Finite Group Databasebeta

← C22×C47×#342 #26060050

Subgroups — C22×C47×#342 #26060050

Order 12032.

4334 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C47C211yesmaximal, characteristic
2C23×C22⋊C4×C47C212yesmaximal
3C2×C47×#342C2112yesmaximal, direct product factor
4C26×C47C2211yescharacteristic
5C24×C4×C47—22no—
6C24×C4×C47C412yescomplemented
7C22×C22⋊C4×C47—26no—
8C22×C22⋊C4×C47—26no—
9C22×C22⋊C4×C47—28no—
10C22×C22⋊C4×C47—22no—
11C22×C22⋊C4×C47C416yescomplemented
12C22×C22⋊C4×C47C4116yescomplemented
13C22×C22⋊C4×C47C2216yes—
14C22×C22⋊C4×C47C22112yes—
15C47×#342C22116yesdirect product factor
16C25×C47—48no—
17C25×C47C2×C411yescharacteristic
18C25×C47C2×C418yes—
19C25×C47C2×C413yes—
20C25×C47D412yes—
21C25×C47D416yes—
22C25×C47D414yes—
23C25×C47Q814yes—
24C25×C47C2313yes—
25C23×C4×C47—26no—
26C23×C4×C47—216no—
27C23×C4×C47—22no—
28C23×C4×C47—212no—
29C23×C4×C47—416no—
30C23×C4×C47—48no—
31C23×C4×C47C2×C4112yescomplemented
32C2×C22⋊C4×C47—212no—
33C2×C22⋊C4×C47—212no—
34C2×C22⋊C4×C47—248no—
35C2×C22⋊C4×C47—212no—
36C2×C22⋊C4×C47—212no—
37C2×C22⋊C4×C47—212no—
38C2×C22⋊C4×C47—224no—
39C2×C22⋊C4×C47C2×C4112yescomplemented
40C2×C22⋊C4×C47C2×C4148yescomplemented
41C2×C22⋊C4×C47C2314yes—
42C2×C22⋊C4×C47C2318yes—
43C24×C47—28no—
44C24×C47—216no—
45C24×C47—432no—
46C24×C47—412no—
47C24×C47—416no—
48C24×C47—424no—
49C24×C47—416no—
50C24×C47—412no—
51C24×C47C4214yes—
52C24×C47C42112yes—
53C24×C47C22⋊C416yes—
54C24×C47C22⋊C418yes—
55C24×C47C22⋊C413yes—
56C24×C47C22⋊C4124yes—
57C24×C47C22⋊C416yes—
58C24×C47C22⋊C411yescharacteristic
59C24×C47C4⋊C414yes—
60C24×C47C4⋊C418yes—
61C24×C47C4⋊C4124yes—
62C24×C47C4⋊C4112yes—
63C24×C47C22×C413yes—
64C24×C47C22×C4112yes—
65C24×C47C22×C413yes—
66C24×C47C2×D416yes—
67C24×C47C2×D416yes—
68C24×C47C2×D416yes—
69C24×C47C2×Q816yes—
70C24×C47C2411yescharacteristic
71C22×C4×C47—212no—
72C22×C4×C47—212no—
73C22×C4×C47—248no—
74C22×C4×C47—28no—
75C22×C4×C47—464no—
76C22×C4×C47—448no—
77C22×C4×C47—424no—
78C22×C4×C47—48no—
79C22×C4×C47—424no—
80C22×C4×C47C22×C418yescomplemented
81C22⋊C4×C47—224no—
82C22⋊C4×C47—248no—
83C22⋊C4×C47—28no—
84C22⋊C4×C47—28no—
85C22⋊C4×C47C22×C4116yescomplemented
86C23×C47—232no—
87C23×C47—216no—
88C23×C47—216no—
89C23×C47—232no—
90C23×C47—212no—
91C23×C47—212no—
92C23×C47—224no—
93C23×C47—224no—
94C23×C47—424no—
95C23×C47—412no—
96C23×C47—448no—
97C23×C47—424no—
98C23×C47—448no—
99C23×C47—46no—
100C23×C47—424no—
101C23×C47—412no—
102C23×C47—412no—
103C23×C47—412no—
104C23×C47—42no—
105C23×C47#95112yes—
106C23×C47#95124yes—
107C23×C47#95124yes—
108C23×C47#9514yes—
109C23×C47#9918yes—
110C23×C47C2×C4216yes—
111C23×C47C2×C4216yes—
112C23×C47C2×C22⋊C416yes—
113C23×C47C2×C22⋊C413yes—
114C23×C47C2×C22⋊C4112yes—
115C23×C47C2×C22⋊C4112yes—
116C23×C47C2×C22⋊C413yes—
117C23×C47C2×C4⋊C416yes—
118C23×C47C2×C4⋊C4112yes—
119C23×C47C2×C4⋊C416yes—
120C23×C47C2×C4⋊C4112yes—
121C23×C47C23×C411yescharacteristic
122C23×C47C23×C412yes—
123C23×C47C22×D412yes—
124C23×C47C22×D411yescharacteristic
125C23×C47C22×Q811yescharacteristic
126C2×C4×C47—28no—
127C2×C4×C47—216no—
128C2×C4×C47—416no—
129C2×C4×C47—496no—
130C2×C4×C47—424no—
131C2×C4×C47—424no—
132C2×C4×C47—48no—
133C22×#342C4711yesmaximal, characteristic, direct product factor, Sylow
134C22×C47—26no—
135C22×C47—22no—
136C22×C47—24no—
137C22×C47—212no—
138C22×C47—224no—
139C22×C47—248no—
140C22×C47—224no—
141C22×C47—212no—
142C22×C47—212no—
143C22×C47—224no—
144C22×C47—424no—
145C22×C47—46no—
146C22×C47—412no—
147C22×C47—46no—
148C22×C47—412no—
149C22×C47—42no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47#342116yesdirect product factor
153C22×C47C2×#9516yes—
154C22×C47C2×#95112yes—
155C22×C47C2×#9516yes—
156C22×C47C2×#99112yes—
157C22×C47C22×C4211yescharacteristic
158C22×C47C22×C22⋊C412yes—
159C22×C47C22×C22⋊C411yescharacteristic
160C22×C47C22×C4⋊C411yescharacteristic
161C22×C47C22×C4⋊C412yes—
162C4×C47—416no—
163C4×C47—48no—
164C23×C22⋊C4C2×C4711yescharacteristic
165C23×C22⋊C4C2×C4712yes—
166C2×#342C2×C47112yesdirect product factor
167C2×C47—22no—
168C2×C47—21no—
169C2×C47—22no—
170C2×C47—26no—
171C2×C47—212no—
172C2×C47—21no—
173C2×C47C2×#342112yesdirect product factor
174C2×C47C22×#9511yescharacteristic
175C2×C47C22×#9912yes—
176C26C22×C4711yescharacteristic
177C24×C4—22no—
178C24×C4C4×C4712yescomplemented
179C22×C22⋊C4—26no—
180C22×C22⋊C4—22no—
181C22×C22⋊C4—26no—
182C22×C22⋊C4—28no—
183C22×C22⋊C4C4×C4716yescomplemented
184C22×C22⋊C4C4×C47116yescomplemented
185C22×C22⋊C4C22×C4716yes—
186C22×C22⋊C4C22×C47112yes—
187#342C22×C47116yesdirect product factor
188C47C22×#34211yescharacteristic, direct product factor, Sylow
189C25—48no—
190C25C2×C4×C4711yescharacteristic
191C25C2×C4×C4718yes—
192C25C2×C4×C4713yes—
193C25D4×C4712yes—
194C25D4×C4716yes—
195C25D4×C4714yes—
196C25Q8×C4714yes—
197C25C23×C4713yes—
198C23×C4—26no—
199C23×C4—22no—
200C23×C4—216no—
201C23×C4—212no—
202C23×C4—416no—
203C23×C4—48no—
204C23×C4C2×C4×C47112yescomplemented
205C2×C22⋊C4—212no—
206C2×C22⋊C4—212no—
207C2×C22⋊C4—248no—
208C2×C22⋊C4—212no—
209C2×C22⋊C4—212no—
210C2×C22⋊C4—212no—
211C2×C22⋊C4—224no—
212C2×C22⋊C4C2×C4×C47112yescomplemented
213C2×C22⋊C4C2×C4×C47148yescomplemented
214C2×C22⋊C4C23×C4714yes—
215C2×C22⋊C4C23×C4718yes—
216C24—28no—
217C24—216no—
218C24—432no—
219C24—412no—
220C24—416no—
221C24—424no—
222C24—416no—
223C24—412no—
224C24C42×C4714yes—
225C24C42×C47112yes—
226C24C22⋊C4×C4716yes—
227C24C22⋊C4×C4718yes—
228C24C22⋊C4×C4713yes—
229C24C22⋊C4×C4716yes—
230C24C22⋊C4×C47124yes—
231C24C22⋊C4×C4711yescharacteristic
232C24C4⋊C4×C4714yes—
233C24C4⋊C4×C4718yes—
234C24C4⋊C4×C47112yes—
235C24C4⋊C4×C47124yes—
236C24C22×C4×C4713yes—
237C24C22×C4×C47112yes—
238C24C22×C4×C4713yes—
239C24C2×D4×C4716yes—
240C24C2×D4×C4716yes—
241C24C2×D4×C4716yes—
242C24C2×Q8×C4716yes—
243C24C24×C4711yescharacteristic
244C22×C4—212no—
245C22×C4—212no—
246C22×C4—248no—
247C22×C4—28no—
248C22×C4—464no—
249C22×C4—448no—
250C22×C4—424no—
251C22×C4—48no—
252C22×C4—424no—
253C22×C4C22×C4×C4718yescomplemented
254C22⋊C4—224no—
255C22⋊C4—248no—
256C22⋊C4—28no—
257C22⋊C4—28no—
258C22⋊C4C22×C4×C47116yescomplemented
259C23—232no—
260C23—216no—
261C23—216no—
262C23—232no—
263C23—212no—
264C23—212no—
265C23—224no—
266C23—224no—
267C23—424no—
268C23—412no—
269C23—448no—
270C23—424no—
271C23—448no—
272C23—46no—
273C23—424no—
274C23—412no—
275C23—412no—
276C23—412no—
277C23—42no—
278C23#95×C47112yes—
279C23#95×C47124yes—
280C23#95×C47124yes—
281C23#95×C4714yes—
282C23#99×C4718yes—
283C23C2×C42×C4716yes—
284C23C2×C42×C4716yes—
285C23C2×C22⋊C4×C4716yes—
286C23C2×C22⋊C4×C4713yes—
287C23C2×C22⋊C4×C47112yes—
288C23C2×C22⋊C4×C47112yes—
289C23C2×C22⋊C4×C4713yes—
290C23C2×C4⋊C4×C4716yes—
291C23C2×C4⋊C4×C47112yes—
292C23C2×C4⋊C4×C4716yes—
293C23C2×C4⋊C4×C47112yes—
294C23C23×C4×C4711yescharacteristic
295C23C23×C4×C4712yes—
296C23C22×D4×C4712yes—
297C23C22×D4×C4711yescharacteristic
298C23C22×Q8×C4711yescharacteristic
299C2×C4—28no—
300C2×C4—216no—
301C2×C4—416no—
302C2×C4—496no—
303C2×C4—424no—
304C2×C4—424no—
305C2×C4—48no—
306C22—26no—
307C22—22no—
308C22—24no—
309C22—212no—
310C22—224no—
311C22—212no—
312C22—212no—
313C22—224no—
314C22—248no—
315C22—224no—
316C22—46no—
317C22—412no—
318C22—46no—
319C22—412no—
320C22—42no—
321C22—41no—
322C22—41no—
323C22—424no—
324C22C47×#342116yesdirect product factor
325C22C2×#95×C4716yes—
326C22C2×#95×C47112yes—
327C22C2×#95×C4716yes—
328C22C2×#99×C47112yes—
329C22C22×C42×C4711yescharacteristic
330C22C22×C22⋊C4×C4712yes—
331C22C22×C22⋊C4×C4711yescharacteristic
332C22C22×C4⋊C4×C4711yescharacteristic
333C22C22×C4⋊C4×C4712yes—
334C4—416no—
335C4—48no—
336C2—22no—
337C2—21no—
338C2—21no—
339C2—22no—
340C2—26no—
341C2—212no—
342C2C2×C47×#342112yesdirect product factor
343C2C22×#95×C4711yescharacteristic
344C2C22×#99×C4712yes—
subgroupG/H
center, socleC24×C47C22⋊C4
commutatorC22C22×C42×C47
Frattini, cosocleC24C24×C47
prime radicalC26×C47C22
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C24×C47 ◁ C26×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C47×#342C2direct (N × H)
6. C24×C4×C47C4semidirect
11. C22×C22⋊C4×C47C4semidirect
12. C22×C22⋊C4×C47C4semidirect
15. C47×#342C22direct (N × H)
31. C23×C4×C47C2×C4semidirect
39. C2×C22⋊C4×C47C2×C4semidirect
40. C2×C22⋊C4×C47C2×C4semidirect
80. C22×C4×C47C22×C4semidirect
85. C22⋊C4×C47C22×C4semidirect
133. C22×#342C47direct (N × H)
152. C22×C47#342direct (N × H)
166. C2×#342C2×C47direct (N × H)
173. C2×C47C2×#342direct (N × H)
178. C24×C4C4×C47semidirect
183. C22×C22⋊C4C4×C47semidirect
184. C22×C22⋊C4C4×C47semidirect
187. #342C22×C47direct (N × H)
188. C47C22×#342direct (N × H)
204. C23×C4C2×C4×C47semidirect
212. C2×C22⋊C4C2×C4×C47semidirect
213. C2×C22⋊C4C2×C4×C47semidirect
253. C22×C4C22×C4×C47semidirect
258. C22⋊C4C22×C4×C47semidirect
324. C22C47×#342direct (N × H)
342. C2C2×C47×#342direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C472
C2×C47×#3422
C22×#34247