Finite Group Databasebeta

← C47×#12998 #26052696

Subgroups — C47×#12998 #26052696

Order 12032.

500 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3054C211yesmaximal, characteristic
2C2×C47×#430C211yesmaximal, characteristic, complemented
3C47×#2143C212yesmaximal, complemented
4C2×C47×#349C211yesmaximal, characteristic, complemented
5C47×#1389C212yesmaximal, complemented
6C2×#135×C47C2211yescharacteristic
7C22×M16×C47—21no—
8C22×M16×C47C2211yescharacteristic
9C47×#525—21no—
10C2×M32×C47C2212yes—
11C47×#470C412yes—
12C47×#469C412yes—
13C47×#468—22no—
14C47×#430—24no—
15C2×#108×C47—21no—
16C2×#108×C47C2212yes—
17C47×#427C2211yescharacteristic
18C47×#416—21no—
19C47×#359—24no—
20C47×#349—22no—
21C2×#41×C47—21no—
22C23×C4×C47D411yescharacteristic
23#135×C47—22no—
24#135×C47—22no—
25C2×Q16×C47C2×C411yescharacteristic
26C2×SD16×C47—21no—
27C2×D8×C47C2×C411yescharacteristic
28C2×M16×C47—22no—
29C2×M16×C47—22no—
30C2×M16×C47—24no—
31C2×M16×C47—22no—
32C2×M16×C47—41no—
33C2×M16×C47—42no—
34C2×M16×C47C2×C412yes—
35C2×M16×C47D412yes—
36C22×C8×C47—41no—
37C22×C8×C47D411yescharacteristic
38C22×C8×C47C2311yescharacteristic
39#123×C47—41no—
40C22⋊Q8×C47—22no—
41#121×C47—22no—
42#120×C47—41no—
43C4×D4×C47—42no—
44#117×C47—21no—
45M32×C47—22no—
46M32×C47—22no—
47C2×C16×C47—22no—
48#108×C47—24no—
49#108×C47—22no—
50#108×C47D414yescomplemented
51#107×C47—21no—
52#106×C47C2×C412yes—
53#103×C47—22no—
54#102×C47—22no—
55C24×C47SD1611yescharacteristic
56#41×C47—41no—
57#41×C47—41no—
58#41×C47—41no—
59#41×C47—41no—
60C2×Q8×C47—21no—
61C2×D4×C47—21no—
62C2×D4×C47—42no—
63C2×D4×C47—41no—
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47—41no—
69C22×C4×C47C22⋊C412yes—
70C22×C4×C47D812yes—
71C22×C4×C47SD1611yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73Q16×C47—22no—
74SD16×C47—42no—
75D8×C47—22no—
76M16×C47—24no—
77M16×C47—24no—
78M16×C47—24no—
79M16×C47—44no—
80M16×C47—42no—
81C2×C8×C47—21no—
82C2×C8×C47—21no—
83C2×C8×C47—44no—
84C2×C8×C47—42no—
85C2×C8×C47C22⋊C412yes—
86C2×C8×C47C22×C411yescharacteristic
87C2×C8×C47C2×D412yes—
88C2×C8×C47C2×D411yescharacteristic
89C2×C8×C47#4112yes—
90C4⋊C4×C47—22no—
91C4⋊C4×C47—42no—
92C22⋊C4×C47—42no—
93C22⋊C4×C47—41no—
94C22⋊C4×C47—42no—
95C42×C47—41no—
96C16×C47—42no—
97C23×C47—21no—
98C23×C47—21no—
99C23×C47—41no—
100C23×C47—81no—
101C23×C47#10212yes—
102C23×C47C2×SD1611yescharacteristic
103Q8×C47—41no—
104Q8×C47—41no—
105D4×C47—41no—
106D4×C47—41no—
107D4×C47—84no—
108D4×C47—81no—
109D4×C47—81no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—22no—
113C2×C4×C47—22no—
114C2×C4×C47—22no—
115C2×C4×C47—22no—
116C2×C4×C47—42no—
117C2×C4×C47—41no—
118C2×C4×C47—81no—
119C2×C4×C47—81no—
120C2×C4×C47#10212yes—
121C2×C4×C47C2×C22⋊C411yescharacteristic
122C2×C4×C47#12011yescharacteristic
123C2×C4×C47#12311yescharacteristic
124C2×C4×C47C2×D811yescharacteristic
125C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C47#13711yescharacteristic
127C8×C47—22no—
128C8×C47—44no—
129C8×C47C4×D412yes—
130C8×C47#12112yes—
131#12998C4711yesmaximal, characteristic, direct product factor, Sylow
132C22×C47—22no—
133C22×C47—41no—
134C22×C47—42no—
135C22×C47—42no—
136C22×C47—81no—
137C22×C47—82no—
138C22×C47—81no—
139C22×C47C2×#10211yescharacteristic
140C22×C47#44811yescharacteristic
141C22×C47#48111yescharacteristic
142C4×C47—22no—
143C4×C47—82no—
144C4×C47—81no—
145C4×C47#38611yescharacteristic
146C4×C47#41711yescharacteristic
147C4×C47#44711yescharacteristic
148C4×C47#48011yescharacteristic
149#3054C2×C4711yescharacteristic
150C2×#430C2×C4711yescharacteristic, complemented
151#2143C2×C4712yescomplemented
152C2×#349C2×C4711yescharacteristic, complemented
153#1389C2×C4712yescomplemented
154C2×C47—21no—
155C2×C47—21no—
156C2×C47—21no—
157C2×C47—42no—
158C2×C47—161no—
159C2×C47#187411yescharacteristic
160C2×#135C22×C4711yescharacteristic
161C22×M16—21no—
162C22×M16C22×C4711yescharacteristic
163#525—21no—
164C2×M32C22×C4712yes—
165#470C4×C4712yes—
166#469C4×C4712yes—
167#468—22no—
168#430—24no—
169C2×#108—21no—
170C2×#108C22×C4712yes—
171#427C22×C4711yescharacteristic
172#416—21no—
173#359—24no—
174#349—22no—
175C47#1299811yescharacteristic, direct product factor, Sylow
176C2×#41—21no—
177C23×C4D4×C4711yescharacteristic
178#135—22no—
179#135—22no—
180C2×Q16C2×C4×C4711yescharacteristic
181C2×SD16—21no—
182C2×D8C2×C4×C4711yescharacteristic
183C2×M16—22no—
184C2×M16—22no—
185C2×M16—24no—
186C2×M16—22no—
187C2×M16—41no—
188C2×M16—42no—
189C2×M16C2×C4×C4712yes—
190C2×M16D4×C4712yes—
191C22×C8—41no—
192C22×C8D4×C4711yescharacteristic
193C22×C8C23×C4711yescharacteristic
194#123—41no—
195C22⋊Q8—22no—
196#121—22no—
197#120—41no—
198C4×D4—42no—
199#117—21no—
200M32—22no—
201M32—22no—
202C2×C16—22no—
203#108—24no—
204#108—22no—
205#108D4×C4714yescomplemented
206#107—21no—
207#106C2×C4×C4712yes—
208#103—22no—
209#102—22no—
210C24SD16×C4711yescharacteristic
211#41—41no—
212#41—41no—
213#41—41no—
214#41—41no—
215C2×Q8—21no—
216C2×D4—21no—
217C2×D4—41no—
218C2×D4—42no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—41no—
224C22×C4C22⋊C4×C4712yes—
225C22×C4D8×C4712yes—
226C22×C4SD16×C4711yescharacteristic
227C22×C4C2×D4×C4711yescharacteristic
228Q16—22no—
229SD16—42no—
230D8—22no—
231M16—24no—
232M16—24no—
233M16—24no—
234M16—44no—
235M16—42no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—44no—
239C2×C8—42no—
240C2×C8C22⋊C4×C4712yes—
241C2×C8C22×C4×C4711yescharacteristic
242C2×C8C2×D4×C4712yes—
243C2×C8C2×D4×C4711yescharacteristic
244C2×C8#41×C4712yes—
245C4⋊C4—22no—
246C4⋊C4—42no—
247C22⋊C4—41no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C42—41no—
251C16—42no—
252C23—21no—
253C23—21no—
254C23—41no—
255C23—81no—
256C23#102×C4712yes—
257C23C2×SD16×C4711yescharacteristic
258Q8—41no—
259Q8—41no—
260D4—41no—
261D4—41no—
262D4—84no—
263D4—81no—
264D4—81no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4#102×C4712yes—
276C2×C4C2×C22⋊C4×C4711yescharacteristic
277C2×C4#120×C4711yescharacteristic
278C2×C4#123×C4711yescharacteristic
279C2×C4C2×D8×C4711yescharacteristic
280C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
281C2×C4#137×C4711yescharacteristic
282C8—22no—
283C8—44no—
284C8C4×D4×C4712yes—
285C8#121×C4712yes—
286C22—22no—
287C22—41no—
288C22—42no—
289C22—42no—
290C22—81no—
291C22—82no—
292C22—81no—
293C22C2×#102×C4711yescharacteristic
294C22C47×#44811yescharacteristic
295C22C47×#48111yescharacteristic
296C4—22no—
297C4—82no—
298C4—81no—
299C4C47×#38611yescharacteristic
300C4C47×#41711yescharacteristic
301C4C47×#44711yescharacteristic
302C4C47×#48011yescharacteristic
303C2—21no—
304C2—21no—
305C2—21no—
306C2—42no—
307C2—161no—
308C2C47×#187411yescharacteristic
subgroupG/H
centerC4×C47#447
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. C2×C47×#430C2semidirect
3. C47×#2143C2semidirect
4. C2×C47×#349C2semidirect
5. C47×#1389C2semidirect
50. #108×C47D4semidirect
131. #12998C47direct (N × H)
150. C2×#430C2×C47semidirect
151. #2143C2×C47semidirect
152. C2×#349C2×C47semidirect
153. #1389C2×C47semidirect
175. C47#12998direct (N × H)
205. #108D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#30542
C2×C47×#4302
C47×#21432
C2×C47×#3492
C47×#13892
#1299847