Finite Group Databasebeta

← C47×#9213 #26048911

Subgroups — C47×#9213 #26048911

Order 12032.

450 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3106C211yesmaximal, characteristic
2C47×#2922C211yesmaximal, characteristic, complemented
3C47×#1525C211yesmaximal, characteristic, complemented
4C47×#1492C211yesmaximal, characteristic, complemented
5C47×#1489C211yesmaximal, characteristic, complemented
6C47×#1299C211yesmaximal, characteristic, complemented
7C47×#1278C211yesmaximal, characteristic, complemented
8C47×#532C2211yescharacteristic
9C4×#41×C47C2211yescharacteristic
10C47×#482—21no—
11C47×#477C411yescharacteristic
12C47×#476C411yescharacteristic
13C47×#460C411yescharacteristic
14C47×#459C411yescharacteristic
15C47×#449—21no—
16C4×SD16×C47—21no—
17C4×D8×C47—21no—
18C47×#433—22no—
19C47×#431—22no—
20C47×#431C2211yescharacteristic
21C47×#424—21no—
22C47×#423C2211yescharacteristic
23C47×#408—21no—
24C4×M16×C47C2211yescharacteristic
25C4×M16×C47C2211yescharacteristic
26C2×C4×C8×C47C2211yescharacteristic
27C47×#329—22no—
28C47×Q8⋊C8—21no—
29C47×D4⋊C8—22no—
30C47×D4⋊C8—21no—
31C2×#41×C47—21no—
32C2×#41×C47D411yescharacteristic
33C2×SD16×C47—21no—
34C2×D8×C47—21no—
35C2×M16×C47—21no—
36C2×M16×C47—21no—
37C2×M16×C47—21no—
38C22×C8×C47—21no—
39C4⋊Q8×C47C2×C411yescharacteristic
40#127×C47C2×C411yescharacteristic
41#124×C47—21no—
42#121×C47—21no—
43#121×C47—21no—
44C4×Q8×C47C2×C411yescharacteristic
45C4×Q8×C47D411yescharacteristic
46C4×D4×C47—21no—
47C4×D4×C47—21no—
48C4×D4×C47—21no—
49C4×D4×C47—21no—
50C4×D4×C47C2×C411yescharacteristic
51C4×D4×C47D411yescharacteristic
52#117×C47—21no—
53#117×C47D411yescharacteristic
54C2×C42×C47—21no—
55C2×C42×C47C2311yescharacteristic
56#107×C47—21no—
57#106×C47—21no—
58C4⋊C8×C47—24no—
59C4⋊C8×C47—21no—
60C4⋊C8×C47—21no—
61C4⋊C8×C47C2×C411yescharacteristic
62C4⋊C8×C47C2×C411yescharacteristic
63#103×C47—21no—
64#102×C47—21no—
65#102×C47—21no—
66#102×C47—21no—
67C22⋊C8×C47—24no—
68C22⋊C8×C47—21no—
69#97×C47—21no—
70#97×C47D412yes—
71C4×C8×C47—21no—
72C4×C8×C47—21no—
73C4×C8×C47—21no—
74C4×C8×C47—21no—
75C4×C8×C47D412yes—
76#41×C47—41no—
77#41×C47—41no—
78#41×C47—81no—
79#41×C47—81no—
80C2×Q8×C47—21no—
81C2×Q8×C47C22⋊C411yescharacteristic
82C2×D4×C47—21no—
83C2×D4×C47—21no—
84C2×D4×C47—21no—
85C2×D4×C47—21no—
86C2×D4×C47—41no—
87C2×D4×C47C22⋊C411yescharacteristic
88C22×C4×C47—21no—
89C22×C4×C47—21no—
90C22×C4×C47—21no—
91C22×C4×C47—41no—
92C22×C4×C47C2×D411yescharacteristic
93C22×C4×C47#4111yescharacteristic
94C22×C4×C47#4111yescharacteristic
95SD16×C47—42no—
96D8×C47—42no—
97M16×C47—22no—
98M16×C47—41no—
99M16×C47—41no—
100M16×C47—41no—
101M16×C47—81no—
102C2×C8×C47—21no—
103C2×C8×C47—21no—
104C2×C8×C47—22no—
105C2×C8×C47—22no—
106C2×C8×C47—41no—
107C2×C8×C47—41no—
108C2×C8×C47—41no—
109C2×C8×C47—41no—
110C4⋊C4×C47—21no—
111C4⋊C4×C47—21no—
112C4⋊C4×C47—21no—
113C4⋊C4×C47—21no—
114C4⋊C4×C47C22⋊C411yescharacteristic
115C4⋊C4×C47C22⋊C411yescharacteristic
116C22⋊C4×C47—21no—
117C22⋊C4×C47—21no—
118C22⋊C4×C47—21no—
119C22⋊C4×C47—41no—
120C22⋊C4×C47—41no—
121C42×C47—21no—
122C42×C47—21no—
123C42×C47—21no—
124C42×C47C22×C411yescharacteristic
125C42×C47C2×D411yescharacteristic
126C42×C47C2×D411yescharacteristic
127C42×C47C2×D411yescharacteristic
128C23×C47—21no—
129C23×C47—41no—
130C23×C47#12311yescharacteristic
131Q8×C47—21no—
132Q8×C47—21no—
133Q8×C47—81no—
134D4×C47—21no—
135D4×C47—21no—
136D4×C47—42no—
137D4×C47—41no—
138D4×C47—41no—
139D4×C47—41no—
140D4×C47—41no—
141D4×C47—81no—
142D4×C47—82no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—42no—
153C2×C4×C47—41no—
154C2×C4×C47—41no—
155C2×C4×C47—41no—
156C2×C4×C47—41no—
157C2×C4×C47—41no—
158C2×C4×C47—81no—
159C2×C4×C47—81no—
160C2×C4×C47C2×C22⋊C411yescharacteristic
161C2×C4×C47C4×D411yescharacteristic
162C2×C4×C47C4×D411yescharacteristic
163C2×C4×C47#12011yescharacteristic
164C2×C4×C47#12111yescharacteristic
165C2×C4×C47#12111yescharacteristic
166C8×C47—42no—
167C8×C47—42no—
168C8×C47—42no—
169C8×C47—41no—
170C8×C47—41no—
171C8×C47—81no—
172#9213C4711yesmaximal, characteristic, direct product factor, Sylow
173C22×C47—21no—
174C22×C47—21no—
175C22×C47—21no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47—41no—
179C22×C47—81no—
180C22×C47—81no—
181C22×C47—81no—
182C22×C47#38611yescharacteristic
183C4×C47—21no—
184C4×C47—21no—
185C4×C47—21no—
186C4×C47—41no—
187C4×C47—41no—
188C4×C47—41no—
189C4×C47—81no—
190C4×C47#42111yescharacteristic
191C4×C47#42111yescharacteristic
192C4×C47#44311yescharacteristic
193C4×C47#44411yescharacteristic
194C4×C47#47111yescharacteristic
195C4×C47#47211yescharacteristic
196#3106C2×C4711yescharacteristic
197#2922C2×C4711yescharacteristic, complemented
198#1525C2×C4711yescharacteristic, complemented
199#1492C2×C4711yescharacteristic, complemented
200#1489C2×C4711yescharacteristic, complemented
201#1299C2×C4711yescharacteristic, complemented
202#1278C2×C4711yescharacteristic, complemented
203C2×C47—41no—
204C2×C47—81no—
205C2×C47—161no—
206C2×C47#187611yescharacteristic
207C2×C47#189711yescharacteristic
208C2×C47#190711yescharacteristic
209#532C22×C4711yescharacteristic
210C4×#41C22×C4711yescharacteristic
211#482—21no—
212#477C4×C4711yescharacteristic
213#476C4×C4711yescharacteristic
214#460C4×C4711yescharacteristic
215#459C4×C4711yescharacteristic
216#449—21no—
217C4×SD16—21no—
218C4×D8—21no—
219#433—22no—
220#431—22no—
221#431C22×C4711yescharacteristic
222#424—21no—
223#423C22×C4711yescharacteristic
224#408—21no—
225C4×M16C22×C4711yescharacteristic
226C4×M16C22×C4711yescharacteristic
227C2×C4×C8C22×C4711yescharacteristic
228#329—22no—
229Q8⋊C8—21no—
230D4⋊C8—21no—
231D4⋊C8—22no—
232C47#921311yescharacteristic, direct product factor, Sylow
233C2×#41—21no—
234C2×#41D4×C4711yescharacteristic
235C2×SD16—21no—
236C2×D8—21no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—21no—
240C22×C8—21no—
241C4⋊Q8C2×C4×C4711yescharacteristic
242#127C2×C4×C4711yescharacteristic
243#124—21no—
244#121—21no—
245#121—21no—
246C4×Q8C2×C4×C4711yescharacteristic
247C4×Q8D4×C4711yescharacteristic
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4C2×C4×C4711yescharacteristic
253C4×D4D4×C4711yescharacteristic
254#117—21no—
255#117D4×C4711yescharacteristic
256C2×C42—21no—
257C2×C42C23×C4711yescharacteristic
258#107—21no—
259#106—21no—
260C4⋊C8—24no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8C2×C4×C4711yescharacteristic
264C4⋊C8C2×C4×C4711yescharacteristic
265#103—21no—
266#102—21no—
267#102—21no—
268#102—21no—
269C22⋊C8—24no—
270C22⋊C8—21no—
271#97—21no—
272#97D4×C4712yes—
273C4×C8—21no—
274C4×C8—21no—
275C4×C8—21no—
276C4×C8—21no—
277C4×C8D4×C4712yes—
278#41—41no—
279#41—41no—
280#41—81no—
281#41—81no—
282C2×Q8—21no—
283C2×Q8C22⋊C4×C4711yescharacteristic
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4C22⋊C4×C4711yescharacteristic
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—41no—
294C22×C4C2×D4×C4711yescharacteristic
295C22×C4#41×C4711yescharacteristic
296C22×C4#41×C4711yescharacteristic
297SD16—42no—
298D8—42no—
299M16—22no—
300M16—41no—
301M16—41no—
302M16—41no—
303M16—81no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4C22⋊C4×C4711yescharacteristic
317C4⋊C4C22⋊C4×C4711yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C42—21no—
324C42—21no—
325C42—21no—
326C42C22×C4×C4711yescharacteristic
327C42C2×D4×C4711yescharacteristic
328C42C2×D4×C4711yescharacteristic
329C42C2×D4×C4711yescharacteristic
330C23—21no—
331C23—41no—
332C23#123×C4711yescharacteristic
333Q8—21no—
334Q8—21no—
335Q8—81no—
336D4—21no—
337D4—21no—
338D4—42no—
339D4—41no—
340D4—41no—
341D4—41no—
342D4—41no—
343D4—81no—
344D4—82no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4C2×C22⋊C4×C4711yescharacteristic
363C2×C4C4×D4×C4711yescharacteristic
364C2×C4C4×D4×C4711yescharacteristic
365C2×C4#120×C4711yescharacteristic
366C2×C4#121×C4711yescharacteristic
367C2×C4#121×C4711yescharacteristic
368C8—42no—
369C8—42no—
370C8—42no—
371C8—41no—
372C8—41no—
373C8—81no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22C47×#38611yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—81no—
391C4C47×#42111yescharacteristic
392C4C47×#42111yescharacteristic
393C4C47×#44311yescharacteristic
394C4C47×#44411yescharacteristic
395C4C47×#47111yescharacteristic
396C4C47×#47211yescharacteristic
397C2—41no—
398C2—81no—
399C2—161no—
400C2C47×#187611yescharacteristic
401C2C47×#189711yescharacteristic
402C2C47×#190711yescharacteristic
subgroupG/H
centerC2×C4×C47#121
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
socleC22×C47#386
prime radicalC47×#3106C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2922C2semidirect
3. C47×#1525C2semidirect
4. C47×#1492C2semidirect
5. C47×#1489C2semidirect
6. C47×#1299C2semidirect
7. C47×#1278C2semidirect
172. #9213C47direct (N × H)
197. #2922C2×C47semidirect
198. #1525C2×C47semidirect
199. #1492C2×C47semidirect
200. #1489C2×C47semidirect
201. #1299C2×C47semidirect
202. #1278C2×C47semidirect
232. C47#9213direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31062
C47×#29222
C47×#15252
C47×#14922
C47×#14892
C47×#12992
C47×#12782
#921347