Finite Group Databasebeta

← C71×#23863 #31844735

Subgroups — C71×#23863 #31844735

Order 18176.

1922 conjugacy classes of subgroups.

The subgroup lattice has 1020 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×#546×C71C211yesmaximal, characteristic, complemented
3C2×#452×C71C211yesmaximal, characteristic, complemented
4C2×#452×C71C211yesmaximal, characteristic, complemented
5C2×#449×C71C211yesmaximal, characteristic, complemented
6C71×#2407C211yesmaximal, characteristic, complemented
7C71×#2015C211yesmaximal, characteristic, complemented
8C71×#2012C211yesmaximal, characteristic, complemented
9C71×#2000C211yesmaximal, characteristic, complemented
10C71×#1999C211yesmaximal, characteristic, complemented
11C71×#1894C211yesmaximal, characteristic, complemented
12C71×#1879C211yesmaximal, characteristic, complemented
13C71×#1877C211yesmaximal, characteristic, complemented
14C71×#1870C211yesmaximal, characteristic, complemented
15C71×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C71C2211yescharacteristic
17C22×#41×C71C2211yescharacteristic
18C23×D4×C71C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C71—24no—
20C2×AGL(1,ℤ/8)×C71—24no—
21C2×AGL(1,ℤ/8)×C71—24no—
22C22×Q16×C71C2211yescharacteristic, complemented
23C22×SD16×C71C2211yescharacteristic
24C22×SD16×C71C2211yescharacteristic
25C22×SD16×C71C2211yescharacteristic, complemented
26C22×D8×C71C2211yescharacteristic
27C22×D8×C71C2211yescharacteristic
28C22×M16×C71C2211yescharacteristic
29#546×C71—24no—
30#546×C71—24no—
31C2×#124×C71C2211yescharacteristic
32C2×#123×C71—21no—
33C2×C22⋊Q8×C71C2211yescharacteristic
34C2×C22⋊Q8×C71C2211yescharacteristic, complemented
35C2×#121×C71—21no—
36C2×#121×C71C2211yescharacteristic
37C2×#121×C71C2211yescharacteristic, complemented
38C2×#120×C71—21no—
39C2×C4×D4×C71C2211yescharacteristic
40C2×C4×D4×C71C2211yescharacteristic
41C22×C22⋊C4×C71—21no—
42#452×C71—24no—
43#452×C71—24no—
44#449×C71—24no—
45C2×#103×C71C2211yescharacteristic, complemented
46C2×#103×C71C2211yescharacteristic, complemented
47C2×#103×C71C2211yescharacteristic, complemented
48C2×#102×C71C2211yescharacteristic
49C2×#102×C71C2211yescharacteristic
50C2×#102×C71C2211yescharacteristic
51C2×#102×C71C2211yescharacteristic
52C2×#102×C71C2211yescharacteristic, complemented
53C2×C22⋊C8×C71C2211yescharacteristic
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
63#340×C71C2211yescharacteristic, complemented
64#340×C71C2211yescharacteristic, complemented
65#336×C71C2211yescharacteristic, complemented
66#336×C71C2211yescharacteristic, complemented
67C25×C71—21no—
68C2×#41×C71—22no—
69C2×#41×C71—22no—
70C2×#41×C71—22no—
71C2×#41×C71—22no—
72C2×#41×C71—22no—
73C2×#41×C71—22no—
74C2×#41×C71—22no—
75C2×#41×C71—22no—
76C2×#41×C71—41no—
77C2×#41×C71—41no—
78C2×#41×C71—41no—
79C2×#41×C71—41no—
80C22×Q8×C71C2311yescharacteristic
81C22×Q8×C71C2311yescharacteristic
82C22×D4×C71—22no—
83C22×D4×C71—22no—
84C22×D4×C71—21no—
85C22×D4×C71—21no—
86C22×D4×C71—21no—
87C22×D4×C71—21no—
88C22×D4×C71—21no—
89C22×D4×C71—22no—
90C22×D4×C71—41no—
91C22×D4×C71—41no—
92C22×D4×C71D411yescharacteristic
93C22×D4×C71D414yescomplemented
94C22×D4×C71C2311yescharacteristic
95C22×D4×C71C2311yescharacteristic
96C22×D4×C71C2311yescharacteristic
97C23×C4×C71—21no—
98C23×C4×C71—21no—
99C23×C4×C71—21no—
100C23×C4×C71C2311yescharacteristic
101C23×C4×C71C2311yescharacteristic
102AGL(1,ℤ/8)×C71—232no—
103C2×Q16×C71—22no—
104C2×Q16×C71—22no—
105C2×Q16×C71—41no—
106C2×SD16×C71—22no—
107C2×SD16×C71—22no—
108C2×SD16×C71—22no—
109C2×SD16×C71—22no—
110C2×SD16×C71—22no—
111C2×SD16×C71—22no—
112C2×SD16×C71—22no—
113C2×SD16×C71—41no—
114C2×SD16×C71D414yescomplemented
115C2×D8×C71—22no—
116C2×D8×C71—22no—
117C2×D8×C71—22no—
118C2×D8×C71—22no—
119C2×D8×C71—22no—
120C2×D8×C71D414yescomplemented
121C2×M16×C71—22no—
122C2×M16×C71—22no—
123C2×M16×C71—22no—
124C22×C8×C71C2311yescharacteristic
125C22×C8×C71C2311yescharacteristic
126C22×C8×C71C2311yescharacteristic
127C22×C8×C71C2311yescharacteristic
128#124×C71—22no—
129#124×C71—22no—
130#123×C71—28no—
131C22⋊Q8×C71—22no—
132C22⋊Q8×C71—22no—
133C22⋊Q8×C71—41no—
134C22⋊Q8×C71D414yescomplemented
135#121×C71—28no—
136#121×C71—22no—
137#121×C71—22no—
138#121×C71—22no—
139#121×C71—41no—
140#120×C71—28no—
141C4×D4×C71—22no—
142C4×D4×C71—22no—
143C4×D4×C71—22no—
144C4×D4×C71—22no—
145C2×C4⋊C4×C71—21no—
146C2×C4⋊C4×C71—21no—
147C2×C4⋊C4×C71D411yescharacteristic
148C2×C4⋊C4×C71C2311yescharacteristic
149C2×C4⋊C4×C71C2311yescharacteristic
150C2×C4⋊C4×C71C2311yescharacteristic
151C2×C22⋊C4×C71—28no—
152C2×C22⋊C4×C71—21no—
153C2×C22⋊C4×C71—21no—
154C2×C22⋊C4×C71—21no—
155C2×C22⋊C4×C71—21no—
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×C71D411yescharacteristic
163C2×C22⋊C4×C71D411yescharacteristic
164C2×C42×C71C2311yescharacteristic
165#103×C71—22no—
166#103×C71—22no—
167#103×C71—22no—
168#102×C71—22no—
169#102×C71—22no—
170#102×C71—22no—
171#102×C71—41no—
172#102×C71—41no—
173C22⋊C8×C71—22no—
174C22⋊C8×C71—22no—
175C22⋊C8×C71—22no—
176#95×C71—21no—
177#95×C71—21no—
178#95×C71—21no—
179C24×C71—21no—
180C24×C71—21no—
181C24×C71—21no—
182C24×C71—24no—
183C24×C71—42no—
184C24×C71—42no—
185C24×C71—42no—
186C24×C71—42no—
187C24×C71—81no—
188C24×C71—81no—
189C24×C71C2×D411yescharacteristic
190C24×C71C2×D411yescharacteristic
191#41×C71—28no—
192#41×C71—44no—
193#41×C71—44no—
194#41×C71—44no—
195#41×C71—44no—
196#41×C71—44no—
197#41×C71—44no—
198#41×C71—44no—
199C2×Q8×C71—21no—
200C2×Q8×C71—21no—
201C2×Q8×C71—21no—
202C2×Q8×C71—21no—
203C2×Q8×C71—21no—
204C2×Q8×C71—21no—
205C2×Q8×C71—21no—
206C2×Q8×C71—21no—
207C2×Q8×C71—21no—
208C2×Q8×C71—21no—
209C2×Q8×C71C2×D412yes—
210C2×Q8×C71C2×D412yes—
211C2×D4×C71—28no—
212C2×D4×C71—24no—
213C2×D4×C71—22no—
214C2×D4×C71—24no—
215C2×D4×C71—24no—
216C2×D4×C71—21no—
217C2×D4×C71—21no—
218C2×D4×C71—21no—
219C2×D4×C71—21no—
220C2×D4×C71—21no—
221C2×D4×C71—21no—
222C2×D4×C71—21no—
223C2×D4×C71—21no—
224C2×D4×C71—21no—
225C2×D4×C71—21no—
226C2×D4×C71—21no—
227C2×D4×C71—21no—
228C2×D4×C71—21no—
229C2×D4×C71—44no—
230C2×D4×C71—44no—
231C2×D4×C71—44no—
232C2×D4×C71—41no—
233C2×D4×C71—41no—
234C2×D4×C71—42no—
235C2×D4×C71—42no—
236C2×D4×C71—42no—
237C2×D4×C71—42no—
238C2×D4×C71—42no—
239C2×D4×C71—42no—
240C2×D4×C71—42no—
241C2×D4×C71—42no—
242C2×D4×C71—42no—
243C2×D4×C71—81no—
244C2×D4×C71—81no—
245C2×D4×C71—81no—
246C2×D4×C71C2×D412yes—
247C2×D4×C71C2×D412yes—
248C2×D4×C71C2×D412yes—
249C2×D4×C71C2×D412yes—
250C2×D4×C71C2×D412yes—
251C22×C4×C71—21no—
252C22×C4×C71—21no—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—24no—
256C22×C4×C71—21no—
257C22×C4×C71—21no—
258C22×C4×C71—21no—
259C22×C4×C71—24no—
260C22×C4×C71—21no—
261C22×C4×C71—21no—
262C22×C4×C71—21no—
263C22×C4×C71—21no—
264C22×C4×C71—21no—
265C22×C4×C71—21no—
266C22×C4×C71—21no—
267C22×C4×C71—21no—
268C22×C4×C71—42no—
269C22×C4×C71—42no—
270C22×C4×C71—42no—
271C22×C4×C71—42no—
272C22×C4×C71—42no—
273C22×C4×C71—81no—
274C22×C4×C71—81no—
275C22×C4×C71C2×D411yescharacteristic
276C22×C4×C71C2×D411yescharacteristic
277C22×C4×C71C2×D411yescharacteristic
278C22×C4×C71C2×D411yescharacteristic
279C22×C4×C71C2×D412yes—
280C22×C4×C71C2×D412yes—
281C22×C4×C71C2411yescharacteristic
282Q16×C71—44no—
283SD16×C71—28no—
284SD16×C71—28no—
285SD16×C71—44no—
286D8×C71—28no—
287D8×C71—28no—
288M16×C71—28no—
289C2×C8×C71—21no—
290C2×C8×C71—21no—
291C2×C8×C71—21no—
292C2×C8×C71—21no—
293C2×C8×C71—21no—
294C2×C8×C71—21no—
295C2×C8×C71—21no—
296C2×C8×C71—21no—
297C2×C8×C71—21no—
298C2×C8×C71—21no—
299C2×C8×C71C2×D412yes—
300C2×C8×C71C2×D412yes—
301C4⋊C4×C71—24no—
302C4⋊C4×C71—22no—
303C4⋊C4×C71—21no—
304C4⋊C4×C71—21no—
305C4⋊C4×C71—21no—
306C4⋊C4×C71—21no—
307C4⋊C4×C71—21no—
308C4⋊C4×C71—42no—
309C4⋊C4×C71C2×D412yes—
310C22⋊C4×C71—24no—
311C22⋊C4×C71—24no—
312C22⋊C4×C71—24no—
313C22⋊C4×C71—24no—
314C22⋊C4×C71—22no—
315C22⋊C4×C71—24no—
316C22⋊C4×C71—22no—
317C22⋊C4×C71—42no—
318C22⋊C4×C71—42no—
319C22⋊C4×C71—42no—
320C22⋊C4×C71—81no—
321C22⋊C4×C71—81no—
322C42×C71—21no—
323C42×C71—21no—
324C23×C71—22no—
325C23×C71—21no—
326C23×C71—21no—
327C23×C71—22no—
328C23×C71—22no—
329C23×C71—21no—
330C23×C71—21no—
331C23×C71—21no—
332C23×C71—21no—
333C23×C71—22no—
334C23×C71—21no—
335C23×C71—21no—
336C23×C71—22no—
337C23×C71—21no—
338C23×C71—21no—
339C23×C71—21no—
340C23×C71—21no—
341C23×C71—21no—
342C23×C71—48no—
343C23×C71—48no—
344C23×C71—41no—
345C23×C71—41no—
346C23×C71—41no—
347C23×C71—41no—
348C23×C71—41no—
349C23×C71—41no—
350C23×C71—41no—
351C23×C71—41no—
352C23×C71—41no—
353C23×C71—41no—
354C23×C71—41no—
355C23×C71—41no—
356C23×C71—41no—
357C23×C71—41no—
358C23×C71—41no—
359C23×C71—41no—
360C23×C71—84no—
361C23×C71—84no—
362C23×C71—84no—
363C23×C71—84no—
364C23×C71—84no—
365C23×C71#12012yes—
366C23×C71C22×D411yescharacteristic
367Q8×C71—22no—
368Q8×C71—22no—
369Q8×C71—22no—
370Q8×C71—22no—
371Q8×C71—41no—
372Q8×C71—41no—
373Q8×C71—41no—
374Q8×C71—41no—
375D4×C71—22no—
376D4×C71—22no—
377D4×C71—22no—
378D4×C71—22no—
379D4×C71—22no—
380D4×C71—22no—
381D4×C71—22no—
382D4×C71—48no—
383D4×C71—44no—
384D4×C71—48no—
385D4×C71—48no—
386D4×C71—41no—
387D4×C71—41no—
388D4×C71—41no—
389D4×C71—41no—
390D4×C71—84no—
391D4×C71—84no—
392D4×C71#12014yes—
393C2×C4×C71—21no—
394C2×C4×C71—21no—
395C2×C4×C71—22no—
396C2×C4×C71—22no—
397C2×C4×C71—22no—
398C2×C4×C71—22no—
399C2×C4×C71—21no—
400C2×C4×C71—21no—
401C2×C4×C71—22no—
402C2×C4×C71—21no—
403C2×C4×C71—22no—
404C2×C4×C71—21no—
405C2×C4×C71—22no—
406C2×C4×C71—21no—
407C2×C4×C71—21no—
408C2×C4×C71—21no—
409C2×C4×C71—21no—
410C2×C4×C71—21no—
411C2×C4×C71—48no—
412C2×C4×C71—48no—
413C2×C4×C71—41no—
414C2×C4×C71—41no—
415C2×C4×C71—41no—
416C2×C4×C71—41no—
417C2×C4×C71—41no—
418C2×C4×C71—41no—
419C2×C4×C71—41no—
420C2×C4×C71—41no—
421C2×C4×C71—41no—
422C2×C4×C71—41no—
423C2×C4×C71—41no—
424C2×C4×C71—41no—
425C2×C4×C71—41no—
426C2×C4×C71—41no—
427C2×C4×C71—41no—
428C2×C4×C71—41no—
429C2×C4×C71—84no—
430C2×C4×C71#12012yes—
431C2×C4×C71C22×D411yescharacteristic
432C2×C4×C71C22×D411yescharacteristic
433C2×C4×C71C22×D411yescharacteristic
434C2×C4×C71C22×D411yescharacteristic
435C2×C4×C71H(5,𝔽2)11yescharacteristic
436C2×C4×C71H(5,𝔽2)11yescharacteristic
437C8×C71—22no—
438C8×C71—22no—
439C8×C71—41no—
440C8×C71—41no—
441C22×C71—22no—
442C22×C71—24no—
443C22×C71—22no—
444C22×C71—22no—
445C22×C71—42no—
446C22×C71—41no—
447C22×C71—42no—
448C22×C71—42no—
449C22×C71—41no—
450C22×C71—42no—
451C22×C71—41no—
452C22×C71—42no—
453C22×C71—41no—
454C22×C71—42no—
455C22×C71—42no—
456C22×C71—41no—
457C22×C71—42no—
458C22×C71—41no—
459C22×C71—42no—
460C22×C71—41no—
461C22×C71—42no—
462C22×C71—41no—
463C22×C71—42no—
464C22×C71—41no—
465C22×C71—41no—
466C22×C71—42no—
467C22×C71—41no—
468C22×C71—816no—
469C22×C71—81no—
470C22×C71—81no—
471C22×C71—81no—
472C22×C71—81no—
473C22×C71—81no—
474C22×C71—81no—
475C22×C71—81no—
476C22×C71—81no—
477C22×C71C2×#12011yescharacteristic
478C22×C71D4211yescharacteristic
479C22×C71D4211yescharacteristic
480C22×C71#57511yescharacteristic
481C22×C71#57511yescharacteristic
482C22×C71#57611yescharacteristic
483C22×C71#57711yescharacteristic
484C4×C71—22no—
485C4×C71—41no—
486C4×C71—42no—
487C4×C71—42no—
488C4×C71—41no—
489C4×C71—41no—
490C4×C71—42no—
491C4×C71—81no—
492C4×C71—81no—
493C4×C71C2×#12011yescharacteristic
494C4×C71#53411yescharacteristic
495C4×C71D4211yescharacteristic
496C4×C71D4211yescharacteristic
497#23863C7111yesmaximal, characteristic, direct product factor, Sylow
498C2×C71—42no—
499C2×C71—44no—
500C2×C71—81no—
501C2×C71—82no—
502C2×C71—82no—
503C2×C71#240311yescharacteristic
504C2×C71#300511yescharacteristic
505C2×C71#301211yescharacteristic
506C2×C71#326711yescharacteristic
507C2×C71#326811yescharacteristic
508C2×C71#327311yescharacteristic
509C2×C71#327511yescharacteristic
510C22×AGL(1,ℤ/8)C2×C7111yescharacteristic, complemented
511C2×#546C2×C7111yescharacteristic, complemented
512C2×#452C2×C7111yescharacteristic, complemented
513C2×#452C2×C7111yescharacteristic, complemented
514C2×#449C2×C7111yescharacteristic, complemented
515#2407C2×C7111yescharacteristic, complemented
516#2015C2×C7111yescharacteristic, complemented
517#2012C2×C7111yescharacteristic, complemented
518#2000C2×C7111yescharacteristic, complemented
519#1999C2×C7111yescharacteristic, complemented
520#1894C2×C7111yescharacteristic, complemented
521#1879C2×C7111yescharacteristic, complemented
522#1877C2×C7111yescharacteristic, complemented
523#1870C2×C7111yescharacteristic, complemented
524#1786C2×C7111yescharacteristic, complemented
525C71#2386311yescharacteristic, direct product factor, Sylow
526C22×#41C22×C7111yescharacteristic
527C22×#41C22×C7111yescharacteristic
528C23×D4C22×C7111yescharacteristic
529C2×AGL(1,ℤ/8)—24no—
530C2×AGL(1,ℤ/8)—24no—
531C2×AGL(1,ℤ/8)—24no—
532C22×Q16C22×C7111yescharacteristic, complemented
533C22×SD16C22×C7111yescharacteristic
534C22×SD16C22×C7111yescharacteristic
535C22×SD16C22×C7111yescharacteristic, complemented
536C22×D8C22×C7111yescharacteristic
537C22×D8C22×C7111yescharacteristic
538C22×M16C22×C7111yescharacteristic
539#546—24no—
540#546—24no—
541C2×#124C22×C7111yescharacteristic
542C2×#123—21no—
543C2×C22⋊Q8C22×C7111yescharacteristic
544C2×C22⋊Q8C22×C7111yescharacteristic, complemented
545C2×#121—21no—
546C2×#121C22×C7111yescharacteristic
547C2×#121C22×C7111yescharacteristic, complemented
548C2×#120—21no—
549C2×C4×D4C22×C7111yescharacteristic
550C2×C4×D4C22×C7111yescharacteristic
551C22×C22⋊C4—21no—
552#452—24no—
553#452—24no—
554#449—24no—
555C2×#103C22×C7111yescharacteristic, complemented
556C2×#103C22×C7111yescharacteristic, complemented
557C2×#103C22×C7111yescharacteristic, complemented
558C2×#102C22×C7111yescharacteristic
559C2×#102C22×C7111yescharacteristic
560C2×#102C22×C7111yescharacteristic
561C2×#102C22×C7111yescharacteristic
562C2×#102C22×C7111yescharacteristic, complemented
563C2×C22⋊C8C22×C7111yescharacteristic
564C2×C22⋊C8C22×C7111yescharacteristic, complemented
565C2×C22⋊C8C22×C7111yescharacteristic, complemented
566#394—21no—
567#392—21no—
568#391C22×C7111yescharacteristic, complemented
569#390C22×C7111yescharacteristic, complemented
570#386—21no—
571#385—21no—
572#380C22×C7111yescharacteristic
573#340C22×C7111yescharacteristic, complemented
574#340C22×C7111yescharacteristic, complemented
575#336C22×C7111yescharacteristic, complemented
576#336C22×C7111yescharacteristic, complemented
577C25—21no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—22no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41—41no—
590C22×Q8C23×C7111yescharacteristic
591C22×Q8C23×C7111yescharacteristic
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—22no—
600C22×D4—41no—
601C22×D4—41no—
602C22×D4D4×C7111yescharacteristic
603C22×D4D4×C7114yescomplemented
604C22×D4C23×C7111yescharacteristic
605C22×D4C23×C7111yescharacteristic
606C22×D4C23×C7111yescharacteristic
607C23×C4—21no—
608C23×C4—21no—
609C23×C4—21no—
610C23×C4C23×C7111yescharacteristic
611C23×C4C23×C7111yescharacteristic
612AGL(1,ℤ/8)—232no—
613C2×Q16—22no—
614C2×Q16—22no—
615C2×Q16—41no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—22no—
621C2×SD16—22no—
622C2×SD16—22no—
623C2×SD16—41no—
624C2×SD16D4×C7114yescomplemented
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—22no—
628C2×D8—22no—
629C2×D8—22no—
630C2×D8D4×C7114yescomplemented
631C2×M16—22no—
632C2×M16—22no—
633C2×M16—22no—
634C22×C8C23×C7111yescharacteristic
635C22×C8C23×C7111yescharacteristic
636C22×C8C23×C7111yescharacteristic
637C22×C8C23×C7111yescharacteristic
638#124—22no—
639#124—22no—
640#123—28no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—41no—
644C22⋊Q8D4×C7114yescomplemented
645#121—28no—
646#121—22no—
647#121—22no—
648#121—22no—
649#121—41no—
650#120—28no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4D4×C7111yescharacteristic
658C2×C4⋊C4C23×C7111yescharacteristic
659C2×C4⋊C4C23×C7111yescharacteristic
660C2×C4⋊C4C23×C7111yescharacteristic
661C2×C22⋊C4—28no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4D4×C7111yescharacteristic
673C2×C22⋊C4D4×C7111yescharacteristic
674C2×C42C23×C7111yescharacteristic
675#103—22no—
676#103—22no—
677#103—22no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—41no—
682#102—41no—
683C22⋊C8—22no—
684C22⋊C8—22no—
685C22⋊C8—22no—
686#95—21no—
687#95—21no—
688#95—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—24no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—81no—
698C24—81no—
699C24C2×D4×C7111yescharacteristic
700C24C2×D4×C7111yescharacteristic
701#41—28no—
702#41—44no—
703#41—44no—
704#41—44no—
705#41—44no—
706#41—44no—
707#41—44no—
708#41—44no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8C2×D4×C7112yes—
720C2×Q8C2×D4×C7112yes—
721C2×D4—28no—
722C2×D4—24no—
723C2×D4—22no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—41no—
743C2×D4—41no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4C2×D4×C7112yes—
757C2×D4C2×D4×C7112yes—
758C2×D4C2×D4×C7112yes—
759C2×D4C2×D4×C7112yes—
760C2×D4C2×D4×C7112yes—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—24no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—24no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4C2×D4×C7111yescharacteristic
786C22×C4C2×D4×C7111yescharacteristic
787C22×C4C2×D4×C7111yescharacteristic
788C22×C4C2×D4×C7111yescharacteristic
789C22×C4C2×D4×C7112yes—
790C22×C4C2×D4×C7112yes—
791C22×C4C24×C7111yescharacteristic
792Q16—44no—
793SD16—28no—
794SD16—28no—
795SD16—44no—
796D8—28no—
797D8—28no—
798M16—28no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8C2×D4×C7112yes—
810C2×C8C2×D4×C7112yes—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C7112yes—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—24no—
826C22⋊C4—22no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C22⋊C4—81no—
832C42—21no—
833C42—21no—
834C23—22no—
835C23—21no—
836C23—21no—
837C23—22no—
838C23—22no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—22no—
844C23—21no—
845C23—21no—
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—48no—
853C23—48no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23#120×C7112yes—
876C23C22×D4×C7111yescharacteristic
877Q8—22no—
878Q8—22no—
879Q8—22no—
880Q8—22no—
881Q8—41no—
882Q8—41no—
883Q8—41no—
884Q8—41no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—22no—
892D4—48no—
893D4—48no—
894D4—44no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—84no—
901D4—84no—
902D4#120×C7114yes—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—21no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—48no—
922C2×C4—48no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—84no—
940C2×C4#120×C7112yes—
941C2×C4C22×D4×C7111yescharacteristic
942C2×C4C22×D4×C7111yescharacteristic
943C2×C4C22×D4×C7111yescharacteristic
944C2×C4C22×D4×C7111yescharacteristic
945C2×C4H(5,𝔽2)×C7111yescharacteristic
946C2×C4H(5,𝔽2)×C7111yescharacteristic
947C8—22no—
948C8—22no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—24no—
953C22—22no—
954C22—22no—
955C22—42no—
956C22—41no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—42no—
963C22—41no—
964C22—42no—
965C22—42no—
966C22—41no—
967C22—42no—
968C22—41no—
969C22—42no—
970C22—41no—
971C22—42no—
972C22—41no—
973C22—42no—
974C22—41no—
975C22—41no—
976C22—42no—
977C22—41no—
978C22—816no—
979C22—81no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22C2×#120×C7111yescharacteristic
988C22D42×C7111yescharacteristic
989C22D42×C7111yescharacteristic
990C22#575×C7111yescharacteristic
991C22#575×C7111yescharacteristic
992C22#576×C7111yescharacteristic
993C22#577×C7111yescharacteristic
994C4—22no—
995C4—41no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C7111yescharacteristic
1004C4#534×C7111yescharacteristic
1005C4D42×C7111yescharacteristic
1006C4D42×C7111yescharacteristic
1007C2—42no—
1008C2—44no—
1009C2—81no—
1010C2—82no—
1011C2—82no—
1012C2C71×#240311yescharacteristic
1013C2C71×#300511yescharacteristic
1014C2C71×#301211yescharacteristic
1015C2C71×#326711yescharacteristic
1016C2C71×#326811yescharacteristic
1017C2C71×#327311yescharacteristic
1018C2C71×#327511yescharacteristic
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×#546×C71C2semidirect
3. C2×#452×C71C2semidirect
4. C2×#452×C71C2semidirect
5. C2×#449×C71C2semidirect
6. C71×#2407C2semidirect
7. C71×#2015C2semidirect
8. C71×#2012C2semidirect
9. C71×#2000C2semidirect
10. C71×#1999C2semidirect
11. C71×#1894C2semidirect
12. C71×#1879C2semidirect
13. C71×#1877C2semidirect
14. C71×#1870C2semidirect
15. C71×#1786C2semidirect
22. C22×Q16×C71C22semidirect
25. C22×SD16×C71C22semidirect
34. C2×C22⋊Q8×C71C22semidirect
37. C2×#121×C71C22semidirect
45. C2×#103×C71C22semidirect
46. C2×#103×C71C22semidirect
47. C2×#103×C71C22semidirect
52. C2×#102×C71C22semidirect
54. C2×C22⋊C8×C71C22semidirect
55. C2×C22⋊C8×C71C22semidirect
58. #391×C71C22semidirect
59. #390×C71C22semidirect
63. #340×C71C22semidirect
64. #340×C71C22semidirect
65. #336×C71C22semidirect
66. #336×C71C22semidirect
93. C22×D4×C71D4semidirect
114. C2×SD16×C71D4semidirect
120. C2×D8×C71D4semidirect
134. C22⋊Q8×C71D4semidirect
497. #23863C71direct (N × H)
510. C22×AGL(1,ℤ/8)C2×C71semidirect
511. C2×#546C2×C71semidirect
512. C2×#452C2×C71semidirect
513. C2×#452C2×C71semidirect
514. C2×#449C2×C71semidirect
515. #2407C2×C71semidirect
516. #2015C2×C71semidirect
517. #2012C2×C71semidirect
518. #2000C2×C71semidirect
519. #1999C2×C71semidirect
520. #1894C2×C71semidirect
521. #1879C2×C71semidirect
522. #1877C2×C71semidirect
523. #1870C2×C71semidirect
524. #1786C2×C71semidirect
525. C71#23863direct (N × H)
532. C22×Q16C22×C71semidirect
535. C22×SD16C22×C71semidirect
544. C2×C22⋊Q8C22×C71semidirect
547. C2×#121C22×C71semidirect
555. C2×#103C22×C71semidirect
556. C2×#103C22×C71semidirect
557. C2×#103C22×C71semidirect
562. C2×#102C22×C71semidirect
564. C2×C22⋊C8C22×C71semidirect
565. C2×C22⋊C8C22×C71semidirect
568. #391C22×C71semidirect
569. #390C22×C71semidirect
573. #340C22×C71semidirect
574. #340C22×C71semidirect
575. #336C22×C71semidirect
576. #336C22×C71semidirect
603. C22×D4D4×C71semidirect
624. C2×SD16D4×C71semidirect
630. C2×D8D4×C71semidirect
644. C22⋊Q8D4×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×#546×C712
C2×#452×C712
C2×#449×C712
C71×#24072
C71×#20152
C71×#20122
C71×#20002
C71×#19992
C71×#18942
C71×#18792
C71×#18772
C71×#18702
C71×#17862
#2386371