Finite Group Databasebeta

← C71×#24029 #31844901

Subgroups — C71×#24029 #31844901

Order 18176.

1264 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71×#3489C211yesmaximal, characteristic
2C71×#3092C211yesmaximal, characteristic, complemented
3C2×#417×C71C211yesmaximal, characteristic, complemented
4C71×#2503C211yesmaximal, characteristic, complemented
5C71×#2040C212yesmaximal, complemented
6C71×#2038C212yesmaximal, complemented
7C71×#1901C211yesmaximal, characteristic, complemented
8C71×#1871C211yesmaximal, characteristic, complemented
9C71×#1860C212yesmaximal, complemented
10C71×#1793C212yesmaximal, complemented
11C71×#1789C211yesmaximal, characteristic, complemented
12C2×2−1+4×C71C2211yescharacteristic
13C22×#41×C71C2211yescharacteristic
14C22×M16×C71C2211yescharacteristic
15D4×Q8×C71—21no—
16#548×C71—21no—
17#547×C71—21no—
18#547×C71—22no—
19#546×C71—21no—
20#546×C71—22no—
21#537×C71—21no—
22#537×C71C2211yescharacteristic
23#536×C71—21no—
24#536×C71C2211yescharacteristic
25#525×C71—21no—
26#525×C71C2211yescharacteristic
27C2×C22⋊Q8×C71—21no—
28C2×C22⋊Q8×C71C2211yescharacteristic
29#520×C71C2211yescharacteristic
30C22×C4⋊C4×C71C2211yescharacteristic
31#484×C71—21no—
32#483×C71—21no—
33#481×C71—21no—
34#480×C71—21no—
35#428×C71C2212yescomplemented
36C2×#104×C71C2212yes—
37C2×#104×C71C2212yes—
38C2×#104×C71C2212yescomplemented
39#417×C71—21no—
40#417×C71—21no—
41#417×C71C2212yes—
42#417×C71C2212yes—
43#417×C71C2212yescomplemented
44C2×#103×C71—21no—
45C2×#102×C71—21no—
46C2×#101×C71C2212yescomplemented
47#407×C71C2211yescharacteristic
48#400×C71—22no—
49#391×C71C2212yescomplemented
50#382×C71C2212yescomplemented
51#381×C71—22no—
52C4×C22⋊C4×C71C2211yescharacteristic
53#343×C71C2212yescomplemented
54#339×C71C2212yescomplemented
552−1+4×C71—24no—
562−1+4×C71—42no—
57C2×#41×C71—21no—
58C2×#41×C71—21no—
59C2×#41×C71—21no—
60C2×#41×C71—22no—
61C2×#41×C71—21no—
62C2×#41×C71—24no—
63C2×#41×C71—42no—
64C2×#41×C71D411yescharacteristic
65C2×#41×C71D411yescharacteristic
66C2×#41×C71C2311yescharacteristic
67C2×#41×C71C2311yescharacteristic
68C2×#41×C71C2311yescharacteristic
69C22×Q8×C71—21no—
70C22×Q8×C71—21no—
71C22×Q8×C71D411yescharacteristic
72C22×Q8×C71C2311yescharacteristic
73C22×D4×C71—21no—
74C22×D4×C71D411yescharacteristic
75C23×C4×C71—21no—
76C23×C4×C71—21no—
77C23×C4×C71C2311yescharacteristic
78C2×M16×C71—21no—
79C2×M16×C71—42no—
80C2×M16×C71C2312yes—
81C2×M16×C71C2312yes—
82C22×C8×C71—21no—
83C4⋊Q8×C71—22no—
84C4⋊Q8×C71—21no—
85#124×C71—22no—
86#124×C71—21no—
87#123×C71—22no—
88#123×C71—22no—
89#123×C71—22no—
90#123×C71—21no—
91#123×C71—22no—
92C22⋊Q8×C71—22no—
93C22⋊Q8×C71—22no—
94C22⋊Q8×C71—22no—
95C22⋊Q8×C71—21no—
96C22⋊Q8×C71—21no—
97C22⋊Q8×C71—21no—
98C22⋊Q8×C71—21no—
99C22⋊Q8×C71—21no—
100C22⋊Q8×C71—21no—
101C22⋊Q8×C71—21no—
102C22⋊Q8×C71—21no—
103C22⋊Q8×C71D411yescharacteristic
104C22⋊Q8×C71D411yescharacteristic
105#121×C71—22no—
106#121×C71—22no—
107#121×C71—22no—
108#121×C71—21no—
109#121×C71—21no—
110#121×C71—22no—
111#121×C71D411yescharacteristic
112#121×C71D411yescharacteristic
113#120×C71—22no—
114#120×C71—21no—
115C4×Q8×C71—21no—
116C4×D4×C71—22no—
117C4×D4×C71—22no—
118C4×D4×C71—21no—
119C4×D4×C71—22no—
120C4×D4×C71—21no—
121C4×D4×C71—21no—
122#117×C71—21no—
123#117×C71C2311yescharacteristic
124C2×C4⋊C4×C71—22no—
125C2×C4⋊C4×C71—21no—
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×C71D412yes—
132C2×C4⋊C4×C71C2312yes—
133C2×C4⋊C4×C71C2311yescharacteristic
134C2×C22⋊C4×C71—22no—
135C2×C22⋊C4×C71—21no—
136C2×C22⋊C4×C71D412yes—
137C2×C42×C71C2312yes—
138#107×C71—22no—
139#106×C71—22no—
140#104×C71—24no—
141#104×C71—42no—
142#104×C71—42no—
143#103×C71—22no—
144#103×C71—22no—
145#103×C71—22no—
146#102×C71—22no—
147#102×C71—22no—
148#102×C71—22no—
149#101×C71—42no—
150C22⋊C8×C71—21no—
151C22⋊C8×C71—21no—
152#95×C71—21no—
153#95×C71—24no—
154#95×C71—24no—
155C24×C71—21no—
156C24×C71C2×D411yescharacteristic
157#41×C71—22no—
158#41×C71—22no—
159#41×C71—22no—
160#41×C71—22no—
161#41×C71—22no—
162#41×C71—22no—
163#41×C71—22no—
164#41×C71—44no—
165#41×C71—41no—
166#41×C71—41no—
167#41×C71—44no—
168#41×C71—44no—
169#41×C71—48no—
170#41×C71—42no—
171#41×C71—42no—
172#41×C71#4114yes—
173C2×Q8×C71—22no—
174C2×Q8×C71—21no—
175C2×Q8×C71—21no—
176C2×Q8×C71—21no—
177C2×Q8×C71—22no—
178C2×Q8×C71—22no—
179C2×Q8×C71—22no—
180C2×Q8×C71—41no—
181C2×Q8×C71—44no—
182C2×Q8×C71—42no—
183C2×Q8×C71—42no—
184C2×Q8×C71C2×D411yescharacteristic
185C2×Q8×C71C2×D411yescharacteristic
186C2×Q8×C71C2×D411yescharacteristic
187C2×D4×C71—21no—
188C2×D4×C71—22no—
189C2×D4×C71—22no—
190C2×D4×C71—21no—
191C2×D4×C71—21no—
192C2×D4×C71—21no—
193C2×D4×C71—21no—
194C2×D4×C71—21no—
195C2×D4×C71—22no—
196C2×D4×C71—21no—
197C2×D4×C71—21no—
198C2×D4×C71—41no—
199C2×D4×C71—44no—
200C2×D4×C71C2×D411yescharacteristic
201C2×D4×C71C2×D411yescharacteristic
202C2×D4×C71C2×D411yescharacteristic
203C22×C4×C71—21no—
204C22×C4×C71—22no—
205C22×C4×C71—22no—
206C22×C4×C71—22no—
207C22×C4×C71—22no—
208C22×C4×C71—21no—
209C22×C4×C71—22no—
210C22×C4×C71—21no—
211C22×C4×C71—21no—
212C22×C4×C71—21no—
213C22×C4×C71—21no—
214C22×C4×C71—22no—
215C22×C4×C71—22no—
216C22×C4×C71—44no—
217C22×C4×C71—44no—
218C22×C4×C71—41no—
219C22×C4×C71—41no—
220C22×C4×C71C2×D412yes—
221C22×C4×C71C2×D411yescharacteristic
222C22×C4×C71C2×D411yescharacteristic
223C22×C4×C71C2×D411yescharacteristic
224C22×C4×C71C2×D411yescharacteristic
225C22×C4×C71C2×D411yescharacteristic
226C22×C4×C71C2×D412yes—
227C22×C4×C71C2411yescharacteristic
228M16×C71—22no—
229M16×C71—22no—
230M16×C71—22no—
231M16×C71—22no—
232M16×C71—42no—
233C2×C8×C71—22no—
234C2×C8×C71—22no—
235C2×C8×C71—42no—
236C4⋊C4×C71—22no—
237C4⋊C4×C71—22no—
238C4⋊C4×C71—22no—
239C4⋊C4×C71—22no—
240C4⋊C4×C71—21no—
241C4⋊C4×C71—22no—
242C4⋊C4×C71—22no—
243C4⋊C4×C71—21no—
244C4⋊C4×C71—21no—
245C4⋊C4×C71—21no—
246C4⋊C4×C71—22no—
247C4⋊C4×C71—22no—
248C4⋊C4×C71—41no—
249C4⋊C4×C71—41no—
250C4⋊C4×C71C2×D411yescharacteristic
251C4⋊C4×C71C2×D411yescharacteristic
252C22⋊C4×C71—22no—
253C22⋊C4×C71—22no—
254C22⋊C4×C71—22no—
255C22⋊C4×C71—22no—
256C22⋊C4×C71—22no—
257C22⋊C4×C71—21no—
258C22⋊C4×C71—22no—
259C22⋊C4×C71—22no—
260C22⋊C4×C71—21no—
261C22⋊C4×C71—21no—
262C22⋊C4×C71—21no—
263C22⋊C4×C71—21no—
264C22⋊C4×C71—42no—
265C42×C71—22no—
266C42×C71—21no—
267C42×C71—22no—
268C42×C71—22no—
269C23×C71—21no—
270C23×C71—22no—
271C23×C71—22no—
272C23×C71—21no—
273C23×C71—21no—
274C23×C71—41no—
275C23×C71—42no—
276C23×C71—42no—
277C23×C71—81no—
278C23×C71#12011yescharacteristic
279C23×C71#12011yescharacteristic
280C23×C71C22×D411yescharacteristic
281Q8×C71—21no—
282Q8×C71—21no—
283Q8×C71—21no—
284Q8×C71—22no—
285Q8×C71—42no—
286Q8×C71—44no—
287Q8×C71—41no—
288Q8×C71—41no—
289Q8×C71—42no—
290Q8×C71#12312yes—
291D4×C71—24no—
292D4×C71—21no—
293D4×C71—21no—
294D4×C71—21no—
295D4×C71—22no—
296D4×C71—42no—
297D4×C71—42no—
298D4×C71—42no—
299D4×C71—44no—
300D4×C71—42no—
301D4×C71—42no—
302D4×C71—42no—
303D4×C71—81no—
304D4×C71—82no—
305D4×C71#12312yes—
306C2×C4×C71—21no—
307C2×C4×C71—22no—
308C2×C4×C71—21no—
309C2×C4×C71—21no—
310C2×C4×C71—21no—
311C2×C4×C71—21no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—24no—
315C2×C4×C71—21no—
316C2×C4×C71—22no—
317C2×C4×C71—21no—
318C2×C4×C71—21no—
319C2×C4×C71—22no—
320C2×C4×C71—21no—
321C2×C4×C71—24no—
322C2×C4×C71—42no—
323C2×C4×C71—42no—
324C2×C4×C71—42no—
325C2×C4×C71—44no—
326C2×C4×C71—44no—
327C2×C4×C71—41no—
328C2×C4×C71—41no—
329C2×C4×C71—42no—
330C2×C4×C71—42no—
331C2×C4×C71—42no—
332C2×C4×C71—42no—
333C2×C4×C71—44no—
334C2×C4×C71—42no—
335C2×C4×C71—42no—
336C2×C4×C71—82no—
337C2×C4×C71—82no—
338C2×C4×C71—82no—
339C2×C4×C71#12011yescharacteristic
340C2×C4×C71#12011yescharacteristic
341C2×C4×C71C22×D411yescharacteristic
342C2×C4×C71C22×D411yescharacteristic
343C2×C4×C71C2×#4112yes—
344C2×C4×C71H(5,𝔽2)12yes—
345C8×C71—42no—
346C8×C71—42no—
347C22×C71—21no—
348C22×C71—21no—
349C22×C71—21no—
350C22×C71—21no—
351C22×C71—21no—
352C22×C71—22no—
353C22×C71—21no—
354C22×C71—21no—
355C22×C71—44no—
356C22×C71—41no—
357C22×C71—41no—
358C22×C71—41no—
359C22×C71—41no—
360C22×C71—41no—
361C22×C71—41no—
362C22×C71—41no—
363C22×C71—41no—
364C22×C71—84no—
365C22×C71#45412yes—
366C22×C71C2×#12011yescharacteristic
367C22×C71#54612yes—
368C4×C71—21no—
369C4×C71—21no—
370C4×C71—22no—
371C4×C71—42no—
372C4×C71—41no—
373C4×C71—41no—
374C4×C71—41no—
375C4×C71—42no—
376C4×C71—41no—
377C4×C71—82no—
378C4×C71—82no—
379C4×C71C2×#12311yescharacteristic
380C4×C71#53411yescharacteristic
381C4×C71#54612yes—
382#24029C7111yesmaximal, characteristic, direct product factor, Sylow
383C2×C71—22no—
384C2×C71—22no—
385C2×C71—41no—
386C2×C71—42no—
387C2×C71—81no—
388C2×C71—81no—
389C2×C71#240511yescharacteristic
390C2×C71C2×#45411yescharacteristic
391C2×C71#302211yescharacteristic
392#3489C2×C7111yescharacteristic
393#3092C2×C7111yescharacteristic, complemented
394C2×#417C2×C7111yescharacteristic, complemented
395#2503C2×C7111yescharacteristic, complemented
396#2040C2×C7112yescomplemented
397#2038C2×C7112yescomplemented
398#1901C2×C7111yescharacteristic, complemented
399#1871C2×C7111yescharacteristic, complemented
400#1860C2×C7112yescomplemented
401#1793C2×C7112yescomplemented
402#1789C2×C7111yescharacteristic, complemented
403C71#2402911yescharacteristic, direct product factor, Sylow
404C2×2−1+4C22×C7111yescharacteristic
405C22×#41C22×C7111yescharacteristic
406C22×M16C22×C7111yescharacteristic
407D4×Q8—21no—
408#548—21no—
409#547—21no—
410#547—22no—
411#546—21no—
412#546—22no—
413#537—21no—
414#537C22×C7111yescharacteristic
415#536—21no—
416#536C22×C7111yescharacteristic
417#525—21no—
418#525C22×C7111yescharacteristic
419C2×C22⋊Q8—21no—
420C2×C22⋊Q8C22×C7111yescharacteristic
421#520C22×C7111yescharacteristic
422C22×C4⋊C4C22×C7111yescharacteristic
423#484—21no—
424#483—21no—
425#481—21no—
426#480—21no—
427#428C22×C7112yescomplemented
428C2×#104C22×C7112yes—
429C2×#104C22×C7112yes—
430C2×#104C22×C7112yescomplemented
431#417—21no—
432#417—21no—
433#417C22×C7112yes—
434#417C22×C7112yes—
435#417C22×C7112yescomplemented
436C2×#103—21no—
437C2×#102—21no—
438C2×#101C22×C7112yescomplemented
439#407C22×C7111yescharacteristic
440#400—22no—
441#391C22×C7112yescomplemented
442#382C22×C7112yescomplemented
443#381—22no—
444C4×C22⋊C4C22×C7111yescharacteristic
445#343C22×C7112yescomplemented
446#339C22×C7112yescomplemented
4472−1+4—24no—
4482−1+4—42no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—22no—
453C2×#41—21no—
454C2×#41—24no—
455C2×#41—42no—
456C2×#41D4×C7111yescharacteristic
457C2×#41D4×C7111yescharacteristic
458C2×#41C23×C7111yescharacteristic
459C2×#41C23×C7111yescharacteristic
460C2×#41C23×C7111yescharacteristic
461C22×Q8—21no—
462C22×Q8—21no—
463C22×Q8D4×C7111yescharacteristic
464C22×Q8C23×C7111yescharacteristic
465C22×D4—21no—
466C22×D4D4×C7111yescharacteristic
467C23×C4—21no—
468C23×C4—21no—
469C23×C4C23×C7111yescharacteristic
470C2×M16—21no—
471C2×M16—42no—
472C2×M16C23×C7112yes—
473C2×M16C23×C7112yes—
474C22×C8—21no—
475C4⋊Q8—22no—
476C4⋊Q8—21no—
477#124—22no—
478#124—21no—
479#123—22no—
480#123—22no—
481#123—22no—
482#123—21no—
483#123—22no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8D4×C7111yescharacteristic
496C22⋊Q8D4×C7111yescharacteristic
497#121—22no—
498#121—22no—
499#121—22no—
500#121—21no—
501#121—21no—
502#121—22no—
503#121D4×C7111yescharacteristic
504#121D4×C7111yescharacteristic
505#120—22no—
506#120—21no—
507C4×Q8—21no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—21no—
511C4×D4—22no—
512C4×D4—21no—
513C4×D4—21no—
514#117—21no—
515#117C23×C7111yescharacteristic
516C2×C4⋊C4—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4D4×C7112yes—
524C2×C4⋊C4C23×C7112yes—
525C2×C4⋊C4C23×C7111yescharacteristic
526C2×C22⋊C4—22no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4D4×C7112yes—
529C2×C42C23×C7112yes—
530#107—22no—
531#106—22no—
532#104—24no—
533#104—42no—
534#104—42no—
535#103—22no—
536#103—22no—
537#103—22no—
538#102—22no—
539#102—22no—
540#102—22no—
541#101—42no—
542C22⋊C8—21no—
543C22⋊C8—21no—
544#95—21no—
545#95—24no—
546#95—24no—
547C24—21no—
548C24C2×D4×C7111yescharacteristic
549#41—22no—
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—44no—
557#41—41no—
558#41—41no—
559#41—44no—
560#41—44no—
561#41—48no—
562#41—42no—
563#41—42no—
564#41#41×C7114yes—
565C2×Q8—22no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—41no—
573C2×Q8—44no—
574C2×Q8—42no—
575C2×Q8—42no—
576C2×Q8C2×D4×C7111yescharacteristic
577C2×Q8C2×D4×C7111yescharacteristic
578C2×Q8C2×D4×C7111yescharacteristic
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—41no—
591C2×D4—44no—
592C2×D4C2×D4×C7111yescharacteristic
593C2×D4C2×D4×C7111yescharacteristic
594C2×D4C2×D4×C7111yescharacteristic
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4C2×D4×C7112yes—
613C22×C4C2×D4×C7111yescharacteristic
614C22×C4C2×D4×C7111yescharacteristic
615C22×C4C2×D4×C7111yescharacteristic
616C22×C4C2×D4×C7111yescharacteristic
617C22×C4C2×D4×C7111yescharacteristic
618C22×C4C2×D4×C7112yes—
619C22×C4C24×C7111yescharacteristic
620M16—22no—
621M16—22no—
622M16—22no—
623M16—22no—
624M16—42no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—42no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—21no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4C2×D4×C7111yescharacteristic
643C4⋊C4C2×D4×C7111yescharacteristic
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—21no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—42no—
657C42—22no—
658C42—21no—
659C42—22no—
660C42—22no—
661C23—22no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—41no—
667C23—42no—
668C23—42no—
669C23—81no—
670C23#120×C7111yescharacteristic
671C23#120×C7111yescharacteristic
672C23C22×D4×C7111yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—21no—
676Q8—22no—
677Q8—42no—
678Q8—44no—
679Q8—41no—
680Q8—41no—
681Q8—42no—
682Q8#123×C7112yes—
683D4—24no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—22no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—44no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—81no—
696D4—82no—
697D4#123×C7112yes—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—24no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—82no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4#120×C7111yescharacteristic
732C2×C4#120×C7111yescharacteristic
733C2×C4C22×D4×C7111yescharacteristic
734C2×C4C22×D4×C7111yescharacteristic
735C2×C4C2×#41×C7112yes—
736C2×C4H(5,𝔽2)×C7112yes—
737C8—42no—
738C8—42no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—22no—
745C22—21no—
746C22—21no—
747C22—44no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—84no—
757C22#454×C7112yes—
758C22C2×#120×C7111yescharacteristic
759C22#546×C7112yes—
760C4—21no—
761C4—21no—
762C4—22no—
763C4—42no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—82no—
770C4—82no—
771C4C2×#123×C7111yescharacteristic
772C4#534×C7111yescharacteristic
773C4#546×C7112yes—
774C2—22no—
775C2—22no—
776C2—41no—
777C2—42no—
778C2—81no—
779C2—81no—
780C2C71×#240511yescharacteristic
781C2C2×#454×C7111yescharacteristic
782C2C71×#302211yescharacteristic
subgroupG/H
center, socleC22×C71C2×#120
commutator, Frattini, cosocleC22×C4C24×C71
prime radicalC71×#3489C2
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×#2503C2semidirect
5. C71×#2040C2semidirect
6. C71×#2038C2semidirect
7. C71×#1901C2semidirect
8. C71×#1871C2semidirect
9. C71×#1860C2semidirect
10. C71×#1793C2semidirect
11. C71×#1789C2semidirect
35. #428×C71C22semidirect
38. C2×#104×C71C22semidirect
43. #417×C71C22semidirect
46. C2×#101×C71C22semidirect
49. #391×C71C22semidirect
50. #382×C71C22semidirect
53. #343×C71C22semidirect
54. #339×C71C22semidirect
382. #24029C71direct (N × H)
393. #3092C2×C71semidirect
394. C2×#417C2×C71semidirect
395. #2503C2×C71semidirect
396. #2040C2×C71semidirect
397. #2038C2×C71semidirect
398. #1901C2×C71semidirect
399. #1871C2×C71semidirect
400. #1860C2×C71semidirect
401. #1793C2×C71semidirect
402. #1789C2×C71semidirect
403. C71#24029direct (N × H)
427. #428C22×C71semidirect
430. C2×#104C22×C71semidirect
435. #417C22×C71semidirect
438. C2×#101C22×C71semidirect
441. #391C22×C71semidirect
442. #382C22×C71semidirect
445. #343C22×C71semidirect
446. #339C22×C71semidirect

Maximal subgroups

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

subgroupindex
C71×#34892
C71×#30922
C2×#417×C712
C71×#25032
C71×#20402
C71×#20382
C71×#19012
C71×#18712
C71×#18602
C71×#17932
C71×#17892
#2402971