Finite Group Databasebeta

← (C3⋊D3)⋊C3×#272 #72228660

Subgroups — (C3⋊D3)⋊C3×#272 #72228660

Order 2916.

1107 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 1107 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
1#13091501C211yesmaximal, characteristic, complemented
2H(3,𝔽3)×#272C211yesmaximal, characteristic, complemented
3H(3,𝔽3)×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
4C3⋊D3×#272C311yesmaximal, characteristic, complemented
5C3×D3×#272—31nomaximal
6C3×D3×(C3⋊D3)⋊C3—34nomaximal
7H(3,𝔽3)2C2211yescharacteristic, complemented, Sylow
8C3⋊(C3⋊#272)C2×C311yescharacteristic, complemented
9C3×C3⋊#272—31no—
10C3⋊D3×H(3,𝔽3)C2×C311yescharacteristic, complemented
11C32×#272—21no—
12C32×#272D311yescharacteristic, complemented
13C32×#272C2×C311yescharacteristic, complemented
14C3×C3⋊((C3⋊D3)⋊C3)—34no—
15C3×D3×H(3,𝔽3)—34no—
16C3×D3×H(3,𝔽3)—31no—
17C32×(C3⋊D3)⋊C3D314yescomplemented
18#92300—64no—
19(C3⋊D3)⋊H(3,𝔽3)—24no—
20C3×D3×C3⋊D3—34no—
21C32×D32—94no—
22C2×C3×#272—91no—
23C2×C3×(C3⋊D3)⋊C3—91no—
24D3×#272—31no—
25D3×#272—91no—
26D3×(C3⋊D3)⋊C3—312no—
27C32×H(3,𝔽3)—21no—
28C32×H(3,𝔽3)C2×D311yescharacteristic, complemented
29C32×H(3,𝔽3)C2×D314yescomplemented
30C32×H(3,𝔽3)C22×C311yescharacteristic, complemented
31C32⋊H(3,𝔽3)—24no—
32C32⋊H(3,𝔽3)—24no—
33C32⋊H(3,𝔽3)—44no—
34C3×C3⋊(C3⋊D3)—34no—
35C32×C3⋊D3—94no—
36C32×C3⋊D3C3×D314yescomplemented
37C33×D3—34no—
38C33×D3—34no—
39C33×D3—34no—
40C33×D3—64no—
41C2×C3×H(3,𝔽3)—91no—
42C2×C3×H(3,𝔽3)—91no—
43C3⋊#272—31no—
44C3⋊#272—64no—
45C3⋊#272—91no—
46C3⋊#272—184no—
47C3×#272—31no—
48C3×#272—31no—
49C3×#272—61no—
50C3×#272—91no—
51C3×#272—184no—
52C3×#272C3×D311yescharacteristic
53C3⋊((C3⋊D3)⋊C3)—312no—
54D3×H(3,𝔽3)—31no—
55D3×H(3,𝔽3)—312no—
56D3×H(3,𝔽3)—64no—
57D3×H(3,𝔽3)—612no—
58D3×H(3,𝔽3)—91no—
59C3×(C3⋊D3)⋊C3—24no—
60C3×(C3⋊D3)⋊C3—312no—
61C3×(C3⋊D3)⋊C3—91no—
62C3×(C3⋊D3)⋊C3—184no—
63C3×(C3⋊D3)⋊C3C3⋊D311yescharacteristic
64C2×C3×C3⋊D3—91no—
65C2×C32×D3—271no—
66C2×C32×D3—274no—
67D3×C3⋊D3—34no—
68C3×D32—94no—
69C3×D32—912no—
70C3×D32—274no—
71C2×#272—91no—
72C2×(C3⋊D3)⋊C3—93no—
73C34—24no—
74C34D3214yescomplemented
75C34C2×C3×D314yescomplemented
76C3×H(3,𝔽3)—24no—
77C3×H(3,𝔽3)—24no—
78C3×H(3,𝔽3)—24no—
79C3×H(3,𝔽3)—24no—
80C3×H(3,𝔽3)—31no—
81C3×H(3,𝔽3)—31no—
82C3×H(3,𝔽3)—312no—
83C3×H(3,𝔽3)—44no—
84C3×H(3,𝔽3)—44no—
85C3×H(3,𝔽3)—412no—
86C3×H(3,𝔽3)—64no—
87C3×H(3,𝔽3)—612no—
88C3×H(3,𝔽3)—64no—
89C3×H(3,𝔽3)—61no—
90C3×H(3,𝔽3)—124no—
91C3×H(3,𝔽3)C2×C3×D311yescharacteristic
92C3×H(3,𝔽3)C2×C3⋊D311yescharacteristic
93C2×C33—91no—
94C2×C33—94no—
95C2×C33—91no—
96C2×C33—181no—
97C3⋊(C3⋊D3)—34no—
98C3×C3⋊D3—34no—
99C3×C3⋊D3—912no—
100C3×C3⋊D3—94no—
101C3×C3⋊D3—91no—
102C3×C3⋊D3—184no—
103C3×C3⋊D3—274no—
104C3×C3⋊D3—544no—
105C3×C3⋊D3C3×C3⋊D311yescharacteristic
106C32×D3—31no—
107C32×D3—34no—
108C32×D3—312no—
109C32×D3—34no—
110C32×D3—34no—
111C32×D3—64no—
112C32×D3—612no—
113C32×D3—64no—
114C32×D3—94no—
115C32×D3—912no—
116C32×D3—94no—
117C32×D3—94no—
118C32×D3—184no—
119C32×D3—184no—
120C32×D3—184no—
121C32×D3—188no—
122C32×D3—274no—
123C32×D3—271no—
124C32×D3—544no—
125C2×H(3,𝔽3)—91no—
126C2×H(3,𝔽3)—93no—
127C2×H(3,𝔽3)—183no—
128C2×H(3,𝔽3)—184no—
129#272—91no—
130#272—184no—
131#272—544no—
132#272—548no—
133#272(C3⋊D3)⋊C311yescharacteristic, direct product factor
134(C3⋊D3)⋊C3—64no—
135(C3⋊D3)⋊C3—93no—
136(C3⋊D3)⋊C3—1812no—
137(C3⋊D3)⋊C3#27213yesdirect product factor
138C22×C32—811no—
139C2×C3⋊D3—91no—
140C2×C3×D3—273no—
141C2×C3×D3—274no—
142C2×C3×D3—271no—
143C2×C3×D3—2712no—
144C2×C3×D3—811no—
145D32—94no—
146D32—274no—
147C33—21no—
148C33—24no—
149C33—24no—
150C33—34no—
151C33—34no—
152C33—312no—
153C33—34no—
154C33—44no—
155C33—64no—
156C33—64no—
157C33—64no—
158C33—612no—
159C33—64no—
160C33—124no—
161C33—184no—
162C33—184no—
163C33—188no—
164C33C3×D3214yes—
165C33D3×C3⋊D311yescharacteristic
166C33C2×C3×C3⋊D311yescharacteristic
167H(3,𝔽3)—24no—
168H(3,𝔽3)—23no—
169H(3,𝔽3)—68no—
170H(3,𝔽3)—64no—
171H(3,𝔽3)—64no—
172H(3,𝔽3)—612no—
173H(3,𝔽3)—64no—
174H(3,𝔽3)—124no—
175H(3,𝔽3)—1212no—
176H(3,𝔽3)—124no—
177H(3,𝔽3)—128no—
178H(3,𝔽3)—124no—
179H(3,𝔽3)—3612no—
180H(3,𝔽3)C2×(C3⋊D3)⋊C311yescharacteristic, complemented
181H(3,𝔽3)C2×#27213yescomplemented
182C2×C32—91no—
183C2×C32—91no—
184C2×C32—94no—
185C2×C32—93no—
186C2×C32—91no—
187C2×C32—183no—
188C2×C32—181no—
189C2×C32—184no—
190C2×C32—271no—
191C2×C32—271no—
192C2×C32—2712no—
193C2×C32—541no—
194C2×C32—541no—
195C2×C32—541no—
196C2×C32—542no—
197C2×C32—811no—
198C3⋊D3—94no—
199C3⋊D3—91no—
200C3⋊D3—184no—
201C3⋊D3—274no—
202C3⋊D3—544no—
203C3⋊D3C3×#27211yescharacteristic, complemented
204C3×D3—34no—
205C3×D3—34no—
206C3×D3—33no—
207C3×D3—31no—
208C3×D3—64no—
209C3×D3—94no—
210C3×D3—94no—
211C3×D3—912no—
212C3×D3—91no—
213C3×D3—184no—
214C3×D3—184no—
215C3×D3—1812no—
216C3×D3—274no—
217C3×D3—2712no—
218C3×D3—274no—
219C3×D3—273no—
220C3×D3—271no—
221C3×D3—544no—
222C3×D3—5412no—
223C3×D3—811no—
224C3×D3—1624no—
225C22×C3—811no—
226C22×C3—813no—
227C2×D3—271no—
228C2×D3—274no—
229C2×D3—811no—
230C32—24no—
231C32—21no—
232C32—23no—
233C32—31no—
234C32—31no—
235C32—34no—
236C32—61no—
237C32—64no—
238C32—61no—
239C32—62no—
240C32—61no—
241C32—64no—
242C32—64no—
243C32—64no—
244C32—64no—
245C32—94no—
246C32—912no—
247C32—124no—
248C32—124no—
249C32—128no—
250C32—124no—
251C32—124no—
252C32—184no—
253C32—1812no—
254C32—184no—
255C32—1812no—
256C32—364no—
257C32—3612no—
258C32D3×(C3⋊D3)⋊C314yescomplemented
259C32D3×#27213yescomplemented
260C32C2×C3×#27211yescharacteristic, complemented
261C32C3×D3×C3⋊D311yescharacteristic
262C2×C3—93no—
263C2×C3—91no—
264C2×C3—91no—
265C2×C3—91no—
266C2×C3—181no—
267C2×C3—274no—
268C2×C3—271no—
269C2×C3—273no—
270C2×C3—541no—
271C2×C3—543no—
272C2×C3—544no—
273C2×C3—813no—
274C2×C3—811no—
275D3—34no—
276D3—31no—
277D3—91no—
278D3—274no—
279D3—271no—
280D3—544no—
281D3—811no—
282D3—1624no—
283C22—811noSylow
284C3—21no—
285C3—34no—
286C3—31no—
287C3—33no—
288C3—64no—
289C3—61no—
290C3—63no—
291C3—184no—
292C3—184no—
293C3—364no—
294C3C3⋊D3×(C3⋊D3)⋊C311yescharacteristic
295C3C3×D3×#27211yescharacteristic
296C2—91no—
297C2—91no—
298C2—811no—
subgroupG/H
center, hypercenterC3C3⋊D3×(C3⋊D3)⋊C3
commutator, cosocle, hypocenterC32×H(3,𝔽3)C22×C3
Frattini, socleC32C3×D3×C3⋊D3
FittingH(3,𝔽3)2C22
LCSG ▷ C32×H(3,𝔽3)
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. #13091501C2semidirect
2. H(3,𝔽3)×#272C2semidirect
3. H(3,𝔽3)×(C3⋊D3)⋊C3C2semidirect
4. C3⋊D3×#272C3semidirect
7. H(3,𝔽3)2C22semidirect
8. C3⋊(C3⋊#272)C2×C3semidirect
10. C3⋊D3×H(3,𝔽3)C2×C3semidirect
12. C32×#272D3semidirect
13. C32×#272C2×C3semidirect
17. C32×(C3⋊D3)⋊C3D3semidirect
28. C32×H(3,𝔽3)C2×D3semidirect
29. C32×H(3,𝔽3)C2×D3semidirect
30. C32×H(3,𝔽3)C22×C3semidirect
36. C32×C3⋊D3C3×D3semidirect
74. C34D32semidirect
75. C34C2×C3×D3semidirect
133. #272(C3⋊D3)⋊C3direct (N × H)
137. (C3⋊D3)⋊C3#272direct (N × H)
180. H(3,𝔽3)C2×(C3⋊D3)⋊C3semidirect
181. H(3,𝔽3)C2×#272semidirect
203. C3⋊D3C3×#272semidirect
258. C32D3×(C3⋊D3)⋊C3semidirect
259. C32D3×#272semidirect
260. C32C2×C3×#272semidirect

Maximal subgroups

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

subgroupindex
#130915012
H(3,𝔽3)×#2722
H(3,𝔽3)×(C3⋊D3)⋊C32
C3⋊D3×#2723
C3×D3×#2723
C3×D3×(C3⋊D3)⋊C33