Finite Group Databasebeta

← C3×#67784 #11772874

Subgroups — C3×#67784 #11772874

Order 1152.

243 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 243 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C32×#490C211yesmaximal, characteristic
2C3×#4545C212yesmaximal
3C3×#1412—31nomaximal
4#67784C311yesmaximal, characteristic, direct product factor
5C32×#127C2211yescharacteristic
6C32×#125C411yescharacteristic, complemented
7C32×#102—22no—
8C32×#97C411yescharacteristic, complemented
9C3×#834—22no—
10C3×#490—21no—
11C3×#490D311yescharacteristic
12C3×#490C2×C311yescharacteristic
13C3×#353—32no—
14#4545C2×C312yes—
15C2×C32×D4—41no—
16C2×C32×D4D412yes—
17C2×C32×C8—21no—
18C32×C4⋊C4—21no—
19C32×C4⋊C4—41no—
20C32×C42C2×C411yescharacteristic
21C3×#217—42no—
22#1412—31noSylow
23C3×#127—21no—
24C3×#127C2×D311yescharacteristic
25C3×#127C22×C311yescharacteristic
26C3×#125—21no—
27C3×#125Dic311yescharacteristic, complemented
28C3×#125C3×C411yescharacteristic, complemented
29C3×#102—24no—
30C3×#102—22no—
31C3×#102—22no—
32C3×#99—62no—
33C3×#97—21no—
34C3×#97Dic311yescharacteristic, complemented
35C3×#97C3×C411yescharacteristic, complemented
36#834—22no—
37C23×C32—22no—
38C32×D4—42no—
39C32×D4—82no—
40C2×C32×C4—21no—
41C2×C32×C4—41no—
42C2×C32×C4C22⋊C411yescharacteristic
43C2×C3×Dic3—82no—
44C32×C8—41no—
45#490C3×D311yescharacteristic
46#353—32no—
47C2×C3×D4—22no—
48C2×C3×D4—41no—
49C2×C3×D4—41no—
50C2×C3×D4—42no—
51C2×C3×D4#6712yes—
52C2×C3×D4C3×D412yes—
53C2×C3×C8—22no—
54C2×C3×C8—21no—
55C2×C3×C8—21no—
56C3×C4⋊C4—22no—
57C3×C4⋊C4—21no—
58C3×C4⋊C4—21no—
59C3×C4⋊C4—41no—
60C3×C4⋊C4—41no—
61C3×C4⋊C4—42no—
62C3×C22⋊C4—122no—
63C3×C42—21no—
64C3×C42C2×Dic311yescharacteristic
65C3×C42C2×C3×C411yescharacteristic
66#217—42no—
67C22×C32—42no—
68C22×C32—82no—
69C22×C32#9911yescharacteristic
70C32×C4—21no—
71C32×C4—41no—
72C32×C4—81no—
73C3×Dic3—162no—
74#127C2×C3×D311yescharacteristic
75#125C3×Dic311yescharacteristic, complemented
76#102—22no—
77#99—62no—
78#97C3×Dic311yescharacteristic, complemented
79C23×C3—22no—
80C23×C3—22no—
81C23×C3—42no—
82C3×D4—42no—
83C3×D4—42no—
84C3×D4—44no—
85C3×D4—82no—
86C3×D4—82no—
87C3×D4—84no—
88C2×C3×C4—22no—
89C2×C3×C4—21no—
90C2×C3×C4—21no—
91C2×C3×C4—21no—
92C2×C3×C4—42no—
93C2×C3×C4—41no—
94C2×C3×C4—41no—
95C2×C3×C4—242no—
96C2×C3×C4#21711yescharacteristic
97C2×C3×C4C3×C22⋊C411yescharacteristic
98C2×Dic3—82no—
99C3×C8—42no—
100C3×C8—41no—
101C3×C8—41no—
102C2×C32—21no—
103C2×C32—82no—
104C2×C32#35411yescharacteristic
105C2×D4—41no—
106C2×D4C3×#6712yes—
107C2×C8—21no—
108C4⋊C4—21no—
109C4⋊C4—41no—
110C22⋊C4—122no—
111C42C2×C3×Dic311yescharacteristic
112C22×C3—21no—
113C22×C3—42no—
114C22×C3—42no—
115C22×C3—82no—
116C22×C3—82no—
117C22×C3—82no—
118C22×C3—84no—
119C22×C3#83411yescharacteristic
120C22×C3C3×#9911yescharacteristic
121C3×C4—22no—
122C3×C4—21no—
123C3×C4—21no—
124C3×C4—42no—
125C3×C4—41no—
126C3×C4—41no—
127C3×C4—82no—
128C3×C4—81no—
129C3×C4—81no—
130C3×C4—482no—
131Dic3—162no—
132C32#141211yescharacteristic, complemented, Sylow
133C23—22no—
134D4—42no—
135D4—82no—
136C2×C4—21no—
137C2×C4—41no—
138C2×C4—242no—
139C2×C4C3×#21711yescharacteristic
140C8—41no—
141C2×C3—22no—
142C2×C3—21no—
143C2×C3—21no—
144C2×C3—21no—
145C2×C3—82no—
146C2×C3—82no—
147C2×C3—162no—
148C2×C3#454111yescharacteristic
149C2×C3C3×#35411yescharacteristic
150C22—42no—
151C22—82no—
152C22C3×#83411yescharacteristic
153C4—21no—
154C4—41no—
155C4—81no—
156C4—482no—
157C3—21no—
158C3#6778411yescharacteristic, direct product factor
159C3C3×#141211yescharacteristic, complemented
160C2—21no—
161C2—82no—
162C2C3×#454111yescharacteristic
subgroupG/H
centerC2×C3#4541
commutatorC3×C42C2×C3×C4
Frattini#127C2×C3×D3
FittingC32×#490C2
socleC2×C32#354
prime radicalC32×#127C22
cosocleC3×#127C22×C3
hypercenterC3×#490D3
hypocenterC3C3×#1412
LCSG ▷ C3×C42 ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#127 ◁ C3×#490

Complements

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

NH ≅ G/Ntype
4. #67784C3direct (N × H)
6. C32×#125C4semidirect
8. C32×#97C4semidirect
27. C3×#125Dic3semidirect
28. C3×#125C3×C4semidirect
34. C3×#97Dic3semidirect
35. C3×#97C3×C4semidirect
75. #125C3×Dic3semidirect
78. #97C3×Dic3semidirect
132. C32#1412semidirect
158. C3#67784direct (N × H)
159. C3C3×#1412semidirect

Maximal subgroups

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

subgroupindex
C32×#4902
C3×#45452
C3×#14123
#677843