Finite Group Databasebeta

← D3×#401⋊C3 #11921201

Subgroups — D3×#401⋊C3 #11921201

Order 1152.

250 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 32 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×#401⋊C3C211yesmaximal, characteristic, complemented
2D3×#95⋊C3C211yesmaximal, characteristic
3C3⋊(#401⋊C3)C211yesmaximal, characteristic, complemented
4D3×#401C311yesmaximal, characteristic, complemented
5C2×#401⋊C3—31nomaximal
6C4×D3×A4—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8C3×#401C2×C311yescharacteristic, complemented
9D3×#95—31no—
10D3×#95—31no—
11D3×#95C2×C311yescharacteristic
12C3⋊#401—31no—
13C3⋊#401—31no—
14C3⋊#401C2×C311yescharacteristic, complemented
15#401⋊C3—21no—
16#401⋊C3—31no—
17#401⋊C3D311yescharacteristic, direct product factor
18C2×#95⋊C3—31no—
19C2×D3×A4—41no—
20C3×C4×A4—41no—
21Dic3×A4—41no—
22C2×#401—31noSylow
23C22×C4×D3—31no—
24C22×C4×D3—31no—
25C22×C4×D3A411yescharacteristic
26C2×C4×A4—121no—
27C3×#95—31no—
28C3×#95—31no—
29C3×#95C22×C311yescharacteristic
30C3⋊#95—32no—
31C3⋊#95—31no—
32C3⋊#95—31no—
33C3⋊#95—31no—
34C3⋊#95—31no—
35C3⋊#95—31no—
36#95⋊C3—21no—
37#95⋊C3C2×D311yescharacteristic
38C2×C3×A4—41no—
39D3×A4—42no—
40C3×C4×D3—161no—
41#401—31no—
42#401—91no—
43#401—91no—
44#401C3×D311yescharacteristic, complemented
45C2×#95—31no—
46C2×#95—91no—
47C2×#95—91no—
48C23×D3C2×A411yescharacteristic
49C22×A4—121no—
50C22×C3×C4—31no—
51C22×C3×C4—31no—
52C22×C3×C4C2×A411yescharacteristic
53C22×Dic3—31no—
54C22×Dic3—31no—
55C22×Dic3C2×A411yescharacteristic
56C2×C4×D3—61no—
57C2×C4×D3—61no—
58C2×C4×D3—61no—
59C2×C4×D3—62no—
60C2×C4×D3—61no—
61C2×C4×D3—61no—
62C2×C4×D3—64no—
63C2×C4×D3—62no—
64C2×C4×D3—61no—
65C4×A4—41no—
66C4×A4—81no—
67C4×A4—121no—
68C2×C3×D3—161no—
69C3×A4—41no—
70C32×C4—161no—
71C3×Dic3—161no—
72C23×C4—31no—
73C23×C4—91no—
74C23×C4—91no—
75#95—31no—
76#95—31no—
77#95—91no—
78#95—91no—
79#95—91no—
80#95—91no—
81#95—92no—
82#95—91no—
83#95C2×C3×D311yescharacteristic
84C23×C3C22×A411yescharacteristic
85C22×D3—31no—
86C22×D3—31no—
87C22×D3—32no—
88C22×D3#41⋊C312yes—
89C2×A4—41no—
90C2×A4—81no—
91C2×A4—122no—
92C2×C3×C4—61no—
93C2×C3×C4—62no—
94C2×C3×C4—61no—
95C2×C3×C4—61no—
96C2×C3×C4—61no—
97C2×C3×C4—61no—
98C2×C3×C4—481no—
99C2×Dic3—61no—
100C2×Dic3—62no—
101C2×Dic3—61no—
102C2×Dic3—61no—
103C2×Dic3—61no—
104C2×Dic3—61no—
105C4×D3—41no—
106C4×D3—121no—
107C4×D3—122no—
108C4×D3—122no—
109C4×D3—122no—
110C4×D3—122no—
111C2×C32—161no—
112C3×D3—162no—
113C24—31no—
114C22×C4—31no—
115C22×C4—31no—
116C22×C4—31no—
117C22×C4—91no—
118C22×C4—91no—
119C22×C4—181no—
120C22×C4—182no—
121C22×C4—181no—
122C22×C4—181no—
123C22×C4—184no—
124C22×C4—181no—
125C22×C4—182no—
126C22×C4—181no—
127C22×C4—181no—
128C22×C4D3×A411yescharacteristic
129C22×C3—31no—
130C22×C3—31no—
131C22×C3—481no—
132C22×C3C2×#41⋊C311yescharacteristic
133C2×D3—32no—
134C2×D3—31no—
135C2×D3—32no—
136C2×D3—32no—
137C2×D3—32no—
138C2×D3#126⋊C311yescharacteristic
139A4—41no—
140A4—81no—
141C3×C4—41no—
142C3×C4—121no—
143C3×C4—121no—
144C3×C4—161no—
145C3×C4—321no—
146C3×C4—481no—
147Dic3—41no—
148Dic3—121no—
149Dic3—121no—
150C32—161noSylow
151C23—32no—
152C23—91no—
153C23—92no—
154C23—91no—
155C23C2×D3×A411yescharacteristic
156C2×C4—61no—
157C2×C4—62no—
158C2×C4—61no—
159C2×C4—61no—
160C2×C4—61no—
161C2×C4—61no—
162C2×C4—121no—
163C2×C4—181no—
164C2×C4—181no—
165C2×C4—182no—
166C2×C4—181no—
167C2×C4—181no—
168C2×C4—181no—
169C2×C4—361no—
170C2×C4—362no—
171C2×C4—362no—
172C2×C4—362no—
173C2×C4—362no—
174C2×C3—31no—
175C2×C3—31no—
176C2×C3—161no—
177C2×C3—321no—
178C2×C3—482no—
179C2×C3C2×#126⋊C311yescharacteristic
180D3—32no—
181D3#401⋊C312yesdirect product factor
182C22—31no—
183C22—31no—
184C22—31no—
185C22—92no—
186C22—92no—
187C22—92no—
188C22—92no—
189C22—91no—
190C22D3×#41⋊C311yescharacteristic
191C4—41no—
192C4—121no—
193C4—121no—
194C4—121no—
195C4—361no—
196C4—361no—
197C3—161no—
198C3—321no—
199C3C2×#401⋊C311yescharacteristic, complemented
200C2—31no—
201C2—31no—
202C2—32no—
203C2—92no—
204C2D3×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#126⋊C3
commutator, cosocle, hypocenterC3×#95C22×C3
FrattiniC23C2×D3×A4
FittingC3×#401C2×C3
socleC23×C3C22×A4
prime radicalD3×#95⋊C3C2
LCSG ▷ C3×#95
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3×#401⋊C3C2semidirect
3. C3⋊(#401⋊C3)C2semidirect
4. D3×#401C3semidirect
8. C3×#401C2×C3semidirect
14. C3⋊#401C2×C3semidirect
17. #401⋊C3D3direct (N × H)
44. #401C3×D3semidirect
181. D3#401⋊C3direct (N × H)
199. C3C2×#401⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#401⋊C32
D3×#95⋊C32
C3⋊(#401⋊C3)2
D3×#4013
C2×#401⋊C33
C4×D3×A44