Finite Group Databasebeta

← C47×#12609 #26052307

Subgroups — C47×#12609 #26052307

Order 12032.

444 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2875C211yesmaximal, characteristic
2C47×#2117C212yesmaximal
3C2×C47×#347C211yesmaximal, characteristic, complemented
4C2×C47×#347C211yesmaximal, characteristic, complemented
5C47×#1378C212yesmaximal, complemented
6C2×#131×C47C411yescharacteristic
7C2×#131×C47C2211yescharacteristic
8C4×#41×C47C411yescharacteristic
9C2×M32×C47C2212yes—
10C2×M32×C47C2212yes—
11C47×#405—21no—
12C47×#405—21no—
13C47×#405C411yescharacteristic
14C47×#405C2211yescharacteristic
15C4×M16×C47—21no—
16C4×M16×C47C411yescharacteristic
17C2×#97×C47—21no—
18C2×#97×C47C2211yescharacteristic
19C47×#350C418yescomplemented
20C47×#347—21no—
21C47×#347—21no—
22C47×#347—21no—
23C47×#347—21no—
24C2×#41×C47C2×C411yescharacteristic
25#131×C47—22no—
26#131×C47—22no—
27#131×C47—22no—
28#131×C47C2×C414yes—
29C2×M16×C47—21no—
30C2×M16×C47—21no—
31C2×M16×C47C2×C411yescharacteristic
32C2×M16×C47C2×C411yescharacteristic
33C22×C8×C47—21no—
34C22×C8×C47—21no—
35C22×C8×C47C2×C411yescharacteristic
36C22×C8×C47C2311yescharacteristic
37C4×Q8×C47—21no—
38C4×D4×C47—21no—
39C4×D4×C47—22no—
40#117×C47—21no—
41#117×C47C2×C411yescharacteristic
42C2×C42×C47—21no—
43C2×C42×C47C2×C411yescharacteristic
44M32×C47—22no—
45M32×C47—22no—
46M32×C47—22no—
47M32×C47C2×C414yescomplemented
48C2×C16×C47—22no—
49C2×C16×C47C2×C414yescomplemented
50#97×C47—21no—
51#97×C47—21no—
52#97×C47—21no—
53#97×C47D411yescharacteristic
54#97×C47D411yescharacteristic
55#97×C47D411yescharacteristic
56#97×C47D411yescharacteristic
57C4×C8×C47—21no—
58C4×C8×C47—21no—
59C4×C8×C47—21no—
60#41×C47—21no—
61#41×C47—21no—
62#41×C47C4212yes—
63#41×C47M1612yes—
64C2×Q8×C47M1611yescharacteristic
65C2×D4×C47—21no—
66C2×D4×C47M1611yescharacteristic
67C22×C4×C47—21no—
68C22×C4×C47—22no—
69C22×C4×C47—21no—
70C22×C4×C47C22×C411yescharacteristic
71M16×C47—24no—
72M16×C47—21no—
73M16×C47—21no—
74M16×C47—24no—
75M16×C47C4212yes—
76M16×C47M1612yes—
77C2×C8×C47—24no—
78C2×C8×C47—21no—
79C2×C8×C47—21no—
80C2×C8×C47—21no—
81C2×C8×C47—21no—
82C2×C8×C47—24no—
83C2×C8×C47C22⋊C411yescharacteristic
84C2×C8×C47C22⋊C411yescharacteristic
85C2×C8×C47C22×C412yes—
86C2×C8×C47C2×D411yescharacteristic
87C2×C8×C47C2×D411yescharacteristic
88C2×C8×C47#4112yes—
89C4⋊C4×C47—22no—
90C4⋊C4×C47—21no—
91C22⋊C4×C47—22no—
92C22⋊C4×C47M1612yes—
93C42×C47—22no—
94C42×C47—21no—
95C42×C47—21no—
96C42×C47C22⋊C411yescharacteristic
97C42×C47C22⋊C411yescharacteristic
98C16×C47—24no—
99C16×C47—24no—
100C23×C47—21no—
101C23×C47C2×M1611yescharacteristic
102Q8×C47—21no—
103Q8×C47#9712yes—
104D4×C47—22no—
105D4×C47—22no—
106D4×C47—21no—
107D4×C47#9712yes—
108C2×C4×C47—21no—
109C2×C4×C47—22no—
110C2×C4×C47—22no—
111C2×C4×C47—21no—
112C2×C4×C47—22no—
113C2×C4×C47—21no—
114C2×C4×C47—81no—
115C2×C4×C47—82no—
116C2×C4×C47C2×C4211yescharacteristic
117C2×C4×C47C2×C22⋊C411yescharacteristic
118C2×C4×C47#11711yescharacteristic
119C2×C4×C47C2×M1611yescharacteristic
120C2×C4×C47C2×M1611yescharacteristic
121C2×C4×C47C2×M1611yescharacteristic
122C8×C47—22no—
123C8×C47—21no—
124C8×C47—22no—
125C8×C47—21no—
126C8×C47C4×D412yes—
127C8×C47C4×D412yes—
128#12609C4711yesmaximal, characteristic, direct product factor, Sylow
129C22×C47—22no—
130C22×C47—41no—
131C22×C47—42no—
132C22×C47C4×M1611yescharacteristic
133C22×C47#40711yescharacteristic
134C22×C47#43211yescharacteristic
135C4×C47—22no—
136C4×C47—42no—
137C4×C47—41no—
138C4×C47—41no—
139C4×C47C4×C22⋊C411yescharacteristic
140C4×C47C2×#9711yescharacteristic
141C4×C47#40711yescharacteristic
142C4×C47#43211yescharacteristic
143#2875C2×C4711yescharacteristic
144#2117C2×C4712yes—
145C2×#347C2×C4711yescharacteristic, complemented
146C2×#347C2×C4711yescharacteristic, complemented
147#1378C2×C4712yescomplemented
148C2×C47—21no—
149C2×C47—21no—
150C2×C47—21no—
151C2×C47—42no—
152C2×C47#174911yescharacteristic
153C2×#131C4×C4711yescharacteristic
154C2×#131C22×C4711yescharacteristic
155C4×#41C4×C4711yescharacteristic
156C2×M32C22×C4712yes—
157C2×M32C22×C4712yes—
158#405—21no—
159#405—21no—
160#405C4×C4711yescharacteristic
161#405C22×C4711yescharacteristic
162C4×M16—21no—
163C4×M16C4×C4711yescharacteristic
164C2×#97—21no—
165C2×#97C22×C4711yescharacteristic
166#350C4×C4718yescomplemented
167#347—21no—
168#347—21no—
169#347—21no—
170#347—21no—
171C47#1260911yescharacteristic, direct product factor, Sylow
172C2×#41C2×C4×C4711yescharacteristic
173#131—22no—
174#131—22no—
175#131—22no—
176#131C2×C4×C4714yes—
177C2×M16—21no—
178C2×M16—21no—
179C2×M16C2×C4×C4711yescharacteristic
180C2×M16C2×C4×C4711yescharacteristic
181C22×C8—21no—
182C22×C8—21no—
183C22×C8C2×C4×C4711yescharacteristic
184C22×C8C23×C4711yescharacteristic
185C4×Q8—21no—
186C4×D4—21no—
187C4×D4—22no—
188#117—21no—
189#117C2×C4×C4711yescharacteristic
190C2×C42—21no—
191C2×C42C2×C4×C4711yescharacteristic
192M32—22no—
193M32—22no—
194M32—22no—
195M32C2×C4×C4714yescomplemented
196C2×C16—22no—
197C2×C16C2×C4×C4714yescomplemented
198#97—21no—
199#97—21no—
200#97—21no—
201#97D4×C4711yescharacteristic
202#97D4×C4711yescharacteristic
203#97D4×C4711yescharacteristic
204#97D4×C4711yescharacteristic
205C4×C8—21no—
206C4×C8—21no—
207C4×C8—21no—
208#41—21no—
209#41—21no—
210#41C42×C4712yes—
211#41M16×C4712yes—
212C2×Q8M16×C4711yescharacteristic
213C2×D4—21no—
214C2×D4M16×C4711yescharacteristic
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—21no—
218C22×C4C22×C4×C4711yescharacteristic
219M16—24no—
220M16—21no—
221M16—21no—
222M16—24no—
223M16C42×C4712yes—
224M16M16×C4712yes—
225C2×C8—24no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—24no—
231C2×C8C22⋊C4×C4711yescharacteristic
232C2×C8C22⋊C4×C4711yescharacteristic
233C2×C8C22×C4×C4712yes—
234C2×C8C2×D4×C4711yescharacteristic
235C2×C8C2×D4×C4711yescharacteristic
236C2×C8#41×C4712yes—
237C4⋊C4—22no—
238C4⋊C4—21no—
239C22⋊C4—22no—
240C22⋊C4M16×C4712yes—
241C42—22no—
242C42—21no—
243C42—21no—
244C42C22⋊C4×C4711yescharacteristic
245C42C22⋊C4×C4711yescharacteristic
246C16—24no—
247C16—24no—
248C23—21no—
249C23C2×M16×C4711yescharacteristic
250Q8—21no—
251Q8#97×C4712yes—
252D4—22no—
253D4—22no—
254D4—21no—
255D4#97×C4712yes—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—81no—
263C2×C4—82no—
264C2×C4C2×C42×C4711yescharacteristic
265C2×C4C2×C22⋊C4×C4711yescharacteristic
266C2×C4#117×C4711yescharacteristic
267C2×C4C2×M16×C4711yescharacteristic
268C2×C4C2×M16×C4711yescharacteristic
269C2×C4C2×M16×C4711yescharacteristic
270C8—22no—
271C8—21no—
272C8—22no—
273C8—21no—
274C8C4×D4×C4712yes—
275C8C4×D4×C4712yes—
276C22—22no—
277C22—41no—
278C22—42no—
279C22C4×M16×C4711yescharacteristic
280C22C47×#40711yescharacteristic
281C22C47×#43211yescharacteristic
282C4—22no—
283C4—41no—
284C4—42no—
285C4—41no—
286C4C4×C22⋊C4×C4711yescharacteristic
287C4C2×#97×C4711yescharacteristic
288C4C47×#40711yescharacteristic
289C4C47×#43211yescharacteristic
290C2—21no—
291C2—21no—
292C2—21no—
293C2—42no—
294C2C47×#174911yescharacteristic
subgroupG/H
centerC4×C47C4×C22⋊C4
commutatorC2×C4C2×C42×C47
Frattini, cosocleC22×C8C23×C47
socleC2×C47#1749
prime radicalC2×#41×C47C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C47 ◁ C2×#97×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C47×#347C2semidirect
4. C2×C47×#347C2semidirect
5. C47×#1378C2semidirect
19. C47×#350C4semidirect
47. M32×C47C2×C4semidirect
49. C2×C16×C47C2×C4semidirect
128. #12609C47direct (N × H)
145. C2×#347C2×C47semidirect
146. C2×#347C2×C47semidirect
147. #1378C2×C47semidirect
166. #350C4×C47semidirect
171. C47#12609direct (N × H)
195. M32C2×C4×C47semidirect
197. C2×C16C2×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#28752
C47×#21172
C2×C47×#3472
C47×#13782
#1260947