Finite Group Databasebeta

← C47×#12833 #26052531

Subgroups — C47×#12833 #26052531

Order 12032.

358 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3407C211yesmaximal, characteristic
2C47×#2155C211yesmaximal, characteristic, complemented
3C2×C47×#365C211yesmaximal, characteristic, complemented
4C47×#1815C211yesmaximal, characteristic
5C47×#1814C211yesmaximal, characteristic
6C47×#1388C211yesmaximal, characteristic, complemented
7C47×#1386C211yesmaximal, characteristic, complemented
8C2×#131×C47C2211yescharacteristic
9C47×#504—22no—
10C47×#504C414yescomplemented
11C2×M32×C47—22no—
12C2×M32×C47C2211yescharacteristic
13C2×M32×C47C2211yescharacteristic
14C2×#108×C47C2211yescharacteristic
15C2×#108×C47C2211yescharacteristic
16C47×#427C2211yescharacteristic
17C2×#106×C47C2211yescharacteristic
18C47×#421—21no—
19C47×#417—21no—
20C47×#365—22no—
21C47×#365—22no—
22C47×#344—21no—
23C47×#343—21no—
24C2×#41×C47D411yescharacteristic
25#131×C47—21no—
26#131×C47—21no—
27#131×C47C2×C412yes—
28#131×C47Q812yes—
29C2×M16×C47—21no—
30C2×M16×C47—21no—
31C2×M16×C47—21no—
32C2×M16×C47D411yescharacteristic
33C22×C8×C47—21no—
34C22×C8×C47C2311yescharacteristic
35#117×C47—21no—
36C2×C4⋊C4×C47—21no—
37M32×C47—21no—
38M32×C47—24no—
39M32×C47C2×C412yes—
40M32×C47D412yes—
41M32×C47D412yes—
42C2×C16×C47—21no—
43C2×C16×C47—24no—
44C2×C16×C47C2×C412yes—
45#108×C47—21no—
46#108×C47—21no—
47#108×C47—21no—
48#108×C47—21no—
49#107×C47—21no—
50#106×C47—21no—
51#106×C47—21no—
52#106×C47—21no—
53#104×C47—42no—
54#103×C47—41no—
55#102×C47—41no—
56#41×C47—21no—
57#41×C47—21no—
58#41×C47C4⋊C412yes—
59#41×C47SD1612yes—
60C2×Q8×C47SD1611yescharacteristic
61C2×D4×C47—21no—
62C2×D4×C47SD1611yescharacteristic
63C22×C4×C47—21no—
64C22×C4×C47—41no—
65C22×C4×C47C2×D411yescharacteristic
66M16×C47—21no—
67M16×C47—22no—
68M16×C47—22no—
69M16×C47—41no—
70M16×C47—41no—
71M16×C47—41no—
72M16×C47—41no—
73M16×C47C4⋊C412yes—
74C2×C8×C47—21no—
75C2×C8×C47—22no—
76C2×C8×C47—22no—
77C2×C8×C47—41no—
78C2×C8×C47—41no—
79C2×C8×C47C22×C411yescharacteristic
80C2×C8×C47C2×D411yescharacteristic
81C2×C8×C47C2×D411yescharacteristic
82C2×C8×C47C2×Q811yescharacteristic
83C2×C8×C47#4111yescharacteristic
84C2×C8×C47#4111yescharacteristic
85C4⋊C4×C47—41no—
86C4⋊C4×C47—41no—
87C4⋊C4×C47—41no—
88C22⋊C4×C47—41no—
89C42×C47—41no—
90C16×C47—22no—
91C16×C47C22⋊C414yes—
92C23×C47—21no—
93C23×C47#13511yescharacteristic
94Q8×C47—21no—
95Q8×C47#10612yes—
96D4×C47—22no—
97D4×C47—22no—
98D4×C47—21no—
99D4×C47#10612yes—
100C2×C4×C47—21no—
101C2×C4×C47—22no—
102C2×C4×C47—22no—
103C2×C4×C47—81no—
104C2×C4×C47—81no—
105C2×C4×C47—161no—
106C2×C4×C47C2×C4⋊C411yescharacteristic
107C2×C4×C47#12111yescharacteristic
108C2×C4×C47#12111yescharacteristic
109C2×C4×C47C2×SD1611yescharacteristic
110C2×C4×C47C2×SD1611yescharacteristic
111C2×C4×C47#13511yescharacteristic
112C8×C47—22no—
113C8×C47—81no—
114C8×C47—81no—
115C8×C47C2×C22⋊C411yescharacteristic
116C8×C47#11711yescharacteristic
117C8×C47C22⋊Q811yescharacteristic
118C8×C47C22⋊Q811yescharacteristic
119#12833C4711yesmaximal, characteristic, direct product factor, Sylow
120C22×C47—22no—
121C22×C47—41no—
122C22×C47—81no—
123C22×C47#42711yescharacteristic
124C22×C47#46511yescharacteristic
125C22×C47#46511yescharacteristic
126C4×C47—22no—
127C4×C47—161no—
128C4×C47—161no—
129C4×C47#38011yescharacteristic
130C4×C47C2×#10611yescharacteristic
131C4×C47#46511yescharacteristic
132C4×C47#46511yescharacteristic
133#3407C2×C4711yescharacteristic
134#2155C2×C4711yescharacteristic, complemented
135C2×#365C2×C4711yescharacteristic, complemented
136#1815C2×C4711yescharacteristic
137#1814C2×C4711yescharacteristic
138#1388C2×C4711yescharacteristic, complemented
139#1386C2×C4711yescharacteristic, complemented
140C2×C47—21no—
141C2×C47—21no—
142C2×C47—21no—
143C2×C47—42no—
144C2×C47#180711yescharacteristic
145C2×#131C22×C4711yescharacteristic
146#504—22no—
147#504C4×C4714yescomplemented
148C2×M32—22no—
149C2×M32C22×C4711yescharacteristic
150C2×M32C22×C4711yescharacteristic
151C2×#108C22×C4711yescharacteristic
152C2×#108C22×C4711yescharacteristic
153#427C22×C4711yescharacteristic
154C2×#106C22×C4711yescharacteristic
155#421—21no—
156#417—21no—
157#365—22no—
158#365—22no—
159#344—21no—
160#343—21no—
161C47#1283311yescharacteristic, direct product factor, Sylow
162C2×#41D4×C4711yescharacteristic
163#131—21no—
164#131—21no—
165#131C2×C4×C4712yes—
166#131Q8×C4712yes—
167C2×M16—21no—
168C2×M16—21no—
169C2×M16—21no—
170C2×M16D4×C4711yescharacteristic
171C22×C8—21no—
172C22×C8C23×C4711yescharacteristic
173#117—21no—
174C2×C4⋊C4—21no—
175M32—21no—
176M32—24no—
177M32C2×C4×C4712yes—
178M32D4×C4712yes—
179M32D4×C4712yes—
180C2×C16—21no—
181C2×C16—24no—
182C2×C16C2×C4×C4712yes—
183#108—21no—
184#108—21no—
185#108—21no—
186#108—21no—
187#107—21no—
188#106—21no—
189#106—21no—
190#106—21no—
191#104—42no—
192#103—41no—
193#102—41no—
194#41—21no—
195#41—21no—
196#41C4⋊C4×C4712yes—
197#41SD16×C4712yes—
198C2×Q8SD16×C4711yescharacteristic
199C2×D4—21no—
200C2×D4SD16×C4711yescharacteristic
201C22×C4—21no—
202C22×C4—41no—
203C22×C4C2×D4×C4711yescharacteristic
204M16—21no—
205M16—22no—
206M16—22no—
207M16—41no—
208M16—41no—
209M16—41no—
210M16—41no—
211M16C4⋊C4×C4712yes—
212C2×C8—21no—
213C2×C8—22no—
214C2×C8—22no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8C22×C4×C4711yescharacteristic
218C2×C8C2×D4×C4711yescharacteristic
219C2×C8C2×D4×C4711yescharacteristic
220C2×C8C2×Q8×C4711yescharacteristic
221C2×C8#41×C4711yescharacteristic
222C2×C8#41×C4711yescharacteristic
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C22⋊C4—41no—
227C42—41no—
228C16—22no—
229C16C22⋊C4×C4714yes—
230C23—21no—
231C23#135×C4711yescharacteristic
232Q8—21no—
233Q8#106×C4712yes—
234D4—22no—
235D4—22no—
236D4—21no—
237D4#106×C4712yes—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—161no—
244C2×C4C2×C4⋊C4×C4711yescharacteristic
245C2×C4#121×C4711yescharacteristic
246C2×C4#121×C4711yescharacteristic
247C2×C4C2×SD16×C4711yescharacteristic
248C2×C4C2×SD16×C4711yescharacteristic
249C2×C4#135×C4711yescharacteristic
250C8—22no—
251C8—81no—
252C8—81no—
253C8C2×C22⋊C4×C4711yescharacteristic
254C8#117×C4711yescharacteristic
255C8C22⋊Q8×C4711yescharacteristic
256C8C22⋊Q8×C4711yescharacteristic
257C22—22no—
258C22—41no—
259C22—81no—
260C22C47×#42711yescharacteristic
261C22C47×#46511yescharacteristic
262C22C47×#46511yescharacteristic
263C4—22no—
264C4—161no—
265C4—161no—
266C4C47×#38011yescharacteristic
267C4C2×#106×C4711yescharacteristic
268C4C47×#46511yescharacteristic
269C4C47×#46511yescharacteristic
270C2—21no—
271C2—21no—
272C2—21no—
273C2—42no—
274C2C47×#180711yescharacteristic
subgroupG/H
center, socleC2×C47#1807
commutatorC2×C8C22×C4×C47
Frattini, cosocleC22×C8C23×C47
prime radicalC2×#41×C47D4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C22×C4×C47 ◁ C2×#131×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2155C2semidirect
3. C2×C47×#365C2semidirect
6. C47×#1388C2semidirect
7. C47×#1386C2semidirect
10. C47×#504C4semidirect
119. #12833C47direct (N × H)
134. #2155C2×C47semidirect
135. C2×#365C2×C47semidirect
138. #1388C2×C47semidirect
139. #1386C2×C47semidirect
147. #504C4×C47semidirect
161. C47#12833direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#34072
C47×#21552
C2×C47×#3652
C47×#18152
C47×#18142
C47×#13882
C47×#13862
#1283347