Finite Group Databasebeta

← C47×#27035 #26066733

Subgroups — C47×#27035 #26066733

Order 12032.

700 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2495C211yesmaximal, characteristic
2C47×#2360C211yesmaximal, characteristic
3C47×#2074C211yesmaximal, characteristic, complemented
4C47×#2068C211yesmaximal, characteristic, complemented
5C47×#2036C211yesmaximal, characteristic
6C47×#2035C211yesmaximal, characteristic
7C47×#1949C211yesmaximal, characteristic, complemented
8C47×#1942C211yesmaximal, characteristic, complemented
9C47×#1923C211yesmaximal, characteristic
10C47×#1920C211yesmaximal, characteristic, complemented
11C47×#1918C211yesmaximal, characteristic, complemented
12C47×#1863C211yesmaximal, characteristic, complemented
13C47×#1852C211yesmaximal, characteristic
14C47×#1823C211yesmaximal, characteristic
15C4×#103×C47C211yesmaximal, characteristic, complemented
16C2×C22⋊Q8×C47C2211yescharacteristic
17C2×C4×Q8×C47C2211yescharacteristic
18C22×C4⋊C4×C47C2211yescharacteristic
19C2×#107×C47C2211yescharacteristic
20C2×#107×C47C2211yescharacteristic
21C2×#107×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×C4×C8×C47C2211yescharacteristic
31C47×#400—21no—
32C47×#397—21no—
33C47×#391C2211yescharacteristic
34C47×#389—21no—
35C47×#389C2211yescharacteristic
36C47×#389C2211yescharacteristic
37C47×#389C2211yescharacteristic
38C47×#388—21no—
39C47×#387—21no—
40C47×#385—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×Q8×C47C2311yescharacteristic
60C23×C4×C47—21no—
61C23×C4×C47C2311yescharacteristic
62C22×C8×C47C2311yescharacteristic
63C22×C8×C47C2311yescharacteristic
64C22×C8×C47C2311yescharacteristic
65C22×C8×C47C2311yescharacteristic
66C22⋊Q8×C47—22no—
67C22⋊Q8×C47—22no—
68C4×Q8×C47—22no—
69C4×Q8×C47—41no—
70C2×C4⋊C4×C47—21no—
71C2×C4⋊C4×C47—22no—
72C2×C4⋊C4×C47—21no—
73C2×C4⋊C4×C47—21no—
74C2×C4⋊C4×C47—21no—
75C2×C4⋊C4×C47—21no—
76C2×C4⋊C4×C47—21no—
77C2×C4⋊C4×C47—41no—
78C2×C4⋊C4×C47C2311yescharacteristic
79C2×C4⋊C4×C47C2311yescharacteristic
80C2×C4⋊C4×C47C2311yescharacteristic
81C2×C4⋊C4×C47C2311yescharacteristic
82C2×C4⋊C4×C47C2311yescharacteristic
83C2×C4⋊C4×C47C2311yescharacteristic
84C2×C4⋊C4×C47C2311yescharacteristic
85C2×C22⋊C4×C47—21no—
86C2×C22⋊C4×C47—21no—
87C2×C22⋊C4×C47—21no—
88C2×C22⋊C4×C47D411yescharacteristic
89C2×C22⋊C4×C47D411yescharacteristic
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—22no—
97#107×C47—41no—
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—
106C4×C8×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×C47—42no—
142C22×C4×C47—42no—
143C22×C4×C47—81no—
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
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#4112yes—
162C4⋊C4×C47—24no—
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—21no—
175C4⋊C4×C47—42no—
176C4⋊C4×C47—42no—
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—22no—
185C22⋊C4×C47—42no—
186C22⋊C4×C47—81no—
187C42×C47—21no—
188C42×C47—21no—
189C42×C47—21no—
190C42×C47—21no—
191C42×C47—42no—
192C42×C47—42no—
193C42×C47—81no—
194C23×C47—21no—
195C23×C47—21no—
196C23×C47—21no—
197C23×C47—21no—
198C23×C47—21no—
199C23×C47—21no—
200C23×C47#13512yes—
201C23×C47C22×D411yescharacteristic
202Q8×C47—22no—
203Q8×C47—22no—
204Q8×C47—41no—
205Q8×C47—41no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—22no—
209C2×C4×C47—22no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—22no—
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—21no—
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×C47—41no—
248C2×C4×C47—84no—
249C2×C4×C47#13712yes—
250C2×C4×C47C2×#4111yescharacteristic
251C2×C4×C47C2×#4111yescharacteristic
252C2×C4×C47C2×#4111yescharacteristic
253C2×C4×C47C2×#4111yescharacteristic
254C2×C4×C47H(5,𝔽2)11yescharacteristic
255C2×C4×C472−1+411yescharacteristic
256C8×C47—22no—
257C8×C47—41no—
258C8×C47—41no—
259C8×C47—41no—
260#27035C4711yesmaximal, characteristic, direct product factor, Sylow
261C22×C47—22no—
262C22×C47—22no—
263C22×C47—22no—
264C22×C47—41no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47—41no—
268C22×C47#52511yescharacteristic
269C22×C47#54611yescharacteristic
270C22×C47#54711yescharacteristic
271C22×C47C2×#13511yescharacteristic
272C22×C47C2×#13711yescharacteristic
273C22×C47#57611yescharacteristic
274C22×C47#57811yescharacteristic
275C4×C47—22no—
276C4×C47—41no—
277C4×C47—41no—
278C4×C47—42no—
279C4×C47—41no—
280C4×C47—42no—
281C4×C47—41no—
282C4×C47—42no—
283C4×C47—81no—
284C4×C47—81no—
285C4×C47—81no—
286C4×C47—81no—
287C4×C47—81no—
288C4×C47#52911yescharacteristic
289C4×C47#53911yescharacteristic
290C4×C47#55311yescharacteristic
291C4×C47#55611yescharacteristic
292#2495C2×C4711yescharacteristic
293#2360C2×C4711yescharacteristic
294#2074C2×C4711yescharacteristic, complemented
295#2068C2×C4711yescharacteristic, complemented
296#2036C2×C4711yescharacteristic
297#2035C2×C4711yescharacteristic
298#1949C2×C4711yescharacteristic, complemented
299#1942C2×C4711yescharacteristic, complemented
300#1923C2×C4711yescharacteristic
301#1920C2×C4711yescharacteristic, complemented
302#1918C2×C4711yescharacteristic, complemented
303#1863C2×C4711yescharacteristic, complemented
304#1852C2×C4711yescharacteristic
305#1823C2×C4711yescharacteristic
306C4×#103C2×C4711yescharacteristic, complemented
307C2×C47—42no—
308C2×C47#246611yescharacteristic
309C2×C47#310811yescharacteristic
310C2×C47#312411yescharacteristic
311C2×C47#329711yescharacteristic
312C2×C47#331211yescharacteristic
313C2×C47#333611yescharacteristic
314C2×C47#335711yescharacteristic
315C2×C22⋊Q8C22×C4711yescharacteristic
316C2×C4×Q8C22×C4711yescharacteristic
317C22×C4⋊C4C22×C4711yescharacteristic
318C2×#107C22×C4711yescharacteristic
319C2×#107C22×C4711yescharacteristic
320C2×#107C22×C4711yescharacteristic
321C2×#106C22×C4711yescharacteristic
322C2×C4⋊C8C22×C4711yescharacteristic
323C2×#103C22×C4711yescharacteristic
324C2×#103C22×C4711yescharacteristic
325C2×#103C22×C4711yescharacteristic
326C2×#103C22×C4711yescharacteristic
327C2×C22⋊C8C22×C4711yescharacteristic
328C2×C22⋊C8C22×C4711yescharacteristic
329C2×C4×C8C22×C4711yescharacteristic
330#400—21no—
331#397—21no—
332#391C22×C4711yescharacteristic
333#389—21no—
334#389C22×C4711yescharacteristic
335#389C22×C4711yescharacteristic
336#389C22×C4711yescharacteristic
337#388—21no—
338#387—21no—
339#385—21no—
340#383—21no—
341#382C22×C4711yescharacteristic
342#380C22×C4711yescharacteristic
343#380C22×C4711yescharacteristic
344C4×C4⋊C4C22×C4711yescharacteristic
345C4×C4⋊C4C22×C4711yescharacteristic
346C4×C22⋊C4—21no—
347C4×C22⋊C4C22×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#336C22×C4711yescharacteristic
357#336C22×C4711yescharacteristic
358C47#2703511yescharacteristic, direct product factor, Sylow
359C22×Q8C23×C4711yescharacteristic
360C23×C4—21no—
361C23×C4C23×C4711yescharacteristic
362C22×C8C23×C4711yescharacteristic
363C22×C8C23×C4711yescharacteristic
364C22×C8C23×C4711yescharacteristic
365C22×C8C23×C4711yescharacteristic
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C4×Q8—22no—
369C4×Q8—41no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—41no—
378C2×C4⋊C4C23×C4711yescharacteristic
379C2×C4⋊C4C23×C4711yescharacteristic
380C2×C4⋊C4C23×C4711yescharacteristic
381C2×C4⋊C4C23×C4711yescharacteristic
382C2×C4⋊C4C23×C4711yescharacteristic
383C2×C4⋊C4C23×C4711yescharacteristic
384C2×C4⋊C4C23×C4711yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4D4×C4711yescharacteristic
389C2×C22⋊C4D4×C4711yescharacteristic
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42C23×C4711yescharacteristic
394C2×C42C23×C4711yescharacteristic
395#107—22no—
396#107—22no—
397#107—41no—
398#106—22no—
399C4⋊C8—22no—
400#103—22no—
401#103—22no—
402#103—22no—
403#103—41no—
404C22⋊C8—22no—
405C22⋊C8—41no—
406C4×C8—41no—
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#95—21no—
416#95—21no—
417#95—21no—
418#95D4×C4711yescharacteristic
419#95D4×C4711yescharacteristic
420C24C2×D4×C4711yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8#41×C4712yes—
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×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—81no—
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#41×C4712yes—
462C4⋊C4—24no—
463C4⋊C4—21no—
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—81no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4#41×C4712yes—
481C4⋊C4#41×C4712yes—
482C22⋊C4—24no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—42no—
486C22⋊C4—81no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—42no—
492C42—42no—
493C42—81no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23#135×C4712yes—
501C23C22×D4×C4711yescharacteristic
502Q8—22no—
503Q8—22no—
504Q8—41no—
505Q8—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
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×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—84no—
549C2×C4#137×C4712yes—
550C2×C4C2×#41×C4711yescharacteristic
551C2×C4C2×#41×C4711yescharacteristic
552C2×C4C2×#41×C4711yescharacteristic
553C2×C4C2×#41×C4711yescharacteristic
554C2×C4H(5,𝔽2)×C4711yescharacteristic
555C2×C42−1+4×C4711yescharacteristic
556C8—22no—
557C8—41no—
558C8—41no—
559C8—41no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22C47×#52511yescharacteristic
568C22C47×#54611yescharacteristic
569C22C47×#54711yescharacteristic
570C22C2×#135×C4711yescharacteristic
571C22C2×#137×C4711yescharacteristic
572C22C47×#57611yescharacteristic
573C22C47×#57811yescharacteristic
574C4—22no—
575C4—41no—
576C4—42no—
577C4—41no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4C47×#52911yescharacteristic
588C4C47×#53911yescharacteristic
589C4C47×#55311yescharacteristic
590C4C47×#55611yescharacteristic
591C2—42no—
592C2C47×#246611yescharacteristic
593C2C47×#310811yescharacteristic
594C2C47×#312411yescharacteristic
595C2C47×#329711yescharacteristic
596C2C47×#331211yescharacteristic
597C2C47×#333611yescharacteristic
598C2C47×#335711yescharacteristic
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×#1942C2semidirect
10. C47×#1920C2semidirect
11. C47×#1918C2semidirect
12. C47×#1863C2semidirect
15. C4×#103×C47C2semidirect
260. #27035C47direct (N × H)
294. #2074C2×C47semidirect
295. #2068C2×C47semidirect
298. #1949C2×C47semidirect
299. #1942C2×C47semidirect
301. #1920C2×C47semidirect
302. #1918C2×C47semidirect
303. #1863C2×C47semidirect
306. C4×#103C2×C47semidirect
358. C47#27035direct (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×#23602
C47×#20742
C47×#20682
C47×#20362
C47×#20352
C47×#19492
C47×#19422
C47×#19232
C47×#19202
C47×#19182
C47×#18632
C47×#18522
C47×#18232
C4×#103×C472
#2703547