Finite Group Databasebeta

← #31720111

Subgroups — #31720111

Order 17152.

2818 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×#16864199C211yesmaximal, characteristic
2C4×#14524089C211yesmaximal, characteristic, complemented
3#22569090C213yesmaximal, complemented
4#22569059C213yesmaximal, complemented
5#22569041C213yesmaximal, complemented
6#22569037C213yesmaximal, complemented
7C4×#14524069C213yesmaximal, complemented
8C4×#14524068C213yesmaximal, complemented
9#22569007C213yesmaximal, complemented
10C2×#16863506C213yesmaximal, complemented
11#22568802C211yesmaximal, characteristic, complemented
12#22568735C211yesmaximal, characteristic, complemented
13#22568732C211yesmaximal, characteristic, complemented
14#22568637C211yesmaximal, characteristic, complemented
15C4×H(5,𝔽2)×C67C211yesmaximal, characteristic, complemented
16C2×#14524089C2211yescharacteristic
17#16864199C4116yescomplemented
18C2×#14524069C2213yes—
19C2×#14524068C2213yes—
20C2×#14524063C2213yes—
21C22×#11761613C2213yes—
22C2×#14524050C2211yescharacteristic
23C2×#14524050C2211yescharacteristic
24#16863879C2211yescharacteristic
25#16863878—21no—
26#16863876C2213yescomplemented
27#16863870C2213yescomplemented
28#16863868—23no—
29C4×#11761629—21no—
30C4×#11761628C2213yescomplemented
31C2×C4×D268C2213yescomplemented
32C4×D4×D67—23no—
33#16863506C2213yescomplemented
34#16863506C2216yescomplemented
35#16863506C2216yescomplemented
36#16863506C2216yescomplemented
37#16863506C2213yescomplemented
38#16863501C2211yescharacteristic, complemented
39#16863501C2213yescomplemented
40#16863496C2213yescomplemented
41#16863496C2213yescomplemented
42#16863494C2213yescomplemented
43#16863494C2213yescomplemented
44C4×#11761615C2216yescomplemented
45C4×#11761616C2216yescomplemented
46C4×#11761613C2216yescomplemented
47C4×#11761613C2216yescomplemented
48#16863439C2213yescomplemented
49#16863436C2213yescomplemented
50#16863432C2213yescomplemented
51C2×#14523974C2213yescomplemented
52#16863401C2213yescomplemented
53#16863400C2213yescomplemented
54#16863397C2213yescomplemented
55#16863395C2213yescomplemented
56#16863392C2213yescomplemented
57#16863390C2213yescomplemented
58C2×#14523964C2213yescomplemented
59C2×#14523963C2213yescomplemented
60#16863352C2213yescomplemented
61#16863352C2213yescomplemented
62C4×#11761612C2213yescomplemented
63C2×#14523954C2213yescomplemented
64C2×H(5,𝔽2)×C67C2211yescharacteristic
65#520×C67—21no—
66#520×C67C2211yescharacteristic
67#520×C67C2213yescomplemented
68#518×C67—23no—
69#518×C67C2213yescomplemented
70C4×#41×C67—21no—
71C4×#41×C67C2211yescharacteristic
72C4×#41×C67C2213yescomplemented
73C2×C4×D4×C67—23no—
74C2×C4×D4×C67C2213yescomplemented
75#14524089—24no—
76#14524089C2×C418yescomplemented
77C2×#11761629—21no—
78C2×#11761628C2313yes—
79C22×D268C2313yes—
80C2×D4×D67—23no—
81C22×C4×D67—23no—
82#14524069C2×C4124yescomplemented
83#14524068C2×C4124yescomplemented
84#14524063C2×C4124yescomplemented
85C2×#11761618C2311yescharacteristic
86C2×#11761616C2313yes—
87C2×#11761615C2313yes—
88C2×#11761613C2×C4124yescomplemented
89C2×#11761613C2313yes—
90C2×#11761613C2316yes—
91#14524050—24no—
92#14524050C2×C418yescomplemented
93C2×#11761612C2313yes—
94C2×#11761612C2313yes—
95C22×C67⋊C8C2313yes—
96C22×C67⋊C8C2313yes—
97Q8×Dic67—21no—
98C4×Dic134C2311yescharacteristic
99C4×Dic134C2313yes—
100C4×D268—23no—
101C4×D268—23no—
102C4×D268C2313yes—
103C4×D268C2313yes—
104C4×D268C2316yes—
105D4×Dic67—23no—
106#14524005—23no—
107#14524005—23no—
108C4×C22⋊D67—23no—
109C4×C22⋊D67—23no—
110(C22⋊D67)⋊C4—26no—
111#14524002C2313yes—
112#14524001—23no—
113#14524000—23no—
114C2×C4⋊Dic67C2313yes—
115C4⋊C4×D67—23no—
116C2×(C2×D67)⋊C4—23no—
117C22⋊C4×D67—26no—
118C42×D67—23no—
119#14523976C2313yes—
120#14523976C2313yes—
121#14523974C2313yes—
122#14523974C2311yescharacteristic
123#14523974C2316yes—
124#14523967C2311yescharacteristic
125#14523967C2313yes—
126#14523966C2311yescharacteristic
127#14523966C2313yes—
128#14523964C2313yes—
129#14523964C2313yes—
130#14523964C2316yes—
131#14523963C2313yes—
132#14523963C2313yes—
133#14523963C2316yes—
134#14523954C2313yes—
135#14523954C2313yes—
136#14523954C2311yescharacteristic
137#14523954C2313yes—
138C4×C67⋊C8C2316yes—
139H(5,𝔽2)×C67—24no—
140H(5,𝔽2)×C67C2×C418yescomplemented
141C2×#41×C67—21no—
142C2×#41×C67C2313yes—
143C2×#41×C67C2311yescharacteristic
144C22×D4×C67—23no—
145C22×D4×C67C2313yes—
146C23×C4×C67—23no—
147C4×Q8×C67—21no—
148C4×Q8×C67D411yescharacteristic
149C4×Q8×C67D411yescharacteristic
150C4×Q8×C67C2311yescharacteristic
151C4×Q8×C67C2313yes—
152C4×D4×C67—23no—
153C4×D4×C67—23no—
154C4×D4×C67—23no—
155C4×D4×C67—23no—
156C4×D4×C67—23no—
157C4×D4×C67—26no—
158C4×D4×C67—23no—
159C4×D4×C67—23no—
160C4×D4×C67D413yes—
161C4×D4×C67D413yes—
162C4×D4×C67C2313yes—
163C4×D4×C67C2313yes—
164C4×D4×C67C2316yes—
165#117×C67—23no—
166#117×C67—23no—
167#117×C67C2313yes—
168#117×C67C2313yes—
169C2×C4⋊C4×C67—23no—
170C2×C4⋊C4×C67C2313yes—
171C2×C22⋊C4×C67—23no—
172C2×C22⋊C4×C67—26no—
173C2×C42×C67—23no—
174C2×C42×C67C2313yes—
175C23×D67—23no—
176#11761629—28no—
177#11761628—26no—
178#11761628C22×C4112yescomplemented
179C2×Dic134C2411yescharacteristic
180C2×D268—23no—
181C2×D268—26no—
182C2×D268C22×C4112yescomplemented
183C2×D268C2413yes—
184C2×C22⋊D67—23no—
185D4×D67—224no—
186C22×Dic67—23no—
187C2×C4×D67—23no—
188C2×C4×D67—23no—
189C2×C4×D67—23no—
190C2×C4×D67—26no—
191C2×C4×D67—86no—
192#11761618C22×C414yescomplemented
193#11761616C22×C4112yescomplemented
194#11761615C22×C4112yescomplemented
195#11761613C22×C4112yescomplemented
196#11761613C22×C4124yescomplemented
197#11761612—26no—
198#11761612C22×C4112yescomplemented
199C2×C67⋊C8—26no—
200C2×C67⋊C8C22×C4112yescomplemented
201C2×C67⋊C8C2413yes—
202C2×C67⋊C8C2411yescharacteristic
203C2×C67⋊C8C2413yes—
204C2×C67⋊C8C2411yescharacteristic
205C4⋊Dic67—23no—
206C4⋊Dic67C2413yes—
207C4⋊Dic67C2411yescharacteristic
208Dic67⋊C4—23no—
209Dic67⋊C4—21no—
210C22⋊Dic67—23no—
211(C2×D67)⋊C4—23no—
212(C2×D67)⋊C4—26no—
213(C2×D67)⋊C4—23no—
214C4×Dic67—21no—
215C4×Dic67—23no—
216C4×Dic67—23no—
217C24×C67—23no—
218#41×C67—28no—
219#41×C67—26no—
220#41×C67C22×C414yes—
221#41×C67C22×C4112yescomplemented
222#41×C67#4114yes—
223C2×Q8×C67C2×D411yescharacteristic
224C2×Q8×C67C2411yescharacteristic
225C2×D4×C67—23no—
226C2×D4×C67—224no—
227C2×D4×C67—23no—
228C2×D4×C67—26no—
229C2×D4×C67C22×C4112yescomplemented
230C2×D4×C67C2×D413yes—
231C2×D4×C67C2413yes—
232C22×C4×C67—23no—
233C22×C4×C67—23no—
234C22×C4×C67—23no—
235C22×C4×C67—23no—
236C22×C4×C67—26no—
237C22×C4×C67—86no—
238C22×C4×C67C2×D413yes—
239C22×C4×C67C2×D413yes—
240C22×C4×C67C2413yes—
241C4⋊C4×C67—23no—
242C4⋊C4×C67—23no—
243C4⋊C4×C67—21no—
244C4⋊C4×C67C2×D413yes—
245C4⋊C4×C67C2×D413yes—
246C4⋊C4×C67C2413yes—
247C4⋊C4×C67C2411yescharacteristic
248C22⋊C4×C67—23no—
249C22⋊C4×C67—23no—
250C22⋊C4×C67—26no—
251C22⋊C4×C67—23no—
252C22⋊C4×C67C2×D416yes—
253C42×C67—21no—
254C42×C67—23no—
255C42×C67—23no—
256C42×C67C2×D413yes—
257C42×C67C2×D413yes—
258C42×C67C2411yescharacteristic
259C42×C67C2413yes—
260C23×C67—23no—
261C23×C67—212no—
262C23×C67—83no—
263C23×C67—83no—
264C23×C67C22×D413yes—
265C22×D67—23no—
266C22×D67—212no—
267C22×D67—83no—
268C22×D67—83no—
269Q8×C67—21no—
270Q8×C67C4×D414yes—
271Q8×C67C23×C412yes—
272D4×C67—212no—
273D4×C67—212no—
274D4×C67—23no—
275D4×C67C4×D4112yes—
276D4×C67C23×C416yes—
277C2×C4×C67—21no—
278C2×C4×C67—212no—
279C2×C4×C67—21no—
280C2×C4×C67—23no—
281C2×C4×C67—43no—
282C2×C4×C67—43no—
283C2×C4×C67—46no—
284C2×C4×C67—83no—
285C2×C4×C67—86no—
286C2×C4×C67—83no—
287C2×C4×C67C23×C416yes—
288C2×C4×C67C22×D411yescharacteristic
289C2×C4×C67C22×D413yes—
290C2×C4×C67C22×D411yescharacteristic
291C2×C4×C67C22×D413yes—
292C2×C4×C67C22×D413yes—
293C2×C4×C67C2×#4116yes—
294C2×C4×C67C2511yescharacteristic
295C22⋊D67—212no—
296C2×Dic67—21no—
297C2×Dic67—21no—
298C2×Dic67—23no—
299C2×Dic67—83no—
300D268—212no—
301D268—23no—
302D268C23×C416yes—
303C4×D67—212no—
304C4×D67—46no—
305C4×D67—83no—
306C4×D67—86no—
307Dic134—21no—
308Dic134C23×C412yes—
309C67⋊C8—21no—
310C67⋊C8—23no—
311C67⋊C8C23×C412yes—
312C67⋊C8C23×C416yes—
313C22×C67—23no—
314C22×C67—23no—
315C22×C67—26no—
316C22×C67—43no—
317C22×C67—43no—
318C22×C67—812no—
319C22×C67C2×C4×D416yes—
320C22×C67C23×D411yescharacteristic
321C2×D67—26no—
322C2×D67—43no—
323C2×D67—43no—
324C2×D67—812no—
325C4×C67—21no—
326C4×C67—23no—
327C4×C67—23no—
328C4×C67—21no—
329C4×C67—22no—
330C4×C67—43no—
331C4×C67—41no—
332C4×C67C2×C4×D416yes—
333C4×C67C24×C411yescharacteristic
334C4×C67C22×#4111yescharacteristic
335Dic67—22no—
336Dic67—43no—
337Dic67—41no—
338#60176—671nomaximal, Sylow
339C2×C67—26no—
340C2×C67—46no—
341C2×C67C22×C4×D411yescharacteristic
342C2×C67#358511yescharacteristic
343C2×C67#358511yescharacteristic
344D67—46no—
345C2×#576—671no—
346C4×H(5,𝔽2)—671no—
347C4×H(5,𝔽2)D6711yescharacteristic, complemented
348#2952—673no—
349#2948—673no—
350#2946—673no—
351#2946—673no—
352C4×AGL(1,ℤ/8)—673no—
353C4×AGL(1,ℤ/8)—673no—
354#2943—673no—
355C2×#442—673no—
356#2912—671no—
357#2897—671no—
358#2897—671no—
359#2875—671no—
360C67#6017611yescharacteristic, complemented, Sylow
361C2×H(5,𝔽2)—671no—
362C2×H(5,𝔽2)C2×D6711yescharacteristic
363#576—6716no—
364C2×AGL(1,ℤ/8)—673no—
365C2×AGL(1,ℤ/8)—673no—
366C2×#135—673no—
367C22×D8—673no—
368C2×#131—671no—
369C2×#131—671no—
370#520—21no—
371#520—671no—
372#520—673no—
373#520—1341no—
374#520C2×D6711yescharacteristic
375#520C2×D6713yescomplemented
376#518—23no—
377#518—673no—
378#518—1343no—
379#518C2×D6713yescomplemented
380C4×#41—21no—
381C4×#41—673no—
382C4×#41—1341no—
383C4×#41C2×D6711yescharacteristic
384C4×#41C2×D6713yescomplemented
385C2×C4×D4—23no—
386C2×C4×D4—673no—
387C2×C4×D4—1343no—
388C2×C4×D4C2×D6713yescomplemented
389#442—673no—
390#442—676no—
391#442—676no—
392#442—676no—
393#442—673no—
394#441—671no—
395#441—673no—
396#440—673no—
397#440—673no—
398#440—673no—
399#440—673no—
400C4×SD16—676no—
401C4×SD16—676no—
402C4×D8—676no—
403C4×D8—676no—
404#428—673no—
405#428—673no—
406#427—673no—
407C2×#106—673no—
408#418—673no—
409#418—673no—
410#417—673no—
411#417—673no—
412#416—673no—
413#416—673no—
414C2×#102—673no—
415C2×#102—673no—
416#405—673no—
417#405—673no—
418C4×M16—673no—
419C2×#97—673no—
420H(5,𝔽2)—24no—
421H(5,𝔽2)—678no—
422H(5,𝔽2)—1344no—
423H(5,𝔽2)C4×D6718yescomplemented
424C2×#41—21no—
425C2×#41—673no—
426C2×#41—1341no—
427C2×#41C22×D6713yes—
428C2×#41C22×D6711yescharacteristic
429C22×D4—23no—
430C22×D4—673no—
431C22×D4—1343no—
432C22×D4C22×D6713yes—
433C23×C4—23no—
434C23×C4—1343no—
435AGL(1,ℤ/8)—6724no—
436AGL(1,ℤ/8)—6724no—
437#135—6724no—
438C2×Q16—671no—
439C2×SD16—673no—
440C2×SD16—673no—
441C2×D8—6724no—
442C2×D8—673no—
443C2×D8—676no—
444#131—678no—
445#131—1344no—
446C2×M16—673no—
447C2×M16—673no—
448C22×C8—673no—
449C22×C8—673no—
450C4×Q8—21no—
451C4×Q8—671no—
452C4×Q8—673no—
453C4×Q8—1341no—
454C4×Q8C22⋊D6711yescharacteristic
455C4×Q8C22⋊D6711yescharacteristic
456C4×Q8C22×D6711yescharacteristic
457C4×Q8C22×D6713yes—
458C4×D4—23no—
459C4×D4—23no—
460C4×D4—23no—
461C4×D4—23no—
462C4×D4—23no—
463C4×D4—26no—
464C4×D4—23no—
465C4×D4—23no—
466C4×D4—673no—
467C4×D4—676no—
468C4×D4—673no—
469C4×D4—1343no—
470C4×D4—1343no—
471C4×D4—1343no—
472C4×D4—1343no—
473C4×D4—1343no—
474C4×D4—1346no—
475C4×D4—1343no—
476C4×D4—1343no—
477C4×D4C22⋊D6713yes—
478C4×D4C22⋊D6713yes—
479C4×D4C22×D6713yes—
480C4×D4C22×D6716yes—
481C4×D4C22×D6713yes—
482#117—23no—
483#117—23no—
484#117—673no—
485#117—1343no—
486#117—1343no—
487#117C22×D6713yes—
488#117C22×D6713yes—
489C2×C4⋊C4—23no—
490C2×C4⋊C4—673no—
491C2×C4⋊C4—1343no—
492C2×C4⋊C4C22×D6713yes—
493C2×C22⋊C4—23no—
494C2×C22⋊C4—26no—
495C2×C22⋊C4—1343no—
496C2×C22⋊C4—1346no—
497C2×C42—23no—
498C2×C42—1343no—
499C2×C42C22×D6713yes—
500#107—673no—
501#107—673no—
502#106—673no—
503#106—676no—
504#106—671no—
505#103—671no—
506#103—673no—
507#103—671no—
508#103—673no—
509#102—673no—
510#102—676no—
511#102—673no—
512#102—673no—
513#102—676no—
514#102—673no—
515#97—671no—
516#97—673no—
517#97—673no—
518#97—673no—
519C4×C8—676no—
520C24—23no—
521C24—1343no—
522#41—28no—
523#41—26no—
524#41—6712no—
525#41—1348no—
526#41—1346no—
527#41C2×C4×D6714yes—
528#41C2×C4×D67112yescomplemented
529#41#1176162814yes—
530C2×Q8—671no—
531C2×Q8C2×C22⋊D6711yescharacteristic
532C2×Q8C23×D6711yescharacteristic
533C2×D4—23no—
534C2×D4—224no—
535C2×D4—23no—
536C2×D4—26no—
537C2×D4—6712no—
538C2×D4—673no—
539C2×D4—1343no—
540C2×D4—13424no—
541C2×D4—1343no—
542C2×D4—1346no—
543C2×D4C2×C4×D67112yescomplemented
544C2×D4C2×C22⋊D6713yes—
545C2×D4C23×D6713yes—
546C22×C4—23no—
547C22×C4—23no—
548C22×C4—23no—
549C22×C4—23no—
550C22×C4—26no—
551C22×C4—86no—
552C22×C4—5366no—
553C22×C4—1343no—
554C22×C4—1343no—
555C22×C4—1343no—
556C22×C4—1346no—
557C22×C4—1343no—
558C22×C4C2×C22⋊D6713yes—
559C22×C4C2×C22⋊D6713yes—
560C22×C4C23×D6713yes—
561Q16—674no—
562SD16—6712no—
563SD16—6712no—
564D8—6712no—
565D8—6724no—
566M16—6712no—
567M16—1346no—
568C2×C8—6712no—
569C2×C8—673no—
570C2×C8—671no—
571C2×C8—673no—
572C2×C8—671no—
573C2×C8—1346no—
574C4⋊C4—23no—
575C4⋊C4—23no—
576C4⋊C4—21no—
577C4⋊C4—673no—
578C4⋊C4—671no—
579C4⋊C4—1343no—
580C4⋊C4—1343no—
581C4⋊C4—1341no—
582C4⋊C4C2×C22⋊D6713yes—
583C4⋊C4C2×C22⋊D6713yes—
584C4⋊C4C23×D6713yes—
585C4⋊C4C23×D6711yescharacteristic
586C22⋊C4—23no—
587C22⋊C4—23no—
588C22⋊C4—26no—
589C22⋊C4—23no—
590C22⋊C4—1343no—
591C22⋊C4—1343no—
592C22⋊C4—1343no—
593C22⋊C4—1346no—
594C22⋊C4C2×C22⋊D6716yes—
595C42—21no—
596C42—23no—
597C42—23no—
598C42—1341no—
599C42—1343no—
600C42—1343no—
601C42C2×C22⋊D6713yes—
602C42C2×C22⋊D6713yes—
603C42C23×D6713yes—
604C42C23×D6711yescharacteristic
605C23—23no—
606C23—212no—
607C23—83no—
608C23—83no—
609C23—5363no—
610C23—5363no—
611C23—1343no—
612C23—13412no—
613C23C22×C22⋊D6713yes—
614Q8—21no—
615Q8—672no—
616Q8—1341no—
617Q8C4×C22⋊D6714yes—
618Q8C22×C4×D6712yes—
619D4—212no—
620D4—212no—
621D4—23no—
622D4—676no—
623D4—13412no—
624D4—13412no—
625D4—1343no—
626D4C4×C22⋊D67112yes—
627D4C22×C4×D6716yes—
628C2×C4—21no—
629C2×C4—212no—
630C2×C4—21no—
631C2×C4—23no—
632C2×C4—43no—
633C2×C4—43no—
634C2×C4—46no—
635C2×C4—86no—
636C2×C4—83no—
637C2×C4—83no—
638C2×C4—2686no—
639C2×C4—5366no—
640C2×C4—5363no—
641C2×C4—5363no—
642C2×C4—1341no—
643C2×C4—1343no—
644C2×C4—1341no—
645C2×C4—13412no—
646C2×C4C22×C4×D6716yes—
647C2×C4C22×C22⋊D6711yescharacteristic
648C2×C4C22×C22⋊D6713yes—
649C2×C4C22×C22⋊D6711yescharacteristic
650C2×C4C22×C22⋊D6713yes—
651C2×C4C22×C22⋊D6713yes—
652C2×C4C2×#1176162816yes—
653C2×C4C24×D6711yescharacteristic
654C8—672no—
655C8—676no—
656C8—1341no—
657C8—1343no—
658C22—23no—
659C22—23no—
660C22—26no—
661C22—43no—
662C22—43no—
663C22—812no—
664C22—2683no—
665C22—2683no—
666C22—53612no—
667C22—1346no—
668C22C2×C4×C22⋊D6716yes—
669C22C23×C22⋊D6711yescharacteristic
670C4—22no—
671C4—21no—
672C4—23no—
673C4—21no—
674C4—23no—
675C4—41no—
676C4—43no—
677C4—2683no—
678C4—2681no—
679C4—1342no—
680C4C2×C4×C22⋊D6716yes—
681C4C23×C4×D6711yescharacteristic
682C4C22×#1176162811yescharacteristic
683C2—26no—
684C2—46no—
685C2—2686no—
686C2C22×C4×C22⋊D6711yescharacteristic
687C2#2257498811yescharacteristic
688C2#2257498911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D67
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
FittingC4×H(5,𝔽2)×C67C2
socleC22×C67C23×D4
prime radicalC2×#16864199C2
cosocleC2×C4×C67C25
hypercenterC4×H(5,𝔽2)D67
hypocenterC67#60176
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C4×#41 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
2. C4×#14524089C2semidirect
3. #22569090C2semidirect
4. #22569059C2semidirect
5. #22569041C2semidirect
6. #22569037C2semidirect
7. C4×#14524069C2semidirect
8. C4×#14524068C2semidirect
9. #22569007C2semidirect
10. C2×#16863506C2semidirect
11. #22568802C2semidirect
12. #22568735C2semidirect
13. #22568732C2semidirect
14. #22568637C2semidirect
15. C4×H(5,𝔽2)×C67C2semidirect
17. #16864199C4semidirect
26. #16863876C22semidirect
27. #16863870C22semidirect
30. C4×#11761628C22semidirect
31. C2×C4×D268C22semidirect
33. #16863506C22semidirect
34. #16863506C22semidirect
35. #16863506C22semidirect
36. #16863506C22semidirect
37. #16863506C22semidirect
38. #16863501C22semidirect
39. #16863501C22semidirect
40. #16863496C22semidirect
41. #16863496C22semidirect
42. #16863494C22semidirect
43. #16863494C22semidirect
44. C4×#11761615C22semidirect
45. C4×#11761616C22semidirect
46. C4×#11761613C22semidirect
47. C4×#11761613C22semidirect
48. #16863439C22semidirect
49. #16863436C22semidirect
50. #16863432C22semidirect
51. C2×#14523974C22semidirect
52. #16863401C22semidirect
53. #16863400C22semidirect
54. #16863397C22semidirect
55. #16863395C22semidirect
56. #16863392C22semidirect
57. #16863390C22semidirect
58. C2×#14523964C22semidirect
59. C2×#14523963C22semidirect
60. #16863352C22semidirect
61. #16863352C22semidirect
62. C4×#11761612C22semidirect
63. C2×#14523954C22semidirect
67. #520×C67C22semidirect
69. #518×C67C22semidirect
72. C4×#41×C67C22semidirect
74. C2×C4×D4×C67C22semidirect
76. #14524089C2×C4semidirect
82. #14524069C2×C4semidirect
83. #14524068C2×C4semidirect
84. #14524063C2×C4semidirect
88. C2×#11761613C2×C4semidirect
92. #14524050C2×C4semidirect
140. H(5,𝔽2)×C67C2×C4semidirect
178. #11761628C22×C4semidirect
182. C2×D268C22×C4semidirect
192. #11761618C22×C4semidirect
193. #11761616C22×C4semidirect
194. #11761615C22×C4semidirect
195. #11761613C22×C4semidirect
196. #11761613C22×C4semidirect
198. #11761612C22×C4semidirect
200. C2×C67⋊C8C22×C4semidirect
221. #41×C67C22×C4semidirect
229. C2×D4×C67C22×C4semidirect
347. C4×H(5,𝔽2)D67semidirect
360. C67#60176semidirect
375. #520C2×D67semidirect
379. #518C2×D67semidirect
384. C4×#41C2×D67semidirect
388. C2×C4×D4C2×D67semidirect
423. H(5,𝔽2)C4×D67semidirect
528. #41C2×C4×D67semidirect
543. C2×D4C2×C4×D67semidirect

Maximal subgroups

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

subgroupindex
C2×#168641992
C4×#145240892
#225690902
#225690592
#225690412
#225690372
C4×#145240692
C4×#145240682
#225690072
C2×#168635062
#225688022
#225687352
#225687322
#225686372
C4×H(5,𝔽2)×C672
#6017667