Finite Group Databasebeta

← C47×#24942 #26064640

Subgroups — C47×#24942 #26064640

Order 12032.

740 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×#2485C211yesmaximal, characteristic
2C47×#2354C211yesmaximal, characteristic
3C47×#2099C211yesmaximal, characteristic, complemented
4C47×#2083C211yesmaximal, characteristic, complemented
5C47×#2076C211yesmaximal, characteristic, complemented
6C47×#2075C211yesmaximal, characteristic, complemented
7C47×#1921C211yesmaximal, characteristic, complemented
8C47×#1919C211yesmaximal, characteristic, complemented
9C47×#1869C211yesmaximal, characteristic
10C47×#1854C211yesmaximal, characteristic, complemented
11C47×#1854C211yesmaximal, characteristic, complemented
12C47×#1825C211yesmaximal, characteristic, complemented
13C47×#1825C211yesmaximal, characteristic, complemented
14C47×#1808C211yesmaximal, characteristic, complemented
15C47×#1735C211yesmaximal, characteristic, complemented
16C23×C8×C47C2211yescharacteristic
17C2×C4×D4×C47C2211yescharacteristic
18C2×#117×C47C2211yescharacteristic
19C2×#117×C47C2211yescharacteristic
20C2×#117×C47C2211yescharacteristic
21C2×#107×C47C2211yescharacteristic
22C2×#107×C47C2211yescharacteristic
23C2×#107×C47C2211yescharacteristic
24C2×#106×C47C2211yescharacteristic
25C2×C22⋊C8×C47C2211yescharacteristic
26C2×C22⋊C8×C47C2211yescharacteristic
27C2×C22⋊C8×C47C2211yescharacteristic
28C47×#397—21no—
29C47×#394—21no—
30C47×#390—21no—
31C47×#389C2211yescharacteristic
32C47×#389C2211yescharacteristic
33C47×#388—21no—
34C47×#388—21no—
35C47×#388—21no—
36C47×#387—21no—
37C47×#384C2211yescharacteristic
38C47×#380C2211yescharacteristic
39C47×#380C2211yescharacteristic
40C47×#380C2211yescharacteristic
41C47×#380C2211yescharacteristic
42C47×#380C2211yescharacteristic
43C4×C4⋊C4×C47—21no—
44C4×C4⋊C4×C47C2211yescharacteristic
45C47×#340C2211yescharacteristic
46C47×#340C2211yescharacteristic
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×D4×C47D411yescharacteristic
60C23×C4×C47C2311yescharacteristic
61C23×C4×C47C2311yescharacteristic
62C22×C8×C47—22no—
63C22×C8×C47—22no—
64C22×C8×C47—41no—
65C22×C8×C47C2311yescharacteristic
66C22×C8×C47C2311yescharacteristic
67C22×C8×C47C2311yescharacteristic
68C22×C8×C47C2311yescharacteristic
69C4×D4×C47—22no—
70C4×D4×C47—22no—
71#117×C47—22no—
72#117×C47—22no—
73#117×C47—22no—
74#117×C47—22no—
75#117×C47—41no—
76#117×C47—41no—
77C2×C4⋊C4×C47—21no—
78C2×C4⋊C4×C47—21no—
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47—21no—
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×C4⋊C4×C47C2311yescharacteristic
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×C22⋊C4×C47—21no—
98C2×C22⋊C4×C47D411yescharacteristic
99C2×C22⋊C4×C47D411yescharacteristic
100C2×C42×C47—21no—
101C2×C42×C47—21no—
102C2×C42×C47—21no—
103C2×C42×C47—21no—
104C2×C42×C47C2311yescharacteristic
105#107×C47—22no—
106#107×C47—41no—
107#107×C47—41no—
108#106×C47—22no—
109C22⋊C8×C47—22no—
110C22⋊C8×C47—22no—
111C22⋊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×C47—21no—
119#95×C47—21no—
120C24×C47C2×D411yescharacteristic
121C24×C47C2×D411yescharacteristic
122C2×D4×C47—22no—
123C2×D4×C47—22no—
124C2×D4×C47—41no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
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—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47#4112yes—
148C22×C4×C47#4112yes—
149C22×C4×C47C2411yescharacteristic
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—
161C2×C8×C47—44no—
162C2×C8×C47#4112yes—
163C4⋊C4×C47—22no—
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—21no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47—21no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—42no—
180C4⋊C4×C47—42no—
181C4⋊C4×C47—81no—
182C4⋊C4×C47—81no—
183C4⋊C4×C47#4112yes—
184C22⋊C4×C47—22no—
185C22⋊C4×C47—22no—
186C22⋊C4×C47—42no—
187C22⋊C4×C47—42no—
188C22⋊C4×C47—42no—
189C22⋊C4×C47—42no—
190C22⋊C4×C47—81no—
191C22⋊C4×C47—81no—
192C22⋊C4×C47—81no—
193C22⋊C4×C47—81no—
194C42×C47—21no—
195C42×C47—21no—
196C42×C47—42no—
197C42×C47—42no—
198C42×C47—42no—
199C42×C47—42no—
200C23×C47—21no—
201C23×C47—21no—
202C23×C47—21no—
203C23×C47—21no—
204C23×C47—21no—
205C23×C47—21no—
206C23×C47—21no—
207C23×C47—21no—
208C23×C47—21no—
209C23×C47—21no—
210C23×C47—21no—
211C23×C47—21no—
212C23×C47—21no—
213C23×C47#12312yes—
214C23×C47C22×D411yescharacteristic
215D4×C47—44no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—22no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
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—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#12312yes—
259C2×C4×C47#13512yes—
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—41no—
268C8×C47—41no—
269C8×C47—41no—
270#24942C4711yesmaximal, characteristic, direct product factor, Sylow
271C22×C47—22no—
272C22×C47—22no—
273C22×C47—22no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47—41no—
279C22×C47—41no—
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47—41no—
285C22×C47C2×#12311yescharacteristic
286C22×C47#54611yescharacteristic
287C22×C47#54711yescharacteristic
288C22×C47C2×#13511yescharacteristic
289C22×C47#57511yescharacteristic
290C22×C47#57611yescharacteristic
291C22×C47#57811yescharacteristic
292C4×C47—22no—
293C4×C47—22no—
294C4×C47—41no—
295C4×C47—41no—
296C4×C47—42no—
297C4×C47—81no—
298C4×C47—81no—
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#55211yescharacteristic
308#2485C2×C4711yescharacteristic
309#2354C2×C4711yescharacteristic
310#2099C2×C4711yescharacteristic, complemented
311#2083C2×C4711yescharacteristic, complemented
312#2076C2×C4711yescharacteristic, complemented
313#2075C2×C4711yescharacteristic, complemented
314#1921C2×C4711yescharacteristic, complemented
315#1919C2×C4711yescharacteristic, complemented
316#1869C2×C4711yescharacteristic
317#1854C2×C4711yescharacteristic, complemented
318#1854C2×C4711yescharacteristic, complemented
319#1825C2×C4711yescharacteristic, complemented
320#1825C2×C4711yescharacteristic, complemented
321#1808C2×C4711yescharacteristic, complemented
322#1735C2×C4711yescharacteristic, complemented
323C2×C47—42no—
324C2×C47—81no—
325C2×C47#241911yescharacteristic
326C2×C47#309111yescharacteristic
327C2×C47#309811yescharacteristic
328C2×C47#330511yescharacteristic
329C2×C47#331511yescharacteristic
330C2×C47#334211yescharacteristic
331C2×C47#334711yescharacteristic
332C23×C8C22×C4711yescharacteristic
333C2×C4×D4C22×C4711yescharacteristic
334C2×#117C22×C4711yescharacteristic
335C2×#117C22×C4711yescharacteristic
336C2×#117C22×C4711yescharacteristic
337C2×#107C22×C4711yescharacteristic
338C2×#107C22×C4711yescharacteristic
339C2×#107C22×C4711yescharacteristic
340C2×#106C22×C4711yescharacteristic
341C2×C22⋊C8C22×C4711yescharacteristic
342C2×C22⋊C8C22×C4711yescharacteristic
343C2×C22⋊C8C22×C4711yescharacteristic
344#397—21no—
345#394—21no—
346#390—21no—
347#389C22×C4711yescharacteristic
348#389C22×C4711yescharacteristic
349#388—21no—
350#388—21no—
351#388—21no—
352#387—21no—
353#384C22×C4711yescharacteristic
354#380C22×C4711yescharacteristic
355#380C22×C4711yescharacteristic
356#380C22×C4711yescharacteristic
357#380C22×C4711yescharacteristic
358#380C22×C4711yescharacteristic
359C4×C4⋊C4—21no—
360C4×C4⋊C4C22×C4711yescharacteristic
361#340C22×C4711yescharacteristic
362#340C22×C4711yescharacteristic
363#340C22×C4711yescharacteristic
364#340C22×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#2494211yescharacteristic, direct product factor, Sylow
376C22×D4D4×C4711yescharacteristic
377C23×C4C23×C4711yescharacteristic
378C23×C4C23×C4711yescharacteristic
379C22×C8—22no—
380C22×C8—22no—
381C22×C8—41no—
382C22×C8C23×C4711yescharacteristic
383C22×C8C23×C4711yescharacteristic
384C22×C8C23×C4711yescharacteristic
385C22×C8C23×C4711yescharacteristic
386C4×D4—22no—
387C4×D4—22no—
388#117—22no—
389#117—22no—
390#117—22no—
391#117—22no—
392#117—41no—
393#117—41no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4D4×C4711yescharacteristic
399C2×C4⋊C4C23×C4711yescharacteristic
400C2×C4⋊C4C23×C4711yescharacteristic
401C2×C4⋊C4C23×C4711yescharacteristic
402C2×C4⋊C4C23×C4711yescharacteristic
403C2×C4⋊C4C23×C4711yescharacteristic
404C2×C4⋊C4C23×C4711yescharacteristic
405C2×C4⋊C4C23×C4711yescharacteristic
406C2×C4⋊C4C23×C4711yescharacteristic
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×C22⋊C4—21no—
415C2×C22⋊C4D4×C4711yescharacteristic
416C2×C22⋊C4D4×C4711yescharacteristic
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42C23×C4711yescharacteristic
422#107—22no—
423#107—41no—
424#107—41no—
425#106—22no—
426C22⋊C8—22no—
427C22⋊C8—22no—
428C22⋊C8—41no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437C24C2×D4×C4711yescharacteristic
438C24C2×D4×C4711yescharacteristic
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—41no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4C2×D4×C4711yescharacteristic
461C22×C4C2×D4×C4711yescharacteristic
462C22×C4C2×D4×C4711yescharacteristic
463C22×C4C2×D4×C4711yescharacteristic
464C22×C4#41×C4712yes—
465C22×C4#41×C4712yes—
466C22×C4C24×C4711yescharacteristic
467C2×C8—21no—
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—44no—
479C2×C8#41×C4712yes—
480C4⋊C4—22no—
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—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—81no—
499C4⋊C4—81no—
500C4⋊C4#41×C4712yes—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—81no—
508C22⋊C4—81no—
509C22⋊C4—81no—
510C22⋊C4—81no—
511C42—21no—
512C42—21no—
513C42—42no—
514C42—42no—
515C42—42no—
516C42—42no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23#123×C4712yes—
531C23C22×D4×C4711yescharacteristic
532D4—44no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
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#123×C4712yes—
576C2×C4#135×C4712yes—
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—41no—
585C8—41no—
586C8—41no—
587C22—22no—
588C22—22no—
589C22—22no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22C2×#123×C4711yescharacteristic
602C22C47×#54611yescharacteristic
603C22C47×#54711yescharacteristic
604C22C2×#135×C4711yescharacteristic
605C22C47×#57511yescharacteristic
606C22C47×#57611yescharacteristic
607C22C47×#57811yescharacteristic
608C4—22no—
609C4—22no—
610C4—42no—
611C4—41no—
612C4—41no—
613C4—81no—
614C4—81no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4—81no—
620C4C47×#52911yescharacteristic
621C4C47×#53911yescharacteristic
622C4C47×#55111yescharacteristic
623C4C47×#55211yescharacteristic
624C2—42no—
625C2—81no—
626C2C47×#241911yescharacteristic
627C2C47×#309111yescharacteristic
628C2C47×#309811yescharacteristic
629C2C47×#330511yescharacteristic
630C2C47×#331511yescharacteristic
631C2C47×#334211yescharacteristic
632C2C47×#334711yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×D4×C47D4
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
3. C47×#2099C2semidirect
4. C47×#2083C2semidirect
5. C47×#2076C2semidirect
6. C47×#2075C2semidirect
7. C47×#1921C2semidirect
8. C47×#1919C2semidirect
10. C47×#1854C2semidirect
11. C47×#1854C2semidirect
12. C47×#1825C2semidirect
13. C47×#1825C2semidirect
14. C47×#1808C2semidirect
15. C47×#1735C2semidirect
270. #24942C47direct (N × H)
310. #2099C2×C47semidirect
311. #2083C2×C47semidirect
312. #2076C2×C47semidirect
313. #2075C2×C47semidirect
314. #1921C2×C47semidirect
315. #1919C2×C47semidirect
317. #1854C2×C47semidirect
318. #1854C2×C47semidirect
319. #1825C2×C47semidirect
320. #1825C2×C47semidirect
321. #1808C2×C47semidirect
322. #1735C2×C47semidirect
375. C47#24942direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#24852
C47×#23542
C47×#20992
C47×#20832
C47×#20762
C47×#20752
C47×#19212
C47×#19192
C47×#18692
C47×#18542
C47×#18252
C47×#18082
C47×#17352
#2494247