Finite Group Databasebeta

← C71×#24444 #31845316

Subgroups — C71×#24444 #31845316

Order 18176.

1662 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C71C211yesmaximal, characteristic, complemented
2C2×#469×C71C211yesmaximal, characteristic, complemented
3C2×#449×C71C211yesmaximal, characteristic, complemented
4C2×#447×C71C211yesmaximal, characteristic, complemented
5C2×#417×C71C211yesmaximal, characteristic, complemented
6C71×#2416C211yesmaximal, characteristic, complemented
7C71×#2042C211yesmaximal, characteristic, complemented
8C71×#2035C211yesmaximal, characteristic, complemented
9C71×#2012C211yesmaximal, characteristic, complemented
10C71×#2000C211yesmaximal, characteristic, complemented
11C71×#1879C211yesmaximal, characteristic, complemented
12C71×#1874C211yesmaximal, characteristic, complemented
13C71×#1870C211yesmaximal, characteristic, complemented
14C71×#1864C211yesmaximal, characteristic, complemented
15C71×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C71C2211yescharacteristic
17C23×D4×C71C2211yescharacteristic
18C22×SD16×C71C2211yescharacteristic, complemented
19C22×D8×C71C2211yescharacteristic
20C22×D8×C71C2211yescharacteristic
21C22×M16×C71C2211yescharacteristic, complemented
22#546×C71—24no—
23#546×C71—24no—
24C2×#124×C71C2211yescharacteristic
25C2×#123×C71—21no—
26C2×C22⋊Q8×C71C2211yescharacteristic
27C2×#121×C71—21no—
28C2×#121×C71—21no—
29C2×#121×C71C2211yescharacteristic
30C2×#121×C71C2211yescharacteristic
31C2×#121×C71C2211yescharacteristic, complemented
32C2×#120×C71—21no—
33C2×C4×D4×C71C2211yescharacteristic
34C2×C4×D4×C71C2211yescharacteristic
35C22×C4⋊C4×C71C2211yescharacteristic, complemented
36C22×C22⋊C4×C71—21no—
37#469×C71—24no—
38#449×C71—24no—
39#447×C71—24no—
40C2×#106×C71C2211yescharacteristic, complemented
41#417×C71—24no—
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
55#396×C71—21no—
56#394×C71—21no—
57#390×C71C2211yescharacteristic, complemented
58#389×C71C2211yescharacteristic, complemented
59#386×C71—21no—
60#380×C71C2211yescharacteristic
61#340×C71C2211yescharacteristic, complemented
62#340×C71C2211yescharacteristic, complemented
63#336×C71C2211yescharacteristic, complemented
64#336×C71C2211yescharacteristic, complemented
65C25×C71—21no—
66C2×#41×C71—22no—
67C2×#41×C71—22no—
68C2×#41×C71—22no—
69C2×#41×C71—41no—
70C2×#41×C71—41no—
71C2×#41×C71D414yescomplemented
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—41no—
95C2×SD16×C71—41no—
96C2×D8×C71—22no—
97C2×D8×C71—22no—
98C2×D8×C71—22no—
99C2×D8×C71—22no—
100C2×D8×C71—22no—
101C2×D8×C71—41no—
102C2×M16×C71—22no—
103C2×M16×C71—22no—
104C2×M16×C71—41no—
105C22×C8×C71C2311yescharacteristic
106C22×C8×C71C2311yescharacteristic
107C22×C8×C71C2311yescharacteristic
108C22×C8×C71C2311yescharacteristic
109#124×C71—22no—
110#124×C71—22no—
111#123×C71—28no—
112C22⋊Q8×C71—22no—
113C22⋊Q8×C71—22no—
114#121×C71—28no—
115#121×C71—22no—
116#121×C71—22no—
117#121×C71—22no—
118#121×C71—22no—
119#121×C71—41no—
120#121×C71—44no—
121#121×C71D414yescomplemented
122#120×C71—28no—
123C4×D4×C71—22no—
124C4×D4×C71—22no—
125C4×D4×C71—22no—
126C4×D4×C71—22no—
127C2×C4⋊C4×C71—21no—
128C2×C4⋊C4×C71—22no—
129C2×C4⋊C4×C71—21no—
130C2×C4⋊C4×C71—21no—
131C2×C4⋊C4×C71—41no—
132C2×C4⋊C4×C71D411yescharacteristic
133C2×C4⋊C4×C71C2311yescharacteristic
134C2×C4⋊C4×C71C2311yescharacteristic
135C2×C4⋊C4×C71C2311yescharacteristic
136C2×C4⋊C4×C71C2311yescharacteristic
137C2×C22⋊C4×C71—28no—
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×C71—21no—
146C2×C22⋊C4×C71—21no—
147C2×C22⋊C4×C71—21no—
148C2×C22⋊C4×C71D411yescharacteristic
149C2×C22⋊C4×C71D411yescharacteristic
150C2×C42×C71C2311yescharacteristic
151#106×C71—22no—
152#103×C71—22no—
153#103×C71—22no—
154#103×C71—22no—
155#102×C71—22no—
156#102×C71—22no—
157#102×C71—22no—
158#102×C71—22no—
159#102×C71—22no—
160#102×C71—41no—
161#102×C71D414yescomplemented
162C22⋊C8×C71—22no—
163C22⋊C8×C71—22no—
164C22⋊C8×C71—41no—
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—28no—
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—22no—
191C2×D4×C71—24no—
192C2×D4×C71—22no—
193C2×D4×C71—24no—
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—21no—
208C2×D4×C71—41no—
209C2×D4×C71—42no—
210C2×D4×C71—42no—
211C2×D4×C71—42no—
212C2×D4×C71—44no—
213C2×D4×C71—44no—
214C2×D4×C71—44no—
215C2×D4×C71—42no—
216C2×D4×C71—42no—
217C2×D4×C71—44no—
218C2×D4×C71—42no—
219C2×D4×C71—42no—
220C2×D4×C71—42no—
221C2×D4×C71—42no—
222C2×D4×C71—81no—
223C2×D4×C71—81no—
224C2×D4×C71—81no—
225C2×D4×C71C2×D412yes—
226C2×D4×C71C2×D412yes—
227C2×D4×C71C2×D412yes—
228C2×D4×C71#4112yes—
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—24no—
237C22×C4×C71—24no—
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—21no—
245C22×C4×C71—21no—
246C22×C4×C71—42no—
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×C71C2×D411yescharacteristic
254C22×C4×C71C2×D411yescharacteristic
255C22×C4×C71C2×D411yescharacteristic
256C22×C4×C71C2×D411yescharacteristic
257C22×C4×C71C2×D412yes—
258C22×C4×C71C2×D412yes—
259C22×C4×C71C2411yescharacteristic
260SD16×C71—44no—
261D8×C71—44no—
262D8×C71—44no—
263M16×C71—44no—
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×C71—21no—
275C2×C8×C71C2×D412yes—
276C4⋊C4×C71—24no—
277C4⋊C4×C71—22no—
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—42no—
286C4⋊C4×C71C2×D412yes—
287C4⋊C4×C71C2×D412yes—
288C22⋊C4×C71—24no—
289C22⋊C4×C71—24no—
290C22⋊C4×C71—24no—
291C22⋊C4×C71—24no—
292C22⋊C4×C71—22no—
293C22⋊C4×C71—22no—
294C22⋊C4×C71—24no—
295C22⋊C4×C71—42no—
296C22⋊C4×C71—42no—
297C22⋊C4×C71—42no—
298C22⋊C4×C71—42no—
299C22⋊C4×C71—81no—
300C42×C71—21no—
301C42×C71—21no—
302C23×C71—21no—
303C23×C71—22no—
304C23×C71—21no—
305C23×C71—21no—
306C23×C71—22no—
307C23×C71—21no—
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—21no—
317C23×C71—22no—
318C23×C71—48no—
319C23×C71—48no—
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—41no—
335C23×C71—41no—
336C23×C71—41no—
337C23×C71—84no—
338C23×C71—84no—
339C23×C71—84no—
340C23×C71—84no—
341C23×C71—84no—
342C23×C71#12012yes—
343C23×C71AGL(1,ℤ/8)12yes—
344C23×C71C22×D411yescharacteristic
345Q8×C71—22no—
346Q8×C71—22no—
347Q8×C71—41no—
348Q8×C71—41no—
349D4×C71—22no—
350D4×C71—22no—
351D4×C71—22no—
352D4×C71—22no—
353D4×C71—22no—
354D4×C71—44no—
355D4×C71—48no—
356D4×C71—48no—
357D4×C71—41no—
358D4×C71—41no—
359D4×C71—41no—
360D4×C71—41no—
361D4×C71—41no—
362D4×C71—41no—
363D4×C71—84no—
364D4×C71—84no—
365D4×C71—84no—
366D4×C71#12114yescomplemented
367C2×C4×C71—21no—
368C2×C4×C71—21no—
369C2×C4×C71—22no—
370C2×C4×C71—22no—
371C2×C4×C71—22no—
372C2×C4×C71—22no—
373C2×C4×C71—21no—
374C2×C4×C71—21no—
375C2×C4×C71—22no—
376C2×C4×C71—22no—
377C2×C4×C71—21no—
378C2×C4×C71—21no—
379C2×C4×C71—22no—
380C2×C4×C71—21no—
381C2×C4×C71—21no—
382C2×C4×C71—21no—
383C2×C4×C71—21no—
384C2×C4×C71—21no—
385C2×C4×C71—48no—
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—41no—
401C2×C4×C71—41no—
402C2×C4×C71—84no—
403C2×C4×C71—84no—
404C2×C4×C71#12012yes—
405C2×C4×C71C22×D411yescharacteristic
406C2×C4×C71C22×D411yescharacteristic
407C2×C4×C71C22×D411yescharacteristic
408C2×C4×C71C2×#4111yescharacteristic
409C2×C4×C71H(5,𝔽2)11yescharacteristic
410C2×C4×C71H(5,𝔽2)11yescharacteristic
411C8×C71—22no—
412C8×C71—41no—
413C8×C71—41no—
414C8×C71—41no—
415C22×C71—22no—
416C22×C71—24no—
417C22×C71—22no—
418C22×C71—22no—
419C22×C71—22no—
420C22×C71—22no—
421C22×C71—22no—
422C22×C71—41no—
423C22×C71—42no—
424C22×C71—41no—
425C22×C71—42no—
426C22×C71—42no—
427C22×C71—41no—
428C22×C71—41no—
429C22×C71—41no—
430C22×C71—42no—
431C22×C71—41no—
432C22×C71—42no—
433C22×C71—41no—
434C22×C71—41no—
435C22×C71—42no—
436C22×C71—42no—
437C22×C71—42no—
438C22×C71—42no—
439C22×C71—816no—
440C22×C71—81no—
441C22×C71—81no—
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×C71—81no—
451C22×C71C2×#12011yescharacteristic
452C22×C71D4211yescharacteristic
453C22×C71#54611yescharacteristic
454C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
455C22×C71#57511yescharacteristic
456C22×C71#57611yescharacteristic
457C22×C71#57711yescharacteristic
458C4×C71—22no—
459C4×C71—41no—
460C4×C71—42no—
461C4×C71—41no—
462C4×C71—42no—
463C4×C71—41no—
464C4×C71—42no—
465C4×C71—81no—
466C4×C71—81no—
467C4×C71C2×#12111yescharacteristic
468C4×C71#53411yescharacteristic
469C4×C71D4211yescharacteristic
470C4×C71#54611yescharacteristic
471#24444C7111yesmaximal, characteristic, direct product factor, Sylow
472C2×C71—42no—
473C2×C71—42no—
474C2×C71—44no—
475C2×C71—82no—
476C2×C71—161no—
477C2×C71#241011yescharacteristic
478C2×C71#300611yescharacteristic
479C2×C71#301211yescharacteristic
480C2×C71#326411yescharacteristic
481C2×C71#327511yescharacteristic
482C2×C71#330611yescharacteristic
483C2×C71#332211yescharacteristic
484C2×#546C2×C7111yescharacteristic, complemented
485C2×#469C2×C7111yescharacteristic, complemented
486C2×#449C2×C7111yescharacteristic, complemented
487C2×#447C2×C7111yescharacteristic, complemented
488C2×#417C2×C7111yescharacteristic, complemented
489#2416C2×C7111yescharacteristic, complemented
490#2042C2×C7111yescharacteristic, complemented
491#2035C2×C7111yescharacteristic, complemented
492#2012C2×C7111yescharacteristic, complemented
493#2000C2×C7111yescharacteristic, complemented
494#1879C2×C7111yescharacteristic, complemented
495#1874C2×C7111yescharacteristic, complemented
496#1870C2×C7111yescharacteristic, complemented
497#1864C2×C7111yescharacteristic, complemented
498#1786C2×C7111yescharacteristic, complemented
499C71#2444411yescharacteristic, direct product factor, Sylow
500C22×#41C22×C7111yescharacteristic
501C23×D4C22×C7111yescharacteristic
502C22×SD16C22×C7111yescharacteristic, complemented
503C22×D8C22×C7111yescharacteristic
504C22×D8C22×C7111yescharacteristic
505C22×M16C22×C7111yescharacteristic, complemented
506#546—24no—
507#546—24no—
508C2×#124C22×C7111yescharacteristic
509C2×#123—21no—
510C2×C22⋊Q8C22×C7111yescharacteristic
511C2×#121—21no—
512C2×#121—21no—
513C2×#121C22×C7111yescharacteristic
514C2×#121C22×C7111yescharacteristic
515C2×#121C22×C7111yescharacteristic, complemented
516C2×#120—21no—
517C2×C4×D4C22×C7111yescharacteristic
518C2×C4×D4C22×C7111yescharacteristic
519C22×C4⋊C4C22×C7111yescharacteristic, complemented
520C22×C22⋊C4—21no—
521#469—24no—
522#449—24no—
523#447—24no—
524C2×#106C22×C7111yescharacteristic, complemented
525#417—24no—
526C2×#103C22×C7111yescharacteristic, complemented
527C2×#103C22×C7111yescharacteristic, complemented
528C2×#103C22×C7111yescharacteristic, complemented
529C2×#102C22×C7111yescharacteristic
530C2×#102C22×C7111yescharacteristic
531C2×#102C22×C7111yescharacteristic
532C2×#102C22×C7111yescharacteristic
533C2×#102C22×C7111yescharacteristic
534C2×#102C22×C7111yescharacteristic
535C2×#102C22×C7111yescharacteristic, complemented
536C2×C22⋊C8C22×C7111yescharacteristic
537C2×C22⋊C8C22×C7111yescharacteristic
538C2×C22⋊C8C22×C7111yescharacteristic, complemented
539#396—21no—
540#394—21no—
541#390C22×C7111yescharacteristic, complemented
542#389C22×C7111yescharacteristic, complemented
543#386—21no—
544#380C22×C7111yescharacteristic
545#340C22×C7111yescharacteristic, complemented
546#340C22×C7111yescharacteristic, complemented
547#336C22×C7111yescharacteristic, complemented
548#336C22×C7111yescharacteristic, complemented
549C25—21no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—41no—
554C2×#41—41no—
555C2×#41D4×C7114yescomplemented
556C22×Q8C23×C7111yescharacteristic
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—22no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4—41no—
567C22×D4—41no—
568C22×D4D4×C7111yescharacteristic
569C22×D4C23×C7111yescharacteristic
570C22×D4C23×C7111yescharacteristic
571C22×D4C23×C7111yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4—21no—
575C23×C4C23×C7111yescharacteristic
576C23×C4C23×C7111yescharacteristic
577C2×SD16—22no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—41no—
586C2×M16—22no—
587C2×M16—22no—
588C2×M16—41no—
589C22×C8C23×C7111yescharacteristic
590C22×C8C23×C7111yescharacteristic
591C22×C8C23×C7111yescharacteristic
592C22×C8C23×C7111yescharacteristic
593#124—22no—
594#124—22no—
595#123—28no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598#121—28no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—41no—
604#121—44no—
605#121D4×C7114yescomplemented
606#120—28no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4D4×C7111yescharacteristic
617C2×C4⋊C4C23×C7111yescharacteristic
618C2×C4⋊C4C23×C7111yescharacteristic
619C2×C4⋊C4C23×C7111yescharacteristic
620C2×C4⋊C4C23×C7111yescharacteristic
621C2×C22⋊C4—28no—
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⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4D4×C7111yescharacteristic
633C2×C22⋊C4D4×C7111yescharacteristic
634C2×C42C23×C7111yescharacteristic
635#106—22no—
636#103—22no—
637#103—22no—
638#103—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—41no—
645#102D4×C7114yescomplemented
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—41no—
649#95—21no—
650#95—21no—
651C24—21no—
652C24—24no—
653C24—21no—
654C24—21no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—42no—
659C24—81no—
660C24—81no—
661C24C2×D4×C7111yescharacteristic
662C24C2×D4×C7111yescharacteristic
663#41—28no—
664#41—44no—
665#41—44no—
666#41—44no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8C2×D4×C7112yes—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—24no—
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—21no—
691C2×D4—21no—
692C2×D4—41no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—44no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4C2×D4×C7112yes—
710C2×D4C2×D4×C7112yes—
711C2×D4C2×D4×C7112yes—
712C2×D4#41×C7112yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4—81no—
736C22×C4—81no—
737C22×C4C2×D4×C7111yescharacteristic
738C22×C4C2×D4×C7111yescharacteristic
739C22×C4C2×D4×C7111yescharacteristic
740C22×C4C2×D4×C7111yescharacteristic
741C22×C4C2×D4×C7112yes—
742C22×C4C2×D4×C7112yes—
743C22×C4C24×C7111yescharacteristic
744SD16—44no—
745D8—44no—
746D8—44no—
747M16—44no—
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×C8—21no—
758C2×C8—21no—
759C2×C8C2×D4×C7112yes—
760C4⋊C4—24no—
761C4⋊C4—22no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—42no—
769C4⋊C4—42no—
770C4⋊C4C2×D4×C7112yes—
771C4⋊C4C2×D4×C7112yes—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—22no—
778C22⋊C4—24no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C22⋊C4—42no—
783C22⋊C4—81no—
784C42—21no—
785C42—21no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—22no—
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—41no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23—84no—
826C23#120×C7112yes—
827C23AGL(1,ℤ/8)×C7112yes—
828C23C22×D4×C7111yescharacteristic
829Q8—22no—
830Q8—22no—
831Q8—41no—
832Q8—41no—
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—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4#121×C7114yescomplemented
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—48no—
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—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—84no—
887C2×C4—84no—
888C2×C4#120×C7112yes—
889C2×C4C22×D4×C7111yescharacteristic
890C2×C4C22×D4×C7111yescharacteristic
891C2×C4C22×D4×C7111yescharacteristic
892C2×C4C2×#41×C7111yescharacteristic
893C2×C4H(5,𝔽2)×C7111yescharacteristic
894C2×C4H(5,𝔽2)×C7111yescharacteristic
895C8—22no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—22no—
900C22—22no—
901C22—24no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—41no—
914C22—42no—
915C22—42no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—816no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22C2×#120×C7111yescharacteristic
936C22D42×C7111yescharacteristic
937C22#546×C7111yescharacteristic
938C22C2×AGL(1,ℤ/8)×C7111yescharacteristic
939C22#575×C7111yescharacteristic
940C22#576×C7111yescharacteristic
941C22#577×C7111yescharacteristic
942C4—22no—
943C4—41no—
944C4—42no—
945C4—41no—
946C4—42no—
947C4—41no—
948C4—42no—
949C4—81no—
950C4—81no—
951C4C2×#121×C7111yescharacteristic
952C4#534×C7111yescharacteristic
953C4D42×C7111yescharacteristic
954C4#546×C7111yescharacteristic
955C2—42no—
956C2—42no—
957C2—44no—
958C2—82no—
959C2—161no—
960C2C71×#241011yescharacteristic
961C2C71×#300611yescharacteristic
962C2C71×#301211yescharacteristic
963C2C71×#326411yescharacteristic
964C2C71×#327511yescharacteristic
965C2C71×#330611yescharacteristic
966C2C71×#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×#469×C71C2semidirect
3. C2×#449×C71C2semidirect
4. C2×#447×C71C2semidirect
5. C2×#417×C71C2semidirect
6. C71×#2416C2semidirect
7. C71×#2042C2semidirect
8. C71×#2035C2semidirect
9. C71×#2012C2semidirect
10. C71×#2000C2semidirect
11. C71×#1879C2semidirect
12. C71×#1874C2semidirect
13. C71×#1870C2semidirect
14. C71×#1864C2semidirect
15. C71×#1786C2semidirect
18. C22×SD16×C71C22semidirect
21. C22×M16×C71C22semidirect
31. C2×#121×C71C22semidirect
35. C22×C4⋊C4×C71C22semidirect
40. C2×#106×C71C22semidirect
42. C2×#103×C71C22semidirect
43. C2×#103×C71C22semidirect
44. C2×#103×C71C22semidirect
51. C2×#102×C71C22semidirect
54. C2×C22⋊C8×C71C22semidirect
57. #390×C71C22semidirect
58. #389×C71C22semidirect
61. #340×C71C22semidirect
62. #340×C71C22semidirect
63. #336×C71C22semidirect
64. #336×C71C22semidirect
71. C2×#41×C71D4semidirect
121. #121×C71D4semidirect
161. #102×C71D4semidirect
366. D4×C71#121semidirect
471. #24444C71direct (N × H)
484. C2×#546C2×C71semidirect
485. C2×#469C2×C71semidirect
486. C2×#449C2×C71semidirect
487. C2×#447C2×C71semidirect
488. C2×#417C2×C71semidirect
489. #2416C2×C71semidirect
490. #2042C2×C71semidirect
491. #2035C2×C71semidirect
492. #2012C2×C71semidirect
493. #2000C2×C71semidirect
494. #1879C2×C71semidirect
495. #1874C2×C71semidirect
496. #1870C2×C71semidirect
497. #1864C2×C71semidirect
498. #1786C2×C71semidirect
499. C71#24444direct (N × H)
502. C22×SD16C22×C71semidirect
505. C22×M16C22×C71semidirect
515. C2×#121C22×C71semidirect
519. C22×C4⋊C4C22×C71semidirect
524. C2×#106C22×C71semidirect
526. C2×#103C22×C71semidirect
527. C2×#103C22×C71semidirect
528. C2×#103C22×C71semidirect
535. C2×#102C22×C71semidirect
538. C2×C22⋊C8C22×C71semidirect
541. #390C22×C71semidirect
542. #389C22×C71semidirect
545. #340C22×C71semidirect
546. #340C22×C71semidirect
547. #336C22×C71semidirect
548. #336C22×C71semidirect
555. C2×#41D4×C71semidirect
605. #121D4×C71semidirect
645. #102D4×C71semidirect
850. 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×#469×C712
C2×#449×C712
C2×#447×C712
C2×#417×C712
C71×#24162
C71×#20422
C71×#20352
C71×#20122
C71×#20002
C71×#18792
C71×#18742
C71×#18702
C71×#18642
C71×#17862
#2444471