Finite Group Databasebeta

← C47×#32713 #26072411

Subgroups — C47×#32713 #26072411

Order 12032.

906 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2616C211yesmaximal, characteristic, complemented
2C47×#2615C211yesmaximal, characteristic
3C47×#2077C211yesmaximal, characteristic, complemented
4C47×#2076C211yesmaximal, characteristic, complemented
5C47×#2075C211yesmaximal, characteristic, complemented
6C47×#2036C211yesmaximal, characteristic, complemented
7C47×#2036C211yesmaximal, characteristic, complemented
8C47×#2035C211yesmaximal, characteristic, complemented
9C47×#2034C211yesmaximal, characteristic, complemented
10C47×#2033C211yesmaximal, characteristic, complemented
11C47×#2033C211yesmaximal, characteristic, complemented
12C47×#2000C211yesmaximal, characteristic, complemented
13C47×#2000C211yesmaximal, characteristic, complemented
14C47×#2000C211yesmaximal, characteristic, complemented
15C47×#1780C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C2×C22⋊Q8×C47C2211yescharacteristic
19C2×C22⋊Q8×C47C2211yescharacteristic
20C2×C22⋊Q8×C47C2211yescharacteristic
21C2×#121×C47C2211yescharacteristic
22C2×#121×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×#107×C47C2211yescharacteristic
25C2×#107×C47C2211yescharacteristic
26C2×#106×C47C2211yescharacteristic
27C2×#103×C47C2211yescharacteristic
28C2×#103×C47C2211yescharacteristic
29C2×#103×C47C2211yescharacteristic
30C2×#102×C47C2211yescharacteristic
31C2×#102×C47C2211yescharacteristic
32C2×#102×C47C2211yescharacteristic
33C2×C22⋊C8×C47C2211yescharacteristic
34C2×C22⋊C8×C47C2211yescharacteristic
35C2×C22⋊C8×C47C2211yescharacteristic
36C2×C22⋊C8×C47C2211yescharacteristic
37C2×C22⋊C8×C47C2211yescharacteristic
38C2×C22⋊C8×C47C2211yescharacteristic
39C47×#395—21no—
40C47×#394—21no—
41C47×#394—21no—
42C47×#394—21no—
43C47×#393—21no—
44C47×#392—21no—
45C47×#392—21no—
46C47×#392—21no—
47C47×#380C2211yescharacteristic
48C47×#380C2211yescharacteristic
49C47×#380C2211yescharacteristic
50C47×#380C2211yescharacteristic
51C47×#380C2211yescharacteristic
52C47×#380C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C2×#41×C47—41no—
60C2×#41×C47—41no—
61C2×#41×C47—41no—
62C2×#41×C47—41no—
63C2×#41×C47—41no—
64C2×#41×C47—41no—
65C22×Q8×C47D411yescharacteristic
66C22×Q8×C47C2311yescharacteristic
67C22×D4×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47—21no—
70C22×D4×C47D411yescharacteristic
71C22×D4×C47D411yescharacteristic
72C22×D4×C47D411yescharacteristic
73C22×D4×C47C2311yescharacteristic
74C23×C4×C47C2311yescharacteristic
75C23×C4×C47C2311yescharacteristic
76C23×C4×C47C2311yescharacteristic
77C2×SD16×C47—41no—
78C2×SD16×C47—41no—
79C2×SD16×C47—41no—
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84C22⋊Q8×C47—41no—
85C22⋊Q8×C47—41no—
86C22⋊Q8×C47—41no—
87C22⋊Q8×C47—41no—
88C22⋊Q8×C47—41no—
89C22⋊Q8×C47—41no—
90#121×C47—41no—
91#121×C47—41no—
92#121×C47—41no—
93#121×C47—41no—
94#121×C47—41no—
95#121×C47—41no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
107C2×C22⋊C4×C47—21no—
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117#107×C47—41no—
118#107×C47—41no—
119#106×C47—41no—
120#103×C47—41no—
121#103×C47—41no—
122#103×C47—41no—
123#102×C47—41no—
124#102×C47—41no—
125#102×C47—41no—
126C22⋊C8×C47—41no—
127C22⋊C8×C47—41no—
128C22⋊C8×C47—41no—
129C22⋊C8×C47—41no—
130C22⋊C8×C47—41no—
131C22⋊C8×C47—41no—
132#95×C47—21no—
133#95×C47—21no—
134#95×C47—21no—
135#95×C47—21no—
136#95×C47—21no—
137#95×C47—21no—
138C24×C47—21no—
139C24×C47C2×D411yescharacteristic
140C24×C47C2×D411yescharacteristic
141C24×C47C2×D411yescharacteristic
142#41×C47—44no—
143#41×C47—44no—
144#41×C47—44no—
145#41×C47—44no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—41no—
153C2×Q8×C47—41no—
154C2×Q8×C47—41no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—41no—
162C2×D4×C47—41no—
163C2×D4×C47—41no—
164C2×D4×C47—41no—
165C2×D4×C47—41no—
166C2×D4×C47—41no—
167C2×D4×C47—41no—
168C2×D4×C47—41no—
169C2×D4×C47—41no—
170C2×D4×C47—42no—
171C2×D4×C47—42no—
172C2×D4×C47—42no—
173C2×D4×C47—81no—
174C2×D4×C47—81no—
175C2×D4×C47—81no—
176C2×D4×C47—81no—
177C2×D4×C47—81no—
178C2×D4×C47—81no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2411yescharacteristic
208SD16×C47—44no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47—21no—
217C2×C8×C47—21no—
218C2×C8×C47—21no—
219C2×C8×C47—21no—
220C2×C8×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—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—42no—
234C4⋊C4×C47—42no—
235C4⋊C4×C47—42no—
236C22⋊C4×C47—42no—
237C22⋊C4×C47—42no—
238C22⋊C4×C47—42no—
239C22⋊C4×C47—42no—
240C22⋊C4×C47—42no—
241C22⋊C4×C47—42no—
242C22⋊C4×C47—81no—
243C22⋊C4×C47—81no—
244C22⋊C4×C47—81no—
245C22⋊C4×C47—81no—
246C22⋊C4×C47—81no—
247C22⋊C4×C47—81no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—41no—
272C23×C47—41no—
273C23×C47—41no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47C22×D411yescharacteristic
277Q8×C47—44no—
278Q8×C47—41no—
279Q8×C47—41no—
280Q8×C47—41no—
281Q8×C47—41no—
282D4×C47—44no—
283D4×C47—44no—
284D4×C47—44no—
285D4×C47—41no—
286D4×C47—41no—
287D4×C47—41no—
288D4×C47—41no—
289D4×C47—84no—
290D4×C47—84no—
291D4×C47—84no—
292C2×C4×C47—21no—
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—21no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47H(5,𝔽2)11yescharacteristic
335C2×C4×C47H(5,𝔽2)11yescharacteristic
336C2×C4×C47H(5,𝔽2)11yescharacteristic
337C2×C4×C47H(5,𝔽2)11yescharacteristic
338C2×C4×C47H(5,𝔽2)11yescharacteristic
339C2×C4×C47H(5,𝔽2)11yescharacteristic
340C8×C47—41no—
341C8×C47—41no—
342C8×C47—41no—
343C8×C47—41no—
344#32713C4711yesmaximal, characteristic, direct product factor, Sylow
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—41no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47—41no—
356C22×C47—41no—
357C22×C47—41no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—81no—
367C22×C47—81no—
368C22×C47—81no—
369C22×C47—81no—
370C22×C47—81no—
371C22×C47—81no—
372C22×C47—81no—
373C22×C47#53411yescharacteristic
374C22×C47#53411yescharacteristic
375C22×C47#53411yescharacteristic
376C22×C47#57611yescharacteristic
377C22×C47#57711yescharacteristic
378C22×C47#57711yescharacteristic
379C22×C47#57811yescharacteristic
380C4×C47—41no—
381C4×C47—41no—
382C4×C47—41no—
383C4×C47—81no—
384C4×C47—81no—
385C4×C47—81no—
386C4×C47—81no—
387C4×C47—81no—
388C4×C47—81no—
389C4×C47—81no—
390C4×C47#56011yescharacteristic
391C4×C47#56011yescharacteristic
392C4×C47#56011yescharacteristic
393C4×C47H(3,𝔽4)11yescharacteristic
394#2616C2×C4711yescharacteristic, complemented
395#2615C2×C4711yescharacteristic
396#2077C2×C4711yescharacteristic, complemented
397#2076C2×C4711yescharacteristic, complemented
398#2075C2×C4711yescharacteristic, complemented
399#2036C2×C4711yescharacteristic, complemented
400#2036C2×C4711yescharacteristic, complemented
401#2035C2×C4711yescharacteristic, complemented
402#2034C2×C4711yescharacteristic, complemented
403#2033C2×C4711yescharacteristic, complemented
404#2033C2×C4711yescharacteristic, complemented
405#2000C2×C4711yescharacteristic, complemented
406#2000C2×C4711yescharacteristic, complemented
407#2000C2×C4711yescharacteristic, complemented
408#1780C2×C4711yescharacteristic, complemented
409C2×C47—81no—
410C2×C47—81no—
411C2×C47—81no—
412C2×C47—161no—
413C2×C47#281211yescharacteristic
414C2×C47#319811yescharacteristic
415C2×C47#319811yescharacteristic
416C2×C47#320011yescharacteristic
417C2×C47#320111yescharacteristic
418C2×C47#320111yescharacteristic
419C2×C47#320311yescharacteristic
420C22×#41C22×C4711yescharacteristic
421C22×SD16C22×C4711yescharacteristic
422C2×C22⋊Q8C22×C4711yescharacteristic
423C2×C22⋊Q8C22×C4711yescharacteristic
424C2×C22⋊Q8C22×C4711yescharacteristic
425C2×#121C22×C4711yescharacteristic
426C2×#121C22×C4711yescharacteristic
427C2×#121C22×C4711yescharacteristic
428C2×#107C22×C4711yescharacteristic
429C2×#107C22×C4711yescharacteristic
430C2×#106C22×C4711yescharacteristic
431C2×#103C22×C4711yescharacteristic
432C2×#103C22×C4711yescharacteristic
433C2×#103C22×C4711yescharacteristic
434C2×#102C22×C4711yescharacteristic
435C2×#102C22×C4711yescharacteristic
436C2×#102C22×C4711yescharacteristic
437C2×C22⋊C8C22×C4711yescharacteristic
438C2×C22⋊C8C22×C4711yescharacteristic
439C2×C22⋊C8C22×C4711yescharacteristic
440C2×C22⋊C8C22×C4711yescharacteristic
441C2×C22⋊C8C22×C4711yescharacteristic
442C2×C22⋊C8C22×C4711yescharacteristic
443#395—21no—
444#394—21no—
445#394—21no—
446#394—21no—
447#393—21no—
448#392—21no—
449#392—21no—
450#392—21no—
451#380C22×C4711yescharacteristic
452#380C22×C4711yescharacteristic
453#380C22×C4711yescharacteristic
454#380C22×C4711yescharacteristic
455#380C22×C4711yescharacteristic
456#380C22×C4711yescharacteristic
457#340C22×C4711yescharacteristic
458#340C22×C4711yescharacteristic
459#340C22×C4711yescharacteristic
460#340C22×C4711yescharacteristic
461#340C22×C4711yescharacteristic
462#340C22×C4711yescharacteristic
463C47#3271311yescharacteristic, direct product factor, Sylow
464C2×#41—41no—
465C2×#41—41no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41—41no—
469C2×#41—41no—
470C22×Q8D4×C4711yescharacteristic
471C22×Q8C23×C4711yescharacteristic
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4D4×C4711yescharacteristic
476C22×D4D4×C4711yescharacteristic
477C22×D4D4×C4711yescharacteristic
478C22×D4C23×C4711yescharacteristic
479C23×C4C23×C4711yescharacteristic
480C23×C4C23×C4711yescharacteristic
481C23×C4C23×C4711yescharacteristic
482C2×SD16—41no—
483C2×SD16—41no—
484C2×SD16—41no—
485C22×C8C23×C4711yescharacteristic
486C22×C8C23×C4711yescharacteristic
487C22×C8C23×C4711yescharacteristic
488C22×C8C23×C4711yescharacteristic
489C22⋊Q8—41no—
490C22⋊Q8—41no—
491C22⋊Q8—41no—
492C22⋊Q8—41no—
493C22⋊Q8—41no—
494C22⋊Q8—41no—
495#121—41no—
496#121—41no—
497#121—41no—
498#121—41no—
499#121—41no—
500#121—41no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4C23×C4711yescharacteristic
505C2×C4⋊C4C23×C4711yescharacteristic
506C2×C4⋊C4C23×C4711yescharacteristic
507C2×C4⋊C4C23×C4711yescharacteristic
508C2×C4⋊C4C23×C4711yescharacteristic
509C2×C4⋊C4C23×C4711yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522#107—41no—
523#107—41no—
524#106—41no—
525#103—41no—
526#103—41no—
527#103—41no—
528#102—41no—
529#102—41no—
530#102—41no—
531C22⋊C8—41no—
532C22⋊C8—41no—
533C22⋊C8—41no—
534C22⋊C8—41no—
535C22⋊C8—41no—
536C22⋊C8—41no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543C24—21no—
544C24C2×D4×C4711yescharacteristic
545C24C2×D4×C4711yescharacteristic
546C24C2×D4×C4711yescharacteristic
547#41—44no—
548#41—44no—
549#41—44no—
550#41—44no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×Q8—41no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
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×C4C2×D4×C4711yescharacteristic
610C22×C4C2×D4×C4711yescharacteristic
611C22×C4C2×D4×C4711yescharacteristic
612C22×C4C24×C4711yescharacteristic
613SD16—44no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C22⋊C4—81no—
650C22⋊C4—81no—
651C22⋊C4—81no—
652C22⋊C4—81no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23C22×D4×C4711yescharacteristic
682Q8—44no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687D4—44no—
688D4—44no—
689D4—44no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—84no—
695D4—84no—
696D4—84no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4H(5,𝔽2)×C4711yescharacteristic
740C2×C4H(5,𝔽2)×C4711yescharacteristic
741C2×C4H(5,𝔽2)×C4711yescharacteristic
742C2×C4H(5,𝔽2)×C4711yescharacteristic
743C2×C4H(5,𝔽2)×C4711yescharacteristic
744C2×C4H(5,𝔽2)×C4711yescharacteristic
745C8—41no—
746C8—41no—
747C8—41no—
748C8—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C47×#53411yescharacteristic
778C22C47×#53411yescharacteristic
779C22C47×#53411yescharacteristic
780C22C47×#57611yescharacteristic
781C22C47×#57711yescharacteristic
782C22C47×#57711yescharacteristic
783C22C47×#57811yescharacteristic
784C4—41no—
785C4—41no—
786C4—41no—
787C4—81no—
788C4—81no—
789C4—81no—
790C4—81no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4C47×#56011yescharacteristic
795C4C47×#56011yescharacteristic
796C4C47×#56011yescharacteristic
797C4C47×H(3,𝔽4)11yescharacteristic
798C2—81no—
799C2—81no—
800C2—81no—
801C2—161no—
802C2C47×#281211yescharacteristic
803C2C47×#319811yescharacteristic
804C2C47×#319811yescharacteristic
805C2C47×#320011yescharacteristic
806C2C47×#320111yescharacteristic
807C2C47×#320111yescharacteristic
808C2C47×#320311yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C22×#41×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#2616C2semidirect
3. C47×#2077C2semidirect
4. C47×#2076C2semidirect
5. C47×#2075C2semidirect
6. C47×#2036C2semidirect
7. C47×#2036C2semidirect
8. C47×#2035C2semidirect
9. C47×#2034C2semidirect
10. C47×#2033C2semidirect
11. C47×#2033C2semidirect
12. C47×#2000C2semidirect
13. C47×#2000C2semidirect
14. C47×#2000C2semidirect
15. C47×#1780C2semidirect
344. #32713C47direct (N × H)
394. #2616C2×C47semidirect
396. #2077C2×C47semidirect
397. #2076C2×C47semidirect
398. #2075C2×C47semidirect
399. #2036C2×C47semidirect
400. #2036C2×C47semidirect
401. #2035C2×C47semidirect
402. #2034C2×C47semidirect
403. #2033C2×C47semidirect
404. #2033C2×C47semidirect
405. #2000C2×C47semidirect
406. #2000C2×C47semidirect
407. #2000C2×C47semidirect
408. #1780C2×C47semidirect
463. C47#32713direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#26162
C47×#26152
C47×#20772
C47×#20762
C47×#20752
C47×#20362
C47×#20352
C47×#20342
C47×#20332
C47×#20002
C47×#17802
#3271347