Finite Group Databasebeta

← C47×#36652 #26076350

Subgroups — C47×#36652 #26076350

Order 12032.

2570 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#525C212yesmaximal, complemented
2C47×#2817C211yesmaximal, characteristic, complemented
3C47×#2816C212yesmaximal, complemented
4C47×#2815C211yesmaximal, characteristic, complemented
5C47×#2814C214yesmaximal, complemented
6C47×#2813C214yesmaximal, complemented
7C47×#2812C214yesmaximal, complemented
8C47×#2395C214yesmaximal, complemented
9C47×#2392C214yesmaximal, complemented
10C47×#2388C214yesmaximal, complemented
11C47×#2280C211yesmaximal, characteristic, complemented
12C22×#41×C47C2212yes—
13C24×C4×C47C2211yescharacteristic
14C47×#525—216no—
15C2×#123×C47C2214yes—
16C2×C22⋊Q8×C47C2212yes—
17C2×C22⋊Q8×C47C2212yes—
18C2×#121×C47C2212yes—
19C2×#121×C47C2212yes—
20C2×#120×C47C2214yes—
21C2×C4×D4×C47C2214yes—
22C2×C4×D4×C47C2214yes—
23C2×C4×D4×C47C2214yescomplemented
24C2×#117×C47C2212yes—
25C2×#117×C47C2212yes—
26C47×#400C2214yescomplemented
27C47×#399C2214yescomplemented
28C47×#398C2214yescomplemented
29C47×#398C2214yescomplemented
30C47×#397C2218yes—
31C47×#397C2214yes—
32C47×#397C2214yescomplemented
33C47×#396C2218yescomplemented
34C47×#395C2214yescomplemented
35C47×#394C2218yes—
36C47×#394C2218yes—
37C47×#394C2218yes—
38C47×#394C2214yescomplemented
39C47×#394C2214yescomplemented
40C47×#393C2214yescomplemented
41C47×#392C2218yes—
42C47×#392C2214yes—
43C47×#392C2214yescomplemented
44C47×#381C2211yescharacteristic
45C47×#381C2211yescharacteristic
46C47×#380C2214yes—
47C47×#379C2212yes—
48C4×C4⋊C4×C47C2214yescomplemented
49C4×C22⋊C4×C47C2214yes—
50C4×C22⋊C4×C47C2218yescomplemented
51C25×C47C2311yescharacteristic
52C2×#41×C47—28no—
53C2×#41×C47—48no—
54C22×Q8×C47C2312yes—
55C22×D4×C47C2314yes—
56C22×D4×C47C2314yes—
57C22×D4×C47C2314yes—
58C22×D4×C47C2312yes—
59C22×D4×C47C2314yes—
60C23×C4×C47—44no—
61C23×C4×C47D418yescomplemented
62C23×C4×C47C2314yes—
63C23×C4×C47C2311yescharacteristic
64C23×C4×C47C2312yes—
65C23×C4×C47C2311yescharacteristic
66C23×C4×C47C2312yes—
67#123×C47—216no—
68C22⋊Q8×C47—28no—
69C22⋊Q8×C47—28no—
70#121×C47—28no—
71#121×C47—28no—
72#120×C47—216no—
73C4×D4×C47—216no—
74C4×D4×C47—216no—
75C4×D4×C47—48no—
76#117×C47—28no—
77#117×C47—44no—
78C2×C4⋊C4×C47C2312yes—
79C2×C4⋊C4×C47C2312yes—
80C2×C4⋊C4×C47C2314yes—
81C2×C4⋊C4×C47C2314yes—
82C2×C4⋊C4×C47C2314yes—
83C2×C4⋊C4×C47C2314yes—
84C2×C4⋊C4×C47C2318yes—
85C2×C22⋊C4×C47C2314yes—
86C2×C22⋊C4×C47C2314yes—
87C2×C22⋊C4×C47C2314yes—
88C2×C22⋊C4×C47C2314yes—
89C2×C22⋊C4×C47C2314yes—
90C2×C22⋊C4×C47C2312yes—
91C2×C22⋊C4×C47C2312yes—
92C2×C22⋊C4×C47C2318yes—
93C2×C22⋊C4×C47C2318yes—
94C2×C22⋊C4×C47C2318yes—
95C2×C22⋊C4×C47C2318yes—
96C2×C42×C47C2314yes—
97C2×C42×C47C2314yes—
98#95×C47C2314yes—
99#95×C47C2314yes—
100#95×C47C2318yes—
101#95×C47C2318yes—
102#95×C47C2314yes—
103#95×C47C2314yes—
104C24×C47—42no—
105C24×C47—44no—
106C24×C47C2×D414yes—
107C24×C47C2414yes—
108C24×C47C2411yescharacteristic
109C24×C47C2412yes—
110#41×C47—432no—
111C2×Q8×C47—24no—
112C2×Q8×C47—44no—
113C2×D4×C47—28no—
114C2×D4×C47—28no—
115C2×D4×C47—28no—
116C2×D4×C47—24no—
117C2×D4×C47—44no—
118C2×D4×C47—44no—
119C2×D4×C47—48no—
120C2×D4×C47—48no—
121C2×D4×C47—44no—
122C2×D4×C47—44no—
123C2×D4×C47—48no—
124C22×C4×C47—24no—
125C22×C4×C47—28no—
126C22×C4×C47—28no—
127C22×C4×C47—216no—
128C22×C4×C47—416no—
129C22×C4×C47—44no—
130C22×C4×C47—42no—
131C22×C4×C47C2×D418yes—
132C22×C4×C47C2×D414yes—
133C22×C4×C47C2×D414yes—
134C22×C4×C47C2×D418yes—
135C22×C4×C47C2414yes—
136C22×C4×C47C2414yes—
137C22×C4×C47C2414yes—
138C22×C4×C47C2414yes—
139C22×C4×C47C2414yes—
140C22×C4×C47C2411yescharacteristic
141C22×C4×C47C2412yes—
142C22×C4×C47C2411yescharacteristic
143C4⋊C4×C47—24no—
144C4⋊C4×C47—24no—
145C4⋊C4×C47—28no—
146C4⋊C4×C47—28no—
147C4⋊C4×C47—48no—
148C4⋊C4×C47—44no—
149C4⋊C4×C47—44no—
150C22⋊C4×C47—28no—
151C22⋊C4×C47—28no—
152C22⋊C4×C47—28no—
153C22⋊C4×C47—28no—
154C22⋊C4×C47—28no—
155C22⋊C4×C47—48no—
156C22⋊C4×C47—48no—
157C22⋊C4×C47—48no—
158C22⋊C4×C47—42no—
159C22⋊C4×C47—42no—
160C22⋊C4×C47—48no—
161C42×C47—28no—
162C42×C47—28no—
163C23×C47—22no—
164C23×C47—24no—
165C23×C47—24no—
166C23×C47—24no—
167C23×C47—24no—
168C23×C47—24no—
169C23×C47—28no—
170C23×C47—24no—
171C23×C47—28no—
172C23×C47—24no—
173C23×C47—44no—
174C23×C47—48no—
175C23×C47—416no—
176C23×C47C22×D414yes—
177C23×C47C22×D412yes—
178C23×C47C2511yescharacteristic
179Q8×C47—48no—
180D4×C47—48no—
181D4×C47—416no—
182D4×C47—416no—
183D4×C47—416no—
184D4×C47—416no—
185C2×C4×C47—22no—
186C2×C4×C47—24no—
187C2×C4×C47—28no—
188C2×C4×C47—216no—
189C2×C4×C47—24no—
190C2×C4×C47—24no—
191C2×C4×C47—24no—
192C2×C4×C47—24no—
193C2×C4×C47—24no—
194C2×C4×C47—28no—
195C2×C4×C47—28no—
196C2×C4×C47—24no—
197C2×C4×C47—28no—
198C2×C4×C47—28no—
199C2×C4×C47—24no—
200C2×C4×C47—48no—
201C2×C4×C47—44no—
202C2×C4×C47—416no—
203C2×C4×C47C22×D412yes—
204C2×C4×C47C22×D414yes—
205C2×C4×C47C22×D412yes—
206C2×C4×C47H(5,𝔽2)14yes—
207#36652C4711yesmaximal, characteristic, direct product factor, Sylow
208C22×C47—24no—
209C22×C47—22no—
210C22×C47—24no—
211C22×C47—24no—
212C22×C47—24no—
213C22×C47—416no—
214C22×C47—44no—
215C22×C47—48no—
216C22×C47—44no—
217C22×C47—44no—
218C22×C47—44no—
219C22×C47—48no—
220C22×C47—48no—
221C22×C47C23×D411yescharacteristic
222C22×C47C2×H(5,𝔽2)12yes—
223C22×C47#58514yes—
224C4×C47—22no—
225C4×C47—24no—
226C4×C47—44no—
227C4×C47—44no—
228C4×C47—44no—
229C4×C47—44no—
230C4×C47—44no—
231C4×C47#53414yes—
232C2×#525C2×C4712yescomplemented
233#2817C2×C4711yescharacteristic, complemented
234#2816C2×C4712yescomplemented
235#2815C2×C4711yescharacteristic, complemented
236#2814C2×C4714yescomplemented
237#2813C2×C4714yescomplemented
238#2812C2×C4714yescomplemented
239#2395C2×C4714yescomplemented
240#2392C2×C4714yescomplemented
241#2388C2×C4714yescomplemented
242#2280C2×C4711yescharacteristic, complemented
243C2×C47—44no—
244C2×C47—42no—
245C2×C47—84no—
246C2×C47C2×#53411yescharacteristic
247C2×C47#344912yes—
248C2×C47#352914yes—
249C22×#41C22×C4712yes—
250C24×C4C22×C4711yescharacteristic
251#525—216no—
252C2×#123C22×C4714yes—
253C2×C22⋊Q8C22×C4712yes—
254C2×C22⋊Q8C22×C4712yes—
255C2×#121C22×C4712yes—
256C2×#121C22×C4712yes—
257C2×#120C22×C4714yes—
258C2×C4×D4C22×C4714yes—
259C2×C4×D4C22×C4714yes—
260C2×C4×D4C22×C4714yescomplemented
261C2×#117C22×C4712yes—
262C2×#117C22×C4712yes—
263#400C22×C4714yescomplemented
264#399C22×C4714yescomplemented
265#398C22×C4714yescomplemented
266#398C22×C4714yescomplemented
267#397C22×C4714yes—
268#397C22×C4718yes—
269#397C22×C4714yescomplemented
270#396C22×C4718yescomplemented
271#395C22×C4714yescomplemented
272#394C22×C4718yes—
273#394C22×C4718yes—
274#394C22×C4718yes—
275#394C22×C4714yescomplemented
276#394C22×C4714yescomplemented
277#393C22×C4714yescomplemented
278#392C22×C4718yes—
279#392C22×C4714yes—
280#392C22×C4714yescomplemented
281#381C22×C4711yescharacteristic
282#381C22×C4711yescharacteristic
283#380C22×C4714yes—
284#379C22×C4712yes—
285C4×C4⋊C4C22×C4714yescomplemented
286C4×C22⋊C4C22×C4714yes—
287C4×C22⋊C4C22×C4718yescomplemented
288C47#3665211yescharacteristic, direct product factor, Sylow
289C25C23×C4711yescharacteristic
290C2×#41—28no—
291C2×#41—48no—
292C22×Q8C23×C4712yes—
293C22×D4C23×C4714yes—
294C22×D4C23×C4714yes—
295C22×D4C23×C4714yes—
296C22×D4C23×C4712yes—
297C22×D4C23×C4714yes—
298C23×C4—44no—
299C23×C4D4×C4718yescomplemented
300C23×C4C23×C4714yes—
301C23×C4C23×C4711yescharacteristic
302C23×C4C23×C4712yes—
303C23×C4C23×C4711yescharacteristic
304C23×C4C23×C4712yes—
305#123—216no—
306C22⋊Q8—28no—
307C22⋊Q8—28no—
308#121—28no—
309#121—28no—
310#120—216no—
311C4×D4—216no—
312C4×D4—216no—
313C4×D4—48no—
314#117—28no—
315#117—44no—
316C2×C4⋊C4C23×C4712yes—
317C2×C4⋊C4C23×C4712yes—
318C2×C4⋊C4C23×C4714yes—
319C2×C4⋊C4C23×C4714yes—
320C2×C4⋊C4C23×C4714yes—
321C2×C4⋊C4C23×C4714yes—
322C2×C4⋊C4C23×C4718yes—
323C2×C22⋊C4C23×C4714yes—
324C2×C22⋊C4C23×C4714yes—
325C2×C22⋊C4C23×C4714yes—
326C2×C22⋊C4C23×C4714yes—
327C2×C22⋊C4C23×C4714yes—
328C2×C22⋊C4C23×C4712yes—
329C2×C22⋊C4C23×C4712yes—
330C2×C22⋊C4C23×C4718yes—
331C2×C22⋊C4C23×C4718yes—
332C2×C22⋊C4C23×C4718yes—
333C2×C22⋊C4C23×C4718yes—
334C2×C42C23×C4714yes—
335C2×C42C23×C4714yes—
336#95C23×C4714yes—
337#95C23×C4714yes—
338#95C23×C4718yes—
339#95C23×C4718yes—
340#95C23×C4714yes—
341#95C23×C4714yes—
342C24—42no—
343C24—44no—
344C24C2×D4×C4714yes—
345C24C24×C4714yes—
346C24C24×C4711yescharacteristic
347C24C24×C4712yes—
348#41—432no—
349C2×Q8—24no—
350C2×Q8—44no—
351C2×D4—28no—
352C2×D4—28no—
353C2×D4—28no—
354C2×D4—24no—
355C2×D4—44no—
356C2×D4—44no—
357C2×D4—48no—
358C2×D4—48no—
359C2×D4—44no—
360C2×D4—44no—
361C2×D4—48no—
362C22×C4—24no—
363C22×C4—28no—
364C22×C4—28no—
365C22×C4—216no—
366C22×C4—416no—
367C22×C4—44no—
368C22×C4—42no—
369C22×C4C2×D4×C4718yes—
370C22×C4C2×D4×C4714yes—
371C22×C4C2×D4×C4714yes—
372C22×C4C2×D4×C4718yes—
373C22×C4C24×C4714yes—
374C22×C4C24×C4714yes—
375C22×C4C24×C4714yes—
376C22×C4C24×C4714yes—
377C22×C4C24×C4714yes—
378C22×C4C24×C4712yes—
379C22×C4C24×C4711yescharacteristic
380C22×C4C24×C4711yescharacteristic
381C4⋊C4—24no—
382C4⋊C4—24no—
383C4⋊C4—28no—
384C4⋊C4—28no—
385C4⋊C4—48no—
386C4⋊C4—44no—
387C4⋊C4—44no—
388C22⋊C4—28no—
389C22⋊C4—28no—
390C22⋊C4—28no—
391C22⋊C4—28no—
392C22⋊C4—28no—
393C22⋊C4—48no—
394C22⋊C4—48no—
395C22⋊C4—48no—
396C22⋊C4—42no—
397C22⋊C4—42no—
398C22⋊C4—48no—
399C42—28no—
400C42—28no—
401C23—22no—
402C23—24no—
403C23—24no—
404C23—24no—
405C23—24no—
406C23—24no—
407C23—28no—
408C23—24no—
409C23—28no—
410C23—24no—
411C23—44no—
412C23—48no—
413C23—416no—
414C23C22×D4×C4714yes—
415C23C22×D4×C4712yes—
416C23C25×C4711yescharacteristic
417Q8—48no—
418D4—48no—
419D4—416no—
420D4—416no—
421D4—416no—
422D4—416no—
423C2×C4—22no—
424C2×C4—24no—
425C2×C4—28no—
426C2×C4—216no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—28no—
433C2×C4—28no—
434C2×C4—24no—
435C2×C4—28no—
436C2×C4—28no—
437C2×C4—24no—
438C2×C4—44no—
439C2×C4—48no—
440C2×C4—416no—
441C2×C4C22×D4×C4712yes—
442C2×C4C22×D4×C4714yes—
443C2×C4C22×D4×C4712yes—
444C2×C4H(5,𝔽2)×C4714yes—
445C22—24no—
446C22—22no—
447C22—24no—
448C22—24no—
449C22—24no—
450C22—416no—
451C22—44no—
452C22—48no—
453C22—44no—
454C22—44no—
455C22—44no—
456C22—48no—
457C22—48no—
458C22C23×D4×C4711yescharacteristic
459C22C2×H(5,𝔽2)×C4712yes—
460C22C47×#58514yes—
461C4—24no—
462C4—22no—
463C4—44no—
464C4—44no—
465C4—44no—
466C4—44no—
467C4—44no—
468C4C47×#53414yes—
469C2—44no—
470C2—42no—
471C2—84no—
472C2C2×C47×#53411yescharacteristic
473C2C47×#344912yes—
474C2C47×#352914yes—
subgroupG/H
centerC22×C4×C47C24
commutator, Frattini, cosocleC23C25×C47
socleC23×C47C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#525C2semidirect
2. C47×#2817C2semidirect
3. C47×#2816C2semidirect
4. C47×#2815C2semidirect
5. C47×#2814C2semidirect
6. C47×#2813C2semidirect
7. C47×#2812C2semidirect
8. C47×#2395C2semidirect
9. C47×#2392C2semidirect
10. C47×#2388C2semidirect
11. C47×#2280C2semidirect
23. C2×C4×D4×C47C22semidirect
26. C47×#400C22semidirect
27. C47×#399C22semidirect
28. C47×#398C22semidirect
29. C47×#398C22semidirect
32. C47×#397C22semidirect
33. C47×#396C22semidirect
34. C47×#395C22semidirect
38. C47×#394C22semidirect
39. C47×#394C22semidirect
40. C47×#393C22semidirect
43. C47×#392C22semidirect
48. C4×C4⋊C4×C47C22semidirect
50. C4×C22⋊C4×C47C22semidirect
61. C23×C4×C47D4semidirect
207. #36652C47direct (N × H)
232. C2×#525C2×C47semidirect
233. #2817C2×C47semidirect
234. #2816C2×C47semidirect
235. #2815C2×C47semidirect
236. #2814C2×C47semidirect
237. #2813C2×C47semidirect
238. #2812C2×C47semidirect
239. #2395C2×C47semidirect
240. #2392C2×C47semidirect
241. #2388C2×C47semidirect
242. #2280C2×C47semidirect
260. C2×C4×D4C22×C47semidirect
263. #400C22×C47semidirect
264. #399C22×C47semidirect
265. #398C22×C47semidirect
266. #398C22×C47semidirect
269. #397C22×C47semidirect
270. #396C22×C47semidirect
271. #395C22×C47semidirect
275. #394C22×C47semidirect
276. #394C22×C47semidirect
277. #393C22×C47semidirect
280. #392C22×C47semidirect
285. C4×C4⋊C4C22×C47semidirect
287. C4×C22⋊C4C22×C47semidirect
288. C47#36652direct (N × H)
299. C23×C4D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5252
C47×#28172
C47×#28162
C47×#28152
C47×#28142
C47×#28132
C47×#28122
C47×#23952
C47×#23922
C47×#23882
C47×#22802
#3665247