Finite Group Databasebeta

← C47×#60191 #26099889

Subgroups — C47×#60191 #26099889

Order 12032.

1810 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
1C47×#3458C211yesmaximal, characteristic
2C47×#2961C2112yesmaximal, complemented
3C47×#2960C2112yesmaximal, complemented
4C47×#2905C213yesmaximal
5C2×C47×#405C213yesmaximal
6C22×M16×C47C2213yes—
7C23×C8×C47C2211yescharacteristic
8C47×#544C4112yes—
9C47×#543C414yes—
10C47×#533C22112yes—
11C2×#117×C47C2213yes—
12C47×#446C22148yescomplemented
13C8×Q8×C47C22116yescomplemented
14C47×#424C22124yes—
15C47×#423C22112yes—
16C47×#405C22112yes—
17C47×#405C22112yes—
18C2×#97×C47C2216yes—
19C2×C4×C8×C47C2216yes—
20C23×C4×C47C2311yescharacteristic
21C2×M16×C47—212no—
22C2×M16×C47C23112yes—
23C22×C8×C47Q818yescomplemented
24C22×C8×C47C2316yes—
25C22×C8×C47C2313yes—
26C22×C8×C47C2313yes—
27C4⋊Q8×C47C2×C4124yes—
28#125×C47C2×C4124yes—
29C22⋊Q8×C47C2×C4148yes—
30C4×Q8×C47C23116yes—
31#117×C47C2×C4112yes—
32#117×C47C23112yes—
33C2×C4⋊C4×C47C2×C416yes—
34C2×C22⋊C4×C47C2×C416yes—
35C2×C42×C47C2316yes—
36C4⋊C8×C47C23148yes—
37#97×C47C23124yes—
38C4×C8×C47C23112yes—
39C4×C8×C47C23112yes—
40C24×C47C22×C411yescharacteristic
41C2×Q8×C47C22×C4116yes—
42C22×C4×C47C22×C4112yes—
43C22×C4×C47C22×C413yes—
44C22×C4×C47C2×Q814yes—
45C22×C4×C47#4114yes—
46C22×C4×C47C2413yes—
47M16×C47—224no—
48C2×C8×C47—212no—
49C2×C8×C47C2×Q8112yes—
50C2×C8×C47C2×Q8112yes—
51C2×C8×C47C24112yes—
52C2×C8×C47C2413yes—
53C2×C8×C47C2411yescharacteristic
54C4⋊C4×C47C22×C4124yes—
55C4⋊C4×C47C22×C4148yes—
56C22⋊C4×C47C22×C4124yes—
57C42×C47C22×C4112yes—
58C42×C47C24112yes—
59C23×C47—42no—
60C23×C47C4×Q814yes—
61C23×C47C23×C413yes—
62Q8×C47—416no—
63C2×C4×C47—412no—
64C2×C4×C47C4×Q8112yes—
65C2×C4×C47C23×C4124yes—
66C2×C4×C47C23×C413yes—
67C2×C4×C47C22×Q816yes—
68C2×C4×C47C2×#4116yes—
69C2×C4×C47C2511yescharacteristic
70C8×C47—212no—
71C8×C47C22×Q816yes—
72C8×C47C22×Q812yes—
73#60191C4711yesmaximal, characteristic, direct product factor, Sylow
74C22×C47—26no—
75C22×C47—44no—
76C22×C47C2×C4×Q816yes—
77C22×C47C24×C411yescharacteristic
78C4×C47—224no—
79C4×C47C2×C4×Q816yes—
80C4×C47C23×Q811yescharacteristic
81C4×C47C22×#4111yescharacteristic
82#3458C2×C4711yescharacteristic
83#2961C2×C47112yescomplemented
84#2960C2×C47112yescomplemented
85#2905C2×C4713yes—
86C2×#405C2×C4713yes—
87C2×C47—26no—
88C2×C47C22×C4×Q811yescharacteristic
89C2×C47#357312yes—
90C22×M16C22×C4713yes—
91C23×C8C22×C4711yescharacteristic
92#544C4×C47112yes—
93#543C4×C4714yes—
94#533C22×C47112yes—
95C2×#117C22×C4713yes—
96#446C22×C47148yescomplemented
97C8×Q8C22×C47116yescomplemented
98#424C22×C47124yes—
99#423C22×C47112yes—
100#405C22×C47112yes—
101#405C22×C47112yes—
102C2×#97C22×C4716yes—
103C2×C4×C8C22×C4716yes—
104C47#6019111yescharacteristic, direct product factor, Sylow
105C23×C4C23×C4711yescharacteristic
106C2×M16—212no—
107C2×M16C23×C47112yes—
108C22×C8Q8×C4718yescomplemented
109C22×C8C23×C4716yes—
110C22×C8C23×C4713yes—
111C22×C8C23×C4713yes—
112C4⋊Q8C2×C4×C47124yes—
113#125C2×C4×C47124yes—
114C22⋊Q8C2×C4×C47148yes—
115C4×Q8C23×C47116yes—
116#117C2×C4×C47112yes—
117#117C23×C47112yes—
118C2×C4⋊C4C2×C4×C4716yes—
119C2×C22⋊C4C2×C4×C4716yes—
120C2×C42C23×C4716yes—
121C4⋊C8C23×C47148yes—
122#97C23×C47124yes—
123C4×C8C23×C47112yes—
124C4×C8C23×C47112yes—
125C24C22×C4×C4711yescharacteristic
126C2×Q8C22×C4×C47116yes—
127C22×C4C22×C4×C47112yes—
128C22×C4C22×C4×C4713yes—
129C22×C4C2×Q8×C4714yes—
130C22×C4#41×C4714yes—
131C22×C4C24×C4713yes—
132M16—224no—
133C2×C8—212no—
134C2×C8C2×Q8×C47112yes—
135C2×C8C2×Q8×C47112yes—
136C2×C8C24×C47112yes—
137C2×C8C24×C4713yes—
138C2×C8C24×C4711yescharacteristic
139C4⋊C4C22×C4×C47124yes—
140C4⋊C4C22×C4×C47148yes—
141C22⋊C4C22×C4×C47124yes—
142C42C22×C4×C47112yes—
143C42C24×C47112yes—
144C23—42no—
145C23C4×Q8×C4714yes—
146C23C23×C4×C4713yes—
147Q8—416no—
148C2×C4—412no—
149C2×C4C4×Q8×C47112yes—
150C2×C4C23×C4×C47124yes—
151C2×C4C23×C4×C4713yes—
152C2×C4C22×Q8×C4716yes—
153C2×C4C2×#41×C4716yes—
154C2×C4C25×C4711yescharacteristic
155C8—212no—
156C8C22×Q8×C4716yes—
157C8C22×Q8×C4712yes—
158C22—26no—
159C22—44no—
160C22C2×C4×Q8×C4716yes—
161C22C24×C4×C4711yescharacteristic
162C4—224no—
163C4C2×C4×Q8×C4716yes—
164C4C23×Q8×C4711yescharacteristic
165C4C22×#41×C4711yescharacteristic
166C2—26no—
167C2C22×C4×Q8×C4711yescharacteristic
168C2C47×#357312yes—
subgroupG/H
centerC2×C8×C47C24
commutatorC22C24×C4×C47
Frattini, cosocleC2×C4C25×C47
socleC22×C47C24×C4
prime radicalC24×C47C22×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2961C2semidirect
3. C47×#2960C2semidirect
12. C47×#446C22semidirect
13. C8×Q8×C47C22semidirect
23. C22×C8×C47Q8semidirect
73. #60191C47direct (N × H)
83. #2961C2×C47semidirect
84. #2960C2×C47semidirect
96. #446C22×C47semidirect
97. C8×Q8C22×C47semidirect
104. C47#60191direct (N × H)
108. C22×C8Q8×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#34582
C47×#29612
C47×#29602
C47×#29052
C2×C47×#4052
#6019147