Finite Group Databasebeta

← C47×#18963 #26058661

Subgroups — C47×#18963 #26058661

Order 12032.

844 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3555C211yesmaximal, characteristic, complemented
2C47×#3254C211yesmaximal, characteristic, complemented
3C47×#3247C211yesmaximal, characteristic
4C47×#3210C211yesmaximal, characteristic, complemented
5C47×#1638C211yesmaximal, characteristic, complemented
6C47×#1636C211yesmaximal, characteristic, complemented
7C47×#1633C211yesmaximal, characteristic, complemented
8C47×#1632C211yesmaximal, characteristic, complemented
9C47×#1628C211yesmaximal, characteristic, complemented
10C47×#1626C211yesmaximal, characteristic, complemented
11C47×#1623C211yesmaximal, characteristic, complemented
12C47×#1622C211yesmaximal, characteristic, complemented
13C47×#1550C211yesmaximal, characteristic, complemented
14C47×#1495C211yesmaximal, characteristic, complemented
15C47×#1481C211yesmaximal, characteristic, complemented
16C47×#563—22no—
17Q82×C47C2211yescharacteristic
18C47×#557—21no—
19C47×#557C2211yescharacteristic
20C47×#556—21no—
21C47×#556—21no—
22C47×#556C2211yescharacteristic
23C47×#554C2211yescharacteristic
24C47×#552—21no—
25C47×#544—21no—
26C47×#542—21no—
27C47×#541—21no—
28C47×#541—21no—
29C47×#541—22no—
30C47×#533C2211yescharacteristic
31C47×#533C2211yescharacteristic
32C47×#532C2211yescharacteristic
33C47×#529C2211yescharacteristic
34C47×#494C2211yescharacteristic
35C47×#492C2211yescharacteristic
36C47×#487C2211yescharacteristic
37C47×#486C2211yescharacteristic
38C47×#478—21no—
39C47×#477C2211yescharacteristic
40C47×#477C2211yescharacteristic
41C47×#477C2211yescharacteristic
42C47×#476C2211yescharacteristic
43C47×#474—21no—
44C47×#468—21no—
45C47×#468—21no—
46C47×#466—21no—
47C47×#465—21no—
48C47×#464—22no—
49C47×#463—21no—
50C47×#461—21no—
51C47×#460C2211yescharacteristic
52C47×#460C2211yescharacteristic
53C47×#460C2211yescharacteristic
54C47×#459C2211yescharacteristic
55C47×#452—22no—
56C47×#431C2211yescharacteristic
57C47×#423C2211yescharacteristic
58C2×C4⋊C8×C47C2211yescharacteristic
59C47×#333C2211yescharacteristic
60C47×#333C2211yescharacteristic
61C47×#332C2211yescharacteristic
62C47×#332C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×Q8⋊C8C2211yescharacteristic
67C47×Q8⋊C8C2211yescharacteristic
68C47×Q8⋊C8C2211yescharacteristic
69C47×D4⋊C8C2211yescharacteristic
70C47×D4⋊C8C2211yescharacteristic
71C2×#41×C47—21no—
72C2×Q16×C47—22no—
73C2×SD16×C47—22no—
74C2×SD16×C47—21no—
75C2×SD16×C47—21no—
76C2×SD16×C47—21no—
77C2×D8×C47—21no—
78C2×M16×C47—21no—
79C22×C8×C47—21no—
80C4⋊Q8×C47—22no—
81C4⋊Q8×C47—21no—
82C4⋊Q8×C47—22no—
83C4⋊Q8×C47—21no—
84C4⋊Q8×C47—21no—
85C4⋊Q8×C47D411yescharacteristic
86C4⋊Q8×C47D411yescharacteristic
87C4⋊Q8×C47C2311yescharacteristic
88C4⋊Q8×C47C2311yescharacteristic
89C4⋊Q8×C47C2311yescharacteristic
90#127×C47C2311yescharacteristic
91#126×C47—22no—
92#126×C47—22no—
93#126×C47—22no—
94#126×C47—22no—
95#126×C47—22no—
96#126×C47—22no—
97#126×C47—21no—
98#125×C47—22no—
99#125×C47—22no—
100#125×C47—22no—
101#125×C47—22no—
102#125×C47—21no—
103#125×C47—22no—
104#125×C47—21no—
105#125×C47—21no—
106#125×C47—21no—
107#125×C47D411yescharacteristic
108#124×C47—22no—
109#124×C47—21no—
110#124×C47—21no—
111#124×C47D411yescharacteristic
112#123×C47—22no—
113#123×C47—21no—
114C22⋊Q8×C47—22no—
115C22⋊Q8×C47—22no—
116C22⋊Q8×C47—21no—
117C22⋊Q8×C47—21no—
118C22⋊Q8×C47—22no—
119C22⋊Q8×C47—21no—
120C22⋊Q8×C47—21no—
121C22⋊Q8×C47D412yes—
122C22⋊Q8×C47D411yescharacteristic
123C22⋊Q8×C47D411yescharacteristic
124C22⋊Q8×C47D411yescharacteristic
125#121×C47—21no—
126#121×C47—21no—
127#121×C47D411yescharacteristic
128C4×Q8×C47—22no—
129C4×Q8×C47—21no—
130C4×Q8×C47—21no—
131C4×Q8×C47—21no—
132C4×Q8×C47—21no—
133C4×Q8×C47—21no—
134C4×Q8×C47—21no—
135C4×Q8×C47—21no—
136C4×Q8×C47D412yes—
137C4×Q8×C47C2311yescharacteristic
138C4×Q8×C47C2311yescharacteristic
139C4×Q8×C47C2311yescharacteristic
140C4×D4×C47—21no—
141C4×D4×C47—21no—
142C4×D4×C47—21no—
143C4×D4×C47—21no—
144C4×D4×C47C2311yescharacteristic
145#117×C47—22no—
146#117×C47—21no—
147#117×C47—21no—
148#117×C47—21no—
149#117×C47—21no—
150C2×C4⋊C4×C47—21no—
151C2×C42×C47C2311yescharacteristic
152#107×C47—21no—
153#107×C47—21no—
154#107×C47—21no—
155#106×C47—21no—
156C4⋊C8×C47—21no—
157C4⋊C8×C47—21no—
158C4⋊C8×C47—21no—
159C4⋊C8×C47C2311yescharacteristic
160C4⋊C8×C47C2311yescharacteristic
161C4⋊C8×C47C2311yescharacteristic
162C4⋊C8×C47C2311yescharacteristic
163#103×C47—21no—
164#103×C47—21no—
165#103×C47—21no—
166#103×C47—22no—
167#102×C47—21no—
168#102×C47—22no—
169#102×C47—21no—
170#102×C47—21no—
171#102×C47—21no—
172#102×C47—21no—
173C22⋊C8×C47—21no—
174C4×C8×C47C2311yescharacteristic
175C4×C8×C47C2311yescharacteristic
176#41×C47—82no—
177C2×Q8×C47—22no—
178C2×Q8×C47—21no—
179C2×Q8×C47—21no—
180C2×Q8×C47—21no—
181C2×Q8×C47C2×D411yescharacteristic
182C2×Q8×C47C2×D411yescharacteristic
183C2×Q8×C47C2×D411yescharacteristic
184C2×Q8×C47C2×D412yes—
185C2×D4×C47—21no—
186C2×D4×C47—21no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—41no—
190C2×D4×C47C2×D411yescharacteristic
191C22×C4×C47—22no—
192C22×C4×C47—21no—
193C22×C4×C47—41no—
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197Q16×C47—82no—
198SD16×C47—81no—
199SD16×C47—81no—
200SD16×C47—81no—
201SD16×C47—82no—
202D8×C47—81no—
203M16×C47—81no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—81no—
211C4⋊C4×C47—22no—
212C4⋊C4×C47—22no—
213C4⋊C4×C47—22no—
214C4⋊C4×C47—22no—
215C4⋊C4×C47—22no—
216C4⋊C4×C47—22no—
217C4⋊C4×C47—22no—
218C4⋊C4×C47—22no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—22no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—22no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47C2×D412yes—
238C4⋊C4×C47C2×D411yescharacteristic
239C4⋊C4×C47C2×D411yescharacteristic
240C4⋊C4×C47C2×D411yescharacteristic
241C4⋊C4×C47C2×D411yescharacteristic
242C22⋊C4×C47—22no—
243C22⋊C4×C47—22no—
244C22⋊C4×C47—22no—
245C22⋊C4×C47—21no—
246C22⋊C4×C47—22no—
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×C47—41no—
254C22⋊C4×C47—41no—
255C42×C47—22no—
256C42×C47—22no—
257C42×C47—22no—
258C42×C47—22no—
259C42×C47—21no—
260C42×C47—21no—
261C42×C47—21no—
262C42×C47C2×D411yescharacteristic
263C42×C47C2×D411yescharacteristic
264C42×C47C2×D411yescharacteristic
265C42×C47C2411yescharacteristic
266C23×C47—21no—
267C23×C47—41no—
268C23×C47#12011yescharacteristic
269Q8×C47—21no—
270Q8×C47—21no—
271Q8×C47—21no—
272Q8×C47—21no—
273Q8×C47—21no—
274Q8×C47—21no—
275Q8×C47—42no—
276Q8×C47—42no—
277Q8×C47—41no—
278Q8×C47—41no—
279Q8×C47—81no—
280Q8×C47—82no—
281D4×C47—21no—
282D4×C47—21no—
283D4×C47—42no—
284D4×C47—41no—
285D4×C47—41no—
286D4×C47—41no—
287D4×C47—41no—
288D4×C47—81no—
289D4×C47—82no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—22no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—22no—
302C2×C4×C47—21no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—82no—
308C2×C4×C47—82no—
309C2×C4×C47#12011yescharacteristic
310C2×C4×C47#12011yescharacteristic
311C2×C4×C47#12011yescharacteristic
312C2×C4×C47C22×D411yescharacteristic
313C2×C4×C47C22×D411yescharacteristic
314C2×C4×C47C22×D411yescharacteristic
315C8×C47—41no—
316C8×C47—41no—
317C8×C47—41no—
318C8×C47—41no—
319C8×C47—41no—
320C8×C47—41no—
321#18963C4711yesmaximal, characteristic, direct product factor, Sylow
322C22×C47—21no—
323C22×C47—21no—
324C22×C47—21no—
325C22×C47—41no—
326C22×C47—41no—
327C22×C47—41no—
328C22×C47—81no—
329C22×C47—81no—
330C22×C47—81no—
331C22×C47C2×#12011yescharacteristic
332C4×C47—21no—
333C4×C47—21no—
334C4×C47—21no—
335C4×C47—21no—
336C4×C47—41no—
337C4×C47—41no—
338C4×C47—41no—
339C4×C47—41no—
340C4×C47—42no—
341C4×C47—41no—
342C4×C47—42no—
343C4×C47—41no—
344C4×C47—41no—
345C4×C47—81no—
346C4×C47#57711yescharacteristic
347C4×C47#57711yescharacteristic
348C4×C47#57811yescharacteristic
349C4×C47#57811yescharacteristic
350#3555C2×C4711yescharacteristic, complemented
351#3254C2×C4711yescharacteristic, complemented
352#3247C2×C4711yescharacteristic
353#3210C2×C4711yescharacteristic, complemented
354#1638C2×C4711yescharacteristic, complemented
355#1636C2×C4711yescharacteristic, complemented
356#1633C2×C4711yescharacteristic, complemented
357#1632C2×C4711yescharacteristic, complemented
358#1628C2×C4711yescharacteristic, complemented
359#1626C2×C4711yescharacteristic, complemented
360#1623C2×C4711yescharacteristic, complemented
361#1622C2×C4711yescharacteristic, complemented
362#1550C2×C4711yescharacteristic, complemented
363#1495C2×C4711yescharacteristic, complemented
364#1481C2×C4711yescharacteristic, complemented
365C2×C47—41no—
366C2×C47—81no—
367C2×C47—161no—
368C2×C47#301311yescharacteristic
369C2×C47#301311yescharacteristic
370C2×C47#302111yescharacteristic
371#563—22no—
372Q82C22×C4711yescharacteristic
373#557—21no—
374#557C22×C4711yescharacteristic
375#556—21no—
376#556—21no—
377#556C22×C4711yescharacteristic
378#554C22×C4711yescharacteristic
379#552—21no—
380#544—21no—
381#542—21no—
382#541—21no—
383#541—21no—
384#541—22no—
385#533C22×C4711yescharacteristic
386#533C22×C4711yescharacteristic
387#532C22×C4711yescharacteristic
388#529C22×C4711yescharacteristic
389#494C22×C4711yescharacteristic
390#492C22×C4711yescharacteristic
391#487C22×C4711yescharacteristic
392#486C22×C4711yescharacteristic
393#478—21no—
394#477C22×C4711yescharacteristic
395#477C22×C4711yescharacteristic
396#477C22×C4711yescharacteristic
397#476C22×C4711yescharacteristic
398#474—21no—
399#468—21no—
400#468—21no—
401#466—21no—
402#465—21no—
403#464—22no—
404#463—21no—
405#461—21no—
406#460C22×C4711yescharacteristic
407#460C22×C4711yescharacteristic
408#460C22×C4711yescharacteristic
409#459C22×C4711yescharacteristic
410#452—22no—
411#431C22×C4711yescharacteristic
412#423C22×C4711yescharacteristic
413C2×C4⋊C8C22×C4711yescharacteristic
414#333C22×C4711yescharacteristic
415#333C22×C4711yescharacteristic
416#332C22×C4711yescharacteristic
417#332C22×C4711yescharacteristic
418Q8⋊C8C22×C4711yescharacteristic
419Q8⋊C8C22×C4711yescharacteristic
420Q8⋊C8C22×C4711yescharacteristic
421Q8⋊C8C22×C4711yescharacteristic
422Q8⋊C8C22×C4711yescharacteristic
423Q8⋊C8C22×C4711yescharacteristic
424D4⋊C8C22×C4711yescharacteristic
425D4⋊C8C22×C4711yescharacteristic
426C47#1896311yescharacteristic, direct product factor, Sylow
427C2×#41—21no—
428C2×Q16—22no—
429C2×SD16—22no—
430C2×SD16—21no—
431C2×SD16—21no—
432C2×SD16—21no—
433C2×D8—21no—
434C2×M16—21no—
435C22×C8—21no—
436C4⋊Q8—22no—
437C4⋊Q8—21no—
438C4⋊Q8—22no—
439C4⋊Q8—21no—
440C4⋊Q8—21no—
441C4⋊Q8D4×C4711yescharacteristic
442C4⋊Q8D4×C4711yescharacteristic
443C4⋊Q8C23×C4711yescharacteristic
444C4⋊Q8C23×C4711yescharacteristic
445C4⋊Q8C23×C4711yescharacteristic
446#127C23×C4711yescharacteristic
447#126—22no—
448#126—22no—
449#126—22no—
450#126—22no—
451#126—22no—
452#126—22no—
453#126—21no—
454#125—22no—
455#125—22no—
456#125—22no—
457#125—22no—
458#125—21no—
459#125—22no—
460#125—21no—
461#125—21no—
462#125—21no—
463#125D4×C4711yescharacteristic
464#124—22no—
465#124—21no—
466#124—21no—
467#124D4×C4711yescharacteristic
468#123—22no—
469#123—21no—
470C22⋊Q8—22no—
471C22⋊Q8—22no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—22no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8D4×C4711yescharacteristic
478C22⋊Q8D4×C4711yescharacteristic
479C22⋊Q8D4×C4711yescharacteristic
480C22⋊Q8D4×C4712yes—
481#121—21no—
482#121—21no—
483#121D4×C4711yescharacteristic
484C4×Q8—22no—
485C4×Q8—21no—
486C4×Q8—21no—
487C4×Q8—21no—
488C4×Q8—21no—
489C4×Q8—21no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8D4×C4712yes—
493C4×Q8C23×C4711yescharacteristic
494C4×Q8C23×C4711yescharacteristic
495C4×Q8C23×C4711yescharacteristic
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4C23×C4711yescharacteristic
501#117—22no—
502#117—21no—
503#117—21no—
504#117—21no—
505#117—21no—
506C2×C4⋊C4—21no—
507C2×C42C23×C4711yescharacteristic
508#107—21no—
509#107—21no—
510#107—21no—
511#106—21no—
512C4⋊C8—21no—
513C4⋊C8—21no—
514C4⋊C8—21no—
515C4⋊C8C23×C4711yescharacteristic
516C4⋊C8C23×C4711yescharacteristic
517C4⋊C8C23×C4711yescharacteristic
518C4⋊C8C23×C4711yescharacteristic
519#103—21no—
520#103—21no—
521#103—21no—
522#103—22no—
523#102—21no—
524#102—22no—
525#102—21no—
526#102—21no—
527#102—21no—
528#102—21no—
529C22⋊C8—21no—
530C4×C8C23×C4711yescharacteristic
531C4×C8C23×C4711yescharacteristic
532#41—82no—
533C2×Q8—22no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8C2×D4×C4711yescharacteristic
538C2×Q8C2×D4×C4711yescharacteristic
539C2×Q8C2×D4×C4711yescharacteristic
540C2×Q8C2×D4×C4712yes—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—41no—
546C2×D4C2×D4×C4711yescharacteristic
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—41no—
550C22×C4C2×D4×C4711yescharacteristic
551C22×C4C2×D4×C4711yescharacteristic
552C22×C4C2×D4×C4711yescharacteristic
553Q16—82no—
554SD16—81no—
555SD16—81no—
556SD16—81no—
557SD16—82no—
558D8—81no—
559M16—81no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—81no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—22no—
583C4⋊C4—21no—
584C4⋊C4—22no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4C2×D4×C4712yes—
594C4⋊C4C2×D4×C4711yescharacteristic
595C4⋊C4C2×D4×C4711yescharacteristic
596C4⋊C4C2×D4×C4711yescharacteristic
597C4⋊C4C2×D4×C4711yescharacteristic
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—21no—
602C22⋊C4—22no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42C2×D4×C4711yescharacteristic
619C42C2×D4×C4711yescharacteristic
620C42C2×D4×C4711yescharacteristic
621C42C24×C4711yescharacteristic
622C23—21no—
623C23—41no—
624C23#120×C4711yescharacteristic
625Q8—21no—
626Q8—21no—
627Q8—21no—
628Q8—21no—
629Q8—21no—
630Q8—21no—
631Q8—42no—
632Q8—42no—
633Q8—41no—
634Q8—41no—
635Q8—81no—
636Q8—82no—
637D4—21no—
638D4—21no—
639D4—42no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—81no—
645D4—82no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—82no—
664C2×C4—82no—
665C2×C4#120×C4711yescharacteristic
666C2×C4#120×C4711yescharacteristic
667C2×C4#120×C4711yescharacteristic
668C2×C4C22×D4×C4711yescharacteristic
669C2×C4C22×D4×C4711yescharacteristic
670C2×C4C22×D4×C4711yescharacteristic
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22C2×#120×C4711yescharacteristic
687C4—21no—
688C4—21no—
689C4—21no—
690C4—21no—
691C4—41no—
692C4—41no—
693C4—41no—
694C4—41no—
695C4—42no—
696C4—41no—
697C4—42no—
698C4—41no—
699C4—41no—
700C4—81no—
701C4C47×#57711yescharacteristic
702C4C47×#57711yescharacteristic
703C4C47×#57811yescharacteristic
704C4C47×#57811yescharacteristic
705C2—41no—
706C2—81no—
707C2—161no—
708C2C47×#301311yescharacteristic
709C2C47×#301311yescharacteristic
710C2C47×#302111yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3247C2
LCSG ▷ C42 ▷ 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×#3555C2semidirect
2. C47×#3254C2semidirect
4. C47×#3210C2semidirect
5. C47×#1638C2semidirect
6. C47×#1636C2semidirect
7. C47×#1633C2semidirect
8. C47×#1632C2semidirect
9. C47×#1628C2semidirect
10. C47×#1626C2semidirect
11. C47×#1623C2semidirect
12. C47×#1622C2semidirect
13. C47×#1550C2semidirect
14. C47×#1495C2semidirect
15. C47×#1481C2semidirect
321. #18963C47direct (N × H)
350. #3555C2×C47semidirect
351. #3254C2×C47semidirect
353. #3210C2×C47semidirect
354. #1638C2×C47semidirect
355. #1636C2×C47semidirect
356. #1633C2×C47semidirect
357. #1632C2×C47semidirect
358. #1628C2×C47semidirect
359. #1626C2×C47semidirect
360. #1623C2×C47semidirect
361. #1622C2×C47semidirect
362. #1550C2×C47semidirect
363. #1495C2×C47semidirect
364. #1481C2×C47semidirect
426. C47#18963direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35552
C47×#32542
C47×#32472
C47×#32102
C47×#16382
C47×#16362
C47×#16332
C47×#16322
C47×#16282
C47×#16262
C47×#16232
C47×#16222
C47×#15502
C47×#14952
C47×#14812
#1896347