Finite Group Databasebeta

← D3×#95⋊C9 #13136825

Subgroups — D3×#95⋊C9 #13136825

Order 1728.

297 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 297 conjugacy classes of subgroups — too many to draw. Only its 37 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×#95⋊C9C211yesmaximal, characteristic, complemented
2C3×D3×#95C311yesmaximal, characteristic
3C2×#95⋊C9—31nomaximal
4C2×D3×C22⋊C9—41nomaximal
5C22×C3×C4×D3—31no—
6C32×#95C2×C311yescharacteristic
7C3×C3⋊#95—31no—
8#95⋊C9—21no—
9#95⋊C9D311yescharacteristic, direct product factor
10C2×C3×C22⋊C9—41no—
11D3×C22⋊C9—42no—
12C2×C3×#95—31no—
13D3×#95C911yescharacteristic, complemented
14C23×C3×D3A411yescharacteristic
15C22×C32×C4—31no—
16C22×C3×Dic3—31no—
17C2×C3×C4×D3—32no—
18C2×C3×C4×D3—32no—
19C2×C3×C4×D3—64no—
20C22×C22⋊C9—121no—
21C2×D3×C9—161no—
22C3×C22⋊C9—41no—
23C23×C3×C4—91no—
24C22×C4×D3—31no—
25C3×#95—21no—
26C3×#95—91no—
27C3×#95C2×C911yescharacteristic, complemented
28C3×#95C3×D311yescharacteristic
29C3⋊#95—31no—
30C23×C32C2×A411yescharacteristic
31C22×C3×D3—31no—
32C22×C3×D3—31no—
33C22×C3×D3—32no—
34C22×C3×D3SL(2,𝔽3)12yes—
35C2×C32×C4—32no—
36C2×C32×C4—62no—
37C2×C3×Dic3—32no—
38C2×C3×Dic3—62no—
39C3×C4×D3—64no—
40C3×C4×D3—64no—
41C2×C22⋊C9—41no—
42C2×C22⋊C9—81no—
43C2×C22⋊C9—122no—
44C2×#95—31noSylow
45C2×C3×C9—161no—
46D3×C9—162no—
47C24×C3—31no—
48C23×D3C22⋊C911yescharacteristic
49C22×C3×C4—31no—
50C22×C3×C4—31no—
51C22×C3×C4—61no—
52C22×C3×C4—92no—
53C22×C3×C4—92no—
54C22×C3×C4—91no—
55C22×C3×C4—184no—
56C22×Dic3—31no—
57C2×C4×D3—32no—
58C2×C4×D3—32no—
59C2×C4×D3—64no—
60C22×C32—31no—
61C22×C32—31no—
62C22×C32C2×SL(2,𝔽3)11yescharacteristic
63C2×C3×D3—32no—
64C2×C3×D3—31no—
65C2×C3×D3—32no—
66C2×C3×D3—32no—
67C2×C3×D3—32no—
68C2×C3×D3C42⋊C311yescharacteristic
69C32×C4—62no—
70C3×Dic3—62no—
71C22×C9—481no—
72C22⋊C9—41no—
73C22⋊C9—81no—
74C23×C4—91no—
75#95—91no—
76#95D3×C911yescharacteristic, complemented
77C3×C9—161noSylow
78C23×C3—21no—
79C23×C3—32no—
80C23×C3—91no—
81C23×C3—91no—
82C23×C3—92no—
83C23×C3C2×C22⋊C911yescharacteristic
84C23×C3D3×A411yescharacteristic
85C22×D3—31no—
86C22×D3—31no—
87C22×D3—32no—
88C22×D3Q8⋊C912yes—
89C2×C3×C4—32no—
90C2×C3×C4—32no—
91C2×C3×C4—62no—
92C2×C3×C4—62no—
93C2×C3×C4—62no—
94C2×C3×C4—92no—
95C2×C3×C4—122no—
96C2×C3×C4—184no—
97C2×C3×C4—184no—
98C2×C3×C4—182no—
99C2×Dic3—32no—
100C2×Dic3—62no—
101C4×D3—64no—
102C4×D3—64no—
103C2×C32—31no—
104C2×C32—31no—
105C2×C32C2×C42⋊C311yescharacteristic
106C3×D3—32no—
107C3×D3#95⋊C312yes—
108C2×C9—161no—
109C2×C9—321no—
110C2×C9—482no—
111C24—31no—
112C22×C4—31no—
113C22×C4—92no—
114C22×C4—92no—
115C22×C4—91no—
116C22×C4—184no—
117C22×C3—21no—
118C22×C3—31no—
119C22×C3—31no—
120C22×C3—31no—
121C22×C3—31no—
122C22×C3—31no—
123C22×C3—61no—
124C22×C3—61no—
125C22×C3—92no—
126C22×C3—92no—
127C22×C3—92no—
128C22×C3—92no—
129C22×C3—91no—
130C22×C3C2×Q8⋊C911yescharacteristic
131C22×C3D3×SL(2,𝔽3)11yescharacteristic
132C2×D3—32no—
133C2×D3—31no—
134C2×D3—32no—
135C2×D3—32no—
136C2×D3—32no—
137C2×D3C42⋊C911yescharacteristic
138C3×C4—62no—
139C3×C4—62no—
140C3×C4—122no—
141C3×C4—182no—
142Dic3—62no—
143C32C2×#95⋊C311yescharacteristic
144C9—161no—
145C9—321no—
146C23—32no—
147C23—91no—
148C23—91no—
149C23—92no—
150C23D3×C22⋊C911yescharacteristic
151C2×C4—32no—
152C2×C4—62no—
153C2×C4—92no—
154C2×C4—184no—
155C2×C4—184no—
156C2×C4—182no—
157C2×C3—21no—
158C2×C3—31no—
159C2×C3—31no—
160C2×C3—31no—
161C2×C3—31no—
162C2×C3—32no—
163C2×C3—61no—
164C2×C3—61no—
165C2×C3—92no—
166C2×C3C2×C42⋊C911yescharacteristic
167C2×C3D3×C42⋊C311yescharacteristic
168D3—32no—
169D3#95⋊C912yesdirect product factor
170C22—31no—
171C22—31no—
172C22—31no—
173C22—92no—
174C22—92no—
175C22—92no—
176C22—92no—
177C22—91no—
178C22D3×Q8⋊C911yescharacteristic
179C4—62no—
180C4—182no—
181C3—21no—
182C3C2×#95⋊C911yescharacteristic, complemented
183C3D3×#95⋊C311yescharacteristic
184C2—31no—
185C2—31no—
186C2—32no—
187C2—92no—
188C2D3×C42⋊C911yescharacteristic
subgroupG/H
center, hypercenterC2×C3D3×C42⋊C3
commutator, hypocenterC3×#95C2×C9
FrattiniC23×C3D3×A4
Fitting, cosocleC32×#95C2×C3
socleC23×C32C2×A4
prime radicalC23×C3×D3A4
LCSG ▷ C3×#95
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C3×#95⋊C9C2semidirect
9. #95⋊C9D3direct (N × H)
13. D3×#95C9semidirect
27. C3×#95C2×C9semidirect
76. #95D3×C9semidirect
169. D3#95⋊C9direct (N × H)
182. C3C2×#95⋊C9semidirect

Maximal subgroups

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

subgroupindex
C3×#95⋊C92
C3×D3×#953
C2×#95⋊C93
C2×D3×C22⋊C94