Finite Group Databasebeta

← C47×#25507 #26065205

Subgroups — C47×#25507 #26065205

Order 12032.

1156 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#540C211yesmaximal, characteristic
2C2×C47×#468C211yesmaximal, characteristic, complemented
3C2×C47×#465C211yesmaximal, characteristic, complemented
4C47×#2625C211yesmaximal, characteristic, complemented
5C47×#2059C211yesmaximal, characteristic, complemented
6C47×#2041C211yesmaximal, characteristic, complemented
7C47×#2026C211yesmaximal, characteristic, complemented
8C47×#2014C211yesmaximal, characteristic, complemented
9C47×#1895C211yesmaximal, characteristic, complemented
10C47×#1893C211yesmaximal, characteristic, complemented
11C47×#1877C211yesmaximal, characteristic, complemented
12C47×#1877C211yesmaximal, characteristic, complemented
13C47×#1864C211yesmaximal, characteristic, complemented
14C47×#1862C211yesmaximal, characteristic, complemented
15C47×#1729C211yesmaximal, characteristic, complemented
16C22×SD16×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C47×#540—24no—
21C47×#540—24no—
22C2×#127×C47C2211yescharacteristic
23C2×#125×C47C2211yescharacteristic
24C2×#123×C47—21no—
25C2×#123×C47—21no—
26C2×C22⋊Q8×C47C2211yescharacteristic
27C2×#121×C47—21no—
28C2×#121×C47—21no—
29C2×#121×C47C2211yescharacteristic
30C2×#121×C47C2211yescharacteristic
31C2×C4×D4×C47C2211yescharacteristic
32C2×C4×D4×C47C2211yescharacteristic
33C2×#117×C47C2211yescharacteristic
34C47×#468—24no—
35C47×#465—24no—
36C2×#107×C47C2211yescharacteristic
37C2×#106×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×#102×C47C2211yescharacteristic
46C47×#400—21no—
47C47×#398—21no—
48C47×#397—21no—
49C47×#397—21no—
50C47×#391C2211yescharacteristic
51C47×#391C2211yescharacteristic
52C47×#389C2211yescharacteristic
53C47×#389C2211yescharacteristic
54C47×#380C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47—21no—
67C22×D4×C47—21no—
68C22×D4×C47C2311yescharacteristic
69C22×D4×C47C2311yescharacteristic
70C23×C4×C47—21no—
71C23×C4×C47—21no—
72C23×C4×C47C2311yescharacteristic
73C2×SD16×C47—22no—
74C2×SD16×C47—22no—
75C2×SD16×C47—22no—
76C2×SD16×C47—22no—
77C2×SD16×C47—41no—
78C2×SD16×C47—41no—
79C2×M16×C47—22no—
80C2×M16×C47—22no—
81C2×M16×C47—41no—
82C22×C8×C47—22no—
83C22×C8×C47—22no—
84C22×C8×C47—41no—
85C22×C8×C47C2311yescharacteristic
86C22×C8×C47C2311yescharacteristic
87C22×C8×C47C2311yescharacteristic
88C22×C8×C47C2311yescharacteristic
89#127×C47—22no—
90#127×C47—22no—
91#125×C47—22no—
92#125×C47—22no—
93#123×C47—28no—
94#123×C47—28no—
95C22⋊Q8×C47—22no—
96C22⋊Q8×C47—22no—
97#121×C47—28no—
98#121×C47—28no—
99#121×C47—22no—
100#121×C47—22no—
101#121×C47D414yes—
102#121×C47D414yes—
103C4×D4×C47—22no—
104C4×D4×C47—22no—
105C4×D4×C47—22no—
106C4×D4×C47—22no—
107#117×C47—22no—
108#117×C47—22no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47—21no—
112C2×C4⋊C4×C47—21no—
113C2×C4⋊C4×C47—21no—
114C2×C4⋊C4×C47D411yescharacteristic
115C2×C4⋊C4×C47D411yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C4⋊C4×C47C2311yescharacteristic
121C2×C22⋊C4×C47—21no—
122C2×C22⋊C4×C47—21no—
123C2×C22⋊C4×C47—21no—
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47—21no—
127C2×C22⋊C4×C47D411yescharacteristic
128C2×C22⋊C4×C47D411yescharacteristic
129C2×C42×C47C2311yescharacteristic
130C2×C42×C47C2311yescharacteristic
131#107×C47—22no—
132#106×C47—22no—
133#103×C47—22no—
134#103×C47—22no—
135#102×C47—22no—
136#102×C47—22no—
137#102×C47—22no—
138#102×C47—22no—
139#102×C47—41no—
140#102×C47—41no—
141#95×C47—21no—
142#95×C47—21no—
143#95×C47—21no—
144#95×C47—21no—
145#95×C47—21no—
146#95×C47—21no—
147#95×C47—21no—
148C24×C47—21no—
149C24×C47—21no—
150C24×C47C2×D411yescharacteristic
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×D4×C47—24no—
158C2×D4×C47—24no—
159C2×D4×C47—24no—
160C2×D4×C47—24no—
161C2×D4×C47—21no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—21no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—81no—
172C2×D4×C47—81no—
173C2×D4×C47—81no—
174C2×D4×C47—81no—
175C2×D4×C47—81no—
176C2×D4×C47—81no—
177C2×D4×C47—81no—
178C2×D4×C47—81no—
179C2×D4×C47C2×D412yes—
180C2×D4×C47C2×D412yes—
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—24no—
188C22×C4×C47—24no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—81no—
194C22×C4×C47—81no—
195C22×C4×C47—81no—
196C22×C4×C47—81no—
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D412yes—
203C22×C4×C47C2×D412yes—
204C22×C4×C47C2411yescharacteristic
205SD16×C47—44no—
206SD16×C47—44no—
207M16×C47—44no—
208C2×C8×C47—21no—
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—44no—
219C2×C8×C47#4112yes—
220C2×C8×C47#4112yes—
221C4⋊C4×C47—24no—
222C4⋊C4×C47—24no—
223C4⋊C4×C47—22no—
224C4⋊C4×C47—22no—
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—81no—
235C4⋊C4×C47—81no—
236C4⋊C4×C47C2×D412yes—
237C4⋊C4×C47C2×D412yes—
238C22⋊C4×C47—24no—
239C22⋊C4×C47—24no—
240C22⋊C4×C47—22no—
241C22⋊C4×C47—22no—
242C22⋊C4×C47—24no—
243C22⋊C4×C47—24no—
244C22⋊C4×C47—42no—
245C22⋊C4×C47—81no—
246C42×C47—21no—
247C42×C47—21no—
248C42×C47—21no—
249C42×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—22no—
257C23×C47—22no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—41no—
263C23×C47—41no—
264C23×C47—41no—
265C23×C47—41no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47#12012yes—
271C23×C47C22×D411yescharacteristic
272Q8×C47—41no—
273Q8×C47—41no—
274Q8×C47—41no—
275Q8×C47—41no—
276D4×C47—22no—
277D4×C47—22no—
278D4×C47—22no—
279D4×C47—22no—
280D4×C47—41no—
281D4×C47—41no—
282D4×C47—41no—
283D4×C47—41no—
284D4×C47—84no—
285D4×C47—84no—
286D4×C47—84no—
287D4×C47—84no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
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—84no—
325C2×C4×C47—84no—
326C2×C4×C47#12012yes—
327C2×C4×C47C22×D411yescharacteristic
328C2×C4×C47C22×D411yescharacteristic
329C2×C4×C47C2×#4111yescharacteristic
330C2×C4×C47C2×#4111yescharacteristic
331C2×C4×C47H(5,𝔽2)11yescharacteristic
332C2×C4×C472−1+411yescharacteristic
333C8×C47—22no—
334C8×C47—22no—
335C8×C47—41no—
336C8×C47—41no—
337#25507C4711yesmaximal, characteristic, direct product factor, Sylow
338C22×C47—22no—
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—42no—
346C22×C47—42no—
347C22×C47—42no—
348C22×C47—42no—
349C22×C47—42no—
350C22×C47—42no—
351C22×C47—81no—
352C22×C47—81no—
353C22×C47—81no—
354C22×C47—81no—
355C22×C47—81no—
356C22×C47—81no—
357C22×C47—81no—
358C22×C47—81no—
359C22×C47C2×#12011yescharacteristic
360C22×C47#53211yescharacteristic
361C22×C47#53711yescharacteristic
362C22×C47#57611yescharacteristic
363C22×C47#57711yescharacteristic
364C22×C47#57711yescharacteristic
365C22×C47#57711yescharacteristic
366C4×C47—22no—
367C4×C47—41no—
368C4×C47—41no—
369C4×C47—42no—
370C4×C47—41no—
371C4×C47—41no—
372C4×C47—42no—
373C4×C47—81no—
374C4×C47—81no—
375C4×C47—81no—
376C4×C47—81no—
377C4×C47#54611yescharacteristic
378C4×C47#54611yescharacteristic
379C4×C47#54711yescharacteristic
380C4×C47#54711yescharacteristic
381C2×#540C2×C4711yescharacteristic
382C2×#468C2×C4711yescharacteristic, complemented
383C2×#465C2×C4711yescharacteristic, complemented
384#2625C2×C4711yescharacteristic, complemented
385#2059C2×C4711yescharacteristic, complemented
386#2041C2×C4711yescharacteristic, complemented
387#2026C2×C4711yescharacteristic, complemented
388#2014C2×C4711yescharacteristic, complemented
389#1895C2×C4711yescharacteristic, complemented
390#1893C2×C4711yescharacteristic, complemented
391#1877C2×C4711yescharacteristic, complemented
392#1877C2×C4711yescharacteristic, complemented
393#1864C2×C4711yescharacteristic, complemented
394#1862C2×C4711yescharacteristic, complemented
395#1729C2×C4711yescharacteristic, complemented
396C2×C47—42no—
397C2×C47—82no—
398C2×C47—82no—
399C2×C47#243011yescharacteristic
400C2×C47#300911yescharacteristic
401C2×C47#301211yescharacteristic
402C2×C47#317411yescharacteristic
403C2×C47#317911yescharacteristic
404C2×C47#325711yescharacteristic
405C2×C47#326011yescharacteristic
406C22×SD16C22×C4711yescharacteristic
407C22×SD16C22×C4711yescharacteristic
408C22×M16C22×C4711yescharacteristic
409C23×C8C22×C4711yescharacteristic
410#540—24no—
411#540—24no—
412C2×#127C22×C4711yescharacteristic
413C2×#125C22×C4711yescharacteristic
414C2×#123—21no—
415C2×#123—21no—
416C2×C22⋊Q8C22×C4711yescharacteristic
417C2×#121—21no—
418C2×#121—21no—
419C2×#121C22×C4711yescharacteristic
420C2×#121C22×C4711yescharacteristic
421C2×C4×D4C22×C4711yescharacteristic
422C2×C4×D4C22×C4711yescharacteristic
423C2×#117C22×C4711yescharacteristic
424#468—24no—
425#465—24no—
426C2×#107C22×C4711yescharacteristic
427C2×#106C22×C4711yescharacteristic
428C2×#103C22×C4711yescharacteristic
429C2×#103C22×C4711yescharacteristic
430C2×#102C22×C4711yescharacteristic
431C2×#102C22×C4711yescharacteristic
432C2×#102C22×C4711yescharacteristic
433C2×#102C22×C4711yescharacteristic
434C2×#102C22×C4711yescharacteristic
435C2×#102C22×C4711yescharacteristic
436#400—21no—
437#398—21no—
438#397—21no—
439#397—21no—
440#391C22×C4711yescharacteristic
441#391C22×C4711yescharacteristic
442#389C22×C4711yescharacteristic
443#389C22×C4711yescharacteristic
444#380C22×C4711yescharacteristic
445#340C22×C4711yescharacteristic
446#340C22×C4711yescharacteristic
447#340C22×C4711yescharacteristic
448#340C22×C4711yescharacteristic
449#336C22×C4711yescharacteristic
450#336C22×C4711yescharacteristic
451#336C22×C4711yescharacteristic
452#336C22×C4711yescharacteristic
453C47#2550711yescharacteristic, direct product factor, Sylow
454C22×Q8C23×C4711yescharacteristic
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C23×C4711yescharacteristic
460C22×D4C23×C4711yescharacteristic
461C23×C4—21no—
462C23×C4—21no—
463C23×C4C23×C4711yescharacteristic
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—41no—
469C2×SD16—41no—
470C2×M16—22no—
471C2×M16—22no—
472C2×M16—41no—
473C22×C8—22no—
474C22×C8—22no—
475C22×C8—41no—
476C22×C8C23×C4711yescharacteristic
477C22×C8C23×C4711yescharacteristic
478C22×C8C23×C4711yescharacteristic
479C22×C8C23×C4711yescharacteristic
480#127—22no—
481#127—22no—
482#125—22no—
483#125—22no—
484#123—28no—
485#123—28no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488#121—28no—
489#121—28no—
490#121—22no—
491#121—22no—
492#121D4×C4714yes—
493#121D4×C4714yes—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498#117—22no—
499#117—22no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4D4×C4711yescharacteristic
506C2×C4⋊C4D4×C4711yescharacteristic
507C2×C4⋊C4C23×C4711yescharacteristic
508C2×C4⋊C4C23×C4711yescharacteristic
509C2×C4⋊C4C23×C4711yescharacteristic
510C2×C4⋊C4C23×C4711yescharacteristic
511C2×C4⋊C4C23×C4711yescharacteristic
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⋊C4D4×C4711yescharacteristic
519C2×C22⋊C4D4×C4711yescharacteristic
520C2×C42C23×C4711yescharacteristic
521C2×C42C23×C4711yescharacteristic
522#107—22no—
523#106—22no—
524#103—22no—
525#103—22no—
526#102—22no—
527#102—22no—
528#102—22no—
529#102—22no—
530#102—41no—
531#102—41no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539C24—21no—
540C24—21no—
541C24C2×D4×C4711yescharacteristic
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4C2×D4×C4712yes—
571C2×D4C2×D4×C4712yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—81no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4C2×D4×C4711yescharacteristic
589C22×C4C2×D4×C4711yescharacteristic
590C22×C4C2×D4×C4711yescharacteristic
591C22×C4C2×D4×C4711yescharacteristic
592C22×C4C2×D4×C4711yescharacteristic
593C22×C4C2×D4×C4712yes—
594C22×C4C2×D4×C4712yes—
595C22×C4C24×C4711yescharacteristic
596SD16—44no—
597SD16—44no—
598M16—44no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—44no—
610C2×C8#41×C4712yes—
611C2×C8#41×C4712yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—42no—
625C4⋊C4—81no—
626C4⋊C4—81no—
627C4⋊C4C2×D4×C4712yes—
628C4⋊C4C2×D4×C4712yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—42no—
636C22⋊C4—81no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23#120×C4712yes—
662C23C22×D4×C4711yescharacteristic
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—41no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—22no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—84no—
676D4—84no—
677D4—84no—
678D4—84no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
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—84no—
716C2×C4—84no—
717C2×C4#120×C4712yes—
718C2×C4C22×D4×C4711yescharacteristic
719C2×C4C22×D4×C4711yescharacteristic
720C2×C4C2×#41×C4711yescharacteristic
721C2×C4C2×#41×C4711yescharacteristic
722C2×C4H(5,𝔽2)×C4711yescharacteristic
723C2×C42−1+4×C4711yescharacteristic
724C8—22no—
725C8—22no—
726C8—41no—
727C8—41no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22C2×#120×C4711yescharacteristic
750C22C47×#53211yescharacteristic
751C22C47×#53711yescharacteristic
752C22C47×#57611yescharacteristic
753C22C47×#57711yescharacteristic
754C22C47×#57711yescharacteristic
755C22C47×#57711yescharacteristic
756C4—22no—
757C4—41no—
758C4—41no—
759C4—42no—
760C4—41no—
761C4—41no—
762C4—42no—
763C4—81no—
764C4—81no—
765C4—81no—
766C4—81no—
767C4C47×#54611yescharacteristic
768C4C47×#54611yescharacteristic
769C4C47×#54711yescharacteristic
770C4C47×#54711yescharacteristic
771C2—42no—
772C2—82no—
773C2—82no—
774C2C47×#243011yescharacteristic
775C2C47×#300911yescharacteristic
776C2C47×#301211yescharacteristic
777C2C47×#317411yescharacteristic
778C2C47×#317911yescharacteristic
779C2C47×#325711yescharacteristic
780C2C47×#326011yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#540C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×#117×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#468C2semidirect
3. C2×C47×#465C2semidirect
4. C47×#2625C2semidirect
5. C47×#2059C2semidirect
6. C47×#2041C2semidirect
7. C47×#2026C2semidirect
8. C47×#2014C2semidirect
9. C47×#1895C2semidirect
10. C47×#1893C2semidirect
11. C47×#1877C2semidirect
12. C47×#1877C2semidirect
13. C47×#1864C2semidirect
14. C47×#1862C2semidirect
15. C47×#1729C2semidirect
337. #25507C47direct (N × H)
382. C2×#468C2×C47semidirect
383. C2×#465C2×C47semidirect
384. #2625C2×C47semidirect
385. #2059C2×C47semidirect
386. #2041C2×C47semidirect
387. #2026C2×C47semidirect
388. #2014C2×C47semidirect
389. #1895C2×C47semidirect
390. #1893C2×C47semidirect
391. #1877C2×C47semidirect
392. #1877C2×C47semidirect
393. #1864C2×C47semidirect
394. #1862C2×C47semidirect
395. #1729C2×C47semidirect
453. C47#25507direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5402
C2×C47×#4682
C2×C47×#4652
C47×#26252
C47×#20592
C47×#20412
C47×#20262
C47×#20142
C47×#18952
C47×#18932
C47×#18772
C47×#18642
C47×#18622
C47×#17292
#2550747