Finite Group Databasebeta

← C71×#23482 #31844354

Subgroups — C71×#23482 #31844354

Order 18176.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C71C211yesmaximal, characteristic
2C2×#428×C71C211yesmaximal, characteristic, complemented
3C2×#417×C71C211yesmaximal, characteristic, complemented
4C2×#417×C71C211yesmaximal, characteristic, complemented
5C2×#407×C71C211yesmaximal, characteristic, complemented
6C2×#380×C71C211yesmaximal, characteristic, complemented
7C71×#2036C212yesmaximal, complemented
8C71×#2035C212yesmaximal, complemented
9C71×#2034C212yesmaximal, complemented
10C71×#2033C212yesmaximal, complemented
11C71×#1736C211yesmaximal, characteristic, complemented
12C22×#41×C71C2211yescharacteristic
13C24×C4×C71C2211yescharacteristic
14C22×M16×C71C2211yescharacteristic
15C22×M16×C71C2211yescharacteristic
16#525×C71—24no—
17#525×C71—24no—
18C2×#123×C71—21no—
19C2×C22⋊Q8×C71C2211yescharacteristic
20C2×C22⋊Q8×C71C2211yescharacteristic
21C2×#121×C71C2211yescharacteristic
22C2×#121×C71C2211yescharacteristic
23C2×#120×C71—21no—
24C2×C4×D4×C71—21no—
25C2×C4×D4×C71—21no—
26C2×#117×C71C2211yescharacteristic
27C22×C4⋊C4×C71C2211yescharacteristic
28C22×C4⋊C4×C71C2211yescharacteristic
29C22×C22⋊C4×C71—21no—
30#428×C71—24no—
31C2×#107×C71C2212yescomplemented
32C2×#106×C71C2212yescomplemented
33#417×C71—24no—
34#417×C71—24no—
35C2×#103×C71C2212yescomplemented
36C2×#103×C71C2212yescomplemented
37C2×#102×C71C2212yescomplemented
38C2×#102×C71C2212yescomplemented
39#407×C71—24no—
40C2×C22⋊C8×C71C2212yes—
41C2×C22⋊C8×C71C2212yes—
42#380×C71—21no—
43#380×C71—21no—
44#380×C71C2212yes—
45#380×C71C2212yes—
46C2×#95×C71—21no—
47#340×C71C2212yescomplemented
48#340×C71C2212yescomplemented
49C25×C71D411yescharacteristic
50C2×#41×C71—22no—
51C2×#41×C71—22no—
52C2×#41×C71—22no—
53C2×#41×C71—22no—
54C2×#41×C71—22no—
55C2×#41×C71D414yes—
56C22×Q8×C71C2311yescharacteristic
57C22×D4×C71—21no—
58C22×D4×C71—21no—
59C22×D4×C71—21no—
60C22×D4×C71C2311yescharacteristic
61C23×C4×C71—22no—
62C23×C4×C71—21no—
63C23×C4×C71—22no—
64C23×C4×C71—22no—
65C23×C4×C71—22no—
66C23×C4×C71—22no—
67C23×C4×C71—22no—
68C23×C4×C71—21no—
69C23×C4×C71—21no—
70C23×C4×C71D411yescharacteristic
71C23×C4×C71D411yescharacteristic
72C23×C4×C71D411yescharacteristic
73C23×C4×C71C2311yescharacteristic
74C23×C4×C71C2311yescharacteristic
75C23×C4×C71C2311yescharacteristic
76C2×M16×C71—22no—
77C2×M16×C71—22no—
78C2×M16×C71—22no—
79C2×M16×C71—22no—
80C2×M16×C71—22no—
81C2×M16×C71D414yescomplemented
82C22×C8×C71C2312yes—
83C22×C8×C71C2312yes—
84#123×C71—28no—
85C22⋊Q8×C71—22no—
86C22⋊Q8×C71—22no—
87C22⋊Q8×C71—22no—
88C22⋊Q8×C71—22no—
89#121×C71—22no—
90#121×C71—22no—
91#121×C71—22no—
92#121×C71—22no—
93#120×C71—28no—
94C4×D4×C71—28no—
95C4×D4×C71—28no—
96#117×C71—22no—
97#117×C71D414yes—
98C2×C4⋊C4×C71—21no—
99C2×C4⋊C4×C71—21no—
100C2×C4⋊C4×C71—22no—
101C2×C4⋊C4×C71—22no—
102C2×C4⋊C4×C71—22no—
103C2×C4⋊C4×C71—22no—
104C2×C4⋊C4×C71—21no—
105C2×C4⋊C4×C71—21no—
106C2×C4⋊C4×C71C2312yes—
107C2×C4⋊C4×C71C2312yes—
108C2×C4⋊C4×C71C2311yescharacteristic
109C2×C4⋊C4×C71C2311yescharacteristic
110C2×C22⋊C4×C71—21no—
111C2×C22⋊C4×C71—21no—
112C2×C22⋊C4×C71—21no—
113C2×C22⋊C4×C71—21no—
114C2×C22⋊C4×C71—21no—
115C2×C22⋊C4×C71—22no—
116C2×C22⋊C4×C71—22no—
117C2×C22⋊C4×C71—44no—
118C2×C42×C71—21no—
119#107×C71—24no—
120#106×C71—24no—
121#103×C71—24no—
122#103×C71—24no—
123#102×C71—24no—
124#102×C71—24no—
125C22⋊C8×C71—24no—
126C22⋊C8×C71—24no—
127#95×C71—22no—
128#95×C71—22no—
129C24×C71—22no—
130C24×C71—22no—
131C24×C71—22no—
132C24×C71—22no—
133C24×C71—22no—
134C24×C71—21no—
135C24×C71—41no—
136C24×C71—41no—
137C24×C71C2×D411yescharacteristic
138C24×C71C2×D411yescharacteristic
139C24×C71C2×D411yescharacteristic
140#41×C71—28no—
141#41×C71—28no—
142#41×C71—44no—
143#41×C71—44no—
144C2×Q8×C71—21no—
145C2×Q8×C71—21no—
146C2×Q8×C71—21no—
147C2×Q8×C71—21no—
148C2×Q8×C71—21no—
149C2×Q8×C71C2×D412yes—
150C2×D4×C71—24no—
151C2×D4×C71—24no—
152C2×D4×C71—24no—
153C2×D4×C71—21no—
154C2×D4×C71—21no—
155C2×D4×C71—21no—
156C2×D4×C71—21no—
157C2×D4×C71—21no—
158C2×D4×C71—42no—
159C2×D4×C71—42no—
160C2×D4×C71—42no—
161C2×D4×C71—42no—
162C2×D4×C71—42no—
163C2×D4×C71—42no—
164C2×D4×C71C2×D412yes—
165C22×C4×C71—22no—
166C22×C4×C71—22no—
167C22×C4×C71—22no—
168C22×C4×C71—21no—
169C22×C4×C71—21no—
170C22×C4×C71—21no—
171C22×C4×C71—22no—
172C22×C4×C71—22no—
173C22×C4×C71—24no—
174C22×C4×C71—22no—
175C22×C4×C71—22no—
176C22×C4×C71—22no—
177C22×C4×C71—22no—
178C22×C4×C71—21no—
179C22×C4×C71—21no—
180C22×C4×C71—21no—
181C22×C4×C71—21no—
182C22×C4×C71—21no—
183C22×C4×C71—21no—
184C22×C4×C71—21no—
185C22×C4×C71—21no—
186C22×C4×C71—21no—
187C22×C4×C71—21no—
188C22×C4×C71—21no—
189C22×C4×C71—21no—
190C22×C4×C71—22no—
191C22×C4×C71—22no—
192C22×C4×C71—44no—
193C22×C4×C71—44no—
194C22×C4×C71—42no—
195C22×C4×C71—44no—
196C22×C4×C71—42no—
197C22×C4×C71—44no—
198C22×C4×C71—42no—
199C22×C4×C71—42no—
200C22×C4×C71—42no—
201C22×C4×C71—42no—
202C22×C4×C71—42no—
203C22×C4×C71—42no—
204C22×C4×C71C2×D411yescharacteristic
205C22×C4×C71C2×D411yescharacteristic
206C22×C4×C71C2×D411yescharacteristic
207C22×C4×C71C2×D412yes—
208C22×C4×C71C2×D412yes—
209C22×C4×C71C2×D412yes—
210C22×C4×C71#4112yes—
211C22×C4×C71#4112yes—
212C22×C4×C71#4112yes—
213C22×C4×C71C2411yescharacteristic
214M16×C71—28no—
215M16×C71—44no—
216C2×C8×C71—22no—
217C2×C8×C71—22no—
218C2×C8×C71—22no—
219C2×C8×C71—22no—
220C2×C8×C71—22no—
221C2×C8×C71C2×D414yes—
222C4⋊C4×C71—24no—
223C4⋊C4×C71—24no—
224C4⋊C4×C71—21no—
225C4⋊C4×C71—21no—
226C4⋊C4×C71—22no—
227C4⋊C4×C71—22no—
228C4⋊C4×C71—22no—
229C4⋊C4×C71—22no—
230C4⋊C4×C71—42no—
231C4⋊C4×C71—42no—
232C4⋊C4×C71C2×D412yes—
233C4⋊C4×C71C2×D412yes—
234C22⋊C4×C71—24no—
235C22⋊C4×C71—24no—
236C22⋊C4×C71—24no—
237C22⋊C4×C71—24no—
238C22⋊C4×C71—24no—
239C22⋊C4×C71—44no—
240C22⋊C4×C71—44no—
241C42×C71—24no—
242C23×C71—21no—
243C23×C71—21no—
244C23×C71—21no—
245C23×C71—21no—
246C23×C71—28no—
247C23×C71—21no—
248C23×C71—21no—
249C23×C71—21no—
250C23×C71—21no—
251C23×C71—21no—
252C23×C71—21no—
253C23×C71—21no—
254C23×C71—21no—
255C23×C71—21no—
256C23×C71—21no—
257C23×C71—21no—
258C23×C71—21no—
259C23×C71—22no—
260C23×C71—44no—
261C23×C71—44no—
262C23×C71—44no—
263C23×C71—44no—
264C23×C71—44no—
265C23×C71—44no—
266C23×C71—41no—
267C23×C71—41no—
268C23×C71—41no—
269C23×C71—41no—
270C23×C71—41no—
271C23×C71—41no—
272C23×C71#12012yes—
273C23×C71#12112yes—
274C23×C71#12312yes—
275C23×C71AGL(1,ℤ/8)12yes—
276C23×C71#13712yes—
277C23×C71C22×D411yescharacteristic
278Q8×C71—22no—
279Q8×C71—22no—
280Q8×C71—41no—
281Q8×C71—41no—
282D4×C71—22no—
283D4×C71—22no—
284D4×C71—48no—
285D4×C71—48no—
286D4×C71—48no—
287D4×C71—41no—
288D4×C71—41no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—21no—
292C2×C4×C71—21no—
293C2×C4×C71—22no—
294C2×C4×C71—21no—
295C2×C4×C71—21no—
296C2×C4×C71—21no—
297C2×C4×C71—21no—
298C2×C4×C71—41no—
299C2×C4×C71—41no—
300C2×C4×C71—41no—
301C2×C4×C71—41no—
302C2×C4×C71—41no—
303C2×C4×C71—41no—
304C2×C4×C71—44no—
305C2×C4×C71—41no—
306C2×C4×C71—41no—
307C2×C4×C71—41no—
308C2×C4×C71—41no—
309C2×C4×C71—41no—
310C2×C4×C71—41no—
311C2×C4×C71—41no—
312C2×C4×C71—41no—
313C2×C4×C71—44no—
314C2×C4×C71—44no—
315C2×C4×C71—48no—
316C2×C4×C71—42no—
317C2×C4×C71—42no—
318C2×C4×C71—42no—
319C2×C4×C71—42no—
320C2×C4×C71—42no—
321C2×C4×C71—42no—
322C2×C4×C71—84no—
323C2×C4×C71—84no—
324C2×C4×C71#12012yes—
325C2×C4×C71#12114yes—
326C2×C4×C71#12114yes—
327C2×C4×C71#12112yes—
328C2×C4×C71#12314yes—
329C2×C4×C71#12312yes—
330C2×C4×C71#12414yes—
331C2×C4×C71C22×D411yescharacteristic
332C2×C4×C71C22×D411yescharacteristic
333C2×C4×C71C22×D411yescharacteristic
334C2×C4×C71C2×#4111yescharacteristic
335C2×C4×C71C2×#4111yescharacteristic
336C2×C4×C71C2×#4111yescharacteristic
337C8×C71—24no—
338C8×C71—42no—
339C22×C71—22no—
340C22×C71—22no—
341C22×C71—22no—
342C22×C71—22no—
343C22×C71—22no—
344C22×C71—22no—
345C22×C71—22no—
346C22×C71—22no—
347C22×C71—22no—
348C22×C71—22no—
349C22×C71—22no—
350C22×C71—22no—
351C22×C71—416no—
352C22×C71—41no—
353C22×C71—41no—
354C22×C71—41no—
355C22×C71—41no—
356C22×C71—41no—
357C22×C71—41no—
358C22×C71—41no—
359C22×C71—41no—
360C22×C71—42no—
361C22×C71—42no—
362C22×C71—42no—
363C22×C71—81no—
364C22×C71—81no—
365C22×C71—81no—
366C22×C71—81no—
367C22×C71#39414yes—
368C22×C71C2×#12011yescharacteristic
369C22×C71C2×#12111yescharacteristic
370C22×C71C2×#12311yescharacteristic
371C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C71C2×#13711yescharacteristic
373C22×C71#57511yescharacteristic
374C22×C71#57511yescharacteristic
375C4×C71—41no—
376C4×C71—41no—
377C4×C71—42no—
378C4×C71—42no—
379C4×C71—42no—
380C4×C71—82no—
381C4×C71—82no—
382C4×C71#39414yes—
383C4×C71C2×#12111yescharacteristic
384C4×C71C2×#12111yescharacteristic
385C4×C71C2×#12311yescharacteristic
386C4×C71C2×#12411yescharacteristic
387#23482C7111yesmaximal, characteristic, direct product factor, Sylow
388C2×C71—24no—
389C2×C71—42no—
390C2×C71—42no—
391C2×C71—82no—
392C2×C71C2×#39411yescharacteristic
393C2×C71#300611yescharacteristic
394C2×C71#300711yescharacteristic
395C2×C71#305511yescharacteristic
396C2×C71#305611yescharacteristic
397C2×C71#309211yescharacteristic
398C2×C71#309311yescharacteristic
399C2×#525C2×C7111yescharacteristic
400C2×#428C2×C7111yescharacteristic, complemented
401C2×#417C2×C7111yescharacteristic, complemented
402C2×#417C2×C7111yescharacteristic, complemented
403C2×#407C2×C7111yescharacteristic, complemented
404C2×#380C2×C7111yescharacteristic, complemented
405#2036C2×C7112yescomplemented
406#2035C2×C7112yescomplemented
407#2034C2×C7112yescomplemented
408#2033C2×C7112yescomplemented
409#1736C2×C7111yescharacteristic, complemented
410C71#2348211yescharacteristic, direct product factor, Sylow
411C22×#41C22×C7111yescharacteristic
412C24×C4C22×C7111yescharacteristic
413C22×M16C22×C7111yescharacteristic
414C22×M16C22×C7111yescharacteristic
415#525—24no—
416#525—24no—
417C2×#123—21no—
418C2×C22⋊Q8C22×C7111yescharacteristic
419C2×C22⋊Q8C22×C7111yescharacteristic
420C2×#121C22×C7111yescharacteristic
421C2×#121C22×C7111yescharacteristic
422C2×#120—21no—
423C2×C4×D4—21no—
424C2×C4×D4—21no—
425C2×#117C22×C7111yescharacteristic
426C22×C4⋊C4C22×C7111yescharacteristic
427C22×C4⋊C4C22×C7111yescharacteristic
428C22×C22⋊C4—21no—
429#428—24no—
430C2×#107C22×C7112yescomplemented
431C2×#106C22×C7112yescomplemented
432#417—24no—
433#417—24no—
434C2×#103C22×C7112yescomplemented
435C2×#103C22×C7112yescomplemented
436C2×#102C22×C7112yescomplemented
437C2×#102C22×C7112yescomplemented
438#407—24no—
439C2×C22⋊C8C22×C7112yes—
440C2×C22⋊C8C22×C7112yes—
441#380—21no—
442#380—21no—
443#380C22×C7112yes—
444#380C22×C7112yes—
445C2×#95—21no—
446#340C22×C7112yescomplemented
447#340C22×C7112yescomplemented
448C25D4×C7111yescharacteristic
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41D4×C7114yes—
455C22×Q8C23×C7111yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C23×C7111yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—21no—
468C23×C4—21no—
469C23×C4D4×C7111yescharacteristic
470C23×C4D4×C7111yescharacteristic
471C23×C4D4×C7111yescharacteristic
472C23×C4C23×C7111yescharacteristic
473C23×C4C23×C7111yescharacteristic
474C23×C4C23×C7111yescharacteristic
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—22no—
480C2×M16D4×C7114yescomplemented
481C22×C8C23×C7112yes—
482C22×C8C23×C7112yes—
483#123—28no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—22no—
492#120—28no—
493C4×D4—28no—
494C4×D4—28no—
495#117—22no—
496#117D4×C7114yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4C23×C7112yes—
506C2×C4⋊C4C23×C7112yes—
507C2×C4⋊C4C23×C7111yescharacteristic
508C2×C4⋊C4C23×C7111yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—44no—
517C2×C42—21no—
518#107—24no—
519#106—24no—
520#103—24no—
521#103—24no—
522#102—24no—
523#102—24no—
524C22⋊C8—24no—
525C22⋊C8—24no—
526#95—22no—
527#95—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—41no—
535C24—41no—
536C24C2×D4×C7111yescharacteristic
537C24C2×D4×C7111yescharacteristic
538C24C2×D4×C7111yescharacteristic
539#41—28no—
540#41—28no—
541#41—44no—
542#41—44no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×D4×C7112yes—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4C2×D4×C7112yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—44no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C7111yescharacteristic
604C22×C4C2×D4×C7111yescharacteristic
605C22×C4C2×D4×C7111yescharacteristic
606C22×C4C2×D4×C7112yes—
607C22×C4C2×D4×C7112yes—
608C22×C4C2×D4×C7112yes—
609C22×C4#41×C7112yes—
610C22×C4#41×C7112yes—
611C22×C4#41×C7112yes—
612C22×C4C24×C7111yescharacteristic
613M16—28no—
614M16—44no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8C2×D4×C7114yes—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4C2×D4×C7112yes—
632C4⋊C4C2×D4×C7112yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C42—24no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#120×C7112yes—
672C23#121×C7112yes—
673C23#123×C7112yes—
674C23AGL(1,ℤ/8)×C7112yes—
675C23#137×C7112yes—
676C23C22×D4×C7111yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—48no—
686D4—41no—
687D4—41no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—44no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—48no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4#120×C7112yes—
724C2×C4#121×C7114yes—
725C2×C4#121×C7114yes—
726C2×C4#121×C7112yes—
727C2×C4#123×C7114yes—
728C2×C4#123×C7112yes—
729C2×C4#124×C7114yes—
730C2×C4C22×D4×C7111yescharacteristic
731C2×C4C22×D4×C7111yescharacteristic
732C2×C4C22×D4×C7111yescharacteristic
733C2×C4C2×#41×C7111yescharacteristic
734C2×C4C2×#41×C7111yescharacteristic
735C2×C4C2×#41×C7111yescharacteristic
736C8—24no—
737C8—42no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22#394×C7114yes—
767C22C2×#120×C7111yescharacteristic
768C22C2×#121×C7111yescharacteristic
769C22C2×#123×C7111yescharacteristic
770C22C2×AGL(1,ℤ/8)×C7111yescharacteristic
771C22C2×#137×C7111yescharacteristic
772C22#575×C7111yescharacteristic
773C22#575×C7111yescharacteristic
774C4—41no—
775C4—41no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—82no—
780C4—82no—
781C4#394×C7114yes—
782C4C2×#121×C7111yescharacteristic
783C4C2×#121×C7111yescharacteristic
784C4C2×#123×C7111yescharacteristic
785C4C2×#124×C7111yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—82no—
790C2C2×#394×C7111yescharacteristic
791C2C71×#300611yescharacteristic
792C2C71×#300711yescharacteristic
793C2C71×#305511yescharacteristic
794C2C71×#305611yescharacteristic
795C2C71×#309211yescharacteristic
796C2C71×#309311yescharacteristic
subgroupG/H
center, socleC23×C71C22×D4
commutator, Frattini, cosocleC22×C4C24×C71
prime radicalC2×#525×C71C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C71 ◁ C24×C4×C71 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#428×C71C2semidirect
3. C2×#417×C71C2semidirect
4. C2×#417×C71C2semidirect
5. C2×#407×C71C2semidirect
6. C2×#380×C71C2semidirect
7. C71×#2036C2semidirect
8. C71×#2035C2semidirect
9. C71×#2034C2semidirect
10. C71×#2033C2semidirect
11. C71×#1736C2semidirect
31. C2×#107×C71C22semidirect
32. C2×#106×C71C22semidirect
35. C2×#103×C71C22semidirect
36. C2×#103×C71C22semidirect
37. C2×#102×C71C22semidirect
38. C2×#102×C71C22semidirect
47. #340×C71C22semidirect
48. #340×C71C22semidirect
81. C2×M16×C71D4semidirect
387. #23482C71direct (N × H)
400. C2×#428C2×C71semidirect
401. C2×#417C2×C71semidirect
402. C2×#417C2×C71semidirect
403. C2×#407C2×C71semidirect
404. C2×#380C2×C71semidirect
405. #2036C2×C71semidirect
406. #2035C2×C71semidirect
407. #2034C2×C71semidirect
408. #2033C2×C71semidirect
409. #1736C2×C71semidirect
410. C71#23482direct (N × H)
430. C2×#107C22×C71semidirect
431. C2×#106C22×C71semidirect
434. C2×#103C22×C71semidirect
435. C2×#103C22×C71semidirect
436. C2×#102C22×C71semidirect
437. C2×#102C22×C71semidirect
446. #340C22×C71semidirect
447. #340C22×C71semidirect
480. C2×M16D4×C71semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C712
C2×#428×C712
C2×#417×C712
C2×#407×C712
C2×#380×C712
C71×#20362
C71×#20352
C71×#20342
C71×#20332
C71×#17362
#2348271