Finite Group Databasebeta

← C47×#9295 #26048993

Subgroups — C47×#9295 #26048993

Order 12032.

594 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3208C211yesmaximal, characteristic
2C47×#2328C211yesmaximal, characteristic
3C47×#1995C211yesmaximal, characteristic, complemented
4C47×#1545C211yesmaximal, characteristic
5C47×#1518C211yesmaximal, characteristic, complemented
6C47×#1286C211yesmaximal, characteristic, complemented
7C47×#1274C211yesmaximal, characteristic, complemented
8C47×#533C2211yescharacteristic
9C2×#127×C47C2211yescharacteristic
10C2×C4×D4×C47—21no—
11C47×#492C412yescomplemented
12C47×#486C412yescomplemented
13C47×#460—22no—
14C47×#450—22no—
15C47×#431C2211yescharacteristic
16C47×#431C2211yescharacteristic
17C47×#423C2211yescharacteristic
18C47×#390—21no—
19C47×#386—22no—
20C47×#386—22no—
21C47×#382C2211yescharacteristic
22C47×#376C2211yescharacteristic
23C47×#339—21no—
24C47×#339—21no—
25C47×#331—22no—
26C47×#328—22no—
27C22×D4×C47—21no—
28C22×D4×C47—21no—
29C22×D4×C47D412yes—
30C23×C4×C47—22no—
31C2×SD16×C47—24no—
32C2×M16×C47—21no—
33C4⋊Q8×C47C2×C411yescharacteristic, complemented
34C4⋊Q8×C47C2×C411yescharacteristic, complemented
35#127×C47—21no—
36#127×C47—21no—
37#127×C47C2×C412yes—
38#127×C47D412yes—
39#125×C47—21no—
40C22⋊Q8×C47—21no—
41C22⋊Q8×C47—21no—
42C4×Q8×C47—21no—
43C4×Q8×C47—21no—
44C4×D4×C47—42no—
45C4×D4×C47—42no—
46#117×C47—21no—
47C2×C4⋊C4×C47—21no—
48C2×C22⋊C4×C47—22no—
49C2×C22⋊C4×C47—22no—
50C2×C22⋊C4×C47—22no—
51C2×C42×C47D411yescharacteristic
52C2×C42×C47D411yescharacteristic
53C2×C42×C47C2311yescharacteristic
54C4⋊C8×C47—21no—
55C4⋊C8×C47—21no—
56C4⋊C8×C47—21no—
57C4⋊C8×C47—21no—
58#102×C47—24no—
59C22⋊C8×C47—21no—
60C22⋊C8×C47—21no—
61C4×C8×C47—21no—
62C4×C8×C47C2×C412yescomplemented
63#95×C47—21no—
64#95×C47—21no—
65#95×C47—21no—
66#95×C47D412yes—
67C24×C47—22no—
68C2×Q8×C47—21no—
69C2×Q8×C47—21no—
70C2×D4×C47—22no—
71C2×D4×C47—22no—
72C2×D4×C47—22no—
73C2×D4×C47—22no—
74C2×D4×C47—22no—
75C2×D4×C47—41no—
76C2×D4×C47—41no—
77C2×D4×C47—41no—
78C2×D4×C47—41no—
79C2×D4×C47—82no—
80C2×D4×C47—82no—
81C2×D4×C47C22⋊C414yes—
82C22×C4×C47—21no—
83C22×C4×C47—21no—
84C22×C4×C47—22no—
85C22×C4×C47—44no—
86C22×C4×C47—82no—
87C22×C4×C47—82no—
88C22×C4×C47C2×D411yescharacteristic
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47C2×D411yescharacteristic
91SD16×C47—84no—
92M16×C47—41no—
93M16×C47—41no—
94C2×C8×C47—22no—
95C2×C8×C47—41no—
96C2×C8×C47—41no—
97C4⋊C4×C47—21no—
98C4⋊C4×C47—21no—
99C4⋊C4×C47—21no—
100C4⋊C4×C47—21no—
101C4⋊C4×C47—41no—
102C4⋊C4×C47—41no—
103C4⋊C4×C47—41no—
104C4⋊C4×C47—41no—
105C22⋊C4×C47—44no—
106C22⋊C4×C47—41no—
107C22⋊C4×C47—82no—
108C22⋊C4×C47—82no—
109C42×C47—21no—
110C42×C47—21no—
111C42×C47—21no—
112C42×C47—41no—
113C42×C47SD1612yescomplemented
114C42×C47C22×C411yescharacteristic
115C42×C47C2×D411yescharacteristic
116C42×C47#4111yescharacteristic
117C42×C47#4111yescharacteristic
118C23×C47—24no—
119C23×C47—42no—
120C23×C47—42no—
121C23×C47—42no—
122C23×C47—42no—
123C23×C47—42no—
124C23×C47—42no—
125C23×C47#12011yescharacteristic
126Q8×C47—42no—
127Q8×C47—81no—
128D4×C47—44no—
129D4×C47—42no—
130D4×C47—42no—
131D4×C47—42no—
132D4×C47—42no—
133D4×C47—82no—
134D4×C47—82no—
135D4×C47—82no—
136C2×C4×C47—22no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—41no—
141C2×C4×C47—41no—
142C2×C4×C47—41no—
143C2×C4×C47—42no—
144C2×C4×C47—42no—
145C2×C4×C47—41no—
146C2×C4×C47—41no—
147C2×C4×C47—42no—
148C2×C4×C47—41no—
149C2×C4×C47—88no—
150C2×C4×C47C2×C22⋊C411yescharacteristic
151C2×C4×C47C4×D411yescharacteristic
152C2×C4×C47C4×D411yescharacteristic
153C2×C4×C47#12111yescharacteristic
154C2×C4×C47#12111yescharacteristic
155C2×C4×C47#12311yescharacteristic
156C2×C4×C47C2×SD1611yescharacteristic
157C2×C4×C47#13511yescharacteristic
158C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C47#13711yescharacteristic
160C8×C47—42no—
161C8×C47—81no—
162C8×C47—81no—
163#9295C4711yesmaximal, characteristic, direct product factor, Sylow
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—44no—
167C22×C47—44no—
168C22×C47—44no—
169C22×C47—82no—
170C22×C47—82no—
171C22×C47—82no—
172C22×C47—82no—
173C22×C47#38611yescharacteristic
174C22×C47#45011yescharacteristic
175C22×C47#45211yescharacteristic
176C4×C47—21no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—42no—
181C4×C47—81no—
182C4×C47—82no—
183C4×C47—81no—
184C4×C47—81no—
185C4×C47C4×SD1611yescharacteristic
186C4×C47#44011yescharacteristic
187C4×C47#46111yescharacteristic
188C4×C47#46311yescharacteristic
189#3208C2×C4711yescharacteristic
190#2328C2×C4711yescharacteristic
191#1995C2×C4711yescharacteristic, complemented
192#1545C2×C4711yescharacteristic
193#1518C2×C4711yescharacteristic, complemented
194#1286C2×C4711yescharacteristic, complemented
195#1274C2×C4711yescharacteristic, complemented
196C2×C47—21no—
197C2×C47—21no—
198C2×C47—84no—
199C2×C47#187711yescharacteristic
200C2×C47#190411yescharacteristic
201C2×C47#191111yescharacteristic
202#533C22×C4711yescharacteristic
203C2×#127C22×C4711yescharacteristic
204C2×C4×D4—21no—
205#492C4×C4712yescomplemented
206#486C4×C4712yescomplemented
207#460—22no—
208#450—22no—
209#431C22×C4711yescharacteristic
210#431C22×C4711yescharacteristic
211#423C22×C4711yescharacteristic
212#390—21no—
213#386—22no—
214#386—22no—
215#382C22×C4711yescharacteristic
216#376C22×C4711yescharacteristic
217#339—21no—
218#339—21no—
219#331—22no—
220#328—22no—
221C47#929511yescharacteristic, direct product factor, Sylow
222C22×D4—21no—
223C22×D4—21no—
224C22×D4D4×C4712yes—
225C23×C4—22no—
226C2×SD16—24no—
227C2×M16—21no—
228C4⋊Q8C2×C4×C4711yescharacteristic, complemented
229C4⋊Q8C2×C4×C4711yescharacteristic, complemented
230#127—21no—
231#127—21no—
232#127C2×C4×C4712yes—
233#127D4×C4712yes—
234#125—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×D4—42no—
240C4×D4—42no—
241#117—21no—
242C2×C4⋊C4—21no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C42D4×C4711yescharacteristic
247C2×C42D4×C4711yescharacteristic
248C2×C42C23×C4711yescharacteristic
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253#102—24no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C4×C8—21no—
257C4×C8C2×C4×C4712yescomplemented
258#95—21no—
259#95—21no—
260#95—21no—
261#95D4×C4712yes—
262C24—22no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—82no—
275C2×D4—82no—
276C2×D4C22⋊C4×C4714yes—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—44no—
281C22×C4—82no—
282C22×C4—82no—
283C22×C4C2×D4×C4711yescharacteristic
284C22×C4C2×D4×C4711yescharacteristic
285C22×C4C2×D4×C4711yescharacteristic
286SD16—84no—
287M16—41no—
288M16—41no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—41no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C22⋊C4—44no—
301C22⋊C4—41no—
302C22⋊C4—82no—
303C22⋊C4—82no—
304C42—21no—
305C42—21no—
306C42—21no—
307C42—41no—
308C42SD16×C4712yescomplemented
309C42C22×C4×C4711yescharacteristic
310C42C2×D4×C4711yescharacteristic
311C42#41×C4711yescharacteristic
312C42#41×C4711yescharacteristic
313C23—24no—
314C23—42no—
315C23—42no—
316C23—42no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23#120×C4711yescharacteristic
321Q8—42no—
322Q8—81no—
323D4—44no—
324D4—42no—
325D4—42no—
326D4—42no—
327D4—42no—
328D4—82no—
329D4—82no—
330D4—82no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—88no—
345C2×C4C2×C22⋊C4×C4711yescharacteristic
346C2×C4C4×D4×C4711yescharacteristic
347C2×C4C4×D4×C4711yescharacteristic
348C2×C4#121×C4711yescharacteristic
349C2×C4#121×C4711yescharacteristic
350C2×C4#123×C4711yescharacteristic
351C2×C4C2×SD16×C4711yescharacteristic
352C2×C4#135×C4711yescharacteristic
353C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
354C2×C4#137×C4711yescharacteristic
355C8—42no—
356C8—81no—
357C8—81no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22—44no—
362C22—44no—
363C22—82no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22C47×#38611yescharacteristic
368C22C47×#45011yescharacteristic
369C22C47×#45211yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—82no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4C4×SD16×C4711yescharacteristic
380C4C47×#44011yescharacteristic
381C4C47×#46111yescharacteristic
382C4C47×#46311yescharacteristic
383C2—21no—
384C2—21no—
385C2—84no—
386C2C47×#187711yescharacteristic
387C2C47×#190411yescharacteristic
388C2C47×#191111yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×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
3. C47×#1995C2semidirect
5. C47×#1518C2semidirect
6. C47×#1286C2semidirect
7. C47×#1274C2semidirect
11. C47×#492C4semidirect
12. C47×#486C4semidirect
33. C4⋊Q8×C47C2×C4semidirect
34. C4⋊Q8×C47C2×C4semidirect
62. C4×C8×C47C2×C4semidirect
113. C42×C47SD16semidirect
163. #9295C47direct (N × H)
191. #1995C2×C47semidirect
193. #1518C2×C47semidirect
194. #1286C2×C47semidirect
195. #1274C2×C47semidirect
205. #492C4×C47semidirect
206. #486C4×C47semidirect
221. C47#9295direct (N × H)
228. C4⋊Q8C2×C4×C47semidirect
229. C4⋊Q8C2×C4×C47semidirect
257. C4×C8C2×C4×C47semidirect
308. C42SD16×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#32082
C47×#23282
C47×#19952
C47×#15452
C47×#15182
C47×#12862
C47×#12742
#929547