Finite Group Databasebeta

← C2×#14539137 #17903559

Subgroups — C2×#14539137 #17903559

Order 4352.

2262 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763439C211yesmaximal, characteristic, complemented
2C2×#11763377C211yesmaximal, characteristic
3#14539137C2116yesmaximal, direct product factor
4C2×#11763175C211yesmaximal, characteristic, complemented
5C2×#11763172C211yesmaximal, characteristic, complemented
6C2×#11763170C211yesmaximal, characteristic, complemented
7C2×#11763168C211yesmaximal, characteristic, complemented
8C2×#11763165C211yesmaximal, characteristic, complemented
9C2×#11763156C211yesmaximal, characteristic, complemented
10C2×#11763154C211yesmaximal, characteristic, complemented
11C2×#11762809C211yesmaximal, characteristic, complemented
12C2×#11762812C211yesmaximal, characteristic, complemented
13C2×#11762804C211yesmaximal, characteristic, complemented
14C2×#102×D17C211yesmaximal, characteristic, complemented
15C2×#11762763C211yesmaximal, characteristic, complemented
16C2×C17×#488C211yesmaximal, characteristic, complemented
17C22×#63256C2211yescharacteristic
18C22×D4×D17C2211yescharacteristic
19C22×#63218C2211yescharacteristic
20C22×C8×D17C2211yescharacteristic
21#11763439—24no—
22#11763439C2218yescomplemented
23#11763377—24no—
24#11763377C2218yes—
25C2×#10587555C2211yescharacteristic, complemented
26C2×#10587574—21no—
27C2×#10587574C2211yescharacteristic, complemented
28C2×#10587560C2211yescharacteristic
29C2×#10587626C2211yescharacteristic
30C2×#10587576C2211yescharacteristic, complemented
31C2×#10587575—21no—
32C2×#10587633C2211yescharacteristic
33C2×#10587583—21no—
34C2×#10587582—21no—
35C2×#10587570—21no—
36C2×#10587570—21no—
37C2×#10587568—21no—
38C2×#10587568—21no—
39C2×#10587578C2211yescharacteristic
40C2×#10587558C2211yescharacteristic
41C2×C4⋊C4×D17C2211yescharacteristic
42#11763175C2218yescomplemented
43#11763172C2218yescomplemented
44#11763170C2218yescomplemented
45#11763168C2218yescomplemented
46#11763165C2218yescomplemented
47#11763156C2218yescomplemented
48#11763154C2218yescomplemented
49#11762812C2218yescomplemented
50#11762809C2218yescomplemented
51#11762804C2218yescomplemented
52C2×#10587506C2211yescharacteristic, complemented
53C2×#10587506C2211yescharacteristic, complemented
54C2×#10587492C2211yescharacteristic
55C2×#10587492C2211yescharacteristic
56C2×#10587492C2211yescharacteristic, complemented
57C2×#10587492C2211yescharacteristic, complemented
58C2×#10587503C2211yescharacteristic
59C2×#10587503C2211yescharacteristic
60C2×#10587480C2211yescharacteristic
61C2×#10587480C2211yescharacteristic
62C2×#10587480C2211yescharacteristic, complemented
63C2×#10587480C2211yescharacteristic, complemented
64#102×D17C2218yescomplemented
65#11762763C2218yescomplemented
66C2×#10587474C2211yescharacteristic, complemented
67C2×#10587486C2211yescharacteristic, complemented
68C2×C8×Dic17C2211yescharacteristic, complemented
69C2×C17×#125C2211yescharacteristic, complemented
70C2×C17×#124C2211yescharacteristic
71C17×#488C2218yescomplemented
72C2×C17×#103C2211yescharacteristic, complemented
73C2×C17×#103C2211yescharacteristic, complemented
74C2×C17×#102C2211yescharacteristic
75C2×C17×#102C2211yescharacteristic
76C2×C4×C8×C17C2211yescharacteristic, complemented
77C24×D17—21no—
78C22×Q8×C17C2311yescharacteristic
79C22×D4×C17C2311yescharacteristic
80C22×C22⋊D17—21no—
81C22×C22⋊D17—21no—
82C22×C22⋊D17—21no—
83C2×#63256—22no—
84C2×#63256—24no—
85C2×#63256—24no—
86C2×#63256C2314yes—
87C2×D4×D17—22no—
88C2×D4×D17—24no—
89C2×D4×D17—24no—
90C2×D4×D17C2314yes—
91C22×D68—21no—
92C22×D68—21no—
93C22×D68—21no—
94C22×D68C2311yescharacteristic
95C22×D68C2311yescharacteristic
96C22×C4×D17—21no—
97C22×C4×D17—21no—
98C22×C4×D17C2311yescharacteristic
99C22×Dic34—21no—
100C22×Dic34—21no—
101C22×C8×C17C2311yescharacteristic
102C22×C8×C17C2311yescharacteristic
103C17×#125—22no—
104C17×#125C2314yescomplemented
105C17×#124—22no—
106C17×#124C2314yes—
107C2×C4⋊C4×C17—21no—
108C2×C4⋊C4×C17—21no—
109C2×C4⋊C4×C17C2311yescharacteristic
110C2×C4⋊C4×C17C2311yescharacteristic
111C2×C22⋊C4×C17—21no—
112C2×C22⋊C4×C17—21no—
113C2×C42×C17C2311yescharacteristic
114#10587633—22no—
115#10587633C2314yes—
116#10587626—22no—
117#10587626C2314yes—
118C2×#63227—21no—
119C2×#63227—21no—
120C2×#63227—21no—
121C2×#63227D411yescharacteristic
122C2×#63227D411yescharacteristic
123C2×C4⋊Dic17—21no—
124C2×C4⋊Dic17—21no—
125C2×C4⋊Dic17C2311yescharacteristic
126C2×C4⋊Dic17C2311yescharacteristic
127C2×#63225—21no—
128C2×#63225—21no—
129C2×#63225—21no—
130C2×#63225D411yescharacteristic
131C2×#63225D411yescharacteristic
132C2×C4×Dic17—21no—
133C2×C4×Dic17C2311yescharacteristic
134C22×#3622C2311yescharacteristic
135C22×#3622C2311yescharacteristic
136C2×#63218—24no—
137C2×#63218C2314yes—
138C2×C8×D17—24no—
139C2×C8×D17C2314yes—
140#10587583—28no—
141#10587582—28no—
142#10587578—22no—
143#10587578C2314yes—
144C4⋊C4×D17—22no—
145C4⋊C4×D17C2314yes—
146#10587576—22no—
147#10587576C2314yescomplemented
148#10587575—28no—
149#10587574—28no—
150#10587574—22no—
151#10587574C2314yescomplemented
152#10587570—28no—
153#10587570—28no—
154#10587568—28no—
155#10587568—28no—
156#10587560—22no—
157#10587560C2314yes—
158#10587558D414yes—
159#10587558C2314yes—
160#10587555—22no—
161#10587555C2314yescomplemented
162C17×#103C2314yescomplemented
163C17×#103C2314yescomplemented
164C17×#102C2314yes—
165C17×#102C2314yes—
166C4×C8×C17C2314yescomplemented
167#10587506C2314yescomplemented
168#10587506C2314yescomplemented
169#10587503C2314yes—
170#10587503C2314yes—
171#10587492C2314yes—
172#10587492C2314yes—
173#10587492C2314yescomplemented
174#10587492C2314yescomplemented
175#10587486C2314yescomplemented
176C8×Dic17C2314yescomplemented
177#10587480C2314yes—
178#10587480C2314yes—
179#10587480C2314yescomplemented
180#10587480C2314yescomplemented
181#10587474C2314yescomplemented
182C24×C17—21no—
183C23×D17—21no—
184C23×D17—21no—
185C23×D17—24no—
186C23×D17—44no—
187C23×D17—82no—
188C23×D17—82no—
189C23×D17C2×D411yescharacteristic
190C2×Q8×C17—21no—
191C2×Q8×C17—22no—
192C2×Q8×C17—22no—
193C2×Q8×C17C2412yes—
194C2×D4×C17—21no—
195C2×D4×C17—22no—
196C2×D4×C17—22no—
197C2×D4×C17C2412yes—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17C2×D411yescharacteristic
202C22×C4×C17C2×D411yescharacteristic
203C22×C4×C17C2411yescharacteristic
204C2×C22⋊D17—24no—
205C2×C22⋊D17—24no—
206C2×C22⋊D17—24no—
207C2×C22⋊D17—44no—
208C2×C22⋊D17—82no—
209C2×C22⋊D17—82no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17C2×D411yescharacteristic
213C22×Dic17C2×D411yescharacteristic
214C22×Dic17C2×D411yescharacteristic
215#63256—28no—
216#63256—28no—
217#63256—48no—
218D4×D17—28no—
219D4×D17—28no—
220D4×D17—48no—
221C2×D68—22no—
222C2×D68—22no—
223C2×D68—22no—
224C2×D68—22no—
225C2×D68—24no—
226C2×D68—21no—
227C2×D68—21no—
228C2×D68—24no—
229C2×D68—24no—
230C2×D68—44no—
231C2×D68—82no—
232C2×D68—82no—
233C2×D68C2412yes—
234C2×D68C2412yes—
235C2×C4×D17—24no—
236C2×C4×D17—24no—
237C2×C4×D17—44no—
238C2×C4×D17—82no—
239C2×C4×D17C2×D412yes—
240C2×C4×D17#4114yes—
241C2×C4×D17#4114yes—
242C2×C4×D17C2412yes—
243C2×Dic34—24no—
244C2×Dic34—24no—
245C2×Dic34—82no—
246C2×Dic34—82no—
247C2×C8×C17—22no—
248C2×C8×C17—22no—
249C2×C8×C17C2412yes—
250C2×C8×C17C2412yes—
251C4⋊C4×C17—21no—
252C4⋊C4×C17—21no—
253C4⋊C4×C17—24no—
254C4⋊C4×C17—24no—
255C4⋊C4×C17C2412yes—
256C4⋊C4×C17C2412yes—
257C22⋊C4×C17—24no—
258C22⋊C4×C17—24no—
259C42×C17C2×D412yes—
260C42×C17C2412yes—
261#63227—24no—
262#63227—24no—
263#63227—24no—
264#63227C2×D414yes—
265#63227C2×D414yes—
266C4⋊Dic17—21no—
267C4⋊Dic17—21no—
268C4⋊Dic17—24no—
269C4⋊Dic17—24no—
270C4⋊Dic17C2412yes—
271C4⋊Dic17C2412yes—
272#63225—24no—
273#63225—24no—
274#63225—24no—
275#63225C2×D414yes—
276#63225C2×D414yes—
277C4×Dic17—24no—
278C4×Dic17C2×D412yes—
279C4×Dic17C2412yes—
280C2×#3622—22no—
281C2×#3622—22no—
282C2×#3622C2412yes—
283C2×#3622C2412yes—
284#63218—28no—
285C8×D17—28no—
286C2×#3136—171nomaximal, Sylow
287C23×C17—22no—
288C23×C17—42no—
289C23×C17—42no—
290C23×C17—42no—
291C23×C17C22×D411yescharacteristic
292C22×D17—22no—
293C22×D17—22no—
294C22×D17—22no—
295C22×D17—22no—
296C22×D17—42no—
297C22×D17—42no—
298C22×D17—42no—
299C22×D17—42no—
300C22×D17—42no—
301C22×D17—42no—
302C22×D17—48no—
303C22×D17—84no—
304C22×D17—84no—
305C22×D17—816no—
306C22×D17#12414yes—
307C22×D17C22×D412yes—
308Q8×C17—22no—
309Q8×C17—22no—
310Q8×C17—42no—
311D4×C17—22no—
312D4×C17—22no—
313D4×C17—42no—
314C2×C4×C17—22no—
315C2×C4×C17—22no—
316C2×C4×C17—22no—
317C2×C4×C17—22no—
318C2×C4×C17—22no—
319C2×C4×C17—42no—
320C2×C4×C17—42no—
321C2×C4×C17—42no—
322C2×C4×C17C22×D412yes—
323C2×C4×C17C22×D412yes—
324C2×C4×C17C22×D411yescharacteristic
325C2×C4×C17C2×#4112yes—
326C2×C4×C17C2×#4112yes—
327C2×C4×C17C2511yescharacteristic
328C22⋊D17—48no—
329C22⋊D17—84no—
330C22⋊D17—84no—
331C2×Dic17—22no—
332C2×Dic17—22no—
333C2×Dic17—22no—
334C2×Dic17—22no—
335C2×Dic17—42no—
336C2×Dic17—42no—
337C2×Dic17#12414yes—
338C2×Dic17C22×D412yes—
339C2×Dic17C22×D412yes—
340C2×Dic17C22×D412yes—
341D68—22no—
342D68—22no—
343D68—22no—
344D68—22no—
345D68—48no—
346D68—42no—
347D68—42no—
348D68—84no—
349D68—84no—
350C4×D17—48no—
351C4×D17—84no—
352C4×D17#12418yes—
353C4×D17C2×#4114yes—
354C4×D17C2×#4114yes—
355Dic34—84no—
356Dic34—84no—
357C8×C17—22no—
358C8×C17—22no—
359#3622—22no—
360#3622—22no—
361C2×#544—171no—
362C2×#535—171no—
363#3136—1716no—
364C2×#490—171no—
365C2×#490—171no—
366C2×#489—171no—
367C2×#489—171no—
368C2×#488—171no—
369C2×#488D1711yescharacteristic, complemented
370C2×#486—171no—
371C2×#486—171no—
372C2×#417—171no—
373C2×#418—171no—
374C2×#416—171no—
375C22×#102—171no—
376C2×#405—171no—
377C22×C17—42no—
378C22×C17—42no—
379C22×C17—42no—
380C22×C17—84no—
381C22×C17C2×#12412yes—
382C22×C17#57612yes—
383C22×C17#57712yes—
384C22×C17C23×D411yescharacteristic
385C2×D17—28no—
386C2×D17—22no—
387C2×D17—22no—
388C2×D17—42no—
389C2×D17—42no—
390C2×D17—42no—
391C2×D17—42no—
392C2×D17—42no—
393C2×D17—42no—
394C2×D17—816no—
395C2×D17—84no—
396C2×D17—84no—
397C2×D17C2×#12414yes—
398C4×C17—22no—
399C4×C17—22no—
400C4×C17—42no—
401C4×C17—42no—
402C4×C17—42no—
403C4×C17C2×#12412yes—
404C4×C17C22×#4111yescharacteristic
405C4×C17C22×#4111yescharacteristic
406Dic17—22no—
407Dic17—22no—
408Dic17—42no—
409Dic17—42no—
410Dic17C2×#12414yes—
411C22×#41—171no—
412C23×D4—171no—
413C22×M16—171no—
414C23×C8—171no—
415#544—178no—
416#544—344no—
417#535—178no—
418#535—344no—
419C2×C4⋊Q8—171no—
420C2×C4⋊Q8—171no—
421C2×C4⋊Q8—341no—
422C2×#127—171no—
423C2×#127—171no—
424C2×#125—171no—
425C2×#125—341no—
426C2×#125C2×D1711yescharacteristic, complemented
427C2×#124—171no—
428C2×#124C2×D1711yescharacteristic
429C2×C22⋊Q8—341no—
430C2×C22⋊Q8—341no—
431C2×#121—341no—
432C2×#121—341no—
433C2×#120—341no—
434C2×#120—341no—
435C2×#117—171no—
436C2×#117—171no—
437C22×C4⋊C4—171no—
438#490—178no—
439#490—178no—
440#489—178no—
441#489—178no—
442#488—178no—
443#488C2×D1718yescomplemented
444#486—178no—
445#486—178no—
446#418—178no—
447#417—178no—
448#416—178no—
449C2×#103—171no—
450C2×#103—171no—
451C2×#103C2×D1711yescharacteristic, complemented
452C2×#103C2×D1711yescharacteristic, complemented
453C2×#102—171no—
454C2×#102—171no—
455C2×#102—171no—
456C2×#102—171no—
457C2×#102—171no—
458C2×#102—171no—
459C2×#102—171no—
460C2×#102—171no—
461C2×#102—171no—
462C2×#102—171no—
463C2×#102—178no—
464C2×#102C2×D1711yescharacteristic
465C2×#102C2×D1711yescharacteristic
466#405—178no—
467C2×#97—171no—
468C2×#97—171no—
469C2×C4×C8—171no—
470C2×C4×C8C2×D1711yescharacteristic, complemented
471C2×C17—82no—
472C2×C17#313614yescomplemented
473C2×C17C22×#12411yescharacteristic
474C2×C17C2×#57611yescharacteristic
475C2×C17C2×#57711yescharacteristic
476D17—24no—
477D17—82no—
478D17—82no—
479C25—341no—
480C2×#41—174no—
481C2×#41—342no—
482C2×#41—344no—
483C2×#41—344no—
484C22×Q8—341no—
485C22×Q8—341no—
486C22×Q8C22×D1711yescharacteristic
487C22×D4—174no—
488C22×D4—171no—
489C22×D4—171no—
490C22×D4—341no—
491C22×D4—344no—
492C22×D4—344no—
493C22×D4—342no—
494C22×D4—341no—
495C22×D4—341no—
496C22×D4—341no—
497C22×D4—341no—
498C22×D4—341no—
499C22×D4C22×D1711yescharacteristic
500C23×C4—171no—
501C23×C4—341no—
502C23×C4—341no—
503C2×M16—174no—
504C2×M16—344no—
505C22×C8—171no—
506C22×C8—171no—
507C22×C8—174no—
508C22×C8—344no—
509C22×C8C22×D1711yescharacteristic
510C22×C8C22×D1711yescharacteristic
511C4⋊Q8—174no—
512C4⋊Q8—174no—
513C4⋊Q8—342no—
514C4⋊Q8—348no—
515C4⋊Q8—342no—
516#127—174no—
517#127—174no—
518#127—342no—
519#127—342no—
520#125—22no—
521#125—174no—
522#125—342no—
523#125—348no—
524#125C22×D1714yescomplemented
525#124—22no—
526#124—174no—
527#124—342no—
528#124C22×D1714yes—
529C22⋊Q8—348no—
530C22⋊Q8—348no—
531#121—348no—
532#121—348no—
533#120—348no—
534#120—348no—
535#117—174no—
536#117—174no—
537#117—174no—
538#117—342no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—171no—
542C2×C4⋊C4—171no—
543C2×C4⋊C4—171no—
544C2×C4⋊C4—171no—
545C2×C4⋊C4—174no—
546C2×C4⋊C4—342no—
547C2×C4⋊C4—341no—
548C2×C4⋊C4—341no—
549C2×C4⋊C4—341no—
550C2×C4⋊C4—341no—
551C2×C4⋊C4—341no—
552C2×C4⋊C4C22×D1711yescharacteristic
553C2×C4⋊C4C22×D1711yescharacteristic
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—171no—
557C2×C22⋊C4—171no—
558C2×C22⋊C4—341no—
559C2×C22⋊C4—341no—
560C2×C22⋊C4—341no—
561C2×C42—171no—
562C2×C42—341no—
563C2×C42C22×D1711yescharacteristic
564#103—174no—
565#103—174no—
566#103C22×D1714yescomplemented
567#103C22×D1714yescomplemented
568#102—174no—
569#102—174no—
570#102—174no—
571#102—174no—
572#102—174no—
573#102—174no—
574#102—174no—
575#102—174no—
576#102—174no—
577#102—174no—
578#102C22×D1714yes—
579#102C22×D1714yes—
580#97—174no—
581#97—174no—
582C4×C8—174no—
583C4×C8C22×D1714yescomplemented
584C17C2×#313611yescharacteristic, complemented, Sylow
585C24—21no—
586C24—171no—
587C24—344no—
588C24—341no—
589C24—341no—
590C24—684no—
591C24—1362no—
592C24—1362no—
593#41—348no—
594#41—348no—
595#41—688no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—22no—
599C2×Q8—344no—
600C2×Q8—344no—
601C2×Q8—1362no—
602C2×Q8—1362no—
603C2×Q8C23×D1712yes—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—172no—
608C2×D4—172no—
609C2×D4—344no—
610C2×D4—348no—
611C2×D4—348no—
612C2×D4—344no—
613C2×D4—344no—
614C2×D4—344no—
615C2×D4—341no—
616C2×D4—341no—
617C2×D4—344no—
618C2×D4—344no—
619C2×D4—342no—
620C2×D4—342no—
621C2×D4—342no—
622C2×D4—342no—
623C2×D4—684no—
624C2×D4—688no—
625C2×D4—684no—
626C2×D4—1362no—
627C2×D4—1362no—
628C2×D4—1362no—
629C2×D4—1362no—
630C2×D4C23×D1712yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—171no—
635C22×C4—172no—
636C22×C4—174no—
637C22×C4—174no—
638C22×C4—172no—
639C22×C4—171no—
640C22×C4—171no—
641C22×C4—344no—
642C22×C4—344no—
643C22×C4—341no—
644C22×C4—341no—
645C22×C4—684no—
646C22×C4—1362no—
647C22×C4D4×D1711yescharacteristic
648C22×C4D4×D1711yescharacteristic
649C22×C4C23×D1711yescharacteristic
650M16—348no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—172no—
654C2×C8—172no—
655C2×C8—348no—
656C2×C8—342no—
657C2×C8—342no—
658C2×C8C23×D1712yes—
659C2×C8C23×D1712yes—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—174no—
665C4⋊C4—174no—
666C4⋊C4—172no—
667C4⋊C4—172no—
668C4⋊C4—344no—
669C4⋊C4—344no—
670C4⋊C4—344no—
671C4⋊C4—344no—
672C4⋊C4—341no—
673C4⋊C4—341no—
674C4⋊C4—344no—
675C4⋊C4C23×D1712yes—
676C4⋊C4C23×D1712yes—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—174no—
680C22⋊C4—174no—
681C22⋊C4—344no—
682C22⋊C4—344no—
683C22⋊C4—344no—
684C42—172no—
685C42—172no—
686C42—344no—
687C42D4×D1712yes—
688C42C23×D1712yes—
689C23—22no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—174no—
694C23—172no—
695C23—342no—
696C23—342no—
697C23—342no—
698C23—342no—
699C23—688no—
700C23—682no—
701C23—682no—
702C23—682no—
703C23—682no—
704C23—682no—
705C23—682no—
706C23—1364no—
707C23—1364no—
708C23—13616no—
709C23C2×D4×D1711yescharacteristic
710Q8—22no—
711Q8—22no—
712Q8—42no—
713Q8—1364no—
714Q8—1364no—
715D4—22no—
716D4—22no—
717D4—42no—
718D4—342no—
719D4—342no—
720D4—342no—
721D4—342no—
722D4—688no—
723D4—688no—
724D4—682no—
725D4—682no—
726D4—1364no—
727D4—1364no—
728D4—1364no—
729D4—1364no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—174no—
739C2×C4—172no—
740C2×C4—178no—
741C2×C4—174no—
742C2×C4—174no—
743C2×C4—172no—
744C2×C4—172no—
745C2×C4—342no—
746C2×C4—342no—
747C2×C4—342no—
748C2×C4—342no—
749C2×C4—688no—
750C2×C4—682no—
751C2×C4—682no—
752C2×C4—1364no—
753C2×C4C2×D4×D1712yes—
754C2×C4C2×D4×D1712yes—
755C2×C4C2×D4×D1711yescharacteristic
756C2×C4#41×D1712yes—
757C2×C4#41×D1712yes—
758C2×C4C24×D1711yescharacteristic
759C8—22no—
760C8—22no—
761C8—342no—
762C8—342no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—84no—
767C22—174no—
768C22—348no—
769C22—342no—
770C22—342no—
771C22—682no—
772C22—682no—
773C22—682no—
774C22—682no—
775C22—682no—
776C22—682no—
777C22—13616no—
778C22—1364no—
779C22—1364no—
780C22#124×D1712yes—
781C22#1176361112yes—
782C22#1176361612yes—
783C22C22×D4×D1711yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—174no—
790C4—342no—
791C4—342no—
792C4—682no—
793C4—682no—
794C4#124×D1712yes—
795C4C2×#41×D1711yescharacteristic
796C4C2×#41×D1711yescharacteristic
797C2—82no—
798C2—344no—
799C2—1362no—
800C2—1362no—
801C2#1453913714yesdirect product factor
802C2C2×#124×D1711yescharacteristic
803C2C2×#1176361111yescharacteristic
804C2C2×#1176361611yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#488C2
socleC23×C17C22×D4
prime radicalC2×#11763377C2
hypercenterC2×#488D17
hypocenterC17C2×#3136
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#11763439C2semidirect
3. #14539137C2direct (N × H)
4. C2×#11763175C2semidirect
5. C2×#11763172C2semidirect
6. C2×#11763170C2semidirect
7. C2×#11763168C2semidirect
8. C2×#11763165C2semidirect
9. C2×#11763156C2semidirect
10. C2×#11763154C2semidirect
11. C2×#11762809C2semidirect
12. C2×#11762812C2semidirect
13. C2×#11762804C2semidirect
14. C2×#102×D17C2semidirect
15. C2×#11762763C2semidirect
16. C2×C17×#488C2semidirect
22. #11763439C22semidirect
25. C2×#10587555C22semidirect
27. C2×#10587574C22semidirect
30. C2×#10587576C22semidirect
42. #11763175C22semidirect
43. #11763172C22semidirect
44. #11763170C22semidirect
45. #11763168C22semidirect
46. #11763165C22semidirect
47. #11763156C22semidirect
48. #11763154C22semidirect
49. #11762812C22semidirect
50. #11762809C22semidirect
51. #11762804C22semidirect
52. C2×#10587506C22semidirect
53. C2×#10587506C22semidirect
56. C2×#10587492C22semidirect
57. C2×#10587492C22semidirect
62. C2×#10587480C22semidirect
63. C2×#10587480C22semidirect
64. #102×D17C22semidirect
65. #11762763C22semidirect
66. C2×#10587474C22semidirect
67. C2×#10587486C22semidirect
68. C2×C8×Dic17C22semidirect
69. C2×C17×#125C22semidirect
71. C17×#488C22semidirect
72. C2×C17×#103C22semidirect
73. C2×C17×#103C22semidirect
76. C2×C4×C8×C17C22semidirect
104. C17×#125C23semidirect
147. #10587576C23semidirect
151. #10587574C23semidirect
161. #10587555C23semidirect
162. C17×#103C23semidirect
163. C17×#103C23semidirect
166. C4×C8×C17C23semidirect
167. #10587506C23semidirect
168. #10587506C23semidirect
173. #10587492C23semidirect
174. #10587492C23semidirect
175. #10587486C23semidirect
176. C8×Dic17C23semidirect
179. #10587480C23semidirect
180. #10587480C23semidirect
181. #10587474C23semidirect
369. C2×#488D17semidirect
426. C2×#125C2×D17semidirect
443. #488C2×D17semidirect
451. C2×#103C2×D17semidirect
452. C2×#103C2×D17semidirect
470. C2×C4×C8C2×D17semidirect
472. C2×C17#3136semidirect
524. #125C22×D17semidirect
566. #103C22×D17semidirect
567. #103C22×D17semidirect
583. C4×C8C22×D17semidirect
584. C17C2×#3136semidirect
801. C2#14539137direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634392
C2×#117633772
#145391372
C2×#117631752
C2×#117631722
C2×#117631702
C2×#117631682
C2×#117631652
C2×#117631562
C2×#117631542
C2×#117628092
C2×#117628122
C2×#117628042
C2×#102×D172
C2×#117627632
C2×C17×#4882
C2×#313617