Finite Group Databasebeta

← C47×#34526 #26074224

Subgroups — C47×#34526 #26074224

Order 12032.

1800 conjugacy classes of subgroups.

The subgroup lattice has 170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#564C211yesmaximal, characteristic
2C47×#2382C213yesmaximal
3C47×#2370C2112yesmaximal
4C47×#2336C2112yesmaximal
5C4×#125×C47C213yesmaximal
6C47×#564C4116yescomplemented
7C2×#125×C47C2213yes—
8C2×#125×C47C22112yes—
9C47×#389C2216yes—
10C47×#389C22112yes—
11C47×#389C22112yes—
12C47×#387C22112yes—
13C47×#387C22112yes—
14C47×#387C22112yes—
15C47×#387C22112yes—
16C47×#387C22112yes—
17C47×#383C2214yes—
18C47×#382C2213yes—
19C4×C4⋊C4×C47C2216yes—
20C4×C4⋊C4×C47C22112yes—
21C4×C4⋊C4×C47C22112yes—
22C4×C4⋊C4×C47C22112yes—
23C43×C47C2211yescharacteristic
24#125×C47C2×C4124yes—
25#125×C47C2×C4196yes—
26C2×C4⋊C4×C47C23112yes—
27C2×C4⋊C4×C47C2316yes—
28C2×C4⋊C4×C47C23112yes—
29C2×C4⋊C4×C47C2316yes—
30C2×C4⋊C4×C47C23112yes—
31C2×C4⋊C4×C47C23112yes—
32C2×C42×C47C2313yes—
33C2×C42×C47C2313yes—
34C2×C42×C47C23112yes—
35C2×C42×C47C23112yes—
36C2×C42×C47C2311yescharacteristic
37C2×C42×C47C2314yes—
38#95×C47C23112yes—
39#95×C47C23112yes—
40#95×C47C23112yes—
41#95×C47C23112yes—
42#95×C47C23112yes—
43C22×C4×C47C24112yes—
44C22×C4×C47C2411yescharacteristic
45C22×C4×C47C2413yes—
46C22×C4×C47C24112yes—
47C22×C4×C47C2413yes—
48C4⋊C4×C47—224no—
49C4⋊C4×C47—412no—
50C4⋊C4×C47—46no—
51C4⋊C4×C47C22×C4124yes—
52C4⋊C4×C47C22×C4148yes—
53C4⋊C4×C47C22×C4148yes—
54C42×C47—26no—
55C42×C47—43no—
56C42×C47—412no—
57C42×C47—412no—
58C42×C47C22×C414yes—
59C42×C47C22×C4116yes—
60C23×C47C2511yescharacteristic
61C2×C4×C47—23no—
62C2×C4×C47—212no—
63C2×C4×C47—26no—
64C2×C4×C47—212no—
65C2×C4×C47—23no—
66C2×C4×C47—23no—
67C2×C4×C47—212no—
68C2×C4×C47—212no—
69C2×C4×C47—212no—
70C2×C4×C47C23×C416yes—
71C2×C4×C47C23×C4124yes—
72C2×C4×C472−1+416yes—
73#34526C4711yesmaximal, characteristic, direct product factor, Sylow
74C22×C47C24×C411yescharacteristic
75C22×C47C2×2−1+413yes—
76C22×C47#58513yes—
77C4×C47—26no—
78C4×C47—224no—
79C4×C47—26no—
80C4×C47—412no—
81C4×C47—41no—
82C2×#564C2×C4711yescharacteristic
83#2382C2×C4713yes—
84#2370C2×C47112yes—
85#2336C2×C47112yes—
86C4×#125C2×C4713yes—
87C2×C47C4×2−1+413yes—
88C2×C47#355313yes—
89C2×C47#355611yescharacteristic
90#564C4×C47116yescomplemented
91C2×#125C22×C4713yes—
92C2×#125C22×C47112yes—
93#389C22×C4716yes—
94#389C22×C47112yes—
95#389C22×C47112yes—
96#387C22×C47112yes—
97#387C22×C47112yes—
98#387C22×C47112yes—
99#387C22×C47112yes—
100#387C22×C47112yes—
101#383C22×C4714yes—
102#382C22×C4713yes—
103C4×C4⋊C4C22×C4716yes—
104C4×C4⋊C4C22×C47112yes—
105C4×C4⋊C4C22×C47112yes—
106C4×C4⋊C4C22×C47112yes—
107C43C22×C4711yescharacteristic
108C47#3452611yescharacteristic, direct product factor, Sylow
109#125C2×C4×C47124yes—
110#125C2×C4×C47196yes—
111C2×C4⋊C4C23×C47112yes—
112C2×C4⋊C4C23×C4716yes—
113C2×C4⋊C4C23×C47112yes—
114C2×C4⋊C4C23×C4716yes—
115C2×C4⋊C4C23×C47112yes—
116C2×C4⋊C4C23×C47112yes—
117C2×C42C23×C4713yes—
118C2×C42C23×C4713yes—
119C2×C42C23×C47112yes—
120C2×C42C23×C47112yes—
121C2×C42C23×C4711yescharacteristic
122C2×C42C23×C4714yes—
123#95C23×C47112yes—
124#95C23×C47112yes—
125#95C23×C47112yes—
126#95C23×C47112yes—
127#95C23×C47112yes—
128C22×C4C24×C4711yescharacteristic
129C22×C4C24×C47112yes—
130C22×C4C24×C4713yes—
131C22×C4C24×C47112yes—
132C22×C4C24×C4713yes—
133C4⋊C4—224no—
134C4⋊C4—412no—
135C4⋊C4—46no—
136C4⋊C4C22×C4×C47124yes—
137C4⋊C4C22×C4×C47148yes—
138C4⋊C4C22×C4×C47148yes—
139C42—26no—
140C42—43no—
141C42—412no—
142C42—412no—
143C42C22×C4×C4714yes—
144C42C22×C4×C47116yes—
145C23C25×C4711yescharacteristic
146C2×C4—23no—
147C2×C4—212no—
148C2×C4—26no—
149C2×C4—212no—
150C2×C4—23no—
151C2×C4—23no—
152C2×C4—212no—
153C2×C4—212no—
154C2×C4—212no—
155C2×C4C23×C4×C4716yes—
156C2×C4C23×C4×C47124yes—
157C2×C42−1+4×C4716yes—
158C22C24×C4×C4711yescharacteristic
159C22C2×2−1+4×C4713yes—
160C22C47×#58513yes—
161C4—26no—
162C4—26no—
163C4—224no—
164C4—412no—
165C4—41no—
166C2C4×2−1+4×C4713yes—
167C2C47×#355313yes—
168C2C47×#355611yescharacteristic
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
6. C47×#564C4semidirect
73. #34526C47direct (N × H)
90. #564C4×C47semidirect
108. C47#34526direct (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×#23702
C47×#23362
C4×#125×C472
#3452647