Finite Group Databasebeta

← C47×#34943 #26074641

Subgroups — C47×#34943 #26074641

Order 12032.

2036 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2572C214yesmaximal, complemented
2C47×#2571C211yesmaximal, characteristic, complemented
3C47×#2563C212yesmaximal, complemented
4C47×#2537C211yesmaximal, characteristic
5C47×#2495C214yesmaximal, complemented
6C47×#2420C214yesmaximal, complemented
7C47×#2398C214yesmaximal, complemented
8C4×C4⋊Q8×C47C211yesmaximal, characteristic, complemented
9C4×#121×C47C214yesmaximal, complemented
10C47×#2283C214yesmaximal, complemented
11C42×D4×C47C212yesmaximal, complemented
12C2×C4⋊Q8×C47C2211yescharacteristic
13C2×#121×C47C2214yes—
14C2×C4×Q8×C47C2212yes—
15C2×C4×D4×C47C2212yes—
16C2×C4×D4×C47C2212yes—
17C2×C4×D4×C47C2212yes—
18C2×C4×D4×C47C2214yes—
19C22×C42×C47C2214yes—
20C47×#400C2214yes—
21C47×#400C2214yes—
22C47×#397C2218yes—
23C47×#394C2214yes—
24C47×#394C2214yes—
25C47×#393C2218yes—
26C47×#391C2212yes—
27C47×#390C2214yes—
28C47×#389C2214yes—
29C47×#389C2214yes—
30C47×#388C2218yes—
31C47×#386C2218yes—
32C47×#384C2211yescharacteristic
33C47×#383C2218yes—
34C47×#382C2214yes—
35C47×#382C2214yes—
36C47×#381C2218yes—
37C47×#380C2214yes—
38C47×#380C2214yes—
39C47×#380C2214yes—
40C4×C4⋊C4×C47C2212yes—
41C4×C4⋊C4×C47C2212yes—
42C4×C4⋊C4×C47C2212yes—
43C4×C4⋊C4×C47C2214yes—
44C4×C22⋊C4×C47C2214yes—
45C4×C22⋊C4×C47C2214yes—
46C4×C22⋊C4×C47C2214yes—
47C4×C22⋊C4×C47C2218yes—
48C47×#376C2214yes—
49C43×C47C2211yescharacteristic
50C22×Q8×C47C2312yes—
51C22×D4×C47C2314yes—
52C22×D4×C47C2312yes—
53C23×C4×C47C2314yes—
54C23×C4×C47C2314yes—
55C23×C4×C47C2314yes—
56C4⋊Q8×C47—24no—
57#121×C47—216no—
58C4×Q8×C47—44no—
59C4×D4×C47—28no—
60C4×D4×C47—28no—
61C4×D4×C47—28no—
62C4×D4×C47—48no—
63C2×C4⋊C4×C47C2312yes—
64C2×C4⋊C4×C47C2312yes—
65C2×C4⋊C4×C47C2312yes—
66C2×C4⋊C4×C47C2314yes—
67C2×C4⋊C4×C47C2314yes—
68C2×C4⋊C4×C47C2314yes—
69C2×C4⋊C4×C47C2312yes—
70C2×C4⋊C4×C47C2314yes—
71C2×C22⋊C4×C47C2314yes—
72C2×C22⋊C4×C47C2314yes—
73C2×C22⋊C4×C47C2314yes—
74C2×C22⋊C4×C47C2318yes—
75C2×C22⋊C4×C47C2318yes—
76C2×C22⋊C4×C47C2318yes—
77C2×C42×C47—216no—
78C2×C42×C47C2314yes—
79C2×C42×C47C2314yes—
80C2×C42×C47C2312yes—
81C2×C42×C47C2314yes—
82C2×C42×C47C2314yes—
83C2×C42×C47C2311yescharacteristic
84C2×C42×C47C2311yescharacteristic
85C2×C42×C47C2311yescharacteristic
86C2×C42×C47C2312yes—
87#95×C47C2314yes—
88#95×C47C2318yes—
89#95×C47C2314yes—
90#95×C47C2314yes—
91#95×C47C2314yes—
92#95×C47C2314yes—
93#95×C47C2318yes—
94#95×C47C2318yes—
95#95×C47C2318yes—
96C24×C47C2414yes—
97C2×Q8×C47—24no—
98C2×Q8×C47—42no—
99C2×Q8×C47—42no—
100C2×D4×C47—216no—
101C2×D4×C47—24no—
102C2×D4×C47—24no—
103C2×D4×C47—44no—
104C2×D4×C47#4118yes—
105C22×C4×C47—28no—
106C22×C4×C47—28no—
107C22×C4×C47—28no—
108C22×C4×C47—28no—
109C22×C4×C47—28no—
110C22×C4×C47—28no—
111C22×C4×C47—28no—
112C22×C4×C47—28no—
113C22×C4×C47—44no—
114C22×C4×C47C2411yescharacteristic
115C22×C4×C47C2414yes—
116C22×C4×C47C2414yes—
117C22×C4×C47C2414yes—
118C22×C4×C47C2414yes—
119C22×C4×C47C2414yes—
120C22×C4×C47C2412yes—
121C22×C4×C47C2411yescharacteristic
122C22×C4×C47C2412yes—
123C22×C4×C47C2411yescharacteristic
124C4⋊C4×C47—24no—
125C4⋊C4×C47—24no—
126C4⋊C4×C47—24no—
127C4⋊C4×C47—28no—
128C4⋊C4×C47—28no—
129C4⋊C4×C47—44no—
130C4⋊C4×C47—42no—
131C4⋊C4×C47—44no—
132C22⋊C4×C47—28no—
133C22⋊C4×C47—216no—
134C22⋊C4×C47—28no—
135C22⋊C4×C47—28no—
136C22⋊C4×C47—48no—
137C22⋊C4×C47—48no—
138C42×C47—28no—
139C42×C47—28no—
140C42×C47—28no—
141C42×C47—24no—
142C42×C47—28no—
143C42×C47—22no—
144C42×C47—41no—
145C42×C47#4118yes—
146C42×C47#4114yes—
147C23×C47—24no—
148C23×C47—24no—
149C23×C47—24no—
150C23×C47—24no—
151C23×C47—24no—
152C23×C47—24no—
153C23×C47C2×#4118yes—
154C23×C47C2511yescharacteristic
155Q8×C47—48no—
156D4×C47—216no—
157D4×C47—416no—
158C2×C4×C47—22no—
159C2×C4×C47—21no—
160C2×C4×C47—22no—
161C2×C4×C47—21no—
162C2×C4×C47—24no—
163C2×C4×C47—24no—
164C2×C4×C47—24no—
165C2×C4×C47—22no—
166C2×C4×C47—24no—
167C2×C4×C47—24no—
168C2×C4×C47—24no—
169C2×C4×C47—24no—
170C2×C4×C47—28no—
171C2×C4×C47—24no—
172C2×C4×C47—24no—
173C2×C4×C47—21no—
174C2×C4×C47—24no—
175C2×C4×C47—24no—
176C2×C4×C47—24no—
177C2×C4×C47—24no—
178C2×C4×C47—416no—
179C2×C4×C47—416no—
180C2×C4×C47—416no—
181C2×C4×C47C2×#4114yes—
182C2×C4×C47C2×#4112yes—
183C2×C4×C47C2×#4114yes—
184C2×C4×C47C2×#4114yes—
185C2×C4×C47C2×#4114yes—
186C2×C4×C47C2×#4114yes—
187C2×C4×C47H(5,𝔽2)12yes—
188#34943C4711yesmaximal, characteristic, direct product factor, Sylow
189C22×C47—28no—
190C22×C47—28no—
191C22×C47—28no—
192C22×C47—44no—
193C22×C47—44no—
194C22×C47—44no—
195C22×C47—44no—
196C22×C47C22×#4111yescharacteristic
197C22×C47C22×#4112yes—
198C22×C47C22×#4112yes—
199C22×C47C2×H(5,𝔽2)11yescharacteristic
200C22×C47#58511yescharacteristic
201C4×C47—22no—
202C4×C47—24no—
203C4×C47—44no—
204C4×C47—44no—
205C4×C47—44no—
206C4×C47—44no—
207C4×C47—41no—
208C4×C47—44no—
209C4×C47#52918yes—
210C4×C47#55514yes—
211#2572C2×C4714yescomplemented
212#2571C2×C4711yescharacteristic, complemented
213#2563C2×C4712yescomplemented
214#2537C2×C4711yescharacteristic
215#2495C2×C4714yescomplemented
216#2420C2×C4714yescomplemented
217#2398C2×C4714yescomplemented
218C4×C4⋊Q8C2×C4711yescharacteristic, complemented
219C4×#121C2×C4714yescomplemented
220#2283C2×C4714yescomplemented
221C42×D4C2×C4712yescomplemented
222C2×C47—48no—
223C2×C47C2×#52912yes—
224C2×C47#346011yescharacteristic
225C2×C47C2×#55511yescharacteristic
226C2×C47#347512yes—
227C2×C47#348111yescharacteristic
228C2×C4⋊Q8C22×C4711yescharacteristic
229C2×#121C22×C4714yes—
230C2×C4×Q8C22×C4712yes—
231C2×C4×D4C22×C4712yes—
232C2×C4×D4C22×C4712yes—
233C2×C4×D4C22×C4712yes—
234C2×C4×D4C22×C4714yes—
235C22×C42C22×C4714yes—
236#400C22×C4714yes—
237#400C22×C4714yes—
238#397C22×C4718yes—
239#394C22×C4714yes—
240#394C22×C4714yes—
241#393C22×C4718yes—
242#391C22×C4712yes—
243#390C22×C4714yes—
244#389C22×C4714yes—
245#389C22×C4714yes—
246#388C22×C4718yes—
247#386C22×C4718yes—
248#384C22×C4711yescharacteristic
249#383C22×C4718yes—
250#382C22×C4714yes—
251#382C22×C4714yes—
252#381C22×C4718yes—
253#380C22×C4714yes—
254#380C22×C4714yes—
255#380C22×C4714yes—
256C4×C4⋊C4C22×C4714yes—
257C4×C4⋊C4C22×C4712yes—
258C4×C4⋊C4C22×C4712yes—
259C4×C4⋊C4C22×C4712yes—
260C4×C22⋊C4C22×C4714yes—
261C4×C22⋊C4C22×C4714yes—
262C4×C22⋊C4C22×C4718yes—
263C4×C22⋊C4C22×C4714yes—
264#376C22×C4714yes—
265C43C22×C4711yescharacteristic
266C47#3494311yescharacteristic, direct product factor, Sylow
267C22×Q8C23×C4712yes—
268C22×D4C23×C4714yes—
269C22×D4C23×C4712yes—
270C23×C4C23×C4714yes—
271C23×C4C23×C4714yes—
272C23×C4C23×C4714yes—
273C4⋊Q8—24no—
274#121—216no—
275C4×Q8—44no—
276C4×D4—28no—
277C4×D4—28no—
278C4×D4—28no—
279C4×D4—48no—
280C2×C4⋊C4C23×C4712yes—
281C2×C4⋊C4C23×C4712yes—
282C2×C4⋊C4C23×C4712yes—
283C2×C4⋊C4C23×C4714yes—
284C2×C4⋊C4C23×C4714yes—
285C2×C4⋊C4C23×C4714yes—
286C2×C4⋊C4C23×C4712yes—
287C2×C4⋊C4C23×C4714yes—
288C2×C22⋊C4C23×C4714yes—
289C2×C22⋊C4C23×C4714yes—
290C2×C22⋊C4C23×C4714yes—
291C2×C22⋊C4C23×C4718yes—
292C2×C22⋊C4C23×C4718yes—
293C2×C22⋊C4C23×C4718yes—
294C2×C42—216no—
295C2×C42C23×C4714yes—
296C2×C42C23×C4712yes—
297C2×C42C23×C4711yescharacteristic
298C2×C42C23×C4714yes—
299C2×C42C23×C4714yes—
300C2×C42C23×C4714yes—
301C2×C42C23×C4711yescharacteristic
302C2×C42C23×C4711yescharacteristic
303C2×C42C23×C4712yes—
304#95C23×C4714yes—
305#95C23×C4718yes—
306#95C23×C4714yes—
307#95C23×C4714yes—
308#95C23×C4714yes—
309#95C23×C4714yes—
310#95C23×C4718yes—
311#95C23×C4718yes—
312#95C23×C4718yes—
313C24C24×C4714yes—
314C2×Q8—24no—
315C2×Q8—42no—
316C2×Q8—42no—
317C2×D4—216no—
318C2×D4—24no—
319C2×D4—24no—
320C2×D4—44no—
321C2×D4#41×C4718yes—
322C22×C4—28no—
323C22×C4—28no—
324C22×C4—28no—
325C22×C4—28no—
326C22×C4—28no—
327C22×C4—28no—
328C22×C4—28no—
329C22×C4—28no—
330C22×C4—44no—
331C22×C4C24×C4714yes—
332C22×C4C24×C4714yes—
333C22×C4C24×C4714yes—
334C22×C4C24×C4714yes—
335C22×C4C24×C4714yes—
336C22×C4C24×C4711yescharacteristic
337C22×C4C24×C4712yes—
338C22×C4C24×C4711yescharacteristic
339C22×C4C24×C4712yes—
340C22×C4C24×C4711yescharacteristic
341C4⋊C4—24no—
342C4⋊C4—24no—
343C4⋊C4—24no—
344C4⋊C4—28no—
345C4⋊C4—28no—
346C4⋊C4—44no—
347C4⋊C4—42no—
348C4⋊C4—44no—
349C22⋊C4—28no—
350C22⋊C4—216no—
351C22⋊C4—28no—
352C22⋊C4—28no—
353C22⋊C4—48no—
354C22⋊C4—48no—
355C42—28no—
356C42—28no—
357C42—28no—
358C42—24no—
359C42—28no—
360C42—22no—
361C42—41no—
362C42#41×C4718yes—
363C42#41×C4714yes—
364C23—24no—
365C23—24no—
366C23—24no—
367C23—24no—
368C23—24no—
369C23—24no—
370C23C2×#41×C4718yes—
371C23C25×C4711yescharacteristic
372Q8—48no—
373D4—216no—
374D4—416no—
375C2×C4—22no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—21no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—22no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—28no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—21no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—416no—
396C2×C4—416no—
397C2×C4—416no—
398C2×C4C2×#41×C4714yes—
399C2×C4C2×#41×C4712yes—
400C2×C4C2×#41×C4714yes—
401C2×C4C2×#41×C4714yes—
402C2×C4C2×#41×C4714yes—
403C2×C4C2×#41×C4714yes—
404C2×C4H(5,𝔽2)×C4712yes—
405C22—28no—
406C22—28no—
407C22—28no—
408C22—44no—
409C22—44no—
410C22—44no—
411C22—44no—
412C22C22×#41×C4711yescharacteristic
413C22C22×#41×C4712yes—
414C22C22×#41×C4712yes—
415C22C2×H(5,𝔽2)×C4711yescharacteristic
416C22C47×#58511yescharacteristic
417C4—22no—
418C4—24no—
419C4—44no—
420C4—44no—
421C4—44no—
422C4—44no—
423C4—44no—
424C4—41no—
425C4C47×#52918yes—
426C4C47×#55514yes—
427C2—48no—
428C2C2×C47×#52912yes—
429C2C47×#346011yescharacteristic
430C2C2×C47×#55511yescharacteristic
431C2C47×#347512yes—
432C2C47×#348111yescharacteristic
subgroupG/H
centerC22×C4×C47C24
commutator, Frattini, cosocleC23C25×C47
socleC23×C47C25
prime radicalC47×#2537C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#2572C2semidirect
2. C47×#2571C2semidirect
3. C47×#2563C2semidirect
5. C47×#2495C2semidirect
6. C47×#2420C2semidirect
7. C47×#2398C2semidirect
8. C4×C4⋊Q8×C47C2semidirect
9. C4×#121×C47C2semidirect
10. C47×#2283C2semidirect
11. C42×D4×C47C2semidirect
188. #34943C47direct (N × H)
211. #2572C2×C47semidirect
212. #2571C2×C47semidirect
213. #2563C2×C47semidirect
215. #2495C2×C47semidirect
216. #2420C2×C47semidirect
217. #2398C2×C47semidirect
218. C4×C4⋊Q8C2×C47semidirect
219. C4×#121C2×C47semidirect
220. #2283C2×C47semidirect
221. C42×D4C2×C47semidirect
266. C47#34943direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#25722
C47×#25712
C47×#25632
C47×#25372
C47×#24952
C47×#24202
C47×#23982
C4×C4⋊Q8×C472
C4×#121×C472
C47×#22832
C42×D4×C472
#3494347