Finite Group Databasebeta

← C47×#9586 #26049284

Subgroups — C47×#9586 #26049284

Order 12032.

312 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#1574C211yesmaximal, characteristic, complemented
2C47×#1543C211yesmaximal, characteristic
3C47×#1492C211yesmaximal, characteristic
4C47×#1484C211yesmaximal, characteristic
5C47×#1450C211yesmaximal, characteristic, complemented
6C47×#1299C211yesmaximal, characteristic, complemented
7C47×#1278C211yesmaximal, characteristic, complemented
8C47×#532C2211yescharacteristic
9C47×#431C2211yescharacteristic
10C47×#431C2211yescharacteristic
11C47×#431C2211yescharacteristic
12C47×#423C2211yescharacteristic
13C4×M16×C47C2211yescharacteristic
14C2×C4×C8×C47C2211yescharacteristic
15C47×#335—21no—
16C47×#334—21no—
17C47×#333C411yescharacteristic
18C47×#333C411yescharacteristic
19C47×#331C411yescharacteristic
20C47×#331C411yescharacteristic
21C47×D4⋊C8—21no—
22C47×D4⋊C8—21no—
23C47×D4⋊C8—21no—
24C47×D4⋊C8—21no—
25C47×#322—21no—
26C82×C47—21no—
27C2×#41×C47—21no—
28C2×M16×C47—21no—
29C2×M16×C47—21no—
30C22×C8×C47—21no—
31C4⋊Q8×C47C2×C411yescharacteristic
32#127×C47C2×C411yescharacteristic
33#124×C47—21no—
34#121×C47—21no—
35#121×C47—21no—
36C4×D4×C47—21no—
37C4×D4×C47—21no—
38C2×C42×C47C2311yescharacteristic
39C4⋊C8×C47—21no—
40C4⋊C8×C47—21no—
41C4⋊C8×C47C2×C411yescharacteristic
42C4⋊C8×C47C2×C411yescharacteristic
43C4⋊C8×C47C2×C411yescharacteristic
44C4⋊C8×C47C2×C411yescharacteristic
45C4⋊C8×C47D411yescharacteristic
46C4⋊C8×C47D411yescharacteristic
47C22⋊C8×C47—21no—
48C22⋊C8×C47—21no—
49C22⋊C8×C47—21no—
50#97×C47—21no—
51C4×C8×C47—21no—
52C4×C8×C47—21no—
53C4×C8×C47—21no—
54C4×C8×C47—21no—
55C4×C8×C47—21no—
56C4×C8×C47D411yescharacteristic
57C4×C8×C47D411yescharacteristic
58#41×C47—81no—
59#41×C47—81no—
60C2×Q8×C47—21no—
61C2×D4×C47—21no—
62C2×D4×C47—21no—
63C2×D4×C47—21no—
64C2×D4×C47—41no—
65C22×C4×C47—41no—
66C22×C4×C47#4111yescharacteristic
67C22×C4×C47#4111yescharacteristic
68C22×C4×C47#4111yescharacteristic
69M16×C47—22no—
70M16×C47—41no—
71M16×C47—81no—
72C2×C8×C47—22no—
73C2×C8×C47—22no—
74C2×C8×C47—21no—
75C2×C8×C47—21no—
76C2×C8×C47—21no—
77C2×C8×C47—21no—
78C2×C8×C47—21no—
79C2×C8×C47—21no—
80C2×C8×C47—21no—
81C2×C8×C47—21no—
82C2×C8×C47—41no—
83C2×C8×C47—41no—
84C4⋊C4×C47—21no—
85C4⋊C4×C47—21no—
86C22⋊C4×C47—41no—
87C22⋊C4×C47—41no—
88C42×C47C22×C411yescharacteristic
89C42×C47C2×D411yescharacteristic
90C42×C47C2×D411yescharacteristic
91C42×C47#4111yescharacteristic
92C23×C47—41no—
93C23×C47#12611yescharacteristic
94Q8×C47—81no—
95D4×C47—41no—
96D4×C47—41no—
97D4×C47—41no—
98D4×C47—41no—
99D4×C47—81no—
100D4×C47—82no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—41no—
108C2×C4×C47—81no—
109C2×C4×C47—81no—
110C2×C4×C47#11711yescharacteristic
111C2×C4×C47C4×D411yescharacteristic
112C2×C4×C47C4×D411yescharacteristic
113C2×C4×C47#12111yescharacteristic
114C2×C4×C47#12311yescharacteristic
115C2×C4×C47#12411yescharacteristic
116C8×C47—22no—
117C8×C47—22no—
118C8×C47—42no—
119C8×C47—41no—
120C8×C47—41no—
121C8×C47—41no—
122C8×C47—41no—
123C8×C47—41no—
124C8×C47—41no—
125C8×C47—81no—
126#9586C4711yesmaximal, characteristic, direct product factor, Sylow
127C22×C47—21no—
128C22×C47—21no—
129C22×C47—21no—
130C22×C47—81no—
131C22×C47—81no—
132C22×C47—81no—
133C22×C47#38811yescharacteristic
134C4×C47—21no—
135C4×C47—21no—
136C4×C47—21no—
137C4×C47—81no—
138C4×C47#44311yescharacteristic
139C4×C47#44311yescharacteristic
140C4×C47#44311yescharacteristic
141C4×C47#44411yescharacteristic
142C4×C47#47111yescharacteristic
143C4×C47#47211yescharacteristic
144#1574C2×C4711yescharacteristic, complemented
145#1543C2×C4711yescharacteristic
146#1492C2×C4711yescharacteristic
147#1484C2×C4711yescharacteristic
148#1450C2×C4711yescharacteristic, complemented
149#1299C2×C4711yescharacteristic, complemented
150#1278C2×C4711yescharacteristic, complemented
151C2×C47—41no—
152C2×C47—161no—
153C2×C47#192911yescharacteristic
154C2×C47#193111yescharacteristic
155C2×C47#193711yescharacteristic
156#532C22×C4711yescharacteristic
157#431C22×C4711yescharacteristic
158#431C22×C4711yescharacteristic
159#431C22×C4711yescharacteristic
160#423C22×C4711yescharacteristic
161C4×M16C22×C4711yescharacteristic
162C2×C4×C8C22×C4711yescharacteristic
163#335—21no—
164#334—21no—
165#333C4×C4711yescharacteristic
166#333C4×C4711yescharacteristic
167#331C4×C4711yescharacteristic
168#331C4×C4711yescharacteristic
169D4⋊C8—21no—
170D4⋊C8—21no—
171D4⋊C8—21no—
172D4⋊C8—21no—
173#322—21no—
174C82—21no—
175C47#958611yescharacteristic, direct product factor, Sylow
176C2×#41—21no—
177C2×M16—21no—
178C2×M16—21no—
179C22×C8—21no—
180C4⋊Q8C2×C4×C4711yescharacteristic
181#127C2×C4×C4711yescharacteristic
182#124—21no—
183#121—21no—
184#121—21no—
185C4×D4—21no—
186C4×D4—21no—
187C2×C42C23×C4711yescharacteristic
188C4⋊C8—21no—
189C4⋊C8—21no—
190C4⋊C8C2×C4×C4711yescharacteristic
191C4⋊C8C2×C4×C4711yescharacteristic
192C4⋊C8C2×C4×C4711yescharacteristic
193C4⋊C8C2×C4×C4711yescharacteristic
194C4⋊C8D4×C4711yescharacteristic
195C4⋊C8D4×C4711yescharacteristic
196C22⋊C8—21no—
197C22⋊C8—21no—
198C22⋊C8—21no—
199#97—21no—
200C4×C8—21no—
201C4×C8—21no—
202C4×C8—21no—
203C4×C8—21no—
204C4×C8—21no—
205C4×C8D4×C4711yescharacteristic
206C4×C8D4×C4711yescharacteristic
207#41—81no—
208#41—81no—
209C2×Q8—21no—
210C2×D4—21no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—41no—
214C22×C4—41no—
215C22×C4#41×C4711yescharacteristic
216C22×C4#41×C4711yescharacteristic
217C22×C4#41×C4711yescharacteristic
218M16—22no—
219M16—41no—
220M16—81no—
221C2×C8—22no—
222C2×C8—22no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—41no—
232C2×C8—41no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C22⋊C4—41no—
236C22⋊C4—41no—
237C42C22×C4×C4711yescharacteristic
238C42C2×D4×C4711yescharacteristic
239C42C2×D4×C4711yescharacteristic
240C42#41×C4711yescharacteristic
241C23—41no—
242C23#126×C4711yescharacteristic
243Q8—81no—
244D4—41no—
245D4—41no—
246D4—41no—
247D4—41no—
248D4—81no—
249D4—82no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4#117×C4711yescharacteristic
260C2×C4C4×D4×C4711yescharacteristic
261C2×C4C4×D4×C4711yescharacteristic
262C2×C4#121×C4711yescharacteristic
263C2×C4#123×C4711yescharacteristic
264C2×C4#124×C4711yescharacteristic
265C8—22no—
266C8—22no—
267C8—42no—
268C8—41no—
269C8—41no—
270C8—41no—
271C8—41no—
272C8—41no—
273C8—41no—
274C8—81no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—81no—
279C22—81no—
280C22—81no—
281C22C47×#38811yescharacteristic
282C4—21no—
283C4—21no—
284C4—21no—
285C4—81no—
286C4C47×#44311yescharacteristic
287C4C47×#44311yescharacteristic
288C4C47×#44311yescharacteristic
289C4C47×#44411yescharacteristic
290C4C47×#47111yescharacteristic
291C4C47×#47211yescharacteristic
292C2—41no—
293C2—161no—
294C2C47×#192911yescharacteristic
295C2C47×#193111yescharacteristic
296C2C47×#193711yescharacteristic
subgroupG/H
centerC2×C4×C47#121
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
socleC22×C47#388
prime radicalC47×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#1574C2semidirect
5. C47×#1450C2semidirect
6. C47×#1299C2semidirect
7. C47×#1278C2semidirect
126. #9586C47direct (N × H)
144. #1574C2×C47semidirect
148. #1450C2×C47semidirect
149. #1299C2×C47semidirect
150. #1278C2×C47semidirect
175. C47#9586direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#15742
C47×#15432
C47×#14922
C47×#14842
C47×#14502
C47×#12992
C47×#12782
#958647