Finite Group Databasebeta

← C71×#24027 #31844899

Subgroups — C71×#24027 #31844899

Order 18176.

1348 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71×#3488C211yesmaximal, characteristic
2C71×#3092C211yesmaximal, characteristic, complemented
3C2×#417×C71C211yesmaximal, characteristic, complemented
4C71×#2504C211yesmaximal, characteristic, complemented
5C71×#2040C212yesmaximal, complemented
6C71×#2037C212yesmaximal, complemented
7C71×#1900C211yesmaximal, characteristic, complemented
8C71×#1871C211yesmaximal, characteristic, complemented
9C71×#1860C212yesmaximal, complemented
10C71×#1792C212yesmaximal, complemented
11C71×#1789C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C71C2211yescharacteristic
13C22×#41×C71C2211yescharacteristic
14C22×M16×C71C2211yescharacteristic, complemented
15#550×C71—21no—
16#548×C71—21no—
17#546×C71—21no—
18#546×C71—22no—
19D42×C71—22no—
20D42×C71—21no—
21#537×C71—21no—
22#537×C71C2211yescharacteristic
23#535×C71—21no—
24#535×C71C2211yescharacteristic
25#525×C71—21no—
26#525×C71C2211yescharacteristic
27C2×#121×C71—21no—
28C2×#121×C71C2211yescharacteristic
29#520×C71C2211yescharacteristic
30C22×C4⋊C4×C71C2211yescharacteristic, complemented
31#484×C71—21no—
32#483×C71—21no—
33#481×C71—21no—
34#480×C71—21no—
35#428×C71C2212yescomplemented
36C2×#104×C71C2212yes—
37C2×#104×C71C2212yescomplemented
38C2×#104×C71C2212yescomplemented
39#417×C71—21no—
40#417×C71—21no—
41#417×C71C2212yes—
42#417×C71C2212yescomplemented
43#417×C71C2212yescomplemented
44C2×#103×C71—21no—
45C2×#102×C71—21no—
46C2×#100×C71C2212yescomplemented
47#407×C71C2211yescharacteristic, complemented
48#397×C71—22no—
49#390×C71C2212yescomplemented
50#386×C71—22no—
51#382×C71C2212yescomplemented
52C4×C22⋊C4×C71C2211yescharacteristic, complemented
53#343×C71C2212yescomplemented
54#339×C71C2212yescomplemented
55H(5,𝔽2)×C71—24no—
56H(5,𝔽2)×C71—42no—
57C2×#41×C71—21no—
58C2×#41×C71—21no—
59C2×#41×C71—21no—
60C2×#41×C71—21no—
61C2×#41×C71—24no—
62C2×#41×C71—42no—
63C2×#41×C71D411yescharacteristic
64C2×#41×C71D411yescharacteristic
65C2×#41×C71C2311yescharacteristic
66C2×#41×C71C2311yescharacteristic
67C2×#41×C71C2311yescharacteristic
68C22×Q8×C71D411yescharacteristic
69C22×D4×C71—21no—
70C22×D4×C71—22no—
71C22×D4×C71—22no—
72C22×D4×C71—21no—
73C22×D4×C71—21no—
74C22×D4×C71D411yescharacteristic
75C22×D4×C71D412yes—
76C22×D4×C71C2311yescharacteristic
77C23×C4×C71—21no—
78C23×C4×C71—21no—
79C23×C4×C71C2311yescharacteristic
80C2×M16×C71—21no—
81C2×M16×C71—42no—
82C2×M16×C71C2312yes—
83C2×M16×C71C2312yes—
84C22×C8×C71—21no—
85#127×C71—22no—
86#127×C71—21no—
87#124×C71—22no—
88#124×C71—21no—
89#123×C71—22no—
90#123×C71—21no—
91C22⋊Q8×C71—22no—
92C22⋊Q8×C71—21no—
93C22⋊Q8×C71—21no—
94C22⋊Q8×C71D411yescharacteristic
95C22⋊Q8×C71D411yescharacteristic
96#121×C71—22no—
97#121×C71—22no—
98#121×C71—22no—
99#121×C71—22no—
100#121×C71—22no—
101#121×C71—21no—
102#121×C71—21no—
103#121×C71—21no—
104#121×C71—21no—
105#121×C71—21no—
106#121×C71—21no—
107#121×C71—22no—
108#121×C71—21no—
109#121×C71—21no—
110#121×C71D411yescharacteristic
111#121×C71D411yescharacteristic
112#120×C71—22no—
113#120×C71—22no—
114#120×C71—22no—
115#120×C71—21no—
116#120×C71—22no—
117C4×Q8×C71—21no—
118C4×D4×C71—22no—
119C4×D4×C71—22no—
120C4×D4×C71—21no—
121C4×D4×C71—22no—
122C4×D4×C71—21no—
123C4×D4×C71—21no—
124#117×C71—21no—
125#117×C71C2311yescharacteristic
126C2×C4⋊C4×C71—21no—
127C2×C4⋊C4×C71—21no—
128C2×C4⋊C4×C71—21no—
129C2×C4⋊C4×C71—21no—
130C2×C4⋊C4×C71—21no—
131C2×C4⋊C4×C71—21no—
132C2×C4⋊C4×C71C2312yes—
133C2×C4⋊C4×C71C2311yescharacteristic
134C2×C22⋊C4×C71—22no—
135C2×C22⋊C4×C71—21no—
136C2×C22⋊C4×C71—24no—
137C2×C22⋊C4×C71D412yes—
138C2×C42×C71C2312yes—
139#107×C71—22no—
140#106×C71—22no—
141#104×C71—24no—
142#104×C71—42no—
143#104×C71—42no—
144#103×C71—22no—
145#103×C71—22no—
146#103×C71—22no—
147#102×C71—22no—
148#102×C71—22no—
149#102×C71—22no—
150#100×C71—42no—
151C22⋊C8×C71—21no—
152C22⋊C8×C71—21no—
153#95×C71—21no—
154#95×C71—24no—
155C24×C71—22no—
156C24×C71—21no—
157C24×C71C2×D411yescharacteristic
158C24×C71C2×D412yes—
159#41×C71—22no—
160#41×C71—22no—
161#41×C71—22no—
162#41×C71—22no—
163#41×C71—22no—
164#41×C71—22no—
165#41×C71—22no—
166#41×C71—44no—
167#41×C71—41no—
168#41×C71—41no—
169#41×C71—44no—
170#41×C71—44no—
171#41×C71—42no—
172#41×C71—42no—
173#41×C71#4114yes—
174C2×Q8×C71—21no—
175C2×Q8×C71—22no—
176C2×Q8×C71—41no—
177C2×Q8×C71C2×D411yescharacteristic
178C2×Q8×C71C2×D411yescharacteristic
179C2×Q8×C71C2×D411yescharacteristic
180C2×D4×C71—21no—
181C2×D4×C71—22no—
182C2×D4×C71—22no—
183C2×D4×C71—22no—
184C2×D4×C71—22no—
185C2×D4×C71—21no—
186C2×D4×C71—21no—
187C2×D4×C71—21no—
188C2×D4×C71—21no—
189C2×D4×C71—21no—
190C2×D4×C71—22no—
191C2×D4×C71—22no—
192C2×D4×C71—22no—
193C2×D4×C71—21no—
194C2×D4×C71—22no—
195C2×D4×C71—21no—
196C2×D4×C71—21no—
197C2×D4×C71—21no—
198C2×D4×C71—22no—
199C2×D4×C71—22no—
200C2×D4×C71—41no—
201C2×D4×C71—44no—
202C2×D4×C71—44no—
203C2×D4×C71—48no—
204C2×D4×C71—42no—
205C2×D4×C71—42no—
206C2×D4×C71—44no—
207C2×D4×C71—84no—
208C2×D4×C71C2×D411yescharacteristic
209C2×D4×C71C2×D411yescharacteristic
210C2×D4×C71C2×D411yescharacteristic
211C22×C4×C71—21no—
212C22×C4×C71—22no—
213C22×C4×C71—22no—
214C22×C4×C71—22no—
215C22×C4×C71—21no—
216C22×C4×C71—22no—
217C22×C4×C71—21no—
218C22×C4×C71—21no—
219C22×C4×C71—21no—
220C22×C4×C71—21no—
221C22×C4×C71—22no—
222C22×C4×C71—22no—
223C22×C4×C71—44no—
224C22×C4×C71—41no—
225C22×C4×C71—41no—
226C22×C4×C71—82no—
227C22×C4×C71C2×D411yescharacteristic
228C22×C4×C71C2×D411yescharacteristic
229C22×C4×C71C2×D411yescharacteristic
230C22×C4×C71C2×D411yescharacteristic
231C22×C4×C71C2×D411yescharacteristic
232C22×C4×C71C2×D412yes—
233C22×C4×C71C2411yescharacteristic
234M16×C71—22no—
235M16×C71—22no—
236M16×C71—22no—
237M16×C71—22no—
238M16×C71—42no—
239C2×C8×C71—22no—
240C2×C8×C71—22no—
241C2×C8×C71—42no—
242C4⋊C4×C71—22no—
243C4⋊C4×C71—22no—
244C4⋊C4×C71—21no—
245C4⋊C4×C71—21no—
246C4⋊C4×C71—21no—
247C4⋊C4×C71—21no—
248C4⋊C4×C71—22no—
249C4⋊C4×C71—22no—
250C4⋊C4×C71—41no—
251C4⋊C4×C71—41no—
252C4⋊C4×C71C2×D411yescharacteristic
253C4⋊C4×C71C2×D411yescharacteristic
254C22⋊C4×C71—22no—
255C22⋊C4×C71—22no—
256C22⋊C4×C71—22no—
257C22⋊C4×C71—22no—
258C22⋊C4×C71—22no—
259C22⋊C4×C71—21no—
260C22⋊C4×C71—21no—
261C22⋊C4×C71—21no—
262C22⋊C4×C71—21no—
263C22⋊C4×C71—22no—
264C22⋊C4×C71—22no—
265C22⋊C4×C71—21no—
266C22⋊C4×C71—42no—
267C22⋊C4×C71—84no—
268C42×C71—22no—
269C42×C71—21no—
270C42×C71—22no—
271C42×C71—22no—
272C23×C71—21no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—22no—
276C23×C71—21no—
277C23×C71—21no—
278C23×C71—24no—
279C23×C71—41no—
280C23×C71—42no—
281C23×C71—44no—
282C23×C71—42no—
283C23×C71—42no—
284C23×C71—42no—
285C23×C71—81no—
286C23×C71—82no—
287C23×C71—82no—
288C23×C71#12011yescharacteristic
289C23×C71#12011yescharacteristic
290C23×C71C22×D411yescharacteristic
291Q8×C71—21no—
292Q8×C71—21no—
293Q8×C71—21no—
294Q8×C71—22no—
295Q8×C71—42no—
296Q8×C71#12312yes—
297D4×C71—24no—
298D4×C71—21no—
299D4×C71—21no—
300D4×C71—21no—
301D4×C71—22no—
302D4×C71—42no—
303D4×C71—42no—
304D4×C71—44no—
305D4×C71—42no—
306D4×C71—44no—
307D4×C71—42no—
308D4×C71—42no—
309D4×C71—44no—
310D4×C71—42no—
311D4×C71—41no—
312D4×C71—41no—
313D4×C71—42no—
314D4×C71—81no—
315D4×C71—82no—
316D4×C71—82no—
317D4×C71—82no—
318D4×C71—82no—
319D4×C71#12312yes—
320C2×C4×C71—21no—
321C2×C4×C71—22no—
322C2×C4×C71—21no—
323C2×C4×C71—21no—
324C2×C4×C71—21no—
325C2×C4×C71—21no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—24no—
329C2×C4×C71—21no—
330C2×C4×C71—22no—
331C2×C4×C71—21no—
332C2×C4×C71—21no—
333C2×C4×C71—21no—
334C2×C4×C71—42no—
335C2×C4×C71—42no—
336C2×C4×C71—42no—
337C2×C4×C71—44no—
338C2×C4×C71—41no—
339C2×C4×C71—41no—
340C2×C4×C71—42no—
341C2×C4×C71—42no—
342C2×C4×C71—42no—
343C2×C4×C71—42no—
344C2×C4×C71—44no—
345C2×C4×C71—42no—
346C2×C4×C71—42no—
347C2×C4×C71—82no—
348C2×C4×C71—82no—
349C2×C4×C71—82no—
350C2×C4×C71#12011yescharacteristic
351C2×C4×C71#12011yescharacteristic
352C2×C4×C71C22×D411yescharacteristic
353C2×C4×C71C22×D411yescharacteristic
354C2×C4×C71C2×#4112yes—
355C2×C4×C71H(5,𝔽2)12yes—
356C8×C71—42no—
357C8×C71—42no—
358C22×C71—21no—
359C22×C71—21no—
360C22×C71—21no—
361C22×C71—21no—
362C22×C71—21no—
363C22×C71—22no—
364C22×C71—21no—
365C22×C71—21no—
366C22×C71—44no—
367C22×C71—41no—
368C22×C71—41no—
369C22×C71—41no—
370C22×C71—41no—
371C22×C71—42no—
372C22×C71—42no—
373C22×C71—41no—
374C22×C71—41no—
375C22×C71—41no—
376C22×C71—42no—
377C22×C71—41no—
378C22×C71—84no—
379C22×C71—84no—
380C22×C71—164no—
381C22×C71#45512yes—
382C22×C71C2×#12011yescharacteristic
383C22×C71#54612yes—
384C4×C71—21no—
385C4×C71—21no—
386C4×C71—22no—
387C4×C71—41no—
388C4×C71—41no—
389C4×C71—42no—
390C4×C71—41no—
391C4×C71—41no—
392C4×C71—82no—
393C4×C71—82no—
394C4×C71C2×#12311yescharacteristic
395C4×C71#53411yescharacteristic
396C4×C71#54612yes—
397#24027C7111yesmaximal, characteristic, direct product factor, Sylow
398C2×C71—22no—
399C2×C71—22no—
400C2×C71—41no—
401C2×C71—42no—
402C2×C71—81no—
403C2×C71—82no—
404C2×C71—81no—
405C2×C71#240511yescharacteristic
406C2×C71C2×#45511yescharacteristic
407C2×C71#302111yescharacteristic
408#3488C2×C7111yescharacteristic
409#3092C2×C7111yescharacteristic, complemented
410C2×#417C2×C7111yescharacteristic, complemented
411#2504C2×C7111yescharacteristic, complemented
412#2040C2×C7112yescomplemented
413#2037C2×C7112yescomplemented
414#1900C2×C7111yescharacteristic, complemented
415#1871C2×C7111yescharacteristic, complemented
416#1860C2×C7112yescomplemented
417#1792C2×C7112yescomplemented
418#1789C2×C7111yescharacteristic, complemented
419C71#2402711yescharacteristic, direct product factor, Sylow
420C2×H(5,𝔽2)C22×C7111yescharacteristic
421C22×#41C22×C7111yescharacteristic
422C22×M16C22×C7111yescharacteristic, complemented
423#550—21no—
424#548—21no—
425#546—21no—
426#546—22no—
427D42—22no—
428D42—21no—
429#537—21no—
430#537C22×C7111yescharacteristic
431#535—21no—
432#535C22×C7111yescharacteristic
433#525—21no—
434#525C22×C7111yescharacteristic
435C2×#121—21no—
436C2×#121C22×C7111yescharacteristic
437#520C22×C7111yescharacteristic
438C22×C4⋊C4C22×C7111yescharacteristic, complemented
439#484—21no—
440#483—21no—
441#481—21no—
442#480—21no—
443#428C22×C7112yescomplemented
444C2×#104C22×C7112yes—
445C2×#104C22×C7112yescomplemented
446C2×#104C22×C7112yescomplemented
447#417—21no—
448#417—21no—
449#417C22×C7112yes—
450#417C22×C7112yescomplemented
451#417C22×C7112yescomplemented
452C2×#103—21no—
453C2×#102—21no—
454C2×#100C22×C7112yescomplemented
455#407C22×C7111yescharacteristic, complemented
456#397—22no—
457#390C22×C7112yescomplemented
458#386—22no—
459#382C22×C7112yescomplemented
460C4×C22⋊C4C22×C7111yescharacteristic, complemented
461#343C22×C7112yescomplemented
462#339C22×C7112yescomplemented
463H(5,𝔽2)—24no—
464H(5,𝔽2)—42no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—24no—
470C2×#41—42no—
471C2×#41D4×C7111yescharacteristic
472C2×#41D4×C7111yescharacteristic
473C2×#41C23×C7111yescharacteristic
474C2×#41C23×C7111yescharacteristic
475C2×#41C23×C7111yescharacteristic
476C22×Q8D4×C7111yescharacteristic
477C22×D4—21no—
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4D4×C7111yescharacteristic
483C22×D4D4×C7112yes—
484C22×D4C23×C7111yescharacteristic
485C23×C4—21no—
486C23×C4—21no—
487C23×C4C23×C7111yescharacteristic
488C2×M16—21no—
489C2×M16—42no—
490C2×M16C23×C7112yes—
491C2×M16C23×C7112yes—
492C22×C8—21no—
493#127—22no—
494#127—21no—
495#124—22no—
496#124—21no—
497#123—22no—
498#123—21no—
499C22⋊Q8—22no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8D4×C7111yescharacteristic
503C22⋊Q8D4×C7111yescharacteristic
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—22no—
516#121—21no—
517#121—21no—
518#121D4×C7111yescharacteristic
519#121D4×C7111yescharacteristic
520#120—22no—
521#120—22no—
522#120—22no—
523#120—21no—
524#120—22no—
525C4×Q8—21no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—21no—
529C4×D4—22no—
530C4×D4—21no—
531C4×D4—21no—
532#117—21no—
533#117C23×C7111yescharacteristic
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4C23×C7112yes—
541C2×C4⋊C4C23×C7111yescharacteristic
542C2×C22⋊C4—22no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4D4×C7112yes—
546C2×C42C23×C7112yes—
547#107—22no—
548#106—22no—
549#104—24no—
550#104—42no—
551#104—42no—
552#103—22no—
553#103—22no—
554#103—22no—
555#102—22no—
556#102—22no—
557#102—22no—
558#100—42no—
559C22⋊C8—21no—
560C22⋊C8—21no—
561#95—21no—
562#95—24no—
563C24—22no—
564C24—21no—
565C24C2×D4×C7111yescharacteristic
566C24C2×D4×C7112yes—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—44no—
575#41—41no—
576#41—41no—
577#41—44no—
578#41—44no—
579#41—42no—
580#41—42no—
581#41#41×C7114yes—
582C2×Q8—21no—
583C2×Q8—22no—
584C2×Q8—41no—
585C2×Q8C2×D4×C7111yescharacteristic
586C2×Q8C2×D4×C7111yescharacteristic
587C2×Q8C2×D4×C7111yescharacteristic
588C2×D4—21no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—21no—
602C2×D4—22no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—41no—
609C2×D4—44no—
610C2×D4—44no—
611C2×D4—48no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—44no—
615C2×D4—84no—
616C2×D4C2×D4×C7111yescharacteristic
617C2×D4C2×D4×C7111yescharacteristic
618C2×D4C2×D4×C7111yescharacteristic
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—44no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—82no—
635C22×C4C2×D4×C7111yescharacteristic
636C22×C4C2×D4×C7111yescharacteristic
637C22×C4C2×D4×C7111yescharacteristic
638C22×C4C2×D4×C7111yescharacteristic
639C22×C4C2×D4×C7111yescharacteristic
640C22×C4C2×D4×C7112yes—
641C22×C4C24×C7111yescharacteristic
642M16—22no—
643M16—22no—
644M16—22no—
645M16—22no—
646M16—42no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—42no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4C2×D4×C7111yescharacteristic
661C4⋊C4C2×D4×C7111yescharacteristic
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—21no—
674C22⋊C4—42no—
675C22⋊C4—84no—
676C42—22no—
677C42—21no—
678C42—22no—
679C42—22no—
680C23—22no—
681C23—21no—
682C23—22no—
683C23—22no—
684C23—21no—
685C23—21no—
686C23—24no—
687C23—41no—
688C23—42no—
689C23—44no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—81no—
694C23—82no—
695C23—82no—
696C23#120×C7111yescharacteristic
697C23#120×C7111yescharacteristic
698C23C22×D4×C7111yescharacteristic
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—22no—
703Q8—42no—
704Q8#123×C7112yes—
705D4—24no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—22no—
710D4—42no—
711D4—42no—
712D4—44no—
713D4—42no—
714D4—44no—
715D4—44no—
716D4—42no—
717D4—42no—
718D4—42no—
719D4—41no—
720D4—41no—
721D4—42no—
722D4—82no—
723D4—81no—
724D4—82no—
725D4—82no—
726D4—82no—
727D4#123×C7112yes—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4—82no—
758C2×C4#120×C7111yescharacteristic
759C2×C4#120×C7111yescharacteristic
760C2×C4C22×D4×C7111yescharacteristic
761C2×C4C22×D4×C7111yescharacteristic
762C2×C4C2×#41×C7112yes—
763C2×C4H(5,𝔽2)×C7112yes—
764C8—42no—
765C8—42no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—22no—
772C22—21no—
773C22—21no—
774C22—44no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—42no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—42no—
785C22—41no—
786C22—84no—
787C22—84no—
788C22—164no—
789C22#455×C7112yes—
790C22C2×#120×C7111yescharacteristic
791C22#546×C7112yes—
792C4—21no—
793C4—21no—
794C4—22no—
795C4—41no—
796C4—41no—
797C4—42no—
798C4—41no—
799C4—41no—
800C4—82no—
801C4—82no—
802C4C2×#123×C7111yescharacteristic
803C4#534×C7111yescharacteristic
804C4#546×C7112yes—
805C2—22no—
806C2—22no—
807C2—41no—
808C2—42no—
809C2—81no—
810C2—82no—
811C2—81no—
812C2C71×#240511yescharacteristic
813C2C2×#455×C7111yescharacteristic
814C2C71×#302111yescharacteristic
subgroupG/H
center, socleC22×C71C2×#120
commutator, Frattini, cosocleC22×C4C24×C71
prime radicalC71×#3488C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C71 ◁ C23×C4×C71 ◁ G

Complements

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

NH ≅ G/Ntype
2. C71×#3092C2semidirect
3. C2×#417×C71C2semidirect
4. C71×#2504C2semidirect
5. C71×#2040C2semidirect
6. C71×#2037C2semidirect
7. C71×#1900C2semidirect
8. C71×#1871C2semidirect
9. C71×#1860C2semidirect
10. C71×#1792C2semidirect
11. C71×#1789C2semidirect
14. C22×M16×C71C22semidirect
30. C22×C4⋊C4×C71C22semidirect
35. #428×C71C22semidirect
37. C2×#104×C71C22semidirect
38. C2×#104×C71C22semidirect
42. #417×C71C22semidirect
43. #417×C71C22semidirect
46. C2×#100×C71C22semidirect
47. #407×C71C22semidirect
49. #390×C71C22semidirect
51. #382×C71C22semidirect
52. C4×C22⋊C4×C71C22semidirect
53. #343×C71C22semidirect
54. #339×C71C22semidirect
397. #24027C71direct (N × H)
409. #3092C2×C71semidirect
410. C2×#417C2×C71semidirect
411. #2504C2×C71semidirect
412. #2040C2×C71semidirect
413. #2037C2×C71semidirect
414. #1900C2×C71semidirect
415. #1871C2×C71semidirect
416. #1860C2×C71semidirect
417. #1792C2×C71semidirect
418. #1789C2×C71semidirect
419. C71#24027direct (N × H)
422. C22×M16C22×C71semidirect
438. C22×C4⋊C4C22×C71semidirect
443. #428C22×C71semidirect
445. C2×#104C22×C71semidirect
446. C2×#104C22×C71semidirect
450. #417C22×C71semidirect
451. #417C22×C71semidirect
454. C2×#100C22×C71semidirect
455. #407C22×C71semidirect
457. #390C22×C71semidirect
459. #382C22×C71semidirect
460. C4×C22⋊C4C22×C71semidirect
461. #343C22×C71semidirect
462. #339C22×C71semidirect

Maximal subgroups

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

subgroupindex
C71×#34882
C71×#30922
C2×#417×C712
C71×#25042
C71×#20402
C71×#20372
C71×#19002
C71×#18712
C71×#18602
C71×#17922
C71×#17892
#2402771