Finite Group Databasebeta

← C47×#13143 #26052841

Subgroups — C47×#13143 #26052841

Order 12032.

338 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#365C211yesmaximal, characteristic, complemented
2C2×C47×#360C211yesmaximal, characteristic
3C47×#2139C211yesmaximal, characteristic
4C47×#1975C211yesmaximal, characteristic
5C47×#1776C211yesmaximal, characteristic, complemented
6C47×#1387C211yesmaximal, characteristic, complemented
7C47×#1375C211yesmaximal, characteristic, complemented
8C2×#135×C47C2211yescharacteristic
9C2×M32×C47C2211yescharacteristic
10C2×M32×C47C2211yescharacteristic
11C2×#108×C47C2211yescharacteristic
12C2×#107×C47C2211yescharacteristic
13C2×#106×C47C2211yescharacteristic
14C2×#104×C47—21no—
15C47×#408—21no—
16C2×#97×C47C2211yescharacteristic
17C4×C4⋊C4×C47—21no—
18C47×#365—22no—
19C47×#360—22no—
20C47×#358C412yescomplemented
21C47×#357C412yescomplemented
22C47×#340—21no—
23C2×#41×C47—21no—
24#135×C47—21no—
25#135×C47—21no—
26#135×C47—21no—
27#135×C47—21no—
28C2×Q16×C47C2×C411yescharacteristic
29C2×SD16×C47—21no—
30C2×D8×C47C2×C411yescharacteristic
31C2×M16×C47—21no—
32C22×C8×C47D411yescharacteristic
33C22×C8×C47C2311yescharacteristic
34C2×C4⋊C4×C47—21no—
35C2×C4⋊C4×C47—21no—
36C2×C42×C47—41no—
37C2×C42×C47D411yescharacteristic
38M32×C47—21no—
39M32×C47—21no—
40M32×C47—21no—
41M32×C47—21no—
42C2×C16×C47—21no—
43C2×C16×C47C2×C412yes—
44#108×C47—21no—
45#108×C47—21no—
46#107×C47—21no—
47#107×C47C2×C412yes—
48#106×C47—21no—
49#106×C47D412yes—
50#104×C47—42no—
51C22⋊C8×C47—42no—
52#97×C47—21no—
53#97×C47—21no—
54#95×C47—41no—
55#41×C47—41no—
56#41×C47—41no—
57#41×C47—41no—
58#41×C47—41no—
59C2×Q8×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47—41no—
62C22×C4×C47—21no—
63C22×C4×C47—41no—
64C22×C4×C47—41no—
65C22×C4×C47—41no—
66C22×C4×C47C2×D411yescharacteristic
67Q16×C47—21no—
68Q16×C47—21no—
69SD16×C47—41no—
70SD16×C47—41no—
71D8×C47—21no—
72D8×C47—21no—
73M16×C47—41no—
74M16×C47—41no—
75C2×C8×C47—21no—
76C2×C8×C47—21no—
77C2×C8×C47—21no—
78C2×C8×C47—41no—
79C2×C8×C47C22×C411yescharacteristic
80C2×C8×C47C2×D411yescharacteristic
81C2×C8×C47#4111yescharacteristic
82C2×C8×C47#4111yescharacteristic
83C2×C8×C47#4111yescharacteristic
84C2×C8×C47#4111yescharacteristic
85C4⋊C4×C47—22no—
86C4⋊C4×C47—22no—
87C4⋊C4×C47—41no—
88C4⋊C4×C47—41no—
89C42×C47—21no—
90C42×C47—82no—
91C42×C47SD1612yes—
92C16×C47—22no—
93C16×C47—41no—
94C23×C47—41no—
95C23×C47AGL(1,ℤ/8)11yescharacteristic
96Q8×C47—41no—
97Q8×C47—41no—
98D4×C47—41no—
99D4×C47—41no—
100D4×C47—81no—
101D4×C47—81no—
102C2×C4×C47—22no—
103C2×C4×C47—41no—
104C2×C4×C47—41no—
105C2×C4×C47—42no—
106C2×C4×C47—41no—
107C2×C4×C47—42no—
108C2×C4×C47—81no—
109C2×C4×C47—81no—
110C2×C4×C47—81no—
111C2×C4×C47—81no—
112C2×C4×C47—81no—
113C2×C4×C47—81no—
114C2×C4×C47C4×D411yescharacteristic
115C2×C4×C47#12111yescharacteristic
116C2×C4×C47#12311yescharacteristic
117C2×C4×C47C2×SD1611yescharacteristic
118C2×C4×C47#13511yescharacteristic
119C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
120C8×C47—41no—
121C8×C47—81no—
122C8×C47#11711yescharacteristic
123C8×C47C4×D411yescharacteristic
124C8×C47#12411yescharacteristic
125C8×C47#12611yescharacteristic
126#13143C4711yesmaximal, characteristic, direct product factor, Sylow
127C22×C47—21no—
128C22×C47—21no—
129C22×C47—81no—
130C22×C47—81no—
131C22×C47—81no—
132C22×C47#44211yescharacteristic
133C22×C47#46311yescharacteristic
134C22×C47#48111yescharacteristic
135C4×C47—42no—
136C4×C47—82no—
137C4×C47—82no—
138C4×C47—81no—
139C4×C47#38811yescharacteristic
140C4×C47C4×SD1611yescharacteristic
141C4×C47#46011yescharacteristic
142C4×C47#48211yescharacteristic
143C2×#365C2×C4711yescharacteristic, complemented
144C2×#360C2×C4711yescharacteristic
145#2139C2×C4711yescharacteristic
146#1975C2×C4711yescharacteristic
147#1776C2×C4711yescharacteristic, complemented
148#1387C2×C4711yescharacteristic, complemented
149#1375C2×C4711yescharacteristic, complemented
150C2×C47—21no—
151C2×C47—21no—
152C2×C47—161no—
153C2×C47#192611yescharacteristic
154C2×C47#218011yescharacteristic
155C2×C47AGL(1,ℤ/16)11yescharacteristic
156C2×#135C22×C4711yescharacteristic
157C2×M32C22×C4711yescharacteristic
158C2×M32C22×C4711yescharacteristic
159C2×#108C22×C4711yescharacteristic
160C2×#107C22×C4711yescharacteristic
161C2×#106C22×C4711yescharacteristic
162C2×#104—21no—
163#408—21no—
164C2×#97C22×C4711yescharacteristic
165C4×C4⋊C4—21no—
166#365—22no—
167#360—22no—
168#358C4×C4712yescomplemented
169#357C4×C4712yescomplemented
170#340—21no—
171C47#1314311yescharacteristic, direct product factor, Sylow
172C2×#41—21no—
173#135—21no—
174#135—21no—
175#135—21no—
176#135—21no—
177C2×Q16C2×C4×C4711yescharacteristic
178C2×SD16—21no—
179C2×D8C2×C4×C4711yescharacteristic
180C2×M16—21no—
181C22×C8D4×C4711yescharacteristic
182C22×C8C23×C4711yescharacteristic
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C42—41no—
186C2×C42D4×C4711yescharacteristic
187M32—21no—
188M32—21no—
189M32—21no—
190M32—21no—
191C2×C16—21no—
192C2×C16C2×C4×C4712yes—
193#108—21no—
194#108—21no—
195#107—21no—
196#107C2×C4×C4712yes—
197#106—21no—
198#106D4×C4712yes—
199#104—42no—
200C22⋊C8—42no—
201#97—21no—
202#97—21no—
203#95—41no—
204#41—41no—
205#41—41no—
206#41—41no—
207#41—41no—
208C2×Q8—21no—
209C2×D4—21no—
210C2×D4—41no—
211C22×C4—21no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4C2×D4×C4711yescharacteristic
216Q16—21no—
217Q16—21no—
218SD16—41no—
219SD16—41no—
220D8—21no—
221D8—21no—
222M16—41no—
223M16—41no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—41no—
228C2×C8C22×C4×C4711yescharacteristic
229C2×C8C2×D4×C4711yescharacteristic
230C2×C8#41×C4711yescharacteristic
231C2×C8#41×C4711yescharacteristic
232C2×C8#41×C4711yescharacteristic
233C2×C8#41×C4711yescharacteristic
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C42—21no—
239C42—82no—
240C42SD16×C4712yes—
241C16—22no—
242C16—41no—
243C23—41no—
244C23AGL(1,ℤ/8)×C4711yescharacteristic
245Q8—41no—
246Q8—41no—
247D4—41no—
248D4—41no—
249D4—81no—
250D4—81no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4C4×D4×C4711yescharacteristic
264C2×C4#121×C4711yescharacteristic
265C2×C4#123×C4711yescharacteristic
266C2×C4C2×SD16×C4711yescharacteristic
267C2×C4#135×C4711yescharacteristic
268C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
269C8—41no—
270C8—81no—
271C8#117×C4711yescharacteristic
272C8C4×D4×C4711yescharacteristic
273C8#124×C4711yescharacteristic
274C8#126×C4711yescharacteristic
275C22—21no—
276C22—21no—
277C22—81no—
278C22—81no—
279C22—81no—
280C22C47×#44211yescharacteristic
281C22C47×#46311yescharacteristic
282C22C47×#48111yescharacteristic
283C4—42no—
284C4—82no—
285C4—82no—
286C4—81no—
287C4C47×#38811yescharacteristic
288C4C4×SD16×C4711yescharacteristic
289C4C47×#46011yescharacteristic
290C4C47×#48211yescharacteristic
291C2—21no—
292C2—21no—
293C2—161no—
294C2C47×#192611yescharacteristic
295C2C47×#218011yescharacteristic
296C2C47×AGL(1,ℤ/16)11yescharacteristic
subgroupG/H
center, socleC22×C47#442
commutatorC2×C8C22×C4×C47
Frattini, cosocleC22×C8C23×C47
prime radicalC2×#135×C47C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C22×C4×C47 ◁ C2×#97×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#365C2semidirect
5. C47×#1776C2semidirect
6. C47×#1387C2semidirect
7. C47×#1375C2semidirect
20. C47×#358C4semidirect
21. C47×#357C4semidirect
126. #13143C47direct (N × H)
143. C2×#365C2×C47semidirect
147. #1776C2×C47semidirect
148. #1387C2×C47semidirect
149. #1375C2×C47semidirect
168. #358C4×C47semidirect
169. #357C4×C47semidirect
171. C47#13143direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#3652
C2×C47×#3602
C47×#21392
C47×#19752
C47×#17762
C47×#13872
C47×#13752
#1314347