Finite Group Databasebeta

← C2×C47×#2643 #26074263

Subgroups — C2×C47×#2643 #26074263

Order 12032.

2546 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2643C2116yesmaximal, direct product factor
2C2×C47×#401C211yesmaximal, characteristic, complemented
3C2×C47×#400C213yesmaximal, complemented
4C2×C47×#397C213yesmaximal, complemented
5C2×C47×#396C211yesmaximal, characteristic, complemented
6C2×C47×#386C213yesmaximal
7C2×C47×#385C213yesmaximal, complemented
8C22×#95×C47C211yesmaximal, characteristic, complemented
9C23×D4×C47C2211yescharacteristic
10C24×C4×C47C2213yes—
11C22×C4⋊C4×C47C2213yes—
12C22×C4⋊C4×C47C2213yes—
13C22×C22⋊C4×C47C2213yes—
14C22×C22⋊C4×C47C2213yes—
15C22×C22⋊C4×C47C2213yes—
16C47×#401C2218yescomplemented
17C47×#400C22124yescomplemented
18C47×#397C22124yescomplemented
19C47×#396C2218yescomplemented
20C47×#386C22124yes—
21C47×#385C22124yescomplemented
22C2×#95×C47C2211yescharacteristic
23C2×#95×C47C2213yes—
24C2×#95×C47C2213yes—
25C2×#95×C47C2213yes—
26C2×#95×C47C2213yes—
27C2×#95×C47C2213yes—
28C2×#95×C47C2218yescomplemented
29C25×C47C2311yescharacteristic
30C25×C47C2311yescharacteristic
31C22×D4×C47—212no—
32C22×D4×C47C2314yes—
33C23×C4×C47—212no—
34C23×C4×C47—46no—
35C23×C4×C47—46no—
36C23×C4×C47C2313yes—
37C23×C4×C47C2313yes—
38C23×C4×C47C2313yes—
39C23×C4×C47C2313yes—
40C23×C4×C47C2311yescharacteristic
41C23×C4×C47C23112yes—
42C2×C4⋊C4×C47—46no—
43C2×C4⋊C4×C47—46no—
44C2×C4⋊C4×C47C23112yes—
45C2×C4⋊C4×C47C23112yes—
46C2×C22⋊C4×C47—212no—
47C2×C22⋊C4×C47—46no—
48C2×C22⋊C4×C47—46no—
49C2×C22⋊C4×C47C23112yes—
50C2×C22⋊C4×C47C23112yes—
51C2×C22⋊C4×C47C23112yes—
52#95×C47C2314yes—
53#95×C47C23112yes—
54#95×C47C23112yes—
55#95×C47C23112yes—
56#95×C47C23112yes—
57#95×C47C23112yes—
58C24×C47—26no—
59C24×C47—22no—
60C24×C47—26no—
61C24×C47—26no—
62C24×C47—22no—
63C24×C47#41112yes—
64C24×C47C2412yes—
65C24×C47C2412yes—
66C24×C47C2411yescharacteristic
67C2×D4×C47—224no—
68C2×D4×C47—416no—
69C22×C4×C47—26no—
70C22×C4×C47—26no—
71C22×C4×C47—224no—
72C22×C4×C47—26no—
73C22×C4×C47—26no—
74C22×C4×C47—26no—
75C22×C4×C47—26no—
76C22×C4×C47—26no—
77C22×C4×C47—26no—
78C22×C4×C47—26no—
79C22×C4×C47—26no—
80C22×C4×C47—26no—
81C22×C4×C47—26no—
82C22×C4×C47—26no—
83C22×C4×C47—412no—
84C22×C4×C47—412no—
85C22×C4×C47—448no—
86C22×C4×C47C2416yes—
87C22×C4×C47C2416yes—
88C22×C4×C47C2416yes—
89C22×C4×C47C2416yes—
90C22×C4×C47C2412yes—
91C4⋊C4×C47—412no—
92C4⋊C4×C47—412no—
93C22⋊C4×C47—224no—
94C22⋊C4×C47—412no—
95C22⋊C4×C47—412no—
96C23×C47—224no—
97C23×C47—224no—
98C23×C47—26no—
99C23×C47—22no—
100C23×C47—26no—
101C23×C47—26no—
102C23×C47—22no—
103C23×C47—44no—
104C23×C47—412no—
105C23×C47—412no—
106C23×C47#126116yes—
107C23×C47C2×#41112yes—
108C23×C47C2×#4116yes—
109C23×C47H(5,𝔽2)16yes—
110C23×C472−1+412yes—
111C23×C47C2511yescharacteristic
112D4×C47—416no—
113C2×C4×C47—26no—
114C2×C4×C47—26no—
115C2×C4×C47—26no—
116C2×C4×C47—26no—
117C2×C4×C47—26no—
118C2×C4×C47—26no—
119C2×C4×C47—26no—
120C2×C4×C47—26no—
121C2×C4×C47—26no—
122C2×C4×C47—26no—
123C2×C4×C47—26no—
124C2×C4×C47—26no—
125C2×C4×C47—26no—
126C2×C4×C47—448no—
127C2×C4×C47—44no—
128C2×C4×C47—412no—
129C2×C4×C47—412no—
130C2×C4×C47—412no—
131C2×C4×C47—412no—
132C2×#2643C4711yesmaximal, characteristic, direct product factor, Sylow
133C22×C47—232no—
134C22×C47—212no—
135C22×C47—212no—
136C22×C47—42no—
137C22×C47—46no—
138C22×C47—46no—
139C22×C47—88no—
140C22×C47C2×#12618yes—
141C22×C47C2×#12614yes—
142C22×C47#538112yes—
143C22×C47#539112yes—
144C22×C47C22×#4113yes—
145C22×C47C2×H(5,𝔽2)13yes—
146C22×C47C2×2−1+411yescharacteristic
147C4×C47—42no—
148C4×C47—46no—
149C4×C47—46no—
150C4×C47—46no—
151C4×C47—46no—
152#2643C2×C47116yesdirect product factor
153C2×#401C2×C4711yescharacteristic, complemented
154C2×#400C2×C4713yescomplemented
155C2×#397C2×C4713yescomplemented
156C2×#396C2×C4711yescharacteristic, complemented
157C2×#386C2×C4713yes—
158C2×#385C2×C4713yescomplemented
159C22×#95C2×C4711yescharacteristic, complemented
160C2×C47—28no—
161C2×C47—82no—
162C2×C47#264318yesdirect product factor
163C2×C47C22×#12611yescharacteristic
164C2×C47C2×#53813yes—
165C2×C47C2×#53913yes—
166C23×D4C22×C4711yescharacteristic
167C24×C4C22×C4713yes—
168C22×C4⋊C4C22×C4713yes—
169C22×C4⋊C4C22×C4713yes—
170C22×C22⋊C4C22×C4713yes—
171C22×C22⋊C4C22×C4713yes—
172C22×C22⋊C4C22×C4713yes—
173#401C22×C4718yescomplemented
174#400C22×C47124yescomplemented
175#397C22×C47124yescomplemented
176#396C22×C4718yescomplemented
177#386C22×C47124yes—
178#385C22×C47124yescomplemented
179C2×#95C22×C4711yescharacteristic
180C2×#95C22×C4713yes—
181C2×#95C22×C4713yes—
182C2×#95C22×C4713yes—
183C2×#95C22×C4713yes—
184C2×#95C22×C4713yes—
185C2×#95C22×C4718yescomplemented
186C47C2×#264311yescharacteristic, direct product factor, Sylow
187C25C23×C4711yescharacteristic
188C25C23×C4711yescharacteristic
189C22×D4—212no—
190C22×D4C23×C4714yes—
191C23×C4—212no—
192C23×C4—46no—
193C23×C4—46no—
194C23×C4C23×C4713yes—
195C23×C4C23×C4713yes—
196C23×C4C23×C4713yes—
197C23×C4C23×C4713yes—
198C23×C4C23×C4711yescharacteristic
199C23×C4C23×C47112yes—
200C2×C4⋊C4—46no—
201C2×C4⋊C4—46no—
202C2×C4⋊C4C23×C47112yes—
203C2×C4⋊C4C23×C47112yes—
204C2×C22⋊C4—212no—
205C2×C22⋊C4—46no—
206C2×C22⋊C4—46no—
207C2×C22⋊C4C23×C47112yes—
208C2×C22⋊C4C23×C47112yes—
209C2×C22⋊C4C23×C47112yes—
210#95C23×C4714yes—
211#95C23×C47112yes—
212#95C23×C47112yes—
213#95C23×C47112yes—
214#95C23×C47112yes—
215#95C23×C47112yes—
216C24—26no—
217C24—22no—
218C24—26no—
219C24—26no—
220C24—22no—
221C24#41×C47112yes—
222C24C24×C4712yes—
223C24C24×C4712yes—
224C24C24×C4711yescharacteristic
225C2×D4—224no—
226C2×D4—416no—
227C22×C4—26no—
228C22×C4—26no—
229C22×C4—224no—
230C22×C4—26no—
231C22×C4—26no—
232C22×C4—26no—
233C22×C4—26no—
234C22×C4—26no—
235C22×C4—26no—
236C22×C4—26no—
237C22×C4—26no—
238C22×C4—26no—
239C22×C4—26no—
240C22×C4—26no—
241C22×C4—412no—
242C22×C4—412no—
243C22×C4—448no—
244C22×C4C24×C4712yes—
245C22×C4C24×C4716yes—
246C22×C4C24×C4716yes—
247C22×C4C24×C4716yes—
248C22×C4C24×C4716yes—
249C4⋊C4—412no—
250C4⋊C4—412no—
251C22⋊C4—224no—
252C22⋊C4—412no—
253C22⋊C4—412no—
254C23—224no—
255C23—224no—
256C23—26no—
257C23—22no—
258C23—26no—
259C23—26no—
260C23—22no—
261C23—44no—
262C23—412no—
263C23—412no—
264C23#126×C47116yes—
265C23C2×#41×C47112yes—
266C23C2×#41×C4716yes—
267C23H(5,𝔽2)×C4716yes—
268C232−1+4×C4712yes—
269C23C25×C4711yescharacteristic
270D4—416no—
271C2×C4—26no—
272C2×C4—26no—
273C2×C4—26no—
274C2×C4—26no—
275C2×C4—26no—
276C2×C4—26no—
277C2×C4—26no—
278C2×C4—26no—
279C2×C4—26no—
280C2×C4—26no—
281C2×C4—26no—
282C2×C4—26no—
283C2×C4—26no—
284C2×C4—448no—
285C2×C4—44no—
286C2×C4—412no—
287C2×C4—412no—
288C2×C4—412no—
289C2×C4—412no—
290C22—232no—
291C22—212no—
292C22—212no—
293C22—42no—
294C22—46no—
295C22—46no—
296C22—88no—
297C22C2×#126×C4718yes—
298C22C2×#126×C4714yes—
299C22C47×#538112yes—
300C22C47×#539112yes—
301C22C22×#41×C4713yes—
302C22C2×H(5,𝔽2)×C4713yes—
303C22C2×2−1+4×C4711yescharacteristic
304C4—42no—
305C4—46no—
306C4—46no—
307C4—46no—
308C4—46no—
309C2—28no—
310C2—82no—
311C2C47×#264318yesdirect product factor
312C2C22×#126×C4711yescharacteristic
313C2C2×C47×#53813yes—
314C2C2×C47×#53913yes—
subgroupG/H
center, socleC24×C47C24
commutator, Frattini, cosocleC23C25×C47
prime radicalC23×D4×C47C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#2643C2direct (N × H)
2. C2×C47×#401C2semidirect
3. C2×C47×#400C2semidirect
4. C2×C47×#397C2semidirect
5. C2×C47×#396C2semidirect
7. C2×C47×#385C2semidirect
8. C22×#95×C47C2semidirect
16. C47×#401C22semidirect
17. C47×#400C22semidirect
18. C47×#397C22semidirect
19. C47×#396C22semidirect
21. C47×#385C22semidirect
28. C2×#95×C47C22semidirect
132. C2×#2643C47direct (N × H)
152. #2643C2×C47direct (N × H)
153. C2×#401C2×C47semidirect
154. C2×#400C2×C47semidirect
155. C2×#397C2×C47semidirect
156. C2×#396C2×C47semidirect
158. C2×#385C2×C47semidirect
159. C22×#95C2×C47semidirect
162. C2×C47#2643direct (N × H)
173. #401C22×C47semidirect
174. #400C22×C47semidirect
175. #397C22×C47semidirect
176. #396C22×C47semidirect
178. #385C22×C47semidirect
185. C2×#95C22×C47semidirect
186. C47C2×#2643direct (N × H)
311. C2C47×#2643direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#26432
C2×C47×#4012
C2×C47×#4002
C2×C47×#3972
C2×C47×#3962
C2×C47×#3862
C2×C47×#3852
C22×#95×C472
C2×#264347