Finite Group Databasebeta

← C47×#25396 #26065094

Subgroups — C47×#25396 #26065094

Order 12032.

1184 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#469C211yesmaximal, characteristic, complemented
2C2×C47×#466C211yesmaximal, characteristic, complemented
3C2×C47×#459C211yesmaximal, characteristic, complemented
4C2×C47×#435C211yesmaximal, characteristic, complemented
5C47×#2541C211yesmaximal, characteristic, complemented
6C47×#2535C211yesmaximal, characteristic, complemented
7C47×#2034C211yesmaximal, characteristic, complemented
8C47×#2033C211yesmaximal, characteristic, complemented
9C47×#1999C211yesmaximal, characteristic, complemented
10C47×#1999C211yesmaximal, characteristic, complemented
11C47×#1961C211yesmaximal, characteristic, complemented
12C47×#1949C211yesmaximal, characteristic, complemented
13C47×#1895C211yesmaximal, characteristic, complemented
14C47×#1893C211yesmaximal, characteristic, complemented
15C47×#1762C211yesmaximal, characteristic, complemented
16C22×D8×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C2×#127×C47—21no—
21C2×#127×C47C2211yescharacteristic
22C2×#121×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×#121×C47C2211yescharacteristic
26C2×#121×C47C2211yescharacteristic
27C2×#121×C47C2211yescharacteristic
28C2×C4×D4×C47C2211yescharacteristic
29C2×C4×D4×C47C2211yescharacteristic
30C47×#469—24no—
31C47×#466—24no—
32C47×#459—24no—
33C47×#435—24no—
34C2×#107×C47C2211yescharacteristic
35C2×#106×C47C2211yescharacteristic
36C2×C4⋊C8×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2211yescharacteristic
46C2×C22⋊C8×C47C2211yescharacteristic
47C2×#97×C47C2211yescharacteristic
48C47×#397—21no—
49C47×#392—21no—
50C47×#392—21no—
51C47×#392—21no—
52C47×#390—21no—
53C47×#386—21no—
54C47×#386—21no—
55C47×#382C2211yescharacteristic
56C47×#380C2211yescharacteristic
57C47×#380C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C22×D4×C47—21no—
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47—21no—
67C22×D4×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47—21no—
70C22×D4×C47—21no—
71C22×D4×C47D411yescharacteristic
72C22×D4×C47C2311yescharacteristic
73C22×D4×C47C2311yescharacteristic
74C22×D4×C47C2311yescharacteristic
75C23×C4×C47—21no—
76C23×C4×C47C2311yescharacteristic
77C23×C4×C47C2311yescharacteristic
78C2×D8×C47—22no—
79C2×D8×C47—22no—
80C2×D8×C47—22no—
81C2×D8×C47—22no—
82C2×D8×C47—41no—
83C2×D8×C47—41no—
84C2×M16×C47—22no—
85C2×M16×C47—22no—
86C2×M16×C47—41no—
87C22×C8×C47—22no—
88C22×C8×C47—22no—
89C22×C8×C47—41no—
90C22×C8×C47C2311yescharacteristic
91C22×C8×C47C2311yescharacteristic
92C22×C8×C47C2311yescharacteristic
93C22×C8×C47C2311yescharacteristic
94#127×C47—22no—
95#127×C47—22no—
96#127×C47—44no—
97#121×C47—22no—
98#121×C47—22no—
99#121×C47—22no—
100#121×C47—22no—
101#121×C47—22no—
102#121×C47—22no—
103#121×C47—41no—
104#121×C47—41no—
105#121×C47—41no—
106#121×C47—41no—
107#121×C47—41no—
108#121×C47—41no—
109C4×D4×C47—22no—
110C4×D4×C47—22no—
111C4×D4×C47—22no—
112C4×D4×C47—22no—
113C2×C4⋊C4×C47D411yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47—21no—
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×C47—21no—
128C2×C22⋊C4×C47D411yescharacteristic
129C2×C22⋊C4×C47D411yescharacteristic
130C2×C42×C47—21no—
131C2×C42×C47C2311yescharacteristic
132#107×C47—22no—
133#106×C47—22no—
134C4⋊C8×C47D414yescomplemented
135#102×C47—22no—
136#102×C47—22no—
137#102×C47—22no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—41no—
141#102×C47—41no—
142#102×C47D414yescomplemented
143C22⋊C8×C47—22no—
144C22⋊C8×C47—22no—
145#97×C47—22no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47—21no—
149#95×C47—21no—
150#95×C47—21no—
151C24×C47—21no—
152C24×C47—21no—
153C24×C47—21no—
154C24×C47C2×D411yescharacteristic
155C24×C47C2×D411yescharacteristic
156C2×D4×C47—22no—
157C2×D4×C47—22no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
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—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—21no—
175C2×D4×C47—41no—
176C2×D4×C47—42no—
177C2×D4×C47—42no—
178C2×D4×C47—42no—
179C2×D4×C47—42no—
180C2×D4×C47—42no—
181C2×D4×C47—42no—
182C2×D4×C47—42no—
183C2×D4×C47—42no—
184C2×D4×C47—42no—
185C2×D4×C47—42no—
186C2×D4×C47—42no—
187C2×D4×C47—42no—
188C2×D4×C47—42no—
189C2×D4×C47—42no—
190C2×D4×C47—42no—
191C2×D4×C47—42no—
192C2×D4×C47—81no—
193C2×D4×C47—81no—
194C2×D4×C47—81no—
195C2×D4×C47—81no—
196C2×D4×C47—81no—
197C2×D4×C47—81no—
198C2×D4×C47—81no—
199C2×D4×C47—81no—
200C2×D4×C47C2×D412yes—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—42no—
219C22×C4×C47—81no—
220C22×C4×C47—81no—
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2411yescharacteristic
226D8×C47—44no—
227D8×C47—44no—
228M16×C47—44no—
229C2×C8×C47—21no—
230C2×C8×C47—21no—
231C2×C8×C47—21no—
232C2×C8×C47—21no—
233C2×C8×C47—21no—
234C2×C8×C47—21no—
235C2×C8×C47—21no—
236C2×C8×C47—21no—
237C2×C8×C47—21no—
238C2×C8×C47—44no—
239C2×C8×C47C2×D412yes—
240C2×C8×C47C2×D412yes—
241C2×C8×C47C2×D412yes—
242C4⋊C4×C47—22no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47C2×D412yes—
252C4⋊C4×C47#4112yes—
253C22⋊C4×C47—22no—
254C22⋊C4×C47—22no—
255C22⋊C4×C47—42no—
256C22⋊C4×C47—42no—
257C22⋊C4×C47—42no—
258C22⋊C4×C47—42no—
259C22⋊C4×C47—42no—
260C22⋊C4×C47—42no—
261C22⋊C4×C47—42no—
262C22⋊C4×C47—81no—
263C22⋊C4×C47—81no—
264C42×C47—42no—
265C42×C47C2×D412yes—
266C42×C47#4112yes—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—22no—
275C23×C47—21no—
276C23×C47—21no—
277C23×C47—21no—
278C23×C47—21no—
279C23×C47—21no—
280C23×C47—21no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—41no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—41no—
298C23×C47—41no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47AGL(1,ℤ/8)12yes—
302C23×C47C22×D411yescharacteristic
303D4×C47—22no—
304D4×C47—22no—
305D4×C47—44no—
306D4×C47—41no—
307D4×C47—41no—
308D4×C47—41no—
309D4×C47—41no—
310D4×C47—41no—
311D4×C47—41no—
312D4×C47—41no—
313D4×C47—41no—
314D4×C47—41no—
315D4×C47—41no—
316D4×C47—84no—
317D4×C47—84no—
318D4×C47—84no—
319D4×C47—84no—
320D4×C47—84no—
321D4×C47—84no—
322D4×C47—84no—
323D4×C47—84no—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—21no—
328C2×C4×C47—21no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—84no—
358C2×C4×C47#12112yes—
359C2×C4×C47#12112yes—
360C2×C4×C47C22×D411yescharacteristic
361C2×C4×C47C22×D411yescharacteristic
362C2×C4×C47C2×#4111yescharacteristic
363C2×C4×C47C2×#4111yescharacteristic
364C2×C4×C47H(5,𝔽2)11yescharacteristic
365C2×C4×C47H(5,𝔽2)11yescharacteristic
366C8×C47—22no—
367C8×C47—22no—
368C8×C47—22no—
369C8×C47—41no—
370#25396C4711yesmaximal, characteristic, direct product factor, Sylow
371C22×C47—22no—
372C22×C47—22no—
373C22×C47—22no—
374C22×C47—41no—
375C22×C47—41no—
376C22×C47—41no—
377C22×C47—41no—
378C22×C47—41no—
379C22×C47—42no—
380C22×C47—41no—
381C22×C47—42no—
382C22×C47—41no—
383C22×C47—42no—
384C22×C47—41no—
385C22×C47—41no—
386C22×C47—41no—
387C22×C47—41no—
388C22×C47—81no—
389C22×C47—81no—
390C22×C47—81no—
391C22×C47—81no—
392C22×C47—81no—
393C22×C47—81no—
394C22×C47—81no—
395C22×C47—81no—
396C22×C47—81no—
397C22×C47—81no—
398C22×C47—81no—
399C22×C47—81no—
400C22×C47—81no—
401C22×C47—81no—
402C22×C47—81no—
403C22×C47—81no—
404C22×C47—81no—
405C22×C47—81no—
406C22×C47C2×#12111yescharacteristic
407C22×C47D4211yescharacteristic
408C22×C47#54611yescharacteristic
409C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C47#57511yescharacteristic
411C22×C47#57611yescharacteristic
412C22×C47#57611yescharacteristic
413C4×C47—22no—
414C4×C47—22no—
415C4×C47—41no—
416C4×C47—41no—
417C4×C47—42no—
418C4×C47—42no—
419C4×C47—81no—
420C4×C47—81no—
421C4×C47—81no—
422C4×C47#53211yescharacteristic
423C4×C47#54011yescharacteristic
424C4×C47D4211yescharacteristic
425C4×C47#55011yescharacteristic
426C2×#469C2×C4711yescharacteristic, complemented
427C2×#466C2×C4711yescharacteristic, complemented
428C2×#459C2×C4711yescharacteristic, complemented
429C2×#435C2×C4711yescharacteristic, complemented
430#2541C2×C4711yescharacteristic, complemented
431#2535C2×C4711yescharacteristic, complemented
432#2034C2×C4711yescharacteristic, complemented
433#2033C2×C4711yescharacteristic, complemented
434#1999C2×C4711yescharacteristic, complemented
435#1999C2×C4711yescharacteristic, complemented
436#1961C2×C4711yescharacteristic, complemented
437#1949C2×C4711yescharacteristic, complemented
438#1895C2×C4711yescharacteristic, complemented
439#1893C2×C4711yescharacteristic, complemented
440#1762C2×C4711yescharacteristic, complemented
441C2×C47—42no—
442C2×C47—81no—
443C2×C47—82no—
444C2×C47—161no—
445C2×C47—161no—
446C2×C47#242811yescharacteristic
447C2×C47#305511yescharacteristic
448C2×C47#305811yescharacteristic
449C2×C47#326411yescharacteristic
450C2×C47#326811yescharacteristic
451C2×C47#330911yescharacteristic
452C2×C47#331811yescharacteristic
453C22×D8C22×C4711yescharacteristic
454C22×D8C22×C4711yescharacteristic
455C22×M16C22×C4711yescharacteristic
456C23×C8C22×C4711yescharacteristic
457C2×#127—21no—
458C2×#127C22×C4711yescharacteristic
459C2×#121C22×C4711yescharacteristic
460C2×#121C22×C4711yescharacteristic
461C2×#121C22×C4711yescharacteristic
462C2×#121C22×C4711yescharacteristic
463C2×#121C22×C4711yescharacteristic
464C2×#121C22×C4711yescharacteristic
465C2×C4×D4C22×C4711yescharacteristic
466C2×C4×D4C22×C4711yescharacteristic
467#469—24no—
468#466—24no—
469#459—24no—
470#435—24no—
471C2×#107C22×C4711yescharacteristic
472C2×#106C22×C4711yescharacteristic
473C2×C4⋊C8C22×C4711yescharacteristic
474C2×#102C22×C4711yescharacteristic
475C2×#102C22×C4711yescharacteristic
476C2×#102C22×C4711yescharacteristic
477C2×#102C22×C4711yescharacteristic
478C2×#102C22×C4711yescharacteristic
479C2×#102C22×C4711yescharacteristic
480C2×#102C22×C4711yescharacteristic
481C2×#102C22×C4711yescharacteristic
482C2×C22⋊C8C22×C4711yescharacteristic
483C2×C22⋊C8C22×C4711yescharacteristic
484C2×#97C22×C4711yescharacteristic
485#397—21no—
486#392—21no—
487#392—21no—
488#392—21no—
489#390—21no—
490#386—21no—
491#386—21no—
492#382C22×C4711yescharacteristic
493#380C22×C4711yescharacteristic
494#380C22×C4711yescharacteristic
495C4×C4⋊C4C22×C4711yescharacteristic
496#340C22×C4711yescharacteristic
497#340C22×C4711yescharacteristic
498#340C22×C4711yescharacteristic
499#340C22×C4711yescharacteristic
500C47#2539611yescharacteristic, direct product factor, Sylow
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4D4×C4711yescharacteristic
510C22×D4C23×C4711yescharacteristic
511C22×D4C23×C4711yescharacteristic
512C22×D4C23×C4711yescharacteristic
513C23×C4—21no—
514C23×C4C23×C4711yescharacteristic
515C23×C4C23×C4711yescharacteristic
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—22no—
520C2×D8—41no—
521C2×D8—41no—
522C2×M16—22no—
523C2×M16—22no—
524C2×M16—41no—
525C22×C8—22no—
526C22×C8—22no—
527C22×C8—41no—
528C22×C8C23×C4711yescharacteristic
529C22×C8C23×C4711yescharacteristic
530C22×C8C23×C4711yescharacteristic
531C22×C8C23×C4711yescharacteristic
532#127—22no—
533#127—22no—
534#127—44no—
535#121—22no—
536#121—22no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—41no—
542#121—41no—
543#121—41no—
544#121—41no—
545#121—41no—
546#121—41no—
547C4×D4—22no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—22no—
551C2×C4⋊C4D4×C4711yescharacteristic
552C2×C4⋊C4C23×C4711yescharacteristic
553C2×C4⋊C4C23×C4711yescharacteristic
554C2×C4⋊C4C23×C4711yescharacteristic
555C2×C4⋊C4C23×C4711yescharacteristic
556C2×C4⋊C4C23×C4711yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4D4×C4711yescharacteristic
567C2×C22⋊C4D4×C4711yescharacteristic
568C2×C42—21no—
569C2×C42C23×C4711yescharacteristic
570#107—22no—
571#106—22no—
572C4⋊C8D4×C4714yescomplemented
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—41no—
579#102—41no—
580#102D4×C4714yescomplemented
581C22⋊C8—22no—
582C22⋊C8—22no—
583#97—22no—
584#95—21no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24—21no—
591C24—21no—
592C24C2×D4×C4711yescharacteristic
593C24C2×D4×C4711yescharacteristic
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—41no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4—81no—
637C2×D4—81no—
638C2×D4C2×D4×C4712yes—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—42no—
657C22×C4—81no—
658C22×C4—81no—
659C22×C4C2×D4×C4711yescharacteristic
660C22×C4C2×D4×C4711yescharacteristic
661C22×C4C2×D4×C4711yescharacteristic
662C22×C4C2×D4×C4711yescharacteristic
663C22×C4C24×C4711yescharacteristic
664D8—44no—
665D8—44no—
666M16—44no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—44no—
677C2×C8C2×D4×C4712yes—
678C2×C8C2×D4×C4712yes—
679C2×C8C2×D4×C4712yes—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4C2×D4×C4712yes—
690C4⋊C4#41×C4712yes—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—81no—
701C22⋊C4—81no—
702C42—42no—
703C42C2×D4×C4712yes—
704C42#41×C4712yes—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23AGL(1,ℤ/8)×C4712yes—
740C23C22×D4×C4711yescharacteristic
741D4—22no—
742D4—22no—
743D4—44no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756D4—84no—
757D4—84no—
758D4—84no—
759D4—84no—
760D4—84no—
761D4—84no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—84no—
796C2×C4#121×C4712yes—
797C2×C4#121×C4712yes—
798C2×C4C22×D4×C4711yescharacteristic
799C2×C4C22×D4×C4711yescharacteristic
800C2×C4C2×#41×C4711yescharacteristic
801C2×C4C2×#41×C4711yescharacteristic
802C2×C4H(5,𝔽2)×C4711yescharacteristic
803C2×C4H(5,𝔽2)×C4711yescharacteristic
804C8—22no—
805C8—22no—
806C8—22no—
807C8—41no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—42no—
821C22—41no—
822C22—42no—
823C22—41no—
824C22—42no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×#121×C4711yescharacteristic
844C22D42×C4711yescharacteristic
845C22C47×#54611yescharacteristic
846C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
847C22C47×#57511yescharacteristic
848C22C47×#57611yescharacteristic
849C22C47×#57611yescharacteristic
850C4—22no—
851C4—22no—
852C4—42no—
853C4—41no—
854C4—41no—
855C4—42no—
856C4—81no—
857C4—81no—
858C4—81no—
859C4C47×#53211yescharacteristic
860C4C47×#54011yescharacteristic
861C4D42×C4711yescharacteristic
862C4C47×#55011yescharacteristic
863C2—42no—
864C2—81no—
865C2—82no—
866C2—161no—
867C2—161no—
868C2C47×#242811yescharacteristic
869C2C47×#305511yescharacteristic
870C2C47×#305811yescharacteristic
871C2C47×#326411yescharacteristic
872C2C47×#326811yescharacteristic
873C2C47×#330911yescharacteristic
874C2C47×#331811yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C4×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#469C2semidirect
2. C2×C47×#466C2semidirect
3. C2×C47×#459C2semidirect
4. C2×C47×#435C2semidirect
5. C47×#2541C2semidirect
6. C47×#2535C2semidirect
7. C47×#2034C2semidirect
8. C47×#2033C2semidirect
9. C47×#1999C2semidirect
10. C47×#1999C2semidirect
11. C47×#1961C2semidirect
12. C47×#1949C2semidirect
13. C47×#1895C2semidirect
14. C47×#1893C2semidirect
15. C47×#1762C2semidirect
134. C4⋊C8×C47D4semidirect
142. #102×C47D4semidirect
370. #25396C47direct (N × H)
426. C2×#469C2×C47semidirect
427. C2×#466C2×C47semidirect
428. C2×#459C2×C47semidirect
429. C2×#435C2×C47semidirect
430. #2541C2×C47semidirect
431. #2535C2×C47semidirect
432. #2034C2×C47semidirect
433. #2033C2×C47semidirect
434. #1999C2×C47semidirect
435. #1999C2×C47semidirect
436. #1961C2×C47semidirect
437. #1949C2×C47semidirect
438. #1895C2×C47semidirect
439. #1893C2×C47semidirect
440. #1762C2×C47semidirect
500. C47#25396direct (N × H)
572. C4⋊C8D4×C47semidirect
580. #102D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4692
C2×C47×#4662
C2×C47×#4592
C2×C47×#4352
C47×#25412
C47×#25352
C47×#20342
C47×#20332
C47×#19992
C47×#19612
C47×#19492
C47×#18952
C47×#18932
C47×#17622
#2539647