Finite Group Databasebeta

← C47×#33693 #26073391

Subgroups — C47×#33693 #26073391

Order 12032.

512 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3177C211yesmaximal, characteristic, complemented
2C47×#2955C211yesmaximal, characteristic
3C47×#2239C212yesmaximal, complemented
4C47×#2231C212yesmaximal, complemented
5C47×#2214C212yesmaximal, complemented
6C47×#2191C212yesmaximal
7C47×#2180C214yesmaximal, complemented
8C47×#2166C211yesmaximal, characteristic, complemented
9C47×#575C2211yescharacteristic
10C2×#131×C47—21no—
11C47×#541—21no—
12C47×#510C2214yes—
13C47×#499C2211yescharacteristic, complemented
14C47×#494C2211yescharacteristic, complemented
15C47×#491—21no—
16C47×#470C2212yes—
17C47×#467—21no—
18C47×#444—21no—
19C47×#444C2212yes—
20C47×#443—21no—
21C47×#443C2212yes—
22C47×#441C2212yescomplemented
23C4×Q16×C47—21no—
24C47×#430C2211yescharacteristic
25C47×#421—21no—
26C47×#405C2211yescharacteristic
27C47×#365C2214yescomplemented
28C47×#364C2212yescomplemented
29C47×#362C2214yescomplemented
30C47×#360C2214yes—
31C47×#349C2212yes—
32C47×#347C2212yescomplemented
33C2×#41×C47—21no—
34#137×C47—22no—
35AGL(1,ℤ/8)×C47—22no—
36#135×C47—21no—
37#135×C47C2312yes—
38C2×Q16×C47—21no—
39C2×Q16×C47C2312yes—
40#131×C47—22no—
41#131×C47—22no—
42#131×C47—41no—
43#131×C47—41no—
44C2×M16×C47—21no—
45C2×M16×C47—41no—
46C2×M16×C47C2311yescharacteristic
47C22×C8×C47—41no—
48C22×C8×C47D411yescharacteristic
49C4⋊Q8×C47—21no—
50#126×C47—42no—
51#125×C47—21no—
52#125×C47—42no—
53C22⋊Q8×C47—22no—
54C4×Q8×C47—22no—
55#117×C47D411yescharacteristic
56Q32×C47—24no—
57SD32×C47—24no—
58M32×C47C2314yes—
59#108×C47—21no—
60#108×C47C2312yes—
61#107×C47—21no—
62#106×C47C2312yes—
63#104×C47—22no—
64#104×C47—22no—
65#103×C47—22no—
66#103×C47—22no—
67#97×C47D411yescharacteristic
68#97×C47C2311yescharacteristic
69C4×C8×C47D411yescharacteristic
70C4×C8×C47C2311yescharacteristic
71#41×C47—22no—
72#41×C47—22no—
73#41×C47—41no—
74#41×C47—41no—
75C2×Q8×C47—21no—
76C2×Q8×C47—22no—
77C2×D4×C47—21no—
78C2×D4×C47—41no—
79C22×C4×C47—41no—
80C22×C4×C47C2×D411yescharacteristic
81Q16×C47—21no—
82Q16×C47—24no—
83Q16×C47—41no—
84Q16×C47—41no—
85Q16×C47#4112yes—
86SD16×C47—22no—
87SD16×C47—22no—
88D8×C47—21no—
89D8×C47#4112yes—
90M16×C47—22no—
91M16×C47—22no—
92M16×C47—42no—
93M16×C47—41no—
94M16×C47—42no—
95C2×C8×C47—21no—
96C2×C8×C47—21no—
97C2×C8×C47—42no—
98C2×C8×C47—41no—
99C2×C8×C47—42no—
100C2×C8×C47C2×D411yescharacteristic
101C2×C8×C47C2×D411yescharacteristic
102C2×C8×C47C2×D411yescharacteristic
103C2×C8×C47C2411yescharacteristic
104C4⋊C4×C47—21no—
105C4⋊C4×C47—22no—
106C4⋊C4×C47—42no—
107C4⋊C4×C47—42no—
108C4⋊C4×C47—42no—
109C4⋊C4×C47—42no—
110C22⋊C4×C47—21no—
111C22⋊C4×C47—42no—
112C42×C47—42no—
113C42×C47C2×D411yescharacteristic
114C42×C47C2×D411yescharacteristic
115C16×C47—24no—
116C23×C47—41no—
117C23×C47AGL(1,ℤ/8)11yescharacteristic
118Q8×C47—22no—
119Q8×C47—41no—
120Q8×C47—42no—
121Q8×C47—42no—
122D4×C47—22no—
123D4×C47—41no—
124D4×C47—42no—
125D4×C47—42no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—42no—
131C2×C4×C47—41no—
132C2×C4×C47—42no—
133C2×C4×C47—42no—
134C2×C4×C47—42no—
135C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C47C22×D411yescharacteristic
137C8×C47—21no—
138C8×C47—21no—
139C8×C47—42no—
140C8×C47AGL(1,ℤ/8)11yescharacteristic
141C8×C47AGL(1,ℤ/8)11yescharacteristic
142C8×C47C2×#4112yes—
143#33693C4711yesmaximal, characteristic, direct product factor, Sylow
144C22×C47—21no—
145C22×C47—41no—
146C22×C47—42no—
147C22×C47—82no—
148C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
149C4×C47—21no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47—42no—
153C4×C47—82no—
154C4×C47—82no—
155C4×C47#52511yescharacteristic
156C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
157#3177C2×C4711yescharacteristic, complemented
158#2955C2×C4711yescharacteristic
159#2239C2×C4712yescomplemented
160#2231C2×C4712yescomplemented
161#2214C2×C4712yescomplemented
162#2191C2×C4712yes—
163#2180C2×C4714yescomplemented
164#2166C2×C4711yescharacteristic, complemented
165C2×C47—21no—
166C2×C47—41no—
167C2×C47—82no—
168C2×C47#310911yescharacteristic
169#575C22×C4711yescharacteristic
170C2×#131—21no—
171#541—21no—
172#510C22×C4714yes—
173#499C22×C4711yescharacteristic, complemented
174#494C22×C4711yescharacteristic, complemented
175#491—21no—
176#470C22×C4712yes—
177#467—21no—
178#444—21no—
179#444C22×C4712yes—
180#443—21no—
181#443C22×C4712yes—
182#441C22×C4712yescomplemented
183C4×Q16—21no—
184#430C22×C4711yescharacteristic
185#421—21no—
186#405C22×C4711yescharacteristic
187#365C22×C4714yescomplemented
188#364C22×C4712yescomplemented
189#362C22×C4714yescomplemented
190#360C22×C4714yes—
191#349C22×C4712yes—
192#347C22×C4712yescomplemented
193C47#3369311yescharacteristic, direct product factor, Sylow
194C2×#41—21no—
195#137—22no—
196AGL(1,ℤ/8)—22no—
197#135—21no—
198#135C23×C4712yes—
199C2×Q16—21no—
200C2×Q16C23×C4712yes—
201#131—22no—
202#131—22no—
203#131—41no—
204#131—41no—
205C2×M16—21no—
206C2×M16—41no—
207C2×M16C23×C4711yescharacteristic
208C22×C8—41no—
209C22×C8D4×C4711yescharacteristic
210C4⋊Q8—21no—
211#126—42no—
212#125—21no—
213#125—42no—
214C22⋊Q8—22no—
215C4×Q8—22no—
216#117D4×C4711yescharacteristic
217Q32—24no—
218SD32—24no—
219M32C23×C4714yes—
220#108—21no—
221#108C23×C4712yes—
222#107—21no—
223#106C23×C4712yes—
224#104—22no—
225#104—22no—
226#103—22no—
227#103—22no—
228#97D4×C4711yescharacteristic
229#97C23×C4711yescharacteristic
230C4×C8D4×C4711yescharacteristic
231C4×C8C23×C4711yescharacteristic
232#41—22no—
233#41—22no—
234#41—41no—
235#41—41no—
236C2×Q8—21no—
237C2×Q8—22no—
238C2×D4—21no—
239C2×D4—41no—
240C22×C4—41no—
241C22×C4C2×D4×C4711yescharacteristic
242Q16—21no—
243Q16—24no—
244Q16—41no—
245Q16—41no—
246Q16#41×C4712yes—
247SD16—22no—
248SD16—22no—
249D8—21no—
250D8#41×C4712yes—
251M16—22no—
252M16—22no—
253M16—42no—
254M16—41no—
255M16—42no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—42no—
259C2×C8—41no—
260C2×C8—42no—
261C2×C8C2×D4×C4711yescharacteristic
262C2×C8C2×D4×C4711yescharacteristic
263C2×C8C2×D4×C4711yescharacteristic
264C2×C8C24×C4711yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—22no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C22⋊C4—21no—
272C22⋊C4—42no—
273C42—42no—
274C42C2×D4×C4711yescharacteristic
275C42C2×D4×C4711yescharacteristic
276C16—24no—
277C23—41no—
278C23AGL(1,ℤ/8)×C4711yescharacteristic
279Q8—22no—
280Q8—41no—
281Q8—42no—
282Q8—42no—
283D4—22no—
284D4—41no—
285D4—42no—
286D4—42no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
297C2×C4C22×D4×C4711yescharacteristic
298C8—21no—
299C8—21no—
300C8—42no—
301C8AGL(1,ℤ/8)×C4711yescharacteristic
302C8AGL(1,ℤ/8)×C4711yescharacteristic
303C8C2×#41×C4712yes—
304C22—21no—
305C22—41no—
306C22—42no—
307C22—82no—
308C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
309C4—21no—
310C4—41no—
311C4—41no—
312C4—42no—
313C4—82no—
314C4—82no—
315C4C47×#52511yescharacteristic
316C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
317C2—21no—
318C2—41no—
319C2—82no—
320C2C47×#310911yescharacteristic
subgroupG/H
center, socleC2×C47#3109
commutator, Frattini, cosocleC2×C8C24×C47
prime radicalC47×#575C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C2×C4×C47 ◁ C47×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3177C2semidirect
3. C47×#2239C2semidirect
4. C47×#2231C2semidirect
5. C47×#2214C2semidirect
7. C47×#2180C2semidirect
8. C47×#2166C2semidirect
13. C47×#499C22semidirect
14. C47×#494C22semidirect
22. C47×#441C22semidirect
27. C47×#365C22semidirect
28. C47×#364C22semidirect
29. C47×#362C22semidirect
32. C47×#347C22semidirect
143. #33693C47direct (N × H)
157. #3177C2×C47semidirect
159. #2239C2×C47semidirect
160. #2231C2×C47semidirect
161. #2214C2×C47semidirect
163. #2180C2×C47semidirect
164. #2166C2×C47semidirect
173. #499C22×C47semidirect
174. #494C22×C47semidirect
182. #441C22×C47semidirect
187. #365C22×C47semidirect
188. #364C22×C47semidirect
189. #362C22×C47semidirect
192. #347C22×C47semidirect
193. C47#33693direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31772
C47×#29552
C47×#22392
C47×#22312
C47×#22142
C47×#21912
C47×#21802
C47×#21662
#3369347