Finite Group Databasebeta

← C3×#89271 #13051136

Subgroups — C3×#89271 #13051136

Order 1344.

136 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 42 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
1C3×#6498C211yesmaximal, characteristic
2C3×C7×#100C211yesmaximal, characteristic
3C3×#6408C211yesmaximal, characteristic
4#89271C311yesmaximal, characteristic, direct product factor, Hall
5C2×C3×C7×D4C2211yescharacteristic
6C22×C3×Dic7C411yescharacteristic, complemented
7C3×C7×M16—21no—
8C3×C22⋊Dic7—21no—
9C3×C22⋊Dic7—21no—
10C3×C22⋊Dic7C411yescharacteristic, complemented
11C3×Dic7⋊C4—21no—
12#6498C2×C311yescharacteristic
13C7×#100C2×C311yescharacteristic
14#6408C2×C311yescharacteristic
15C3×#352—71nomaximal, Hall
16C23×C3×C7C2×C411yescharacteristic
17C23×C3×C7D411yescharacteristic
18C3×C7×D4—41no—
19C2×C3×C4×C7D411yescharacteristic
20C2×C3×Dic7—21no—
21C2×C3×Dic7—21no—
22C2×C3×Dic7—41no—
23C2×C3×Dic7—41no—
24C3×C7×C8—41no—
25C2×C7×D4C22×C311yescharacteristic
26C22×Dic7C3×C411yescharacteristic, complemented
27C7×M16—21no—
28C22⋊Dic7—21no—
29C22⋊Dic7—21no—
30C22⋊Dic7C3×C411yescharacteristic, complemented
31Dic7⋊C4—21no—
32C3×#123—71no—
33C3×#100D711yescharacteristic
34C3×#99—71no—
35C22×C3×C7—21no—
36C22×C3×C7—21no—
37C22×C3×C7—41no—
38C22×C3×C7—41no—
39C22×C3×C7C22⋊C411yescharacteristic
40C3×C4×C7—21no—
41C3×Dic7—41no—
42C3×Dic7—41no—
43C3×Dic7—81no—
44#352—71noSylow
45C23×C7C2×C3×C411yescharacteristic
46C23×C7C3×D411yescharacteristic
47C7×D4—41no—
48C2×C4×C7C3×D411yescharacteristic
49C2×Dic7—21no—
50C2×Dic7—21no—
51C2×Dic7—41no—
52C2×Dic7—41no—
53C7×C8—41no—
54C2×C3×D4C2×D711yescharacteristic
55C22×C3×C4—71no—
56C3×M16—21no—
57C3×C4⋊C4—141no—
58C3×C22⋊C4—71no—
59C3×C22⋊C4—141no—
60C3×C22⋊C4—141no—
61C2×C3×C7—21no—
62C2×C3×C7—41no—
63C2×C3×C7—41no—
64C2×C3×C7#9911yescharacteristic
65#123—71no—
66#100C3×D711yescharacteristic
67#99—71no—
68C22×C7—21no—
69C22×C7—21no—
70C22×C7—41no—
71C22×C7—41no—
72C22×C7C3×C22⋊C411yescharacteristic
73C4×C7—21no—
74Dic7—41no—
75Dic7—41no—
76Dic7—81no—
77C23×C3C4×D711yescharacteristic
78C23×C3D2811yescharacteristic
79C3×D4—41no—
80C2×C3×C4—141no—
81C2×C3×C4—141no—
82C2×C3×C4—281no—
83C2×C3×C4—281no—
84C2×C3×C4C22⋊D711yescharacteristic
85C3×C8—41no—
86C3×C7#35211yescharacteristic, complemented, Hall
87C2×D4C2×C3×D711yescharacteristic
88C22×C4—71no—
89M16—21no—
90C4⋊C4—141no—
91C22⋊C4—71no—
92C22⋊C4—141no—
93C22⋊C4—141no—
94C2×C7—21no—
95C2×C7—41no—
96C2×C7—41no—
97C2×C7C3×#9911yescharacteristic
98C22×C3—21no—
99C22×C3—21no—
100C22×C3—41no—
101C22×C3—41no—
102C22×C3(C2×D7)⋊C411yescharacteristic
103C3×C4—21no—
104C3×C4—281no—
105C3×C4—281no—
106C3×C4—561no—
107C23C3×C4×D711yescharacteristic
108C23C3×D2811yescharacteristic
109D4—41no—
110C2×C4—141no—
111C2×C4—141no—
112C2×C4—281no—
113C2×C4—281no—
114C2×C4C3×C22⋊D711yescharacteristic
115C8—41no—
116C7C3×#35211yescharacteristic, complemented, Sylow
117C2×C3—21no—
118C2×C3—41no—
119C2×C3—41no—
120C2×C3#638011yescharacteristic
121C22—21no—
122C22—21no—
123C22—41no—
124C22—41no—
125C22C3×(C2×D7)⋊C411yescharacteristic
126C4—21no—
127C4—281no—
128C4—281no—
129C4—561no—
130C3#8927111yescharacteristic, direct product factor, Sylow
131C2—21no—
132C2—41no—
133C2—41no—
134C2C3×#638011yescharacteristic
subgroupG/H
centerC2×C3#6380
commutatorC23×C7C2×C3×C4
FrattiniC2×D4C2×C3×D7
FittingC3×C7×#100C2
socleC2×C3×C7#99
prime radicalC2×C3×C7×D4C22
cosocleC2×C7×D4C22×C3
hypercenterC3×#100D7
hypocenterC7C3×#352
LCSG ▷ C23×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#100

Complements

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

NH ≅ G/Ntype
4. #89271C3direct (N × H)
6. C22×C3×Dic7C4semidirect
10. C3×C22⋊Dic7C4semidirect
26. C22×Dic7C3×C4semidirect
30. C22⋊Dic7C3×C4semidirect
86. C3×C7#352semidirect
116. C7C3×#352semidirect
130. C3#89271direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#64982
C3×C7×#1002
C3×#64082
#892713
C3×#3527