Finite Group Databasebeta

← C47×#18661 #26058359

Subgroups — C47×#18661 #26058359

Order 12032.

874 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×#3515C211yesmaximal, characteristic
2C47×#3233C211yesmaximal, characteristic, complemented
3C47×#3170C211yesmaximal, characteristic, complemented
4C47×#3116C211yesmaximal, characteristic, complemented
5C47×#1648C211yesmaximal, characteristic, complemented
6C47×#1647C211yesmaximal, characteristic, complemented
7C47×#1644C211yesmaximal, characteristic, complemented
8C47×#1643C211yesmaximal, characteristic, complemented
9C47×#1636C211yesmaximal, characteristic, complemented
10C47×#1635C211yesmaximal, characteristic, complemented
11C47×#1632C211yesmaximal, characteristic, complemented
12C47×#1632C211yesmaximal, characteristic, complemented
13C47×#1554C211yesmaximal, characteristic, complemented
14C47×#1494C211yesmaximal, characteristic, complemented
15C47×#1476C211yesmaximal, characteristic, complemented
16C47×#557C2211yescharacteristic
17C47×#554C2211yescharacteristic
18C47×#554C2211yescharacteristic
19C47×#553—21no—
20C47×#552—21no—
21C47×#552—22no—
22C47×#552—21no—
23C47×#547—21no—
24C47×#547C2211yescharacteristic
25C47×#541—21no—
26C47×#539—22no—
27C47×#533C2211yescharacteristic
28C47×#533C2211yescharacteristic
29C47×#529—21no—
30C47×#529C2211yescharacteristic
31C2×#125×C47—21no—
32C47×#520—21no—
33C4×#41×C47C2211yescharacteristic
34C47×#500C2211yescharacteristic
35C47×#499—21no—
36C47×#494C2211yescharacteristic
37C47×#488—21no—
38C47×#487C2211yescharacteristic
39C47×#487C2211yescharacteristic
40C47×#485—21no—
41C47×#485—21no—
42C47×#482—21no—
43C47×#477C2211yescharacteristic
44C47×#477C2211yescharacteristic
45C47×#476C2211yescharacteristic
46C47×#476C2211yescharacteristic
47C47×#475C2211yescharacteristic
48C47×#474C2211yescharacteristic
49C47×#467—22no—
50C47×#462C2211yescharacteristic
51C47×#461C2211yescharacteristic
52C47×#452—21no—
53C47×#441—21no—
54C47×#440—21no—
55C4×Q16×C47—22no—
56C47×#432C2211yescharacteristic
57C47×#431C2211yescharacteristic
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×D4⋊C8C2211yescharacteristic
68C47×D4⋊C8C2211yescharacteristic
69C47×D4⋊C8C2211yescharacteristic
70C47×D4⋊C8C2211yescharacteristic
71C2×#41×C47—21no—
72C2×#41×C47D411yescharacteristic
73C2×Q16×C47—21no—
74C2×Q16×C47—22no—
75C2×SD16×C47—21no—
76C22×C8×C47—21no—
77C4⋊Q8×C47—21no—
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81C4⋊Q8×C47C2311yescharacteristic
82#126×C47—22no—
83#126×C47—22no—
84#126×C47—22no—
85#126×C47—21no—
86#125×C47—22no—
87#125×C47—22no—
88#125×C47—22no—
89#125×C47—21no—
90#125×C47—21no—
91#125×C47—22no—
92#125×C47—21no—
93#125×C47—21no—
94#125×C47—21no—
95#125×C47D411yescharacteristic
96#124×C47D411yescharacteristic
97#123×C47—22no—
98#123×C47—22no—
99#123×C47—22no—
100#123×C47—21no—
101#123×C47—22no—
102C22⋊Q8×C47—21no—
103C22⋊Q8×C47—22no—
104C22⋊Q8×C47—22no—
105C22⋊Q8×C47—21no—
106C22⋊Q8×C47—21no—
107C22⋊Q8×C47—21no—
108C22⋊Q8×C47—21no—
109C22⋊Q8×C47—21no—
110C22⋊Q8×C47D412yes—
111C22⋊Q8×C47D411yescharacteristic
112#121×C47—22no—
113#121×C47—21no—
114#121×C47D411yescharacteristic
115C4×Q8×C47—21no—
116C4×Q8×C47—21no—
117C4×Q8×C47—21no—
118C4×Q8×C47—21no—
119C4×Q8×C47—21no—
120C4×Q8×C47D411yescharacteristic
121C4×Q8×C47D412yes—
122C4×Q8×C47C2311yescharacteristic
123C4×Q8×C47C2311yescharacteristic
124C4×D4×C47—22no—
125C4×D4×C47—22no—
126C4×D4×C47—21no—
127C4×D4×C47—21no—
128C4×D4×C47—21no—
129C4×D4×C47—21no—
130C4×D4×C47—21no—
131C4×D4×C47D411yescharacteristic
132C4×D4×C47C2311yescharacteristic
133C4×D4×C47C2311yescharacteristic
134#117×C47—22no—
135#117×C47—22no—
136#117×C47—21no—
137#117×C47—21no—
138#117×C47—21no—
139#117×C47—21no—
140#117×C47D411yescharacteristic
141C2×C4⋊C4×C47—22no—
142C2×C4⋊C4×C47—22no—
143C2×C4⋊C4×C47—21no—
144C2×C4⋊C4×C47—21no—
145C2×C4⋊C4×C47—21no—
146C2×C42×C47—21no—
147C2×C42×C47C2311yescharacteristic
148#107×C47—22no—
149#107×C47—21no—
150#107×C47—21no—
151#107×C47—21no—
152#106×C47—21no—
153#106×C47—21no—
154#106×C47—21no—
155C4⋊C8×C47C2311yescharacteristic
156C4⋊C8×C47C2311yescharacteristic
157C4⋊C8×C47C2311yescharacteristic
158C4⋊C8×C47C2311yescharacteristic
159#103×C47—21no—
160#103×C47—22no—
161#103×C47—21no—
162#103×C47—21no—
163#103×C47—21no—
164#103×C47—21no—
165#103×C47—22no—
166#102×C47—21no—
167#102×C47—21no—
168#102×C47—21no—
169C22⋊C8×C47—21no—
170C22⋊C8×C47—21no—
171#97×C47—21no—
172C4×C8×C47—21no—
173C4×C8×C47—21no—
174C4×C8×C47C2311yescharacteristic
175C4×C8×C47C2311yescharacteristic
176#41×C47—22no—
177#41×C47—41no—
178#41×C47—42no—
179#41×C47—42no—
180C2×Q8×C47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47C2×D411yescharacteristic
184C2×Q8×C47C2×D411yescharacteristic
185C2×Q8×C47C2×D412yes—
186C2×D4×C47—22no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47C2×D411yescharacteristic
190C2×D4×C47C2×D411yescharacteristic
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201Q16×C47—44no—
202Q16×C47—42no—
203SD16×C47—42no—
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—42no—
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—22no—
222C4⋊C4×C47—22no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—41no—
235C4⋊C4×C47—41no—
236C4⋊C4×C47C2×D411yescharacteristic
237C4⋊C4×C47C2×D411yescharacteristic
238C4⋊C4×C47C2×D412yes—
239C4⋊C4×C47C2×D411yescharacteristic
240C4⋊C4×C47C2×D411yescharacteristic
241C22⋊C4×C47—22no—
242C22⋊C4×C47—22no—
243C22⋊C4×C47—22no—
244C22⋊C4×C47—22no—
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×C47—41no—
254C42×C47—22no—
255C42×C47—21no—
256C42×C47—21no—
257C42×C47—22no—
258C42×C47—21no—
259C42×C47—21no—
260C42×C47—41no—
261C42×C47C2×D411yescharacteristic
262C42×C47C2×D411yescharacteristic
263C42×C47C2×D411yescharacteristic
264C42×C47C2411yescharacteristic
265C23×C47—21no—
266C23×C47—21no—
267C23×C47#12011yescharacteristic
268Q8×C47—21no—
269Q8×C47—21no—
270Q8×C47—21no—
271Q8×C47—21no—
272Q8×C47—42no—
273Q8×C47—42no—
274Q8×C47—41no—
275Q8×C47—41no—
276Q8×C47—41no—
277Q8×C47—41no—
278D4×C47—21no—
279D4×C47—21no—
280D4×C47—21no—
281D4×C47—42no—
282D4×C47—44no—
283D4×C47—81no—
284D4×C47#13512yes—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—41no—
298C2×C4×C47—42no—
299C2×C4×C47—44no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—81no—
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—22no—
316C8×C47—41no—
317C8×C47—41no—
318C8×C47—41no—
319C8×C47—41no—
320C8×C47—41no—
321#18661C4711yesmaximal, characteristic, direct product factor, Sylow
322C22×C47—21no—
323C22×C47—22no—
324C22×C47—21no—
325C22×C47—21no—
326C22×C47—41no—
327C22×C47—41no—
328C22×C47—41no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47C2×#12011yescharacteristic
332C4×C47—21no—
333C4×C47—21no—
334C4×C47—21no—
335C4×C47—21no—
336C4×C47—41no—
337C4×C47—41no—
338C4×C47—42no—
339C4×C47—41no—
340C4×C47—41no—
341C4×C47—41no—
342C4×C47—41no—
343C4×C47—42no—
344C4×C47—81no—
345C4×C47—81no—
346C4×C47C2×#13511yescharacteristic
347C4×C47#57511yescharacteristic
348C4×C47#57811yescharacteristic
349C4×C47#57811yescharacteristic
350#3515C2×C4711yescharacteristic
351#3233C2×C4711yescharacteristic, complemented
352#3170C2×C4711yescharacteristic, complemented
353#3116C2×C4711yescharacteristic, complemented
354#1648C2×C4711yescharacteristic, complemented
355#1647C2×C4711yescharacteristic, complemented
356#1644C2×C4711yescharacteristic, complemented
357#1643C2×C4711yescharacteristic, complemented
358#1636C2×C4711yescharacteristic, complemented
359#1635C2×C4711yescharacteristic, complemented
360#1632C2×C4711yescharacteristic, complemented
361#1632C2×C4711yescharacteristic, complemented
362#1554C2×C4711yescharacteristic, complemented
363#1494C2×C4711yescharacteristic, complemented
364#1476C2×C4711yescharacteristic, complemented
365C2×C47—41no—
366C2×C47—42no—
367C2×C47—81no—
368C2×C47#300211yescharacteristic
369C2×C47#301111yescharacteristic
370C2×C47#301811yescharacteristic
371#557C22×C4711yescharacteristic
372#554C22×C4711yescharacteristic
373#554C22×C4711yescharacteristic
374#553—21no—
375#552—21no—
376#552—22no—
377#552—21no—
378#547—21no—
379#547C22×C4711yescharacteristic
380#541—21no—
381#539—22no—
382#533C22×C4711yescharacteristic
383#533C22×C4711yescharacteristic
384#529—21no—
385#529C22×C4711yescharacteristic
386C2×#125—21no—
387#520—21no—
388C4×#41C22×C4711yescharacteristic
389#500C22×C4711yescharacteristic
390#499—21no—
391#494C22×C4711yescharacteristic
392#488—21no—
393#487C22×C4711yescharacteristic
394#487C22×C4711yescharacteristic
395#485—21no—
396#485—21no—
397#482—21no—
398#477C22×C4711yescharacteristic
399#477C22×C4711yescharacteristic
400#476C22×C4711yescharacteristic
401#476C22×C4711yescharacteristic
402#475C22×C4711yescharacteristic
403#474C22×C4711yescharacteristic
404#467—22no—
405#462C22×C4711yescharacteristic
406#461C22×C4711yescharacteristic
407#452—21no—
408#441—21no—
409#440—21no—
410C4×Q16—22no—
411#432C22×C4711yescharacteristic
412#431C22×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
422D4⋊C8C22×C4711yescharacteristic
423D4⋊C8C22×C4711yescharacteristic
424D4⋊C8C22×C4711yescharacteristic
425D4⋊C8C22×C4711yescharacteristic
426C47#1866111yescharacteristic, direct product factor, Sylow
427C2×#41—21no—
428C2×#41D4×C4711yescharacteristic
429C2×Q16—22no—
430C2×Q16—21no—
431C2×SD16—21no—
432C22×C8—21no—
433C4⋊Q8—21no—
434C4⋊Q8C23×C4711yescharacteristic
435C4⋊Q8C23×C4711yescharacteristic
436C4⋊Q8C23×C4711yescharacteristic
437C4⋊Q8C23×C4711yescharacteristic
438#126—22no—
439#126—22no—
440#126—22no—
441#126—21no—
442#125—22no—
443#125—22no—
444#125—22no—
445#125—21no—
446#125—21no—
447#125—22no—
448#125—21no—
449#125—21no—
450#125—21no—
451#125D4×C4711yescharacteristic
452#124D4×C4711yescharacteristic
453#123—22no—
454#123—22no—
455#123—22no—
456#123—21no—
457#123—22no—
458C22⋊Q8—21no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8—21no—
462C22⋊Q8—21no—
463C22⋊Q8—21no—
464C22⋊Q8—21no—
465C22⋊Q8—21no—
466C22⋊Q8D4×C4711yescharacteristic
467C22⋊Q8D4×C4712yes—
468#121—22no—
469#121—21no—
470#121D4×C4711yescharacteristic
471C4×Q8—21no—
472C4×Q8—21no—
473C4×Q8—21no—
474C4×Q8—21no—
475C4×Q8—21no—
476C4×Q8D4×C4711yescharacteristic
477C4×Q8D4×C4712yes—
478C4×Q8C23×C4711yescharacteristic
479C4×Q8C23×C4711yescharacteristic
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—21no—
485C4×D4—21no—
486C4×D4—21no—
487C4×D4D4×C4711yescharacteristic
488C4×D4C23×C4711yescharacteristic
489C4×D4C23×C4711yescharacteristic
490#117—22no—
491#117—22no—
492#117—21no—
493#117—21no—
494#117—21no—
495#117—21no—
496#117D4×C4711yescharacteristic
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C42—21no—
503C2×C42C23×C4711yescharacteristic
504#107—22no—
505#107—21no—
506#107—21no—
507#107—21no—
508#106—21no—
509#106—21no—
510#106—21no—
511C4⋊C8C23×C4711yescharacteristic
512C4⋊C8C23×C4711yescharacteristic
513C4⋊C8C23×C4711yescharacteristic
514C4⋊C8C23×C4711yescharacteristic
515#103—22no—
516#103—21no—
517#103—21no—
518#103—21no—
519#103—22no—
520#103—21no—
521#103—21no—
522#102—21no—
523#102—21no—
524#102—21no—
525C22⋊C8—21no—
526C22⋊C8—21no—
527#97—21no—
528C4×C8—21no—
529C4×C8—21no—
530C4×C8C23×C4711yescharacteristic
531C4×C8C23×C4711yescharacteristic
532#41—22no—
533#41—41no—
534#41—42no—
535#41—42no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8C2×D4×C4711yescharacteristic
540C2×Q8C2×D4×C4711yescharacteristic
541C2×Q8C2×D4×C4712yes—
542C2×D4—22no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4C2×D4×C4711yescharacteristic
546C2×D4C2×D4×C4711yescharacteristic
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4C2×D4×C4711yescharacteristic
555C22×C4C2×D4×C4711yescharacteristic
556C22×C4C2×D4×C4711yescharacteristic
557Q16—44no—
558Q16—42no—
559SD16—42no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—42no—
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—22no—
578C4⋊C4—22no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4C2×D4×C4711yescharacteristic
593C4⋊C4C2×D4×C4711yescharacteristic
594C4⋊C4C2×D4×C4712yes—
595C4⋊C4C2×D4×C4711yescharacteristic
596C4⋊C4C2×D4×C4711yescharacteristic
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—41no—
610C42—22no—
611C42—21no—
612C42—21no—
613C42—22no—
614C42—21no—
615C42—21no—
616C42—41no—
617C42C2×D4×C4711yescharacteristic
618C42C2×D4×C4711yescharacteristic
619C42C2×D4×C4711yescharacteristic
620C42C24×C4711yescharacteristic
621C23—21no—
622C23—21no—
623C23#120×C4711yescharacteristic
624Q8—21no—
625Q8—21no—
626Q8—21no—
627Q8—21no—
628Q8—42no—
629Q8—42no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633Q8—41no—
634D4—21no—
635D4—21no—
636D4—21no—
637D4—42no—
638D4—44no—
639D4—81no—
640D4#135×C4712yes—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—44no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—81no—
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—22no—
672C8—41no—
673C8—41no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—21no—
678C22—22no—
679C22—21no—
680C22—21no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22C2×#120×C4711yescharacteristic
687C4—21no—
688C4—21no—
689C4—21no—
690C4—21no—
691C4—41no—
692C4—41no—
693C4—42no—
694C4—41no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—42no—
699C4—81no—
700C4—81no—
701C4C2×#135×C4711yescharacteristic
702C4C47×#57511yescharacteristic
703C4C47×#57811yescharacteristic
704C4C47×#57811yescharacteristic
705C2—41no—
706C2—42no—
707C2—81no—
708C2C47×#300211yescharacteristic
709C2C47×#301111yescharacteristic
710C2C47×#301811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3515C2
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
2. C47×#3233C2semidirect
3. C47×#3170C2semidirect
4. C47×#3116C2semidirect
5. C47×#1648C2semidirect
6. C47×#1647C2semidirect
7. C47×#1644C2semidirect
8. C47×#1643C2semidirect
9. C47×#1636C2semidirect
10. C47×#1635C2semidirect
11. C47×#1632C2semidirect
12. C47×#1632C2semidirect
13. C47×#1554C2semidirect
14. C47×#1494C2semidirect
15. C47×#1476C2semidirect
321. #18661C47direct (N × H)
351. #3233C2×C47semidirect
352. #3170C2×C47semidirect
353. #3116C2×C47semidirect
354. #1648C2×C47semidirect
355. #1647C2×C47semidirect
356. #1644C2×C47semidirect
357. #1643C2×C47semidirect
358. #1636C2×C47semidirect
359. #1635C2×C47semidirect
360. #1632C2×C47semidirect
361. #1632C2×C47semidirect
362. #1554C2×C47semidirect
363. #1494C2×C47semidirect
364. #1476C2×C47semidirect
426. C47#18661direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35152
C47×#32332
C47×#31702
C47×#31162
C47×#16482
C47×#16472
C47×#16442
C47×#16432
C47×#16362
C47×#16352
C47×#16322
C47×#15542
C47×#14942
C47×#14762
#1866147