Finite Group Databasebeta

← C71×#24218 #31845090

Subgroups — C71×#24218 #31845090

Order 18176.

1612 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C71C211yesmaximal, characteristic, complemented
2C2×#463×C71C211yesmaximal, characteristic, complemented
3C2×#459×C71C211yesmaximal, characteristic, complemented
4C2×#449×C71C211yesmaximal, characteristic, complemented
5C2×#447×C71C211yesmaximal, characteristic, complemented
6C71×#2324C211yesmaximal, characteristic, complemented
7C71×#2042C211yesmaximal, characteristic, complemented
8C71×#2041C211yesmaximal, characteristic, complemented
9C71×#2012C211yesmaximal, characteristic, complemented
10C71×#2011C211yesmaximal, characteristic, complemented
11C71×#1983C211yesmaximal, characteristic, complemented
12C71×#1982C211yesmaximal, characteristic, complemented
13C71×#1798C211yesmaximal, characteristic, complemented
14C71×#1788C211yesmaximal, characteristic, complemented
15C71×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C71C2211yescharacteristic
17C23×D4×C71C2211yescharacteristic
18C22×SD16×C71C2211yescharacteristic, complemented
19C22×D8×C71C2211yescharacteristic
20C22×D8×C71C2211yescharacteristic
21C22×D8×C71C2211yescharacteristic, complemented
22#535×C71—24no—
23#535×C71—24no—
24C2×#127×C71C2211yescharacteristic
25C2×#127×C71C2211yescharacteristic
26C2×#124×C71C2211yescharacteristic
27C2×#124×C71C2211yescharacteristic
28C2×#121×C71—21no—
29C2×#121×C71—21no—
30C2×#121×C71C2211yescharacteristic
31C2×#120×C71—21no—
32C2×#120×C71—21no—
33C2×C4×D4×C71C2211yescharacteristic, complemented
34C2×#117×C71C2211yescharacteristic
35#463×C71—24no—
36#459×C71—24no—
37#449×C71—24no—
38#447×C71—24no—
39C2×C4⋊C8×C71C2211yescharacteristic, complemented
40C2×C4⋊C8×C71C2211yescharacteristic, complemented
41C2×#103×C71C2211yescharacteristic, complemented
42C2×#103×C71C2211yescharacteristic, complemented
43C2×#103×C71C2211yescharacteristic, complemented
44C2×#102×C71C2211yescharacteristic
45C2×#102×C71C2211yescharacteristic
46C2×#102×C71C2211yescharacteristic
47C2×#102×C71C2211yescharacteristic
48C2×#102×C71C2211yescharacteristic
49C2×#102×C71C2211yescharacteristic
50C2×#102×C71C2211yescharacteristic, complemented
51C2×#102×C71C2211yescharacteristic, complemented
52C2×#102×C71C2211yescharacteristic, complemented
53C2×C22⋊C8×C71C2211yescharacteristic
54C2×C22⋊C8×C71C2211yescharacteristic
55#390×C71—21no—
56#390×C71C2211yescharacteristic, complemented
57#389×C71C2211yescharacteristic, complemented
58#388×C71—21no—
59#386×C71—21no—
60#385×C71—21no—
61#380×C71C2211yescharacteristic
62C4×C4⋊C4×C71C2211yescharacteristic, complemented
63#336×C71C2211yescharacteristic, complemented
64#336×C71C2211yescharacteristic, complemented
65C25×C71—21no—
66C2×#41×C71—22no—
67C2×#41×C71—22no—
68C2×#41×C71—22no—
69C2×#41×C71—22no—
70C2×#41×C71—41no—
71C2×#41×C71—41no—
72C22×Q8×C71C2311yescharacteristic
73C22×D4×C71—21no—
74C22×D4×C71—21no—
75C22×D4×C71—22no—
76C22×D4×C71—22no—
77C22×D4×C71—21no—
78C22×D4×C71—21no—
79C22×D4×C71—21no—
80C22×D4×C71—21no—
81C22×D4×C71—21no—
82C22×D4×C71—22no—
83C22×D4×C71—22no—
84C22×D4×C71—41no—
85C22×D4×C71—41no—
86C22×D4×C71C2311yescharacteristic
87C22×D4×C71C2311yescharacteristic
88C22×D4×C71C2311yescharacteristic
89C22×D4×C71C2311yescharacteristic
90C23×C4×C71—21no—
91C23×C4×C71—21no—
92C23×C4×C71C2311yescharacteristic
93C2×SD16×C71—22no—
94C2×SD16×C71—22no—
95C2×SD16×C71—41no—
96C2×D8×C71—22no—
97C2×D8×C71—22no—
98C2×D8×C71—22no—
99C2×D8×C71—22no—
100C2×D8×C71—22no—
101C2×D8×C71—22no—
102C2×D8×C71—41no—
103C2×D8×C71—41no—
104C2×D8×C71—41no—
105C22×C8×C71C2311yescharacteristic
106C22×C8×C71C2311yescharacteristic
107C22×C8×C71C2311yescharacteristic
108C22×C8×C71C2311yescharacteristic
109#127×C71—22no—
110#127×C71—22no—
111#127×C71—22no—
112#127×C71D414yescomplemented
113#124×C71—22no—
114#124×C71—22no—
115#124×C71—22no—
116#124×C71D414yescomplemented
117#121×C71—28no—
118#121×C71—28no—
119#121×C71—22no—
120#121×C71D414yescomplemented
121#120×C71—28no—
122#120×C71—28no—
123C4×D4×C71—22no—
124C4×D4×C71—22no—
125#117×C71—22no—
126#117×C71—22no—
127C2×C4⋊C4×C71—21no—
128C2×C4⋊C4×C71D411yescharacteristic
129C2×C4⋊C4×C71D411yescharacteristic
130C2×C4⋊C4×C71C2311yescharacteristic
131C2×C4⋊C4×C71C2311yescharacteristic
132C2×C4⋊C4×C71C2311yescharacteristic
133C2×C22⋊C4×C71—21no—
134C2×C22⋊C4×C71—21no—
135C2×C22⋊C4×C71—21no—
136C2×C22⋊C4×C71—21no—
137C2×C22⋊C4×C71—21no—
138C2×C22⋊C4×C71—21no—
139C2×C22⋊C4×C71—21no—
140C2×C22⋊C4×C71—21no—
141C2×C22⋊C4×C71—21no—
142C2×C22⋊C4×C71D411yescharacteristic
143C2×C22⋊C4×C71D411yescharacteristic
144C2×C42×C71—21no—
145C2×C42×C71C2311yescharacteristic
146C2×C42×C71C2311yescharacteristic
147C4⋊C8×C71—22no—
148C4⋊C8×C71—22no—
149#103×C71—22no—
150#103×C71—22no—
151#103×C71—41no—
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—41no—
159#102×C71—41no—
160#102×C71—41no—
161C22⋊C8×C71—22no—
162C22⋊C8×C71—22no—
163#95×C71—21no—
164#95×C71—21no—
165#95×C71—21no—
166C24×C71—24no—
167C24×C71—21no—
168C24×C71—21no—
169C24×C71—21no—
170C24×C71—21no—
171C24×C71—42no—
172C24×C71—42no—
173C24×C71—81no—
174C24×C71—81no—
175C24×C71—81no—
176C24×C71—81no—
177C24×C71C2×D411yescharacteristic
178#41×C71—44no—
179#41×C71—44no—
180#41×C71—44no—
181#41×C71—44no—
182C2×Q8×C71—21no—
183C2×Q8×C71—21no—
184C2×Q8×C71—21no—
185C2×Q8×C71—21no—
186C2×Q8×C71—21no—
187C2×Q8×C71C2×D412yes—
188C2×D4×C71—24no—
189C2×D4×C71—24no—
190C2×D4×C71—24no—
191C2×D4×C71—24no—
192C2×D4×C71—24no—
193C2×D4×C71—24no—
194C2×D4×C71—24no—
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—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—44no—
219C2×D4×C71—42no—
220C2×D4×C71—42no—
221C2×D4×C71—42no—
222C2×D4×C71—42no—
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×C71—81no—
230C2×D4×C71—81no—
231C2×D4×C71—81no—
232C2×D4×C71—81no—
233C2×D4×C71C2×D412yes—
234C2×D4×C71C2×D412yes—
235C2×D4×C71C2×D412yes—
236C2×D4×C71C2×D412yes—
237C22×C4×C71—21no—
238C22×C4×C71—21no—
239C22×C4×C71—21no—
240C22×C4×C71—21no—
241C22×C4×C71—24no—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—42no—
247C22×C4×C71—42no—
248C22×C4×C71—42no—
249C22×C4×C71—81no—
250C22×C4×C71—81no—
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71C2×D411yescharacteristic
253C22×C4×C71C2×D411yescharacteristic
254C22×C4×C71C2×D411yescharacteristic
255C22×C4×C71C2×D411yescharacteristic
256C22×C4×C71C2×D412yes—
257C22×C4×C71#4112yes—
258C22×C4×C71C2411yescharacteristic
259SD16×C71—44no—
260D8×C71—44no—
261D8×C71—44no—
262D8×C71—44no—
263C2×C8×C71—21no—
264C2×C8×C71—21no—
265C2×C8×C71—21no—
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—
275C4⋊C4×C71—22no—
276C4⋊C4×C71—22no—
277C4⋊C4×C71—21no—
278C4⋊C4×C71—21no—
279C4⋊C4×C71—21no—
280C4⋊C4×C71—21no—
281C4⋊C4×C71—21no—
282C4⋊C4×C71—81no—
283C4⋊C4×C71C2×D412yes—
284C22⋊C4×C71—24no—
285C22⋊C4×C71—24no—
286C22⋊C4×C71—24no—
287C22⋊C4×C71—24no—
288C22⋊C4×C71—22no—
289C22⋊C4×C71—22no—
290C22⋊C4×C71—24no—
291C22⋊C4×C71—42no—
292C22⋊C4×C71—81no—
293C22⋊C4×C71—81no—
294C22⋊C4×C71—81no—
295C42×C71—21no—
296C42×C71—21no—
297C42×C71—81no—
298C42×C71C2×D412yes—
299C42×C71C2×D412yes—
300C23×C71—21no—
301C23×C71—21no—
302C23×C71—21no—
303C23×C71—21no—
304C23×C71—21no—
305C23×C71—21no—
306C23×C71—22no—
307C23×C71—22no—
308C23×C71—22no—
309C23×C71—22no—
310C23×C71—48no—
311C23×C71—41no—
312C23×C71—41no—
313C23×C71—41no—
314C23×C71—41no—
315C23×C71—41no—
316C23×C71—41no—
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—84no—
336C23×C71—84no—
337C23×C71—84no—
338C23×C71—84no—
339C23×C71—84no—
340C23×C71—84no—
341C23×C71#12112yes—
342C23×C71C22×D411yescharacteristic
343Q8×C71—22no—
344Q8×C71—22no—
345Q8×C71—41no—
346Q8×C71—41no—
347D4×C71—22no—
348D4×C71—22no—
349D4×C71—22no—
350D4×C71—22no—
351D4×C71—22no—
352D4×C71—22no—
353D4×C71—22no—
354D4×C71—22no—
355D4×C71—48no—
356D4×C71—48no—
357D4×C71—41no—
358D4×C71—41no—
359D4×C71—41no—
360D4×C71—41no—
361D4×C71—41no—
362D4×C71—41no—
363D4×C71—41no—
364D4×C71—41no—
365D4×C71—84no—
366D4×C71—84no—
367D4×C71—84no—
368D4×C71—84no—
369D4×C71—84no—
370C2×C4×C71—21no—
371C2×C4×C71—21no—
372C2×C4×C71—21no—
373C2×C4×C71—21no—
374C2×C4×C71—21no—
375C2×C4×C71—21no—
376C2×C4×C71—22no—
377C2×C4×C71—22no—
378C2×C4×C71—22no—
379C2×C4×C71—22no—
380C2×C4×C71—21no—
381C2×C4×C71—21no—
382C2×C4×C71—22no—
383C2×C4×C71—22no—
384C2×C4×C71—21no—
385C2×C4×C71—21no—
386C2×C4×C71—21no—
387C2×C4×C71—21no—
388C2×C4×C71—48no—
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—41no—
399C2×C4×C71—84no—
400C2×C4×C71#12012yes—
401C2×C4×C71#12012yes—
402C2×C4×C71#12112yes—
403C2×C4×C71C22×D411yescharacteristic
404C2×C4×C71C22×D411yescharacteristic
405C2×C4×C71C22×D411yescharacteristic
406C2×C4×C71C2×#4111yescharacteristic
407C2×C4×C71H(5,𝔽2)11yescharacteristic
408C2×C4×C71H(5,𝔽2)11yescharacteristic
409C8×C71—41no—
410C8×C71—41no—
411C8×C71—41no—
412C8×C71—41no—
413C22×C71—22no—
414C22×C71—22no—
415C22×C71—22no—
416C22×C71—41no—
417C22×C71—41no—
418C22×C71—41no—
419C22×C71—41no—
420C22×C71—42no—
421C22×C71—42no—
422C22×C71—42no—
423C22×C71—42no—
424C22×C71—42no—
425C22×C71—42no—
426C22×C71—42no—
427C22×C71—42no—
428C22×C71—42no—
429C22×C71—42no—
430C22×C71—42no—
431C22×C71—42no—
432C22×C71—816no—
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×C71—81no—
447C22×C71—81no—
448C22×C71—81no—
449C22×C71C2×#12011yescharacteristic
450C22×C71C2×#12111yescharacteristic
451C22×C71#53511yescharacteristic
452C22×C71#57611yescharacteristic
453C22×C71#57611yescharacteristic
454C22×C71#57611yescharacteristic
455C22×C71#57711yescharacteristic
456C4×C71—22no—
457C4×C71—22no—
458C4×C71—22no—
459C4×C71—42no—
460C4×C71—41no—
461C4×C71—41no—
462C4×C71—42no—
463C4×C71—81no—
464C4×C71—81no—
465C4×C71D4211yescharacteristic
466C4×C71D4211yescharacteristic
467C4×C71#54611yescharacteristic
468C4×C71#54611yescharacteristic
469#24218C7111yesmaximal, characteristic, direct product factor, Sylow
470C2×C71—42no—
471C2×C71—82no—
472C2×C71—82no—
473C2×C71—82no—
474C2×C71—82no—
475C2×C71#240811yescharacteristic
476C2×C71#300811yescharacteristic
477C2×C71#301211yescharacteristic
478C2×C71#304111yescharacteristic
479C2×C71#304511yescharacteristic
480C2×C71#322011yescharacteristic
481C2×C71#322411yescharacteristic
482C2×#535C2×C7111yescharacteristic, complemented
483C2×#463C2×C7111yescharacteristic, complemented
484C2×#459C2×C7111yescharacteristic, complemented
485C2×#449C2×C7111yescharacteristic, complemented
486C2×#447C2×C7111yescharacteristic, complemented
487#2324C2×C7111yescharacteristic, complemented
488#2042C2×C7111yescharacteristic, complemented
489#2041C2×C7111yescharacteristic, complemented
490#2012C2×C7111yescharacteristic, complemented
491#2011C2×C7111yescharacteristic, complemented
492#1983C2×C7111yescharacteristic, complemented
493#1982C2×C7111yescharacteristic, complemented
494#1798C2×C7111yescharacteristic, complemented
495#1788C2×C7111yescharacteristic, complemented
496#1786C2×C7111yescharacteristic, complemented
497C71#2421811yescharacteristic, direct product factor, Sylow
498C22×#41C22×C7111yescharacteristic
499C23×D4C22×C7111yescharacteristic
500C22×SD16C22×C7111yescharacteristic, complemented
501C22×D8C22×C7111yescharacteristic
502C22×D8C22×C7111yescharacteristic
503C22×D8C22×C7111yescharacteristic, complemented
504#535—24no—
505#535—24no—
506C2×#127C22×C7111yescharacteristic
507C2×#127C22×C7111yescharacteristic
508C2×#124C22×C7111yescharacteristic
509C2×#124C22×C7111yescharacteristic
510C2×#121—21no—
511C2×#121—21no—
512C2×#121C22×C7111yescharacteristic
513C2×#120—21no—
514C2×#120—21no—
515C2×C4×D4C22×C7111yescharacteristic, complemented
516C2×#117C22×C7111yescharacteristic
517#463—24no—
518#459—24no—
519#449—24no—
520#447—24no—
521C2×C4⋊C8C22×C7111yescharacteristic, complemented
522C2×C4⋊C8C22×C7111yescharacteristic, complemented
523C2×#103C22×C7111yescharacteristic, complemented
524C2×#103C22×C7111yescharacteristic, complemented
525C2×#103C22×C7111yescharacteristic, complemented
526C2×#102C22×C7111yescharacteristic
527C2×#102C22×C7111yescharacteristic
528C2×#102C22×C7111yescharacteristic
529C2×#102C22×C7111yescharacteristic
530C2×#102C22×C7111yescharacteristic
531C2×#102C22×C7111yescharacteristic
532C2×#102C22×C7111yescharacteristic, complemented
533C2×#102C22×C7111yescharacteristic, complemented
534C2×#102C22×C7111yescharacteristic, complemented
535C2×C22⋊C8C22×C7111yescharacteristic
536C2×C22⋊C8C22×C7111yescharacteristic
537#390—21no—
538#390C22×C7111yescharacteristic, complemented
539#389C22×C7111yescharacteristic, complemented
540#388—21no—
541#386—21no—
542#385—21no—
543#380C22×C7111yescharacteristic
544C4×C4⋊C4C22×C7111yescharacteristic, complemented
545#336C22×C7111yescharacteristic, complemented
546#336C22×C7111yescharacteristic, complemented
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8C23×C7111yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—22no—
565C22×D4—22no—
566C22×D4—41no—
567C22×D4—41no—
568C22×D4C23×C7111yescharacteristic
569C22×D4C23×C7111yescharacteristic
570C22×D4C23×C7111yescharacteristic
571C22×D4C23×C7111yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C7111yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—41no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—41no—
585C2×D8—41no—
586C2×D8—41no—
587C22×C8C23×C7111yescharacteristic
588C22×C8C23×C7111yescharacteristic
589C22×C8C23×C7111yescharacteristic
590C22×C8C23×C7111yescharacteristic
591#127—22no—
592#127—22no—
593#127—22no—
594#127D4×C7114yescomplemented
595#124—22no—
596#124—22no—
597#124—22no—
598#124D4×C7114yescomplemented
599#121—28no—
600#121—28no—
601#121—22no—
602#121D4×C7114yescomplemented
603#120—28no—
604#120—28no—
605C4×D4—22no—
606C4×D4—22no—
607#117—22no—
608#117—22no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4D4×C7111yescharacteristic
611C2×C4⋊C4D4×C7111yescharacteristic
612C2×C4⋊C4C23×C7111yescharacteristic
613C2×C4⋊C4C23×C7111yescharacteristic
614C2×C4⋊C4C23×C7111yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4D4×C7111yescharacteristic
625C2×C22⋊C4D4×C7111yescharacteristic
626C2×C42—21no—
627C2×C42C23×C7111yescharacteristic
628C2×C42C23×C7111yescharacteristic
629C4⋊C8—22no—
630C4⋊C8—22no—
631#103—22no—
632#103—22no—
633#103—41no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—41no—
641#102—41no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—42no—
654C24—42no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24—81no—
659C24C2×D4×C7111yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8C2×D4×C7112yes—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—24no—
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—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4—81no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4C2×D4×C7112yes—
716C2×D4C2×D4×C7112yes—
717C2×D4C2×D4×C7112yes—
718C2×D4C2×D4×C7112yes—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—24no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—81no—
732C22×C4—81no—
733C22×C4C2×D4×C7111yescharacteristic
734C22×C4C2×D4×C7111yescharacteristic
735C22×C4C2×D4×C7111yescharacteristic
736C22×C4C2×D4×C7111yescharacteristic
737C22×C4C2×D4×C7111yescharacteristic
738C22×C4C2×D4×C7112yes—
739C22×C4#41×C7112yes—
740C22×C4C24×C7111yescharacteristic
741SD16—44no—
742D8—44no—
743D8—44no—
744D8—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×C8—21no—
757C4⋊C4—22no—
758C4⋊C4—22no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—81no—
765C4⋊C4C2×D4×C7112yes—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—24no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
777C42—21no—
778C42—21no—
779C42—81no—
780C42C2×D4×C7112yes—
781C42C2×D4×C7112yes—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—48no—
793C23—41no—
794C23—41no—
795C23—41no—
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—41no—
816C23—41no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23#121×C7112yes—
824C23C22×D4×C7111yescharacteristic
825Q8—22no—
826Q8—22no—
827Q8—41no—
828Q8—41no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—48no—
838D4—48no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4—84no—
851D4—84no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—48no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—84no—
882C2×C4#120×C7112yes—
883C2×C4#120×C7112yes—
884C2×C4#121×C7112yes—
885C2×C4C22×D4×C7111yescharacteristic
886C2×C4C22×D4×C7111yescharacteristic
887C2×C4C22×D4×C7111yescharacteristic
888C2×C4C2×#41×C7111yescharacteristic
889C2×C4H(5,𝔽2)×C7111yescharacteristic
890C2×C4H(5,𝔽2)×C7111yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—816no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C7111yescharacteristic
932C22C2×#121×C7111yescharacteristic
933C22#535×C7111yescharacteristic
934C22#576×C7111yescharacteristic
935C22#576×C7111yescharacteristic
936C22#576×C7111yescharacteristic
937C22#577×C7111yescharacteristic
938C4—22no—
939C4—22no—
940C4—22no—
941C4—42no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—81no—
946C4—81no—
947C4D42×C7111yescharacteristic
948C4D42×C7111yescharacteristic
949C4#546×C7111yescharacteristic
950C4#546×C7111yescharacteristic
951C2—42no—
952C2—82no—
953C2—82no—
954C2—82no—
955C2—82no—
956C2C71×#240811yescharacteristic
957C2C71×#300811yescharacteristic
958C2C71×#301211yescharacteristic
959C2C71×#304111yescharacteristic
960C2C71×#304511yescharacteristic
961C2C71×#322011yescharacteristic
962C2C71×#322411yescharacteristic
subgroupG/H
center, socleC23×C71C22×D4
commutator, Frattini, cosocleC22×C4C24×C71
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C71 ◁ C2×#117×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#535×C71C2semidirect
2. C2×#463×C71C2semidirect
3. C2×#459×C71C2semidirect
4. C2×#449×C71C2semidirect
5. C2×#447×C71C2semidirect
6. C71×#2324C2semidirect
7. C71×#2042C2semidirect
8. C71×#2041C2semidirect
9. C71×#2012C2semidirect
10. C71×#2011C2semidirect
11. C71×#1983C2semidirect
12. C71×#1982C2semidirect
13. C71×#1798C2semidirect
14. C71×#1788C2semidirect
15. C71×#1786C2semidirect
18. C22×SD16×C71C22semidirect
21. C22×D8×C71C22semidirect
33. C2×C4×D4×C71C22semidirect
39. C2×C4⋊C8×C71C22semidirect
40. C2×C4⋊C8×C71C22semidirect
41. C2×#103×C71C22semidirect
42. C2×#103×C71C22semidirect
43. C2×#103×C71C22semidirect
50. C2×#102×C71C22semidirect
51. C2×#102×C71C22semidirect
52. C2×#102×C71C22semidirect
56. #390×C71C22semidirect
57. #389×C71C22semidirect
62. C4×C4⋊C4×C71C22semidirect
63. #336×C71C22semidirect
64. #336×C71C22semidirect
112. #127×C71D4semidirect
116. #124×C71D4semidirect
120. #121×C71D4semidirect
469. #24218C71direct (N × H)
482. C2×#535C2×C71semidirect
483. C2×#463C2×C71semidirect
484. C2×#459C2×C71semidirect
485. C2×#449C2×C71semidirect
486. C2×#447C2×C71semidirect
487. #2324C2×C71semidirect
488. #2042C2×C71semidirect
489. #2041C2×C71semidirect
490. #2012C2×C71semidirect
491. #2011C2×C71semidirect
492. #1983C2×C71semidirect
493. #1982C2×C71semidirect
494. #1798C2×C71semidirect
495. #1788C2×C71semidirect
496. #1786C2×C71semidirect
497. C71#24218direct (N × H)
500. C22×SD16C22×C71semidirect
503. C22×D8C22×C71semidirect
515. C2×C4×D4C22×C71semidirect
521. C2×C4⋊C8C22×C71semidirect
522. C2×C4⋊C8C22×C71semidirect
523. C2×#103C22×C71semidirect
524. C2×#103C22×C71semidirect
525. C2×#103C22×C71semidirect
532. C2×#102C22×C71semidirect
533. C2×#102C22×C71semidirect
534. C2×#102C22×C71semidirect
538. #390C22×C71semidirect
539. #389C22×C71semidirect
544. C4×C4⋊C4C22×C71semidirect
545. #336C22×C71semidirect
546. #336C22×C71semidirect
594. #127D4×C71semidirect
598. #124D4×C71semidirect
602. #121D4×C71semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C712
C2×#463×C712
C2×#459×C712
C2×#449×C712
C2×#447×C712
C71×#23242
C71×#20422
C71×#20412
C71×#20122
C71×#20112
C71×#19832
C71×#19822
C71×#17982
C71×#17882
C71×#17862
#2421871