Finite Group Databasebeta

← D3×#504⋊C3 #11921238

Subgroups — D3×#504⋊C3 #11921238

Order 1152.

215 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 215 conjugacy classes of subgroups — too many to draw. Only its 49 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
1D3×#131⋊C3C211yesmaximal, characteristic
2C3×#504⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#504⋊C3)C211yesmaximal, characteristic, complemented
4D3×#504C311yesmaximal, characteristic, complemented
5C2×#504⋊C3—31nomaximal
6D3×#41⋊C3C411yescharacteristic
7C3×#131⋊C3C2211yescharacteristic
8C3⋊(#131⋊C3)C411yescharacteristic
9C3×D3×C16—41nomaximal
10D3×#131C2×C311yescharacteristic
11C2×#131⋊C3—31no—
12C3×#504C2×C311yescharacteristic, complemented
13#5140C2×C311yescharacteristic, complemented
14#4907—31no—
15D3×M32—31no—
16#4901—31no—
17C2×D3×C16—31no—
18#504⋊C3—21no—
19#504⋊C3—31no—
20#504⋊C3D311yescharacteristic, direct product factor
21C3×#41⋊C3C2×C411yescharacteristic
22D3×SL(2,𝔽3)C811yescharacteristic
23C3⋊(#41⋊C3)C811yescharacteristic
24C3×D3×C8—41no—
25C32×C16—41no—
26C3×C3⋊C16—41no—
27C2×#504—31noSylow
28D3×#41C3×C411yescharacteristic
29C2×#41⋊C3—31no—
30C3×#131C22×C311yescharacteristic
31#948C3×C411yescharacteristic
32#907—31no—
33D3×M16—31no—
34#901—31no—
35C2×D3×C8—31no—
36#131⋊C3—21no—
37#131⋊C3—31no—
38#131⋊C3C2×D311yescharacteristic
39C3×M32—31no—
40C2×C3×C16—31no—
41C2×C3×C16—121no—
42#812—31no—
43C2×C3⋊C16—31no—
44#798—32no—
45D3×C16—31no—
46D3×C16—31no—
47D3×C16—31no—
48D3×C16A411yescharacteristic
49C3×C4×D3—41no—
50C3×SL(2,𝔽3)C2×C811yescharacteristic
51C32×C8—41no—
52C3×C3⋊C8—41no—
53C2×#131—31no—
54#504—31no—
55#504—91no—
56#504—91no—
57#504C3×D311yescharacteristic, complemented
58C2×M32—91no—
59C22×C16—91no—
60C3×#41C2×C3×C411yescharacteristic
61#239C3×C811yescharacteristic
62D3×Q8C3×C811yescharacteristic
63#237—31no—
64D3×D4—31no—
65#235—31no—
66C2×C4×D3—31no—
67#41⋊C3—21no—
68#41⋊C3—31no—
69#41⋊C3C4×D311yescharacteristic
70C2×SL(2,𝔽3)—31no—
71C3×M16—31no—
72C2×C3×C8—31no—
73C2×C3×C8—121no—
74#208—31no—
75C2×C3⋊C8—31no—
76ΓL(1,𝔽25)—32no—
77D3×C8—31no—
78D3×C8—31no—
79D3×C8—31no—
80D3×C8C2×A411yescharacteristic
81C3×C16—31no—
82C3×C16—41no—
83C3×C16—81no—
84C3×C16—121no—
85C3×C16C2×A411yescharacteristic
86C3⋊C16—31no—
87C3⋊C16C2×A411yescharacteristic
88C2×C3×D3—41no—
89C32×C4—41no—
90C3×Dic3—41no—
91C2×#41—31no—
92#131—31no—
93#131—91no—
94#131—91no—
95#131C2×C3×D311yescharacteristic
96C2×M16—91no—
97C22×C8—91no—
98M32—31no—
99M32—92no—
100M32—91no—
101C2×C16—31no—
102C2×C16—31no—
103C2×C16—91no—
104C2×C16—91no—
105C2×C16—91no—
106C2×C16—91no—
107C22×D3—31no—
108C3×Q8C2×C3×C811yescharacteristic
109C3×D4—31no—
110C2×C3×C4—31no—
111C2×C3×C4—121no—
112#67—32no—
113C2×Dic3—31no—
114D12—31no—
115C4×D3—31no—
116C4×D3—31no—
117C4×D3—31no—
118C4×D3C4×A411yescharacteristic
119Dic6—31no—
120SL(2,𝔽3)—21no—
121SL(2,𝔽3)D3×C811yescharacteristic
122C3×C8—31no—
123C3×C8—41no—
124C3×C8—81no—
125C3×C8—121no—
126C3×C8C22×A411yescharacteristic
127C3⋊C8—31no—
128C3⋊C8C4×A411yescharacteristic
129C2×C32—41no—
130C3×D3—42no—
131#41—31no—
132#41—91no—
133#41—91no—
134#41C3×C4×D311yescharacteristic
135C2×Q8—31no—
136C2×D4—91no—
137C22×C4—91no—
138M16—31no—
139M16—92no—
140M16—91no—
141C2×C8—31no—
142C2×C8—31no—
143C2×C8—91no—
144C2×C8—91no—
145C2×C8—91no—
146C2×C8—91no—
147C16—31no—
148C16—31no—
149C16—91no—
150C16D3×A411yescharacteristic
151C22×C3—31no—
152C22×C3—121no—
153C2×D3—31no—
154C2×D3—62no—
155C2×D3C8×A411yescharacteristic
156C3×C4—31no—
157C3×C4—41no—
158C3×C4—81no—
159C3×C4—121no—
160C3×C4C2×C4×A411yescharacteristic
161Dic3—31no—
162Dic3C8×A411yescharacteristic
163C32—41noSylow
164C23—91no—
165Q8—91no—
166Q8C3×D3×C811yescharacteristic
167D4—31no—
168D4—91no—
169D4—92no—
170C2×C4—31no—
171C2×C4—31no—
172C2×C4—91no—
173C2×C4—91no—
174C2×C4—91no—
175C2×C4—91no—
176C8—31no—
177C8—31no—
178C8—91no—
179C8C2×D3×A411yescharacteristic
180C2×C3—41no—
181C2×C3—61no—
182C2×C3—81no—
183C2×C3—122no—
184C2×C3C2×C8×A411yescharacteristic
185D3—61no—
186D3#504⋊C312yesdirect product factor
187C22—31no—
188C22—31no—
189C22—91no—
190C22—182no—
191C4—31no—
192C4—31no—
193C4—91no—
194C4C4×D3×A411yescharacteristic
195C3—41no—
196C3—81no—
197C3C2×#504⋊C311yescharacteristic, complemented
198C2—32no—
199C2—61no—
200C2—181no—
201C2D3×C8×A411yescharacteristic
subgroupG/H
center, hypercenterC16D3×A4
commutator, hypocenterC3×Q8C2×C3×C8
FrattiniC8C2×D3×A4
FittingC3×#504C2×C3
socleC2×C3C2×C8×A4
prime radicalD3×#41⋊C3C4
cosocleC3×#131C22×C3
LCSG ▷ C3×Q8
UCSC1 ◁ C16

Complements

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

NH ≅ G/Ntype
2. C3×#504⋊C3C2semidirect
3. C3⋊(#504⋊C3)C2semidirect
4. D3×#504C3semidirect
12. C3×#504C2×C3semidirect
13. #5140C2×C3semidirect
20. #504⋊C3D3direct (N × H)
57. #504C3×D3semidirect
186. D3#504⋊C3direct (N × H)
197. C3C2×#504⋊C3semidirect

Maximal subgroups

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

subgroupindex
D3×#131⋊C32
C3×#504⋊C32
C3⋊(#504⋊C3)2
D3×#5043
C2×#504⋊C33
C3×D3×C164