Finite Group Databasebeta

← C47×#27059 #26066757

Subgroups — C47×#27059 #26066757

Order 12032.

672 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2495C211yesmaximal, characteristic
2C47×#2362C211yesmaximal, characteristic
3C47×#2074C211yesmaximal, characteristic, complemented
4C47×#2068C211yesmaximal, characteristic, complemented
5C47×#2036C211yesmaximal, characteristic
6C47×#2035C211yesmaximal, characteristic
7C47×#1949C211yesmaximal, characteristic, complemented
8C47×#1944C211yesmaximal, characteristic, complemented
9C47×#1924C211yesmaximal, characteristic
10C47×#1921C211yesmaximal, characteristic, complemented
11C47×#1919C211yesmaximal, characteristic, complemented
12C47×#1865C211yesmaximal, characteristic, complemented
13C47×#1854C211yesmaximal, characteristic
14C47×#1825C211yesmaximal, characteristic
15C47×#1763C211yesmaximal, characteristic, complemented
16C2×C22⋊Q8×C47C2211yescharacteristic
17C2×C4×Q8×C47C2211yescharacteristic
18C2×#117×C47C2211yescharacteristic
19C2×#107×C47C2211yescharacteristic
20C2×#107×C47C2211yescharacteristic
21C2×#106×C47C2211yescharacteristic
22C2×#106×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×#103×C47C2211yescharacteristic
25C2×#103×C47C2211yescharacteristic
26C2×#103×C47C2211yescharacteristic
27C2×#103×C47C2211yescharacteristic
28C2×C22⋊C8×C47C2211yescharacteristic
29C2×C22⋊C8×C47C2211yescharacteristic
30C2×#97×C47C2211yescharacteristic
31C47×#400—21no—
32C47×#397—21no—
33C47×#391C2211yescharacteristic
34C47×#389C2211yescharacteristic
35C47×#389C2211yescharacteristic
36C47×#389C2211yescharacteristic
37C47×#388—21no—
38C47×#388—21no—
39C47×#388—21no—
40C47×#387—21no—
41C47×#383—21no—
42C47×#382C2211yescharacteristic
43C47×#380C2211yescharacteristic
44C47×#380C2211yescharacteristic
45C4×C4⋊C4×C47—21no—
46C4×C4⋊C4×C47C2211yescharacteristic
47C4×C4⋊C4×C47C2211yescharacteristic
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×Q8×C47C2311yescharacteristic
60C23×C4×C47C2311yescharacteristic
61C22×C8×C47C2311yescharacteristic
62C22×C8×C47C2311yescharacteristic
63C22×C8×C47C2311yescharacteristic
64C22×C8×C47C2311yescharacteristic
65C22⋊Q8×C47—22no—
66C22⋊Q8×C47—22no—
67C4×Q8×C47—22no—
68C4×Q8×C47—41no—
69#117×C47—22no—
70#117×C47—41no—
71C2×C4⋊C4×C47—21no—
72C2×C4⋊C4×C47—21no—
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×C47D411yescharacteristic
88C2×C22⋊C4×C47D411yescharacteristic
89C2×C42×C47—21no—
90C2×C42×C47—21no—
91C2×C42×C47—21no—
92C2×C42×C47—21no—
93C2×C42×C47C2311yescharacteristic
94C2×C42×C47C2311yescharacteristic
95#107×C47—22no—
96#107×C47—41no—
97#106×C47—22no—
98#106×C47—22no—
99C4⋊C8×C47—22no—
100#103×C47—22no—
101#103×C47—22no—
102#103×C47—22no—
103#103×C47—41no—
104C22⋊C8×C47—22no—
105C22⋊C8×C47—41no—
106#97×C47—41no—
107#95×C47—21no—
108#95×C47—21no—
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×C47C2×D411yescharacteristic
121C2×Q8×C47—21no—
122C2×Q8×C47—21no—
123C2×Q8×C47—21no—
124C2×Q8×C47—21no—
125C2×Q8×C47—21no—
126C2×Q8×C47#4112yes—
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×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2411yescharacteristic
147C2×C8×C47—21no—
148C2×C8×C47—21no—
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#4112yes—
159C4⋊C4×C47—24no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
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—42no—
173C4⋊C4×C47—42no—
174C4⋊C4×C47—81no—
175C4⋊C4×C47—81no—
176C4⋊C4×C47#4112yes—
177C4⋊C4×C47#4112yes—
178C22⋊C4×C47—24no—
179C22⋊C4×C47—41no—
180C22⋊C4×C47—41no—
181C22⋊C4×C47—42no—
182C22⋊C4×C47—42no—
183C22⋊C4×C47—81no—
184C42×C47—21no—
185C42×C47—21no—
186C42×C47—21no—
187C42×C47—21no—
188C42×C47—42no—
189C42×C47—42no—
190C42×C47—42no—
191C42×C47—42no—
192C23×C47—21no—
193C23×C47—21no—
194C23×C47—21no—
195C23×C47—21no—
196C23×C47—21no—
197C23×C47—21no—
198C23×C47—21no—
199C23×C47C22×D411yescharacteristic
200Q8×C47—22no—
201Q8×C47—22no—
202Q8×C47—41no—
203Q8×C47—41no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—22no—
210C2×C4×C47—21no—
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—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
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—41no—
247C2×C4×C47C2×#4111yescharacteristic
248C2×C4×C47C2×#4111yescharacteristic
249C2×C4×C47C2×#4111yescharacteristic
250C2×C4×C47C2×#4111yescharacteristic
251C2×C4×C47H(5,𝔽2)11yescharacteristic
252C2×C4×C472−1+411yescharacteristic
253C8×C47—22no—
254C8×C47—41no—
255C8×C47—41no—
256C8×C47—41no—
257#27059C4711yesmaximal, characteristic, direct product factor, Sylow
258C22×C47—41no—
259C22×C47—41no—
260C22×C47—41no—
261C22×C47—41no—
262C22×C47—41no—
263C22×C47—41no—
264C22×C47—41no—
265C22×C47#52511yescharacteristic
266C22×C47#54611yescharacteristic
267C22×C47#54711yescharacteristic
268C22×C47#57511yescharacteristic
269C22×C47#57511yescharacteristic
270C22×C47#57711yescharacteristic
271C22×C47#57811yescharacteristic
272C4×C47—41no—
273C4×C47—41no—
274C4×C47—42no—
275C4×C47—41no—
276C4×C47—42no—
277C4×C47—41no—
278C4×C47—42no—
279C4×C47—41no—
280C4×C47—81no—
281C4×C47—81no—
282C4×C47—81no—
283C4×C47—81no—
284C4×C47—81no—
285C4×C47#52911yescharacteristic
286C4×C47#53911yescharacteristic
287C4×C47#55311yescharacteristic
288C4×C47#55611yescharacteristic
289#2495C2×C4711yescharacteristic
290#2362C2×C4711yescharacteristic
291#2074C2×C4711yescharacteristic, complemented
292#2068C2×C4711yescharacteristic, complemented
293#2036C2×C4711yescharacteristic
294#2035C2×C4711yescharacteristic
295#1949C2×C4711yescharacteristic, complemented
296#1944C2×C4711yescharacteristic, complemented
297#1924C2×C4711yescharacteristic
298#1921C2×C4711yescharacteristic, complemented
299#1919C2×C4711yescharacteristic, complemented
300#1865C2×C4711yescharacteristic, complemented
301#1854C2×C4711yescharacteristic
302#1825C2×C4711yescharacteristic
303#1763C2×C4711yescharacteristic, complemented
304C2×C47—81no—
305C2×C47#246611yescharacteristic
306C2×C47#311111yescharacteristic
307C2×C47#312111yescharacteristic
308C2×C47#331511yescharacteristic
309C2×C47#332611yescharacteristic
310C2×C47#334811yescharacteristic
311C2×C47#334911yescharacteristic
312C2×C22⋊Q8C22×C4711yescharacteristic
313C2×C4×Q8C22×C4711yescharacteristic
314C2×#117C22×C4711yescharacteristic
315C2×#107C22×C4711yescharacteristic
316C2×#107C22×C4711yescharacteristic
317C2×#106C22×C4711yescharacteristic
318C2×#106C22×C4711yescharacteristic
319C2×C4⋊C8C22×C4711yescharacteristic
320C2×#103C22×C4711yescharacteristic
321C2×#103C22×C4711yescharacteristic
322C2×#103C22×C4711yescharacteristic
323C2×#103C22×C4711yescharacteristic
324C2×C22⋊C8C22×C4711yescharacteristic
325C2×C22⋊C8C22×C4711yescharacteristic
326C2×#97C22×C4711yescharacteristic
327#400—21no—
328#397—21no—
329#391C22×C4711yescharacteristic
330#389C22×C4711yescharacteristic
331#389C22×C4711yescharacteristic
332#389C22×C4711yescharacteristic
333#388—21no—
334#388—21no—
335#388—21no—
336#387—21no—
337#383—21no—
338#382C22×C4711yescharacteristic
339#380C22×C4711yescharacteristic
340#380C22×C4711yescharacteristic
341C4×C4⋊C4—21no—
342C4×C4⋊C4C22×C4711yescharacteristic
343C4×C4⋊C4C22×C4711yescharacteristic
344C4×C22⋊C4C22×C4711yescharacteristic
345#340C22×C4711yescharacteristic
346#340C22×C4711yescharacteristic
347#340C22×C4711yescharacteristic
348#340C22×C4711yescharacteristic
349#340C22×C4711yescharacteristic
350#340C22×C4711yescharacteristic
351#340C22×C4711yescharacteristic
352#340C22×C4711yescharacteristic
353#336C22×C4711yescharacteristic
354#336C22×C4711yescharacteristic
355C47#2705911yescharacteristic, direct product factor, Sylow
356C22×Q8C23×C4711yescharacteristic
357C23×C4C23×C4711yescharacteristic
358C22×C8C23×C4711yescharacteristic
359C22×C8C23×C4711yescharacteristic
360C22×C8C23×C4711yescharacteristic
361C22×C8C23×C4711yescharacteristic
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C4×Q8—22no—
365C4×Q8—41no—
366#117—22no—
367#117—41no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4C23×C4711yescharacteristic
374C2×C4⋊C4C23×C4711yescharacteristic
375C2×C4⋊C4C23×C4711yescharacteristic
376C2×C4⋊C4C23×C4711yescharacteristic
377C2×C4⋊C4C23×C4711yescharacteristic
378C2×C4⋊C4C23×C4711yescharacteristic
379C2×C4⋊C4C23×C4711yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4D4×C4711yescharacteristic
385C2×C22⋊C4D4×C4711yescharacteristic
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42C23×C4711yescharacteristic
391C2×C42C23×C4711yescharacteristic
392#107—22no—
393#107—41no—
394#106—22no—
395#106—22no—
396C4⋊C8—22no—
397#103—22no—
398#103—22no—
399#103—22no—
400#103—41no—
401C22⋊C8—22no—
402C22⋊C8—41no—
403#97—41no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95D4×C4711yescharacteristic
416#95D4×C4711yescharacteristic
417C24C2×D4×C4711yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8#41×C4712yes—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4C2×D4×C4711yescharacteristic
439C22×C4C2×D4×C4711yescharacteristic
440C22×C4C2×D4×C4711yescharacteristic
441C22×C4C2×D4×C4711yescharacteristic
442C22×C4C2×D4×C4711yescharacteristic
443C22×C4C24×C4711yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8#41×C4712yes—
456C4⋊C4—24no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4—81no—
472C4⋊C4—81no—
473C4⋊C4#41×C4712yes—
474C4⋊C4#41×C4712yes—
475C22⋊C4—24no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—42no—
479C22⋊C4—42no—
480C22⋊C4—81no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—42no—
486C42—42no—
487C42—42no—
488C42—42no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23C22×D4×C4711yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—41no—
500Q8—41no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
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×C4C2×#41×C4711yescharacteristic
545C2×C4C2×#41×C4711yescharacteristic
546C2×C4C2×#41×C4711yescharacteristic
547C2×C4C2×#41×C4711yescharacteristic
548C2×C4H(5,𝔽2)×C4711yescharacteristic
549C2×C42−1+4×C4711yescharacteristic
550C8—22no—
551C8—41no—
552C8—41no—
553C8—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22C47×#52511yescharacteristic
562C22C47×#54611yescharacteristic
563C22C47×#54711yescharacteristic
564C22C47×#57511yescharacteristic
565C22C47×#57511yescharacteristic
566C22C47×#57711yescharacteristic
567C22C47×#57811yescharacteristic
568C4—41no—
569C4—42no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—42no—
574C4—41no—
575C4—42no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4C47×#52911yescharacteristic
582C4C47×#53911yescharacteristic
583C4C47×#55311yescharacteristic
584C4C47×#55611yescharacteristic
585C2—81no—
586C2C47×#246611yescharacteristic
587C2C47×#311111yescharacteristic
588C2C47×#312111yescharacteristic
589C2C47×#331511yescharacteristic
590C2C47×#332611yescharacteristic
591C2C47×#334811yescharacteristic
592C2C47×#334911yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC24×C47C2×D4
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
3. C47×#2074C2semidirect
4. C47×#2068C2semidirect
7. C47×#1949C2semidirect
8. C47×#1944C2semidirect
10. C47×#1921C2semidirect
11. C47×#1919C2semidirect
12. C47×#1865C2semidirect
15. C47×#1763C2semidirect
257. #27059C47direct (N × H)
291. #2074C2×C47semidirect
292. #2068C2×C47semidirect
295. #1949C2×C47semidirect
296. #1944C2×C47semidirect
298. #1921C2×C47semidirect
299. #1919C2×C47semidirect
300. #1865C2×C47semidirect
303. #1763C2×C47semidirect
355. C47#27059direct (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×#23622
C47×#20742
C47×#20682
C47×#20362
C47×#20352
C47×#19492
C47×#19442
C47×#19242
C47×#19212
C47×#19192
C47×#18652
C47×#18542
C47×#18252
C47×#17632
#2705947