Subgroups — C₃×#69884 #11795936

Order 1152.

385 conjugacy classes of subgroups.

The subgroup lattice has 213 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#405	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#812	C₂	1	2	yes	maximal
3	C₃×#4466	C₂	1	4	yes	maximal, complemented
4	C₃×#2110	—	3	1	no	maximal
5	#69884	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃²×M₁₆	C₄	1	1	yes	characteristic
7	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
8	C₃²×#117	C₄	1	1	yes	characteristic
9	C₃²×#97	C₂²	1	2	yes	—
10	C₃²×C₄×C₈	C₄	1	2	yes	—
11	C₃×#812	C₄	1	4	yes	complemented
12	C₃×#812	C₂²	1	4	yes	—
13	C₂×C₃×C₃⋊C₁₆	C₄	1	4	yes	complemented
14	C₂×C₃×M₃₂	—	3	2	no	—
15	C₃×#405	—	2	1	no	—
16	C₃×#405	D₃	1	1	yes	characteristic
17	C₃×#405	C₂×C₃	1	1	yes	characteristic
18	C₂×#812	C₂×C₃	1	2	yes	—
19	C₃×#347	—	3	4	no	—
20	#4466	C₂×C₃	1	4	yes	complemented
21	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
22	C₃²×M₁₆	—	2	2	no	—
23	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
24	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
25	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
26	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
27	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
28	C₃²×C₄⋊C₄	—	2	1	no	—
29	C₃²×C₂²⋊C₄	—	2	1	no	—
30	C₃²×C₄²	C₂×C₄	1	2	yes	—
31	C₃×C₃⋊C₁₆	C₂×C₄	1	8	yes	—
32	#2110	—	3	1	no	Sylow
33	C₂×C₃×M₁₆	—	2	1	no	—
34	C₂×C₃×M₁₆	Dic₃	1	1	yes	characteristic
35	C₂×C₃×M₁₆	C₃×C₄	1	1	yes	characteristic
36	C₂²×C₃×C₈	—	2	1	no	—
37	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
38	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
39	C₃×#117	—	2	1	no	—
40	C₃×#117	Dic₃	1	1	yes	characteristic
41	C₃×#117	C₃×C₄	1	1	yes	characteristic
42	C₃×M₃₂	—	3	4	no	—
43	C₃×M₃₂	—	3	4	no	—
44	C₂×C₃×C₁₆	—	3	4	no	—
45	C₃×#97	—	2	2	no	—
46	C₃×#97	C₂×D₃	1	2	yes	—
47	C₃×#97	C₂²×C₃	1	2	yes	—
48	C₃×C₄×C₈	—	2	2	no	—
49	C₃×C₄×C₈	Dic₃	1	2	yes	—
50	C₃×C₄×C₈	C₃×C₄	1	2	yes	—
51	#812	C₃×C₄	1	4	yes	complemented
52	#812	C₂²×C₃	1	4	yes	—
53	C₂×C₃⋊C₁₆	C₃×C₄	1	4	yes	complemented
54	C₂³×C₃²	M₁₆	1	1	yes	characteristic
55	C₂×C₃²×C₄	—	2	2	no	—
56	C₂×C₃²×C₄	C₄²	1	2	yes	—
57	C₂×C₃²×C₄	M₁₆	1	1	yes	characteristic
58	C₂×C₃²×C₄	M₁₆	1	2	yes	—
59	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
60	C₃²×C₈	—	2	2	no	—
61	C₃²×C₈	C₄²	1	1	yes	characteristic
62	C₃²×C₈	C₄²	1	1	yes	characteristic
63	C₃²×C₈	C₂²×C₄	1	2	yes	—
64	C₂×M₃₂	—	3	2	no	—
65	#405	C₃×D₃	1	1	yes	characteristic
66	#347	—	3	4	no	—
67	C₂²×C₃×C₄	—	2	1	no	—
68	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
69	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
70	C₃×M₁₆	—	2	4	no	—
71	C₃×M₁₆	—	2	2	no	—
72	C₃×M₁₆	—	2	2	no	—
73	C₂×C₃×C₈	—	2	2	no	—
74	C₂×C₃×C₈	—	2	2	no	—
75	C₂×C₃×C₈	—	2	1	no	—
76	C₂×C₃×C₈	—	2	2	no	—
77	C₂×C₃×C₈	—	2	1	no	—
78	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
79	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
80	C₂×C₃×C₈	C₂×Dic₃	1	2	yes	—
81	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
82	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
83	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
84	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
85	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
86	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
87	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
88	C₃×C₄⋊C₄	—	2	2	no	—
89	C₃×C₄⋊C₄	—	2	1	no	—
90	C₃×C₄⋊C₄	—	2	1	no	—
91	C₃×C₂²⋊C₄	—	2	2	no	—
92	C₃×C₂²⋊C₄	—	2	1	no	—
93	C₃×C₂²⋊C₄	—	2	1	no	—
94	C₃×C₄²	—	2	2	no	—
95	C₃×C₄²	C₂×Dic₃	1	2	yes	—
96	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
97	C₃×C₁₆	—	3	8	no	—
98	C₃⋊C₁₆	C₂×C₃×C₄	1	8	yes	—
99	C₂²×C₃²	—	4	1	no	—
100	C₂²×C₃²	#97	1	2	yes	—
101	C₂²×C₃²	C₂×M₁₆	1	1	yes	characteristic
102	C₃²×C₄	—	4	2	no	—
103	C₃²×C₄	#97	1	2	yes	—
104	C₃²×C₄	C₂×C₄²	1	1	yes	characteristic
105	C₃²×C₄	C₂×M₁₆	1	1	yes	characteristic
106	C₂×M₁₆	C₃×Dic₃	1	1	yes	characteristic
107	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
108	#117	C₃×Dic₃	1	1	yes	characteristic
109	M₃₂	—	3	4	no	—
110	M₃₂	—	3	4	no	—
111	C₂×C₁₆	—	3	4	no	—
112	#97	C₂×C₃×D₃	1	2	yes	—
113	C₄×C₈	C₃×Dic₃	1	2	yes	—
114	C₂³×C₃	—	2	1	no	—
115	C₂³×C₃	#208	1	1	yes	characteristic
116	C₂³×C₃	C₃×M₁₆	1	1	yes	characteristic
117	C₂×C₃×C₄	—	2	4	no	—
118	C₂×C₃×C₄	—	2	2	no	—
119	C₂×C₃×C₄	—	2	2	no	—
120	C₂×C₃×C₄	—	2	1	no	—
121	C₂×C₃×C₄	—	2	2	no	—
122	C₂×C₃×C₄	—	2	2	no	—
123	C₂×C₃×C₄	—	2	1	no	—
124	C₂×C₃×C₄	#208	1	1	yes	characteristic
125	C₂×C₃×C₄	#208	1	2	yes	—
126	C₂×C₃×C₄	C₄×Dic₃	1	2	yes	—
127	C₂×C₃×C₄	C₃×C₄²	1	2	yes	—
128	C₂×C₃×C₄	C₃×M₁₆	1	1	yes	characteristic
129	C₂×C₃×C₄	C₃×M₁₆	1	2	yes	—
130	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
131	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
132	C₃×C₈	—	2	4	no	—
133	C₃×C₈	—	2	2	no	—
134	C₃×C₈	—	2	2	no	—
135	C₃×C₈	—	2	1	no	—
136	C₃×C₈	—	2	1	no	—
137	C₃×C₈	—	2	2	no	—
138	C₃×C₈	C₄×Dic₃	1	1	yes	characteristic
139	C₃×C₈	C₄×Dic₃	1	1	yes	characteristic
140	C₃×C₈	C₃×C₄²	1	1	yes	characteristic
141	C₃×C₈	C₃×C₄²	1	1	yes	characteristic
142	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
143	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
144	C₂×C₃²	—	2	1	no	—
145	C₂×C₃²	—	2	2	no	—
146	C₂×C₃²	C₂×#97	1	1	yes	characteristic
147	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
148	M₁₆	—	2	2	no	—
149	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
150	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
151	C₂×C₈	C₂×C₃×Dic₃	1	2	yes	—
152	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
153	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
154	C₄⋊C₄	—	2	1	no	—
155	C₂²⋊C₄	—	2	1	no	—
156	C₄²	C₂×C₃×Dic₃	1	2	yes	—
157	C₁₆	—	3	8	no	—
158	C₂²×C₃	—	2	1	no	—
159	C₂²×C₃	—	2	2	no	—
160	C₂²×C₃	—	4	1	no	—
161	C₂²×C₃	—	4	1	no	—
162	C₂²×C₃	—	4	2	no	—
163	C₂²×C₃	#803	1	2	yes	—
164	C₂²×C₃	C₃×#97	1	2	yes	—
165	C₂²×C₃	C₂×#208	1	1	yes	characteristic
166	C₂²×C₃	C₂×C₃×M₁₆	1	1	yes	characteristic
167	C₃×C₄	—	2	1	no	—
168	C₃×C₄	—	2	1	no	—
169	C₃×C₄	—	2	2	no	—
170	C₃×C₄	—	4	4	no	—
171	C₃×C₄	—	4	2	no	—
172	C₃×C₄	—	4	2	no	—
173	C₃×C₄	#803	1	2	yes	—
174	C₃×C₄	C₃×#97	1	2	yes	—
175	C₃×C₄	C₂×#208	1	1	yes	characteristic
176	C₃×C₄	C₂×C₄×Dic₃	1	1	yes	characteristic
177	C₃×C₄	C₂×C₃×C₄²	1	1	yes	characteristic
178	C₃×C₄	C₂×C₃×M₁₆	1	1	yes	characteristic
179	C₃²	#2110	1	1	yes	characteristic, complemented, Sylow
180	C₂³	C₃×#208	1	1	yes	characteristic
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	C₃×#208	1	2	yes	—
183	C₂×C₄	C₃×#208	1	1	yes	characteristic
184	C₂×C₄	C₃×C₄×Dic₃	1	2	yes	—
185	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
186	C₈	—	2	2	no	—
187	C₈	C₃×C₄×Dic₃	1	1	yes	characteristic
188	C₈	C₃×C₄×Dic₃	1	1	yes	characteristic
189	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
190	C₂×C₃	—	2	2	no	—
191	C₂×C₃	—	2	1	no	—
192	C₂×C₃	—	2	2	no	—
193	C₂×C₃	—	2	1	no	—
194	C₂×C₃	—	2	2	no	—
195	C₂×C₃	—	2	1	no	—
196	C₂×C₃	—	4	2	no	—
197	C₂×C₃	C₂×#803	1	1	yes	characteristic
198	C₂×C₃	C₂×C₃×#97	1	1	yes	characteristic
199	C₂²	—	4	1	no	—
200	C₂²	C₃×#803	1	2	yes	—
201	C₂²	C₂×C₃×#208	1	1	yes	characteristic
202	C₄	—	4	2	no	—
203	C₄	C₃×#803	1	2	yes	—
204	C₄	C₂×C₃×#208	1	1	yes	characteristic
205	C₄	C₂×C₃×C₄×Dic₃	1	1	yes	characteristic
206	C₃	—	2	1	no	—
207	C₃	#69884	1	1	yes	characteristic, direct product factor
208	C₃	C₃×#2110	1	1	yes	characteristic, complemented
209	C₂	—	2	1	no	—
210	C₂	—	2	2	no	—
211	C₂	C₂×C₃×#803	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₈	C₄×Dic₃
commutator	C₃×C₄	C₂×C₃×C₄²
Frattini	C₂×C₈	C₂²×C₃×D₃
Fitting	C₃²×#405	C₂
socle	C₂×C₃²	C₂×#97
prime radical	C₂³×C₃²	M₁₆
cosocle	C₂×C₃×C₈	C₂³×C₃
hypercenter	C₃×#405	D₃
hypocenter	C₃	C₃×#2110
LCS	G ▷ C₃×C₄ ▷ C₃
UCS	C₁ ◁ C₃×C₈ ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
3. C₃×#4466	C₂	semidirect
5. #69884	C₃	direct (N × H)
11. C₃×#812	C₄	semidirect
13. C₂×C₃×C₃⋊C₁₆	C₄	semidirect
20. #4466	C₂×C₃	semidirect
51. #812	C₃×C₄	semidirect
53. C₂×C₃⋊C₁₆	C₃×C₄	semidirect
179. C₃²	#2110	semidirect
207. C₃	#69884	direct (N × H)
208. C₃	C₃×#2110	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#405	2
C₂×C₃×#812	2
C₃×#4466	2
C₃×#2110	3
#69884	3

Subgroups — C3×#69884 #11795936

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#69884 #11795936