Finite Group Databasebeta

← C47×#26036 #26065734

Subgroups — C47×#26036 #26065734

Order 12032.

744 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2551C211yesmaximal, characteristic, complemented
2C47×#2357C211yesmaximal, characteristic
3C47×#2067C211yesmaximal, characteristic
4C47×#2065C211yesmaximal, characteristic
5C47×#2023C211yesmaximal, characteristic
6C47×#2023C211yesmaximal, characteristic
7C47×#1988C211yesmaximal, characteristic, complemented
8C47×#1987C211yesmaximal, characteristic, complemented
9C47×#1949C211yesmaximal, characteristic, complemented
10C47×#1940C211yesmaximal, characteristic, complemented
11C47×#1921C211yesmaximal, characteristic, complemented
12C47×#1919C211yesmaximal, characteristic, complemented
13C47×#1836C211yesmaximal, characteristic, complemented
14C47×#1802C211yesmaximal, characteristic
15C47×#1762C211yesmaximal, characteristic
16C2×C4⋊Q8×C47—21no—
17C2×C4⋊Q8×C47C2211yescharacteristic
18C2×C4⋊Q8×C47C2211yescharacteristic
19C2×C4×D4×C47C2211yescharacteristic
20C2×#107×C47C2211yescharacteristic
21C2×#106×C47C2211yescharacteristic
22C2×C4⋊C8×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C2×#102×C47C2211yescharacteristic
26C2×#102×C47C2211yescharacteristic
27C2×#102×C47C2211yescharacteristic
28C2×#102×C47C2211yescharacteristic
29C2×#97×C47C2211yescharacteristic
30C47×#395—21no—
31C47×#395—21no—
32C47×#390C2211yescharacteristic
33C47×#390C2211yescharacteristic
34C47×#389—21no—
35C47×#389C2211yescharacteristic
36C47×#389C2211yescharacteristic
37C47×#388—21no—
38C47×#388—21no—
39C47×#384C2211yescharacteristic
40C47×#382C2211yescharacteristic
41C47×#381—21no—
42C4×C4⋊C4×C47C2211yescharacteristic
43C4×C4⋊C4×C47C2211yescharacteristic
44C4×C4⋊C4×C47C2211yescharacteristic
45C4×C4⋊C4×C47C2211yescharacteristic
46C4×C22⋊C4×C47—21no—
47C47×#340C2211yescharacteristic
48C47×#340C2211yescharacteristic
49C47×#340C2211yescharacteristic
50C47×#340C2211yescharacteristic
51C47×#340C2211yescharacteristic
52C47×#340C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×Q8×C47—21no—
60C22×Q8×C47—21no—
61C22×D4×C47C2311yescharacteristic
62C23×C4×C47—21no—
63C22×C8×C47C2311yescharacteristic
64C22×C8×C47C2311yescharacteristic
65C22×C8×C47C2311yescharacteristic
66C22×C8×C47C2311yescharacteristic
67C4⋊Q8×C47—22no—
68C4⋊Q8×C47—22no—
69C4⋊Q8×C47—41no—
70C4⋊Q8×C47—41no—
71C4⋊Q8×C47—44no—
72C4×D4×C47—22no—
73C4×D4×C47Q814yescomplemented
74C2×C4⋊C4×C47—21no—
75C2×C4⋊C4×C47—21no—
76C2×C4⋊C4×C47—21no—
77C2×C4⋊C4×C47—21no—
78C2×C4⋊C4×C47—21no—
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47D411yescharacteristic
81C2×C4⋊C4×C47D411yescharacteristic
82C2×C4⋊C4×C47C2311yescharacteristic
83C2×C4⋊C4×C47C2311yescharacteristic
84C2×C4⋊C4×C47C2311yescharacteristic
85C2×C4⋊C4×C47C2311yescharacteristic
86C2×C4⋊C4×C47C2311yescharacteristic
87C2×C4⋊C4×C47C2311yescharacteristic
88C2×C4⋊C4×C47C2311yescharacteristic
89C2×C22⋊C4×C47—21no—
90C2×C22⋊C4×C47—21no—
91C2×C22⋊C4×C47—21no—
92C2×C22⋊C4×C47—21no—
93C2×C22⋊C4×C47—21no—
94C2×C42×C47—21no—
95C2×C42×C47—21no—
96C2×C42×C47—21no—
97C2×C42×C47C2311yescharacteristic
98C2×C42×C47C2311yescharacteristic
99C2×C42×C47C2311yescharacteristic
100#107×C47—22no—
101#106×C47—22no—
102C4⋊C8×C47—22no—
103C4⋊C8×C47—41no—
104C4⋊C8×C47—41no—
105#102×C47—22no—
106#102×C47—22no—
107#102×C47—41no—
108#102×C47—41no—
109#97×C47—22no—
110#95×C47—21no—
111#95×C47—21no—
112#95×C47—21no—
113#95×C47—21no—
114#95×C47—21no—
115#95×C47—21no—
116#95×C47—21no—
117#95×C47D411yescharacteristic
118#95×C47D411yescharacteristic
119C24×C47—21no—
120C2×Q8×C47—42no—
121C2×Q8×C47—42no—
122C2×Q8×C47—42no—
123C2×Q8×C47—42no—
124C2×Q8×C47—81no—
125C2×Q8×C47—81no—
126C2×D4×C47—21no—
127C2×D4×C47—21no—
128C2×D4×C47—21no—
129C2×D4×C47—21no—
130C2×D4×C47—21no—
131C2×D4×C47C2×Q812yes—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—24no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—81no—
141C22×C4×C47—81no—
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2411yescharacteristic
149C2×C8×C47—21no—
150C2×C8×C47—21no—
151C2×C8×C47—21no—
152C2×C8×C47—21no—
153C2×C8×C47—21no—
154C2×C8×C47—21no—
155C2×C8×C47—21no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C4⋊C4×C47—22no—
162C4⋊C4×C47—22no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—42no—
175C4⋊C4×C47—42no—
176C4⋊C4×C47—42no—
177C4⋊C4×C47—42no—
178C4⋊C4×C47—42no—
179C4⋊C4×C47—81no—
180C4⋊C4×C47C2×Q812yes—
181C4⋊C4×C47#4112yes—
182C4⋊C4×C47#4112yes—
183C22⋊C4×C47—24no—
184C22⋊C4×C47—42no—
185C22⋊C4×C47—42no—
186C22⋊C4×C47—81no—
187C22⋊C4×C47—81no—
188C42×C47—21no—
189C42×C47—21no—
190C42×C47—21no—
191C42×C47—21no—
192C42×C47—42no—
193C42×C47—81no—
194C42×C47—81no—
195C42×C47C2×Q812yes—
196C42×C47#4112yes—
197C23×C47—22no—
198C23×C47—41no—
199C23×C47—41no—
200C23×C47—41no—
201C23×C47—41no—
202C23×C47—41no—
203C23×C47—41no—
204C23×C47C22×D411yescharacteristic
205Q8×C47—84no—
206Q8×C47—84no—
207D4×C47—22no—
208D4×C47—22no—
209D4×C47—41no—
210D4×C47—41no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—22no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—84no—
247C2×C4×C47C22⋊Q812yes—
248C2×C4×C47C22⋊Q812yes—
249C2×C4×C47AGL(1,ℤ/8)12yes—
250C2×C4×C47#13712yes—
251C2×C4×C47C22×Q811yescharacteristic
252C2×C4×C47C2×#4111yescharacteristic
253C2×C4×C47C2×#4111yescharacteristic
254C2×C4×C47C2×#4111yescharacteristic
255C2×C4×C47H(5,𝔽2)11yescharacteristic
256C2×C4×C472−1+411yescharacteristic
257C8×C47—41no—
258C8×C47—41no—
259C8×C47—41no—
260C8×C47—41no—
261#26036C4711yesmaximal, characteristic, direct product factor, Sylow
262C22×C47—42no—
263C22×C47—42no—
264C22×C47—42no—
265C22×C47—81no—
266C22×C47—81no—
267C22×C47—81no—
268C22×C47—81no—
269C22×C47C2×C22⋊Q811yescharacteristic
270C22×C47#54611yescharacteristic
271C22×C47#54811yescharacteristic
272C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C47C2×#13711yescharacteristic
274C22×C47#57611yescharacteristic
275C22×C47#57711yescharacteristic
276C4×C47—22no—
277C4×C47—22no—
278C4×C47—22no—
279C4×C47—22no—
280C4×C47—42no—
281C4×C47—42no—
282C4×C47—41no—
283C4×C47—42no—
284C4×C47—41no—
285C4×C47—81no—
286C4×C47—81no—
287C4×C47—81no—
288C4×C47—81no—
289C4×C47#53311yescharacteristic
290C4×C47#54411yescharacteristic
291C4×C47#55511yescharacteristic
292C4×C47#55611yescharacteristic
293#2551C2×C4711yescharacteristic, complemented
294#2357C2×C4711yescharacteristic
295#2067C2×C4711yescharacteristic
296#2065C2×C4711yescharacteristic
297#2023C2×C4711yescharacteristic
298#2023C2×C4711yescharacteristic
299#1988C2×C4711yescharacteristic, complemented
300#1987C2×C4711yescharacteristic, complemented
301#1949C2×C4711yescharacteristic, complemented
302#1940C2×C4711yescharacteristic, complemented
303#1921C2×C4711yescharacteristic, complemented
304#1919C2×C4711yescharacteristic, complemented
305#1836C2×C4711yescharacteristic, complemented
306#1802C2×C4711yescharacteristic
307#1762C2×C4711yescharacteristic
308C2×C47—82no—
309C2×C47#243911yescharacteristic
310C2×C47#307911yescharacteristic
311C2×C47#308111yescharacteristic
312C2×C47#331811yescharacteristic
313C2×C47#332011yescharacteristic
314C2×C47#337311yescharacteristic
315C2×C47#337511yescharacteristic
316C2×C4⋊Q8—21no—
317C2×C4⋊Q8C22×C4711yescharacteristic
318C2×C4⋊Q8C22×C4711yescharacteristic
319C2×C4×D4C22×C4711yescharacteristic
320C2×#107C22×C4711yescharacteristic
321C2×#106C22×C4711yescharacteristic
322C2×C4⋊C8C22×C4711yescharacteristic
323C2×C4⋊C8C22×C4711yescharacteristic
324C2×C4⋊C8C22×C4711yescharacteristic
325C2×#102C22×C4711yescharacteristic
326C2×#102C22×C4711yescharacteristic
327C2×#102C22×C4711yescharacteristic
328C2×#102C22×C4711yescharacteristic
329C2×#97C22×C4711yescharacteristic
330#395—21no—
331#395—21no—
332#390C22×C4711yescharacteristic
333#390C22×C4711yescharacteristic
334#389—21no—
335#389C22×C4711yescharacteristic
336#389C22×C4711yescharacteristic
337#388—21no—
338#388—21no—
339#384C22×C4711yescharacteristic
340#382C22×C4711yescharacteristic
341#381—21no—
342C4×C4⋊C4C22×C4711yescharacteristic
343C4×C4⋊C4C22×C4711yescharacteristic
344C4×C4⋊C4C22×C4711yescharacteristic
345C4×C4⋊C4C22×C4711yescharacteristic
346C4×C22⋊C4—21no—
347#340C22×C4711yescharacteristic
348#340C22×C4711yescharacteristic
349#340C22×C4711yescharacteristic
350#340C22×C4711yescharacteristic
351#340C22×C4711yescharacteristic
352#340C22×C4711yescharacteristic
353#340C22×C4711yescharacteristic
354#340C22×C4711yescharacteristic
355#340C22×C4711yescharacteristic
356#340C22×C4711yescharacteristic
357#336C22×C4711yescharacteristic
358#336C22×C4711yescharacteristic
359C47#2603611yescharacteristic, direct product factor, Sylow
360C22×Q8—21no—
361C22×Q8—21no—
362C22×D4C23×C4711yescharacteristic
363C23×C4—21no—
364C22×C8C23×C4711yescharacteristic
365C22×C8C23×C4711yescharacteristic
366C22×C8C23×C4711yescharacteristic
367C22×C8C23×C4711yescharacteristic
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8—41no—
371C4⋊Q8—41no—
372C4⋊Q8—44no—
373C4×D4—22no—
374C4×D4Q8×C4714yescomplemented
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4D4×C4711yescharacteristic
382C2×C4⋊C4D4×C4711yescharacteristic
383C2×C4⋊C4C23×C4711yescharacteristic
384C2×C4⋊C4C23×C4711yescharacteristic
385C2×C4⋊C4C23×C4711yescharacteristic
386C2×C4⋊C4C23×C4711yescharacteristic
387C2×C4⋊C4C23×C4711yescharacteristic
388C2×C4⋊C4C23×C4711yescharacteristic
389C2×C4⋊C4C23×C4711yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42C23×C4711yescharacteristic
399C2×C42C23×C4711yescharacteristic
400C2×C42C23×C4711yescharacteristic
401#107—22no—
402#106—22no—
403C4⋊C8—22no—
404C4⋊C8—41no—
405C4⋊C8—41no—
406#102—22no—
407#102—22no—
408#102—41no—
409#102—41no—
410#97—22no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95D4×C4711yescharacteristic
419#95D4×C4711yescharacteristic
420C24—21no—
421C2×Q8—42no—
422C2×Q8—42no—
423C2×Q8—42no—
424C2×Q8—42no—
425C2×Q8—81no—
426C2×Q8—81no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4C2×Q8×C4712yes—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—24no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—81no—
442C22×C4—81no—
443C22×C4C2×D4×C4711yescharacteristic
444C22×C4C2×D4×C4711yescharacteristic
445C22×C4C2×D4×C4711yescharacteristic
446C22×C4C2×D4×C4711yescharacteristic
447C22×C4C2×D4×C4711yescharacteristic
448C22×C4C2×D4×C4711yescharacteristic
449C22×C4C24×C4711yescharacteristic
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—81no—
481C4⋊C4C2×Q8×C4712yes—
482C4⋊C4#41×C4712yes—
483C4⋊C4#41×C4712yes—
484C22⋊C4—24no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—42no—
494C42—81no—
495C42—81no—
496C42C2×Q8×C4712yes—
497C42#41×C4712yes—
498C23—22no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23C22×D4×C4711yescharacteristic
506Q8—84no—
507Q8—84no—
508D4—22no—
509D4—22no—
510D4—41no—
511D4—41no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—84no—
548C2×C4C22⋊Q8×C4712yes—
549C2×C4C22⋊Q8×C4712yes—
550C2×C4AGL(1,ℤ/8)×C4712yes—
551C2×C4#137×C4712yes—
552C2×C4C22×Q8×C4711yescharacteristic
553C2×C4C2×#41×C4711yescharacteristic
554C2×C4C2×#41×C4711yescharacteristic
555C2×C4C2×#41×C4711yescharacteristic
556C2×C4H(5,𝔽2)×C4711yescharacteristic
557C2×C42−1+4×C4711yescharacteristic
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22C2×C22⋊Q8×C4711yescharacteristic
570C22C47×#54611yescharacteristic
571C22C47×#54811yescharacteristic
572C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
573C22C2×#137×C4711yescharacteristic
574C22C47×#57611yescharacteristic
575C22C47×#57711yescharacteristic
576C4—22no—
577C4—22no—
578C4—22no—
579C4—22no—
580C4—41no—
581C4—42no—
582C4—41no—
583C4—42no—
584C4—42no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4C47×#53311yescharacteristic
590C4C47×#54411yescharacteristic
591C4C47×#55511yescharacteristic
592C4C47×#55611yescharacteristic
593C2—82no—
594C2C47×#243911yescharacteristic
595C2C47×#307911yescharacteristic
596C2C47×#308111yescharacteristic
597C2C47×#331811yescharacteristic
598C2C47×#332011yescharacteristic
599C2C47×#337311yescharacteristic
600C2C47×#337511yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×D4×C47C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C4⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#2551C2semidirect
7. C47×#1988C2semidirect
8. C47×#1987C2semidirect
9. C47×#1949C2semidirect
10. C47×#1940C2semidirect
11. C47×#1921C2semidirect
12. C47×#1919C2semidirect
13. C47×#1836C2semidirect
73. C4×D4×C47Q8semidirect
261. #26036C47direct (N × H)
293. #2551C2×C47semidirect
299. #1988C2×C47semidirect
300. #1987C2×C47semidirect
301. #1949C2×C47semidirect
302. #1940C2×C47semidirect
303. #1921C2×C47semidirect
304. #1919C2×C47semidirect
305. #1836C2×C47semidirect
359. C47#26036direct (N × H)
374. C4×D4Q8×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#25512
C47×#23572
C47×#20672
C47×#20652
C47×#20232
C47×#19882
C47×#19872
C47×#19492
C47×#19402
C47×#19212
C47×#19192
C47×#18362
C47×#18022
C47×#17622
#2603647