Finite Group Databasebeta

← C71×#23860 #31844732

Subgroups — C71×#23860 #31844732

Order 18176.

2240 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C71C211yesmaximal, characteristic, complemented
2C2×D42×C71C211yesmaximal, characteristic, complemented
3C2×#449×C71C211yesmaximal, characteristic, complemented
4C2×#450×C71C211yesmaximal, characteristic, complemented
5C2×#447×C71C211yesmaximal, characteristic, complemented
6C71×#2407C211yesmaximal, characteristic, complemented
7C71×#2014C211yesmaximal, characteristic, complemented
8C71×#2011C211yesmaximal, characteristic, complemented
9C71×#2000C211yesmaximal, characteristic, complemented
10C71×#1999C211yesmaximal, characteristic, complemented
11C71×#1895C211yesmaximal, characteristic, complemented
12C71×#1879C211yesmaximal, characteristic, complemented
13C71×#1877C211yesmaximal, characteristic, complemented
14C71×#1870C211yesmaximal, characteristic, complemented
15C71×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C71C2211yescharacteristic, complemented
17C23×D4×C71—21no—
18C23×D4×C71C2211yescharacteristic
19C23×D4×C71C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C71—24no—
21C2×AGL(1,ℤ/8)×C71—24no—
22C2×AGL(1,ℤ/8)×C71—24no—
23C22×SD16×C71C2211yescharacteristic
24C22×SD16×C71C2211yescharacteristic, complemented
25C22×SD16×C71C2211yescharacteristic, complemented
26C22×D8×C71C2211yescharacteristic
27C22×D8×C71C2211yescharacteristic, complemented
28C22×D8×C71C2211yescharacteristic, complemented
29C22×M16×C71C2211yescharacteristic, complemented
30D42×C71—24no—
31D42×C71—24no—
32C2×#127×C71C2211yescharacteristic
33C2×C22⋊Q8×C71C2211yescharacteristic, complemented
34C2×#121×C71—21no—
35C2×#121×C71C2211yescharacteristic
36C2×#121×C71C2211yescharacteristic
37C2×#121×C71C2211yescharacteristic, complemented
38C2×#120×C71—21no—
39C2×#120×C71—21no—
40C2×C4×D4×C71C2211yescharacteristic
41C2×C4×D4×C71C2211yescharacteristic
42#450×C71—24no—
43#449×C71—24no—
44#447×C71—24no—
45C2×#103×C71C2211yescharacteristic, complemented
46C2×#102×C71C2211yescharacteristic
47C2×#102×C71C2211yescharacteristic
48C2×#102×C71C2211yescharacteristic, complemented
49C2×#102×C71C2211yescharacteristic, complemented
50C2×#102×C71C2211yescharacteristic, complemented
51C2×#102×C71C2211yescharacteristic, complemented
52C2×#102×C71C2211yescharacteristic, complemented
53C2×C22⋊C8×C71C2211yescharacteristic, complemented
54C2×C22⋊C8×C71C2211yescharacteristic, complemented
55C2×C22⋊C8×C71C2211yescharacteristic, complemented
56#394×C71—21no—
57#392×C71—21no—
58#391×C71C2211yescharacteristic, complemented
59#390×C71C2211yescharacteristic, complemented
60#386×C71—21no—
61#385×C71—21no—
62#380×C71C2211yescharacteristic, complemented
63#340×C71C2211yescharacteristic, complemented
64#340×C71C2211yescharacteristic, complemented
65#336×C71C2211yescharacteristic, complemented
66#336×C71C2211yescharacteristic, complemented
67C25×C71—21no—
68C25×C71—21no—
69C2×#41×C71—22no—
70C2×#41×C71—22no—
71C2×#41×C71—22no—
72C2×#41×C71—22no—
73C2×#41×C71—41no—
74C2×#41×C71—41no—
75C22×Q8×C71C2311yescharacteristic
76C22×D4×C71—22no—
77C22×D4×C71—22no—
78C22×D4×C71—28no—
79C22×D4×C71—21no—
80C22×D4×C71—21no—
81C22×D4×C71—22no—
82C22×D4×C71—22no—
83C22×D4×C71—22no—
84C22×D4×C71—22no—
85C22×D4×C71—21no—
86C22×D4×C71—21no—
87C22×D4×C71—21no—
88C22×D4×C71—21no—
89C22×D4×C71—21no—
90C22×D4×C71—22no—
91C22×D4×C71—21no—
92C22×D4×C71—41no—
93C22×D4×C71—41no—
94C22×D4×C71—41no—
95C22×D4×C71—41no—
96C22×D4×C71—44no—
97C22×D4×C71—44no—
98C22×D4×C71D411yescharacteristic
99C22×D4×C71D414yescomplemented
100C22×D4×C71C2311yescharacteristic
101C22×D4×C71C2311yescharacteristic
102C22×D4×C71C2311yescharacteristic
103C22×D4×C71C2311yescharacteristic
104C23×C4×C71—21no—
105C23×C4×C71—21no—
106C23×C4×C71C2311yescharacteristic
107C23×C4×C71C2311yescharacteristic
108AGL(1,ℤ/8)×C71—232no—
109C2×SD16×C71—22no—
110C2×SD16×C71—22no—
111C2×SD16×C71—22no—
112C2×SD16×C71—22no—
113C2×SD16×C71—22no—
114C2×SD16×C71—22no—
115C2×SD16×C71—22no—
116C2×SD16×C71—41no—
117C2×SD16×C71D414yescomplemented
118C2×D8×C71—22no—
119C2×D8×C71—22no—
120C2×D8×C71—22no—
121C2×D8×C71—22no—
122C2×D8×C71—22no—
123C2×D8×C71—22no—
124C2×D8×C71—22no—
125C2×D8×C71—41no—
126C2×D8×C71D414yescomplemented
127C2×M16×C71—22no—
128C2×M16×C71—22no—
129C2×M16×C71—22no—
130C22×C8×C71C2311yescharacteristic
131C22×C8×C71C2311yescharacteristic
132C22×C8×C71C2311yescharacteristic
133C22×C8×C71C2311yescharacteristic
134#127×C71—22no—
135#127×C71—22no—
136C22⋊Q8×C71—22no—
137C22⋊Q8×C71—41no—
138#121×C71—28no—
139#121×C71—22no—
140#121×C71—22no—
141#121×C71—22no—
142#121×C71—22no—
143#121×C71—41no—
144#121×C71D414yescomplemented
145#120×C71—28no—
146#120×C71—28no—
147C4×D4×C71—22no—
148C4×D4×C71—22no—
149C4×D4×C71—22no—
150C4×D4×C71—22no—
151C2×C4⋊C4×C71—21no—
152C2×C4⋊C4×C71D411yescharacteristic
153C2×C4⋊C4×C71C2311yescharacteristic
154C2×C4⋊C4×C71C2311yescharacteristic
155C2×C4⋊C4×C71C2311yescharacteristic
156C2×C22⋊C4×C71—21no—
157C2×C22⋊C4×C71—21no—
158C2×C22⋊C4×C71—21no—
159C2×C22⋊C4×C71—21no—
160C2×C22⋊C4×C71—21no—
161C2×C22⋊C4×C71—21no—
162C2×C22⋊C4×C71—21no—
163C2×C22⋊C4×C71—21no—
164C2×C22⋊C4×C71D411yescharacteristic
165C2×C22⋊C4×C71D411yescharacteristic
166C2×C42×C71C2311yescharacteristic
167#103×C71—22no—
168#102×C71—22no—
169#102×C71—22no—
170#102×C71—22no—
171#102×C71—22no—
172#102×C71—22no—
173#102×C71—41no—
174#102×C71—41no—
175C22⋊C8×C71—22no—
176C22⋊C8×C71—22no—
177C22⋊C8×C71—22no—
178#95×C71—21no—
179#95×C71—21no—
180#95×C71—21no—
181C24×C71—21no—
182C24×C71—24no—
183C24×C71—21no—
184C24×C71—21no—
185C24×C71—21no—
186C24×C71—24no—
187C24×C71—42no—
188C24×C71—42no—
189C24×C71—42no—
190C24×C71—42no—
191C24×C71—42no—
192C24×C71—42no—
193C24×C71—42no—
194C24×C71—42no—
195C24×C71—81no—
196C24×C71—81no—
197C24×C71—81no—
198C24×C71—81no—
199C24×C71C2×D411yescharacteristic
200C24×C71C2×D411yescharacteristic
201#41×C71—28no—
202#41×C71—44no—
203#41×C71—44no—
204#41×C71—44no—
205C2×Q8×C71—21no—
206C2×Q8×C71—21no—
207C2×Q8×C71—21no—
208C2×Q8×C71—21no—
209C2×Q8×C71—21no—
210C2×Q8×C71C2×D412yescomplemented
211C2×D4×C71—22no—
212C2×D4×C71—22no—
213C2×D4×C71—28no—
214C2×D4×C71—24no—
215C2×D4×C71—24no—
216C2×D4×C71—24no—
217C2×D4×C71—24no—
218C2×D4×C71—24no—
219C2×D4×C71—24no—
220C2×D4×C71—22no—
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—21no—
236C2×D4×C71—21no—
237C2×D4×C71—21no—
238C2×D4×C71—21no—
239C2×D4×C71—44no—
240C2×D4×C71—44no—
241C2×D4×C71—44no—
242C2×D4×C71—42no—
243C2×D4×C71—42no—
244C2×D4×C71—42no—
245C2×D4×C71—42no—
246C2×D4×C71—42no—
247C2×D4×C71—42no—
248C2×D4×C71—44no—
249C2×D4×C71—44no—
250C2×D4×C71—432no—
251C2×D4×C71—44no—
252C2×D4×C71—42no—
253C2×D4×C71—42no—
254C2×D4×C71—42no—
255C2×D4×C71—42no—
256C2×D4×C71—42no—
257C2×D4×C71—42no—
258C2×D4×C71—44no—
259C2×D4×C71—42no—
260C2×D4×C71—42no—
261C2×D4×C71—42no—
262C2×D4×C71—81no—
263C2×D4×C71—81no—
264C2×D4×C71—81no—
265C2×D4×C71C2×D412yes—
266C2×D4×C71C2×D412yes—
267C2×D4×C71C2×D412yes—
268C2×D4×C71C2×D412yes—
269C2×D4×C71C2×D412yes—
270C2×D4×C71C2×D412yescomplemented
271C22×C4×C71—21no—
272C22×C4×C71—21no—
273C22×C4×C71—21no—
274C22×C4×C71—21no—
275C22×C4×C71—24no—
276C22×C4×C71—21no—
277C22×C4×C71—21no—
278C22×C4×C71—21no—
279C22×C4×C71—21no—
280C22×C4×C71—21no—
281C22×C4×C71—21no—
282C22×C4×C71—21no—
283C22×C4×C71—21no—
284C22×C4×C71—21no—
285C22×C4×C71—21no—
286C22×C4×C71—42no—
287C22×C4×C71—42no—
288C22×C4×C71—42no—
289C22×C4×C71—42no—
290C22×C4×C71—42no—
291C22×C4×C71C2×D411yescharacteristic
292C22×C4×C71C2×D411yescharacteristic
293C22×C4×C71C2×D411yescharacteristic
294C22×C4×C71C2×D412yes—
295C22×C4×C71C2×D412yes—
296C22×C4×C71C2×D411yescharacteristic
297C22×C4×C71C2411yescharacteristic
298SD16×C71—28no—
299SD16×C71—28no—
300SD16×C71—44no—
301D8×C71—28no—
302D8×C71—28no—
303D8×C71—44no—
304M16×C71—28no—
305C2×C8×C71—21no—
306C2×C8×C71—21no—
307C2×C8×C71—21no—
308C2×C8×C71—21no—
309C2×C8×C71—21no—
310C2×C8×C71—21no—
311C2×C8×C71—21no—
312C2×C8×C71—21no—
313C2×C8×C71—21no—
314C2×C8×C71—21no—
315C2×C8×C71C2×D412yescomplemented
316C2×C8×C71C2×D412yescomplemented
317C4⋊C4×C71—22no—
318C4⋊C4×C71—21no—
319C4⋊C4×C71—21no—
320C4⋊C4×C71—21no—
321C4⋊C4×C71—21no—
322C4⋊C4×C71—21no—
323C4⋊C4×C71—42no—
324C4⋊C4×C71C2×D412yes—
325C22⋊C4×C71—24no—
326C22⋊C4×C71—24no—
327C22⋊C4×C71—22no—
328C22⋊C4×C71—24no—
329C22⋊C4×C71—22no—
330C22⋊C4×C71—42no—
331C22⋊C4×C71—42no—
332C22⋊C4×C71—42no—
333C22⋊C4×C71—81no—
334C22⋊C4×C71—81no—
335C42×C71—21no—
336C42×C71—21no—
337C23×C71—21no—
338C23×C71—22no—
339C23×C71—21no—
340C23×C71—21no—
341C23×C71—21no—
342C23×C71—21no—
343C23×C71—22no—
344C23×C71—22no—
345C23×C71—21no—
346C23×C71—21no—
347C23×C71—21no—
348C23×C71—21no—
349C23×C71—21no—
350C23×C71—21no—
351C23×C71—21no—
352C23×C71—22no—
353C23×C71—22no—
354C23×C71—22no—
355C23×C71—48no—
356C23×C71—48no—
357C23×C71—48no—
358C23×C71—48no—
359C23×C71—41no—
360C23×C71—41no—
361C23×C71—41no—
362C23×C71—41no—
363C23×C71—41no—
364C23×C71—41no—
365C23×C71—41no—
366C23×C71—41no—
367C23×C71—41no—
368C23×C71—41no—
369C23×C71—41no—
370C23×C71—41no—
371C23×C71—41no—
372C23×C71—41no—
373C23×C71—41no—
374C23×C71—41no—
375C23×C71—41no—
376C23×C71—41no—
377C23×C71—41no—
378C23×C71—41no—
379C23×C71—41no—
380C23×C71—41no—
381C23×C71—84no—
382C23×C71—84no—
383C23×C71—84no—
384C23×C71—84no—
385C23×C71—84no—
386C23×C71—84no—
387C23×C71—84no—
388C23×C71—84no—
389C23×C71—84no—
390C23×C71—84no—
391C23×C71#12012yes—
392C23×C71AGL(1,ℤ/8)12yescomplemented
393C23×C71C22×D411yescharacteristic
394Q8×C71—22no—
395Q8×C71—22no—
396Q8×C71—41no—
397Q8×C71—41no—
398D4×C71—28no—
399D4×C71—22no—
400D4×C71—22no—
401D4×C71—22no—
402D4×C71—22no—
403D4×C71—22no—
404D4×C71—22no—
405D4×C71—22no—
406D4×C71—22no—
407D4×C71—22no—
408D4×C71—48no—
409D4×C71—48no—
410D4×C71—48no—
411D4×C71—48no—
412D4×C71—48no—
413D4×C71—48no—
414D4×C71—41no—
415D4×C71—41no—
416D4×C71—41no—
417D4×C71—41no—
418D4×C71—41no—
419D4×C71—41no—
420D4×C71—84no—
421D4×C71—84no—
422D4×C71#12014yes—
423C2×C4×C71—21no—
424C2×C4×C71—21no—
425C2×C4×C71—21no—
426C2×C4×C71—21no—
427C2×C4×C71—22no—
428C2×C4×C71—22no—
429C2×C4×C71—22no—
430C2×C4×C71—22no—
431C2×C4×C71—21no—
432C2×C4×C71—21no—
433C2×C4×C71—22no—
434C2×C4×C71—21no—
435C2×C4×C71—22no—
436C2×C4×C71—21no—
437C2×C4×C71—21no—
438C2×C4×C71—21no—
439C2×C4×C71—48no—
440C2×C4×C71—48no—
441C2×C4×C71—41no—
442C2×C4×C71—41no—
443C2×C4×C71—41no—
444C2×C4×C71—41no—
445C2×C4×C71—41no—
446C2×C4×C71—41no—
447C2×C4×C71—41no—
448C2×C4×C71—41no—
449C2×C4×C71—41no—
450C2×C4×C71—41no—
451C2×C4×C71—41no—
452C2×C4×C71—41no—
453C2×C4×C71—41no—
454C2×C4×C71—41no—
455C2×C4×C71#12012yes—
456C2×C4×C71AGL(1,ℤ/8)12yescomplemented
457C2×C4×C71C22×D411yescharacteristic
458C2×C4×C71C22×D411yescharacteristic
459C2×C4×C71C22×D411yescharacteristic
460C2×C4×C71C22×D411yescharacteristic
461C2×C4×C71H(5,𝔽2)11yescharacteristic
462C2×C4×C71H(5,𝔽2)11yescharacteristic
463C8×C71—22no—
464C8×C71—22no—
465C8×C71—41no—
466C8×C71—41no—
467C22×C71—22no—
468C22×C71—24no—
469C22×C71—22no—
470C22×C71—22no—
471C22×C71—22no—
472C22×C71—22no—
473C22×C71—22no—
474C22×C71—41no—
475C22×C71—42no—
476C22×C71—41no—
477C22×C71—42no—
478C22×C71—41no—
479C22×C71—42no—
480C22×C71—41no—
481C22×C71—42no—
482C22×C71—41no—
483C22×C71—41no—
484C22×C71—42no—
485C22×C71—41no—
486C22×C71—41no—
487C22×C71—42no—
488C22×C71—42no—
489C22×C71—42no—
490C22×C71—42no—
491C22×C71—42no—
492C22×C71—42no—
493C22×C71—42no—
494C22×C71—42no—
495C22×C71—42no—
496C22×C71—42no—
497C22×C71—816no—
498C22×C71—816no—
499C22×C71—81no—
500C22×C71—81no—
501C22×C71—81no—
502C22×C71—81no—
503C22×C71—81no—
504C22×C71—81no—
505C22×C71—81no—
506C22×C71—81no—
507C22×C71—81no—
508C22×C71—81no—
509C22×C71—81no—
510C22×C71—81no—
511C22×C71C2×#12011yescharacteristic
512C22×C71D4211yescharacteristic
513C22×C71D4211yescharacteristic
514C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
515C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
516C22×C71#57611yescharacteristic
517C22×C71#57711yescharacteristic
518C4×C71—22no—
519C4×C71—22no—
520C4×C71—41no—
521C4×C71—42no—
522C4×C71—42no—
523C4×C71—41no—
524C4×C71—81no—
525C4×C71—81no—
526C4×C71C2×#12011yescharacteristic
527C4×C71#53411yescharacteristic
528C4×C71D4211yescharacteristic
529C4×C71D4211yescharacteristic
530#23860C7111yesmaximal, characteristic, direct product factor, Sylow
531C2×C71—42no—
532C2×C71—42no—
533C2×C71—44no—
534C2×C71—82no—
535C2×C71—82no—
536C2×C71—82no—
537C2×C71#240311yescharacteristic
538C2×C71#300311yescharacteristic
539C2×C71#301211yescharacteristic
540C2×C71#326411yescharacteristic
541C2×C71#326511yescharacteristic
542C2×C71#327211yescharacteristic
543C2×C71#327411yescharacteristic
544C22×AGL(1,ℤ/8)C2×C7111yescharacteristic, complemented
545C2×D42C2×C7111yescharacteristic, complemented
546C2×#449C2×C7111yescharacteristic, complemented
547C2×#450C2×C7111yescharacteristic, complemented
548C2×#447C2×C7111yescharacteristic, complemented
549#2407C2×C7111yescharacteristic, complemented
550#2014C2×C7111yescharacteristic, complemented
551#2011C2×C7111yescharacteristic, complemented
552#2000C2×C7111yescharacteristic, complemented
553#1999C2×C7111yescharacteristic, complemented
554#1895C2×C7111yescharacteristic, complemented
555#1879C2×C7111yescharacteristic, complemented
556#1877C2×C7111yescharacteristic, complemented
557#1870C2×C7111yescharacteristic, complemented
558#1786C2×C7111yescharacteristic, complemented
559C71#2386011yescharacteristic, direct product factor, Sylow
560C22×#41C22×C7111yescharacteristic, complemented
561C23×D4—21no—
562C23×D4C22×C7111yescharacteristic
563C23×D4C22×C7111yescharacteristic
564C2×AGL(1,ℤ/8)—24no—
565C2×AGL(1,ℤ/8)—24no—
566C2×AGL(1,ℤ/8)—24no—
567C22×SD16C22×C7111yescharacteristic
568C22×SD16C22×C7111yescharacteristic, complemented
569C22×SD16C22×C7111yescharacteristic, complemented
570C22×D8C22×C7111yescharacteristic
571C22×D8C22×C7111yescharacteristic, complemented
572C22×D8C22×C7111yescharacteristic, complemented
573C22×M16C22×C7111yescharacteristic, complemented
574D42—24no—
575D42—24no—
576C2×#127C22×C7111yescharacteristic
577C2×C22⋊Q8C22×C7111yescharacteristic, complemented
578C2×#121—21no—
579C2×#121C22×C7111yescharacteristic
580C2×#121C22×C7111yescharacteristic
581C2×#121C22×C7111yescharacteristic, complemented
582C2×#120—21no—
583C2×#120—21no—
584C2×C4×D4C22×C7111yescharacteristic
585C2×C4×D4C22×C7111yescharacteristic
586#450—24no—
587#449—24no—
588#447—24no—
589C2×#103C22×C7111yescharacteristic, complemented
590C2×#102C22×C7111yescharacteristic
591C2×#102C22×C7111yescharacteristic
592C2×#102C22×C7111yescharacteristic, complemented
593C2×#102C22×C7111yescharacteristic, complemented
594C2×#102C22×C7111yescharacteristic, complemented
595C2×#102C22×C7111yescharacteristic, complemented
596C2×#102C22×C7111yescharacteristic, complemented
597C2×C22⋊C8C22×C7111yescharacteristic, complemented
598C2×C22⋊C8C22×C7111yescharacteristic, complemented
599C2×C22⋊C8C22×C7111yescharacteristic, complemented
600#394—21no—
601#392—21no—
602#391C22×C7111yescharacteristic, complemented
603#390C22×C7111yescharacteristic, complemented
604#386—21no—
605#385—21no—
606#380C22×C7111yescharacteristic, complemented
607#340C22×C7111yescharacteristic, complemented
608#340C22×C7111yescharacteristic, complemented
609#336C22×C7111yescharacteristic, complemented
610#336C22×C7111yescharacteristic, complemented
611C25—21no—
612C25—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C22×Q8C23×C7111yescharacteristic
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—28no—
623C22×D4—21no—
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4—21no—
632C22×D4—21no—
633C22×D4—21no—
634C22×D4—22no—
635C22×D4—21no—
636C22×D4—41no—
637C22×D4—41no—
638C22×D4—41no—
639C22×D4—41no—
640C22×D4—44no—
641C22×D4—44no—
642C22×D4D4×C7111yescharacteristic
643C22×D4D4×C7114yescomplemented
644C22×D4C23×C7111yescharacteristic
645C22×D4C23×C7111yescharacteristic
646C22×D4C23×C7111yescharacteristic
647C22×D4C23×C7111yescharacteristic
648C23×C4—21no—
649C23×C4—21no—
650C23×C4C23×C7111yescharacteristic
651C23×C4C23×C7111yescharacteristic
652AGL(1,ℤ/8)—232no—
653C2×SD16—22no—
654C2×SD16—22no—
655C2×SD16—22no—
656C2×SD16—22no—
657C2×SD16—22no—
658C2×SD16—22no—
659C2×SD16—22no—
660C2×SD16—41no—
661C2×SD16D4×C7114yescomplemented
662C2×D8—22no—
663C2×D8—22no—
664C2×D8—22no—
665C2×D8—22no—
666C2×D8—22no—
667C2×D8—22no—
668C2×D8—22no—
669C2×D8—41no—
670C2×D8D4×C7114yescomplemented
671C2×M16—22no—
672C2×M16—22no—
673C2×M16—22no—
674C22×C8C23×C7111yescharacteristic
675C22×C8C23×C7111yescharacteristic
676C22×C8C23×C7111yescharacteristic
677C22×C8C23×C7111yescharacteristic
678#127—22no—
679#127—22no—
680C22⋊Q8—22no—
681C22⋊Q8—41no—
682#121—28no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—41no—
688#121D4×C7114yescomplemented
689#120—28no—
690#120—28no—
691C4×D4—22no—
692C4×D4—22no—
693C4×D4—22no—
694C4×D4—22no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4D4×C7111yescharacteristic
697C2×C4⋊C4C23×C7111yescharacteristic
698C2×C4⋊C4C23×C7111yescharacteristic
699C2×C4⋊C4C23×C7111yescharacteristic
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4D4×C7111yescharacteristic
709C2×C22⋊C4D4×C7111yescharacteristic
710C2×C42C23×C7111yescharacteristic
711#103—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—41no—
718#102—41no—
719C22⋊C8—22no—
720C22⋊C8—22no—
721C22⋊C8—22no—
722#95—21no—
723#95—21no—
724#95—21no—
725C24—21no—
726C24—24no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—24no—
731C24—42no—
732C24—42no—
733C24—42no—
734C24—42no—
735C24—42no—
736C24—42no—
737C24—42no—
738C24—42no—
739C24—81no—
740C24—81no—
741C24—81no—
742C24—81no—
743C24C2×D4×C7111yescharacteristic
744C24C2×D4×C7111yescharacteristic
745#41—28no—
746#41—44no—
747#41—44no—
748#41—44no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8C2×D4×C7112yescomplemented
755C2×D4—22no—
756C2×D4—22no—
757C2×D4—28no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—24no—
764C2×D4—22no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—432no—
795C2×D4—44no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—44no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4C2×D4×C7112yes—
810C2×D4C2×D4×C7112yes—
811C2×D4C2×D4×C7112yes—
812C2×D4C2×D4×C7112yes—
813C2×D4C2×D4×C7112yes—
814C2×D4C2×D4×C7112yescomplemented
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—24no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4C2×D4×C7111yescharacteristic
836C22×C4C2×D4×C7111yescharacteristic
837C22×C4C2×D4×C7111yescharacteristic
838C22×C4C2×D4×C7112yes—
839C22×C4C2×D4×C7112yes—
840C22×C4C2×D4×C7111yescharacteristic
841C22×C4C24×C7111yescharacteristic
842SD16—28no—
843SD16—28no—
844SD16—44no—
845D8—28no—
846D8—28no—
847D8—44no—
848M16—28no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8C2×D4×C7112yescomplemented
860C2×C8C2×D4×C7112yescomplemented
861C4⋊C4—22no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4C2×D4×C7112yes—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—22no—
872C22⋊C4—24no—
873C22⋊C4—22no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4—42no—
877C22⋊C4—81no—
878C22⋊C4—81no—
879C42—21no—
880C42—21no—
881C23—21no—
882C23—22no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—22no—
888C23—22no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—48no—
900C23—48no—
901C23—48no—
902C23—48no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—84no—
926C23—84no—
927C23—84no—
928C23—84no—
929C23—84no—
930C23—84no—
931C23—84no—
932C23—84no—
933C23—84no—
934C23—84no—
935C23#120×C7112yes—
936C23AGL(1,ℤ/8)×C7112yescomplemented
937C23C22×D4×C7111yescharacteristic
938Q8—22no—
939Q8—22no—
940Q8—41no—
941Q8—41no—
942D4—28no—
943D4—22no—
944D4—22no—
945D4—22no—
946D4—22no—
947D4—22no—
948D4—22no—
949D4—22no—
950D4—22no—
951D4—22no—
952D4—48no—
953D4—48no—
954D4—48no—
955D4—48no—
956D4—48no—
957D4—48no—
958D4—41no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—84no—
965D4—84no—
966D4#120×C7114yes—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4#120×C7112yes—
1000C2×C4AGL(1,ℤ/8)×C7112yescomplemented
1001C2×C4C22×D4×C7111yescharacteristic
1002C2×C4C22×D4×C7111yescharacteristic
1003C2×C4C22×D4×C7111yescharacteristic
1004C2×C4C22×D4×C7111yescharacteristic
1005C2×C4H(5,𝔽2)×C7111yescharacteristic
1006C2×C4H(5,𝔽2)×C7111yescharacteristic
1007C8—22no—
1008C8—22no—
1009C8—41no—
1010C8—41no—
1011C22—22no—
1012C22—24no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—42no—
1022C22—41no—
1023C22—42no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—41no—
1028C22—42no—
1029C22—41no—
1030C22—41no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—816no—
1042C22—816no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22C2×#120×C7111yescharacteristic
1056C22D42×C7111yescharacteristic
1057C22D42×C7111yescharacteristic
1058C22C2×AGL(1,ℤ/8)×C7111yescharacteristic
1059C22C2×AGL(1,ℤ/8)×C7111yescharacteristic
1060C22#576×C7111yescharacteristic
1061C22#577×C7111yescharacteristic
1062C4—22no—
1063C4—22no—
1064C4—41no—
1065C4—42no—
1066C4—42no—
1067C4—41no—
1068C4—81no—
1069C4—81no—
1070C4C2×#120×C7111yescharacteristic
1071C4#534×C7111yescharacteristic
1072C4D42×C7111yescharacteristic
1073C4D42×C7111yescharacteristic
1074C2—42no—
1075C2—42no—
1076C2—44no—
1077C2—82no—
1078C2—82no—
1079C2—82no—
1080C2C71×#240311yescharacteristic
1081C2C71×#300311yescharacteristic
1082C2C71×#301211yescharacteristic
1083C2C71×#326411yescharacteristic
1084C2C71×#326511yescharacteristic
1085C2C71×#327211yescharacteristic
1086C2C71×#327411yescharacteristic
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. C22×AGL(1,ℤ/8)×C71C2semidirect
2. C2×D42×C71C2semidirect
3. C2×#449×C71C2semidirect
4. C2×#450×C71C2semidirect
5. C2×#447×C71C2semidirect
6. C71×#2407C2semidirect
7. C71×#2014C2semidirect
8. C71×#2011C2semidirect
9. C71×#2000C2semidirect
10. C71×#1999C2semidirect
11. C71×#1895C2semidirect
12. C71×#1879C2semidirect
13. C71×#1877C2semidirect
14. C71×#1870C2semidirect
15. C71×#1786C2semidirect
16. C22×#41×C71C22semidirect
24. C22×SD16×C71C22semidirect
25. C22×SD16×C71C22semidirect
27. C22×D8×C71C22semidirect
28. C22×D8×C71C22semidirect
29. C22×M16×C71C22semidirect
33. C2×C22⋊Q8×C71C22semidirect
37. C2×#121×C71C22semidirect
45. C2×#103×C71C22semidirect
48. C2×#102×C71C22semidirect
49. C2×#102×C71C22semidirect
50. C2×#102×C71C22semidirect
51. C2×#102×C71C22semidirect
52. C2×#102×C71C22semidirect
53. C2×C22⋊C8×C71C22semidirect
54. C2×C22⋊C8×C71C22semidirect
55. C2×C22⋊C8×C71C22semidirect
58. #391×C71C22semidirect
59. #390×C71C22semidirect
62. #380×C71C22semidirect
63. #340×C71C22semidirect
64. #340×C71C22semidirect
65. #336×C71C22semidirect
66. #336×C71C22semidirect
99. C22×D4×C71D4semidirect
117. C2×SD16×C71D4semidirect
126. C2×D8×C71D4semidirect
144. #121×C71D4semidirect
210. C2×Q8×C71C2×D4semidirect
270. C2×D4×C71C2×D4semidirect
315. C2×C8×C71C2×D4semidirect
316. C2×C8×C71C2×D4semidirect
392. C23×C71AGL(1,ℤ/8)semidirect
456. C2×C4×C71AGL(1,ℤ/8)semidirect
530. #23860C71direct (N × H)
544. C22×AGL(1,ℤ/8)C2×C71semidirect
545. C2×D42C2×C71semidirect
546. C2×#449C2×C71semidirect
547. C2×#450C2×C71semidirect
548. C2×#447C2×C71semidirect
549. #2407C2×C71semidirect
550. #2014C2×C71semidirect
551. #2011C2×C71semidirect
552. #2000C2×C71semidirect
553. #1999C2×C71semidirect
554. #1895C2×C71semidirect
555. #1879C2×C71semidirect
556. #1877C2×C71semidirect
557. #1870C2×C71semidirect
558. #1786C2×C71semidirect
559. C71#23860direct (N × H)
560. C22×#41C22×C71semidirect
568. C22×SD16C22×C71semidirect
569. C22×SD16C22×C71semidirect
571. C22×D8C22×C71semidirect
572. C22×D8C22×C71semidirect
573. C22×M16C22×C71semidirect
577. C2×C22⋊Q8C22×C71semidirect
581. C2×#121C22×C71semidirect
589. C2×#103C22×C71semidirect
592. C2×#102C22×C71semidirect
593. C2×#102C22×C71semidirect
594. C2×#102C22×C71semidirect
595. C2×#102C22×C71semidirect
596. C2×#102C22×C71semidirect
597. C2×C22⋊C8C22×C71semidirect
598. C2×C22⋊C8C22×C71semidirect
599. C2×C22⋊C8C22×C71semidirect
602. #391C22×C71semidirect
603. #390C22×C71semidirect
606. #380C22×C71semidirect
607. #340C22×C71semidirect
608. #340C22×C71semidirect
609. #336C22×C71semidirect
610. #336C22×C71semidirect
643. C22×D4D4×C71semidirect
661. C2×SD16D4×C71semidirect
670. C2×D8D4×C71semidirect
688. #121D4×C71semidirect
754. C2×Q8C2×D4×C71semidirect
814. C2×D4C2×D4×C71semidirect
859. C2×C8C2×D4×C71semidirect
860. C2×C8C2×D4×C71semidirect
936. C23AGL(1,ℤ/8)×C71semidirect
1000. C2×C4AGL(1,ℤ/8)×C71semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C712
C2×D42×C712
C2×#449×C712
C2×#450×C712
C2×#447×C712
C71×#24072
C71×#20142
C71×#20112
C71×#20002
C71×#19992
C71×#18952
C71×#18792
C71×#18772
C71×#18702
C71×#17862
#2386071