Finite Group Databasebeta

← C71×#24424 #31845296

Subgroups — C71×#24424 #31845296

Order 18176.

1992 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C71C211yesmaximal, characteristic, complemented
2C2×#466×C71C211yesmaximal, characteristic, complemented
3C2×#447×C71C211yesmaximal, characteristic, complemented
4C2×#447×C71C211yesmaximal, characteristic, complemented
5C22×#102×C71C211yesmaximal, characteristic, complemented
6C71×#2416C211yesmaximal, characteristic, complemented
7C71×#2041C211yesmaximal, characteristic, complemented
8C71×#2033C211yesmaximal, characteristic, complemented
9C71×#2011C211yesmaximal, characteristic, complemented
10C71×#1999C211yesmaximal, characteristic, complemented
11C71×#1879C211yesmaximal, characteristic, complemented
12C71×#1874C211yesmaximal, characteristic, complemented
13C71×#1869C211yesmaximal, characteristic, complemented
14C71×#1862C211yesmaximal, characteristic, complemented
15C71×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C71—21no—
17C23×D4×C71C2211yescharacteristic
18C23×D4×C71C2211yescharacteristic
19C22×D8×C71C2211yescharacteristic
20C22×D8×C71C2211yescharacteristic, complemented
21C22×D8×C71C2211yescharacteristic, complemented
22C23×C8×C71C2211yescharacteristic, complemented
23D42×C71—24no—
24D42×C71—24no—
25C2×#127×C71C2211yescharacteristic
26C2×#121×C71—21no—
27C2×#121×C71—21no—
28C2×#121×C71C2211yescharacteristic
29C2×#121×C71C2211yescharacteristic
30C2×#121×C71C2211yescharacteristic, complemented
31C2×#121×C71C2211yescharacteristic, complemented
32C2×#120×C71—21no—
33C2×#120×C71—21no—
34C2×C4×D4×C71C2211yescharacteristic
35C2×C4×D4×C71C2211yescharacteristic
36C22×C4⋊C4×C71C2211yescharacteristic, complemented
37#466×C71—24no—
38#447×C71—24no—
39#447×C71—24no—
40C2×#107×C71C2211yescharacteristic, complemented
41C2×#102×C71—24no—
42C2×#102×C71C2211yescharacteristic
43C2×#102×C71C2211yescharacteristic
44C2×#102×C71C2211yescharacteristic
45C2×#102×C71C2211yescharacteristic, complemented
46C2×#102×C71C2211yescharacteristic, complemented
47C2×#102×C71C2211yescharacteristic, complemented
48C2×#102×C71C2211yescharacteristic, complemented
49C2×#102×C71C2211yescharacteristic, complemented
50C2×#102×C71C2211yescharacteristic, complemented
51C2×#102×C71C2211yescharacteristic, complemented
52C2×C22⋊C8×C71C2211yescharacteristic, complemented
53C2×C22⋊C8×C71C2211yescharacteristic, complemented
54C2×C22⋊C8×C71C2211yescharacteristic, complemented
55#396×C71—21no—
56#394×C71—21no—
57#390×C71C2211yescharacteristic, complemented
58#389×C71C2211yescharacteristic, complemented
59#386×C71—21no—
60#380×C71C2211yescharacteristic, complemented
61#340×C71C2211yescharacteristic, complemented
62#340×C71C2211yescharacteristic, complemented
63#336×C71C2211yescharacteristic, complemented
64#336×C71C2211yescharacteristic, complemented
65C25×C71—21no—
66C25×C71—21no—
67C22×D4×C71—22no—
68C22×D4×C71—22no—
69C22×D4×C71—28no—
70C22×D4×C71—21no—
71C22×D4×C71—21no—
72C22×D4×C71—22no—
73C22×D4×C71—22no—
74C22×D4×C71—22no—
75C22×D4×C71—22no—
76C22×D4×C71—21no—
77C22×D4×C71—21no—
78C22×D4×C71—21no—
79C22×D4×C71—21no—
80C22×D4×C71—21no—
81C22×D4×C71—22no—
82C22×D4×C71—21no—
83C22×D4×C71—41no—
84C22×D4×C71—41no—
85C22×D4×C71—41no—
86C22×D4×C71—41no—
87C22×D4×C71—44no—
88C22×D4×C71—44no—
89C22×D4×C71D411yescharacteristic
90C22×D4×C71D414yescomplemented
91C22×D4×C71C2311yescharacteristic
92C22×D4×C71C2311yescharacteristic
93C22×D4×C71C2311yescharacteristic
94C22×D4×C71C2311yescharacteristic
95C23×C4×C71—21no—
96C23×C4×C71—21no—
97C23×C4×C71C2311yescharacteristic
98C23×C4×C71C2311yescharacteristic
99C2×D8×C71—22no—
100C2×D8×C71—22no—
101C2×D8×C71—22no—
102C2×D8×C71—22no—
103C2×D8×C71—22no—
104C2×D8×C71—22no—
105C2×D8×C71—41no—
106C2×D8×C71—41no—
107C2×D8×C71—41no—
108C22×C8×C71—22no—
109C22×C8×C71—22no—
110C22×C8×C71—41no—
111C22×C8×C71C2311yescharacteristic
112C22×C8×C71C2311yescharacteristic
113C22×C8×C71C2311yescharacteristic
114C22×C8×C71C2311yescharacteristic
115#127×C71—22no—
116#127×C71—22no—
117#121×C71—28no—
118#121×C71—22no—
119#121×C71—22no—
120#121×C71—22no—
121#121×C71—22no—
122#121×C71—22no—
123#121×C71—22no—
124#121×C71—41no—
125#121×C71—44no—
126#121×C71D414yescomplemented
127#120×C71—28no—
128#120×C71—28no—
129C4×D4×C71—22no—
130C4×D4×C71—22no—
131C4×D4×C71—22no—
132C4×D4×C71—22no—
133C2×C4⋊C4×C71—22no—
134C2×C4⋊C4×C71—21no—
135C2×C4⋊C4×C71—21no—
136C2×C4⋊C4×C71—41no—
137C2×C4⋊C4×C71D411yescharacteristic
138C2×C4⋊C4×C71C2311yescharacteristic
139C2×C4⋊C4×C71C2311yescharacteristic
140C2×C4⋊C4×C71C2311yescharacteristic
141C2×C4⋊C4×C71C2311yescharacteristic
142C2×C22⋊C4×C71—21no—
143C2×C22⋊C4×C71—21no—
144C2×C22⋊C4×C71—21no—
145C2×C22⋊C4×C71—21no—
146C2×C22⋊C4×C71—21no—
147C2×C22⋊C4×C71—21no—
148C2×C22⋊C4×C71—21no—
149C2×C22⋊C4×C71—21no—
150C2×C22⋊C4×C71D411yescharacteristic
151C2×C22⋊C4×C71D411yescharacteristic
152C2×C42×C71C2311yescharacteristic
153#107×C71—22no—
154#102×C71—22no—
155#102×C71—22no—
156#102×C71—22no—
157#102×C71—22no—
158#102×C71—22no—
159#102×C71—22no—
160#102×C71—22no—
161#102×C71—22no—
162#102×C71—41no—
163#102×C71D414yescomplemented
164C22⋊C8×C71—22no—
165C22⋊C8×C71—22no—
166C22⋊C8×C71—41no—
167#95×C71—21no—
168#95×C71—21no—
169C24×C71—21no—
170C24×C71—24no—
171C24×C71—21no—
172C24×C71—21no—
173C24×C71—24no—
174C24×C71—21no—
175C24×C71—42no—
176C24×C71—42no—
177C24×C71—42no—
178C24×C71—42no—
179C24×C71—42no—
180C24×C71—42no—
181C24×C71—42no—
182C24×C71—42no—
183C24×C71—81no—
184C24×C71—81no—
185C24×C71—81no—
186C24×C71—81no—
187C24×C71C2×D411yescharacteristic
188C24×C71C2×D411yescharacteristic
189C2×D4×C71—22no—
190C2×D4×C71—22no—
191C2×D4×C71—28no—
192C2×D4×C71—24no—
193C2×D4×C71—24no—
194C2×D4×C71—24no—
195C2×D4×C71—24no—
196C2×D4×C71—24no—
197C2×D4×C71—24no—
198C2×D4×C71—21no—
199C2×D4×C71—21no—
200C2×D4×C71—21no—
201C2×D4×C71—21no—
202C2×D4×C71—21no—
203C2×D4×C71—21no—
204C2×D4×C71—21no—
205C2×D4×C71—21no—
206C2×D4×C71—21no—
207C2×D4×C71—21no—
208C2×D4×C71—21no—
209C2×D4×C71—21no—
210C2×D4×C71—21no—
211C2×D4×C71—21no—
212C2×D4×C71—21no—
213C2×D4×C71—21no—
214C2×D4×C71—21no—
215C2×D4×C71—21no—
216C2×D4×C71—21no—
217C2×D4×C71—44no—
218C2×D4×C71—44no—
219C2×D4×C71—44no—
220C2×D4×C71—42no—
221C2×D4×C71—42no—
222C2×D4×C71—42no—
223C2×D4×C71—42no—
224C2×D4×C71—42no—
225C2×D4×C71—42no—
226C2×D4×C71—44no—
227C2×D4×C71—44no—
228C2×D4×C71—432no—
229C2×D4×C71—44no—
230C2×D4×C71—42no—
231C2×D4×C71—42no—
232C2×D4×C71—42no—
233C2×D4×C71—42no—
234C2×D4×C71—44no—
235C2×D4×C71—42no—
236C2×D4×C71—42no—
237C2×D4×C71—42no—
238C2×D4×C71—42no—
239C2×D4×C71—42no—
240C2×D4×C71—81no—
241C2×D4×C71—81no—
242C2×D4×C71—81no—
243C2×D4×C71D814yescomplemented
244C2×D4×C71C2×D412yes—
245C2×D4×C71C2×D412yes—
246C2×D4×C71C2×D412yes—
247C2×D4×C71C2×D412yes—
248C2×D4×C71#4112yes—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71—21no—
252C22×C4×C71—21no—
253C22×C4×C71—24no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71—21no—
257C22×C4×C71—21no—
258C22×C4×C71—21no—
259C22×C4×C71—21no—
260C22×C4×C71—21no—
261C22×C4×C71—21no—
262C22×C4×C71—21no—
263C22×C4×C71—21no—
264C22×C4×C71—42no—
265C22×C4×C71—42no—
266C22×C4×C71—42no—
267C22×C4×C71—42no—
268C22×C4×C71—81no—
269C22×C4×C71C2×D411yescharacteristic
270C22×C4×C71C2×D411yescharacteristic
271C22×C4×C71C2×D411yescharacteristic
272C22×C4×C71C2×D412yes—
273C22×C4×C71C2×D412yes—
274C22×C4×C71C2×D411yescharacteristic
275C22×C4×C71C2411yescharacteristic
276D8×C71—44no—
277D8×C71—44no—
278D8×C71—44no—
279C2×C8×C71—21no—
280C2×C8×C71—21no—
281C2×C8×C71—21no—
282C2×C8×C71—21no—
283C2×C8×C71—21no—
284C2×C8×C71—21no—
285C2×C8×C71—21no—
286C2×C8×C71—21no—
287C2×C8×C71—21no—
288C2×C8×C71—21no—
289C2×C8×C71—21no—
290C2×C8×C71—44no—
291C2×C8×C71C2×D412yescomplemented
292C4⋊C4×C71—22no—
293C4⋊C4×C71—21no—
294C4⋊C4×C71—21no—
295C4⋊C4×C71—21no—
296C4⋊C4×C71—21no—
297C4⋊C4×C71—21no—
298C4⋊C4×C71—21no—
299C4⋊C4×C71—42no—
300C4⋊C4×C71—42no—
301C4⋊C4×C71C2×D412yes—
302C4⋊C4×C71C2×D412yescomplemented
303C22⋊C4×C71—24no—
304C22⋊C4×C71—24no—
305C22⋊C4×C71—22no—
306C22⋊C4×C71—24no—
307C22⋊C4×C71—22no—
308C22⋊C4×C71—42no—
309C22⋊C4×C71—42no—
310C22⋊C4×C71—42no—
311C22⋊C4×C71—42no—
312C22⋊C4×C71—81no—
313C42×C71—21no—
314C42×C71—21no—
315C23×C71—21no—
316C23×C71—21no—
317C23×C71—21no—
318C23×C71—21no—
319C23×C71—21no—
320C23×C71—22no—
321C23×C71—21no—
322C23×C71—22no—
323C23×C71—21no—
324C23×C71—22no—
325C23×C71—21no—
326C23×C71—21no—
327C23×C71—21no—
328C23×C71—22no—
329C23×C71—22no—
330C23×C71—48no—
331C23×C71—48no—
332C23×C71—48no—
333C23×C71—41no—
334C23×C71—41no—
335C23×C71—41no—
336C23×C71—41no—
337C23×C71—41no—
338C23×C71—41no—
339C23×C71—41no—
340C23×C71—41no—
341C23×C71—41no—
342C23×C71—41no—
343C23×C71—41no—
344C23×C71—41no—
345C23×C71—41no—
346C23×C71—41no—
347C23×C71—41no—
348C23×C71—41no—
349C23×C71—48no—
350C23×C71—41no—
351C23×C71—41no—
352C23×C71—41no—
353C23×C71—41no—
354C23×C71—41no—
355C23×C71—41no—
356C23×C71—41no—
357C23×C71—84no—
358C23×C71—84no—
359C23×C71—84no—
360C23×C71—84no—
361C23×C71—84no—
362C23×C71—84no—
363C23×C71—84no—
364C23×C71—84no—
365C23×C71—84no—
366C23×C71—84no—
367C23×C71#12012yes—
368C23×C71C2×D812yes—
369C23×C71C2×D812yes—
370C23×C71AGL(1,ℤ/8)12yes—
371C23×C71C22×D411yescharacteristic
372D4×C71—28no—
373D4×C71—22no—
374D4×C71—22no—
375D4×C71—22no—
376D4×C71—22no—
377D4×C71—22no—
378D4×C71—22no—
379D4×C71—22no—
380D4×C71—48no—
381D4×C71—48no—
382D4×C71—48no—
383D4×C71—48no—
384D4×C71—48no—
385D4×C71—41no—
386D4×C71—41no—
387D4×C71—41no—
388D4×C71—41no—
389D4×C71—41no—
390D4×C71—41no—
391D4×C71—41no—
392D4×C71—41no—
393D4×C71—84no—
394D4×C71—84no—
395D4×C71—84no—
396D4×C71#12114yescomplemented
397C2×C4×C71—21no—
398C2×C4×C71—21no—
399C2×C4×C71—21no—
400C2×C4×C71—21no—
401C2×C4×C71—22no—
402C2×C4×C71—22no—
403C2×C4×C71—22no—
404C2×C4×C71—22no—
405C2×C4×C71—21no—
406C2×C4×C71—21no—
407C2×C4×C71—22no—
408C2×C4×C71—21no—
409C2×C4×C71—22no—
410C2×C4×C71—21no—
411C2×C4×C71—21no—
412C2×C4×C71—21no—
413C2×C4×C71—48no—
414C2×C4×C71—41no—
415C2×C4×C71—41no—
416C2×C4×C71—41no—
417C2×C4×C71—41no—
418C2×C4×C71—41no—
419C2×C4×C71—41no—
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—41no—
427C2×C4×C71—41no—
428C2×C4×C71—84no—
429C2×C4×C71#12012yes—
430C2×C4×C71C2×D812yes—
431C2×C4×C71C22×D411yescharacteristic
432C2×C4×C71C22×D411yescharacteristic
433C2×C4×C71C22×D411yescharacteristic
434C2×C4×C71C2×#4111yescharacteristic
435C2×C4×C71H(5,𝔽2)11yescharacteristic
436C2×C4×C71H(5,𝔽2)11yescharacteristic
437C8×C71—22no—
438C8×C71—41no—
439C8×C71—41no—
440C8×C71—41no—
441C22×C71—22no—
442C22×C71—22no—
443C22×C71—22no—
444C22×C71—22no—
445C22×C71—22no—
446C22×C71—22no—
447C22×C71—24no—
448C22×C71—22no—
449C22×C71—22no—
450C22×C71—22no—
451C22×C71—41no—
452C22×C71—42no—
453C22×C71—41no—
454C22×C71—42no—
455C22×C71—41no—
456C22×C71—42no—
457C22×C71—42no—
458C22×C71—42no—
459C22×C71—41no—
460C22×C71—42no—
461C22×C71—42no—
462C22×C71—42no—
463C22×C71—42no—
464C22×C71—42no—
465C22×C71—42no—
466C22×C71—42no—
467C22×C71—816no—
468C22×C71—816no—
469C22×C71—81no—
470C22×C71—81no—
471C22×C71—81no—
472C22×C71—81no—
473C22×C71—81no—
474C22×C71—81no—
475C22×C71—81no—
476C22×C71—81no—
477C22×C71—81no—
478C22×C71—81no—
479C22×C71—81no—
480C22×C71—81no—
481C22×C71—81no—
482C22×C71—81no—
483C22×C71—81no—
484C22×C71#44714yescomplemented
485C22×C71C2×#12011yescharacteristic
486C22×C71D4211yescharacteristic
487C22×C71#54611yescharacteristic
488C22×C71C22×D811yescharacteristic
489C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
490C22×C71#57611yescharacteristic
491C22×C71#57711yescharacteristic
492C4×C71—22no—
493C4×C71—22no—
494C4×C71—41no—
495C4×C71—42no—
496C4×C71—41no—
497C4×C71—42no—
498C4×C71—81no—
499C4×C71—81no—
500C4×C71C2×#12111yescharacteristic
501C4×C71#53411yescharacteristic
502C4×C71D4211yescharacteristic
503C4×C71#54611yescharacteristic
504#24424C7111yesmaximal, characteristic, direct product factor, Sylow
505C2×C71—24no—
506C2×C71—42no—
507C2×C71—44no—
508C2×C71—82no—
509C2×C71—82no—
510C2×C71—161no—
511C2×C71#241011yescharacteristic
512C2×C71C2×#44711yescharacteristic
513C2×C71#301211yescharacteristic
514C2×C71#326511yescharacteristic
515C2×C71D4×D811yescharacteristic
516C2×C71#329411yescharacteristic
517C2×C71#331811yescharacteristic
518C2×D42C2×C7111yescharacteristic, complemented
519C2×#466C2×C7111yescharacteristic, complemented
520C2×#447C2×C7111yescharacteristic, complemented
521C2×#447C2×C7111yescharacteristic, complemented
522C22×#102C2×C7111yescharacteristic, complemented
523#2416C2×C7111yescharacteristic, complemented
524#2041C2×C7111yescharacteristic, complemented
525#2033C2×C7111yescharacteristic, complemented
526#2011C2×C7111yescharacteristic, complemented
527#1999C2×C7111yescharacteristic, complemented
528#1879C2×C7111yescharacteristic, complemented
529#1874C2×C7111yescharacteristic, complemented
530#1869C2×C7111yescharacteristic, complemented
531#1862C2×C7111yescharacteristic, complemented
532#1786C2×C7111yescharacteristic, complemented
533C71#2442411yescharacteristic, direct product factor, Sylow
534C23×D4—21no—
535C23×D4C22×C7111yescharacteristic
536C23×D4C22×C7111yescharacteristic
537C22×D8C22×C7111yescharacteristic
538C22×D8C22×C7111yescharacteristic, complemented
539C22×D8C22×C7111yescharacteristic, complemented
540C23×C8C22×C7111yescharacteristic, complemented
541D42—24no—
542D42—24no—
543C2×#127C22×C7111yescharacteristic
544C2×#121—21no—
545C2×#121—21no—
546C2×#121C22×C7111yescharacteristic
547C2×#121C22×C7111yescharacteristic
548C2×#121C22×C7111yescharacteristic, complemented
549C2×#121C22×C7111yescharacteristic, complemented
550C2×#120—21no—
551C2×#120—21no—
552C2×C4×D4C22×C7111yescharacteristic
553C2×C4×D4C22×C7111yescharacteristic
554C22×C4⋊C4C22×C7111yescharacteristic, complemented
555#466—24no—
556#447—24no—
557#447—24no—
558C2×#107C22×C7111yescharacteristic, complemented
559C2×#102—24no—
560C2×#102C22×C7111yescharacteristic
561C2×#102C22×C7111yescharacteristic
562C2×#102C22×C7111yescharacteristic
563C2×#102C22×C7111yescharacteristic, complemented
564C2×#102C22×C7111yescharacteristic, complemented
565C2×#102C22×C7111yescharacteristic, complemented
566C2×#102C22×C7111yescharacteristic, complemented
567C2×#102C22×C7111yescharacteristic, complemented
568C2×#102C22×C7111yescharacteristic, complemented
569C2×#102C22×C7111yescharacteristic, complemented
570C2×C22⋊C8C22×C7111yescharacteristic, complemented
571C2×C22⋊C8C22×C7111yescharacteristic, complemented
572C2×C22⋊C8C22×C7111yescharacteristic, complemented
573#396—21no—
574#394—21no—
575#390C22×C7111yescharacteristic, complemented
576#389C22×C7111yescharacteristic, complemented
577#386—21no—
578#380C22×C7111yescharacteristic, complemented
579#340C22×C7111yescharacteristic, complemented
580#340C22×C7111yescharacteristic, complemented
581#336C22×C7111yescharacteristic, complemented
582#336C22×C7111yescharacteristic, complemented
583C25—21no—
584C25—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—28no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—22no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—22no—
600C22×D4—21no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4—41no—
604C22×D4—41no—
605C22×D4—44no—
606C22×D4—44no—
607C22×D4D4×C7111yescharacteristic
608C22×D4D4×C7114yescomplemented
609C22×D4C23×C7111yescharacteristic
610C22×D4C23×C7111yescharacteristic
611C22×D4C23×C7111yescharacteristic
612C22×D4C23×C7111yescharacteristic
613C23×C4—21no—
614C23×C4—21no—
615C23×C4C23×C7111yescharacteristic
616C23×C4C23×C7111yescharacteristic
617C2×D8—22no—
618C2×D8—22no—
619C2×D8—22no—
620C2×D8—22no—
621C2×D8—22no—
622C2×D8—22no—
623C2×D8—41no—
624C2×D8—41no—
625C2×D8—41no—
626C22×C8—22no—
627C22×C8—22no—
628C22×C8—41no—
629C22×C8C23×C7111yescharacteristic
630C22×C8C23×C7111yescharacteristic
631C22×C8C23×C7111yescharacteristic
632C22×C8C23×C7111yescharacteristic
633#127—22no—
634#127—22no—
635#121—28no—
636#121—22no—
637#121—22no—
638#121—22no—
639#121—22no—
640#121—22no—
641#121—22no—
642#121—41no—
643#121—44no—
644#121D4×C7114yescomplemented
645#120—28no—
646#120—28no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4D4×C7111yescharacteristic
656C2×C4⋊C4C23×C7111yescharacteristic
657C2×C4⋊C4C23×C7111yescharacteristic
658C2×C4⋊C4C23×C7111yescharacteristic
659C2×C4⋊C4C23×C7111yescharacteristic
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4D4×C7111yescharacteristic
669C2×C22⋊C4D4×C7111yescharacteristic
670C2×C42C23×C7111yescharacteristic
671#107—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—22no—
677#102—22no—
678#102—22no—
679#102—22no—
680#102—41no—
681#102D4×C7114yescomplemented
682C22⋊C8—22no—
683C22⋊C8—22no—
684C22⋊C8—41no—
685#95—21no—
686#95—21no—
687C24—21no—
688C24—24no—
689C24—21no—
690C24—21no—
691C24—24no—
692C24—21no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—42no—
698C24—42no—
699C24—42no—
700C24—42no—
701C24—81no—
702C24—81no—
703C24—81no—
704C24—81no—
705C24C2×D4×C7111yescharacteristic
706C24C2×D4×C7111yescharacteristic
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—28no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—432no—
747C2×D4—44no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—81no—
759C2×D4—81no—
760C2×D4—81no—
761C2×D4D8×C7114yescomplemented
762C2×D4C2×D4×C7112yes—
763C2×D4C2×D4×C7112yes—
764C2×D4C2×D4×C7112yes—
765C2×D4C2×D4×C7112yes—
766C2×D4#41×C7112yes—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—24no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—81no—
787C22×C4C2×D4×C7111yescharacteristic
788C22×C4C2×D4×C7111yescharacteristic
789C22×C4C2×D4×C7111yescharacteristic
790C22×C4C2×D4×C7112yes—
791C22×C4C2×D4×C7112yes—
792C22×C4C2×D4×C7111yescharacteristic
793C22×C4C24×C7111yescharacteristic
794D8—44no—
795D8—44no—
796D8—44no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—44no—
809C2×C8C2×D4×C7112yescomplemented
810C4⋊C4—22no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C7112yes—
820C4⋊C4C2×D4×C7112yescomplemented
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—22no—
824C22⋊C4—24no—
825C22⋊C4—22no—
826C22⋊C4—42no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C42—21no—
832C42—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—22no—
839C23—21no—
840C23—22no—
841C23—21no—
842C23—22no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—22no—
847C23—22no—
848C23—48no—
849C23—48no—
850C23—48no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—48no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23—84no—
881C23—84no—
882C23—84no—
883C23—84no—
884C23—84no—
885C23#120×C7112yes—
886C23C2×D8×C7112yes—
887C23C2×D8×C7112yes—
888C23AGL(1,ℤ/8)×C7112yes—
889C23C22×D4×C7111yescharacteristic
890D4—28no—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—22no—
897D4—22no—
898D4—48no—
899D4—48no—
900D4—48no—
901D4—48no—
902D4—48no—
903D4—41no—
904D4—41no—
905D4—41no—
906D4—41no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—84no—
912D4—84no—
913D4—84no—
914D4#121×C7114yescomplemented
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—48no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—84no—
947C2×C4#120×C7112yes—
948C2×C4C2×D8×C7112yes—
949C2×C4C22×D4×C7111yescharacteristic
950C2×C4C22×D4×C7111yescharacteristic
951C2×C4C22×D4×C7111yescharacteristic
952C2×C4C2×#41×C7111yescharacteristic
953C2×C4H(5,𝔽2)×C7111yescharacteristic
954C2×C4H(5,𝔽2)×C7111yescharacteristic
955C8—22no—
956C8—41no—
957C8—41no—
958C8—41no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—24no—
967C22—22no—
968C22—22no—
969C22—42no—
970C22—41no—
971C22—42no—
972C22—41no—
973C22—42no—
974C22—41no—
975C22—42no—
976C22—41no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—816no—
986C22—816no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22—81no—
996C22—81no—
997C22—81no—
998C22—81no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22#447×C7114yescomplemented
1003C22C2×#120×C7111yescharacteristic
1004C22D42×C7111yescharacteristic
1005C22#546×C7111yescharacteristic
1006C22C22×D8×C7111yescharacteristic
1007C22C2×AGL(1,ℤ/8)×C7111yescharacteristic
1008C22#576×C7111yescharacteristic
1009C22#577×C7111yescharacteristic
1010C4—22no—
1011C4—22no—
1012C4—41no—
1013C4—42no—
1014C4—41no—
1015C4—42no—
1016C4—81no—
1017C4—81no—
1018C4C2×#121×C7111yescharacteristic
1019C4#534×C7111yescharacteristic
1020C4D42×C7111yescharacteristic
1021C4#546×C7111yescharacteristic
1022C2—24no—
1023C2—42no—
1024C2—44no—
1025C2—82no—
1026C2—82no—
1027C2—161no—
1028C2C71×#241011yescharacteristic
1029C2C2×#447×C7111yescharacteristic
1030C2C71×#301211yescharacteristic
1031C2C71×#326511yescharacteristic
1032C2D4×D8×C7111yescharacteristic
1033C2C71×#329411yescharacteristic
1034C2C71×#331811yescharacteristic
subgroupG/H
center, socleC23×C71C22×D4
commutator, Frattini, cosocleC22×C4C24×C71
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C71 ◁ C2×C4×D4×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×D42×C71C2semidirect
2. C2×#466×C71C2semidirect
3. C2×#447×C71C2semidirect
4. C2×#447×C71C2semidirect
5. C22×#102×C71C2semidirect
6. C71×#2416C2semidirect
7. C71×#2041C2semidirect
8. C71×#2033C2semidirect
9. C71×#2011C2semidirect
10. C71×#1999C2semidirect
11. C71×#1879C2semidirect
12. C71×#1874C2semidirect
13. C71×#1869C2semidirect
14. C71×#1862C2semidirect
15. C71×#1786C2semidirect
20. C22×D8×C71C22semidirect
21. C22×D8×C71C22semidirect
22. C23×C8×C71C22semidirect
30. C2×#121×C71C22semidirect
31. C2×#121×C71C22semidirect
36. C22×C4⋊C4×C71C22semidirect
40. C2×#107×C71C22semidirect
45. C2×#102×C71C22semidirect
46. C2×#102×C71C22semidirect
47. C2×#102×C71C22semidirect
48. C2×#102×C71C22semidirect
49. C2×#102×C71C22semidirect
50. C2×#102×C71C22semidirect
51. C2×#102×C71C22semidirect
52. C2×C22⋊C8×C71C22semidirect
53. C2×C22⋊C8×C71C22semidirect
54. C2×C22⋊C8×C71C22semidirect
57. #390×C71C22semidirect
58. #389×C71C22semidirect
60. #380×C71C22semidirect
61. #340×C71C22semidirect
62. #340×C71C22semidirect
63. #336×C71C22semidirect
64. #336×C71C22semidirect
90. C22×D4×C71D4semidirect
126. #121×C71D4semidirect
163. #102×C71D4semidirect
243. C2×D4×C71D8semidirect
291. C2×C8×C71C2×D4semidirect
302. C4⋊C4×C71C2×D4semidirect
396. D4×C71#121semidirect
484. C22×C71#447semidirect
504. #24424C71direct (N × H)
518. C2×D42C2×C71semidirect
519. C2×#466C2×C71semidirect
520. C2×#447C2×C71semidirect
521. C2×#447C2×C71semidirect
522. C22×#102C2×C71semidirect
523. #2416C2×C71semidirect
524. #2041C2×C71semidirect
525. #2033C2×C71semidirect
526. #2011C2×C71semidirect
527. #1999C2×C71semidirect
528. #1879C2×C71semidirect
529. #1874C2×C71semidirect
530. #1869C2×C71semidirect
531. #1862C2×C71semidirect
532. #1786C2×C71semidirect
533. C71#24424direct (N × H)
538. C22×D8C22×C71semidirect
539. C22×D8C22×C71semidirect
540. C23×C8C22×C71semidirect
548. C2×#121C22×C71semidirect
549. C2×#121C22×C71semidirect
554. C22×C4⋊C4C22×C71semidirect
558. C2×#107C22×C71semidirect
563. C2×#102C22×C71semidirect
564. C2×#102C22×C71semidirect
565. C2×#102C22×C71semidirect
566. C2×#102C22×C71semidirect
567. C2×#102C22×C71semidirect
568. C2×#102C22×C71semidirect
569. C2×#102C22×C71semidirect
570. C2×C22⋊C8C22×C71semidirect
571. C2×C22⋊C8C22×C71semidirect
572. C2×C22⋊C8C22×C71semidirect
575. #390C22×C71semidirect
576. #389C22×C71semidirect
578. #380C22×C71semidirect
579. #340C22×C71semidirect
580. #340C22×C71semidirect
581. #336C22×C71semidirect
582. #336C22×C71semidirect
608. C22×D4D4×C71semidirect
644. #121D4×C71semidirect
681. #102D4×C71semidirect
761. C2×D4D8×C71semidirect
809. C2×C8C2×D4×C71semidirect
820. C4⋊C4C2×D4×C71semidirect
914. D4#121×C71semidirect
1002. C22#447×C71semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C712
C2×#466×C712
C2×#447×C712
C22×#102×C712
C71×#24162
C71×#20412
C71×#20332
C71×#20112
C71×#19992
C71×#18792
C71×#18742
C71×#18692
C71×#18622
C71×#17862
#2442471