Finite Group Databasebeta

← C47×#13608 #26053306

Subgroups — C47×#13608 #26053306

Order 12032.

308 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 86 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×#3223C211yesmaximal, characteristic
2C47×#2133C211yesmaximal, characteristic
3C47×#2129C211yesmaximal, characteristic
4C47×#1414C212yesmaximal, complemented
5C47×#1407C212yesmaximal, complemented
6C47×#541C411yescharacteristic, complemented
7C47×#536C2211yescharacteristic
8C47×#497C2211yescharacteristic
9C47×#494C411yescharacteristic, complemented
10C47×#491C411yescharacteristic, complemented
11C47×#488C2211yescharacteristic
12C47×#464—21no—
13C47×#462—21no—
14C47×#452—21no—
15C47×#451—21no—
16C47×#433C411yescharacteristic, complemented
17C2×#101×C47—21no—
18C47×#410—21no—
19C47×#356—21no—
20C47×#355C2212yes—
21C47×#354—21no—
22C47×#354C2212yes—
23C2×#41×C47D411yescharacteristic
24C22×Q8×C47D411yescharacteristic
25C2×Q16×C47—21no—
26C2×Q16×C47—21no—
27C2×Q16×C47—21no—
28C2×SD16×C47—21no—
29C2×M16×C47—41no—
30C4⋊Q8×C47C2×C411yescharacteristic
31C4⋊Q8×C47C2×C411yescharacteristic
32C4⋊Q8×C47D411yescharacteristic
33#126×C47—41no—
34#125×C47—41no—
35#125×C47C2×C411yescharacteristic
36#124×C47D411yescharacteristic
37#124×C47C2311yescharacteristic
38#123×C47—41no—
39C22⋊Q8×C47—21no—
40C22⋊Q8×C47—41no—
41C4×Q8×C47—21no—
42#117×C47—41no—
43#117×C47C2×C411yescharacteristic
44C4⋊C8×C47—21no—
45#103×C47—21no—
46#103×C47—21no—
47#103×C47—21no—
48#102×C47—21no—
49#101×C47—22no—
50#101×C47—41no—
51#99×C47—22no—
52#99×C47—41no—
53C22⋊C8×C47—21no—
54#97×C47C2×C411yescharacteristic
55C4×C8×C47C2×C411yescharacteristic
56#41×C47—81no—
57C2×Q8×C47—21no—
58C2×Q8×C47—21no—
59C2×Q8×C47—81no—
60C2×Q8×C47C22⋊C411yescharacteristic
61C2×Q8×C47C22⋊C411yescharacteristic
62C2×Q8×C47C2×D411yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47C2×D411yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47C22⋊C411yescharacteristic
68Q16×C47—81no—
69Q16×C47—81no—
70Q16×C47—81no—
71SD16×C47—81no—
72M16×C47—42no—
73M16×C47—81no—
74C2×C8×C47—21no—
75C2×C8×C47—21no—
76C2×C8×C47—81no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47—41no—
80C4⋊C4×C47—41no—
81C4⋊C4×C47—41no—
82C4⋊C4×C47—41no—
83C4⋊C4×C47—41no—
84C4⋊C4×C47—41no—
85C4⋊C4×C47—81no—
86C22⋊C4×C47—21no—
87C22⋊C4×C47—41no—
88C22⋊C4×C47—41no—
89C22⋊C4×C47—41no—
90C22⋊C4×C47—42no—
91C42×C47—41no—
92C42×C47—81no—
93C42×C47C22⋊C411yescharacteristic
94C42×C47C22×C411yescharacteristic
95C23×C47—21no—
96C23×C47#9911yescharacteristic
97Q8×C47—41no—
98Q8×C47—41no—
99Q8×C47—41no—
100Q8×C47—41no—
101Q8×C47—41no—
102Q8×C47—81no—
103D4×C47—41no—
104D4×C47—81no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—41no—
111C2×C4×C47—41no—
112C2×C4×C47—41no—
113C2×C4×C47—41no—
114C2×C4×C47—41no—
115C2×C4×C47—41no—
116C2×C4×C47—41no—
117C2×C4×C47—82no—
118C2×C4×C47#9911yescharacteristic
119C2×C4×C47C2×C22⋊C411yescharacteristic
120C8×C47—41no—
121C8×C47—41no—
122C8×C47—82no—
123#13608C4711yesmaximal, characteristic, direct product factor, Sylow
124C22×C47—21no—
125C22×C47—41no—
126C22×C47—41no—
127C22×C47—81no—
128C22×C47C2×#9911yescharacteristic
129C4×C47—21no—
130C4×C47—21no—
131C4×C47—41no—
132C4×C47—41no—
133C4×C47—41no—
134C4×C47—41no—
135C4×C47—41no—
136C4×C47—81no—
137C4×C47—81no—
138C4×C47—162no—
139#3223C2×C4711yescharacteristic
140#2133C2×C4711yescharacteristic
141#2129C2×C4711yescharacteristic
142#1414C2×C4712yescomplemented
143#1407C2×C4712yescomplemented
144C2×C47—21no—
145C2×C47—41no—
146C2×C47—81no—
147C2×C47#212711yescharacteristic
148#541C4×C4711yescharacteristic, complemented
149#536C22×C4711yescharacteristic
150#497C22×C4711yescharacteristic
151#494C4×C4711yescharacteristic, complemented
152#491C4×C4711yescharacteristic, complemented
153#488C22×C4711yescharacteristic
154#464—21no—
155#462—21no—
156#452—21no—
157#451—21no—
158#433C4×C4711yescharacteristic, complemented
159C2×#101—21no—
160#410—21no—
161#356—21no—
162#355C22×C4712yes—
163#354—21no—
164#354C22×C4712yes—
165C47#1360811yescharacteristic, direct product factor, Sylow
166C2×#41D4×C4711yescharacteristic
167C22×Q8D4×C4711yescharacteristic
168C2×Q16—21no—
169C2×Q16—21no—
170C2×Q16—21no—
171C2×SD16—21no—
172C2×M16—41no—
173C4⋊Q8C2×C4×C4711yescharacteristic
174C4⋊Q8C2×C4×C4711yescharacteristic
175C4⋊Q8D4×C4711yescharacteristic
176#126—41no—
177#125—41no—
178#125C2×C4×C4711yescharacteristic
179#124D4×C4711yescharacteristic
180#124C23×C4711yescharacteristic
181#123—41no—
182C22⋊Q8—21no—
183C22⋊Q8—41no—
184C4×Q8—21no—
185#117—41no—
186#117C2×C4×C4711yescharacteristic
187C4⋊C8—21no—
188#103—21no—
189#103—21no—
190#103—21no—
191#102—21no—
192#101—22no—
193#101—41no—
194#99—22no—
195#99—41no—
196C22⋊C8—21no—
197#97C2×C4×C4711yescharacteristic
198C4×C8C2×C4×C4711yescharacteristic
199#41—81no—
200C2×Q8—21no—
201C2×Q8—21no—
202C2×Q8—81no—
203C2×Q8C22⋊C4×C4711yescharacteristic
204C2×Q8C22⋊C4×C4711yescharacteristic
205C2×Q8C2×D4×C4711yescharacteristic
206C2×D4—21no—
207C2×D4C2×D4×C4711yescharacteristic
208C22×C4—21no—
209C22×C4—21no—
210C22×C4C22⋊C4×C4711yescharacteristic
211Q16—81no—
212Q16—81no—
213Q16—81no—
214SD16—81no—
215M16—42no—
216M16—81no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—81no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—81no—
229C22⋊C4—21no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—42no—
234C42—41no—
235C42—81no—
236C42C22⋊C4×C4711yescharacteristic
237C42C22×C4×C4711yescharacteristic
238C23—21no—
239C23#99×C4711yescharacteristic
240Q8—41no—
241Q8—41no—
242Q8—41no—
243Q8—41no—
244Q8—41no—
245Q8—81no—
246D4—41no—
247D4—81no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—82no—
261C2×C4#99×C4711yescharacteristic
262C2×C4C2×C22⋊C4×C4711yescharacteristic
263C8—41no—
264C8—41no—
265C8—82no—
266C22—21no—
267C22—41no—
268C22—41no—
269C22—81no—
270C22C2×#99×C4711yescharacteristic
271C4—21no—
272C4—21no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—41no—
278C4—81no—
279C4—81no—
280C4—162no—
281C2—21no—
282C2—41no—
283C2—81no—
284C2C47×#212711yescharacteristic
subgroupG/H
center, socleC2×C47#2127
commutatorC42C22×C4×C47
Frattini, cosocle#124C23×C47
prime radicalC2×#41×C47D4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C22×C47 ◁ C22×C4×C47 ◁ C47×#536 ◁ G

Complements

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

NH ≅ G/Ntype
4. C47×#1414C2semidirect
5. C47×#1407C2semidirect
6. C47×#541C4semidirect
9. C47×#494C4semidirect
10. C47×#491C4semidirect
16. C47×#433C4semidirect
123. #13608C47direct (N × H)
142. #1414C2×C47semidirect
143. #1407C2×C47semidirect
148. #541C4×C47semidirect
151. #494C4×C47semidirect
152. #491C4×C47semidirect
158. #433C4×C47semidirect
165. C47#13608direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32232
C47×#21332
C47×#21292
C47×#14142
C47×#14072
#1360847