Finite Group Databasebeta

← C2×C3⋊(#504⋊C3) #11921330

Subgroups — C2×C3⋊(#504⋊C3) #11921330

Order 1152.

225 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 225 conjugacy classes of subgroups — too many to draw. Only its 63 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⋊(#504⋊C3)C212yesmaximal, direct product factor
3C2×#5140C311yesmaximal, characteristic, complemented
4C2×#504⋊C3—31nomaximal
5C2×C3×#41⋊C3C411yescharacteristic
6C3×#131⋊C3C411yescharacteristic
7C3×#131⋊C3C2211yescharacteristic
8C2×C3×C3⋊C16—41nomaximal
9C2×C3×#131C2×C311yescharacteristic
10C2×#131⋊C3—21no—
11C2×#131⋊C3D311yescharacteristic
12#5140—32no—
13#5140C2×C312yescomplemented
14C2×#812—31no—
15C22×C3⋊C16—31no—
16#504⋊C3—32no—
17C3×#41⋊C3C811yescharacteristic
18C3×#41⋊C3C2×C411yescharacteristic
19C2×C3×SL(2,𝔽3)C811yescharacteristic
20C2×C32×C8—41no—
21C3×C3⋊C16—42no—
22C2×#504—31noSylow
23C2×C3×#41C3×C411yescharacteristic
24C2×#41⋊C3—21no—
25C2×#41⋊C3Dic311yescharacteristic
26C3×#131—31no—
27C3×#131—31no—
28C3×#131C3×C411yescharacteristic
29C3×#131C22×C311yescharacteristic
30C2×C3×M16—31no—
31C22×C3×C8—31no—
32#131⋊C3—21no—
33#131⋊C3—21no—
34#131⋊C3Dic311yescharacteristic
35#131⋊C3C2×D311yescharacteristic
36C2×C3×C16—121no—
37#812—32no—
38#812—32no—
39C2×C3⋊C16—31no—
40C2×C3⋊C16—32no—
41C2×C3⋊C16—32no—
42C2×C3⋊C16A411yescharacteristic
43C2×C32×C4—41no—
44C3×SL(2,𝔽3)C2×C811yescharacteristic
45C32×C8—41no—
46C32×C8—41no—
47C2×#131C3×D311yescharacteristic
48#504—32no—
49#504—92no—
50C2×M32—91no—
51C22×C16—91no—
52C3×#41—31no—
53C3×#41—31no—
54C3×#41C3×C811yescharacteristic
55C3×#41C2×C3×C411yescharacteristic
56C2×C3×Q8C3×C811yescharacteristic
57C2×C3×D4—31no—
58C22×C3×C4—31no—
59#41⋊C3—21no—
60#41⋊C3—21no—
61#41⋊C3C3⋊C811yescharacteristic
62#41⋊C3C2×Dic311yescharacteristic
63C2×SL(2,𝔽3)—21no—
64C2×SL(2,𝔽3)C3⋊C811yescharacteristic
65C3×M16—32no—
66C3×M16—31no—
67C3×M16—31no—
68C2×C3×C8—31no—
69C2×C3×C8—31no—
70C2×C3×C8—31no—
71C2×C3×C8—31no—
72C2×C3×C8—31no—
73C2×C3×C8—41no—
74C2×C3×C8—81no—
75C2×C3×C8C2×A411yescharacteristic
76C3×C16—122no—
77C3⋊C16—32no—
78C3⋊C16C2×A412yes—
79C22×C32—41no—
80C32×C4—41no—
81C32×C4—41no—
82C2×#41C3×Dic311yescharacteristic
83#131—31no—
84#131—31no—
85#131C3×Dic311yescharacteristic
86#131C2×C3×D311yescharacteristic
87C2×M16—31no—
88C22×C8—31no—
89M32—92no—
90M32—92no—
91C2×C16—31no—
92C2×C16—92no—
93C2×C16—92no—
94C2×C16—91no—
95C23×C3—31no—
96C3×Q8—31no—
97C3×Q8C2×C3×C811yescharacteristic
98C3×D4—31no—
99C3×D4—31no—
100C3×D4—32no—
101C2×C3×C4—31no—
102C2×C3×C4—31no—
103C2×C3×C4—31no—
104C2×C3×C4—31no—
105C2×C3×C4—31no—
106C2×C3×C4—41no—
107C2×C3×C4—81no—
108C2×C3×C4C4×A411yescharacteristic
109SL(2,𝔽3)—21no—
110SL(2,𝔽3)C2×C3⋊C811yescharacteristic
111C3×C8—31no—
112C3×C8—31no—
113C3×C8—41no—
114C3×C8—41no—
115C3×C8—81no—
116C3×C8—81no—
117C3×C8C4×A411yescharacteristic
118C3×C8C22×A411yescharacteristic
119C2×C32—42no—
120C2×C32—41no—
121#41—31no—
122#41—31no—
123#41C3×C3⋊C811yescharacteristic
124#41C2×C3×Dic311yescharacteristic
125C2×Q8C3×C3⋊C811yescharacteristic
126C2×D4—31no—
127C22×C4—31no—
128M16—32no—
129M16—31no—
130M16—31no—
131C2×C8—31no—
132C2×C8—31no—
133C2×C8—31no—
134C2×C8—31no—
135C2×C8—31no—
136C2×C8D3×A411yescharacteristic
137C16—32no—
138C16—92no—
139C22×C3—31no—
140C22×C3—31no—
141C22×C3—41no—
142C22×C3—62no—
143C22×C3—81no—
144C22×C3C8×A411yescharacteristic
145C3×C4—31no—
146C3×C4—31no—
147C3×C4—41no—
148C3×C4—41no—
149C3×C4—81no—
150C3×C4—81no—
151C3×C4C8×A411yescharacteristic
152C3×C4C2×C4×A411yescharacteristic
153C32—41noSylow
154C23—31no—
155Q8—31no—
156Q8C2×C3×C3⋊C811yescharacteristic
157D4—31no—
158D4—31no—
159D4—32no—
160C2×C4—31no—
161C2×C4—31no—
162C2×C4—31no—
163C2×C4—31no—
164C2×C4—31no—
165C2×C4Dic3×A411yescharacteristic
166C8—31no—
167C8—31no—
168C8Dic3×A411yescharacteristic
169C8C2×D3×A411yescharacteristic
170C2×C3—41no—
171C2×C3—42no—
172C2×C3—61no—
173C2×C3—61no—
174C2×C3—81no—
175C2×C3—82no—
176C2×C3#504⋊C312yescomplemented
177C2×C3C2×C8×A411yescharacteristic
178C22—31no—
179C22—31no—
180C22—62no—
181C22A4×C3⋊C811yescharacteristic
182C4—31no—
183C4—31no—
184C4A4×C3⋊C811yescharacteristic
185C4C2×Dic3×A411yescharacteristic
186C3—41no—
187C3—81no—
188C3C2×#504⋊C311yescharacteristic, complemented
189C2—61no—
190C2—61no—
191C2C3⋊(#504⋊C3)12yesdirect product factor
192C2C2×A4×C3⋊C811yescharacteristic
subgroupG/H
center, hypercenterC2×C8D3×A4
commutator, hypocenterC3×Q8C2×C3×C8
FrattiniC8C2×D3×A4
FittingC2×C3×#131C2×C3
socleC22×C3C8×A4
prime radicalC2×C3×#41⋊C3C4
cosocleC3×#131C22×C3
LCSG ▷ C3×Q8
UCSC1 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C3⋊(#504⋊C3)C2direct (N × H)
3. C2×#5140C3semidirect
13. #5140C2×C3semidirect
176. C2×C3#504⋊C3semidirect
188. C3C2×#504⋊C3semidirect
191. C2C3⋊(#504⋊C3)direct (N × H)

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⋊(#504⋊C3)2
C2×#51403
C2×#504⋊C33
C2×C3×C3⋊C164