Finite Group Databasebeta

← C47×#10266 #26049964

Subgroups — C47×#10266 #26049964

Order 12032.

710 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#492C211yesmaximal, characteristic, complemented
2C2×C47×#474C211yesmaximal, characteristic, complemented
3C2×C47×#459C211yesmaximal, characteristic
4C47×#1954C211yesmaximal, characteristic, complemented
5C2×C47×#332C211yesmaximal, characteristic, complemented
6C2×C47×#331C211yesmaximal, characteristic, complemented
7C47×#1277C211yesmaximal, characteristic, complemented
8C22×SD16×C47—22no—
9C22×D8×C47—21no—
10C2×C4⋊Q8×C47C2211yescharacteristic
11C2×#127×C47C2211yescharacteristic
12C2×C4×D4×C47C2211yescharacteristic
13C47×#492—22no—
14C47×#492—22no—
15C47×#474—22no—
16C47×#474—22no—
17C47×#459—22no—
18C47×#459—22no—
19C2×#107×C47—21no—
20C2×C4⋊C8×C47C2211yescharacteristic
21C2×C4⋊C8×C47C2211yescharacteristic
22C2×C4⋊C8×C47C2211yescharacteristic
23C2×#102×C47—21no—
24C2×#102×C47—21no—
25C2×C22⋊C8×C47—22no—
26C2×C4×C8×C47C2211yescharacteristic
27C47×#332—22no—
28C47×#331—22no—
29C22×Q8×C47—21no—
30C22×D4×C47—21no—
31C22×D4×C47—21no—
32C22×D4×C47—21no—
33C22×D4×C47D411yescharacteristic
34C23×C4×C47—21no—
35C2×SD16×C47—28no—
36C2×SD16×C47—44no—
37C2×SD16×C47—44no—
38C2×D8×C47—24no—
39C2×D8×C47—42no—
40C2×D8×C47—42no—
41C22×C8×C47—21no—
42C22×C8×C47—21no—
43C22×C8×C47—21no—
44C22×C8×C47D412yes—
45C4⋊Q8×C47—21no—
46C4⋊Q8×C47—21no—
47C4⋊Q8×C47—21no—
48C4⋊Q8×C47D412yes—
49#127×C47—21no—
50#127×C47—21no—
51#127×C47—21no—
52#127×C47D412yes—
53C4×D4×C47—21no—
54C4×D4×C47—21no—
55C4×D4×C47—21no—
56C4×D4×C47—21no—
57C2×C4⋊C4×C47—21no—
58C2×C4⋊C4×C47—21no—
59C2×C4⋊C4×C47D411yescharacteristic
60C2×C22⋊C4×C47—21no—
61C2×C42×C47C2311yescharacteristic
62#107×C47—24no—
63C4⋊C8×C47—21no—
64C4⋊C8×C47—21no—
65C4⋊C8×C47—21no—
66C4⋊C8×C47—21no—
67C4⋊C8×C47D412yes—
68C4⋊C8×C47D412yes—
69#102×C47—24no—
70#102×C47—24no—
71C22⋊C8×C47—44no—
72C4×C8×C47—21no—
73C4×C8×C47—21no—
74C24×C47—21no—
75C24×C47—41no—
76C2×Q8×C47—22no—
77C2×Q8×C47—41no—
78C2×Q8×C47—42no—
79C2×Q8×C47—42no—
80C2×D4×C47—21no—
81C2×D4×C47—21no—
82C2×D4×C47—22no—
83C2×D4×C47—22no—
84C2×D4×C47—22no—
85C2×D4×C47—21no—
86C2×D4×C47—21no—
87C2×D4×C47—21no—
88C2×D4×C47—41no—
89C2×D4×C47—41no—
90C2×D4×C47—41no—
91C2×D4×C47—42no—
92C2×D4×C47—41no—
93C2×D4×C47—41no—
94C2×D4×C47—41no—
95C2×D4×C47—42no—
96C2×D4×C47—41no—
97C2×D4×C47—82no—
98C2×D4×C47SD1612yescomplemented
99C22×C4×C47—21no—
100C22×C4×C47—41no—
101C22×C4×C47—41no—
102C22×C4×C47—41no—
103C22×C4×C47—42no—
104C22×C4×C47—42no—
105C22×C4×C47C2×D411yescharacteristic
106C22×C4×C47C2×D411yescharacteristic
107C22×C4×C47#4111yescharacteristic
108SD16×C47—416no—
109D8×C47—48no—
110C2×C8×C47—22no—
111C2×C8×C47—22no—
112C2×C8×C47—22no—
113C2×C8×C47—22no—
114C2×C8×C47—41no—
115C2×C8×C47—41no—
116C2×C8×C47—41no—
117C2×C8×C47—41no—
118C2×C8×C47—41no—
119C2×C8×C47—42no—
120C2×C8×C47D814yescomplemented
121C4⋊C4×C47—21no—
122C4⋊C4×C47—22no—
123C4⋊C4×C47—21no—
124C4⋊C4×C47—22no—
125C4⋊C4×C47—41no—
126C4⋊C4×C47—41no—
127C22⋊C4×C47—41no—
128C22⋊C4×C47—41no—
129C42×C47C2×D411yescharacteristic
130C42×C47C2×D411yescharacteristic
131C42×C47C2×D411yescharacteristic
132C42×C47C2×D411yescharacteristic
133C23×C47—22no—
134C23×C47—41no—
135C23×C47—42no—
136C23×C47—41no—
137C23×C47—42no—
138C23×C47—42no—
139C23×C47—82no—
140C23×C47—81no—
141C23×C47—81no—
142C23×C47—82no—
143C23×C47#12111yescharacteristic
144Q8×C47—44no—
145Q8×C47—81no—
146Q8×C47—81no—
147D4×C47—22no—
148D4×C47—22no—
149D4×C47—44no—
150D4×C47—41no—
151D4×C47—42no—
152D4×C47—41no—
153D4×C47—42no—
154D4×C47—82no—
155D4×C47—82no—
156D4×C47—81no—
157D4×C47—81no—
158D4×C47—81no—
159D4×C47—81no—
160C2×C4×C47—22no—
161C2×C4×C47—41no—
162C2×C4×C47—42no—
163C2×C4×C47—42no—
164C2×C4×C47—82no—
165C2×C4×C47—82no—
166C2×C4×C47—81no—
167C2×C4×C47—81no—
168C2×C4×C47#12011yescharacteristic
169C2×C4×C47#12011yescharacteristic
170C2×C4×C47#12011yescharacteristic
171C2×C4×C47#12111yescharacteristic
172C2×C4×C47#12111yescharacteristic
173C2×C4×C47#12711yescharacteristic
174C2×C4×C47C2×D812yes—
175C2×C4×C47C2×SD1611yescharacteristic
176C2×C4×C47#13511yescharacteristic
177C2×C4×C47AGL(1,ℤ/8)12yes—
178C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C47#13711yescharacteristic
180C8×C47—24no—
181C8×C47—42no—
182C8×C47—42no—
183C8×C47—81no—
184#10266C4711yesmaximal, characteristic, direct product factor, Sylow
185C22×C47—44no—
186C22×C47—42no—
187C22×C47—82no—
188C22×C47—81no—
189C22×C47—81no—
190C22×C47—82no—
191C22×C47—82no—
192C22×C47—82no—
193C22×C47—162no—
194C22×C47—162no—
195C22×C47#39211yescharacteristic
196C22×C47#45912yes—
197C22×C47#46511yescharacteristic
198C22×C47#46811yescharacteristic
199C22×C47#47112yes—
200C4×C47—21no—
201C4×C47—21no—
202C4×C47—81no—
203C4×C47—82no—
204C4×C47#44712yes—
205C4×C47#44811yescharacteristic
206C4×C47#44911yescharacteristic
207C4×C47#45011yescharacteristic
208C4×C47#45211yescharacteristic
209C4×C47#49311yescharacteristic
210C4×C47#49611yescharacteristic
211C2×#492C2×C4711yescharacteristic, complemented
212C2×#474C2×C4711yescharacteristic, complemented
213C2×#459C2×C4711yescharacteristic
214#1954C2×C4711yescharacteristic, complemented
215C2×#332C2×C4711yescharacteristic, complemented
216C2×#331C2×C4711yescharacteristic, complemented
217#1277C2×C4711yescharacteristic, complemented
218C2×C47—82no—
219C2×C47—162no—
220C2×C47#166512yes—
221C2×C47#168512yes—
222C2×C47#200011yescharacteristic
223C2×C47#201111yescharacteristic
224C2×C47#201911yescharacteristic
225C22×SD16—22no—
226C22×D8—21no—
227C2×C4⋊Q8C22×C4711yescharacteristic
228C2×#127C22×C4711yescharacteristic
229C2×C4×D4C22×C4711yescharacteristic
230#492—22no—
231#492—22no—
232#474—22no—
233#474—22no—
234#459—22no—
235#459—22no—
236C2×#107—21no—
237C2×C4⋊C8C22×C4711yescharacteristic
238C2×C4⋊C8C22×C4711yescharacteristic
239C2×C4⋊C8C22×C4711yescharacteristic
240C2×#102—21no—
241C2×#102—21no—
242C2×C22⋊C8—22no—
243C2×C4×C8C22×C4711yescharacteristic
244#332—22no—
245#331—22no—
246C47#1026611yescharacteristic, direct product factor, Sylow
247C22×Q8—21no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4—21no—
251C22×D4D4×C4711yescharacteristic
252C23×C4—21no—
253C2×SD16—28no—
254C2×SD16—44no—
255C2×SD16—44no—
256C2×D8—24no—
257C2×D8—42no—
258C2×D8—42no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8D4×C4712yes—
263C4⋊Q8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8D4×C4712yes—
267#127—21no—
268#127—21no—
269#127—21no—
270#127D4×C4712yes—
271C4×D4—21no—
272C4×D4—21no—
273C4×D4—21no—
274C4×D4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4D4×C4711yescharacteristic
278C2×C22⋊C4—21no—
279C2×C42C23×C4711yescharacteristic
280#107—24no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8D4×C4712yes—
286C4⋊C8D4×C4712yes—
287#102—24no—
288#102—24no—
289C22⋊C8—44no—
290C4×C8—21no—
291C4×C8—21no—
292C24—21no—
293C24—41no—
294C2×Q8—22no—
295C2×Q8—41no—
296C2×Q8—42no—
297C2×Q8—42no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—42no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—42no—
314C2×D4—41no—
315C2×D4—82no—
316C2×D4SD16×C4712yescomplemented
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4C2×D4×C4711yescharacteristic
324C22×C4C2×D4×C4711yescharacteristic
325C22×C4#41×C4711yescharacteristic
326SD16—416no—
327D8—48no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—42no—
338C2×C8D8×C4714yescomplemented
339C4⋊C4—21no—
340C4⋊C4—22no—
341C4⋊C4—21no—
342C4⋊C4—22no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C42C2×D4×C4711yescharacteristic
348C42C2×D4×C4711yescharacteristic
349C42C2×D4×C4711yescharacteristic
350C42C2×D4×C4711yescharacteristic
351C23—22no—
352C23—42no—
353C23—41no—
354C23—42no—
355C23—41no—
356C23—42no—
357C23—82no—
358C23—81no—
359C23—81no—
360C23—82no—
361C23#121×C4711yescharacteristic
362Q8—44no—
363Q8—81no—
364Q8—81no—
365D4—22no—
366D4—22no—
367D4—41no—
368D4—42no—
369D4—41no—
370D4—42no—
371D4—44no—
372D4—82no—
373D4—82no—
374D4—81no—
375D4—81no—
376D4—81no—
377D4—81no—
378C2×C4—22no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—82no—
386C2×C4#120×C4711yescharacteristic
387C2×C4#120×C4711yescharacteristic
388C2×C4#120×C4711yescharacteristic
389C2×C4#121×C4711yescharacteristic
390C2×C4#121×C4711yescharacteristic
391C2×C4#127×C4711yescharacteristic
392C2×C4C2×D8×C4712yes—
393C2×C4C2×SD16×C4711yescharacteristic
394C2×C4#135×C4711yescharacteristic
395C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
396C2×C4AGL(1,ℤ/8)×C4712yes—
397C2×C4#137×C4711yescharacteristic
398C8—24no—
399C8—42no—
400C8—42no—
401C8—81no—
402C22—44no—
403C22—42no—
404C22—81no—
405C22—81no—
406C22—82no—
407C22—82no—
408C22—82no—
409C22—82no—
410C22—162no—
411C22—162no—
412C22C47×#39211yescharacteristic
413C22C47×#45912yes—
414C22C47×#46511yescharacteristic
415C22C47×#46811yescharacteristic
416C22C47×#47112yes—
417C4—21no—
418C4—21no—
419C4—81no—
420C4—82no—
421C4C47×#44712yes—
422C4C47×#44811yescharacteristic
423C4C47×#44911yescharacteristic
424C4C47×#45011yescharacteristic
425C4C47×#45211yescharacteristic
426C4C47×#49311yescharacteristic
427C4C47×#49611yescharacteristic
428C2—82no—
429C2—162no—
430C2C47×#166512yes—
431C2C47×#168512yes—
432C2C47×#200011yescharacteristic
433C2C47×#201111yescharacteristic
434C2C47×#201911yescharacteristic
subgroupG/H
center, socleC23×C47#121
commutator, Frattini, cosocleC2×C42C23×C47
prime radicalC2×C47×#459C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#492C2semidirect
2. C2×C47×#474C2semidirect
4. C47×#1954C2semidirect
5. C2×C47×#332C2semidirect
6. C2×C47×#331C2semidirect
7. C47×#1277C2semidirect
98. C2×D4×C47SD16semidirect
120. C2×C8×C47D8semidirect
184. #10266C47direct (N × H)
211. C2×#492C2×C47semidirect
212. C2×#474C2×C47semidirect
214. #1954C2×C47semidirect
215. C2×#332C2×C47semidirect
216. C2×#331C2×C47semidirect
217. #1277C2×C47semidirect
246. C47#10266direct (N × H)
316. C2×D4SD16×C47semidirect
338. C2×C8D8×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4922
C2×C47×#4742
C2×C47×#4592
C47×#19542
C2×C47×#3322
C2×C47×#3312
C47×#12772
#1026647