Finite Group Databasebeta

← C47×#13777 #26053475

Subgroups — C47×#13777 #26053475

Order 12032.

2102 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#117×C47C211yesmaximal, characteristic
2C2×C47×#380C212yesmaximal
3C2×C4×C4⋊C4×C47C212yesmaximal, complemented
4C47×#1437C214yesmaximal
5C47×#1436C214yesmaximal, complemented
6C47×C4⋊#95C212yesmaximal, complemented
7C24×C4×C47C2211yescharacteristic
8C2×#117×C47—28no—
9C2×#117×C47C418yescomplemented
10C22×C4⋊C4×C47C2214yes—
11C22×C4⋊C4×C47C2212yes—
12C22×C22⋊C4×C47C2212yes—
13C22×C22⋊C4×C47C2214yes—
14C22×C42×C47C2211yescharacteristic
15C22×C42×C47C2214yes—
16C22×C42×C47C2211yescharacteristic
17C47×#380C4116yescomplemented
18C4×C4⋊C4×C47—28no—
19C2×#95×C47C2214yes—
20C2×#95×C47C2218yes—
21C2×#95×C47C2214yes—
22C25×C47C2311yescharacteristic
23C23×C4×C47—24no—
24C23×C4×C47—24no—
25C23×C4×C47C2×C414yes—
26C23×C4×C47C2×C418yes—
27C23×C4×C47C2312yes—
28C23×C4×C47C2318yes—
29C23×C4×C47C2311yescharacteristic
30C23×C4×C47C2312yes—
31C23×C4×C47C2311yescharacteristic
32#117×C47—232no—
33C2×C4⋊C4×C47—24no—
34C2×C4⋊C4×C47—24no—
35C2×C4⋊C4×C47—28no—
36C2×C4⋊C4×C47—28no—
37C2×C4⋊C4×C47C2×C418yes—
38C2×C4⋊C4×C47C2×C4116yes—
39C2×C22⋊C4×C47—24no—
40C2×C22⋊C4×C47—24no—
41C2×C22⋊C4×C47—48no—
42C2×C22⋊C4×C47C2×C418yes—
43C2×C22⋊C4×C47C2×C4116yes—
44C2×C42×C47—24no—
45C2×C42×C47—28no—
46C2×C42×C47—48no—
47C2×C42×C47C2×C414yes—
48C2×C42×C47C2×C414yes—
49C2×C42×C47D418yes—
50#95×C47—28no—
51#95×C47—48no—
52#95×C47C2×C4116yes—
53C24×C47—22no—
54C24×C47—22no—
55C24×C47—24no—
56C24×C47—24no—
57C24×C47C22×C412yes—
58C24×C47C22×C414yes—
59C24×C47C2411yescharacteristic
60C22×C4×C47—22no—
61C22×C4×C47—22no—
62C22×C4×C47—24no—
63C22×C4×C47—24no—
64C22×C4×C47—28no—
65C22×C4×C47—28no—
66C22×C4×C47—232no—
67C22×C4×C47—22no—
68C22×C4×C47—22no—
69C22×C4×C47—28no—
70C22×C4×C47—28no—
71C22×C4×C47—28no—
72C22×C4×C47—28no—
73C22×C4×C47—28no—
74C22×C4×C47—24no—
75C22×C4×C47—24no—
76C22×C4×C47—28no—
77C22×C4×C47C42116yescomplemented
78C22×C4×C47C22×C414yes—
79C22×C4×C47C22×C4116yes—
80C22×C4×C47C22×C412yes—
81C22×C4×C47C22×C414yes—
82C22×C4×C47C22×C414yes—
83C22×C4×C47C22×C412yes—
84C22×C4×C47C22×C414yes—
85C22×C4×C47C2×D414yes—
86C22×C4×C47C2×D414yes—
87C22×C4×C47C2×D414yes—
88C22×C4×C47#4114yes—
89C4⋊C4×C47—216no—
90C4⋊C4×C47—232no—
91C22⋊C4×C47—216no—
92C22⋊C4×C47—416no—
93C42×C47—28no—
94C42×C47—416no—
95C42×C47C22⋊C4116yescomplemented
96C23×C47—22no—
97C23×C47—22no—
98C23×C47—28no—
99C23×C47—24no—
100C23×C47—24no—
101C23×C47—28no—
102C23×C47—28no—
103C23×C47—42no—
104C23×C47—42no—
105C23×C47—44no—
106C23×C47—42no—
107C23×C47—42no—
108C23×C47—44no—
109C23×C47C2×C4214yes—
110C23×C47C23×C411yescharacteristic
111C23×C47C23×C412yes—
112C23×C47C22×D412yes—
113C23×C47C2×#4112yes—
114C23×C47H(5,𝔽2)14yes—
115C23×C472−1+414yes—
116C2×C4×C47—22no—
117C2×C4×C47—22no—
118C2×C4×C47—28no—
119C2×C4×C47—28no—
120C2×C4×C47—24no—
121C2×C4×C47—24no—
122C2×C4×C47—28no—
123C2×C4×C47—232no—
124C2×C4×C47—24no—
125C2×C4×C47—216no—
126C2×C4×C47—216no—
127C2×C4×C47—28no—
128C2×C4×C47—216no—
129C2×C4×C47—48no—
130C2×C4×C47—42no—
131C2×C4×C47—42no—
132C2×C4×C47—44no—
133C2×C4×C47—48no—
134C2×C4×C47—48no—
135C2×C4×C47—48no—
136C2×C4×C47C2×C4214yes—
137C2×C4×C47C2×C4214yes—
138C2×C4×C47C2×C22⋊C418yes—
139C2×C4×C47C2×C22⋊C414yes—
140C2×C4×C47#11714yes—
141C2×C4×C47C4×D4116yes—
142#13777C4711yesmaximal, characteristic, direct product factor, Sylow
143C22×C47—24no—
144C22×C47—28no—
145C22×C47—44no—
146C22×C47—44no—
147C22×C47—48no—
148C22×C47—48no—
149C22×C47C22×C4211yescharacteristic
150C22×C47C22×C22⋊C411yescharacteristic
151C22×C47C2×#11711yescharacteristic
152C22×C47C2×C4×D414yes—
153C22×C47#51812yes—
154C22×C47#51912yes—
155C22×C47#52014yes—
156C22×C47#52014yes—
157C22×C47#53512yes—
158C22×C47#53612yes—
159C22×C47#53714yes—
160C22×C47#54012yes—
161C22×C47#54112yes—
162C22×C47#54214yes—
163C4×C47—28no—
164C4×C47—24no—
165C4×C47—44no—
166C4×C47—416no—
167C4×C47C4×C22⋊C418yes—
168C22×#117C2×C4711yescharacteristic
169C2×#380C2×C4712yes—
170C2×C4×C4⋊C4C2×C4712yescomplemented
171#1437C2×C4714yes—
172#1436C2×C4714yescomplemented
173C4⋊#95C2×C4712yescomplemented
174C2×C47—44no—
175C2×C47C2×C4×C22⋊C411yescharacteristic
176C2×C47#227412yes—
177C2×C47#231112yes—
178C2×C47#231412yes—
179C2×C47#232314yes—
180C2×C47#232414yes—
181C24×C4C22×C4711yescharacteristic
182C2×#117—28no—
183C2×#117C4×C4718yescomplemented
184C22×C4⋊C4C22×C4712yes—
185C22×C4⋊C4C22×C4714yes—
186C22×C22⋊C4C22×C4712yes—
187C22×C22⋊C4C22×C4714yes—
188C22×C42C22×C4711yescharacteristic
189C22×C42C22×C4714yes—
190C22×C42C22×C4711yescharacteristic
191#380C4×C47116yescomplemented
192C4×C4⋊C4—28no—
193C2×#95C22×C4714yes—
194C2×#95C22×C4718yes—
195C2×#95C22×C4714yes—
196C47#1377711yescharacteristic, direct product factor, Sylow
197C25C23×C4711yescharacteristic
198C23×C4—24no—
199C23×C4—24no—
200C23×C4C2×C4×C4714yes—
201C23×C4C2×C4×C4718yes—
202C23×C4C23×C4718yes—
203C23×C4C23×C4712yes—
204C23×C4C23×C4711yescharacteristic
205C23×C4C23×C4712yes—
206C23×C4C23×C4711yescharacteristic
207#117—232no—
208C2×C4⋊C4—24no—
209C2×C4⋊C4—24no—
210C2×C4⋊C4—28no—
211C2×C4⋊C4—28no—
212C2×C4⋊C4C2×C4×C4718yes—
213C2×C4⋊C4C2×C4×C47116yes—
214C2×C22⋊C4—24no—
215C2×C22⋊C4—24no—
216C2×C22⋊C4—48no—
217C2×C22⋊C4C2×C4×C4718yes—
218C2×C22⋊C4C2×C4×C47116yes—
219C2×C42—24no—
220C2×C42—28no—
221C2×C42—48no—
222C2×C42C2×C4×C4714yes—
223C2×C42C2×C4×C4714yes—
224C2×C42D4×C4718yes—
225#95—28no—
226#95—48no—
227#95C2×C4×C47116yes—
228C24—22no—
229C24—22no—
230C24—24no—
231C24—24no—
232C24C22×C4×C4712yes—
233C24C22×C4×C4714yes—
234C24C24×C4711yescharacteristic
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—28no—
240C22×C4—28no—
241C22×C4—232no—
242C22×C4—28no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—28no—
246C22×C4—24no—
247C22×C4—28no—
248C22×C4—28no—
249C22×C4—28no—
250C22×C4—24no—
251C22×C4—28no—
252C22×C4C42×C47116yescomplemented
253C22×C4C22×C4×C47116yes—
254C22×C4C22×C4×C4714yes—
255C22×C4C22×C4×C4714yes—
256C22×C4C22×C4×C4712yes—
257C22×C4C22×C4×C4714yes—
258C22×C4C22×C4×C4712yes—
259C22×C4C22×C4×C4714yes—
260C22×C4C2×D4×C4714yes—
261C22×C4C2×D4×C4714yes—
262C22×C4C2×D4×C4714yes—
263C22×C4#41×C4714yes—
264C4⋊C4—216no—
265C4⋊C4—232no—
266C22⋊C4—216no—
267C22⋊C4—416no—
268C42—28no—
269C42—416no—
270C42C22⋊C4×C47116yescomplemented
271C23—22no—
272C23—22no—
273C23—28no—
274C23—24no—
275C23—24no—
276C23—28no—
277C23—28no—
278C23—42no—
279C23—42no—
280C23—44no—
281C23—42no—
282C23—42no—
283C23—44no—
284C23C2×C42×C4714yes—
285C23C23×C4×C4711yescharacteristic
286C23C23×C4×C4712yes—
287C23C22×D4×C4712yes—
288C23C2×#41×C4712yes—
289C23H(5,𝔽2)×C4714yes—
290C232−1+4×C4714yes—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—28no—
294C2×C4—28no—
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—28no—
298C2×C4—232no—
299C2×C4—24no—
300C2×C4—216no—
301C2×C4—216no—
302C2×C4—28no—
303C2×C4—216no—
304C2×C4—48no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—44no—
308C2×C4—48no—
309C2×C4—48no—
310C2×C4—48no—
311C2×C4C2×C42×C4714yes—
312C2×C4C2×C42×C4714yes—
313C2×C4C2×C22⋊C4×C4718yes—
314C2×C4C2×C22⋊C4×C4714yes—
315C2×C4#117×C4714yes—
316C2×C4C4×D4×C47116yes—
317C22—24no—
318C22—28no—
319C22—44no—
320C22—44no—
321C22—48no—
322C22—48no—
323C22C22×C42×C4711yescharacteristic
324C22C22×C22⋊C4×C4711yescharacteristic
325C22C2×#117×C4711yescharacteristic
326C22C2×C4×D4×C4714yes—
327C22C47×#51812yes—
328C22C47×#51912yes—
329C22C47×#52014yes—
330C22C47×#52014yes—
331C22C47×#53512yes—
332C22C47×#53612yes—
333C22C47×#53714yes—
334C22C47×#54012yes—
335C22C47×#54112yes—
336C22C47×#54214yes—
337C4—24no—
338C4—28no—
339C4—44no—
340C4—416no—
341C4C4×C22⋊C4×C4718yes—
342C2—44no—
343C2C2×C4×C22⋊C4×C4711yescharacteristic
344C2C47×#227412yes—
345C2C47×#231112yes—
346C2C47×#231412yes—
347C2C47×#232314yes—
348C2C47×#232414yes—
subgroupG/H
center, socleC24×C47C24
commutatorC22C22×C42×C47
Frattini, cosocleC24C24×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
3. C2×C4×C4⋊C4×C47C2semidirect
5. C47×#1436C2semidirect
6. C47×C4⋊#95C2semidirect
9. C2×#117×C47C4semidirect
17. C47×#380C4semidirect
77. C22×C4×C47C42semidirect
95. C42×C47C22⋊C4semidirect
142. #13777C47direct (N × H)
170. C2×C4×C4⋊C4C2×C47semidirect
172. #1436C2×C47semidirect
173. C4⋊#95C2×C47semidirect
183. C2×#117C4×C47semidirect
191. #380C4×C47semidirect
196. C47#13777direct (N × H)
252. C22×C4C42×C47semidirect
270. C42C22⋊C4×C47semidirect

Maximal subgroups

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

subgroupindex
C22×#117×C472
C2×C47×#3802
C2×C4×C4⋊C4×C472
C47×#14372
C47×#14362
C47×C4⋊#952
#1377747