Finite Group Databasebeta

← C47×#60333 #26100031

Subgroups — C47×#60333 #26100031

Order 12032.

1926 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×2−1+4×C47C211yesmaximal, characteristic
2C47×#2991C214yesmaximal, complemented
3C47×#2989C216yesmaximal, complemented
4C47×#2984C214yesmaximal, complemented
5C47×#2982C211yesmaximal, characteristic, complemented
6C47×#2971C214yesmaximal, complemented
7C47×#2965C216yesmaximal, complemented
8Q8×M16×C47C214yesmaximal, complemented
9C2×C8×Q8×C47C211yesmaximal, characteristic, complemented
10C2×2−1+4×C47C411yescharacteristic
11C47×#520C414yes—
12C47×#520C416yes—
13C47×#519C414yes—
14C47×#519C411yescharacteristic
15C4×#41×C47C2216yes—
16C4×#41×C47C2214yes—
17C2×C4×Q8×C47C2211yescharacteristic
18C2×C4×Q8×C47C2214yes—
19C47×#446C2216yes—
20C47×#446C22112yes—
21C47×#446C2216yes—
22C8×Q8×C47C2214yes—
23C8×Q8×C47C2214yes—
24C8×Q8×C47C2214yes—
25C8×Q8×C47C2214yes—
26C47×#436C2216yes—
27C47×#436C2216yes—
28C47×#436C22112yes—
29C47×#435C2214yes—
30C47×#435C22112yes—
31C47×#432C22112yes—
32C47×#431C2216yes—
33C47×#431C22112yes—
34C47×#423C22112yes—
35C2×C4⋊C8×C47C2213yes—
36C4×M16×C47C22112yes—
37C2×C4×C8×C47C2213yes—
382−1+4×C47—28no—
39C2×#41×C47C2×C414yes—
40C2×#41×C47C2×C416yes—
41C22×Q8×C47C2×C414yes—
42C22×Q8×C47C2×C411yescharacteristic
43C2×M16×C47C2314yes—
44C2×M16×C47C23112yes—
45C22×C8×C47C2311yescharacteristic
46C22×C8×C47C2313yes—
47C4×Q8×C47C2×C4112yes—
48C4×Q8×C47C2×C414yes—
49C4×Q8×C47C2×C414yes—
50C4×Q8×C47C2×C416yes—
51C4×Q8×C47C2×C414yes—
52C4×Q8×C47C2314yes—
53C4×Q8×C47C2316yes—
54C4×D4×C47C2×C4112yes—
55C4×D4×C47C2×C416yes—
56C4×D4×C47C2×C4112yes—
57C4×D4×C47C2314yes—
58C4×D4×C47C2316yes—
59#117×C47C2×C4112yes—
60#117×C47C2×C4112yes—
61#117×C47C2×C416yes—
62C2×C4⋊C4×C47C2×C4112yes—
63C2×C4⋊C4×C47C2×C413yes—
64C2×C42×C47C2313yes—
65C2×C42×C47C23112yes—
66C4⋊C8×C47C23112yes—
67C4⋊C8×C47C23112yes—
68C4⋊C8×C47C2316yes—
69C4⋊C8×C47C2314yes—
70C4⋊C8×C47C2316yes—
71C22⋊C8×C47C2314yes—
72C22⋊C8×C47C2314yes—
73C22⋊C8×C47C23112yes—
74#97×C47C2314yes—
75#97×C47C23112yes—
76C4×C8×C47C2316yes—
77C4×C8×C47C2316yes—
78C4×C8×C47C23112yes—
79#41×C47—216no—
80#41×C47—224no—
81C2×Q8×C47—216no—
82C2×Q8×C47M1618yescomplemented
83C2×Q8×C47C22×C416yes—
84C2×Q8×C47C22×C414yes—
85C2×D4×C47C22×C414yes—
86C2×D4×C47C22×C416yes—
87C22×C4×C47C22×C4112yes—
88C22×C4×C47C22×C4112yes—
89C22×C4×C47C22×C413yes—
90C22×C4×C47C22×C413yes—
91C22×C4×C47C2411yescharacteristic
92C22×C4×C47C2414yes—
93M16×C47—28no—
94M16×C47—412no—
95C2×C8×C47—22no—
96C2×C8×C47—43no—
97C2×C8×C47C2416yes—
98C2×C8×C47C2414yes—
99C2×C8×C47C2411yescharacteristic
100C2×C8×C47C2414yes—
101C2×C8×C47C2411yescharacteristic
102C4⋊C4×C47C22×C4112yes—
103C4⋊C4×C47C22×C4112yes—
104C4⋊C4×C47C22×C416yes—
105C4⋊C4×C47C22×C414yes—
106C4⋊C4×C47C22×C416yes—
107C22⋊C4×C47C22×C414yes—
108C22⋊C4×C47C22×C4112yes—
109C22⋊C4×C47C22×C414yes—
110C42×C47C22×C4112yes—
111C42×C47C22×C416yes—
112C42×C47C22×C4112yes—
113C42×C47C2416yes—
114C42×C47C2414yes—
115C23×C47C23×C414yes—
116C23×C47C23×C411yescharacteristic
117Q8×C47—212no—
118Q8×C47C2×M16116yes—
119D4×C47—28no—
120D4×C47—212no—
121C2×C4×C47—224no—
122C2×C4×C47—21no—
123C2×C4×C47—24no—
124C2×C4×C47—21no—
125C2×C4×C47—24no—
126C2×C4×C47—43no—
127C2×C4×C47—412no—
128C2×C4×C47C2×M16112yes—
129C2×C4×C47C23×C411yescharacteristic
130C2×C4×C47C23×C414yes—
131C2×C4×C47C23×C416yes—
132C2×C4×C47C23×C414yes—
133C2×C4×C47C23×C414yes—
134C2×C4×C47C23×C416yes—
135C2×C4×C47C2511yescharacteristic
136C8×C47—21no—
137C8×C47—24no—
138C8×C47—26no—
139C8×C47—24no—
140C8×C472−1+412yescomplemented
141#60333C4711yesmaximal, characteristic, direct product factor, Sylow
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—24no—
145C22×C47—24no—
146C22×C47—24no—
147C22×C47C22×M1612yes—
148C22×C47C24×C411yescharacteristic
149C4×C47—21no—
150C4×C47—24no—
151C4×C47—24no—
152C4×C47—26no—
153C4×C47—24no—
154C4×C47C22×M16112yes—
155C4×C47C2×2−1+411yescharacteristic
156C4×C47#58511yescharacteristic
157C4×2−1+4C2×C4711yescharacteristic
158#2991C2×C4714yescomplemented
159#2989C2×C4716yescomplemented
160#2984C2×C4714yescomplemented
161#2982C2×C4711yescharacteristic, complemented
162#2971C2×C4714yescomplemented
163#2965C2×C4716yescomplemented
164Q8×M16C2×C4714yescomplemented
165C2×C8×Q8C2×C4711yescharacteristic, complemented
166C2×C47—22no—
167C2×C47—44no—
168C2×C47C4×2−1+411yescharacteristic
169C2×C47C23×M1611yescharacteristic
170C2×C47#357311yescharacteristic
171C2×2−1+4C4×C4711yescharacteristic
172#520C4×C4714yes—
173#520C4×C4716yes—
174#519C4×C4714yes—
175#519C4×C4711yescharacteristic
176C4×#41C22×C4716yes—
177C4×#41C22×C4714yes—
178C2×C4×Q8C22×C4711yescharacteristic
179C2×C4×Q8C22×C4714yes—
180#446C22×C4716yes—
181#446C22×C47112yes—
182#446C22×C4716yes—
183C8×Q8C22×C4714yes—
184C8×Q8C22×C4714yes—
185C8×Q8C22×C4714yes—
186C8×Q8C22×C4714yes—
187#436C22×C4716yes—
188#436C22×C4716yes—
189#436C22×C47112yes—
190#435C22×C4714yes—
191#435C22×C47112yes—
192#432C22×C47112yes—
193#431C22×C4716yes—
194#431C22×C47112yes—
195#423C22×C47112yes—
196C2×C4⋊C8C22×C4713yes—
197C4×M16C22×C47112yes—
198C2×C4×C8C22×C4713yes—
199C47#6033311yescharacteristic, direct product factor, Sylow
2002−1+4—28no—
201C2×#41C2×C4×C4714yes—
202C2×#41C2×C4×C4716yes—
203C22×Q8C2×C4×C4714yes—
204C22×Q8C2×C4×C4711yescharacteristic
205C2×M16C23×C4714yes—
206C2×M16C23×C47112yes—
207C22×C8C23×C4711yescharacteristic
208C22×C8C23×C4713yes—
209C4×Q8C2×C4×C47112yes—
210C4×Q8C2×C4×C4714yes—
211C4×Q8C2×C4×C4714yes—
212C4×Q8C2×C4×C4716yes—
213C4×Q8C2×C4×C4714yes—
214C4×Q8C23×C4714yes—
215C4×Q8C23×C4716yes—
216C4×D4C2×C4×C47112yes—
217C4×D4C2×C4×C4716yes—
218C4×D4C2×C4×C47112yes—
219C4×D4C23×C4714yes—
220C4×D4C23×C4716yes—
221#117C2×C4×C47112yes—
222#117C2×C4×C47112yes—
223#117C2×C4×C4716yes—
224C2×C4⋊C4C2×C4×C47112yes—
225C2×C4⋊C4C2×C4×C4713yes—
226C2×C42C23×C4713yes—
227C2×C42C23×C47112yes—
228C4⋊C8C23×C47112yes—
229C4⋊C8C23×C47112yes—
230C4⋊C8C23×C4716yes—
231C4⋊C8C23×C4714yes—
232C4⋊C8C23×C4716yes—
233C22⋊C8C23×C4714yes—
234C22⋊C8C23×C4714yes—
235C22⋊C8C23×C47112yes—
236#97C23×C4714yes—
237#97C23×C47112yes—
238C4×C8C23×C4716yes—
239C4×C8C23×C4716yes—
240C4×C8C23×C47112yes—
241#41—216no—
242#41—224no—
243C2×Q8—216no—
244C2×Q8M16×C4718yescomplemented
245C2×Q8C22×C4×C4716yes—
246C2×Q8C22×C4×C4714yes—
247C2×D4C22×C4×C4714yes—
248C2×D4C22×C4×C4716yes—
249C22×C4C22×C4×C47112yes—
250C22×C4C22×C4×C47112yes—
251C22×C4C22×C4×C4713yes—
252C22×C4C22×C4×C4713yes—
253C22×C4C24×C4711yescharacteristic
254C22×C4C24×C4714yes—
255M16—28no—
256M16—412no—
257C2×C8—22no—
258C2×C8—43no—
259C2×C8C24×C4711yescharacteristic
260C2×C8C24×C4714yes—
261C2×C8C24×C4714yes—
262C2×C8C24×C4716yes—
263C2×C8C24×C4711yescharacteristic
264C4⋊C4C22×C4×C47112yes—
265C4⋊C4C22×C4×C47112yes—
266C4⋊C4C22×C4×C4716yes—
267C4⋊C4C22×C4×C4714yes—
268C4⋊C4C22×C4×C4716yes—
269C22⋊C4C22×C4×C4714yes—
270C22⋊C4C22×C4×C47112yes—
271C22⋊C4C22×C4×C4714yes—
272C42C22×C4×C47112yes—
273C42C22×C4×C4716yes—
274C42C22×C4×C47112yes—
275C42C24×C4716yes—
276C42C24×C4714yes—
277C23C23×C4×C4714yes—
278C23C23×C4×C4711yescharacteristic
279Q8—212no—
280Q8C2×M16×C47116yes—
281D4—28no—
282D4—212no—
283C2×C4—224no—
284C2×C4—21no—
285C2×C4—24no—
286C2×C4—21no—
287C2×C4—24no—
288C2×C4—43no—
289C2×C4—412no—
290C2×C4C2×M16×C47112yes—
291C2×C4C23×C4×C4711yescharacteristic
292C2×C4C23×C4×C4714yes—
293C2×C4C23×C4×C4716yes—
294C2×C4C23×C4×C4714yes—
295C2×C4C23×C4×C4714yes—
296C2×C4C23×C4×C4716yes—
297C2×C4C25×C4711yescharacteristic
298C8—21no—
299C8—24no—
300C8—26no—
301C8—24no—
302C82−1+4×C4712yescomplemented
303C22—21no—
304C22—21no—
305C22—24no—
306C22—24no—
307C22—24no—
308C22C22×M16×C4712yes—
309C22C24×C4×C4711yescharacteristic
310C4—24no—
311C4—26no—
312C4—24no—
313C4—21no—
314C4—24no—
315C4C22×M16×C47112yes—
316C4C2×2−1+4×C4711yescharacteristic
317C4C47×#58511yescharacteristic
318C2—22no—
319C2—44no—
320C2C4×2−1+4×C4711yescharacteristic
321C2C23×M16×C4711yescharacteristic
322C2C47×#357311yescharacteristic
subgroupG/H
centerC2×C4×C47C25
commutatorC22C24×C4×C47
Frattini, cosocleC2×C4C25×C47
socleC22×C47C24×C4
prime radicalC2×2−1+4×C47C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2991C2semidirect
3. C47×#2989C2semidirect
4. C47×#2984C2semidirect
5. C47×#2982C2semidirect
6. C47×#2971C2semidirect
7. C47×#2965C2semidirect
8. Q8×M16×C47C2semidirect
9. C2×C8×Q8×C47C2semidirect
82. C2×Q8×C47M16semidirect
140. C8×C472−1+4semidirect
141. #60333C47direct (N × H)
158. #2991C2×C47semidirect
159. #2989C2×C47semidirect
160. #2984C2×C47semidirect
161. #2982C2×C47semidirect
162. #2971C2×C47semidirect
163. #2965C2×C47semidirect
164. Q8×M16C2×C47semidirect
165. C2×C8×Q8C2×C47semidirect
199. C47#60333direct (N × H)
244. C2×Q8M16×C47semidirect
302. C82−1+4×C47semidirect

Maximal subgroups

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

subgroupindex
C4×2−1+4×C472
C47×#29912
C47×#29892
C47×#29842
C47×#29822
C47×#29712
C47×#29652
Q8×M16×C472
C2×C8×Q8×C472
#6033347