Finite Group Databasebeta

← C47×#15105 #26054803

Subgroups — C47×#15105 #26054803

Order 12032.

1226 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#387C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C47C211yesmaximal, characteristic
3C47×#1445C211yesmaximal, characteristic
4C47×#1445C211yesmaximal, characteristic
5C47×#1444C211yesmaximal, characteristic
6C47×#1442C211yesmaximal, characteristic
7C47×#1441C212yesmaximal
8C47×#1441C212yesmaximal
9C47×#1436C212yesmaximal
10C47×#1436C212yesmaximal
11C47×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊C4×C47C2211yescharacteristic
13C22×C4⋊C4×C47C2211yescharacteristic
14C22×C4⋊C4×C47C2212yes—
15C22×C4⋊C4×C47C2211yescharacteristic
16C22×C4⋊C4×C47C2211yescharacteristic
17C22×C4⋊C4×C47C2212yes—
18C22×C42×C47C2211yescharacteristic
19C22×C42×C47C2212yes—
20C47×#387—24no—
21C4×C4⋊C4×C47—24no—
22C2×#95×C47C2212yes—
23C2×#95×C47C2211yescharacteristic
24C2×#95×C47C2211yescharacteristic
25C2×#95×C47C2211yescharacteristic
26C2×#95×C47C2211yescharacteristic
27C2×#95×C47C2212yes—
28C2×#95×C47C2211yescharacteristic
29C2×#95×C47C2211yescharacteristic
30C2×#95×C47C2212yes—
31C2×#95×C47C2212yes—
32C2×#95×C47C2212yes—
33C2×#95×C47C2212yes—
34C2×#95×C47C2212yes—
35C2×#95×C47C2212yes—
36C2×#95×C47C2212yes—
37C23×C4×C47C2311yescharacteristic
38C23×C4×C47C2311yescharacteristic
39C23×C4×C47C2312yes—
40C23×C4×C47C2312yes—
41C23×C4×C47C2311yescharacteristic
42C23×C4×C47C2311yescharacteristic
43C23×C4×C47C2312yes—
44C23×C4×C47C2312yes—
45C23×C4×C47C2311yescharacteristic
46C23×C4×C47C2311yescharacteristic
47C23×C4×C47C2311yescharacteristic
48C2×C4⋊C4×C47—22no—
49C2×C4⋊C4×C47—22no—
50C2×C4⋊C4×C47—22no—
51C2×C4⋊C4×C47—24no—
52C2×C4⋊C4×C47—22no—
53C2×C4⋊C4×C47—22no—
54C2×C4⋊C4×C47—22no—
55C2×C4⋊C4×C47—24no—
56C2×C4⋊C4×C47—24no—
57C2×C4⋊C4×C47—24no—
58C2×C4⋊C4×C47—24no—
59C2×C4⋊C4×C47—42no—
60C2×C4⋊C4×C47—42no—
61C2×C4⋊C4×C47—42no—
62C2×C4⋊C4×C47Q814yes—
63C2×C4⋊C4×C47Q814yes—
64C2×C42×C47—24no—
65C2×C42×C47—24no—
66C2×C42×C47—42no—
67C2×C42×C47—42no—
68C2×C42×C47D414yes—
69#95×C47—24no—
70#95×C47—22no—
71#95×C47—22no—
72#95×C47—22no—
73#95×C47—22no—
74#95×C47—24no—
75#95×C47—22no—
76#95×C47—24no—
77#95×C47—24no—
78#95×C47—24no—
79#95×C47—22no—
80#95×C47—42no—
81#95×C47—42no—
82#95×C47—42no—
83#95×C47—42no—
84C24×C47C2411yescharacteristic
85C22×C4×C47—22no—
86C22×C4×C47—22no—
87C22×C4×C47—22no—
88C22×C4×C47—22no—
89C22×C4×C47—22no—
90C22×C4×C47—21no—
91C22×C4×C47—21no—
92C22×C4×C47—22no—
93C22×C4×C47—22no—
94C22×C4×C47—21no—
95C22×C4×C47—21no—
96C22×C4×C47—21no—
97C22×C4×C47—22no—
98C22×C4×C47—21no—
99C22×C4×C47—22no—
100C22×C4×C47—22no—
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—22no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—21no—
119C22×C4×C47—21no—
120C22×C4×C47—22no—
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—21no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—21no—
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×Q814yes—
140C22×C4×C47C2×Q812yes—
141C22×C4×C47C2×Q812yes—
142C22×C4×C47C2×Q812yes—
143C22×C4×C47#4114yes—
144C22×C4×C47#4114yes—
145C22×C4×C47#4112yes—
146C22×C4×C47#4112yes—
147C22×C4×C47#4114yes—
148C4⋊C4×C47—28no—
149C4⋊C4×C47—28no—
150C4⋊C4×C47—28no—
151C4⋊C4×C47—48no—
152C4⋊C4×C47—48no—
153C4⋊C4×C47—44no—
154C42×C47—28no—
155C42×C47—48no—
156C23×C47C22×D411yescharacteristic
157C23×C47C22×Q811yescharacteristic
158C23×C47C22×Q811yescharacteristic
159C23×C47C2×#4111yescharacteristic
160C23×C47C2×#4111yescharacteristic
161C23×C47C2×#4112yes—
162C23×C47C2×#4112yes—
163C23×C47C2×#4112yes—
164C23×C47H(5,𝔽2)12yes—
165C23×C47H(5,𝔽2)11yescharacteristic
166C23×C472−1+411yescharacteristic
167C2×C4×C47—22no—
168C2×C4×C47—22no—
169C2×C4×C47—22no—
170C2×C4×C47—24no—
171C2×C4×C47—22no—
172C2×C4×C47—24no—
173C2×C4×C47—22no—
174C2×C4×C47—22no—
175C2×C4×C47—24no—
176C2×C4×C47—24no—
177C2×C4×C47—24no—
178C2×C4×C47—24no—
179C2×C4×C47—24no—
180C2×C4×C47—22no—
181C2×C4×C47—22no—
182C2×C4×C47—24no—
183C2×C4×C47—24no—
184C2×C4×C47—24no—
185C2×C4×C47—24no—
186C2×C4×C47—24no—
187C2×C4×C47—24no—
188C2×C4×C47—24no—
189C2×C4×C47—24no—
190C2×C4×C47—24no—
191C2×C4×C47—24no—
192C2×C4×C47—41no—
193C2×C4×C47—41no—
194C2×C4×C47—42no—
195C2×C4×C47—42no—
196C2×C4×C47—42no—
197C2×C4×C47—41no—
198C2×C4×C47—42no—
199C2×C4×C47—42no—
200C2×C4×C47—41no—
201C2×C4×C47—42no—
202C2×C4×C47—42no—
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—41no—
211C2×C4×C47—41no—
212C2×C4×C47—42no—
213C2×C4×C47—42no—
214C2×C4×C47—41no—
215C2×C4×C47—41no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47—42no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
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×C47C22⋊Q814yes—
228C2×C4×C47C22⋊Q814yes—
229C2×C4×C47#12314yes—
230#15105C4711yesmaximal, characteristic, direct product factor, Sylow
231C22×C47C2×C22⋊Q811yescharacteristic
232C22×C47C2×C22⋊Q811yescharacteristic
233C22×C47C2×#12311yescharacteristic
234C22×C47#52511yescharacteristic
235C22×C47#52912yes—
236C22×C47#52912yes—
237C22×C47#53211yescharacteristic
238C22×C47#53312yes—
239C22×C47#53312yes—
240C22×C47#53511yescharacteristic
241C22×C47#53711yescharacteristic
242C22×C47#53812yes—
243C22×C47#53912yes—
244C22×C47#55112yes—
245C22×C47#55212yes—
246C22×C47#55312yes—
247C22×C47#55312yes—
248C22×C47#55412yes—
249C22×C47#55412yes—
250C22×C47#55711yescharacteristic
251C22×C47#55711yescharacteristic
252C22×C47Q8211yescharacteristic
253C22×C47#55911yescharacteristic
254C4×C47—24no—
255C4×C47—24no—
256C4×C47—24no—
257C4×C47—44no—
258C4×C47—44no—
259C4×C47—44no—
260C4×C47—42no—
261C4×C47—42no—
262C4×C47—82no—
263C4×C47—81no—
264C4×C47—81no—
265C2×#387C2×C4711yescharacteristic
266C2×C4×C4⋊C4C2×C4711yescharacteristic
267#1445C2×C4711yescharacteristic
268#1445C2×C4711yescharacteristic
269#1444C2×C4711yescharacteristic
270#1442C2×C4711yescharacteristic
271#1441C2×C4712yes—
272#1441C2×C4712yes—
273#1436C2×C4712yes—
274#1436C2×C4712yes—
275C4⋊#95C2×C4711yescharacteristic
276C2×C47#239611yescharacteristic
277C2×C47#248711yescharacteristic
278C2×C47#249811yescharacteristic
279C2×C47#256611yescharacteristic
280C2×C47#258211yescharacteristic
281C2×C47#258512yes—
282C2×C47#258612yes—
283C2×C47#259012yes—
284C2×C47#259712yes—
285C2×C47#263611yescharacteristic
286C2×C47#285511yescharacteristic
287C22×C4⋊C4C22×C4711yescharacteristic
288C22×C4⋊C4C22×C4711yescharacteristic
289C22×C4⋊C4C22×C4712yes—
290C22×C4⋊C4C22×C4711yescharacteristic
291C22×C4⋊C4C22×C4711yescharacteristic
292C22×C4⋊C4C22×C4712yes—
293C22×C42C22×C4711yescharacteristic
294C22×C42C22×C4712yes—
295#387—24no—
296C4×C4⋊C4—24no—
297C2×#95C22×C4712yes—
298C2×#95C22×C4711yescharacteristic
299C2×#95C22×C4711yescharacteristic
300C2×#95C22×C4711yescharacteristic
301C2×#95C22×C4712yes—
302C2×#95C22×C4712yes—
303C2×#95C22×C4712yes—
304C2×#95C22×C4712yes—
305C2×#95C22×C4711yescharacteristic
306C2×#95C22×C4711yescharacteristic
307C2×#95C22×C4711yescharacteristic
308C2×#95C22×C4712yes—
309C2×#95C22×C4712yes—
310C2×#95C22×C4712yes—
311C2×#95C22×C4712yes—
312C47#1510511yescharacteristic, direct product factor, Sylow
313C23×C4C23×C4711yescharacteristic
314C23×C4C23×C4711yescharacteristic
315C23×C4C23×C4712yes—
316C23×C4C23×C4711yescharacteristic
317C23×C4C23×C4711yescharacteristic
318C23×C4C23×C4712yes—
319C23×C4C23×C4712yes—
320C23×C4C23×C4712yes—
321C23×C4C23×C4711yescharacteristic
322C23×C4C23×C4711yescharacteristic
323C23×C4C23×C4711yescharacteristic
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4Q8×C4714yes—
339C2×C4⋊C4Q8×C4714yes—
340C2×C42—24no—
341C2×C42—24no—
342C2×C42—42no—
343C2×C42—42no—
344C2×C42D4×C4714yes—
345#95—24no—
346#95—22no—
347#95—22no—
348#95—22no—
349#95—22no—
350#95—24no—
351#95—22no—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—22no—
356#95—42no—
357#95—42no—
358#95—42no—
359#95—42no—
360C24C24×C4711yescharacteristic
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4C2×D4×C4712yes—
412C22×C4C2×D4×C4712yes—
413C22×C4C2×D4×C4712yes—
414C22×C4C2×Q8×C4712yes—
415C22×C4C2×Q8×C4712yes—
416C22×C4C2×Q8×C4714yes—
417C22×C4C2×Q8×C4712yes—
418C22×C4C2×Q8×C4712yes—
419C22×C4#41×C4714yes—
420C22×C4#41×C4714yes—
421C22×C4#41×C4712yes—
422C22×C4#41×C4712yes—
423C22×C4#41×C4714yes—
424C4⋊C4—28no—
425C4⋊C4—28no—
426C4⋊C4—28no—
427C4⋊C4—48no—
428C4⋊C4—48no—
429C4⋊C4—44no—
430C42—28no—
431C42—48no—
432C23C22×D4×C4711yescharacteristic
433C23C22×Q8×C4711yescharacteristic
434C23C22×Q8×C4711yescharacteristic
435C23C2×#41×C4711yescharacteristic
436C23C2×#41×C4711yescharacteristic
437C23C2×#41×C4712yes—
438C23C2×#41×C4712yes—
439C23C2×#41×C4712yes—
440C23H(5,𝔽2)×C4712yes—
441C23H(5,𝔽2)×C4711yescharacteristic
442C232−1+4×C4711yescharacteristic
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4C22⋊Q8×C4714yes—
504C2×C4C22⋊Q8×C4714yes—
505C2×C4#123×C4714yes—
506C22C2×C22⋊Q8×C4711yescharacteristic
507C22C2×C22⋊Q8×C4711yescharacteristic
508C22C2×#123×C4711yescharacteristic
509C22C47×#52511yescharacteristic
510C22C47×#52912yes—
511C22C47×#52912yes—
512C22C47×#53211yescharacteristic
513C22C47×#53312yes—
514C22C47×#53312yes—
515C22C47×#53511yescharacteristic
516C22C47×#53711yescharacteristic
517C22C47×#53812yes—
518C22C47×#53912yes—
519C22C47×#55112yes—
520C22C47×#55212yes—
521C22C47×#55312yes—
522C22C47×#55312yes—
523C22C47×#55412yes—
524C22C47×#55412yes—
525C22C47×#55711yescharacteristic
526C22C47×#55711yescharacteristic
527C22Q82×C4711yescharacteristic
528C22C47×#55911yescharacteristic
529C4—24no—
530C4—24no—
531C4—24no—
532C4—44no—
533C4—44no—
534C4—44no—
535C4—42no—
536C4—42no—
537C4—82no—
538C4—81no—
539C4—81no—
540C2C47×#239611yescharacteristic
541C2C47×#248711yescharacteristic
542C2C47×#249811yescharacteristic
543C2C47×#256611yescharacteristic
544C2C47×#258211yescharacteristic
545C2C47×#258512yes—
546C2C47×#258612yes—
547C2C47×#259012yes—
548C2C47×#259712yes—
549C2C47×#263611yescharacteristic
550C2C47×#285511yescharacteristic
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
230. #15105C47direct (N × H)
312. C47#15105direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#3872
C2×C4×C4⋊C4×C472
C47×#14452
C47×#14442
C47×#14422
C47×#14412
C47×#14362
C47×C4⋊#952
#1510547