Finite Group Databasebeta

← #11920948

Subgroups — #11920948

Order 1152.

262 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 31 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×#384⋊C3C211yesmaximal, characteristic
2C3⋊#4623C212yesmaximal
3#72992—33nomaximal
4#69573—31nomaximal
5#64259—41nomaximal
6C2×C3×C42⋊C3C2211yescharacteristic
7#5500—31no—
8C3×#384D311yescharacteristic
9#4964—32no—
10#384⋊C3D313yes—
11#4623—36no—
12#4530—31no—
13#4523—32no—
14C3×C4×A4—41no—
15C3⋊SL(2,ℤ/4)—42no—
16C3×C42⋊C3Q811yescharacteristic, complemented
17#2060—91noSylow
18A4⋊Q8—123no—
19C2×C3×C4⋊C4—31no—
20C2×C3×C4⋊C4—31no—
21C2×C3×C42C2×D311yescharacteristic
22#926—32no—
23#924—61no—
24#924—61no—
25C2×#208—32no—
26#890—62no—
27#888—62no—
28C2×C42⋊C3C2×D313yes—
29#808—62no—
30#807—62no—
31C2×C3×A4—41no—
32#634—161no—
33#544—91no—
34#428—92no—
35#384C3⋊D311yescharacteristic
36#343—91no—
37#339—92no—
38C22×C3×C4—31no—
39C22×C3×C4—31no—
40C22×C3×C4S411yescharacteristic
41C2×Dic6—61no—
42C2×Dic6—61no—
43C4×A4—43no—
44SL(2,ℤ/4)—126no—
45C3×C4⋊C4—62no—
46C3×C4⋊C4—62no—
47C3×C42—31no—
48C3×C42Dic611yescharacteristic, complemented
49#217—62no—
50C4⋊Dic3—32no—
51C4⋊Dic3—32no—
52C4⋊Dic3—61no—
53C4⋊Dic3—61no—
54Dic3⋊C4—62no—
55Dic3⋊C4—62no—
56C4×Dic3—62no—
57#208—34no—
58#208—62no—
59C2×C3⋊C8—62no—
60C42⋊C3Dic613yescomplemented
61C3×A4—41no—
62C32×C4—161no—
63C3⋊Dic3—162no—
64C2×M16—92no—
65C4⋊Q8—182no—
66#125—182no—
67C22⋊Q8—181no—
68C22⋊Q8—181no—
69#117—92no—
70C2×C4⋊C4—31no—
71C2×C4⋊C4—31no—
72C2×C42C2×C3⋊D311yescharacteristic
73#107—182no—
74#106—182no—
75C23×C3C2×S411yescharacteristic
76C2×A4—43no—
77C2×C3×C4—32no—
78C2×C3×C4—32no—
79C2×C3×C4—31no—
80C2×C3×C4—31no—
81C2×C3×C4—61no—
82C2×C3×C4—61no—
83C2×C3×C4—121no—
84C2×Dic3—62no—
85C2×Dic3—62no—
86Dic6—241no—
87Dic6—241no—
88Dic6—483no—
89C3⋊C8—64no—
90C2×C32—161no—
91C2×Q8—181no—
92C2×Q8—181no—
93C22×C4—31no—
94C22×C4—31no—
95C22×C4C3⋊S411yescharacteristic
96M16—94no—
97M16—182no—
98C2×C8—182no—
99C4⋊C4—62no—
100C4⋊C4—62no—
101C4⋊C4—92no—
102C4⋊C4—92no—
103C4⋊C4—181no—
104C4⋊C4—181no—
105C4⋊C4—182no—
106C4⋊C4—182no—
107C22⋊C4—182no—
108C42—31no—
109C42—182no—
110C42#63411yescharacteristic, complemented
111C22×C3—31no—
112C22×C3—31no—
113C22×C3A4⋊Q811yescharacteristic
114A4—43no—
115C3×C4—32no—
116C3×C4—32no—
117C3×C4—41no—
118C3×C4—121no—
119C3×C4—163no—
120Dic3—122no—
121Dic3—122no—
122Dic3—486no—
123C32—161noSylow
124C23C2×C3⋊S411yescharacteristic
125Q8—721no—
126Q8—721no—
127C2×C4—32no—
128C2×C4—32no—
129C2×C4—31no—
130C2×C4—31no—
131C2×C4—61no—
132C2×C4—61no—
133C2×C4—121no—
134C2×C4—182no—
135C2×C4—182no—
136C8—184no—
137C2×C3—31no—
138C2×C3—31no—
139C2×C3—163no—
140C2×C3#857⋊C211yescharacteristic
141C22—31no—
142C22—31no—
143C22#6425911yescharacteristic
144C4—32no—
145C4—32no—
146C4—41no—
147C4—121no—
148C4—362no—
149C4—362no—
150C3—163no—
151C3#7299211yescharacteristic, complemented
152C2—31no—
153C2—31no—
154C2#1059363111yescharacteristic
subgroupG/H
center, hypercenterC2#10593631
commutator, prime radical, cosocleC2×C3×C42⋊C3C22
FrattiniC23C2×C3⋊S4
FittingC3×#384D3
socleC23×C3C2×S4
hypocenterC3×C42⋊C3Q8
LCSG ▷ C2×C3×C42⋊C3 ▷ C3×C42⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
16. C3×C42⋊C3Q8semidirect
48. C3×C42Dic6semidirect
60. C42⋊C3Dic6semidirect
110. C42#634semidirect
151. C3#72992semidirect

Maximal subgroups

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

subgroupindex
C3×#384⋊C32
C3⋊#46232
#729923
#695733
#642594