Finite Group Databasebeta

← C71×#18418 #31839290

Subgroups — C71×#18418 #31839290

Order 18176.

1176 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71×#3537C211yesmaximal, characteristic, complemented
2C71×#3192C211yesmaximal, characteristic, complemented
3C71×#3188C211yesmaximal, characteristic, complemented
4C71×#2656C211yesmaximal, characteristic, complemented
5C71×#1618C212yesmaximal, complemented
6C71×#1613C212yesmaximal, complemented
7C71×#1600C212yesmaximal, complemented
8C71×#1595C212yesmaximal, complemented
9C71×#1504C211yesmaximal, characteristic, complemented
10C2×#327×C71C211yesmaximal, characteristic, complemented
11C71×#1471C211yesmaximal, characteristic, complemented
12#560×C71—22no—
13#553×C71—21no—
14#553×C71—21no—
15D42×C71—22no—
16D42×C71—21no—
17D42×C71—21no—
18#540×C71—21no—
19#538×C71—21no—
20#538×C71C2212yes—
21#535×C71—21no—
22#534×C71—21no—
23#534×C71C2212yes—
24#525×C71C2211yescharacteristic
25C2×#121×C71—22no—
26C2×#121×C71C2211yescharacteristic
27C2×#121×C71C2211yescharacteristic
28C2×#121×C71C2211yescharacteristic, complemented
29#484×C71C2211yescharacteristic, complemented
30#482×C71—21no—
31#481×C71—21no—
32#481×C71C2211yescharacteristic, complemented
33#481×C71C2212yescomplemented
34#469×C71—22no—
35#466×C71—21no—
36#465×C71—21no—
37#450×C71C2211yescharacteristic, complemented
38#449×C71—21no—
39#447×C71—21no—
40#447×C71C2211yescharacteristic, complemented
41#447×C71C2212yescomplemented
42#407×C71C2211yescharacteristic, complemented
43C2×C22⋊C8×C71C2211yescharacteristic, complemented
44#399×C71—21no—
45#399×C71C2212yescomplemented
46#392×C71—21no—
47#392×C71C2212yescomplemented
48C2×#95×C71C2211yescharacteristic, complemented
49#328×C71C2212yescomplemented
50#327×C71C2212yescomplemented
51#327×C71C2212yescomplemented
52#327×C71C2212yescomplemented
53#323×C71C2212yescomplemented
54#323×C71C2212yescomplemented
55C2×#41×C71D411yescharacteristic, complemented
56C22×D4×C71—22no—
57C22×D4×C71—21no—
58C22×D4×C71—21no—
59C22×D4×C71—22no—
60C22×D4×C71—21no—
61C22×D4×C71—22no—
62C22×D4×C71D412yes—
63C22×D4×C71D411yescharacteristic
64C22×D4×C71D411yescharacteristic, complemented
65C22×D4×C71C2311yescharacteristic
66C23×C4×C71—21no—
67C23×C4×C71C2311yescharacteristic
68C2×SD16×C71—21no—
69C2×D8×C71—22no—
70C2×D8×C71—21no—
71C2×M16×C71—21no—
72C22×C8×C71—21no—
73#127×C71—22no—
74#127×C71—21no—
75#126×C71—22no—
76#126×C71—22no—
77#125×C71—21no—
78#124×C71—22no—
79#123×C71—22no—
80#123×C71—21no—
81#123×C71—22no—
82#123×C71—22no—
83#123×C71—22no—
84C22⋊Q8×C71D411yescharacteristic, complemented
85C22⋊Q8×C71C2311yescharacteristic
86#121×C71—22no—
87#121×C71—21no—
88#121×C71—21no—
89#121×C71—22no—
90#121×C71—22no—
91#121×C71—22no—
92#121×C71—22no—
93#121×C71—21no—
94#121×C71—21no—
95#121×C71—21no—
96#121×C71—21no—
97#121×C71—21no—
98#121×C71—21no—
99#121×C71—22no—
100#121×C71—21no—
101#121×C71—21no—
102#121×C71—21no—
103#121×C71—21no—
104#121×C71—48no—
105#121×C71D411yescharacteristic, complemented
106#121×C71D412yescomplemented
107#121×C71C2312yes—
108#121×C71C2311yescharacteristic
109#120×C71—22no—
110#120×C71—22no—
111#120×C71—22no—
112#120×C71—21no—
113#120×C71—22no—
114#120×C71—22no—
115#120×C71—22no—
116C4×D4×C71—22no—
117C4×D4×C71—21no—
118C4×D4×C71—21no—
119C4×D4×C71—21no—
120C4×D4×C71—21no—
121C4×D4×C71—22no—
122#117×C71—21no—
123#117×C71D411yescharacteristic, complemented
124C2×C4⋊C4×C71—22no—
125C2×C4⋊C4×C71D411yescharacteristic
126C2×C4⋊C4×C71D411yescharacteristic, complemented
127C2×C4⋊C4×C71C2311yescharacteristic
128C2×C22⋊C4×C71—21no—
129C2×C22⋊C4×C71—22no—
130C2×C22⋊C4×C71—22no—
131C2×C22⋊C4×C71—21no—
132C2×C22⋊C4×C71C2312yes—
133#107×C71—21no—
134#106×C71—21no—
135#106×C71—22no—
136#103×C71—21no—
137#102×C71—22no—
138#102×C71—21no—
139#102×C71—21no—
140#102×C71—22no—
141#102×C71—21no—
142C22⋊C8×C71—21no—
143C22⋊C8×C71—21no—
144C22⋊C8×C71C2311yescharacteristic
145C22⋊C8×C71C2311yescharacteristic
146C22⋊C8×C71C2312yes—
147#95×C71—21no—
148#95×C71C2312yes—
149C24×C71—22no—
150C24×C71—21no—
151C24×C71—21no—
152C24×C71C2×D411yescharacteristic
153C24×C71C2×D412yes—
154#41×C71—81no—
155C2×Q8×C71C2×D411yescharacteristic
156C2×D4×C71—22no—
157C2×D4×C71—21no—
158C2×D4×C71—21no—
159C2×D4×C71—22no—
160C2×D4×C71—22no—
161C2×D4×C71—22no—
162C2×D4×C71—22no—
163C2×D4×C71—22no—
164C2×D4×C71—22no—
165C2×D4×C71—21no—
166C2×D4×C71—22no—
167C2×D4×C71—22no—
168C2×D4×C71—21no—
169C2×D4×C71—21no—
170C2×D4×C71—21no—
171C2×D4×C71—21no—
172C2×D4×C71—21no—
173C2×D4×C71—44no—
174C2×D4×C71—44no—
175C2×D4×C71—44no—
176C2×D4×C71—41no—
177C2×D4×C71—41no—
178C2×D4×C71—81no—
179C2×D4×C71—81no—
180C2×D4×C71—82no—
181C2×D4×C71—81no—
182C2×D4×C71—82no—
183C2×D4×C71—82no—
184C2×D4×C71—81no—
185C2×D4×C71—81no—
186C2×D4×C71—82no—
187C2×D4×C71—82no—
188C2×D4×C71—84no—
189C2×D4×C71C2×D411yescharacteristic
190C2×D4×C71C2×D412yes—
191C22×C4×C71—22no—
192C22×C4×C71—22no—
193C22×C4×C71—22no—
194C22×C4×C71—24no—
195C22×C4×C71—21no—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—81no—
199C22×C4×C71—81no—
200C22×C4×C71—81no—
201C22×C4×C71C2×D412yes—
202C22×C4×C71C2×D411yescharacteristic
203C22×C4×C71C2×D411yescharacteristic
204C22×C4×C71C2×D411yescharacteristic
205C22×C4×C71C2×D411yescharacteristic
206C22×C4×C71C2×D411yescharacteristic
207C22×C4×C71C2411yescharacteristic
208SD16×C71—81no—
209D8×C71—81no—
210D8×C71—82no—
211M16×C71—81no—
212C2×C8×C71—21no—
213C2×C8×C71—22no—
214C2×C8×C71—21no—
215C2×C8×C71—81no—
216C4⋊C4×C71—22no—
217C4⋊C4×C71—22no—
218C4⋊C4×C71—21no—
219C4⋊C4×C71—21no—
220C4⋊C4×C71—21no—
221C4⋊C4×C71—21no—
222C4⋊C4×C71—21no—
223C4⋊C4×C71—21no—
224C4⋊C4×C71—21no—
225C4⋊C4×C71—44no—
226C4⋊C4×C71C2×D412yes—
227C4⋊C4×C71C2×D411yescharacteristic
228C4⋊C4×C71C2×D411yescharacteristic
229C22⋊C4×C71—22no—
230C22⋊C4×C71—22no—
231C22⋊C4×C71—22no—
232C22⋊C4×C71—22no—
233C22⋊C4×C71—22no—
234C22⋊C4×C71—21no—
235C22⋊C4×C71—21no—
236C22⋊C4×C71—21no—
237C22⋊C4×C71—22no—
238C22⋊C4×C71—21no—
239C22⋊C4×C71—22no—
240C22⋊C4×C71—22no—
241C22⋊C4×C71—22no—
242C22⋊C4×C71—21no—
243C22⋊C4×C71—44no—
244C22⋊C4×C71—44no—
245C22⋊C4×C71—41no—
246C22⋊C4×C71—41no—
247C42×C71—22no—
248C42×C71—21no—
249C23×C71—21no—
250C23×C71—21no—
251C23×C71—22no—
252C23×C71—22no—
253C23×C71—22no—
254C23×C71—21no—
255C23×C71—22no—
256C23×C71—22no—
257C23×C71—41no—
258C23×C71—42no—
259C23×C71—42no—
260C23×C71—42no—
261C23×C71—42no—
262C23×C71—42no—
263C23×C71—41no—
264C23×C71—41no—
265C23×C71—41no—
266C23×C71—81no—
267C23×C71—81no—
268C23×C71—82no—
269C23×C71—82no—
270C23×C71—82no—
271C23×C71#12011yescharacteristic
272C23×C71#12011yescharacteristic
273C23×C71C22×D411yescharacteristic
274Q8×C71—41no—
275D4×C71—42no—
276D4×C71—41no—
277D4×C71—42no—
278D4×C71—42no—
279D4×C71—42no—
280D4×C71—41no—
281D4×C71—41no—
282D4×C71—42no—
283D4×C71—41no—
284D4×C71—42no—
285D4×C71—41no—
286D4×C71—44no—
287D4×C71—42no—
288D4×C71—81no—
289D4×C71—82no—
290D4×C71—82no—
291D4×C71—81no—
292D4×C71—82no—
293D4×C71—82no—
294D4×C71—82no—
295D4×C71—82no—
296D4×C71—82no—
297D4×C71—88no—
298D4×C71—82no—
299D4×C71—82no—
300C2×C4×C71—24no—
301C2×C4×C71—21no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
304C2×C4×C71—21no—
305C2×C4×C71—21no—
306C2×C4×C71—41no—
307C2×C4×C71—41no—
308C2×C4×C71—41no—
309C2×C4×C71—41no—
310C2×C4×C71—41no—
311C2×C4×C71—41no—
312C2×C4×C71—42no—
313C2×C4×C71—42no—
314C2×C4×C71—42no—
315C2×C4×C71—42no—
316C2×C4×C71—42no—
317C2×C4×C71—41no—
318C2×C4×C71—81no—
319C2×C4×C71—84no—
320C2×C4×C71—82no—
321C2×C4×C71—82no—
322C2×C4×C71#12011yescharacteristic
323C2×C4×C71#12011yescharacteristic
324C2×C4×C71C22×D411yescharacteristic
325C2×C4×C71C22×D411yescharacteristic
326C8×C71—41no—
327C8×C71—41no—
328C8×C71—42no—
329C22×C71—21no—
330C22×C71—21no—
331C22×C71—21no—
332C22×C71—21no—
333C22×C71—21no—
334C22×C71—21no—
335C22×C71—21no—
336C22×C71—42no—
337C22×C71—42no—
338C22×C71—42no—
339C22×C71—42no—
340C22×C71—41no—
341C22×C71—42no—
342C22×C71—42no—
343C22×C71—41no—
344C22×C71—41no—
345C22×C71—42no—
346C22×C71—42no—
347C22×C71—82no—
348C22×C71—82no—
349C22×C71—82no—
350C22×C71—82no—
351C22×C71—81no—
352C22×C71—81no—
353C22×C71—81no—
354C22×C71—162no—
355C22×C71—164no—
356C22×C71#45312yes—
357C22×C71C2×#12011yescharacteristic
358C22×C71#57611yescharacteristic
359C22×C71#57711yescharacteristic
360C4×C71—21no—
361C4×C71—21no—
362C4×C71—21no—
363C4×C71—21no—
364C4×C71—44no—
365C4×C71—42no—
366C4×C71—41no—
367C4×C71—42no—
368C4×C71—41no—
369C4×C71—41no—
370C4×C71—81no—
371#18418C7111yesmaximal, characteristic, direct product factor, Sylow
372C2×C71—21no—
373C2×C71—21no—
374C2×C71—22no—
375C2×C71—41no—
376C2×C71—82no—
377C2×C71—82no—
378C2×C71—81no—
379C2×C71—161no—
380C2×C71#301211yescharacteristic
381C2×C71C2×#45311yescharacteristic
382C2×C71#302611yescharacteristic
383#3537C2×C7111yescharacteristic, complemented
384#3192C2×C7111yescharacteristic, complemented
385#3188C2×C7111yescharacteristic, complemented
386#2656C2×C7111yescharacteristic, complemented
387#1618C2×C7112yescomplemented
388#1613C2×C7112yescomplemented
389#1600C2×C7112yescomplemented
390#1595C2×C7112yescomplemented
391#1504C2×C7111yescharacteristic, complemented
392C2×#327C2×C7111yescharacteristic, complemented
393#1471C2×C7111yescharacteristic, complemented
394C71#1841811yescharacteristic, direct product factor, Sylow
395#560—22no—
396#553—21no—
397#553—21no—
398D42—22no—
399D42—21no—
400D42—21no—
401#540—21no—
402#538—21no—
403#538C22×C7112yes—
404#535—21no—
405#534—21no—
406#534C22×C7112yes—
407#525C22×C7111yescharacteristic
408C2×#121—22no—
409C2×#121C22×C7111yescharacteristic
410C2×#121C22×C7111yescharacteristic
411C2×#121C22×C7111yescharacteristic, complemented
412#484C22×C7111yescharacteristic, complemented
413#482—21no—
414#481—21no—
415#481C22×C7111yescharacteristic, complemented
416#481C22×C7112yescomplemented
417#469—22no—
418#466—21no—
419#465—21no—
420#450C22×C7111yescharacteristic, complemented
421#449—21no—
422#447—21no—
423#447C22×C7111yescharacteristic, complemented
424#447C22×C7112yescomplemented
425#407C22×C7111yescharacteristic, complemented
426C2×C22⋊C8C22×C7111yescharacteristic, complemented
427#399—21no—
428#399C22×C7112yescomplemented
429#392—21no—
430#392C22×C7112yescomplemented
431C2×#95C22×C7111yescharacteristic, complemented
432#328C22×C7112yescomplemented
433#327C22×C7112yescomplemented
434#327C22×C7112yescomplemented
435#327C22×C7112yescomplemented
436#323C22×C7112yescomplemented
437#323C22×C7112yescomplemented
438C2×#41D4×C7111yescharacteristic, complemented
439C22×D4—22no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—22no—
443C22×D4—21no—
444C22×D4—22no—
445C22×D4D4×C7112yes—
446C22×D4D4×C7111yescharacteristic
447C22×D4D4×C7111yescharacteristic, complemented
448C22×D4C23×C7111yescharacteristic
449C23×C4—21no—
450C23×C4C23×C7111yescharacteristic
451C2×SD16—21no—
452C2×D8—22no—
453C2×D8—21no—
454C2×M16—21no—
455C22×C8—21no—
456#127—22no—
457#127—21no—
458#126—22no—
459#126—22no—
460#125—21no—
461#124—22no—
462#123—22no—
463#123—21no—
464#123—22no—
465#123—22no—
466#123—22no—
467C22⋊Q8D4×C7111yescharacteristic, complemented
468C22⋊Q8C23×C7111yescharacteristic
469#121—22no—
470#121—21no—
471#121—21no—
472#121—22no—
473#121—22no—
474#121—22no—
475#121—22no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—22no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—48no—
488#121D4×C7112yescomplemented
489#121D4×C7111yescharacteristic, complemented
490#121C23×C7112yes—
491#121C23×C7111yescharacteristic
492#120—22no—
493#120—22no—
494#120—22no—
495#120—21no—
496#120—22no—
497#120—22no—
498#120—22no—
499C4×D4—22no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—22no—
505#117—21no—
506#117D4×C7111yescharacteristic, complemented
507C2×C4⋊C4—22no—
508C2×C4⋊C4D4×C7111yescharacteristic
509C2×C4⋊C4D4×C7111yescharacteristic, complemented
510C2×C4⋊C4C23×C7111yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4C23×C7112yes—
516#107—21no—
517#106—21no—
518#106—22no—
519#103—21no—
520#102—22no—
521#102—21no—
522#102—21no—
523#102—22no—
524#102—21no—
525C22⋊C8—21no—
526C22⋊C8—21no—
527C22⋊C8C23×C7111yescharacteristic
528C22⋊C8C23×C7111yescharacteristic
529C22⋊C8C23×C7112yes—
530#95—21no—
531#95C23×C7112yes—
532C24—22no—
533C24—21no—
534C24—21no—
535C24C2×D4×C7111yescharacteristic
536C24C2×D4×C7112yes—
537#41—81no—
538C2×Q8C2×D4×C7111yescharacteristic
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—82no—
564C2×D4—81no—
565C2×D4—82no—
566C2×D4—82no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—82no—
570C2×D4—82no—
571C2×D4—84no—
572C2×D4C2×D4×C7111yescharacteristic
573C2×D4C2×D4×C7112yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4C2×D4×C7112yes—
585C22×C4C2×D4×C7111yescharacteristic
586C22×C4C2×D4×C7111yescharacteristic
587C22×C4C2×D4×C7111yescharacteristic
588C22×C4C2×D4×C7111yescharacteristic
589C22×C4C2×D4×C7111yescharacteristic
590C22×C4C24×C7111yescharacteristic
591SD16—81no—
592D8—81no—
593D8—82no—
594M16—81no—
595C2×C8—21no—
596C2×C8—22no—
597C2×C8—21no—
598C2×C8—81no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—44no—
609C4⋊C4C2×D4×C7112yes—
610C4⋊C4C2×D4×C7111yescharacteristic
611C4⋊C4C2×D4×C7111yescharacteristic
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—41no—
629C22⋊C4—41no—
630C42—22no—
631C42—21no—
632C23—22no—
633C23—21no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—81no—
650C23—81no—
651C23—82no—
652C23—82no—
653C23—82no—
654C23#120×C7111yescharacteristic
655C23#120×C7111yescharacteristic
656C23C22×D4×C7111yescharacteristic
657Q8—41no—
658D4—42no—
659D4—41no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—41no—
664D4—41no—
665D4—44no—
666D4—42no—
667D4—42no—
668D4—41no—
669D4—42no—
670D4—41no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—82no—
679D4—82no—
680D4—88no—
681D4—82no—
682D4—82no—
683C2×C4—24no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—81no—
702C2×C4—84no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4#120×C7111yescharacteristic
706C2×C4#120×C7111yescharacteristic
707C2×C4C22×D4×C7111yescharacteristic
708C2×C4C22×D4×C7111yescharacteristic
709C8—41no—
710C8—41no—
711C8—42no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—162no—
738C22—164no—
739C22#453×C7112yes—
740C22C2×#120×C7111yescharacteristic
741C22#576×C7111yescharacteristic
742C22#577×C7111yescharacteristic
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—44no—
748C4—42no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—81no—
754C2—21no—
755C2—21no—
756C2—22no—
757C2—41no—
758C2—82no—
759C2—82no—
760C2—81no—
761C2—161no—
762C2C71×#301211yescharacteristic
763C2C2×#453×C7111yescharacteristic
764C2C71×#302611yescharacteristic
subgroupG/H
center, socleC22×C71C2×#120
commutator, Frattini, cosocleC22×C4C24×C71
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C71 ◁ C23×C4×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C71×#3537C2semidirect
2. C71×#3192C2semidirect
3. C71×#3188C2semidirect
4. C71×#2656C2semidirect
5. C71×#1618C2semidirect
6. C71×#1613C2semidirect
7. C71×#1600C2semidirect
8. C71×#1595C2semidirect
9. C71×#1504C2semidirect
10. C2×#327×C71C2semidirect
11. C71×#1471C2semidirect
28. C2×#121×C71C22semidirect
29. #484×C71C22semidirect
32. #481×C71C22semidirect
33. #481×C71C22semidirect
37. #450×C71C22semidirect
40. #447×C71C22semidirect
41. #447×C71C22semidirect
42. #407×C71C22semidirect
43. C2×C22⋊C8×C71C22semidirect
45. #399×C71C22semidirect
47. #392×C71C22semidirect
48. C2×#95×C71C22semidirect
49. #328×C71C22semidirect
50. #327×C71C22semidirect
51. #327×C71C22semidirect
52. #327×C71C22semidirect
53. #323×C71C22semidirect
54. #323×C71C22semidirect
55. C2×#41×C71D4semidirect
64. C22×D4×C71D4semidirect
84. C22⋊Q8×C71D4semidirect
105. #121×C71D4semidirect
106. #121×C71D4semidirect
123. #117×C71D4semidirect
126. C2×C4⋊C4×C71D4semidirect
371. #18418C71direct (N × H)
383. #3537C2×C71semidirect
384. #3192C2×C71semidirect
385. #3188C2×C71semidirect
386. #2656C2×C71semidirect
387. #1618C2×C71semidirect
388. #1613C2×C71semidirect
389. #1600C2×C71semidirect
390. #1595C2×C71semidirect
391. #1504C2×C71semidirect
392. C2×#327C2×C71semidirect
393. #1471C2×C71semidirect
394. C71#18418direct (N × H)
411. C2×#121C22×C71semidirect
412. #484C22×C71semidirect
415. #481C22×C71semidirect
416. #481C22×C71semidirect
420. #450C22×C71semidirect
423. #447C22×C71semidirect
424. #447C22×C71semidirect
425. #407C22×C71semidirect
426. C2×C22⋊C8C22×C71semidirect
428. #399C22×C71semidirect
430. #392C22×C71semidirect
431. C2×#95C22×C71semidirect
432. #328C22×C71semidirect
433. #327C22×C71semidirect
434. #327C22×C71semidirect
435. #327C22×C71semidirect
436. #323C22×C71semidirect
437. #323C22×C71semidirect
438. C2×#41D4×C71semidirect
447. C22×D4D4×C71semidirect
467. C22⋊Q8D4×C71semidirect
488. #121D4×C71semidirect
489. #121D4×C71semidirect
506. #117D4×C71semidirect
509. C2×C4⋊C4D4×C71semidirect

Maximal subgroups

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

subgroupindex
C71×#35372
C71×#31922
C71×#31882
C71×#26562
C71×#16182
C71×#16132
C71×#16002
C71×#15952
C71×#15042
C2×#327×C712
C71×#14712
#1841871