Finite Group Databasebeta

← #17898608

Subgroups — #17898608

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×#11763610C211yesmaximal, characteristic
2#14541988C212yesmaximal, complemented
3#14537669C211yesmaximal, characteristic, complemented
4#14537666C212yesmaximal, complemented
5#14537633C212yesmaximal, complemented
6#14537616C212yesmaximal, complemented
7#14537609C214yesmaximal, complemented
8#14537588C212yesmaximal, complemented
9C4×#10587597C214yesmaximal, complemented
10#14537584C211yesmaximal, characteristic, complemented
11#14537581C212yesmaximal, complemented
12C2×#11762921C211yesmaximal, characteristic, complemented
13D17×#442C212yesmaximal, complemented
14#14537376C211yesmaximal, characteristic, complemented
15#14537309C212yesmaximal, complemented
16#14537211C211yesmaximal, characteristic, complemented
17C17×#2948C211yesmaximal, characteristic, complemented
18C2×#10587691C2212yes—
19#11763610C4116yescomplemented
20C2×#10587618C2212yes—
21C2×#10587597C2214yes—
22C2×#10587590C2211yescharacteristic
23C2×#10587598C2212yes—
24C2×D8×D17C2212yes—
25C2×#10587593C2211yescharacteristic
26C2×#10587587C2211yescharacteristic
27#11763289C2212yes—
28#11763289C2212yescomplemented
29#11763288—22no—
30#11763288C2214yescomplemented
31#11763282—24no—
32#11763281—22no—
33#11763281C2214yescomplemented
34#11763277C2211yescharacteristic
35#11763277C2212yescomplemented
36C4×#63254—22no—
37C4×#63254C2214yescomplemented
38C2×D4×Dic17C2212yescomplemented
39C2×#10587567—24no—
40C4×D4×D17—22no—
41C4×D4×D17C2214yescomplemented
42#11762922C2212yescomplemented
43#11762921C2212yescomplemented
44#11762921C2212yescomplemented
45#11762921C2212yescomplemented
46#11762921C2212yescomplemented
47#11762920C2211yescharacteristic, complemented
48#11762920C2211yescharacteristic, complemented
49#11762919C2214yescomplemented
50#11762918C2214yescomplemented
51#11762917C2212yescomplemented
52#11762915C2211yescharacteristic, complemented
53#11762915C2211yescharacteristic, complemented
54#11762909C2214yescomplemented
55#11762908C2212yescomplemented
56#11762908C2212yescomplemented
57#11762906C2214yescomplemented
58#11762900C2214yescomplemented
59C4×#63219C2214yescomplemented
60C4×#63229C2214yescomplemented
61C4×#63228C2214yescomplemented
62#11762889C2214yescomplemented
63#11762852C2212yescomplemented
64#11762850C2214yescomplemented
65#11762844C2212yescomplemented
66C2×#10587488C2211yescharacteristic, complemented
67#106×D17C2212yescomplemented
68#11762812C2214yescomplemented
69#11762811C2212yescomplemented
70#11762807C2214yescomplemented
71#11762803C2212yescomplemented
72#11762802C2214yescomplemented
73C2×#10587503C2212yescomplemented
74#102×D17C2214yescomplemented
75#11762766C2212yescomplemented
76#11762765C2211yescharacteristic, complemented
77#11762763C2212yescomplemented
78M16×Dic17C2211yescharacteristic, complemented
79C4×#63218C2212yescomplemented
80C2×#10587486C2211yescharacteristic, complemented
81#97×D17C2212yescomplemented
82C22×D8×C17C2211yescharacteristic
83C17×#518C2212yescomplemented
84C17×#442C2212yescomplemented
85C17×#442C2212yescomplemented
86C4×D8×C17C2214yescomplemented
87C17×#427C2211yescharacteristic, complemented
88C17×#418C2212yescomplemented
89C17×#405C2211yescharacteristic, complemented
90C22×D4×C17C2312yes—
91C22×C22⋊D17—24no—
92C23×Dic17—22no—
93#10587691—28no—
94#10587691C2×C4116yescomplemented
95C2×#63254—22no—
96C2×#63254C2314yes—
97C2×D4×D17—22no—
98C2×D4×D17C2314yes—
99C2×#63252C2311yescharacteristic
100C2×#63252C2312yes—
101C22×C4×D17—24no—
102C2×D8×C17C2×C418yescomplemented
103C2×D8×C17C2312yes—
104C2×D8×C17C2312yes—
105C2×M16×C17C2311yescharacteristic
106C22×C8×C17C2311yescharacteristic
107C4×D4×C17—22no—
108C4×D4×C17—22no—
109C4×D4×C17C2314yes—
110C4×D4×C17C2314yes—
111C17×#117C2312yes—
112C17×#117C2311yescharacteristic
113C2×C22⋊C4×C17—24no—
114C2×C22⋊Dic17—22no—
115D4×Dic17—22no—
116D4×Dic17—22no—
117D4×Dic17C2314yes—
118D4×Dic17C2314yes—
119C2×#63229C2314yes—
120#10587618C2×C4116yescomplemented
121C2×#63228C2314yes—
122C4×C22⋊D17—24no—
123C4×C22⋊D17—24no—
124C4×C22⋊D17—24no—
125C4×C22⋊D17—24no—
126C2×#63227—24no—
127C2×C4⋊Dic17C2312yes—
128C2×#63225—24no—
129C2×C4×Dic17—24no—
130C2×C4×Dic17C2311yescharacteristic
131C2×#63223C2311yescharacteristic
132C22×#3622C2311yescharacteristic
133#10587598C2×C4116yescomplemented
134#10587597C2×C4132yescomplemented
135D8×D17C2×C4116yescomplemented
136#10587593—24no—
137C2×Dic68C2311yescharacteristic
138#10587590C2×C418yescomplemented
139C2×D136C2311yescharacteristic
140C2×#63219C2312yes—
141#10587587C2×C418yescomplemented
142C2×#63218C2312yes—
143C2×#63218C2312yes—
144C2×C8×D17C2312yes—
145C2×C8×D17C2312yes—
146#10587579D412yes—
147#10587579C2312yes—
148#10587579C2312yes—
149#10587578—22no—
150#10587578C2314yes—
151C4⋊C4×D17—22no—
152C4⋊C4×D17C2314yes—
153#10587573D412yes—
154#10587573C2312yes—
155#10587573C2312yes—
156#10587567—24no—
157#10587567—24no—
158#10587567—24no—
159#10587567—24no—
160#10587567—22no—
161#10587567—22no—
162#10587567—24no—
163#10587567—24no—
164#10587567D414yes—
165C22⋊C4×D17—24no—
166C22⋊C4×D17—24no—
167#10587563—24no—
168#10587563—24no—
169C4×D68—22no—
170C4×D68C2314yes—
171#10587558—22no—
172#10587558C2312yes—
173C42×D17—22no—
174C42×D17C2312yes—
175C4×Dic34—22no—
176C4×Dic34C2314yes—
177C17×#107C2312yes—
178C17×#106C2311yescharacteristic
179C17×#106C2311yescharacteristic
180C17×#102C2314yes—
181C17×#102C2314yes—
182C17×#97C2312yes—
183C4×C8×C17C2312yes—
184#10587503C2314yes—
185#10587503C2314yes—
186#10587492C2314yes—
187#10587488C2312yes—
188#10587488C2312yes—
189#10587487C2314yes—
190#10587486C2311yescharacteristic
191#10587486C2312yes—
192#10587486C2311yescharacteristic
193#10587486C2311yescharacteristic
194#10587486C2311yescharacteristic
195C8×Dic17C2312yes—
196#10587481C2312yes—
197#10587481C2312yes—
198#10587480C2312yes—
199#10587480C2312yes—
200#10587479C2314yes—
201#10587478C2314yes—
202#10587474C2312yes—
203C4×#3622C2312yes—
204C24×C17—22no—
205C23×D17—24no—
206C2×D4×C17—22no—
207C2×D4×C17—24no—
208C2×D4×C17C22×C418yescomplemented
209C2×D4×C17C2414yes—
210C22×C4×C17—24no—
211C22×C4×C17—24no—
212C22×C4×C17C2411yescharacteristic
213C2×C22⋊D17—22no—
214C2×C22⋊D17—24no—
215C2×C22⋊D17—232no—
216C2×C22⋊D17—24no—
217C2×C22⋊D17C2×D412yes—
218C22×Dic17—24no—
219C22×Dic17—22no—
220C22×Dic17—24no—
221C22×Dic17—24no—
222C22×Dic17—84no—
223C22×Dic17C2×D412yes—
224#63254—28no—
225#63254—216no—
226#63254C22×C4116yescomplemented
227D4×D17—216no—
228D4×D17—28no—
229D4×D17C22×C4116yescomplemented
230#63252—24no—
231#63252C22×C414yes—
232#63252C22×C418yescomplemented
233#63252#4114yes—
234C2×D68C2×D411yescharacteristic
235C2×D68C2412yes—
236C2×C4×D17—22no—
237C2×C4×D17—22no—
238C2×C4×D17—24no—
239C2×C4×D17—24no—
240C2×C4×D17—22no—
241C2×C4×D17—88no—
242C2×C4×D17C2×D414yes—
243C2×C4×D17C2412yes—
244C2×Dic34C2×D411yescharacteristic
245C2×Dic34C2412yes—
246D8×C17C22×C418yescomplemented
247D8×C17C22×C418yescomplemented
248M16×C17—22no—
249C2×C8×C17C22×C414yescomplemented
250C2×C8×C17C2412yes—
251C2×C8×C17C2411yescharacteristic
252C2×C8×C17C2411yescharacteristic
253C4⋊C4×C17C2×D412yes—
254C4⋊C4×C17C2412yes—
255C4⋊C4×C17C2412yes—
256C22⋊C4×C17—22no—
257C22⋊C4×C17—24no—
258C22⋊C4×C17—24no—
259C22⋊C4×C17C2×D412yes—
260C42×C17—22no—
261C42×C17C2412yes—
262C22⋊Dic17—24no—
263C22⋊Dic17—24no—
264#63229C22×C4116yescomplemented
265#63228C22×C4116yescomplemented
266#63227—24no—
267#63227—24no—
268#63227—22no—
269#63227—22no—
270#63227C2×D414yes—
271C4⋊Dic17—22no—
272C4⋊Dic17C2414yes—
273#63225—24no—
274#63225—24no—
275#63225—22no—
276#63225—22no—
277#63225C2×D414yes—
278C4×Dic17—24no—
279C4×Dic17—24no—
280C4×Dic17—22no—
281C4×Dic17—22no—
282C4×Dic17C2×D412yes—
283C4×Dic17C2×D414yes—
284C4×Dic17C2411yescharacteristic
285C4×Dic17C2411yescharacteristic
286#63223C22×C414yescomplemented
287C2×#3622—22no—
288C2×#3622C2411yescharacteristic
289C2×#3622C2411yescharacteristic
290C2×#3622C2412yes—
291Dic68C22×C414yescomplemented
292D136C22×C414yescomplemented
293#63219C22×C418yescomplemented
294#63218—24no—
295#63218C22×C418yescomplemented
296C8×D17—24no—
297C8×D17C22×C418yescomplemented
298#60176—171nomaximal, Sylow
299C23×C17—24no—
300C23×C17—28no—
301C23×C17—82no—
302C23×C17—82no—
303C23×C17C22×D411yescharacteristic
304C22×D17—22no—
305C22×D17—216no—
306C22×D17—84no—
307C22×D17—84no—
308C22×D17C22×D412yes—
309D4×C17—28no—
310D4×C17—24no—
311D4×C17C23×C418yes—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—84no—
315C2×C4×C17—84no—
316C2×C4×C17C23×C412yes—
317C2×C4×C17C22×D414yes—
318C2×C4×C17C22×D411yescharacteristic
319C2×C4×C17C2×#4112yes—
320C2×C4×C17C2511yescharacteristic
321C22⋊D17—28no—
322C22⋊D17—216no—
323C22⋊D17—216no—
324C22⋊D17C4×D418yes—
325C2×Dic17—22no—
326C2×Dic17—216no—
327C2×Dic17—24no—
328C2×Dic17—42no—
329C2×Dic17—48no—
330C2×Dic17—84no—
331C2×Dic17—82no—
332C2×Dic17C22×D412yes—
333C2×Dic17C22×D412yes—
334C2×Dic17C22×D412yes—
335D68—22no—
336D68C4×D414yes—
337D68C23×C414yes—
338C4×D17—28no—
339C4×D17—44no—
340C4×D17—44no—
341C4×D17—82no—
342C4×D17—84no—
343C4×D17—84no—
344C4×D17C23×C414yes—
345C4×D17C2×#4114yes—
346Dic34—22no—
347Dic34C4×D414yes—
348Dic34C23×C414yes—
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#2952—171no—
359#2948—172no—
360#2948D1711yescharacteristic, complemented
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—28no—
374C22×C17—44no—
375C22×C17—44no—
376C22×C17—88no—
377C22×C17C2×C4×D412yes—
378C22×C17C23×D411yescharacteristic
379C2×D17—24no—
380C2×D17—24no—
381C2×D17—42no—
382C2×D17—42no—
383C2×D17—816no—
384C2×D17C2×C4×D414yes—
385C4×C17—24no—
386C4×C17—42no—
387C4×C17—42no—
388C4×C17C2×C4×D412yes—
389C4×C17C24×C411yescharacteristic
390C4×C17C22×#4111yescharacteristic
391Dic17—22no—
392Dic17—22no—
393Dic17—24no—
394Dic17—44no—
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×#135—171no—
402C22×D8—172no—
403C22×D8C2×D1711yescharacteristic
404C2×#131—171no—
405C2×#131—171no—
406#520—172no—
407#520—174no—
408#520—172no—
409#520—342no—
410#518—174no—
411#518—344no—
412#518—342no—
413#518C2×D1712yescomplemented
414C4×#41—171no—
415C4×#41—174no—
416C4×#41—172no—
417C4×#41—342no—
418C2×C4×D4—172no—
419C2×C4×D4—174no—
420C2×C4×D4—344no—
421C2×C4×D4—342no—
422#442—172no—
423#442—172no—
424#442—172no—
425#442—172no—
426#442—174no—
427#442—171no—
428#442—171no—
429#442—174no—
430#442—172no—
431#442C2×D1712yescomplemented
432#442C2×D1712yescomplemented
433#441—171no—
434#441—171no—
435#441—172no—
436#440—174no—
437#440—172no—
438#440—172no—
439#440—174no—
440C4×SD16—174no—
441C4×SD16—174no—
442C4×SD16—174no—
443C4×D8—174no—
444C4×D8—174no—
445C4×D8C2×D1714yescomplemented
446#428—172no—
447#428—174no—
448#427—172no—
449#427C2×D1711yescharacteristic, complemented
450C2×#106—171no—
451C2×#106—172no—
452#418—174no—
453#418C2×D1712yescomplemented
454#417—172no—
455#417—174no—
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—48no—
470C2×C17C22×C4×D411yescharacteristic
471C2×C17#358512yes—
472D17—24no—
473D17—44no—
474H(5,𝔽2)—1716no—
475H(5,𝔽2)—348no—
476C2×#41—171no—
477C2×#41—174no—
478C2×#41—172no—
479C2×#41—342no—
480C22×D4—174no—
481C22×D4—342no—
482C22×D4—344no—
483C22×D4C22×D1712yes—
484C23×C4—344no—
485C23×C4—342no—
486AGL(1,ℤ/8)—1716no—
487AGL(1,ℤ/8)—1732no—
488#135—1716no—
489#135—178no—
490C2×Q16—171no—
491C2×SD16—174no—
492C2×SD16—172no—
493C2×D8—174no—
494C2×D8—1716no—
495C2×D8—171no—
496C2×D8C4×D1718yescomplemented
497C2×D8C22×D1712yes—
498C2×D8C22×D1712yes—
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—174no—
513C4×Q8—342no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—172no—
517C4×D4—174no—
518C4×D4—174no—
519C4×D4—174no—
520C4×D4—172no—
521C4×D4—172no—
522C4×D4—174no—
523C4×D4—342no—
524C4×D4—344no—
525C4×D4—344no—
526C4×D4—342no—
527C4×D4—342no—
528C4×D4—344no—
529C4×D4—344no—
530C4×D4—342no—
531C4×D4—344no—
532C4×D4—342no—
533C4×D4—344no—
534C4×D4—344no—
535C4×D4—344no—
536C4×D4—344no—
537C4×D4—344no—
538C4×D4C22×D1714yes—
539C4×D4C22×D1714yes—
540#117—172no—
541#117—174no—
542#117—342no—
543#117—344no—
544#117—344no—
545#117—342no—
546#117C22×D1712yes—
547#117C22×D1711yescharacteristic
548C2×C4⋊C4—172no—
549C2×C4⋊C4—174no—
550C2×C4⋊C4—344no—
551C2×C4⋊C4—342no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—344no—
554C2×C22⋊C4—344no—
555C2×C22⋊C4—344no—
556C2×C22⋊C4—342no—
557C2×C42—171no—
558C2×C42—172no—
559C2×C42—342no—
560C2×C42—344no—
561#107—174no—
562#107C22×D1712yes—
563#106—172no—
564#106—172no—
565#106—174no—
566#106C22×D1711yescharacteristic
567#106C22×D1711yescharacteristic
568#103—174no—
569#103—172no—
570#103—172no—
571#102—174no—
572#102—174no—
573#102—174no—
574#102—172no—
575#102—172no—
576#102C22×D1714yes—
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—22no—
590C24—344no—
591#41—174no—
592#41—174no—
593#41—1716no—
594#41—178no—
595#41—348no—
596#41—3416no—
597#41—344no—
598C2×Q8—171no—
599C2×Q8—172no—
600C2×D4—22no—
601C2×D4—24no—
602C2×D4—172no—
603C2×D4—1716no—
604C2×D4—171no—
605C2×D4—172no—
606C2×D4—348no—
607C2×D4—344no—
608C2×D4—3416no—
609C2×D4—3432no—
610C2×D4—344no—
611C2×D4—342no—
612C2×D4C2×C4×D1718yescomplemented
613C2×D4C23×D1714yes—
614C22×C4—24no—
615C22×C4—24no—
616C22×C4—172no—
617C22×C4—172no—
618C22×C4—174no—
619C22×C4—342no—
620C22×C4—342no—
621C22×C4—344no—
622C22×C4—344no—
623C22×C4—344no—
624C22×C4—344no—
625C22×C4—342no—
626C22×C4—342no—
627C22×C4—344no—
628C22×C4—1368no—
629C22×C4—1364no—
630C22×C4C23×D1711yescharacteristic
631Q16—174no—
632SD16—1716no—
633SD16—178no—
634D8—1716no—
635D8—174no—
636D8C2×C4×D1718yescomplemented
637D8C2×C4×D1718yescomplemented
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—174no—
653C4⋊C4—174no—
654C4⋊C4—344no—
655C4⋊C4—342no—
656C4⋊C4—342no—
657C4⋊C4—342no—
658C4⋊C4—344no—
659C4⋊C4D4×D1712yes—
660C4⋊C4C23×D1712yes—
661C4⋊C4C23×D1712yes—
662C22⋊C4—22no—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—174no—
666C22⋊C4—342no—
667C22⋊C4—342no—
668C22⋊C4—344no—
669C22⋊C4—344no—
670C22⋊C4—344no—
671C22⋊C4—344no—
672C22⋊C4D4×D1712yes—
673C42—22no—
674C42—174no—
675C42—172no—
676C42—171no—
677C42—171no—
678C42—342no—
679C42—344no—
680C42—342no—
681C42—344no—
682C42C23×D1712yes—
683C23—24no—
684C23—28no—
685C23—82no—
686C23—82no—
687C23—172no—
688C23—3416no—
689C23—342no—
690C23—1364no—
691C23—1364no—
692C23C2×D4×D1711yescharacteristic
693Q8—174no—
694Q8—174no—
695Q8—342no—
696D4—28no—
697D4—24no—
698D4—178no—
699D4—174no—
700D4—174no—
701D4—3416no—
702D4—3416no—
703D4—348no—
704D4—342no—
705D4C22×C4×D1718yes—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—84no—
709C2×C4—84no—
710C2×C4—172no—
711C2×C4—174no—
712C2×C4—174no—
713C2×C4—172no—
714C2×C4—172no—
715C2×C4—3416no—
716C2×C4—342no—
717C2×C4—348no—
718C2×C4—344no—
719C2×C4—684no—
720C2×C4—684no—
721C2×C4—682no—
722C2×C4—688no—
723C2×C4—1364no—
724C2×C4—1362no—
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—28no—
741C22—44no—
742C22—44no—
743C22—88no—
744C22—174no—
745C22—344no—
746C22—344no—
747C22—682no—
748C22—682no—
749C22—13616no—
750C22C4×D4×D1712yes—
751C22C22×D4×D1711yescharacteristic
752C4—24no—
753C4—42no—
754C4—42no—
755C4—174no—
756C4—344no—
757C4—342no—
758C4—342no—
759C4—684no—
760C4C4×D4×D1712yes—
761C4C23×C4×D1711yescharacteristic
762C4C2×#41×D1711yescharacteristic
763C2—22no—
764C2—48no—
765C2—344no—
766C2—684no—
767C2C2×C4×D4×D1711yescharacteristic
768C2#1454355912yes—
subgroupG/H
centerC22C22×D4×D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC17×#2948C2
socleC22×C17C23×D4
prime radicalC2×#11763610C2
cosocleC2×C4×C17C25
hypercenter#2948D17
hypocenterC17#60176
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ #117 ◁ #2948

Complements

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

NH ≅ G/Ntype
2. #14541988C2semidirect
3. #14537669C2semidirect
4. #14537666C2semidirect
5. #14537633C2semidirect
6. #14537616C2semidirect
7. #14537609C2semidirect
8. #14537588C2semidirect
9. C4×#10587597C2semidirect
10. #14537584C2semidirect
11. #14537581C2semidirect
12. C2×#11762921C2semidirect
13. D17×#442C2semidirect
14. #14537376C2semidirect
15. #14537309C2semidirect
16. #14537211C2semidirect
17. C17×#2948C2semidirect
19. #11763610C4semidirect
28. #11763289C22semidirect
30. #11763288C22semidirect
33. #11763281C22semidirect
35. #11763277C22semidirect
37. C4×#63254C22semidirect
38. C2×D4×Dic17C22semidirect
41. C4×D4×D17C22semidirect
42. #11762922C22semidirect
43. #11762921C22semidirect
44. #11762921C22semidirect
45. #11762921C22semidirect
46. #11762921C22semidirect
47. #11762920C22semidirect
48. #11762920C22semidirect
49. #11762919C22semidirect
50. #11762918C22semidirect
51. #11762917C22semidirect
52. #11762915C22semidirect
53. #11762915C22semidirect
54. #11762909C22semidirect
55. #11762908C22semidirect
56. #11762908C22semidirect
57. #11762906C22semidirect
58. #11762900C22semidirect
59. C4×#63219C22semidirect
60. C4×#63229C22semidirect
61. C4×#63228C22semidirect
62. #11762889C22semidirect
63. #11762852C22semidirect
64. #11762850C22semidirect
65. #11762844C22semidirect
66. C2×#10587488C22semidirect
67. #106×D17C22semidirect
68. #11762812C22semidirect
69. #11762811C22semidirect
70. #11762807C22semidirect
71. #11762803C22semidirect
72. #11762802C22semidirect
73. C2×#10587503C22semidirect
74. #102×D17C22semidirect
75. #11762766C22semidirect
76. #11762765C22semidirect
77. #11762763C22semidirect
78. M16×Dic17C22semidirect
79. C4×#63218C22semidirect
80. C2×#10587486C22semidirect
81. #97×D17C22semidirect
83. C17×#518C22semidirect
84. C17×#442C22semidirect
85. C17×#442C22semidirect
86. C4×D8×C17C22semidirect
87. C17×#427C22semidirect
88. C17×#418C22semidirect
89. C17×#405C22semidirect
94. #10587691C2×C4semidirect
102. C2×D8×C17C2×C4semidirect
120. #10587618C2×C4semidirect
133. #10587598C2×C4semidirect
134. #10587597C2×C4semidirect
135. D8×D17C2×C4semidirect
138. #10587590C2×C4semidirect
141. #10587587C2×C4semidirect
208. C2×D4×C17C22×C4semidirect
226. #63254C22×C4semidirect
229. D4×D17C22×C4semidirect
232. #63252C22×C4semidirect
246. D8×C17C22×C4semidirect
247. D8×C17C22×C4semidirect
249. C2×C8×C17C22×C4semidirect
264. #63229C22×C4semidirect
265. #63228C22×C4semidirect
286. #63223C22×C4semidirect
291. Dic68C22×C4semidirect
292. D136C22×C4semidirect
293. #63219C22×C4semidirect
295. #63218C22×C4semidirect
297. C8×D17C22×C4semidirect
360. #2948D17semidirect
413. #518C2×D17semidirect
431. #442C2×D17semidirect
432. #442C2×D17semidirect
445. C4×D8C2×D17semidirect
449. #427C2×D17semidirect
453. #418C2×D17semidirect
463. #405C2×D17semidirect
496. C2×D8C4×D17semidirect
588. C17#60176semidirect
612. C2×D4C2×C4×D17semidirect
636. D8C2×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×#117636102
#145419882
#145376692
#145376662
#145376332
#145376162
#145376092
#145375882
C4×#105875972
#145375842
#145375812
C2×#117629212
D17×#4422
#145373762
#145373092
#145372112
C17×#29482
#6017617