Finite Group Databasebeta

← C47×#11499 #26051197

Subgroups — C47×#11499 #26051197

Order 12032.

1866 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 1866 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#379C211yesmaximal, characteristic
2C47×#1462C212yesmaximal, complemented
3C47×#1316C214yesmaximal, complemented
4C26×C47C411yescharacteristic
5C22×C22⋊C4×C47—22no—
6C22×C22⋊C4×C47C411yescharacteristic
7C22×C22⋊C4×C47C2211yescharacteristic
8C47×#407—22no—
9C47×#379—22no—
10C47×#379C412yes—
11C47×#379C2212yes—
12C47×#323—22no—
13C47×#323C2214yescomplemented
14C25×C47—21no—
15C25×C47—21no—
16C25×C47—24no—
17C25×C47—48no—
18C25×C47—42no—
19C25×C47—42no—
20C25×C47C2×C411yescharacteristic
21C25×C47C2×C412yes—
22C23×C4×C47—21no—
23C23×C4×C47D412yes—
24C2×M16×C47—42no—
25C2×C22⋊C4×C47—21no—
26C2×C22⋊C4×C47—24no—
27C2×C22⋊C4×C47—24no—
28C2×C22⋊C4×C47—42no—
29C2×C22⋊C4×C47—48no—
30C2×C22⋊C4×C47—42no—
31C2×C22⋊C4×C47C2×C412yes—
32C2×C22⋊C4×C47C2×C411yescharacteristic
33C2×C22⋊C4×C47D412yes—
34C2×C22⋊C4×C47C2311yescharacteristic
35C22⋊C8×C47—24no—
36C22⋊C8×C47—42no—
37C24×C47—28no—
38C24×C47—24no—
39C24×C47—22no—
40C24×C47—22no—
41C24×C47—22no—
42C24×C47—22no—
43C24×C47—24no—
44C24×C47—22no—
45C24×C47—44no—
46C24×C47—42no—
47C24×C47—48no—
48C24×C47—432no—
49C24×C47—416no—
50C24×C47—42no—
51C24×C47—44no—
52C24×C47—48no—
53C24×C47—42no—
54C24×C47—42no—
55C24×C47—416no—
56C24×C47—432no—
57C24×C47—48no—
58C24×C47—42no—
59C24×C47—42no—
60C24×C47—48no—
61C24×C47C22⋊C411yescharacteristic
62C24×C47C22⋊C411yescharacteristic
63C24×C47M1614yescomplemented
64C24×C47C22×C411yescharacteristic
65C22×C4×C47—22no—
66C22×C4×C47—22no—
67C22×C4×C47—22no—
68C22×C4×C47—44no—
69C22×C4×C47—44no—
70C22×C4×C47—42no—
71C22×C4×C47C22⋊C412yes—
72C22×C4×C47C2×D412yes—
73M16×C47—84no—
74C2×C8×C47—44no—
75C22⋊C4×C47—41no—
76C22⋊C4×C47—42no—
77C22⋊C4×C47—41no—
78C22⋊C4×C47—48no—
79C22⋊C4×C47—48no—
80C22⋊C4×C47—42no—
81C22⋊C4×C47—42no—
82C23×C47—24no—
83C23×C47—21no—
84C23×C47—21no—
85C23×C47—28no—
86C23×C47—216no—
87C23×C47—28no—
88C23×C47—21no—
89C23×C47—24no—
90C23×C47—21no—
91C23×C47—21no—
92C23×C47—21no—
93C23×C47—42no—
94C23×C47—48no—
95C23×C47—44no—
96C23×C47—42no—
97C23×C47—48no—
98C23×C47—416no—
99C23×C47—48no—
100C23×C47—48no—
101C23×C47—44no—
102C23×C47—48no—
103C23×C47—44no—
104C23×C47—48no—
105C23×C47—48no—
106C23×C47—416no—
107C23×C47—48no—
108C23×C47—44no—
109C23×C47—48no—
110C23×C47—416no—
111C23×C47—464no—
112C23×C47—416no—
113C23×C47—464no—
114C23×C47—416no—
115C23×C47—48no—
116C23×C47—48no—
117C23×C47—44no—
118C23×C47—42no—
119C23×C47—42no—
120C23×C47#9912yes—
121C23×C47#10012yes—
122C23×C47C2×C22⋊C411yescharacteristic
123C23×C47C2×M1612yes—
124C2×C4×C47—22no—
125C2×C4×C47—22no—
126C2×C4×C47—44no—
127C2×C4×C47—42no—
128C2×C4×C47—42no—
129C2×C4×C47—44no—
130C2×C4×C47—42no—
131C2×C4×C47—82no—
132C2×C4×C47—84no—
133C8×C47—84no—
134#11499C4711yesmaximal, characteristic, direct product factor, Sylow
135C22×C47—24no—
136C22×C47—24no—
137C22×C47—22no—
138C22×C47—22no—
139C22×C47—22no—
140C22×C47—28no—
141C22×C47—22no—
142C22×C47—22no—
143C22×C47—42no—
144C22×C47—42no—
145C22×C47—48no—
146C22×C47—42no—
147C22×C47—42no—
148C22×C47—44no—
149C22×C47—432no—
150C22×C47—416no—
151C22×C47—48no—
152C22×C47—48no—
153C22×C47—416no—
154C22×C47—432no—
155C22×C47—48no—
156C22×C47—42no—
157C22×C47—42no—
158C22×C47—44no—
159C22×C47AΣL(1,𝔽16)14yes—
160C22×C47#40711yescharacteristic
161C22×C47C2×#9911yescharacteristic
162C22×C47C2×#10011yescharacteristic
163C4×C47—42no—
164C4×C47—42no—
165C4×C47—82no—
166C2×#379C2×C4711yescharacteristic
167#1462C2×C4712yescomplemented
168#1316C2×C4714yescomplemented
169C2×C47—21no—
170C2×C47—21no—
171C2×C47—24no—
172C2×C47—48no—
173C2×C47—42no—
174C2×C47—42no—
175C2×C47#146211yescharacteristic
176C2×C47C2×AΣL(1,𝔽16)12yes—
177C26C4×C4711yescharacteristic
178C22×C22⋊C4—22no—
179C22×C22⋊C4C4×C4711yescharacteristic
180C22×C22⋊C4C22×C4711yescharacteristic
181#407—22no—
182#379—22no—
183#379C4×C4712yes—
184#379C22×C4712yes—
185#323—22no—
186#323C22×C4714yescomplemented
187C47#1149911yescharacteristic, direct product factor, Sylow
188C25—21no—
189C25—21no—
190C25—24no—
191C25—48no—
192C25—42no—
193C25—42no—
194C25C2×C4×C4711yescharacteristic
195C25C2×C4×C4712yes—
196C23×C4—21no—
197C23×C4D4×C4712yes—
198C2×M16—42no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—24no—
201C2×C22⋊C4—24no—
202C2×C22⋊C4—42no—
203C2×C22⋊C4—48no—
204C2×C22⋊C4—42no—
205C2×C22⋊C4C2×C4×C4712yes—
206C2×C22⋊C4C2×C4×C4711yescharacteristic
207C2×C22⋊C4D4×C4712yes—
208C2×C22⋊C4C23×C4711yescharacteristic
209C22⋊C8—24no—
210C22⋊C8—42no—
211C24—28no—
212C24—24no—
213C24—22no—
214C24—22no—
215C24—22no—
216C24—22no—
217C24—24no—
218C24—22no—
219C24—44no—
220C24—48no—
221C24—42no—
222C24—42no—
223C24—44no—
224C24—42no—
225C24—48no—
226C24—432no—
227C24—416no—
228C24—42no—
229C24—48no—
230C24—416no—
231C24—432no—
232C24—48no—
233C24—42no—
234C24—42no—
235C24C22⋊C4×C4711yescharacteristic
236C24C22⋊C4×C4711yescharacteristic
237C24M16×C4714yescomplemented
238C24C22×C4×C4711yescharacteristic
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—44no—
243C22×C4—44no—
244C22×C4—42no—
245C22×C4C22⋊C4×C4712yes—
246C22×C4C2×D4×C4712yes—
247M16—84no—
248C2×C8—44no—
249C22⋊C4—41no—
250C22⋊C4—42no—
251C22⋊C4—41no—
252C22⋊C4—48no—
253C22⋊C4—48no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C23—24no—
257C23—21no—
258C23—21no—
259C23—28no—
260C23—216no—
261C23—28no—
262C23—21no—
263C23—24no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—42no—
268C23—48no—
269C23—44no—
270C23—42no—
271C23—48no—
272C23—416no—
273C23—48no—
274C23—48no—
275C23—44no—
276C23—48no—
277C23—44no—
278C23—48no—
279C23—48no—
280C23—416no—
281C23—44no—
282C23—48no—
283C23—48no—
284C23—416no—
285C23—416no—
286C23—464no—
287C23—464no—
288C23—48no—
289C23—416no—
290C23—48no—
291C23—44no—
292C23—42no—
293C23—42no—
294C23#99×C4712yes—
295C23#100×C4712yes—
296C23C2×C22⋊C4×C4711yescharacteristic
297C23C2×M16×C4712yes—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—44no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—44no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4—84no—
307C8—84no—
308C22—24no—
309C22—24no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—28no—
314C22—22no—
315C22—22no—
316C22—42no—
317C22—42no—
318C22—48no—
319C22—42no—
320C22—42no—
321C22—44no—
322C22—432no—
323C22—416no—
324C22—48no—
325C22—48no—
326C22—416no—
327C22—432no—
328C22—48no—
329C22—42no—
330C22—42no—
331C22—44no—
332C22C47×AΣL(1,𝔽16)14yes—
333C22C47×#40711yescharacteristic
334C22C2×#99×C4711yescharacteristic
335C22C2×#100×C4711yescharacteristic
336C4—42no—
337C4—42no—
338C4—82no—
339C2—21no—
340C2—21no—
341C2—24no—
342C2—48no—
343C2—42no—
344C2—42no—
345C2C47×#146211yescharacteristic
346C2C2×C47×AΣL(1,𝔽16)12yes—
subgroupG/H
center, socleC22×C47C2×#99
commutatorC24C22×C4×C47
Frattini, cosocleC2×C22⋊C4C23×C47
prime radicalC26×C47C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C24×C47 ◁ C22×C22⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#1462C2semidirect
3. C47×#1316C2semidirect
13. C47×#323C22semidirect
63. C24×C47M16semidirect
134. #11499C47direct (N × H)
167. #1462C2×C47semidirect
168. #1316C2×C47semidirect
186. #323C22×C47semidirect
187. C47#11499direct (N × H)
237. C24M16×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#3792
C47×#14622
C47×#13162
#1149947