Finite Group Databasebeta

← C71×#18446 #31839318

Subgroups — C71×#18446 #31839318

Order 18176.

1032 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71×#3534C211yesmaximal, characteristic, complemented
2C71×#3192C211yesmaximal, characteristic, complemented
3C71×#3188C211yesmaximal, characteristic, complemented
4C71×#2813C211yesmaximal, characteristic, complemented
5C71×#1618C211yesmaximal, characteristic, complemented
6C71×#1616C211yesmaximal, characteristic, complemented
7C71×#1615C211yesmaximal, characteristic, complemented
8C71×#1613C211yesmaximal, characteristic, complemented
9C71×#1600C211yesmaximal, characteristic, complemented
10C71×#1598C211yesmaximal, characteristic, complemented
11C71×#1597C211yesmaximal, characteristic, complemented
12C71×#1595C211yesmaximal, characteristic, complemented
13C71×#1519C211yesmaximal, characteristic, complemented
14C71×#1513C211yesmaximal, characteristic, complemented
15C71×#1468C211yesmaximal, characteristic, complemented
16#562×C71—21no—
17#560×C71—21no—
18#553×C71—21no—
19#551×C71—21no—
20#546×C71—21no—
21#546×C71—21no—
22#546×C71—21no—
23D42×C71—21no—
24#540×C71—21no—
25#539×C71—21no—
26#539×C71C2211yescharacteristic
27#538×C71—21no—
28#538×C71C2211yescharacteristic
29#537×C71C2211yescharacteristic
30#534×C71—21no—
31#534×C71C2211yescharacteristic
32#525×C71C2211yescharacteristic
33C2×#123×C71C2211yescharacteristic
34C2×#121×C71C2211yescharacteristic
35C2×#121×C71C2211yescharacteristic, complemented
36#484×C71C2211yescharacteristic, complemented
37#482×C71—21no—
38#481×C71—21no—
39#481×C71C2211yescharacteristic
40#481×C71C2211yescharacteristic, complemented
41#481×C71C2211yescharacteristic, complemented
42#469×C71—21no—
43#469×C71—21no—
44#466×C71—21no—
45#465×C71—21no—
46#450×C71C2211yescharacteristic, complemented
47#449×C71—21no—
48#447×C71—21no—
49#447×C71C2211yescharacteristic
50#447×C71C2211yescharacteristic, complemented
51#447×C71C2211yescharacteristic, complemented
52#407×C71C2211yescharacteristic, complemented
53C2×C22⋊C8×C71C2211yescharacteristic, complemented
54#400×C71C2211yescharacteristic, complemented
55#399×C71C2211yescharacteristic, complemented
56#396×C71—21no—
57#394×C71—21no—
58#394×C71—21no—
59#394×C71C2211yescharacteristic, complemented
60#392×C71—21no—
61#392×C71C2211yescharacteristic, complemented
62#380×C71C2211yescharacteristic, complemented
63#328×C71C2211yescharacteristic, complemented
64#328×C71C2211yescharacteristic, complemented
65#327×C71C2211yescharacteristic
66#327×C71C2211yescharacteristic
67#327×C71C2211yescharacteristic, complemented
68#327×C71C2211yescharacteristic, complemented
69#327×C71C2211yescharacteristic, complemented
70#327×C71C2211yescharacteristic, complemented
71#324×C71C2211yescharacteristic, complemented
72#324×C71C2211yescharacteristic, complemented
73#323×C71C2211yescharacteristic, complemented
74#323×C71C2211yescharacteristic, complemented
75C2×#41×C71—21no—
76C2×#41×C71D411yescharacteristic, complemented
77C22×D4×C71—21no—
78C22×D4×C71—21no—
79C22×D4×C71—21no—
80C22×D4×C71—21no—
81C22×D4×C71—21no—
82C22×D4×C71D411yescharacteristic
83C22×D4×C71D411yescharacteristic, complemented
84C22×D4×C71C2311yescharacteristic
85C23×C4×C71C2311yescharacteristic
86C2×SD16×C71—21no—
87C2×D8×C71—21no—
88C2×D8×C71—21no—
89C2×D8×C71—21no—
90C2×M16×C71—21no—
91C22×C8×C71—21no—
92#127×C71—21no—
93#126×C71—21no—
94#126×C71—21no—
95#126×C71—21no—
96#126×C71—21no—
97#125×C71—21no—
98#125×C71—21no—
99#124×C71—21no—
100#124×C71—21no—
101#124×C71—21no—
102#123×C71—21no—
103#123×C71—21no—
104#123×C71—21no—
105#123×C71—21no—
106#123×C71—21no—
107#123×C71—21no—
108#123×C71—21no—
109#123×C71—21no—
110#123×C71—21no—
111#123×C71—21no—
112#123×C71—21no—
113#123×C71—21no—
114#123×C71—21no—
115#123×C71—21no—
116C22⋊Q8×C71—21no—
117C22⋊Q8×C71—21no—
118C22⋊Q8×C71—21no—
119C22⋊Q8×C71—21no—
120C22⋊Q8×C71—21no—
121C22⋊Q8×C71D411yescharacteristic, complemented
122C22⋊Q8×C71C2311yescharacteristic
123#121×C71—21no—
124#121×C71—21no—
125#121×C71—21no—
126#121×C71—21no—
127#121×C71—21no—
128#121×C71—21no—
129#121×C71—21no—
130#121×C71—21no—
131#121×C71—21no—
132#121×C71—21no—
133#121×C71—21no—
134#121×C71—21no—
135#121×C71—21no—
136#121×C71—21no—
137#121×C71—21no—
138#121×C71—21no—
139#121×C71—21no—
140#121×C71—21no—
141#121×C71—21no—
142#121×C71D411yescharacteristic, complemented
143#121×C71D411yescharacteristic, complemented
144#121×C71D411yescharacteristic, complemented
145#121×C71C2311yescharacteristic
146#121×C71C2311yescharacteristic
147#121×C71C2311yescharacteristic
148#120×C71—21no—
149#120×C71—21no—
150#120×C71—21no—
151#120×C71—21no—
152#120×C71—21no—
153#120×C71—21no—
154#120×C71—21no—
155#120×C71—21no—
156C4×D4×C71—21no—
157C4×D4×C71—21no—
158C4×D4×C71—21no—
159C4×D4×C71—21no—
160C4×D4×C71—21no—
161C4×D4×C71—21no—
162C4×D4×C71—21no—
163C4×D4×C71—21no—
164#117×C71—21no—
165#117×C71D411yescharacteristic, complemented
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71D411yescharacteristic
169C2×C4⋊C4×C71D411yescharacteristic, complemented
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C22⋊C4×C71—21no—
173C2×C22⋊C4×C71—21no—
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71—21no—
177C2×C22⋊C4×C71—21no—
178C2×C22⋊C4×C71—21no—
179C2×C22⋊C4×C71—21no—
180C2×C22⋊C4×C71—21no—
181C2×C22⋊C4×C71D411yescharacteristic
182C2×C22⋊C4×C71D411yescharacteristic
183C2×C22⋊C4×C71C2311yescharacteristic
184#107×C71—21no—
185#106×C71—21no—
186#106×C71—21no—
187#106×C71—21no—
188#103×C71—21no—
189#102×C71—21no—
190#102×C71—21no—
191#102×C71—21no—
192#102×C71—21no—
193#102×C71—21no—
194#102×C71—21no—
195#102×C71—21no—
196C22⋊C8×C71—21no—
197C22⋊C8×C71—21no—
198C22⋊C8×C71C2311yescharacteristic
199C22⋊C8×C71C2311yescharacteristic
200C22⋊C8×C71C2311yescharacteristic
201C22⋊C8×C71C2311yescharacteristic
202#95×C71—21no—
203#95×C71—21no—
204#95×C71C2311yescharacteristic
205#95×C71C2311yescharacteristic
206C24×C71—21no—
207C24×C71—21no—
208C24×C71—21no—
209C24×C71C2×D411yescharacteristic
210C24×C71C2×D411yescharacteristic
211#41×C71—81no—
212#41×C71—81no—
213#41×C71—81no—
214C2×Q8×C71—21no—
215C2×Q8×C71C2×D411yescharacteristic
216C2×D4×C71—21no—
217C2×D4×C71—21no—
218C2×D4×C71—21no—
219C2×D4×C71—21no—
220C2×D4×C71—21no—
221C2×D4×C71—21no—
222C2×D4×C71—21no—
223C2×D4×C71—21no—
224C2×D4×C71—21no—
225C2×D4×C71—21no—
226C2×D4×C71—21no—
227C2×D4×C71—21no—
228C2×D4×C71—21no—
229C2×D4×C71—21no—
230C2×D4×C71—21no—
231C2×D4×C71—21no—
232C2×D4×C71—21no—
233C2×D4×C71—21no—
234C2×D4×C71—21no—
235C2×D4×C71—41no—
236C2×D4×C71—41no—
237C2×D4×C71—81no—
238C2×D4×C71—81no—
239C2×D4×C71—81no—
240C2×D4×C71—81no—
241C2×D4×C71—81no—
242C2×D4×C71—81no—
243C2×D4×C71—81no—
244C2×D4×C71—81no—
245C2×D4×C71—81no—
246C2×D4×C71—81no—
247C2×D4×C71—81no—
248C2×D4×C71—81no—
249C2×D4×C71—82no—
250C2×D4×C71C2×D411yescharacteristic
251C2×D4×C71C2×D411yescharacteristic
252C2×D4×C71C2×D411yescharacteristic
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71—21no—
257C22×C4×C71—21no—
258C22×C4×C71—21no—
259C22×C4×C71—21no—
260C22×C4×C71—21no—
261C22×C4×C71—21no—
262C22×C4×C71—21no—
263C22×C4×C71—81no—
264C22×C4×C71C2×D411yescharacteristic
265C22×C4×C71C2×D411yescharacteristic
266C22×C4×C71C2×D411yescharacteristic
267C22×C4×C71C2×D411yescharacteristic
268C22×C4×C71C2×D411yescharacteristic
269C22×C4×C71C2×D411yescharacteristic
270C22×C4×C71C2×D411yescharacteristic
271C22×C4×C71C2×D411yescharacteristic
272C22×C4×C71C2411yescharacteristic
273SD16×C71—81no—
274D8×C71—81no—
275D8×C71—81no—
276D8×C71—81no—
277M16×C71—81no—
278C2×C8×C71—21no—
279C2×C8×C71—21no—
280C2×C8×C71—21no—
281C2×C8×C71—21no—
282C2×C8×C71—81no—
283C4⋊C4×C71—21no—
284C4⋊C4×C71—21no—
285C4⋊C4×C71—21no—
286C4⋊C4×C71—21no—
287C4⋊C4×C71—21no—
288C4⋊C4×C71—21no—
289C4⋊C4×C71—21no—
290C4⋊C4×C71—21no—
291C4⋊C4×C71—21no—
292C4⋊C4×C71—21no—
293C4⋊C4×C71—21no—
294C4⋊C4×C71—21no—
295C4⋊C4×C71—21no—
296C4⋊C4×C71—21no—
297C4⋊C4×C71—21no—
298C4⋊C4×C71—81no—
299C4⋊C4×C71—81no—
300C4⋊C4×C71C2×D411yescharacteristic
301C4⋊C4×C71C2×D411yescharacteristic
302C4⋊C4×C71C2×D411yescharacteristic
303C4⋊C4×C71C2×D411yescharacteristic
304C22⋊C4×C71—21no—
305C22⋊C4×C71—21no—
306C22⋊C4×C71—21no—
307C22⋊C4×C71—21no—
308C22⋊C4×C71—21no—
309C22⋊C4×C71—21no—
310C22⋊C4×C71—21no—
311C22⋊C4×C71—21no—
312C22⋊C4×C71—21no—
313C22⋊C4×C71—21no—
314C22⋊C4×C71—21no—
315C22⋊C4×C71—21no—
316C22⋊C4×C71—21no—
317C22⋊C4×C71—21no—
318C22⋊C4×C71—21no—
319C22⋊C4×C71—21no—
320C22⋊C4×C71—21no—
321C22⋊C4×C71—21no—
322C22⋊C4×C71—21no—
323C22⋊C4×C71—21no—
324C22⋊C4×C71—21no—
325C22⋊C4×C71—21no—
326C22⋊C4×C71—21no—
327C22⋊C4×C71—21no—
328C22⋊C4×C71—21no—
329C22⋊C4×C71—41no—
330C22⋊C4×C71—41no—
331C22⋊C4×C71—81no—
332C22⋊C4×C71—81no—
333C22⋊C4×C71—81no—
334C22⋊C4×C71—81no—
335C22⋊C4×C71—81no—
336C42×C71—21no—
337C42×C71—21no—
338C42×C71—21no—
339C23×C71—21no—
340C23×C71—21no—
341C23×C71—21no—
342C23×C71—21no—
343C23×C71—21no—
344C23×C71—21no—
345C23×C71—21no—
346C23×C71—21no—
347C23×C71—41no—
348C23×C71—41no—
349C23×C71—42no—
350C23×C71—41no—
351C23×C71—41no—
352C23×C71—41no—
353C23×C71—41no—
354C23×C71—41no—
355C23×C71—41no—
356C23×C71—41no—
357C23×C71—41no—
358C23×C71—41no—
359C23×C71—81no—
360C23×C71—81no—
361C23×C71—81no—
362C23×C71—81no—
363C23×C71—81no—
364C23×C71#12011yescharacteristic
365C23×C71#12011yescharacteristic
366C23×C71C22×D411yescharacteristic
367Q8×C71—41no—
368Q8×C71—81no—
369D4×C71—41no—
370D4×C71—41no—
371D4×C71—41no—
372D4×C71—41no—
373D4×C71—41no—
374D4×C71—41no—
375D4×C71—41no—
376D4×C71—42no—
377D4×C71—42no—
378D4×C71—41no—
379D4×C71—41no—
380D4×C71—41no—
381D4×C71—41no—
382D4×C71—41no—
383D4×C71—41no—
384D4×C71—81no—
385D4×C71—81no—
386D4×C71—81no—
387D4×C71—81no—
388D4×C71—81no—
389D4×C71—81no—
390D4×C71—81no—
391D4×C71—81no—
392D4×C71—81no—
393D4×C71—81no—
394D4×C71—81no—
395D4×C71—81no—
396D4×C71—82no—
397D4×C71—82no—
398D4×C71—84no—
399C2×C4×C71—21no—
400C2×C4×C71—21no—
401C2×C4×C71—21no—
402C2×C4×C71—21no—
403C2×C4×C71—21no—
404C2×C4×C71—21no—
405C2×C4×C71—21no—
406C2×C4×C71—21no—
407C2×C4×C71—21no—
408C2×C4×C71—21no—
409C2×C4×C71—41no—
410C2×C4×C71—41no—
411C2×C4×C71—41no—
412C2×C4×C71—41no—
413C2×C4×C71—41no—
414C2×C4×C71—41no—
415C2×C4×C71—41no—
416C2×C4×C71—41no—
417C2×C4×C71—41no—
418C2×C4×C71—41no—
419C2×C4×C71—41no—
420C2×C4×C71—41no—
421C2×C4×C71—41no—
422C2×C4×C71—41no—
423C2×C4×C71—41no—
424C2×C4×C71—41no—
425C2×C4×C71—41no—
426C2×C4×C71—81no—
427C2×C4×C71—81no—
428C2×C4×C71—81no—
429C2×C4×C71—81no—
430C2×C4×C71—81no—
431C2×C4×C71—81no—
432C2×C4×C71—81no—
433C2×C4×C71#12011yescharacteristic
434C2×C4×C71#12011yescharacteristic
435C2×C4×C71C22×D411yescharacteristic
436C2×C4×C71C22×D411yescharacteristic
437C8×C71—41no—
438C8×C71—41no—
439C8×C71—41no—
440C8×C71—41no—
441C22×C71—21no—
442C22×C71—21no—
443C22×C71—21no—
444C22×C71—21no—
445C22×C71—21no—
446C22×C71—21no—
447C22×C71—21no—
448C22×C71—21no—
449C22×C71—41no—
450C22×C71—41no—
451C22×C71—41no—
452C22×C71—41no—
453C22×C71—41no—
454C22×C71—41no—
455C22×C71—41no—
456C22×C71—41no—
457C22×C71—41no—
458C22×C71—41no—
459C22×C71—41no—
460C22×C71—41no—
461C22×C71—81no—
462C22×C71—81no—
463C22×C71—81no—
464C22×C71—81no—
465C22×C71—81no—
466C22×C71—81no—
467C22×C71—81no—
468C22×C71—81no—
469C22×C71—81no—
470C22×C71—81no—
471C22×C71—81no—
472C22×C71—162no—
473C22×C71—162no—
474C22×C71C2×#12011yescharacteristic
475C22×C71#57611yescharacteristic
476C22×C71#57711yescharacteristic
477C4×C71—21no—
478C4×C71—21no—
479C4×C71—21no—
480C4×C71—21no—
481C4×C71—41no—
482C4×C71—41no—
483C4×C71—41no—
484C4×C71—41no—
485C4×C71—41no—
486C4×C71—41no—
487C4×C71—41no—
488C4×C71—41no—
489C4×C71—81no—
490C4×C71—81no—
491C4×C71—81no—
492#18446C7111yesmaximal, characteristic, direct product factor, Sylow
493C2×C71—21no—
494C2×C71—21no—
495C2×C71—41no—
496C2×C71—41no—
497C2×C71—81no—
498C2×C71—81no—
499C2×C71—81no—
500C2×C71—81no—
501C2×C71—161no—
502C2×C71#301211yescharacteristic
503C2×C71#302111yescharacteristic
504C2×C71#302611yescharacteristic
505#3534C2×C7111yescharacteristic, complemented
506#3192C2×C7111yescharacteristic, complemented
507#3188C2×C7111yescharacteristic, complemented
508#2813C2×C7111yescharacteristic, complemented
509#1618C2×C7111yescharacteristic, complemented
510#1616C2×C7111yescharacteristic, complemented
511#1615C2×C7111yescharacteristic, complemented
512#1613C2×C7111yescharacteristic, complemented
513#1600C2×C7111yescharacteristic, complemented
514#1598C2×C7111yescharacteristic, complemented
515#1597C2×C7111yescharacteristic, complemented
516#1595C2×C7111yescharacteristic, complemented
517#1519C2×C7111yescharacteristic, complemented
518#1513C2×C7111yescharacteristic, complemented
519#1468C2×C7111yescharacteristic, complemented
520C71#1844611yescharacteristic, direct product factor, Sylow
521#562—21no—
522#560—21no—
523#553—21no—
524#551—21no—
525#546—21no—
526#546—21no—
527#546—21no—
528D42—21no—
529#540—21no—
530#539—21no—
531#539C22×C7111yescharacteristic
532#538—21no—
533#538C22×C7111yescharacteristic
534#537C22×C7111yescharacteristic
535#534—21no—
536#534C22×C7111yescharacteristic
537#525C22×C7111yescharacteristic
538C2×#123C22×C7111yescharacteristic
539C2×#121C22×C7111yescharacteristic
540C2×#121C22×C7111yescharacteristic, complemented
541#484C22×C7111yescharacteristic, complemented
542#482—21no—
543#481—21no—
544#481C22×C7111yescharacteristic
545#481C22×C7111yescharacteristic, complemented
546#481C22×C7111yescharacteristic, complemented
547#469—21no—
548#469—21no—
549#466—21no—
550#465—21no—
551#450C22×C7111yescharacteristic, complemented
552#449—21no—
553#447—21no—
554#447C22×C7111yescharacteristic
555#447C22×C7111yescharacteristic, complemented
556#447C22×C7111yescharacteristic, complemented
557#407C22×C7111yescharacteristic, complemented
558C2×C22⋊C8C22×C7111yescharacteristic, complemented
559#400C22×C7111yescharacteristic, complemented
560#399C22×C7111yescharacteristic, complemented
561#396—21no—
562#394—21no—
563#394—21no—
564#394C22×C7111yescharacteristic, complemented
565#392—21no—
566#392C22×C7111yescharacteristic, complemented
567#380C22×C7111yescharacteristic, complemented
568#328C22×C7111yescharacteristic, complemented
569#328C22×C7111yescharacteristic, complemented
570#327C22×C7111yescharacteristic
571#327C22×C7111yescharacteristic
572#327C22×C7111yescharacteristic, complemented
573#327C22×C7111yescharacteristic, complemented
574#327C22×C7111yescharacteristic, complemented
575#327C22×C7111yescharacteristic, complemented
576#324C22×C7111yescharacteristic, complemented
577#324C22×C7111yescharacteristic, complemented
578#323C22×C7111yescharacteristic, complemented
579#323C22×C7111yescharacteristic, complemented
580C2×#41—21no—
581C2×#41D4×C7111yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C7111yescharacteristic
588C22×D4D4×C7111yescharacteristic, complemented
589C22×D4C23×C7111yescharacteristic
590C23×C4C23×C7111yescharacteristic
591C2×SD16—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×M16—21no—
596C22×C8—21no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8D4×C7111yescharacteristic, complemented
627C22⋊Q8C23×C7111yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121D4×C7111yescharacteristic, complemented
648#121D4×C7111yescharacteristic, complemented
649#121D4×C7111yescharacteristic, complemented
650#121C23×C7111yescharacteristic
651#121C23×C7111yescharacteristic
652#121C23×C7111yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117D4×C7111yescharacteristic, complemented
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4D4×C7111yescharacteristic
674C2×C4⋊C4D4×C7111yescharacteristic, complemented
675C2×C4⋊C4C23×C7111yescharacteristic
676C2×C4⋊C4C23×C7111yescharacteristic
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4D4×C7111yescharacteristic
687C2×C22⋊C4D4×C7111yescharacteristic
688C2×C22⋊C4C23×C7111yescharacteristic
689#107—21no—
690#106—21no—
691#106—21no—
692#106—21no—
693#103—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C7111yescharacteristic
704C22⋊C8C23×C7111yescharacteristic
705C22⋊C8C23×C7111yescharacteristic
706C22⋊C8C23×C7111yescharacteristic
707#95—21no—
708#95—21no—
709#95C23×C7111yescharacteristic
710#95C23×C7111yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C7111yescharacteristic
715C24C2×D4×C7111yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C7111yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C7111yescharacteristic
756C2×D4C2×D4×C7111yescharacteristic
757C2×D4C2×D4×C7111yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C7111yescharacteristic
770C22×C4C2×D4×C7111yescharacteristic
771C22×C4C2×D4×C7111yescharacteristic
772C22×C4C2×D4×C7111yescharacteristic
773C22×C4C2×D4×C7111yescharacteristic
774C22×C4C2×D4×C7111yescharacteristic
775C22×C4C2×D4×C7111yescharacteristic
776C22×C4C2×D4×C7111yescharacteristic
777C22×C4C24×C7111yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4—81no—
805C4⋊C4C2×D4×C7111yescharacteristic
806C4⋊C4C2×D4×C7111yescharacteristic
807C4⋊C4C2×D4×C7111yescharacteristic
808C4⋊C4C2×D4×C7111yescharacteristic
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—81no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C22⋊C4—81no—
841C42—21no—
842C42—21no—
843C42—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23#120×C7111yescharacteristic
870C23#120×C7111yescharacteristic
871C23C22×D4×C7111yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—82no—
902D4—82no—
903D4—84no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4#120×C7111yescharacteristic
939C2×C4#120×C7111yescharacteristic
940C2×C4C22×D4×C7111yescharacteristic
941C2×C4C22×D4×C7111yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×#120×C7111yescharacteristic
980C22#576×C7111yescharacteristic
981C22#577×C7111yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—81no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C71×#301211yescharacteristic
1007C2C71×#302111yescharacteristic
1008C2C71×#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×#3534C2semidirect
2. C71×#3192C2semidirect
3. C71×#3188C2semidirect
4. C71×#2813C2semidirect
5. C71×#1618C2semidirect
6. C71×#1616C2semidirect
7. C71×#1615C2semidirect
8. C71×#1613C2semidirect
9. C71×#1600C2semidirect
10. C71×#1598C2semidirect
11. C71×#1597C2semidirect
12. C71×#1595C2semidirect
13. C71×#1519C2semidirect
14. C71×#1513C2semidirect
15. C71×#1468C2semidirect
35. C2×#121×C71C22semidirect
36. #484×C71C22semidirect
40. #481×C71C22semidirect
41. #481×C71C22semidirect
46. #450×C71C22semidirect
50. #447×C71C22semidirect
51. #447×C71C22semidirect
52. #407×C71C22semidirect
53. C2×C22⋊C8×C71C22semidirect
54. #400×C71C22semidirect
55. #399×C71C22semidirect
59. #394×C71C22semidirect
61. #392×C71C22semidirect
62. #380×C71C22semidirect
63. #328×C71C22semidirect
64. #328×C71C22semidirect
67. #327×C71C22semidirect
68. #327×C71C22semidirect
69. #327×C71C22semidirect
70. #327×C71C22semidirect
71. #324×C71C22semidirect
72. #324×C71C22semidirect
73. #323×C71C22semidirect
74. #323×C71C22semidirect
76. C2×#41×C71D4semidirect
83. C22×D4×C71D4semidirect
121. C22⋊Q8×C71D4semidirect
142. #121×C71D4semidirect
143. #121×C71D4semidirect
144. #121×C71D4semidirect
165. #117×C71D4semidirect
169. C2×C4⋊C4×C71D4semidirect
492. #18446C71direct (N × H)
505. #3534C2×C71semidirect
506. #3192C2×C71semidirect
507. #3188C2×C71semidirect
508. #2813C2×C71semidirect
509. #1618C2×C71semidirect
510. #1616C2×C71semidirect
511. #1615C2×C71semidirect
512. #1613C2×C71semidirect
513. #1600C2×C71semidirect
514. #1598C2×C71semidirect
515. #1597C2×C71semidirect
516. #1595C2×C71semidirect
517. #1519C2×C71semidirect
518. #1513C2×C71semidirect
519. #1468C2×C71semidirect
520. C71#18446direct (N × H)
540. C2×#121C22×C71semidirect
541. #484C22×C71semidirect
545. #481C22×C71semidirect
546. #481C22×C71semidirect
551. #450C22×C71semidirect
555. #447C22×C71semidirect
556. #447C22×C71semidirect
557. #407C22×C71semidirect
558. C2×C22⋊C8C22×C71semidirect
559. #400C22×C71semidirect
560. #399C22×C71semidirect
564. #394C22×C71semidirect
566. #392C22×C71semidirect
567. #380C22×C71semidirect
568. #328C22×C71semidirect
569. #328C22×C71semidirect
572. #327C22×C71semidirect
573. #327C22×C71semidirect
574. #327C22×C71semidirect
575. #327C22×C71semidirect
576. #324C22×C71semidirect
577. #324C22×C71semidirect
578. #323C22×C71semidirect
579. #323C22×C71semidirect
581. C2×#41D4×C71semidirect
588. C22×D4D4×C71semidirect
626. C22⋊Q8D4×C71semidirect
647. #121D4×C71semidirect
648. #121D4×C71semidirect
649. #121D4×C71semidirect
670. #117D4×C71semidirect
674. 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×#35342
C71×#31922
C71×#31882
C71×#28132
C71×#16182
C71×#16162
C71×#16152
C71×#16132
C71×#16002
C71×#15982
C71×#15972
C71×#15952
C71×#15192
C71×#15132
C71×#14682
#1844671