Finite Group Databasebeta

← #32861732

Subgroups — #32861732

Order 18176.

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×#17986802C211yesmaximal, characteristic
2C4×#14556174C211yesmaximal, characteristic, complemented
3#22597221C213yesmaximal, complemented
4#22597190C213yesmaximal, complemented
5#22597172C213yesmaximal, complemented
6#22597168C213yesmaximal, complemented
7C4×#14556154C213yesmaximal, complemented
8C4×#14556153C213yesmaximal, complemented
9#22597138C213yesmaximal, complemented
10C2×#17986109C213yesmaximal, complemented
11#22596933C211yesmaximal, characteristic, complemented
12#22596866C211yesmaximal, characteristic, complemented
13#22596863C211yesmaximal, characteristic, complemented
14#22596768C211yesmaximal, characteristic, complemented
15C4×H(5,𝔽2)×C71C211yesmaximal, characteristic, complemented
16C2×#14556174C2211yescharacteristic
17#17986802C4116yescomplemented
18C2×#14556154C2213yes—
19C2×#14556153C2213yes—
20C2×#14556148C2213yes—
21C22×#11765850C2213yes—
22C2×#14556135C2211yescharacteristic
23C2×#14556135C2211yescharacteristic
24#17986482C2211yescharacteristic
25#17986481—21no—
26#17986479C2213yescomplemented
27#17986473C2213yescomplemented
28#17986471—23no—
29C4×#11765866—21no—
30C4×#11765865C2213yescomplemented
31C2×C4×D284C2213yescomplemented
32C4×D4×D71—23no—
33#17986109C2213yescomplemented
34#17986109C2216yescomplemented
35#17986109C2216yescomplemented
36#17986109C2216yescomplemented
37#17986109C2213yescomplemented
38#17986104C2211yescharacteristic, complemented
39#17986104C2213yescomplemented
40#17986099C2213yescomplemented
41#17986099C2213yescomplemented
42#17986097C2213yescomplemented
43#17986097C2213yescomplemented
44C4×#11765852C2216yescomplemented
45C4×#11765853C2216yescomplemented
46C4×#11765850C2216yescomplemented
47C4×#11765850C2216yescomplemented
48#17986042C2213yescomplemented
49#17986039C2213yescomplemented
50#17986035C2213yescomplemented
51C2×#14556059C2213yescomplemented
52#17986004C2213yescomplemented
53#17986003C2213yescomplemented
54#17986000C2213yescomplemented
55#17985998C2213yescomplemented
56#17985995C2213yescomplemented
57#17985993C2213yescomplemented
58C2×#14556049C2213yescomplemented
59C2×#14556048C2213yescomplemented
60#17985955C2213yescomplemented
61#17985955C2213yescomplemented
62C4×#11765849C2213yescomplemented
63C2×#14556039C2213yescomplemented
64C2×H(5,𝔽2)×C71C2211yescharacteristic
65#520×C71—21no—
66#520×C71C2211yescharacteristic
67#520×C71C2213yescomplemented
68#518×C71—23no—
69#518×C71C2213yescomplemented
70C4×#41×C71—21no—
71C4×#41×C71C2211yescharacteristic
72C4×#41×C71C2213yescomplemented
73C2×C4×D4×C71—23no—
74C2×C4×D4×C71C2213yescomplemented
75#14556174—24no—
76#14556174C2×C418yescomplemented
77C2×#11765866—21no—
78C2×#11765865C2313yes—
79C22×D284C2313yes—
80C2×D4×D71—23no—
81C22×C4×D71—23no—
82#14556154C2×C4124yescomplemented
83#14556153C2×C4124yescomplemented
84#14556148C2×C4124yescomplemented
85C2×#11765855C2311yescharacteristic
86C2×#11765853C2313yes—
87C2×#11765852C2313yes—
88C2×#11765850C2×C4124yescomplemented
89C2×#11765850C2316yes—
90C2×#11765850C2313yes—
91#14556135—24no—
92#14556135C2×C418yescomplemented
93C2×#11765849C2313yes—
94C2×#11765849C2313yes—
95C22×C71⋊C8C2313yes—
96C22×C71⋊C8C2313yes—
97Q8×Dic71—21no—
98C4×Dic142C2313yes—
99C4×Dic142C2311yescharacteristic
100C4×D284—23no—
101C4×D284—23no—
102C4×D284C2313yes—
103C4×D284C2316yes—
104C4×D284C2313yes—
105D4×Dic71—23no—
106#14556090—23no—
107#14556090—23no—
108C4×C22⋊D71—23no—
109C4×C22⋊D71—23no—
110(C22⋊D71)⋊C4—26no—
111#14556087C2313yes—
112#14556086—23no—
113#14556085—23no—
114C2×C4⋊Dic71C2313yes—
115C4⋊C4×D71—23no—
116C2×(C2×D71)⋊C4—23no—
117C22⋊C4×D71—26no—
118C42×D71—23no—
119#14556061C2313yes—
120#14556061C2313yes—
121#14556059C2316yes—
122#14556059C2313yes—
123#14556059C2311yescharacteristic
124#14556052C2313yes—
125#14556052C2311yescharacteristic
126#14556051C2313yes—
127#14556051C2311yescharacteristic
128#14556049C2313yes—
129#14556049C2316yes—
130#14556049C2313yes—
131#14556048C2313yes—
132#14556048C2316yes—
133#14556048C2313yes—
134#14556039C2313yes—
135#14556039C2313yes—
136#14556039C2311yescharacteristic
137#14556039C2313yes—
138C4×C71⋊C8C2316yes—
139H(5,𝔽2)×C71—24no—
140H(5,𝔽2)×C71C2×C418yescomplemented
141C2×#41×C71—21no—
142C2×#41×C71C2313yes—
143C2×#41×C71C2311yescharacteristic
144C22×D4×C71—23no—
145C22×D4×C71C2313yes—
146C23×C4×C71—23no—
147C4×Q8×C71—21no—
148C4×Q8×C71D411yescharacteristic
149C4×Q8×C71D411yescharacteristic
150C4×Q8×C71C2313yes—
151C4×Q8×C71C2311yescharacteristic
152C4×D4×C71—23no—
153C4×D4×C71—23no—
154C4×D4×C71—23no—
155C4×D4×C71—23no—
156C4×D4×C71—23no—
157C4×D4×C71—26no—
158C4×D4×C71—23no—
159C4×D4×C71—23no—
160C4×D4×C71D413yes—
161C4×D4×C71D413yes—
162C4×D4×C71C2313yes—
163C4×D4×C71C2316yes—
164C4×D4×C71C2313yes—
165#117×C71—23no—
166#117×C71—23no—
167#117×C71C2313yes—
168#117×C71C2313yes—
169C2×C4⋊C4×C71—23no—
170C2×C4⋊C4×C71C2313yes—
171C2×C22⋊C4×C71—23no—
172C2×C22⋊C4×C71—26no—
173C2×C42×C71—23no—
174C2×C42×C71C2313yes—
175C23×D71—23no—
176#11765866—28no—
177#11765865—26no—
178#11765865C22×C4112yescomplemented
179C2×Dic142C2411yescharacteristic
180C2×D284—23no—
181C2×D284—26no—
182C2×D284C22×C4112yescomplemented
183C2×D284C2413yes—
184C2×C22⋊D71—23no—
185D4×D71—224no—
186C22×Dic71—23no—
187C2×C4×D71—23no—
188C2×C4×D71—23no—
189C2×C4×D71—26no—
190C2×C4×D71—23no—
191C2×C4×D71—86no—
192#11765855C22×C414yescomplemented
193#11765853C22×C4112yescomplemented
194#11765852C22×C4112yescomplemented
195#11765850C22×C4112yescomplemented
196#11765850C22×C4124yescomplemented
197#11765849—26no—
198#11765849C22×C4112yescomplemented
199C2×C71⋊C8—26no—
200C2×C71⋊C8C22×C4112yescomplemented
201C2×C71⋊C8C2413yes—
202C2×C71⋊C8C2411yescharacteristic
203C2×C71⋊C8C2413yes—
204C2×C71⋊C8C2411yescharacteristic
205C4⋊Dic71—23no—
206C4⋊Dic71C2413yes—
207C4⋊Dic71C2411yescharacteristic
208Dic71⋊C4—23no—
209Dic71⋊C4—21no—
210C22⋊Dic71—23no—
211(C2×D71)⋊C4—23no—
212(C2×D71)⋊C4—26no—
213(C2×D71)⋊C4—23no—
214C4×Dic71—21no—
215C4×Dic71—23no—
216C4×Dic71—23no—
217C24×C71—23no—
218#41×C71—28no—
219#41×C71—26no—
220#41×C71C22×C414yes—
221#41×C71C22×C4112yescomplemented
222#41×C71#4114yes—
223C2×Q8×C71C2×D411yescharacteristic
224C2×Q8×C71C2411yescharacteristic
225C2×D4×C71—23no—
226C2×D4×C71—224no—
227C2×D4×C71—23no—
228C2×D4×C71—26no—
229C2×D4×C71C22×C4112yescomplemented
230C2×D4×C71C2×D413yes—
231C2×D4×C71C2413yes—
232C22×C4×C71—23no—
233C22×C4×C71—23no—
234C22×C4×C71—23no—
235C22×C4×C71—23no—
236C22×C4×C71—26no—
237C22×C4×C71—86no—
238C22×C4×C71C2×D413yes—
239C22×C4×C71C2×D413yes—
240C22×C4×C71C2413yes—
241C4⋊C4×C71—23no—
242C4⋊C4×C71—23no—
243C4⋊C4×C71—21no—
244C4⋊C4×C71C2×D413yes—
245C4⋊C4×C71C2×D413yes—
246C4⋊C4×C71C2413yes—
247C4⋊C4×C71C2411yescharacteristic
248C22⋊C4×C71—23no—
249C22⋊C4×C71—23no—
250C22⋊C4×C71—26no—
251C22⋊C4×C71—23no—
252C22⋊C4×C71C2×D416yes—
253C42×C71—21no—
254C42×C71—23no—
255C42×C71—23no—
256C42×C71C2×D413yes—
257C42×C71C2×D413yes—
258C42×C71C2411yescharacteristic
259C42×C71C2413yes—
260C23×C71—23no—
261C23×C71—212no—
262C23×C71—83no—
263C23×C71—83no—
264C23×C71C22×D413yes—
265C22×D71—23no—
266C22×D71—212no—
267C22×D71—83no—
268C22×D71—83no—
269Q8×C71—21no—
270Q8×C71C4×D414yes—
271Q8×C71C23×C412yes—
272D4×C71—212no—
273D4×C71—212no—
274D4×C71—23no—
275D4×C71C4×D4112yes—
276D4×C71C23×C416yes—
277C2×C4×C71—21no—
278C2×C4×C71—212no—
279C2×C4×C71—21no—
280C2×C4×C71—23no—
281C2×C4×C71—43no—
282C2×C4×C71—43no—
283C2×C4×C71—46no—
284C2×C4×C71—83no—
285C2×C4×C71—86no—
286C2×C4×C71—83no—
287C2×C4×C71C23×C416yes—
288C2×C4×C71C22×D411yescharacteristic
289C2×C4×C71C22×D413yes—
290C2×C4×C71C22×D411yescharacteristic
291C2×C4×C71C22×D413yes—
292C2×C4×C71C22×D413yes—
293C2×C4×C71C2×#4116yes—
294C2×C4×C71C2511yescharacteristic
295C22⋊D71—212no—
296C2×Dic71—21no—
297C2×Dic71—21no—
298C2×Dic71—23no—
299C2×Dic71—83no—
300D284—212no—
301D284—23no—
302D284C23×C416yes—
303C4×D71—212no—
304C4×D71—46no—
305C4×D71—83no—
306C4×D71—86no—
307Dic142—21no—
308Dic142C23×C412yes—
309C71⋊C8—21no—
310C71⋊C8—23no—
311C71⋊C8C23×C412yes—
312C71⋊C8C23×C416yes—
313C22×C71—23no—
314C22×C71—23no—
315C22×C71—26no—
316C22×C71—43no—
317C22×C71—43no—
318C22×C71—812no—
319C22×C71C2×C4×D416yes—
320C22×C71C23×D411yescharacteristic
321C2×D71—26no—
322C2×D71—43no—
323C2×D71—43no—
324C2×D71—812no—
325C4×C71—21no—
326C4×C71—23no—
327C4×C71—23no—
328C4×C71—21no—
329C4×C71—22no—
330C4×C71—43no—
331C4×C71—41no—
332C4×C71C2×C4×D416yes—
333C4×C71C24×C411yescharacteristic
334C4×C71C22×#4111yescharacteristic
335Dic71—22no—
336Dic71—43no—
337Dic71—41no—
338#60176—711nomaximal, Sylow
339C2×C71—26no—
340C2×C71—46no—
341C2×C71C22×C4×D411yescharacteristic
342C2×C71#358511yescharacteristic
343C2×C71#358511yescharacteristic
344D71—46no—
345C2×#576—711no—
346C4×H(5,𝔽2)—711no—
347C4×H(5,𝔽2)D7111yescharacteristic, complemented
348#2952—713no—
349#2948—713no—
350#2946—713no—
351#2946—713no—
352C4×AGL(1,ℤ/8)—713no—
353C4×AGL(1,ℤ/8)—713no—
354#2943—713no—
355C2×#442—713no—
356#2912—711no—
357#2897—711no—
358#2897—711no—
359#2875—711no—
360C71#6017611yescharacteristic, complemented, Sylow
361C2×H(5,𝔽2)—711no—
362C2×H(5,𝔽2)C2×D7111yescharacteristic
363#576—7116no—
364C2×AGL(1,ℤ/8)—713no—
365C2×AGL(1,ℤ/8)—713no—
366C2×#135—713no—
367C22×D8—713no—
368C2×#131—711no—
369C2×#131—711no—
370#520—21no—
371#520—711no—
372#520—713no—
373#520—1421no—
374#520C2×D7111yescharacteristic
375#520C2×D7113yescomplemented
376#518—23no—
377#518—713no—
378#518—1423no—
379#518C2×D7113yescomplemented
380C4×#41—21no—
381C4×#41—713no—
382C4×#41—1421no—
383C4×#41C2×D7111yescharacteristic
384C4×#41C2×D7113yescomplemented
385C2×C4×D4—23no—
386C2×C4×D4—713no—
387C2×C4×D4—1423no—
388C2×C4×D4C2×D7113yescomplemented
389#442—713no—
390#442—716no—
391#442—716no—
392#442—716no—
393#442—713no—
394#441—711no—
395#441—713no—
396#440—713no—
397#440—713no—
398#440—713no—
399#440—713no—
400C4×SD16—716no—
401C4×SD16—716no—
402C4×D8—716no—
403C4×D8—716no—
404#428—713no—
405#428—713no—
406#427—713no—
407C2×#106—713no—
408#418—713no—
409#418—713no—
410#417—713no—
411#417—713no—
412#416—713no—
413#416—713no—
414C2×#102—713no—
415C2×#102—713no—
416#405—713no—
417#405—713no—
418C4×M16—713no—
419C2×#97—713no—
420H(5,𝔽2)—24no—
421H(5,𝔽2)—718no—
422H(5,𝔽2)—1424no—
423H(5,𝔽2)C4×D7118yescomplemented
424C2×#41—21no—
425C2×#41—713no—
426C2×#41—1421no—
427C2×#41C22×D7113yes—
428C2×#41C22×D7111yescharacteristic
429C22×D4—23no—
430C22×D4—713no—
431C22×D4—1423no—
432C22×D4C22×D7113yes—
433C23×C4—23no—
434C23×C4—1423no—
435AGL(1,ℤ/8)—7124no—
436AGL(1,ℤ/8)—7124no—
437#135—7124no—
438C2×Q16—711no—
439C2×SD16—713no—
440C2×SD16—713no—
441C2×D8—7124no—
442C2×D8—713no—
443C2×D8—716no—
444#131—718no—
445#131—1424no—
446C2×M16—713no—
447C2×M16—713no—
448C22×C8—713no—
449C22×C8—713no—
450C4×Q8—21no—
451C4×Q8—711no—
452C4×Q8—713no—
453C4×Q8—1421no—
454C4×Q8C22⋊D7111yescharacteristic
455C4×Q8C22⋊D7111yescharacteristic
456C4×Q8C22×D7111yescharacteristic
457C4×Q8C22×D7113yes—
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—713no—
467C4×D4—716no—
468C4×D4—713no—
469C4×D4—1423no—
470C4×D4—1423no—
471C4×D4—1423no—
472C4×D4—1423no—
473C4×D4—1423no—
474C4×D4—1426no—
475C4×D4—1423no—
476C4×D4—1423no—
477C4×D4C22⋊D7113yes—
478C4×D4C22⋊D7113yes—
479C4×D4C22×D7113yes—
480C4×D4C22×D7116yes—
481C4×D4C22×D7113yes—
482#117—23no—
483#117—23no—
484#117—713no—
485#117—1423no—
486#117—1423no—
487#117C22×D7113yes—
488#117C22×D7113yes—
489C2×C4⋊C4—23no—
490C2×C4⋊C4—713no—
491C2×C4⋊C4—1423no—
492C2×C4⋊C4C22×D7113yes—
493C2×C22⋊C4—23no—
494C2×C22⋊C4—26no—
495C2×C22⋊C4—1423no—
496C2×C22⋊C4—1426no—
497C2×C42—23no—
498C2×C42—1423no—
499C2×C42C22×D7113yes—
500#107—713no—
501#107—713no—
502#106—713no—
503#106—716no—
504#106—711no—
505#103—711no—
506#103—713no—
507#103—711no—
508#103—713no—
509#102—713no—
510#102—716no—
511#102—713no—
512#102—713no—
513#102—716no—
514#102—713no—
515#97—711no—
516#97—713no—
517#97—713no—
518#97—713no—
519C4×C8—716no—
520C24—23no—
521C24—1423no—
522#41—28no—
523#41—26no—
524#41—7112no—
525#41—1428no—
526#41—1426no—
527#41C2×C4×D7114yes—
528#41C2×C4×D71112yescomplemented
529#41#1176586514yes—
530C2×Q8—711no—
531C2×Q8C2×C22⋊D7111yescharacteristic
532C2×Q8C23×D7111yescharacteristic
533C2×D4—23no—
534C2×D4—224no—
535C2×D4—23no—
536C2×D4—26no—
537C2×D4—7112no—
538C2×D4—713no—
539C2×D4—1423no—
540C2×D4—14224no—
541C2×D4—1423no—
542C2×D4—1426no—
543C2×D4C2×C4×D71112yescomplemented
544C2×D4C2×C22⋊D7113yes—
545C2×D4C23×D7113yes—
546C22×C4—23no—
547C22×C4—23no—
548C22×C4—23no—
549C22×C4—23no—
550C22×C4—26no—
551C22×C4—86no—
552C22×C4—5686no—
553C22×C4—1423no—
554C22×C4—1423no—
555C22×C4—1423no—
556C22×C4—1426no—
557C22×C4—1423no—
558C22×C4C2×C22⋊D7113yes—
559C22×C4C2×C22⋊D7113yes—
560C22×C4C23×D7113yes—
561Q16—714no—
562SD16—7112no—
563SD16—7112no—
564D8—7112no—
565D8—7124no—
566M16—7112no—
567M16—1426no—
568C2×C8—7112no—
569C2×C8—713no—
570C2×C8—711no—
571C2×C8—713no—
572C2×C8—711no—
573C2×C8—1426no—
574C4⋊C4—23no—
575C4⋊C4—23no—
576C4⋊C4—21no—
577C4⋊C4—713no—
578C4⋊C4—711no—
579C4⋊C4—1423no—
580C4⋊C4—1421no—
581C4⋊C4—1423no—
582C4⋊C4C2×C22⋊D7113yes—
583C4⋊C4C2×C22⋊D7113yes—
584C4⋊C4C23×D7113yes—
585C4⋊C4C23×D7111yescharacteristic
586C22⋊C4—23no—
587C22⋊C4—23no—
588C22⋊C4—26no—
589C22⋊C4—23no—
590C22⋊C4—1423no—
591C22⋊C4—1423no—
592C22⋊C4—1423no—
593C22⋊C4—1426no—
594C22⋊C4C2×C22⋊D7116yes—
595C42—21no—
596C42—23no—
597C42—23no—
598C42—1421no—
599C42—1423no—
600C42—1423no—
601C42C2×C22⋊D7113yes—
602C42C2×C22⋊D7113yes—
603C42C23×D7113yes—
604C42C23×D7111yescharacteristic
605C23—23no—
606C23—212no—
607C23—83no—
608C23—83no—
609C23—5683no—
610C23—5683no—
611C23—1423no—
612C23—14212no—
613C23C22×C22⋊D7113yes—
614Q8—21no—
615Q8—712no—
616Q8—1421no—
617Q8C4×C22⋊D7114yes—
618Q8C22×C4×D7112yes—
619D4—212no—
620D4—23no—
621D4—212no—
622D4—716no—
623D4—14212no—
624D4—1423no—
625D4—14212no—
626D4C4×C22⋊D71112yes—
627D4C22×C4×D7116yes—
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—2846no—
639C2×C4—5686no—
640C2×C4—5683no—
641C2×C4—5683no—
642C2×C4—1421no—
643C2×C4—1423no—
644C2×C4—1421no—
645C2×C4—14212no—
646C2×C4C22×C4×D7116yes—
647C2×C4C22×C22⋊D7111yescharacteristic
648C2×C4C22×C22⋊D7113yes—
649C2×C4C22×C22⋊D7111yescharacteristic
650C2×C4C22×C22⋊D7113yes—
651C2×C4C22×C22⋊D7113yes—
652C2×C4C2×#1176586516yes—
653C2×C4C24×D7111yescharacteristic
654C8—712no—
655C8—716no—
656C8—1421no—
657C8—1423no—
658C22—23no—
659C22—23no—
660C22—26no—
661C22—43no—
662C22—43no—
663C22—812no—
664C22—2843no—
665C22—2843no—
666C22—56812no—
667C22—1426no—
668C22C2×C4×C22⋊D7116yes—
669C22C23×C22⋊D7111yescharacteristic
670C4—22no—
671C4—21no—
672C4—23no—
673C4—21no—
674C4—23no—
675C4—41no—
676C4—43no—
677C4—2843no—
678C4—2841no—
679C4—1422no—
680C4C2×C4×C22⋊D7116yes—
681C4C23×C4×D7111yescharacteristic
682C4C22×#1176586511yescharacteristic
683C2—26no—
684C2—46no—
685C2—2846no—
686C2C22×C4×C22⋊D7111yescharacteristic
687C2#2260311911yescharacteristic
688C2#2260312011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D71
commutatorC4×C71C24×C4
FrattiniC2×C4C24×D71
FittingC4×H(5,𝔽2)×C71C2
socleC22×C71C23×D4
prime radicalC2×#17986802C2
cosocleC2×C4×C71C25
hypercenterC4×H(5,𝔽2)D71
hypocenterC71#60176
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×#41 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
2. C4×#14556174C2semidirect
3. #22597221C2semidirect
4. #22597190C2semidirect
5. #22597172C2semidirect
6. #22597168C2semidirect
7. C4×#14556154C2semidirect
8. C4×#14556153C2semidirect
9. #22597138C2semidirect
10. C2×#17986109C2semidirect
11. #22596933C2semidirect
12. #22596866C2semidirect
13. #22596863C2semidirect
14. #22596768C2semidirect
15. C4×H(5,𝔽2)×C71C2semidirect
17. #17986802C4semidirect
26. #17986479C22semidirect
27. #17986473C22semidirect
30. C4×#11765865C22semidirect
31. C2×C4×D284C22semidirect
33. #17986109C22semidirect
34. #17986109C22semidirect
35. #17986109C22semidirect
36. #17986109C22semidirect
37. #17986109C22semidirect
38. #17986104C22semidirect
39. #17986104C22semidirect
40. #17986099C22semidirect
41. #17986099C22semidirect
42. #17986097C22semidirect
43. #17986097C22semidirect
44. C4×#11765852C22semidirect
45. C4×#11765853C22semidirect
46. C4×#11765850C22semidirect
47. C4×#11765850C22semidirect
48. #17986042C22semidirect
49. #17986039C22semidirect
50. #17986035C22semidirect
51. C2×#14556059C22semidirect
52. #17986004C22semidirect
53. #17986003C22semidirect
54. #17986000C22semidirect
55. #17985998C22semidirect
56. #17985995C22semidirect
57. #17985993C22semidirect
58. C2×#14556049C22semidirect
59. C2×#14556048C22semidirect
60. #17985955C22semidirect
61. #17985955C22semidirect
62. C4×#11765849C22semidirect
63. C2×#14556039C22semidirect
67. #520×C71C22semidirect
69. #518×C71C22semidirect
72. C4×#41×C71C22semidirect
74. C2×C4×D4×C71C22semidirect
76. #14556174C2×C4semidirect
82. #14556154C2×C4semidirect
83. #14556153C2×C4semidirect
84. #14556148C2×C4semidirect
88. C2×#11765850C2×C4semidirect
92. #14556135C2×C4semidirect
140. H(5,𝔽2)×C71C2×C4semidirect
178. #11765865C22×C4semidirect
182. C2×D284C22×C4semidirect
192. #11765855C22×C4semidirect
193. #11765853C22×C4semidirect
194. #11765852C22×C4semidirect
195. #11765850C22×C4semidirect
196. #11765850C22×C4semidirect
198. #11765849C22×C4semidirect
200. C2×C71⋊C8C22×C4semidirect
221. #41×C71C22×C4semidirect
229. C2×D4×C71C22×C4semidirect
347. C4×H(5,𝔽2)D71semidirect
360. C71#60176semidirect
375. #520C2×D71semidirect
379. #518C2×D71semidirect
384. C4×#41C2×D71semidirect
388. C2×C4×D4C2×D71semidirect
423. H(5,𝔽2)C4×D71semidirect
528. #41C2×C4×D71semidirect
543. C2×D4C2×C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179868022
C4×#145561742
#225972212
#225971902
#225971722
#225971682
C4×#145561542
C4×#145561532
#225971382
C2×#179861092
#225969332
#225968662
#225968632
#225967682
C4×H(5,𝔽2)×C712
#6017671