Finite Group Databasebeta

← C47×#27034 #26066732

Subgroups — C47×#27034 #26066732

Order 12032.

728 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2496C211yesmaximal, characteristic
2C47×#2360C211yesmaximal, characteristic
3C47×#2072C211yesmaximal, characteristic, complemented
4C47×#2066C211yesmaximal, characteristic, complemented
5C47×#2035C211yesmaximal, characteristic
6C47×#2035C211yesmaximal, characteristic
7C47×#1948C211yesmaximal, characteristic, complemented
8C47×#1941C211yesmaximal, characteristic, complemented
9C47×#1923C211yesmaximal, characteristic
10C47×#1920C211yesmaximal, characteristic, complemented
11C47×#1919C211yesmaximal, characteristic, complemented
12C47×#1865C211yesmaximal, characteristic, complemented
13C47×#1853C211yesmaximal, characteristic
14C47×#1824C211yesmaximal, characteristic
15C4×#103×C47C211yesmaximal, characteristic, complemented
16C2×#126×C47—21no—
17C2×C22⋊Q8×C47C2211yescharacteristic
18C2×C4×Q8×C47C2211yescharacteristic
19C22×C4⋊C4×C47C2211yescharacteristic
20C2×#106×C47C2211yescharacteristic
21C2×#106×C47C2211yescharacteristic
22C2×#106×C47C2211yescharacteristic
23C2×#106×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C2×#103×C47C2211yescharacteristic
26C2×#103×C47C2211yescharacteristic
27C2×#103×C47C2211yescharacteristic
28C2×#103×C47C2211yescharacteristic
29C2×C22⋊C8×C47C2211yescharacteristic
30C2×C22⋊C8×C47C2211yescharacteristic
31C2×C4×C8×C47C2211yescharacteristic
32C47×#400—21no—
33C47×#397—21no—
34C47×#391C2211yescharacteristic
35C47×#389—21no—
36C47×#389C2211yescharacteristic
37C47×#389C2211yescharacteristic
38C47×#389C2211yescharacteristic
39C47×#387—21no—
40C47×#387—21no—
41C47×#385—21no—
42C47×#384C2211yescharacteristic
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
66#126×C47—44no—
67C22⋊Q8×C47—22no—
68C22⋊Q8×C47—22no—
69C4×Q8×C47—22no—
70C4×Q8×C47—41no—
71C2×C4⋊C4×C47—21no—
72C2×C4⋊C4×C47—22no—
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×C47—21no—
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47—41no—
81C2×C4⋊C4×C47C2311yescharacteristic
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×C22⋊C4×C47—21no—
89C2×C22⋊C4×C47—21no—
90C2×C22⋊C4×C47—21no—
91C2×C22⋊C4×C47D411yescharacteristic
92C2×C22⋊C4×C47D411yescharacteristic
93C2×C42×C47—21no—
94C2×C42×C47—21no—
95C2×C42×C47—21no—
96C2×C42×C47C2311yescharacteristic
97C2×C42×C47C2311yescharacteristic
98#106×C47—22no—
99#106×C47—22no—
100#106×C47—22no—
101#106×C47—41no—
102C4⋊C8×C47—22no—
103#103×C47—22no—
104#103×C47—22no—
105#103×C47—22no—
106#103×C47—41no—
107C22⋊C8×C47—22no—
108C22⋊C8×C47—41no—
109C4×C8×C47—41no—
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×C47—21no—
119#95×C47D411yescharacteristic
120#95×C47D411yescharacteristic
121C24×C47C2×D411yescharacteristic
122C2×Q8×C47—21no—
123C2×Q8×C47—21no—
124C2×Q8×C47—21no—
125C2×Q8×C47—21no—
126C2×Q8×C47—21no—
127C2×Q8×C47#4112yes—
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—42no—
143C22×C4×C47—42no—
144C22×C4×C47—81no—
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2411yescharacteristic
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—21no—
162C2×C8×C47#4112yes—
163C4⋊C4×C47—24no—
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—42no—
177C4⋊C4×C47—42no—
178C4⋊C4×C47—42no—
179C4⋊C4×C47—42no—
180C4⋊C4×C47—42no—
181C4⋊C4×C47—42no—
182C4⋊C4×C47—81no—
183C4⋊C4×C47#4112yes—
184C4⋊C4×C47#4112yes—
185C22⋊C4×C47—24no—
186C22⋊C4×C47—41no—
187C22⋊C4×C47—42no—
188C22⋊C4×C47—42no—
189C22⋊C4×C47SD1614yes—
190C42×C47—21no—
191C42×C47—21no—
192C42×C47—21no—
193C42×C47—21no—
194C42×C47—42no—
195C42×C47—42no—
196C42×C47—81no—
197C23×C47—21no—
198C23×C47—21no—
199C23×C47—21no—
200C23×C47—21no—
201C23×C47—21no—
202C23×C47—21no—
203C23×C47C2×SD1612yes—
204C23×C47C22×D411yescharacteristic
205Q8×C47—22no—
206Q8×C47—22no—
207Q8×C47—41no—
208Q8×C47—41no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—22no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
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—41no—
249C2×C4×C47—41no—
250C2×C4×C47—84no—
251C2×C4×C47C2×SD1612yes—
252C2×C4×C47C2×SD1612yes—
253C2×C4×C47C2×#4111yescharacteristic
254C2×C4×C47C2×#4111yescharacteristic
255C2×C4×C47C2×#4111yescharacteristic
256C2×C4×C47C2×#4111yescharacteristic
257C2×C4×C47H(5,𝔽2)11yescharacteristic
258C2×C4×C472−1+411yescharacteristic
259C8×C47—22no—
260C8×C47—41no—
261C8×C47—41no—
262C8×C47—41no—
263#27034C4711yesmaximal, characteristic, direct product factor, Sylow
264C22×C47—22no—
265C22×C47—22no—
266C22×C47—22no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47—41no—
270C22×C47—41no—
271C22×C47#52511yescharacteristic
272C22×C47#54611yescharacteristic
273C22×C47#54711yescharacteristic
274C22×C47C22×SD1611yescharacteristic
275C22×C47#57511yescharacteristic
276C22×C47#57711yescharacteristic
277C22×C47#57811yescharacteristic
278C4×C47—22no—
279C4×C47—22no—
280C4×C47—41no—
281C4×C47—42no—
282C4×C47—41no—
283C4×C47—42no—
284C4×C47—41no—
285C4×C47—42no—
286C4×C47—81no—
287C4×C47—81no—
288C4×C47—81no—
289C4×C47—81no—
290C4×C47—81no—
291C4×C47#52911yescharacteristic
292C4×C47#53911yescharacteristic
293C4×C47#55311yescharacteristic
294C4×C47#55611yescharacteristic
295#2496C2×C4711yescharacteristic
296#2360C2×C4711yescharacteristic
297#2072C2×C4711yescharacteristic, complemented
298#2066C2×C4711yescharacteristic, complemented
299#2035C2×C4711yescharacteristic
300#2035C2×C4711yescharacteristic
301#1948C2×C4711yescharacteristic, complemented
302#1941C2×C4711yescharacteristic, complemented
303#1923C2×C4711yescharacteristic
304#1920C2×C4711yescharacteristic, complemented
305#1919C2×C4711yescharacteristic, complemented
306#1865C2×C4711yescharacteristic, complemented
307#1853C2×C4711yescharacteristic
308#1824C2×C4711yescharacteristic
309C4×#103C2×C4711yescharacteristic, complemented
310C2×C47—42no—
311C2×C47#246611yescharacteristic
312C2×C47#310311yescharacteristic
313C2×C47#312011yescharacteristic
314C2×C47#329811yescharacteristic
315C2×C47#331111yescharacteristic
316C2×C47#333511yescharacteristic
317C2×C47#335211yescharacteristic
318C2×#126—21no—
319C2×C22⋊Q8C22×C4711yescharacteristic
320C2×C4×Q8C22×C4711yescharacteristic
321C22×C4⋊C4C22×C4711yescharacteristic
322C2×#106C22×C4711yescharacteristic
323C2×#106C22×C4711yescharacteristic
324C2×#106C22×C4711yescharacteristic
325C2×#106C22×C4711yescharacteristic
326C2×C4⋊C8C22×C4711yescharacteristic
327C2×#103C22×C4711yescharacteristic
328C2×#103C22×C4711yescharacteristic
329C2×#103C22×C4711yescharacteristic
330C2×#103C22×C4711yescharacteristic
331C2×C22⋊C8C22×C4711yescharacteristic
332C2×C22⋊C8C22×C4711yescharacteristic
333C2×C4×C8C22×C4711yescharacteristic
334#400—21no—
335#397—21no—
336#391C22×C4711yescharacteristic
337#389—21no—
338#389C22×C4711yescharacteristic
339#389C22×C4711yescharacteristic
340#389C22×C4711yescharacteristic
341#387—21no—
342#387—21no—
343#385—21no—
344#384C22×C4711yescharacteristic
345#380C22×C4711yescharacteristic
346#380C22×C4711yescharacteristic
347C4×C4⋊C4C22×C4711yescharacteristic
348C4×C4⋊C4C22×C4711yescharacteristic
349C4×C22⋊C4—21no—
350C4×C22⋊C4C22×C4711yescharacteristic
351#340C22×C4711yescharacteristic
352#340C22×C4711yescharacteristic
353#340C22×C4711yescharacteristic
354#340C22×C4711yescharacteristic
355#340C22×C4711yescharacteristic
356#340C22×C4711yescharacteristic
357#340C22×C4711yescharacteristic
358#340C22×C4711yescharacteristic
359#336C22×C4711yescharacteristic
360#336C22×C4711yescharacteristic
361C47#2703411yescharacteristic, direct product factor, Sylow
362C22×Q8C23×C4711yescharacteristic
363C23×C4—21no—
364C23×C4C23×C4711yescharacteristic
365C22×C8C23×C4711yescharacteristic
366C22×C8C23×C4711yescharacteristic
367C22×C8C23×C4711yescharacteristic
368C22×C8C23×C4711yescharacteristic
369#126—44no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C4×Q8—22no—
373C4×Q8—41no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—41no—
384C2×C4⋊C4C23×C4711yescharacteristic
385C2×C4⋊C4C23×C4711yescharacteristic
386C2×C4⋊C4C23×C4711yescharacteristic
387C2×C4⋊C4C23×C4711yescharacteristic
388C2×C4⋊C4C23×C4711yescharacteristic
389C2×C4⋊C4C23×C4711yescharacteristic
390C2×C4⋊C4C23×C4711yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4D4×C4711yescharacteristic
395C2×C22⋊C4D4×C4711yescharacteristic
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42C23×C4711yescharacteristic
400C2×C42C23×C4711yescharacteristic
401#106—22no—
402#106—22no—
403#106—22no—
404#106—41no—
405C4⋊C8—22no—
406#103—22no—
407#103—22no—
408#103—22no—
409#103—41no—
410C22⋊C8—22no—
411C22⋊C8—41no—
412C4×C8—41no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95D4×C4711yescharacteristic
423#95D4×C4711yescharacteristic
424C24C2×D4×C4711yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8#41×C4712yes—
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—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—81no—
448C22×C4C2×D4×C4711yescharacteristic
449C22×C4C2×D4×C4711yescharacteristic
450C22×C4C2×D4×C4711yescharacteristic
451C22×C4C2×D4×C4711yescharacteristic
452C22×C4C2×D4×C4711yescharacteristic
453C22×C4C24×C4711yescharacteristic
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8#41×C4712yes—
466C4⋊C4—24no—
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—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—81no—
486C4⋊C4#41×C4712yes—
487C4⋊C4#41×C4712yes—
488C22⋊C4—24no—
489C22⋊C4—41no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4SD16×C4714yes—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—42no—
498C42—42no—
499C42—81no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23C2×SD16×C4712yes—
507C23C22×D4×C4711yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—41no—
511Q8—41no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
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—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—84no—
554C2×C4C2×SD16×C4712yes—
555C2×C4C2×SD16×C4712yes—
556C2×C4C2×#41×C4711yescharacteristic
557C2×C4C2×#41×C4711yescharacteristic
558C2×C4C2×#41×C4711yescharacteristic
559C2×C4C2×#41×C4711yescharacteristic
560C2×C4H(5,𝔽2)×C4711yescharacteristic
561C2×C42−1+4×C4711yescharacteristic
562C8—22no—
563C8—41no—
564C8—41no—
565C8—41no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22C47×#52511yescharacteristic
574C22C47×#54611yescharacteristic
575C22C47×#54711yescharacteristic
576C22C22×SD16×C4711yescharacteristic
577C22C47×#57511yescharacteristic
578C22C47×#57711yescharacteristic
579C22C47×#57811yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—42no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—42no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4C47×#52911yescharacteristic
594C4C47×#53911yescharacteristic
595C4C47×#55311yescharacteristic
596C4C47×#55611yescharacteristic
597C2—42no—
598C2C47×#246611yescharacteristic
599C2C47×#310311yescharacteristic
600C2C47×#312011yescharacteristic
601C2C47×#329811yescharacteristic
602C2C47×#331111yescharacteristic
603C2C47×#333511yescharacteristic
604C2C47×#335211yescharacteristic
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×#2072C2semidirect
4. C47×#2066C2semidirect
7. C47×#1948C2semidirect
8. C47×#1941C2semidirect
10. C47×#1920C2semidirect
11. C47×#1919C2semidirect
12. C47×#1865C2semidirect
15. C4×#103×C47C2semidirect
263. #27034C47direct (N × H)
297. #2072C2×C47semidirect
298. #2066C2×C47semidirect
301. #1948C2×C47semidirect
302. #1941C2×C47semidirect
304. #1920C2×C47semidirect
305. #1919C2×C47semidirect
306. #1865C2×C47semidirect
309. C4×#103C2×C47semidirect
361. C47#27034direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#24962
C47×#23602
C47×#20722
C47×#20662
C47×#20352
C47×#19482
C47×#19412
C47×#19232
C47×#19202
C47×#19192
C47×#18652
C47×#18532
C47×#18242
C4×#103×C472
#2703447