Finite Group Databasebeta

← #17898670

Subgroups — #17898670

Order 4352.

2604 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14543553C211yesmaximal, characteristic
2#14543497C212yesmaximal, complemented
3#14537702C211yesmaximal, characteristic, complemented
4#14537698C214yesmaximal, complemented
5#14537691C212yesmaximal, complemented
6#14537689C214yesmaximal, complemented
7#14537683C212yesmaximal, complemented
8#14537682C214yesmaximal, complemented
9C2×#11762931C211yesmaximal, characteristic, complemented
10C2×#11762930C211yesmaximal, characteristic, complemented
11D17×#444C214yesmaximal, complemented
12#14537392C211yesmaximal, characteristic, complemented
13#14537330C212yesmaximal, complemented
14#14537211C211yesmaximal, characteristic, complemented
15C17×#2957C211yesmaximal, characteristic, complemented
16#11763645C2212yes—
17#11763623C412yescomplemented
18#11763622C412yescomplemented
19#11763616C414yescomplemented
20#11763615C414yescomplemented
21#11763611C412yescomplemented
22#11763610C412yescomplemented
23#11763607C2212yes—
24#11763606C2214yes—
25C2×#10587590C2211yescharacteristic
26#135×D17C2214yes—
27#11763575—24no—
28#11763575C2212yes—
29#11763575C2212yescomplemented
30#11763574—24no—
31#11763574C2218yescomplemented
32C2×#10587593—24no—
33C2×#10587593C2211yescharacteristic
34C2×#10587593C2212yescomplemented
35C2×#10587634C2212yescomplemented
36C2×#10587587C2211yescharacteristic
37#131×D17—24no—
38#131×D17C2218yescomplemented
39#11763277C2211yescharacteristic
40#11762932C2214yescomplemented
41#11762931C2212yescomplemented
42#11762931C2212yescomplemented
43#11762931C2212yescomplemented
44#11762931C2212yescomplemented
45#11762930C2212yescomplemented
46#11762930C2212yescomplemented
47#11762930C2212yescomplemented
48#11762930C2212yescomplemented
49#11762929C2218yescomplemented
50#11762928C2218yescomplemented
51#11762927C2214yescomplemented
52#11762924C2218yescomplemented
53#11762923C2218yescomplemented
54#11762857C2212yescomplemented
55#11762856C2214yescomplemented
56C2×#10587490C2211yescharacteristic, complemented
57#108×D17C2214yescomplemented
58#11762827C2212yescomplemented
59#11762824C2218yescomplemented
60C2×#10587508C2212yescomplemented
61C2×#10587496C2212yescomplemented
62#104×D17C2218yescomplemented
63#11762766C2212yescomplemented
64#11762765C2211yescharacteristic, complemented
65#11762763C2212yescomplemented
66M16×Dic17C2211yescharacteristic, complemented
67C4×#63218C2212yescomplemented
68C2×#10587486C2211yescharacteristic, complemented
69#97×D17C2212yescomplemented
70C2×C17×#135C2211yescharacteristic
71C17×#568C2212yescomplemented
72C17×#444C2214yescomplemented
73C17×#443C2214yescomplemented
74C2×C17×#108C2211yescharacteristic, complemented
75C17×#421C2212yescomplemented
76C17×#405C2211yescharacteristic, complemented
77C2×#41×C17C2312yes—
78#10587697—22no—
79#10587697C2×C414yes—
80#10587696—22no—
81#10587696C2×C414yes—
82#41×D17—24no—
83#41×D17C2318yes—
84#10587694C2×C414yes—
85#10587691—24no—
86#10587691C2×C414yes—
87C2×#63252—24no—
88C2×#63252C2312yes—
89C2×#63252C2311yescharacteristic
90C17×#135C2×C412yescomplemented
91C17×#135C2×C412yescomplemented
92C17×#135C2312yes—
93C17×#135C2312yes—
94C2×Q16×C17C2×C411yescharacteristic, complemented
95C2×SD16×C17C2×C412yescomplemented
96C2×D8×C17C2×C411yescharacteristic, complemented
97C17×#131—24no—
98C17×#131C2318yes—
99C2×M16×C17—24no—
100C2×M16×C17C2312yes—
101C2×M16×C17C2311yescharacteristic
102C22×C8×C17C2311yescharacteristic
103C17×#117C2311yescharacteristic
104#10587637C2×C414yescomplemented
105#10587636C2318yes—
106#10587635C2×C414yescomplemented
107#10587634—22no—
108#10587634—22no—
109#10587634C2314yes—
110#10587634C2314yes—
111#10587628C2×C414yescomplemented
112#10587618C2×C414yescomplemented
113C2×C4×Dic17C2311yescharacteristic
114C2×#63223—22no—
115C2×#63223C2312yes—
116C2×#63223C2311yescharacteristic
117C22×#3622—22no—
118C22×#3622C2311yescharacteristic
119#10587605C2×C414yescomplemented
120#10587604C2×C418yescomplemented
121Q16×D17C2×C414yescomplemented
122#10587602C2×C418yescomplemented
123#10587601C2×C418yescomplemented
124#10587600C2×C418yescomplemented
125SD16×D17C2×C418yescomplemented
126#10587598C2×C414yescomplemented
127#10587597C2×C418yescomplemented
128D8×D17C2×C414yescomplemented
129#10587593—22no—
130#10587593—22no—
131#10587593—28no—
132#10587593—28no—
133#10587593—24no—
134#10587593—24no—
135#10587593D414yes—
136#10587593D414yes—
137#10587593C2314yes—
138#10587593C2314yes—
139M16×D17—28no—
140M16×D17—28no—
141M16×D17—24no—
142M16×D17C2318yes—
143C2×Dic68C2×C411yescharacteristic, complemented
144#10587590C2×C412yescomplemented
145#10587590C2×C412yescomplemented
146#10587590C2312yes—
147#10587590C2312yes—
148C2×D136C2×C411yescharacteristic, complemented
149C2×#63219C2×C412yescomplemented
150#10587587—28no—
151#10587587—28no—
152#10587587—24no—
153#10587587C2×C412yes—
154#10587587C2×C412yes—
155#10587587C2×C412yes—
156#10587587C2×C412yes—
157#10587587C2318yes—
158C2×#63218—22no—
159C2×#63218—28no—
160C2×#63218C2312yes—
161C2×#63218C2312yes—
162C2×C8×D17—22no—
163C2×C8×D17—28no—
164C2×C8×D17C2312yes—
165C2×C8×D17C2312yes—
166#10587579—21no—
167#10587573—21no—
168#10587567—22no—
169#10587558C2312yes—
170C42×D17C2312yes—
171C17×#108C2312yes—
172C17×#108C2312yes—
173C17×#104C2318yes—
174C17×#97C2312yes—
175C4×C8×C17C2312yes—
176#10587508C2314yes—
177#10587508C2314yes—
178#10587496C2314yes—
179#10587496C2314yes—
180#10587493C2318yes—
181#10587490C2312yes—
182#10587490C2312yes—
183#10587486C2311yescharacteristic
184#10587486C2312yes—
185#10587486C2311yescharacteristic
186#10587486C2311yescharacteristic
187#10587486C2311yescharacteristic
188C8×Dic17C2312yes—
189#10587476C2318yes—
190#10587474C2312yes—
191C4×#3622C2312yes—
192#41×C17—22no—
193#41×C17—22no—
194#41×C17C22×C414yes—
195#41×C17C2414yes—
196C2×Q8×C17C22×C412yes—
197C2×D4×C17—22no—
198C2×D4×C17C22×C412yes—
199C22×C4×C17—22no—
200C22×C4×C17C2411yescharacteristic
201C2×C22⋊D17—22no—
202C2×C22⋊D17—28no—
203C2×C22⋊D17#4112yes—
204C22×Dic17—21no—
205#63256—24no—
206#63256C22×C418yes—
207Q8×D17—24no—
208Q8×D17C22×C418yes—
209#63254—28no—
210#63254—28no—
211#63254—24no—
212#63254C22×C418yes—
213D4×D17—28no—
214D4×D17—28no—
215D4×D17—24no—
216D4×D17C22×C418yes—
217#63252—22no—
218#63252—22no—
219#63252—28no—
220#63252—24no—
221#63252—28no—
222#63252—24no—
223#63252C22×C412yes—
224#63252C22×C412yes—
225#63252C22×C414yes—
226#63252C2×D412yes—
227#63252C2×D412yes—
228#63252C2414yes—
229C2×D68—24no—
230C2×D68C22×C412yes—
231C2×D68#4111yescharacteristic
232C2×C4×D17—22no—
233C2×C4×D17—28no—
234C2×C4×D17—22no—
235C2×C4×D17C2412yes—
236C2×Dic34—24no—
237C2×Dic34C22×C412yes—
238C2×Dic34#4111yescharacteristic
239Q16×C17C22×C412yes—
240Q16×C17C22×C412yes—
241SD16×C17C22×C414yes—
242SD16×C17C22×C414yes—
243D8×C17C22×C412yes—
244D8×C17C22×C412yes—
245M16×C17—22no—
246M16×C17—28no—
247M16×C17C2×D412yes—
248M16×C17C2×D412yes—
249M16×C17C2414yes—
250C2×C8×C17—22no—
251C2×C8×C17—28no—
252C2×C8×C17C22×C411yescharacteristic
253C2×C8×C17C22×C411yescharacteristic
254C2×C8×C17C22×C411yescharacteristic
255C2×C8×C17C22×C411yescharacteristic
256C2×C8×C17C2411yescharacteristic
257C2×C8×C17C2411yescharacteristic
258C2×C8×C17C2412yes—
259C4⋊C4×C17—21no—
260C22⋊C4×C17—21no—
261C42×C17C2412yes—
262#63231C22×C418yes—
263#63230C22×C418yes—
264#63229C22×C418yes—
265#63228C22×C418yes—
266#63227—22no—
267#63225—22no—
268C4×Dic17—21no—
269C4×Dic17—22no—
270C4×Dic17C2411yescharacteristic
271C4×Dic17C2411yescharacteristic
272#63223—22no—
273#63223—24no—
274#63223—24no—
275#63223C22×C412yes—
276#63223C22×C412yes—
277#63223C2414yes—
278C2×#3622—22no—
279C2×#3622—24no—
280C2×#3622—24no—
281C2×#3622C2×D412yes—
282C2×#3622C2×D412yes—
283C2×#3622C2412yes—
284C2×#3622C2411yescharacteristic
285C2×#3622C2411yescharacteristic
286Dic68C22×C412yes—
287Dic68C22×C412yes—
288D136C22×C412yes—
289D136C22×C412yes—
290#63219C22×C414yes—
291#63219C22×C414yes—
292#63218—28no—
293#63218—28no—
294#63218—24no—
295#63218—24no—
296#63218C22×C414yes—
297#63218C22×C414yes—
298#63218C2×D418yes—
299C8×D17—28no—
300C8×D17—28no—
301C8×D17—24no—
302C8×D17—24no—
303C8×D17C22×C414yes—
304C8×D17C22×C414yes—
305C8×D17C2×D418yes—
306#60184—171nomaximal, Sylow
307C23×C17—22no—
308C23×C17C2×#4111yescharacteristic
309C22×D17—22no—
310C22×D17—28no—
311C22×D17C2×#4112yes—
312Q8×C17—22no—
313Q8×C17C23×C414yes—
314D4×C17—24no—
315D4×C17—24no—
316D4×C17—22no—
317D4×C17C23×C414yes—
318C2×C4×C17—22no—
319C2×C4×C17—24no—
320C2×C4×C17—24no—
321C2×C4×C17—22no—
322C2×C4×C17C23×C411yescharacteristic
323C2×C4×C17C23×C411yescharacteristic
324C2×C4×C17C22×D411yescharacteristic
325C2×C4×C17C22×D411yescharacteristic
326C2×C4×C17C2×#4111yescharacteristic
327C2×C4×C17C2511yescharacteristic
328C22⋊D17—24no—
329C22⋊D17—24no—
330C22⋊D17—28no—
331C22⋊D17—28no—
332C22⋊D17C4×D414yes—
333C22⋊D17C4×D414yes—
334C2×Dic17—22no—
335C2×Dic17—28no—
336C2×Dic17—21no—
337C2×Dic17—21no—
338C2×Dic17—81no—
339C2×Dic17C2×#4112yes—
340D68—28no—
341D68—22no—
342D68C4×D412yes—
343D68C4×D412yes—
344D68C23×C414yes—
345C4×D17—28no—
346C4×D17—24no—
347C4×D17—24no—
348C4×D17—28no—
349C4×D17—82no—
350C4×D17C23×C414yes—
351C4×D17C22×D414yes—
352Dic34—22no—
353Dic34—28no—
354Dic34C4×D412yes—
355Dic34C4×D412yes—
356Dic34C23×C414yes—
357C8×C17—24no—
358C8×C17C23×C411yescharacteristic
359C8×C17C23×C411yescharacteristic
360C8×C17C23×C411yescharacteristic
361C8×C17C23×C411yescharacteristic
362C8×C17C22×D414yes—
363#3622—24no—
364#3622C23×C414yes—
365#3622C22×D412yes—
366#3622C22×D412yes—
367#3584—171no—
368#3573—172no—
369#2957—174no—
370#2957—171no—
371#2957D1711yescharacteristic, complemented
372#2956—174no—
373#2956—172no—
374#2955—174no—
375#2955—172no—
376C2×#444—174no—
377C2×#444—171no—
378C2×#444—171no—
379#2916—171no—
380#2901—172no—
381#2875—171no—
382C22×C17—24no—
383C22×C17—41no—
384C22×C17—82no—
385C22×C17C2×C4×D411yescharacteristic
386C22×C17C2×C4×D411yescharacteristic
387C22×C17C22×#4111yescharacteristic
388C2×D17—24no—
389C2×D17—42no—
390C2×D17—88no—
391C2×D17—82no—
392C2×D17C2×C4×D414yes—
393C4×C17—24no—
394C4×C17—42no—
395C4×C17C2×C4×D411yescharacteristic
396C4×C17C2×C4×D411yescharacteristic
397C4×C17C24×C411yescharacteristic
398C4×C17C23×D411yescharacteristic
399Dic17—24no—
400Dic17—41no—
401Dic17—41no—
402Dic17C2×C4×D414yes—
403#585—172no—
404#578—172no—
405#578—172no—
406#577—174no—
407#577—174no—
408#576—172no—
409#576—172no—
410#575—172no—
411#575—174no—
412C2×#135—174no—
413C2×#135—171no—
414C2×#135C2×D1711yescharacteristic
415#568—172no—
416#568—178no—
417#568—172no—
418#568—344no—
419#568—344no—
420#568C2×D1712yescomplemented
421C2×#131—171no—
422C2×#131—171no—
423C2×#131—172no—
424C2×#131—178no—
425C2×#131—172no—
426C2×#131—344no—
427C2×#131—344no—
428C4×#41—171no—
429#444—172no—
430#444—172no—
431#444—172no—
432#444—172no—
433#444—178no—
434#444—172no—
435#444—172no—
436#444—172no—
437#444—172no—
438#444—178no—
439#444—174no—
440#444C2×D1714yescomplemented
441#443—178no—
442#443—178no—
443#443—174no—
444#443C2×D1714yescomplemented
445#430—172no—
446#430—174no—
447C2×#108—171no—
448C2×#108—174no—
449C2×#108C2×D1711yescharacteristic, complemented
450#421—172no—
451#421—178no—
452#421C2×D1712yescomplemented
453C2×#104—172no—
454C2×#104—172no—
455C2×#104—178no—
456#405—171no—
457#405—172no—
458#405—172no—
459#405C2×D1711yescharacteristic, complemented
460C4×M16—171no—
461C4×M16—172no—
462C2×#97—171no—
463C2×#97—172no—
464C2×C17—21no—
465C2×C17—21no—
466C2×C17—21no—
467C2×C17—44no—
468C2×C17C22×C4×D411yescharacteristic
469D17—24no—
470D17—44no—
4712−1+4—174no—
4722−1+4—174no—
4732−1+4—342no—
474H(5,𝔽2)—174no—
475H(5,𝔽2)—174no—
476H(5,𝔽2)—344no—
477H(5,𝔽2)—342no—
478C2×#41—171no—
479C2×#41—178no—
480C2×#41—172no—
481C2×#41—344no—
482C2×#41—344no—
483C2×#41C22×D1712yes—
484#137—174no—
485#137—174no—
486#137—178no—
487#137—178no—
488AGL(1,ℤ/8)—174no—
489AGL(1,ℤ/8)—174no—
490AGL(1,ℤ/8)—178no—
491AGL(1,ℤ/8)—178no—
492#135—178no—
493#135—174no—
494#135—178no—
495#135—174no—
496#135—172no—
497#135—172no—
498#135—172no—
499#135—172no—
500#135C4×D1712yescomplemented
501#135C4×D1712yescomplemented
502#135C22×D1712yes—
503#135C22×D1712yes—
504C2×Q16—174no—
505C2×Q16—171no—
506C2×Q16C4×D1711yescharacteristic, complemented
507C2×SD16—178no—
508C2×SD16—172no—
509C2×SD16C4×D1712yescomplemented
510C2×D8—174no—
511C2×D8—171no—
512C2×D8C4×D1711yescharacteristic, complemented
513#131—24no—
514#131—174no—
515#131—174no—
516#131—172no—
517#131—172no—
518#131—172no—
519#131—172no—
520#131—174no—
521#131—174no—
522#131—174no—
523#131—174no—
524#131—178no—
525#131—348no—
526#131—348no—
527#131—344no—
528#131—342no—
529#131—348no—
530#131—342no—
531#131—342no—
532#131—342no—
533#131—348no—
534#131—344no—
535#131—344no—
536#131C22×D1718yes—
537C2×M16—24no—
538C2×M16—171no—
539C2×M16—172no—
540C2×M16—172no—
541C2×M16—172no—
542C2×M16—178no—
543C2×M16—342no—
544C2×M16—348no—
545C2×M16—348no—
546C2×M16—342no—
547C2×M16—348no—
548C2×M16—344no—
549C2×M16C22×D1712yes—
550C2×M16C22×D1711yescharacteristic
551C22×C8—171no—
552C22×C8—172no—
553C22×C8—172no—
554C22×C8—342no—
555C22×C8—348no—
556C22×C8—342no—
557C22×C8C22×D1711yescharacteristic
558C4×Q8—341no—
559C4×D4—342no—
560C4×D4—341no—
561#117—172no—
562#117C22×D1711yescharacteristic
563C2×C42—171no—
564C2×C42—172no—
565#108—178no—
566#108—172no—
567#108—172no—
568#108C22×D1712yes—
569#108C22×D1712yes—
570#104—174no—
571#104—174no—
572#104—174no—
573#104—174no—
574#104—178no—
575#104C22×D1718yes—
576#97—171no—
577#97—172no—
578#97—171no—
579#97—171no—
580#97—171no—
581#97—172no—
582#97C22×D1712yes—
583C4×C8—172no—
584C4×C8—172no—
585C4×C8C22×D1712yes—
586C17#6018411yescharacteristic, complemented, Sylow
587#41—22no—
588#41—22no—
589#41—172no—
590#41—172no—
591#41—172no—
592#41—172no—
593#41—178no—
594#41—178no—
595#41—174no—
596#41—174no—
597#41—348no—
598#41—348no—
599#41—344no—
600#41—344no—
601#41—348no—
602#41—348no—
603#41—344no—
604#41—344no—
605#41—342no—
606#41—342no—
607#41C2×C4×D1714yes—
608#41C23×D1714yes—
609C2×Q8—171no—
610C2×Q8—178no—
611C2×Q8—172no—
612C2×Q8—344no—
613C2×Q8—344no—
614C2×Q8C2×C4×D1712yes—
615C2×D4—22no—
616C2×D4—172no—
617C2×D4—178no—
618C2×D4—172no—
619C2×D4—171no—
620C2×D4—344no—
621C2×D4—348no—
622C2×D4—344no—
623C2×D4—348no—
624C2×D4—348no—
625C2×D4—342no—
626C2×D4C2×C4×D1712yes—
627C22×C4—22no—
628C22×C4—172no—
629C22×C4—348no—
630C22×C4—342no—
631C22×C4—342no—
632C22×C4—341no—
633C22×C4C23×D1711yescharacteristic
634Q16—178no—
635Q16—172no—
636Q16—172no—
637Q16C2×C4×D1712yes—
638Q16C2×C4×D1712yes—
639SD16—178no—
640SD16—178no—
641SD16—174no—
642SD16—174no—
643SD16C2×C4×D1714yes—
644SD16C2×C4×D1714yes—
645D8—178no—
646D8—172no—
647D8—172no—
648D8C2×C4×D1712yes—
649D8C2×C4×D1712yes—
650M16—22no—
651M16—28no—
652M16—172no—
653M16—172no—
654M16—174no—
655M16—174no—
656M16—178no—
657M16—174no—
658M16—344no—
659M16—344no—
660M16—348no—
661M16—344no—
662M16—344no—
663M16—342no—
664M16—348no—
665M16D4×D1712yes—
666M16D4×D1712yes—
667M16C23×D1714yes—
668C2×C8—22no—
669C2×C8—28no—
670C2×C8—172no—
671C2×C8—172no—
672C2×C8—172no—
673C2×C8—171no—
674C2×C8—171no—
675C2×C8—174no—
676C2×C8—174no—
677C2×C8—178no—
678C2×C8—344no—
679C2×C8—344no—
680C2×C8—348no—
681C2×C8—344no—
682C2×C8—344no—
683C2×C8—342no—
684C2×C8—348no—
685C2×C8C2×C4×D1711yescharacteristic
686C2×C8C2×C4×D1711yescharacteristic
687C2×C8C2×C4×D1711yescharacteristic
688C2×C8C2×C4×D1711yescharacteristic
689C2×C8C23×D1711yescharacteristic
690C2×C8C23×D1711yescharacteristic
691C2×C8C23×D1712yes—
692C4⋊C4—21no—
693C4⋊C4—342no—
694C22⋊C4—21no—
695C22⋊C4—342no—
696C42—171no—
697C42—171no—
698C42—342no—
699C42—341no—
700C42C23×D1712yes—
701C23—22no—
702C23—172no—
703C23—348no—
704C23—342no—
705C23#41×D1711yescharacteristic
706Q8—22no—
707Q8—172no—
708Q8—172no—
709Q8—174no—
710Q8—348no—
711Q8—342no—
712Q8C22×C4×D1714yes—
713D4—24no—
714D4—24no—
715D4—22no—
716D4—174no—
717D4—174no—
718D4—172no—
719D4—172no—
720D4—174no—
721D4—348no—
722D4—348no—
723D4—348no—
724D4—344no—
725D4—344no—
726D4—342no—
727D4C22×C4×D1714yes—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—172no—
733C2×C4—174no—
734C2×C4—174no—
735C2×C4—348no—
736C2×C4—348no—
737C2×C4—348no—
738C2×C4—342no—
739C2×C4—344no—
740C2×C4—344no—
741C2×C4—341no—
742C2×C4—341no—
743C2×C4—1362no—
744C2×C4—1361no—
745C2×C4C22×C4×D1711yescharacteristic
746C2×C4C22×C4×D1711yescharacteristic
747C2×C4C2×D4×D1711yescharacteristic
748C2×C4C2×D4×D1711yescharacteristic
749C2×C4#41×D1711yescharacteristic
750C2×C4C24×D1711yescharacteristic
751C8—24no—
752C8—174no—
753C8—172no—
754C8—172no—
755C8—344no—
756C8C22×C4×D1711yescharacteristic
757C8C22×C4×D1711yescharacteristic
758C8C22×C4×D1711yescharacteristic
759C8C22×C4×D1711yescharacteristic
760C8C2×D4×D1714yes—
761C22—24no—
762C22—41no—
763C22—82no—
764C22—174no—
765C22—344no—
766C22—682no—
767C22—1362no—
768C22—1368no—
769C22C4×D4×D1711yescharacteristic
770C22C4×D4×D1711yescharacteristic
771C22C2×#41×D1711yescharacteristic
772C4—24no—
773C4—42no—
774C4—174no—
775C4—344no—
776C4—681no—
777C4—681no—
778C4C4×D4×D1711yescharacteristic
779C4C4×D4×D1711yescharacteristic
780C4C23×C4×D1711yescharacteristic
781C4C22×D4×D1711yescharacteristic
782C2—21no—
783C2—21no—
784C2—21no—
785C2—44no—
786C2—344no—
787C2—684no—
788C2C2×C4×D4×D1711yescharacteristic
subgroupG/H
centerC4C22×D4×D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC17×#2957C2
socleC2×C17C22×C4×D4
prime radical#14543553C2
cosocleC2×C4×C17C25
hypercenter#2957D17
hypocenterC17#60184
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×M16 ◁ #2957

Complements

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

NH ≅ G/Ntype
2. #14543497C2semidirect
3. #14537702C2semidirect
4. #14537698C2semidirect
5. #14537691C2semidirect
6. #14537689C2semidirect
7. #14537683C2semidirect
8. #14537682C2semidirect
9. C2×#11762931C2semidirect
10. C2×#11762930C2semidirect
11. D17×#444C2semidirect
12. #14537392C2semidirect
13. #14537330C2semidirect
14. #14537211C2semidirect
15. C17×#2957C2semidirect
17. #11763623C4semidirect
18. #11763622C4semidirect
19. #11763616C4semidirect
20. #11763615C4semidirect
21. #11763611C4semidirect
22. #11763610C4semidirect
29. #11763575C22semidirect
31. #11763574C22semidirect
34. C2×#10587593C22semidirect
35. C2×#10587634C22semidirect
38. #131×D17C22semidirect
40. #11762932C22semidirect
41. #11762931C22semidirect
42. #11762931C22semidirect
43. #11762931C22semidirect
44. #11762931C22semidirect
45. #11762930C22semidirect
46. #11762930C22semidirect
47. #11762930C22semidirect
48. #11762930C22semidirect
49. #11762929C22semidirect
50. #11762928C22semidirect
51. #11762927C22semidirect
52. #11762924C22semidirect
53. #11762923C22semidirect
54. #11762857C22semidirect
55. #11762856C22semidirect
56. C2×#10587490C22semidirect
57. #108×D17C22semidirect
58. #11762827C22semidirect
59. #11762824C22semidirect
60. C2×#10587508C22semidirect
61. C2×#10587496C22semidirect
62. #104×D17C22semidirect
63. #11762766C22semidirect
64. #11762765C22semidirect
65. #11762763C22semidirect
66. M16×Dic17C22semidirect
67. C4×#63218C22semidirect
68. C2×#10587486C22semidirect
69. #97×D17C22semidirect
71. C17×#568C22semidirect
72. C17×#444C22semidirect
73. C17×#443C22semidirect
74. C2×C17×#108C22semidirect
75. C17×#421C22semidirect
76. C17×#405C22semidirect
90. C17×#135C2×C4semidirect
91. C17×#135C2×C4semidirect
94. C2×Q16×C17C2×C4semidirect
95. C2×SD16×C17C2×C4semidirect
96. C2×D8×C17C2×C4semidirect
104. #10587637C2×C4semidirect
106. #10587635C2×C4semidirect
111. #10587628C2×C4semidirect
112. #10587618C2×C4semidirect
119. #10587605C2×C4semidirect
120. #10587604C2×C4semidirect
121. Q16×D17C2×C4semidirect
122. #10587602C2×C4semidirect
123. #10587601C2×C4semidirect
124. #10587600C2×C4semidirect
125. SD16×D17C2×C4semidirect
126. #10587598C2×C4semidirect
127. #10587597C2×C4semidirect
128. D8×D17C2×C4semidirect
143. C2×Dic68C2×C4semidirect
144. #10587590C2×C4semidirect
145. #10587590C2×C4semidirect
148. C2×D136C2×C4semidirect
149. C2×#63219C2×C4semidirect
371. #2957D17semidirect
420. #568C2×D17semidirect
440. #444C2×D17semidirect
444. #443C2×D17semidirect
449. C2×#108C2×D17semidirect
452. #421C2×D17semidirect
459. #405C2×D17semidirect
500. #135C4×D17semidirect
501. #135C4×D17semidirect
506. C2×Q16C4×D17semidirect
509. C2×SD16C4×D17semidirect
512. C2×D8C4×D17semidirect
586. C17#60184semidirect

Maximal subgroups

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

subgroupindex
#145435532
#145434972
#145377022
#145376982
#145376912
#145376892
#145376832
#145376822
C2×#117629312
C2×#117629302
D17×#4442
#145373922
#145373302
#145372112
C17×#29572
#6018417