Finite Group Databasebeta

← C71×#24257 #31845129

Subgroups — C71×#24257 #31845129

Order 18176.

1650 conjugacy classes of subgroups.

The subgroup lattice has 966 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×#442×C71C211yesmaximal, characteristic, complemented
6C71×#2537C211yesmaximal, characteristic, complemented
7C71×#2035C211yesmaximal, characteristic, complemented
8C71×#2034C211yesmaximal, characteristic, complemented
9C71×#2000C211yesmaximal, characteristic, complemented
10C71×#1999C211yesmaximal, characteristic, complemented
11C71×#1959C211yesmaximal, characteristic, complemented
12C71×#1955C211yesmaximal, characteristic, complemented
13C71×#1802C211yesmaximal, 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×C71—21no—
28C2×#121×C71C2211yescharacteristic
29C2×#121×C71C2211yescharacteristic
30C2×#121×C71C2211yescharacteristic, complemented
31C2×#120×C71—21no—
32C2×C4×D4×C71C2211yescharacteristic
33C2×C4×D4×C71C2211yescharacteristic
34C2×C4×D4×C71C2211yescharacteristic, complemented
35C22×C22⋊C4×C71—21no—
36#463×C71—24no—
37#449×C71—24no—
38#447×C71—24no—
39#442×C71—24no—
40C2×#106×C71C2211yescharacteristic, complemented
41C2×C4⋊C8×C71C2211yescharacteristic, complemented
42C2×#103×C71C2211yescharacteristic, complemented
43C2×#103×C71C2211yescharacteristic, complemented
44C2×#103×C71C2211yescharacteristic, complemented
45C2×#102×C71C2211yescharacteristic
46C2×#102×C71C2211yescharacteristic
47C2×#102×C71C2211yescharacteristic
48C2×#102×C71C2211yescharacteristic
49C2×#102×C71C2211yescharacteristic
50C2×#102×C71C2211yescharacteristic
51C2×#102×C71C2211yescharacteristic, complemented
52C2×C22⋊C8×C71C2211yescharacteristic
53C2×C22⋊C8×C71C2211yescharacteristic
54C2×C22⋊C8×C71C2211yescharacteristic, complemented
55C2×C22⋊C8×C71C2211yescharacteristic, complemented
56C2×#97×C71C2211yescharacteristic, complemented
57#394×C71—21no—
58#394×C71—21no—
59#384×C71C2211yescharacteristic, complemented
60#380×C71—21no—
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#121×C71—44no—
119#120×C71—28no—
120C4×D4×C71—22no—
121C4×D4×C71—22no—
122C4×D4×C71—22no—
123C4×D4×C71—22no—
124C4×D4×C71—22no—
125C4×D4×C71D414yescomplemented
126C2×C4⋊C4×C71—21no—
127C2×C4⋊C4×C71—21no—
128C2×C4⋊C4×C71—21no—
129C2×C4⋊C4×C71D411yescharacteristic
130C2×C4⋊C4×C71C2311yescharacteristic
131C2×C4⋊C4×C71C2311yescharacteristic
132C2×C4⋊C4×C71C2311yescharacteristic
133C2×C4⋊C4×C71C2311yescharacteristic
134C2×C22⋊C4×C71—28no—
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×C71—21no—
143C2×C22⋊C4×C71—21no—
144C2×C22⋊C4×C71—21no—
145C2×C22⋊C4×C71D411yescharacteristic
146C2×C22⋊C4×C71D411yescharacteristic
147C2×C42×C71C2311yescharacteristic
148#106×C71—22no—
149C4⋊C8×C71—22no—
150#103×C71—22no—
151#103×C71—22no—
152#103×C71—41no—
153#102×C71—22no—
154#102×C71—22no—
155#102×C71—22no—
156#102×C71—22no—
157#102×C71—22no—
158#102×C71—22no—
159#102×C71—41no—
160C22⋊C8×C71—22no—
161C22⋊C8×C71—22no—
162C22⋊C8×C71—41no—
163C22⋊C8×C71—41no—
164#97×C71—22no—
165#95×C71—21no—
166#95×C71—21no—
167C24×C71—21no—
168C24×C71—24no—
169C24×C71—21no—
170C24×C71—21no—
171C24×C71—42no—
172C24×C71—42no—
173C24×C71—42no—
174C24×C71—42no—
175C24×C71—81no—
176C24×C71—81no—
177C24×C71C2×D411yescharacteristic
178C24×C71C2×D411yescharacteristic
179#41×C71—44no—
180#41×C71—44no—
181#41×C71—44no—
182#41×C71—44no—
183C2×Q8×C71—21no—
184C2×Q8×C71—21no—
185C2×Q8×C71—21no—
186C2×Q8×C71—21no—
187C2×Q8×C71—21no—
188C2×Q8×C71C2×D412yes—
189C2×D4×C71—24no—
190C2×D4×C71—24no—
191C2×D4×C71—22no—
192C2×D4×C71—24no—
193C2×D4×C71—22no—
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—21no—
207C2×D4×C71—41no—
208C2×D4×C71—42no—
209C2×D4×C71—42no—
210C2×D4×C71—44no—
211C2×D4×C71—44no—
212C2×D4×C71—44no—
213C2×D4×C71—42no—
214C2×D4×C71—42no—
215C2×D4×C71—44no—
216C2×D4×C71—42no—
217C2×D4×C71—42no—
218C2×D4×C71—42no—
219C2×D4×C71—42no—
220C2×D4×C71—81no—
221C2×D4×C71—81no—
222C2×D4×C71—81no—
223C2×D4×C71—81no—
224C2×D4×C71C2×D412yes—
225C2×D4×C71C2×D412yes—
226C2×D4×C71C2×D412yes—
227C2×D4×C71C2×D412yes—
228C2×D4×C71#4112yes—
229C22×C4×C71—24no—
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—21no—
244C22×C4×C71—24no—
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71—42no—
249C22×C4×C71—42no—
250C22×C4×C71—42no—
251C22×C4×C71—42no—
252C22×C4×C71—42no—
253C22×C4×C71—81no—
254C22×C4×C71—81no—
255C22×C4×C71C2×D411yescharacteristic
256C22×C4×C71C2×D411yescharacteristic
257C22×C4×C71C2×D411yescharacteristic
258C22×C4×C71C2×D411yescharacteristic
259C22×C4×C71C2411yescharacteristic
260SD16×C71—44no—
261D8×C71—28no—
262D8×C71—44no—
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×C71—21no—
274C2×C8×C71C2×D412yes—
275C4⋊C4×C71—24no—
276C4⋊C4×C71—22no—
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—42no—
285C4⋊C4×C71—81no—
286C4⋊C4×C71C2×D412yes—
287C22⋊C4×C71—24no—
288C22⋊C4×C71—24no—
289C22⋊C4×C71—22no—
290C22⋊C4×C71—24no—
291C22⋊C4×C71—24no—
292C22⋊C4×C71—24no—
293C22⋊C4×C71—22no—
294C22⋊C4×C71—42no—
295C22⋊C4×C71—42no—
296C22⋊C4×C71—42no—
297C22⋊C4×C71—42no—
298C22⋊C4×C71—42no—
299C42×C71C2×D412yes—
300C42×C71C2×D412yes—
301C23×C71—21no—
302C23×C71—22no—
303C23×C71—21no—
304C23×C71—22no—
305C23×C71—21no—
306C23×C71—22no—
307C23×C71—21no—
308C23×C71—21no—
309C23×C71—21no—
310C23×C71—22no—
311C23×C71—21no—
312C23×C71—22no—
313C23×C71—21no—
314C23×C71—21no—
315C23×C71—21no—
316C23×C71—21no—
317C23×C71—21no—
318C23×C71—21no—
319C23×C71—48no—
320C23×C71—48no—
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—41no—
335C23×C71—41no—
336C23×C71—41no—
337C23×C71—84no—
338C23×C71—84no—
339C23×C71—84no—
340C23×C71—84no—
341C23×C71—84no—
342C23×C71AGL(1,ℤ/8)12yes—
343C23×C71C22×D411yescharacteristic
344Q8×C71—22no—
345Q8×C71—22no—
346Q8×C71—41no—
347Q8×C71—41no—
348D4×C71—22no—
349D4×C71—22no—
350D4×C71—22no—
351D4×C71—22no—
352D4×C71—22no—
353D4×C71—22no—
354D4×C71—22no—
355D4×C71—44no—
356D4×C71—48no—
357D4×C71—48no—
358D4×C71—41no—
359D4×C71—41no—
360D4×C71—41no—
361D4×C71—41no—
362D4×C71—84no—
363D4×C71—84no—
364D4×C71—84no—
365D4×C71#12114yescomplemented
366C2×C4×C71—21no—
367C2×C4×C71—21no—
368C2×C4×C71—21no—
369C2×C4×C71—21no—
370C2×C4×C71—22no—
371C2×C4×C71—21no—
372C2×C4×C71—22no—
373C2×C4×C71—21no—
374C2×C4×C71—21no—
375C2×C4×C71—21no—
376C2×C4×C71—21no—
377C2×C4×C71—21no—
378C2×C4×C71—48no—
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—41no—
398C2×C4×C71—41no—
399C2×C4×C71—41no—
400C2×C4×C71—84no—
401C2×C4×C71—84no—
402C2×C4×C71#12012yes—
403C2×C4×C71#12012yes—
404C2×C4×C71C22×D411yescharacteristic
405C2×C4×C71C22×D411yescharacteristic
406C2×C4×C71C22×D411yescharacteristic
407C2×C4×C71C2×#4111yescharacteristic
408C2×C4×C71H(5,𝔽2)11yescharacteristic
409C2×C4×C71H(5,𝔽2)11yescharacteristic
410C8×C71—22no—
411C8×C71—41no—
412C8×C71—41no—
413C8×C71—41no—
414C22×C71—24no—
415C22×C71—22no—
416C22×C71—22no—
417C22×C71—22no—
418C22×C71—41no—
419C22×C71—42no—
420C22×C71—42no—
421C22×C71—41no—
422C22×C71—42no—
423C22×C71—42no—
424C22×C71—41no—
425C22×C71—42no—
426C22×C71—41no—
427C22×C71—42no—
428C22×C71—41no—
429C22×C71—42no—
430C22×C71—42no—
431C22×C71—41no—
432C22×C71—42no—
433C22×C71—41no—
434C22×C71—42no—
435C22×C71—41no—
436C22×C71—42no—
437C22×C71—41no—
438C22×C71—42no—
439C22×C71—41no—
440C22×C71—41no—
441C22×C71—816no—
442C22×C71—81no—
443C22×C71—81no—
444C22×C71—81no—
445C22×C71—81no—
446C22×C71—81no—
447C22×C71—81no—
448C22×C71—81no—
449C22×C71—81no—
450C22×C71C2×#12011yescharacteristic
451C22×C71D4211yescharacteristic
452C22×C71#54611yescharacteristic
453C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
454C22×C71#57511yescharacteristic
455C22×C71#57611yescharacteristic
456C22×C71#57711yescharacteristic
457C4×C71—22no—
458C4×C71—22no—
459C4×C71—41no—
460C4×C71—41no—
461C4×C71—42no—
462C4×C71—42no—
463C4×C71—81no—
464C4×C71—81no—
465C4×C71—81no—
466C4×C71C2×#12111yescharacteristic
467C4×C71#53511yescharacteristic
468C4×C71D4211yescharacteristic
469C4×C71#54611yescharacteristic
470#24257C7111yesmaximal, characteristic, direct product factor, Sylow
471C2×C71—42no—
472C2×C71—44no—
473C2×C71—81no—
474C2×C71—82no—
475C2×C71—82no—
476C2×C71#240811yescharacteristic
477C2×C71#300611yescharacteristic
478C2×C71#301211yescharacteristic
479C2×C71#326411yescharacteristic
480C2×C71#326711yescharacteristic
481C2×C71#330611yescharacteristic
482C2×C71#331911yescharacteristic
483C2×#546C2×C7111yescharacteristic, complemented
484C2×#463C2×C7111yescharacteristic, complemented
485C2×#449C2×C7111yescharacteristic, complemented
486C2×#447C2×C7111yescharacteristic, complemented
487C2×#442C2×C7111yescharacteristic, complemented
488#2537C2×C7111yescharacteristic, complemented
489#2035C2×C7111yescharacteristic, complemented
490#2034C2×C7111yescharacteristic, complemented
491#2000C2×C7111yescharacteristic, complemented
492#1999C2×C7111yescharacteristic, complemented
493#1959C2×C7111yescharacteristic, complemented
494#1955C2×C7111yescharacteristic, complemented
495#1802C2×C7111yescharacteristic, complemented
496#1788C2×C7111yescharacteristic, complemented
497#1786C2×C7111yescharacteristic, complemented
498C71#2425711yescharacteristic, direct product factor, Sylow
499C22×#41C22×C7111yescharacteristic
500C23×D4C22×C7111yescharacteristic
501C22×SD16C22×C7111yescharacteristic, complemented
502C22×D8C22×C7111yescharacteristic
503C22×D8C22×C7111yescharacteristic
504#546—24no—
505#546—24no—
506C2×#124C22×C7111yescharacteristic
507C2×#123—21no—
508C2×C22⋊Q8C22×C7111yescharacteristic
509C2×#121—21no—
510C2×#121—21no—
511C2×#121C22×C7111yescharacteristic
512C2×#121C22×C7111yescharacteristic
513C2×#121C22×C7111yescharacteristic, complemented
514C2×#120—21no—
515C2×C4×D4C22×C7111yescharacteristic
516C2×C4×D4C22×C7111yescharacteristic
517C2×C4×D4C22×C7111yescharacteristic, complemented
518C22×C22⋊C4—21no—
519#463—24no—
520#449—24no—
521#447—24no—
522#442—24no—
523C2×#106C22×C7111yescharacteristic, complemented
524C2×C4⋊C8C22×C7111yescharacteristic, complemented
525C2×#103C22×C7111yescharacteristic, complemented
526C2×#103C22×C7111yescharacteristic, complemented
527C2×#103C22×C7111yescharacteristic, complemented
528C2×#102C22×C7111yescharacteristic
529C2×#102C22×C7111yescharacteristic
530C2×#102C22×C7111yescharacteristic
531C2×#102C22×C7111yescharacteristic
532C2×#102C22×C7111yescharacteristic
533C2×#102C22×C7111yescharacteristic
534C2×#102C22×C7111yescharacteristic, complemented
535C2×C22⋊C8C22×C7111yescharacteristic
536C2×C22⋊C8C22×C7111yescharacteristic
537C2×C22⋊C8C22×C7111yescharacteristic, complemented
538C2×C22⋊C8C22×C7111yescharacteristic, complemented
539C2×#97C22×C7111yescharacteristic, complemented
540#394—21no—
541#394—21no—
542#384C22×C7111yescharacteristic, complemented
543#380—21no—
544#380C22×C7111yescharacteristic
545#380C22×C7111yescharacteristic, complemented
546#340C22×C7111yescharacteristic, complemented
547#340C22×C7111yescharacteristic, complemented
548C25—21no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—41no—
554C2×#41—41no—
555C22×Q8C23×C7111yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C7111yescharacteristic
568C22×D4C23×C7111yescharacteristic
569C22×D4C23×C7111yescharacteristic
570C22×D4C23×C7111yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C7111yescharacteristic
575C23×C4C23×C7111yescharacteristic
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—41no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—41no—
584C2×D8D4×C7114yescomplemented
585C22×C8C23×C7111yescharacteristic
586C22×C8C23×C7111yescharacteristic
587C22×C8C23×C7111yescharacteristic
588C22×C8C23×C7111yescharacteristic
589#124—22no—
590#124D4×C7114yescomplemented
591#123—28no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#121—41no—
601#121—44no—
602#120—28no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4D4×C7114yescomplemented
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4D4×C7111yescharacteristic
613C2×C4⋊C4C23×C7111yescharacteristic
614C2×C4⋊C4C23×C7111yescharacteristic
615C2×C4⋊C4C23×C7111yescharacteristic
616C2×C4⋊C4C23×C7111yescharacteristic
617C2×C22⋊C4—28no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4D4×C7111yescharacteristic
629C2×C22⋊C4D4×C7111yescharacteristic
630C2×C42C23×C7111yescharacteristic
631#106—22no—
632C4⋊C8—22no—
633#103—22no—
634#103—22no—
635#103—41no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645C22⋊C8—41no—
646C22⋊C8—41no—
647#97—22no—
648#95—21no—
649#95—21no—
650C24—21no—
651C24—24no—
652C24—21no—
653C24—21no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—81no—
659C24—81no—
660C24C2×D4×C7111yescharacteristic
661C24C2×D4×C7111yescharacteristic
662#41—44no—
663#41—44no—
664#41—44no—
665#41—44no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8C2×D4×C7112yes—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
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—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—44no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4C2×D4×C7112yes—
708C2×D4C2×D4×C7112yes—
709C2×D4C2×D4×C7112yes—
710C2×D4C2×D4×C7112yes—
711C2×D4#41×C7112yes—
712C22×C4—24no—
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—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—24no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—81no—
737C22×C4—81no—
738C22×C4C2×D4×C7111yescharacteristic
739C22×C4C2×D4×C7111yescharacteristic
740C22×C4C2×D4×C7111yescharacteristic
741C22×C4C2×D4×C7111yescharacteristic
742C22×C4C24×C7111yescharacteristic
743SD16—44no—
744D8—28no—
745D8—44no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8C2×D4×C7112yes—
758C4⋊C4—24no—
759C4⋊C4—22no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C7112yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—42no—
778C22⋊C4—42no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C42C2×D4×C7112yes—
783C42C2×D4×C7112yes—
784C23—21no—
785C23—22no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—48no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23AGL(1,ℤ/8)×C7112yes—
826C23C22×D4×C7111yescharacteristic
827Q8—22no—
828Q8—22no—
829Q8—41no—
830Q8—41no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—44no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—84no—
846D4—84no—
847D4—84no—
848D4#121×C7114yescomplemented
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
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—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—84no—
884C2×C4—84no—
885C2×C4#120×C7112yes—
886C2×C4#120×C7112yes—
887C2×C4C22×D4×C7111yescharacteristic
888C2×C4C22×D4×C7111yescharacteristic
889C2×C4C22×D4×C7111yescharacteristic
890C2×C4C2×#41×C7111yescharacteristic
891C2×C4H(5,𝔽2)×C7111yescharacteristic
892C2×C4H(5,𝔽2)×C7111yescharacteristic
893C8—22no—
894C8—41no—
895C8—41no—
896C8—41no—
897C22—22no—
898C22—24no—
899C22—22no—
900C22—22no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—42no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—42no—
915C22—42no—
916C22—41no—
917C22—42no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—42no—
922C22—41no—
923C22—42no—
924C22—816no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22C2×#120×C7111yescharacteristic
934C22D42×C7111yescharacteristic
935C22#546×C7111yescharacteristic
936C22C2×AGL(1,ℤ/8)×C7111yescharacteristic
937C22#575×C7111yescharacteristic
938C22#576×C7111yescharacteristic
939C22#577×C7111yescharacteristic
940C4—22no—
941C4—22no—
942C4—41no—
943C4—41no—
944C4—42no—
945C4—42no—
946C4—81no—
947C4—81no—
948C4—81no—
949C4C2×#121×C7111yescharacteristic
950C4#535×C7111yescharacteristic
951C4D42×C7111yescharacteristic
952C4#546×C7111yescharacteristic
953C2—42no—
954C2—44no—
955C2—81no—
956C2—82no—
957C2—82no—
958C2C71×#240811yescharacteristic
959C2C71×#300611yescharacteristic
960C2C71×#301211yescharacteristic
961C2C71×#326411yescharacteristic
962C2C71×#326711yescharacteristic
963C2C71×#330611yescharacteristic
964C2C71×#331911yescharacteristic
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×#442×C71C2semidirect
6. C71×#2537C2semidirect
7. C71×#2035C2semidirect
8. C71×#2034C2semidirect
9. C71×#2000C2semidirect
10. C71×#1999C2semidirect
11. C71×#1959C2semidirect
12. C71×#1955C2semidirect
13. C71×#1802C2semidirect
14. C71×#1788C2semidirect
15. C71×#1786C2semidirect
18. C22×SD16×C71C22semidirect
30. C2×#121×C71C22semidirect
34. C2×C4×D4×C71C22semidirect
40. C2×#106×C71C22semidirect
41. C2×C4⋊C8×C71C22semidirect
42. C2×#103×C71C22semidirect
43. C2×#103×C71C22semidirect
44. C2×#103×C71C22semidirect
51. C2×#102×C71C22semidirect
54. C2×C22⋊C8×C71C22semidirect
55. C2×C22⋊C8×C71C22semidirect
56. C2×#97×C71C22semidirect
59. #384×C71C22semidirect
62. #380×C71C22semidirect
63. #340×C71C22semidirect
64. #340×C71C22semidirect
101. C2×D8×C71D4semidirect
107. #124×C71D4semidirect
125. C4×D4×C71D4semidirect
365. D4×C71#121semidirect
470. #24257C71direct (N × H)
483. C2×#546C2×C71semidirect
484. C2×#463C2×C71semidirect
485. C2×#449C2×C71semidirect
486. C2×#447C2×C71semidirect
487. C2×#442C2×C71semidirect
488. #2537C2×C71semidirect
489. #2035C2×C71semidirect
490. #2034C2×C71semidirect
491. #2000C2×C71semidirect
492. #1999C2×C71semidirect
493. #1959C2×C71semidirect
494. #1955C2×C71semidirect
495. #1802C2×C71semidirect
496. #1788C2×C71semidirect
497. #1786C2×C71semidirect
498. C71#24257direct (N × H)
501. C22×SD16C22×C71semidirect
513. C2×#121C22×C71semidirect
517. C2×C4×D4C22×C71semidirect
523. C2×#106C22×C71semidirect
524. C2×C4⋊C8C22×C71semidirect
525. C2×#103C22×C71semidirect
526. C2×#103C22×C71semidirect
527. C2×#103C22×C71semidirect
534. C2×#102C22×C71semidirect
537. C2×C22⋊C8C22×C71semidirect
538. C2×C22⋊C8C22×C71semidirect
539. C2×#97C22×C71semidirect
542. #384C22×C71semidirect
545. #380C22×C71semidirect
546. #340C22×C71semidirect
547. #340C22×C71semidirect
584. C2×D8D4×C71semidirect
590. #124D4×C71semidirect
608. C4×D4D4×C71semidirect
848. D4#121×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×#442×C712
C71×#25372
C71×#20352
C71×#20342
C71×#20002
C71×#19992
C71×#19592
C71×#19552
C71×#18022
C71×#17882
C71×#17862
#2425771