Finite Group Databasebeta

← C3×D3×#95⋊C3 #13157026

Subgroups — C3×D3×#95⋊C3 #13157026

Order 1728.

399 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 399 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C32×#95⋊C3C211yesmaximal, characteristic, complemented
2C3×D3×#95C311yesmaximal, characteristic, complemented
3C2×C3×#95⋊C3—31nomaximal
4D3×#95⋊C3C313yesmaximal, direct product factor
5C2×C3×D3×A4—41nomaximal
6C22×C3×C4×D3—31no—
7C32×#95C2×C311yescharacteristic, complemented
8C3×C3⋊#95—31no—
9C3×#95⋊C3—21no—
10C3×#95⋊C3—23no—
11C3×#95⋊C3D311yescharacteristic, direct product factor
12C3×#95⋊C3C2×C313yescomplemented
13C2×C32×A4—41no—
14C3×D3×A4—42no—
15C2×C3×#95—31no—
16D3×#95C3211yescharacteristic, complemented
17C2×#95⋊C3—33no—
18C23×C3×D3A411yescharacteristic
19C22×C3×A4—121no—
20C2×D3×A4—43no—
21C22×C32×C4—31no—
22C22×C3×Dic3—31no—
23C2×C3×C4×D3—32no—
24C2×C3×C4×D3—32no—
25C2×C3×C4×D3—64no—
26C2×C32×D3—161no—
27C32×A4—41no—
28C23×C3×C4—91no—
29C22×C4×D3—31no—
30C3×#95—21no—
31C3×#95—91no—
32C3×#95C3×D311yescharacteristic, complemented
33C3×#95C2×C3211yescharacteristic, complemented
34C3⋊#95—31no—
35#95⋊C3—23no—
36#95⋊C3C3×D313yesdirect product factor
37C23×C32C2×A411yescharacteristic
38C22×C3×D3—31no—
39C22×C3×D3—31no—
40C22×C3×D3—32no—
41C22×C3×D3SL(2,𝔽3)12yes—
42C2×C3×A4—41no—
43C2×C3×A4—43no—
44C2×C3×A4—83no—
45C2×C3×A4—81no—
46C2×C3×A4—122no—
47D3×A4—46no—
48C2×C32×C4—32no—
49C2×C32×C4—62no—
50C2×C3×Dic3—32no—
51C2×C3×Dic3—62no—
52C3×C4×D3—64no—
53C3×C4×D3—64no—
54C2×#95—31noSylow
55C2×C33—161no—
56C32×D3—162no—
57C24×C3—31no—
58C23×D3C3×A411yescharacteristic
59C22×A4—123no—
60C22×C3×C4—31no—
61C22×C3×C4—31no—
62C22×C3×C4—61no—
63C22×C3×C4—92no—
64C22×C3×C4—92no—
65C22×C3×C4—91no—
66C22×C3×C4—184no—
67C22×Dic3—31no—
68C2×C4×D3—32no—
69C2×C4×D3—32no—
70C2×C4×D3—64no—
71C22×C32—31no—
72C22×C32—31no—
73C22×C32—481no—
74C22×C32C2×SL(2,𝔽3)11yescharacteristic
75C2×C3×D3—32no—
76C2×C3×D3—31no—
77C2×C3×D3—32no—
78C2×C3×D3—32no—
79C2×C3×D3—32no—
80C2×C3×D3—163no—
81C2×C3×D3C42⋊C311yescharacteristic
82C3×A4—41no—
83C3×A4—43no—
84C3×A4—83no—
85C3×A4—81no—
86C32×C4—62no—
87C3×Dic3—62no—
88C23×C4—91no—
89#95—91no—
90#95C32×D311yescharacteristic, complemented
91C33—161noSylow
92C23×C3—21no—
93C23×C3—32no—
94C23×C3—91no—
95C23×C3—91no—
96C23×C3—92no—
97C23×C3D3×A411yescharacteristic
98C23×C3C2×C3×A411yescharacteristic
99C22×D3—31no—
100C22×D3—31no—
101C22×D3—32no—
102C22×D3C3×SL(2,𝔽3)12yes—
103C2×A4—43no—
104C2×A4—83no—
105C2×A4—126no—
106C2×C3×C4—32no—
107C2×C3×C4—32no—
108C2×C3×C4—62no—
109C2×C3×C4—62no—
110C2×C3×C4—62no—
111C2×C3×C4—92no—
112C2×C3×C4—122no—
113C2×C3×C4—184no—
114C2×C3×C4—184no—
115C2×C3×C4—182no—
116C2×Dic3—32no—
117C2×Dic3—62no—
118C4×D3—64no—
119C4×D3—64no—
120C2×C32—31no—
121C2×C32—31no—
122C2×C32—161no—
123C2×C32—163no—
124C2×C32—323no—
125C2×C32—321no—
126C2×C32—482no—
127C2×C32C2×C42⋊C311yescharacteristic
128C3×D3—32no—
129C3×D3—166no—
130C3×D3#95⋊C312yesdirect product factor
131C24—31no—
132C22×C4—31no—
133C22×C4—92no—
134C22×C4—92no—
135C22×C4—91no—
136C22×C4—184no—
137C22×C3—21no—
138C22×C3—31no—
139C22×C3—31no—
140C22×C3—31no—
141C22×C3—31no—
142C22×C3—31no—
143C22×C3—61no—
144C22×C3—61no—
145C22×C3—92no—
146C22×C3—92no—
147C22×C3—92no—
148C22×C3—92no—
149C22×C3—91no—
150C22×C3—483no—
151C22×C3D3×SL(2,𝔽3)11yescharacteristic
152C22×C3C2×C3×SL(2,𝔽3)11yescharacteristic
153C2×D3—32no—
154C2×D3—31no—
155C2×D3—32no—
156C2×D3—32no—
157C2×D3—32no—
158C2×D3C3×C42⋊C311yescharacteristic
159A4—43no—
160A4—83no—
161C3×C4—62no—
162C3×C4—62no—
163C3×C4—122no—
164C3×C4—182no—
165Dic3—62no—
166C32—161no—
167C32—163no—
168C32—323no—
169C32—321no—
170C32C2×#95⋊C311yescharacteristic, complemented
171C23—32no—
172C23—91no—
173C23—91no—
174C23—92no—
175C23C3×D3×A411yescharacteristic
176C2×C4—32no—
177C2×C4—62no—
178C2×C4—92no—
179C2×C4—184no—
180C2×C4—184no—
181C2×C4—182no—
182C2×C3—21no—
183C2×C3—31no—
184C2×C3—31no—
185C2×C3—32no—
186C2×C3—31no—
187C2×C3—31no—
188C2×C3—61no—
189C2×C3—61no—
190C2×C3—92no—
191C2×C3—163no—
192C2×C3—323no—
193C2×C3—486no—
194C2×C3D3×C42⋊C311yescharacteristic
195C2×C3C2×C3×C42⋊C311yescharacteristic
196D3—32no—
197D3C3×#95⋊C312yesdirect product factor
198C22—31no—
199C22—31no—
200C22—31no—
201C22—92no—
202C22—92no—
203C22—92no—
204C22—92no—
205C22—91no—
206C22C3×D3×SL(2,𝔽3)11yescharacteristic
207C4—62no—
208C4—182no—
209C3—21no—
210C3—163no—
211C3—323no—
212C3D3×#95⋊C311yescharacteristic, direct product factor
213C3C2×C3×#95⋊C311yescharacteristic, complemented
214C2—31no—
215C2—31no—
216C2—32no—
217C2—92no—
218C2C3×D3×C42⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2×C3D3×C42⋊C3
commutator, cosocle, hypocenterC3×#95C2×C32
FrattiniC23C3×D3×A4
FittingC32×#95C2×C3
socleC23×C32C2×A4
LCSG ▷ C3×#95
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C32×#95⋊C3C2semidirect
2. C3×D3×#95C3semidirect
4. D3×#95⋊C3C3direct (N × H)
7. C32×#95C2×C3semidirect
11. C3×#95⋊C3D3direct (N × H)
12. C3×#95⋊C3C2×C3semidirect
16. D3×#95C32semidirect
32. C3×#95C3×D3semidirect
33. C3×#95C2×C32semidirect
36. #95⋊C3C3×D3direct (N × H)
90. #95C32×D3semidirect
130. C3×D3#95⋊C3direct (N × H)
170. C32C2×#95⋊C3semidirect
197. D3C3×#95⋊C3direct (N × H)
212. C3D3×#95⋊C3direct (N × H)
213. C3C2×C3×#95⋊C3semidirect

Maximal subgroups

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

subgroupindex
C32×#95⋊C32
C3×D3×#953
C2×C3×#95⋊C33
D3×#95⋊C33
C2×C3×D3×A44