Finite Group Databasebeta

← C71×#24440 #31845312

Subgroups — C71×#24440 #31845312

Order 18176.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C71C211yesmaximal, characteristic, complemented
2C2×#469×C71C211yesmaximal, characteristic, complemented
3C2×#447×C71C211yesmaximal, characteristic, complemented
4C2×#447×C71C211yesmaximal, characteristic, complemented
5C2×#418×C71C211yesmaximal, characteristic, complemented
6C71×#2414C211yesmaximal, characteristic, complemented
7C71×#2041C211yesmaximal, characteristic, complemented
8C71×#2034C211yesmaximal, characteristic, complemented
9C71×#2011C211yesmaximal, characteristic, complemented
10C71×#1999C211yesmaximal, characteristic, complemented
11C71×#1879C211yesmaximal, characteristic, complemented
12C71×#1875C211yesmaximal, characteristic, complemented
13C71×#1870C211yesmaximal, characteristic, complemented
14C71×#1864C211yesmaximal, 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
22C22×M16×C71C2211yescharacteristic, complemented
23D42×C71—24no—
24D42×C71—24no—
25C2×#127×C71C2211yescharacteristic
26C2×#121×C71—21no—
27C2×#121×C71C2211yescharacteristic
28C2×#121×C71C2211yescharacteristic
29C2×#121×C71C2211yescharacteristic, complemented
30C2×#121×C71C2211yescharacteristic, complemented
31C2×#120×C71—21no—
32C2×#120×C71—21no—
33C2×C4×D4×C71C2211yescharacteristic
34C2×C4×D4×C71C2211yescharacteristic
35C2×#117×C71C2211yescharacteristic, complemented
36#469×C71—24no—
37#447×C71—24no—
38#447×C71—24no—
39C2×#106×C71C2211yescharacteristic, complemented
40#418×C71—24no—
41C2×#102×C71C2211yescharacteristic
42C2×#102×C71C2211yescharacteristic
43C2×#102×C71C2211yescharacteristic
44C2×#102×C71C2211yescharacteristic, complemented
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×C22⋊C8×C71C2211yescharacteristic, complemented
52C2×C22⋊C8×C71C2211yescharacteristic, complemented
53C2×C22⋊C8×C71C2211yescharacteristic, complemented
54#394×C71—21no—
55#392×C71—21no—
56#390×C71—21no—
57#390×C71C2211yescharacteristic, complemented
58#389×C71C2211yescharacteristic, complemented
59#388×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×C71C2311yescharacteristic
97C23×C4×C71C2311yescharacteristic
98C2×D8×C71—22no—
99C2×D8×C71—22no—
100C2×D8×C71—22no—
101C2×D8×C71—22no—
102C2×D8×C71—22no—
103C2×D8×C71—22no—
104C2×D8×C71—41no—
105C2×D8×C71—41no—
106C2×D8×C71—41no—
107C2×M16×C71—22no—
108C2×M16×C71—22no—
109C2×M16×C71—41no—
110C22×C8×C71C2311yescharacteristic
111C22×C8×C71C2311yescharacteristic
112C22×C8×C71C2311yescharacteristic
113C22×C8×C71C2311yescharacteristic
114#127×C71—22no—
115#127×C71—22no—
116#121×C71—28no—
117#121×C71—22no—
118#121×C71—22no—
119#121×C71—22no—
120#121×C71—22no—
121#121×C71—22no—
122#121×C71—22no—
123#121×C71—41no—
124#121×C71D414yescomplemented
125#120×C71—28no—
126#120×C71—28no—
127C4×D4×C71—22no—
128C4×D4×C71—22no—
129C4×D4×C71—22no—
130C4×D4×C71—22no—
131#117×C71—22no—
132#117×C71—41no—
133C2×C4⋊C4×C71—21no—
134C2×C4⋊C4×C71D411yescharacteristic
135C2×C4⋊C4×C71C2311yescharacteristic
136C2×C4⋊C4×C71C2311yescharacteristic
137C2×C4⋊C4×C71C2311yescharacteristic
138C2×C4⋊C4×C71C2311yescharacteristic
139C2×C22⋊C4×C71—21no—
140C2×C22⋊C4×C71—21no—
141C2×C22⋊C4×C71—21no—
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×C71D411yescharacteristic
149C2×C22⋊C4×C71D411yescharacteristic
150C2×C42×C71—21no—
151C2×C42×C71C2311yescharacteristic
152#106×C71—22no—
153#102×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—41no—
162#102×C71D414yescomplemented
163C22⋊C8×C71—22no—
164C22⋊C8×C71—22no—
165C22⋊C8×C71—41no—
166#95×C71—21no—
167#95×C71—21no—
168C24×C71—21no—
169C24×C71—24no—
170C24×C71—21no—
171C24×C71—21no—
172C24×C71—24no—
173C24×C71—21no—
174C24×C71—42no—
175C24×C71—42no—
176C24×C71—42no—
177C24×C71—42no—
178C24×C71—42no—
179C24×C71—42no—
180C24×C71—42no—
181C24×C71—42no—
182C24×C71—81no—
183C24×C71—81no—
184C24×C71—81no—
185C24×C71—81no—
186C24×C71C2×D411yescharacteristic
187C24×C71C2×D411yescharacteristic
188C2×D4×C71—22no—
189C2×D4×C71—22no—
190C2×D4×C71—28no—
191C2×D4×C71—24no—
192C2×D4×C71—24no—
193C2×D4×C71—24no—
194C2×D4×C71—24no—
195C2×D4×C71—24no—
196C2×D4×C71—24no—
197C2×D4×C71—22no—
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—81no—
239C2×D4×C71—81no—
240C2×D4×C71—81no—
241C2×D4×C71—81no—
242C2×D4×C71—81no—
243C2×D4×C71C2×D412yes—
244C2×D4×C71C2×D412yes—
245C2×D4×C71C2×D412yes—
246C2×D4×C71C2×D412yes—
247C2×D4×C71#4112yes—
248C22×C4×C71—21no—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71—21no—
252C22×C4×C71—24no—
253C22×C4×C71—21no—
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—42no—
264C22×C4×C71—42no—
265C22×C4×C71C2×D411yescharacteristic
266C22×C4×C71C2×D411yescharacteristic
267C22×C4×C71C2×D411yescharacteristic
268C22×C4×C71C2×D412yes—
269C22×C4×C71C2×D412yes—
270C22×C4×C71C2×D411yescharacteristic
271C22×C4×C71C2411yescharacteristic
272D8×C71—44no—
273D8×C71—44no—
274D8×C71—44no—
275M16×C71—44no—
276C2×C8×C71—21no—
277C2×C8×C71—21no—
278C2×C8×C71—21no—
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×C71C2×D412yescomplemented
288C4⋊C4×C71—22no—
289C4⋊C4×C71—21no—
290C4⋊C4×C71—21no—
291C4⋊C4×C71—21no—
292C4⋊C4×C71—21no—
293C4⋊C4×C71—21no—
294C4⋊C4×C71—21no—
295C4⋊C4×C71—81no—
296C4⋊C4×C71C2×D412yes—
297C4⋊C4×C71C2×D412yescomplemented
298C22⋊C4×C71—24no—
299C22⋊C4×C71—24no—
300C22⋊C4×C71—22no—
301C22⋊C4×C71—24no—
302C22⋊C4×C71—22no—
303C22⋊C4×C71—42no—
304C22⋊C4×C71—42no—
305C22⋊C4×C71—42no—
306C22⋊C4×C71—42no—
307C22⋊C4×C71—81no—
308C22⋊C4×C71—81no—
309C42×C71—21no—
310C42×C71—21no—
311C42×C71—42no—
312C23×C71—21no—
313C23×C71—22no—
314C23×C71—21no—
315C23×C71—21no—
316C23×C71—22no—
317C23×C71—21no—
318C23×C71—21no—
319C23×C71—22no—
320C23×C71—21no—
321C23×C71—21no—
322C23×C71—21no—
323C23×C71—21no—
324C23×C71—21no—
325C23×C71—21no—
326C23×C71—21no—
327C23×C71—22no—
328C23×C71—22no—
329C23×C71—48no—
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—41no—
350C23×C71—41no—
351C23×C71—41no—
352C23×C71—41no—
353C23×C71—41no—
354C23×C71—41no—
355C23×C71—41no—
356C23×C71—84no—
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#12012yes—
367C23×C71AGL(1,ℤ/8)12yes—
368C23×C71C22×D411yescharacteristic
369D4×C71—28no—
370D4×C71—22no—
371D4×C71—22no—
372D4×C71—22no—
373D4×C71—22no—
374D4×C71—22no—
375D4×C71—22no—
376D4×C71—22no—
377D4×C71—48no—
378D4×C71—48no—
379D4×C71—48no—
380D4×C71—48no—
381D4×C71—48no—
382D4×C71—41no—
383D4×C71—41no—
384D4×C71—41no—
385D4×C71—41no—
386D4×C71—41no—
387D4×C71—41no—
388D4×C71—41no—
389D4×C71—41no—
390D4×C71—84no—
391D4×C71—84no—
392D4×C71—84no—
393D4×C71#12114yes—
394C2×C4×C71—21no—
395C2×C4×C71—21no—
396C2×C4×C71—21no—
397C2×C4×C71—21no—
398C2×C4×C71—22no—
399C2×C4×C71—22no—
400C2×C4×C71—22no—
401C2×C4×C71—22no—
402C2×C4×C71—21no—
403C2×C4×C71—21no—
404C2×C4×C71—22no—
405C2×C4×C71—22no—
406C2×C4×C71—21no—
407C2×C4×C71—21no—
408C2×C4×C71—21no—
409C2×C4×C71—21no—
410C2×C4×C71—48no—
411C2×C4×C71—41no—
412C2×C4×C71—41no—
413C2×C4×C71—41no—
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#12012yes—
426C2×C4×C71AGL(1,ℤ/8)12yes—
427C2×C4×C71C22×D411yescharacteristic
428C2×C4×C71C22×D411yescharacteristic
429C2×C4×C71C22×D411yescharacteristic
430C2×C4×C71C2×#4111yescharacteristic
431C2×C4×C71H(5,𝔽2)11yescharacteristic
432C2×C4×C71H(5,𝔽2)11yescharacteristic
433C8×C71—22no—
434C8×C71—41no—
435C8×C71—41no—
436C8×C71—41no—
437C22×C71—22no—
438C22×C71—24no—
439C22×C71—22no—
440C22×C71—22no—
441C22×C71—22no—
442C22×C71—22no—
443C22×C71—22no—
444C22×C71—41no—
445C22×C71—42no—
446C22×C71—41no—
447C22×C71—42no—
448C22×C71—41no—
449C22×C71—42no—
450C22×C71—41no—
451C22×C71—41no—
452C22×C71—42no—
453C22×C71—41no—
454C22×C71—42no—
455C22×C71—41no—
456C22×C71—41no—
457C22×C71—42no—
458C22×C71—42no—
459C22×C71—42no—
460C22×C71—42no—
461C22×C71—42no—
462C22×C71—42no—
463C22×C71—42no—
464C22×C71—816no—
465C22×C71—816no—
466C22×C71—81no—
467C22×C71—81no—
468C22×C71—81no—
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×C71C2×#12011yescharacteristic
482C22×C71D4211yescharacteristic
483C22×C71#54611yescharacteristic
484C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
485C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
486C22×C71#57611yescharacteristic
487C22×C71#57611yescharacteristic
488C4×C71—22no—
489C4×C71—22no—
490C4×C71—41no—
491C4×C71—42no—
492C4×C71—41no—
493C4×C71—42no—
494C4×C71—81no—
495C4×C71—81no—
496C4×C71C2×#12111yescharacteristic
497C4×C71#53411yescharacteristic
498C4×C71D4211yescharacteristic
499C4×C71#54611yescharacteristic
500#24440C7111yesmaximal, characteristic, direct product factor, Sylow
501C2×C71—42no—
502C2×C71—42no—
503C2×C71—44no—
504C2×C71—82no—
505C2×C71—82no—
506C2×C71—161no—
507C2×C71#241011yescharacteristic
508C2×C71#300311yescharacteristic
509C2×C71#300811yescharacteristic
510C2×C71#326411yescharacteristic
511C2×C71#327411yescharacteristic
512C2×C71#331811yescharacteristic
513C2×C71#332511yescharacteristic
514C2×D42C2×C7111yescharacteristic, complemented
515C2×#469C2×C7111yescharacteristic, complemented
516C2×#447C2×C7111yescharacteristic, complemented
517C2×#447C2×C7111yescharacteristic, complemented
518C2×#418C2×C7111yescharacteristic, complemented
519#2414C2×C7111yescharacteristic, complemented
520#2041C2×C7111yescharacteristic, complemented
521#2034C2×C7111yescharacteristic, complemented
522#2011C2×C7111yescharacteristic, complemented
523#1999C2×C7111yescharacteristic, complemented
524#1879C2×C7111yescharacteristic, complemented
525#1875C2×C7111yescharacteristic, complemented
526#1870C2×C7111yescharacteristic, complemented
527#1864C2×C7111yescharacteristic, complemented
528#1786C2×C7111yescharacteristic, complemented
529C71#2444011yescharacteristic, direct product factor, Sylow
530C23×D4—21no—
531C23×D4C22×C7111yescharacteristic
532C23×D4C22×C7111yescharacteristic
533C22×D8C22×C7111yescharacteristic
534C22×D8C22×C7111yescharacteristic, complemented
535C22×D8C22×C7111yescharacteristic, complemented
536C22×M16C22×C7111yescharacteristic, complemented
537D42—24no—
538D42—24no—
539C2×#127C22×C7111yescharacteristic
540C2×#121—21no—
541C2×#121C22×C7111yescharacteristic
542C2×#121C22×C7111yescharacteristic
543C2×#121C22×C7111yescharacteristic, complemented
544C2×#121C22×C7111yescharacteristic, complemented
545C2×#120—21no—
546C2×#120—21no—
547C2×C4×D4C22×C7111yescharacteristic
548C2×C4×D4C22×C7111yescharacteristic
549C2×#117C22×C7111yescharacteristic, complemented
550#469—24no—
551#447—24no—
552#447—24no—
553C2×#106C22×C7111yescharacteristic, complemented
554#418—24no—
555C2×#102C22×C7111yescharacteristic
556C2×#102C22×C7111yescharacteristic
557C2×#102C22×C7111yescharacteristic
558C2×#102C22×C7111yescharacteristic, complemented
559C2×#102C22×C7111yescharacteristic, complemented
560C2×#102C22×C7111yescharacteristic, complemented
561C2×#102C22×C7111yescharacteristic, complemented
562C2×#102C22×C7111yescharacteristic, complemented
563C2×#102C22×C7111yescharacteristic, complemented
564C2×#102C22×C7111yescharacteristic, complemented
565C2×C22⋊C8C22×C7111yescharacteristic, complemented
566C2×C22⋊C8C22×C7111yescharacteristic, complemented
567C2×C22⋊C8C22×C7111yescharacteristic, complemented
568#394—21no—
569#392—21no—
570#390—21no—
571#390C22×C7111yescharacteristic, complemented
572#389C22×C7111yescharacteristic, complemented
573#388—21no—
574#380C22×C7111yescharacteristic, complemented
575#340C22×C7111yescharacteristic, complemented
576#340C22×C7111yescharacteristic, complemented
577#336C22×C7111yescharacteristic, complemented
578#336C22×C7111yescharacteristic, complemented
579C25—21no—
580C25—21no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—28no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—41no—
598C22×D4—41no—
599C22×D4—41no—
600C22×D4—41no—
601C22×D4—44no—
602C22×D4—44no—
603C22×D4D4×C7111yescharacteristic
604C22×D4D4×C7114yescomplemented
605C22×D4C23×C7111yescharacteristic
606C22×D4C23×C7111yescharacteristic
607C22×D4C23×C7111yescharacteristic
608C22×D4C23×C7111yescharacteristic
609C23×C4—21no—
610C23×C4C23×C7111yescharacteristic
611C23×C4C23×C7111yescharacteristic
612C2×D8—22no—
613C2×D8—22no—
614C2×D8—22no—
615C2×D8—22no—
616C2×D8—22no—
617C2×D8—22no—
618C2×D8—41no—
619C2×D8—41no—
620C2×D8—41no—
621C2×M16—22no—
622C2×M16—22no—
623C2×M16—41no—
624C22×C8C23×C7111yescharacteristic
625C22×C8C23×C7111yescharacteristic
626C22×C8C23×C7111yescharacteristic
627C22×C8C23×C7111yescharacteristic
628#127—22no—
629#127—22no—
630#121—28no—
631#121—22no—
632#121—22no—
633#121—22no—
634#121—22no—
635#121—22no—
636#121—22no—
637#121—41no—
638#121D4×C7114yescomplemented
639#120—28no—
640#120—28no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645#117—22no—
646#117—41no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4D4×C7111yescharacteristic
649C2×C4⋊C4C23×C7111yescharacteristic
650C2×C4⋊C4C23×C7111yescharacteristic
651C2×C4⋊C4C23×C7111yescharacteristic
652C2×C4⋊C4C23×C7111yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4D4×C7111yescharacteristic
663C2×C22⋊C4D4×C7111yescharacteristic
664C2×C42—21no—
665C2×C42C23×C7111yescharacteristic
666#106—22no—
667#102—22no—
668#102—22no—
669#102—22no—
670#102—22no—
671#102—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—41no—
676#102D4×C7114yescomplemented
677C22⋊C8—22no—
678C22⋊C8—22no—
679C22⋊C8—41no—
680#95—21no—
681#95—21no—
682C24—21no—
683C24—24no—
684C24—21no—
685C24—21no—
686C24—24no—
687C24—21no—
688C24—42no—
689C24—42no—
690C24—42no—
691C24—42no—
692C24—42no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24—81no—
700C24C2×D4×C7111yescharacteristic
701C24C2×D4×C7111yescharacteristic
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—22no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
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—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—432no—
743C2×D4—44no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—44no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4—81no—
757C2×D4C2×D4×C7112yes—
758C2×D4C2×D4×C7112yes—
759C2×D4C2×D4×C7112yes—
760C2×D4C2×D4×C7112yes—
761C2×D4#41×C7112yes—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4C2×D4×C7111yescharacteristic
780C22×C4C2×D4×C7111yescharacteristic
781C22×C4C2×D4×C7111yescharacteristic
782C22×C4C2×D4×C7112yes—
783C22×C4C2×D4×C7112yes—
784C22×C4C2×D4×C7111yescharacteristic
785C22×C4C24×C7111yescharacteristic
786D8—44no—
787D8—44no—
788D8—44no—
789M16—44no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8C2×D4×C7112yescomplemented
802C4⋊C4—22no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—81no—
810C4⋊C4C2×D4×C7112yes—
811C4⋊C4C2×D4×C7112yescomplemented
812C22⋊C4—24no—
813C22⋊C4—24no—
814C22⋊C4—22no—
815C22⋊C4—24no—
816C22⋊C4—22no—
817C22⋊C4—42no—
818C22⋊C4—42no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—81no—
822C22⋊C4—81no—
823C42—21no—
824C42—21no—
825C42—42no—
826C23—21no—
827C23—22no—
828C23—21no—
829C23—21no—
830C23—22no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—22no—
842C23—22no—
843C23—48no—
844C23—48no—
845C23—48no—
846C23—48no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
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—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23#120×C7112yes—
881C23AGL(1,ℤ/8)×C7112yes—
882C23C22×D4×C7111yescharacteristic
883D4—28no—
884D4—22no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—48no—
892D4—48no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—41no—
901D4—41no—
902D4—41no—
903D4—41no—
904D4—84no—
905D4—84no—
906D4—84no—
907D4#121×C7114yes—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—48no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4#120×C7112yes—
940C2×C4AGL(1,ℤ/8)×C7112yes—
941C2×C4C22×D4×C7111yescharacteristic
942C2×C4C22×D4×C7111yescharacteristic
943C2×C4C22×D4×C7111yescharacteristic
944C2×C4C2×#41×C7111yescharacteristic
945C2×C4H(5,𝔽2)×C7111yescharacteristic
946C2×C4H(5,𝔽2)×C7111yescharacteristic
947C8—22no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—22no—
953C22—24no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—41no—
959C22—42no—
960C22—41no—
961C22—41no—
962C22—42no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—816no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22C2×#120×C7111yescharacteristic
996C22D42×C7111yescharacteristic
997C22#546×C7111yescharacteristic
998C22C2×AGL(1,ℤ/8)×C7111yescharacteristic
999C22C2×AGL(1,ℤ/8)×C7111yescharacteristic
1000C22#576×C7111yescharacteristic
1001C22#576×C7111yescharacteristic
1002C4—22no—
1003C4—22no—
1004C4—41no—
1005C4—42no—
1006C4—41no—
1007C4—42no—
1008C4—81no—
1009C4—81no—
1010C4C2×#121×C7111yescharacteristic
1011C4#534×C7111yescharacteristic
1012C4D42×C7111yescharacteristic
1013C4#546×C7111yescharacteristic
1014C2—42no—
1015C2—42no—
1016C2—44no—
1017C2—82no—
1018C2—82no—
1019C2—161no—
1020C2C71×#241011yescharacteristic
1021C2C71×#300311yescharacteristic
1022C2C71×#300811yescharacteristic
1023C2C71×#326411yescharacteristic
1024C2C71×#327411yescharacteristic
1025C2C71×#331811yescharacteristic
1026C2C71×#332511yescharacteristic
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×#469×C71C2semidirect
3. C2×#447×C71C2semidirect
4. C2×#447×C71C2semidirect
5. C2×#418×C71C2semidirect
6. C71×#2414C2semidirect
7. C71×#2041C2semidirect
8. C71×#2034C2semidirect
9. C71×#2011C2semidirect
10. C71×#1999C2semidirect
11. C71×#1879C2semidirect
12. C71×#1875C2semidirect
13. C71×#1870C2semidirect
14. C71×#1864C2semidirect
15. C71×#1786C2semidirect
20. C22×D8×C71C22semidirect
21. C22×D8×C71C22semidirect
22. C22×M16×C71C22semidirect
29. C2×#121×C71C22semidirect
30. C2×#121×C71C22semidirect
35. C2×#117×C71C22semidirect
39. C2×#106×C71C22semidirect
44. C2×#102×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×C22⋊C8×C71C22semidirect
52. C2×C22⋊C8×C71C22semidirect
53. 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
124. #121×C71D4semidirect
162. #102×C71D4semidirect
287. C2×C8×C71C2×D4semidirect
297. C4⋊C4×C71C2×D4semidirect
500. #24440C71direct (N × H)
514. C2×D42C2×C71semidirect
515. C2×#469C2×C71semidirect
516. C2×#447C2×C71semidirect
517. C2×#447C2×C71semidirect
518. C2×#418C2×C71semidirect
519. #2414C2×C71semidirect
520. #2041C2×C71semidirect
521. #2034C2×C71semidirect
522. #2011C2×C71semidirect
523. #1999C2×C71semidirect
524. #1879C2×C71semidirect
525. #1875C2×C71semidirect
526. #1870C2×C71semidirect
527. #1864C2×C71semidirect
528. #1786C2×C71semidirect
529. C71#24440direct (N × H)
534. C22×D8C22×C71semidirect
535. C22×D8C22×C71semidirect
536. C22×M16C22×C71semidirect
543. C2×#121C22×C71semidirect
544. C2×#121C22×C71semidirect
549. C2×#117C22×C71semidirect
553. C2×#106C22×C71semidirect
558. C2×#102C22×C71semidirect
559. C2×#102C22×C71semidirect
560. C2×#102C22×C71semidirect
561. C2×#102C22×C71semidirect
562. C2×#102C22×C71semidirect
563. C2×#102C22×C71semidirect
564. C2×#102C22×C71semidirect
565. C2×C22⋊C8C22×C71semidirect
566. C2×C22⋊C8C22×C71semidirect
567. C2×C22⋊C8C22×C71semidirect
571. #390C22×C71semidirect
572. #389C22×C71semidirect
574. #380C22×C71semidirect
575. #340C22×C71semidirect
576. #340C22×C71semidirect
577. #336C22×C71semidirect
578. #336C22×C71semidirect
604. C22×D4D4×C71semidirect
638. #121D4×C71semidirect
676. #102D4×C71semidirect
801. C2×C8C2×D4×C71semidirect
811. C4⋊C4C2×D4×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×#469×C712
C2×#447×C712
C2×#418×C712
C71×#24142
C71×#20412
C71×#20342
C71×#20112
C71×#19992
C71×#18792
C71×#18752
C71×#18702
C71×#18642
C71×#17862
#2444071