Finite Group Databasebeta

← C71×#24469 #31845341

Subgroups — C71×#24469 #31845341

Order 18176.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71×#3489C211yesmaximal, characteristic, complemented
2C71×#3055C211yesmaximal, characteristic, complemented
3C2×#454×C71C211yesmaximal, characteristic, complemented
4C71×#3006C211yesmaximal, characteristic, complemented
5C2×#421×C71C211yesmaximal, characteristic, complemented
6C71×#2620C211yesmaximal, characteristic, complemented
7C71×#2039C211yesmaximal, characteristic, complemented
8C71×#2038C211yesmaximal, characteristic, complemented
9C71×#2006C211yesmaximal, characteristic, complemented
10C71×#2003C211yesmaximal, characteristic, complemented
11C71×#1901C211yesmaximal, characteristic, complemented
12C71×#1897C211yesmaximal, characteristic, complemented
13C71×#1883C211yesmaximal, characteristic, complemented
14C71×#1859C211yesmaximal, characteristic, complemented
15C71×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C71C2211yescharacteristic
17C22×#41×C71C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C71C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C71C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C71C2211yescharacteristic, complemented
21C22×M16×C71C2211yescharacteristic
22D4×Q8×C71—21no—
23#548×C71—21no—
24#547×C71—21no—
25#547×C71—22no—
26#546×C71—21no—
27#546×C71—22no—
28#537×C71—21no—
29#537×C71C2211yescharacteristic
30#536×C71—21no—
31#536×C71C2211yescharacteristic
32C2×#124×C71C2211yescharacteristic, complemented
33#525×C71—21no—
34#525×C71C2211yescharacteristic
35C2×C22⋊Q8×C71—21no—
36C2×C22⋊Q8×C71C2211yescharacteristic
37C2×#121×C71C2211yescharacteristic
38#520×C71C2211yescharacteristic
39C2×#117×C71C2211yescharacteristic
40#469×C71—21no—
41#468×C71—21no—
42#466×C71—21no—
43#465×C71—21no—
44#454×C71—24no—
45#449×C71—21no—
46#449×C71—21no—
47#448×C71—21no—
48#447×C71—21no—
49#428×C71C2211yescharacteristic, complemented
50#421×C71—24no—
51C2×#104×C71C2211yescharacteristic
52C2×#104×C71C2211yescharacteristic
53C2×#104×C71C2211yescharacteristic
54C2×#104×C71C2211yescharacteristic
55C2×#104×C71C2211yescharacteristic, complemented
56C2×#104×C71C2211yescharacteristic, complemented
57#418×C71C2211yescharacteristic, complemented
58#417×C71C2211yescharacteristic
59#417×C71C2211yescharacteristic
60#417×C71C2211yescharacteristic, complemented
61C2×#101×C71C2211yescharacteristic, complemented
62C2×#101×C71C2211yescharacteristic, complemented
63#407×C71C2211yescharacteristic
64#396×C71—22no—
65#394×C71—22no—
66#391×C71C2211yescharacteristic, complemented
67#390×C71C2211yescharacteristic, complemented
68#384×C71C2211yescharacteristic, complemented
69#343×C71C2211yescharacteristic, complemented
70#343×C71C2211yescharacteristic, complemented
71#339×C71C2211yescharacteristic, complemented
72#339×C71C2211yescharacteristic, complemented
732−1+4×C71—22no—
742−1+4×C71—22no—
752−1+4×C71—41no—
762−1+4×C71—41no—
77C2×#41×C71—21no—
78C2×#41×C71—21no—
79C2×#41×C71—21no—
80C2×#41×C71—22no—
81C2×#41×C71—21no—
82C2×#41×C71—22no—
83C2×#41×C71—22no—
84C2×#41×C71—41no—
85C2×#41×C71—41no—
86C2×#41×C71D411yescharacteristic
87C2×#41×C71D411yescharacteristic
88C2×#41×C71C2311yescharacteristic
89C2×#41×C71C2311yescharacteristic
90C2×#41×C71C2311yescharacteristic
91C22×Q8×C71—21no—
92C22×Q8×C71—21no—
93C22×Q8×C71D411yescharacteristic
94C22×Q8×C71C2311yescharacteristic
95C22×D4×C71—21no—
96C22×D4×C71—21no—
97C22×D4×C71D411yescharacteristic
98C22×D4×C71C2311yescharacteristic
99C23×C4×C71—21no—
100C23×C4×C71C2311yescharacteristic
101AGL(1,ℤ/8)×C71—22no—
102AGL(1,ℤ/8)×C71—22no—
103AGL(1,ℤ/8)×C71—22no—
104AGL(1,ℤ/8)×C71—41no—
105AGL(1,ℤ/8)×C71—41no—
106AGL(1,ℤ/8)×C71—41no—
107C2×SD16×C71—21no—
108C2×SD16×C71—21no—
109C2×SD16×C71—21no—
110C2×D8×C71—21no—
111C2×D8×C71—21no—
112C2×D8×C71—21no—
113C2×M16×C71—21no—
114C2×M16×C71—22no—
115C2×M16×C71—41no—
116C2×M16×C71C2311yescharacteristic
117C2×M16×C71C2311yescharacteristic
118C2×M16×C71C2311yescharacteristic
119C2×M16×C71C2311yescharacteristic
120C22×C8×C71—21no—
121C4⋊Q8×C71—22no—
122C4⋊Q8×C71—21no—
123#124×C71—22no—
124#124×C71—21no—
125#124×C71—22no—
126#124×C71—41no—
127#123×C71—22no—
128#123×C71—22no—
129#123×C71—22no—
130#123×C71—21no—
131#123×C71—22no—
132C22⋊Q8×C71—22no—
133C22⋊Q8×C71—22no—
134C22⋊Q8×C71—22no—
135C22⋊Q8×C71—21no—
136C22⋊Q8×C71—21no—
137C22⋊Q8×C71—21no—
138C22⋊Q8×C71—21no—
139C22⋊Q8×C71—21no—
140C22⋊Q8×C71—21no—
141C22⋊Q8×C71—21no—
142C22⋊Q8×C71—21no—
143C22⋊Q8×C71D411yescharacteristic
144C22⋊Q8×C71D411yescharacteristic
145#121×C71—22no—
146#121×C71—22no—
147#121×C71—22no—
148#121×C71—21no—
149#121×C71—21no—
150#121×C71—22no—
151#121×C71—21no—
152#121×C71—21no—
153#121×C71—21no—
154#121×C71—21no—
155#121×C71D411yescharacteristic
156#121×C71D411yescharacteristic
157#120×C71—22no—
158#120×C71—21no—
159C4×Q8×C71—21no—
160C4×D4×C71—22no—
161C4×D4×C71—22no—
162C4×D4×C71—21no—
163C4×D4×C71—22no—
164C4×D4×C71—21no—
165C4×D4×C71—21no—
166#117×C71—21no—
167#117×C71—22no—
168#117×C71—41no—
169#117×C71C2311yescharacteristic
170C2×C4⋊C4×C71—22no—
171C2×C4⋊C4×C71—21no—
172C2×C4⋊C4×C71—21no—
173C2×C4⋊C4×C71—22no—
174C2×C4⋊C4×C71D412yes—
175C2×C4⋊C4×C71C2311yescharacteristic
176C2×C4⋊C4×C71C2311yescharacteristic
177C2×C22⋊C4×C71—22no—
178C2×C22⋊C4×C71—21no—
179C2×C22⋊C4×C71—21no—
180C2×C22⋊C4×C71—22no—
181C2×C22⋊C4×C71—22no—
182C2×C22⋊C4×C71D412yes—
183C2×C42×C71C2311yescharacteristic
184C2×C42×C71C2311yescharacteristic
185#107×C71—21no—
186#106×C71—21no—
187#104×C71—22no—
188#104×C71—22no—
189#104×C71—22no—
190#104×C71—22no—
191#104×C71—41no—
192#104×C71D414yescomplemented
193#103×C71—21no—
194#103×C71—21no—
195#103×C71—21no—
196#102×C71—21no—
197#102×C71—21no—
198#102×C71—21no—
199#102×C71—21no—
200#102×C71—21no—
201#101×C71—22no—
202#101×C71—41no—
203C22⋊C8×C71—21no—
204C22⋊C8×C71—21no—
205#95×C71—22no—
206C24×C71—21no—
207C24×C71—21no—
208C24×C71C2×D411yescharacteristic
209#41×C71—21no—
210#41×C71—21no—
211#41×C71—22no—
212#41×C71—22no—
213#41×C71—21no—
214#41×C71—21no—
215#41×C71—21no—
216#41×C71—21no—
217#41×C71—21no—
218#41×C71—21no—
219#41×C71—21no—
220#41×C71—21no—
221#41×C71—42no—
222#41×C71—42no—
223#41×C71—41no—
224#41×C71—41no—
225#41×C71—42no—
226#41×C71—42no—
227#41×C71—42no—
228#41×C71—42no—
229#41×C71—44no—
230#41×C71—44no—
231#41×C71—42no—
232#41×C71—42no—
233#41×C71C2×D412yes—
234#41×C71#4112yes—
235C2×Q8×C71—22no—
236C2×Q8×C71—21no—
237C2×Q8×C71—21no—
238C2×Q8×C71—21no—
239C2×Q8×C71—21no—
240C2×Q8×C71—21no—
241C2×Q8×C71—21no—
242C2×Q8×C71—21no—
243C2×Q8×C71—22no—
244C2×Q8×C71—41no—
245C2×Q8×C71—42no—
246C2×Q8×C71—42no—
247C2×Q8×C71—42no—
248C2×Q8×C71—42no—
249C2×Q8×C71C2×D411yescharacteristic
250C2×Q8×C71C2×D411yescharacteristic
251C2×Q8×C71C2×D411yescharacteristic
252C2×D4×C71—21no—
253C2×D4×C71—22no—
254C2×D4×C71—22no—
255C2×D4×C71—21no—
256C2×D4×C71—21no—
257C2×D4×C71—21no—
258C2×D4×C71—21no—
259C2×D4×C71—21no—
260C2×D4×C71—22no—
261C2×D4×C71—21no—
262C2×D4×C71—21no—
263C2×D4×C71—21no—
264C2×D4×C71—21no—
265C2×D4×C71—21no—
266C2×D4×C71—21no—
267C2×D4×C71—21no—
268C2×D4×C71—21no—
269C2×D4×C71—41no—
270C2×D4×C71—42no—
271C2×D4×C71—42no—
272C2×D4×C71—41no—
273C2×D4×C71—41no—
274C2×D4×C71—82no—
275C2×D4×C71C2×D411yescharacteristic
276C2×D4×C71C2×D411yescharacteristic
277C2×D4×C71C2×D411yescharacteristic
278C22×C4×C71—21no—
279C22×C4×C71—21no—
280C22×C4×C71—21no—
281C22×C4×C71—21no—
282C22×C4×C71—21no—
283C22×C4×C71—22no—
284C22×C4×C71—22no—
285C22×C4×C71—21no—
286C22×C4×C71—21no—
287C22×C4×C71—22no—
288C22×C4×C71—21no—
289C22×C4×C71—21no—
290C22×C4×C71—21no—
291C22×C4×C71—21no—
292C22×C4×C71—21no—
293C22×C4×C71—21no—
294C22×C4×C71—42no—
295C22×C4×C71—42no—
296C22×C4×C71C2×D412yes—
297C22×C4×C71C2×D411yescharacteristic
298C22×C4×C71C2×D411yescharacteristic
299C22×C4×C71C2×D411yescharacteristic
300C22×C4×C71C2×D411yescharacteristic
301C22×C4×C71C2×D411yescharacteristic
302C22×C4×C71C2×D412yes—
303C22×C4×C71C2411yescharacteristic
304SD16×C71—42no—
305SD16×C71—42no—
306SD16×C71—42no—
307D8×C71—42no—
308D8×C71—42no—
309D8×C71—42no—
310M16×C71—21no—
311M16×C71—21no—
312M16×C71—21no—
313M16×C71—21no—
314M16×C71—21no—
315M16×C71—21no—
316M16×C71—21no—
317M16×C71—42no—
318M16×C71C2×D412yes—
319C2×C8×C71—21no—
320C2×C8×C71—21no—
321C2×C8×C71—21no—
322C2×C8×C71—21no—
323C2×C8×C71—42no—
324C4⋊C4×C71—22no—
325C4⋊C4×C71—22no—
326C4⋊C4×C71—22no—
327C4⋊C4×C71—22no—
328C4⋊C4×C71—21no—
329C4⋊C4×C71—22no—
330C4⋊C4×C71—22no—
331C4⋊C4×C71—21no—
332C4⋊C4×C71—21no—
333C4⋊C4×C71—21no—
334C4⋊C4×C71—21no—
335C4⋊C4×C71—21no—
336C4⋊C4×C71—42no—
337C4⋊C4×C71—82no—
338C4⋊C4×C71C2×D411yescharacteristic
339C4⋊C4×C71C2×D411yescharacteristic
340C22⋊C4×C71—22no—
341C22⋊C4×C71—22no—
342C22⋊C4×C71—22no—
343C22⋊C4×C71—22no—
344C22⋊C4×C71—22no—
345C22⋊C4×C71—21no—
346C22⋊C4×C71—22no—
347C22⋊C4×C71—22no—
348C22⋊C4×C71—21no—
349C22⋊C4×C71—21no—
350C22⋊C4×C71—21no—
351C22⋊C4×C71—21no—
352C22⋊C4×C71—44no—
353C22⋊C4×C71—42no—
354C22⋊C4×C71—41no—
355C22⋊C4×C71—41no—
356C22⋊C4×C71—82no—
357C42×C71—22no—
358C42×C71—21no—
359C42×C71—21no—
360C42×C71—21no—
361C42×C71—21no—
362C42×C71C2×D412yes—
363C23×C71—21no—
364C23×C71—21no—
365C23×C71—21no—
366C23×C71—21no—
367C23×C71—21no—
368C23×C71—41no—
369C23×C71—41no—
370C23×C71—42no—
371C23×C71—42no—
372C23×C71—42no—
373C23×C71—42no—
374C23×C71—41no—
375C23×C71—41no—
376C23×C71—41no—
377C23×C71—81no—
378C23×C71#12011yescharacteristic
379C23×C71#12011yescharacteristic
380C23×C71C22×D411yescharacteristic
381Q8×C71—21no—
382Q8×C71—21no—
383Q8×C71—21no—
384Q8×C71—21no—
385Q8×C71—21no—
386Q8×C71—42no—
387Q8×C71—44no—
388Q8×C71—41no—
389Q8×C71—41no—
390Q8×C71—41no—
391Q8×C71—41no—
392Q8×C71#12112yes—
393D4×C71—22no—
394D4×C71—22no—
395D4×C71—21no—
396D4×C71—21no—
397D4×C71—21no—
398D4×C71—21no—
399D4×C71—21no—
400D4×C71—42no—
401D4×C71—42no—
402D4×C71—42no—
403D4×C71—42no—
404D4×C71—44no—
405D4×C71—41no—
406D4×C71—41no—
407D4×C71—41no—
408D4×C71—41no—
409D4×C71—41no—
410D4×C71—41no—
411D4×C71—41no—
412D4×C71—41no—
413D4×C71—81no—
414D4×C71—82no—
415D4×C71—82no—
416D4×C71—82no—
417D4×C71#12112yes—
418C2×C4×C71—21no—
419C2×C4×C71—21no—
420C2×C4×C71—21no—
421C2×C4×C71—21no—
422C2×C4×C71—21no—
423C2×C4×C71—21no—
424C2×C4×C71—21no—
425C2×C4×C71—21no—
426C2×C4×C71—21no—
427C2×C4×C71—22no—
428C2×C4×C71—21no—
429C2×C4×C71—21no—
430C2×C4×C71—22no—
431C2×C4×C71—21no—
432C2×C4×C71—22no—
433C2×C4×C71—21no—
434C2×C4×C71—21no—
435C2×C4×C71—22no—
436C2×C4×C71—21no—
437C2×C4×C71—22no—
438C2×C4×C71—22no—
439C2×C4×C71—22no—
440C2×C4×C71—42no—
441C2×C4×C71—42no—
442C2×C4×C71—42no—
443C2×C4×C71—44no—
444C2×C4×C71—41no—
445C2×C4×C71—41no—
446C2×C4×C71—44no—
447C2×C4×C71—41no—
448C2×C4×C71—41no—
449C2×C4×C71—41no—
450C2×C4×C71—41no—
451C2×C4×C71—42no—
452C2×C4×C71—41no—
453C2×C4×C71—42no—
454C2×C4×C71—41no—
455C2×C4×C71—41no—
456C2×C4×C71—41no—
457C2×C4×C71—82no—
458C2×C4×C71#12011yescharacteristic
459C2×C4×C71#12011yescharacteristic
460C2×C4×C71C22×D411yescharacteristic
461C2×C4×C71C22×D411yescharacteristic
462C2×C4×C71C22×D411yescharacteristic
463C2×C4×C71C2×#4111yescharacteristic
464C2×C4×C71H(5,𝔽2)11yescharacteristic
465C2×C4×C71H(5,𝔽2)11yescharacteristic
466C8×C71—22no—
467C8×C71—41no—
468C8×C71—41no—
469C8×C71—41no—
470C22×C71—21no—
471C22×C71—21no—
472C22×C71—21no—
473C22×C71—21no—
474C22×C71—22no—
475C22×C71—21no—
476C22×C71—21no—
477C22×C71—21no—
478C22×C71—21no—
479C22×C71—41no—
480C22×C71—41no—
481C22×C71—41no—
482C22×C71—41no—
483C22×C71—41no—
484C22×C71—41no—
485C22×C71—41no—
486C22×C71—41no—
487C22×C71—81no—
488C22×C71—81no—
489C22×C71—82no—
490C22×C71—82no—
491C22×C71—84no—
492C22×C71—81no—
493C22×C71—81no—
494C22×C71—81no—
495C22×C71C2×#12011yescharacteristic
496C22×C71D4211yescharacteristic
497C22×C71#54611yescharacteristic
498C4×C71—21no—
499C4×C71—21no—
500C4×C71—22no—
501C4×C71—42no—
502C4×C71—42no—
503C4×C71—41no—
504C4×C71—41no—
505C4×C71—41no—
506C4×C71—42no—
507C4×C71—41no—
508C4×C71—81no—
509C4×C71—81no—
510C4×C71C2×#12111yescharacteristic
511C4×C71#53411yescharacteristic
512C4×C71D4211yescharacteristic
513C4×C71#54611yescharacteristic
514#24469C7111yesmaximal, characteristic, direct product factor, Sylow
515C2×C71—21no—
516C2×C71—21no—
517C2×C71—41no—
518C2×C71—41no—
519C2×C71—42no—
520C2×C71—81no—
521C2×C71—81no—
522C2×C71—161no—
523C2×C71#241011yescharacteristic
524C2×C71#302011yescharacteristic
525C2×C71#302111yescharacteristic
526#3489C2×C7111yescharacteristic, complemented
527#3055C2×C7111yescharacteristic, complemented
528C2×#454C2×C7111yescharacteristic, complemented
529#3006C2×C7111yescharacteristic, complemented
530C2×#421C2×C7111yescharacteristic, complemented
531#2620C2×C7111yescharacteristic, complemented
532#2039C2×C7111yescharacteristic, complemented
533#2038C2×C7111yescharacteristic, complemented
534#2006C2×C7111yescharacteristic, complemented
535#2003C2×C7111yescharacteristic, complemented
536#1901C2×C7111yescharacteristic, complemented
537#1897C2×C7111yescharacteristic, complemented
538#1883C2×C7111yescharacteristic, complemented
539#1859C2×C7111yescharacteristic, complemented
540#1793C2×C7111yescharacteristic, complemented
541C71#2446911yescharacteristic, direct product factor, Sylow
542C2×2−1+4C22×C7111yescharacteristic
543C22×#41C22×C7111yescharacteristic
544C2×AGL(1,ℤ/8)C22×C7111yescharacteristic
545C2×AGL(1,ℤ/8)C22×C7111yescharacteristic
546C2×AGL(1,ℤ/8)C22×C7111yescharacteristic, complemented
547C22×M16C22×C7111yescharacteristic
548D4×Q8—21no—
549#548—21no—
550#547—21no—
551#547—22no—
552#546—21no—
553#546—22no—
554#537—21no—
555#537C22×C7111yescharacteristic
556#536—21no—
557#536C22×C7111yescharacteristic
558C2×#124C22×C7111yescharacteristic, complemented
559#525—21no—
560#525C22×C7111yescharacteristic
561C2×C22⋊Q8—21no—
562C2×C22⋊Q8C22×C7111yescharacteristic
563C2×#121C22×C7111yescharacteristic
564#520C22×C7111yescharacteristic
565C2×#117C22×C7111yescharacteristic
566#469—21no—
567#468—21no—
568#466—21no—
569#465—21no—
570#454—24no—
571#449—21no—
572#449—21no—
573#448—21no—
574#447—21no—
575#428C22×C7111yescharacteristic, complemented
576#421—24no—
577C2×#104C22×C7111yescharacteristic
578C2×#104C22×C7111yescharacteristic
579C2×#104C22×C7111yescharacteristic
580C2×#104C22×C7111yescharacteristic
581C2×#104C22×C7111yescharacteristic, complemented
582C2×#104C22×C7111yescharacteristic, complemented
583#418C22×C7111yescharacteristic, complemented
584#417C22×C7111yescharacteristic
585#417C22×C7111yescharacteristic
586#417C22×C7111yescharacteristic, complemented
587C2×#101C22×C7111yescharacteristic, complemented
588C2×#101C22×C7111yescharacteristic, complemented
589#407C22×C7111yescharacteristic
590#396—22no—
591#394—22no—
592#391C22×C7111yescharacteristic, complemented
593#390C22×C7111yescharacteristic, complemented
594#384C22×C7111yescharacteristic, complemented
595#343C22×C7111yescharacteristic, complemented
596#343C22×C7111yescharacteristic, complemented
597#339C22×C7111yescharacteristic, complemented
598#339C22×C7111yescharacteristic, complemented
5992−1+4—22no—
6002−1+4—22no—
6012−1+4—41no—
6022−1+4—41no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—22no—
607C2×#41—21no—
608C2×#41—22no—
609C2×#41—22no—
610C2×#41—41no—
611C2×#41—41no—
612C2×#41D4×C7111yescharacteristic
613C2×#41D4×C7111yescharacteristic
614C2×#41C23×C7111yescharacteristic
615C2×#41C23×C7111yescharacteristic
616C2×#41C23×C7111yescharacteristic
617C22×Q8—21no—
618C22×Q8—21no—
619C22×Q8D4×C7111yescharacteristic
620C22×Q8C23×C7111yescharacteristic
621C22×D4—21no—
622C22×D4—21no—
623C22×D4D4×C7111yescharacteristic
624C22×D4C23×C7111yescharacteristic
625C23×C4—21no—
626C23×C4C23×C7111yescharacteristic
627AGL(1,ℤ/8)—22no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—22no—
630AGL(1,ℤ/8)—41no—
631AGL(1,ℤ/8)—41no—
632AGL(1,ℤ/8)—41no—
633C2×SD16—21no—
634C2×SD16—21no—
635C2×SD16—21no—
636C2×D8—21no—
637C2×D8—21no—
638C2×D8—21no—
639C2×M16—21no—
640C2×M16—22no—
641C2×M16—41no—
642C2×M16C23×C7111yescharacteristic
643C2×M16C23×C7111yescharacteristic
644C2×M16C23×C7111yescharacteristic
645C2×M16C23×C7111yescharacteristic
646C22×C8—21no—
647C4⋊Q8—22no—
648C4⋊Q8—21no—
649#124—22no—
650#124—21no—
651#124—22no—
652#124—41no—
653#123—22no—
654#123—22no—
655#123—22no—
656#123—21no—
657#123—22no—
658C22⋊Q8—22no—
659C22⋊Q8—22no—
660C22⋊Q8—22no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C7111yescharacteristic
670C22⋊Q8D4×C7111yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—21no—
675#121—21no—
676#121—22no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121D4×C7111yescharacteristic
682#121D4×C7111yescharacteristic
683#120—22no—
684#120—21no—
685C4×Q8—21no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—21no—
689C4×D4—22no—
690C4×D4—21no—
691C4×D4—21no—
692#117—21no—
693#117—22no—
694#117—41no—
695#117C23×C7111yescharacteristic
696C2×C4⋊C4—22no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4D4×C7112yes—
701C2×C4⋊C4C23×C7111yescharacteristic
702C2×C4⋊C4C23×C7111yescharacteristic
703C2×C22⋊C4—22no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4D4×C7112yes—
709C2×C42C23×C7111yescharacteristic
710C2×C42C23×C7111yescharacteristic
711#107—21no—
712#106—21no—
713#104—22no—
714#104—22no—
715#104—22no—
716#104—22no—
717#104—41no—
718#104D4×C7114yescomplemented
719#103—21no—
720#103—21no—
721#103—21no—
722#102—21no—
723#102—21no—
724#102—21no—
725#102—21no—
726#102—21no—
727#101—22no—
728#101—41no—
729C22⋊C8—21no—
730C22⋊C8—21no—
731#95—22no—
732C24—21no—
733C24—21no—
734C24C2×D4×C7111yescharacteristic
735#41—21no—
736#41—21no—
737#41—22no—
738#41—22no—
739#41—21no—
740#41—21no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—42no—
748#41—42no—
749#41—41no—
750#41—41no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—44no—
756#41—44no—
757#41—42no—
758#41—42no—
759#41C2×D4×C7112yes—
760#41#41×C7112yes—
761C2×Q8—22no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—41no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8C2×D4×C7111yescharacteristic
776C2×Q8C2×D4×C7111yescharacteristic
777C2×Q8C2×D4×C7111yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—41no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—82no—
801C2×D4C2×D4×C7111yescharacteristic
802C2×D4C2×D4×C7111yescharacteristic
803C2×D4C2×D4×C7111yescharacteristic
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4C2×D4×C7112yes—
823C22×C4C2×D4×C7111yescharacteristic
824C22×C4C2×D4×C7111yescharacteristic
825C22×C4C2×D4×C7111yescharacteristic
826C22×C4C2×D4×C7111yescharacteristic
827C22×C4C2×D4×C7111yescharacteristic
828C22×C4C2×D4×C7112yes—
829C22×C4C24×C7111yescharacteristic
830SD16—42no—
831SD16—42no—
832SD16—42no—
833D8—42no—
834D8—42no—
835D8—42no—
836M16—21no—
837M16—21no—
838M16—21no—
839M16—21no—
840M16—21no—
841M16—21no—
842M16—21no—
843M16—42no—
844M16C2×D4×C7112yes—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—42no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—21no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—42no—
863C4⋊C4—82no—
864C4⋊C4C2×D4×C7111yescharacteristic
865C4⋊C4C2×D4×C7111yescharacteristic
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—21no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—44no—
879C22⋊C4—42no—
880C22⋊C4—41no—
881C22⋊C4—41no—
882C22⋊C4—82no—
883C42—22no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42C2×D4×C7112yes—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—81no—
904C23#120×C7111yescharacteristic
905C23#120×C7111yescharacteristic
906C23C22×D4×C7111yescharacteristic
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—42no—
913Q8—44no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8—41no—
918Q8#121×C7112yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—44no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—81no—
940D4—82no—
941D4—82no—
942D4—82no—
943D4#121×C7112yes—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—44no—
970C2×C4—41no—
971C2×C4—44no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—41no—
979C2×C4—42no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—82no—
984C2×C4#120×C7111yescharacteristic
985C2×C4#120×C7111yescharacteristic
986C2×C4C22×D4×C7111yescharacteristic
987C2×C4C22×D4×C7111yescharacteristic
988C2×C4C22×D4×C7111yescharacteristic
989C2×C4C2×#41×C7111yescharacteristic
990C2×C4H(5,𝔽2)×C7111yescharacteristic
991C2×C4H(5,𝔽2)×C7111yescharacteristic
992C8—22no—
993C8—41no—
994C8—41no—
995C8—41no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—22no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—82no—
1016C22—82no—
1017C22—84no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22C2×#120×C7111yescharacteristic
1022C22D42×C7111yescharacteristic
1023C22#546×C7111yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—22no—
1027C4—42no—
1028C4—42no—
1029C4—41no—
1030C4—41no—
1031C4—41no—
1032C4—42no—
1033C4—41no—
1034C4—81no—
1035C4—81no—
1036C4C2×#121×C7111yescharacteristic
1037C4#534×C7111yescharacteristic
1038C4D42×C7111yescharacteristic
1039C4#546×C7111yescharacteristic
1040C2—21no—
1041C2—21no—
1042C2—41no—
1043C2—41no—
1044C2—42no—
1045C2—81no—
1046C2—81no—
1047C2—161no—
1048C2C71×#241011yescharacteristic
1049C2C71×#302011yescharacteristic
1050C2C71×#302111yescharacteristic
subgroupG/H
center, socleC22×C71C2×#120
commutator, Frattini, cosocleC22×C4C24×C71
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C71 ◁ C23×C4×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C71×#3489C2semidirect
2. C71×#3055C2semidirect
3. C2×#454×C71C2semidirect
4. C71×#3006C2semidirect
5. C2×#421×C71C2semidirect
6. C71×#2620C2semidirect
7. C71×#2039C2semidirect
8. C71×#2038C2semidirect
9. C71×#2006C2semidirect
10. C71×#2003C2semidirect
11. C71×#1901C2semidirect
12. C71×#1897C2semidirect
13. C71×#1883C2semidirect
14. C71×#1859C2semidirect
15. C71×#1793C2semidirect
20. C2×AGL(1,ℤ/8)×C71C22semidirect
32. C2×#124×C71C22semidirect
49. #428×C71C22semidirect
55. C2×#104×C71C22semidirect
56. C2×#104×C71C22semidirect
57. #418×C71C22semidirect
60. #417×C71C22semidirect
61. C2×#101×C71C22semidirect
62. C2×#101×C71C22semidirect
66. #391×C71C22semidirect
67. #390×C71C22semidirect
68. #384×C71C22semidirect
69. #343×C71C22semidirect
70. #343×C71C22semidirect
71. #339×C71C22semidirect
72. #339×C71C22semidirect
192. #104×C71D4semidirect
514. #24469C71direct (N × H)
526. #3489C2×C71semidirect
527. #3055C2×C71semidirect
528. C2×#454C2×C71semidirect
529. #3006C2×C71semidirect
530. C2×#421C2×C71semidirect
531. #2620C2×C71semidirect
532. #2039C2×C71semidirect
533. #2038C2×C71semidirect
534. #2006C2×C71semidirect
535. #2003C2×C71semidirect
536. #1901C2×C71semidirect
537. #1897C2×C71semidirect
538. #1883C2×C71semidirect
539. #1859C2×C71semidirect
540. #1793C2×C71semidirect
541. C71#24469direct (N × H)
546. C2×AGL(1,ℤ/8)C22×C71semidirect
558. C2×#124C22×C71semidirect
575. #428C22×C71semidirect
581. C2×#104C22×C71semidirect
582. C2×#104C22×C71semidirect
583. #418C22×C71semidirect
586. #417C22×C71semidirect
587. C2×#101C22×C71semidirect
588. C2×#101C22×C71semidirect
592. #391C22×C71semidirect
593. #390C22×C71semidirect
594. #384C22×C71semidirect
595. #343C22×C71semidirect
596. #343C22×C71semidirect
597. #339C22×C71semidirect
598. #339C22×C71semidirect
718. #104D4×C71semidirect

Maximal subgroups

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

subgroupindex
C71×#34892
C71×#30552
C2×#454×C712
C71×#30062
C2×#421×C712
C71×#26202
C71×#20392
C71×#20382
C71×#20062
C71×#20032
C71×#19012
C71×#18972
C71×#18832
C71×#18592
C71×#17932
#2446971