Finite Group Databasebeta

← C71×#24432 #31845304

Subgroups — C71×#24432 #31845304

Order 18176.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C71C211yesmaximal, characteristic
2C2×#465×C71C211yesmaximal, characteristic, complemented
3C2×#450×C71C211yesmaximal, characteristic, complemented
4C2×#450×C71C211yesmaximal, characteristic, complemented
5C22×#102×C71C211yesmaximal, characteristic, complemented
6C71×#2417C211yesmaximal, characteristic, complemented
7C71×#2041C211yesmaximal, characteristic, complemented
8C71×#2034C211yesmaximal, characteristic, complemented
9C71×#2014C211yesmaximal, characteristic, complemented
10C71×#2000C211yesmaximal, characteristic, complemented
11C71×#1877C211yesmaximal, characteristic, complemented
12C71×#1874C211yesmaximal, characteristic, complemented
13C71×#1869C211yesmaximal, characteristic, complemented
14C71×#1864C211yesmaximal, characteristic, complemented
15C71×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C71—21no—
17C23×D4×C71C2211yescharacteristic
18C23×D4×C71C2211yescharacteristic
19C22×SD16×C71C2211yescharacteristic
20C22×SD16×C71C2211yescharacteristic, complemented
21C22×SD16×C71C2211yescharacteristic, complemented
22C23×C8×C71C2211yescharacteristic, complemented
23D42×C71—24no—
24D42×C71—24no—
25C2×#127×C71C2211yescharacteristic
26C2×C22⋊Q8×C71C2211yescharacteristic, complemented
27C2×C22⋊Q8×C71C2211yescharacteristic, complemented
28C2×#121×C71—21no—
29C2×#121×C71C2211yescharacteristic
30C2×#121×C71C2211yescharacteristic
31C2×#120×C71—21no—
32C2×#120×C71—21no—
33C2×C4×D4×C71C2211yescharacteristic
34C2×C4×D4×C71C2211yescharacteristic
35C22×C4⋊C4×C71C2211yescharacteristic, complemented
36#465×C71—24no—
37#450×C71—24no—
38#450×C71—24no—
39C2×#106×C71C2211yescharacteristic, complemented
40C2×#103×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×C22⋊C8×C71C2211yescharacteristic, complemented
52C2×C22⋊C8×C71C2211yescharacteristic, complemented
53C2×C22⋊C8×C71C2211yescharacteristic, complemented
54#398×C71—21no—
55#396×C71—21no—
56#391×C71C2211yescharacteristic, complemented
57#389×C71C2211yescharacteristic, complemented
58#386×C71—21no—
59#380×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×Q8×C71C2311yescharacteristic
68C22×D4×C71—22no—
69C22×D4×C71—22no—
70C22×D4×C71—28no—
71C22×D4×C71—21no—
72C22×D4×C71—21no—
73C22×D4×C71—22no—
74C22×D4×C71—22no—
75C22×D4×C71—22no—
76C22×D4×C71—22no—
77C22×D4×C71—21no—
78C22×D4×C71—21no—
79C22×D4×C71—21no—
80C22×D4×C71—22no—
81C22×D4×C71—21no—
82C22×D4×C71—41no—
83C22×D4×C71—41no—
84C22×D4×C71—41no—
85C22×D4×C71—41no—
86C22×D4×C71—44no—
87C22×D4×C71—44no—
88C22×D4×C71D411yescharacteristic
89C22×D4×C71D414yes—
90C22×D4×C71C2311yescharacteristic
91C22×D4×C71C2311yescharacteristic
92C22×D4×C71C2311yescharacteristic
93C23×C4×C71—21no—
94C23×C4×C71—21no—
95C23×C4×C71C2311yescharacteristic
96C23×C4×C71C2311yescharacteristic
97C2×SD16×C71—22no—
98C2×SD16×C71—22no—
99C2×SD16×C71—22no—
100C2×SD16×C71—22no—
101C2×SD16×C71—22no—
102C2×SD16×C71—22no—
103C2×SD16×C71—41no—
104C2×SD16×C71—41no—
105C2×SD16×C71—41no—
106C22×C8×C71—22no—
107C22×C8×C71—22no—
108C22×C8×C71—41no—
109C22×C8×C71C2311yescharacteristic
110C22×C8×C71C2311yescharacteristic
111C22×C8×C71C2311yescharacteristic
112C22×C8×C71C2311yescharacteristic
113#127×C71—22no—
114#127×C71—22no—
115C22⋊Q8×C71—22no—
116C22⋊Q8×C71—22no—
117C22⋊Q8×C71—22no—
118C22⋊Q8×C71—41no—
119#121×C71—28no—
120#121×C71—22no—
121#121×C71—22no—
122#121×C71—22no—
123#121×C71D414yes—
124#120×C71—28no—
125#120×C71—28no—
126C4×D4×C71—22no—
127C4×D4×C71—22no—
128C4×D4×C71—22no—
129C4×D4×C71—22no—
130C2×C4⋊C4×C71—22no—
131C2×C4⋊C4×C71—21no—
132C2×C4⋊C4×C71—21no—
133C2×C4⋊C4×C71—21no—
134C2×C4⋊C4×C71—21no—
135C2×C4⋊C4×C71—41no—
136C2×C4⋊C4×C71D411yescharacteristic
137C2×C4⋊C4×C71C2311yescharacteristic
138C2×C4⋊C4×C71C2311yescharacteristic
139C2×C4⋊C4×C71C2311yescharacteristic
140C2×C4⋊C4×C71C2311yescharacteristic
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×C71D411yescharacteristic
148C2×C22⋊C4×C71D411yescharacteristic
149C2×C42×C71C2311yescharacteristic
150#106×C71—22no—
151#103×C71—22no—
152#102×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—41no—
160#102×C71D414yescomplemented
161C22⋊C8×C71—22no—
162C22⋊C8×C71—22no—
163C22⋊C8×C71—41no—
164#95×C71—21no—
165#95×C71—21no—
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—42no—
174C24×C71—42no—
175C24×C71—42no—
176C24×C71—42no—
177C24×C71—42no—
178C24×C71—42no—
179C24×C71—42no—
180C24×C71—42no—
181C24×C71—81no—
182C24×C71—81no—
183C24×C71—81no—
184C24×C71—81no—
185C24×C71C2×D411yescharacteristic
186C24×C71C2×D411yescharacteristic
187C2×Q8×C71—21no—
188C2×Q8×C71—21no—
189C2×Q8×C71—21no—
190C2×Q8×C71—21no—
191C2×Q8×C71—21no—
192C2×Q8×C71—21no—
193C2×D4×C71—22no—
194C2×D4×C71—22no—
195C2×D4×C71—28no—
196C2×D4×C71—24no—
197C2×D4×C71—24no—
198C2×D4×C71—24no—
199C2×D4×C71—24no—
200C2×D4×C71—24no—
201C2×D4×C71—24no—
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—44no—
216C2×D4×C71—44no—
217C2×D4×C71—44no—
218C2×D4×C71—42no—
219C2×D4×C71—42no—
220C2×D4×C71—42no—
221C2×D4×C71—42no—
222C2×D4×C71—42no—
223C2×D4×C71—44no—
224C2×D4×C71—44no—
225C2×D4×C71—432no—
226C2×D4×C71—44no—
227C2×D4×C71—42no—
228C2×D4×C71—42no—
229C2×D4×C71—42no—
230C2×D4×C71—42no—
231C2×D4×C71—44no—
232C2×D4×C71—42no—
233C2×D4×C71—81no—
234C2×D4×C71—81no—
235C2×D4×C71SD1614yescomplemented
236C2×D4×C71C2×D412yes—
237C2×D4×C71C2×D412yes—
238C2×D4×C71C2×D412yes—
239C2×D4×C71C2×D412yes—
240C2×D4×C71#4112yes—
241C22×C4×C71—21no—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71—24no—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71—21no—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71—21no—
252C22×C4×C71—21no—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71—21no—
257C22×C4×C71—42no—
258C22×C4×C71—42no—
259C22×C4×C71—42no—
260C22×C4×C71—42no—
261C22×C4×C71—81no—
262C22×C4×C71C2×D411yescharacteristic
263C22×C4×C71C2×D411yescharacteristic
264C22×C4×C71C2×D411yescharacteristic
265C22×C4×C71C2×D412yes—
266C22×C4×C71C2×D412yes—
267C22×C4×C71C2×D411yescharacteristic
268C22×C4×C71C2411yescharacteristic
269SD16×C71—44no—
270SD16×C71—44no—
271SD16×C71—44no—
272C2×C8×C71—21no—
273C2×C8×C71—21no—
274C2×C8×C71—21no—
275C2×C8×C71—21no—
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—44no—
284C2×C8×C71C2×D412yescomplemented
285C4⋊C4×C71—22no—
286C4⋊C4×C71—21no—
287C4⋊C4×C71—21no—
288C4⋊C4×C71—21no—
289C4⋊C4×C71—21no—
290C4⋊C4×C71—21no—
291C4⋊C4×C71—21no—
292C4⋊C4×C71—42no—
293C4⋊C4×C71—42no—
294C4⋊C4×C71—42no—
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—81no—
306C42×C71—21no—
307C42×C71—21no—
308C23×C71—21no—
309C23×C71—21no—
310C23×C71—21no—
311C23×C71—21no—
312C23×C71—21no—
313C23×C71—22no—
314C23×C71—21no—
315C23×C71—22no—
316C23×C71—21no—
317C23×C71—22no—
318C23×C71—21no—
319C23×C71—21no—
320C23×C71—21no—
321C23×C71—22no—
322C23×C71—22no—
323C23×C71—48no—
324C23×C71—48no—
325C23×C71—48no—
326C23×C71—41no—
327C23×C71—41no—
328C23×C71—41no—
329C23×C71—41no—
330C23×C71—41no—
331C23×C71—41no—
332C23×C71—41no—
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—48no—
343C23×C71—84no—
344C23×C71—84no—
345C23×C71—84no—
346C23×C71—84no—
347C23×C71—84no—
348C23×C71—84no—
349C23×C71—84no—
350C23×C71—84no—
351C23×C71—84no—
352C23×C71—84no—
353C23×C71#12012yes—
354C23×C71C2×SD1612yes—
355C23×C71C2×SD1612yes—
356C23×C71AGL(1,ℤ/8)12yes—
357C23×C71C22×D411yescharacteristic
358Q8×C71—41no—
359Q8×C71—41no—
360Q8×C71—41no—
361Q8×C71—41no—
362D4×C71—28no—
363D4×C71—22no—
364D4×C71—22no—
365D4×C71—22no—
366D4×C71—22no—
367D4×C71—22no—
368D4×C71—22no—
369D4×C71—22no—
370D4×C71—48no—
371D4×C71—48no—
372D4×C71—48no—
373D4×C71—48no—
374D4×C71—48no—
375D4×C71—41no—
376D4×C71—41no—
377D4×C71—41no—
378D4×C71—41no—
379D4×C71—84no—
380D4×C71#12114yes—
381C2×C4×C71—21no—
382C2×C4×C71—21no—
383C2×C4×C71—21no—
384C2×C4×C71—21no—
385C2×C4×C71—22no—
386C2×C4×C71—22no—
387C2×C4×C71—22no—
388C2×C4×C71—22no—
389C2×C4×C71—21no—
390C2×C4×C71—21no—
391C2×C4×C71—22no—
392C2×C4×C71—22no—
393C2×C4×C71—21no—
394C2×C4×C71—21no—
395C2×C4×C71—21no—
396C2×C4×C71—21no—
397C2×C4×C71—48no—
398C2×C4×C71—41no—
399C2×C4×C71—41no—
400C2×C4×C71—41no—
401C2×C4×C71—41no—
402C2×C4×C71—41no—
403C2×C4×C71—41no—
404C2×C4×C71—41no—
405C2×C4×C71—41no—
406C2×C4×C71—41no—
407C2×C4×C71—41no—
408C2×C4×C71—41no—
409C2×C4×C71—41no—
410C2×C4×C71—41no—
411C2×C4×C71—41no—
412C2×C4×C71—41no—
413C2×C4×C71—41no—
414C2×C4×C71—41no—
415C2×C4×C71—84no—
416C2×C4×C71#12012yes—
417C2×C4×C71C2×SD1612yes—
418C2×C4×C71C22×D411yescharacteristic
419C2×C4×C71C22×D411yescharacteristic
420C2×C4×C71C22×D411yescharacteristic
421C2×C4×C71C2×#4111yescharacteristic
422C2×C4×C71H(5,𝔽2)11yescharacteristic
423C2×C4×C71H(5,𝔽2)11yescharacteristic
424C8×C71—22no—
425C8×C71—41no—
426C8×C71—41no—
427C8×C71—41no—
428C22×C71—22no—
429C22×C71—22no—
430C22×C71—22no—
431C22×C71—22no—
432C22×C71—22no—
433C22×C71—22no—
434C22×C71—24no—
435C22×C71—22no—
436C22×C71—22no—
437C22×C71—22no—
438C22×C71—41no—
439C22×C71—42no—
440C22×C71—41no—
441C22×C71—42no—
442C22×C71—41no—
443C22×C71—42no—
444C22×C71—42no—
445C22×C71—42no—
446C22×C71—41no—
447C22×C71—42no—
448C22×C71—42no—
449C22×C71—42no—
450C22×C71—42no—
451C22×C71—42no—
452C22×C71—42no—
453C22×C71—42no—
454C22×C71—816no—
455C22×C71—816no—
456C22×C71—81no—
457C22×C71—81no—
458C22×C71—81no—
459C22×C71—81no—
460C22×C71—81no—
461C22×C71—81no—
462C22×C71—81no—
463C22×C71—81no—
464C22×C71#45014yescomplemented
465C22×C71C2×#12011yescharacteristic
466C22×C71D4211yescharacteristic
467C22×C71#54611yescharacteristic
468C22×C71C22×SD1611yescharacteristic
469C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
470C22×C71#57611yescharacteristic
471C22×C71#57711yescharacteristic
472C4×C71—22no—
473C4×C71—22no—
474C4×C71—41no—
475C4×C71—42no—
476C4×C71—42no—
477C4×C71—41no—
478C4×C71—81no—
479C4×C71—81no—
480C4×C71—81no—
481C4×C71C2×#12111yescharacteristic
482C4×C71#53411yescharacteristic
483C4×C71D4211yescharacteristic
484C4×C71#54611yescharacteristic
485#24432C7111yesmaximal, characteristic, direct product factor, Sylow
486C2×C71—24no—
487C2×C71—42no—
488C2×C71—44no—
489C2×C71—82no—
490C2×C71—82no—
491C2×C71#241011yescharacteristic
492C2×C71C2×#45011yescharacteristic
493C2×C71#301211yescharacteristic
494C2×C71#326411yescharacteristic
495C2×C71D4×SD1611yescharacteristic
496C2×C71#329511yescharacteristic
497C2×C71#331011yescharacteristic
498C2×D42C2×C7111yescharacteristic
499C2×#465C2×C7111yescharacteristic, complemented
500C2×#450C2×C7111yescharacteristic, complemented
501C2×#450C2×C7111yescharacteristic, complemented
502C22×#102C2×C7111yescharacteristic, complemented
503#2417C2×C7111yescharacteristic, complemented
504#2041C2×C7111yescharacteristic, complemented
505#2034C2×C7111yescharacteristic, complemented
506#2014C2×C7111yescharacteristic, complemented
507#2000C2×C7111yescharacteristic, complemented
508#1877C2×C7111yescharacteristic, complemented
509#1874C2×C7111yescharacteristic, complemented
510#1869C2×C7111yescharacteristic, complemented
511#1864C2×C7111yescharacteristic, complemented
512#1786C2×C7111yescharacteristic, complemented
513C71#2443211yescharacteristic, direct product factor, Sylow
514C23×D4—21no—
515C23×D4C22×C7111yescharacteristic
516C23×D4C22×C7111yescharacteristic
517C22×SD16C22×C7111yescharacteristic
518C22×SD16C22×C7111yescharacteristic, complemented
519C22×SD16C22×C7111yescharacteristic, complemented
520C23×C8C22×C7111yescharacteristic, complemented
521D42—24no—
522D42—24no—
523C2×#127C22×C7111yescharacteristic
524C2×C22⋊Q8C22×C7111yescharacteristic, complemented
525C2×C22⋊Q8C22×C7111yescharacteristic, complemented
526C2×#121—21no—
527C2×#121C22×C7111yescharacteristic
528C2×#121C22×C7111yescharacteristic
529C2×#120—21no—
530C2×#120—21no—
531C2×C4×D4C22×C7111yescharacteristic
532C2×C4×D4C22×C7111yescharacteristic
533C22×C4⋊C4C22×C7111yescharacteristic, complemented
534#465—24no—
535#450—24no—
536#450—24no—
537C2×#106C22×C7111yescharacteristic, complemented
538C2×#103C22×C7111yescharacteristic, complemented
539C2×#102—24no—
540C2×#102C22×C7111yescharacteristic
541C2×#102C22×C7111yescharacteristic
542C2×#102C22×C7111yescharacteristic
543C2×#102C22×C7111yescharacteristic, complemented
544C2×#102C22×C7111yescharacteristic, complemented
545C2×#102C22×C7111yescharacteristic, complemented
546C2×#102C22×C7111yescharacteristic, complemented
547C2×#102C22×C7111yescharacteristic, complemented
548C2×#102C22×C7111yescharacteristic, complemented
549C2×C22⋊C8C22×C7111yescharacteristic, complemented
550C2×C22⋊C8C22×C7111yescharacteristic, complemented
551C2×C22⋊C8C22×C7111yescharacteristic, complemented
552#398—21no—
553#396—21no—
554#391C22×C7111yescharacteristic, complemented
555#389C22×C7111yescharacteristic, complemented
556#386—21no—
557#380—21no—
558#380C22×C7111yescharacteristic, complemented
559#340C22×C7111yescharacteristic, complemented
560#340C22×C7111yescharacteristic, complemented
561#336C22×C7111yescharacteristic, complemented
562#336C22×C7111yescharacteristic, complemented
563C25—21no—
564C25—21no—
565C22×Q8C23×C7111yescharacteristic
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—28no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—22no—
579C22×D4—21no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—41no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4D4×C7111yescharacteristic
587C22×D4D4×C7114yes—
588C22×D4C23×C7111yescharacteristic
589C22×D4C23×C7111yescharacteristic
590C22×D4C23×C7111yescharacteristic
591C23×C4—21no—
592C23×C4—21no—
593C23×C4C23×C7111yescharacteristic
594C23×C4C23×C7111yescharacteristic
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—22no—
601C2×SD16—41no—
602C2×SD16—41no—
603C2×SD16—41no—
604C22×C8—22no—
605C22×C8—22no—
606C22×C8—41no—
607C22×C8C23×C7111yescharacteristic
608C22×C8C23×C7111yescharacteristic
609C22×C8C23×C7111yescharacteristic
610C22×C8C23×C7111yescharacteristic
611#127—22no—
612#127—22no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—41no—
617#121—28no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121D4×C7114yes—
622#120—28no—
623#120—28no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4D4×C7111yescharacteristic
635C2×C4⋊C4C23×C7111yescharacteristic
636C2×C4⋊C4C23×C7111yescharacteristic
637C2×C4⋊C4C23×C7111yescharacteristic
638C2×C4⋊C4C23×C7111yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4D4×C7111yescharacteristic
646C2×C22⋊C4D4×C7111yescharacteristic
647C2×C42C23×C7111yescharacteristic
648#106—22no—
649#103—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—41no—
658#102D4×C7114yescomplemented
659C22⋊C8—22no—
660C22⋊C8—22no—
661C22⋊C8—41no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666C24—21no—
667C24—24no—
668C24—21no—
669C24—21no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—42no—
678C24—42no—
679C24—81no—
680C24—81no—
681C24—81no—
682C24—81no—
683C24C2×D4×C7111yescharacteristic
684C24C2×D4×C7111yescharacteristic
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—432no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4SD16×C7114yescomplemented
734C2×D4C2×D4×C7112yes—
735C2×D4C2×D4×C7112yes—
736C2×D4C2×D4×C7112yes—
737C2×D4C2×D4×C7112yes—
738C2×D4#41×C7112yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—81no—
760C22×C4C2×D4×C7111yescharacteristic
761C22×C4C2×D4×C7111yescharacteristic
762C22×C4C2×D4×C7111yescharacteristic
763C22×C4C2×D4×C7112yes—
764C22×C4C2×D4×C7112yes—
765C22×C4C2×D4×C7111yescharacteristic
766C22×C4C24×C7111yescharacteristic
767SD16—44no—
768SD16—44no—
769SD16—44no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—44no—
782C2×C8C2×D4×C7112yescomplemented
783C4⋊C4—22no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—81no—
794C4⋊C4C2×D4×C7112yes—
795C4⋊C4C2×D4×C7112yescomplemented
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—81no—
804C42—21no—
805C42—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—22no—
814C23—21no—
815C23—22no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—48no—
822C23—48no—
823C23—48no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—48no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23#120×C7112yes—
852C23C2×SD16×C7112yes—
853C23C2×SD16×C7112yes—
854C23AGL(1,ℤ/8)×C7112yes—
855C23C22×D4×C7111yescharacteristic
856Q8—41no—
857Q8—41no—
858Q8—41no—
859Q8—41no—
860D4—28no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—48no—
869D4—48no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—84no—
878D4#121×C7114yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—48no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—84no—
914C2×C4#120×C7112yes—
915C2×C4C2×SD16×C7112yes—
916C2×C4C22×D4×C7111yescharacteristic
917C2×C4C22×D4×C7111yescharacteristic
918C2×C4C22×D4×C7111yescharacteristic
919C2×C4C2×#41×C7111yescharacteristic
920C2×C4H(5,𝔽2)×C7111yescharacteristic
921C2×C4H(5,𝔽2)×C7111yescharacteristic
922C8—22no—
923C8—41no—
924C8—41no—
925C8—41no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—24no—
934C22—22no—
935C22—22no—
936C22—42no—
937C22—41no—
938C22—42no—
939C22—41no—
940C22—42no—
941C22—41no—
942C22—42no—
943C22—41no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—816no—
953C22—816no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22#450×C7114yescomplemented
963C22C2×#120×C7111yescharacteristic
964C22D42×C7111yescharacteristic
965C22#546×C7111yescharacteristic
966C22C22×SD16×C7111yescharacteristic
967C22C2×AGL(1,ℤ/8)×C7111yescharacteristic
968C22#576×C7111yescharacteristic
969C22#577×C7111yescharacteristic
970C4—22no—
971C4—22no—
972C4—41no—
973C4—42no—
974C4—42no—
975C4—41no—
976C4—81no—
977C4—81no—
978C4—81no—
979C4C2×#121×C7111yescharacteristic
980C4#534×C7111yescharacteristic
981C4D42×C7111yescharacteristic
982C4#546×C7111yescharacteristic
983C2—24no—
984C2—42no—
985C2—44no—
986C2—82no—
987C2—82no—
988C2C71×#241011yescharacteristic
989C2C2×#450×C7111yescharacteristic
990C2C71×#301211yescharacteristic
991C2C71×#326411yescharacteristic
992C2D4×SD16×C7111yescharacteristic
993C2C71×#329511yescharacteristic
994C2C71×#331011yescharacteristic
subgroupG/H
center, socleC23×C71C22×D4
commutator, Frattini, cosocleC22×C4C24×C71
prime radicalC2×D42×C71C2
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
2. C2×#465×C71C2semidirect
3. C2×#450×C71C2semidirect
4. C2×#450×C71C2semidirect
5. C22×#102×C71C2semidirect
6. C71×#2417C2semidirect
7. C71×#2041C2semidirect
8. C71×#2034C2semidirect
9. C71×#2014C2semidirect
10. C71×#2000C2semidirect
11. C71×#1877C2semidirect
12. C71×#1874C2semidirect
13. C71×#1869C2semidirect
14. C71×#1864C2semidirect
15. C71×#1786C2semidirect
20. C22×SD16×C71C22semidirect
21. C22×SD16×C71C22semidirect
22. C23×C8×C71C22semidirect
26. C2×C22⋊Q8×C71C22semidirect
27. C2×C22⋊Q8×C71C22semidirect
35. C22×C4⋊C4×C71C22semidirect
39. C2×#106×C71C22semidirect
40. C2×#103×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
56. #391×C71C22semidirect
57. #389×C71C22semidirect
60. #380×C71C22semidirect
61. #340×C71C22semidirect
62. #340×C71C22semidirect
63. #336×C71C22semidirect
64. #336×C71C22semidirect
160. #102×C71D4semidirect
235. C2×D4×C71SD16semidirect
284. C2×C8×C71C2×D4semidirect
297. C4⋊C4×C71C2×D4semidirect
464. C22×C71#450semidirect
485. #24432C71direct (N × H)
499. C2×#465C2×C71semidirect
500. C2×#450C2×C71semidirect
501. C2×#450C2×C71semidirect
502. C22×#102C2×C71semidirect
503. #2417C2×C71semidirect
504. #2041C2×C71semidirect
505. #2034C2×C71semidirect
506. #2014C2×C71semidirect
507. #2000C2×C71semidirect
508. #1877C2×C71semidirect
509. #1874C2×C71semidirect
510. #1869C2×C71semidirect
511. #1864C2×C71semidirect
512. #1786C2×C71semidirect
513. C71#24432direct (N × H)
518. C22×SD16C22×C71semidirect
519. C22×SD16C22×C71semidirect
520. C23×C8C22×C71semidirect
524. C2×C22⋊Q8C22×C71semidirect
525. C2×C22⋊Q8C22×C71semidirect
533. C22×C4⋊C4C22×C71semidirect
537. C2×#106C22×C71semidirect
538. C2×#103C22×C71semidirect
543. C2×#102C22×C71semidirect
544. C2×#102C22×C71semidirect
545. C2×#102C22×C71semidirect
546. C2×#102C22×C71semidirect
547. C2×#102C22×C71semidirect
548. C2×#102C22×C71semidirect
549. C2×C22⋊C8C22×C71semidirect
550. C2×C22⋊C8C22×C71semidirect
551. C2×C22⋊C8C22×C71semidirect
554. #391C22×C71semidirect
555. #389C22×C71semidirect
558. #380C22×C71semidirect
559. #340C22×C71semidirect
560. #340C22×C71semidirect
561. #336C22×C71semidirect
562. #336C22×C71semidirect
658. #102D4×C71semidirect
733. C2×D4SD16×C71semidirect
782. C2×C8C2×D4×C71semidirect
795. C4⋊C4C2×D4×C71semidirect
962. C22#450×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×#465×C712
C2×#450×C712
C22×#102×C712
C71×#24172
C71×#20412
C71×#20342
C71×#20142
C71×#20002
C71×#18772
C71×#18742
C71×#18692
C71×#18642
C71×#17862
#2443271