Finite Group Databasebeta

← C71×#24448 #31845320

Subgroups — C71×#24448 #31845320

Order 18176.

1888 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C71C211yesmaximal, characteristic
2C2×#468×C71C211yesmaximal, characteristic, complemented
3C2×#450×C71C211yesmaximal, characteristic, complemented
4C2×#450×C71C211yesmaximal, characteristic, complemented
5C2×#418×C71C211yesmaximal, characteristic, complemented
6C71×#2415C211yesmaximal, characteristic, complemented
7C71×#2041C211yesmaximal, characteristic, complemented
8C71×#2033C211yesmaximal, characteristic, complemented
9C71×#2014C211yesmaximal, characteristic, complemented
10C71×#2000C211yesmaximal, characteristic, complemented
11C71×#1877C211yesmaximal, characteristic, complemented
12C71×#1875C211yesmaximal, characteristic, complemented
13C71×#1870C211yesmaximal, characteristic, complemented
14C71×#1862C211yesmaximal, 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
22C22×M16×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
35C2×#117×C71C2211yescharacteristic, complemented
36#468×C71—24no—
37#450×C71—24no—
38#450×C71—24no—
39C2×#107×C71C2211yescharacteristic, complemented
40#418×C71—24no—
41C2×#103×C71C2211yescharacteristic, complemented
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#397×C71—21no—
55#394×C71—21no—
56#391×C71C2211yescharacteristic, complemented
57#389×C71—21no—
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×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×C71C2311yescharacteristic
95C23×C4×C71C2311yescharacteristic
96C2×SD16×C71—22no—
97C2×SD16×C71—22no—
98C2×SD16×C71—22no—
99C2×SD16×C71—22no—
100C2×SD16×C71—22no—
101C2×SD16×C71—22no—
102C2×SD16×C71—41no—
103C2×SD16×C71—41no—
104C2×SD16×C71—41no—
105C2×M16×C71—22no—
106C2×M16×C71—22no—
107C2×M16×C71—41no—
108C22×C8×C71C2311yescharacteristic
109C22×C8×C71C2311yescharacteristic
110C22×C8×C71C2311yescharacteristic
111C22×C8×C71C2311yescharacteristic
112#127×C71—22no—
113#127×C71—22no—
114C22⋊Q8×C71—22no—
115C22⋊Q8×C71—22no—
116C22⋊Q8×C71—22no—
117C22⋊Q8×C71—41no—
118#121×C71—28no—
119#121×C71—22no—
120#121×C71—22no—
121#121×C71—22no—
122#121×C71D414yes—
123#120×C71—28no—
124#120×C71—28no—
125C4×D4×C71—22no—
126C4×D4×C71—22no—
127C4×D4×C71—22no—
128C4×D4×C71—22no—
129#117×C71—22no—
130#117×C71—41no—
131C2×C4⋊C4×C71—21no—
132C2×C4⋊C4×C71—21no—
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×C71D411yescharacteristic
147C2×C22⋊C4×C71D411yescharacteristic
148C2×C42×C71—21no—
149C2×C42×C71C2311yescharacteristic
150#107×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—22no—
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—44no—
217C2×D4×C71—44no—
218C2×D4×C71—44no—
219C2×D4×C71—42no—
220C2×D4×C71—42no—
221C2×D4×C71—42no—
222C2×D4×C71—42no—
223C2×D4×C71—42no—
224C2×D4×C71—44no—
225C2×D4×C71—44no—
226C2×D4×C71—432no—
227C2×D4×C71—44no—
228C2×D4×C71—42no—
229C2×D4×C71—42no—
230C2×D4×C71—42no—
231C2×D4×C71—42no—
232C2×D4×C71—44no—
233C2×D4×C71—42no—
234C2×D4×C71—81no—
235C2×D4×C71—81no—
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×C71C2×D411yescharacteristic
260C22×C4×C71C2×D411yescharacteristic
261C22×C4×C71C2×D411yescharacteristic
262C22×C4×C71C2×D412yes—
263C22×C4×C71C2×D412yes—
264C22×C4×C71C2×D411yescharacteristic
265C22×C4×C71C2411yescharacteristic
266SD16×C71—44no—
267SD16×C71—44no—
268SD16×C71—44no—
269M16×C71—44no—
270C2×C8×C71—21no—
271C2×C8×C71—21no—
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×C71C2×D412yescomplemented
282C4⋊C4×C71—22no—
283C4⋊C4×C71—21no—
284C4⋊C4×C71—21no—
285C4⋊C4×C71—21no—
286C4⋊C4×C71—21no—
287C4⋊C4×C71—21no—
288C4⋊C4×C71—21no—
289C4⋊C4×C71—42no—
290C4⋊C4×C71—42no—
291C4⋊C4×C71—42no—
292C4⋊C4×C71C2×D412yes—
293C4⋊C4×C71C2×D412yescomplemented
294C22⋊C4×C71—24no—
295C22⋊C4×C71—24no—
296C22⋊C4×C71—22no—
297C22⋊C4×C71—24no—
298C22⋊C4×C71—22no—
299C22⋊C4×C71—42no—
300C22⋊C4×C71—42no—
301C22⋊C4×C71—42no—
302C22⋊C4×C71—42no—
303C42×C71—21no—
304C42×C71—21no—
305C42×C71—42no—
306C23×C71—21no—
307C23×C71—22no—
308C23×C71—21no—
309C23×C71—21no—
310C23×C71—22no—
311C23×C71—21no—
312C23×C71—21no—
313C23×C71—22no—
314C23×C71—21no—
315C23×C71—21no—
316C23×C71—21no—
317C23×C71—21no—
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—48no—
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—41no—
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×C71AGL(1,ℤ/8)12yes—
355C23×C71C22×D411yescharacteristic
356Q8×C71—41no—
357Q8×C71—41no—
358Q8×C71—41no—
359Q8×C71—41no—
360D4×C71—28no—
361D4×C71—22no—
362D4×C71—22no—
363D4×C71—22no—
364D4×C71—22no—
365D4×C71—22no—
366D4×C71—22no—
367D4×C71—22no—
368D4×C71—48no—
369D4×C71—48no—
370D4×C71—48no—
371D4×C71—48no—
372D4×C71—48no—
373D4×C71—41no—
374D4×C71—41no—
375D4×C71—41no—
376D4×C71—41no—
377D4×C71—84no—
378D4×C71#12114yes—
379C2×C4×C71—21no—
380C2×C4×C71—21no—
381C2×C4×C71—21no—
382C2×C4×C71—21no—
383C2×C4×C71—22no—
384C2×C4×C71—22no—
385C2×C4×C71—22no—
386C2×C4×C71—22no—
387C2×C4×C71—21no—
388C2×C4×C71—21no—
389C2×C4×C71—22no—
390C2×C4×C71—22no—
391C2×C4×C71—21no—
392C2×C4×C71—21no—
393C2×C4×C71—21no—
394C2×C4×C71—21no—
395C2×C4×C71—48no—
396C2×C4×C71—41no—
397C2×C4×C71—41no—
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#12012yes—
414C2×C4×C71AGL(1,ℤ/8)12yes—
415C2×C4×C71C22×D411yescharacteristic
416C2×C4×C71C22×D411yescharacteristic
417C2×C4×C71C22×D411yescharacteristic
418C2×C4×C71C2×#4111yescharacteristic
419C2×C4×C71H(5,𝔽2)11yescharacteristic
420C2×C4×C71H(5,𝔽2)11yescharacteristic
421C8×C71—22no—
422C8×C71—41no—
423C8×C71—41no—
424C8×C71—41no—
425C22×C71—22no—
426C22×C71—24no—
427C22×C71—22no—
428C22×C71—22no—
429C22×C71—22no—
430C22×C71—22no—
431C22×C71—22no—
432C22×C71—41no—
433C22×C71—42no—
434C22×C71—41no—
435C22×C71—42no—
436C22×C71—41no—
437C22×C71—42no—
438C22×C71—41no—
439C22×C71—41no—
440C22×C71—42no—
441C22×C71—41no—
442C22×C71—42no—
443C22×C71—41no—
444C22×C71—41no—
445C22×C71—42no—
446C22×C71—42no—
447C22×C71—42no—
448C22×C71—42no—
449C22×C71—42no—
450C22×C71—42no—
451C22×C71—42no—
452C22×C71—816no—
453C22×C71—816no—
454C22×C71—81no—
455C22×C71—81no—
456C22×C71—81no—
457C22×C71—81no—
458C22×C71—81no—
459C22×C71—81no—
460C22×C71—81no—
461C22×C71—81no—
462C22×C71C2×#12011yescharacteristic
463C22×C71D4211yescharacteristic
464C22×C71#54611yescharacteristic
465C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
466C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
467C22×C71#57711yescharacteristic
468C22×C71#57711yescharacteristic
469C4×C71—22no—
470C4×C71—22no—
471C4×C71—41no—
472C4×C71—42no—
473C4×C71—41no—
474C4×C71—42no—
475C4×C71—81no—
476C4×C71—81no—
477C4×C71—81no—
478C4×C71C2×#12111yescharacteristic
479C4×C71#53411yescharacteristic
480C4×C71D4211yescharacteristic
481C4×C71#54611yescharacteristic
482#24448C7111yesmaximal, characteristic, direct product factor, Sylow
483C2×C71—42no—
484C2×C71—42no—
485C2×C71—44no—
486C2×C71—82no—
487C2×C71—82no—
488C2×C71#241011yescharacteristic
489C2×C71#300311yescharacteristic
490C2×C71#300911yescharacteristic
491C2×C71#326511yescharacteristic
492C2×C71#327211yescharacteristic
493C2×C71#331011yescharacteristic
494C2×C71#332411yescharacteristic
495C2×D42C2×C7111yescharacteristic
496C2×#468C2×C7111yescharacteristic, complemented
497C2×#450C2×C7111yescharacteristic, complemented
498C2×#450C2×C7111yescharacteristic, complemented
499C2×#418C2×C7111yescharacteristic, complemented
500#2415C2×C7111yescharacteristic, complemented
501#2041C2×C7111yescharacteristic, complemented
502#2033C2×C7111yescharacteristic, complemented
503#2014C2×C7111yescharacteristic, complemented
504#2000C2×C7111yescharacteristic, complemented
505#1877C2×C7111yescharacteristic, complemented
506#1875C2×C7111yescharacteristic, complemented
507#1870C2×C7111yescharacteristic, complemented
508#1862C2×C7111yescharacteristic, complemented
509#1786C2×C7111yescharacteristic, complemented
510C71#2444811yescharacteristic, direct product factor, Sylow
511C23×D4—21no—
512C23×D4C22×C7111yescharacteristic
513C23×D4C22×C7111yescharacteristic
514C22×SD16C22×C7111yescharacteristic
515C22×SD16C22×C7111yescharacteristic, complemented
516C22×SD16C22×C7111yescharacteristic, complemented
517C22×M16C22×C7111yescharacteristic, complemented
518D42—24no—
519D42—24no—
520C2×#127C22×C7111yescharacteristic
521C2×C22⋊Q8C22×C7111yescharacteristic, complemented
522C2×C22⋊Q8C22×C7111yescharacteristic, complemented
523C2×#121—21no—
524C2×#121C22×C7111yescharacteristic
525C2×#121C22×C7111yescharacteristic
526C2×#120—21no—
527C2×#120—21no—
528C2×C4×D4C22×C7111yescharacteristic
529C2×C4×D4C22×C7111yescharacteristic
530C2×#117C22×C7111yescharacteristic, complemented
531#468—24no—
532#450—24no—
533#450—24no—
534C2×#107C22×C7111yescharacteristic, complemented
535#418—24no—
536C2×#103C22×C7111yescharacteristic, complemented
537C2×#102C22×C7111yescharacteristic
538C2×#102C22×C7111yescharacteristic
539C2×#102C22×C7111yescharacteristic
540C2×#102C22×C7111yescharacteristic, complemented
541C2×#102C22×C7111yescharacteristic, complemented
542C2×#102C22×C7111yescharacteristic, complemented
543C2×#102C22×C7111yescharacteristic, complemented
544C2×#102C22×C7111yescharacteristic, complemented
545C2×#102C22×C7111yescharacteristic, complemented
546C2×C22⋊C8C22×C7111yescharacteristic, complemented
547C2×C22⋊C8C22×C7111yescharacteristic, complemented
548C2×C22⋊C8C22×C7111yescharacteristic, complemented
549#397—21no—
550#394—21no—
551#391C22×C7111yescharacteristic, complemented
552#389—21no—
553#389C22×C7111yescharacteristic, complemented
554#388—21no—
555#380C22×C7111yescharacteristic, complemented
556#340C22×C7111yescharacteristic, complemented
557#340C22×C7111yescharacteristic, complemented
558#336C22×C7111yescharacteristic, complemented
559#336C22×C7111yescharacteristic, complemented
560C25—21no—
561C25—21no—
562C22×Q8C23×C7111yescharacteristic
563C22×D4—22no—
564C22×D4—22no—
565C22×D4—28no—
566C22×D4—21no—
567C22×D4—21no—
568C22×D4—22no—
569C22×D4—22no—
570C22×D4—22no—
571C22×D4—22no—
572C22×D4—21no—
573C22×D4—21no—
574C22×D4—21no—
575C22×D4—22no—
576C22×D4—21no—
577C22×D4—41no—
578C22×D4—41no—
579C22×D4—41no—
580C22×D4—41no—
581C22×D4—44no—
582C22×D4—44no—
583C22×D4D4×C7111yescharacteristic
584C22×D4D4×C7114yes—
585C22×D4C23×C7111yescharacteristic
586C22×D4C23×C7111yescharacteristic
587C22×D4C23×C7111yescharacteristic
588C23×C4—21no—
589C23×C4C23×C7111yescharacteristic
590C23×C4C23×C7111yescharacteristic
591C2×SD16—22no—
592C2×SD16—22no—
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—41no—
598C2×SD16—41no—
599C2×SD16—41no—
600C2×M16—22no—
601C2×M16—22no—
602C2×M16—41no—
603C22×C8C23×C7111yescharacteristic
604C22×C8C23×C7111yescharacteristic
605C22×C8C23×C7111yescharacteristic
606C22×C8C23×C7111yescharacteristic
607#127—22no—
608#127—22no—
609C22⋊Q8—22no—
610C22⋊Q8—22no—
611C22⋊Q8—22no—
612C22⋊Q8—41no—
613#121—28no—
614#121—22no—
615#121—22no—
616#121—22no—
617#121D4×C7114yes—
618#120—28no—
619#120—28no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—22no—
624#117—22no—
625#117—41no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4D4×C7111yescharacteristic
630C2×C4⋊C4C23×C7111yescharacteristic
631C2×C4⋊C4C23×C7111yescharacteristic
632C2×C4⋊C4C23×C7111yescharacteristic
633C2×C4⋊C4C23×C7111yescharacteristic
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4D4×C7111yescharacteristic
642C2×C22⋊C4D4×C7111yescharacteristic
643C2×C42—21no—
644C2×C42C23×C7111yescharacteristic
645#107—22no—
646#103—22no—
647#102—22no—
648#102—22no—
649#102—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—41no—
655#102D4×C7114yescomplemented
656C22⋊C8—22no—
657C22⋊C8—22no—
658C22⋊C8—41no—
659#95—21no—
660#95—21no—
661#95—21no—
662#95—21no—
663C24—21no—
664C24—24no—
665C24—21no—
666C24—21no—
667C24—24no—
668C24—42no—
669C24—42no—
670C24—42no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—81no—
677C24—81no—
678C24—81no—
679C24—81no—
680C24C2×D4×C7111yescharacteristic
681C24C2×D4×C7111yescharacteristic
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—28no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—22no—
698C2×D4—21no—
699C2×D4—21no—
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—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—432no—
722C2×D4—44no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—44no—
728C2×D4—42no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4C2×D4×C7112yes—
732C2×D4C2×D4×C7112yes—
733C2×D4C2×D4×C7112yes—
734C2×D4C2×D4×C7112yes—
735C2×D4#41×C7112yes—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—24no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
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—42no—
753C22×C4—42no—
754C22×C4C2×D4×C7111yescharacteristic
755C22×C4C2×D4×C7111yescharacteristic
756C22×C4C2×D4×C7111yescharacteristic
757C22×C4C2×D4×C7112yes—
758C22×C4C2×D4×C7112yes—
759C22×C4C2×D4×C7111yescharacteristic
760C22×C4C24×C7111yescharacteristic
761SD16—44no—
762SD16—44no—
763SD16—44no—
764M16—44no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8C2×D4×C7112yescomplemented
777C4⋊C4—22no—
778C4⋊C4—21no—
779C4⋊C4—21no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—42no—
785C4⋊C4—42no—
786C4⋊C4—42no—
787C4⋊C4C2×D4×C7112yes—
788C4⋊C4C2×D4×C7112yescomplemented
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—22no—
792C22⋊C4—24no—
793C22⋊C4—22no—
794C22⋊C4—42no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C42—21no—
799C42—21no—
800C42—42no—
801C23—21no—
802C23—22no—
803C23—21no—
804C23—21no—
805C23—22no—
806C23—21no—
807C23—21no—
808C23—22no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—22no—
817C23—22no—
818C23—48no—
819C23—48no—
820C23—48no—
821C23—48no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—84no—
839C23—84no—
840C23—84no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23#120×C7112yes—
849C23AGL(1,ℤ/8)×C7112yes—
850C23C22×D4×C7111yescharacteristic
851Q8—41no—
852Q8—41no—
853Q8—41no—
854Q8—41no—
855D4—28no—
856D4—22no—
857D4—22no—
858D4—22no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—48no—
864D4—48no—
865D4—48no—
866D4—48no—
867D4—48no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—84no—
873D4#121×C7114yes—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—48no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
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#120×C7112yes—
909C2×C4AGL(1,ℤ/8)×C7112yes—
910C2×C4C22×D4×C7111yescharacteristic
911C2×C4C22×D4×C7111yescharacteristic
912C2×C4C22×D4×C7111yescharacteristic
913C2×C4C2×#41×C7111yescharacteristic
914C2×C4H(5,𝔽2)×C7111yescharacteristic
915C2×C4H(5,𝔽2)×C7111yescharacteristic
916C8—22no—
917C8—41no—
918C8—41no—
919C8—41no—
920C22—22no—
921C22—22no—
922C22—24no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—41no—
928C22—42no—
929C22—41no—
930C22—41no—
931C22—42no—
932C22—41no—
933C22—42no—
934C22—41no—
935C22—42no—
936C22—41no—
937C22—42no—
938C22—41no—
939C22—41no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—816no—
948C22—816no—
949C22—81no—
950C22—81no—
951C22—81no—
952C22—81no—
953C22—81no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22C2×#120×C7111yescharacteristic
958C22D42×C7111yescharacteristic
959C22#546×C7111yescharacteristic
960C22C2×AGL(1,ℤ/8)×C7111yescharacteristic
961C22C2×AGL(1,ℤ/8)×C7111yescharacteristic
962C22#577×C7111yescharacteristic
963C22#577×C7111yescharacteristic
964C4—22no—
965C4—22no—
966C4—41no—
967C4—42no—
968C4—41no—
969C4—42no—
970C4—81no—
971C4—81no—
972C4—81no—
973C4C2×#121×C7111yescharacteristic
974C4#534×C7111yescharacteristic
975C4D42×C7111yescharacteristic
976C4#546×C7111yescharacteristic
977C2—42no—
978C2—42no—
979C2—44no—
980C2—82no—
981C2—82no—
982C2C71×#241011yescharacteristic
983C2C71×#300311yescharacteristic
984C2C71×#300911yescharacteristic
985C2C71×#326511yescharacteristic
986C2C71×#327211yescharacteristic
987C2C71×#331011yescharacteristic
988C2C71×#332411yescharacteristic
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×#468×C71C2semidirect
3. C2×#450×C71C2semidirect
4. C2×#450×C71C2semidirect
5. C2×#418×C71C2semidirect
6. C71×#2415C2semidirect
7. C71×#2041C2semidirect
8. C71×#2033C2semidirect
9. C71×#2014C2semidirect
10. C71×#2000C2semidirect
11. C71×#1877C2semidirect
12. C71×#1875C2semidirect
13. C71×#1870C2semidirect
14. C71×#1862C2semidirect
15. C71×#1786C2semidirect
20. C22×SD16×C71C22semidirect
21. C22×SD16×C71C22semidirect
22. C22×M16×C71C22semidirect
26. C2×C22⋊Q8×C71C22semidirect
27. C2×C22⋊Q8×C71C22semidirect
35. C2×#117×C71C22semidirect
39. C2×#107×C71C22semidirect
41. 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
58. #389×C71C22semidirect
60. #380×C71C22semidirect
61. #340×C71C22semidirect
62. #340×C71C22semidirect
63. #336×C71C22semidirect
64. #336×C71C22semidirect
160. #102×C71D4semidirect
281. C2×C8×C71C2×D4semidirect
293. C4⋊C4×C71C2×D4semidirect
482. #24448C71direct (N × H)
496. C2×#468C2×C71semidirect
497. C2×#450C2×C71semidirect
498. C2×#450C2×C71semidirect
499. C2×#418C2×C71semidirect
500. #2415C2×C71semidirect
501. #2041C2×C71semidirect
502. #2033C2×C71semidirect
503. #2014C2×C71semidirect
504. #2000C2×C71semidirect
505. #1877C2×C71semidirect
506. #1875C2×C71semidirect
507. #1870C2×C71semidirect
508. #1862C2×C71semidirect
509. #1786C2×C71semidirect
510. C71#24448direct (N × H)
515. C22×SD16C22×C71semidirect
516. C22×SD16C22×C71semidirect
517. C22×M16C22×C71semidirect
521. C2×C22⋊Q8C22×C71semidirect
522. C2×C22⋊Q8C22×C71semidirect
530. C2×#117C22×C71semidirect
534. C2×#107C22×C71semidirect
536. C2×#103C22×C71semidirect
540. C2×#102C22×C71semidirect
541. C2×#102C22×C71semidirect
542. C2×#102C22×C71semidirect
543. C2×#102C22×C71semidirect
544. C2×#102C22×C71semidirect
545. C2×#102C22×C71semidirect
546. C2×C22⋊C8C22×C71semidirect
547. C2×C22⋊C8C22×C71semidirect
548. C2×C22⋊C8C22×C71semidirect
551. #391C22×C71semidirect
553. #389C22×C71semidirect
555. #380C22×C71semidirect
556. #340C22×C71semidirect
557. #340C22×C71semidirect
558. #336C22×C71semidirect
559. #336C22×C71semidirect
655. #102D4×C71semidirect
776. C2×C8C2×D4×C71semidirect
788. 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×#468×C712
C2×#450×C712
C2×#418×C712
C71×#24152
C71×#20412
C71×#20332
C71×#20142
C71×#20002
C71×#18772
C71×#18752
C71×#18702
C71×#18622
C71×#17862
#2444871