Finite Group Databasebeta

← C71×#24467 #31845339

Subgroups — C71×#24467 #31845339

Order 18176.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71×#3488C211yesmaximal, characteristic
2C71×#3056C211yesmaximal, characteristic, complemented
3C2×#455×C71C211yesmaximal, characteristic, complemented
4C71×#3007C211yesmaximal, characteristic, complemented
5C22×#104×C71C211yesmaximal, characteristic, complemented
6C71×#2850C211yesmaximal, characteristic, complemented
7C71×#2040C211yesmaximal, characteristic, complemented
8C71×#2037C211yesmaximal, characteristic, complemented
9C71×#2007C211yesmaximal, characteristic, complemented
10C71×#2004C211yesmaximal, characteristic, complemented
11C71×#1900C211yesmaximal, characteristic, complemented
12C71×#1896C211yesmaximal, characteristic, complemented
13C71×#1882C211yesmaximal, characteristic, complemented
14C71×#1860C211yesmaximal, characteristic, complemented
15C71×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C71C2211yescharacteristic
17C22×#41×C71C2211yescharacteristic
18C2×#137×C71C2211yescharacteristic
19C2×#137×C71C2211yescharacteristic, complemented
20C2×#137×C71C2211yescharacteristic, complemented
21C22×M16×C71C2211yescharacteristic, complemented
22#550×C71—21no—
23#548×C71—21no—
24#546×C71—21no—
25#546×C71—22no—
26D42×C71—22no—
27D42×C71—21no—
28#537×C71—21no—
29#537×C71C2211yescharacteristic
30#535×C71—21no—
31#535×C71C2211yescharacteristic
32C2×#124×C71C2211yescharacteristic, complemented
33#525×C71—21no—
34#525×C71C2211yescharacteristic
35C2×C22⋊Q8×C71C2211yescharacteristic, complemented
36C2×#121×C71—21no—
37C2×#121×C71C2211yescharacteristic
38#520×C71C2211yescharacteristic
39C22×C42×C71C2211yescharacteristic, complemented
40#470×C71—21no—
41#468×C71—21no—
42#467×C71—21no—
43#465×C71—21no—
44#455×C71—24no—
45#452×C71—21no—
46#452×C71—21no—
47#451×C71—21no—
48#450×C71—21no—
49#428×C71C2211yescharacteristic, complemented
50C2×#104×C71—24no—
51C2×#104×C71C2211yescharacteristic
52C2×#104×C71C2211yescharacteristic
53C2×#104×C71C2211yescharacteristic, complemented
54C2×#104×C71C2211yescharacteristic, complemented
55C2×#104×C71C2211yescharacteristic, complemented
56C2×#104×C71C2211yescharacteristic, complemented
57#419×C71C2211yescharacteristic, complemented
58#417×C71C2211yescharacteristic
59#417×C71C2211yescharacteristic, complemented
60#417×C71C2211yescharacteristic, complemented
61C2×#100×C71C2211yescharacteristic, complemented
62C2×#100×C71C2211yescharacteristic, complemented
63#407×C71C2211yescharacteristic, complemented
64#391×C71C2211yescharacteristic, complemented
65#390×C71C2211yescharacteristic, complemented
66#388×C71—22no—
67#386×C71—22no—
68#382×C71C2211yescharacteristic, complemented
69#343×C71C2211yescharacteristic, complemented
70#343×C71C2211yescharacteristic, complemented
71#339×C71C2211yescharacteristic, complemented
72#339×C71C2211yescharacteristic, complemented
73H(5,𝔽2)×C71—22no—
74H(5,𝔽2)×C71—22no—
75H(5,𝔽2)×C71—41no—
76H(5,𝔽2)×C71—41no—
77C2×#41×C71—21no—
78C2×#41×C71—21no—
79C2×#41×C71—21no—
80C2×#41×C71—21no—
81C2×#41×C71—22no—
82C2×#41×C71—22no—
83C2×#41×C71—41no—
84C2×#41×C71—41no—
85C2×#41×C71D411yescharacteristic
86C2×#41×C71D411yescharacteristic
87C2×#41×C71C2311yescharacteristic
88C2×#41×C71C2311yescharacteristic
89C2×#41×C71C2311yescharacteristic
90C22×Q8×C71D411yescharacteristic
91C22×Q8×C71C2311yescharacteristic
92C22×D4×C71—21no—
93C22×D4×C71—22no—
94C22×D4×C71—22no—
95C22×D4×C71—21no—
96C22×D4×C71—21no—
97C22×D4×C71D411yescharacteristic
98C22×D4×C71D412yes—
99C22×D4×C71C2311yescharacteristic
100C23×C4×C71—21no—
101C23×C4×C71—21no—
102C23×C4×C71C2311yescharacteristic
103#137×C71—22no—
104#137×C71—22no—
105#137×C71—22no—
106#137×C71—41no—
107#137×C71—41no—
108#137×C71—41no—
109C2×Q16×C71—21no—
110C2×Q16×C71—21no—
111C2×Q16×C71—21no—
112C2×SD16×C71—21no—
113C2×SD16×C71—21no—
114C2×SD16×C71—21no—
115C2×M16×C71—21no—
116C2×M16×C71—22no—
117C2×M16×C71—41no—
118C2×M16×C71C2311yescharacteristic
119C2×M16×C71C2311yescharacteristic
120C2×M16×C71C2311yescharacteristic
121C2×M16×C71C2311yescharacteristic
122C22×C8×C71—21no—
123#127×C71—22no—
124#127×C71—21no—
125#124×C71—22no—
126#124×C71—21no—
127#124×C71—22no—
128#124×C71—41no—
129#123×C71—22no—
130#123×C71—21no—
131C22⋊Q8×C71—22no—
132C22⋊Q8×C71—21no—
133C22⋊Q8×C71—21no—
134C22⋊Q8×C71—21no—
135C22⋊Q8×C71—21no—
136C22⋊Q8×C71—21no—
137C22⋊Q8×C71—21no—
138C22⋊Q8×C71D411yescharacteristic
139C22⋊Q8×C71D411yescharacteristic
140#121×C71—22no—
141#121×C71—22no—
142#121×C71—22no—
143#121×C71—22no—
144#121×C71—22no—
145#121×C71—21no—
146#121×C71—21no—
147#121×C71—21no—
148#121×C71—21no—
149#121×C71—21no—
150#121×C71—21no—
151#121×C71—22no—
152#121×C71—21no—
153#121×C71—21no—
154#121×C71D411yescharacteristic
155#121×C71D411yescharacteristic
156#120×C71—22no—
157#120×C71—22no—
158#120×C71—22no—
159#120×C71—21no—
160#120×C71—22no—
161C4×Q8×C71—21no—
162C4×D4×C71—22no—
163C4×D4×C71—22no—
164C4×D4×C71—21no—
165C4×D4×C71—22no—
166C4×D4×C71—21no—
167C4×D4×C71—21no—
168#117×C71—21no—
169#117×C71C2311yescharacteristic
170C2×C4⋊C4×C71—21no—
171C2×C4⋊C4×C71—21no—
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C22⋊C4×C71—22no—
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71—22no—
177C2×C22⋊C4×C71—22no—
178C2×C22⋊C4×C71D412yes—
179C2×C42×C71—22no—
180C2×C42×C71—21no—
181C2×C42×C71—41no—
182C2×C42×C71C2311yescharacteristic
183C2×C42×C71C2311yescharacteristic
184#107×C71—21no—
185#106×C71—21no—
186#104×C71—22no—
187#104×C71—22no—
188#104×C71—22no—
189#104×C71—22no—
190#104×C71—41no—
191#104×C71D414yescomplemented
192#103×C71—21no—
193#103×C71—21no—
194#103×C71—21no—
195#103×C71—21no—
196#103×C71—21no—
197#102×C71—21no—
198#102×C71—21no—
199#102×C71—21no—
200#100×C71—22no—
201#100×C71—41no—
202C22⋊C8×C71—21no—
203C22⋊C8×C71—21no—
204#95×C71—22no—
205#95×C71—22no—
206C24×C71—22no—
207C24×C71—21no—
208C24×C71C2×D411yescharacteristic
209C24×C71C2×D412yes—
210#41×C71—21no—
211#41×C71—21no—
212#41×C71—22no—
213#41×C71—22no—
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—21no—
222#41×C71—42no—
223#41×C71—42no—
224#41×C71—41no—
225#41×C71—41no—
226#41×C71—42no—
227#41×C71—42no—
228#41×C71—42no—
229#41×C71—42no—
230#41×C71—42no—
231#41×C71—42no—
232#41×C71C2×D412yes—
233#41×C71#4112yes—
234C2×Q8×C71—21no—
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—41no—
243C2×Q8×C71C2×D411yescharacteristic
244C2×Q8×C71C2×D411yescharacteristic
245C2×Q8×C71C2×D411yescharacteristic
246C2×D4×C71—21no—
247C2×D4×C71—22no—
248C2×D4×C71—22no—
249C2×D4×C71—22no—
250C2×D4×C71—22no—
251C2×D4×C71—21no—
252C2×D4×C71—21no—
253C2×D4×C71—21no—
254C2×D4×C71—21no—
255C2×D4×C71—21no—
256C2×D4×C71—22no—
257C2×D4×C71—22no—
258C2×D4×C71—22no—
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—41no—
269C2×D4×C71—42no—
270C2×D4×C71—42no—
271C2×D4×C71—42no—
272C2×D4×C71—42no—
273C2×D4×C71—44no—
274C2×D4×C71—44no—
275C2×D4×C71—42no—
276C2×D4×C71—42no—
277C2×D4×C71—44no—
278C2×D4×C71—84no—
279C2×D4×C71C2×D411yescharacteristic
280C2×D4×C71C2×D411yescharacteristic
281C2×D4×C71C2×D411yescharacteristic
282C22×C4×C71—21no—
283C22×C4×C71—21no—
284C22×C4×C71—21no—
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—22no—
292C22×C4×C71—21no—
293C22×C4×C71—21no—
294C22×C4×C71—21no—
295C22×C4×C71—21no—
296C22×C4×C71—21no—
297C22×C4×C71—21no—
298C22×C4×C71—42no—
299C22×C4×C71—42no—
300C22×C4×C71—42no—
301C22×C4×C71—42no—
302C22×C4×C71—42no—
303C22×C4×C71C2×D411yescharacteristic
304C22×C4×C71C2×D411yescharacteristic
305C22×C4×C71C2×D411yescharacteristic
306C22×C4×C71C2×D411yescharacteristic
307C22×C4×C71C2×D411yescharacteristic
308C22×C4×C71C2×D412yes—
309C22×C4×C71C2411yescharacteristic
310Q16×C71—42no—
311Q16×C71—42no—
312Q16×C71—42no—
313SD16×C71—42no—
314SD16×C71—42no—
315SD16×C71—42no—
316M16×C71—21no—
317M16×C71—21no—
318M16×C71—21no—
319M16×C71—21no—
320M16×C71—21no—
321M16×C71—21no—
322M16×C71—21no—
323M16×C71—42no—
324M16×C71C2×D412yescomplemented
325C2×C8×C71—21no—
326C2×C8×C71—21no—
327C2×C8×C71—21no—
328C2×C8×C71—21no—
329C2×C8×C71—42no—
330C4⋊C4×C71—22no—
331C4⋊C4×C71—22no—
332C4⋊C4×C71—21no—
333C4⋊C4×C71—21no—
334C4⋊C4×C71—21no—
335C4⋊C4×C71—21no—
336C4⋊C4×C71—21no—
337C4⋊C4×C71—21no—
338C4⋊C4×C71—41no—
339C4⋊C4×C71—41no—
340C4⋊C4×C71C2×D411yescharacteristic
341C4⋊C4×C71C2×D411yescharacteristic
342C22⋊C4×C71—22no—
343C22⋊C4×C71—22no—
344C22⋊C4×C71—22no—
345C22⋊C4×C71—22no—
346C22⋊C4×C71—22no—
347C22⋊C4×C71—21no—
348C22⋊C4×C71—21no—
349C22⋊C4×C71—21no—
350C22⋊C4×C71—21no—
351C22⋊C4×C71—22no—
352C22⋊C4×C71—22no—
353C22⋊C4×C71—21no—
354C22⋊C4×C71—44no—
355C22⋊C4×C71—44no—
356C22⋊C4×C71—41no—
357C22⋊C4×C71—41no—
358C42×C71—22no—
359C42×C71—21no—
360C42×C71—21no—
361C42×C71—21no—
362C42×C71—21no—
363C42×C71—42no—
364C42×C71C2×D412yescomplemented
365C23×C71—21no—
366C23×C71—21no—
367C23×C71—21no—
368C23×C71—22no—
369C23×C71—22no—
370C23×C71—21no—
371C23×C71—21no—
372C23×C71—22no—
373C23×C71—22no—
374C23×C71—41no—
375C23×C71—42no—
376C23×C71—44no—
377C23×C71—42no—
378C23×C71—42no—
379C23×C71—42no—
380C23×C71—81no—
381C23×C71—82no—
382C23×C71—82no—
383C23×C71#12011yescharacteristic
384C23×C71#12011yescharacteristic
385C23×C71C22×D411yescharacteristic
386Q8×C71—21no—
387Q8×C71—21no—
388Q8×C71—21no—
389Q8×C71—21no—
390Q8×C71—21no—
391Q8×C71—42no—
392Q8×C71—41no—
393Q8×C71—41no—
394Q8×C71—41no—
395Q8×C71—41no—
396Q8×C71#12112yes—
397D4×C71—22no—
398D4×C71—22no—
399D4×C71—21no—
400D4×C71—21no—
401D4×C71—21no—
402D4×C71—21no—
403D4×C71—21no—
404D4×C71—42no—
405D4×C71—42no—
406D4×C71—44no—
407D4×C71—42no—
408D4×C71—44no—
409D4×C71—41no—
410D4×C71—41no—
411D4×C71—41no—
412D4×C71—41no—
413D4×C71—44no—
414D4×C71—42no—
415D4×C71—41no—
416D4×C71—41no—
417D4×C71—41no—
418D4×C71—41no—
419D4×C71—81no—
420D4×C71—82no—
421D4×C71—82no—
422D4×C71—82no—
423D4×C71—82no—
424D4×C71#12112yes—
425C2×C4×C71—21no—
426C2×C4×C71—21no—
427C2×C4×C71—21no—
428C2×C4×C71—21no—
429C2×C4×C71—21no—
430C2×C4×C71—21no—
431C2×C4×C71—21no—
432C2×C4×C71—21no—
433C2×C4×C71—21no—
434C2×C4×C71—22no—
435C2×C4×C71—21no—
436C2×C4×C71—21no—
437C2×C4×C71—22no—
438C2×C4×C71—22no—
439C2×C4×C71—21no—
440C2×C4×C71—22no—
441C2×C4×C71—21no—
442C2×C4×C71—21no—
443C2×C4×C71—21no—
444C2×C4×C71—22no—
445C2×C4×C71—42no—
446C2×C4×C71—42no—
447C2×C4×C71—42no—
448C2×C4×C71—44no—
449C2×C4×C71—41no—
450C2×C4×C71—41no—
451C2×C4×C71—41no—
452C2×C4×C71—48no—
453C2×C4×C71—41no—
454C2×C4×C71—41no—
455C2×C4×C71—41no—
456C2×C4×C71—41no—
457C2×C4×C71—41no—
458C2×C4×C71—42no—
459C2×C4×C71—42no—
460C2×C4×C71—41no—
461C2×C4×C71—41no—
462C2×C4×C71—41no—
463C2×C4×C71—41no—
464C2×C4×C71—82no—
465C2×C4×C71#12011yescharacteristic
466C2×C4×C71#12011yescharacteristic
467C2×C4×C71C22×D411yescharacteristic
468C2×C4×C71C22×D411yescharacteristic
469C2×C4×C71C22×D411yescharacteristic
470C2×C4×C71C2×#4111yescharacteristic
471C2×C4×C71H(5,𝔽2)11yescharacteristic
472C2×C4×C71H(5,𝔽2)11yescharacteristic
473C8×C71—22no—
474C8×C71—41no—
475C8×C71—41no—
476C8×C71—41no—
477C22×C71—21no—
478C22×C71—21no—
479C22×C71—21no—
480C22×C71—21no—
481C22×C71—21no—
482C22×C71—22no—
483C22×C71—21no—
484C22×C71—21no—
485C22×C71—42no—
486C22×C71—42no—
487C22×C71—41no—
488C22×C71—41no—
489C22×C71—41no—
490C22×C71—41no—
491C22×C71—42no—
492C22×C71—42no—
493C22×C71—41no—
494C22×C71—41no—
495C22×C71—41no—
496C22×C71—42no—
497C22×C71—41no—
498C22×C71—84no—
499C22×C71—82no—
500C22×C71—82no—
501C22×C71—164no—
502C22×C71#45512yescomplemented
503C22×C71C2×#12011yescharacteristic
504C22×C71D4211yescharacteristic
505C22×C71#54611yescharacteristic
506C4×C71—21no—
507C4×C71—21no—
508C4×C71—22no—
509C4×C71—42no—
510C4×C71—42no—
511C4×C71—41no—
512C4×C71—41no—
513C4×C71—42no—
514C4×C71—41no—
515C4×C71—41no—
516C4×C71—81no—
517C4×C71—81no—
518C4×C71C2×#12111yescharacteristic
519C4×C71#53411yescharacteristic
520C4×C71D4211yescharacteristic
521C4×C71#54611yescharacteristic
522#24467C7111yesmaximal, characteristic, direct product factor, Sylow
523C2×C71—21no—
524C2×C71—21no—
525C2×C71—22no—
526C2×C71—41no—
527C2×C71—42no—
528C2×C71—81no—
529C2×C71—82no—
530C2×C71—81no—
531C2×C71#241011yescharacteristic
532C2×C71C2×#45511yescharacteristic
533C2×C71#301811yescharacteristic
534#3488C2×C7111yescharacteristic
535#3056C2×C7111yescharacteristic, complemented
536C2×#455C2×C7111yescharacteristic, complemented
537#3007C2×C7111yescharacteristic, complemented
538C22×#104C2×C7111yescharacteristic, complemented
539#2850C2×C7111yescharacteristic, complemented
540#2040C2×C7111yescharacteristic, complemented
541#2037C2×C7111yescharacteristic, complemented
542#2007C2×C7111yescharacteristic, complemented
543#2004C2×C7111yescharacteristic, complemented
544#1900C2×C7111yescharacteristic, complemented
545#1896C2×C7111yescharacteristic, complemented
546#1882C2×C7111yescharacteristic, complemented
547#1860C2×C7111yescharacteristic, complemented
548#1792C2×C7111yescharacteristic, complemented
549C71#2446711yescharacteristic, direct product factor, Sylow
550C2×H(5,𝔽2)C22×C7111yescharacteristic
551C22×#41C22×C7111yescharacteristic
552C2×#137C22×C7111yescharacteristic
553C2×#137C22×C7111yescharacteristic, complemented
554C2×#137C22×C7111yescharacteristic, complemented
555C22×M16C22×C7111yescharacteristic, complemented
556#550—21no—
557#548—21no—
558#546—21no—
559#546—22no—
560D42—22no—
561D42—21no—
562#537—21no—
563#537C22×C7111yescharacteristic
564#535—21no—
565#535C22×C7111yescharacteristic
566C2×#124C22×C7111yescharacteristic, complemented
567#525—21no—
568#525C22×C7111yescharacteristic
569C2×C22⋊Q8C22×C7111yescharacteristic, complemented
570C2×#121—21no—
571C2×#121C22×C7111yescharacteristic
572#520C22×C7111yescharacteristic
573C22×C42C22×C7111yescharacteristic, complemented
574#470—21no—
575#468—21no—
576#467—21no—
577#465—21no—
578#455—24no—
579#452—21no—
580#452—21no—
581#451—21no—
582#450—21no—
583#428C22×C7111yescharacteristic, complemented
584C2×#104—24no—
585C2×#104C22×C7111yescharacteristic
586C2×#104C22×C7111yescharacteristic
587C2×#104C22×C7111yescharacteristic, complemented
588C2×#104C22×C7111yescharacteristic, complemented
589C2×#104C22×C7111yescharacteristic, complemented
590C2×#104C22×C7111yescharacteristic, complemented
591#419C22×C7111yescharacteristic, complemented
592#417C22×C7111yescharacteristic
593#417C22×C7111yescharacteristic, complemented
594#417C22×C7111yescharacteristic, complemented
595C2×#100C22×C7111yescharacteristic, complemented
596C2×#100C22×C7111yescharacteristic, complemented
597#407C22×C7111yescharacteristic, complemented
598#391C22×C7111yescharacteristic, complemented
599#390C22×C7111yescharacteristic, complemented
600#388—22no—
601#386—22no—
602#382C22×C7111yescharacteristic, complemented
603#343C22×C7111yescharacteristic, complemented
604#343C22×C7111yescharacteristic, complemented
605#339C22×C7111yescharacteristic, complemented
606#339C22×C7111yescharacteristic, complemented
607H(5,𝔽2)—22no—
608H(5,𝔽2)—22no—
609H(5,𝔽2)—41no—
610H(5,𝔽2)—41no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C2×#41D4×C7111yescharacteristic
620C2×#41D4×C7111yescharacteristic
621C2×#41C23×C7111yescharacteristic
622C2×#41C23×C7111yescharacteristic
623C2×#41C23×C7111yescharacteristic
624C22×Q8D4×C7111yescharacteristic
625C22×Q8C23×C7111yescharacteristic
626C22×D4—21no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4D4×C7111yescharacteristic
632C22×D4D4×C7112yes—
633C22×D4C23×C7111yescharacteristic
634C23×C4—21no—
635C23×C4—21no—
636C23×C4C23×C7111yescharacteristic
637#137—22no—
638#137—22no—
639#137—22no—
640#137—41no—
641#137—41no—
642#137—41no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×M16—21no—
650C2×M16—22no—
651C2×M16—41no—
652C2×M16C23×C7111yescharacteristic
653C2×M16C23×C7111yescharacteristic
654C2×M16C23×C7111yescharacteristic
655C2×M16C23×C7111yescharacteristic
656C22×C8—21no—
657#127—22no—
658#127—21no—
659#124—22no—
660#124—21no—
661#124—22no—
662#124—41no—
663#123—22no—
664#123—21no—
665C22⋊Q8—22no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8—21no—
672C22⋊Q8D4×C7111yescharacteristic
673C22⋊Q8D4×C7111yescharacteristic
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—22no—
686#121—21no—
687#121—21no—
688#121D4×C7111yescharacteristic
689#121D4×C7111yescharacteristic
690#120—22no—
691#120—22no—
692#120—22no—
693#120—21no—
694#120—22no—
695C4×Q8—21no—
696C4×D4—22no—
697C4×D4—22no—
698C4×D4—21no—
699C4×D4—22no—
700C4×D4—21no—
701C4×D4—21no—
702#117—21no—
703#117C23×C7111yescharacteristic
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4C23×C7111yescharacteristic
707C2×C4⋊C4C23×C7111yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4D4×C7112yes—
713C2×C42—22no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42C23×C7111yescharacteristic
717C2×C42C23×C7111yescharacteristic
718#107—21no—
719#106—21no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—22no—
724#104—41no—
725#104D4×C7114yescomplemented
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#103—21no—
731#102—21no—
732#102—21no—
733#102—21no—
734#100—22no—
735#100—41no—
736C22⋊C8—21no—
737C22⋊C8—21no—
738#95—22no—
739#95—22no—
740C24—22no—
741C24—21no—
742C24C2×D4×C7111yescharacteristic
743C24C2×D4×C7112yes—
744#41—21no—
745#41—21no—
746#41—22no—
747#41—22no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—42no—
757#41—42no—
758#41—41no—
759#41—41no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41—42no—
766#41C2×D4×C7112yes—
767#41#41×C7112yes—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—41no—
777C2×Q8C2×D4×C7111yescharacteristic
778C2×Q8C2×D4×C7111yescharacteristic
779C2×Q8C2×D4×C7111yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—84no—
813C2×D4C2×D4×C7111yescharacteristic
814C2×D4C2×D4×C7111yescharacteristic
815C2×D4C2×D4×C7111yescharacteristic
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4C2×D4×C7111yescharacteristic
838C22×C4C2×D4×C7111yescharacteristic
839C22×C4C2×D4×C7111yescharacteristic
840C22×C4C2×D4×C7111yescharacteristic
841C22×C4C2×D4×C7111yescharacteristic
842C22×C4C2×D4×C7112yes—
843C22×C4C24×C7111yescharacteristic
844Q16—42no—
845Q16—42no—
846Q16—42no—
847SD16—42no—
848SD16—42no—
849SD16—42no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—42no—
858M16C2×D4×C7112yescomplemented
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—42no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4C2×D4×C7111yescharacteristic
875C4⋊C4C2×D4×C7111yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C42—22no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—42no—
898C42C2×D4×C7112yescomplemented
899C23—22no—
900C23—21no—
901C23—21no—
902C23—21no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23#120×C7111yescharacteristic
918C23#120×C7111yescharacteristic
919C23C22×D4×C7111yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8#121×C7112yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—44no—
944D4—42no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—82no—
954D4—81no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4#121×C7112yes—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4#120×C7111yescharacteristic
1000C2×C4#120×C7111yescharacteristic
1001C2×C4C22×D4×C7111yescharacteristic
1002C2×C4C22×D4×C7111yescharacteristic
1003C2×C4C22×D4×C7111yescharacteristic
1004C2×C4C2×#41×C7111yescharacteristic
1005C2×C4H(5,𝔽2)×C7111yescharacteristic
1006C2×C4H(5,𝔽2)×C7111yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—22no—
1017C22—21no—
1018C22—21no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—42no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—42no—
1031C22—41no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22#455×C7112yescomplemented
1037C22C2×#120×C7111yescharacteristic
1038C22D42×C7111yescharacteristic
1039C22#546×C7111yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×#121×C7111yescharacteristic
1053C4#534×C7111yescharacteristic
1054C4D42×C7111yescharacteristic
1055C4#546×C7111yescharacteristic
1056C2—21no—
1057C2—22no—
1058C2—21no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2C71×#241011yescharacteristic
1065C2C2×#455×C7111yescharacteristic
1066C2C71×#301811yescharacteristic
subgroupG/H
center, socleC22×C71C2×#120
commutator, Frattini, cosocleC22×C4C24×C71
prime radicalC71×#3488C2
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
2. C71×#3056C2semidirect
3. C2×#455×C71C2semidirect
4. C71×#3007C2semidirect
5. C22×#104×C71C2semidirect
6. C71×#2850C2semidirect
7. C71×#2040C2semidirect
8. C71×#2037C2semidirect
9. C71×#2007C2semidirect
10. C71×#2004C2semidirect
11. C71×#1900C2semidirect
12. C71×#1896C2semidirect
13. C71×#1882C2semidirect
14. C71×#1860C2semidirect
15. C71×#1792C2semidirect
19. C2×#137×C71C22semidirect
20. C2×#137×C71C22semidirect
21. C22×M16×C71C22semidirect
32. C2×#124×C71C22semidirect
35. C2×C22⋊Q8×C71C22semidirect
39. C22×C42×C71C22semidirect
49. #428×C71C22semidirect
53. C2×#104×C71C22semidirect
54. C2×#104×C71C22semidirect
55. C2×#104×C71C22semidirect
56. C2×#104×C71C22semidirect
57. #419×C71C22semidirect
59. #417×C71C22semidirect
60. #417×C71C22semidirect
61. C2×#100×C71C22semidirect
62. C2×#100×C71C22semidirect
63. #407×C71C22semidirect
64. #391×C71C22semidirect
65. #390×C71C22semidirect
68. #382×C71C22semidirect
69. #343×C71C22semidirect
70. #343×C71C22semidirect
71. #339×C71C22semidirect
72. #339×C71C22semidirect
191. #104×C71D4semidirect
324. M16×C71C2×D4semidirect
364. C42×C71C2×D4semidirect
502. C22×C71#455semidirect
522. #24467C71direct (N × H)
535. #3056C2×C71semidirect
536. C2×#455C2×C71semidirect
537. #3007C2×C71semidirect
538. C22×#104C2×C71semidirect
539. #2850C2×C71semidirect
540. #2040C2×C71semidirect
541. #2037C2×C71semidirect
542. #2007C2×C71semidirect
543. #2004C2×C71semidirect
544. #1900C2×C71semidirect
545. #1896C2×C71semidirect
546. #1882C2×C71semidirect
547. #1860C2×C71semidirect
548. #1792C2×C71semidirect
549. C71#24467direct (N × H)
553. C2×#137C22×C71semidirect
554. C2×#137C22×C71semidirect
555. C22×M16C22×C71semidirect
566. C2×#124C22×C71semidirect
569. C2×C22⋊Q8C22×C71semidirect
573. C22×C42C22×C71semidirect
583. #428C22×C71semidirect
587. C2×#104C22×C71semidirect
588. C2×#104C22×C71semidirect
589. C2×#104C22×C71semidirect
590. C2×#104C22×C71semidirect
591. #419C22×C71semidirect
593. #417C22×C71semidirect
594. #417C22×C71semidirect
595. C2×#100C22×C71semidirect
596. C2×#100C22×C71semidirect
597. #407C22×C71semidirect
598. #391C22×C71semidirect
599. #390C22×C71semidirect
602. #382C22×C71semidirect
603. #343C22×C71semidirect
604. #343C22×C71semidirect
605. #339C22×C71semidirect
606. #339C22×C71semidirect
725. #104D4×C71semidirect
858. M16C2×D4×C71semidirect
898. C42C2×D4×C71semidirect
1036. C22#455×C71semidirect

Maximal subgroups

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

subgroupindex
C71×#34882
C71×#30562
C2×#455×C712
C71×#30072
C22×#104×C712
C71×#28502
C71×#20402
C71×#20372
C71×#20072
C71×#20042
C71×#19002
C71×#18962
C71×#18822
C71×#18602
C71×#17922
#2446771