Subgroups — C₃×Dic₃×#97 #11783018

Order 1152.

793 conjugacy classes of subgroups.

The subgroup lattice has 263 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#97	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#815	C₂	1	2	yes	maximal
3	C₂×C₃×C₈×Dic₃	C₂	1	2	yes	maximal
4	C₃×C₄²×Dic₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×#803	C₂	1	1	yes	maximal, characteristic
6	C₃×C₄×#97	—	3	1	no	maximal
7	Dic₃×#97	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂²×C₃²×C₈	C₂²	1	2	yes	—
9	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₄×Dic₃	C₄	1	4	yes	—
11	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
14	C₃²×#97	C₄	1	4	yes	complemented
15	C₃×#815	C₄	1	8	yes	complemented
16	C₃×C₈×Dic₃	C₄	1	8	yes	complemented
17	C₃×#803	C₄	1	4	yes	complemented
18	C₂×C₃×#97	—	2	1	no	—
19	C₂×C₃×#97	—	3	2	no	—
20	C₂×C₃×#97	—	3	1	no	—
21	C₂×C₃×#97	D₃	1	1	yes	characteristic
22	C₂×C₃×#97	C₂×C₃	1	1	yes	characteristic
23	C₂×C₃×C₄×C₈	—	3	2	no	—
24	C₃×C₄³	—	3	1	no	—
25	C₂×#815	C₂×C₃	1	2	yes	—
26	C₂×C₈×Dic₃	C₂×C₃	1	2	yes	—
27	C₄²×Dic₃	C₂×C₃	1	1	yes	characteristic
28	C₂×#803	C₂×C₃	1	1	yes	characteristic
29	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
30	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
31	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
32	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
33	C₂×C₃²×C₈	C₂×C₄	1	4	yes	—
34	C₂×C₃²×C₈	C₂×C₄	1	4	yes	—
35	C₂×C₃²×C₈	C₂×C₄	1	4	yes	—
36	C₃²×C₄²	C₂×C₄	1	2	yes	—
37	C₃²×C₄²	C₂×C₄	1	2	yes	—
38	C₃×C₄×Dic₃	—	2	8	no	—
39	C₃×C₄×Dic₃	C₂×C₄	1	4	yes	—
40	C₃×C₄×Dic₃	C₂×C₄	1	4	yes	—
41	C₂×C₃×C₃⋊C₈	C₂×C₄	1	4	yes	—
42	C₂×C₃×C₃⋊C₈	C₂×C₄	1	4	yes	—
43	C₂×C₃×C₃⋊C₈	C₂×C₄	1	4	yes	—
44	C₄×#97	—	3	1	no	Sylow
45	C₂²×C₃×C₈	—	2	2	no	—
46	C₂²×C₃×C₈	—	3	2	no	—
47	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
48	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
49	C₂×C₃×C₄²	—	2	1	no	—
50	C₂×C₃×C₄²	—	3	1	no	—
51	C₂×C₃×C₄²	—	3	1	no	—
52	C₂×C₃×C₄²	—	3	4	no	—
53	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
54	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
55	C₂×C₄×Dic₃	C₃×C₄	1	4	yes	—
56	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
57	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
58	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
59	C₃×#97	—	2	4	no	—
60	C₃×#97	—	3	8	no	—
61	C₃×#97	—	3	4	no	—
62	C₃×#97	Dic₃	1	4	yes	direct product factor
63	C₃×#97	C₃×C₄	1	4	yes	complemented
64	C₃×C₄×C₈	—	3	8	no	—
65	#815	C₃×C₄	1	8	yes	complemented
66	C₈×Dic₃	C₃×C₄	1	8	yes	complemented
67	#803	C₃×C₄	1	4	yes	complemented
68	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₃²×C₄	—	2	4	no	—
70	C₂×C₃²×C₄	C₄²	1	4	yes	—
71	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
73	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
74	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₃×Dic₃	—	2	4	no	—
76	C₂×C₃×Dic₃	C₄²	1	4	yes	—
77	C₂×C₃×Dic₃	C₄²	1	4	yes	—
78	C₂×C₃×Dic₃	M₁₆	1	8	yes	—
79	C₃²×C₈	C₄²	1	8	yes	complemented
80	C₃×C₃⋊C₈	C₄²	1	8	yes	complemented
81	C₂×#97	—	3	2	no	—
82	C₂×#97	—	3	1	no	—
83	C₂×#97	C₃×D₃	1	1	yes	characteristic
84	C₂×C₄×C₈	—	3	2	no	—
85	C₄³	—	3	1	no	—
86	C₂²×C₃×C₄	—	2	2	no	—
87	C₂²×C₃×C₄	—	2	1	no	—
88	C₂²×C₃×C₄	—	3	2	no	—
89	C₂²×C₃×C₄	—	3	2	no	—
90	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
91	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
92	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
93	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
94	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
95	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
96	C₂×C₃×C₈	—	2	4	no	—
97	C₂×C₃×C₈	—	2	4	no	—
98	C₂×C₃×C₈	—	2	4	no	—
99	C₂×C₃×C₈	—	3	4	no	—
100	C₂×C₃×C₈	—	3	4	no	—
101	C₂×C₃×C₈	—	3	4	no	—
102	C₂×C₃×C₈	C₄×D₃	1	4	yes	—
103	C₂×C₃×C₈	C₄×D₃	1	4	yes	—
104	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	—
105	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	—
106	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	—
107	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	—
108	C₃×C₄²	—	2	2	no	—
109	C₃×C₄²	—	2	2	no	—
110	C₃×C₄²	—	3	4	no	—
111	C₃×C₄²	—	3	4	no	—
112	C₃×C₄²	—	6	8	no	—
113	C₃×C₄²	C₄×D₃	1	2	yes	—
114	C₃×C₄²	C₂×Dic₃	1	2	yes	—
115	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
116	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
117	C₄×Dic₃	—	2	8	no	—
118	C₄×Dic₃	C₂×C₃×C₄	1	4	yes	—
119	C₄×Dic₃	C₂×C₃×C₄	1	4	yes	—
120	C₂×C₃⋊C₈	C₂×C₃×C₄	1	4	yes	—
121	C₂×C₃⋊C₈	C₂×C₃×C₄	1	4	yes	—
122	C₂×C₃⋊C₈	C₂×C₃×C₄	1	4	yes	—
123	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
124	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
125	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
126	C₂²×C₃²	C₂×M₁₆	1	4	yes	—
127	C₃²×C₄	—	2	4	no	—
128	C₃²×C₄	C₂×C₄²	1	2	yes	—
129	C₃²×C₄	C₂×C₄²	1	2	yes	—
130	C₃×Dic₃	—	2	4	no	—
131	C₃×Dic₃	#97	1	8	yes	direct product factor
132	C₂²×C₈	—	3	2	no	—
133	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
134	C₂×C₄²	—	3	1	no	—
135	C₂×C₄²	—	3	1	no	—
136	C₂×C₄²	—	3	4	no	—
137	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
138	#97	—	3	8	no	—
139	#97	—	3	4	no	—
140	#97	C₃×Dic₃	1	4	yes	direct product factor
141	C₄×C₈	—	3	8	no	—
142	C₂³×C₃	—	2	1	no	—
143	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
144	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
145	C₂×C₃×C₄	—	2	4	no	—
146	C₂×C₃×C₄	—	2	4	no	—
147	C₂×C₃×C₄	—	2	4	no	—
148	C₂×C₃×C₄	—	2	1	no	—
149	C₂×C₃×C₄	—	2	2	no	—
150	C₂×C₃×C₄	—	2	2	no	—
151	C₂×C₃×C₄	—	2	1	no	—
152	C₂×C₃×C₄	—	3	4	no	—
153	C₂×C₃×C₄	—	3	8	no	—
154	C₂×C₃×C₄	—	3	4	no	—
155	C₂×C₃×C₄	—	4	4	no	—
156	C₂×C₃×C₄	—	6	4	no	—
157	C₂×C₃×C₄	C₄×Dic₃	1	4	yes	—
158	C₂×C₃×C₄	C₃×C₄²	1	4	yes	—
159	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
160	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
161	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
162	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
163	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
164	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
165	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
166	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
167	C₂×Dic₃	—	2	4	no	—
168	C₂×Dic₃	C₃×C₄²	1	4	yes	—
169	C₂×Dic₃	C₃×C₄²	1	4	yes	—
170	C₂×Dic₃	C₃×M₁₆	1	8	yes	—
171	C₃×C₈	—	2	8	no	—
172	C₃×C₈	—	3	8	no	—
173	C₃×C₈	C₄×Dic₃	1	8	yes	complemented
174	C₃×C₈	C₃×C₄²	1	8	yes	complemented
175	C₃⋊C₈	C₃×C₄²	1	8	yes	complemented
176	C₂×C₃²	C₄³	1	1	yes	characteristic
177	C₂×C₃²	C₂×#97	1	2	yes	—
178	C₂×C₃²	C₄×M₁₆	1	2	yes	—
179	C₂×C₃²	C₄×M₁₆	1	2	yes	—
180	C₂²×C₄	—	3	2	no	—
181	C₂²×C₄	—	3	2	no	—
182	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
183	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
184	C₂×C₈	—	3	4	no	—
185	C₂×C₈	—	3	4	no	—
186	C₂×C₈	—	3	4	no	—
187	C₂×C₈	C₃×C₄×D₃	1	4	yes	—
188	C₂×C₈	C₃×C₄×D₃	1	4	yes	—
189	C₂×C₈	C₂×C₃×Dic₃	1	4	yes	—
190	C₄²	—	3	4	no	—
191	C₄²	—	3	4	no	—
192	C₄²	—	6	8	no	—
193	C₄²	C₃×C₄×D₃	1	2	yes	—
194	C₄²	C₂×C₃×Dic₃	1	2	yes	—
195	C₂²×C₃	—	2	4	no	—
196	C₂²×C₃	—	2	1	no	—
197	C₂²×C₃	—	2	1	no	—
198	C₂²×C₃	—	2	1	no	—
199	C₂²×C₃	C₄²×D₃	1	1	yes	characteristic
200	C₂²×C₃	C₄²×D₃	1	1	yes	characteristic
201	C₂²×C₃	D₃×M₁₆	1	4	yes	—
202	C₂²×C₃	C₂×C₄×Dic₃	1	1	yes	characteristic
203	C₂²×C₃	C₂×C₃×C₄²	1	1	yes	characteristic
204	C₂²×C₃	C₂×C₃×C₄²	1	1	yes	characteristic
205	C₂²×C₃	C₂×C₃×C₄²	1	1	yes	characteristic
206	C₂²×C₃	C₂×C₃×M₁₆	1	4	yes	—
207	C₃×C₄	—	2	4	no	—
208	C₃×C₄	—	2	4	no	—
209	C₃×C₄	—	2	2	no	—
210	C₃×C₄	—	2	2	no	—
211	C₃×C₄	—	3	8	no	—
212	C₃×C₄	—	4	4	no	—
213	C₃×C₄	—	6	4	no	—
214	C₃×C₄	C₄²×D₃	1	2	yes	—
215	C₃×C₄	C₂×C₄×Dic₃	1	2	yes	—
216	C₃×C₄	C₂×C₃×C₄²	1	2	yes	—
217	C₃×C₄	C₂×C₃×C₄²	1	2	yes	—
218	Dic₃	—	2	4	no	—
219	Dic₃	C₃×#97	1	8	yes	direct product factor
220	C₃²	C₄×#97	1	1	yes	characteristic, complemented, Sylow
221	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
222	C₂×C₄	—	2	4	no	—
223	C₂×C₄	—	3	8	no	—
224	C₂×C₄	—	3	4	no	—
225	C₂×C₄	—	3	4	no	—
226	C₂×C₄	—	6	4	no	—
227	C₂×C₄	C₃×C₄×Dic₃	1	4	yes	—
228	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
229	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
230	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
231	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
232	C₈	—	3	8	no	—
233	C₈	C₃×C₄×Dic₃	1	8	yes	complemented
234	C₂×C₃	—	2	1	no	—
235	C₂×C₃	—	2	2	no	—
236	C₂×C₃	—	2	2	no	—
237	C₂×C₃	—	2	2	no	—
238	C₂×C₃	D₃×#97	1	2	yes	—
239	C₂×C₃	#4707	1	2	yes	—
240	C₂×C₃	C₄²×Dic₃	1	1	yes	characteristic
241	C₂×C₃	Dic₃×M₁₆	1	2	yes	—
242	C₂×C₃	C₃×C₄³	1	1	yes	characteristic
243	C₂×C₃	C₂×C₃×#97	1	2	yes	—
244	C₂×C₃	C₃×C₄×M₁₆	1	2	yes	—
245	C₂×C₃	C₃×C₄×M₁₆	1	2	yes	—
246	C₂²	C₃×C₄²×D₃	1	1	yes	characteristic
247	C₂²	C₃×C₄²×D₃	1	1	yes	characteristic
248	C₂²	C₃×D₃×M₁₆	1	4	yes	—
249	C₂²	C₂×C₃×C₄×Dic₃	1	1	yes	characteristic
250	C₄	—	2	4	no	—
251	C₄	—	3	8	no	—
252	C₄	—	6	4	no	—
253	C₄	C₃×C₄²×D₃	1	2	yes	—
254	C₄	C₂×C₃×C₄×Dic₃	1	2	yes	—
255	C₃	—	2	1	no	—
256	C₃	Dic₃×#97	1	1	yes	characteristic, direct product factor
257	C₃	C₃×C₄×#97	1	1	yes	characteristic, complemented
258	C₂	C₃×D₃×#97	1	2	yes	—
259	C₂	C₃×#4707	1	2	yes	—
260	C₂	C₃×C₄²×Dic₃	1	1	yes	characteristic
261	C₂	C₃×Dic₃×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₃
commutator	C₂×C₃	C₃×C₄³
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃²×#97	C₂
socle, prime radical	C₂³×C₃²	C₂²×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₂×C₃×#97	D₃
hypocenter	C₃	C₃×C₄×#97
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#97

Complements

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

N	H ≅ G/N	type
7. Dic₃×#97	C₃	direct (N × H)
14. C₃²×#97	C₄	semidirect
15. C₃×#815	C₄	semidirect
16. C₃×C₈×Dic₃	C₄	semidirect
17. C₃×#803	C₄	semidirect
62. C₃×#97	Dic₃	direct (N × H)
63. C₃×#97	C₃×C₄	semidirect
65. #815	C₃×C₄	semidirect
66. C₈×Dic₃	C₃×C₄	semidirect
67. #803	C₃×C₄	semidirect
79. C₃²×C₈	C₄²	semidirect
80. C₃×C₃⋊C₈	C₄²	semidirect
131. C₃×Dic₃	#97	direct (N × H)
140. #97	C₃×Dic₃	direct (N × H)
173. C₃×C₈	C₄×Dic₃	semidirect
174. C₃×C₈	C₃×C₄²	semidirect
175. C₃⋊C₈	C₃×C₄²	semidirect
219. Dic₃	C₃×#97	direct (N × H)
220. C₃²	C₄×#97	semidirect
233. C₈	C₃×C₄×Dic₃	semidirect
256. C₃	Dic₃×#97	direct (N × H)
257. C₃	C₃×C₄×#97	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#97	2
C₂×C₃×#815	2
C₂×C₃×C₈×Dic₃	2
C₃×C₄²×Dic₃	2
C₂×C₃×#803	2
C₃×C₄×#97	3
Dic₃×#97	3

Subgroups — C3×Dic3×#97 #11783018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₃×#97 #11783018