Finite Group Databasebeta

← D3×#64218 #13180370

Subgroups — D3×#64218 #13180370

Order 1728.

250 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 64 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×D3×#622C211yesmaximal, characteristic
2#11724242C211yesmaximal, characteristic, complemented
3C3×#64218C211yesmaximal, characteristic, complemented
4#11724093C212yesmaximal, complemented
5D3×#3771C212yesmaximal, complemented
6C2×#64218—31nomaximal
7C2×D3×C3⋊Dic3C411yescharacteristic
8C2×C3⋊#622C411yescharacteristic
9C2×C3×#622C2211yescharacteristic
10D3×#622C411yescharacteristic
11D3×#622C411yescharacteristic
12D3×#622C2211yescharacteristic
13D3×#622C2211yescharacteristic
14C3⋊#3771C2212yescomplemented
15C3×#3771C2212yescomplemented
16C22×#622—31no—
17#64218—31no—
18#64218—32no—
19#64218D311yescharacteristic, direct product factor
20C2×#3771—32no—
21C22×C32×D3C811yescharacteristic
22C2×C3⋊(C3⋊Dic3)C811yescharacteristic
23C2×C3×C3⋊Dic3C2×C411yescharacteristic
24D3×C3⋊Dic3C811yescharacteristic
25D3×C3⋊Dic3C811yescharacteristic
26D3×C3⋊Dic3C2×C411yescharacteristic
27D3×C3⋊Dic3C2×C411yescharacteristic
28C3⋊#622C2×C411yescharacteristic
29C3⋊#622C2×C411yescharacteristic
30C3×#622C2×C411yescharacteristic
31C3×#622C2311yescharacteristic
32D3×M32—91nomaximal
33C22×C3⋊Dic3—31no—
34C2×D3×Dic3—121no—
35C2×#622—31no—
36C2×#622—31no—
37C2×#622—31no—
38C2×#622—31no—
39C2×#622—31no—
40C2×#622C2×D311yescharacteristic
41#3771—32no—
42#3771C2×D312yescomplemented
43C22×C33C2×C811yescharacteristic
44C2×C32×D3—22no—
45C2×C32×D3C2×C811yescharacteristic
46C2×C32×D3C2×C811yescharacteristic
47C3⋊(C3⋊Dic3)C2×C811yescharacteristic
48C3⋊(C3⋊Dic3)C2×C811yescharacteristic
49C3×C3⋊Dic3C2×C811yescharacteristic
50C3×C3⋊Dic3C22×C411yescharacteristic
51C2×D3×C8—91no—
52C3×M32—91no—
53#812—91no—
54#798—92no—
55D3×C16—92no—
56C23×C32—31no—
57C22×C3×D3—41no—
58C2×C3⋊Dic3—31no—
59C2×C3⋊Dic3—31no—
60C2×C3⋊Dic3—31no—
61C2×C3⋊Dic3—31no—
62C2×C3⋊Dic3—31no—
63C2×C3⋊Dic3—121no—
64C2×C3⋊Dic3—241no—
65C2×C3⋊Dic3C4×D311yescharacteristic
66C2×C3×Dic3—121no—
67D3×Dic3—121no—
68D3×Dic3—121no—
69D3×Dic3—121no—
70D3×Dic3—121no—
71#622—31no—
72#622—31no—
73#622C4×D311yescharacteristic
74#622C22×D311yescharacteristic
75C2×M32—271noSylow
76C2×C33—21no—
77C2×C33C22×C811yescharacteristic
78C32×D3—21no—
79C32×D3M3212yescomplemented
80C22×Dic3—361no—
81C2×C4×D3—91no—
82C2×C3×C8—91no—
83C2×C3⋊C8—91no—
84D3×C8—91no—
85D3×C8—91no—
86D3×C8—91no—
87D3×C8—91no—
88C3×C16—92no—
89C3⋊C16—92no—
90C22×C32—31no—
91C22×C32—31no—
92C22×C32—41no—
93C22×C32—62no—
94C22×C32—81no—
95C22×C32D3×C811yescharacteristic
96C2×C3×D3—44no—
97C2×C3×D3—41no—
98C2×C3×D3—41no—
99C3⋊Dic3—31no—
100C3⋊Dic3—31no—
101C3⋊Dic3—121no—
102C3⋊Dic3—121no—
103C3⋊Dic3—241no—
104C3⋊Dic3—241no—
105C3⋊Dic3D3×C811yescharacteristic
106C3⋊Dic3C2×C4×D311yescharacteristic
107C3×Dic3—121no—
108C3×Dic3—121no—
109C22×C8—271no—
110M32—91no—
111M32—272no—
112M32—271no—
113C2×C16—272no—
114C33C2×M3211yescharacteristic, complemented, Sylow
115C23×C3—121no—
116C22×D3AGL(1,𝔽9)11yescharacteristic
117C2×C3×C4—91no—
118C2×Dic3—91no—
119C2×Dic3—121no—
120C2×Dic3—361no—
121C2×Dic3—361no—
122C2×Dic3—361no—
123C2×Dic3—361no—
124C2×Dic3—361no—
125C2×Dic3—721no—
126C4×D3—91no—
127C4×D3—91no—
128C4×D3—91no—
129C4×D3—91no—
130C3×C8—91no—
131C3×C8—91no—
132C3⋊C8—91no—
133C3⋊C8—91no—
134C2×C32—21no—
135C2×C32—32no—
136C2×C32—42no—
137C2×C32—41no—
138C2×C32—61no—
139C2×C32—82no—
140C2×C32—81no—
141C2×C32C2×D3×C811yescharacteristic
142C3×D3—42no—
143C3×D3—42no—
144C22×C4—271no—
145C2×C8—91no—
146C2×C8—271no—
147C2×C8—271no—
148C2×C8—271no—
149C2×C8—271no—
150C2×C8—271no—
151C16—92no—
152C16—272no—
153C22×C3—41no—
154C22×C3—81no—
155C22×C3—121no—
156C22×C3—121no—
157C22×C3—124no—
158C22×C3C2×AGL(1,𝔽9)11yescharacteristic
159C2×D3—22no—
160C2×D3C2×AGL(1,𝔽9)11yescharacteristic
161C2×D3C2×AGL(1,𝔽9)11yescharacteristic
162C3×C4—91no—
163C3×C4—91no—
164Dic3—91no—
165Dic3—91no—
166Dic3—121no—
167Dic3—121no—
168Dic3—361no—
169Dic3—361no—
170Dic3—721no—
171Dic3—721no—
172C32—41no—
173C32—81no—
174C32D3×M3211yescharacteristic, complemented
175C23—31no—
176C2×C4—91no—
177C2×C4—271no—
178C2×C4—271no—
179C2×C4—271no—
180C2×C4—271no—
181C2×C4—271no—
182C8—91no—
183C8—91no—
184C8—271no—
185C8—271no—
186C2×C3—21no—
187C2×C3—42no—
188C2×C3—41no—
189C2×C3—82no—
190C2×C3—81no—
191C2×C3—122no—
192C2×C3—122no—
193C2×C3C22×AGL(1,𝔽9)11yescharacteristic
194D3—21no—
195D3#6421812yesdirect product factor
196C22—31no—
197C22—31no—
198C22—62no—
199C22D3×AGL(1,𝔽9)11yescharacteristic
200C4—91no—
201C4—91no—
202C4—271no—
203C4—271no—
204C3—41no—
205C3—81no—
206C3C2×#6421811yescharacteristic, complemented
207C2—21no—
208C2—32no—
209C2—61no—
210C2C2×D3×AGL(1,𝔽9)11yescharacteristic
subgroupG/H
center, FrattiniC2C2×D3×AGL(1,𝔽9)
commutator, socleC2×C33C22×C8
FittingC22×C33C2×C8
prime radicalC22×C32×D3C8
cosocleC3×#622C23
hypercenterC22D3×AGL(1,𝔽9)
hypocenterC33C2×M32
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #11724242C2semidirect
3. C3×#64218C2semidirect
4. #11724093C2semidirect
5. D3×#3771C2semidirect
14. C3⋊#3771C22semidirect
15. C3×#3771C22semidirect
19. #64218D3direct (N × H)
42. #3771C2×D3semidirect
79. C32×D3M32semidirect
114. C33C2×M32semidirect
174. C32D3×M32semidirect
195. D3#64218direct (N × H)
206. C3C2×#64218semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6222
#117242422
C3×#642182
#117240932
D3×#37712
C2×#642183
D3×M329