Finite Group Databasebeta

← C71×#24262 #31845134

Subgroups — C71×#24262 #31845134

Order 18176.

1654 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71×#3496C211yesmaximal, characteristic, complemented
2C2×B(4,𝔽2)×C71C212yesmaximal, complemented
3C71×#2617C212yesmaximal, complemented
4C71×#2321C211yesmaximal, characteristic, complemented
5C71×#2044C212yesmaximal, complemented
6C71×#2021C212yesmaximal, complemented
7C71×#1964C212yesmaximal, complemented
8C71×#1799C211yesmaximal, characteristic, complemented
9C71×#1790C212yesmaximal, complemented
10C2×H(5,𝔽2)×C71C2212yes—
11#547×C71—22no—
12#546×C71—24no—
13D42×C71—22no—
14#537×C71—21no—
15#534×C71—21no—
16#534×C71C2212yes—
17#532×C71—21no—
18C2×#121×C71—21no—
19C2×#121×C71C2212yes—
20C2×#120×C71C2211yescharacteristic
21C2×#120×C71C2214yescomplemented
22C2×C4×D4×C71C2211yescharacteristic
23C22×C22⋊C4×C71C2211yescharacteristic, complemented
24B(4,𝔽2)×C71—28no—
25C2×#99×C71C2212yes—
26C2×#99×C71C2214yescomplemented
27C2×#99×C71C2214yescomplemented
28#397×C71—22no—
29#394×C71—24no—
30#392×C71—22no—
31#390×C71—21no—
32#388×C71—21no—
33#388×C71—21no—
34#386×C71—21no—
35#386×C71C2211yescharacteristic
36#386×C71C2214yescomplemented
37#385×C71C2211yescharacteristic, complemented
38#380×C71C2212yescomplemented
39#379×C71C2211yescharacteristic, complemented
40C4×C22⋊C4×C71C2211yescharacteristic, complemented
41#342×C71C2212yescomplemented
42C25×C71C2311yescharacteristic
43H(5,𝔽2)×C71—24no—
44H(5,𝔽2)×C71—24no—
45H(5,𝔽2)×C71—44no—
46C2×#41×C71—22no—
47C2×#41×C71—24no—
48C22×D4×C71—22no—
49C22×D4×C71—24no—
50C22×D4×C71—21no—
51C22×D4×C71—21no—
52C22×D4×C71—24no—
53C22×D4×C71D412yescomplemented
54C22×D4×C71C2314yes—
55C22×D4×C71C2311yescharacteristic
56C23×C4×C71D411yescharacteristic, complemented
57C23×C4×C71C2311yescharacteristic
58C23×C4×C71C2311yescharacteristic
59C4⋊Q8×C71—21no—
60#127×C71—21no—
61#124×C71—22no—
62#123×C71—24no—
63#123×C71—24no—
64C22⋊Q8×C71—24no—
65#121×C71—22no—
66#121×C71—22no—
67#121×C71—24no—
68#121×C71—22no—
69#121×C71—22no—
70#121×C71—22no—
71#121×C71—22no—
72#121×C71—22no—
73#121×C71—22no—
74#120×C71—24no—
75#120×C71—24no—
76#120×C71—22no—
77#120×C71—28no—
78#120×C71—44no—
79#120×C71D414yescomplemented
80C4×D4×C71—22no—
81C4×D4×C71—22no—
82C4×D4×C71—22no—
83C4×D4×C71—22no—
84C2×C4⋊C4×C71—21no—
85C2×C4⋊C4×C71—22no—
86C2×C4⋊C4×C71—21no—
87C2×C4⋊C4×C71D411yescharacteristic, complemented
88C2×C4⋊C4×C71D412yescomplemented
89C2×C22⋊C4×C71—22no—
90C2×C22⋊C4×C71—21no—
91C2×C22⋊C4×C71—21no—
92C2×C22⋊C4×C71—21no—
93C2×C22⋊C4×C71—22no—
94C2×C22⋊C4×C71—22no—
95C2×C22⋊C4×C71—24no—
96C2×C22⋊C4×C71—21no—
97C2×C22⋊C4×C71—24no—
98C2×C22⋊C4×C71—21no—
99C2×C22⋊C4×C71—21no—
100C2×C22⋊C4×C71D411yescharacteristic, complemented
101C2×C22⋊C4×C71D414yescomplemented
102C2×C22⋊C4×C71C2314yes—
103C2×C22⋊C4×C71C2311yescharacteristic
104C2×C22⋊C4×C71C2311yescharacteristic
105C2×C22⋊C4×C71C2311yescharacteristic
106C2×C42×C71—21no—
107C2×C42×C71D411yescharacteristic, complemented
108#99×C71—24no—
109#99×C71—28no—
110#99×C71—44no—
111#95×C71—21no—
112#95×C71—22no—
113#95×C71—21no—
114#95×C71—21no—
115#95×C71—24no—
116C24×C71—22no—
117C24×C71—21no—
118C24×C71—22no—
119C24×C71—21no—
120C24×C71—22no—
121C24×C71—81no—
122C24×C71—81no—
123C24×C71C2×D414yes—
124C24×C71C2×D411yescharacteristic
125C24×C71C2×D412yescomplemented
126C24×C71C2411yescharacteristic
127#41×C71—48no—
128#41×C71—48no—
129#41×C71—44no—
130#41×C71—44no—
131C2×Q8×C71—22no—
132C2×D4×C71—22no—
133C2×D4×C71—22no—
134C2×D4×C71—24no—
135C2×D4×C71—22no—
136C2×D4×C71—24no—
137C2×D4×C71—24no—
138C2×D4×C71—24no—
139C2×D4×C71—24no—
140C2×D4×C71—24no—
141C2×D4×C71—24no—
142C2×D4×C71—22no—
143C2×D4×C71—22no—
144C2×D4×C71—24no—
145C2×D4×C71—22no—
146C2×D4×C71—22no—
147C2×D4×C71—48no—
148C2×D4×C71—48no—
149C2×D4×C71—44no—
150C2×D4×C71—44no—
151C2×D4×C71—48no—
152C2×D4×C71—82no—
153C2×D4×C71—82no—
154C2×D4×C71—81no—
155C2×D4×C71—81no—
156C2×D4×C71—84no—
157C2×D4×C71—84no—
158C2×D4×C71C2×D412yes—
159C2×D4×C71#4112yes—
160C22×C4×C71—22no—
161C22×C4×C71—24no—
162C22×C4×C71—21no—
163C22×C4×C71—21no—
164C22×C4×C71—21no—
165C22×C4×C71—21no—
166C22×C4×C71—22no—
167C22×C4×C71—21no—
168C22×C4×C71—24no—
169C22×C4×C71—81no—
170C22×C4×C71—81no—
171C22×C4×C71—81no—
172C22×C4×C71C2×D414yes—
173C22×C4×C71C2×D411yescharacteristic
174C22×C4×C71C2×D411yescharacteristic
175C22×C4×C71C2×D411yescharacteristic
176C22×C4×C71C2×D411yescharacteristic
177C22×C4×C71C2×D412yes—
178C22×C4×C71C2×D411yescharacteristic
179C22×C4×C71C2×D412yes—
180C4⋊C4×C71—22no—
181C4⋊C4×C71—22no—
182C4⋊C4×C71—22no—
183C4⋊C4×C71—22no—
184C4⋊C4×C71—22no—
185C4⋊C4×C71—82no—
186C4⋊C4×C71—81no—
187C22⋊C4×C71—24no—
188C22⋊C4×C71—24no—
189C22⋊C4×C71—22no—
190C22⋊C4×C71—21no—
191C22⋊C4×C71—24no—
192C22⋊C4×C71—22no—
193C22⋊C4×C71—24no—
194C22⋊C4×C71—24no—
195C22⋊C4×C71—24no—
196C22⋊C4×C71—22no—
197C22⋊C4×C71—24no—
198C22⋊C4×C71—48no—
199C22⋊C4×C71—41no—
200C22⋊C4×C71—41no—
201C22⋊C4×C71—42no—
202C22⋊C4×C71—81no—
203C22⋊C4×C71—81no—
204C22⋊C4×C71—81no—
205C22⋊C4×C71—84no—
206C22⋊C4×C71C2×D412yescomplemented
207C42×C71—21no—
208C42×C71—21no—
209C42×C71—81no—
210C23×C71—21no—
211C23×C71—21no—
212C23×C71—24no—
213C23×C71—22no—
214C23×C71—24no—
215C23×C71—24no—
216C23×C71—24no—
217C23×C71—41no—
218C23×C71—41no—
219C23×C71—41no—
220C23×C71—41no—
221C23×C71—41no—
222C23×C71—41no—
223C23×C71—41no—
224C23×C71—44no—
225C23×C71—41no—
226C23×C71—44no—
227C23×C71—44no—
228C23×C71—44no—
229C23×C71—44no—
230C23×C71—41no—
231C23×C71—41no—
232C23×C71—42no—
233C23×C71—82no—
234C23×C71—82no—
235C23×C71—84no—
236C23×C71—82no—
237C23×C71—82no—
238C23×C71#12112yes—
239C23×C71C22×D411yescharacteristic
240C23×C71C22×D412yes—
241C23×C71C22×D411yescharacteristic
242C23×C71C2×#4111yescharacteristic
243C23×C71H(5,𝔽2)12yes—
244Q8×C71—44no—
245D4×C71—24no—
246D4×C71—24no—
247D4×C71—44no—
248D4×C71—44no—
249D4×C71—48no—
250D4×C71—44no—
251D4×C71—44no—
252D4×C71—44no—
253D4×C71—44no—
254D4×C71—82no—
255D4×C71—82no—
256D4×C71—84no—
257D4×C71—82no—
258D4×C71—816no—
259C2×C4×C71—21no—
260C2×C4×C71—21no—
261C2×C4×C71—21no—
262C2×C4×C71—21no—
263C2×C4×C71—24no—
264C2×C4×C71—22no—
265C2×C4×C71—24no—
266C2×C4×C71—24no—
267C2×C4×C71—41no—
268C2×C4×C71—42no—
269C2×C4×C71—41no—
270C2×C4×C71—42no—
271C2×C4×C71—42no—
272C2×C4×C71—48no—
273C2×C4×C71—41no—
274C2×C4×C71—41no—
275C2×C4×C71—44no—
276C2×C4×C71—41no—
277C2×C4×C71—41no—
278C2×C4×C71—41no—
279C2×C4×C71—41no—
280C2×C4×C71—41no—
281C2×C4×C71—44no—
282C2×C4×C71—44no—
283C2×C4×C71—41no—
284C2×C4×C71—44no—
285C2×C4×C71—41no—
286C2×C4×C71—41no—
287C2×C4×C71—44no—
288C2×C4×C71—81no—
289C2×C4×C71#12011yescharacteristic
290C2×C4×C71#12011yescharacteristic
291C2×C4×C71#12012yes—
292C2×C4×C71#12112yes—
293C22×C71—21no—
294C22×C71—22no—
295C22×C71—21no—
296C22×C71—22no—
297C22×C71—22no—
298C22×C71—41no—
299C22×C71—41no—
300C22×C71—42no—
301C22×C71—42no—
302C22×C71—42no—
303C22×C71—48no—
304C22×C71—42no—
305C22×C71—41no—
306C22×C71—41no—
307C22×C71—44no—
308C22×C71—42no—
309C22×C71—44no—
310C22×C71—44no—
311C22×C71—81no—
312C22×C71—84no—
313C22×C71—84no—
314C22×C71—81no—
315C22×C71—81no—
316C22×C71—84no—
317C22×C71—81no—
318C22×C71—81no—
319C22×C71—164no—
320C22×C71C2×#12011yescharacteristic
321C22×C71C2×#12111yescharacteristic
322C22×C71#53511yescharacteristic
323C22×C71D4212yes—
324C22×C71#54612yes—
325C4×C71—22no—
326C4×C71—21no—
327C4×C71—21no—
328C4×C71—22no—
329C4×C71—42no—
330C4×C71—44no—
331C4×C71—41no—
332C4×C71—41no—
333C4×C71—81no—
334C4×C71—84no—
335C4×C71—81no—
336#24262C7111yesmaximal, characteristic, direct product factor, Sylow
337C2×C71—21no—
338C2×C71—22no—
339C2×C71—21no—
340C2×C71—22no—
341C2×C71—42no—
342C2×C71—82no—
343C2×C71—84no—
344C2×C71#240811yescharacteristic
345C2×C71#302611yescharacteristic
346C2×C71#302711yescharacteristic
347#3496C2×C7111yescharacteristic, complemented
348C2×B(4,𝔽2)C2×C7112yescomplemented
349#2617C2×C7112yescomplemented
350#2321C2×C7111yescharacteristic, complemented
351#2044C2×C7112yescomplemented
352#2021C2×C7112yescomplemented
353#1964C2×C7112yescomplemented
354#1799C2×C7111yescharacteristic, complemented
355#1790C2×C7112yescomplemented
356C71#2426211yescharacteristic, direct product factor, Sylow
357C2×H(5,𝔽2)C22×C7112yes—
358#547—22no—
359#546—24no—
360D42—22no—
361#537—21no—
362#534—21no—
363#534C22×C7112yes—
364#532—21no—
365C2×#121—21no—
366C2×#121C22×C7112yes—
367C2×#120C22×C7111yescharacteristic
368C2×#120C22×C7114yescomplemented
369C2×C4×D4C22×C7111yescharacteristic
370C22×C22⋊C4C22×C7111yescharacteristic, complemented
371B(4,𝔽2)—28no—
372C2×#99C22×C7112yes—
373C2×#99C22×C7114yescomplemented
374C2×#99C22×C7114yescomplemented
375#397—22no—
376#394—24no—
377#392—22no—
378#390—21no—
379#388—21no—
380#388—21no—
381#386—21no—
382#386C22×C7111yescharacteristic
383#386C22×C7114yescomplemented
384#385C22×C7111yescharacteristic, complemented
385#380C22×C7112yescomplemented
386#379C22×C7111yescharacteristic, complemented
387C4×C22⋊C4C22×C7111yescharacteristic, complemented
388#342C22×C7112yescomplemented
389C25C23×C7111yescharacteristic
390H(5,𝔽2)—24no—
391H(5,𝔽2)—24no—
392H(5,𝔽2)—44no—
393C2×#41—22no—
394C2×#41—24no—
395C22×D4—22no—
396C22×D4—24no—
397C22×D4—21no—
398C22×D4—21no—
399C22×D4—24no—
400C22×D4D4×C7112yescomplemented
401C22×D4C23×C7114yes—
402C22×D4C23×C7111yescharacteristic
403C23×C4D4×C7111yescharacteristic, complemented
404C23×C4C23×C7111yescharacteristic
405C23×C4C23×C7111yescharacteristic
406C4⋊Q8—21no—
407#127—21no—
408#124—22no—
409#123—24no—
410#123—24no—
411C22⋊Q8—24no—
412#121—22no—
413#121—22no—
414#121—24no—
415#121—22no—
416#121—22no—
417#121—22no—
418#121—22no—
419#121—22no—
420#121—22no—
421#120—24no—
422#120—24no—
423#120—22no—
424#120—28no—
425#120—44no—
426#120D4×C7114yescomplemented
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4D4×C7111yescharacteristic, complemented
435C2×C4⋊C4D4×C7112yescomplemented
436C2×C22⋊C4—22no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4D4×C7111yescharacteristic, complemented
448C2×C22⋊C4D4×C7114yescomplemented
449C2×C22⋊C4C23×C7114yes—
450C2×C22⋊C4C23×C7111yescharacteristic
451C2×C22⋊C4C23×C7111yescharacteristic
452C2×C22⋊C4C23×C7111yescharacteristic
453C2×C42—21no—
454C2×C42D4×C7111yescharacteristic, complemented
455#99—24no—
456#99—28no—
457#99—44no—
458#95—21no—
459#95—22no—
460#95—21no—
461#95—21no—
462#95—24no—
463C24—22no—
464C24—21no—
465C24—22no—
466C24—21no—
467C24—22no—
468C24—81no—
469C24—81no—
470C24C2×D4×C7114yes—
471C24C2×D4×C7111yescharacteristic
472C24C2×D4×C7112yescomplemented
473C24C24×C7111yescharacteristic
474#41—48no—
475#41—48no—
476#41—44no—
477#41—44no—
478C2×Q8—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—24no—
482C2×D4—22no—
483C2×D4—24no—
484C2×D4—24no—
485C2×D4—24no—
486C2×D4—24no—
487C2×D4—24no—
488C2×D4—24no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—24no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—48no—
499C2×D4—82no—
500C2×D4—82no—
501C2×D4—81no—
502C2×D4—81no—
503C2×D4—84no—
504C2×D4—84no—
505C2×D4C2×D4×C7112yes—
506C2×D4#41×C7112yes—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—24no—
516C22×C4—81no—
517C22×C4—81no—
518C22×C4—81no—
519C22×C4C2×D4×C7114yes—
520C22×C4C2×D4×C7111yescharacteristic
521C22×C4C2×D4×C7111yescharacteristic
522C22×C4C2×D4×C7111yescharacteristic
523C22×C4C2×D4×C7111yescharacteristic
524C22×C4C2×D4×C7112yes—
525C22×C4C2×D4×C7111yescharacteristic
526C22×C4C2×D4×C7112yes—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—82no—
533C4⋊C4—81no—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—22no—
537C22⋊C4—21no—
538C22⋊C4—24no—
539C22⋊C4—22no—
540C22⋊C4—24no—
541C22⋊C4—24no—
542C22⋊C4—24no—
543C22⋊C4—22no—
544C22⋊C4—24no—
545C22⋊C4—48no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—42no—
549C22⋊C4—81no—
550C22⋊C4—81no—
551C22⋊C4—81no—
552C22⋊C4—84no—
553C22⋊C4C2×D4×C7112yescomplemented
554C42—21no—
555C42—21no—
556C42—81no—
557C23—21no—
558C23—21no—
559C23—24no—
560C23—22no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—44no—
572C23—41no—
573C23—44no—
574C23—44no—
575C23—44no—
576C23—44no—
577C23—41no—
578C23—41no—
579C23—42no—
580C23—82no—
581C23—82no—
582C23—84no—
583C23—82no—
584C23—82no—
585C23#121×C7112yes—
586C23C22×D4×C7111yescharacteristic
587C23C22×D4×C7112yes—
588C23C22×D4×C7111yescharacteristic
589C23C2×#41×C7111yescharacteristic
590C23H(5,𝔽2)×C7112yes—
591Q8—44no—
592D4—24no—
593D4—24no—
594D4—44no—
595D4—44no—
596D4—48no—
597D4—44no—
598D4—44no—
599D4—44no—
600D4—44no—
601D4—82no—
602D4—84no—
603D4—82no—
604D4—82no—
605D4—816no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—48no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—44no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—44no—
629C2×C4—44no—
630C2×C4—41no—
631C2×C4—44no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—44no—
635C2×C4—81no—
636C2×C4#120×C7111yescharacteristic
637C2×C4#120×C7111yescharacteristic
638C2×C4#120×C7112yes—
639C2×C4#121×C7112yes—
640C22—21no—
641C22—22no—
642C22—21no—
643C22—22no—
644C22—22no—
645C22—41no—
646C22—41no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—48no—
651C22—42no—
652C22—41no—
653C22—41no—
654C22—44no—
655C22—42no—
656C22—44no—
657C22—44no—
658C22—81no—
659C22—84no—
660C22—84no—
661C22—81no—
662C22—81no—
663C22—84no—
664C22—81no—
665C22—81no—
666C22—164no—
667C22C2×#120×C7111yescharacteristic
668C22C2×#121×C7111yescharacteristic
669C22#535×C7111yescharacteristic
670C22D42×C7112yes—
671C22#546×C7112yes—
672C4—22no—
673C4—21no—
674C4—21no—
675C4—22no—
676C4—42no—
677C4—44no—
678C4—41no—
679C4—41no—
680C4—84no—
681C4—81no—
682C4—81no—
683C2—21no—
684C2—22no—
685C2—21no—
686C2—22no—
687C2—42no—
688C2—82no—
689C2—84no—
690C2C71×#240811yescharacteristic
691C2C71×#302611yescharacteristic
692C2C71×#302711yescharacteristic
subgroupG/H
center, socleC22×C71C2×#120
commutator, Frattini, cosocleC24C24×C71
LCSG ▷ C24 ▷ 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×#3496C2semidirect
2. C2×B(4,𝔽2)×C71C2semidirect
3. C71×#2617C2semidirect
4. C71×#2321C2semidirect
5. C71×#2044C2semidirect
6. C71×#2021C2semidirect
7. C71×#1964C2semidirect
8. C71×#1799C2semidirect
9. C71×#1790C2semidirect
21. C2×#120×C71C22semidirect
23. C22×C22⋊C4×C71C22semidirect
26. C2×#99×C71C22semidirect
27. C2×#99×C71C22semidirect
36. #386×C71C22semidirect
37. #385×C71C22semidirect
38. #380×C71C22semidirect
39. #379×C71C22semidirect
40. C4×C22⋊C4×C71C22semidirect
41. #342×C71C22semidirect
53. C22×D4×C71D4semidirect
56. C23×C4×C71D4semidirect
79. #120×C71D4semidirect
87. C2×C4⋊C4×C71D4semidirect
88. C2×C4⋊C4×C71D4semidirect
100. C2×C22⋊C4×C71D4semidirect
101. C2×C22⋊C4×C71D4semidirect
107. C2×C42×C71D4semidirect
125. C24×C71C2×D4semidirect
206. C22⋊C4×C71C2×D4semidirect
336. #24262C71direct (N × H)
347. #3496C2×C71semidirect
348. C2×B(4,𝔽2)C2×C71semidirect
349. #2617C2×C71semidirect
350. #2321C2×C71semidirect
351. #2044C2×C71semidirect
352. #2021C2×C71semidirect
353. #1964C2×C71semidirect
354. #1799C2×C71semidirect
355. #1790C2×C71semidirect
356. C71#24262direct (N × H)
368. C2×#120C22×C71semidirect
370. C22×C22⋊C4C22×C71semidirect
373. C2×#99C22×C71semidirect
374. C2×#99C22×C71semidirect
383. #386C22×C71semidirect
384. #385C22×C71semidirect
385. #380C22×C71semidirect
386. #379C22×C71semidirect
387. C4×C22⋊C4C22×C71semidirect
388. #342C22×C71semidirect
400. C22×D4D4×C71semidirect
403. C23×C4D4×C71semidirect
426. #120D4×C71semidirect
434. C2×C4⋊C4D4×C71semidirect
435. C2×C4⋊C4D4×C71semidirect
447. C2×C22⋊C4D4×C71semidirect
448. C2×C22⋊C4D4×C71semidirect
454. C2×C42D4×C71semidirect
472. C24C2×D4×C71semidirect
553. C22⋊C4C2×D4×C71semidirect

Maximal subgroups

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

subgroupindex
C71×#34962
C2×B(4,𝔽2)×C712
C71×#26172
C71×#23212
C71×#20442
C71×#20212
C71×#19642
C71×#17992
C71×#17902
#2426271