Finite Group Databasebeta

← C71×#24451 #31845323

Subgroups — C71×#24451 #31845323

Order 18176.

1580 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C71C211yesmaximal, characteristic, complemented
2C2×#469×C71C211yesmaximal, characteristic, complemented
3C2×#449×C71C211yesmaximal, characteristic, complemented
4C2×#449×C71C211yesmaximal, characteristic, complemented
5C2×#417×C71C211yesmaximal, characteristic, complemented
6C71×#2416C211yesmaximal, characteristic, complemented
7C71×#2041C211yesmaximal, characteristic, complemented
8C71×#2034C211yesmaximal, characteristic, complemented
9C71×#2011C211yesmaximal, characteristic, complemented
10C71×#1999C211yesmaximal, characteristic, complemented
11C71×#1880C211yesmaximal, characteristic, complemented
12C71×#1874C211yesmaximal, characteristic, complemented
13C71×#1870C211yesmaximal, characteristic, complemented
14C71×#1865C211yesmaximal, characteristic, complemented
15C71×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C71C2211yescharacteristic
17C22×#41×C71C2211yescharacteristic
18C22×SD16×C71C2211yescharacteristic
19C22×D8×C71C2211yescharacteristic
20C22×D8×C71C2211yescharacteristic
21C22×M16×C71C2211yescharacteristic
22#550×C71—24no—
23#550×C71—24no—
24C2×#127×C71—21no—
25C2×#127×C71C2211yescharacteristic
26C2×#121×C71—21no—
27C2×#121×C71—21no—
28C2×#121×C71—21no—
29C2×#121×C71C2211yescharacteristic
30C2×#121×C71C2211yescharacteristic
31C2×#121×C71C2211yescharacteristic
32C2×#121×C71C2211yescharacteristic
33C2×C4×Q8×C71C2211yescharacteristic
34C2×C4×D4×C71—21no—
35C2×C4×D4×C71C2211yescharacteristic
36C22×C4⋊C4×C71C2211yescharacteristic
37#469×C71—24no—
38#449×C71—24no—
39#449×C71—24no—
40C2×#106×C71C2211yescharacteristic
41#417×C71—24no—
42C2×#103×C71C2211yescharacteristic
43C2×#103×C71C2211yescharacteristic
44C2×#103×C71C2211yescharacteristic
45C2×#102×C71C2211yescharacteristic
46C2×#102×C71C2211yescharacteristic
47C2×#102×C71C2211yescharacteristic
48C2×#102×C71C2211yescharacteristic
49C2×#102×C71C2211yescharacteristic
50C2×#102×C71C2211yescharacteristic
51C2×#102×C71C2211yescharacteristic
52C2×C22⋊C8×C71C2211yescharacteristic
53C2×C22⋊C8×C71C2211yescharacteristic
54C2×C22⋊C8×C71C2211yescharacteristic
55#396×C71—21no—
56#394×C71—21no—
57#390×C71C2211yescharacteristic
58#389×C71C2211yescharacteristic
59#386×C71—21no—
60#380×C71C2211yescharacteristic
61#340×C71C2211yescharacteristic
62#340×C71C2211yescharacteristic
63#336×C71C2211yescharacteristic
64#336×C71C2211yescharacteristic
65C2×#41×C71—22no—
66C2×#41×C71—22no—
67C2×#41×C71—22no—
68C2×#41×C71—22no—
69C2×#41×C71—22no—
70C2×#41×C71—22no—
71C2×#41×C71—22no—
72C2×#41×C71—41no—
73C2×#41×C71—41no—
74C2×#41×C71—41no—
75C2×#41×C71—41no—
76C2×#41×C71D414yescomplemented
77C22×Q8×C71C2311yescharacteristic
78C22×D4×C71—21no—
79C22×D4×C71—21no—
80C22×D4×C71—21no—
81C22×D4×C71—21no—
82C22×D4×C71—21no—
83C22×D4×C71—21no—
84C22×D4×C71—21no—
85C22×D4×C71—21no—
86C22×D4×C71D411yescharacteristic
87C22×D4×C71C2311yescharacteristic
88C22×D4×C71C2311yescharacteristic
89C22×D4×C71C2311yescharacteristic
90C23×C4×C71—21no—
91C23×C4×C71—21no—
92C23×C4×C71—21no—
93C23×C4×C71C2311yescharacteristic
94C23×C4×C71C2311yescharacteristic
95C2×SD16×C71—22no—
96C2×SD16×C71—22no—
97C2×SD16×C71—22no—
98C2×D8×C71—22no—
99C2×D8×C71—22no—
100C2×D8×C71—22no—
101C2×D8×C71—41no—
102C2×D8×C71—41no—
103C2×D8×C71—41no—
104C2×M16×C71—22no—
105C2×M16×C71—22no—
106C2×M16×C71—41no—
107C22×C8×C71C2311yescharacteristic
108C22×C8×C71C2311yescharacteristic
109C22×C8×C71C2311yescharacteristic
110C22×C8×C71C2311yescharacteristic
111#127×C71—28no—
112#127×C71—22no—
113#127×C71—22no—
114#121×C71—28no—
115#121×C71—28no—
116#121×C71—22no—
117#121×C71—22no—
118#121×C71—22no—
119#121×C71—22no—
120#121×C71—22no—
121#121×C71—22no—
122#121×C71—41no—
123#121×C71—44no—
124#121×C71D414yescomplemented
125C4×Q8×C71—22no—
126C4×Q8×C71—22no—
127C4×D4×C71—28no—
128C4×D4×C71—22no—
129C4×D4×C71—22no—
130C2×C4⋊C4×C71—21no—
131C2×C4⋊C4×C71—22no—
132C2×C4⋊C4×C71—21no—
133C2×C4⋊C4×C71—21no—
134C2×C4⋊C4×C71—41no—
135C2×C4⋊C4×C71D411yescharacteristic
136C2×C4⋊C4×C71C2311yescharacteristic
137C2×C4⋊C4×C71C2311yescharacteristic
138C2×C4⋊C4×C71C2311yescharacteristic
139C2×C4⋊C4×C71C2311yescharacteristic
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×C71D411yescharacteristic
148C2×C22⋊C4×C71D411yescharacteristic
149C2×C42×C71—21no—
150C2×C42×C71C2311yescharacteristic
151#106×C71—22no—
152#103×C71—22no—
153#103×C71—22no—
154#103×C71D414yescomplemented
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—
162C22⋊C8×C71—22no—
163C22⋊C8×C71—22no—
164C22⋊C8×C71—41no—
165#95×C71—21no—
166#95×C71—21no—
167C24×C71—21no—
168C24×C71—21no—
169C24×C71—21no—
170C24×C71C2×D411yescharacteristic
171C24×C71C2×D411yescharacteristic
172#41×C71—28no—
173#41×C71—44no—
174#41×C71—44no—
175#41×C71—44no—
176#41×C71—44no—
177#41×C71—44no—
178#41×C71—44no—
179#41×C71—44no—
180C2×Q8×C71—21no—
181C2×Q8×C71—21no—
182C2×Q8×C71—21no—
183C2×Q8×C71C2×D412yes—
184C2×Q8×C71C2×D412yes—
185C2×Q8×C71#4112yes—
186C2×D4×C71—24no—
187C2×D4×C71—24no—
188C2×D4×C71—22no—
189C2×D4×C71—24no—
190C2×D4×C71—24no—
191C2×D4×C71—24no—
192C2×D4×C71—24no—
193C2×D4×C71—22no—
194C2×D4×C71—21no—
195C2×D4×C71—21no—
196C2×D4×C71—21no—
197C2×D4×C71—21no—
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—41no—
211C2×D4×C71—42no—
212C2×D4×C71—42no—
213C2×D4×C71—42no—
214C2×D4×C71—42no—
215C2×D4×C71—42no—
216C2×D4×C71—42no—
217C2×D4×C71—42no—
218C2×D4×C71—42no—
219C2×D4×C71—42no—
220C2×D4×C71—42no—
221C2×D4×C71—42no—
222C2×D4×C71—81no—
223C2×D4×C71—81no—
224C2×D4×C71—81no—
225C2×D4×C71—81no—
226C2×D4×C71—81no—
227C2×D4×C71—81no—
228C2×D4×C71—81no—
229C2×D4×C71C2×D412yes—
230C2×D4×C71C2×D412yes—
231C22×C4×C71—21no—
232C22×C4×C71—21no—
233C22×C4×C71—21no—
234C22×C4×C71—21no—
235C22×C4×C71—21no—
236C22×C4×C71—24no—
237C22×C4×C71—21no—
238C22×C4×C71—21no—
239C22×C4×C71—24no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71—42no—
249C22×C4×C71—42no—
250C22×C4×C71—42no—
251C22×C4×C71—42no—
252C22×C4×C71—42no—
253C22×C4×C71—42no—
254C22×C4×C71—81no—
255C22×C4×C71C2×D411yescharacteristic
256C22×C4×C71C2×D411yescharacteristic
257C22×C4×C71C2×D411yescharacteristic
258C22×C4×C71C2×D412yes—
259C22×C4×C71C2×D412yes—
260C22×C4×C71C2×D411yescharacteristic
261C22×C4×C71C2411yescharacteristic
262SD16×C71—44no—
263D8×C71—44no—
264D8×C71—44no—
265M16×C71—44no—
266C2×C8×C71—21no—
267C2×C8×C71—21no—
268C2×C8×C71—21no—
269C2×C8×C71—21no—
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×C71C2×D412yes—
278C4⋊C4×C71—24no—
279C4⋊C4×C71—22no—
280C4⋊C4×C71—21no—
281C4⋊C4×C71—21no—
282C4⋊C4×C71—21no—
283C4⋊C4×C71—21no—
284C4⋊C4×C71—21no—
285C4⋊C4×C71—21no—
286C4⋊C4×C71—42no—
287C4⋊C4×C71—42no—
288C4⋊C4×C71C2×D412yes—
289C4⋊C4×C71C2×D412yes—
290C22⋊C4×C71—24no—
291C22⋊C4×C71—22no—
292C22⋊C4×C71—24no—
293C22⋊C4×C71—22no—
294C22⋊C4×C71—42no—
295C22⋊C4×C71—42no—
296C22⋊C4×C71—42no—
297C22⋊C4×C71—42no—
298C22⋊C4×C71—81no—
299C42×C71—24no—
300C42×C71—21no—
301C42×C71—21no—
302C23×C71—21no—
303C23×C71—21no—
304C23×C71—21no—
305C23×C71—21no—
306C23×C71—21no—
307C23×C71—21no—
308C23×C71—21no—
309C23×C71—22no—
310C23×C71—22no—
311C23×C71—21no—
312C23×C71—21no—
313C23×C71—21no—
314C23×C71—21no—
315C23×C71—21no—
316C23×C71—21no—
317C23×C71—41no—
318C23×C71—41no—
319C23×C71—41no—
320C23×C71—41no—
321C23×C71—41no—
322C23×C71—41no—
323C23×C71—41no—
324C23×C71—41no—
325C23×C71—41no—
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#12012yes—
337C23×C71C22×D411yescharacteristic
338Q8×C71—22no—
339Q8×C71—22no—
340Q8×C71—22no—
341Q8×C71#12114yescomplemented
342D4×C71—22no—
343D4×C71—22no—
344D4×C71—22no—
345D4×C71—22no—
346D4×C71—44no—
347D4×C71—48no—
348D4×C71—48no—
349D4×C71—48no—
350D4×C71—41no—
351D4×C71—41no—
352D4×C71—41no—
353D4×C71—41no—
354D4×C71—41no—
355D4×C71—41no—
356D4×C71—41no—
357D4×C71—41no—
358D4×C71—84no—
359D4×C71—84no—
360D4×C71—84no—
361D4×C71—84no—
362D4×C71—84no—
363C2×C4×C71—21no—
364C2×C4×C71—22no—
365C2×C4×C71—21no—
366C2×C4×C71—22no—
367C2×C4×C71—21no—
368C2×C4×C71—22no—
369C2×C4×C71—21no—
370C2×C4×C71—22no—
371C2×C4×C71—22no—
372C2×C4×C71—22no—
373C2×C4×C71—22no—
374C2×C4×C71—21no—
375C2×C4×C71—22no—
376C2×C4×C71—21no—
377C2×C4×C71—21no—
378C2×C4×C71—22no—
379C2×C4×C71—21no—
380C2×C4×C71—21no—
381C2×C4×C71—21no—
382C2×C4×C71—48no—
383C2×C4×C71—48no—
384C2×C4×C71—41no—
385C2×C4×C71—41no—
386C2×C4×C71—41no—
387C2×C4×C71—41no—
388C2×C4×C71—41no—
389C2×C4×C71—41no—
390C2×C4×C71—41no—
391C2×C4×C71—41no—
392C2×C4×C71—41no—
393C2×C4×C71—41no—
394C2×C4×C71—41no—
395C2×C4×C71—41no—
396C2×C4×C71—41no—
397C2×C4×C71—41no—
398C2×C4×C71—84no—
399C2×C4×C71#12012yes—
400C2×C4×C71AGL(1,ℤ/8)12yes—
401C2×C4×C71C22×D411yescharacteristic
402C2×C4×C71C22×D411yescharacteristic
403C2×C4×C71C22×D411yescharacteristic
404C2×C4×C71C2×#4111yescharacteristic
405C2×C4×C71H(5,𝔽2)11yescharacteristic
406C2×C4×C71H(5,𝔽2)11yescharacteristic
407C8×C71—22no—
408C8×C71—41no—
409C8×C71—41no—
410C8×C71—41no—
411C22×C71—22no—
412C22×C71—22no—
413C22×C71—22no—
414C22×C71—41no—
415C22×C71—41no—
416C22×C71—41no—
417C22×C71—41no—
418C22×C71—41no—
419C22×C71—42no—
420C22×C71—42no—
421C22×C71—41no—
422C22×C71—41no—
423C22×C71—42no—
424C22×C71—42no—
425C22×C71—41no—
426C22×C71—42no—
427C22×C71—42no—
428C22×C71—41no—
429C22×C71—41no—
430C22×C71—41no—
431C22×C71—81no—
432C22×C71—81no—
433C22×C71—81no—
434C22×C71—81no—
435C22×C71—81no—
436C22×C71—81no—
437C22×C71—81no—
438C22×C71—81no—
439C22×C71—81no—
440C22×C71—81no—
441C22×C71—81no—
442C22×C71—81no—
443C22×C71—81no—
444C22×C71—81no—
445C22×C71—81no—
446C22×C71C2×#12011yescharacteristic
447C22×C71D4211yescharacteristic
448C22×C71#54611yescharacteristic
449C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
450C22×C71#57511yescharacteristic
451C22×C71#57611yescharacteristic
452C22×C71#57711yescharacteristic
453C4×C71—22no—
454C4×C71—24no—
455C4×C71—22no—
456C4×C71—41no—
457C4×C71—41no—
458C4×C71—42no—
459C4×C71—42no—
460C4×C71—81no—
461C4×C71—81no—
462C4×C71C2×#12111yescharacteristic
463C4×C71#53411yescharacteristic
464C4×C71D4211yescharacteristic
465C4×C71#54611yescharacteristic
466#24451C7111yesmaximal, characteristic, direct product factor, Sylow
467C2×C71—42no—
468C2×C71—81no—
469C2×C71—82no—
470C2×C71—82no—
471C2×C71—161no—
472C2×C71#241011yescharacteristic
473C2×C71#300611yescharacteristic
474C2×C71#301211yescharacteristic
475C2×C71#327111yescharacteristic
476C2×C71#327411yescharacteristic
477C2×C71#330911yescharacteristic
478C2×C71#333211yescharacteristic
479C2×#550C2×C7111yescharacteristic, complemented
480C2×#469C2×C7111yescharacteristic, complemented
481C2×#449C2×C7111yescharacteristic, complemented
482C2×#449C2×C7111yescharacteristic, complemented
483C2×#417C2×C7111yescharacteristic, complemented
484#2416C2×C7111yescharacteristic, complemented
485#2041C2×C7111yescharacteristic, complemented
486#2034C2×C7111yescharacteristic, complemented
487#2011C2×C7111yescharacteristic, complemented
488#1999C2×C7111yescharacteristic, complemented
489#1880C2×C7111yescharacteristic, complemented
490#1874C2×C7111yescharacteristic, complemented
491#1870C2×C7111yescharacteristic, complemented
492#1865C2×C7111yescharacteristic, complemented
493#1788C2×C7111yescharacteristic, complemented
494C71#2445111yescharacteristic, direct product factor, Sylow
495C22×#41C22×C7111yescharacteristic
496C22×#41C22×C7111yescharacteristic
497C22×SD16C22×C7111yescharacteristic
498C22×D8C22×C7111yescharacteristic
499C22×D8C22×C7111yescharacteristic
500C22×M16C22×C7111yescharacteristic
501#550—24no—
502#550—24no—
503C2×#127—21no—
504C2×#127C22×C7111yescharacteristic
505C2×#121—21no—
506C2×#121—21no—
507C2×#121—21no—
508C2×#121C22×C7111yescharacteristic
509C2×#121C22×C7111yescharacteristic
510C2×#121C22×C7111yescharacteristic
511C2×#121C22×C7111yescharacteristic
512C2×C4×Q8C22×C7111yescharacteristic
513C2×C4×D4—21no—
514C2×C4×D4C22×C7111yescharacteristic
515C22×C4⋊C4C22×C7111yescharacteristic
516#469—24no—
517#449—24no—
518#449—24no—
519C2×#106C22×C7111yescharacteristic
520#417—24no—
521C2×#103C22×C7111yescharacteristic
522C2×#103C22×C7111yescharacteristic
523C2×#103C22×C7111yescharacteristic
524C2×#102C22×C7111yescharacteristic
525C2×#102C22×C7111yescharacteristic
526C2×#102C22×C7111yescharacteristic
527C2×#102C22×C7111yescharacteristic
528C2×#102C22×C7111yescharacteristic
529C2×#102C22×C7111yescharacteristic
530C2×#102C22×C7111yescharacteristic
531C2×C22⋊C8C22×C7111yescharacteristic
532C2×C22⋊C8C22×C7111yescharacteristic
533C2×C22⋊C8C22×C7111yescharacteristic
534#396—21no—
535#394—21no—
536#390C22×C7111yescharacteristic
537#389C22×C7111yescharacteristic
538#386—21no—
539#380C22×C7111yescharacteristic
540#340C22×C7111yescharacteristic
541#340C22×C7111yescharacteristic
542#336C22×C7111yescharacteristic
543#336C22×C7111yescharacteristic
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C2×#41—41no—
555C2×#41D4×C7114yescomplemented
556C22×Q8C23×C7111yescharacteristic
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4D4×C7111yescharacteristic
566C22×D4C23×C7111yescharacteristic
567C22×D4C23×C7111yescharacteristic
568C22×D4C23×C7111yescharacteristic
569C23×C4—21no—
570C23×C4—21no—
571C23×C4—21no—
572C23×C4C23×C7111yescharacteristic
573C23×C4C23×C7111yescharacteristic
574C2×SD16—22no—
575C2×SD16—22no—
576C2×SD16—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C2×D8—41no—
582C2×D8—41no—
583C2×M16—22no—
584C2×M16—22no—
585C2×M16—41no—
586C22×C8C23×C7111yescharacteristic
587C22×C8C23×C7111yescharacteristic
588C22×C8C23×C7111yescharacteristic
589C22×C8C23×C7111yescharacteristic
590#127—28no—
591#127—22no—
592#127—22no—
593#121—28no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—41no—
602#121—44no—
603#121D4×C7114yescomplemented
604C4×Q8—22no—
605C4×Q8—22no—
606C4×D4—28no—
607C4×D4—22no—
608C4×D4—22no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4D4×C7111yescharacteristic
615C2×C4⋊C4C23×C7111yescharacteristic
616C2×C4⋊C4C23×C7111yescharacteristic
617C2×C4⋊C4C23×C7111yescharacteristic
618C2×C4⋊C4C23×C7111yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4D4×C7111yescharacteristic
627C2×C22⋊C4D4×C7111yescharacteristic
628C2×C42—21no—
629C2×C42C23×C7111yescharacteristic
630#106—22no—
631#103—22no—
632#103—22no—
633#103D4×C7114yescomplemented
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—41no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—41no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24C2×D4×C7111yescharacteristic
650C24C2×D4×C7111yescharacteristic
651#41—28no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656#41—44no—
657#41—44no—
658#41—44no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8C2×D4×C7112yes—
663C2×Q8C2×D4×C7112yes—
664C2×Q8#41×C7112yes—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—22no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—41no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4C2×D4×C7112yes—
709C2×D4C2×D4×C7112yes—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—81no—
734C22×C4C2×D4×C7111yescharacteristic
735C22×C4C2×D4×C7111yescharacteristic
736C22×C4C2×D4×C7111yescharacteristic
737C22×C4C2×D4×C7112yes—
738C22×C4C2×D4×C7112yes—
739C22×C4C2×D4×C7111yescharacteristic
740C22×C4C24×C7111yescharacteristic
741SD16—44no—
742D8—44no—
743D8—44no—
744M16—44no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8C2×D4×C7112yes—
757C4⋊C4—24no—
758C4⋊C4—22no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4C2×D4×C7112yes—
768C4⋊C4C2×D4×C7112yes—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—42no—
774C22⋊C4—42no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—81no—
778C42—24no—
779C42—21no—
780C42—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23#120×C7112yes—
816C23C22×D4×C7111yescharacteristic
817Q8—22no—
818Q8—22no—
819Q8—22no—
820Q8#121×C7114yescomplemented
821D4—22no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—44no—
826D4—48no—
827D4—48no—
828D4—48no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—84no—
838D4—84no—
839D4—84no—
840D4—84no—
841D4—84no—
842C2×C4—21no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—22no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—48no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—84no—
878C2×C4#120×C7112yes—
879C2×C4AGL(1,ℤ/8)×C7112yes—
880C2×C4C22×D4×C7111yescharacteristic
881C2×C4C22×D4×C7111yescharacteristic
882C2×C4C22×D4×C7111yescharacteristic
883C2×C4C2×#41×C7111yescharacteristic
884C2×C4H(5,𝔽2)×C7111yescharacteristic
885C2×C4H(5,𝔽2)×C7111yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—42no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22C2×#120×C7111yescharacteristic
926C22D42×C7111yescharacteristic
927C22#546×C7111yescharacteristic
928C22C2×AGL(1,ℤ/8)×C7111yescharacteristic
929C22#575×C7111yescharacteristic
930C22#576×C7111yescharacteristic
931C22#577×C7111yescharacteristic
932C4—22no—
933C4—24no—
934C4—22no—
935C4—41no—
936C4—41no—
937C4—42no—
938C4—42no—
939C4—81no—
940C4—81no—
941C4C2×#121×C7111yescharacteristic
942C4#534×C7111yescharacteristic
943C4D42×C7111yescharacteristic
944C4#546×C7111yescharacteristic
945C2—42no—
946C2—81no—
947C2—82no—
948C2—82no—
949C2—161no—
950C2C71×#241011yescharacteristic
951C2C71×#300611yescharacteristic
952C2C71×#301211yescharacteristic
953C2C71×#327111yescharacteristic
954C2C71×#327411yescharacteristic
955C2C71×#330911yescharacteristic
956C2C71×#333211yescharacteristic
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×#550×C71C2semidirect
2. C2×#469×C71C2semidirect
3. C2×#449×C71C2semidirect
4. C2×#449×C71C2semidirect
5. C2×#417×C71C2semidirect
6. C71×#2416C2semidirect
7. C71×#2041C2semidirect
8. C71×#2034C2semidirect
9. C71×#2011C2semidirect
10. C71×#1999C2semidirect
11. C71×#1880C2semidirect
12. C71×#1874C2semidirect
13. C71×#1870C2semidirect
14. C71×#1865C2semidirect
15. C71×#1788C2semidirect
76. C2×#41×C71D4semidirect
124. #121×C71D4semidirect
154. #103×C71D4semidirect
341. Q8×C71#121semidirect
466. #24451C71direct (N × H)
479. C2×#550C2×C71semidirect
480. C2×#469C2×C71semidirect
481. C2×#449C2×C71semidirect
482. C2×#449C2×C71semidirect
483. C2×#417C2×C71semidirect
484. #2416C2×C71semidirect
485. #2041C2×C71semidirect
486. #2034C2×C71semidirect
487. #2011C2×C71semidirect
488. #1999C2×C71semidirect
489. #1880C2×C71semidirect
490. #1874C2×C71semidirect
491. #1870C2×C71semidirect
492. #1865C2×C71semidirect
493. #1788C2×C71semidirect
494. C71#24451direct (N × H)
555. C2×#41D4×C71semidirect
603. #121D4×C71semidirect
633. #103D4×C71semidirect
820. Q8#121×C71semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C712
C2×#469×C712
C2×#449×C712
C2×#417×C712
C71×#24162
C71×#20412
C71×#20342
C71×#20112
C71×#19992
C71×#18802
C71×#18742
C71×#18702
C71×#18652
C71×#17882
#2445171