristic
18C22×#63228C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20#11762952C418yescomplemented
21C2×#10587478C2211yescharacteristic
22C2×#10587478C2211yescharacteristic
23C2×#10587481C2211yescharacteristic
24C2×#10587481C2211yescharacteristic
25C2×#10587481C2211yescharacteristic
26C2×#10587503C2211yescharacteristic
27C2×#10587503C2211yescharacteristic
28C2×#10587480C2211yescharacteristic
29C2×#10587480C2211yescharacteristic
30C2×#10587480C2211yescharacteristic
31C2×C22⋊#3622C2211yescharacteristic
32C2×C22⋊#3622C2211yescharacteristic
33C2×#10587474C2211yescharacteristic
34C2×C4×#3622C2211yescharacteristic
35#11762715C2211yescharacteristic
36#11762715C2211yescharacteristic
37#11762711C2211yescharacteristic
38#11762711C2211yescharacteristic
39#11762686—21no—
40#11762686—21no—
41#11762666—21no—
42#11762666—21no—
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762564C2211yescharacteristic
48#11762564C2211yescharacteristic
49C2×C17×#121C2211yescharacteristic
50C2×C4×D4×C17C2211yescharacteristic
51C2×C17×#117C2211yescharacteristic
52C17×#390—21no—
53C17×#390C2211yescharacteristic
54C17×#389C2211yescharacteristic
55C17×#388—21no—
56C17×#386—21no—
57C17×#385—21no—
58C17×#380C2211yescharacteristic
59C4×C4⋊C4×C17C2211yescharacteristic
60C22×D4×C17—21no—
61C22×D4×C17C2311yescharacteristic
62C23×C4×C17—21no—
63C23×C4×C17C2311yescharacteristic
64C22×C22⋊D17—21no—
65C23×Dic17—21no—
66C2×#63252—22no—
67C2×#63252—41no—
68C2×#63252—41no—
69C2×#63252—41no—
70C2×#63252—41no—
71C2×#63252C2×C414yescomplemented
72C22×D68C2311yescharacteristic
73C22×C4×D17—21no—
74C22×Dic34C2311yescharacteristic
75C17×#121—22no—
76C17×#121C2×C414yes—
77C4×D4×C17—41no—
78C4×D4×C17—41no—
79C17×#117—41no—
80C17×#117—41no—
81C2×C4⋊C4×C17—21no—
82C2×C4⋊C4×C17D411yescharacteristic
83C2×C4⋊C4×C17D411yescharacteristic
84C2×C4⋊C4×C17C2311yescharacteristic
85C2×C4⋊C4×C17C2311yescharacteristic
86C2×C4⋊C4×C17C2311yescharacteristic
87C2×C22⋊C4×C17—21no—
88C2×C22⋊C4×C17—21no—
89C2×C22⋊C4×C17—21no—
90C2×C22⋊C4×C17—21no—
91C2×C22⋊C4×C17—21no—
92C2×C22⋊C4×C17D411yescharacteristic
93C2×C22⋊C4×C17D411yescharacteristic
94C2×C42×C17—21no—
95C2×C42×C17C2311yescharacteristic
96C2×C42×C17C2311yescharacteristic
97C2×#63229—41no—
98C2×#63229—41no—
99C2×#63229C2×C414yescomplemented
100C2×#63228—41no—
101C2×#63228—41no—
102C2×#63228C2×C414yescomplemented
103C2×#63227—21no—
104C2×#63227—21no—
105C2×#63227—21no—
106C2×#63227—21no—
107C2×C4⋊Dic17—21no—
108C2×C4⋊Dic17—41no—
109C2×C4⋊Dic17—41no—
110C2×C4⋊Dic17C2311yescharacteristic
111C2×C4⋊Dic17C2311yescharacteristic
112C22×#3622C2311yescharacteristic
113C22×#3622C2311yescharacteristic
114C22×#3622C2311yescharacteristic
115C22×#3622C2311yescharacteristic
116C17×#95—21no—
117C17×#95—21no—
118C17×#95—21no—
119#10587503—41no—
120#10587503—41no—
121#10587502—21no—
122#10587502—21no—
123#10587502—21no—
124#10587502—21no—
125C22⋊#3622—22no—
126C22⋊#3622C2×C414yescomplemented
127#10587481—41no—
128#10587481—41no—
129#10587481C2×C414yescomplemented
130#10587480—41no—
131#10587480—41no—
132#10587480C2×C414yescomplemented
133#10587478—41no—
134#10587478—41no—
135#10587474—41no—
136C4×#3622—41no—
137C24×C17—21no—
138C24×C17C2×D411yescharacteristic
139C23×D17—21no—
140C2×D4×C17—24no—
141C2×D4×C17—21no—
142C2×D4×C17—21no—
143C2×D4×C17—21no—
144C2×D4×C17—21no—
145C2×D4×C17—21no—
146C2×D4×C17—81no—
147C2×D4×C17—81no—
148C2×D4×C17C22×C412yes—
149C22×C4×C17—21no—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—42no—
157C22×C4×C17—81no—
158C22×C4×C17—81no—
159C22×C4×C17C22×C412yes—
160C22×C4×C17C2×D411yescharacteristic
161C22×C4×C17C2×D411yescharacteristic
162C22×C4×C17C2×D411yescharacteristic
163C22×C4×C17C2×D411yescharacteristic
164C22×C4×C17C2×D411yescharacteristic
165C22×C4×C17#4112yes—
166C22×C4×C17C2411yescharacteristic
167C2×C22⋊D17—24no—
168C2×C22⋊D17—42no—
169C2×C22⋊D17—42no—
170C22×Dic17—21no—
171C22×Dic17—21no—
172C22×Dic17—21no—
173C22×Dic17—42no—
174C22×Dic17—81no—
175C22×Dic17—81no—
176#63252—44no—
177#63252—44no—
178#63252—44no—
179#63252—44no—
180C2×D68—21no—
181C2×D68—21no—
182C2×D68—21no—
183C2×D68—21no—
184C2×D68—21no—
185C2×D68C22×C412yes—
186C2×C4×D17—24no—
187C2×C4×D17—42no—
188C2×C4×D17—42no—
189C2×Dic34—21no—
190C2×Dic34—21no—
191C2×Dic34—21no—
192C2×Dic34—21no—
193C2×Dic34—21no—
194C2×Dic34C22×C412yes—
195C4⋊C4×C17—21no—
196C4⋊C4×C17—21no—
197C4⋊C4×C17—21no—
198C4⋊C4×C17—21no—
199C4⋊C4×C17—21no—
200C4⋊C4×C17—41no—
201C4⋊C4×C17—41no—
202C4⋊C4×C17—81no—
203C4⋊C4×C17C22×C412yes—
204C22⋊C4×C17—24no—
205C22⋊C4×C17—41no—
206C22⋊C4×C17—41no—
207C22⋊C4×C17—42no—
208C22⋊C4×C17—81no—
209C22⋊C4×C17—81no—
210C22⋊C4×C17—81no—
211C42×C17—21no—
212C42×C17—21no—
213C42×C17—21no—
214C42×C17—21no—
215C42×C17—81no—
216#63229—44no—
217#63228—44no—
218#63227—81no—
219#63227—81no—
220#63227—81no—
221#63227—81no—
222C4⋊Dic17—21no—
223C4⋊Dic17—21no—
224C4⋊Dic17—21no—
225C4⋊Dic17—21no—
226C4⋊Dic17—42no—
227C2×#3622—21no—
228C2×#3622—21no—
229C2×#3622—21no—
230C2×#3622—21no—
231C2×#3622—21no—
232C2×#3622—21no—
233C2×#3622—21no—
234C2×#3622—21no—
235C2×#3622—21no—
236C2×#3622—21no—
237C2×#3622C22×C412yes—
238C2×#3622C22×C412yes—
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—41no—
248C23×C17—41no—
249C23×C17—41no—
250C23×C17—41no—
251C23×C17—41no—
252C23×C17—41no—
253C23×C17C4×D412yes—
254C23×C17C22×D411yescharacteristic
255C22×D17—22no—
256C22×D17—41no—
257C22×D17—41no—
258C22×D17—41no—
259C22×D17—41no—
260C22×D17—41no—
261C22×D17—41no—
262D4×C17—22no—
263D4×C17—22no—
264D4×C17—41no—
265D4×C17—41no—
266D4×C17—84no—
267C2×C4×C17—21no—
268C2×C4×C17—21no—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—21no—
275C2×C4×C17—21no—
276C2×C4×C17—21no—
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—41no—
293C2×C4×C17—41no—
294C2×C4×C17—84no—
295C2×C4×C17C4×D412yes—
296C2×C4×C17C23×C411yescharacteristic
297C2×C4×C17C2×#4111yescharacteristic
298C2×C4×C17H(5,𝔽2)11yescharacteristic
299C2×C4×C17H(5,𝔽2)11yescharacteristic
300C2×C4×C17H(5,𝔽2)11yescharacteristic
301C2×C4×C17H(5,𝔽2)11yescharacteristic
302C22⋊D17—48no—
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—84no—
313D68—22no—
314D68—22no—
315D68—41no—
316D68—41no—
317C4×D17—48no—
318Dic34—22no—
319Dic34—22no—
320Dic34—41no—
321Dic34—41no—
322#3622—22no—
323#3622—22no—
324#3622—41no—
325#3622—41no—
326C2×#449—171no—
327#2324D1711yescharacteristic, complemented
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—81no—
352C22×C17—81no—
353C22×C17—81no—
354C22×C17—81no—
355C22×C17C2×C4×D411yescharacteristic
356C22×C17#53411yescharacteristic
357C22×C17#53511yescharacteristic
358C22×C17#57611yescharacteristic
359C22×C17#57611yescharacteristic
360C22×C17#57711yescharacteristic
361C22×C17#57811yescharacteristic
362C2×D17—42no—
363C2×D17—42no—
364C2×D17—42no—
365C2×D17—81no—
366C2×D17—81no—
367C2×D17—81no—
368C2×D17—81no—
369C4×C17—22no—
370C4×C17—41no—
371C4×C17—41no—
372C4×C17—42no—
373C4×C17—41no—
374C4×C17—41no—
375C4×C17—81no—
376C4×C17—81no—
377C4×C17#51811yescharacteristic
378C4×C17#51811yescharacteristic
379C4×C17#53811yescharacteristic
380C4×C17#53811yescharacteristic
381Dic17—42no—
382Dic17—81no—
383Dic17—81no—
384C22×#41—171no—
385C22×SD16—171no—
386C22×D8—171no—
387C2×#121C2×D1711yescharacteristic
388C2×C4×D4C2×D1711yescharacteristic
389C2×#117C2×D1711yescharacteristic
390C22×C4⋊C4—171no—
391#449—178no—
392C2×#107—171no—
393C2×#107—171no—
394C2×#103—171no—
395C2×#103—171no—
396C2×#103—171no—
397C2×#102—171no—
398C2×#102—171no—
399C2×#102—171no—
400C2×#102—171no—
401C2×#102—171no—
402C2×C22⋊C8—171no—
403C2×C22⋊C8—171no—
404C2×#97—171no—
405C2×C4×C8—171no—
406#391—171no—
407#391—171no—
408#390—21no—
409#390—171no—
410#390—171no—
411#390C2×D1711yescharacteristic
412#389C2×D1711yescharacteristic
413#388—21no—
414#386—21no—
415#386—341no—
416#386—341no—
417#385—21no—
418#380—341no—
419#380—341no—
420#380C2×D1711yescharacteristic
421C4×C4⋊C4C2×D1711yescharacteristic
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#232111yescharacteristic
431C2×C17#294611yescharacteristic
432C2×C17#295111yescharacteristic
433C2×C17#319811yescharacteristic
434C2×C17#320311yescharacteristic
435C2×C17#322011yescharacteristic
436C2×C17#322511yescharacteristic
437D17—82no—
438C2×#41—174no—
439C2×#41—342no—
440C2×#41—681no—
441C2×#41—681no—
442C2×#41—681no—
443C2×#41—681no—
444C22×Q8—171no—
445C22×D4—21no—
446C22×D4—171no—
447C22×D4—341no—
448C22×D4C22×D1711yescharacteristic
449C23×C4—21no—
450C23×C4—341no—
451C23×C4—341no—
452C23×C4C22×D1711yescharacteristic
453C2×SD16—174no—
454C2×SD16—681no—
455C2×SD16—681no—
456C2×D8—174no—
457C2×D8—681no—
458C2×D8—681no—
459C22×C8—171no—
460C22×C8—171no—
461C22×C8—171no—
462C22×C8—171no—
463#121—22no—
464#121C4×D1714yes—
465C4×D4—41no—
466C4×D4—41no—
467#117—41no—
468#117—41no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—171no—
471C2×C4⋊C4—171no—
472C2×C4⋊C4—341no—
473C2×C4⋊C4—681no—
474C2×C4⋊C4—681no—
475C2×C4⋊C4C22⋊D1711yescharacteristic
476C2×C4⋊C4C22⋊D1711yescharacteristic
477C2×C4⋊C4C22×D1711yescharacteristic
478C2×C4⋊C4C22×D1711yescharacteristic
479C2×C4⋊C4C22×D1711yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—341no—
486C2×C22⋊C4—341no—
487C2×C22⋊C4—341no—
488C2×C22⋊C4—341no—
489C2×C22⋊C4C22⋊D1711yescharacteristic
490C2×C22⋊C4C22⋊D1711yescharacteristic
491C2×C42—21no—
492C2×C42C22×D1711yescharacteristic
493C2×C42C22×D1711yescharacteristic
494#107—681no—
495#107—681no—
496#103—174no—
497#103—681no—
498#103—681no—
499#102—174no—
500#102—681no—
501#102—681no—
502#102—681no—
503#102—681no—
504C22⋊C8—174no—
505C22⋊C8—342no—
506#97—681no—
507C4×C8—681no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—341no—
512#95—341no—
513#95—341no—
514#95—341no—
515C17#2205511yescharacteristic, complemented, Sylow
516C24—21no—
517C24—341no—
518C24C2×C22⋊D1711yescharacteristic
519#41—684no—
520#41—684no—
521#41—684no—
522#41—684no—
523C2×Q8—172no—
524C2×Q8—341no—
525C2×Q8—341no—
526C2×Q8—341no—
527C2×Q8—341no—
528C2×Q8—341no—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—81no—
536C2×D4—81no—
537C2×D4—172no—
538C2×D4—344no—
539C2×D4—341no—
540C2×D4—341no—
541C2×D4—341no—
542C2×D4—341no—
543C2×D4—341no—
544C2×D4—682no—
545C2×D4—682no—
546C2×D4C2×C4×D1712yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—42no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—341no—
558C22×C4—344no—
559C22×C4—341no—
560C22×C4—341no—
561C22×C4—682no—
562C22×C4—682no—
563C22×C4—682no—
564C22×C4—1361no—
565C22×C4—1361no—
566C22×C4C2×C4×D1712yes—
567C22×C4#6325212yes—
568C22×C4C2×C22⋊D1711yescharacteristic
569C22×C4C2×C22⋊D1711yescharacteristic
570C22×C4C2×C22⋊D1711yescharacteristic
571C22×C4C2×C22⋊D1711yescharacteristic
572C22×C4C2×C22⋊D1711yescharacteristic
573C22×C4C23×D1711yescharacteristic
574SD16—684no—
575D8—684no—
576C2×C8—172no—
577C2×C8—172no—
578C2×C8—341no—
579C2×C8—341no—
580C2×C8—341no—
581C2×C8—341no—
582C2×C8—341no—
583C2×C8—341no—
584C2×C8—341no—
585C2×C8—341no—
586C2×C8—341no—
587C2×C8—341no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—81no—
596C4⋊C4—341no—
597C4⋊C4—341no—
598C4⋊C4—341no—
599C4⋊C4—341no—
600C4⋊C4—682no—
601C4⋊C4C2×C4×D1712yes—
602C22⋊C4—24no—
603C22⋊C4—41no—
604C22⋊C4—41no—
605C22⋊C4—42no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—1361no—
610C22⋊C4—1361no—
611C22⋊C4—1361no—
612C22⋊C4—1361no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—81no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—342no—
632C23—681no—
633C23—681no—
634C23—681no—
635C23—681no—
636C23—681no—
637C23—681no—
638C23C4×C22⋊D1712yes—
639C23C22×C22⋊D1711yescharacteristic
640Q8—342no—
641Q8—342no—
642Q8—681no—
643Q8—681no—
644D4—22no—
645D4—22no—
646D4—41no—
647D4—41no—
648D4—84no—
649D4—342no—
650D4—342no—
651D4—688no—
652D4—681no—
653D4—681no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—84no—
682C2×C4—342no—
683C2×C4—688no—
684C2×C4—681no—
685C2×C4—681no—
686C2×C4—681no—
687C2×C4—681no—
688C2×C4—681no—
689C2×C4—681no—
690C2×C4—681no—
691C2×C4—681no—
692C2×C4—1364no—
693C2×C4C4×C22⋊D1712yes—
694C2×C4C22×C4×D1711yescharacteristic
695C2×C4C2×#6325211yescharacteristic
696C2×C4#1058769111yescharacteristic
697C2×C4#1058769111yescharacteristic
698C2×C4#1058769611yescharacteristic
699C2×C4#1058769611yescharacteristic
700C8—342no—
701C8—342no—
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—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—682no—
719C22—682no—
720C22—682no—
721C22—1361no—
722C22—1361no—
723C22—1361no—
724C22—1361no—
725C22C2×C4×C22⋊D1711yescharacteristic
726C22#1176336811yescharacteristic
727C22#1176337311yescharacteristic
728C22#1176361211yescharacteristic
729C22#1176361211yescharacteristic
730C22#1176362011yescharacteristic
731C22#1176362411yescharacteristic
732C4—22no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—41no—
737C4—41no—
738C4—81no—
739C4—81no—
740C4—682no—
741C4—1361no—
742C4—1361no—
743C4#1176328111yescharacteristic
744C4#1176328111yescharacteristic
745C4#1176339211yescharacteristic
746C4#1176339211yescharacteristic
747C2—42no—
748C2—82no—
749C2—1362no—
750C2#1453143811yescharacteristic
751C2#1453761611yescharacteristic
752C2#1453765711yescharacteristic
753C2#1453963611yescharacteristic
754C2#1453968111yescharacteristic
755C2#1453982811yescharacteristic
756C2#1453988711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2324C2
socleC23×C17C22×D4
prime radicalC2×#11762952C2
cosocleC22×C4×C17C24
hypercenter#2324D17
hypocenterC17#22055
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. #14531372C2semidirect
3. #14529664C2semidirect
4. #14529649C2semidirect
5. #14529480C2semidirect
6. #14529459C2semidirect
7. #14529425C2semidirect
8. #14529404C2semidirect
9. #14529132C2semidirect
10. #14529118C2semidirect
11. #14529102C2semidirect
12. #14528971C2semidirect
13. #14528722C2semidirect
14. #14528550C2semidirect
15. C17×#2324C2semidirect
20. #11762952C4semidirect
71. C2×#63252C2×C4semidirect
99. C2×#63229C2×C4semidirect
102. C2×#63228C2×C4semidirect
126. C22⋊#3622C2×C4semidirect
129. #10587481C2×C4semidirect
132. #10587480C2×C4semidirect
327. #2324D17semidirect
515. C17#22055semidirect

Maximal subgroups

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

subgroupindex
C2×#117629522
#145313722
#145296642
#145296492
#145294802
#145294592
#145294252
#145294042
#145291322
#145291182
#145291022
#145289712
#145287222
#145285502
C17×#23242
#2205517