Finite Group Databasebeta

← C47×#19242 #26058940

Subgroups — C47×#19242 #26058940

Order 12032.

636 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3249C211yesmaximal, characteristic, complemented
2C47×#3208C211yesmaximal, characteristic
3C47×#3138C211yesmaximal, characteristic
4C47×#2962C211yesmaximal, characteristic, complemented
5C47×#1702C212yesmaximal, complemented
6C47×#1698C212yesmaximal, complemented
7C47×#1682C212yesmaximal, complemented
8C47×#1678C212yesmaximal, complemented
9C47×#1565C211yesmaximal, characteristic, complemented
10C47×#1542C211yesmaximal, characteristic, complemented
11C2×C47×#331C211yesmaximal, characteristic
12C47×#533C2211yescharacteristic
13C47×#533C2211yescharacteristic
14C2×#127×C47C2211yescharacteristic
15C47×#492—21no—
16C47×#490—22no—
17C47×#486—21no—
18C47×#486C2212yes—
19C47×#486C2212yes—
20C47×#477—21no—
21C47×#477C2212yescomplemented
22C47×#467—22no—
23C47×#462—21no—
24C47×#462C2212yescomplemented
25C47×#460C2212yes—
26C47×#460C2212yes—
27C47×#450—22no—
28C47×#446—22no—
29C47×#446C2212yescomplemented
30C8×Q8×C47C2212yescomplemented
31C47×#431C2211yescharacteristic
32C47×#424—21no—
33C2×C4⋊C8×C47C2211yescharacteristic
34C2×C4⋊C8×C47C2211yescharacteristic
35C47×#418—21no—
36C47×#418—21no—
37C47×#405—21no—
38C4×M16×C47C2211yescharacteristic
39C47×#335C2212yescomplemented
40C47×#334C2212yescomplemented
41C47×#333C2211yescharacteristic, complemented
42C47×#333C2211yescharacteristic, complemented
43C47×#332C2211yescharacteristic, complemented
44C47×#332C2211yescharacteristic, complemented
45C47×#331C2212yes—
46C47×#331C2212yes—
47C22×D4×C47—21no—
48C22×D4×C47—21no—
49C22×D4×C47—21no—
50C2×Q16×C47—22no—
51C2×SD16×C47—22no—
52C2×SD16×C47—22no—
53C2×M16×C47D411yescharacteristic
54C2×M16×C47D411yescharacteristic
55C22×C8×C47—21no—
56C22×C8×C47—21no—
57C4⋊Q8×C47D411yescharacteristic
58C4⋊Q8×C47D411yescharacteristic
59C4⋊Q8×C47C2311yescharacteristic
60C4⋊Q8×C47C2311yescharacteristic
61#127×C47—21no—
62#127×C47—21no—
63#127×C47—21no—
64#127×C47C2312yes—
65#125×C47—21no—
66#125×C47—21no—
67C22⋊Q8×C47—21no—
68C22⋊Q8×C47—21no—
69C22⋊Q8×C47—21no—
70C22⋊Q8×C47D412yes—
71C4×Q8×C47—21no—
72C4×Q8×C47—21no—
73C4×Q8×C47—21no—
74C4×Q8×C47C2312yes—
75#117×C47—21no—
76#117×C47—21no—
77C2×C42×C47C2311yescharacteristic
78#107×C47—22no—
79C4⋊C8×C47—22no—
80C4⋊C8×C47—22no—
81C4⋊C8×C47—21no—
82C4⋊C8×C47—21no—
83C4⋊C8×C47C2311yescharacteristic
84C4⋊C8×C47C2311yescharacteristic
85C4⋊C8×C47C2312yes—
86C4⋊C8×C47C2311yescharacteristic
87C4⋊C8×C47C2311yescharacteristic
88#103×C47—22no—
89#103×C47—22no—
90#102×C47—22no—
91#102×C47—22no—
92#102×C47—22no—
93#102×C47—22no—
94#102×C47—22no—
95#102×C47—22no—
96C22⋊C8×C47—21no—
97#97×C47—22no—
98#97×C47D412yes—
99C4×C8×C47—22no—
100C4×C8×C47—21no—
101C4×C8×C47C2312yes—
102C24×C47—41no—
103C2×Q8×C47—21no—
104C2×Q8×C47—21no—
105C2×Q8×C47—21no—
106C2×Q8×C47C2×D412yes—
107C2×D4×C47—22no—
108C2×D4×C47—22no—
109C2×D4×C47—22no—
110C2×D4×C47—41no—
111C2×D4×C47—41no—
112C2×D4×C47—41no—
113C2×D4×C47—42no—
114C2×D4×C47—42no—
115C2×D4×C47—81no—
116C2×D4×C47—81no—
117C2×D4×C47—82no—
118C22×C4×C47C2×D411yescharacteristic
119C22×C4×C47C2×D411yescharacteristic
120C22×C4×C47#4111yescharacteristic
121Q16×C47—82no—
122SD16×C47—82no—
123SD16×C47—82no—
124M16×C47—22no—
125M16×C47—22no—
126C2×C8×C47—22no—
127C2×C8×C47—21no—
128C2×C8×C47—21no—
129C2×C8×C47—21no—
130C2×C8×C47—21no—
131C2×C8×C47—42no—
132C2×C8×C47—81no—
133C2×C8×C47C2×D412yes—
134C2×C8×C47C2×D412yes—
135C4⋊C4×C47—21no—
136C4⋊C4×C47—21no—
137C4⋊C4×C47—21no—
138C4⋊C4×C47—22no—
139C4⋊C4×C47—22no—
140C4⋊C4×C47—21no—
141C4⋊C4×C47—21no—
142C4⋊C4×C47—21no—
143C4⋊C4×C47—21no—
144C4⋊C4×C47—41no—
145C4⋊C4×C47—41no—
146C4⋊C4×C47C2×D412yes—
147C22⋊C4×C47—22no—
148C22⋊C4×C47—41no—
149C42×C47—22no—
150C42×C47—41no—
151C42×C47C2×D411yescharacteristic
152C42×C47C2×D411yescharacteristic
153C42×C47#4111yescharacteristic
154C42×C47C2411yescharacteristic
155C23×C47—42no—
156C23×C47—82no—
157C23×C47—82no—
158C23×C47—82no—
159C23×C47#12111yescharacteristic
160Q8×C47—22no—
161Q8×C47—22no—
162Q8×C47—41no—
163Q8×C47—41no—
164Q8×C47—81no—
165Q8×C47—81no—
166D4×C47—42no—
167D4×C47—42no—
168D4×C47—42no—
169D4×C47—42no—
170D4×C47—82no—
171D4×C47—82no—
172D4×C47—82no—
173D4×C47—82no—
174C2×C4×C47—21no—
175C2×C4×C47—21no—
176C2×C4×C47—22no—
177C2×C4×C47—22no—
178C2×C4×C47—41no—
179C2×C4×C47—41no—
180C2×C4×C47—41no—
181C2×C4×C47#12111yescharacteristic
182C2×C4×C47#12111yescharacteristic
183C2×C4×C47#12111yescharacteristic
184C2×C4×C47#13512yes—
185C2×C4×C47#13712yes—
186C2×C4×C47C22×D411yescharacteristic
187C2×C4×C47C22×D411yescharacteristic
188C2×C4×C47C2×#4111yescharacteristic
189C8×C47—22no—
190C8×C47—22no—
191C8×C47—41no—
192C8×C47—41no—
193C8×C47—42no—
194C8×C47—41no—
195C8×C47—41no—
196#19242C4711yesmaximal, characteristic, direct product factor, Sylow
197C22×C47—21no—
198C22×C47—21no—
199C22×C47—82no—
200C22×C47—82no—
201C22×C47—82no—
202C22×C47—164no—
203C22×C47#46412yes—
204C22×C47C2×#12111yescharacteristic
205C4×C47—21no—
206C4×C47—21no—
207C4×C47—21no—
208C4×C47—42no—
209C4×C47—42no—
210C4×C47—81no—
211C4×C47—81no—
212C4×C47#46412yes—
213C4×C47C2×#13511yescharacteristic
214C4×C47C2×#13711yescharacteristic
215C4×C47#57611yescharacteristic
216C4×C47#57711yescharacteristic
217#3249C2×C4711yescharacteristic, complemented
218#3208C2×C4711yescharacteristic
219#3138C2×C4711yescharacteristic
220#2962C2×C4711yescharacteristic, complemented
221#1702C2×C4712yescomplemented
222#1698C2×C4712yescomplemented
223#1682C2×C4712yescomplemented
224#1678C2×C4712yescomplemented
225#1565C2×C4711yescharacteristic, complemented
226#1542C2×C4711yescharacteristic, complemented
227C2×#331C2×C4711yescharacteristic
228C2×C47—22no—
229C2×C47—162no—
230C2×C47C2×#46411yescharacteristic
231C2×C47#306211yescharacteristic
232C2×C47#306811yescharacteristic
233#533C22×C4711yescharacteristic
234#533C22×C4711yescharacteristic
235C2×#127C22×C4711yescharacteristic
236#492—21no—
237#490—22no—
238#486—21no—
239#486C22×C4712yes—
240#486C22×C4712yes—
241#477—21no—
242#477C22×C4712yescomplemented
243#467—22no—
244#462—21no—
245#462C22×C4712yescomplemented
246#460C22×C4712yes—
247#460C22×C4712yes—
248#450—22no—
249#446—22no—
250#446C22×C4712yescomplemented
251C8×Q8C22×C4712yescomplemented
252#431C22×C4711yescharacteristic
253#424—21no—
254C2×C4⋊C8C22×C4711yescharacteristic
255C2×C4⋊C8C22×C4711yescharacteristic
256#418—21no—
257#418—21no—
258#405—21no—
259C4×M16C22×C4711yescharacteristic
260#335C22×C4712yescomplemented
261#334C22×C4712yescomplemented
262#333C22×C4711yescharacteristic, complemented
263#333C22×C4711yescharacteristic, complemented
264#332C22×C4711yescharacteristic, complemented
265#332C22×C4711yescharacteristic, complemented
266#331C22×C4712yes—
267#331C22×C4712yes—
268C47#1924211yescharacteristic, direct product factor, Sylow
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—21no—
272C2×Q16—22no—
273C2×SD16—22no—
274C2×SD16—22no—
275C2×M16D4×C4711yescharacteristic
276C2×M16D4×C4711yescharacteristic
277C22×C8—21no—
278C22×C8—21no—
279C4⋊Q8D4×C4711yescharacteristic
280C4⋊Q8D4×C4711yescharacteristic
281C4⋊Q8C23×C4711yescharacteristic
282C4⋊Q8C23×C4711yescharacteristic
283#127—21no—
284#127—21no—
285#127—21no—
286#127C23×C4712yes—
287#125—21no—
288#125—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8D4×C4712yes—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8C23×C4712yes—
297#117—21no—
298#117—21no—
299C2×C42C23×C4711yescharacteristic
300#107—22no—
301C4⋊C8—22no—
302C4⋊C8—22no—
303C4⋊C8—21no—
304C4⋊C8—21no—
305C4⋊C8C23×C4711yescharacteristic
306C4⋊C8C23×C4711yescharacteristic
307C4⋊C8C23×C4712yes—
308C4⋊C8C23×C4711yescharacteristic
309C4⋊C8C23×C4711yescharacteristic
310#103—22no—
311#103—22no—
312#102—22no—
313#102—22no—
314#102—22no—
315#102—22no—
316#102—22no—
317#102—22no—
318C22⋊C8—21no—
319#97—22no—
320#97D4×C4712yes—
321C4×C8—22no—
322C4×C8—21no—
323C4×C8C23×C4712yes—
324C24—41no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8C2×D4×C4712yes—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—42no—
336C2×D4—42no—
337C2×D4—81no—
338C2×D4—81no—
339C2×D4—82no—
340C22×C4C2×D4×C4711yescharacteristic
341C22×C4C2×D4×C4711yescharacteristic
342C22×C4#41×C4711yescharacteristic
343Q16—82no—
344SD16—82no—
345SD16—82no—
346M16—22no—
347M16—22no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—22no—
353C2×C8—42no—
354C2×C8—81no—
355C2×C8C2×D4×C4712yes—
356C2×C8C2×D4×C4712yes—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4C2×D4×C4712yes—
369C22⋊C4—22no—
370C22⋊C4—41no—
371C42—22no—
372C42—41no—
373C42C2×D4×C4711yescharacteristic
374C42C2×D4×C4711yescharacteristic
375C42#41×C4711yescharacteristic
376C42C24×C4711yescharacteristic
377C23—42no—
378C23—82no—
379C23—82no—
380C23—82no—
381C23#121×C4711yescharacteristic
382Q8—22no—
383Q8—22no—
384Q8—41no—
385Q8—41no—
386Q8—81no—
387Q8—81no—
388D4—42no—
389D4—42no—
390D4—42no—
391D4—42no—
392D4—82no—
393D4—82no—
394D4—82no—
395D4—82no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4#121×C4711yescharacteristic
404C2×C4#121×C4711yescharacteristic
405C2×C4#121×C4711yescharacteristic
406C2×C4#135×C4712yes—
407C2×C4#137×C4712yes—
408C2×C4C22×D4×C4711yescharacteristic
409C2×C4C22×D4×C4711yescharacteristic
410C2×C4C2×#41×C4711yescharacteristic
411C8—22no—
412C8—22no—
413C8—41no—
414C8—41no—
415C8—42no—
416C8—41no—
417C8—41no—
418C22—21no—
419C22—21no—
420C22—82no—
421C22—82no—
422C22—82no—
423C22—164no—
424C22C47×#46412yes—
425C22C2×#121×C4711yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—42no—
430C4—42no—
431C4—81no—
432C4—81no—
433C4C47×#46412yes—
434C4C2×#135×C4711yescharacteristic
435C4C2×#137×C4711yescharacteristic
436C4C47×#57611yescharacteristic
437C4C47×#57711yescharacteristic
438C2—22no—
439C2—162no—
440C2C2×C47×#46411yescharacteristic
441C2C47×#306211yescharacteristic
442C2C47×#306811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC42C24×C47
prime radicalC2×#127×C47C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3249C2semidirect
4. C47×#2962C2semidirect
5. C47×#1702C2semidirect
6. C47×#1698C2semidirect
7. C47×#1682C2semidirect
8. C47×#1678C2semidirect
9. C47×#1565C2semidirect
10. C47×#1542C2semidirect
21. C47×#477C22semidirect
24. C47×#462C22semidirect
29. C47×#446C22semidirect
30. C8×Q8×C47C22semidirect
39. C47×#335C22semidirect
40. C47×#334C22semidirect
41. C47×#333C22semidirect
42. C47×#333C22semidirect
43. C47×#332C22semidirect
44. C47×#332C22semidirect
196. #19242C47direct (N × H)
217. #3249C2×C47semidirect
220. #2962C2×C47semidirect
221. #1702C2×C47semidirect
222. #1698C2×C47semidirect
223. #1682C2×C47semidirect
224. #1678C2×C47semidirect
225. #1565C2×C47semidirect
226. #1542C2×C47semidirect
242. #477C22×C47semidirect
245. #462C22×C47semidirect
250. #446C22×C47semidirect
251. C8×Q8C22×C47semidirect
260. #335C22×C47semidirect
261. #334C22×C47semidirect
262. #333C22×C47semidirect
263. #333C22×C47semidirect
264. #332C22×C47semidirect
265. #332C22×C47semidirect
268. C47#19242direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32492
C47×#32082
C47×#31382
C47×#29622
C47×#17022
C47×#16982
C47×#16822
C47×#16782
C47×#15652
C47×#15422
C2×C47×#3312
#1924247