Finite Group Databasebeta

← #11921075

Subgroups — #11921075

Order 1152.

240 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C2×C3×#131⋊C3C211yesmaximal, characteristic
2C3⋊#4628C212yesmaximal, complemented
3#73119—33nomaximal
4#72006—31nomaximal
5C2×C3×#41⋊C3C411yescharacteristic
6C3×#131⋊C3C411yescharacteristic
7C3×#131⋊C3C2211yescharacteristic
8#63639—41nomaximal
9C2×C3×#131D311yescharacteristic
10C2×#131⋊C3D313yes—
11C2×#812—31no—
12C2×#812—31no—
13#4628—36no—
14#4561—32no—
15#4561—32no—
16C3×#41⋊C3C811yescharacteristic
17C3×#41⋊C3C2×C411yescharacteristic
18C2×C3×SL(2,𝔽3)C811yescharacteristic
19C2×C32×C8—41no—
20C3⋊(C3⋊C16)—42no—
21#2117—91noSylow
22C2×C3×#41Dic311yescharacteristic
23C2×#41⋊C3Dic313yes—
24C3×#131—31no—
25C3×#131—31no—
26C3×#131Dic311yescharacteristic
27C3×#131C2×D311yescharacteristic
28C2×C3×M16—31no—
29C22×C3×C8—31no—
30#131⋊C3Dic313yes—
31#131⋊C3C2×D313yes—
32#812—32no—
33#812—61no—
34#812—61no—
35#812—61no—
36#812—123no—
37C2×C3⋊C16—32no—
38C2×C3⋊C16—61no—
39C2×C32×C4—41no—
40C3×SL(2,𝔽3)C2×C811yescharacteristic
41C32×C8—41no—
42C32×C8—41no—
43C2×#131C3⋊D311yescharacteristic
44C2×M32—91no—
45C2×M32—91no—
46#350—92no—
47#350—92no—
48C3×#41—31no—
49C3×#41—31no—
50C3×#41C3⋊C811yescharacteristic
51C3×#41C2×Dic311yescharacteristic
52C2×C3×Q8C3⋊C811yescharacteristic
53C2×C3×D4—31no—
54C22×C3×C4—31no—
55#41⋊C3C3⋊C813yes—
56#41⋊C3C2×Dic313yes—
57C2×SL(2,𝔽3)C3⋊C813yes—
58C3×M16—31no—
59C3×M16—31no—
60C3×M16—61no—
61C2×C3×C8—31no—
62C2×C3×C8—31no—
63C2×C3×C8—31no—
64C2×C3×C8—31no—
65C2×C3×C8—31no—
66C2×C3×C8—43no—
67C2×C3×C8S411yescharacteristic
68C3⋊C16—62no—
69C3⋊C16—62no—
70C3⋊C16—126no—
71C22×C32—41no—
72C32×C4—41no—
73C32×C4—41no—
74C2×#41C3⋊Dic311yescharacteristic
75#131—31no—
76#131—31no—
77#131C3⋊Dic311yescharacteristic
78#131C2×C3⋊D311yescharacteristic
79C2×M16—31no—
80C22×C8—31no—
81M32—92no—
82M32—181no—
83M32—181no—
84M32—181no—
85C2×C16—92no—
86C2×C16—181no—
87C23×C3—31no—
88C3×Q8—31no—
89C3×Q8C2×C3⋊C811yescharacteristic
90C3×D4—31no—
91C3×D4—31no—
92C3×D4—61no—
93C2×C3×C4—31no—
94C2×C3×C4—31no—
95C2×C3×C4—31no—
96C2×C3×C4—31no—
97C2×C3×C4—31no—
98C2×C3×C4—43no—
99C2×C3×C4SL(2,ℤ/4)11yescharacteristic
100SL(2,𝔽3)C2×C3⋊C813yes—
101C3×C8—31no—
102C3×C8—31no—
103C3×C8—43no—
104C3×C8—43no—
105C3×C8SL(2,ℤ/4)11yescharacteristic
106C3×C8C2×S411yescharacteristic
107C2×C32—41no—
108C2×C32—81no—
109#41—31no—
110#41—31no—
111#41C3⋊(C3⋊C8)11yescharacteristic
112#41C2×C3⋊Dic311yescharacteristic
113C2×Q8C3⋊(C3⋊C8)11yescharacteristic
114C2×D4—31no—
115C22×C4—31no—
116M16—31no—
117M16—31no—
118M16—61no—
119C2×C8—31no—
120C2×C8—31no—
121C2×C8—31no—
122C2×C8—31no—
123C2×C8—31no—
124C2×C8C3⋊S411yescharacteristic
125C16—182no—
126C16—182no—
127C22×C3—31no—
128C22×C3—31no—
129C22×C3—43no—
130C22×C3—121no—
131C22×C3A4⋊C811yescharacteristic
132C3×C4—31no—
133C3×C4—31no—
134C3×C4—43no—
135C3×C4—43no—
136C3×C4A4⋊C811yescharacteristic
137C3×C4C2×SL(2,ℤ/4)11yescharacteristic
138C32—41noSylow
139C23—31no—
140Q8—31no—
141Q8C2×C3⋊(C3⋊C8)11yescharacteristic
142D4—31no—
143D4—31no—
144D4—61no—
145C2×C4—31no—
146C2×C4—31no—
147C2×C4—31no—
148C2×C4—31no—
149C2×C4—31no—
150C2×C4C3⋊SL(2,ℤ/4)11yescharacteristic
151C8—31no—
152C8—31no—
153C8C3⋊SL(2,ℤ/4)11yescharacteristic
154C8C2×C3⋊S411yescharacteristic
155C2×C3—21no—
156C2×C3—43no—
157C2×C3—61no—
158C2×C3—61no—
159C2×C3—83no—
160C2×C3C2×A4⋊C811yescharacteristic
161C22—31no—
162C22—31no—
163C22—121no—
164C22C3⋊(A4⋊C8)11yescharacteristic
165C4—31no—
166C4—31no—
167C4C3⋊(A4⋊C8)11yescharacteristic
168C4C2×C3⋊SL(2,ℤ/4)11yescharacteristic
169C3—43no—
170C3#7311911yescharacteristic, complemented
171C2—21no—
172C2—61no—
173C2—61no—
174C2C2×C3⋊(A4⋊C8)11yescharacteristic
subgroupG/H
center, FrattiniC8C2×C3⋊S4
commutator, hypocenterC3×SL(2,𝔽3)C2×C8
FittingC2×C3×#131D3
socleC2×C3C2×A4⋊C8
prime radicalC2×C3×#41⋊C3C4
cosocleC3×#131⋊C3C22
hypercenterC2×C8C3⋊S4
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C8 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C3⋊#4628C2semidirect
170. C3#73119semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#131⋊C32
C3⋊#46282
#731193
#720063
#636394