Finite Group Databasebeta

← C47×#13123 #26052821

Subgroups — C47×#13123 #26052821

Order 12032.

312 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2153C211yesmaximal, characteristic, complemented
2C47×#2117C211yesmaximal, characteristic
3C2×C47×#350C211yesmaximal, characteristic
4C47×#2108C211yesmaximal, characteristic, complemented
5C47×#1757C211yesmaximal, characteristic
6C47×#1379C211yesmaximal, characteristic, complemented
7C47×#1378C211yesmaximal, characteristic, complemented
8C2×#131×C47C2211yescharacteristic
9C2×M32×C47C2211yescharacteristic
10C2×M32×C47C2211yescharacteristic
11C2×M32×C47C2211yescharacteristic
12C22×C16×C47C2211yescharacteristic
13C47×#413C411yescharacteristic
14C47×#410C411yescharacteristic
15C47×#405C2211yescharacteristic
16C47×#405C2211yescharacteristic
17C47×#364—22no—
18C47×#350—22no—
19C47×#350—21no—
20C47×#350—21no—
21C47×#346—21no—
22C4×C16×C47—21no—
23C47×#344C411yescharacteristic
24C47×#344C411yescharacteristic
25C2×#41×C47C2×C411yescharacteristic
26#131×C47—21no—
27#131×C47—21no—
28#131×C47—21no—
29#131×C47—21no—
30C2×M16×C47—21no—
31C2×M16×C47C2×C411yescharacteristic
32C2×M16×C47C2×C411yescharacteristic
33C2×M16×C47C2×C411yescharacteristic
34C22×C8×C47—21no—
35C22×C8×C47C2311yescharacteristic
36#117×C47C2×C411yescharacteristic
37#117×C47C2×C411yescharacteristic
38M32×C47—21no—
39M32×C47—21no—
40M32×C47—21no—
41M32×C47—21no—
42M32×C47—21no—
43M32×C47D412yes—
44C2×C16×C47—21no—
45C2×C16×C47—21no—
46C2×C16×C47—21no—
47C2×C16×C47—21no—
48C2×C16×C47—21no—
49C2×C16×C47D411yescharacteristic
50C2×C16×C47D411yescharacteristic
51#101×C47C812yes—
52#100×C47C812yes—
53#99×C47—22no—
54#97×C47—21no—
55#97×C47—21no—
56C4×C8×C47—21no—
57C4×C8×C47—21no—
58#41×C47—21no—
59#41×C47—21no—
60#41×C47—21no—
61#41×C47—21no—
62C2×Q8×C47C2×C811yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47C2×C811yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47C22×C411yescharacteristic
67M16×C47—21no—
68M16×C47—21no—
69M16×C47—21no—
70M16×C47—21no—
71M16×C47—41no—
72M16×C47—41no—
73M16×C47C2×C812yes—
74M16×C47C2×C812yes—
75C2×C8×C47—21no—
76C2×C8×C47—21no—
77C2×C8×C47—21no—
78C2×C8×C47—41no—
79C2×C8×C47—41no—
80C2×C8×C47C2×D411yescharacteristic
81C2×C8×C47C2×D411yescharacteristic
82C2×C8×C47#4111yescharacteristic
83C2×C8×C47#4111yescharacteristic
84C2×C8×C47#4111yescharacteristic
85C2×C8×C47#4111yescharacteristic
86C4⋊C4×C47—21no—
87C4⋊C4×C47—21no—
88C22⋊C4×C47—21no—
89C22⋊C4×C47M1612yes—
90C42×C47—21no—
91C42×C47—21no—
92C16×C47—22no—
93C16×C47—21no—
94C16×C47—21no—
95C16×C47—41no—
96C16×C47—41no—
97C23×C47—21no—
98C23×C47C2×M1611yescharacteristic
99Q8×C47—21no—
100Q8×C47—21no—
101D4×C47—21no—
102D4×C47—21no—
103D4×C47—41no—
104D4×C47—41no—
105C2×C4×C47—21no—
106C2×C4×C47—22no—
107C2×C4×C47—41no—
108C2×C4×C47—41no—
109C2×C4×C47—41no—
110C2×C4×C47#11711yescharacteristic
111C2×C4×C47C4×D411yescharacteristic
112C2×C4×C47C4×D411yescharacteristic
113C2×C4×C47C22×C811yescharacteristic
114C2×C4×C47#13111yescharacteristic
115C2×C4×C47#13111yescharacteristic
116C8×C47—22no—
117C8×C47—22no—
118C8×C47—41no—
119C8×C47#12111yescharacteristic
120C8×C47#12311yescharacteristic
121C8×C47#12411yescharacteristic
122C8×C47#12611yescharacteristic
123#13123C4711yesmaximal, characteristic, direct product factor, Sylow
124C22×C47—41no—
125C22×C47—41no—
126C22×C47—81no—
127C22×C47#43111yescharacteristic
128C22×C47#43511yescharacteristic
129C22×C47#43611yescharacteristic
130C4×C47—42no—
131C4×C47—41no—
132C4×C47—81no—
133C4×C47#38811yescharacteristic
134C4×C47#43311yescharacteristic
135C4×C47C8×D411yescharacteristic
136C4×C47C8×D411yescharacteristic
137#2153C2×C4711yescharacteristic, complemented
138#2117C2×C4711yescharacteristic
139C2×#350C2×C4711yescharacteristic
140#2108C2×C4711yescharacteristic, complemented
141#1757C2×C4711yescharacteristic
142#1379C2×C4711yescharacteristic, complemented
143#1378C2×C4711yescharacteristic, complemented
144C2×C47—21no—
145C2×C47—21no—
146C2×C47—21no—
147C2×C47—81no—
148C2×C47#192311yescharacteristic
149C2×#131C22×C4711yescharacteristic
150C2×M32C22×C4711yescharacteristic
151C2×M32C22×C4711yescharacteristic
152C2×M32C22×C4711yescharacteristic
153C22×C16C22×C4711yescharacteristic
154#413C4×C4711yescharacteristic
155#410C4×C4711yescharacteristic
156#405C22×C4711yescharacteristic
157#405C22×C4711yescharacteristic
158#364—22no—
159#350—22no—
160#350—21no—
161#350—21no—
162#346—21no—
163C4×C16—21no—
164#344C4×C4711yescharacteristic
165#344C4×C4711yescharacteristic
166C47#1312311yescharacteristic, direct product factor, Sylow
167C2×#41C2×C4×C4711yescharacteristic
168#131—21no—
169#131—21no—
170#131—21no—
171#131—21no—
172C2×M16—21no—
173C2×M16C2×C4×C4711yescharacteristic
174C2×M16C2×C4×C4711yescharacteristic
175C2×M16C2×C4×C4711yescharacteristic
176C22×C8—21no—
177C22×C8C23×C4711yescharacteristic
178#117C2×C4×C4711yescharacteristic
179#117C2×C4×C4711yescharacteristic
180M32—21no—
181M32—21no—
182M32—21no—
183M32—21no—
184M32—21no—
185M32D4×C4712yes—
186C2×C16—21no—
187C2×C16—21no—
188C2×C16—21no—
189C2×C16—21no—
190C2×C16—21no—
191C2×C16D4×C4711yescharacteristic
192C2×C16D4×C4711yescharacteristic
193#101C8×C4712yes—
194#100C8×C4712yes—
195#99—22no—
196#97—21no—
197#97—21no—
198C4×C8—21no—
199C4×C8—21no—
200#41—21no—
201#41—21no—
202#41—21no—
203#41—21no—
204C2×Q8C2×C8×C4711yescharacteristic
205C2×D4—21no—
206C2×D4C2×C8×C4711yescharacteristic
207C22×C4—21no—
208C22×C4C22×C4×C4711yescharacteristic
209M16—21no—
210M16—21no—
211M16—21no—
212M16—21no—
213M16—41no—
214M16—41no—
215M16C2×C8×C4712yes—
216M16C2×C8×C4712yes—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8C2×D4×C4711yescharacteristic
223C2×C8C2×D4×C4711yescharacteristic
224C2×C8#41×C4711yescharacteristic
225C2×C8#41×C4711yescharacteristic
226C2×C8#41×C4711yescharacteristic
227C2×C8#41×C4711yescharacteristic
228C4⋊C4—21no—
229C4⋊C4—21no—
230C22⋊C4—21no—
231C22⋊C4M16×C4712yes—
232C42—21no—
233C42—21no—
234C16—22no—
235C16—21no—
236C16—21no—
237C16—41no—
238C16—41no—
239C23—21no—
240C23C2×M16×C4711yescharacteristic
241Q8—21no—
242Q8—21no—
243D4—21no—
244D4—21no—
245D4—41no—
246D4—41no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4#117×C4711yescharacteristic
253C2×C4C4×D4×C4711yescharacteristic
254C2×C4C4×D4×C4711yescharacteristic
255C2×C4C22×C8×C4711yescharacteristic
256C2×C4#131×C4711yescharacteristic
257C2×C4#131×C4711yescharacteristic
258C8—22no—
259C8—22no—
260C8—41no—
261C8#121×C4711yescharacteristic
262C8#123×C4711yescharacteristic
263C8#124×C4711yescharacteristic
264C8#126×C4711yescharacteristic
265C22—41no—
266C22—41no—
267C22—81no—
268C22C47×#43111yescharacteristic
269C22C47×#43511yescharacteristic
270C22C47×#43611yescharacteristic
271C4—42no—
272C4—41no—
273C4—81no—
274C4C47×#38811yescharacteristic
275C4C47×#43311yescharacteristic
276C4C8×D4×C4711yescharacteristic
277C4C8×D4×C4711yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—81no—
282C2C47×#192311yescharacteristic
subgroupG/H
centerC8×C47#121
commutatorC2×C4C22×C8×C47
Frattini, cosocleC22×C8C23×C47
socleC2×C47#1923
prime radicalC2×#41×C47C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C8×C47 ◁ C22×C8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#2153C2semidirect
4. C47×#2108C2semidirect
6. C47×#1379C2semidirect
7. C47×#1378C2semidirect
123. #13123C47direct (N × H)
137. #2153C2×C47semidirect
140. #2108C2×C47semidirect
142. #1379C2×C47semidirect
143. #1378C2×C47semidirect
166. C47#13123direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#21532
C47×#21172
C2×C47×#3502
C47×#21082
C47×#17572
C47×#13792
C47×#13782
#1312347