Finite Group Databasebeta

← #17898607

Subgroups — #17898607

Order 4352.

2818 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763611C211yesmaximal, characteristic
2#14541990C212yesmaximal, complemented
3#14537664C212yesmaximal, complemented
4#14537637C211yesmaximal, characteristic, complemented
5#14537633C212yesmaximal, complemented
6#14537612C212yesmaximal, complemented
7#14537611C214yesmaximal, complemented
8#14537597C212yesmaximal, complemented
9C4×#10587600C214yesmaximal, complemented
10#14537585C211yesmaximal, characteristic, complemented
11#14537583C212yesmaximal, complemented
12C2×#11762920C211yesmaximal, characteristic, complemented
13D17×#442C212yesmaximal, complemented
14#14537375C211yesmaximal, characteristic, complemented
15#14537308C212yesmaximal, complemented
16#14537211C211yesmaximal, characteristic, complemented
17C17×#2952C211yesmaximal, characteristic, complemented
18C2×#10587696C2212yes—
19#11763611C4116yescomplemented
20C2×#10587600C2214yes—
21C2×#10587635C2212yes—
22C2×#10587605C2212yes—
23C22×D136C2211yescharacteristic
24C2×D8×D17C2212yes—
25C2×#10587593C2211yescharacteristic
26C2×#10587587C2211yescharacteristic
27#11763291C2214yescomplemented
28#11763290—22no—
29#11763290C2212yes—
30#11763283—22no—
31#11763283C2212yescomplemented
32#11763281—24no—
33#11763281C2214yescomplemented
34#41×Dic17C2212yescomplemented
35C4×#63256C2214yescomplemented
36#11763277—22no—
37#11763277C2211yescharacteristic
38C2×#10587579—22no—
39C2×#10587579C2212yescomplemented
40C4×D4×D17—24no—
41C4×D4×D17C2214yescomplemented
42#11762922C2212yescomplemented
43#11762922C2212yescomplemented
44#11762921C2211yescharacteristic, complemented
45#11762921C2211yescharacteristic, complemented
46#11762920C2212yescomplemented
47#11762920C2212yescomplemented
48#11762920C2212yescomplemented
49#11762920C2212yescomplemented
50#11762919C2214yescomplemented
51#11762918C2214yescomplemented
52#11762916C2211yescharacteristic, complemented
53#11762916C2211yescharacteristic, complemented
54#11762912C2214yescomplemented
55#11762910C2212yescomplemented
56#11762910C2212yescomplemented
57#11762907C2214yescomplemented
58C4×#63230C2214yescomplemented
59#11762894C2214yescomplemented
60C4×D136C2214yescomplemented
61C4×#63228C2214yescomplemented
62#11762889C2214yescomplemented
63#11762849C2212yescomplemented
64#11762848C2214yescomplemented
65#11762847C2211yescharacteristic, complemented
66#11762844C2212yescomplemented
67#106×D17C2212yescomplemented
68#11762815C2212yescomplemented
69#11762812C2214yescomplemented
70#11762809C2214yescomplemented
71#11762805C2212yescomplemented
72#11762804C2214yescomplemented
73C2×#10587480C2212yescomplemented
74#102×D17C2214yescomplemented
75#11762766C2212yescomplemented
76#11762765C2211yescharacteristic, complemented
77#11762763C2212yescomplemented
78M16×Dic17C2211yescharacteristic, complemented
79C4×#63218C2212yescomplemented
80C2×#10587486C2211yescharacteristic, complemented
81#97×D17C2212yescomplemented
82C2×C17×#135C2211yescharacteristic
83C17×#520C2212yescomplemented
84C17×#442C2212yescomplemented
85C17×#441C2212yescomplemented
86C4×SD16×C17C2214yescomplemented
87C2×C17×#106C2211yescharacteristic, complemented
88C17×#417C2212yescomplemented
89C17×#405C2211yescharacteristic, complemented
90C2×#41×C17C2312yes—
91#10587696—28no—
92#10587696C2×C4116yescomplemented
93C2×#63256C2314yes—
94C2×D4×D17—24no—
95C2×D4×D17C2314yes—
96C2×#63252—22no—
97C2×#63252C2311yescharacteristic
98C22×D68—22no—
99C22×D68C2312yes—
100C22×C4×D17—22no—
101C22×C4×D17—24no—
102C17×#135C2×C418yescomplemented
103C2×Q16×C17C2311yescharacteristic
104C2×SD16×C17C2312yes—
105C2×D8×C17C2311yescharacteristic
106C2×M16×C17C2311yescharacteristic
107C22×C8×C17C2311yescharacteristic
108C4×Q8×C17C2314yes—
109C4×D4×C17—24no—
110C4×D4×C17C2314yes—
111C17×#117—22no—
112C17×#117C2311yescharacteristic
113C2×C4⋊C4×C17—22no—
114C2×C4⋊C4×C17C2312yes—
115#10587635C2×C4116yescomplemented
116Q8×Dic17C2312yes—
117Q8×Dic17C2312yes—
118C2×#63230C2314yes—
119D4×Dic17—22no—
120D4×Dic17—22no—
121D4×Dic17C2312yes—
122D4×Dic17C2312yes—
123C2×#63228C2314yes—
124C4×C22⋊D17—24no—
125C4×C22⋊D17—24no—
126C4×C22⋊D17—24no—
127C2×#63227—24no—
128C2×#63227—22no—
129#10587612—22no—
130#10587612C2312yes—
131C2×C4×Dic17—22no—
132C2×C4×Dic17C2311yescharacteristic
133C2×#63223C2311yescharacteristic
134C22×#3622C2311yescharacteristic
135#10587605C2×C4116yescomplemented
136#10587600C2×C4132yescomplemented
137D8×D17C2×C4116yescomplemented
138#10587593—24no—
139C2×D136C2×C418yescomplemented
140C2×D136C2312yes—
141C2×D136C2312yes—
142#10587587C2×C418yescomplemented
143C2×#63218C2312yes—
144C2×#63218C2312yes—
145C2×C8×D17C2312yes—
146C2×C8×D17C2312yes—
147#10587579—24no—
148#10587579—22no—
149#10587579—22no—
150#10587579—22no—
151#10587579—24no—
152#10587579—22no—
153#10587579—22no—
154#10587579D412yes—
155#10587579C2314yes—
156#10587579C2314yes—
157#10587578—24no—
158#10587578C2314yes—
159C4⋊C4×D17—24no—
160C4⋊C4×D17C2314yes—
161#10587573—22no—
162#10587573D412yes—
163#10587567—24no—
164#10587567—24no—
165#10587567D414yes—
166C22⋊C4×D17—24no—
167C22⋊C4×D17—24no—
168C22⋊C4×D17—24no—
169C4×D68—24no—
170C4×D68—24no—
171C4×D68C2314yes—
172C4×D68C2314yes—
173#10587558—24no—
174#10587558C2312yes—
175C42×D17—24no—
176C42×D17C2312yes—
177C17×#106C2312yes—
178C17×#106C2312yes—
179C17×#103C2314yes—
180C17×#102C2314yes—
181C17×#97C2312yes—
182C4×C8×C17C2312yes—
183#10587506C2312yes—
184#10587506C2312yes—
185#10587503C2312yes—
186#10587503C2312yes—
187#10587492C2314yes—
188#10587492C2314yes—
189#10587489C2312yes—
190#10587488C2311yescharacteristic
191#10587488C2311yescharacteristic
192#10587486C2311yescharacteristic
193#10587486C2312yes—
194#10587486C2311yescharacteristic
195#10587486C2311yescharacteristic
196#10587486C2311yescharacteristic
197C8×Dic17C2312yes—
198#10587480C2314yes—
199#10587480C2314yes—
200#10587479C2314yes—
201#10587478C2314yes—
202#10587474C2312yes—
203C4×#3622C2312yes—
204C23×D17—22no—
205C23×D17—24no—
206#41×C17—24no—
207#41×C17C22×C418yescomplemented
208C2×Q8×C17C2412yes—
209C2×D4×C17—22no—
210C2×D4×C17C2412yes—
211C22×C4×C17—22no—
212C22×C4×C17—22no—
213C22×C4×C17—24no—
214C22×C4×C17C2411yescharacteristic
215C2×C22⋊D17—24no—
216C2×C22⋊D17C2×D412yes—
217C22×Dic17—22no—
218C22×Dic17—22no—
219C22×Dic17C2×D412yes—
220#63256—28no—
221#63256C22×C4116yescomplemented
222D4×D17—232no—
223D4×D17—28no—
224D4×D17C22×C4116yescomplemented
225#63252—216no—
226#63252C22×C414yes—
227#63252#4114yes—
228C2×D68—24no—
229C2×D68—22no—
230C2×D68—24no—
231C2×D68—216no—
232C2×D68C22×C418yescomplemented
233C2×D68C2×D411yescharacteristic
234C2×D68C2414yes—
235C2×C4×D17—24no—
236C2×C4×D17—24no—
237C2×C4×D17—24no—
238C2×C4×D17—24no—
239C2×C4×D17—24no—
240C2×C4×D17—24no—
241C2×C4×D17—88no—
242C2×C4×D17—84no—
243C2×C4×D17C2×D414yes—
244C2×C4×D17C2412yes—
245C2×Dic34C2×D411yescharacteristic
246Q16×C17C22×C414yescomplemented
247SD16×C17C22×C418yescomplemented
248D8×C17C22×C414yescomplemented
249M16×C17—22no—
250C2×C8×C17C22×C414yescomplemented
251C2×C8×C17C2412yes—
252C2×C8×C17C2411yescharacteristic
253C2×C8×C17C2411yescharacteristic
254C4⋊C4×C17—22no—
255C4⋊C4×C17—24no—
256C4⋊C4×C17C2×D412yes—
257C4⋊C4×C17C2414yes—
258C22⋊C4×C17—24no—
259C22⋊C4×C17C2×D412yes—
260C42×C17—24no—
261C42×C17C2412yes—
262C22⋊Dic17—22no—
263C22⋊Dic17—22no—
264C22⋊Dic17—22no—
265#63230C22×C4116yescomplemented
266#63228C22×C4116yescomplemented
267#63227—24no—
268#63227—24no—
269#63227—24no—
270#63227—24no—
271#63227—24no—
272#63227C2×D414yes—
273C4⋊Dic17—22no—
274C4⋊Dic17—22no—
275C4⋊Dic17C2412yes—
276C4⋊Dic17C2412yes—
277#63225—24no—
278#63225C2×D414yes—
279C4×Dic17—22no—
280C4×Dic17—22no—
281C4×Dic17—24no—
282C4×Dic17—22no—
283C4×Dic17C2×D414yes—
284C4×Dic17C2×D412yes—
285C4×Dic17C2411yescharacteristic
286C4×Dic17C2411yescharacteristic
287#63223C22×C414yescomplemented
288C2×#3622—22no—
289C2×#3622C2411yescharacteristic
290C2×#3622C2411yescharacteristic
291C2×#3622C2412yes—
292D136C22×C418yescomplemented
293D136C22×C418yescomplemented
294#63218—24no—
295#63218C22×C418yescomplemented
296C8×D17—24no—
297C8×D17C22×C418yescomplemented
298#60176—171nomaximal, Sylow
299C23×C17—22no—
300C23×C17C22×D411yescharacteristic
301C22×D17—24no—
302C22×D17—28no—
303C22×D17—216no—
304C22×D17—84no—
305C22×D17—84no—
306C22×D17—82no—
307C22×D17—82no—
308C22×D17C22×D412yes—
309Q8×C17—22no—
310Q8×C17C23×C414yes—
311D4×C17—28no—
312D4×C17—22no—
313D4×C17C23×C414yes—
314C2×C4×C17—22no—
315C2×C4×C17—28no—
316C2×C4×C17—24no—
317C2×C4×C17—84no—
318C2×C4×C17—82no—
319C2×C4×C17C23×C412yes—
320C2×C4×C17C22×D414yes—
321C2×C4×C17C22×D411yescharacteristic
322C2×C4×C17C2×#4112yes—
323C2×C4×C17C2511yescharacteristic
324C22⋊D17—216no—
325C22⋊D17C4×D418yes—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—42no—
329C2×Dic17—44no—
330C2×Dic17—82no—
331C2×Dic17C22×D412yes—
332C2×Dic17C22×D412yes—
333C2×Dic17C22×D412yes—
334D68—216no—
335D68—28no—
336D68—24no—
337D68C4×D414yes—
338D68C23×C418yes—
339C4×D17—216no—
340C4×D17—44no—
341C4×D17—48no—
342C4×D17—84no—
343C4×D17—84no—
344C4×D17—84no—
345C4×D17—84no—
346C4×D17C23×C414yes—
347C4×D17C2×#4114yes—
348Dic34C4×D414yes—
349C8×C17—22no—
350C8×C17C23×C412yes—
351C8×C17C23×C412yes—
352#3622—21no—
353#3622—21no—
354#3622C23×C414yes—
355C2×#576—171no—
356C4×H(5,𝔽2)—172no—
357#2952—172no—
358#2952D1711yescharacteristic, complemented
359#2948—172no—
360#2948—171no—
361#2946—174no—
362#2946—172no—
363C4×AGL(1,ℤ/8)—174no—
364C4×AGL(1,ℤ/8)—172no—
365#2943—172no—
366#2943—171no—
367C2×#442—172no—
368C2×#442—171no—
369#2912—171no—
370#2897—172no—
371#2875—171no—
372C22×C17—22no—
373C22×C17—24no—
374C22×C17—42no—
375C22×C17—42no—
376C22×C17C2×C4×D412yes—
377C22×C17C23×D411yescharacteristic
378C2×D17—24no—
379C2×D17—28no—
380C2×D17—44no—
381C2×D17—44no—
382C2×D17—816no—
383C2×D17—88no—
384C2×D17C2×C4×D414yes—
385C4×C17—24no—
386C4×C17—24no—
387C4×C17—44no—
388C4×C17C2×C4×D412yes—
389C4×C17C24×C411yescharacteristic
390C4×C17C22×#4111yescharacteristic
391Dic17—22no—
392Dic17—22no—
393Dic17—42no—
394Dic17—42no—
395Dic17C2×C4×D414yes—
396C2×H(5,𝔽2)—172no—
397#576—1716no—
398C2×AGL(1,ℤ/8)—172no—
399C2×AGL(1,ℤ/8)—174no—
400C2×#135—172no—
401C2×#135C2×D1711yescharacteristic
402C22×D8—172no—
403C22×D8—171no—
404C2×#131—171no—
405C2×#131—171no—
406#520—172no—
407#520—174no—
408#520—342no—
409#520C2×D1712yescomplemented
410#518—174no—
411#518—172no—
412#518—342no—
413#518—344no—
414C4×#41—171no—
415C4×#41—172no—
416C4×#41—174no—
417C4×#41—342no—
418C2×C4×D4—174no—
419C2×C4×D4—172no—
420C2×C4×D4—342no—
421C2×C4×D4—344no—
422#442—171no—
423#442—171no—
424#442—174no—
425#442—172no—
426#442—172no—
427#442—172no—
428#442—172no—
429#442—174no—
430#442—172no—
431#442—172no—
432#442C2×D1712yescomplemented
433#441—171no—
434#441—171no—
435#441C2×D1712yescomplemented
436#440—172no—
437#440—172no—
438#440—174no—
439#440—174no—
440C4×SD16—174no—
441C4×SD16—174no—
442C4×SD16C2×D1714yescomplemented
443C4×D8—174no—
444C4×D8—174no—
445C4×D8—174no—
446#428—172no—
447#428—174no—
448#427—171no—
449#427—172no—
450C2×#106—172no—
451C2×#106C2×D1711yescharacteristic, complemented
452#418—172no—
453#418—174no—
454#417—174no—
455#417C2×D1712yescomplemented
456#416—172no—
457#416—174no—
458C2×#102—172no—
459C2×#102—174no—
460#405—171no—
461#405—172no—
462#405—172no—
463#405C2×D1711yescharacteristic, complemented
464C4×M16—171no—
465C4×M16—172no—
466C2×#97—171no—
467C2×#97—172no—
468C2×C17—22no—
469C2×C17—44no—
470C2×C17C22×C4×D411yescharacteristic
471C2×C17#358512yes—
472D17—24no—
473D17—48no—
474H(5,𝔽2)—1716no—
475H(5,𝔽2)—348no—
476C2×#41—171no—
477C2×#41—174no—
478C2×#41—342no—
479C2×#41C22×D1712yes—
480C22×D4—174no—
481C22×D4—172no—
482C22×D4—342no—
483C22×D4—344no—
484C23×C4—342no—
485C23×C4—344no—
486AGL(1,ℤ/8)—1716no—
487AGL(1,ℤ/8)—1732no—
488#135—1716no—
489#135C4×D1718yescomplemented
490C2×Q16C22×D1711yescharacteristic
491C2×SD16—174no—
492C2×SD16C22×D1712yes—
493C2×D8—174no—
494C2×D8—1716no—
495C2×D8—178no—
496C2×D8—172no—
497C2×D8—172no—
498C2×D8C22×D1711yescharacteristic
499#131—178no—
500#131—344no—
501C2×M16—171no—
502C2×M16—172no—
503C2×M16—172no—
504C2×M16C22×D1711yescharacteristic
505C22×C8—172no—
506C22×C8—171no—
507C22×C8—172no—
508C22×C8C22×D1711yescharacteristic
509C4×Q8—172no—
510C4×Q8—172no—
511C4×Q8—172no—
512C4×Q8—342no—
513C4×Q8C22×D1714yes—
514C4×D4—24no—
515C4×D4—172no—
516C4×D4—174no—
517C4×D4—172no—
518C4×D4—172no—
519C4×D4—174no—
520C4×D4—174no—
521C4×D4—174no—
522C4×D4—174no—
523C4×D4—344no—
524C4×D4—344no—
525C4×D4—344no—
526C4×D4—342no—
527C4×D4—342no—
528C4×D4—344no—
529C4×D4—344no—
530C4×D4—344no—
531C4×D4—344no—
532C4×D4—342no—
533C4×D4—344no—
534C4×D4—344no—
535C4×D4—342no—
536C4×D4—342no—
537C4×D4—342no—
538C4×D4—342no—
539C4×D4C22×D1714yes—
540#117—22no—
541#117—172no—
542#117—172no—
543#117—174no—
544#117—344no—
545#117—344no—
546#117—342no—
547#117C22×D1711yescharacteristic
548C2×C4⋊C4—22no—
549C2×C4⋊C4—174no—
550C2×C4⋊C4—344no—
551C2×C4⋊C4C22×D1712yes—
552C2×C22⋊C4—344no—
553C2×C22⋊C4—344no—
554C2×C22⋊C4—344no—
555C2×C22⋊C4—342no—
556C2×C22⋊C4—344no—
557C2×C42—171no—
558C2×C42—172no—
559C2×C42—344no—
560C2×C42—342no—
561#107—172no—
562#107—174no—
563#106—171no—
564#106—171no—
565#106—174no—
566#106C22×D1712yes—
567#106C22×D1712yes—
568#103—172no—
569#103—172no—
570#103C22×D1714yes—
571#102—172no—
572#102—172no—
573#102—174no—
574#102—174no—
575#102—174no—
576#102—174no—
577#102C22×D1714yes—
578#97—171no—
579#97—172no—
580#97—171no—
581#97—171no—
582#97—171no—
583#97—172no—
584#97C22×D1712yes—
585C4×C8—172no—
586C4×C8—172no—
587C4×C8C22×D1712yes—
588C17#6017611yescharacteristic, complemented, Sylow
589C24—344no—
590C24—342no—
591#41—24no—
592#41—174no—
593#41—174no—
594#41—1716no—
595#41—3416no—
596#41—348no—
597#41C2×C4×D1718yescomplemented
598C2×Q8—171no—
599C2×Q8C23×D1712yes—
600C2×D4—22no—
601C2×D4—172no—
602C2×D4—1716no—
603C2×D4—178no—
604C2×D4—171no—
605C2×D4—174no—
606C2×D4—3416no—
607C2×D4—344no—
608C2×D4—348no—
609C2×D4—344no—
610C2×D4—3432no—
611C2×D4—342no—
612C2×D4—344no—
613C2×D4C23×D1712yes—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—24no—
617C22×C4—172no—
618C22×C4—172no—
619C22×C4—174no—
620C22×C4—344no—
621C22×C4—344no—
622C22×C4—344no—
623C22×C4—344no—
624C22×C4—342no—
625C22×C4—342no—
626C22×C4—344no—
627C22×C4—344no—
628C22×C4—1368no—
629C22×C4—1364no—
630C22×C4C23×D1711yescharacteristic
631Q16C2×C4×D1714yescomplemented
632SD16—1716no—
633SD16C2×C4×D1718yescomplemented
634D8—1716no—
635D8—178no—
636D8—178no—
637D8C2×C4×D1714yescomplemented
638M16—22no—
639M16—174no—
640M16—178no—
641M16—344no—
642C2×C8—172no—
643C2×C8—178no—
644C2×C8—171no—
645C2×C8—171no—
646C2×C8—344no—
647C2×C8—342no—
648C2×C8C2×C4×D1714yescomplemented
649C2×C8C23×D1712yes—
650C2×C8C23×D1711yescharacteristic
651C2×C8C23×D1711yescharacteristic
652C4⋊C4—24no—
653C4⋊C4—22no—
654C4⋊C4—174no—
655C4⋊C4—172no—
656C4⋊C4—172no—
657C4⋊C4—344no—
658C4⋊C4—342no—
659C4⋊C4—342no—
660C4⋊C4D4×D1712yes—
661C4⋊C4C23×D1714yes—
662C22⋊C4—24no—
663C22⋊C4—174no—
664C22⋊C4—344no—
665C22⋊C4—344no—
666C22⋊C4—344no—
667C22⋊C4—342no—
668C22⋊C4—342no—
669C22⋊C4—342no—
670C22⋊C4—344no—
671C22⋊C4—344no—
672C22⋊C4D4×D1712yes—
673C42—24no—
674C42—174no—
675C42—172no—
676C42—171no—
677C42—171no—
678C42—342no—
679C42—344no—
680C42—342no—
681C42—342no—
682C42C23×D1712yes—
683C23—22no—
684C23—172no—
685C23—3416no—
686C23—344no—
687C23—348no—
688C23—1362no—
689C23—1362no—
690C23—1364no—
691C23—1364no—
692C23C2×D4×D1711yescharacteristic
693Q8—22no—
694Q8—174no—
695Q8C22×C4×D1714yes—
696D4—28no—
697D4—22no—
698D4—178no—
699D4—174no—
700D4—178no—
701D4—3416no—
702D4—3416no—
703D4—348no—
704D4—344no—
705D4C22×C4×D1714yes—
706C2×C4—22no—
707C2×C4—28no—
708C2×C4—24no—
709C2×C4—84no—
710C2×C4—82no—
711C2×C4—172no—
712C2×C4—174no—
713C2×C4—174no—
714C2×C4—172no—
715C2×C4—172no—
716C2×C4—3416no—
717C2×C4—342no—
718C2×C4—342no—
719C2×C4—684no—
720C2×C4—688no—
721C2×C4—682no—
722C2×C4—684no—
723C2×C4—1364no—
724C2×C4—1364no—
725C2×C4—1364no—
726C2×C4—1364no—
727C2×C4—1362no—
728C2×C4C22×C4×D1712yes—
729C2×C4C2×D4×D1714yes—
730C2×C4C2×D4×D1711yescharacteristic
731C2×C4#41×D1712yes—
732C2×C4C24×D1711yescharacteristic
733C8—22no—
734C8—174no—
735C8—341no—
736C8—341no—
737C8C22×C4×D1712yes—
738C8C22×C4×D1712yes—
739C22—22no—
740C22—24no—
741C22—42no—
742C22—42no—
743C22—174no—
744C22—344no—
745C22—348no—
746C22—684no—
747C22—684no—
748C22—1368no—
749C22—13616no—
750C22C4×D4×D1712yes—
751C22C22×D4×D1711yescharacteristic
752C4—24no—
753C4—24no—
754C4—44no—
755C4—174no—
756C4—342no—
757C4—342no—
758C4—682no—
759C4—682no—
760C4C4×D4×D1712yes—
761C4C23×C4×D1711yescharacteristic
762C4C2×#41×D1711yescharacteristic
763C2—22no—
764C2—44no—
765C2—344no—
766C2—688no—
767C2C2×C4×D4×D1711yescharacteristic
768C2#1454356212yes—
subgroupG/H
centerC22C22×D4×D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC17×#2952C2
socleC22×C17C23×D4
prime radicalC2×#11763611C2
cosocleC2×C4×C17C25
hypercenter#2952D17
hypocenterC17#60176
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ #117 ◁ #2952

Complements

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

NH ≅ G/Ntype
2. #14541990C2semidirect
3. #14537664C2semidirect
4. #14537637C2semidirect
5. #14537633C2semidirect
6. #14537612C2semidirect
7. #14537611C2semidirect
8. #14537597C2semidirect
9. C4×#10587600C2semidirect
10. #14537585C2semidirect
11. #14537583C2semidirect
12. C2×#11762920C2semidirect
13. D17×#442C2semidirect
14. #14537375C2semidirect
15. #14537308C2semidirect
16. #14537211C2semidirect
17. C17×#2952C2semidirect
19. #11763611C4semidirect
27. #11763291C22semidirect
31. #11763283C22semidirect
33. #11763281C22semidirect
34. #41×Dic17C22semidirect
35. C4×#63256C22semidirect
39. C2×#10587579C22semidirect
41. C4×D4×D17C22semidirect
42. #11762922C22semidirect
43. #11762922C22semidirect
44. #11762921C22semidirect
45. #11762921C22semidirect
46. #11762920C22semidirect
47. #11762920C22semidirect
48. #11762920C22semidirect
49. #11762920C22semidirect
50. #11762919C22semidirect
51. #11762918C22semidirect
52. #11762916C22semidirect
53. #11762916C22semidirect
54. #11762912C22semidirect
55. #11762910C22semidirect
56. #11762910C22semidirect
57. #11762907C22semidirect
58. C4×#63230C22semidirect
59. #11762894C22semidirect
60. C4×D136C22semidirect
61. C4×#63228C22semidirect
62. #11762889C22semidirect
63. #11762849C22semidirect
64. #11762848C22semidirect
65. #11762847C22semidirect
66. #11762844C22semidirect
67. #106×D17C22semidirect
68. #11762815C22semidirect
69. #11762812C22semidirect
70. #11762809C22semidirect
71. #11762805C22semidirect
72. #11762804C22semidirect
73. C2×#10587480C22semidirect
74. #102×D17C22semidirect
75. #11762766C22semidirect
76. #11762765C22semidirect
77. #11762763C22semidirect
78. M16×Dic17C22semidirect
79. C4×#63218C22semidirect
80. C2×#10587486C22semidirect
81. #97×D17C22semidirect
83. C17×#520C22semidirect
84. C17×#442C22semidirect
85. C17×#441C22semidirect
86. C4×SD16×C17C22semidirect
87. C2×C17×#106C22semidirect
88. C17×#417C22semidirect
89. C17×#405C22semidirect
92. #10587696C2×C4semidirect
102. C17×#135C2×C4semidirect
115. #10587635C2×C4semidirect
135. #10587605C2×C4semidirect
136. #10587600C2×C4semidirect
137. D8×D17C2×C4semidirect
139. C2×D136C2×C4semidirect
142. #10587587C2×C4semidirect
207. #41×C17C22×C4semidirect
221. #63256C22×C4semidirect
224. D4×D17C22×C4semidirect
232. C2×D68C22×C4semidirect
246. Q16×C17C22×C4semidirect
247. SD16×C17C22×C4semidirect
248. D8×C17C22×C4semidirect
250. C2×C8×C17C22×C4semidirect
265. #63230C22×C4semidirect
266. #63228C22×C4semidirect
287. #63223C22×C4semidirect
292. D136C22×C4semidirect
293. D136C22×C4semidirect
295. #63218C22×C4semidirect
297. C8×D17C22×C4semidirect
358. #2952D17semidirect
409. #520C2×D17semidirect
432. #442C2×D17semidirect
435. #441C2×D17semidirect
442. C4×SD16C2×D17semidirect
451. C2×#106C2×D17semidirect
455. #417C2×D17semidirect
463. #405C2×D17semidirect
489. #135C4×D17semidirect
588. C17#60176semidirect
597. #41C2×C4×D17semidirect
631. Q16C2×C4×D17semidirect
633. SD16C2×C4×D17semidirect
637. D8C2×C4×D17semidirect
648. C2×C8C2×C4×D17semidirect

Maximal subgroups

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

subgroupindex
C2×#117636112
#145419902
#145376642
#145376372
#145376332
#145376122
#145376112
#145375972
C4×#105876002
#145375852
#145375832
C2×#117629202
D17×#4422
#145373752
#145373082
#145372112
C17×#29522
#6017617