Finite Group Databasebeta

← C3×#67995 #11920116

Subgroups — C3×#67995 #11920116

Order 1152.

161 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 161 conjugacy classes of subgroups — too many to draw. Only its 26 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×C4×C42⋊C3C211yesmaximal, characteristic
2#67995C311yesmaximal, characteristic, direct product factor
3C3×#1276—31nomaximal
4C2×C3×C42⋊C3C411yescharacteristic
5C3×A4⋊C8—41nomaximal
6C3×#431—31no—
7C3×#431—31no—
8C3×C43D311yescharacteristic
9C4×C42⋊C3—21no—
10C4×C42⋊C3C2×C311yescharacteristic
11C3×C4×A4—41no—
12C3×C42⋊C3C811yescharacteristic, complemented
13#1276—31noSylow
14C2×C3×C42—31no—
15C2×C3×C42—31no—
16C2×C3×C42Dic311yescharacteristic
17C2×C42⋊C3—21no—
18C2×C42⋊C3C3×C411yescharacteristic
19A4⋊C8—41no—
20C3×C4⋊C8—32no—
21C3×C4⋊C8—31no—
22C3×C4⋊C8—31no—
23C3×C22⋊C8—61no—
24C3×C22⋊C8—61no—
25C3×C4×C8—61no—
26C3×C4×C8—61no—
27C2×C3×A4—41no—
28C3×C3⋊C8—161no—
29#431—31no—
30#431—31no—
31C43C3×D311yescharacteristic
32C22×C3×C4—31no—
33C22×C3×C4—31no—
34C22×C3×C4S411yescharacteristic
35C4×A4—41no—
36C4×A4—81no—
37C2×C3×C8—62no—
38C2×C3×C8—61no—
39C2×C3×C8—61no—
40C3×C42—31no—
41C3×C42—31no—
42C3×C42—31no—
43C3×C42—31no—
44C3×C42—31no—
45C3×C42—32no—
46C3×C42—61no—
47C3×C42C3⋊C811yescharacteristic, complemented
48C42⋊C3—21no—
49C42⋊C3C3×C811yescharacteristic, complemented
50C3×A4—41no—
51C32×C4—161no—
52C2×C42—31no—
53C2×C42—31no—
54C2×C42C3×Dic311yescharacteristic
55C4⋊C8—32no—
56C4⋊C8—31no—
57C4⋊C8—31no—
58C22⋊C8—61no—
59C22⋊C8—61no—
60C4×C8—61no—
61C4×C8—61no—
62C23×C3SL(2,ℤ/4)11yescharacteristic
63C2×A4—41no—
64C2×A4—81no—
65C2×C3×C4—31no—
66C2×C3×C4—31no—
67C2×C3×C4—31no—
68C2×C3×C4—31no—
69C2×C3×C4—31no—
70C2×C3×C4—31no—
71C2×C3×C4—31no—
72C2×C3×C4—31no—
73C2×C3×C4—31no—
74C2×C3×C4—31no—
75C2×C3×C4—62no—
76C3×C8—122no—
77C3×C8—121no—
78C3×C8—121no—
79C3⋊C8—161no—
80C2×C32—161no—
81C22×C4—31no—
82C22×C4—31no—
83C22×C4C3×S411yescharacteristic
84C2×C8—62no—
85C2×C8—61no—
86C2×C8—61no—
87C42—31no—
88C42—31no—
89C42—31no—
90C42—31no—
91C42—31no—
92C42—32no—
93C42—61no—
94C42C3×C3⋊C811yescharacteristic, complemented
95C22×C3—31no—
96C22×C3—31no—
97C22×C3A4⋊C811yescharacteristic
98A4—41no—
99A4—81no—
100C3×C4—32no—
101C3×C4—31no—
102C3×C4—31no—
103C3×C4—31no—
104C3×C4—31no—
105C3×C4—31no—
106C3×C4—61no—
107C3×C4—161no—
108C3×C4—321no—
109C3×C4#85711yescharacteristic
110C32—161noSylow
111C23C3×SL(2,ℤ/4)11yescharacteristic
112C2×C4—31no—
113C2×C4—31no—
114C2×C4—31no—
115C2×C4—31no—
116C2×C4—31no—
117C2×C4—31no—
118C2×C4—31no—
119C2×C4—31no—
120C2×C4—31no—
121C2×C4—31no—
122C2×C4—62no—
123C8—122no—
124C8—121no—
125C8—121no—
126C2×C3—31no—
127C2×C3—31no—
128C2×C3—161no—
129C2×C3—321no—
130C2×C3#462311yescharacteristic
131C22—31no—
132C22—31no—
133C22C3×A4⋊C811yescharacteristic
134C4—32no—
135C4—31no—
136C4—31no—
137C4—31no—
138C4—31no—
139C4—31no—
140C4—61no—
141C4C3×#85711yescharacteristic
142C3—161no—
143C3—321no—
144C3#6799511yescharacteristic, direct product factor
145C2—31no—
146C2—31no—
147C2C3×#462311yescharacteristic
subgroupG/H
center, hypercenterC3×C4#857
commutator, hypocenterC42⋊C3C3×C8
FrattiniC22×C4C3×S4
FittingC3×C43D3
socleC23×C3SL(2,ℤ/4)
prime radicalC2×C3×C42⋊C3C4
cosocleC4×C42⋊C3C2×C3
LCSG ▷ C42⋊C3
UCSC1 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
2. #67995C3direct (N × H)
12. C3×C42⋊C3C8semidirect
47. C3×C42C3⋊C8semidirect
49. C42⋊C3C3×C8semidirect
94. C42C3×C3⋊C8semidirect
144. C3#67995direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×C42⋊C32
#679953
C3×#12763
C3×A4⋊C84