Finite Group Databasebeta

← C47×#13008 #26052706

Subgroups — C47×#13008 #26052706

Order 12032.

516 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3054C211yesmaximal, characteristic
2C47×#2911C211yesmaximal, characteristic, complemented
3C47×#2145C212yesmaximal, complemented
4C2×C47×#349C211yesmaximal, characteristic, complemented
5C47×#1384C212yesmaximal, complemented
6C2×#135×C47C2211yescharacteristic
7C22×M16×C47C2211yescharacteristic
8C47×#525—21no—
9C2×#117×C47—21no—
10C2×M32×C47C2212yes—
11C47×#470C412yescomplemented
12C47×#469C412yescomplemented
13C47×#468—22no—
14C47×#428—24no—
15C47×#427—21no—
16C47×#427C2211yescharacteristic
17C47×#427C2212yes—
18C47×#416—21no—
19C47×#360—24no—
20C47×#349—22no—
21C2×#41×C47—21no—
22C23×C4×C47D411yescharacteristic
23#135×C47—22no—
24#135×C47—22no—
25C2×Q16×C47C2×C411yescharacteristic, complemented
26C2×SD16×C47—21no—
27C2×D8×C47C2×C411yescharacteristic, complemented
28C2×M16×C47—22no—
29C2×M16×C47—22no—
30C2×M16×C47C2×C412yes—
31C2×M16×C47D412yes—
32C22×C8×C47D411yescharacteristic
33C22×C8×C47C2311yescharacteristic
34#123×C47—41no—
35C22⋊Q8×C47—22no—
36#121×C47—22no—
37#120×C47—41no—
38C4×D4×C47—42no—
39#117×C47—22no—
40#117×C47—22no—
41#117×C47—21no—
42#117×C47—41no—
43#117×C47—41no—
44C2×C4⋊C4×C47—22no—
45C2×C22⋊C4×C47—41no—
46C2×C42×C47—41no—
47M32×C47—22no—
48M32×C47—22no—
49C2×C16×C47—22no—
50#107×C47—22no—
51#107×C47—21no—
52#107×C47—22no—
53#106×C47—22no—
54#106×C47C2×C412yescomplemented
55#106×C47D414yescomplemented
56#103×C47—22no—
57#102×C47—22no—
58C24×C47D811yescharacteristic
59#41×C47—41no—
60#41×C47—41no—
61#41×C47—41no—
62#41×C47—41no—
63C2×Q8×C47—21no—
64C2×D4×C47—21no—
65C2×D4×C47—42no—
66C2×D4×C47—41no—
67C22×C4×C47—21no—
68C22×C4×C47—21no—
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47—42no—
72C22×C4×C47—41no—
73C22×C4×C47C22⋊C412yes—
74C22×C4×C47D811yescharacteristic
75C22×C4×C47SD1612yes—
76C22×C4×C47C2×D411yescharacteristic
77Q16×C47—22no—
78SD16×C47—42no—
79D8×C47—22no—
80M16×C47—24no—
81M16×C47—24no—
82C2×C8×C47—21no—
83C2×C8×C47—21no—
84C2×C8×C47C22⋊C412yes—
85C2×C8×C47C22×C411yescharacteristic
86C2×C8×C47C2×D412yes—
87C2×C8×C47C2×D411yescharacteristic
88C2×C8×C47#4112yes—
89C4⋊C4×C47—22no—
90C4⋊C4×C47—24no—
91C4⋊C4×C47—42no—
92C4⋊C4×C47—42no—
93C22⋊C4×C47—42no—
94C22⋊C4×C47—42no—
95C22⋊C4×C47—42no—
96C22⋊C4×C47—41no—
97C22⋊C4×C47—42no—
98C42×C47—42no—
99C42×C47—41no—
100C42×C47—42no—
101C16×C47—42no—
102C23×C47—21no—
103C23×C47—21no—
104C23×C47—41no—
105C23×C47—81no—
106C23×C47#10212yes—
107C23×C47C2×D811yescharacteristic
108Q8×C47—41no—
109Q8×C47—41no—
110D4×C47—41no—
111D4×C47—41no—
112D4×C47—84no—
113D4×C47—81no—
114D4×C47—81no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—22no—
118C2×C4×C47—22no—
119C2×C4×C47—22no—
120C2×C4×C47—22no—
121C2×C4×C47—42no—
122C2×C4×C47—41no—
123C2×C4×C47—44no—
124C2×C4×C47—84no—
125C2×C4×C47—81no—
126C2×C4×C47—81no—
127C2×C4×C47#10212yes—
128C2×C4×C47C2×C22⋊C411yescharacteristic
129C2×C4×C47#12011yescharacteristic
130C2×C4×C47#12311yescharacteristic
131C2×C4×C47C2×SD1611yescharacteristic
132C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C47#13711yescharacteristic
134C8×C47—22no—
135C8×C47C4×D412yes—
136C8×C47#12112yes—
137#13008C4711yesmaximal, characteristic, direct product factor, Sylow
138C22×C47—22no—
139C22×C47—41no—
140C22×C47—42no—
141C22×C47—42no—
142C22×C47—81no—
143C22×C47—82no—
144C22×C47—81no—
145C22×C47C2×#10211yescharacteristic
146C22×C47#44711yescharacteristic
147C22×C47#48011yescharacteristic
148C4×C47—22no—
149C4×C47—84no—
150C4×C47—82no—
151C4×C47—81no—
152C4×C47#38611yescharacteristic
153C4×C47#41711yescharacteristic
154C4×C47#44811yescharacteristic
155C4×C47#48111yescharacteristic
156#3054C2×C4711yescharacteristic
157#2911C2×C4711yescharacteristic, complemented
158#2145C2×C4712yescomplemented
159C2×#349C2×C4711yescharacteristic, complemented
160#1384C2×C4712yescomplemented
161C2×C47—21no—
162C2×C47—21no—
163C2×C47—21no—
164C2×C47—42no—
165C2×C47—161no—
166C2×C47#187411yescharacteristic
167C2×#135C22×C4711yescharacteristic
168C22×M16C22×C4711yescharacteristic
169#525—21no—
170C2×#117—21no—
171C2×M32C22×C4712yes—
172#470C4×C4712yescomplemented
173#469C4×C4712yescomplemented
174#468—22no—
175#428—24no—
176#427—21no—
177#427C22×C4711yescharacteristic
178#427C22×C4712yes—
179#416—21no—
180#360—24no—
181#349—22no—
182C47#1300811yescharacteristic, direct product factor, Sylow
183C2×#41—21no—
184C23×C4D4×C4711yescharacteristic
185#135—22no—
186#135—22no—
187C2×Q16C2×C4×C4711yescharacteristic, complemented
188C2×SD16—21no—
189C2×D8C2×C4×C4711yescharacteristic, complemented
190C2×M16—22no—
191C2×M16—22no—
192C2×M16C2×C4×C4712yes—
193C2×M16D4×C4712yes—
194C22×C8D4×C4711yescharacteristic
195C22×C8C23×C4711yescharacteristic
196#123—41no—
197C22⋊Q8—22no—
198#121—22no—
199#120—41no—
200C4×D4—42no—
201#117—22no—
202#117—22no—
203#117—21no—
204#117—41no—
205#117—41no—
206C2×C4⋊C4—22no—
207C2×C22⋊C4—41no—
208C2×C42—41no—
209M32—22no—
210M32—22no—
211C2×C16—22no—
212#107—22no—
213#107—22no—
214#107—21no—
215#106—22no—
216#106C2×C4×C4712yescomplemented
217#106D4×C4714yescomplemented
218#103—22no—
219#102—22no—
220C24D8×C4711yescharacteristic
221#41—41no—
222#41—41no—
223#41—41no—
224#41—41no—
225C2×Q8—21no—
226C2×D4—21no—
227C2×D4—41no—
228C2×D4—42no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—41no—
235C22×C4C22⋊C4×C4712yes—
236C22×C4D8×C4711yescharacteristic
237C22×C4SD16×C4712yes—
238C22×C4C2×D4×C4711yescharacteristic
239Q16—22no—
240SD16—42no—
241D8—22no—
242M16—24no—
243M16—24no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8C22⋊C4×C4712yes—
247C2×C8C22×C4×C4711yescharacteristic
248C2×C8C2×D4×C4712yes—
249C2×C8C2×D4×C4711yescharacteristic
250C2×C8#41×C4712yes—
251C4⋊C4—22no—
252C4⋊C4—24no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—41no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C42—42no—
261C42—41no—
262C42—42no—
263C16—42no—
264C23—21no—
265C23—21no—
266C23—41no—
267C23—81no—
268C23#102×C4712yes—
269C23C2×D8×C4711yescharacteristic
270Q8—41no—
271Q8—41no—
272D4—41no—
273D4—41no—
274D4—84no—
275D4—81no—
276D4—81no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—44no—
286C2×C4—84no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4#102×C4712yes—
290C2×C4C2×C22⋊C4×C4711yescharacteristic
291C2×C4#120×C4711yescharacteristic
292C2×C4#123×C4711yescharacteristic
293C2×C4C2×SD16×C4711yescharacteristic
294C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
295C2×C4#137×C4711yescharacteristic
296C8—22no—
297C8C4×D4×C4712yes—
298C8#121×C4712yes—
299C22—22no—
300C22—41no—
301C22—42no—
302C22—42no—
303C22—81no—
304C22—82no—
305C22—81no—
306C22C2×#102×C4711yescharacteristic
307C22C47×#44711yescharacteristic
308C22C47×#48011yescharacteristic
309C4—22no—
310C4—84no—
311C4—82no—
312C4—81no—
313C4C47×#38611yescharacteristic
314C4C47×#41711yescharacteristic
315C4C47×#44811yescharacteristic
316C4C47×#48111yescharacteristic
317C2—21no—
318C2—21no—
319C2—21no—
320C2—42no—
321C2—161no—
322C2C47×#187411yescharacteristic
subgroupG/H
centerC4×C47#481
commutatorC2×C8C22×C4×C47
Frattini, cosocleC22×C8C23×C47
socleC2×C47#1874
prime radicalC47×#3054C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C47 ◁ C22×C4×C47 ◁ C22×M16×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2911C2semidirect
3. C47×#2145C2semidirect
4. C2×C47×#349C2semidirect
5. C47×#1384C2semidirect
11. C47×#470C4semidirect
12. C47×#469C4semidirect
25. C2×Q16×C47C2×C4semidirect
27. C2×D8×C47C2×C4semidirect
54. #106×C47C2×C4semidirect
55. #106×C47D4semidirect
137. #13008C47direct (N × H)
157. #2911C2×C47semidirect
158. #2145C2×C47semidirect
159. C2×#349C2×C47semidirect
160. #1384C2×C47semidirect
172. #470C4×C47semidirect
173. #469C4×C47semidirect
182. C47#13008direct (N × H)
187. C2×Q16C2×C4×C47semidirect
189. C2×D8C2×C4×C47semidirect
216. #106C2×C4×C47semidirect
217. #106D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#30542
C47×#29112
C47×#21452
C2×C47×#3492
C47×#13842
#1300847