Finite Group Databasebeta

← C2×C47×#2314 #26073745

Subgroups — C2×C47×#2314 #26073745

Order 12032.

2678 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#117×C47C211yesmaximal, characteristic
2C47×#2314C2116yesmaximal, direct product factor
3C2×C47×#388C214yesmaximal
4C2×C47×#387C214yesmaximal, complemented
5C2×C47×#384C211yesmaximal, characteristic, complemented
6C2×C47×#382C211yesmaximal, characteristic, complemented
7C2×C47×#380C212yesmaximal
8C2×C4×C4⋊C4×C47C212yesmaximal, complemented
9C24×C4×C47C2211yescharacteristic
10C2×#117×C47C4116yescomplemented
11C2×#117×C47C2218yes—
12C22×C4⋊C4×C47C2212yes—
13C22×C4⋊C4×C47C2212yes—
14C22×C4⋊C4×C47C2214yes—
15C22×C4⋊C4×C47C2212yes—
16C22×C22⋊C4×C47C2214yes—
17C22×C22⋊C4×C47C2212yes—
18C22×C42×C47C2214yes—
19C22×C42×C47C2211yescharacteristic
20C22×C42×C47C2211yescharacteristic
21C47×#388C22132yes—
22C47×#387C22132yescomplemented
23C47×#384C2218yescomplemented
24C47×#382C2218yescomplemented
25C47×#380C22116yes—
26C4×C4⋊C4×C47C22116yescomplemented
27C2×#95×C47C2214yes—
28C2×#95×C47C2214yes—
29C2×#95×C47C2214yes—
30C25×C47C2311yescharacteristic
31C23×C4×C47—24no—
32C23×C4×C47—24no—
33C23×C4×C47C2×C418yes—
34C23×C4×C47C2314yes—
35C23×C4×C47C2314yes—
36C23×C4×C47C2314yes—
37C23×C4×C47C2312yes—
38C23×C4×C47C2312yes—
39C23×C4×C47C2311yescharacteristic
40C23×C4×C47C2311yescharacteristic
41#117×C47C2×C4164yescomplemented
42C2×C4⋊C4×C47—28no—
43C2×C4⋊C4×C47—28no—
44C2×C4⋊C4×C47—48no—
45C2×C4⋊C4×C47C2×C4116yes—
46C2×C4⋊C4×C47C2318yes—
47C2×C4⋊C4×C47C2318yes—
48C2×C4⋊C4×C47C23116yes—
49C2×C4⋊C4×C47C2318yes—
50C2×C22⋊C4×C47—48no—
51C2×C22⋊C4×C47C2×C4116yes—
52C2×C22⋊C4×C47C23116yes—
53C2×C22⋊C4×C47C2318yes—
54C2×C42×C47—48no—
55C2×C42×C47C2×C418yes—
56C2×C42×C47C2×C418yes—
57C2×C42×C47C23116yes—
58C2×C42×C47C2314yes—
59C2×C42×C47C2314yes—
60#95×C47C23116yes—
61#95×C47C23116yes—
62#95×C47C23116yes—
63C24×C47—22no—
64C24×C47—22no—
65C24×C47—24no—
66C24×C47—24no—
67C24×C47C22×C414yes—
68C24×C47C2412yes—
69C24×C47C2411yescharacteristic
70C22×C4×C47—22no—
71C22×C4×C47—22no—
72C22×C4×C47—24no—
73C22×C4×C47—24no—
74C22×C4×C47—24no—
75C22×C4×C47—24no—
76C22×C4×C47—232no—
77C22×C4×C47—28no—
78C22×C4×C47—28no—
79C22×C4×C47—28no—
80C22×C4×C47—28no—
81C22×C4×C47—28no—
82C22×C4×C47—28no—
83C22×C4×C47—28no—
84C22×C4×C47—28no—
85C22×C4×C47C22×C418yes—
86C22×C4×C47C22×C418yes—
87C22×C4×C47C22×C414yes—
88C22×C4×C47C22×C4116yes—
89C22×C4×C47C22×C414yes—
90C22×C4×C47#4114yes—
91C22×C4×C47#4114yes—
92C22×C4×C47C2418yes—
93C22×C4×C47C2418yes—
94C22×C4×C47C2414yes—
95C22×C4×C47C2414yes—
96C22×C4×C47C2412yes—
97C22×C4×C47C2412yes—
98C4⋊C4×C47—216no—
99C4⋊C4×C47—216no—
100C4⋊C4×C47—416no—
101C4⋊C4×C47C22×C4132yes—
102C22⋊C4×C47—416no—
103C22⋊C4×C47C22×C4132yes—
104C42×C47—416no—
105C42×C47C22×C4116yes—
106C42×C47C22×C4116yes—
107C23×C47—28no—
108C23×C47—216no—
109C23×C47—22no—
110C23×C47—22no—
111C23×C47—24no—
112C23×C47—24no—
113C23×C47—44no—
114C23×C47—44no—
115C23×C47—48no—
116C23×C47C23×C414yes—
117C23×C47C23×C412yes—
118C23×C47C2×#4112yes—
119C23×C47C2×#4112yes—
120C23×C47H(5,𝔽2)14yes—
121C23×C472−1+414yes—
122C23×C47C2511yescharacteristic
123C2×C4×C47—28no—
124C2×C4×C47—216no—
125C2×C4×C47—216no—
126C2×C4×C47—22no—
127C2×C4×C47—22no—
128C2×C4×C47—24no—
129C2×C4×C47—24no—
130C2×C4×C47—24no—
131C2×C4×C47—24no—
132C2×C4×C47—232no—
133C2×C4×C47—28no—
134C2×C4×C47—28no—
135C2×C4×C47—28no—
136C2×C4×C47—28no—
137C2×C4×C47—28no—
138C2×C4×C47—28no—
139C2×C4×C47—416no—
140C2×C4×C47—416no—
141C2×C4×C47#117116yes—
142C2×C4×C47C23×C418yes—
143C2×C4×C47C23×C418yes—
144C2×C4×C47C23×C414yes—
145C2×C4×C47C23×C414yes—
146C2×C4×C47C2×#4114yes—
147C2×C4×C47C2×#4114yes—
148C2×#2314C4711yesmaximal, characteristic, direct product factor, Sylow
149C22×C47—24no—
150C22×C47—28no—
151C22×C47—416no—
152C22×C47—42no—
153C22×C47—42no—
154C22×C47—44no—
155C22×C47C2×#11714yes—
156C22×C47#52018yes—
157C22×C47#54014yes—
158C22×C47#54114yes—
159C22×C47#54218yes—
160C22×C47C24×C411yescharacteristic
161C22×C47C22×#4111yescharacteristic
162C22×C47C22×#4111yescharacteristic
163C22×C47C2×H(5,𝔽2)12yes—
164C22×C47C2×2−1+412yes—
165C4×C47—24no—
166C4×C47—28no—
167C4×C47—28no—
168C4×C47—48no—
169C4×C47—48no—
170C4×C47C2×#11718yes—
171C22×#117C2×C4711yescharacteristic
172#2314C2×C47116yesdirect product factor
173C2×#388C2×C4714yes—
174C2×#387C2×C4714yescomplemented
175C2×#384C2×C4711yescharacteristic, complemented
176C2×#382C2×C4711yescharacteristic, complemented
177C2×#380C2×C4712yes—
178C2×C4×C4⋊C4C2×C4712yescomplemented
179C2×C47—44no—
180C2×C47#231418yesdirect product factor
181C2×C47C22×#11711yescharacteristic
182C2×C47C2×#52012yes—
183C2×C47C2×#54011yescharacteristic
184C2×C47C2×#54111yescharacteristic
185C2×C47C2×#54212yes—
186C24×C4C22×C4711yescharacteristic
187C2×#117C4×C47116yescomplemented
188C2×#117C22×C4718yes—
189C22×C4⋊C4C22×C4712yes—
190C22×C4⋊C4C22×C4712yes—
191C22×C4⋊C4C22×C4714yes—
192C22×C4⋊C4C22×C4712yes—
193C22×C22⋊C4C22×C4714yes—
194C22×C22⋊C4C22×C4712yes—
195C22×C42C22×C4714yes—
196C22×C42C22×C4711yescharacteristic
197C22×C42C22×C4711yescharacteristic
198#388C22×C47132yes—
199#387C22×C47132yescomplemented
200#384C22×C4718yescomplemented
201#382C22×C4718yescomplemented
202#380C22×C47116yes—
203C4×C4⋊C4C22×C47116yescomplemented
204C2×#95C22×C4714yes—
205C2×#95C22×C4714yes—
206C2×#95C22×C4714yes—
207C47C2×#231411yescharacteristic, direct product factor, Sylow
208C25C23×C4711yescharacteristic
209C23×C4—24no—
210C23×C4—24no—
211C23×C4C2×C4×C4718yes—
212C23×C4C23×C4714yes—
213C23×C4C23×C4714yes—
214C23×C4C23×C4712yes—
215C23×C4C23×C4712yes—
216C23×C4C23×C4711yescharacteristic
217C23×C4C23×C4714yes—
218C23×C4C23×C4711yescharacteristic
219#117C2×C4×C47164yescomplemented
220C2×C4⋊C4—28no—
221C2×C4⋊C4—28no—
222C2×C4⋊C4—48no—
223C2×C4⋊C4C2×C4×C47116yes—
224C2×C4⋊C4C23×C4718yes—
225C2×C4⋊C4C23×C4718yes—
226C2×C4⋊C4C23×C47116yes—
227C2×C4⋊C4C23×C4718yes—
228C2×C22⋊C4—48no—
229C2×C22⋊C4C2×C4×C47116yes—
230C2×C22⋊C4C23×C47116yes—
231C2×C22⋊C4C23×C4718yes—
232C2×C42—48no—
233C2×C42C2×C4×C4718yes—
234C2×C42C2×C4×C4718yes—
235C2×C42C23×C47116yes—
236C2×C42C23×C4714yes—
237C2×C42C23×C4714yes—
238#95C23×C47116yes—
239#95C23×C47116yes—
240#95C23×C47116yes—
241C24—22no—
242C24—22no—
243C24—24no—
244C24—24no—
245C24C22×C4×C4714yes—
246C24C24×C4712yes—
247C24C24×C4711yescharacteristic
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—24no—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—232no—
255C22×C4—28no—
256C22×C4—28no—
257C22×C4—28no—
258C22×C4—28no—
259C22×C4—28no—
260C22×C4—28no—
261C22×C4—28no—
262C22×C4—28no—
263C22×C4C22×C4×C4718yes—
264C22×C4C22×C4×C4718yes—
265C22×C4C22×C4×C4714yes—
266C22×C4C22×C4×C47116yes—
267C22×C4C22×C4×C4714yes—
268C22×C4#41×C4714yes—
269C22×C4#41×C4714yes—
270C22×C4C24×C4718yes—
271C22×C4C24×C4718yes—
272C22×C4C24×C4712yes—
273C22×C4C24×C4714yes—
274C22×C4C24×C4714yes—
275C22×C4C24×C4712yes—
276C4⋊C4—216no—
277C4⋊C4—216no—
278C4⋊C4—416no—
279C4⋊C4C22×C4×C47132yes—
280C22⋊C4—416no—
281C22⋊C4C22×C4×C47132yes—
282C42—416no—
283C42C22×C4×C47116yes—
284C42C22×C4×C47116yes—
285C23—28no—
286C23—216no—
287C23—22no—
288C23—22no—
289C23—24no—
290C23—24no—
291C23—44no—
292C23—44no—
293C23—48no—
294C23C23×C4×C4714yes—
295C23C23×C4×C4712yes—
296C23C2×#41×C4712yes—
297C23C2×#41×C4712yes—
298C23H(5,𝔽2)×C4714yes—
299C232−1+4×C4714yes—
300C23C25×C4711yescharacteristic
301C2×C4—28no—
302C2×C4—216no—
303C2×C4—216no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—232no—
311C2×C4—28no—
312C2×C4—28no—
313C2×C4—28no—
314C2×C4—28no—
315C2×C4—28no—
316C2×C4—28no—
317C2×C4—416no—
318C2×C4—416no—
319C2×C4#117×C47116yes—
320C2×C4C23×C4×C4718yes—
321C2×C4C23×C4×C4718yes—
322C2×C4C23×C4×C4714yes—
323C2×C4C23×C4×C4714yes—
324C2×C4C2×#41×C4714yes—
325C2×C4C2×#41×C4714yes—
326C22—24no—
327C22—28no—
328C22—416no—
329C22—42no—
330C22—42no—
331C22—44no—
332C22C2×#117×C4714yes—
333C22C47×#52018yes—
334C22C47×#54014yes—
335C22C47×#54114yes—
336C22C47×#54218yes—
337C22C24×C4×C4711yescharacteristic
338C22C22×#41×C4711yescharacteristic
339C22C22×#41×C4711yescharacteristic
340C22C2×H(5,𝔽2)×C4712yes—
341C22C2×2−1+4×C4712yes—
342C4—24no—
343C4—28no—
344C4—28no—
345C4—48no—
346C4—48no—
347C4C2×#117×C4718yes—
348C2—44no—
349C2C47×#231418yesdirect product factor
350C2C22×#117×C4711yescharacteristic
351C2C2×C47×#52012yes—
352C2C2×C47×#54011yescharacteristic
353C2C2×C47×#54111yescharacteristic
354C2C2×C47×#54212yes—
subgroupG/H
center, socleC24×C47C24
commutatorC22C24×C4×C47
Frattini, cosocleC23C25×C47
prime radicalC25×C47C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2314C2direct (N × H)
4. C2×C47×#387C2semidirect
5. C2×C47×#384C2semidirect
6. C2×C47×#382C2semidirect
8. C2×C4×C4⋊C4×C47C2semidirect
10. C2×#117×C47C4semidirect
22. C47×#387C22semidirect
23. C47×#384C22semidirect
24. C47×#382C22semidirect
26. C4×C4⋊C4×C47C22semidirect
41. #117×C47C2×C4semidirect
148. C2×#2314C47direct (N × H)
172. #2314C2×C47direct (N × H)
174. C2×#387C2×C47semidirect
175. C2×#384C2×C47semidirect
176. C2×#382C2×C47semidirect
178. C2×C4×C4⋊C4C2×C47semidirect
180. C2×C47#2314direct (N × H)
187. C2×#117C4×C47semidirect
199. #387C22×C47semidirect
200. #384C22×C47semidirect
201. #382C22×C47semidirect
203. C4×C4⋊C4C22×C47semidirect
207. C47C2×#2314direct (N × H)
219. #117C2×C4×C47semidirect
349. C2C47×#2314direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#117×C472
C47×#23142
C2×C47×#3882
C2×C47×#3872
C2×C47×#3842
C2×C47×#3822
C2×C47×#3802
C2×C4×C4⋊C4×C472
C2×#231447