Finite Group Databasebeta

← C47×#3523 #20241133

Subgroups — C47×#3523 #20241133

Order 6016.

992 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#557C211yesmaximal, characteristic, complemented
2C47×#557C213yesmaximal, complemented
3C47×#556C213yesmaximal, complemented
4C47×#552C216yesmaximal, complemented
5D4×Q8×C47C212yesmaximal, complemented
6D4×Q8×C47C211yesmaximal, characteristic, complemented
7C47×#541C216yesmaximal, complemented
8C47×#533C213yesmaximal, complemented
9C47×#529C213yesmaximal
10C47×#519C212yesmaximal, complemented
11C2×C4×Q8×C47C211yesmaximal, characteristic, complemented
12C22×Q8×C47C2211yescharacteristic
13C22×Q8×C47C2212yes—
14C4⋊Q8×C47C2213yes—
15C4⋊Q8×C47C2213yes—
16C4⋊Q8×C47C2216yes—
17#126×C47C2216yes—
18#126×C47C22112yes—
19#125×C47C2213yes—
20#125×C47C2216yes—
21#125×C47C22112yes—
22#125×C47C2216yes—
23#124×C47C2213yes—
24#123×C47C2216yes—
25C22⋊Q8×C47C2213yes—
26C22⋊Q8×C47C2216yes—
27C22⋊Q8×C47C2216yes—
28C22⋊Q8×C47C2216yes—
29#121×C47C2211yescharacteristic
30C4×Q8×C47C2211yescharacteristic
31C4×Q8×C47C2213yes—
32C4×Q8×C47C2211yescharacteristic
33C4×Q8×C47C2213yes—
34C4×Q8×C47C2216yes—
35C4×Q8×C47C2212yes—
36C4×Q8×C47C2216yes—
37C4×Q8×C47C2213yes—
38C4×Q8×C47C2216yes—
39C4×D4×C47C2216yes—
40C4×D4×C47C2213yes—
41#117×C47C2216yes—
42#117×C47C2216yes—
43#117×C47C2216yes—
44C2×C4⋊C4×C47C2213yes—
45C2×C42×C47C2213yes—
46C2×Q8×C47—24no—
47C2×Q8×C47—28no—
48C2×Q8×C47C2313yes—
49C2×Q8×C47C2313yes—
50C2×Q8×C47C2316yes—
51C2×Q8×C47C2311yescharacteristic
52C2×D4×C47C2312yes—
53C2×D4×C47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2313yes—
56C22×C4×C47C2313yes—
57C22×C4×C47C2316yes—
58C4⋊C4×C47C2313yes—
59C4⋊C4×C47C2313yes—
60C4⋊C4×C47C2316yes—
61C4⋊C4×C47C2316yes—
62C4⋊C4×C47C2316yes—
63C4⋊C4×C47C2316yes—
64C4⋊C4×C47C2316yes—
65C4⋊C4×C47C2316yes—
66C4⋊C4×C47C2313yes—
67C4⋊C4×C47C2316yes—
68C4⋊C4×C47C2311yescharacteristic
69C4⋊C4×C47C23112yes—
70C4⋊C4×C47C2316yes—
71C22⋊C4×C47C2312yes—
72C22⋊C4×C47C2316yes—
73C22⋊C4×C47C2316yes—
74C22⋊C4×C47C2316yes—
75C22⋊C4×C47C2316yes—
76C42×C47C2313yes—
77C42×C47C2313yes—
78C42×C47C2313yes—
79C42×C47C2313yes—
80C42×C47C23112yes—
81C42×C47C2316yes—
82C23×C47C2412yes—
83C23×C47C2411yescharacteristic
84Q8×C47—26no—
85Q8×C47—212no—
86Q8×C47—26no—
87Q8×C47#4114yes—
88D4×C47—24no—
89D4×C47—22no—
90C2×C4×C47—26no—
91C2×C4×C47—26no—
92C2×C4×C47—212no—
93C2×C4×C47—22no—
94C2×C4×C47C2411yescharacteristic
95C2×C4×C47C2413yes—
96C2×C4×C47C2416yes—
97C2×C4×C47C2412yes—
98C2×C4×C47C2413yes—
99C2×C4×C47C2413yes—
100C2×C4×C47C2416yes—
101C2×C4×C47C2413yes—
102C2×C4×C47C2411yescharacteristic
103C22×C47—21no—
104C22×C47—21no—
105C22×C47—22no—
106C22×C47—22no—
107C22×C47—22no—
108C22×C472−1+412yes—
109C22×C47C2511yescharacteristic
110C4×C47—23no—
111C4×C47—26no—
112C4×C47—23no—
113C4×C47—23no—
114C4×C47—21no—
115C4×C47—22no—
116C4×C47—26no—
117C4×C47C2×#4116yes—
118C4×C472−1+412yes—
119#3523C4711yesmaximal, characteristic, direct product factor, Sylow
120C2×C47—22no—
121C2×C47—42no—
122C2×C47C22×#4111yescharacteristic
123C2×C47C2×2−1+411yescharacteristic
124C2×C47C2×2−1+411yescharacteristic
125#557C2×C4711yescharacteristic, complemented
126#557C2×C4713yescomplemented
127#556C2×C4713yescomplemented
128#552C2×C4716yescomplemented
129D4×Q8C2×C4712yescomplemented
130D4×Q8C2×C4711yescharacteristic, complemented
131#541C2×C4716yescomplemented
132#533C2×C4713yescomplemented
133#529C2×C4713yes—
134#519C2×C4712yescomplemented
135C2×C4×Q8C2×C4711yescharacteristic, complemented
136C47#352311yescharacteristic, direct product factor, Sylow
137C22×Q8C22×C4711yescharacteristic
138C22×Q8C22×C4712yes—
139C4⋊Q8C22×C4713yes—
140C4⋊Q8C22×C4713yes—
141C4⋊Q8C22×C4716yes—
142#126C22×C4716yes—
143#126C22×C47112yes—
144#125C22×C4713yes—
145#125C22×C4716yes—
146#125C22×C47112yes—
147#125C22×C4716yes—
148#124C22×C4713yes—
149#123C22×C4716yes—
150C22⋊Q8C22×C4713yes—
151C22⋊Q8C22×C4716yes—
152C22⋊Q8C22×C4716yes—
153C22⋊Q8C22×C4716yes—
154#121C22×C4711yescharacteristic
155C4×Q8C22×C4711yescharacteristic
156C4×Q8C22×C4713yes—
157C4×Q8C22×C4711yescharacteristic
158C4×Q8C22×C4713yes—
159C4×Q8C22×C4716yes—
160C4×Q8C22×C4712yes—
161C4×Q8C22×C4716yes—
162C4×Q8C22×C4713yes—
163C4×Q8C22×C4716yes—
164C4×D4C22×C4716yes—
165C4×D4C22×C4713yes—
166#117C22×C4716yes—
167#117C22×C4716yes—
168#117C22×C4716yes—
169C2×C4⋊C4C22×C4713yes—
170C2×C42C22×C4713yes—
171C2×Q8—24no—
172C2×Q8—28no—
173C2×Q8C23×C4713yes—
174C2×Q8C23×C4713yes—
175C2×Q8C23×C4716yes—
176C2×Q8C23×C4711yescharacteristic
177C2×D4C23×C4712yes—
178C2×D4C23×C4711yescharacteristic
179C22×C4C23×C4711yescharacteristic
180C22×C4C23×C4713yes—
181C22×C4C23×C4713yes—
182C22×C4C23×C4716yes—
183C4⋊C4C23×C4713yes—
184C4⋊C4C23×C4713yes—
185C4⋊C4C23×C4716yes—
186C4⋊C4C23×C4716yes—
187C4⋊C4C23×C4716yes—
188C4⋊C4C23×C4716yes—
189C4⋊C4C23×C4716yes—
190C4⋊C4C23×C4716yes—
191C4⋊C4C23×C4713yes—
192C4⋊C4C23×C4716yes—
193C4⋊C4C23×C4711yescharacteristic
194C4⋊C4C23×C47112yes—
195C4⋊C4C23×C4716yes—
196C22⋊C4C23×C4712yes—
197C22⋊C4C23×C4716yes—
198C22⋊C4C23×C4716yes—
199C22⋊C4C23×C4716yes—
200C22⋊C4C23×C4716yes—
201C42C23×C4713yes—
202C42C23×C4713yes—
203C42C23×C4713yes—
204C42C23×C4713yes—
205C42C23×C47112yes—
206C42C23×C4716yes—
207C23C24×C4712yes—
208C23C24×C4711yescharacteristic
209Q8—26no—
210Q8—212no—
211Q8—26no—
212Q8#41×C4714yes—
213D4—24no—
214D4—22no—
215C2×C4—26no—
216C2×C4—26no—
217C2×C4—212no—
218C2×C4—22no—
219C2×C4C24×C4711yescharacteristic
220C2×C4C24×C4713yes—
221C2×C4C24×C4716yes—
222C2×C4C24×C4712yes—
223C2×C4C24×C4713yes—
224C2×C4C24×C4713yes—
225C2×C4C24×C4716yes—
226C2×C4C24×C4713yes—
227C2×C4C24×C4711yescharacteristic
228C22—21no—
229C22—21no—
230C22—22no—
231C22—22no—
232C22—22no—
233C222−1+4×C4712yes—
234C22C25×C4711yescharacteristic
235C4—23no—
236C4—26no—
237C4—23no—
238C4—23no—
239C4—21no—
240C4—22no—
241C4—26no—
242C4C2×#41×C4716yes—
243C42−1+4×C4712yes—
244C2—22no—
245C2—42no—
246C2C22×#41×C4711yescharacteristic
247C2C2×2−1+4×C4711yescharacteristic
248C2C2×2−1+4×C4711yescharacteristic
subgroupG/H
center, socleC22×C47C25
commutator, Frattini, cosocleC22C25×C47
prime radical#121×C47C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#557C2semidirect
2. C47×#557C2semidirect
3. C47×#556C2semidirect
4. C47×#552C2semidirect
5. D4×Q8×C47C2semidirect
6. D4×Q8×C47C2semidirect
7. C47×#541C2semidirect
8. C47×#533C2semidirect
10. C47×#519C2semidirect
11. C2×C4×Q8×C47C2semidirect
119. #3523C47direct (N × H)
125. #557C2×C47semidirect
126. #557C2×C47semidirect
127. #556C2×C47semidirect
128. #552C2×C47semidirect
129. D4×Q8C2×C47semidirect
130. D4×Q8C2×C47semidirect
131. #541C2×C47semidirect
132. #533C2×C47semidirect
134. #519C2×C47semidirect
135. C2×C4×Q8C2×C47semidirect
136. C47#3523direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#5572
C47×#5562
C47×#5522
D4×Q8×C472
C47×#5412
C47×#5332
C47×#5292
C47×#5192
C2×C4×Q8×C472
#352347