Finite Group Databasebeta

← C47×#11598 #26051296

Subgroups — C47×#11598 #26051296

Order 12032.

402 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
1C4×#135×C47C211yesmaximal, characteristic
2C4×M32×C47C211yesmaximal, characteristic, complemented
3C2×C47×#334C211yesmaximal, characteristic, complemented
4C47×#1334C212yesmaximal, complemented
5C47×#1333C212yesmaximal, complemented
6C2×#135×C47C411yescharacteristic
7C4×#41×C47—21no—
8C2×M32×C47—21no—
9C4×Q16×C47C411yescharacteristic
10C4×Q16×C47C2211yescharacteristic
11C4×SD16×C47—21no—
12C4×SD16×C47—21no—
13C4×D8×C47C411yescharacteristic
14C4×D8×C47C2211yescharacteristic
15C47×#427C411yescharacteristic
16C2×C4⋊C8×C47—21no—
17C47×#416—21no—
18C2×C4×C8×C47C2211yescharacteristic
19C47×#346C2212yes—
20C4×C16×C47—21no—
21C47×#334—21no—
22C47×#334C2212yes—
23C2×#41×C47—21no—
24#135×C47—22no—
25#135×C47C814yescomplemented
26C2×Q16×C47C2×C411yescharacteristic
27C2×SD16×C47—21no—
28C2×D8×C47C2×C411yescharacteristic
29C22×C8×C47—41no—
30C22×C8×C47C2×C411yescharacteristic
31C22×C8×C47D411yescharacteristic
32C4×Q8×C47—21no—
33C4×Q8×C47—21no—
34C4×D4×C47—21no—
35C4×D4×C47—21no—
36C4×D4×C47—41no—
37C4×D4×C47—41no—
38#117×C47—21no—
39#117×C47—41no—
40C2×C42×C47—41no—
41C2×C42×C47D411yescharacteristic
42M32×C47—24no—
43C2×C16×C47—22no—
44#107×C47C2×C411yescharacteristic
45#107×C47C2×C411yescharacteristic
46#106×C47—21no—
47C4⋊C8×C47—22no—
48C4⋊C8×C47—41no—
49#103×C47—21no—
50#103×C47—21no—
51#102×C47—21no—
52#102×C47—21no—
53C4×C8×C47C2×C411yescharacteristic
54C4×C8×C47D411yescharacteristic
55C4×C8×C47D411yescharacteristic
56C4×C8×C47C2311yescharacteristic
57#41×C47—24no—
58#41×C47—42no—
59C2×Q8×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47—41no—
62C22×C4×C47—41no—
63C22×C4×C47—41no—
64C22×C4×C47—41no—
65C22×C4×C47C22⋊C411yescharacteristic
66C22×C4×C47D811yescharacteristic
67C22×C4×C47SD1611yescharacteristic
68Q16×C47—21no—
69Q16×C47C2×C812yescomplemented
70SD16×C47—24no—
71D8×C47—21no—
72D8×C47C2×C812yescomplemented
73C2×C8×C47—22no—
74C2×C8×C47—42no—
75C2×C8×C47—82no—
76C2×C8×C47C22⋊C411yescharacteristic
77C2×C8×C47C22⋊C411yescharacteristic
78C2×C8×C47C2×C812yes—
79C2×C8×C47M1612yes—
80C2×C8×C47C22×C411yescharacteristic
81C2×C8×C47C2×D411yescharacteristic
82C4⋊C4×C47—21no—
83C4⋊C4×C47—21no—
84C4⋊C4×C47—41no—
85C4⋊C4×C47—41no—
86C22⋊C4×C47—41no—
87C22⋊C4×C47—41no—
88C22⋊C4×C47—41no—
89C42×C47—41no—
90C42×C47—41no—
91C42×C47—41no—
92C42×C47C22⋊C411yescharacteristic
93C42×C47D811yescharacteristic
94C42×C47SD1611yescharacteristic
95C42×C47C2×D411yescharacteristic
96C16×C47—24no—
97C23×C47—41no—
98C23×C47#10211yescharacteristic
99Q8×C47—22no—
100Q8×C47—41no—
101D4×C47—22no—
102D4×C47—44no—
103D4×C47—41no—
104C2×C4×C47—22no—
105C2×C4×C47—41no—
106C2×C4×C47—41no—
107C2×C4×C47—44no—
108C2×C4×C47—41no—
109C2×C4×C47—41no—
110C2×C4×C47—82no—
111C2×C4×C47—82no—
112C2×C4×C47C22⋊C812yes—
113C2×C4×C47#10211yescharacteristic
114C2×C4×C47#10211yescharacteristic
115C2×C4×C47#10211yescharacteristic
116C2×C4×C47#10412yes—
117C2×C4×C47C2×C22⋊C411yescharacteristic
118C2×C4×C47C2×D811yescharacteristic
119C2×C4×C47C2×SD1611yescharacteristic
120C8×C47—21no—
121C8×C47—21no—
122C8×C47—82no—
123C8×C47C22⋊C812yes—
124C8×C47C22×C811yescharacteristic
125C8×C47C2×M1611yescharacteristic
126#11598C4711yesmaximal, characteristic, direct product factor, Sylow
127C22×C47—21no—
128C22×C47—21no—
129C22×C47—42no—
130C22×C47—81no—
131C22×C47—81no—
132C22×C47D4⋊C812yes—
133C22×C47C2×#10211yescharacteristic
134C4×C47—21no—
135C4×C47—21no—
136C4×C47—21no—
137C4×C47—42no—
138C4×C47—81no—
139C4×C47—81no—
140C4×C47D4⋊C812yes—
141C4×C47#36012yes—
142C4×C47C2×C22⋊C811yescharacteristic
143C4×C47C2×#10411yescharacteristic
144C4×#135C2×C4711yescharacteristic
145C4×M32C2×C4711yescharacteristic, complemented
146C2×#334C2×C4711yescharacteristic, complemented
147#1334C2×C4712yescomplemented
148#1333C2×C4712yescomplemented
149C2×C47—22no—
150C2×C47—82no—
151C2×C47C2×D4⋊C811yescharacteristic
152C2×C47C2×#36011yescharacteristic
153C2×C47#214811yescharacteristic
154C2×#135C4×C4711yescharacteristic
155C4×#41—21no—
156C2×M32—21no—
157C4×Q16C4×C4711yescharacteristic
158C4×Q16C22×C4711yescharacteristic
159C4×SD16—21no—
160C4×SD16—21no—
161C4×D8C4×C4711yescharacteristic
162C4×D8C22×C4711yescharacteristic
163#427C4×C4711yescharacteristic
164C2×C4⋊C8—21no—
165#416—21no—
166C2×C4×C8C22×C4711yescharacteristic
167#346C22×C4712yes—
168C4×C16—21no—
169#334—21no—
170#334C22×C4712yes—
171C47#1159811yescharacteristic, direct product factor, Sylow
172C2×#41—21no—
173#135—22no—
174#135C8×C4714yescomplemented
175C2×Q16C2×C4×C4711yescharacteristic
176C2×SD16—21no—
177C2×D8C2×C4×C4711yescharacteristic
178C22×C8—41no—
179C22×C8C2×C4×C4711yescharacteristic
180C22×C8D4×C4711yescharacteristic
181C4×Q8—21no—
182C4×Q8—21no—
183C4×D4—21no—
184C4×D4—21no—
185C4×D4—41no—
186C4×D4—41no—
187#117—21no—
188#117—41no—
189C2×C42—41no—
190C2×C42D4×C4711yescharacteristic
191M32—24no—
192C2×C16—22no—
193#107C2×C4×C4711yescharacteristic
194#107C2×C4×C4711yescharacteristic
195#106—21no—
196C4⋊C8—22no—
197C4⋊C8—41no—
198#103—21no—
199#103—21no—
200#102—21no—
201#102—21no—
202C4×C8C2×C4×C4711yescharacteristic
203C4×C8D4×C4711yescharacteristic
204C4×C8D4×C4711yescharacteristic
205C4×C8C23×C4711yescharacteristic
206#41—24no—
207#41—42no—
208C2×Q8—21no—
209C2×D4—21no—
210C2×D4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4C22⋊C4×C4711yescharacteristic
215C22×C4D8×C4711yescharacteristic
216C22×C4SD16×C4711yescharacteristic
217Q16—21no—
218Q16C2×C8×C4712yescomplemented
219SD16—24no—
220D8—21no—
221D8C2×C8×C4712yescomplemented
222C2×C8—22no—
223C2×C8—42no—
224C2×C8—82no—
225C2×C8C22⋊C4×C4711yescharacteristic
226C2×C8C22⋊C4×C4711yescharacteristic
227C2×C8C2×C8×C4712yes—
228C2×C8M16×C4712yes—
229C2×C8C22×C4×C4711yescharacteristic
230C2×C8C2×D4×C4711yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C22⋊C4—41no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C42—41no—
239C42—41no—
240C42—41no—
241C42C22⋊C4×C4711yescharacteristic
242C42D8×C4711yescharacteristic
243C42SD16×C4711yescharacteristic
244C42C2×D4×C4711yescharacteristic
245C16—24no—
246C23—41no—
247C23#102×C4711yescharacteristic
248Q8—22no—
249Q8—41no—
250D4—22no—
251D4—44no—
252D4—41no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—44no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4C22⋊C8×C4712yes—
262C2×C4#102×C4711yescharacteristic
263C2×C4#102×C4711yescharacteristic
264C2×C4#102×C4711yescharacteristic
265C2×C4#104×C4712yes—
266C2×C4C2×C22⋊C4×C4711yescharacteristic
267C2×C4C2×D8×C4711yescharacteristic
268C2×C4C2×SD16×C4711yescharacteristic
269C8—21no—
270C8—21no—
271C8—82no—
272C8C22⋊C8×C4712yes—
273C8C22×C8×C4711yescharacteristic
274C8C2×M16×C4711yescharacteristic
275C22—21no—
276C22—21no—
277C22—42no—
278C22—81no—
279C22—81no—
280C22C47×D4⋊C812yes—
281C22C2×#102×C4711yescharacteristic
282C4—21no—
283C4—21no—
284C4—21no—
285C4—42no—
286C4—81no—
287C4—81no—
288C4C47×D4⋊C812yes—
289C4C47×#36012yes—
290C4C2×C22⋊C8×C4711yescharacteristic
291C4C2×#104×C4711yescharacteristic
292C2—22no—
293C2—82no—
294C2C2×C47×D4⋊C811yescharacteristic
295C2C2×C47×#36011yescharacteristic
296C2C47×#214811yescharacteristic
subgroupG/H
centerC2×C4×C47#102
commutatorC8C22×C8×C47
Frattini, cosocleC4×C8C23×C47
socleC22×C47C2×#102
prime radicalC2×#135×C47C4
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C2×C42×C47 ◁ C2×C4×C8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×M32×C47C2semidirect
3. C2×C47×#334C2semidirect
4. C47×#1334C2semidirect
5. C47×#1333C2semidirect
25. #135×C47C8semidirect
69. Q16×C47C2×C8semidirect
72. D8×C47C2×C8semidirect
126. #11598C47direct (N × H)
145. C4×M32C2×C47semidirect
146. C2×#334C2×C47semidirect
147. #1334C2×C47semidirect
148. #1333C2×C47semidirect
171. C47#11598direct (N × H)
174. #135C8×C47semidirect
218. Q16C2×C8×C47semidirect
221. D8C2×C8×C47semidirect

Maximal subgroups

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

subgroupindex
C4×#135×C472
C4×M32×C472
C2×C47×#3342
C47×#13342
C47×#13332
#1159847