Finite Group Databasebeta

← C47×#18744 #26058442

Subgroups — C47×#18744 #26058442

Order 12032.

852 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3555C211yesmaximal, characteristic, complemented
2C47×#3246C211yesmaximal, characteristic, complemented
3C47×#3212C211yesmaximal, characteristic
4C47×#3182C211yesmaximal, characteristic, complemented
5C47×#1650C211yesmaximal, characteristic, complemented
6C47×#1648C211yesmaximal, characteristic, complemented
7C47×#1645C211yesmaximal, characteristic, complemented
8C47×#1643C211yesmaximal, characteristic, complemented
9C47×#1628C211yesmaximal, characteristic, complemented
10C47×#1626C211yesmaximal, characteristic, complemented
11C47×#1623C211yesmaximal, characteristic, complemented
12C47×#1622C211yesmaximal, characteristic, complemented
13C47×#1542C211yesmaximal, characteristic, complemented
14C47×#1485C211yesmaximal, characteristic, complemented
15C47×#1483C211yesmaximal, 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×#500C2211yescharacteristic
35C47×#495—21no—
36C47×#492C2211yescharacteristic
37C47×#488—21no—
38C47×#487C2211yescharacteristic
39C47×#486C2211yescharacteristic
40C47×#476—21no—
41C47×#475C2211yescharacteristic
42C47×#475C2211yescharacteristic
43C47×#468—22no—
44C47×#465—21no—
45C47×#465—21no—
46C47×#462C2211yescharacteristic
47C47×#461—21no—
48C47×#461C2211yescharacteristic
49C47×#460C2211yescharacteristic
50C47×#460C2211yescharacteristic
51C47×#460C2211yescharacteristic
52C47×#459C2211yescharacteristic
53C47×#452—21no—
54C47×#449—21no—
55C47×#440—22no—
56C47×#431C2211yescharacteristic
57C2×C4⋊C8×C47C2211yescharacteristic
58C4×M16×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—21no—
73C2×SD16×C47—22no—
74C2×SD16×C47—21no—
75C2×SD16×C47—21no—
76C2×SD16×C47—21no—
77C2×SD16×C47—21no—
78C2×D8×C47—21no—
79C2×M16×C47—21no—
80C22×C8×C47—21no—
81C4⋊Q8×C47—22no—
82C4⋊Q8×C47—21no—
83C4⋊Q8×C47—22no—
84C4⋊Q8×C47—21no—
85C4⋊Q8×C47—21no—
86C4⋊Q8×C47D411yescharacteristic
87C4⋊Q8×C47D411yescharacteristic
88C4⋊Q8×C47C2311yescharacteristic
89C4⋊Q8×C47C2311yescharacteristic
90C4⋊Q8×C47C2311yescharacteristic
91#127×C47C2311yescharacteristic
92#126×C47—22no—
93#126×C47—22no—
94#126×C47—22no—
95#126×C47—22no—
96#126×C47—22no—
97#126×C47—22no—
98#126×C47—21no—
99#125×C47—22no—
100#125×C47—22no—
101#125×C47—22no—
102#125×C47—22no—
103#125×C47—21no—
104#125×C47—22no—
105#125×C47—21no—
106#125×C47—21no—
107#125×C47—21no—
108#125×C47D411yescharacteristic
109#124×C47—22no—
110#124×C47—21no—
111#124×C47—21no—
112#124×C47D411yescharacteristic
113#123×C47—22no—
114#123×C47—21no—
115C22⋊Q8×C47—22no—
116C22⋊Q8×C47—22no—
117C22⋊Q8×C47—21no—
118C22⋊Q8×C47—21no—
119C22⋊Q8×C47—22no—
120C22⋊Q8×C47—21no—
121C22⋊Q8×C47—21no—
122C22⋊Q8×C47D411yescharacteristic
123C22⋊Q8×C47D411yescharacteristic
124C22⋊Q8×C47D411yescharacteristic
125C22⋊Q8×C47D412yes—
126#121×C47—21no—
127#121×C47—21no—
128#121×C47D411yescharacteristic
129C4×Q8×C47—22no—
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×C47—21no—
137C4×Q8×C47D412yes—
138C4×Q8×C47C2311yescharacteristic
139C4×Q8×C47C2311yescharacteristic
140C4×Q8×C47C2311yescharacteristic
141C4×D4×C47—21no—
142C4×D4×C47—21no—
143C4×D4×C47—21no—
144C4×D4×C47—21no—
145C4×D4×C47C2311yescharacteristic
146#117×C47—22no—
147#117×C47—21no—
148#117×C47—21no—
149#117×C47—21no—
150#117×C47—21no—
151C2×C4⋊C4×C47—21no—
152C2×C42×C47C2311yescharacteristic
153#107×C47—22no—
154#106×C47—21no—
155#106×C47—21no—
156C4⋊C8×C47—21no—
157C4⋊C8×C47C2311yescharacteristic
158C4⋊C8×C47C2311yescharacteristic
159C4⋊C8×C47C2311yescharacteristic
160C4⋊C8×C47C2311yescharacteristic
161#103×C47—21no—
162#103×C47—21no—
163#103×C47—22no—
164#103×C47—21no—
165#103×C47—21no—
166#102×C47—21no—
167#102×C47—21no—
168#102×C47—21no—
169#102×C47—21no—
170#102×C47—22no—
171C22⋊C8×C47—21no—
172#97×C47—21no—
173C4×C8×C47—21no—
174C4×C8×C47C2311yescharacteristic
175C4×C8×C47C2311yescharacteristic
176#41×C47—81no—
177#41×C47—81no—
178C2×Q8×C47—22no—
179C2×Q8×C47—21no—
180C2×Q8×C47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47C2×D411yescharacteristic
183C2×Q8×C47C2×D411yescharacteristic
184C2×Q8×C47C2×D411yescharacteristic
185C2×Q8×C47C2×D412yes—
186C2×D4×C47—21no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—21no—
190C2×D4×C47—41no—
191C2×D4×C47C2×D411yescharacteristic
192C22×C4×C47—22no—
193C22×C4×C47—21no—
194C22×C4×C47—41no—
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198Q16×C47—81no—
199SD16×C47—44no—
200SD16×C47—81no—
201SD16×C47—81no—
202SD16×C47—81no—
203SD16×C47—81no—
204D8×C47—81no—
205M16×C47—42no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—81no—
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—22no—
220C4⋊C4×C47—22no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—22no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—22no—
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×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47C2×D411yescharacteristic
240C4⋊C4×C47C2×D411yescharacteristic
241C4⋊C4×C47C2×D411yescharacteristic
242C4⋊C4×C47C2×D411yescharacteristic
243C4⋊C4×C47C2×D412yes—
244C22⋊C4×C47—22no—
245C22⋊C4×C47—22no—
246C22⋊C4×C47—22no—
247C22⋊C4×C47—21no—
248C22⋊C4×C47—22no—
249C22⋊C4×C47—21no—
250C22⋊C4×C47—21no—
251C22⋊C4×C47—21no—
252C22⋊C4×C47—21no—
253C22⋊C4×C47—21no—
254C22⋊C4×C47—21no—
255C22⋊C4×C47—41no—
256C22⋊C4×C47—41no—
257C42×C47—22no—
258C42×C47—22no—
259C42×C47—22no—
260C42×C47—22no—
261C42×C47—21no—
262C42×C47—21no—
263C42×C47—21no—
264C42×C47C2×D411yescharacteristic
265C42×C47C2×D411yescharacteristic
266C42×C47C2×D411yescharacteristic
267C42×C47C2411yescharacteristic
268C23×C47—21no—
269C23×C47—41no—
270C23×C47#12011yescharacteristic
271Q8×C47—21no—
272Q8×C47—21no—
273Q8×C47—21no—
274Q8×C47—21no—
275Q8×C47—21no—
276Q8×C47—21no—
277Q8×C47—42no—
278Q8×C47—41no—
279Q8×C47—41no—
280Q8×C47—41no—
281Q8×C47—41no—
282Q8×C47—81no—
283Q8×C47—82no—
284D4×C47—21no—
285D4×C47—21no—
286D4×C47—42no—
287D4×C47—41no—
288D4×C47—41no—
289D4×C47—41no—
290D4×C47—41no—
291D4×C47—81no—
292D4×C47—82no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—22no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—22no—
305C2×C4×C47—21no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—82no—
311C2×C4×C47—82no—
312C2×C4×C47#12011yescharacteristic
313C2×C4×C47#12011yescharacteristic
314C2×C4×C47#12011yescharacteristic
315C2×C4×C47C22×D411yescharacteristic
316C2×C4×C47C22×D411yescharacteristic
317C2×C4×C47C22×D411yescharacteristic
318C8×C47—22no—
319C8×C47—41no—
320C8×C47—41no—
321C8×C47—41no—
322C8×C47—41no—
323C8×C47—41no—
324#18744C4711yesmaximal, characteristic, direct product factor, Sylow
325C22×C47—21no—
326C22×C47—21no—
327C22×C47—21no—
328C22×C47—41no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47—81no—
332C22×C47—81no—
333C22×C47—81no—
334C22×C47C2×#12011yescharacteristic
335C4×C47—21no—
336C4×C47—21no—
337C4×C47—21no—
338C4×C47—21no—
339C4×C47—41no—
340C4×C47—42no—
341C4×C47—41no—
342C4×C47—41no—
343C4×C47—41no—
344C4×C47—41no—
345C4×C47—42no—
346C4×C47—41no—
347C4×C47—41no—
348C4×C47—81no—
349C4×C47#57711yescharacteristic
350C4×C47#57711yescharacteristic
351C4×C47#57711yescharacteristic
352C4×C47#57811yescharacteristic
353#3555C2×C4711yescharacteristic, complemented
354#3246C2×C4711yescharacteristic, complemented
355#3212C2×C4711yescharacteristic
356#3182C2×C4711yescharacteristic, complemented
357#1650C2×C4711yescharacteristic, complemented
358#1648C2×C4711yescharacteristic, complemented
359#1645C2×C4711yescharacteristic, complemented
360#1643C2×C4711yescharacteristic, complemented
361#1628C2×C4711yescharacteristic, complemented
362#1626C2×C4711yescharacteristic, complemented
363#1623C2×C4711yescharacteristic, complemented
364#1622C2×C4711yescharacteristic, complemented
365#1542C2×C4711yescharacteristic, complemented
366#1485C2×C4711yescharacteristic, complemented
367#1483C2×C4711yescharacteristic, complemented
368C2×C47—41no—
369C2×C47—81no—
370C2×C47—161no—
371C2×C47#301011yescharacteristic
372C2×C47#301311yescharacteristic
373C2×C47#301811yescharacteristic
374#563—22no—
375Q82C22×C4711yescharacteristic
376#557—21no—
377#557C22×C4711yescharacteristic
378#556—21no—
379#556—21no—
380#556C22×C4711yescharacteristic
381#554C22×C4711yescharacteristic
382#552—21no—
383#544—21no—
384#542—21no—
385#541—21no—
386#541—21no—
387#541—22no—
388#533C22×C4711yescharacteristic
389#533C22×C4711yescharacteristic
390#532C22×C4711yescharacteristic
391#529C22×C4711yescharacteristic
392#500C22×C4711yescharacteristic
393#495—21no—
394#492C22×C4711yescharacteristic
395#488—21no—
396#487C22×C4711yescharacteristic
397#486C22×C4711yescharacteristic
398#476—21no—
399#475C22×C4711yescharacteristic
400#475C22×C4711yescharacteristic
401#468—22no—
402#465—21no—
403#465—21no—
404#462C22×C4711yescharacteristic
405#461—21no—
406#461C22×C4711yescharacteristic
407#460C22×C4711yescharacteristic
408#460C22×C4711yescharacteristic
409#460C22×C4711yescharacteristic
410#459C22×C4711yescharacteristic
411#452—21no—
412#449—21no—
413#440—22no—
414#431C22×C4711yescharacteristic
415C2×C4⋊C8C22×C4711yescharacteristic
416C4×M16C22×C4711yescharacteristic
417#333C22×C4711yescharacteristic
418#333C22×C4711yescharacteristic
419#332C22×C4711yescharacteristic
420#332C22×C4711yescharacteristic
421Q8⋊C8C22×C4711yescharacteristic
422Q8⋊C8C22×C4711yescharacteristic
423Q8⋊C8C22×C4711yescharacteristic
424Q8⋊C8C22×C4711yescharacteristic
425Q8⋊C8C22×C4711yescharacteristic
426Q8⋊C8C22×C4711yescharacteristic
427D4⋊C8C22×C4711yescharacteristic
428D4⋊C8C22×C4711yescharacteristic
429C47#1874411yescharacteristic, direct product factor, Sylow
430C2×#41—21no—
431C2×Q16—21no—
432C2×SD16—22no—
433C2×SD16—21no—
434C2×SD16—21no—
435C2×SD16—21no—
436C2×SD16—21no—
437C2×D8—21no—
438C2×M16—21no—
439C22×C8—21no—
440C4⋊Q8—22no—
441C4⋊Q8—21no—
442C4⋊Q8—22no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8D4×C4711yescharacteristic
446C4⋊Q8D4×C4711yescharacteristic
447C4⋊Q8C23×C4711yescharacteristic
448C4⋊Q8C23×C4711yescharacteristic
449C4⋊Q8C23×C4711yescharacteristic
450#127C23×C4711yescharacteristic
451#126—22no—
452#126—22no—
453#126—22no—
454#126—22no—
455#126—22no—
456#126—22no—
457#126—21no—
458#125—22no—
459#125—22no—
460#125—22no—
461#125—22no—
462#125—21no—
463#125—22no—
464#125—21no—
465#125—21no—
466#125—21no—
467#125D4×C4711yescharacteristic
468#124—22no—
469#124—21no—
470#124—21no—
471#124D4×C4711yescharacteristic
472#123—22no—
473#123—21no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—22no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8D4×C4711yescharacteristic
482C22⋊Q8D4×C4711yescharacteristic
483C22⋊Q8D4×C4711yescharacteristic
484C22⋊Q8D4×C4712yes—
485#121—21no—
486#121—21no—
487#121D4×C4711yescharacteristic
488C4×Q8—22no—
489C4×Q8—21no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8—21no—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8D4×C4712yes—
497C4×Q8C23×C4711yescharacteristic
498C4×Q8C23×C4711yescharacteristic
499C4×Q8C23×C4711yescharacteristic
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4C23×C4711yescharacteristic
505#117—22no—
506#117—21no—
507#117—21no—
508#117—21no—
509#117—21no—
510C2×C4⋊C4—21no—
511C2×C42C23×C4711yescharacteristic
512#107—22no—
513#106—21no—
514#106—21no—
515C4⋊C8—21no—
516C4⋊C8C23×C4711yescharacteristic
517C4⋊C8C23×C4711yescharacteristic
518C4⋊C8C23×C4711yescharacteristic
519C4⋊C8C23×C4711yescharacteristic
520#103—22no—
521#103—21no—
522#103—21no—
523#103—21no—
524#103—21no—
525#102—22no—
526#102—21no—
527#102—21no—
528#102—21no—
529#102—21no—
530C22⋊C8—21no—
531#97—21no—
532C4×C8—21no—
533C4×C8C23×C4711yescharacteristic
534C4×C8C23×C4711yescharacteristic
535#41—81no—
536#41—81no—
537C2×Q8—22no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8C2×D4×C4711yescharacteristic
542C2×Q8C2×D4×C4711yescharacteristic
543C2×Q8C2×D4×C4711yescharacteristic
544C2×Q8C2×D4×C4712yes—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—41no—
550C2×D4C2×D4×C4711yescharacteristic
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—41no—
554C22×C4C2×D4×C4711yescharacteristic
555C22×C4C2×D4×C4711yescharacteristic
556C22×C4C2×D4×C4711yescharacteristic
557Q16—81no—
558SD16—44no—
559SD16—81no—
560SD16—81no—
561SD16—81no—
562SD16—81no—
563D8—81no—
564M16—42no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—81no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—22no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4C2×D4×C4711yescharacteristic
599C4⋊C4C2×D4×C4711yescharacteristic
600C4⋊C4C2×D4×C4711yescharacteristic
601C4⋊C4C2×D4×C4711yescharacteristic
602C4⋊C4C2×D4×C4712yes—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—21no—
607C22⋊C4—22no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—41no—
615C22⋊C4—41no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42C2×D4×C4711yescharacteristic
624C42C2×D4×C4711yescharacteristic
625C42C2×D4×C4711yescharacteristic
626C42C24×C4711yescharacteristic
627C23—21no—
628C23—41no—
629C23#120×C4711yescharacteristic
630Q8—21no—
631Q8—21no—
632Q8—21no—
633Q8—21no—
634Q8—21no—
635Q8—21no—
636Q8—42no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—81no—
642Q8—82no—
643D4—21no—
644D4—21no—
645D4—42no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—81no—
651D4—82no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—82no—
670C2×C4—82no—
671C2×C4#120×C4711yescharacteristic
672C2×C4#120×C4711yescharacteristic
673C2×C4#120×C4711yescharacteristic
674C2×C4C22×D4×C4711yescharacteristic
675C2×C4C22×D4×C4711yescharacteristic
676C2×C4C22×D4×C4711yescharacteristic
677C8—22no—
678C8—41no—
679C8—41no—
680C8—41no—
681C8—41no—
682C8—41no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22C2×#120×C4711yescharacteristic
693C4—21no—
694C4—21no—
695C4—21no—
696C4—21no—
697C4—41no—
698C4—42no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—41no—
703C4—42no—
704C4—41no—
705C4—41no—
706C4—81no—
707C4C47×#57711yescharacteristic
708C4C47×#57711yescharacteristic
709C4C47×#57711yescharacteristic
710C4C47×#57811yescharacteristic
711C2—41no—
712C2—81no—
713C2—161no—
714C2C47×#301011yescharacteristic
715C2C47×#301311yescharacteristic
716C2C47×#301811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3212C2
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×#3246C2semidirect
4. C47×#3182C2semidirect
5. C47×#1650C2semidirect
6. C47×#1648C2semidirect
7. C47×#1645C2semidirect
8. C47×#1643C2semidirect
9. C47×#1628C2semidirect
10. C47×#1626C2semidirect
11. C47×#1623C2semidirect
12. C47×#1622C2semidirect
13. C47×#1542C2semidirect
14. C47×#1485C2semidirect
15. C47×#1483C2semidirect
324. #18744C47direct (N × H)
353. #3555C2×C47semidirect
354. #3246C2×C47semidirect
356. #3182C2×C47semidirect
357. #1650C2×C47semidirect
358. #1648C2×C47semidirect
359. #1645C2×C47semidirect
360. #1643C2×C47semidirect
361. #1628C2×C47semidirect
362. #1626C2×C47semidirect
363. #1623C2×C47semidirect
364. #1622C2×C47semidirect
365. #1542C2×C47semidirect
366. #1485C2×C47semidirect
367. #1483C2×C47semidirect
429. C47#18744direct (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×#32462
C47×#32122
C47×#31822
C47×#16502
C47×#16482
C47×#16452
C47×#16432
C47×#16282
C47×#16262
C47×#16232
C47×#16222
C47×#15422
C47×#14852
C47×#14832
#1874447