Finite Group Databasebeta

← C47×#9507 #26049205

Subgroups — C47×#9507 #26049205

Order 12032.

544 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 126 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
1C47×#2973C211yesmaximal, characteristic
2C47×#2486C211yesmaximal, characteristic
3C47×#1821C212yesmaximal, complemented
4C47×#1465C211yesmaximal, characteristic
5C47×#1305C212yesmaximal, complemented
6C2×#123×C47C412yes—
7C2×C4×D4×C47C2211yescharacteristic
8C22×C4⋊C4×C47C2211yescharacteristic
9C47×#435—24no—
10C47×#432—21no—
11C47×#407C2212yes—
12C47×#407C2212yes—
13C2×C22⋊C8×C47—21no—
14C47×#398—21no—
15C47×#397—21no—
16C47×#389—21no—
17C47×#381C412yes—
18C47×#380—21no—
19C47×#380C2211yescharacteristic
20C47×#343—24no—
21C47×#324—21no—
22C47×#323—21no—
23C22×D4×C47C2×C411yescharacteristic
24C23×C4×C47C2×C412yes—
25C23×C4×C47D411yescharacteristic
26C23×C4×C47C2311yescharacteristic
27C2×M16×C47—22no—
28C2×M16×C47D414yes—
29C22×C8×C47—22no—
30#123×C47—44no—
31C4×D4×C47—22no—
32C4×D4×C47—22no—
33C2×C4⋊C4×C47—22no—
34C2×C4⋊C4×C47—22no—
35C2×C4⋊C4×C47—21no—
36C2×C4⋊C4×C47—21no—
37C2×C4⋊C4×C47—21no—
38C2×C4⋊C4×C47—22no—
39C2×C4⋊C4×C47D411yescharacteristic
40C2×C22⋊C4×C47—22no—
41C2×C22⋊C4×C47C2×C411yescharacteristic
42C2×C22⋊C4×C47C2×C412yes—
43C2×C22⋊C4×C47D411yescharacteristic
44C2×C42×C47D411yescharacteristic
45C4⋊C8×C47—22no—
46C22⋊C8×C47—22no—
47C22⋊C8×C47—22no—
48C22⋊C8×C47—22no—
49C22⋊C8×C47—22no—
50C22⋊C8×C47—22no—
51#97×C47—22no—
52#95×C47—22no—
53#95×C47—22no—
54#95×C47—21no—
55C24×C47C22⋊C411yescharacteristic
56C24×C47C22×C411yescharacteristic
57C2×D4×C47—22no—
58C2×D4×C47—22no—
59C2×D4×C47—41no—
60C22×C4×C47—21no—
61C22×C4×C47—21no—
62C22×C4×C47—22no—
63C22×C4×C47—22no—
64C22×C4×C47—24no—
65C22×C4×C47—42no—
66C22×C4×C47—42no—
67C22×C4×C47—42no—
68C22×C4×C47—42no—
69C22×C4×C47C22⋊C411yescharacteristic
70C22×C4×C47C22⋊C411yescharacteristic
71C22×C4×C47C22⋊C411yescharacteristic
72C22×C4×C47C2×D412yes—
73C22×C4×C47C2×D411yescharacteristic
74C22×C4×C47C2×D411yescharacteristic
75C22×C4×C47#4112yes—
76M16×C47—44no—
77M16×C47—44no—
78C2×C8×C47—24no—
79C2×C8×C47—42no—
80C2×C8×C47—82no—
81C4⋊C4×C47—22no—
82C4⋊C4×C47—42no—
83C4⋊C4×C47—44no—
84C4⋊C4×C47—41no—
85C4⋊C4×C47—42no—
86C4⋊C4×C47—41no—
87C22⋊C4×C47—22no—
88C22⋊C4×C47—22no—
89C22⋊C4×C47—44no—
90C22⋊C4×C47—42no—
91C42×C47—21no—
92C42×C47—21no—
93C23×C47—21no—
94C23×C47—21no—
95C23×C47—21no—
96C23×C47—21no—
97C23×C47—41no—
98C23×C47—41no—
99C23×C47—41no—
100C23×C47—41no—
101C23×C47#10012yes—
102C23×C47C2×C22⋊C411yescharacteristic
103C23×C47C4×D412yes—
104D4×C47—44no—
105C2×C4×C47—22no—
106C2×C4×C47—24no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—41no—
113C2×C4×C47—42no—
114C2×C4×C47—42no—
115C2×C4×C47—41no—
116C2×C4×C47—41no—
117C2×C4×C47—42no—
118C2×C4×C47—42no—
119C2×C4×C47—42no—
120C2×C4×C47—42no—
121C2×C4×C47—42no—
122C2×C4×C47—42no—
123C2×C4×C47—81no—
124C2×C4×C47—84no—
125C2×C4×C47#12011yescharacteristic
126C2×C4×C47#12112yes—
127C2×C4×C47#12311yescharacteristic
128C8×C47—44no—
129C8×C47—82no—
130#9507C4711yesmaximal, characteristic, direct product factor, Sylow
131C22×C47—21no—
132C22×C47—21no—
133C22×C47—22no—
134C22×C47—22no—
135C22×C47—22no—
136C22×C47—22no—
137C22×C47—42no—
138C22×C47—42no—
139C22×C47—42no—
140C22×C47—41no—
141C22×C47—41no—
142C22×C47—81no—
143C22×C47#38611yescharacteristic
144C22×C47C2×#10011yescharacteristic
145C22×C47#41311yescharacteristic
146C4×C47—22no—
147C4×C47—21no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47—82no—
152C4×C47—82no—
153C4×C47#45812yes—
154#2973C2×C4711yescharacteristic
155#2486C2×C4711yescharacteristic
156#1821C2×C4712yescomplemented
157#1465C2×C4711yescharacteristic
158#1305C2×C4712yescomplemented
159C2×C47—21no—
160C2×C47—21no—
161C2×C47—42no—
162C2×C47—42no—
163C2×C47#189011yescharacteristic
164C2×C47#190011yescharacteristic
165C2×C47#191511yescharacteristic
166C2×#123C4×C4712yes—
167C2×C4×D4C22×C4711yescharacteristic
168C22×C4⋊C4C22×C4711yescharacteristic
169#435—24no—
170#432—21no—
171#407C22×C4712yes—
172#407C22×C4712yes—
173C2×C22⋊C8—21no—
174#398—21no—
175#397—21no—
176#389—21no—
177#381C4×C4712yes—
178#380—21no—
179#380C22×C4711yescharacteristic
180#343—24no—
181#324—21no—
182#323—21no—
183C47#950711yescharacteristic, direct product factor, Sylow
184C22×D4C2×C4×C4711yescharacteristic
185C23×C4C2×C4×C4712yes—
186C23×C4D4×C4711yescharacteristic
187C23×C4C23×C4711yescharacteristic
188C2×M16—22no—
189C2×M16D4×C4714yes—
190C22×C8—22no—
191#123—44no—
192C4×D4—22no—
193C4×D4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4D4×C4711yescharacteristic
201C2×C22⋊C4—22no—
202C2×C22⋊C4C2×C4×C4711yescharacteristic
203C2×C22⋊C4C2×C4×C4712yes—
204C2×C22⋊C4D4×C4711yescharacteristic
205C2×C42D4×C4711yescharacteristic
206C4⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—22no—
209C22⋊C8—22no—
210C22⋊C8—22no—
211C22⋊C8—22no—
212#97—22no—
213#95—22no—
214#95—22no—
215#95—21no—
216C24C22⋊C4×C4711yescharacteristic
217C24C22×C4×C4711yescharacteristic
218C2×D4—22no—
219C2×D4—22no—
220C2×D4—41no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—24no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4C22⋊C4×C4711yescharacteristic
231C22×C4C22⋊C4×C4711yescharacteristic
232C22×C4C22⋊C4×C4711yescharacteristic
233C22×C4C2×D4×C4712yes—
234C22×C4C2×D4×C4711yescharacteristic
235C22×C4C2×D4×C4711yescharacteristic
236C22×C4#41×C4712yes—
237M16—44no—
238M16—44no—
239C2×C8—24no—
240C2×C8—42no—
241C2×C8—82no—
242C4⋊C4—22no—
243C4⋊C4—42no—
244C4⋊C4—44no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—41no—
248C22⋊C4—22no—
249C22⋊C4—22no—
250C22⋊C4—44no—
251C22⋊C4—42no—
252C42—21no—
253C42—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23#100×C4712yes—
263C23C2×C22⋊C4×C4711yescharacteristic
264C23C4×D4×C4712yes—
265D4—44no—
266C2×C4—22no—
267C2×C4—24no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—81no—
285C2×C4—84no—
286C2×C4#120×C4711yescharacteristic
287C2×C4#121×C4712yes—
288C2×C4#123×C4711yescharacteristic
289C8—44no—
290C8—82no—
291C22—21no—
292C22—21no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C47×#38611yescharacteristic
304C22C2×#100×C4711yescharacteristic
305C22C47×#41311yescharacteristic
306C4—22no—
307C4—21no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—82no—
312C4—82no—
313C4C47×#45812yes—
314C2—21no—
315C2—21no—
316C2—42no—
317C2—42no—
318C2C47×#189011yescharacteristic
319C2C47×#190011yescharacteristic
320C2C47×#191511yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC24C22×C4×C47
Frattini, cosocleC23×C4C23×C47
prime radicalC22×D4×C47C2×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#1821C2semidirect
5. C47×#1305C2semidirect
130. #9507C47direct (N × H)
156. #1821C2×C47semidirect
158. #1305C2×C47semidirect
183. C47#9507direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#29732
C47×#24862
C47×#18212
C47×#14652
C47×#13052
#950747