Finite Group Databasebeta

← C47×#13468 #26053166

Subgroups — C47×#13468 #26053166

Order 12032.

304 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2155C211yesmaximal, characteristic, complemented
2C47×#2151C211yesmaximal, characteristic, complemented
3C47×#2143C211yesmaximal, characteristic
4C2×C47×#359C211yesmaximal, characteristic
5C47×#1976C211yesmaximal, characteristic
6C47×#1953C211yesmaximal, characteristic, complemented
7C47×#1382C211yesmaximal, characteristic, complemented
8C2×#135×C47C2211yescharacteristic
9C2×M32×C47C2211yescharacteristic
10C22×C16×C47C2211yescharacteristic
11C47×#430—21no—
12C2×#108×C47C2211yescharacteristic
13C2×#108×C47C2211yescharacteristic
14C47×#427C2211yescharacteristic
15C47×#421—21no—
16C47×#410—21no—
17C47×#405C2211yescharacteristic
18C47×#365—22no—
19C47×C4⋊C16—22no—
20C47×#359—22no—
21C47×#359—22no—
22C47×#344—21no—
23C2×#41×C47—21no—
24#135×C47—21no—
25#135×C47—21no—
26#135×C47—21no—
27#135×C47—21no—
28C2×Q16×C47Q811yescharacteristic
29C2×SD16×C47—21no—
30C2×D8×C47Q811yescharacteristic
31C2×M16×C47—21no—
32C2×M16×C47—21no—
33C2×M16×C47D411yescharacteristic
34C22×C8×C47C2311yescharacteristic
35#117×C47—21no—
36#117×C47D411yescharacteristic
37M32×C47—21no—
38M32×C47—21no—
39C2×C16×C47—21no—
40C2×C16×C47—21no—
41C2×C16×C47—21no—
42C2×C16×C47D412yes—
43#108×C47—21no—
44#108×C47—21no—
45#108×C47—21no—
46#108×C47—42no—
47#108×C47D412yes—
48#107×C47—21no—
49#106×C47—21no—
50#104×C47—42no—
51#99×C47—42no—
52#97×C47—21no—
53C4×C8×C47—21no—
54#41×C47—41no—
55#41×C47—41no—
56#41×C47—41no—
57#41×C47—41no—
58C2×Q8×C47—21no—
59C2×D4×C47—21no—
60C2×D4×C47—41no—
61C22×C4×C47—41no—
62C22×C4×C47C2×D411yescharacteristic
63Q16×C47—21no—
64Q16×C47—21no—
65SD16×C47—41no—
66SD16×C47—41no—
67D8×C47—21no—
68D8×C47—21no—
69M16×C47—22no—
70M16×C47—21no—
71M16×C47—21no—
72M16×C47—41no—
73M16×C47—41no—
74M16×C47—41no—
75C2×C8×C47—21no—
76C2×C8×C47—41no—
77C2×C8×C47—41no—
78C2×C8×C47C2×D411yescharacteristic
79C2×C8×C47C2×D411yescharacteristic
80C2×C8×C47C2×Q811yescharacteristic
81C2×C8×C47#4111yescharacteristic
82C2×C8×C47#4111yescharacteristic
83C2×C8×C47#4111yescharacteristic
84C4⋊C4×C47—21no—
85C4⋊C4×C47—41no—
86C22⋊C4×C47—41no—
87C22⋊C4×C47SD1612yes—
88C42×C47—21no—
89C42×C47—41no—
90C16×C47—22no—
91C16×C47—41no—
92C23×C47—41no—
93C23×C47C2×SD1611yescharacteristic
94Q8×C47—41no—
95Q8×C47—41no—
96D4×C47—41no—
97D4×C47—41no—
98D4×C47—81no—
99D4×C47—81no—
100C2×C4×C47—22no—
101C2×C4×C47—41no—
102C2×C4×C47—81no—
103C2×C4×C47—81no—
104C2×C4×C47—81no—
105C2×C4×C47#12111yescharacteristic
106C2×C4×C47#12111yescharacteristic
107C2×C4×C47C22⋊Q811yescharacteristic
108C2×C4×C47#13511yescharacteristic
109C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
110C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
111C8×C47—42no—
112C8×C47—41no—
113C8×C47—81no—
114C8×C47#12111yescharacteristic
115C8×C47C22⋊Q811yescharacteristic
116C8×C47C22⋊Q811yescharacteristic
117C8×C47#12611yescharacteristic
118#13468C4711yesmaximal, characteristic, direct product factor, Sylow
119C22×C47—41no—
120C22×C47—81no—
121C22×C47—161no—
122C22×C47#46011yescharacteristic
123C22×C47#46511yescharacteristic
124C22×C47#47611yescharacteristic
125C4×C47—42no—
126C4×C47—81no—
127C4×C47—161no—
128C4×C47#39611yescharacteristic
129C4×C47#46311yescharacteristic
130C4×C47#46911yescharacteristic
131C4×C47#47811yescharacteristic
132#2155C2×C4711yescharacteristic, complemented
133#2151C2×C4711yescharacteristic, complemented
134#2143C2×C4711yescharacteristic
135C2×#359C2×C4711yescharacteristic
136#1976C2×C4711yescharacteristic
137#1953C2×C4711yescharacteristic, complemented
138#1382C2×C4711yescharacteristic, complemented
139C2×C47—21no—
140C2×C47—21no—
141C2×C47—21no—
142C2×C47—161no—
143C2×C47#206511yescharacteristic
144C2×#135C22×C4711yescharacteristic
145C2×M32C22×C4711yescharacteristic
146C22×C16C22×C4711yescharacteristic
147#430—21no—
148C2×#108C22×C4711yescharacteristic
149C2×#108C22×C4711yescharacteristic
150#427C22×C4711yescharacteristic
151#421—21no—
152#410—21no—
153#405C22×C4711yescharacteristic
154#365—22no—
155C4⋊C16—22no—
156#359—22no—
157#359—22no—
158#344—21no—
159C47#1346811yescharacteristic, direct product factor, Sylow
160C2×#41—21no—
161#135—21no—
162#135—21no—
163#135—21no—
164#135—21no—
165C2×Q16Q8×C4711yescharacteristic
166C2×SD16—21no—
167C2×D8Q8×C4711yescharacteristic
168C2×M16—21no—
169C2×M16—21no—
170C2×M16D4×C4711yescharacteristic
171C22×C8C23×C4711yescharacteristic
172#117—21no—
173#117D4×C4711yescharacteristic
174M32—21no—
175M32—21no—
176C2×C16—21no—
177C2×C16—21no—
178C2×C16—21no—
179C2×C16D4×C4712yes—
180#108—21no—
181#108—21no—
182#108—21no—
183#108—42no—
184#108D4×C4712yes—
185#107—21no—
186#106—21no—
187#104—42no—
188#99—42no—
189#97—21no—
190C4×C8—21no—
191#41—41no—
192#41—41no—
193#41—41no—
194#41—41no—
195C2×Q8—21no—
196C2×D4—21no—
197C2×D4—41no—
198C22×C4—41no—
199C22×C4C2×D4×C4711yescharacteristic
200Q16—21no—
201Q16—21no—
202SD16—41no—
203SD16—41no—
204D8—21no—
205D8—21no—
206M16—22no—
207M16—21no—
208M16—21no—
209M16—41no—
210M16—41no—
211M16—41no—
212C2×C8—21no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8C2×D4×C4711yescharacteristic
216C2×C8C2×D4×C4711yescharacteristic
217C2×C8C2×Q8×C4711yescharacteristic
218C2×C8#41×C4711yescharacteristic
219C2×C8#41×C4711yescharacteristic
220C2×C8#41×C4711yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—41no—
223C22⋊C4—41no—
224C22⋊C4SD16×C4712yes—
225C42—21no—
226C42—41no—
227C16—22no—
228C16—41no—
229C23—41no—
230C23C2×SD16×C4711yescharacteristic
231Q8—41no—
232Q8—41no—
233D4—41no—
234D4—41no—
235D4—81no—
236D4—81no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4#121×C4711yescharacteristic
243C2×C4#121×C4711yescharacteristic
244C2×C4C22⋊Q8×C4711yescharacteristic
245C2×C4#135×C4711yescharacteristic
246C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
247C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
248C8—42no—
249C8—41no—
250C8—81no—
251C8#121×C4711yescharacteristic
252C8C22⋊Q8×C4711yescharacteristic
253C8C22⋊Q8×C4711yescharacteristic
254C8#126×C4711yescharacteristic
255C22—41no—
256C22—81no—
257C22—161no—
258C22C47×#46011yescharacteristic
259C22C47×#46511yescharacteristic
260C22C47×#47611yescharacteristic
261C4—42no—
262C4—81no—
263C4—161no—
264C4C47×#39611yescharacteristic
265C4C47×#46311yescharacteristic
266C4C47×#46911yescharacteristic
267C4C47×#47811yescharacteristic
268C2—21no—
269C2—21no—
270C2—21no—
271C2—161no—
272C2C47×#206511yescharacteristic
subgroupG/H
centerC4×C47#469
commutator, Frattini, cosocleC22×C8C23×C47
socleC2×C47#2065
prime radicalC2×#135×C47C22
LCSG ▷ C22×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
1. C47×#2155C2semidirect
2. C47×#2151C2semidirect
6. C47×#1953C2semidirect
7. C47×#1382C2semidirect
118. #13468C47direct (N × H)
132. #2155C2×C47semidirect
133. #2151C2×C47semidirect
137. #1953C2×C47semidirect
138. #1382C2×C47semidirect
159. C47#13468direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#21552
C47×#21512
C47×#21432
C2×C47×#3592
C47×#19762
C47×#19532
C47×#13822
#1346847