Finite Group Databasebeta

← C47×#12947 #26052645

Subgroups — C47×#12947 #26052645

Order 12032.

380 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2957C211yesmaximal, characteristic
2C2×C47×#368C211yesmaximal, characteristic, complemented
3C47×#2143C211yesmaximal, characteristic
4C2×C47×#359C211yesmaximal, characteristic
5C47×#1953C211yesmaximal, characteristic, complemented
6C47×#1388C211yesmaximal, characteristic, complemented
7C47×#1379C211yesmaximal, characteristic, complemented
8C2×#135×C47C2211yescharacteristic
9C47×#568—21no—
10C2×M32×C47C2211yescharacteristic
11C22×C16×C47C2211yescharacteristic
12C47×#444—22no—
13C47×#443—22no—
14C47×#430—21no—
15C2×#108×C47C2211yescharacteristic
16C2×#108×C47C2211yescharacteristic
17C2×#108×C47C2211yescharacteristic
18C47×#421—21no—
19C47×#405C2211yescharacteristic
20C47×#368—22no—
21C47×#359—22no—
22C47×#359C414yescomplemented
23C47×#344—21no—
24C2×#41×C47—21no—
25#135×C47—21no—
26#135×C47—21no—
27#135×C47C2×C412yes—
28#135×C47D412yes—
29C2×Q16×C47Q811yescharacteristic
30C2×SD16×C47—21no—
31C2×D8×C47Q811yescharacteristic
32#131×C47—24no—
33#131×C47—42no—
34C2×M16×C47—21no—
35C2×M16×C47—21no—
36C2×M16×C47—21no—
37C2×M16×C47—42no—
38C2×M16×C47D411yescharacteristic
39C22×C8×C47C2311yescharacteristic
40#117×C47D411yescharacteristic
41M32×C47—21no—
42M32×C47—21no—
43C2×C16×C47—21no—
44C2×C16×C47—21no—
45C2×C16×C47—21no—
46C2×C16×C47C2×C412yes—
47#108×C47—21no—
48#108×C47—21no—
49#108×C47—21no—
50#108×C47—21no—
51#108×C47—42no—
52#108×C47C2×C412yes—
53#108×C47D412yes—
54#104×C47—24no—
55#97×C47—21no—
56C4×C8×C47—21no—
57#41×C47—22no—
58#41×C47—22no—
59#41×C47—41no—
60#41×C47—41no—
61C2×Q8×C47—21no—
62C2×D4×C47—21no—
63C2×D4×C47—41no—
64C22×C4×C47—41no—
65C22×C4×C47C2×D411yescharacteristic
66Q16×C47—21no—
67Q16×C47C4⋊C412yes—
68SD16×C47—22no—
69SD16×C47—22no—
70D8×C47—21no—
71D8×C47C4⋊C412yes—
72M16×C47—21no—
73M16×C47—22no—
74M16×C47—22no—
75M16×C47—44no—
76M16×C47—41no—
77M16×C47—41no—
78M16×C47—41no—
79M16×C47—41no—
80M16×C47D812yes—
81C2×C8×C47—21no—
82C2×C8×C47—44no—
83C2×C8×C47—41no—
84C2×C8×C47—41no—
85C2×C8×C47—41no—
86C2×C8×C47C22×C411yescharacteristic
87C2×C8×C47C2×D411yescharacteristic
88C2×C8×C47C2×D411yescharacteristic
89C2×C8×C47C2×Q811yescharacteristic
90C2×C8×C47#4111yescharacteristic
91C2×C8×C47#4111yescharacteristic
92C4⋊C4×C47—21no—
93C22⋊C4×C47—21no—
94C42×C47—21no—
95C16×C47—22no—
96C16×C47—41no—
97C23×C47—41no—
98C23×C47#13711yescharacteristic
99Q8×C47—22no—
100Q8×C47—41no—
101D4×C47—22no—
102D4×C47—42no—
103D4×C47—42no—
104D4×C47—41no—
105C2×C4×C47—41no—
106C2×C4×C47—42no—
107C2×C4×C47—42no—
108C2×C4×C47—41no—
109C2×C4×C47C4×D411yescharacteristic
110C2×C4×C47#12011yescharacteristic
111C2×C4×C47C22⋊Q811yescharacteristic
112C2×C4×C47C2×D811yescharacteristic
113C2×C4×C47#13511yescharacteristic
114C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
115C8×C47—22no—
116C8×C47—42no—
117C8×C47—42no—
118C8×C47—81no—
119C8×C47C2×C4⋊C411yescharacteristic
120C8×C47C4×D411yescharacteristic
121C8×C47C22⋊Q811yescharacteristic
122C8×C47#12311yescharacteristic
123#12947C4711yesmaximal, characteristic, direct product factor, Sylow
124C22×C47—41no—
125C22×C47—42no—
126C22×C47—161no—
127C22×C47#44011yescharacteristic
128C22×C47#45211yescharacteristic
129C22×C47#47411yescharacteristic
130C4×C47—42no—
131C4×C47—81no—
132C4×C47#38511yescharacteristic
133C4×C47C4×D811yescharacteristic
134C4×C47#44711yescharacteristic
135C4×C47#47811yescharacteristic
136#2957C2×C4711yescharacteristic
137C2×#368C2×C4711yescharacteristic, complemented
138#2143C2×C4711yescharacteristic
139C2×#359C2×C4711yescharacteristic
140#1953C2×C4711yescharacteristic, complemented
141#1388C2×C4711yescharacteristic, complemented
142#1379C2×C4711yescharacteristic, complemented
143C2×C47—21no—
144C2×C47—21no—
145C2×C47—21no—
146C2×C47—82no—
147C2×C47#186211yescharacteristic
148C2×#135C22×C4711yescharacteristic
149#568—21no—
150C2×M32C22×C4711yescharacteristic
151C22×C16C22×C4711yescharacteristic
152#444—22no—
153#443—22no—
154#430—21no—
155C2×#108C22×C4711yescharacteristic
156C2×#108C22×C4711yescharacteristic
157C2×#108C22×C4711yescharacteristic
158#421—21no—
159#405C22×C4711yescharacteristic
160#368—22no—
161#359—22no—
162#359C4×C4714yescomplemented
163#344—21no—
164C47#1294711yescharacteristic, direct product factor, Sylow
165C2×#41—21no—
166#135—21no—
167#135—21no—
168#135C2×C4×C4712yes—
169#135D4×C4712yes—
170C2×Q16Q8×C4711yescharacteristic
171C2×SD16—21no—
172C2×D8Q8×C4711yescharacteristic
173#131—24no—
174#131—42no—
175C2×M16—21no—
176C2×M16—21no—
177C2×M16—21no—
178C2×M16—42no—
179C2×M16D4×C4711yescharacteristic
180C22×C8C23×C4711yescharacteristic
181#117D4×C4711yescharacteristic
182M32—21no—
183M32—21no—
184C2×C16—21no—
185C2×C16—21no—
186C2×C16—21no—
187C2×C16C2×C4×C4712yes—
188#108—21no—
189#108—21no—
190#108—21no—
191#108—21no—
192#108—42no—
193#108C2×C4×C4712yes—
194#108D4×C4712yes—
195#104—24no—
196#97—21no—
197C4×C8—21no—
198#41—22no—
199#41—22no—
200#41—41no—
201#41—41no—
202C2×Q8—21no—
203C2×D4—21no—
204C2×D4—41no—
205C22×C4—41no—
206C22×C4C2×D4×C4711yescharacteristic
207Q16—21no—
208Q16C4⋊C4×C4712yes—
209SD16—22no—
210SD16—22no—
211D8—21no—
212D8C4⋊C4×C4712yes—
213M16—21no—
214M16—22no—
215M16—22no—
216M16—44no—
217M16—41no—
218M16—41no—
219M16—41no—
220M16—41no—
221M16D8×C4712yes—
222C2×C8—21no—
223C2×C8—44no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8C22×C4×C4711yescharacteristic
228C2×C8C2×D4×C4711yescharacteristic
229C2×C8C2×D4×C4711yescharacteristic
230C2×C8C2×Q8×C4711yescharacteristic
231C2×C8#41×C4711yescharacteristic
232C2×C8#41×C4711yescharacteristic
233C4⋊C4—21no—
234C22⋊C4—21no—
235C42—21no—
236C16—22no—
237C16—41no—
238C23—41no—
239C23#137×C4711yescharacteristic
240Q8—22no—
241Q8—41no—
242D4—22no—
243D4—42no—
244D4—42no—
245D4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4C4×D4×C4711yescharacteristic
251C2×C4#120×C4711yescharacteristic
252C2×C4C22⋊Q8×C4711yescharacteristic
253C2×C4C2×D8×C4711yescharacteristic
254C2×C4#135×C4711yescharacteristic
255C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
256C8—22no—
257C8—42no—
258C8—42no—
259C8—81no—
260C8C2×C4⋊C4×C4711yescharacteristic
261C8C4×D4×C4711yescharacteristic
262C8C22⋊Q8×C4711yescharacteristic
263C8#123×C4711yescharacteristic
264C22—41no—
265C22—42no—
266C22—161no—
267C22C47×#44011yescharacteristic
268C22C47×#45211yescharacteristic
269C22C47×#47411yescharacteristic
270C4—42no—
271C4—81no—
272C4C47×#38511yescharacteristic
273C4C4×D8×C4711yescharacteristic
274C4C47×#44711yescharacteristic
275C4C47×#47811yescharacteristic
276C2—21no—
277C2—21no—
278C2—21no—
279C2—82no—
280C2C47×#186211yescharacteristic
subgroupG/H
centerC4×C47#447
commutatorC2×C8C22×C4×C47
Frattini, cosocleC22×C8C23×C47
socleC2×C47#1862
prime radicalC2×#135×C47C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C47 ◁ C22×C4×C47 ◁ C47×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#368C2semidirect
5. C47×#1953C2semidirect
6. C47×#1388C2semidirect
7. C47×#1379C2semidirect
22. C47×#359C4semidirect
123. #12947C47direct (N × H)
137. C2×#368C2×C47semidirect
140. #1953C2×C47semidirect
141. #1388C2×C47semidirect
142. #1379C2×C47semidirect
162. #359C4×C47semidirect
164. C47#12947direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#29572
C2×C47×#3682
C47×#21432
C2×C47×#3592
C47×#19532
C47×#13882
C47×#13792
#1294747