Finite Group Databasebeta

← #11920957

Subgroups — #11920957

Order 1152.

268 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 25 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⋊#5930C212yesmaximal
2C3×#395⋊C3C211yesmaximal, characteristic
3#73001—33nomaximal
4#69707—31nomaximal
5C3×C22⋊SL(2,𝔽3)C2211yescharacteristic
6#64259—41nomaximal
7#5930—36no—
8#5500—31no—
9C3×#395D311yescharacteristic
10#5228—32no—
11#395⋊C3D313yes—
12#4528—31no—
13#4452—32no—
14C3×C4×A4—41no—
15C3⋊SL(2,ℤ/4)—42no—
16C3⋊#226—82no—
17#1605—91noSylow
18C22×C3×Q8C2×D311yescharacteristic
19C22⋊SL(2,𝔽3)C2×D313yes—
20A4⋊Q8—123no—
21C2×C3×C4⋊C4—31no—
22C2×#216—62no—
23#926—61no—
24#924—32no—
25#924—61no—
26#890—62no—
27#888—62no—
28C3×#95—31no—
29#835—62no—
30#830—32no—
31C2×C3×A4—41no—
32#634—161no—
33C3×SL(2,𝔽3)—82no—
34#544—91no—
35#451—92no—
36#395C3⋊D311yescharacteristic
37#328—92no—
38#324—91no—
39C2×C3×Q8—62no—
40C22×C3×C4—31no—
41C22×C3×C4—31no—
42C22×C3×C4S411yescharacteristic
43C2×Dic6—32no—
44C2×Dic6—61no—
45C4×A4—43no—
46SL(2,ℤ/4)—126no—
47#226—246no—
48C3×C4⋊C4—62no—
49#217—62no—
50#216—122no—
51#216—122no—
52C4⋊Dic3—32no—
53C4⋊Dic3—61no—
54C4⋊Dic3—61no—
55C4⋊Dic3—61no—
56Dic3⋊C4—62no—
57Dic3⋊C4—62no—
58C4×Dic3—62no—
59C2×C3⋊C8—62no—
60C3×A4—41no—
61C32×C4—161no—
62C3⋊Dic3—162no—
63C22×Q8C2×C3⋊D311yescharacteristic
64C2×Q16—182no—
65C4⋊Q8—182no—
66#125—182no—
67C22⋊Q8—92no—
68C22⋊Q8—181no—
69#117—181no—
70C2×C4⋊C4—31no—
71#103—182no—
72C22⋊C8—92no—
73#95—31no—
74C23×C3C2×S411yescharacteristic
75C2×A4—43no—
76C3×Q8—22no—
77C3×Q8—62no—
78C2×C3×C4—32no—
79C2×C3×C4—32no—
80C2×C3×C4—61no—
81C2×C3×C4—61no—
82C2×C3×C4—61no—
83C2×C3×C4—121no—
84C2×Dic3—62no—
85C2×Dic3—62no—
86Dic6—122no—
87Dic6—241no—
88Dic6—483no—
89SL(2,𝔽3)—86no—
90C3⋊C8—122no—
91C2×C32—161no—
92C2×Q8—62no—
93C2×Q8—92no—
94C2×Q8—181no—
95C22×C4—31no—
96C22×C4—31no—
97C22×C4C3⋊S411yescharacteristic
98Q16—362no—
99Q16—362no—
100C2×C8—182no—
101C4⋊C4—62no—
102C4⋊C4—92no—
103C4⋊C4—182no—
104C4⋊C4—181no—
105C4⋊C4—181no—
106C4⋊C4—181no—
107C4⋊C4—182no—
108C22⋊C4—182no—
109C42—182no—
110C22×C3—31no—
111C22×C3—31no—
112C22×C3#98411yescharacteristic
113A4—43no—
114C3×C4—41no—
115C3×C4—62no—
116C3×C4—62no—
117C3×C4—163no—
118Dic3—122no—
119Dic3—122no—
120Dic3—486no—
121C32—161noSylow
122C23C2×C3⋊S411yescharacteristic
123Q8—22no—
124Q8—62no—
125Q8—362no—
126Q8—721no—
127C2×C4—32no—
128C2×C4—32no—
129C2×C4—61no—
130C2×C4—61no—
131C2×C4—61no—
132C2×C4—121no—
133C2×C4—182no—
134C2×C4—182no—
135C8—362no—
136C2×C3—31no—
137C2×C3—31no—
138C2×C3—163no—
139C2×C3#1020⋊C211yescharacteristic
140C22—31no—
141C22—31no—
142C22#6426511yescharacteristic
143C4—41no—
144C4—62no—
145C4—62no—
146C4—362no—
147C4—362no—
148C3—163no—
149C3#7300111yescharacteristic, complemented
150C2—31no—
151C2—31no—
152C2#1059363011yescharacteristic
subgroupG/H
center, hypercenterC2#10593630
commutator, prime radical, cosocle, hypocenterC3×C22⋊SL(2,𝔽3)C22
FrattiniC23C2×C3⋊S4
FittingC3×#395D3
socleC23×C3C2×S4
LCSG ▷ C3×C22⋊SL(2,𝔽3)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
149. C3#73001semidirect

Maximal subgroups

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

subgroupindex
C3⋊#59302
C3×#395⋊C32
#730013
#697073
#642594