Finite Group Databasebeta

← C47×#18434 #26058132

Subgroups — C47×#18434 #26058132

Order 12032.

982 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
1C47×#3560C211yesmaximal, characteristic, complemented
2C47×#3213C211yesmaximal, characteristic, complemented
3C47×#3211C211yesmaximal, characteristic, complemented
4C47×#2662C211yesmaximal, characteristic, complemented
5C47×#1606C211yesmaximal, characteristic, complemented
6C47×#1604C211yesmaximal, characteristic, complemented
7C47×#1603C211yesmaximal, characteristic, complemented
8C47×#1601C211yesmaximal, characteristic, complemented
9C47×#1600C211yesmaximal, characteristic, complemented
10C47×#1598C211yesmaximal, characteristic, complemented
11C47×#1597C211yesmaximal, characteristic, complemented
12C47×#1595C211yesmaximal, characteristic, complemented
13C47×#1509C211yesmaximal, characteristic, complemented
14C47×#1502C211yesmaximal, characteristic, complemented
15C47×#1473C211yesmaximal, characteristic, complemented
16C47×#563—21no—
17C47×#560—21no—
18C47×#553—21no—
19C47×#553—21no—
20C47×#551—21no—
21C47×#547—21no—
22C47×#546—21no—
23C47×#546—21no—
24C47×#542—21no—
25C47×#539—21no—
26C47×#539C2211yescharacteristic
27C47×#538—21no—
28C47×#538—21no—
29C47×#538C2211yescharacteristic
30C47×#537C2211yescharacteristic
31C47×#534C2211yescharacteristic
32C47×#532C2211yescharacteristic
33C47×#529C2211yescharacteristic
34C2×#126×C47C2211yescharacteristic
35C2×#124×C47C2211yescharacteristic, complemented
36C47×#496—21no—
37C47×#495—21no—
38C47×#489—21no—
39C47×#488—21no—
40C47×#464—21no—
41C47×#463—21no—
42C47×#463—21no—
43C47×#463—21no—
44C47×#451C2211yescharacteristic, complemented
45C47×#450C2211yescharacteristic, complemented
46C47×#448C2211yescharacteristic
47C47×#448C2211yescharacteristic
48C47×#448C2211yescharacteristic, complemented
49C47×#447C2211yescharacteristic
50C47×#447C2211yescharacteristic
51C47×#447C2211yescharacteristic, complemented
52C47×#432C2211yescharacteristic, complemented
53C47×#431C2211yescharacteristic, complemented
54C47×#396—21no—
55C47×#395C2211yescharacteristic, complemented
56C47×#394—21no—
57C47×#394C2211yescharacteristic, complemented
58C47×#393C2211yescharacteristic
59C47×#392C2211yescharacteristic
60C47×#390—21no—
61C47×#388—21no—
62C4×C4⋊C4×C47C2211yescharacteristic, complemented
63C47×#328C2211yescharacteristic, complemented
64C47×#328C2211yescharacteristic, complemented
65C47×#327C2211yescharacteristic
66C47×#327C2211yescharacteristic
67C47×#327C2211yescharacteristic
68C47×#327C2211yescharacteristic
69C47×#327C2211yescharacteristic, complemented
70C47×#327C2211yescharacteristic, complemented
71C47×#324C2211yescharacteristic, complemented
72C47×#324C2211yescharacteristic, complemented
73C47×#323C2211yescharacteristic
74C47×#323C2211yescharacteristic
75C2×#41×C47—21no—
76C2×#41×C47—21no—
77C22×Q8×C47C2311yescharacteristic
78C22×D4×C47—21no—
79C22×D4×C47—21no—
80C22×D4×C47C2311yescharacteristic
81C2×Q16×C47—21no—
82C2×SD16×C47—21no—
83C2×SD16×C47—21no—
84C2×SD16×C47—21no—
85C2×SD16×C47—21no—
86C2×D8×C47—21no—
87C2×D8×C47—21no—
88C2×D8×C47—21no—
89C4⋊Q8×C47—21no—
90C4⋊Q8×C47D411yescharacteristic, complemented
91#127×C47D411yescharacteristic, complemented
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#126×C47—21no—
99#126×C47—21no—
100#126×C47—21no—
101#125×C47—21no—
102#125×C47—21no—
103#125×C47D411yescharacteristic, complemented
104#124×C47—21no—
105#124×C47—21no—
106#124×C47—21no—
107#124×C47—21no—
108#124×C47—21no—
109#124×C47—21no—
110#124×C47—21no—
111#124×C47—21no—
112#124×C47D411yescharacteristic, complemented
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—
121#123×C47—21no—
122#123×C47—21no—
123#123×C47—21no—
124#123×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×C47C2311yescharacteristic
133#121×C47—21no—
134#121×C47—21no—
135#121×C47—21no—
136#121×C47—21no—
137#121×C47—21no—
138#121×C47—21no—
139#121×C47—21no—
140#121×C47—21no—
141#121×C47—21no—
142#121×C47—21no—
143#121×C47—21no—
144#121×C47—21no—
145#121×C47C2311yescharacteristic
146#121×C47C2311yescharacteristic
147#121×C47C2311yescharacteristic
148#120×C47—21no—
149#120×C47—21no—
150#120×C47—21no—
151#120×C47—21no—
152#120×C47—21no—
153C4×Q8×C47D411yescharacteristic, complemented
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—
161C4×D4×C47—21no—
162C4×D4×C47D411yescharacteristic, complemented
163C4×D4×C47D411yescharacteristic, complemented
164C4×D4×C47D411yescharacteristic, complemented
165#117×C47—21no—
166#117×C47—21no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47D411yescharacteristic
171C2×C4⋊C4×C47D411yescharacteristic
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
184C2×C42×C47—21no—
185C2×C42×C47C2311yescharacteristic
186C4⋊C8×C47—21no—
187C4⋊C8×C47—21no—
188#103×C47—21no—
189#103×C47—21no—
190#103×C47—21no—
191#103×C47—21no—
192#102×C47—21no—
193#102×C47—21no—
194#102×C47—21no—
195#102×C47—21no—
196C22⋊C8×C47C2311yescharacteristic
197C22⋊C8×C47C2311yescharacteristic
198C22⋊C8×C47C2311yescharacteristic
199C22⋊C8×C47C2311yescharacteristic
200#97×C47—21no—
201C4×C8×C47—21no—
202#95×C47—21no—
203#95×C47—21no—
204#95×C47C2311yescharacteristic
205#95×C47C2311yescharacteristic
206C24×C47—21no—
207C24×C47—21no—
208C24×C47C2×D411yescharacteristic
209#41×C47—81no—
210#41×C47—81no—
211#41×C47—81no—
212#41×C47—81no—
213C2×Q8×C47—21no—
214C2×Q8×C47—21no—
215C2×Q8×C47—21no—
216C2×Q8×C47—21no—
217C2×Q8×C47—81no—
218C2×Q8×C47C2×D411yescharacteristic
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—21no—
228C2×D4×C47—21no—
229C2×D4×C47—21no—
230C2×D4×C47—21no—
231C2×D4×C47—21no—
232C2×D4×C47—21no—
233C2×D4×C47—42no—
234C2×D4×C47—81no—
235C2×D4×C47—81no—
236C2×D4×C47—81no—
237C2×D4×C47—81no—
238C2×D4×C47—81no—
239C2×D4×C47C2×D411yescharacteristic
240C2×D4×C47C2×D411yescharacteristic
241C2×D4×C47C2×D411yescharacteristic
242C22×C4×C47—21no—
243C22×C4×C47—21no—
244C22×C4×C47—21no—
245C22×C4×C47—21no—
246C22×C4×C47—21no—
247C22×C4×C47—21no—
248C22×C4×C47—21no—
249C22×C4×C47—21no—
250C22×C4×C47—21no—
251C22×C4×C47—21no—
252C22×C4×C47—21no—
253C22×C4×C47C2×D411yescharacteristic
254C22×C4×C47C2×D411yescharacteristic
255C22×C4×C47C2×D411yescharacteristic
256C22×C4×C47C2×D411yescharacteristic
257C22×C4×C47C2×D411yescharacteristic
258C22×C4×C47C2411yescharacteristic
259Q16×C47—81no—
260SD16×C47—81no—
261SD16×C47—81no—
262SD16×C47—81no—
263SD16×C47—81no—
264D8×C47—81no—
265D8×C47—81no—
266D8×C47—81no—
267C2×C8×C47—21no—
268C2×C8×C47—21no—
269C2×C8×C47—21no—
270C2×C8×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—42no—
289C4⋊C4×C47—81no—
290C4⋊C4×C47C2×D411yescharacteristic
291C4⋊C4×C47C2×D411yescharacteristic
292C4⋊C4×C47C2×D411yescharacteristic
293C4⋊C4×C47C2×D411yescharacteristic
294C22⋊C4×C47—21no—
295C22⋊C4×C47—21no—
296C22⋊C4×C47—21no—
297C22⋊C4×C47—21no—
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—42no—
320C22⋊C4×C47—41no—
321C22⋊C4×C47—41no—
322C22⋊C4×C47—41no—
323C22⋊C4×C47—41no—
324C22⋊C4×C47—81no—
325C22⋊C4×C47—81no—
326C22⋊C4×C47—81no—
327C42×C47—21no—
328C42×C47—21no—
329C42×C47—21no—
330C42×C47—81no—
331C42×C47C2×D411yescharacteristic
332C42×C47C2×D411yescharacteristic
333C42×C47C2×D411yescharacteristic
334C42×C47C2×D411yescharacteristic
335C23×C47—21no—
336C23×C47—21no—
337C23×C47—21no—
338C23×C47—21no—
339C23×C47—21no—
340C23×C47—21no—
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—81no—
351C23×C47—81no—
352C23×C47—81no—
353C23×C47C22×D411yescharacteristic
354Q8×C47—41no—
355Q8×C47—41no—
356Q8×C47—41no—
357Q8×C47—41no—
358Q8×C47—41no—
359Q8×C47—81no—
360Q8×C47—81no—
361D4×C47—41no—
362D4×C47—41no—
363D4×C47—41no—
364D4×C47—41no—
365D4×C47—41no—
366D4×C47—41no—
367D4×C47—41no—
368D4×C47—41no—
369D4×C47—41no—
370D4×C47—41no—
371D4×C47—41no—
372D4×C47—41no—
373D4×C47—41no—
374D4×C47—81no—
375D4×C47—81no—
376D4×C47—81no—
377D4×C47—81no—
378D4×C47—81no—
379D4×C47—81no—
380D4×C47—81no—
381D4×C47—81no—
382D4×C47—81no—
383D4×C47—84no—
384C2×C4×C47—21no—
385C2×C4×C47—21no—
386C2×C4×C47—22no—
387C2×C4×C47—21no—
388C2×C4×C47—21no—
389C2×C4×C47—21no—
390C2×C4×C47—21no—
391C2×C4×C47—21no—
392C2×C4×C47—21no—
393C2×C4×C47—21no—
394C2×C4×C47—21no—
395C2×C4×C47—21no—
396C2×C4×C47—21no—
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—41no—
406C2×C4×C47—41no—
407C2×C4×C47—41no—
408C2×C4×C47—41no—
409C2×C4×C47—81no—
410C2×C4×C47—81no—
411C2×C4×C47—81no—
412C2×C4×C47—81no—
413C2×C4×C47—81no—
414C2×C4×C47—81no—
415C2×C4×C47—81no—
416C2×C4×C47—81no—
417C2×C4×C47#12011yescharacteristic
418C2×C4×C47#12011yescharacteristic
419C2×C4×C47#12011yescharacteristic
420C2×C4×C47#12011yescharacteristic
421C2×C4×C47C22×D411yescharacteristic
422C2×C4×C47C22×D411yescharacteristic
423C8×C47—41no—
424C8×C47—41no—
425C8×C47—41no—
426C8×C47—41no—
427#18434C4711yesmaximal, characteristic, direct product factor, Sylow
428C22×C47—21no—
429C22×C47—21no—
430C22×C47—41no—
431C22×C47—41no—
432C22×C47—41no—
433C22×C47—41no—
434C22×C47—41no—
435C22×C47—41no—
436C22×C47—41no—
437C22×C47—41no—
438C22×C47—41no—
439C22×C47—41no—
440C22×C47—41no—
441C22×C47—41no—
442C22×C47—81no—
443C22×C47—81no—
444C22×C47—81no—
445C22×C47—81no—
446C22×C47—81no—
447C22×C47—81no—
448C22×C47—81no—
449C22×C47—81no—
450C22×C47—81no—
451C22×C47—162no—
452C22×C47C2×#12011yescharacteristic
453C22×C47#57611yescharacteristic
454C22×C47#57711yescharacteristic
455C4×C47—21no—
456C4×C47—21no—
457C4×C47—21no—
458C4×C47—21no—
459C4×C47—21no—
460C4×C47—21no—
461C4×C47—42no—
462C4×C47—41no—
463C4×C47—41no—
464C4×C47—41no—
465C4×C47—41no—
466C4×C47—41no—
467C4×C47—41no—
468C4×C47—41no—
469C4×C47—41no—
470C4×C47—81no—
471C4×C47—81no—
472#3560C2×C4711yescharacteristic, complemented
473#3213C2×C4711yescharacteristic, complemented
474#3211C2×C4711yescharacteristic, complemented
475#2662C2×C4711yescharacteristic, complemented
476#1606C2×C4711yescharacteristic, complemented
477#1604C2×C4711yescharacteristic, complemented
478#1603C2×C4711yescharacteristic, complemented
479#1601C2×C4711yescharacteristic, complemented
480#1600C2×C4711yescharacteristic, complemented
481#1598C2×C4711yescharacteristic, complemented
482#1597C2×C4711yescharacteristic, complemented
483#1595C2×C4711yescharacteristic, complemented
484#1509C2×C4711yescharacteristic, complemented
485#1502C2×C4711yescharacteristic, complemented
486#1473C2×C4711yescharacteristic, complemented
487C2×C47—21no—
488C2×C47—21no—
489C2×C47—81no—
490C2×C47—81no—
491C2×C47—81no—
492C2×C47—81no—
493C2×C47—161no—
494C2×C47#301211yescharacteristic
495C2×C47#301811yescharacteristic
496C2×C47#302711yescharacteristic
497#563—21no—
498#560—21no—
499#553—21no—
500#553—21no—
501#551—21no—
502#547—21no—
503#546—21no—
504#546—21no—
505#542—21no—
506#539—21no—
507#539C22×C4711yescharacteristic
508#538—21no—
509#538—21no—
510#538C22×C4711yescharacteristic
511#537C22×C4711yescharacteristic
512#534C22×C4711yescharacteristic
513#532C22×C4711yescharacteristic
514#529C22×C4711yescharacteristic
515C2×#126C22×C4711yescharacteristic
516C2×#124C22×C4711yescharacteristic, complemented
517#496—21no—
518#495—21no—
519#489—21no—
520#488—21no—
521#464—21no—
522#463—21no—
523#463—21no—
524#463—21no—
525#451C22×C4711yescharacteristic, complemented
526#450C22×C4711yescharacteristic, complemented
527#448C22×C4711yescharacteristic
528#448C22×C4711yescharacteristic
529#448C22×C4711yescharacteristic, complemented
530#447C22×C4711yescharacteristic
531#447C22×C4711yescharacteristic
532#447C22×C4711yescharacteristic, complemented
533#432C22×C4711yescharacteristic, complemented
534#431C22×C4711yescharacteristic, complemented
535#396—21no—
536#395C22×C4711yescharacteristic, complemented
537#394—21no—
538#394C22×C4711yescharacteristic, complemented
539#393C22×C4711yescharacteristic
540#392C22×C4711yescharacteristic
541#390—21no—
542#388—21no—
543C4×C4⋊C4C22×C4711yescharacteristic, complemented
544#328C22×C4711yescharacteristic, complemented
545#328C22×C4711yescharacteristic, complemented
546#327C22×C4711yescharacteristic
547#327C22×C4711yescharacteristic
548#327C22×C4711yescharacteristic
549#327C22×C4711yescharacteristic
550#327C22×C4711yescharacteristic, complemented
551#327C22×C4711yescharacteristic, complemented
552#324C22×C4711yescharacteristic, complemented
553#324C22×C4711yescharacteristic, complemented
554#323C22×C4711yescharacteristic
555#323C22×C4711yescharacteristic
556C47#1843411yescharacteristic, direct product factor, Sylow
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C4711yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C4711yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C4711yescharacteristic, complemented
573#127D4×C4711yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C4711yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C4711yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C4711yescharacteristic
615#121—21no—
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#121—21no—
625#121—21no—
626#121—21no—
627#121C23×C4711yescharacteristic
628#121C23×C4711yescharacteristic
629#121C23×C4711yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C4711yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C4711yescharacteristic, complemented
645C4×D4D4×C4711yescharacteristic, complemented
646C4×D4D4×C4711yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C4711yescharacteristic
653C2×C4⋊C4D4×C4711yescharacteristic
654C2×C4⋊C4C23×C4711yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C4711yescharacteristic
664C2×C22⋊C4D4×C4711yescharacteristic
665C2×C22⋊C4C23×C4711yescharacteristic
666C2×C42—21no—
667C2×C42C23×C4711yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C4711yescharacteristic
679C22⋊C8C23×C4711yescharacteristic
680C22⋊C8C23×C4711yescharacteristic
681C22⋊C8C23×C4711yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C4711yescharacteristic
687#95C23×C4711yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C4711yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C4711yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C4711yescharacteristic
722C2×D4C2×D4×C4711yescharacteristic
723C2×D4C2×D4×C4711yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C4711yescharacteristic
736C22×C4C2×D4×C4711yescharacteristic
737C22×C4C2×D4×C4711yescharacteristic
738C22×C4C2×D4×C4711yescharacteristic
739C22×C4C2×D4×C4711yescharacteristic
740C22×C4C24×C4711yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—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—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C4711yescharacteristic
773C4⋊C4C2×D4×C4711yescharacteristic
774C4⋊C4C2×D4×C4711yescharacteristic
775C4⋊C4C2×D4×C4711yescharacteristic
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—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C4711yescharacteristic
814C42C2×D4×C4711yescharacteristic
815C42C2×D4×C4711yescharacteristic
816C42C2×D4×C4711yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C4711yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C4711yescharacteristic
900C2×C4#120×C4711yescharacteristic
901C2×C4#120×C4711yescharacteristic
902C2×C4#120×C4711yescharacteristic
903C2×C4C22×D4×C4711yescharacteristic
904C2×C4C22×D4×C4711yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C4711yescharacteristic
934C22C47×#57611yescharacteristic
935C22C47×#57711yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C47×#301211yescharacteristic
961C2C47×#301811yescharacteristic
962C2C47×#302711yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3560C2semidirect
2. C47×#3213C2semidirect
3. C47×#3211C2semidirect
4. C47×#2662C2semidirect
5. C47×#1606C2semidirect
6. C47×#1604C2semidirect
7. C47×#1603C2semidirect
8. C47×#1601C2semidirect
9. C47×#1600C2semidirect
10. C47×#1598C2semidirect
11. C47×#1597C2semidirect
12. C47×#1595C2semidirect
13. C47×#1509C2semidirect
14. C47×#1502C2semidirect
15. C47×#1473C2semidirect
35. C2×#124×C47C22semidirect
44. C47×#451C22semidirect
45. C47×#450C22semidirect
48. C47×#448C22semidirect
51. C47×#447C22semidirect
52. C47×#432C22semidirect
53. C47×#431C22semidirect
55. C47×#395C22semidirect
57. C47×#394C22semidirect
62. C4×C4⋊C4×C47C22semidirect
63. C47×#328C22semidirect
64. C47×#328C22semidirect
69. C47×#327C22semidirect
70. C47×#327C22semidirect
71. C47×#324C22semidirect
72. C47×#324C22semidirect
90. C4⋊Q8×C47D4semidirect
91. #127×C47D4semidirect
103. #125×C47D4semidirect
112. #124×C47D4semidirect
153. C4×Q8×C47D4semidirect
162. C4×D4×C47D4semidirect
163. C4×D4×C47D4semidirect
164. C4×D4×C47D4semidirect
427. #18434C47direct (N × H)
472. #3560C2×C47semidirect
473. #3213C2×C47semidirect
474. #3211C2×C47semidirect
475. #2662C2×C47semidirect
476. #1606C2×C47semidirect
477. #1604C2×C47semidirect
478. #1603C2×C47semidirect
479. #1601C2×C47semidirect
480. #1600C2×C47semidirect
481. #1598C2×C47semidirect
482. #1597C2×C47semidirect
483. #1595C2×C47semidirect
484. #1509C2×C47semidirect
485. #1502C2×C47semidirect
486. #1473C2×C47semidirect
516. C2×#124C22×C47semidirect
525. #451C22×C47semidirect
526. #450C22×C47semidirect
529. #448C22×C47semidirect
532. #447C22×C47semidirect
533. #432C22×C47semidirect
534. #431C22×C47semidirect
536. #395C22×C47semidirect
538. #394C22×C47semidirect
543. C4×C4⋊C4C22×C47semidirect
544. #328C22×C47semidirect
545. #328C22×C47semidirect
550. #327C22×C47semidirect
551. #327C22×C47semidirect
552. #324C22×C47semidirect
553. #324C22×C47semidirect
556. C47#18434direct (N × H)
572. C4⋊Q8D4×C47semidirect
573. #127D4×C47semidirect
585. #125D4×C47semidirect
594. #124D4×C47semidirect
635. C4×Q8D4×C47semidirect
644. C4×D4D4×C47semidirect
645. C4×D4D4×C47semidirect
646. C4×D4D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#35602
C47×#32132
C47×#32112
C47×#26622
C47×#16062
C47×#16042
C47×#16032
C47×#16012
C47×#16002
C47×#15982
C47×#15972
C47×#15952
C47×#15092
C47×#15022
C47×#14732
#1843447