Finite Group Databasebeta

← #11759443

Subgroups — #11759443

Order 1008.

176 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 46 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
1#92696C211yesmaximal, characteristic, complemented
2D3×Dic21C212yesmaximal, complemented
3C7×#625C211yesmaximal, characteristic, complemented
4D7×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#4245C212yesmaximal, complemented
6#66684—32nomaximal
7C2×C3×D3×C7C2212yes—
8C2×C32×D7C2211yescharacteristic
9C3⋊Dic21C2211yescharacteristic
10C7×C3⋊Dic3C2211yescharacteristic
11C3×Dic21C2212yes—
12C2×Dic21—32no—
13C7×#67—32no—
14C3×C22⋊D7—32no—
15#4248—32no—
16#4245D312yescomplemented
17D3×Dic7—32no—
18Dic3×D7—32no—
19Dic3×D7—61no—
20#3805—71nomaximal, Hall
21C2×C32×C7C2311yescharacteristic
22C3×D3×C7—22no—
23C32×D7—21no—
24#1159—91noHall
25C22×C3×C7—32no—
26C2×D3×C7C2×D312yes—
27C2×C3×D7—21no—
28C2×C3×D7C2×D312yes—
29Dic21—32no—
30Dic21—61no—
31Dic21C2×D312yes—
32C3×Dic7—32no—
33C7×Dic3—32no—
34C7×Dic3—61no—
35C2×C3⋊Dic3—71no—
36C3×#67—72no—
37#627—71no—
38#625D711yescharacteristic, complemented
39D3×Dic3—72no—
40C32×C7#4111yescharacteristic, complemented, Hall
41C7×D4—91no—
42C22⋊D7—32no—
43C2×Dic7—92no—
44C4×D7—91no—
45Dic14—91no—
46#237—212no—
47C2×C3×C7—21no—
48C2×C3×C7—62no—
49C2×C3×C7C22×D312yes—
50C3×D7—22no—
51C3×D7—22no—
52D3×C7—22no—
53C22×C32—71no—
54C2×C3×D3C2×D712yes—
55C3⋊Dic3—71no—
56C3⋊Dic3C2×D711yescharacteristic
57C3×Dic3—72no—
58C22×C7—32no—
59C2×D7D3211yescharacteristic
60C4×C7—91no—
61Dic7—32no—
62Dic7—91no—
63C3×D4—212no—
64#67—32no—
65#67—72no—
66C2×Dic3—212no—
67C2×Dic3—212no—
68C2×Dic3—421no—
69C4×D3—212no—
70Dic6—212no—
71C3×C7—21no—
72C3×C7#23712yescomplemented
73C2×C32—141no—
74C2×C32C22×D711yescharacteristic
75C3×D3—22no—
76#41—631noSylow
77C2×C7—62no—
78C2×C7C2×D3211yescharacteristic
79D7—21no—
80C22×C3—32no—
81C22×C3—72no—
82C22×C3—141no—
83C2×D3D3×D712yes—
84C3×C4—212no—
85Dic3—32no—
86Dic3—61no—
87Dic3—72no—
88Dic3—212no—
89Dic3—421no—
90C32#115911yescharacteristic, complemented, Sylow
91Q8—631no—
92D4—91no—
93D4—212no—
94C2×C4—631no—
95C2×C4—632no—
96C7#380511yescharacteristic, complemented, Sylow
97C2×C3—21no—
98C2×C3—62no—
99C2×C3—142no—
100C2×C3—142no—
101C2×C3C2×D3×D712yes—
102D3—22no—
103C22—32no—
104C22—71no—
105C4—91no—
106C4—212no—
107C4—631no—
108C3—21no—
109C3#6668412yescomplemented
110C2—62no—
111C2—141no—
112C2D32×D711yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D32×D7
commutator, Fitting, socle, cosocleC2×C32×C7C23
hypocenterC32×C7#41
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #92696C2semidirect
2. D3×Dic21C2semidirect
3. C7×#625C2semidirect
4. D7×C3⋊Dic3C2semidirect
5. C3×#4245C2semidirect
16. #4245D3semidirect
38. #625D7semidirect
40. C32×C7#41semidirect
72. C3×C7#237semidirect
90. C32#1159semidirect
96. C7#3805semidirect
109. C3#66684semidirect

Maximal subgroups

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

subgroupindex
#926962
D3×Dic212
C7×#6252
D7×C3⋊Dic32
C3×#42452
#666843
#38057