Finite Group Databasebeta

← C47×#15068 #26054766

Subgroups — C47×#15068 #26054766

Order 12032.

1254 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#389C211yesmaximal, characteristic
2C2×C47×#387C211yesmaximal, characteristic
3C47×#1444C211yesmaximal, characteristic
4C47×#1444C212yesmaximal
5C47×#1444C211yesmaximal, characteristic
6C47×#1442C211yesmaximal, characteristic
7C47×#1442C211yesmaximal, characteristic
8C47×#1441C212yesmaximal
9C47×#1436C212yesmaximal
10C47×C4⋊#95C212yesmaximal
11C4×#95×C47C211yesmaximal, characteristic
12C22×C4⋊C4×C47C2211yescharacteristic
13C22×C4⋊C4×C47C2212yes—
14C22×C4⋊C4×C47C2211yescharacteristic
15C22×C4⋊C4×C47C2211yescharacteristic
16C22×C4⋊C4×C47C2212yes—
17C22×C4⋊C4×C47C2211yescharacteristic
18C22×C4⋊C4×C47C2212yes—
19C22×C42×C47C2212yes—
20C22×C42×C47C2211yescharacteristic
21C47×#389—24no—
22C47×#387—24no—
23C2×#95×C47C2211yescharacteristic
24C2×#95×C47C2211yescharacteristic
25C2×#95×C47C2211yescharacteristic
26C2×#95×C47C2211yescharacteristic
27C2×#95×C47C2212yes—
28C2×#95×C47C2212yes—
29C2×#95×C47C2212yes—
30C2×#95×C47C2212yes—
31C2×#95×C47C2212yes—
32C2×#95×C47C2212yes—
33C2×#95×C47C2212yes—
34C2×#95×C47C2212yes—
35C2×#95×C47C2211yescharacteristic
36C2×#95×C47C2211yescharacteristic
37C23×C4×C47C2312yes—
38C23×C4×C47C2311yescharacteristic
39C23×C4×C47C2311yescharacteristic
40C23×C4×C47C2311yescharacteristic
41C23×C4×C47C2312yes—
42C23×C4×C47C2311yescharacteristic
43C23×C4×C47C2311yescharacteristic
44C23×C4×C47C2312yes—
45C23×C4×C47C2311yescharacteristic
46C23×C4×C47C2311yescharacteristic
47C23×C4×C47C2312yes—
48C2×C4⋊C4×C47—22no—
49C2×C4⋊C4×C47—22no—
50C2×C4⋊C4×C47—24no—
51C2×C4⋊C4×C47—22no—
52C2×C4⋊C4×C47—22no—
53C2×C4⋊C4×C47—24no—
54C2×C4⋊C4×C47—22no—
55C2×C4⋊C4×C47—24no—
56C2×C4⋊C4×C47—24no—
57C2×C4⋊C4×C47—24no—
58C2×C4⋊C4×C47—42no—
59C2×C4⋊C4×C47—42no—
60C2×C4⋊C4×C47—42no—
61C2×C4⋊C4×C47—42no—
62C2×C4⋊C4×C47—42no—
63C2×C4⋊C4×C47—42no—
64C2×C4⋊C4×C47—42no—
65C2×C4⋊C4×C47Q814yes—
66C2×C42×C47—24no—
67C2×C42×C47—24no—
68C2×C42×C47—42no—
69C2×C42×C47—42no—
70C2×C42×C47D414yes—
71#95×C47—22no—
72#95×C47—22no—
73#95×C47—22no—
74#95×C47—22no—
75#95×C47—24no—
76#95×C47—24no—
77#95×C47—24no—
78#95×C47—24no—
79#95×C47—24no—
80#95×C47—42no—
81#95×C47—42no—
82#95×C47—42no—
83#95×C47Q814yes—
84#95×C47Q814yes—
85C24×C47C2411yescharacteristic
86C22×C4×C47—22no—
87C22×C4×C47—22no—
88C22×C4×C47—22no—
89C22×C4×C47—22no—
90C22×C4×C47—22no—
91C22×C4×C47—22no—
92C22×C4×C47—22no—
93C22×C4×C47—22no—
94C22×C4×C47—21no—
95C22×C4×C47—22no—
96C22×C4×C47—21no—
97C22×C4×C47—22no—
98C22×C4×C47—22no—
99C22×C4×C47—21no—
100C22×C4×C47—21no—
101C22×C4×C47—22no—
102C22×C4×C47—22no—
103C22×C4×C47—22no—
104C22×C4×C47—22no—
105C22×C4×C47—22no—
106C22×C4×C47—22no—
107C22×C4×C47—22no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—21no—
113C22×C4×C47—21no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—22no—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47C2×D412yes—
136C22×C4×C47C2×D412yes—
137C22×C4×C47C2×D412yes—
138C22×C4×C47C2×Q812yes—
139C22×C4×C47C2×Q812yes—
140C22×C4×C47C2×Q814yes—
141C22×C4×C47C2×Q812yes—
142C22×C4×C47C2×Q814yes—
143C22×C4×C47C2×Q812yes—
144C22×C4×C47C2×Q812yes—
145C22×C4×C47#4114yes—
146C22×C4×C47#4112yes—
147C22×C4×C47#4114yes—
148C22×C4×C47#4114yes—
149C4⋊C4×C47—28no—
150C4⋊C4×C47—28no—
151C4⋊C4×C47—48no—
152C4⋊C4×C47—44no—
153C4⋊C4×C47—48no—
154C4⋊C4×C47—44no—
155C4⋊C4×C47—48no—
156C42×C47—44no—
157C42×C47—48no—
158C23×C47C22×D411yescharacteristic
159C23×C47C22×Q811yescharacteristic
160C23×C47C22×Q811yescharacteristic
161C23×C47C22×Q811yescharacteristic
162C23×C47C2×#4111yescharacteristic
163C23×C47C2×#4112yes—
164C23×C47C2×#4112yes—
165C23×C47C2×#4112yes—
166C23×C47H(5,𝔽2)12yes—
167C23×C47H(5,𝔽2)11yescharacteristic
168C23×C47H(5,𝔽2)11yescharacteristic
169C2×C4×C47—22no—
170C2×C4×C47—24no—
171C2×C4×C47—22no—
172C2×C4×C47—22no—
173C2×C4×C47—22no—
174C2×C4×C47—24no—
175C2×C4×C47—24no—
176C2×C4×C47—24no—
177C2×C4×C47—24no—
178C2×C4×C47—24no—
179C2×C4×C47—24no—
180C2×C4×C47—24no—
181C2×C4×C47—24no—
182C2×C4×C47—24no—
183C2×C4×C47—22no—
184C2×C4×C47—22no—
185C2×C4×C47—24no—
186C2×C4×C47—22no—
187C2×C4×C47—24no—
188C2×C4×C47—24no—
189C2×C4×C47—22no—
190C2×C4×C47—22no—
191C2×C4×C47—24no—
192C2×C4×C47—24no—
193C2×C4×C47—24no—
194C2×C4×C47—24no—
195C2×C4×C47—24no—
196C2×C4×C47—41no—
197C2×C4×C47—42no—
198C2×C4×C47—42no—
199C2×C4×C47—41no—
200C2×C4×C47—42no—
201C2×C4×C47—41no—
202C2×C4×C47—41no—
203C2×C4×C47—42no—
204C2×C4×C47—42no—
205C2×C4×C47—42no—
206C2×C4×C47—42no—
207C2×C4×C47—42no—
208C2×C4×C47—42no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47—41no—
213C2×C4×C47—41no—
214C2×C4×C47—42no—
215C2×C4×C47—41no—
216C2×C4×C47—42no—
217C2×C4×C47—41no—
218C2×C4×C47—42no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47—42no—
226C2×C4×C47—42no—
227C2×C4×C47—42no—
228C2×C4×C47—42no—
229C2×C4×C47C22⋊Q814yes—
230C2×C4×C47#12518yes—
231C2×C4×C47C4⋊Q814yes—
232#15068C4711yesmaximal, characteristic, direct product factor, Sylow
233C22×C47C2×C22⋊Q811yescharacteristic
234C22×C47#52511yescharacteristic
235C22×C47C2×#12512yes—
236C22×C47#52912yes—
237C22×C47C2×C4⋊Q811yescharacteristic
238C22×C47#53211yescharacteristic
239C22×C47#53211yescharacteristic
240C22×C47#53312yes—
241C22×C47#53312yes—
242C22×C47#53411yescharacteristic
243C22×C47#53511yescharacteristic
244C22×C47#53812yes—
245C22×C47#54012yes—
246C22×C47#55112yes—
247C22×C47#55112yes—
248C22×C47#55312yes—
249C22×C47#55412yes—
250C22×C47#55411yescharacteristic
251C22×C47#55411yescharacteristic
252C22×C47#55412yes—
253C22×C47#55412yes—
254C22×C47Q8211yescharacteristic
255C22×C47Q8211yescharacteristic
256C4×C47—24no—
257C4×C47—24no—
258C4×C47—28no—
259C4×C47—42no—
260C4×C47—44no—
261C4×C47—42no—
262C4×C47—42no—
263C4×C47—44no—
264C4×C47—81no—
265C4×C47—82no—
266C4×C47—81no—
267C2×#389C2×C4711yescharacteristic
268C2×#387C2×C4711yescharacteristic
269#1444C2×C4711yescharacteristic
270#1444C2×C4711yescharacteristic
271#1444C2×C4712yes—
272#1442C2×C4711yescharacteristic
273#1442C2×C4711yescharacteristic
274#1441C2×C4712yes—
275#1436C2×C4712yes—
276C4⋊#95C2×C4712yes—
277C4×#95C2×C4711yescharacteristic
278C2×C47#239611yescharacteristic
279C2×C47#250512yes—
280C2×C47#250712yes—
281C2×C47#252212yes—
282C2×C47#256411yescharacteristic
283C2×C47#256711yescharacteristic
284C2×C47#258311yescharacteristic
285C2×C47#258612yes—
286C2×C47#260311yescharacteristic
287C2×C47#266111yescharacteristic
288C2×C47#285911yescharacteristic
289C22×C4⋊C4C22×C4711yescharacteristic
290C22×C4⋊C4C22×C4712yes—
291C22×C4⋊C4C22×C4711yescharacteristic
292C22×C4⋊C4C22×C4712yes—
293C22×C4⋊C4C22×C4712yes—
294C22×C4⋊C4C22×C4711yescharacteristic
295C22×C4⋊C4C22×C4711yescharacteristic
296C22×C42C22×C4712yes—
297C22×C42C22×C4711yescharacteristic
298#389—24no—
299#387—24no—
300C2×#95C22×C4712yes—
301C2×#95C22×C4711yescharacteristic
302C2×#95C22×C4712yes—
303C2×#95C22×C4712yes—
304C2×#95C22×C4712yes—
305C2×#95C22×C4712yes—
306C2×#95C22×C4711yescharacteristic
307C2×#95C22×C4711yescharacteristic
308C2×#95C22×C4711yescharacteristic
309C2×#95C22×C4712yes—
310C2×#95C22×C4712yes—
311C2×#95C22×C4712yes—
312C2×#95C22×C4711yescharacteristic
313C2×#95C22×C4711yescharacteristic
314C47#1506811yescharacteristic, direct product factor, Sylow
315C23×C4C23×C4711yescharacteristic
316C23×C4C23×C4712yes—
317C23×C4C23×C4711yescharacteristic
318C23×C4C23×C4711yescharacteristic
319C23×C4C23×C4711yescharacteristic
320C23×C4C23×C4711yescharacteristic
321C23×C4C23×C4712yes—
322C23×C4C23×C4712yes—
323C23×C4C23×C4711yescharacteristic
324C23×C4C23×C4711yescharacteristic
325C23×C4C23×C4712yes—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4Q8×C4714yes—
344C2×C42—24no—
345C2×C42—24no—
346C2×C42—42no—
347C2×C42—42no—
348C2×C42D4×C4714yes—
349#95—22no—
350#95—22no—
351#95—22no—
352#95—22no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—24no—
357#95—24no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95Q8×C4714yes—
362#95Q8×C4714yes—
363C24C24×C4711yescharacteristic
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4C2×D4×C4712yes—
414C22×C4C2×D4×C4712yes—
415C22×C4C2×D4×C4712yes—
416C22×C4C2×Q8×C4714yes—
417C22×C4C2×Q8×C4712yes—
418C22×C4C2×Q8×C4712yes—
419C22×C4C2×Q8×C4712yes—
420C22×C4C2×Q8×C4714yes—
421C22×C4C2×Q8×C4712yes—
422C22×C4C2×Q8×C4712yes—
423C22×C4#41×C4714yes—
424C22×C4#41×C4712yes—
425C22×C4#41×C4714yes—
426C22×C4#41×C4714yes—
427C4⋊C4—28no—
428C4⋊C4—28no—
429C4⋊C4—48no—
430C4⋊C4—44no—
431C4⋊C4—48no—
432C4⋊C4—44no—
433C4⋊C4—48no—
434C42—44no—
435C42—48no—
436C23C22×D4×C4711yescharacteristic
437C23C22×Q8×C4711yescharacteristic
438C23C22×Q8×C4711yescharacteristic
439C23C22×Q8×C4711yescharacteristic
440C23C2×#41×C4711yescharacteristic
441C23C2×#41×C4712yes—
442C23C2×#41×C4712yes—
443C23C2×#41×C4712yes—
444C23H(5,𝔽2)×C4712yes—
445C23H(5,𝔽2)×C4711yescharacteristic
446C23H(5,𝔽2)×C4711yescharacteristic
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4C22⋊Q8×C4714yes—
508C2×C4#125×C4718yes—
509C2×C4C4⋊Q8×C4714yes—
510C22C2×C22⋊Q8×C4711yescharacteristic
511C22C47×#52511yescharacteristic
512C22C2×#125×C4712yes—
513C22C47×#52912yes—
514C22C2×C4⋊Q8×C4711yescharacteristic
515C22C47×#53211yescharacteristic
516C22C47×#53211yescharacteristic
517C22C47×#53312yes—
518C22C47×#53312yes—
519C22C47×#53411yescharacteristic
520C22C47×#53511yescharacteristic
521C22C47×#53812yes—
522C22C47×#54012yes—
523C22C47×#55112yes—
524C22C47×#55112yes—
525C22C47×#55312yes—
526C22C47×#55411yescharacteristic
527C22C47×#55412yes—
528C22C47×#55412yes—
529C22C47×#55411yescharacteristic
530C22C47×#55412yes—
531C22Q82×C4711yescharacteristic
532C22Q82×C4711yescharacteristic
533C4—24no—
534C4—24no—
535C4—28no—
536C4—44no—
537C4—42no—
538C4—44no—
539C4—42no—
540C4—42no—
541C4—81no—
542C4—82no—
543C4—81no—
544C2C47×#239611yescharacteristic
545C2C47×#250512yes—
546C2C47×#250712yes—
547C2C47×#252212yes—
548C2C47×#256411yescharacteristic
549C2C47×#256711yescharacteristic
550C2C47×#258311yescharacteristic
551C2C47×#258612yes—
552C2C47×#260311yescharacteristic
553C2C47×#266111yescharacteristic
554C2C47×#285911yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C47C24
commutator, Frattini, cosocleC24C24×C47
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
232. #15068C47direct (N × H)
314. C47#15068direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#3892
C2×C47×#3872
C47×#14442
C47×#14422
C47×#14412
C47×#14362
C47×C4⋊#952
C4×#95×C472
#1506847