Finite Group Databasebeta

← C71×#24245 #31845117

Subgroups — C71×#24245 #31845117

Order 18176.

1628 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C71C211yesmaximal, characteristic, complemented
2C2×#463×C71C211yesmaximal, characteristic, complemented
3C2×#449×C71C211yesmaximal, characteristic, complemented
4C2×#447×C71C211yesmaximal, characteristic, complemented
5C2×C4×D8×C71C211yesmaximal, characteristic, complemented
6C71×#2535C211yesmaximal, characteristic, complemented
7C71×#2036C211yesmaximal, characteristic, complemented
8C71×#2033C211yesmaximal, characteristic, complemented
9C71×#2000C211yesmaximal, characteristic, complemented
10C71×#1999C211yesmaximal, characteristic, complemented
11C71×#1958C211yesmaximal, characteristic, complemented
12C71×#1954C211yesmaximal, characteristic, complemented
13C71×#1804C211yesmaximal, characteristic, complemented
14C71×#1788C211yesmaximal, characteristic, complemented
15C71×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C71C2211yescharacteristic
17C23×D4×C71C2211yescharacteristic
18C22×SD16×C71C2211yescharacteristic, complemented
19C22×D8×C71C2211yescharacteristic
20C22×D8×C71C2211yescharacteristic
21#546×C71—24no—
22#546×C71—24no—
23C2×#124×C71C2211yescharacteristic
24C2×#123×C71—21no—
25C2×C22⋊Q8×C71C2211yescharacteristic
26C2×#121×C71—21no—
27C2×#121×C71C2211yescharacteristic
28C2×#121×C71C2211yescharacteristic
29C2×#121×C71C2211yescharacteristic, complemented
30C2×#120×C71—21no—
31C2×C4×D4×C71C2211yescharacteristic
32C2×C4×D4×C71C2211yescharacteristic
33C2×C4×D4×C71C2211yescharacteristic, complemented
34C22×C22⋊C4×C71—21no—
35#463×C71—24no—
36#449×C71—24no—
37#447×C71—24no—
38C4×D8×C71—24no—
39C2×#107×C71C2211yescharacteristic, complemented
40C2×C4⋊C8×C71C2211yescharacteristic, complemented
41C2×#103×C71C2211yescharacteristic, complemented
42C2×#103×C71C2211yescharacteristic, complemented
43C2×#103×C71C2211yescharacteristic, complemented
44C2×#102×C71C2211yescharacteristic
45C2×#102×C71C2211yescharacteristic
46C2×#102×C71C2211yescharacteristic
47C2×#102×C71C2211yescharacteristic
48C2×#102×C71C2211yescharacteristic
49C2×#102×C71C2211yescharacteristic
50C2×#102×C71C2211yescharacteristic, complemented
51C2×C22⋊C8×C71C2211yescharacteristic
52C2×C22⋊C8×C71C2211yescharacteristic
53C2×C22⋊C8×C71C2211yescharacteristic, complemented
54C2×C22⋊C8×C71C2211yescharacteristic, complemented
55C2×C4×C8×C71C2211yescharacteristic, complemented
56#397×C71—21no—
57#392×C71—21no—
58#386×C71—21no—
59#386×C71—21no—
60#382×C71C2211yescharacteristic, complemented
61#380×C71C2211yescharacteristic
62#380×C71C2211yescharacteristic, complemented
63#340×C71C2211yescharacteristic, complemented
64#340×C71C2211yescharacteristic, complemented
65C25×C71—21no—
66C2×#41×C71—22no—
67C2×#41×C71—22no—
68C2×#41×C71—22no—
69C2×#41×C71—22no—
70C2×#41×C71—41no—
71C2×#41×C71—41no—
72C22×Q8×C71C2311yescharacteristic
73C22×D4×C71—21no—
74C22×D4×C71—21no—
75C22×D4×C71—22no—
76C22×D4×C71—22no—
77C22×D4×C71—22no—
78C22×D4×C71—22no—
79C22×D4×C71—21no—
80C22×D4×C71—21no—
81C22×D4×C71—21no—
82C22×D4×C71—41no—
83C22×D4×C71—41no—
84C22×D4×C71D411yescharacteristic
85C22×D4×C71C2311yescharacteristic
86C22×D4×C71C2311yescharacteristic
87C22×D4×C71C2311yescharacteristic
88C23×C4×C71—21no—
89C23×C4×C71—21no—
90C23×C4×C71—21no—
91C23×C4×C71C2311yescharacteristic
92C23×C4×C71C2311yescharacteristic
93C2×SD16×C71—22no—
94C2×SD16×C71—22no—
95C2×SD16×C71—41no—
96C2×D8×C71—22no—
97C2×D8×C71—22no—
98C2×D8×C71—22no—
99C2×D8×C71—22no—
100C2×D8×C71—41no—
101C2×D8×C71D414yescomplemented
102C22×C8×C71C2311yescharacteristic
103C22×C8×C71C2311yescharacteristic
104C22×C8×C71C2311yescharacteristic
105C22×C8×C71C2311yescharacteristic
106#124×C71—22no—
107#124×C71D414yescomplemented
108#123×C71—28no—
109C22⋊Q8×C71—22no—
110C22⋊Q8×C71—22no—
111#121×C71—28no—
112#121×C71—22no—
113#121×C71—22no—
114#121×C71—22no—
115#121×C71—22no—
116#121×C71—41no—
117#121×C71—41no—
118#120×C71—28no—
119C4×D4×C71—22no—
120C4×D4×C71—22no—
121C4×D4×C71—22no—
122C4×D4×C71—22no—
123C4×D4×C71—22no—
124C4×D4×C71D414yescomplemented
125C2×C4⋊C4×C71—21no—
126C2×C4⋊C4×C71D411yescharacteristic
127C2×C4⋊C4×C71C2311yescharacteristic
128C2×C4⋊C4×C71C2311yescharacteristic
129C2×C4⋊C4×C71C2311yescharacteristic
130C2×C4⋊C4×C71C2311yescharacteristic
131C2×C22⋊C4×C71—28no—
132C2×C22⋊C4×C71—21no—
133C2×C22⋊C4×C71—21no—
134C2×C22⋊C4×C71—21no—
135C2×C22⋊C4×C71—21no—
136C2×C22⋊C4×C71—21no—
137C2×C22⋊C4×C71—21no—
138C2×C22⋊C4×C71—21no—
139C2×C22⋊C4×C71—21no—
140C2×C22⋊C4×C71—21no—
141C2×C22⋊C4×C71—21no—
142C2×C22⋊C4×C71D411yescharacteristic
143C2×C22⋊C4×C71D411yescharacteristic
144C2×C42×C71C2311yescharacteristic
145#107×C71—22no—
146C4⋊C8×C71—22no—
147#103×C71—22no—
148#103×C71—22no—
149#103×C71—41no—
150#102×C71—22no—
151#102×C71—22no—
152#102×C71—22no—
153#102×C71—22no—
154#102×C71—22no—
155#102×C71—22no—
156#102×C71—41no—
157C22⋊C8×C71—22no—
158C22⋊C8×C71—22no—
159C22⋊C8×C71—41no—
160C22⋊C8×C71—41no—
161C4×C8×C71—22no—
162#95×C71—21no—
163#95×C71—21no—
164#95×C71—21no—
165#95×C71—21no—
166C24×C71—21no—
167C24×C71—24no—
168C24×C71—21no—
169C24×C71—21no—
170C24×C71—42no—
171C24×C71—42no—
172C24×C71—42no—
173C24×C71—42no—
174C24×C71—81no—
175C24×C71—81no—
176C24×C71C2×D411yescharacteristic
177C24×C71C2×D411yescharacteristic
178#41×C71—44no—
179#41×C71—44no—
180#41×C71—44no—
181#41×C71—44no—
182C2×Q8×C71—21no—
183C2×Q8×C71—21no—
184C2×Q8×C71—21no—
185C2×Q8×C71—21no—
186C2×Q8×C71—21no—
187C2×Q8×C71C2×D412yes—
188C2×D4×C71—24no—
189C2×D4×C71—24no—
190C2×D4×C71—22no—
191C2×D4×C71—24no—
192C2×D4×C71—22no—
193C2×D4×C71—21no—
194C2×D4×C71—21no—
195C2×D4×C71—21no—
196C2×D4×C71—21no—
197C2×D4×C71—21no—
198C2×D4×C71—21no—
199C2×D4×C71—21no—
200C2×D4×C71—21no—
201C2×D4×C71—21no—
202C2×D4×C71—21no—
203C2×D4×C71—21no—
204C2×D4×C71—21no—
205C2×D4×C71—21no—
206C2×D4×C71—41no—
207C2×D4×C71—42no—
208C2×D4×C71—42no—
209C2×D4×C71—44no—
210C2×D4×C71—44no—
211C2×D4×C71—44no—
212C2×D4×C71—42no—
213C2×D4×C71—42no—
214C2×D4×C71—44no—
215C2×D4×C71—42no—
216C2×D4×C71—42no—
217C2×D4×C71—42no—
218C2×D4×C71—42no—
219C2×D4×C71—81no—
220C2×D4×C71—81no—
221C2×D4×C71—81no—
222C2×D4×C71—81no—
223C2×D4×C71C2×D412yes—
224C2×D4×C71C2×D412yes—
225C2×D4×C71C2×D412yes—
226C2×D4×C71C2×D412yes—
227C2×D4×C71#4112yes—
228C22×C4×C71—24no—
229C22×C4×C71—21no—
230C22×C4×C71—21no—
231C22×C4×C71—21no—
232C22×C4×C71—21no—
233C22×C4×C71—21no—
234C22×C4×C71—21no—
235C22×C4×C71—21no—
236C22×C4×C71—21no—
237C22×C4×C71—21no—
238C22×C4×C71—21no—
239C22×C4×C71—21no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71—21no—
243C22×C4×C71—24no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—42no—
248C22×C4×C71—42no—
249C22×C4×C71—42no—
250C22×C4×C71—81no—
251C22×C4×C71—81no—
252C22×C4×C71—81no—
253C22×C4×C71—81no—
254C22×C4×C71C2×D411yescharacteristic
255C22×C4×C71C2×D411yescharacteristic
256C22×C4×C71C2×D411yescharacteristic
257C22×C4×C71C2×D411yescharacteristic
258C22×C4×C71C2411yescharacteristic
259SD16×C71—44no—
260D8×C71—28no—
261D8×C71—44no—
262C2×C8×C71—21no—
263C2×C8×C71—21no—
264C2×C8×C71—21no—
265C2×C8×C71—21no—
266C2×C8×C71—21no—
267C2×C8×C71—21no—
268C2×C8×C71—21no—
269C2×C8×C71—21no—
270C2×C8×C71—21no—
271C2×C8×C71—21no—
272C2×C8×C71—21no—
273C2×C8×C71C2×D412yes—
274C4⋊C4×C71—24no—
275C4⋊C4×C71—22no—
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×C71C2×D412yes—
284C22⋊C4×C71—24no—
285C22⋊C4×C71—24no—
286C22⋊C4×C71—22no—
287C22⋊C4×C71—24no—
288C22⋊C4×C71—24no—
289C22⋊C4×C71—24no—
290C22⋊C4×C71—22no—
291C22⋊C4×C71—42no—
292C22⋊C4×C71—42no—
293C22⋊C4×C71—42no—
294C22⋊C4×C71—81no—
295C22⋊C4×C71—81no—
296C42×C71C2×D412yes—
297C42×C71C2×D412yes—
298C23×C71—21no—
299C23×C71—22no—
300C23×C71—21no—
301C23×C71—22no—
302C23×C71—21no—
303C23×C71—22no—
304C23×C71—21no—
305C23×C71—21no—
306C23×C71—21no—
307C23×C71—22no—
308C23×C71—21no—
309C23×C71—22no—
310C23×C71—21no—
311C23×C71—21no—
312C23×C71—21no—
313C23×C71—21no—
314C23×C71—21no—
315C23×C71—21no—
316C23×C71—48no—
317C23×C71—48no—
318C23×C71—41no—
319C23×C71—41no—
320C23×C71—41no—
321C23×C71—41no—
322C23×C71—41no—
323C23×C71—41no—
324C23×C71—41no—
325C23×C71—41no—
326C23×C71—41no—
327C23×C71—41no—
328C23×C71—41no—
329C23×C71—41no—
330C23×C71—41no—
331C23×C71—41no—
332C23×C71—41no—
333C23×C71—41no—
334C23×C71—84no—
335C23×C71—84no—
336C23×C71—84no—
337C23×C71—84no—
338C23×C71—84no—
339C23×C71#13512yes—
340C23×C71C22×D411yescharacteristic
341Q8×C71—22no—
342Q8×C71—22no—
343Q8×C71—41no—
344Q8×C71—41no—
345D4×C71—22no—
346D4×C71—22no—
347D4×C71—22no—
348D4×C71—22no—
349D4×C71—22no—
350D4×C71—22no—
351D4×C71—22no—
352D4×C71—44no—
353D4×C71—48no—
354D4×C71—48no—
355D4×C71—41no—
356D4×C71—41no—
357D4×C71—41no—
358D4×C71—41no—
359D4×C71—84no—
360D4×C71—84no—
361D4×C71—84no—
362D4×C71#12114yes—
363C2×C4×C71—21no—
364C2×C4×C71—21no—
365C2×C4×C71—21no—
366C2×C4×C71—21no—
367C2×C4×C71—22no—
368C2×C4×C71—21no—
369C2×C4×C71—22no—
370C2×C4×C71—21no—
371C2×C4×C71—21no—
372C2×C4×C71—21no—
373C2×C4×C71—21no—
374C2×C4×C71—21no—
375C2×C4×C71—48no—
376C2×C4×C71—41no—
377C2×C4×C71—41no—
378C2×C4×C71—41no—
379C2×C4×C71—41no—
380C2×C4×C71—41no—
381C2×C4×C71—41no—
382C2×C4×C71—41no—
383C2×C4×C71—41no—
384C2×C4×C71—41no—
385C2×C4×C71—41no—
386C2×C4×C71—41no—
387C2×C4×C71—41no—
388C2×C4×C71—41no—
389C2×C4×C71—41no—
390C2×C4×C71—41no—
391C2×C4×C71—41no—
392C2×C4×C71—41no—
393C2×C4×C71—41no—
394C2×C4×C71—41no—
395C2×C4×C71—41no—
396C2×C4×C71—41no—
397C2×C4×C71—84no—
398C2×C4×C71—84no—
399C2×C4×C71#12012yes—
400C2×C4×C71#12012yes—
401C2×C4×C71C22×D411yescharacteristic
402C2×C4×C71C22×D411yescharacteristic
403C2×C4×C71C22×D411yescharacteristic
404C2×C4×C71C2×#4111yescharacteristic
405C2×C4×C71H(5,𝔽2)11yescharacteristic
406C2×C4×C71H(5,𝔽2)11yescharacteristic
407C8×C71—22no—
408C8×C71—41no—
409C8×C71—41no—
410C8×C71—41no—
411C22×C71—24no—
412C22×C71—22no—
413C22×C71—22no—
414C22×C71—22no—
415C22×C71—41no—
416C22×C71—42no—
417C22×C71—42no—
418C22×C71—41no—
419C22×C71—41no—
420C22×C71—42no—
421C22×C71—42no—
422C22×C71—42no—
423C22×C71—41no—
424C22×C71—42no—
425C22×C71—41no—
426C22×C71—42no—
427C22×C71—42no—
428C22×C71—41no—
429C22×C71—42no—
430C22×C71—41no—
431C22×C71—42no—
432C22×C71—41no—
433C22×C71—42no—
434C22×C71—42no—
435C22×C71—41no—
436C22×C71—41no—
437C22×C71—41no—
438C22×C71—816no—
439C22×C71—81no—
440C22×C71—81no—
441C22×C71—81no—
442C22×C71—81no—
443C22×C71—81no—
444C22×C71—81no—
445C22×C71—81no—
446C22×C71—81no—
447C22×C71C2×#12011yescharacteristic
448C22×C71D4211yescharacteristic
449C22×C71#54611yescharacteristic
450C22×C71C2×#13511yescharacteristic
451C22×C71#57511yescharacteristic
452C22×C71#57611yescharacteristic
453C22×C71#57611yescharacteristic
454C4×C71—22no—
455C4×C71—22no—
456C4×C71—41no—
457C4×C71—41no—
458C4×C71—42no—
459C4×C71—42no—
460C4×C71—81no—
461C4×C71—81no—
462C4×C71—81no—
463C4×C71C2×#12111yescharacteristic
464C4×C71#53511yescharacteristic
465C4×C71D4211yescharacteristic
466C4×C71#54611yescharacteristic
467#24245C7111yesmaximal, characteristic, direct product factor, Sylow
468C2×C71—42no—
469C2×C71—44no—
470C2×C71—81no—
471C2×C71—82no—
472C2×C71—82no—
473C2×C71#240811yescharacteristic
474C2×C71#300211yescharacteristic
475C2×C71#300811yescharacteristic
476C2×C71#327311yescharacteristic
477C2×C71#328011yescharacteristic
478C2×C71#329711yescharacteristic
479C2×C71#332211yescharacteristic
480C2×#546C2×C7111yescharacteristic, complemented
481C2×#463C2×C7111yescharacteristic, complemented
482C2×#449C2×C7111yescharacteristic, complemented
483C2×#447C2×C7111yescharacteristic, complemented
484C2×C4×D8C2×C7111yescharacteristic, complemented
485#2535C2×C7111yescharacteristic, complemented
486#2036C2×C7111yescharacteristic, complemented
487#2033C2×C7111yescharacteristic, complemented
488#2000C2×C7111yescharacteristic, complemented
489#1999C2×C7111yescharacteristic, complemented
490#1958C2×C7111yescharacteristic, complemented
491#1954C2×C7111yescharacteristic, complemented
492#1804C2×C7111yescharacteristic, complemented
493#1788C2×C7111yescharacteristic, complemented
494#1786C2×C7111yescharacteristic, complemented
495C71#2424511yescharacteristic, direct product factor, Sylow
496C22×#41C22×C7111yescharacteristic
497C23×D4C22×C7111yescharacteristic
498C22×SD16C22×C7111yescharacteristic, complemented
499C22×D8C22×C7111yescharacteristic
500C22×D8C22×C7111yescharacteristic
501#546—24no—
502#546—24no—
503C2×#124C22×C7111yescharacteristic
504C2×#123—21no—
505C2×C22⋊Q8C22×C7111yescharacteristic
506C2×#121—21no—
507C2×#121C22×C7111yescharacteristic
508C2×#121C22×C7111yescharacteristic
509C2×#121C22×C7111yescharacteristic, complemented
510C2×#120—21no—
511C2×C4×D4C22×C7111yescharacteristic
512C2×C4×D4C22×C7111yescharacteristic
513C2×C4×D4C22×C7111yescharacteristic, complemented
514C22×C22⋊C4—21no—
515#463—24no—
516#449—24no—
517#447—24no—
518C4×D8—24no—
519C2×#107C22×C7111yescharacteristic, complemented
520C2×C4⋊C8C22×C7111yescharacteristic, complemented
521C2×#103C22×C7111yescharacteristic, complemented
522C2×#103C22×C7111yescharacteristic, complemented
523C2×#103C22×C7111yescharacteristic, complemented
524C2×#102C22×C7111yescharacteristic
525C2×#102C22×C7111yescharacteristic
526C2×#102C22×C7111yescharacteristic
527C2×#102C22×C7111yescharacteristic
528C2×#102C22×C7111yescharacteristic
529C2×#102C22×C7111yescharacteristic
530C2×#102C22×C7111yescharacteristic, complemented
531C2×C22⋊C8C22×C7111yescharacteristic
532C2×C22⋊C8C22×C7111yescharacteristic
533C2×C22⋊C8C22×C7111yescharacteristic, complemented
534C2×C22⋊C8C22×C7111yescharacteristic, complemented
535C2×C4×C8C22×C7111yescharacteristic, complemented
536#397—21no—
537#392—21no—
538#386—21no—
539#386—21no—
540#382C22×C7111yescharacteristic, complemented
541#380C22×C7111yescharacteristic
542#380C22×C7111yescharacteristic, complemented
543#340C22×C7111yescharacteristic, complemented
544#340C22×C7111yescharacteristic, complemented
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C22×Q8C23×C7111yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—41no—
563C22×D4—41no—
564C22×D4D4×C7111yescharacteristic
565C22×D4C23×C7111yescharacteristic
566C22×D4C23×C7111yescharacteristic
567C22×D4C23×C7111yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4—21no—
571C23×C4C23×C7111yescharacteristic
572C23×C4C23×C7111yescharacteristic
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—41no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C2×D8D4×C7114yescomplemented
582C22×C8C23×C7111yescharacteristic
583C22×C8C23×C7111yescharacteristic
584C22×C8C23×C7111yescharacteristic
585C22×C8C23×C7111yescharacteristic
586#124—22no—
587#124D4×C7114yescomplemented
588#123—28no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591#121—28no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—41no—
597#121—41no—
598#120—28no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4D4×C7114yescomplemented
605C2×C4⋊C4—21no—
606C2×C4⋊C4D4×C7111yescharacteristic
607C2×C4⋊C4C23×C7111yescharacteristic
608C2×C4⋊C4C23×C7111yescharacteristic
609C2×C4⋊C4C23×C7111yescharacteristic
610C2×C4⋊C4C23×C7111yescharacteristic
611C2×C22⋊C4—28no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4D4×C7111yescharacteristic
623C2×C22⋊C4D4×C7111yescharacteristic
624C2×C42C23×C7111yescharacteristic
625#107—22no—
626C4⋊C8—22no—
627#103—22no—
628#103—22no—
629#103—41no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636#102—41no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639C22⋊C8—41no—
640C22⋊C8—41no—
641C4×C8—22no—
642#95—21no—
643#95—21no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—24no—
648C24—21no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C7111yescharacteristic
657C24C2×D4×C7111yescharacteristic
658#41—44no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C7112yes—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—22no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—44no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C7112yes—
704C2×D4C2×D4×C7112yes—
705C2×D4C2×D4×C7112yes—
706C2×D4C2×D4×C7112yes—
707C2×D4#41×C7112yes—
708C22×C4—24no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—24no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—81no—
731C22×C4—81no—
732C22×C4—81no—
733C22×C4—81no—
734C22×C4C2×D4×C7111yescharacteristic
735C22×C4C2×D4×C7111yescharacteristic
736C22×C4C2×D4×C7111yescharacteristic
737C22×C4C2×D4×C7111yescharacteristic
738C22×C4C24×C7111yescharacteristic
739SD16—44no—
740D8—28no—
741D8—44no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8C2×D4×C7112yes—
754C4⋊C4—24no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4C2×D4×C7112yes—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—22no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42C2×D4×C7112yes—
777C42C2×D4×C7112yes—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—22no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—48no—
797C23—48no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23#135×C7112yes—
820C23C22×D4×C7111yescharacteristic
821Q8—22no—
822Q8—22no—
823Q8—41no—
824Q8—41no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—44no—
833D4—48no—
834D4—48no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—84no—
840D4—84no—
841D4—84no—
842D4#121×C7114yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—48no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—84no—
878C2×C4—84no—
879C2×C4#120×C7112yes—
880C2×C4#120×C7112yes—
881C2×C4C22×D4×C7111yescharacteristic
882C2×C4C22×D4×C7111yescharacteristic
883C2×C4C22×D4×C7111yescharacteristic
884C2×C4C2×#41×C7111yescharacteristic
885C2×C4H(5,𝔽2)×C7111yescharacteristic
886C2×C4H(5,𝔽2)×C7111yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—22no—
892C22—24no—
893C22—22no—
894C22—22no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—42no—
904C22—42no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—42no—
909C22—42no—
910C22—41no—
911C22—42no—
912C22—41no—
913C22—42no—
914C22—41no—
915C22—42no—
916C22—42no—
917C22—41no—
918C22—816no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×#120×C7111yescharacteristic
928C22D42×C7111yescharacteristic
929C22#546×C7111yescharacteristic
930C22C2×#135×C7111yescharacteristic
931C22#575×C7111yescharacteristic
932C22#576×C7111yescharacteristic
933C22#576×C7111yescharacteristic
934C4—22no—
935C4—22no—
936C4—41no—
937C4—41no—
938C4—42no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4C2×#121×C7111yescharacteristic
944C4#535×C7111yescharacteristic
945C4D42×C7111yescharacteristic
946C4#546×C7111yescharacteristic
947C2—42no—
948C2—44no—
949C2—81no—
950C2—82no—
951C2—82no—
952C2C71×#240811yescharacteristic
953C2C71×#300211yescharacteristic
954C2C71×#300811yescharacteristic
955C2C71×#327311yescharacteristic
956C2C71×#328011yescharacteristic
957C2C71×#329711yescharacteristic
958C2C71×#332211yescharacteristic
subgroupG/H
center, socleC23×C71C22×D4
commutator, Frattini, cosocleC22×C4C24×C71
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C71 ◁ C2×C4×D4×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#546×C71C2semidirect
2. C2×#463×C71C2semidirect
3. C2×#449×C71C2semidirect
4. C2×#447×C71C2semidirect
5. C2×C4×D8×C71C2semidirect
6. C71×#2535C2semidirect
7. C71×#2036C2semidirect
8. C71×#2033C2semidirect
9. C71×#2000C2semidirect
10. C71×#1999C2semidirect
11. C71×#1958C2semidirect
12. C71×#1954C2semidirect
13. C71×#1804C2semidirect
14. C71×#1788C2semidirect
15. C71×#1786C2semidirect
18. C22×SD16×C71C22semidirect
29. C2×#121×C71C22semidirect
33. C2×C4×D4×C71C22semidirect
39. C2×#107×C71C22semidirect
40. C2×C4⋊C8×C71C22semidirect
41. C2×#103×C71C22semidirect
42. C2×#103×C71C22semidirect
43. C2×#103×C71C22semidirect
50. C2×#102×C71C22semidirect
53. C2×C22⋊C8×C71C22semidirect
54. C2×C22⋊C8×C71C22semidirect
55. C2×C4×C8×C71C22semidirect
60. #382×C71C22semidirect
62. #380×C71C22semidirect
63. #340×C71C22semidirect
64. #340×C71C22semidirect
101. C2×D8×C71D4semidirect
107. #124×C71D4semidirect
124. C4×D4×C71D4semidirect
467. #24245C71direct (N × H)
480. C2×#546C2×C71semidirect
481. C2×#463C2×C71semidirect
482. C2×#449C2×C71semidirect
483. C2×#447C2×C71semidirect
484. C2×C4×D8C2×C71semidirect
485. #2535C2×C71semidirect
486. #2036C2×C71semidirect
487. #2033C2×C71semidirect
488. #2000C2×C71semidirect
489. #1999C2×C71semidirect
490. #1958C2×C71semidirect
491. #1954C2×C71semidirect
492. #1804C2×C71semidirect
493. #1788C2×C71semidirect
494. #1786C2×C71semidirect
495. C71#24245direct (N × H)
498. C22×SD16C22×C71semidirect
509. C2×#121C22×C71semidirect
513. C2×C4×D4C22×C71semidirect
519. C2×#107C22×C71semidirect
520. C2×C4⋊C8C22×C71semidirect
521. C2×#103C22×C71semidirect
522. C2×#103C22×C71semidirect
523. C2×#103C22×C71semidirect
530. C2×#102C22×C71semidirect
533. C2×C22⋊C8C22×C71semidirect
534. C2×C22⋊C8C22×C71semidirect
535. C2×C4×C8C22×C71semidirect
540. #382C22×C71semidirect
542. #380C22×C71semidirect
543. #340C22×C71semidirect
544. #340C22×C71semidirect
581. C2×D8D4×C71semidirect
587. #124D4×C71semidirect
604. C4×D4D4×C71semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C712
C2×#463×C712
C2×#449×C712
C2×#447×C712
C2×C4×D8×C712
C71×#25352
C71×#20362
C71×#20332
C71×#20002
C71×#19992
C71×#19582
C71×#19542
C71×#18042
C71×#17882
C71×#17862
#2424571