Finite Group Databasebeta

← #11759613

Subgroups — #11759613

Order 1008.

232 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 52 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×D3×D21C212yesmaximal, complemented
2C4×C3⋊D21C211yesmaximal, characteristic, complemented
3C3×D84C211yesmaximal, characteristic, complemented
4C3×C7×D12C211yesmaximal, characteristic, complemented
5#92688C212yesmaximal, complemented
6D4×D21—31nomaximal
7#66681—31nomaximal
8C2×C3⋊D21C2211yescharacteristic
9C2×C3×D21C2212yescomplemented
10C2×C3×D3×C7C2212yescomplemented
11D3×D21—24no—
12C32×C4×C7C2211yescharacteristic, complemented
13C3⋊Dic21C2211yescharacteristic, complemented
14C22×D21—32no—
15C2×D3×D7—32no—
16C3×C7×D4—31no—
17#4268—32no—
18D84D311yescharacteristic, complemented
19C4×D21—31no—
20C4×D21—31no—
21C4×D21—61no—
22C7×D12D311yescharacteristic, complemented
23C3×D28—31no—
24#4245—32no—
25#3802—71nomaximal, Hall
26C2×C32×C7C2311yescharacteristic
27C3⋊D21D412yescomplemented
28C3×D21—22no—
29C3×D3×C7—22no—
30D4×D7—91noHall
31C22×C3×C7—32no—
32C2×D21—31no—
33C2×D21—31no—
34C2×D21—61no—
35C2×D21—64no—
36C2×D21C2×D312yescomplemented
37C2×D3×C7C2×D312yescomplemented
38C2×C3×D7—32no—
39D3×D7—64no—
40C3×C4×C7—21no—
41C3×C4×C7C2×D311yescharacteristic, complemented
42C3×C4×C7C2×D311yescharacteristic, complemented
43Dic21—31no—
44Dic21—31no—
45Dic21—61no—
46C2×D32—72no—
47C4×C3⋊D3—71no—
48C3×D12—71no—
49C3×D12D711yescharacteristic, complemented
50#625—72no—
51C32×C7C2×D411yescharacteristic, complemented, Hall
52C22×D7—92no—
53C7×D4—31no—
54C22⋊D7—92no—
55D28—31no—
56C4×D7—91no—
57D3×D4—211no—
58D3×D4—211no—
59C2×C3×C7—21no—
60C2×C3×C7—62no—
61C2×C3×C7C22×D311yescharacteristic
62C2×C3×C7C22×D311yescharacteristic
63D21—22no—
64D21—32no—
65D21—32no—
66D21—62no—
67C3×D7—62no—
68D3×C7—22no—
69C2×C3⋊D3—71no—
70C2×C3×D3—72no—
71C2×C3×D3C2×D712yescomplemented
72D32—144no—
73C32×C4C2×D711yescharacteristic, complemented
74C3⋊Dic3—71no—
75C22×C7—32no—
76C2×D7—32no—
77C2×D7—91no—
78C2×D7—184no—
79C4×C7D3211yescharacteristic, complemented
80Dic7—91no—
81C22×D3—212no—
82C22×D3—212no—
83C3×D4—31no—
84C3×D4—211no—
85#67—212no—
86#67—212no—
87D12—71no—
88D12D2111yescharacteristic, complemented
89C4×D3—211no—
90C4×D3—211no—
91C4×D3—421no—
92C3×C7—21no—
93C3×C7D3×D411yescharacteristic, complemented
94C3×C7D3×D411yescharacteristic, complemented
95C2×C32C22×D711yescharacteristic
96C3⋊D3—72no—
97C3×D3—22no—
98C3×D3—142no—
99C2×D4—631noSylow
100C2×C7—62no—
101C2×C7C2×D3211yescharacteristic
102D7—62no—
103D7—92no—
104C22×C3—32no—
105C22×C3—212no—
106C2×D3—72no—
107C2×D3—211no—
108C2×D3—211no—
109C2×D3—421no—
110C2×D3—424no—
111C2×D3—424no—
112C2×D3C2×D2112yescomplemented
113C3×C4—21no—
114C3×C4D3×D711yescharacteristic, complemented
115C3×C4C2×D2111yescharacteristic, complemented
116Dic3—211no—
117Dic3—211no—
118Dic3—421no—
119C32D4×D711yescharacteristic, complemented, Sylow
120C23—632no—
121D4—31no—
122D4—211no—
123D4—632no—
124C2×C4—631no—
125C7#380211yescharacteristic, complemented, Sylow
126C2×C3—21no—
127C2×C3—62no—
128C2×C3—422no—
129C2×C3C2×D3×D711yescharacteristic
130C2×C3C22×D2111yescharacteristic
131D3—22no—
132D3—142no—
133D3—212no—
134D3—212no—
135D3—422no—
136C22—32no—
137C22—212no—
138C22—631no—
139C22—1264no—
140C4—631no—
141C4D3×D2111yescharacteristic, complemented
142C3—21no—
143C3#6668111yescharacteristic, complemented
144C3D4×D2111yescharacteristic, complemented
145C2—62no—
146C2—422no—
147C2—632no—
148C2C2×D3×D2111yescharacteristic
subgroupG/H
center, FrattiniC2C2×D3×D21
commutator, socle, cosocleC2×C32×C7C23
FittingC32×C4×C7C22
hypercenterC4D3×D21
hypocenterC32×C7C2×D4
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×D21C2semidirect
2. C4×C3⋊D21C2semidirect
3. C3×D84C2semidirect
4. C3×C7×D12C2semidirect
5. #92688C2semidirect
9. C2×C3×D21C22semidirect
10. C2×C3×D3×C7C22semidirect
12. C32×C4×C7C22semidirect
13. C3⋊Dic21C22semidirect
18. D84D3semidirect
22. C7×D12D3semidirect
27. C3⋊D21D4semidirect
36. C2×D21C2×D3semidirect
37. C2×D3×C7C2×D3semidirect
41. C3×C4×C7C2×D3semidirect
42. C3×C4×C7C2×D3semidirect
49. C3×D12D7semidirect
51. C32×C7C2×D4semidirect
71. C2×C3×D3C2×D7semidirect
73. C32×C4C2×D7semidirect
79. C4×C7D32semidirect
88. D12D21semidirect
93. C3×C7D3×D4semidirect
94. C3×C7D3×D4semidirect
112. C2×D3C2×D21semidirect
114. C3×C4D3×D7semidirect
115. C3×C4C2×D21semidirect
119. C32D4×D7semidirect
125. C7#3802semidirect
141. C4D3×D21semidirect
143. C3#66681semidirect
144. C3D4×D21semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D212
C4×C3⋊D212
C3×D842
C3×C7×D122
#926882
D4×D213
#666813
#38027