Finite Group Databasebeta

← C71×#18415 #31839287

Subgroups — C71×#18415 #31839287

Order 18176.

992 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71×#3534C211yesmaximal, characteristic
2C71×#3196C211yesmaximal, characteristic, complemented
3C71×#3187C211yesmaximal, characteristic, complemented
4C71×#2663C211yesmaximal, characteristic, complemented
5C71×#1618C211yesmaximal, characteristic, complemented
6C71×#1616C211yesmaximal, characteristic, complemented
7C71×#1615C211yesmaximal, characteristic, complemented
8C71×#1613C211yesmaximal, characteristic, complemented
9C71×#1606C211yesmaximal, characteristic, complemented
10C71×#1604C211yesmaximal, characteristic, complemented
11C71×#1603C211yesmaximal, characteristic, complemented
12C71×#1601C211yesmaximal, characteristic, complemented
13C71×#1507C211yesmaximal, characteristic, complemented
14C71×#1501C211yesmaximal, 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×C22⋊Q8×C71C2211yescharacteristic, complemented
35C2×#121×C71C2211yescharacteristic
36#485×C71—21no—
37#484×C71C2211yescharacteristic, complemented
38#483×C71—21no—
39#481×C71C2211yescharacteristic
40#481×C71C2211yescharacteristic, complemented
41#481×C71C2211yescharacteristic, complemented
42#470×C71—21no—
43#468×C71—21no—
44#465×C71—21no—
45#465×C71—21no—
46#452×C71—21no—
47#451×C71C2211yescharacteristic, complemented
48#450×C71—21no—
49#448×C71C2211yescharacteristic
50#448×C71C2211yescharacteristic, complemented
51#448×C71C2211yescharacteristic, complemented
52#407×C71C2211yescharacteristic, complemented
53C2×C22⋊C8×C71C2211yescharacteristic, complemented
54#400×C71C2211yescharacteristic, complemented
55#399×C71C2211yescharacteristic, complemented
56#397×C71—21no—
57#395×C71C2211yescharacteristic, complemented
58#394×C71—21no—
59#393×C71C2211yescharacteristic, complemented
60#389×C71—21no—
61#388×C71—21no—
62C4×C22⋊C4×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
77C22×Q8×C71C2311yescharacteristic
78C22×D4×C71—21no—
79C22×D4×C71—21no—
80C22×D4×C71—21no—
81C22×D4×C71D411yescharacteristic
82C22×D4×C71D411yescharacteristic
83C23×C4×C71C2311yescharacteristic
84C2×Q16×C71—21no—
85C2×SD16×C71—21no—
86C2×SD16×C71—21no—
87C2×SD16×C71—21no—
88C2×M16×C71—21no—
89C22×C8×C71—21no—
90#127×C71—21no—
91#126×C71—21no—
92#126×C71—21no—
93#126×C71—21no—
94#126×C71—21no—
95#125×C71—21no—
96#125×C71—21no—
97#124×C71—21no—
98#124×C71—21no—
99#124×C71—21no—
100#123×C71—21no—
101#123×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—
114C22⋊Q8×C71—21no—
115C22⋊Q8×C71—21no—
116C22⋊Q8×C71—21no—
117C22⋊Q8×C71—21no—
118C22⋊Q8×C71—21no—
119C22⋊Q8×C71—21no—
120C22⋊Q8×C71—21no—
121C22⋊Q8×C71—21no—
122C22⋊Q8×C71—21no—
123C22⋊Q8×C71D411yescharacteristic
124C22⋊Q8×C71C2311yescharacteristic
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×C71D411yescharacteristic
141#121×C71D411yescharacteristic
142#121×C71D411yescharacteristic
143#121×C71C2311yescharacteristic
144#121×C71C2311yescharacteristic
145#121×C71C2311yescharacteristic
146#120×C71—21no—
147#120×C71—21no—
148#120×C71—21no—
149#120×C71—21no—
150#120×C71—21no—
151#120×C71—21no—
152#120×C71—21no—
153#120×C71—21no—
154C4×D4×C71—21no—
155C4×D4×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—
162#117×C71—21no—
163#117×C71D411yescharacteristic
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71D411yescharacteristic
168C2×C4⋊C4×C71D411yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C22⋊C4×C71—21no—
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×C71D411yescharacteristic
179C2×C22⋊C4×C71D411yescharacteristic
180C2×C22⋊C4×C71C2311yescharacteristic
181C2×C42×C71—21no—
182#107×C71—21no—
183#106×C71—21no—
184#106×C71—21no—
185#106×C71—21no—
186#103×C71—21no—
187#103×C71—21no—
188#103×C71—21no—
189#103×C71—21no—
190#103×C71—21no—
191#102×C71—21no—
192#102×C71—21no—
193#102×C71—21no—
194C22⋊C8×C71—21no—
195C22⋊C8×C71—21no—
196C22⋊C8×C71C2311yescharacteristic
197C22⋊C8×C71C2311yescharacteristic
198C22⋊C8×C71C2311yescharacteristic
199C22⋊C8×C71C2311yescharacteristic
200#95×C71—21no—
201#95×C71—21no—
202#95×C71—21no—
203#95×C71—21no—
204#95×C71C2311yescharacteristic
205#95×C71C2311yescharacteristic
206C24×C71—21no—
207C24×C71—21no—
208C24×C71C2×D411yescharacteristic
209C24×C71C2×D411yescharacteristic
210#41×C71—81no—
211#41×C71—81no—
212#41×C71—81no—
213C2×Q8×C71—21no—
214C2×Q8×C71—21no—
215C2×Q8×C71—21no—
216C2×Q8×C71—81no—
217C2×Q8×C71C2×D411yescharacteristic
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—81no—
236C2×D4×C71—81no—
237C2×D4×C71—81no—
238C2×D4×C71—81no—
239C2×D4×C71—81no—
240C2×D4×C71—81no—
241C2×D4×C71—82no—
242C2×D4×C71C2×D411yescharacteristic
243C2×D4×C71C2×D411yescharacteristic
244C2×D4×C71C2×D411yescharacteristic
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71—21no—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71—21no—
252C22×C4×C71—21no—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71—81no—
257C22×C4×C71C2×D411yescharacteristic
258C22×C4×C71C2×D411yescharacteristic
259C22×C4×C71C2×D411yescharacteristic
260C22×C4×C71C2×D411yescharacteristic
261C22×C4×C71C2×D411yescharacteristic
262C22×C4×C71C2×D411yescharacteristic
263C22×C4×C71C2×D411yescharacteristic
264C22×C4×C71C2×D411yescharacteristic
265C22×C4×C71C2411yescharacteristic
266Q16×C71—81no—
267SD16×C71—81no—
268SD16×C71—81no—
269SD16×C71—81no—
270M16×C71—81no—
271C2×C8×C71—21no—
272C2×C8×C71—21no—
273C2×C8×C71—21no—
274C2×C8×C71—21no—
275C2×C8×C71—81no—
276C4⋊C4×C71—21no—
277C4⋊C4×C71—21no—
278C4⋊C4×C71—21no—
279C4⋊C4×C71—21no—
280C4⋊C4×C71—21no—
281C4⋊C4×C71—21no—
282C4⋊C4×C71—21no—
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—42no—
292C4⋊C4×C71—41no—
293C4⋊C4×C71—41no—
294C4⋊C4×C71—81no—
295C4⋊C4×C71C2×D411yescharacteristic
296C4⋊C4×C71C2×D411yescharacteristic
297C4⋊C4×C71C2×D411yescharacteristic
298C4⋊C4×C71C2×D411yescharacteristic
299C22⋊C4×C71—21no—
300C22⋊C4×C71—21no—
301C22⋊C4×C71—21no—
302C22⋊C4×C71—21no—
303C22⋊C4×C71—21no—
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—42no—
325C22⋊C4×C71—42no—
326C22⋊C4×C71—41no—
327C22⋊C4×C71—41no—
328C22⋊C4×C71—81no—
329C42×C71—21no—
330C42×C71—21no—
331C42×C71—21no—
332C42×C71—81no—
333C23×C71—21no—
334C23×C71—21no—
335C23×C71—21no—
336C23×C71—21no—
337C23×C71—21no—
338C23×C71—21no—
339C23×C71—21no—
340C23×C71—21no—
341C23×C71—41no—
342C23×C71—41no—
343C23×C71—42no—
344C23×C71—41no—
345C23×C71—41no—
346C23×C71—81no—
347C23×C71—81no—
348C23×C71—81no—
349C23×C71—81no—
350C23×C71—81no—
351C23×C71#12011yescharacteristic
352C23×C71#12011yescharacteristic
353C23×C71C22×D411yescharacteristic
354Q8×C71—41no—
355Q8×C71—41no—
356Q8×C71—41no—
357Q8×C71—41no—
358Q8×C71—41no—
359Q8×C71—81no—
360D4×C71—41no—
361D4×C71—41no—
362D4×C71—41no—
363D4×C71—42no—
364D4×C71—42no—
365D4×C71—41no—
366D4×C71—41no—
367D4×C71—41no—
368D4×C71—41no—
369D4×C71—41no—
370D4×C71—41no—
371D4×C71—81no—
372D4×C71—81no—
373D4×C71—81no—
374D4×C71—81no—
375D4×C71—81no—
376D4×C71—81no—
377D4×C71—81no—
378D4×C71—81no—
379D4×C71—81no—
380D4×C71—81no—
381D4×C71—81no—
382D4×C71—81no—
383C2×C4×C71—22no—
384C2×C4×C71—21no—
385C2×C4×C71—21no—
386C2×C4×C71—21no—
387C2×C4×C71—21no—
388C2×C4×C71—21no—
389C2×C4×C71—21no—
390C2×C4×C71—21no—
391C2×C4×C71—21no—
392C2×C4×C71—21no—
393C2×C4×C71—21no—
394C2×C4×C71—41no—
395C2×C4×C71—41no—
396C2×C4×C71—41no—
397C2×C4×C71—41no—
398C2×C4×C71—41no—
399C2×C4×C71—41no—
400C2×C4×C71—41no—
401C2×C4×C71—41no—
402C2×C4×C71—41no—
403C2×C4×C71—41no—
404C2×C4×C71—41no—
405C2×C4×C71—41no—
406C2×C4×C71—41no—
407C2×C4×C71—41no—
408C2×C4×C71—41no—
409C2×C4×C71—41no—
410C2×C4×C71—41no—
411C2×C4×C71—41no—
412C2×C4×C71—41no—
413C2×C4×C71—81no—
414C2×C4×C71—81no—
415C2×C4×C71—81no—
416C2×C4×C71—81no—
417C2×C4×C71—81no—
418C2×C4×C71—81no—
419C2×C4×C71—81no—
420C2×C4×C71#12011yescharacteristic
421C2×C4×C71#12011yescharacteristic
422C2×C4×C71C22×D411yescharacteristic
423C2×C4×C71C22×D411yescharacteristic
424C8×C71—41no—
425C8×C71—41no—
426C8×C71—41no—
427C8×C71—41no—
428C22×C71—21no—
429C22×C71—21no—
430C22×C71—21no—
431C22×C71—21no—
432C22×C71—21no—
433C22×C71—21no—
434C22×C71—21no—
435C22×C71—21no—
436C22×C71—41no—
437C22×C71—41no—
438C22×C71—41no—
439C22×C71—41no—
440C22×C71—41no—
441C22×C71—41no—
442C22×C71—41no—
443C22×C71—41no—
444C22×C71—41no—
445C22×C71—41no—
446C22×C71—41no—
447C22×C71—41no—
448C22×C71—81no—
449C22×C71—81no—
450C22×C71—81no—
451C22×C71—81no—
452C22×C71—162no—
453C22×C71—162no—
454C22×C71C2×#12011yescharacteristic
455C22×C71#57711yescharacteristic
456C22×C71#57711yescharacteristic
457C4×C71—21no—
458C4×C71—21no—
459C4×C71—21no—
460C4×C71—21no—
461C4×C71—42no—
462C4×C71—41no—
463C4×C71—41no—
464C4×C71—41no—
465C4×C71—41no—
466C4×C71—41no—
467C4×C71—41no—
468C4×C71—41no—
469C4×C71—41no—
470C4×C71—81no—
471C4×C71—81no—
472C4×C71—81no—
473#18415C7111yesmaximal, characteristic, direct product factor, Sylow
474C2×C71—21no—
475C2×C71—21no—
476C2×C71—41no—
477C2×C71—41no—
478C2×C71—81no—
479C2×C71—81no—
480C2×C71—81no—
481C2×C71—81no—
482C2×C71#300911yescharacteristic
483C2×C71#301811yescharacteristic
484C2×C71#302611yescharacteristic
485#3534C2×C7111yescharacteristic
486#3196C2×C7111yescharacteristic, complemented
487#3187C2×C7111yescharacteristic, complemented
488#2663C2×C7111yescharacteristic, complemented
489#1618C2×C7111yescharacteristic, complemented
490#1616C2×C7111yescharacteristic, complemented
491#1615C2×C7111yescharacteristic, complemented
492#1613C2×C7111yescharacteristic, complemented
493#1606C2×C7111yescharacteristic, complemented
494#1604C2×C7111yescharacteristic, complemented
495#1603C2×C7111yescharacteristic, complemented
496#1601C2×C7111yescharacteristic, complemented
497#1507C2×C7111yescharacteristic, complemented
498#1501C2×C7111yescharacteristic, complemented
499#1468C2×C7111yescharacteristic, complemented
500C71#1841511yescharacteristic, direct product factor, Sylow
501#562—21no—
502#560—21no—
503#553—21no—
504#551—21no—
505#546—21no—
506#546—21no—
507#546—21no—
508D42—21no—
509#540—21no—
510#539—21no—
511#539C22×C7111yescharacteristic
512#538—21no—
513#538C22×C7111yescharacteristic
514#537C22×C7111yescharacteristic
515#534—21no—
516#534C22×C7111yescharacteristic
517#525C22×C7111yescharacteristic
518C2×#123C22×C7111yescharacteristic
519C2×C22⋊Q8C22×C7111yescharacteristic, complemented
520C2×#121C22×C7111yescharacteristic
521#485—21no—
522#484C22×C7111yescharacteristic, complemented
523#483—21no—
524#481C22×C7111yescharacteristic
525#481C22×C7111yescharacteristic, complemented
526#481C22×C7111yescharacteristic, complemented
527#470—21no—
528#468—21no—
529#465—21no—
530#465—21no—
531#452—21no—
532#451C22×C7111yescharacteristic, complemented
533#450—21no—
534#448C22×C7111yescharacteristic
535#448C22×C7111yescharacteristic, complemented
536#448C22×C7111yescharacteristic, complemented
537#407C22×C7111yescharacteristic, complemented
538C2×C22⋊C8C22×C7111yescharacteristic, complemented
539#400C22×C7111yescharacteristic, complemented
540#399C22×C7111yescharacteristic, complemented
541#397—21no—
542#395C22×C7111yescharacteristic, complemented
543#394—21no—
544#393C22×C7111yescharacteristic, complemented
545#389—21no—
546#388—21no—
547C4×C22⋊C4C22×C7111yescharacteristic, complemented
548#328C22×C7111yescharacteristic, complemented
549#328C22×C7111yescharacteristic, complemented
550#327C22×C7111yescharacteristic
551#327C22×C7111yescharacteristic
552#327C22×C7111yescharacteristic, complemented
553#327C22×C7111yescharacteristic, complemented
554#327C22×C7111yescharacteristic, complemented
555#327C22×C7111yescharacteristic, complemented
556#324C22×C7111yescharacteristic, complemented
557#324C22×C7111yescharacteristic, complemented
558#323C22×C7111yescharacteristic, complemented
559#323C22×C7111yescharacteristic, complemented
560C2×#41—21no—
561C2×#41D4×C7111yescharacteristic
562C22×Q8C23×C7111yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C7111yescharacteristic
567C22×D4D4×C7111yescharacteristic
568C23×C4C23×C7111yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8D4×C7111yescharacteristic
609C22⋊Q8C23×C7111yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121D4×C7111yescharacteristic
626#121D4×C7111yescharacteristic
627#121D4×C7111yescharacteristic
628#121C23×C7111yescharacteristic
629#121C23×C7111yescharacteristic
630#121C23×C7111yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C7111yescharacteristic
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C7111yescharacteristic
653C2×C4⋊C4D4×C7111yescharacteristic
654C2×C4⋊C4C23×C7111yescharacteristic
655C2×C4⋊C4C23×C7111yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C7111yescharacteristic
664C2×C22⋊C4D4×C7111yescharacteristic
665C2×C22⋊C4C23×C7111yescharacteristic
666C2×C42—21no—
667#107—21no—
668#106—21no—
669#106—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C7111yescharacteristic
682C22⋊C8C23×C7111yescharacteristic
683C22⋊C8C23×C7111yescharacteristic
684C22⋊C8C23×C7111yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C7111yescharacteristic
690#95C23×C7111yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C7111yescharacteristic
694C24C2×D4×C7111yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C7111yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C7111yescharacteristic
728C2×D4C2×D4×C7111yescharacteristic
729C2×D4C2×D4×C7111yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—81no—
742C22×C4C2×D4×C7111yescharacteristic
743C22×C4C2×D4×C7111yescharacteristic
744C22×C4C2×D4×C7111yescharacteristic
745C22×C4C2×D4×C7111yescharacteristic
746C22×C4C2×D4×C7111yescharacteristic
747C22×C4C2×D4×C7111yescharacteristic
748C22×C4C2×D4×C7111yescharacteristic
749C22×C4C2×D4×C7111yescharacteristic
750C22×C4C24×C7111yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—42no—
777C4⋊C4—41no—
778C4⋊C4—41no—
779C4⋊C4—81no—
780C4⋊C4C2×D4×C7111yescharacteristic
781C4⋊C4C2×D4×C7111yescharacteristic
782C4⋊C4C2×D4×C7111yescharacteristic
783C4⋊C4C2×D4×C7111yescharacteristic
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—42no—
810C22⋊C4—42no—
811C22⋊C4—41no—
812C22⋊C4—41no—
813C22⋊C4—81no—
814C42—21no—
815C42—21no—
816C42—21no—
817C42—81no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C7111yescharacteristic
837C23#120×C7111yescharacteristic
838C23C22×D4×C7111yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C7111yescharacteristic
906C2×C4#120×C7111yescharacteristic
907C2×C4C22×D4×C7111yescharacteristic
908C2×C4C22×D4×C7111yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C7111yescharacteristic
940C22#577×C7111yescharacteristic
941C22#577×C7111yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—42no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—41no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C71×#300911yescharacteristic
967C2C71×#301811yescharacteristic
968C2C71×#302611yescharacteristic
subgroupG/H
center, socleC22×C71C2×#120
commutator, Frattini, cosocleC22×C4C24×C71
prime radicalC71×#3534C2
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
2. C71×#3196C2semidirect
3. C71×#3187C2semidirect
4. C71×#2663C2semidirect
5. C71×#1618C2semidirect
6. C71×#1616C2semidirect
7. C71×#1615C2semidirect
8. C71×#1613C2semidirect
9. C71×#1606C2semidirect
10. C71×#1604C2semidirect
11. C71×#1603C2semidirect
12. C71×#1601C2semidirect
13. C71×#1507C2semidirect
14. C71×#1501C2semidirect
15. C71×#1468C2semidirect
34. C2×C22⋊Q8×C71C22semidirect
37. #484×C71C22semidirect
40. #481×C71C22semidirect
41. #481×C71C22semidirect
47. #451×C71C22semidirect
50. #448×C71C22semidirect
51. #448×C71C22semidirect
52. #407×C71C22semidirect
53. C2×C22⋊C8×C71C22semidirect
54. #400×C71C22semidirect
55. #399×C71C22semidirect
57. #395×C71C22semidirect
59. #393×C71C22semidirect
62. C4×C22⋊C4×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
473. #18415C71direct (N × H)
486. #3196C2×C71semidirect
487. #3187C2×C71semidirect
488. #2663C2×C71semidirect
489. #1618C2×C71semidirect
490. #1616C2×C71semidirect
491. #1615C2×C71semidirect
492. #1613C2×C71semidirect
493. #1606C2×C71semidirect
494. #1604C2×C71semidirect
495. #1603C2×C71semidirect
496. #1601C2×C71semidirect
497. #1507C2×C71semidirect
498. #1501C2×C71semidirect
499. #1468C2×C71semidirect
500. C71#18415direct (N × H)
519. C2×C22⋊Q8C22×C71semidirect
522. #484C22×C71semidirect
525. #481C22×C71semidirect
526. #481C22×C71semidirect
532. #451C22×C71semidirect
535. #448C22×C71semidirect
536. #448C22×C71semidirect
537. #407C22×C71semidirect
538. C2×C22⋊C8C22×C71semidirect
539. #400C22×C71semidirect
540. #399C22×C71semidirect
542. #395C22×C71semidirect
544. #393C22×C71semidirect
547. C4×C22⋊C4C22×C71semidirect
548. #328C22×C71semidirect
549. #328C22×C71semidirect
552. #327C22×C71semidirect
553. #327C22×C71semidirect
554. #327C22×C71semidirect
555. #327C22×C71semidirect
556. #324C22×C71semidirect
557. #324C22×C71semidirect
558. #323C22×C71semidirect
559. #323C22×C71semidirect

Maximal subgroups

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

subgroupindex
C71×#35342
C71×#31962
C71×#31872
C71×#26632
C71×#16182
C71×#16162
C71×#16152
C71×#16132
C71×#16062
C71×#16042
C71×#16032
C71×#16012
C71×#15072
C71×#15012
C71×#14682
#1841571