Finite Group Databasebeta

← C47×#34530 #26074228

Subgroups — C47×#34530 #26074228

Order 12032.

1800 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#564C211yesmaximal, characteristic
2C47×#2382C213yesmaximal
3C47×#2371C216yesmaximal
4C47×#2370C216yesmaximal
5C47×#2336C216yesmaximal
6C47×#2330C216yesmaximal
7C4×#125×C47C213yesmaximal
8C47×#564C4116yescomplemented
9C2×#125×C47C2213yes—
10C2×#125×C47C2216yes—
11C2×#125×C47C2216yes—
12C47×#389C2213yes—
13C47×#389C2213yes—
14C47×#389C2216yes—
15C47×#389C2216yes—
16C47×#389C2216yes—
17C47×#389C2216yes—
18C47×#387C2216yes—
19C47×#387C2216yes—
20C47×#387C2216yes—
21C47×#387C2216yes—
22C47×#387C2216yes—
23C47×#387C2216yes—
24C47×#387C2216yes—
25C47×#387C2216yes—
26C47×#387C2216yes—
27C47×#387C2216yes—
28C47×#384C2212yes—
29C47×#383C2212yes—
30C47×#382C2213yes—
31C4×C4⋊C4×C47C2216yes—
32C4×C4⋊C4×C47C2213yes—
33C4×C4⋊C4×C47C2216yes—
34C4×C4⋊C4×C47C2213yes—
35C4×C4⋊C4×C47C2216yes—
36C4×C4⋊C4×C47C2216yes—
37C4×C4⋊C4×C47C2216yes—
38C47×#376C2216yes—
39C43×C47C2211yescharacteristic
40#125×C47C2×C4124yes—
41#125×C47C2×C4148yes—
42#125×C47C2×C4148yes—
43C2×C4⋊C4×C47C2316yes—
44C2×C4⋊C4×C47C2313yes—
45C2×C4⋊C4×C47C2313yes—
46C2×C4⋊C4×C47C2316yes—
47C2×C4⋊C4×C47C2316yes—
48C2×C4⋊C4×C47C2316yes—
49C2×C4⋊C4×C47C2313yes—
50C2×C4⋊C4×C47C2316yes—
51C2×C4⋊C4×C47C2316yes—
52C2×C4⋊C4×C47C2313yes—
53C2×C4⋊C4×C47C2316yes—
54C2×C4⋊C4×C47C2316yes—
55C2×C42×C47C2313yes—
56C2×C42×C47C2316yes—
57C2×C42×C47C2313yes—
58C2×C42×C47C2316yes—
59C2×C42×C47C2316yes—
60C2×C42×C47C2316yes—
61C2×C42×C47C2311yescharacteristic
62C2×C42×C47C2312yes—
63C2×C42×C47C2312yes—
64#95×C47C2316yes—
65#95×C47C2316yes—
66#95×C47C2316yes—
67#95×C47C2316yes—
68#95×C47C2316yes—
69#95×C47C2316yes—
70#95×C47C2316yes—
71#95×C47C2316yes—
72#95×C47C2316yes—
73#95×C47C2316yes—
74C22×C4×C47C2416yes—
75C22×C4×C47C2411yescharacteristic
76C22×C4×C47C2416yes—
77C22×C4×C47C2413yes—
78C22×C4×C47C2416yes—
79C22×C4×C47C2416yes—
80C22×C4×C47C2413yes—
81C4⋊C4×C47—212no—
82C4⋊C4×C47—46no—
83C4⋊C4×C47—43no—
84C4⋊C4×C47—46no—
85C4⋊C4×C47—46no—
86C4⋊C4×C47—43no—
87C4⋊C4×C47C22×C4112yes—
88C4⋊C4×C47C22×C4124yes—
89C4⋊C4×C47C22×C4124yes—
90C4⋊C4×C47C22×C4112yes—
91C4⋊C4×C47C22×C4124yes—
92C4⋊C4×C47C22×C4124yes—
93C42×C47—26no—
94C42×C47—212no—
95C42×C47—46no—
96C42×C47—43no—
97C42×C47—46no—
98C42×C47—46no—
99C42×C47C22×C414yes—
100C42×C47C22×C418yes—
101C42×C47C22×C418yes—
102C23×C47C2511yescharacteristic
103C2×C4×C47—23no—
104C2×C4×C47—26no—
105C2×C4×C47—23no—
106C2×C4×C47—26no—
107C2×C4×C47—23no—
108C2×C4×C47—26no—
109C2×C4×C47—23no—
110C2×C4×C47—26no—
111C2×C4×C47—26no—
112C2×C4×C47—26no—
113C2×C4×C47—26no—
114C2×C4×C47—26no—
115C2×C4×C47—26no—
116C2×C4×C47—23no—
117C2×C4×C47—26no—
118C2×C4×C47C23×C416yes—
119C2×C4×C47C23×C4112yes—
120C2×C4×C47C23×C4112yes—
121C2×C4×C472−1+416yes—
122#34530C4711yesmaximal, characteristic, direct product factor, Sylow
123C22×C47C24×C411yescharacteristic
124C22×C47C2×2−1+413yes—
125C22×C47#58513yes—
126C4×C47—26no—
127C4×C47—212no—
128C4×C47—212no—
129C4×C47—26no—
130C4×C47—46no—
131C4×C47—46no—
132C4×C47—41no—
133C2×#564C2×C4711yescharacteristic
134#2382C2×C4713yes—
135#2371C2×C4716yes—
136#2370C2×C4716yes—
137#2336C2×C4716yes—
138#2330C2×C4716yes—
139C4×#125C2×C4713yes—
140C2×C47C4×2−1+413yes—
141C2×C47#356313yes—
142C2×C47#356711yescharacteristic
143#564C4×C47116yescomplemented
144C2×#125C22×C4713yes—
145C2×#125C22×C4716yes—
146C2×#125C22×C4716yes—
147#389C22×C4713yes—
148#389C22×C4713yes—
149#389C22×C4716yes—
150#389C22×C4716yes—
151#389C22×C4716yes—
152#389C22×C4716yes—
153#387C22×C4716yes—
154#387C22×C4716yes—
155#387C22×C4716yes—
156#387C22×C4716yes—
157#387C22×C4716yes—
158#387C22×C4716yes—
159#387C22×C4716yes—
160#387C22×C4716yes—
161#387C22×C4716yes—
162#387C22×C4716yes—
163#384C22×C4712yes—
164#383C22×C4712yes—
165#382C22×C4713yes—
166C4×C4⋊C4C22×C4716yes—
167C4×C4⋊C4C22×C4713yes—
168C4×C4⋊C4C22×C4716yes—
169C4×C4⋊C4C22×C4713yes—
170C4×C4⋊C4C22×C4716yes—
171C4×C4⋊C4C22×C4716yes—
172C4×C4⋊C4C22×C4716yes—
173#376C22×C4716yes—
174C43C22×C4711yescharacteristic
175C47#3453011yescharacteristic, direct product factor, Sylow
176#125C2×C4×C47124yes—
177#125C2×C4×C47148yes—
178#125C2×C4×C47148yes—
179C2×C4⋊C4C23×C4716yes—
180C2×C4⋊C4C23×C4713yes—
181C2×C4⋊C4C23×C4713yes—
182C2×C4⋊C4C23×C4716yes—
183C2×C4⋊C4C23×C4716yes—
184C2×C4⋊C4C23×C4716yes—
185C2×C4⋊C4C23×C4713yes—
186C2×C4⋊C4C23×C4716yes—
187C2×C4⋊C4C23×C4716yes—
188C2×C4⋊C4C23×C4713yes—
189C2×C4⋊C4C23×C4716yes—
190C2×C4⋊C4C23×C4716yes—
191C2×C42C23×C4713yes—
192C2×C42C23×C4716yes—
193C2×C42C23×C4713yes—
194C2×C42C23×C4716yes—
195C2×C42C23×C4716yes—
196C2×C42C23×C4716yes—
197C2×C42C23×C4711yescharacteristic
198C2×C42C23×C4712yes—
199C2×C42C23×C4712yes—
200#95C23×C4716yes—
201#95C23×C4716yes—
202#95C23×C4716yes—
203#95C23×C4716yes—
204#95C23×C4716yes—
205#95C23×C4716yes—
206#95C23×C4716yes—
207#95C23×C4716yes—
208#95C23×C4716yes—
209#95C23×C4716yes—
210C22×C4C24×C4716yes—
211C22×C4C24×C4716yes—
212C22×C4C24×C4711yescharacteristic
213C22×C4C24×C4716yes—
214C22×C4C24×C4713yes—
215C22×C4C24×C4716yes—
216C22×C4C24×C4713yes—
217C4⋊C4—212no—
218C4⋊C4—46no—
219C4⋊C4—43no—
220C4⋊C4—46no—
221C4⋊C4—46no—
222C4⋊C4—43no—
223C4⋊C4C22×C4×C47112yes—
224C4⋊C4C22×C4×C47124yes—
225C4⋊C4C22×C4×C47124yes—
226C4⋊C4C22×C4×C47112yes—
227C4⋊C4C22×C4×C47124yes—
228C4⋊C4C22×C4×C47124yes—
229C42—26no—
230C42—212no—
231C42—46no—
232C42—43no—
233C42—46no—
234C42—46no—
235C42C22×C4×C4714yes—
236C42C22×C4×C4718yes—
237C42C22×C4×C4718yes—
238C23C25×C4711yescharacteristic
239C2×C4—23no—
240C2×C4—23no—
241C2×C4—26no—
242C2×C4—26no—
243C2×C4—23no—
244C2×C4—26no—
245C2×C4—23no—
246C2×C4—26no—
247C2×C4—26no—
248C2×C4—26no—
249C2×C4—26no—
250C2×C4—26no—
251C2×C4—26no—
252C2×C4—23no—
253C2×C4—26no—
254C2×C4C23×C4×C4716yes—
255C2×C4C23×C4×C47112yes—
256C2×C4C23×C4×C47112yes—
257C2×C42−1+4×C4716yes—
258C22C24×C4×C4711yescharacteristic
259C22C2×2−1+4×C4713yes—
260C22C47×#58513yes—
261C4—26no—
262C4—26no—
263C4—212no—
264C4—212no—
265C4—46no—
266C4—46no—
267C4—41no—
268C2C4×2−1+4×C4713yes—
269C2C47×#356313yes—
270C2C47×#356711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C47C25
commutatorC22C24×C4×C47
Frattini, cosocleC23C25×C47
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ G

Complements

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

NH ≅ G/Ntype
8. C47×#564C4semidirect
122. #34530C47direct (N × H)
143. #564C4×C47semidirect
175. C47#34530direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5642
C47×#23822
C47×#23712
C47×#23702
C47×#23362
C47×#23302
C4×#125×C472
#3453047