Finite Group Databasebeta

← C47×#27038 #26066736

Subgroups — C47×#27038 #26066736

Order 12032.

734 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2495C211yesmaximal, characteristic, complemented
2C47×#2363C211yesmaximal, characteristic
3C47×#2073C211yesmaximal, characteristic, complemented
4C47×#2067C211yesmaximal, characteristic, complemented
5C47×#2034C211yesmaximal, characteristic
6C47×#2033C211yesmaximal, characteristic
7C47×#1949C211yesmaximal, characteristic, complemented
8C47×#1942C211yesmaximal, characteristic, complemented
9C47×#1923C211yesmaximal, characteristic, complemented
10C47×#1920C211yesmaximal, characteristic, complemented
11C47×#1920C211yesmaximal, characteristic, complemented
12C47×#1864C211yesmaximal, characteristic, complemented
13C47×#1854C211yesmaximal, characteristic, complemented
14C47×#1825C211yesmaximal, characteristic, complemented
15C4×#102×C47C211yesmaximal, characteristic, complemented
16C2×#121×C47C2211yescharacteristic
17C2×C4×D4×C47C2211yescharacteristic
18C2×#117×C47C2211yescharacteristic
19C2×#107×C47C2211yescharacteristic
20C2×#107×C47C2211yescharacteristic
21C2×#106×C47C2211yescharacteristic
22C2×#106×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×#102×C47C2211yescharacteristic
25C2×#102×C47C2211yescharacteristic
26C2×#102×C47C2211yescharacteristic
27C2×#102×C47C2211yescharacteristic
28C2×C22⋊C8×C47C2211yescharacteristic
29C2×C22⋊C8×C47C2211yescharacteristic
30C2×C4×C8×C47C2211yescharacteristic
31C47×#400—21no—
32C47×#397—21no—
33C47×#390—21no—
34C47×#390C2211yescharacteristic
35C47×#389C2211yescharacteristic
36C47×#389C2211yescharacteristic
37C47×#389C2211yescharacteristic
38C47×#388—21no—
39C47×#388—21no—
40C47×#386—21no—
41C47×#383—21no—
42C47×#382C2211yescharacteristic
43C47×#380C2211yescharacteristic
44C47×#380C2211yescharacteristic
45C4×C4⋊C4×C47C2211yescharacteristic
46C4×C4⋊C4×C47C2211yescharacteristic
47C4×C22⋊C4×C47—21no—
48C4×C22⋊C4×C47C2211yescharacteristic
49C47×#340C2211yescharacteristic
50C47×#340C2211yescharacteristic
51C47×#340C2211yescharacteristic
52C47×#340C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×D4×C47—21no—
60C22×D4×C47C2311yescharacteristic
61C23×C4×C47—21no—
62C23×C4×C47C2311yescharacteristic
63C22×C8×C47C2311yescharacteristic
64C22×C8×C47C2311yescharacteristic
65C22×C8×C47C2311yescharacteristic
66C22×C8×C47C2311yescharacteristic
67#121×C47—22no—
68#121×C47—22no—
69C4×D4×C47—22no—
70C4×D4×C47—41no—
71#117×C47—22no—
72#117×C47—41no—
73C2×C4⋊C4×C47—21no—
74C2×C4⋊C4×C47—21no—
75C2×C4⋊C4×C47—21no—
76C2×C4⋊C4×C47C2311yescharacteristic
77C2×C4⋊C4×C47C2311yescharacteristic
78C2×C4⋊C4×C47C2311yescharacteristic
79C2×C4⋊C4×C47C2311yescharacteristic
80C2×C4⋊C4×C47C2311yescharacteristic
81C2×C4⋊C4×C47C2311yescharacteristic
82C2×C4⋊C4×C47C2311yescharacteristic
83C2×C22⋊C4×C47—21no—
84C2×C22⋊C4×C47—21no—
85C2×C22⋊C4×C47—21no—
86C2×C22⋊C4×C47—21no—
87C2×C22⋊C4×C47—21no—
88C2×C22⋊C4×C47—21no—
89C2×C22⋊C4×C47—21no—
90C2×C22⋊C4×C47D411yescharacteristic
91C2×C22⋊C4×C47D411yescharacteristic
92C2×C42×C47—21no—
93C2×C42×C47—21no—
94C2×C42×C47—21no—
95C2×C42×C47C2311yescharacteristic
96C2×C42×C47C2311yescharacteristic
97#107×C47—22no—
98#107×C47—41no—
99#106×C47—22no—
100#106×C47—22no—
101C4⋊C8×C47—22no—
102#102×C47—22no—
103#102×C47—22no—
104#102×C47—22no—
105#102×C47—41no—
106C22⋊C8×C47—22no—
107C22⋊C8×C47—41no—
108C4×C8×C47—41no—
109#95×C47—21no—
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×C47—21no—
118#95×C47D411yescharacteristic
119#95×C47D411yescharacteristic
120C24×C47—21no—
121C24×C47C2×D411yescharacteristic
122C2×D4×C47—24no—
123C2×D4×C47—21no—
124C2×D4×C47—21no—
125C2×D4×C47—21no—
126C2×D4×C47—21no—
127C2×D4×C47—21no—
128C2×D4×C47—81no—
129C2×D4×C47—81no—
130C2×D4×C47#4112yes—
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×C47—21no—
144C22×C4×C47—42no—
145C22×C4×C47—42no—
146C22×C4×C47—81no—
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2411yescharacteristic
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—21no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47#4112yes—
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—81no—
178C4⋊C4×C47—81no—
179C4⋊C4×C47—81no—
180C4⋊C4×C47#4112yes—
181C4⋊C4×C47#4112yes—
182C22⋊C4×C47—24no—
183C22⋊C4×C47—22no—
184C22⋊C4×C47—41no—
185C22⋊C4×C47—42no—
186C22⋊C4×C47—42no—
187C22⋊C4×C47—42no—
188C22⋊C4×C47—42no—
189C22⋊C4×C47—81no—
190C22⋊C4×C47—81no—
191C42×C47—21no—
192C42×C47—21no—
193C42×C47—21no—
194C42×C47—21no—
195C42×C47—42no—
196C42×C47—42no—
197C42×C47—81no—
198C23×C47—22no—
199C23×C47—21no—
200C23×C47—21no—
201C23×C47—21no—
202C23×C47—21no—
203C23×C47—21no—
204C23×C47—21no—
205C23×C47—21no—
206C23×C47—41no—
207C23×C47—41no—
208C23×C47—41no—
209C23×C47—41no—
210C23×C47—41no—
211C23×C47—41no—
212C23×C47C22×D411yescharacteristic
213D4×C47—22no—
214D4×C47—22no—
215D4×C47—41no—
216D4×C47—41no—
217D4×C47—84no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—22no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—22no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
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—84no—
258C2×C4×C47#13512yes—
259C2×C4×C47C2×#4111yescharacteristic
260C2×C4×C47C2×#4111yescharacteristic
261C2×C4×C47C2×#4111yescharacteristic
262C2×C4×C47C2×#4111yescharacteristic
263C2×C4×C47H(5,𝔽2)11yescharacteristic
264C2×C4×C472−1+411yescharacteristic
265C8×C47—22no—
266C8×C47—41no—
267C8×C47—41no—
268C8×C47—41no—
269#27038C4711yesmaximal, characteristic, direct product factor, Sylow
270C22×C47—41no—
271C22×C47—41no—
272C22×C47—41no—
273C22×C47—42no—
274C22×C47—41no—
275C22×C47—42no—
276C22×C47—41no—
277C22×C47—42no—
278C22×C47—41no—
279C22×C47—41no—
280C22×C47—81no—
281C22×C47—81no—
282C22×C47—81no—
283C22×C47—81no—
284C22×C47#52511yescharacteristic
285C22×C47#54611yescharacteristic
286C22×C47#54711yescharacteristic
287C22×C47C2×#13511yescharacteristic
288C22×C47#57511yescharacteristic
289C22×C47#57611yescharacteristic
290C22×C47#57711yescharacteristic
291C4×C47—22no—
292C4×C47—41no—
293C4×C47—41no—
294C4×C47—42no—
295C4×C47—41no—
296C4×C47—42no—
297C4×C47—41no—
298C4×C47—81no—
299C4×C47—81no—
300C4×C47—81no—
301C4×C47—81no—
302C4×C47—81no—
303C4×C47#52911yescharacteristic
304C4×C47#53911yescharacteristic
305C4×C47#55311yescharacteristic
306C4×C47#55611yescharacteristic
307#2495C2×C4711yescharacteristic, complemented
308#2363C2×C4711yescharacteristic
309#2073C2×C4711yescharacteristic, complemented
310#2067C2×C4711yescharacteristic, complemented
311#2034C2×C4711yescharacteristic
312#2033C2×C4711yescharacteristic
313#1949C2×C4711yescharacteristic, complemented
314#1942C2×C4711yescharacteristic, complemented
315#1923C2×C4711yescharacteristic, complemented
316#1920C2×C4711yescharacteristic, complemented
317#1920C2×C4711yescharacteristic, complemented
318#1864C2×C4711yescharacteristic, complemented
319#1854C2×C4711yescharacteristic, complemented
320#1825C2×C4711yescharacteristic, complemented
321C4×#102C2×C4711yescharacteristic, complemented
322C2×C47—81no—
323C2×C47—82no—
324C2×C47#246611yescharacteristic
325C2×C47#310211yescharacteristic
326C2×C47#311811yescharacteristic
327C2×C47#329611yescharacteristic
328C2×C47#330911yescharacteristic
329C2×C47#334111yescharacteristic
330C2×C47#335111yescharacteristic
331C2×#121C22×C4711yescharacteristic
332C2×C4×D4C22×C4711yescharacteristic
333C2×#117C22×C4711yescharacteristic
334C2×#107C22×C4711yescharacteristic
335C2×#107C22×C4711yescharacteristic
336C2×#106C22×C4711yescharacteristic
337C2×#106C22×C4711yescharacteristic
338C2×C4⋊C8C22×C4711yescharacteristic
339C2×#102C22×C4711yescharacteristic
340C2×#102C22×C4711yescharacteristic
341C2×#102C22×C4711yescharacteristic
342C2×#102C22×C4711yescharacteristic
343C2×C22⋊C8C22×C4711yescharacteristic
344C2×C22⋊C8C22×C4711yescharacteristic
345C2×C4×C8C22×C4711yescharacteristic
346#400—21no—
347#397—21no—
348#390—21no—
349#390C22×C4711yescharacteristic
350#389C22×C4711yescharacteristic
351#389C22×C4711yescharacteristic
352#389C22×C4711yescharacteristic
353#388—21no—
354#388—21no—
355#386—21no—
356#383—21no—
357#382C22×C4711yescharacteristic
358#380C22×C4711yescharacteristic
359#380C22×C4711yescharacteristic
360C4×C4⋊C4C22×C4711yescharacteristic
361C4×C4⋊C4C22×C4711yescharacteristic
362C4×C22⋊C4—21no—
363C4×C22⋊C4C22×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#336C22×C4711yescharacteristic
373#336C22×C4711yescharacteristic
374C47#2703811yescharacteristic, direct product factor, Sylow
375C22×D4—21no—
376C22×D4C23×C4711yescharacteristic
377C23×C4—21no—
378C23×C4C23×C4711yescharacteristic
379C22×C8C23×C4711yescharacteristic
380C22×C8C23×C4711yescharacteristic
381C22×C8C23×C4711yescharacteristic
382C22×C8C23×C4711yescharacteristic
383#121—22no—
384#121—22no—
385C4×D4—22no—
386C4×D4—41no—
387#117—22no—
388#117—41no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4C23×C4711yescharacteristic
393C2×C4⋊C4C23×C4711yescharacteristic
394C2×C4⋊C4C23×C4711yescharacteristic
395C2×C4⋊C4C23×C4711yescharacteristic
396C2×C4⋊C4C23×C4711yescharacteristic
397C2×C4⋊C4C23×C4711yescharacteristic
398C2×C4⋊C4C23×C4711yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4D4×C4711yescharacteristic
407C2×C22⋊C4D4×C4711yescharacteristic
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42C23×C4711yescharacteristic
412C2×C42C23×C4711yescharacteristic
413#107—22no—
414#107—41no—
415#106—22no—
416#106—22no—
417C4⋊C8—22no—
418#102—22no—
419#102—22no—
420#102—22no—
421#102—41no—
422C22⋊C8—22no—
423C22⋊C8—41no—
424C4×C8—41no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95D4×C4711yescharacteristic
435#95D4×C4711yescharacteristic
436C24—21no—
437C24C2×D4×C4711yescharacteristic
438C2×D4—24no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—81no—
445C2×D4—81no—
446C2×D4#41×C4712yes—
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×C4—42no—
461C22×C4—42no—
462C22×C4—81no—
463C22×C4C2×D4×C4711yescharacteristic
464C22×C4C2×D4×C4711yescharacteristic
465C22×C4C2×D4×C4711yescharacteristic
466C22×C4C2×D4×C4711yescharacteristic
467C22×C4C2×D4×C4711yescharacteristic
468C22×C4C24×C4711yescharacteristic
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—21no—
479C2×C8—21no—
480C2×C8#41×C4712yes—
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—81no—
494C4⋊C4—81no—
495C4⋊C4—81no—
496C4⋊C4#41×C4712yes—
497C4⋊C4#41×C4712yes—
498C22⋊C4—24no—
499C22⋊C4—22no—
500C22⋊C4—41no—
501C22⋊C4—42no—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—81no—
506C22⋊C4—81no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—42no—
512C42—42no—
513C42—81no—
514C23—22no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23C22×D4×C4711yescharacteristic
529D4—22no—
530D4—22no—
531D4—41no—
532D4—41no—
533D4—84no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
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—84no—
574C2×C4#135×C4712yes—
575C2×C4C2×#41×C4711yescharacteristic
576C2×C4C2×#41×C4711yescharacteristic
577C2×C4C2×#41×C4711yescharacteristic
578C2×C4C2×#41×C4711yescharacteristic
579C2×C4H(5,𝔽2)×C4711yescharacteristic
580C2×C42−1+4×C4711yescharacteristic
581C8—22no—
582C8—41no—
583C8—41no—
584C8—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—42no—
591C22—41no—
592C22—42no—
593C22—41no—
594C22—42no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22C47×#52511yescharacteristic
600C22C47×#54611yescharacteristic
601C22C47×#54711yescharacteristic
602C22C2×#135×C4711yescharacteristic
603C22C47×#57511yescharacteristic
604C22C47×#57611yescharacteristic
605C22C47×#57711yescharacteristic
606C4—22no—
607C4—42no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—42no—
612C4—41no—
613C4—81no—
614C4—81no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4C47×#52911yescharacteristic
619C4C47×#53911yescharacteristic
620C4C47×#55311yescharacteristic
621C4C47×#55611yescharacteristic
622C2—81no—
623C2—82no—
624C2C47×#246611yescharacteristic
625C2C47×#310211yescharacteristic
626C2C47×#311811yescharacteristic
627C2C47×#329611yescharacteristic
628C2C47×#330911yescharacteristic
629C2C47×#334111yescharacteristic
630C2C47×#335111yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×#121×C47C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C22⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#2495C2semidirect
3. C47×#2073C2semidirect
4. C47×#2067C2semidirect
7. C47×#1949C2semidirect
8. C47×#1942C2semidirect
9. C47×#1923C2semidirect
10. C47×#1920C2semidirect
11. C47×#1920C2semidirect
12. C47×#1864C2semidirect
13. C47×#1854C2semidirect
14. C47×#1825C2semidirect
15. C4×#102×C47C2semidirect
269. #27038C47direct (N × H)
307. #2495C2×C47semidirect
309. #2073C2×C47semidirect
310. #2067C2×C47semidirect
313. #1949C2×C47semidirect
314. #1942C2×C47semidirect
315. #1923C2×C47semidirect
316. #1920C2×C47semidirect
317. #1920C2×C47semidirect
318. #1864C2×C47semidirect
319. #1854C2×C47semidirect
320. #1825C2×C47semidirect
321. C4×#102C2×C47semidirect
374. C47#27038direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#24952
C47×#23632
C47×#20732
C47×#20672
C47×#20342
C47×#20332
C47×#19492
C47×#19422
C47×#19232
C47×#19202
C47×#18642
C47×#18542
C47×#18252
C4×#102×C472
#2703847