Finite Group Databasebeta

← C47×#18448 #26058146

Subgroups — C47×#18448 #26058146

Order 12032.

968 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3535C211yesmaximal, characteristic, complemented
2C47×#3193C211yesmaximal, characteristic, complemented
3C47×#3188C211yesmaximal, characteristic, complemented
4C47×#2813C211yesmaximal, characteristic, complemented
5C47×#1618C211yesmaximal, characteristic, complemented
6C47×#1617C211yesmaximal, characteristic, complemented
7C47×#1615C211yesmaximal, characteristic, complemented
8C47×#1614C211yesmaximal, characteristic, complemented
9C47×#1600C211yesmaximal, characteristic, complemented
10C47×#1599C211yesmaximal, characteristic, complemented
11C47×#1597C211yesmaximal, characteristic, complemented
12C47×#1596C211yesmaximal, characteristic, complemented
13C47×#1520C211yesmaximal, characteristic, complemented
14C47×#1513C211yesmaximal, characteristic, complemented
15C47×#1468C211yesmaximal, characteristic, complemented
16C47×#563—21no—
17C47×#562—21no—
18C47×#554—21no—
19C47×#552—21no—
20C47×#551—21no—
21C47×#551—21no—
22C47×#547—21no—
23C47×#546—21no—
24C47×#544C2211yescharacteristic
25C47×#543C2211yescharacteristic
26C47×#542—21no—
27C47×#539—21no—
28C47×#539—21no—
29C47×#539C2211yescharacteristic
30C47×#538C2211yescharacteristic
31C47×#536—21no—
32C47×#525C2211yescharacteristic
33C2×#123×C47C2211yescharacteristic
34C2×C22⋊Q8×C47C2211yescharacteristic
35C2×#121×C47C2211yescharacteristic
36C47×#484C2211yescharacteristic
37C47×#484C2211yescharacteristic
38C47×#484C2211yescharacteristic
39C47×#482—21no—
40C47×#481C2211yescharacteristic
41C47×#480—21no—
42C47×#468—21no—
43C47×#468—21no—
44C47×#466—21no—
45C47×#465—21no—
46C47×#450C2211yescharacteristic
47C47×#450C2211yescharacteristic
48C47×#450C2211yescharacteristic
49C47×#449—21no—
50C47×#448—21no—
51C47×#447C2211yescharacteristic
52C47×#407C2211yescharacteristic
53C2×C22⋊C8×C47C2211yescharacteristic
54C47×#400C2211yescharacteristic
55C47×#399C2211yescharacteristic
56C47×#396—21no—
57C47×#394—21no—
58C47×#394—21no—
59C47×#394C2211yescharacteristic
60C47×#392—21no—
61C47×#392C2211yescharacteristic
62C47×#380C2211yescharacteristic
63C47×#328C2211yescharacteristic
64C47×#328C2211yescharacteristic
65C47×#328C2211yescharacteristic
66C47×#328C2211yescharacteristic
67C47×#328C2211yescharacteristic
68C47×#328C2211yescharacteristic
69C47×#327C2211yescharacteristic
70C47×#327C2211yescharacteristic
71C47×#324C2211yescharacteristic
72C47×#324C2211yescharacteristic
73C47×#323C2211yescharacteristic
74C47×#323C2211yescharacteristic
75C2×#41×C47—21no—
76C2×#41×C47D411yescharacteristic, complemented
77C22×Q8×C47D411yescharacteristic, complemented
78C22×D4×C47—21no—
79C22×D4×C47—21no—
80C22×D4×C47D411yescharacteristic
81C22×D4×C47C2311yescharacteristic
82C23×C4×C47C2311yescharacteristic
83C2×SD16×C47—21no—
84C2×SD16×C47—21no—
85C2×SD16×C47—21no—
86C2×D8×C47—21no—
87C2×M16×C47—21no—
88C22×C8×C47—21no—
89C4⋊Q8×C47—21no—
90C4⋊Q8×C47—21no—
91C4⋊Q8×C47—21no—
92#126×C47—21no—
93#126×C47—21no—
94#126×C47—21no—
95#126×C47—21no—
96#126×C47—21no—
97#126×C47—21no—
98#125×C47—21no—
99#125×C47—21no—
100#125×C47—21no—
101#125×C47—21no—
102#125×C47—21no—
103#124×C47—21no—
104#124×C47—21no—
105#124×C47—21no—
106#124×C47—21no—
107#123×C47—21no—
108#123×C47—21no—
109#123×C47—21no—
110#123×C47—21no—
111#123×C47—21no—
112#123×C47—21no—
113#123×C47—21no—
114#123×C47—21no—
115#123×C47—21no—
116#123×C47—21no—
117#123×C47—21no—
118#123×C47—21no—
119#123×C47—21no—
120#123×C47—21no—
121C22⋊Q8×C47—21no—
122C22⋊Q8×C47—21no—
123C22⋊Q8×C47—21no—
124C22⋊Q8×C47—21no—
125C22⋊Q8×C47—21no—
126C22⋊Q8×C47—21no—
127C22⋊Q8×C47—21no—
128C22⋊Q8×C47—21no—
129C22⋊Q8×C47—21no—
130C22⋊Q8×C47—21no—
131C22⋊Q8×C47—21no—
132C22⋊Q8×C47—21no—
133C22⋊Q8×C47—21no—
134C22⋊Q8×C47—21no—
135C22⋊Q8×C47D411yescharacteristic, complemented
136C22⋊Q8×C47D411yescharacteristic, complemented
137C22⋊Q8×C47D411yescharacteristic, complemented
138C22⋊Q8×C47C2311yescharacteristic
139C22⋊Q8×C47C2311yescharacteristic
140C22⋊Q8×C47C2311yescharacteristic
141#121×C47—21no—
142#121×C47—21no—
143#121×C47—21no—
144#121×C47—21no—
145#121×C47—21no—
146#121×C47—21no—
147#121×C47—21no—
148#121×C47—21no—
149#121×C47D411yescharacteristic, complemented
150#121×C47C2311yescharacteristic
151#120×C47—21no—
152#120×C47—21no—
153C4×Q8×C47—21no—
154C4×D4×C47—21no—
155C4×D4×C47—21no—
156C4×D4×C47—21no—
157C4×D4×C47—21no—
158C4×D4×C47—21no—
159C4×D4×C47—21no—
160C4×D4×C47—21no—
161#117×C47—21no—
162#117×C47—21no—
163#117×C47—21no—
164#117×C47D411yescharacteristic, complemented
165C2×C4⋊C4×C47—21no—
166C2×C4⋊C4×C47—21no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47D411yescharacteristic
170C2×C4⋊C4×C47D411yescharacteristic, complemented
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C22⋊C4×C47—21no—
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176C2×C22⋊C4×C47—21no—
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47D411yescharacteristic
182C2×C22⋊C4×C47D411yescharacteristic
183C2×C22⋊C4×C47C2311yescharacteristic
184#107×C47—21no—
185#107×C47—21no—
186#107×C47—21no—
187#106×C47—21no—
188#103×C47—21no—
189#103×C47—21no—
190#103×C47—21no—
191#102×C47—21no—
192#102×C47—21no—
193#102×C47—21no—
194#102×C47—21no—
195#102×C47—21no—
196C22⋊C8×C47—21no—
197C22⋊C8×C47—21no—
198C22⋊C8×C47C2311yescharacteristic
199C22⋊C8×C47C2311yescharacteristic
200C22⋊C8×C47C2311yescharacteristic
201C22⋊C8×C47C2311yescharacteristic
202#95×C47—21no—
203#95×C47—21no—
204#95×C47C2311yescharacteristic
205#95×C47C2311yescharacteristic
206C24×C47—21no—
207C24×C47C2×D411yescharacteristic
208C24×C47C2×D411yescharacteristic
209#41×C47—82no—
210#41×C47—81no—
211C2×Q8×C47—21no—
212C2×Q8×C47—21no—
213C2×Q8×C47—21no—
214C2×Q8×C47—81no—
215C2×Q8×C47C2×D411yescharacteristic
216C2×Q8×C47C2×D411yescharacteristic
217C2×Q8×C47C2×D411yescharacteristic
218C2×D4×C47—21no—
219C2×D4×C47—21no—
220C2×D4×C47—21no—
221C2×D4×C47—21no—
222C2×D4×C47—21no—
223C2×D4×C47—21no—
224C2×D4×C47—21no—
225C2×D4×C47—21no—
226C2×D4×C47—21no—
227C2×D4×C47—41no—
228C2×D4×C47—41no—
229C2×D4×C47—81no—
230C2×D4×C47—81no—
231C2×D4×C47—81no—
232C2×D4×C47—81no—
233C2×D4×C47—81no—
234C2×D4×C47—81no—
235C2×D4×C47—81no—
236C2×D4×C47C2×D411yescharacteristic
237C22×C4×C47—21no—
238C22×C4×C47—21no—
239C22×C4×C47—21no—
240C22×C4×C47—21no—
241C22×C4×C47—21no—
242C22×C4×C47—21no—
243C22×C4×C47—21no—
244C22×C4×C47—21no—
245C22×C4×C47—21no—
246C22×C4×C47—21no—
247C22×C4×C47—81no—
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D411yescharacteristic
250C22×C4×C47C2×D411yescharacteristic
251C22×C4×C47C2×D411yescharacteristic
252C22×C4×C47C2×D411yescharacteristic
253C22×C4×C47C2×D411yescharacteristic
254C22×C4×C47C2×D411yescharacteristic
255C22×C4×C47C2×D411yescharacteristic
256C22×C4×C47C2411yescharacteristic
257SD16×C47—81no—
258SD16×C47—81no—
259SD16×C47—81no—
260D8×C47—81no—
261M16×C47—81no—
262C2×C8×C47—21no—
263C2×C8×C47—21no—
264C2×C8×C47—21no—
265C2×C8×C47—21no—
266C2×C8×C47—81no—
267C4⋊C4×C47—21no—
268C4⋊C4×C47—21no—
269C4⋊C4×C47—21no—
270C4⋊C4×C47—21no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47—21no—
273C4⋊C4×C47—21no—
274C4⋊C4×C47—21no—
275C4⋊C4×C47—21no—
276C4⋊C4×C47—21no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47—21no—
279C4⋊C4×C47—21no—
280C4⋊C4×C47—21no—
281C4⋊C4×C47—21no—
282C4⋊C4×C47—21no—
283C4⋊C4×C47—21no—
284C4⋊C4×C47—21no—
285C4⋊C4×C47—21no—
286C4⋊C4×C47—21no—
287C4⋊C4×C47—21no—
288C4⋊C4×C47—21no—
289C4⋊C4×C47—21no—
290C4⋊C4×C47—21no—
291C4⋊C4×C47—21no—
292C4⋊C4×C47—81no—
293C4⋊C4×C47—81no—
294C4⋊C4×C47C2×D411yescharacteristic
295C4⋊C4×C47C2×D411yescharacteristic
296C4⋊C4×C47C2×D411yescharacteristic
297C4⋊C4×C47C2×D411yescharacteristic
298C22⋊C4×C47—21no—
299C22⋊C4×C47—21no—
300C22⋊C4×C47—21no—
301C22⋊C4×C47—21no—
302C22⋊C4×C47—21no—
303C22⋊C4×C47—21no—
304C22⋊C4×C47—21no—
305C22⋊C4×C47—21no—
306C22⋊C4×C47—21no—
307C22⋊C4×C47—21no—
308C22⋊C4×C47—21no—
309C22⋊C4×C47—21no—
310C22⋊C4×C47—21no—
311C22⋊C4×C47—21no—
312C22⋊C4×C47—21no—
313C22⋊C4×C47—21no—
314C22⋊C4×C47—21no—
315C22⋊C4×C47—21no—
316C22⋊C4×C47—21no—
317C22⋊C4×C47—21no—
318C22⋊C4×C47—21no—
319C22⋊C4×C47—21no—
320C22⋊C4×C47—21no—
321C22⋊C4×C47—41no—
322C22⋊C4×C47—41no—
323C22⋊C4×C47—81no—
324C22⋊C4×C47—81no—
325C22⋊C4×C47—81no—
326C22⋊C4×C47—81no—
327C22⋊C4×C47—81no—
328C42×C47—21no—
329C42×C47—21no—
330C42×C47—21no—
331C42×C47—21no—
332C42×C47—21no—
333C23×C47—21no—
334C23×C47—21no—
335C23×C47—21no—
336C23×C47—21no—
337C23×C47—21no—
338C23×C47—21no—
339C23×C47—41no—
340C23×C47—41no—
341C23×C47—41no—
342C23×C47—41no—
343C23×C47—41no—
344C23×C47—41no—
345C23×C47—41no—
346C23×C47—41no—
347C23×C47—41no—
348C23×C47—41no—
349C23×C47—41no—
350C23×C47#12011yescharacteristic
351C23×C47#12011yescharacteristic
352C23×C47C22×D411yescharacteristic
353Q8×C47—41no—
354Q8×C47—41no—
355Q8×C47—41no—
356Q8×C47—81no—
357Q8×C47—81no—
358Q8×C47—81no—
359D4×C47—41no—
360D4×C47—41no—
361D4×C47—41no—
362D4×C47—41no—
363D4×C47—41no—
364D4×C47—42no—
365D4×C47—42no—
366D4×C47—41no—
367D4×C47—41no—
368D4×C47—81no—
369D4×C47—81no—
370D4×C47—81no—
371D4×C47—81no—
372D4×C47—82no—
373D4×C47—82no—
374D4×C47—84no—
375C2×C4×C47—21no—
376C2×C4×C47—21no—
377C2×C4×C47—21no—
378C2×C4×C47—21no—
379C2×C4×C47—21no—
380C2×C4×C47—21no—
381C2×C4×C47—21no—
382C2×C4×C47—21no—
383C2×C4×C47—21no—
384C2×C4×C47—21no—
385C2×C4×C47—21no—
386C2×C4×C47—21no—
387C2×C4×C47—41no—
388C2×C4×C47—41no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—41no—
393C2×C4×C47—42no—
394C2×C4×C47—41no—
395C2×C4×C47—41no—
396C2×C4×C47—41no—
397C2×C4×C47—41no—
398C2×C4×C47—41no—
399C2×C4×C47—41no—
400C2×C4×C47—41no—
401C2×C4×C47—41no—
402C2×C4×C47—41no—
403C2×C4×C47—41no—
404C2×C4×C47—41no—
405C2×C4×C47—81no—
406C2×C4×C47—81no—
407C2×C4×C47—81no—
408C2×C4×C47—81no—
409C2×C4×C47—81no—
410C2×C4×C47—81no—
411C2×C4×C47#12011yescharacteristic
412C2×C4×C47#12011yescharacteristic
413C2×C4×C47C22×D411yescharacteristic
414C2×C4×C47C22×D411yescharacteristic
415C8×C47—41no—
416C8×C47—41no—
417C8×C47—41no—
418C8×C47—41no—
419#18448C4711yesmaximal, characteristic, direct product factor, Sylow
420C22×C47—21no—
421C22×C47—21no—
422C22×C47—21no—
423C22×C47—21no—
424C22×C47—21no—
425C22×C47—21no—
426C22×C47—21no—
427C22×C47—21no—
428C22×C47—41no—
429C22×C47—41no—
430C22×C47—41no—
431C22×C47—41no—
432C22×C47—41no—
433C22×C47—41no—
434C22×C47—81no—
435C22×C47—81no—
436C22×C47—81no—
437C22×C47—81no—
438C22×C47—81no—
439C22×C47—81no—
440C22×C47—81no—
441C22×C47—81no—
442C22×C47—81no—
443C22×C47—81no—
444C22×C47—81no—
445C22×C47C2×#12011yescharacteristic
446C22×C47#57711yescharacteristic
447C22×C47#57811yescharacteristic
448C4×C47—21no—
449C4×C47—21no—
450C4×C47—21no—
451C4×C47—21no—
452C4×C47—41no—
453C4×C47—41no—
454C4×C47—41no—
455C4×C47—41no—
456C4×C47—41no—
457C4×C47—41no—
458C4×C47—41no—
459C4×C47—41no—
460C4×C47—41no—
461C4×C47—41no—
462C4×C47—81no—
463C4×C47—81no—
464C4×C47—81no—
465#3535C2×C4711yescharacteristic, complemented
466#3193C2×C4711yescharacteristic, complemented
467#3188C2×C4711yescharacteristic, complemented
468#2813C2×C4711yescharacteristic, complemented
469#1618C2×C4711yescharacteristic, complemented
470#1617C2×C4711yescharacteristic, complemented
471#1615C2×C4711yescharacteristic, complemented
472#1614C2×C4711yescharacteristic, complemented
473#1600C2×C4711yescharacteristic, complemented
474#1599C2×C4711yescharacteristic, complemented
475#1597C2×C4711yescharacteristic, complemented
476#1596C2×C4711yescharacteristic, complemented
477#1520C2×C4711yescharacteristic, complemented
478#1513C2×C4711yescharacteristic, complemented
479#1468C2×C4711yescharacteristic, complemented
480C2×C47—21no—
481C2×C47—21no—
482C2×C47—41no—
483C2×C47—41no—
484C2×C47—81no—
485C2×C47—81no—
486C2×C47—161no—
487C2×C47#301311yescharacteristic
488C2×C47#302111yescharacteristic
489C2×C47#302611yescharacteristic
490#563—21no—
491#562—21no—
492#554—21no—
493#552—21no—
494#551—21no—
495#551—21no—
496#547—21no—
497#546—21no—
498#544C22×C4711yescharacteristic
499#543C22×C4711yescharacteristic
500#542—21no—
501#539—21no—
502#539—21no—
503#539C22×C4711yescharacteristic
504#538C22×C4711yescharacteristic
505#536—21no—
506#525C22×C4711yescharacteristic
507C2×#123C22×C4711yescharacteristic
508C2×C22⋊Q8C22×C4711yescharacteristic
509C2×#121C22×C4711yescharacteristic
510#484C22×C4711yescharacteristic
511#484C22×C4711yescharacteristic
512#484C22×C4711yescharacteristic
513#482—21no—
514#481C22×C4711yescharacteristic
515#480—21no—
516#468—21no—
517#468—21no—
518#466—21no—
519#465—21no—
520#450C22×C4711yescharacteristic
521#450C22×C4711yescharacteristic
522#450C22×C4711yescharacteristic
523#449—21no—
524#448—21no—
525#447C22×C4711yescharacteristic
526#407C22×C4711yescharacteristic
527C2×C22⋊C8C22×C4711yescharacteristic
528#400C22×C4711yescharacteristic
529#399C22×C4711yescharacteristic
530#396—21no—
531#394—21no—
532#394—21no—
533#394C22×C4711yescharacteristic
534#392—21no—
535#392C22×C4711yescharacteristic
536#380C22×C4711yescharacteristic
537#328C22×C4711yescharacteristic
538#328C22×C4711yescharacteristic
539#328C22×C4711yescharacteristic
540#328C22×C4711yescharacteristic
541#328C22×C4711yescharacteristic
542#328C22×C4711yescharacteristic
543#327C22×C4711yescharacteristic
544#327C22×C4711yescharacteristic
545#324C22×C4711yescharacteristic
546#324C22×C4711yescharacteristic
547#323C22×C4711yescharacteristic
548#323C22×C4711yescharacteristic
549C47#1844811yescharacteristic, direct product factor, Sylow
550C2×#41—21no—
551C2×#41D4×C4711yescharacteristic, complemented
552C22×Q8D4×C4711yescharacteristic, complemented
553C22×D4—21no—
554C22×D4—21no—
555C22×D4D4×C4711yescharacteristic
556C22×D4C23×C4711yescharacteristic
557C23×C4C23×C4711yescharacteristic
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×D8—21no—
562C2×M16—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#125—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C4711yescharacteristic, complemented
611C22⋊Q8D4×C4711yescharacteristic, complemented
612C22⋊Q8D4×C4711yescharacteristic, complemented
613C22⋊Q8C23×C4711yescharacteristic
614C22⋊Q8C23×C4711yescharacteristic
615C22⋊Q8C23×C4711yescharacteristic
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121D4×C4711yescharacteristic, complemented
625#121C23×C4711yescharacteristic
626#120—21no—
627#120—21no—
628C4×Q8—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—21no—
638#117—21no—
639#117D4×C4711yescharacteristic, complemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4D4×C4711yescharacteristic
645C2×C4⋊C4D4×C4711yescharacteristic, complemented
646C2×C4⋊C4C23×C4711yescharacteristic
647C2×C4⋊C4C23×C4711yescharacteristic
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4D4×C4711yescharacteristic
657C2×C22⋊C4D4×C4711yescharacteristic
658C2×C22⋊C4C23×C4711yescharacteristic
659#107—21no—
660#107—21no—
661#107—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C4711yescharacteristic
674C22⋊C8C23×C4711yescharacteristic
675C22⋊C8C23×C4711yescharacteristic
676C22⋊C8C23×C4711yescharacteristic
677#95—21no—
678#95—21no—
679#95C23×C4711yescharacteristic
680#95C23×C4711yescharacteristic
681C24—21no—
682C24C2×D4×C4711yescharacteristic
683C24C2×D4×C4711yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C4711yescharacteristic
691C2×Q8C2×D4×C4711yescharacteristic
692C2×Q8C2×D4×C4711yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C4711yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C4711yescharacteristic
724C22×C4C2×D4×C4711yescharacteristic
725C22×C4C2×D4×C4711yescharacteristic
726C22×C4C2×D4×C4711yescharacteristic
727C22×C4C2×D4×C4711yescharacteristic
728C22×C4C2×D4×C4711yescharacteristic
729C22×C4C2×D4×C4711yescharacteristic
730C22×C4C2×D4×C4711yescharacteristic
731C22×C4C24×C4711yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C4711yescharacteristic
770C4⋊C4C2×D4×C4711yescharacteristic
771C4⋊C4C2×D4×C4711yescharacteristic
772C4⋊C4C2×D4×C4711yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—41no—
797C22⋊C4—41no—
798C22⋊C4—81no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C22⋊C4—81no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#120×C4711yescharacteristic
826C23#120×C4711yescharacteristic
827C23C22×D4×C4711yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—82no—
848D4—82no—
849D4—84no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—42no—
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—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4#120×C4711yescharacteristic
887C2×C4#120×C4711yescharacteristic
888C2×C4C22×D4×C4711yescharacteristic
889C2×C4C22×D4×C4711yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×#120×C4711yescharacteristic
920C22C47×#57711yescharacteristic
921C22C47×#57811yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—41no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C47×#301311yescharacteristic
947C2C47×#302111yescharacteristic
948C2C47×#302611yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3535C2semidirect
2. C47×#3193C2semidirect
3. C47×#3188C2semidirect
4. C47×#2813C2semidirect
5. C47×#1618C2semidirect
6. C47×#1617C2semidirect
7. C47×#1615C2semidirect
8. C47×#1614C2semidirect
9. C47×#1600C2semidirect
10. C47×#1599C2semidirect
11. C47×#1597C2semidirect
12. C47×#1596C2semidirect
13. C47×#1520C2semidirect
14. C47×#1513C2semidirect
15. C47×#1468C2semidirect
76. C2×#41×C47D4semidirect
77. C22×Q8×C47D4semidirect
135. C22⋊Q8×C47D4semidirect
136. C22⋊Q8×C47D4semidirect
137. C22⋊Q8×C47D4semidirect
149. #121×C47D4semidirect
164. #117×C47D4semidirect
170. C2×C4⋊C4×C47D4semidirect
419. #18448C47direct (N × H)
465. #3535C2×C47semidirect
466. #3193C2×C47semidirect
467. #3188C2×C47semidirect
468. #2813C2×C47semidirect
469. #1618C2×C47semidirect
470. #1617C2×C47semidirect
471. #1615C2×C47semidirect
472. #1614C2×C47semidirect
473. #1600C2×C47semidirect
474. #1599C2×C47semidirect
475. #1597C2×C47semidirect
476. #1596C2×C47semidirect
477. #1520C2×C47semidirect
478. #1513C2×C47semidirect
479. #1468C2×C47semidirect
549. C47#18448direct (N × H)
551. C2×#41D4×C47semidirect
552. C22×Q8D4×C47semidirect
610. C22⋊Q8D4×C47semidirect
611. C22⋊Q8D4×C47semidirect
612. C22⋊Q8D4×C47semidirect
624. #121D4×C47semidirect
639. #117D4×C47semidirect
645. C2×C4⋊C4D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#35352
C47×#31932
C47×#31882
C47×#28132
C47×#16182
C47×#16172
C47×#16152
C47×#16142
C47×#16002
C47×#15992
C47×#15972
C47×#15962
C47×#15202
C47×#15132
C47×#14682
#1844847