Finite Group Databasebeta

← C3⋊#85666 #11923435

Subgroups — C3⋊#85666 #11923435

Order 1152.

576 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 42 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×#5950C211yesmaximal, characteristic
2#87296C311yesmaximal, characteristic, complemented
3#85666—31nomaximal
4C3×#997C411yescharacteristic
5C3⋊(#131⋊C3)—42nomaximal
6A4×C3⋊C8—43nomaximal
7C3×#585C2×C311yescharacteristic
8#5950—21no—
9#5950D311yescharacteristic
10#5819—32no—
11#5819—33no—
12C2×#948—32no—
13C2×#948—33no—
14C3×#41⋊C3—42no—
15C3×C4×A4—43no—
16#3573—31noSylow
17C3×2−1+4—32no—
18C3×H(5,𝔽2)—33no—
19C3×H(5,𝔽2)C3×C411yescharacteristic
20C2×C3×#41—32no—
21C2×C3×#41—33no—
22#997—21no—
23#997Dic311yescharacteristic
24#948—36no—
25#948—36no—
26#948—312no—
27#948—32no—
28#948A412yescomplemented
29C2×#208—36no—
30C2×#208—33no—
31C2×#208—33no—
32C2×#208—33no—
33C22×C3⋊C8—33no—
34C22×C3⋊C8—31no—
35C22×C3⋊C8A413yescomplemented
36#131⋊C3—122no—
37C8×A4—123no—
38C2×C3×A4—43no—
39C3×SL(2,𝔽3)—42no—
40C3×C3⋊C8—161no—
41#585C3×D311yescharacteristic
42#568—92no—
43#568—93no—
44C2×#131—93no—
45C2×#131—92no—
46C3×#41—36no—
47C3×#41—36no—
48C3×#41—312no—
49C3×#41—32no—
50C3×#41C2×A412yes—
51C2×C3×Q8—33no—
52C2×C3×Q8—32no—
53C2×C3×D4—36no—
54C2×C3×D4—33no—
55C2×C3×D4—33no—
56C2×C3×D4—33no—
57C22×C3×C4—33no—
58C22×C3×C4—31no—
59C22×C3×C4C2×A413yes—
60#41⋊C3—42no—
61#41⋊C3—82no—
62C4×A4—43no—
63C4×A4—83no—
64#208—312no—
65#208—36no—
66#208—32no—
67C2×C3⋊C8—33no—
68C2×C3⋊C8—36no—
69C2×C3⋊C8—33no—
70C2×C3⋊C8—32no—
71C2×C3⋊C8—33no—
72C2×C3⋊C8—33no—
73C3×A4—43no—
74C32×C4—161no—
752−1+4—32no—
76H(5,𝔽2)—33no—
77H(5,𝔽2)C3×Dic311yescharacteristic
78C2×#41—32no—
79C2×#41—33no—
80#131—32no—
81#131—96no—
82#131—96no—
83#131—912no—
84#131—92no—
85C2×M16—96no—
86C2×M16—93no—
87C2×M16—93no—
88C2×M16—93no—
89C22×C8—33no—
90C22×C8—91no—
91C22×C8—93no—
92C23×C3—31no—
93C23×C3—33no—
94C23×C3C4×A413yes—
95C2×A4—43no—
96C2×A4—83no—
97C3×Q8—36no—
98C3×Q8C4×A412yes—
99C3×D4—32no—
100C3×D4—36no—
101C3×D4—312no—
102C2×C3×C4—33no—
103C2×C3×C4—36no—
104C2×C3×C4—33no—
105C2×C3×C4—32no—
106C2×C3×C4—33no—
107C2×C3×C4—33no—
108SL(2,𝔽3)—42no—
109SL(2,𝔽3)—82no—
110C3×C8—481no—
111C3⋊C8—32no—
112C3⋊C8—33no—
113C3⋊C8C22⋊A411yescharacteristic
114C2×C32—161no—
115#41—36no—
116#41—36no—
117#41—312no—
118#41—32no—
119#41D3×A412yes—
120C2×Q8—33no—
121C2×Q8—32no—
122C2×D4—36no—
123C2×D4—33no—
124C2×D4—33no—
125C2×D4—33no—
126C22×C4—33no—
127C22×C4—31no—
128C22×C4D3×A413yes—
129M16—912no—
130M16—96no—
131M16—92no—
132C2×C8—93no—
133C2×C8—92no—
134C2×C8—93no—
135C2×C8—96no—
136C2×C8—93no—
137C2×C8—93no—
138C22×C3—33no—
139C22×C3—32no—
140C22×C3—43no—
141C22×C3—121no—
142C22×C3—123no—
143A4—43no—
144A4—83no—
145C3×C4—32no—
146C3×C4—33no—
147C3×C4—161no—
148C3×C4—321no—
149C3×C4C2×C22⋊A411yescharacteristic
150C32—161noSylow
151C23—31no—
152C23—33no—
153C23Dic3×A413yes—
154Q8—36no—
155Q8Dic3×A412yes—
156D4—32no—
157D4—36no—
158D4—312no—
159C2×C4—33no—
160C2×C4—36no—
161C2×C4—33no—
162C2×C4—32no—
163C2×C4—33no—
164C2×C4—33no—
165C8—31no—
166C8—92no—
167C8—93no—
168C2×C3—63no—
169C2×C3—62no—
170C2×C3—161no—
171C2×C3—321no—
172C2×C3C4×C22⋊A411yescharacteristic
173C22—33no—
174C22—32no—
175C22—43no—
176C22—121no—
177C22—123no—
178C4—32no—
179C4—33no—
180C4D3×C22⋊A411yescharacteristic
181C3—161no—
182C3—321no—
183C3#8566611yescharacteristic, complemented
184C2—63no—
185C2—62no—
186C2Dic3×C22⋊A411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC4D3×C22⋊A4
commutator, hypocenterC3×H(5,𝔽2)C3×C4
Fitting, cosocleC3×#585C2×C3
socleC2×C3C4×C22⋊A4
prime radicalC3×#5950C2
LCSG ▷ C3×H(5,𝔽2)
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. #87296C3semidirect
28. #948A4semidirect
35. C22×C3⋊C8A4semidirect
183. C3#85666semidirect

Maximal subgroups

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

subgroupindex
C3×#59502
#872963
#856663
C3⋊(#131⋊C3)4
A4×C3⋊C84