Finite Group Databasebeta

← C47×#29096 #26068794

Subgroups — C47×#29096 #26068794

Order 12032.

716 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2513C211yesmaximal, characteristic, complemented
2C47×#2454C211yesmaximal, characteristic, complemented
3C47×#2086C211yesmaximal, characteristic, complemented
4C47×#2073C211yesmaximal, characteristic, complemented
5C47×#2054C211yesmaximal, characteristic
6C47×#2025C211yesmaximal, characteristic, complemented
7C47×#1991C211yesmaximal, characteristic, complemented
8C47×#1970C211yesmaximal, characteristic
9C47×#1936C211yesmaximal, characteristic, complemented
10C47×#1936C211yesmaximal, characteristic, complemented
11C47×#1936C211yesmaximal, characteristic, complemented
12C47×#1918C211yesmaximal, characteristic, complemented
13C47×#1879C211yesmaximal, characteristic
14C47×#1771C211yesmaximal, characteristic, complemented
15C47×#1762C211yesmaximal, characteristic, complemented
16C22×D8×C47C2211yescharacteristic
17C2×#125×C47C2211yescharacteristic
18C2×C4×D4×C47C2211yescharacteristic
19C2×#107×C47C2211yescharacteristic
20C2×C4⋊C8×C47C2211yescharacteristic
21C2×#102×C47C2211yescharacteristic
22C2×#102×C47C2211yescharacteristic
23C2×#102×C47C2211yescharacteristic
24C2×#102×C47C2211yescharacteristic
25C2×#102×C47C2211yescharacteristic
26C2×#102×C47C2211yescharacteristic
27C2×#97×C47C2211yescharacteristic
28C2×#97×C47C2211yescharacteristic
29C2×C4×C8×C47C2211yescharacteristic
30C47×#399—21no—
31C47×#397—21no—
32C47×#397—21no—
33C47×#396—21no—
34C47×#390C2211yescharacteristic
35C47×#390C2211yescharacteristic
36C47×#390C2211yescharacteristic
37C47×#390C2211yescharacteristic
38C47×#390C2211yescharacteristic
39C47×#389C2211yescharacteristic
40C47×#389C2211yescharacteristic
41C47×#389C2211yescharacteristic
42C47×#388—21no—
43C47×#388—21no—
44C47×#385—21no—
45C47×#382C2211yescharacteristic
46C47×#380—21no—
47C4×C4⋊C4×C47C2211yescharacteristic
48C4×C4⋊C4×C47C2211yescharacteristic
49C47×#340C2211yescharacteristic
50C47×#340C2211yescharacteristic
51C47×#340C2211yescharacteristic
52C47×#340C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×D4×C47C2311yescharacteristic
60C22×D4×C47C2311yescharacteristic
61C23×C4×C47—21no—
62C2×D8×C47—22no—
63C2×D8×C47—22no—
64C2×D8×C47—41no—
65C22×C8×C47C2311yescharacteristic
66C22×C8×C47C2311yescharacteristic
67C22×C8×C47C2311yescharacteristic
68C22×C8×C47C2311yescharacteristic
69#125×C47—22no—
70#125×C47—41no—
71C4×D4×C47—22no—
72C4×D4×C47—41no—
73C2×C4⋊C4×C47—21no—
74C2×C4⋊C4×C47—21no—
75C2×C4⋊C4×C47—21no—
76C2×C4⋊C4×C47—21no—
77C2×C4⋊C4×C47—21no—
78C2×C4⋊C4×C47D411yescharacteristic
79C2×C4⋊C4×C47D411yescharacteristic
80C2×C4⋊C4×C47C2311yescharacteristic
81C2×C4⋊C4×C47C2311yescharacteristic
82C2×C4⋊C4×C47C2311yescharacteristic
83C2×C4⋊C4×C47C2311yescharacteristic
84C2×C4⋊C4×C47C2311yescharacteristic
85C2×C4⋊C4×C47C2311yescharacteristic
86C2×C22⋊C4×C47—21no—
87C2×C22⋊C4×C47—21no—
88C2×C22⋊C4×C47—21no—
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×C22⋊C4×C47—21no—
95C2×C22⋊C4×C47—21no—
96C2×C22⋊C4×C47—21no—
97C2×C42×C47—21no—
98C2×C42×C47C2311yescharacteristic
99C2×C42×C47C2311yescharacteristic
100C2×C42×C47C2311yescharacteristic
101#107×C47—22no—
102C4⋊C8×C47—22no—
103#102×C47—22no—
104#102×C47—22no—
105#102×C47—22no—
106#102×C47—22no—
107#102×C47—22no—
108#102×C47—41no—
109#97×C47—22no—
110#97×C47—41no—
111C4×C8×C47—41no—
112#95×C47—21no—
113#95×C47—21no—
114#95×C47—21no—
115#95×C47—21no—
116#95×C47—21no—
117#95×C47—21no—
118#95×C47D411yescharacteristic
119#95×C47D411yescharacteristic
120C24×C47—21no—
121C24×C47—21no—
122C2×D4×C47—21no—
123C2×D4×C47—21no—
124C2×D4×C47—21no—
125C2×D4×C47—21no—
126C2×D4×C47—21no—
127C2×D4×C47—21no—
128C2×D4×C47—21no—
129C2×D4×C47—21no—
130C2×D4×C47—21no—
131C2×D4×C47—21no—
132C2×D4×C47—21no—
133C2×D4×C47#4112yes—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—42no—
141C22×C4×C47—42no—
142C22×C4×C47—81no—
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2411yescharacteristic
150D8×C47—44no—
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—
161C2×C8×C47#4112yes—
162C2×C8×C47#4112yes—
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—41no—
175C4⋊C4×C47—41no—
176C4⋊C4×C47—42no—
177C4⋊C4×C47—42no—
178C4⋊C4×C47—81no—
179C4⋊C4×C47—81no—
180C4⋊C4×C47—81no—
181C4⋊C4×C47#4112yes—
182C22⋊C4×C47—42no—
183C22⋊C4×C47—42no—
184C22⋊C4×C47—42no—
185C22⋊C4×C47—42no—
186C22⋊C4×C47—81no—
187C22⋊C4×C47—81no—
188C22⋊C4×C47—81no—
189C22⋊C4×C47—81no—
190C22⋊C4×C47—81no—
191C22⋊C4×C47—81no—
192C22⋊C4×C47—81no—
193C42×C47—21no—
194C42×C47—21no—
195C42×C47—21no—
196C42×C47—21no—
197C42×C47—21no—
198C42×C47—21no—
199C42×C47—81no—
200C23×C47—22no—
201C23×C47—41no—
202C23×C47—41no—
203C23×C47—41no—
204C23×C47—41no—
205C23×C47—41no—
206C23×C47—41no—
207C23×C47—41no—
208C23×C47—41no—
209C23×C47—41no—
210C23×C47—41no—
211C23×C47—41no—
212C23×C47—41no—
213C23×C47—41no—
214C23×C47C22×D411yescharacteristic
215D4×C47—22no—
216D4×C47—22no—
217D4×C47—41no—
218D4×C47—41no—
219D4×C47—41no—
220D4×C47—41no—
221D4×C47—41no—
222D4×C47—41no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—22no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—41no—
258C2×C4×C47—41no—
259C2×C4×C47—84no—
260C2×C4×C47C2×#4111yescharacteristic
261C2×C4×C47C2×#4111yescharacteristic
262C2×C4×C47C2×#4111yescharacteristic
263C2×C4×C47C2×#4111yescharacteristic
264C2×C4×C47H(5,𝔽2)11yescharacteristic
265C2×C4×C472−1+411yescharacteristic
266C8×C47—22no—
267C8×C47—22no—
268C8×C47—41no—
269C8×C47—41no—
270#29096C4711yesmaximal, characteristic, direct product factor, Sylow
271C22×C47—42no—
272C22×C47—42no—
273C22×C47—42no—
274C22×C47—81no—
275C22×C47—81no—
276C22×C47—81no—
277C22×C47—81no—
278C22×C47—81no—
279C22×C47—81no—
280C22×C47—81no—
281C22×C47—81no—
282C22×C47—81no—
283C22×C47—81no—
284C22×C47—81no—
285C22×C47#53211yescharacteristic
286C22×C47#54611yescharacteristic
287C22×C47#54811yescharacteristic
288C22×C47#57511yescharacteristic
289C22×C47#57511yescharacteristic
290C22×C47#57611yescharacteristic
291C22×C47#57611yescharacteristic
292C4×C47—41no—
293C4×C47—41no—
294C4×C47—41no—
295C4×C47—41no—
296C4×C47—41no—
297C4×C47—41no—
298C4×C47—42no—
299C4×C47—81no—
300C4×C47—81no—
301C4×C47—81no—
302C4×C47—81no—
303C4×C47—81no—
304C4×C47#52911yescharacteristic
305C4×C47#53911yescharacteristic
306C4×C47#55111yescharacteristic
307C4×C47#55611yescharacteristic
308#2513C2×C4711yescharacteristic, complemented
309#2454C2×C4711yescharacteristic, complemented
310#2086C2×C4711yescharacteristic, complemented
311#2073C2×C4711yescharacteristic, complemented
312#2054C2×C4711yescharacteristic
313#2025C2×C4711yescharacteristic, complemented
314#1991C2×C4711yescharacteristic, complemented
315#1970C2×C4711yescharacteristic
316#1936C2×C4711yescharacteristic, complemented
317#1936C2×C4711yescharacteristic, complemented
318#1936C2×C4711yescharacteristic, complemented
319#1918C2×C4711yescharacteristic, complemented
320#1879C2×C4711yescharacteristic
321#1771C2×C4711yescharacteristic, complemented
322#1762C2×C4711yescharacteristic, complemented
323C2×C47—82no—
324C2×C47—161no—
325C2×C47#256011yescharacteristic
326C2×C47#317611yescharacteristic
327C2×C47#318311yescharacteristic
328C2×C47#330911yescharacteristic
329C2×C47#331911yescharacteristic
330C2×C47#337011yescharacteristic
331C2×C47#337011yescharacteristic
332C22×D8C22×C4711yescharacteristic
333C2×#125C22×C4711yescharacteristic
334C2×C4×D4C22×C4711yescharacteristic
335C2×#107C22×C4711yescharacteristic
336C2×C4⋊C8C22×C4711yescharacteristic
337C2×#102C22×C4711yescharacteristic
338C2×#102C22×C4711yescharacteristic
339C2×#102C22×C4711yescharacteristic
340C2×#102C22×C4711yescharacteristic
341C2×#102C22×C4711yescharacteristic
342C2×#102C22×C4711yescharacteristic
343C2×#97C22×C4711yescharacteristic
344C2×#97C22×C4711yescharacteristic
345C2×C4×C8C22×C4711yescharacteristic
346#399—21no—
347#397—21no—
348#397—21no—
349#396—21no—
350#390C22×C4711yescharacteristic
351#390C22×C4711yescharacteristic
352#390C22×C4711yescharacteristic
353#390C22×C4711yescharacteristic
354#390C22×C4711yescharacteristic
355#389C22×C4711yescharacteristic
356#389C22×C4711yescharacteristic
357#389C22×C4711yescharacteristic
358#388—21no—
359#388—21no—
360#385—21no—
361#382C22×C4711yescharacteristic
362#380—21no—
363C4×C4⋊C4C22×C4711yescharacteristic
364C4×C4⋊C4C22×C4711yescharacteristic
365#340C22×C4711yescharacteristic
366#340C22×C4711yescharacteristic
367#340C22×C4711yescharacteristic
368#340C22×C4711yescharacteristic
369#340C22×C4711yescharacteristic
370#340C22×C4711yescharacteristic
371#340C22×C4711yescharacteristic
372#340C22×C4711yescharacteristic
373#336C22×C4711yescharacteristic
374#336C22×C4711yescharacteristic
375C47#2909611yescharacteristic, direct product factor, Sylow
376C22×D4C23×C4711yescharacteristic
377C22×D4C23×C4711yescharacteristic
378C23×C4—21no—
379C2×D8—22no—
380C2×D8—22no—
381C2×D8—41no—
382C22×C8C23×C4711yescharacteristic
383C22×C8C23×C4711yescharacteristic
384C22×C8C23×C4711yescharacteristic
385C22×C8C23×C4711yescharacteristic
386#125—22no—
387#125—41no—
388C4×D4—22no—
389C4×D4—41no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4D4×C4711yescharacteristic
396C2×C4⋊C4D4×C4711yescharacteristic
397C2×C4⋊C4C23×C4711yescharacteristic
398C2×C4⋊C4C23×C4711yescharacteristic
399C2×C4⋊C4C23×C4711yescharacteristic
400C2×C4⋊C4C23×C4711yescharacteristic
401C2×C4⋊C4C23×C4711yescharacteristic
402C2×C4⋊C4C23×C4711yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C42—21no—
415C2×C42C23×C4711yescharacteristic
416C2×C42C23×C4711yescharacteristic
417C2×C42C23×C4711yescharacteristic
418#107—22no—
419C4⋊C8—22no—
420#102—22no—
421#102—22no—
422#102—22no—
423#102—22no—
424#102—22no—
425#102—41no—
426#97—22no—
427#97—41no—
428C4×C8—41no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95D4×C4711yescharacteristic
436#95D4×C4711yescharacteristic
437C24—21no—
438C24—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4#41×C4712yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—81no—
460C22×C4C2×D4×C4711yescharacteristic
461C22×C4C2×D4×C4711yescharacteristic
462C22×C4C2×D4×C4711yescharacteristic
463C22×C4C2×D4×C4711yescharacteristic
464C22×C4C2×D4×C4711yescharacteristic
465C22×C4C2×D4×C4711yescharacteristic
466C22×C4C24×C4711yescharacteristic
467D8—44no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8#41×C4712yes—
479C2×C8#41×C4712yes—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—81no—
496C4⋊C4—81no—
497C4⋊C4—81no—
498C4⋊C4#41×C4712yes—
499C22⋊C4—42no—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C22⋊C4—42no—
503C22⋊C4—81no—
504C22⋊C4—81no—
505C22⋊C4—81no—
506C22⋊C4—81no—
507C22⋊C4—81no—
508C22⋊C4—81no—
509C22⋊C4—81no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—81no—
517C23—22no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23C22×D4×C4711yescharacteristic
532D4—22no—
533D4—22no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—84no—
577C2×C4C2×#41×C4711yescharacteristic
578C2×C4C2×#41×C4711yescharacteristic
579C2×C4C2×#41×C4711yescharacteristic
580C2×C4C2×#41×C4711yescharacteristic
581C2×C4H(5,𝔽2)×C4711yescharacteristic
582C2×C42−1+4×C4711yescharacteristic
583C8—22no—
584C8—22no—
585C8—41no—
586C8—41no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22C47×#53211yescharacteristic
602C22C47×#54611yescharacteristic
603C22C47×#54811yescharacteristic
604C22C47×#57511yescharacteristic
605C22C47×#57511yescharacteristic
606C22C47×#57611yescharacteristic
607C22C47×#57611yescharacteristic
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—42no—
613C4—41no—
614C4—41no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4—81no—
620C4C47×#52911yescharacteristic
621C4C47×#53911yescharacteristic
622C4C47×#55111yescharacteristic
623C4C47×#55611yescharacteristic
624C2—82no—
625C2—161no—
626C2C47×#256011yescharacteristic
627C2C47×#317611yescharacteristic
628C2C47×#318311yescharacteristic
629C2C47×#330911yescharacteristic
630C2C47×#331911yescharacteristic
631C2C47×#337011yescharacteristic
632C2C47×#337011yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×D8×C47C22
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×#2513C2semidirect
2. C47×#2454C2semidirect
3. C47×#2086C2semidirect
4. C47×#2073C2semidirect
6. C47×#2025C2semidirect
7. C47×#1991C2semidirect
9. C47×#1936C2semidirect
10. C47×#1936C2semidirect
11. C47×#1936C2semidirect
12. C47×#1918C2semidirect
14. C47×#1771C2semidirect
15. C47×#1762C2semidirect
270. #29096C47direct (N × H)
308. #2513C2×C47semidirect
309. #2454C2×C47semidirect
310. #2086C2×C47semidirect
311. #2073C2×C47semidirect
313. #2025C2×C47semidirect
314. #1991C2×C47semidirect
316. #1936C2×C47semidirect
317. #1936C2×C47semidirect
318. #1936C2×C47semidirect
319. #1918C2×C47semidirect
321. #1771C2×C47semidirect
322. #1762C2×C47semidirect
375. C47#29096direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#25132
C47×#24542
C47×#20862
C47×#20732
C47×#20542
C47×#20252
C47×#19912
C47×#19702
C47×#19362
C47×#19182
C47×#18792
C47×#17712
C47×#17622
#2909647