Finite Group Databasebeta

← C71×#23712 #31844584

Subgroups — C71×#23712 #31844584

Order 18176.

932 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#442×C71C211yesmaximal, characteristic, complemented
2C2×#433×C71C211yesmaximal, characteristic, complemented
3C71×#2324C211yesmaximal, characteristic, complemented
4C71×#2324C211yesmaximal, characteristic, complemented
5C71×#2088C211yesmaximal, characteristic, complemented
6C71×#2077C211yesmaximal, characteristic, complemented
7C71×#2067C211yesmaximal, characteristic, complemented
8C71×#2065C211yesmaximal, characteristic, complemented
9C71×#2054C211yesmaximal, characteristic, complemented
10C71×#2034C211yesmaximal, characteristic, complemented
11C71×#2033C211yesmaximal, characteristic, complemented
12C71×#1999C211yesmaximal, characteristic
13C71×#1776C211yesmaximal, characteristic, complemented
14C4×#102×C71C211yesmaximal, characteristic, complemented
15C4×#102×C71C211yesmaximal, characteristic, complemented
16C22×D8×C71C2211yescharacteristic
17C2×#121×C71C2211yescharacteristic
18C2×#121×C71C2211yescharacteristic
19C2×C4×D4×C71C2211yescharacteristic
20C2×C4×D4×C71C2211yescharacteristic
21C2×#117×C71C2211yescharacteristic
22#442×C71—24no—
23#433×C71—24no—
24C2×#107×C71C2211yescharacteristic
25C2×#106×C71C2211yescharacteristic
26C2×#106×C71C2211yescharacteristic
27C2×C4⋊C8×C71C2211yescharacteristic
28C2×C4⋊C8×C71C2211yescharacteristic
29C2×#102×C71C2211yescharacteristic
30C2×#102×C71C2211yescharacteristic
31C2×#102×C71C2211yescharacteristic
32C2×#102×C71C2211yescharacteristic
33C2×#102×C71C2211yescharacteristic
34C2×#102×C71C2211yescharacteristic
35C2×C22⋊C8×C71C2211yescharacteristic
36C2×C22⋊C8×C71C2211yescharacteristic
37C2×#97×C71C2211yescharacteristic
38C2×C4×C8×C71C2211yescharacteristic
39#390×C71—21no—
40#390×C71—21no—
41#390×C71C2211yescharacteristic
42#390×C71C2211yescharacteristic
43#389×C71C2211yescharacteristic
44#389×C71C2211yescharacteristic
45#388×C71—21no—
46#388×C71—21no—
47#386×C71—21no—
48#386×C71—21no—
49#385×C71—21no—
50#385×C71—21no—
51#380×C71C2211yescharacteristic
52#380×C71C2211yescharacteristic
53C4×C4⋊C4×C71C2211yescharacteristic
54C4×C4⋊C4×C71C2211yescharacteristic
55#340×C71C2211yescharacteristic
56#340×C71C2211yescharacteristic
57#340×C71C2211yescharacteristic
58#340×C71C2211yescharacteristic
59#340×C71C2211yescharacteristic
60#340×C71C2211yescharacteristic
61C22×D4×C71—21no—
62C22×D4×C71—21no—
63C22×D4×C71C2311yescharacteristic
64C22×D4×C71C2311yescharacteristic
65C23×C4×C71—21no—
66C23×C4×C71—21no—
67C23×C4×C71C2311yescharacteristic
68C2×D8×C71—22no—
69C2×D8×C71—22no—
70C2×D8×C71—22no—
71C22×C8×C71C2311yescharacteristic
72C22×C8×C71C2311yescharacteristic
73C22×C8×C71C2311yescharacteristic
74C22×C8×C71C2311yescharacteristic
75#121×C71—22no—
76#121×C71—22no—
77#121×C71—22no—
78#121×C71—22no—
79C4×D4×C71—22no—
80C4×D4×C71—22no—
81C4×D4×C71—22no—
82C4×D4×C71—22no—
83#117×C71—22no—
84#117×C71—22no—
85C2×C4⋊C4×C71—21no—
86C2×C4⋊C4×C71—21no—
87C2×C4⋊C4×C71D411yescharacteristic
88C2×C4⋊C4×C71D411yescharacteristic
89C2×C4⋊C4×C71C2311yescharacteristic
90C2×C4⋊C4×C71C2311yescharacteristic
91C2×C4⋊C4×C71C2311yescharacteristic
92C2×C4⋊C4×C71C2311yescharacteristic
93C2×C4⋊C4×C71C2311yescharacteristic
94C2×C4⋊C4×C71C2311yescharacteristic
95C2×C22⋊C4×C71—21no—
96C2×C22⋊C4×C71—21no—
97C2×C22⋊C4×C71—21no—
98C2×C22⋊C4×C71—21no—
99C2×C22⋊C4×C71—21no—
100C2×C22⋊C4×C71—21no—
101C2×C22⋊C4×C71—21no—
102C2×C22⋊C4×C71—21no—
103C2×C22⋊C4×C71—21no—
104C2×C22⋊C4×C71—21no—
105C2×C22⋊C4×C71D411yescharacteristic
106C2×C22⋊C4×C71D411yescharacteristic
107C2×C42×C71—21no—
108C2×C42×C71—21no—
109C2×C42×C71C2311yescharacteristic
110C2×C42×C71C2311yescharacteristic
111#107×C71—22no—
112#106×C71—22no—
113#106×C71—22no—
114C4⋊C8×C71—22no—
115C4⋊C8×C71—22no—
116#102×C71—22no—
117#102×C71—22no—
118#102×C71—22no—
119#102×C71—22no—
120#102×C71—22no—
121#102×C71—22no—
122C22⋊C8×C71—22no—
123C22⋊C8×C71—22no—
124#97×C71D414yescomplemented
125C4×C8×C71—22no—
126#95×C71—21no—
127#95×C71—21no—
128#95×C71—21no—
129#95×C71—21no—
130#95×C71—21no—
131#95×C71—21no—
132C24×C71—21no—
133C24×C71—21no—
134C24×C71C2×D411yescharacteristic
135C2×D4×C71—24no—
136C2×D4×C71—24no—
137C2×D4×C71—21no—
138C2×D4×C71—21no—
139C2×D4×C71—21no—
140C2×D4×C71—21no—
141C2×D4×C71—21no—
142C2×D4×C71—21no—
143C2×D4×C71—21no—
144C2×D4×C71—21no—
145C2×D4×C71—21no—
146C2×D4×C71—21no—
147C2×D4×C71—81no—
148C2×D4×C71—81no—
149C2×D4×C71—81no—
150C2×D4×C71—81no—
151C2×D4×C71#4112yes—
152C2×D4×C71#4112yes—
153C22×C4×C71—21no—
154C22×C4×C71—21no—
155C22×C4×C71—21no—
156C22×C4×C71—21no—
157C22×C4×C71—21no—
158C22×C4×C71—21no—
159C22×C4×C71—21no—
160C22×C4×C71—21no—
161C22×C4×C71—21no—
162C22×C4×C71—21no—
163C22×C4×C71—21no—
164C22×C4×C71—21no—
165C22×C4×C71—42no—
166C22×C4×C71—42no—
167C22×C4×C71—81no—
168C22×C4×C71—81no—
169C22×C4×C71—81no—
170C22×C4×C71—81no—
171C22×C4×C71C2×D411yescharacteristic
172C22×C4×C71C2×D411yescharacteristic
173C22×C4×C71C2×D411yescharacteristic
174C22×C4×C71C2×D411yescharacteristic
175C22×C4×C71C2×D411yescharacteristic
176C22×C4×C71C2411yescharacteristic
177D8×C71—28no—
178C2×C8×C71—21no—
179C2×C8×C71—21no—
180C2×C8×C71—21no—
181C2×C8×C71—21no—
182C2×C8×C71—21no—
183C2×C8×C71—21no—
184C2×C8×C71—21no—
185C2×C8×C71—21no—
186C2×C8×C71—21no—
187C2×C8×C71—21no—
188C2×C8×C71C2×D412yes—
189C2×C8×C71C2×D412yes—
190C4⋊C4×C71—22no—
191C4⋊C4×C71—22no—
192C4⋊C4×C71—21no—
193C4⋊C4×C71—21no—
194C4⋊C4×C71—21no—
195C4⋊C4×C71—21no—
196C4⋊C4×C71—21no—
197C4⋊C4×C71—21no—
198C4⋊C4×C71—21no—
199C4⋊C4×C71—21no—
200C4⋊C4×C71—21no—
201C4⋊C4×C71—21no—
202C4⋊C4×C71—81no—
203C4⋊C4×C71—81no—
204C4⋊C4×C71#4112yes—
205C4⋊C4×C71#4112yes—
206C22⋊C4×C71—24no—
207C22⋊C4×C71—24no—
208C22⋊C4×C71—22no—
209C22⋊C4×C71—22no—
210C22⋊C4×C71—42no—
211C22⋊C4×C71—42no—
212C22⋊C4×C71—81no—
213C22⋊C4×C71—81no—
214C22⋊C4×C71—81no—
215C22⋊C4×C71—81no—
216C22⋊C4×C71—81no—
217C22⋊C4×C71—81no—
218C42×C71—21no—
219C42×C71—21no—
220C42×C71—81no—
221C42×C71—81no—
222C42×C71C2×D412yes—
223C42×C71#4112yes—
224C23×C71—21no—
225C23×C71—22no—
226C23×C71—22no—
227C23×C71—21no—
228C23×C71—21no—
229C23×C71—21no—
230C23×C71—21no—
231C23×C71—21no—
232C23×C71—21no—
233C23×C71—41no—
234C23×C71—41no—
235C23×C71—41no—
236C23×C71—41no—
237C23×C71—41no—
238C23×C71—41no—
239C23×C71—41no—
240C23×C71—41no—
241C23×C71—41no—
242C23×C71—41no—
243C23×C71—41no—
244C23×C71—41no—
245C23×C71C22×D411yescharacteristic
246D4×C71—22no—
247D4×C71—22no—
248D4×C71—22no—
249D4×C71—22no—
250D4×C71—41no—
251D4×C71—41no—
252D4×C71—41no—
253D4×C71—41no—
254D4×C71—84no—
255D4×C71—84no—
256C2×C4×C71—21no—
257C2×C4×C71—21no—
258C2×C4×C71—21no—
259C2×C4×C71—21no—
260C2×C4×C71—21no—
261C2×C4×C71—21no—
262C2×C4×C71—21no—
263C2×C4×C71—21no—
264C2×C4×C71—21no—
265C2×C4×C71—22no—
266C2×C4×C71—22no—
267C2×C4×C71—21no—
268C2×C4×C71—21no—
269C2×C4×C71—21no—
270C2×C4×C71—21no—
271C2×C4×C71—41no—
272C2×C4×C71—41no—
273C2×C4×C71—41no—
274C2×C4×C71—41no—
275C2×C4×C71—41no—
276C2×C4×C71—41no—
277C2×C4×C71—41no—
278C2×C4×C71—41no—
279C2×C4×C71—41no—
280C2×C4×C71—41no—
281C2×C4×C71—41no—
282C2×C4×C71—41no—
283C2×C4×C71—41no—
284C2×C4×C71—41no—
285C2×C4×C71—41no—
286C2×C4×C71—41no—
287C2×C4×C71—41no—
288C2×C4×C71—41no—
289C2×C4×C71—41no—
290C2×C4×C71—41no—
291C2×C4×C71—84no—
292C2×C4×C71—84no—
293C2×C4×C71#12112yes—
294C2×C4×C71#12112yes—
295C2×C4×C71C22×D411yescharacteristic
296C2×C4×C71C2×#4111yescharacteristic
297C2×C4×C71C2×#4111yescharacteristic
298C2×C4×C71C2×#4111yescharacteristic
299C2×C4×C71C2×#4111yescharacteristic
300C2×C4×C71C2×#4111yescharacteristic
301C8×C71—22no—
302C8×C71—22no—
303C8×C71—41no—
304C8×C71—41no—
305C22×C71—41no—
306C22×C71—42no—
307C22×C71—41no—
308C22×C71—42no—
309C22×C71—41no—
310C22×C71—42no—
311C22×C71—41no—
312C22×C71—42no—
313C22×C71—41no—
314C22×C71—42no—
315C22×C71—42no—
316C22×C71—41no—
317C22×C71—41no—
318C22×C71—81no—
319C22×C71—81no—
320C22×C71—81no—
321C22×C71—81no—
322C22×C71—81no—
323C22×C71—81no—
324C22×C71—81no—
325C22×C71—81no—
326C22×C71C2×#12111yescharacteristic
327C22×C71#52511yescharacteristic
328C22×C71#52511yescharacteristic
329C22×C71#57611yescharacteristic
330C22×C71#57611yescharacteristic
331C22×C71#57711yescharacteristic
332C22×C71#57711yescharacteristic
333C4×C71—22no—
334C4×C71—22no—
335C4×C71—42no—
336C4×C71—42no—
337C4×C71—41no—
338C4×C71—41no—
339C4×C71—41no—
340C4×C71—81no—
341C4×C71—81no—
342C4×C71—81no—
343C4×C71—81no—
344C4×C71#52511yescharacteristic
345C4×C71#52911yescharacteristic
346C4×C71#52911yescharacteristic
347C4×C71#53211yescharacteristic
348#23712C7111yesmaximal, characteristic, direct product factor, Sylow
349C2×C71—81no—
350C2×C71—82no—
351C2×C71—82no—
352C2×C71#239211yescharacteristic
353C2×C71#306211yescharacteristic
354C2×C71#306211yescharacteristic
355C2×C71#311811yescharacteristic
356C2×C71#311911yescharacteristic
357C2×C71#312211yescharacteristic
358C2×C71#312511yescharacteristic
359C2×#442C2×C7111yescharacteristic, complemented
360C2×#433C2×C7111yescharacteristic, complemented
361#2324C2×C7111yescharacteristic, complemented
362#2324C2×C7111yescharacteristic, complemented
363#2088C2×C7111yescharacteristic, complemented
364#2077C2×C7111yescharacteristic, complemented
365#2067C2×C7111yescharacteristic, complemented
366#2065C2×C7111yescharacteristic, complemented
367#2054C2×C7111yescharacteristic, complemented
368#2034C2×C7111yescharacteristic, complemented
369#2033C2×C7111yescharacteristic, complemented
370#1999C2×C7111yescharacteristic
371#1776C2×C7111yescharacteristic, complemented
372C4×#102C2×C7111yescharacteristic, complemented
373C4×#102C2×C7111yescharacteristic, complemented
374C71#2371211yescharacteristic, direct product factor, Sylow
375C22×D8C22×C7111yescharacteristic
376C2×#121C22×C7111yescharacteristic
377C2×#121C22×C7111yescharacteristic
378C2×C4×D4C22×C7111yescharacteristic
379C2×C4×D4C22×C7111yescharacteristic
380C2×#117C22×C7111yescharacteristic
381#442—24no—
382#433—24no—
383C2×#107C22×C7111yescharacteristic
384C2×#106C22×C7111yescharacteristic
385C2×#106C22×C7111yescharacteristic
386C2×C4⋊C8C22×C7111yescharacteristic
387C2×C4⋊C8C22×C7111yescharacteristic
388C2×#102C22×C7111yescharacteristic
389C2×#102C22×C7111yescharacteristic
390C2×#102C22×C7111yescharacteristic
391C2×#102C22×C7111yescharacteristic
392C2×#102C22×C7111yescharacteristic
393C2×#102C22×C7111yescharacteristic
394C2×C22⋊C8C22×C7111yescharacteristic
395C2×C22⋊C8C22×C7111yescharacteristic
396C2×#97C22×C7111yescharacteristic
397C2×C4×C8C22×C7111yescharacteristic
398#390—21no—
399#390—21no—
400#390C22×C7111yescharacteristic
401#390C22×C7111yescharacteristic
402#389C22×C7111yescharacteristic
403#389C22×C7111yescharacteristic
404#388—21no—
405#388—21no—
406#386—21no—
407#386—21no—
408#385—21no—
409#385—21no—
410#380C22×C7111yescharacteristic
411#380C22×C7111yescharacteristic
412C4×C4⋊C4C22×C7111yescharacteristic
413C4×C4⋊C4C22×C7111yescharacteristic
414#340C22×C7111yescharacteristic
415#340C22×C7111yescharacteristic
416#340C22×C7111yescharacteristic
417#340C22×C7111yescharacteristic
418#340C22×C7111yescharacteristic
419#340C22×C7111yescharacteristic
420C22×D4—21no—
421C22×D4—21no—
422C22×D4C23×C7111yescharacteristic
423C22×D4C23×C7111yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4C23×C7111yescharacteristic
427C2×D8—22no—
428C2×D8—22no—
429C2×D8—22no—
430C22×C8C23×C7111yescharacteristic
431C22×C8C23×C7111yescharacteristic
432C22×C8C23×C7111yescharacteristic
433C22×C8C23×C7111yescharacteristic
434#121—22no—
435#121—22no—
436#121—22no—
437#121—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442#117—22no—
443#117—22no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4D4×C7111yescharacteristic
447C2×C4⋊C4D4×C7111yescharacteristic
448C2×C4⋊C4C23×C7111yescharacteristic
449C2×C4⋊C4C23×C7111yescharacteristic
450C2×C4⋊C4C23×C7111yescharacteristic
451C2×C4⋊C4C23×C7111yescharacteristic
452C2×C4⋊C4C23×C7111yescharacteristic
453C2×C4⋊C4C23×C7111yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4D4×C7111yescharacteristic
465C2×C22⋊C4D4×C7111yescharacteristic
466C2×C42—21no—
467C2×C42—21no—
468C2×C42C23×C7111yescharacteristic
469C2×C42C23×C7111yescharacteristic
470#107—22no—
471#106—22no—
472#106—22no—
473C4⋊C8—22no—
474C4⋊C8—22no—
475#102—22no—
476#102—22no—
477#102—22no—
478#102—22no—
479#102—22no—
480#102—22no—
481C22⋊C8—22no—
482C22⋊C8—22no—
483#97D4×C7114yescomplemented
484C4×C8—22no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491C24—21no—
492C24—21no—
493C24C2×D4×C7111yescharacteristic
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—81no—
507C2×D4—81no—
508C2×D4—81no—
509C2×D4—81no—
510C2×D4#41×C7112yes—
511C2×D4#41×C7112yes—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4C2×D4×C7111yescharacteristic
531C22×C4C2×D4×C7111yescharacteristic
532C22×C4C2×D4×C7111yescharacteristic
533C22×C4C2×D4×C7111yescharacteristic
534C22×C4C2×D4×C7111yescharacteristic
535C22×C4C24×C7111yescharacteristic
536D8—28no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8C2×D4×C7112yes—
548C2×C8C2×D4×C7112yes—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—81no—
562C4⋊C4—81no—
563C4⋊C4#41×C7112yes—
564C4⋊C4#41×C7112yes—
565C22⋊C4—24no—
566C22⋊C4—24no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C42—21no—
578C42—21no—
579C42—81no—
580C42—81no—
581C42C2×D4×C7112yes—
582C42#41×C7112yes—
583C23—21no—
584C23—22no—
585C23—22no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23C22×D4×C7111yescharacteristic
605D4—22no—
606D4—22no—
607D4—22no—
608D4—22no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—84no—
614D4—84no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—84no—
651C2×C4—84no—
652C2×C4#121×C7112yes—
653C2×C4#121×C7112yes—
654C2×C4C22×D4×C7111yescharacteristic
655C2×C4C2×#41×C7111yescharacteristic
656C2×C4C2×#41×C7111yescharacteristic
657C2×C4C2×#41×C7111yescharacteristic
658C2×C4C2×#41×C7111yescharacteristic
659C2×C4C2×#41×C7111yescharacteristic
660C8—22no—
661C8—22no—
662C8—41no—
663C8—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—42no—
668C22—41no—
669C22—42no—
670C22—41no—
671C22—42no—
672C22—41no—
673C22—42no—
674C22—41no—
675C22—42no—
676C22—42no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22C2×#121×C7111yescharacteristic
686C22#525×C7111yescharacteristic
687C22#525×C7111yescharacteristic
688C22#576×C7111yescharacteristic
689C22#576×C7111yescharacteristic
690C22#577×C7111yescharacteristic
691C22#577×C7111yescharacteristic
692C4—22no—
693C4—22no—
694C4—41no—
695C4—41no—
696C4—42no—
697C4—42no—
698C4—41no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4#525×C7111yescharacteristic
704C4#529×C7111yescharacteristic
705C4#529×C7111yescharacteristic
706C4#532×C7111yescharacteristic
707C2—81no—
708C2—82no—
709C2—82no—
710C2C71×#239211yescharacteristic
711C2C71×#306211yescharacteristic
712C2C71×#306211yescharacteristic
713C2C71×#311811yescharacteristic
714C2C71×#311911yescharacteristic
715C2C71×#312211yescharacteristic
716C2C71×#312511yescharacteristic
subgroupG/H
center, socleC23×C71C22×D4
commutator, Frattini, cosocleC22×C4C24×C71
prime radicalC71×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C71 ◁ C2×#117×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#442×C71C2semidirect
2. C2×#433×C71C2semidirect
3. C71×#2324C2semidirect
4. C71×#2324C2semidirect
5. C71×#2088C2semidirect
6. C71×#2077C2semidirect
7. C71×#2067C2semidirect
8. C71×#2065C2semidirect
9. C71×#2054C2semidirect
10. C71×#2034C2semidirect
11. C71×#2033C2semidirect
13. C71×#1776C2semidirect
14. C4×#102×C71C2semidirect
15. C4×#102×C71C2semidirect
124. #97×C71D4semidirect
348. #23712C71direct (N × H)
359. C2×#442C2×C71semidirect
360. C2×#433C2×C71semidirect
361. #2324C2×C71semidirect
362. #2324C2×C71semidirect
363. #2088C2×C71semidirect
364. #2077C2×C71semidirect
365. #2067C2×C71semidirect
366. #2065C2×C71semidirect
367. #2054C2×C71semidirect
368. #2034C2×C71semidirect
369. #2033C2×C71semidirect
371. #1776C2×C71semidirect
372. C4×#102C2×C71semidirect
373. C4×#102C2×C71semidirect
374. C71#23712direct (N × H)
483. #97D4×C71semidirect

Maximal subgroups

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

subgroupindex
C2×#442×C712
C2×#433×C712
C71×#23242
C71×#20882
C71×#20772
C71×#20672
C71×#20652
C71×#20542
C71×#20342
C71×#20332
C71×#19992
C71×#17762
C4×#102×C712
#2371271