Finite Group Databasebeta

← C47×#25402 #26065100

Subgroups — C47×#25402 #26065100

Order 12032.

1120 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#468C211yesmaximal, characteristic, complemented
2C2×C47×#465C211yesmaximal, characteristic, complemented
3C2×C47×#460C211yesmaximal, characteristic, complemented
4C2×C47×#435C211yesmaximal, characteristic, complemented
5C47×#2541C211yesmaximal, characteristic
6C47×#2536C211yesmaximal, characteristic, complemented
7C47×#2034C211yesmaximal, characteristic, complemented
8C47×#2033C211yesmaximal, characteristic, complemented
9C47×#2000C211yesmaximal, characteristic, complemented
10C47×#2000C211yesmaximal, characteristic, complemented
11C47×#1961C211yesmaximal, characteristic, complemented
12C47×#1949C211yesmaximal, characteristic, complemented
13C47×#1895C211yesmaximal, characteristic, complemented
14C47×#1893C211yesmaximal, characteristic, complemented
15C47×#1763C211yesmaximal, characteristic, complemented
16C22×SD16×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C2×#127×C47—21no—
21C2×#127×C47C2211yescharacteristic
22C2×C22⋊Q8×C47C2211yescharacteristic
23C2×C22⋊Q8×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×#121×C47C2211yescharacteristic
26C2×#121×C47C2211yescharacteristic
27C2×#121×C47C2211yescharacteristic
28C2×C4×Q8×C47C2211yescharacteristic
29C2×C4×D4×C47C2211yescharacteristic
30C47×#468—24no—
31C47×#465—24no—
32C47×#460—24no—
33C47×#435—24no—
34C2×#107×C47C2211yescharacteristic
35C2×#106×C47C2211yescharacteristic
36C2×C4⋊C8×C47C2211yescharacteristic
37C2×#103×C47C2211yescharacteristic
38C2×#103×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×#398—21no—
49C47×#394—21no—
50C47×#392—21no—
51C47×#392—21no—
52C47×#390—21no—
53C47×#388—21no—
54C47×#388—21no—
55C47×#382C2211yescharacteristic
56C47×#380C2211yescharacteristic
57C47×#380C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
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×C47D411yescharacteristic
71C22×D4×C47C2311yescharacteristic
72C22×D4×C47C2311yescharacteristic
73C23×C4×C47C2311yescharacteristic
74C23×C4×C47C2311yescharacteristic
75C2×SD16×C47—22no—
76C2×SD16×C47—22no—
77C2×SD16×C47—22no—
78C2×SD16×C47—22no—
79C2×SD16×C47—41no—
80C2×SD16×C47—41no—
81C2×M16×C47—22no—
82C2×M16×C47—22no—
83C2×M16×C47—41no—
84C22×C8×C47—22no—
85C22×C8×C47—22no—
86C22×C8×C47—41no—
87C22×C8×C47C2311yescharacteristic
88C22×C8×C47C2311yescharacteristic
89C22×C8×C47C2311yescharacteristic
90C22×C8×C47C2311yescharacteristic
91#127×C47—22no—
92#127×C47—22no—
93#127×C47—44no—
94C22⋊Q8×C47—22no—
95C22⋊Q8×C47—22no—
96C22⋊Q8×C47—41no—
97C22⋊Q8×C47—41no—
98#121×C47—22no—
99#121×C47—22no—
100#121×C47—22no—
101#121×C47—22no—
102#121×C47—41no—
103#121×C47—41no—
104#121×C47—41no—
105#121×C47—41no—
106C4×Q8×C47—22no—
107C4×Q8×C47—22no—
108C4×D4×C47—22no—
109C4×D4×C47—22no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47—21no—
112C2×C4⋊C4×C47—21no—
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×C47D411yescharacteristic
128C2×C22⋊C4×C47D411yescharacteristic
129C2×C42×C47—21no—
130C2×C42×C47—21no—
131C2×C42×C47C2311yescharacteristic
132#107×C47—22no—
133#106×C47—22no—
134C4⋊C8×C47D414yescomplemented
135#103×C47—22no—
136#103×C47D414yescomplemented
137#102×C47—22no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47—41no—
142#102×C47—41no—
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×C47C2×D411yescharacteristic
154C24×C47C2×D411yescharacteristic
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47C2×D412yes—
161C2×D4×C47—22no—
162C2×D4×C47—22no—
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—81no—
189C2×D4×C47—81no—
190C2×D4×C47—81no—
191C2×D4×C47—81no—
192C2×D4×C47—81no—
193C2×D4×C47—81no—
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×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×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2411yescharacteristic
217SD16×C47—44no—
218SD16×C47—44no—
219M16×C47—44no—
220C2×C8×C47—21no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—44no—
230C2×C8×C47C2×D412yes—
231C2×C8×C47C2×D412yes—
232C2×C8×C47C2×D412yes—
233C4⋊C4×C47—22no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—42no—
243C4⋊C4×C47—42no—
244C4⋊C4×C47—42no—
245C4⋊C4×C47C2×D412yes—
246C4⋊C4×C47#4112yes—
247C22⋊C4×C47—22no—
248C22⋊C4×C47—22no—
249C22⋊C4×C47—42no—
250C22⋊C4×C47—42no—
251C22⋊C4×C47—42no—
252C22⋊C4×C47—42no—
253C22⋊C4×C47—42no—
254C22⋊C4×C47—42no—
255C22⋊C4×C47—42no—
256C22⋊C4×C47—42no—
257C42×C47—42no—
258C42×C47—42no—
259C42×C47C2×D412yes—
260C42×C47#4112yes—
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—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—41no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47AGL(1,ℤ/8)12yes—
289C23×C47C22×D411yescharacteristic
290Q8×C47—22no—
291Q8×C47—22no—
292Q8×C47—41no—
293Q8×C47—41no—
294D4×C47—44no—
295D4×C47—41no—
296D4×C47—41no—
297D4×C47—41no—
298D4×C47—41no—
299D4×C47—41no—
300D4×C47—41no—
301D4×C47—41no—
302D4×C47—41no—
303D4×C47—84no—
304D4×C47—84no—
305D4×C47—84no—
306D4×C47—84no—
307D4×C47—84no—
308D4×C47—84no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—22no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
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×C47—41no—
335C2×C4×C47—41no—
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#12112yes—
346C2×C4×C47#12112yes—
347C2×C4×C47C22×D411yescharacteristic
348C2×C4×C47C22×D411yescharacteristic
349C2×C4×C47C2×#4111yescharacteristic
350C2×C4×C47C2×#4111yescharacteristic
351C2×C4×C47H(5,𝔽2)11yescharacteristic
352C2×C4×C47H(5,𝔽2)11yescharacteristic
353C8×C47—22no—
354C8×C47—22no—
355C8×C47—22no—
356C8×C47—41no—
357#25402C4711yesmaximal, characteristic, direct product factor, Sylow
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—22no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—41no—
367C22×C47—41no—
368C22×C47—41no—
369C22×C47—41no—
370C22×C47—41no—
371C22×C47—41no—
372C22×C47—81no—
373C22×C47—81no—
374C22×C47—81no—
375C22×C47—81no—
376C22×C47—81no—
377C22×C47—81no—
378C22×C47—81no—
379C22×C47—81no—
380C22×C47—81no—
381C22×C47—81no—
382C22×C47—81no—
383C22×C47—81no—
384C22×C47—81no—
385C22×C47—81no—
386C22×C47C2×#12111yescharacteristic
387C22×C47D4211yescharacteristic
388C22×C47#54611yescharacteristic
389C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
390C22×C47#57511yescharacteristic
391C22×C47#57711yescharacteristic
392C22×C47#57711yescharacteristic
393C4×C47—22no—
394C4×C47—22no—
395C4×C47—41no—
396C4×C47—41no—
397C4×C47—42no—
398C4×C47—42no—
399C4×C47—42no—
400C4×C47—81no—
401C4×C47—81no—
402C4×C47—81no—
403C4×C47#53211yescharacteristic
404C4×C47#54011yescharacteristic
405C4×C47D4211yescharacteristic
406C4×C47#55011yescharacteristic
407C2×#468C2×C4711yescharacteristic, complemented
408C2×#465C2×C4711yescharacteristic, complemented
409C2×#460C2×C4711yescharacteristic, complemented
410C2×#435C2×C4711yescharacteristic, complemented
411#2541C2×C4711yescharacteristic
412#2536C2×C4711yescharacteristic, complemented
413#2034C2×C4711yescharacteristic, complemented
414#2033C2×C4711yescharacteristic, complemented
415#2000C2×C4711yescharacteristic, complemented
416#2000C2×C4711yescharacteristic, complemented
417#1961C2×C4711yescharacteristic, complemented
418#1949C2×C4711yescharacteristic, complemented
419#1895C2×C4711yescharacteristic, complemented
420#1893C2×C4711yescharacteristic, complemented
421#1763C2×C4711yescharacteristic, complemented
422C2×C47—42no—
423C2×C47—81no—
424C2×C47—161no—
425C2×C47—161no—
426C2×C47#242811yescharacteristic
427C2×C47#305511yescharacteristic
428C2×C47#305711yescharacteristic
429C2×C47#326511yescharacteristic
430C2×C47#327111yescharacteristic
431C2×C47#331011yescharacteristic
432C2×C47#331711yescharacteristic
433C22×SD16C22×C4711yescharacteristic
434C22×SD16C22×C4711yescharacteristic
435C22×M16C22×C4711yescharacteristic
436C23×C8C22×C4711yescharacteristic
437C2×#127—21no—
438C2×#127C22×C4711yescharacteristic
439C2×C22⋊Q8C22×C4711yescharacteristic
440C2×C22⋊Q8C22×C4711yescharacteristic
441C2×#121C22×C4711yescharacteristic
442C2×#121C22×C4711yescharacteristic
443C2×#121C22×C4711yescharacteristic
444C2×#121C22×C4711yescharacteristic
445C2×C4×Q8C22×C4711yescharacteristic
446C2×C4×D4C22×C4711yescharacteristic
447#468—24no—
448#465—24no—
449#460—24no—
450#435—24no—
451C2×#107C22×C4711yescharacteristic
452C2×#106C22×C4711yescharacteristic
453C2×C4⋊C8C22×C4711yescharacteristic
454C2×#103C22×C4711yescharacteristic
455C2×#103C22×C4711yescharacteristic
456C2×#102C22×C4711yescharacteristic
457C2×#102C22×C4711yescharacteristic
458C2×#102C22×C4711yescharacteristic
459C2×#102C22×C4711yescharacteristic
460C2×#102C22×C4711yescharacteristic
461C2×#102C22×C4711yescharacteristic
462C2×C22⋊C8C22×C4711yescharacteristic
463C2×C22⋊C8C22×C4711yescharacteristic
464C2×#97C22×C4711yescharacteristic
465#398—21no—
466#394—21no—
467#392—21no—
468#392—21no—
469#390—21no—
470#388—21no—
471#388—21no—
472#382C22×C4711yescharacteristic
473#380C22×C4711yescharacteristic
474#380C22×C4711yescharacteristic
475C4×C4⋊C4C22×C4711yescharacteristic
476#340C22×C4711yescharacteristic
477#340C22×C4711yescharacteristic
478#340C22×C4711yescharacteristic
479#340C22×C4711yescharacteristic
480C47#2540211yescharacteristic, direct product factor, Sylow
481C22×Q8C23×C4711yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4D4×C4711yescharacteristic
489C22×D4C23×C4711yescharacteristic
490C22×D4C23×C4711yescharacteristic
491C23×C4C23×C4711yescharacteristic
492C23×C4C23×C4711yescharacteristic
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—41no—
498C2×SD16—41no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—41no—
502C22×C8—22no—
503C22×C8—22no—
504C22×C8—41no—
505C22×C8C23×C4711yescharacteristic
506C22×C8C23×C4711yescharacteristic
507C22×C8C23×C4711yescharacteristic
508C22×C8C23×C4711yescharacteristic
509#127—22no—
510#127—22no—
511#127—44no—
512C22⋊Q8—22no—
513C22⋊Q8—22no—
514C22⋊Q8—41no—
515C22⋊Q8—41no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—41no—
521#121—41no—
522#121—41no—
523#121—41no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×D4—22no—
527C4×D4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4D4×C4711yescharacteristic
532C2×C4⋊C4C23×C4711yescharacteristic
533C2×C4⋊C4C23×C4711yescharacteristic
534C2×C4⋊C4C23×C4711yescharacteristic
535C2×C4⋊C4C23×C4711yescharacteristic
536C2×C4⋊C4C23×C4711yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4D4×C4711yescharacteristic
546C2×C22⋊C4D4×C4711yescharacteristic
547C2×C42—21no—
548C2×C42—21no—
549C2×C42C23×C4711yescharacteristic
550#107—22no—
551#106—22no—
552C4⋊C8D4×C4714yescomplemented
553#103—22no—
554#103D4×C4714yescomplemented
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—41no—
560#102—41no—
561C22⋊C8—22no—
562C22⋊C8—22no—
563#97—22no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95—21no—
569C24—21no—
570C24—21no—
571C24C2×D4×C4711yescharacteristic
572C24C2×D4×C4711yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8C2×D4×C4712yes—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—41no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—81no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4C2×D4×C4711yescharacteristic
631C22×C4C2×D4×C4711yescharacteristic
632C22×C4C2×D4×C4711yescharacteristic
633C22×C4C2×D4×C4711yescharacteristic
634C22×C4C24×C4711yescharacteristic
635SD16—44no—
636SD16—44no—
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—44no—
648C2×C8C2×D4×C4712yes—
649C2×C8C2×D4×C4712yes—
650C2×C8C2×D4×C4712yes—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4C2×D4×C4712yes—
664C4⋊C4#41×C4712yes—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C42—42no—
676C42—42no—
677C42C2×D4×C4712yes—
678C42#41×C4712yes—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23AGL(1,ℤ/8)×C4712yes—
707C23C22×D4×C4711yescharacteristic
708Q8—22no—
709Q8—22no—
710Q8—41no—
711Q8—41no—
712D4—44no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—84no—
722D4—84no—
723D4—84no—
724D4—84no—
725D4—84no—
726D4—84no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4#121×C4712yes—
764C2×C4#121×C4712yes—
765C2×C4C22×D4×C4711yescharacteristic
766C2×C4C22×D4×C4711yescharacteristic
767C2×C4C2×#41×C4711yescharacteristic
768C2×C4C2×#41×C4711yescharacteristic
769C2×C4H(5,𝔽2)×C4711yescharacteristic
770C2×C4H(5,𝔽2)×C4711yescharacteristic
771C8—22no—
772C8—22no—
773C8—22no—
774C8—41no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22C2×#121×C4711yescharacteristic
804C22D42×C4711yescharacteristic
805C22C47×#54611yescharacteristic
806C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
807C22C47×#57511yescharacteristic
808C22C47×#57711yescharacteristic
809C22C47×#57711yescharacteristic
810C4—22no—
811C4—22no—
812C4—42no—
813C4—41no—
814C4—41no—
815C4—42no—
816C4—42no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4C47×#53211yescharacteristic
821C4C47×#54011yescharacteristic
822C4D42×C4711yescharacteristic
823C4C47×#55011yescharacteristic
824C2—42no—
825C2—81no—
826C2—161no—
827C2—161no—
828C2C47×#242811yescharacteristic
829C2C47×#305511yescharacteristic
830C2C47×#305711yescharacteristic
831C2C47×#326511yescharacteristic
832C2C47×#327111yescharacteristic
833C2C47×#331011yescharacteristic
834C2C47×#331711yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#2541C2
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×#468C2semidirect
2. C2×C47×#465C2semidirect
3. C2×C47×#460C2semidirect
4. C2×C47×#435C2semidirect
6. C47×#2536C2semidirect
7. C47×#2034C2semidirect
8. C47×#2033C2semidirect
9. C47×#2000C2semidirect
10. C47×#2000C2semidirect
11. C47×#1961C2semidirect
12. C47×#1949C2semidirect
13. C47×#1895C2semidirect
14. C47×#1893C2semidirect
15. C47×#1763C2semidirect
134. C4⋊C8×C47D4semidirect
136. #103×C47D4semidirect
357. #25402C47direct (N × H)
407. C2×#468C2×C47semidirect
408. C2×#465C2×C47semidirect
409. C2×#460C2×C47semidirect
410. C2×#435C2×C47semidirect
412. #2536C2×C47semidirect
413. #2034C2×C47semidirect
414. #2033C2×C47semidirect
415. #2000C2×C47semidirect
416. #2000C2×C47semidirect
417. #1961C2×C47semidirect
418. #1949C2×C47semidirect
419. #1895C2×C47semidirect
420. #1893C2×C47semidirect
421. #1763C2×C47semidirect
480. C47#25402direct (N × H)
552. C4⋊C8D4×C47semidirect
554. #103D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4682
C2×C47×#4652
C2×C47×#4602
C2×C47×#4352
C47×#25412
C47×#25362
C47×#20342
C47×#20332
C47×#20002
C47×#19612
C47×#19492
C47×#18952
C47×#18932
C47×#17632
#2540247