Finite Group Databasebeta

← C2×C47×#1655 #26058676

Subgroups — C2×C47×#1655 #26058676

Order 12032.

1330 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 1330 conjugacy classes of subgroups — too many to draw. Only its 238 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
1C2×C47×H(3,𝔽4)C211yesmaximal, characteristic, complemented
2C2×C47×#496C213yesmaximal, complemented
3C47×#1655C218yesmaximal, direct product factor
4C2×C47×#329C213yesmaximal, complemented
5C22×SD16×C47—23no—
6C22×D8×C47—23no—
7C47×H(3,𝔽4)—26no—
8C47×H(3,𝔽4)C2214yescomplemented
9C2×#127×C47C2211yescharacteristic, complemented
10C2×#124×C47—23no—
11C2×#124×C47C2213yes—
12C2×#120×C47—23no—
13C47×#496—26no—
14C47×#496C22112yescomplemented
15C2×#97×C47C2213yescomplemented
16C47×#329C22112yescomplemented
17C25×C47—21no—
18C22×Q8×C47D413yes—
19C22×D4×C47—23no—
20C22×D4×C47—23no—
21C22×D4×C47D413yes—
22C2×SD16×C47—212no—
23C2×SD16×C47—412no—
24C2×D8×C47—212no—
25C2×D8×C47—412no—
26C22×C8×C47—23no—
27#127×C47—23no—
28#127×C47C2312yescomplemented
29#124×C47—212no—
30#124×C47—212no—
31#124×C47—26no—
32#124×C47D416yes—
33#124×C47C2316yes—
34#120×C47—212no—
35#120×C47—212no—
36C2×C22⋊C4×C47—23no—
37C2×C22⋊C4×C47—26no—
38C2×C42×C47—21no—
39C2×C42×C47C2311yescharacteristic
40#97×C47—23no—
41#97×C47C2316yescomplemented
42C24×C47—24no—
43C24×C47—23no—
44C24×C47—41no—
45C24×C47—86no—
46C2×Q8×C47—23no—
47C2×Q8×C47—46no—
48C2×Q8×C47C2×D416yes—
49C2×D4×C47—212no—
50C2×D4×C47—23no—
51C2×D4×C47—26no—
52C2×D4×C47—46no—
53C2×D4×C47—46no—
54C2×D4×C47—46no—
55C2×D4×C47—43no—
56C2×D4×C47—86no—
57C2×D4×C47C2×D416yes—
58C22×C4×C47—23no—
59C22×C4×C47C2×D413yes—
60SD16×C47—424no—
61D8×C47—424no—
62C2×C8×C47—212no—
63C2×C8×C47—26no—
64C22⋊C4×C47—212no—
65C22⋊C4×C47—212no—
66C22⋊C4×C47—212no—
67C42×C47—24no—
68C42×C47C2×D413yes—
69C42×C47C2411yescharacteristic
70C23×C47—26no—
71C23×C47—46no—
72C23×C47—412no—
73C23×C47—42no—
74C23×C47—812no—
75C23×C47—816no—
76C23×C47—86no—
77C23×C47#12011yescharacteristic
78Q8×C47—46no—
79Q8×C47—83no—
80D4×C47—46no—
81D4×C47—46no—
82D4×C47—46no—
83D4×C47—83no—
84D4×C47—86no—
85D4×C47—812no—
86C2×C4×C47—26no—
87C2×C4×C47—26no—
88C2×C4×C47—46no—
89C2×C4×C47#12013yes—
90C2×C4×C47C22×D413yes—
91C8×C47—212no—
92C2×#1655C4711yesmaximal, characteristic, direct product factor, Sylow
93C22×C47—46no—
94C22×C47—412no—
95C22×C47—816no—
96C22×C47—812no—
97C22×C47—86no—
98C22×C47—164no—
99C22×C47#45316yes—
100C22×C47C2×#12011yescharacteristic
101C4×C47—23no—
102C4×C47—23no—
103C4×C47—46no—
104C2×H(3,𝔽4)C2×C4711yescharacteristic, complemented
105C2×#496C2×C4713yescomplemented
106#1655C2×C4718yesdirect product factor
107C2×#329C2×C4713yescomplemented
108C2×C47—86no—
109C2×C47—162no—
110C2×C47#165514yesdirect product factor
111C2×C47C2×#45313yes—
112C22×SD16—23no—
113C22×D8—23no—
114H(3,𝔽4)—26no—
115H(3,𝔽4)C22×C4714yescomplemented
116C2×#127C22×C4711yescharacteristic, complemented
117C2×#124—23no—
118C2×#124C22×C4713yes—
119C2×#120—23no—
120#496—26no—
121#496C22×C47112yescomplemented
122C2×#97C22×C4713yescomplemented
123#329C22×C47112yescomplemented
124C47C2×#165511yescharacteristic, direct product factor, Sylow
125C25—21no—
126C22×Q8D4×C4713yes—
127C22×D4—23no—
128C22×D4—23no—
129C22×D4D4×C4713yes—
130C2×SD16—212no—
131C2×SD16—412no—
132C2×D8—212no—
133C2×D8—412no—
134C22×C8—23no—
135#127—23no—
136#127C23×C4712yescomplemented
137#124—212no—
138#124—212no—
139#124—26no—
140#124D4×C4716yes—
141#124C23×C4716yes—
142#120—212no—
143#120—212no—
144C2×C22⋊C4—23no—
145C2×C22⋊C4—26no—
146C2×C42—21no—
147C2×C42C23×C4711yescharacteristic
148#97—23no—
149#97C23×C4716yescomplemented
150C24—24no—
151C24—23no—
152C24—41no—
153C24—86no—
154C2×Q8—23no—
155C2×Q8—46no—
156C2×Q8C2×D4×C4716yes—
157C2×D4—212no—
158C2×D4—23no—
159C2×D4—26no—
160C2×D4—46no—
161C2×D4—46no—
162C2×D4—46no—
163C2×D4—43no—
164C2×D4—86no—
165C2×D4C2×D4×C4716yes—
166C22×C4—23no—
167C22×C4C2×D4×C4713yes—
168SD16—424no—
169D8—424no—
170C2×C8—212no—
171C2×C8—26no—
172C22⋊C4—212no—
173C22⋊C4—212no—
174C22⋊C4—212no—
175C42—24no—
176C42C2×D4×C4713yes—
177C42C24×C4711yescharacteristic
178C23—26no—
179C23—46no—
180C23—412no—
181C23—42no—
182C23—812no—
183C23—816no—
184C23—86no—
185C23#120×C4711yescharacteristic
186Q8—46no—
187Q8—83no—
188D4—46no—
189D4—46no—
190D4—46no—
191D4—83no—
192D4—86no—
193D4—812no—
194C2×C4—26no—
195C2×C4—26no—
196C2×C4—46no—
197C2×C4#120×C4713yes—
198C2×C4C22×D4×C4713yes—
199C8—212no—
200C22—46no—
201C22—412no—
202C22—816no—
203C22—812no—
204C22—86no—
205C22—164no—
206C22C47×#45316yes—
207C22C2×#120×C4711yescharacteristic
208C4—23no—
209C4—23no—
210C4—46no—
211C2—86no—
212C2—162no—
213C2C47×#165514yesdirect product factor
214C2C2×C47×#45313yes—
subgroupG/H
center, socleC23×C47#120
commutator, Frattini, cosocleC42C24×C47
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×H(3,𝔽4)C2semidirect
2. C2×C47×#496C2semidirect
3. C47×#1655C2direct (N × H)
4. C2×C47×#329C2semidirect
8. C47×H(3,𝔽4)C22semidirect
9. C2×#127×C47C22semidirect
14. C47×#496C22semidirect
15. C2×#97×C47C22semidirect
16. C47×#329C22semidirect
28. #127×C47C23semidirect
41. #97×C47C23semidirect
92. C2×#1655C47direct (N × H)
104. C2×H(3,𝔽4)C2×C47semidirect
105. C2×#496C2×C47semidirect
106. #1655C2×C47direct (N × H)
107. C2×#329C2×C47semidirect
110. C2×C47#1655direct (N × H)
115. H(3,𝔽4)C22×C47semidirect
116. C2×#127C22×C47semidirect
121. #496C22×C47semidirect
122. C2×#97C22×C47semidirect
123. #329C22×C47semidirect
124. C47C2×#1655direct (N × H)
136. #127C23×C47semidirect
149. #97C23×C47semidirect
213. C2C47×#1655direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×H(3,𝔽4)2
C2×C47×#4962
C47×#16552
C2×C47×#3292
C2×#165547