Finite Group Databasebeta

← C71×#24031 #31844903

Subgroups — C71×#24031 #31844903

Order 18176.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71×#3488C211yesmaximal, characteristic
2C71×#3093C211yesmaximal, characteristic, complemented
3C71×#2896C211yesmaximal, characteristic, complemented
4C71×#2500C211yesmaximal, characteristic, complemented
5C71×#2040C211yesmaximal, characteristic, complemented
6C71×#2039C211yesmaximal, characteristic, complemented
7C71×#2037C211yesmaximal, characteristic, complemented
8C71×#2037C211yesmaximal, characteristic, complemented
9C71×#1900C211yesmaximal, characteristic, complemented
10C71×#1871C211yesmaximal, characteristic, complemented
11C71×#1860C211yesmaximal, characteristic, complemented
12C71×#1859C211yesmaximal, characteristic, complemented
13C71×#1792C211yesmaximal, characteristic, complemented
14C71×#1792C211yesmaximal, characteristic, complemented
15C71×#1789C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C71C2211yescharacteristic
17C22×#41×C71C2211yescharacteristic
18C22×M16×C71C2211yescharacteristic, complemented
19#550×C71—21no—
20#548×C71—21no—
21#546×C71—21no—
22#546×C71—22no—
23D42×C71—22no—
24D42×C71—21no—
25#537×C71—21no—
26#537×C71C2211yescharacteristic
27#535×C71—21no—
28#535×C71C2211yescharacteristic
29#525×C71—21no—
30#525×C71C2211yescharacteristic
31C2×#121×C71—21no—
32C2×#121×C71C2211yescharacteristic
33#520×C71C2211yescharacteristic
34C2×#117×C71C2211yescharacteristic, complemented
35#485×C71—21no—
36#485×C71—21no—
37#482×C71—21no—
38#482×C71—21no—
39#428×C71C2211yescharacteristic, complemented
40#428×C71C2211yescharacteristic, complemented
41C2×#104×C71C2211yescharacteristic
42C2×#104×C71C2211yescharacteristic
43C2×#104×C71C2211yescharacteristic, complemented
44C2×#104×C71C2211yescharacteristic, complemented
45C2×#104×C71C2211yescharacteristic, complemented
46C2×#104×C71C2211yescharacteristic, complemented
47#419×C71—21no—
48#418×C71—21no—
49#417×C71C2211yescharacteristic
50#417×C71C2211yescharacteristic
51#417×C71C2211yescharacteristic, complemented
52#417×C71C2211yescharacteristic, complemented
53#417×C71C2211yescharacteristic, complemented
54#417×C71C2211yescharacteristic, complemented
55#416×C71—21no—
56#416×C71—21no—
57C2×#100×C71C2211yescharacteristic, complemented
58C2×#100×C71C2211yescharacteristic, complemented
59#407×C71C2211yescharacteristic, complemented
60#394×C71—22no—
61#390×C71C2211yescharacteristic, complemented
62#390×C71C2211yescharacteristic, complemented
63#388×C71—22no—
64#384×C71C2211yescharacteristic, complemented
65#382×C71C2211yescharacteristic, complemented
66C4×C22⋊C4×C71C2211yescharacteristic, complemented
67#343×C71C2211yescharacteristic, complemented
68#343×C71C2211yescharacteristic, complemented
69#339×C71C2211yescharacteristic, complemented
70#339×C71C2211yescharacteristic, complemented
71H(5,𝔽2)×C71—22no—
72H(5,𝔽2)×C71—22no—
73H(5,𝔽2)×C71—41no—
74H(5,𝔽2)×C71—41no—
75C2×#41×C71—21no—
76C2×#41×C71—21no—
77C2×#41×C71—21no—
78C2×#41×C71—21no—
79C2×#41×C71—22no—
80C2×#41×C71—22no—
81C2×#41×C71—41no—
82C2×#41×C71—41no—
83C2×#41×C71D411yescharacteristic
84C2×#41×C71D411yescharacteristic
85C2×#41×C71C2311yescharacteristic
86C2×#41×C71C2311yescharacteristic
87C2×#41×C71C2311yescharacteristic
88C22×Q8×C71D411yescharacteristic
89C22×D4×C71—21no—
90C22×D4×C71—22no—
91C22×D4×C71—22no—
92C22×D4×C71—21no—
93C22×D4×C71—21no—
94C22×D4×C71D411yescharacteristic
95C22×D4×C71D412yes—
96C22×D4×C71C2311yescharacteristic
97C23×C4×C71—21no—
98C23×C4×C71C2311yescharacteristic
99C2×M16×C71—21no—
100C2×M16×C71—41no—
101C2×M16×C71—41no—
102C2×M16×C71C2311yescharacteristic
103C2×M16×C71C2311yescharacteristic
104C2×M16×C71C2311yescharacteristic
105C2×M16×C71C2311yescharacteristic
106C22×C8×C71—21no—
107#127×C71—22no—
108#127×C71—21no—
109#124×C71—22no—
110#124×C71—21no—
111#123×C71—22no—
112#123×C71—21no—
113C22⋊Q8×C71—22no—
114C22⋊Q8×C71—21no—
115C22⋊Q8×C71—21no—
116C22⋊Q8×C71D411yescharacteristic
117C22⋊Q8×C71D411yescharacteristic
118#121×C71—22no—
119#121×C71—22no—
120#121×C71—22no—
121#121×C71—22no—
122#121×C71—22no—
123#121×C71—21no—
124#121×C71—21no—
125#121×C71—21no—
126#121×C71—21no—
127#121×C71—21no—
128#121×C71—21no—
129#121×C71—22no—
130#121×C71—21no—
131#121×C71—21no—
132#121×C71D411yescharacteristic
133#121×C71D411yescharacteristic
134#120×C71—22no—
135#120×C71—22no—
136#120×C71—22no—
137#120×C71—21no—
138#120×C71—22no—
139C4×Q8×C71—21no—
140C4×D4×C71—22no—
141C4×D4×C71—22no—
142C4×D4×C71—21no—
143C4×D4×C71—22no—
144C4×D4×C71—21no—
145C4×D4×C71—21no—
146#117×C71—21no—
147#117×C71—21no—
148#117×C71—21no—
149#117×C71—21no—
150#117×C71—21no—
151#117×C71C2311yescharacteristic
152C2×C4⋊C4×C71—21no—
153C2×C4⋊C4×C71—22no—
154C2×C4⋊C4×C71C2311yescharacteristic
155C2×C4⋊C4×C71C2311yescharacteristic
156C2×C4⋊C4×C71C2311yescharacteristic
157C2×C22⋊C4×C71—22no—
158C2×C22⋊C4×C71—21no—
159C2×C22⋊C4×C71—21no—
160C2×C22⋊C4×C71—22no—
161C2×C22⋊C4×C71—22no—
162C2×C22⋊C4×C71D412yes—
163C2×C42×C71—21no—
164C2×C42×C71C2311yescharacteristic
165C2×C42×C71C2311yescharacteristic
166#107×C71—21no—
167#107×C71—21no—
168#106×C71—21no—
169#106×C71—21no—
170#104×C71—22no—
171#104×C71—22no—
172#104×C71—41no—
173#104×C71—41no—
174#104×C71—41no—
175#104×C71—41no—
176#103×C71—21no—
177#103×C71—21no—
178#103×C71—21no—
179#103×C71—21no—
180#103×C71—21no—
181#103×C71—21no—
182#102×C71—21no—
183#102×C71—21no—
184#102×C71—21no—
185#102×C71—21no—
186#102×C71—21no—
187#102×C71—21no—
188#100×C71—41no—
189#100×C71—41no—
190C22⋊C8×C71—21no—
191C22⋊C8×C71—21no—
192#95×C71—21no—
193#95×C71—22no—
194C24×C71—22no—
195C24×C71—21no—
196C24×C71C2×D412yes—
197C24×C71C2×D411yescharacteristic
198#41×C71—21no—
199#41×C71—21no—
200#41×C71—22no—
201#41×C71—22no—
202#41×C71—21no—
203#41×C71—21no—
204#41×C71—21no—
205#41×C71—21no—
206#41×C71—21no—
207#41×C71—21no—
208#41×C71—21no—
209#41×C71—21no—
210#41×C71—42no—
211#41×C71—42no—
212#41×C71—41no—
213#41×C71—41no—
214#41×C71—42no—
215#41×C71—42no—
216#41×C71—42no—
217#41×C71—42no—
218#41×C71—42no—
219#41×C71—42no—
220#41×C71#4112yes—
221#41×C71#4112yes—
222C2×Q8×C71—21no—
223C2×Q8×C71—22no—
224C2×Q8×C71—41no—
225C2×Q8×C71C2×D411yescharacteristic
226C2×Q8×C71C2×D411yescharacteristic
227C2×Q8×C71C2×D411yescharacteristic
228C2×D4×C71—21no—
229C2×D4×C71—22no—
230C2×D4×C71—22no—
231C2×D4×C71—22no—
232C2×D4×C71—22no—
233C2×D4×C71—21no—
234C2×D4×C71—21no—
235C2×D4×C71—21no—
236C2×D4×C71—21no—
237C2×D4×C71—21no—
238C2×D4×C71—22no—
239C2×D4×C71—22no—
240C2×D4×C71—22no—
241C2×D4×C71—21no—
242C2×D4×C71—22no—
243C2×D4×C71—21no—
244C2×D4×C71—21no—
245C2×D4×C71—21no—
246C2×D4×C71—21no—
247C2×D4×C71—21no—
248C2×D4×C71—21no—
249C2×D4×C71—21no—
250C2×D4×C71—41no—
251C2×D4×C71—42no—
252C2×D4×C71—42no—
253C2×D4×C71—42no—
254C2×D4×C71—42no—
255C2×D4×C71—44no—
256C2×D4×C71—44no—
257C2×D4×C71—42no—
258C2×D4×C71—42no—
259C2×D4×C71—82no—
260C2×D4×C71—84no—
261C2×D4×C71C2×D411yescharacteristic
262C2×D4×C71C2×D411yescharacteristic
263C2×D4×C71C2×D411yescharacteristic
264C22×C4×C71—21no—
265C22×C4×C71—21no—
266C22×C4×C71—21no—
267C22×C4×C71—21no—
268C22×C4×C71—21no—
269C22×C4×C71—22no—
270C22×C4×C71—21no—
271C22×C4×C71—21no—
272C22×C4×C71—22no—
273C22×C4×C71—21no—
274C22×C4×C71—21no—
275C22×C4×C71—21no—
276C22×C4×C71—21no—
277C22×C4×C71—21no—
278C22×C4×C71—21no—
279C22×C4×C71—21no—
280C22×C4×C71—42no—
281C22×C4×C71—42no—
282C22×C4×C71C2×D411yescharacteristic
283C22×C4×C71C2×D411yescharacteristic
284C22×C4×C71C2×D411yescharacteristic
285C22×C4×C71C2×D411yescharacteristic
286C22×C4×C71C2×D411yescharacteristic
287C22×C4×C71C2×D412yes—
288C22×C4×C71C2411yescharacteristic
289M16×C71—21no—
290M16×C71—21no—
291M16×C71—21no—
292M16×C71—21no—
293M16×C71—21no—
294M16×C71—21no—
295M16×C71—21no—
296M16×C71—21no—
297M16×C71—42no—
298C2×C8×C71—21no—
299C2×C8×C71—21no—
300C2×C8×C71—21no—
301C2×C8×C71—21no—
302C2×C8×C71—42no—
303C4⋊C4×C71—22no—
304C4⋊C4×C71—22no—
305C4⋊C4×C71—21no—
306C4⋊C4×C71—21no—
307C4⋊C4×C71—21no—
308C4⋊C4×C71—21no—
309C4⋊C4×C71—21no—
310C4⋊C4×C71—21no—
311C4⋊C4×C71—21no—
312C4⋊C4×C71—21no—
313C4⋊C4×C71—82no—
314C4⋊C4×C71C2×D411yescharacteristic
315C4⋊C4×C71C2×D411yescharacteristic
316C22⋊C4×C71—22no—
317C22⋊C4×C71—22no—
318C22⋊C4×C71—22no—
319C22⋊C4×C71—22no—
320C22⋊C4×C71—22no—
321C22⋊C4×C71—21no—
322C22⋊C4×C71—21no—
323C22⋊C4×C71—21no—
324C22⋊C4×C71—21no—
325C22⋊C4×C71—22no—
326C22⋊C4×C71—22no—
327C22⋊C4×C71—21no—
328C22⋊C4×C71—42no—
329C22⋊C4×C71—44no—
330C22⋊C4×C71—41no—
331C22⋊C4×C71—41no—
332C22⋊C4×C71—82no—
333C42×C71—22no—
334C42×C71—21no—
335C42×C71—21no—
336C42×C71—21no—
337C42×C71—21no—
338C42×C71—21no—
339C42×C71—41no—
340C42×C71—41no—
341C23×C71—21no—
342C23×C71—21no—
343C23×C71—21no—
344C23×C71—22no—
345C23×C71—21no—
346C23×C71—21no—
347C23×C71—22no—
348C23×C71—22no—
349C23×C71—41no—
350C23×C71—41no—
351C23×C71—42no—
352C23×C71—42no—
353C23×C71—44no—
354C23×C71—42no—
355C23×C71—42no—
356C23×C71—81no—
357C23×C71—82no—
358C23×C71—82no—
359C23×C71#12011yescharacteristic
360C23×C71#12011yescharacteristic
361C23×C71C22×D411yescharacteristic
362Q8×C71—21no—
363Q8×C71—21no—
364Q8×C71—21no—
365Q8×C71—21no—
366Q8×C71—21no—
367Q8×C71—42no—
368Q8×C71#12312yes—
369D4×C71—22no—
370D4×C71—22no—
371D4×C71—21no—
372D4×C71—21no—
373D4×C71—21no—
374D4×C71—21no—
375D4×C71—21no—
376D4×C71—42no—
377D4×C71—42no—
378D4×C71—44no—
379D4×C71—42no—
380D4×C71—44no—
381D4×C71—44no—
382D4×C71—42no—
383D4×C71—41no—
384D4×C71—41no—
385D4×C71—41no—
386D4×C71—41no—
387D4×C71—41no—
388D4×C71—41no—
389D4×C71—41no—
390D4×C71—41no—
391D4×C71—81no—
392D4×C71—82no—
393D4×C71—82no—
394D4×C71—82no—
395D4×C71—82no—
396D4×C71#12312yes—
397C2×C4×C71—21no—
398C2×C4×C71—21no—
399C2×C4×C71—21no—
400C2×C4×C71—21no—
401C2×C4×C71—21no—
402C2×C4×C71—21no—
403C2×C4×C71—21no—
404C2×C4×C71—21no—
405C2×C4×C71—21no—
406C2×C4×C71—21no—
407C2×C4×C71—21no—
408C2×C4×C71—22no—
409C2×C4×C71—22no—
410C2×C4×C71—22no—
411C2×C4×C71—21no—
412C2×C4×C71—22no—
413C2×C4×C71—21no—
414C2×C4×C71—21no—
415C2×C4×C71—21no—
416C2×C4×C71—42no—
417C2×C4×C71—42no—
418C2×C4×C71—42no—
419C2×C4×C71—44no—
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—42no—
427C2×C4×C71—41no—
428C2×C4×C71—42no—
429C2×C4×C71—41no—
430C2×C4×C71—42no—
431C2×C4×C71—41no—
432C2×C4×C71—41no—
433C2×C4×C71—41no—
434C2×C4×C71—82no—
435C2×C4×C71#12011yescharacteristic
436C2×C4×C71#12011yescharacteristic
437C2×C4×C71C22×D411yescharacteristic
438C2×C4×C71C22×D411yescharacteristic
439C2×C4×C71C2×#4111yescharacteristic
440C2×C4×C71C2×#4111yescharacteristic
441C2×C4×C71H(5,𝔽2)11yescharacteristic
442C2×C4×C71H(5,𝔽2)11yescharacteristic
443C8×C71—41no—
444C8×C71—41no—
445C8×C71—41no—
446C8×C71—41no—
447C22×C71—21no—
448C22×C71—21no—
449C22×C71—21no—
450C22×C71—21no—
451C22×C71—22no—
452C22×C71—21no—
453C22×C71—21no—
454C22×C71—21no—
455C22×C71—21no—
456C22×C71—41no—
457C22×C71—41no—
458C22×C71—41no—
459C22×C71—41no—
460C22×C71—42no—
461C22×C71—41no—
462C22×C71—42no—
463C22×C71—41no—
464C22×C71—42no—
465C22×C71—41no—
466C22×C71—41no—
467C22×C71—81no—
468C22×C71—81no—
469C22×C71—82no—
470C22×C71—82no—
471C22×C71—84no—
472C22×C71—164no—
473C22×C71C2×#12011yescharacteristic
474C22×C71#54611yescharacteristic
475C22×C71#54611yescharacteristic
476C4×C71—21no—
477C4×C71—21no—
478C4×C71—22no—
479C4×C71—42no—
480C4×C71—41no—
481C4×C71—41no—
482C4×C71—41no—
483C4×C71—42no—
484C4×C71—41no—
485C4×C71—81no—
486C4×C71—81no—
487C4×C71—81no—
488C4×C71C2×#12311yescharacteristic
489C4×C71#53411yescharacteristic
490C4×C71#54611yescharacteristic
491C4×C71#54611yescharacteristic
492#24031C7111yesmaximal, characteristic, direct product factor, Sylow
493C2×C71—21no—
494C2×C71—21no—
495C2×C71—41no—
496C2×C71—41no—
497C2×C71—42no—
498C2×C71—81no—
499C2×C71—82no—
500C2×C71—81no—
501C2×C71#240511yescharacteristic
502C2×C71#301811yescharacteristic
503C2×C71#301911yescharacteristic
504#3488C2×C7111yescharacteristic
505#3093C2×C7111yescharacteristic, complemented
506#2896C2×C7111yescharacteristic, complemented
507#2500C2×C7111yescharacteristic, complemented
508#2040C2×C7111yescharacteristic, complemented
509#2039C2×C7111yescharacteristic, complemented
510#2037C2×C7111yescharacteristic, complemented
511#2037C2×C7111yescharacteristic, complemented
512#1900C2×C7111yescharacteristic, complemented
513#1871C2×C7111yescharacteristic, complemented
514#1860C2×C7111yescharacteristic, complemented
515#1859C2×C7111yescharacteristic, complemented
516#1792C2×C7111yescharacteristic, complemented
517#1792C2×C7111yescharacteristic, complemented
518#1789C2×C7111yescharacteristic, complemented
519C71#2403111yescharacteristic, direct product factor, Sylow
520C2×H(5,𝔽2)C22×C7111yescharacteristic
521C22×#41C22×C7111yescharacteristic
522C22×M16C22×C7111yescharacteristic, complemented
523#550—21no—
524#548—21no—
525#546—21no—
526#546—22no—
527D42—22no—
528D42—21no—
529#537—21no—
530#537C22×C7111yescharacteristic
531#535—21no—
532#535C22×C7111yescharacteristic
533#525—21no—
534#525C22×C7111yescharacteristic
535C2×#121—21no—
536C2×#121C22×C7111yescharacteristic
537#520C22×C7111yescharacteristic
538C2×#117C22×C7111yescharacteristic, complemented
539#485—21no—
540#485—21no—
541#482—21no—
542#482—21no—
543#428C22×C7111yescharacteristic, complemented
544#428C22×C7111yescharacteristic, complemented
545C2×#104C22×C7111yescharacteristic
546C2×#104C22×C7111yescharacteristic
547C2×#104C22×C7111yescharacteristic, complemented
548C2×#104C22×C7111yescharacteristic, complemented
549C2×#104C22×C7111yescharacteristic, complemented
550C2×#104C22×C7111yescharacteristic, complemented
551#419—21no—
552#418—21no—
553#417C22×C7111yescharacteristic
554#417C22×C7111yescharacteristic
555#417C22×C7111yescharacteristic, complemented
556#417C22×C7111yescharacteristic, complemented
557#417C22×C7111yescharacteristic, complemented
558#417C22×C7111yescharacteristic, complemented
559#416—21no—
560#416—21no—
561C2×#100C22×C7111yescharacteristic, complemented
562C2×#100C22×C7111yescharacteristic, complemented
563#407C22×C7111yescharacteristic, complemented
564#394—22no—
565#390C22×C7111yescharacteristic, complemented
566#390C22×C7111yescharacteristic, complemented
567#388—22no—
568#384C22×C7111yescharacteristic, complemented
569#382C22×C7111yescharacteristic, complemented
570C4×C22⋊C4C22×C7111yescharacteristic, complemented
571#343C22×C7111yescharacteristic, complemented
572#343C22×C7111yescharacteristic, complemented
573#339C22×C7111yescharacteristic, complemented
574#339C22×C7111yescharacteristic, complemented
575H(5,𝔽2)—22no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—41no—
578H(5,𝔽2)—41no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41D4×C7111yescharacteristic
588C2×#41D4×C7111yescharacteristic
589C2×#41C23×C7111yescharacteristic
590C2×#41C23×C7111yescharacteristic
591C2×#41C23×C7111yescharacteristic
592C22×Q8D4×C7111yescharacteristic
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4D4×C7111yescharacteristic
599C22×D4D4×C7112yes—
600C22×D4C23×C7111yescharacteristic
601C23×C4—21no—
602C23×C4C23×C7111yescharacteristic
603C2×M16—21no—
604C2×M16—41no—
605C2×M16—41no—
606C2×M16C23×C7111yescharacteristic
607C2×M16C23×C7111yescharacteristic
608C2×M16C23×C7111yescharacteristic
609C2×M16C23×C7111yescharacteristic
610C22×C8—21no—
611#127—22no—
612#127—21no—
613#124—22no—
614#124—21no—
615#123—22no—
616#123—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8D4×C7111yescharacteristic
621C22⋊Q8D4×C7111yescharacteristic
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—22no—
634#121—21no—
635#121—21no—
636#121D4×C7111yescharacteristic
637#121D4×C7111yescharacteristic
638#120—22no—
639#120—22no—
640#120—22no—
641#120—21no—
642#120—22no—
643C4×Q8—21no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650#117—21no—
651#117—21no—
652#117—21no—
653#117—21no—
654#117—21no—
655#117C23×C7111yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4C23×C7111yescharacteristic
659C2×C4⋊C4C23×C7111yescharacteristic
660C2×C4⋊C4C23×C7111yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4D4×C7112yes—
667C2×C42—21no—
668C2×C42C23×C7111yescharacteristic
669C2×C42C23×C7111yescharacteristic
670#107—21no—
671#107—21no—
672#106—21no—
673#106—21no—
674#104—22no—
675#104—22no—
676#104—41no—
677#104—41no—
678#104—41no—
679#104—41no—
680#103—21no—
681#103—21no—
682#103—21no—
683#103—21no—
684#103—21no—
685#103—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#102—21no—
692#100—41no—
693#100—41no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696#95—21no—
697#95—22no—
698C24—22no—
699C24—21no—
700C24C2×D4×C7112yes—
701C24C2×D4×C7111yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#41×C7112yes—
725#41#41×C7112yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×D4×C7111yescharacteristic
730C2×Q8C2×D4×C7111yescharacteristic
731C2×Q8C2×D4×C7111yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×D4×C7111yescharacteristic
766C2×D4C2×D4×C7111yescharacteristic
767C2×D4C2×D4×C7111yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4C2×D4×C7111yescharacteristic
787C22×C4C2×D4×C7111yescharacteristic
788C22×C4C2×D4×C7111yescharacteristic
789C22×C4C2×D4×C7111yescharacteristic
790C22×C4C2×D4×C7111yescharacteristic
791C22×C4C2×D4×C7112yes—
792C22×C4C24×C7111yescharacteristic
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—42no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—82no—
818C4⋊C4C2×D4×C7111yescharacteristic
819C4⋊C4C2×D4×C7111yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—82no—
837C42—22no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#120×C7111yescharacteristic
864C23#120×C7111yescharacteristic
865C23C22×D4×C7111yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#123×C7112yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—82no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#123×C7112yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4#120×C7111yescharacteristic
940C2×C4#120×C7111yescharacteristic
941C2×C4C22×D4×C7111yescharacteristic
942C2×C4C22×D4×C7111yescharacteristic
943C2×C4C2×#41×C7111yescharacteristic
944C2×C4C2×#41×C7111yescharacteristic
945C2×C4H(5,𝔽2)×C7111yescharacteristic
946C2×C4H(5,𝔽2)×C7111yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—22no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×#120×C7111yescharacteristic
978C22#546×C7111yescharacteristic
979C22#546×C7111yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×#123×C7111yescharacteristic
993C4#534×C7111yescharacteristic
994C4#546×C7111yescharacteristic
995C4#546×C7111yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2C71×#240511yescharacteristic
1005C2C71×#301811yescharacteristic
1006C2C71×#301911yescharacteristic
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×#3093C2semidirect
3. C71×#2896C2semidirect
4. C71×#2500C2semidirect
5. C71×#2040C2semidirect
6. C71×#2039C2semidirect
7. C71×#2037C2semidirect
8. C71×#2037C2semidirect
9. C71×#1900C2semidirect
10. C71×#1871C2semidirect
11. C71×#1860C2semidirect
12. C71×#1859C2semidirect
13. C71×#1792C2semidirect
14. C71×#1792C2semidirect
15. C71×#1789C2semidirect
18. C22×M16×C71C22semidirect
34. C2×#117×C71C22semidirect
39. #428×C71C22semidirect
40. #428×C71C22semidirect
43. C2×#104×C71C22semidirect
44. C2×#104×C71C22semidirect
45. C2×#104×C71C22semidirect
46. C2×#104×C71C22semidirect
51. #417×C71C22semidirect
52. #417×C71C22semidirect
53. #417×C71C22semidirect
54. #417×C71C22semidirect
57. C2×#100×C71C22semidirect
58. C2×#100×C71C22semidirect
59. #407×C71C22semidirect
61. #390×C71C22semidirect
62. #390×C71C22semidirect
64. #384×C71C22semidirect
65. #382×C71C22semidirect
66. C4×C22⋊C4×C71C22semidirect
67. #343×C71C22semidirect
68. #343×C71C22semidirect
69. #339×C71C22semidirect
70. #339×C71C22semidirect
492. #24031C71direct (N × H)
505. #3093C2×C71semidirect
506. #2896C2×C71semidirect
507. #2500C2×C71semidirect
508. #2040C2×C71semidirect
509. #2039C2×C71semidirect
510. #2037C2×C71semidirect
511. #2037C2×C71semidirect
512. #1900C2×C71semidirect
513. #1871C2×C71semidirect
514. #1860C2×C71semidirect
515. #1859C2×C71semidirect
516. #1792C2×C71semidirect
517. #1792C2×C71semidirect
518. #1789C2×C71semidirect
519. C71#24031direct (N × H)
522. C22×M16C22×C71semidirect
538. C2×#117C22×C71semidirect
543. #428C22×C71semidirect
544. #428C22×C71semidirect
547. C2×#104C22×C71semidirect
548. C2×#104C22×C71semidirect
549. C2×#104C22×C71semidirect
550. C2×#104C22×C71semidirect
555. #417C22×C71semidirect
556. #417C22×C71semidirect
557. #417C22×C71semidirect
558. #417C22×C71semidirect
561. C2×#100C22×C71semidirect
562. C2×#100C22×C71semidirect
563. #407C22×C71semidirect
565. #390C22×C71semidirect
566. #390C22×C71semidirect
568. #384C22×C71semidirect
569. #382C22×C71semidirect
570. C4×C22⋊C4C22×C71semidirect
571. #343C22×C71semidirect
572. #343C22×C71semidirect
573. #339C22×C71semidirect
574. #339C22×C71semidirect

Maximal subgroups

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

subgroupindex
C71×#34882
C71×#30932
C71×#28962
C71×#25002
C71×#20402
C71×#20392
C71×#20372
C71×#19002
C71×#18712
C71×#18602
C71×#18592
C71×#17922
C71×#17892
#2403171