Finite Group Databasebeta

← C3×#72986 #11920764

Subgroups — C3×#72986 #11920764

Order 1152.

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

normal subgroups only

This group has 216 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×#376⋊C3C211yesmaximal, characteristic
2C3×#4621C212yesmaximal
3#72986C311yesmaximal, characteristic, direct product factor
4C3×#1506—31nomaximal
5C3×A4⋊Q8—41nomaximal
6C3×#95⋊C3C2211yescharacteristic
7C3×#533—31no—
8C3×#432—31no—
9C3×#376D311yescharacteristic
10#376⋊C3—21no—
11#376⋊C3C2×C311yescharacteristic
12#4621C2×C312yes—
13C3×#328—32no—
14C3×#328—32no—
15C3×C4×A4—41no—
16C3×SL(2,ℤ/4)—42no—
17#1506—31noSylow
18A4⋊Q8—41no—
19C3×C4⋊Q8—31no—
20C3×C4⋊Q8—31no—
21C3×#125—61no—
22C3×C22⋊Q8—32no—
23C3×C22⋊Q8—61no—
24C3×C4×Q8—32no—
25C3×C4×Q8—61no—
26C3×#117—61no—
27C2×C3×C42—31no—
28C3×C4⋊C8—61no—
29C3×C22⋊C8—32no—
30C3×#97—61no—
31C3×#95—31no—
32C3×#95C2×D311yescharacteristic
33#95⋊C3—21no—
34#95⋊C3C22×C311yescharacteristic
35C2×C3×A4—41no—
36C3×Dic6—161no—
37#533—31no—
38#432—31no—
39#376C3×D311yescharacteristic
40#328—32no—
41#328—32no—
42C2×C3×Q8—32no—
43C2×C3×Q8—61no—
44C22×C3×C4—31no—
45C22×C3×C4—31no—
46C22×C3×C4S411yescharacteristic
47C4×A4—41no—
48C4×A4—81no—
49SL(2,ℤ/4)—42no—
50C2×C3×C8—62no—
51C3×C4⋊C4—32no—
52C3×C4⋊C4—61no—
53C3×C4⋊C4—61no—
54C3×C4⋊C4—62no—
55C3×C4⋊C4—62no—
56C3×C4⋊C4—61no—
57C3×C22⋊C4—62no—
58C3×C42—31no—
59C3×C42—31no—
60C3×C42—31no—
61C3×C42—31no—
62C3×C42—62no—
63C3×A4—41no—
64C32×C4—161no—
65C3×Dic3—162no—
66C4⋊Q8—31no—
67C4⋊Q8—31no—
68#125—61no—
69C22⋊Q8—32no—
70C22⋊Q8—61no—
71C4×Q8—32no—
72C4×Q8—61no—
73#117—61no—
74C2×C42—31no—
75C4⋊C8—61no—
76C22⋊C8—32no—
77#97—61no—
78#95—31no—
79#95C2×C3×D311yescharacteristic
80C23×C3C2×S411yescharacteristic
81C2×A4—41no—
82C2×A4—81no—
83C3×Q8—121no—
84C3×Q8—122no—
85C3×Q8—121no—
86C2×C3×C4—31no—
87C2×C3×C4—31no—
88C2×C3×C4—31no—
89C2×C3×C4—31no—
90C2×C3×C4—31no—
91C2×C3×C4—31no—
92C2×C3×C4—61no—
93C2×C3×C4—61no—
94C2×C3×C4—62no—
95C2×C3×C4—62no—
96C2×C3×C4—121no—
97Dic6—161no—
98C3×C8—122no—
99C2×C32—161no—
100C2×Q8—32no—
101C2×Q8—61no—
102C22×C4—31no—
103C22×C4—31no—
104C22×C4C3×S411yescharacteristic
105C2×C8—62no—
106C4⋊C4—32no—
107C4⋊C4—61no—
108C4⋊C4—61no—
109C4⋊C4—62no—
110C4⋊C4—62no—
111C4⋊C4—61no—
112C22⋊C4—62no—
113C42—31no—
114C42—31no—
115C42—31no—
116C42—31no—
117C42—62no—
118C22×C3—31no—
119C22×C3—31no—
120C22×C3#98411yescharacteristic
121A4—41no—
122A4—81no—
123C3×C4—31no—
124C3×C4—61no—
125C3×C4—61no—
126C3×C4—61no—
127C3×C4—61no—
128C3×C4—122no—
129C3×C4—122no—
130C3×C4—161no—
131C3×C4—321no—
132C3×C4#85711yescharacteristic
133Dic3—162no—
134C32—161noSylow
135C23C2×C3×S411yescharacteristic
136Q8—121no—
137Q8—122no—
138Q8—121no—
139C2×C4—31no—
140C2×C4—31no—
141C2×C4—31no—
142C2×C4—31no—
143C2×C4—31no—
144C2×C4—31no—
145C2×C4—61no—
146C2×C4—61no—
147C2×C4—62no—
148C2×C4—62no—
149C2×C4—121no—
150C8—122no—
151C2×C3—31no—
152C2×C3—31no—
153C2×C3—161no—
154C2×C3—321no—
155C2×C3C2×#85711yescharacteristic
156C22—31no—
157C22—31no—
158C22C3×#98411yescharacteristic
159C4—31no—
160C4—61no—
161C4—61no—
162C4—61no—
163C4—61no—
164C4—122no—
165C4—122no—
166C4C3×#85711yescharacteristic
167C3—161no—
168C3—321no—
169C3#7298611yescharacteristic, direct product factor
170C2—31no—
171C2—31no—
172C2C2×C3×#85711yescharacteristic
subgroupG/H
centerC2×C3C2×#857
commutator, cosocle, hypocenter#95⋊C3C22×C3
FrattiniC23C2×C3×S4
FittingC3×#376D3
socleC23×C3C2×S4
prime radicalC3×#95⋊C3C22
hypercenterC3×C4#857
LCSG ▷ #95⋊C3
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
3. #72986C3direct (N × H)
169. C3#72986direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#376⋊C32
C3×#46212
#729863
C3×#15063
C3×A4⋊Q84