Finite Group Databasebeta

← C4×#11763612 #17898541

Subgroups — C4×#11763612 #17898541

Order 4352.

2826 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763612C211yesmaximal, characteristic
2C4×#10587696C211yesmaximal, characteristic, complemented
3#14537657C213yesmaximal, complemented
4#14537634C213yesmaximal, complemented
5#14537616C213yesmaximal, complemented
6#14537612C213yesmaximal, complemented
7C4×#10587618C213yesmaximal, complemented
8C4×#10587635C213yesmaximal, complemented
9C4×#10587636C213yesmaximal, complemented
10C2×C4×#63228C213yesmaximal, complemented
11#14537382C211yesmaximal, characteristic, complemented
12#14537310C211yesmaximal, characteristic, complemented
13#14537307C211yesmaximal, characteristic, complemented
14C4×#10587634C211yesmaximal, characteristic, complemented
15C4×C17×H(5,𝔽2)C211yesmaximal, characteristic, complemented
16C2×#10587696C2211yescharacteristic
17#11763612C4116yesdirect product factor
18C2×#10587618C2213yes—
19C2×#10587635C2213yes—
20C2×#10587636C2213yes—
21C22×#63228C2213yes—
22C2×#10587634C2211yescharacteristic
23C2×#10587634C2211yescharacteristic
24#11763292C2211yescharacteristic
25#11763291—21no—
26#11763289C2213yescomplemented
27#11763283C2213yescomplemented
28#11763281—23no—
29C4×#63256—21no—
30C4×#63252C2213yescomplemented
31C2×C4×D68C2213yescomplemented
32C4×D4×D17—23no—
33#11762919C2216yescomplemented
34#11762919C2216yescomplemented
35#11762909C2216yescomplemented
36#11762907C2216yescomplemented
37C4×#63231C2211yescharacteristic, complemented
38C4×#63231C2213yescomplemented
39C4×#63230C2213yescomplemented
40C4×#63230C2213yescomplemented
41C4×#63229C2213yescomplemented
42C4×#63229C2213yescomplemented
43C4×#63228C2213yescomplemented
44C4×#63228C2216yescomplemented
45C4×#63228C2216yescomplemented
46C4×#63228C2216yescomplemented
47C4×#63228C2213yescomplemented
48#11762852C2213yescomplemented
49#11762849C2213yescomplemented
50#11762845C2213yescomplemented
51C2×#10587478C2213yescomplemented
52#11762814C2213yescomplemented
53#11762813C2213yescomplemented
54#11762810C2213yescomplemented
55#11762808C2213yescomplemented
56#11762805C2213yescomplemented
57#11762803C2213yescomplemented
58C2×#10587503C2213yescomplemented
59C2×#10587480C2213yescomplemented
60#11762765C2213yescomplemented
61#11762765C2213yescomplemented
62C4×#63223C2213yescomplemented
63C2×C4×#3622C2213yescomplemented
64C2×C17×H(5,𝔽2)C2211yescharacteristic
65C17×#520—21no—
66C17×#520C2211yescharacteristic
67C17×#520C2213yescomplemented
68C17×#518—23no—
69C17×#518C2213yescomplemented
70C4×#41×C17—21no—
71C4×#41×C17C2211yescharacteristic
72C4×#41×C17C2213yescomplemented
73C2×C4×D4×C17—23no—
74C2×C4×D4×C17C2213yescomplemented
75C17×H(5,𝔽2)—24no—
76C17×H(5,𝔽2)C2×C418yescomplemented
77C2×#41×C17—21no—
78C2×#41×C17C2313yes—
79C2×#41×C17C2311yescharacteristic
80C22×D4×C17—23no—
81C22×D4×C17C2313yes—
82C23×C4×C17—23no—
83#10587696—24no—
84#10587696C2×C418yescomplemented
85C2×#63256—21no—
86C2×D4×D17—23no—
87C2×#63252C2313yes—
88C22×D68C2313yes—
89C22×C4×D17—23no—
90C4×Q8×C17—21no—
91C4×Q8×C17D411yescharacteristic
92C4×Q8×C17D411yescharacteristic
93C4×Q8×C17C2311yescharacteristic
94C4×Q8×C17C2313yes—
95C4×D4×C17—23no—
96C4×D4×C17—23no—
97C4×D4×C17—23no—
98C4×D4×C17—23no—
99C4×D4×C17—23no—
100C4×D4×C17—26no—
101C4×D4×C17—23no—
102C4×D4×C17—23no—
103C4×D4×C17D413yes—
104C4×D4×C17D413yes—
105C4×D4×C17C2313yes—
106C4×D4×C17C2316yes—
107C4×D4×C17C2313yes—
108C17×#117—23no—
109C17×#117—23no—
110C17×#117C2313yes—
111C17×#117C2313yes—
112C2×C4⋊C4×C17—23no—
113C2×C4⋊C4×C17C2313yes—
114C2×C22⋊C4×C17—23no—
115C2×C22⋊C4×C17—26no—
116C2×C42×C17—23no—
117C2×C42×C17C2313yes—
118#10587636C2×C4124yescomplemented
119#10587635C2×C4124yescomplemented
120#10587634—24no—
121#10587634C2×C418yescomplemented
122Q8×Dic17—21no—
123C2×#63231C2311yescharacteristic
124C2×#63230C2313yes—
125D4×Dic17—23no—
126C2×#63229C2313yes—
127#10587618C2×C4124yescomplemented
128C2×#63228C2×C4124yescomplemented
129C2×#63228C2313yes—
130C2×#63228C2316yes—
131C4×C22⋊D17—23no—
132C4×C22⋊D17—23no—
133C2×#63227—23no—
134#10587612C2313yes—
135C2×C4⋊Dic17C2313yes—
136C2×#63223C2313yes—
137C2×#63223C2313yes—
138C22×#3622C2313yes—
139C22×#3622C2313yes—
140#10587579—23no—
141#10587579—23no—
142#10587578—23no—
143C4⋊C4×D17—23no—
144#10587567—26no—
145C22⋊C4×D17—26no—
146C4×D68—23no—
147C4×D68—23no—
148C4×D68C2313yes—
149C4×D68C2316yes—
150C4×D68C2313yes—
151#10587558—23no—
152C42×D17—23no—
153C4×Dic34C2311yescharacteristic
154C4×Dic34C2313yes—
155#10587506C2311yescharacteristic
156#10587506C2313yes—
157#10587503C2313yes—
158#10587503C2316yes—
159#10587503C2313yes—
160#10587481C2311yescharacteristic
161#10587481C2313yes—
162#10587480C2313yes—
163#10587480C2316yes—
164#10587480C2313yes—
165#10587479C2313yes—
166#10587479C2313yes—
167#10587478C2313yes—
168#10587478C2316yes—
169#10587478C2311yescharacteristic
170#10587474C2316yes—
171C4×#3622C2311yescharacteristic
172C4×#3622C2313yes—
173C4×#3622C2313yes—
174C4×#3622C2313yes—
175C24×C17—23no—
176C23×D17—23no—
177#41×C17—28no—
178#41×C17—26no—
179#41×C17C22×C414yes—
180#41×C17C22×C4112yescomplemented
181#41×C17#4114yes—
182C2×Q8×C17C2×D411yescharacteristic
183C2×Q8×C17C2411yescharacteristic
184C2×D4×C17—23no—
185C2×D4×C17—224no—
186C2×D4×C17—23no—
187C2×D4×C17—26no—
188C2×D4×C17C22×C4112yescomplemented
189C2×D4×C17C2×D413yes—
190C2×D4×C17C2413yes—
191C22×C4×C17—23no—
192C22×C4×C17—23no—
193C22×C4×C17—23no—
194C22×C4×C17—26no—
195C22×C4×C17—23no—
196C22×C4×C17—86no—
197C22×C4×C17C2×D413yes—
198C22×C4×C17C2×D413yes—
199C22×C4×C17C2413yes—
200C2×C22⋊D17—23no—
201C22×Dic17—23no—
202#63256—28no—
203D4×D17—224no—
204#63252—26no—
205#63252C22×C4112yescomplemented
206C2×D68—23no—
207C2×D68—26no—
208C2×D68C22×C4112yescomplemented
209C2×D68C2413yes—
210C2×C4×D17—23no—
211C2×C4×D17—23no—
212C2×C4×D17—26no—
213C2×C4×D17—23no—
214C2×C4×D17—86no—
215C2×Dic34C2411yescharacteristic
216C4⋊C4×C17—23no—
217C4⋊C4×C17—23no—
218C4⋊C4×C17—21no—
219C4⋊C4×C17C2×D413yes—
220C4⋊C4×C17C2×D413yes—
221C4⋊C4×C17C2413yes—
222C4⋊C4×C17C2411yescharacteristic
223C22⋊C4×C17—23no—
224C22⋊C4×C17—23no—
225C22⋊C4×C17—26no—
226C22⋊C4×C17—23no—
227C22⋊C4×C17C2×D416yes—
228C42×C17—21no—
229C42×C17—23no—
230C42×C17—23no—
231C42×C17C2×D413yes—
232C42×C17C2×D413yes—
233C42×C17C2411yescharacteristic
234C42×C17C2413yes—
235C22⋊Dic17—23no—
236#63231C22×C414yescomplemented
237#63230C22×C4112yescomplemented
238#63229C22×C4112yescomplemented
239#63228C22×C4112yescomplemented
240#63228C22×C4124yescomplemented
241#63227—23no—
242#63227—23no—
243#63227—26no—
244C4⋊Dic17—23no—
245C4⋊Dic17C2413yes—
246C4⋊Dic17C2411yescharacteristic
247#63225—21no—
248#63225—23no—
249C4×Dic17—21no—
250C4×Dic17—23no—
251C4×Dic17—23no—
252#63223—26no—
253#63223C22×C4112yescomplemented
254C2×#3622—26no—
255C2×#3622C22×C4112yescomplemented
256C2×#3622C2411yescharacteristic
257C2×#3622C2413yes—
258C2×#3622C2411yescharacteristic
259C2×#3622C2413yes—
260C4×#576—171nomaximal, Sylow
261C23×C17—23no—
262C23×C17—212no—
263C23×C17—83no—
264C23×C17—83no—
265C23×C17C22×D413yes—
266C22×D17—23no—
267C22×D17—212no—
268C22×D17—83no—
269C22×D17—83no—
270Q8×C17—21no—
271Q8×C17C4×D414yes—
272Q8×C17C23×C412yes—
273D4×C17—212no—
274D4×C17—212no—
275D4×C17—23no—
276D4×C17C4×D4112yes—
277D4×C17C23×C416yes—
278C2×C4×C17—21no—
279C2×C4×C17—212no—
280C2×C4×C17—26no—
281C2×C4×C17—21no—
282C2×C4×C17—23no—
283C2×C4×C17—43no—
284C2×C4×C17—46no—
285C2×C4×C17—83no—
286C2×C4×C17—86no—
287C2×C4×C17—83no—
288C2×C4×C17C23×C416yes—
289C2×C4×C17C22×D413yes—
290C2×C4×C17C22×D411yescharacteristic
291C2×C4×C17C22×D413yes—
292C2×C4×C17C22×D413yes—
293C2×C4×C17C22×D411yescharacteristic
294C2×C4×C17C2×#4116yes—
295C2×C4×C17C2511yescharacteristic
296C22⋊D17—212no—
297C2×Dic17—21no—
298C2×Dic17—21no—
299C2×Dic17—23no—
300C2×Dic17—83no—
301D68—212no—
302D68—23no—
303D68C23×C416yes—
304C4×D17—212no—
305C4×D17—46no—
306C4×D17—83no—
307C4×D17—86no—
308Dic34—21no—
309Dic34C23×C412yes—
310#3622—21no—
311#3622—23no—
312#3622C23×C412yes—
313#3622C23×C416yes—
314C2×#576—171no—
315C4×H(5,𝔽2)—171no—
316C4×H(5,𝔽2)D1711yescharacteristic, complemented
317#2951—173no—
318#2948—173no—
319#2946—173no—
320#2946—173no—
321C4×AGL(1,ℤ/8)—173no—
322C4×AGL(1,ℤ/8)—173no—
323C4×#135—173no—
324C2×C4×D8—173no—
325#2913—171no—
326#2897—171no—
327#2897—171no—
328C4×#131—171no—
329C22×C17—23no—
330C22×C17—23no—
331C22×C17—26no—
332C22×C17—43no—
333C22×C17—43no—
334C22×C17—812no—
335C22×C17C2×C4×D416yes—
336C22×C17C23×D411yescharacteristic
337C2×D17—26no—
338C2×D17—43no—
339C2×D17—43no—
340C2×D17—812no—
341C4×C17—23no—
342C4×C17—21no—
343C4×C17—22no—
344C4×C17—23no—
345C4×C17—41no—
346C4×C17—43no—
347C4×C17C2×C4×D416yes—
348C4×C17#57612yescomplemented
349C4×C17C24×C411yescharacteristic
350C4×C17C22×#4111yescharacteristic
351Dic17—22no—
352Dic17—41no—
353Dic17—43no—
354C2×H(5,𝔽2)—171no—
355C2×H(5,𝔽2)C2×D1711yescharacteristic
356#576—1716no—
357C2×AGL(1,ℤ/8)—173no—
358C2×AGL(1,ℤ/8)—173no—
359C2×#135—173no—
360C22×D8—173no—
361C2×#131—171no—
362C2×#131—171no—
363#520—21no—
364#520—171no—
365#520—173no—
366#520—341no—
367#520C2×D1711yescharacteristic
368#520C2×D1713yescomplemented
369#518—23no—
370#518—173no—
371#518—343no—
372#518C2×D1713yescomplemented
373C4×#41—21no—
374C4×#41—173no—
375C4×#41—341no—
376C4×#41C2×D1711yescharacteristic
377C4×#41C2×D1713yescomplemented
378C2×C4×D4—23no—
379C2×C4×D4—173no—
380C2×C4×D4—343no—
381C2×C4×D4C2×D1713yescomplemented
382#442—176no—
383#442—176no—
384#440—176no—
385#440—176no—
386C4×Q16—171no—
387C4×Q16—173no—
388C4×SD16—173no—
389C4×SD16—173no—
390C4×SD16—173no—
391C4×SD16—173no—
392C4×D8—173no—
393C4×D8—176no—
394C4×D8—176no—
395C4×D8—176no—
396C4×D8—173no—
397#428—173no—
398#428—173no—
399#427—173no—
400C2×#107—173no—
401#418—173no—
402#418—173no—
403#417—173no—
404#417—173no—
405#416—173no—
406#416—173no—
407C2×#102—173no—
408C2×#102—173no—
409#405—173no—
410#405—173no—
411C4×M16—173no—
412C2×C4×C8—173no—
413C2×C17—26no—
414C2×C17—46no—
415C2×C17C22×C4×D411yescharacteristic
416C2×C17C2×#57611yescharacteristic
417C2×C17#358411yescharacteristic
418D17—46no—
419H(5,𝔽2)—24no—
420H(5,𝔽2)—178no—
421H(5,𝔽2)—344no—
422H(5,𝔽2)C4×D1718yescomplemented
423C2×#41—21no—
424C2×#41—173no—
425C2×#41—341no—
426C2×#41C22×D1713yes—
427C2×#41C22×D1711yescharacteristic
428C22×D4—23no—
429C22×D4—173no—
430C22×D4—343no—
431C22×D4C22×D1713yes—
432C23×C4—23no—
433C23×C4—343no—
434AGL(1,ℤ/8)—1724no—
435AGL(1,ℤ/8)—1724no—
436#135—1724no—
437C2×Q16—171no—
438C2×SD16—173no—
439C2×SD16—173no—
440C2×D8—1724no—
441C2×D8—173no—
442C2×D8—176no—
443#131—178no—
444#131—344no—
445C2×M16—173no—
446C2×M16—173no—
447C22×C8—173no—
448C22×C8—173no—
449C4×Q8—21no—
450C4×Q8—171no—
451C4×Q8—173no—
452C4×Q8—341no—
453C4×Q8C22⋊D1711yescharacteristic
454C4×Q8C22⋊D1711yescharacteristic
455C4×Q8C22×D1711yescharacteristic
456C4×Q8C22×D1713yes—
457C4×D4—23no—
458C4×D4—23no—
459C4×D4—23no—
460C4×D4—23no—
461C4×D4—23no—
462C4×D4—26no—
463C4×D4—23no—
464C4×D4—23no—
465C4×D4—173no—
466C4×D4—176no—
467C4×D4—173no—
468C4×D4—343no—
469C4×D4—343no—
470C4×D4—343no—
471C4×D4—343no—
472C4×D4—343no—
473C4×D4—346no—
474C4×D4—343no—
475C4×D4—343no—
476C4×D4C22⋊D1713yes—
477C4×D4C22⋊D1713yes—
478C4×D4C22×D1713yes—
479C4×D4C22×D1716yes—
480C4×D4C22×D1713yes—
481#117—23no—
482#117—23no—
483#117—173no—
484#117—343no—
485#117—343no—
486#117C22×D1713yes—
487#117C22×D1713yes—
488C2×C4⋊C4—23no—
489C2×C4⋊C4—173no—
490C2×C4⋊C4—343no—
491C2×C4⋊C4C22×D1713yes—
492C2×C22⋊C4—23no—
493C2×C22⋊C4—26no—
494C2×C22⋊C4—343no—
495C2×C22⋊C4—346no—
496C2×C42—23no—
497C2×C42—343no—
498C2×C42C22×D1713yes—
499#107—173no—
500#107—176no—
501#107—171no—
502#106—173no—
503#106—173no—
504#103—171no—
505#103—173no—
506#103—171no—
507#103—173no—
508#102—173no—
509#102—176no—
510#102—173no—
511#102—173no—
512#102—176no—
513#102—173no—
514#97—176no—
515C4×C8—171no—
516C4×C8—173no—
517C4×C8—173no—
518C4×C8—173no—
519C17C4×#57611yescharacteristic, complemented, Sylow
520C24—23no—
521C24—343no—
522#41—28no—
523#41—26no—
524#41—1712no—
525#41—348no—
526#41—346no—
527#41C2×C4×D1714yes—
528#41C2×C4×D17112yescomplemented
529#41#6325214yes—
530C2×Q8—171no—
531C2×Q8C2×C22⋊D1711yescharacteristic
532C2×Q8C23×D1711yescharacteristic
533C2×D4—23no—
534C2×D4—224no—
535C2×D4—26no—
536C2×D4—23no—
537C2×D4—1712no—
538C2×D4—173no—
539C2×D4—343no—
540C2×D4—3424no—
541C2×D4—346no—
542C2×D4—343no—
543C2×D4C2×C4×D17112yescomplemented
544C2×D4C2×C22⋊D1713yes—
545C2×D4C23×D1713yes—
546C22×C4—23no—
547C22×C4—23no—
548C22×C4—23no—
549C22×C4—23no—
550C22×C4—26no—
551C22×C4—86no—
552C22×C4—343no—
553C22×C4—343no—
554C22×C4—343no—
555C22×C4—343no—
556C22×C4—346no—
557C22×C4—1366no—
558C22×C4C2×C22⋊D1713yes—
559C22×C4C2×C22⋊D1713yes—
560C22×C4C23×D1713yes—
561Q16—174no—
562SD16—1712no—
563SD16—1712no—
564D8—1712no—
565D8—1724no—
566M16—1712no—
567M16—346no—
568C2×C8—1712no—
569C2×C8—171no—
570C2×C8—173no—
571C2×C8—171no—
572C2×C8—173no—
573C2×C8—346no—
574C4⋊C4—23no—
575C4⋊C4—23no—
576C4⋊C4—21no—
577C4⋊C4—171no—
578C4⋊C4—173no—
579C4⋊C4—343no—
580C4⋊C4—343no—
581C4⋊C4—341no—
582C4⋊C4C2×C22⋊D1713yes—
583C4⋊C4C2×C22⋊D1713yes—
584C4⋊C4C23×D1711yescharacteristic
585C4⋊C4C23×D1713yes—
586C22⋊C4—23no—
587C22⋊C4—23no—
588C22⋊C4—26no—
589C22⋊C4—23no—
590C22⋊C4—343no—
591C22⋊C4—343no—
592C22⋊C4—346no—
593C22⋊C4—343no—
594C22⋊C4C2×C22⋊D1716yes—
595C42—23no—
596C42—23no—
597C42—21no—
598C42—343no—
599C42—343no—
600C42—341no—
601C42C2×C22⋊D1713yes—
602C42C2×C22⋊D1713yes—
603C42C23×D1713yes—
604C42C23×D1711yescharacteristic
605C23—23no—
606C23—212no—
607C23—83no—
608C23—83no—
609C23—343no—
610C23—3412no—
611C23—1363no—
612C23—1363no—
613C23C22×C22⋊D1713yes—
614Q8—21no—
615Q8—172no—
616Q8—341no—
617Q8C4×C22⋊D1714yes—
618Q8C22×C4×D1712yes—
619D4—212no—
620D4—212no—
621D4—23no—
622D4—176no—
623D4—3412no—
624D4—3412no—
625D4—343no—
626D4C4×C22⋊D17112yes—
627D4C22×C4×D1716yes—
628C2×C4—21no—
629C2×C4—212no—
630C2×C4—26no—
631C2×C4—21no—
632C2×C4—23no—
633C2×C4—43no—
634C2×C4—46no—
635C2×C4—86no—
636C2×C4—83no—
637C2×C4—83no—
638C2×C4—341no—
639C2×C4—3412no—
640C2×C4—341no—
641C2×C4—343no—
642C2×C4—686no—
643C2×C4—1366no—
644C2×C4—1363no—
645C2×C4—1363no—
646C2×C4C22×C4×D1716yes—
647C2×C4C2×#6325216yes—
648C2×C4C22×C22⋊D1713yes—
649C2×C4C22×C22⋊D1711yescharacteristic
650C2×C4C22×C22⋊D1713yes—
651C2×C4C22×C22⋊D1713yes—
652C2×C4C22×C22⋊D1711yescharacteristic
653C2×C4C24×D1711yescharacteristic
654C8—172no—
655C8—176no—
656C8—341no—
657C8—343no—
658C22—23no—
659C22—23no—
660C22—26no—
661C22—43no—
662C22—43no—
663C22—812no—
664C22—346no—
665C22—683no—
666C22—683no—
667C22—13612no—
668C22C2×C4×C22⋊D1716yes—
669C22C23×C22⋊D1711yescharacteristic
670C4—22no—
671C4—23no—
672C4—21no—
673C4—23no—
674C4—43no—
675C4—41no—
676C4—342no—
677C4—683no—
678C4—681no—
679C4C2×C4×C22⋊D1716yes—
680C4#1176361212yesdirect product factor
681C4C23×C4×D1711yescharacteristic
682C4C22×#6325211yescharacteristic
683C2—26no—
684C2—46no—
685C2—686no—
686C2C22×C4×C22⋊D1711yescharacteristic
687C2C2×#1176361211yescharacteristic
688C2#1454355511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC4×C17×H(5,𝔽2)C2
socleC22×C17C23×D4
prime radicalC2×#11763612C2
cosocleC2×C4×C17C25
hypercenterC4×H(5,𝔽2)D17
hypocenterC17C4×#576
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
2. C4×#10587696C2semidirect
3. #14537657C2semidirect
4. #14537634C2semidirect
5. #14537616C2semidirect
6. #14537612C2semidirect
7. C4×#10587618C2semidirect
8. C4×#10587635C2semidirect
9. C4×#10587636C2semidirect
10. C2×C4×#63228C2semidirect
11. #14537382C2semidirect
12. #14537310C2semidirect
13. #14537307C2semidirect
14. C4×#10587634C2semidirect
15. C4×C17×H(5,𝔽2)C2semidirect
17. #11763612C4direct (N × H)
26. #11763289C22semidirect
27. #11763283C22semidirect
30. C4×#63252C22semidirect
31. C2×C4×D68C22semidirect
33. #11762919C22semidirect
34. #11762919C22semidirect
35. #11762909C22semidirect
36. #11762907C22semidirect
37. C4×#63231C22semidirect
38. C4×#63231C22semidirect
39. C4×#63230C22semidirect
40. C4×#63230C22semidirect
41. C4×#63229C22semidirect
42. C4×#63229C22semidirect
43. C4×#63228C22semidirect
44. C4×#63228C22semidirect
45. C4×#63228C22semidirect
46. C4×#63228C22semidirect
47. C4×#63228C22semidirect
48. #11762852C22semidirect
49. #11762849C22semidirect
50. #11762845C22semidirect
51. C2×#10587478C22semidirect
52. #11762814C22semidirect
53. #11762813C22semidirect
54. #11762810C22semidirect
55. #11762808C22semidirect
56. #11762805C22semidirect
57. #11762803C22semidirect
58. C2×#10587503C22semidirect
59. C2×#10587480C22semidirect
60. #11762765C22semidirect
61. #11762765C22semidirect
62. C4×#63223C22semidirect
63. C2×C4×#3622C22semidirect
67. C17×#520C22semidirect
69. C17×#518C22semidirect
72. C4×#41×C17C22semidirect
74. C2×C4×D4×C17C22semidirect
76. C17×H(5,𝔽2)C2×C4semidirect
84. #10587696C2×C4semidirect
118. #10587636C2×C4semidirect
119. #10587635C2×C4semidirect
121. #10587634C2×C4semidirect
127. #10587618C2×C4semidirect
128. C2×#63228C2×C4semidirect
180. #41×C17C22×C4semidirect
188. C2×D4×C17C22×C4semidirect
205. #63252C22×C4semidirect
208. C2×D68C22×C4semidirect
236. #63231C22×C4semidirect
237. #63230C22×C4semidirect
238. #63229C22×C4semidirect
239. #63228C22×C4semidirect
240. #63228C22×C4semidirect
253. #63223C22×C4semidirect
255. C2×#3622C22×C4semidirect
316. C4×H(5,𝔽2)D17semidirect
348. C4×C17#576semidirect
368. #520C2×D17semidirect
372. #518C2×D17semidirect
377. C4×#41C2×D17semidirect
381. C2×C4×D4C2×D17semidirect
422. H(5,𝔽2)C4×D17semidirect
519. C17C4×#576semidirect
528. #41C2×C4×D17semidirect
543. C2×D4C2×C4×D17semidirect
680. C4#11763612direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117636122
C4×#105876962
#145376572
#145376342
#145376162
#145376122
C4×#105876182
C4×#105876352
C4×#105876362
C2×C4×#632282
#145373822
#145373102
#145373072
C4×#105876342
C4×C17×H(5,𝔽2)2
C4×#57617