Subgroups — C₂×D₃×C₈×C₃⋊D₃ #13176611

Order 1728.

2332 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃²×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#88785	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃⋊D₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₃×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	D₃×C₈×C₃⋊D₃	C₂	1	8	yes	maximal, direct product factor
9	C₂²×C₈×C₃⋊D₃	—	3	1	no	maximal
10	C₂×D₃²×C₈	—	3	4	no	maximal
11	C₂²×D₃×C₃⋊D₃	C₄	1	1	yes	characteristic
12	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
14	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
15	C₂×#6289	C₄	1	1	yes	characteristic
16	C₂×Dic₃×C₃⋊D₃	C₄	1	1	yes	characteristic
17	C₂×D₃×C₃⋊Dic₃	C₄	1	1	yes	characteristic
18	C₄×D₃×C₃⋊D₃	C₄	1	4	yes	—
19	C₄×D₃×C₃⋊D₃	C₂²	1	4	yes	—
20	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃⋊(C₃⋊(C₃⋊C₈))	C₂²	1	1	yes	characteristic, complemented
22	C₈×C₃⋊(C₃⋊D₃)	C₂²	1	4	yes	complemented
23	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₈×C₃⋊D₃	C₂²	1	4	yes	complemented
25	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
26	C₃²×D₃×C₈	C₂²	1	4	yes	complemented
27	#88785	C₂²	1	4	yes	complemented
28	C₃⋊D₃×C₃⋊C₈	C₂²	1	4	yes	complemented
29	D₃×C₃⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
30	C₂²×C₄×C₃⋊D₃	—	3	1	no	—
31	C₂×C₄×D₃²	—	3	4	no	—
32	C₂²×C₃²×C₈	—	3	1	no	—
33	C₂²×C₃⋊(C₃⋊C₈)	—	3	1	no	—
34	C₂×C₈×C₃⋊D₃	—	3	1	no	—
35	C₂×C₈×C₃⋊D₃	—	3	1	no	—
36	C₂×C₈×C₃⋊D₃	—	3	1	no	—
37	C₂×C₈×C₃⋊D₃	—	3	8	no	—
38	C₂×C₈×C₃⋊D₃	—	3	4	no	—
39	C₂×C₈×C₃⋊D₃	—	6	4	no	—
40	C₂×C₈×C₃⋊D₃	D₃	1	1	yes	characteristic, direct product factor
41	C₂×C₃×D₃×C₈	—	3	4	no	—
42	C₂×C₃×D₃×C₈	D₃	1	4	yes	complemented
43	C₂×#3710	—	3	4	no	—
44	C₂×D₃×C₃⋊C₈	—	3	4	no	—
45	C₂×D₃×C₃⋊C₈	—	3	4	no	—
46	D₃²×C₈	—	3	32	no	—
47	C₂²×C₃⋊(C₃⋊D₃)	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₃×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₃²×D₃	C₂×C₄	1	1	yes	characteristic
50	C₂×D₃×C₃⋊D₃	C₈	1	8	yes	direct product factor
51	C₂×D₃×C₃⋊D₃	C₂×C₄	1	4	yes	—
52	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
53	C₂×C₃⋊(C₃⋊Dic₃)	C₂×C₄	1	1	yes	characteristic
54	C₄×C₃⋊(C₃⋊D₃)	C₂×C₄	1	2	yes	—
55	C₄×C₃⋊(C₃⋊D₃)	C₂³	1	2	yes	—
56	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
57	C₃×C₄×C₃⋊D₃	C₂×C₄	1	2	yes	—
58	C₃×C₄×C₃⋊D₃	C₂³	1	2	yes	—
59	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
60	C₃²×C₄×D₃	C₂×C₄	1	2	yes	—
61	C₃²×C₄×D₃	C₂³	1	2	yes	—
62	#6289	C₂×C₄	1	4	yes	—
63	Dic₃×C₃⋊D₃	C₂×C₄	1	4	yes	—
64	D₃×C₃⋊Dic₃	C₂×C₄	1	4	yes	—
65	C₃³×C₈	C₂³	1	2	yes	complemented
66	C₃⋊(C₃⋊(C₃⋊C₈))	C₂³	1	2	yes	complemented
67	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	complemented
68	C₃²×C₃⋊C₈	C₂³	1	2	yes	complemented
69	C₂²×D₃×C₈	—	9	4	no	—
70	C₂²×D₃×C₈	—	9	1	no	—
71	C₂³×C₃⋊D₃	—	3	1	no	—
72	C₂²×D₃²	—	3	4	no	—
73	C₂²×C₃²×C₄	—	3	1	no	—
74	C₂²×C₃⋊Dic₃	—	3	1	no	—
75	C₂×C₄×C₃⋊D₃	—	3	1	no	—
76	C₂×C₄×C₃⋊D₃	—	3	1	no	—
77	C₂×C₄×C₃⋊D₃	—	3	4	no	—
78	C₂×C₄×C₃⋊D₃	—	3	1	no	—
79	C₂×C₄×C₃⋊D₃	—	3	4	no	—
80	C₂×C₄×C₃⋊D₃	—	3	4	no	—
81	C₂×C₄×C₃⋊D₃	—	6	4	no	—
82	C₂×C₄×C₃⋊D₃	C₂×D₃	1	1	yes	characteristic
83	C₂×C₃×C₄×D₃	—	3	4	no	—
84	C₂×C₃×C₄×D₃	C₂×D₃	1	4	yes	—
85	C₂×#624	—	3	4	no	—
86	C₂×D₃×Dic₃	—	3	4	no	—
87	C₂×D₃×Dic₃	—	3	4	no	—
88	C₄×D₃²	—	3	16	no	—
89	C₄×D₃²	—	3	16	no	—
90	C₂×C₃²×C₈	—	2	4	no	—
91	C₂×C₃²×C₈	—	3	1	no	—
92	C₂×C₃²×C₈	—	3	4	no	—
93	C₂×C₃²×C₈	C₂×D₃	1	4	yes	complemented
94	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic, complemented
95	C₂×C₃⋊(C₃⋊C₈)	—	3	1	no	—
96	C₂×C₃⋊(C₃⋊C₈)	—	3	4	no	—
97	C₂×C₃⋊(C₃⋊C₈)	—	3	4	no	—
98	C₂×C₃⋊(C₃⋊C₈)	—	6	4	no	—
99	C₂×C₃⋊(C₃⋊C₈)	C₂×D₃	1	1	yes	characteristic, complemented
100	C₈×C₃⋊D₃	—	3	4	no	—
101	C₈×C₃⋊D₃	—	3	4	no	—
102	C₈×C₃⋊D₃	—	3	16	no	—
103	C₈×C₃⋊D₃	—	3	4	no	—
104	C₈×C₃⋊D₃	—	6	16	no	—
105	C₈×C₃⋊D₃	C₂×D₃	1	4	yes	direct product factor
106	C₂×C₃×C₃⋊C₈	—	3	4	no	—
107	C₂×C₃×C₃⋊C₈	C₂×D₃	1	4	yes	complemented
108	C₃×D₃×C₈	—	3	16	no	—
109	C₃×D₃×C₈	C₂×D₃	1	16	yes	complemented
110	#3710	—	3	16	no	—
111	D₃×C₃⋊C₈	—	3	16	no	—
112	D₃×C₃⋊C₈	—	3	16	no	—
113	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₃⋊(C₃⋊D₃)	C₂×C₈	1	4	yes	complemented
115	C₂×C₃⋊(C₃⋊D₃)	C₂²×C₄	1	2	yes	—
116	C₂×C₃×C₃⋊D₃	C₂×C₈	1	4	yes	complemented
117	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	2	yes	—
118	C₂×C₃²×D₃	C₂×C₈	1	4	yes	complemented
119	C₂×C₃²×D₃	C₂²×C₄	1	2	yes	—
120	D₃×C₃⋊D₃	C₂×C₈	1	16	yes	direct product factor
121	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
122	C₃³×C₄	C₂⁴	1	1	yes	characteristic
123	C₃⋊(C₃⋊Dic₃)	C₂²×C₄	1	2	yes	—
124	C₃×C₃⋊Dic₃	C₂²×C₄	1	2	yes	—
125	C₃²×Dic₃	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×D₃	—	9	4	no	—
127	C₂²×C₄×D₃	—	9	1	no	—
128	C₂²×C₃×C₈	—	3	4	no	—
129	C₂²×C₃×C₈	—	9	1	no	—
130	C₂²×C₃⋊C₈	—	9	4	no	—
131	C₂²×C₃⋊C₈	—	9	1	no	—
132	C₂×D₃×C₈	—	3	4	no	—
133	C₂×D₃×C₈	—	9	32	no	—
134	C₂×D₃×C₈	—	9	4	no	—
135	C₂×D₃×C₈	—	9	4	no	—
136	C₂×D₃×C₈	—	9	1	no	—
137	C₂×D₃×C₈	—	9	4	no	—
138	C₂×D₃×C₈	—	9	1	no	—
139	C₂×D₃×C₈	—	9	1	no	—
140	C₂×D₃×C₈	—	9	8	no	—
141	C₂×D₃×C₈	—	18	4	no	—
142	C₂×D₃×C₈	C₃⋊D₃	1	1	yes	characteristic, direct product factor
143	C₂³×C₃²	—	3	1	no	—
144	C₂²×C₃⋊D₃	—	3	1	no	—
145	C₂²×C₃⋊D₃	—	3	8	no	—
146	C₂²×C₃⋊D₃	—	3	4	no	—
147	C₂²×C₃⋊D₃	—	3	4	no	—
148	C₂²×C₃⋊D₃	—	6	4	no	—
149	C₂²×C₃⋊D₃	C₄×D₃	1	1	yes	characteristic
150	C₂²×C₃×D₃	—	3	4	no	—
151	C₂²×C₃×D₃	C₄×D₃	1	4	yes	—
152	C₂×D₃²	—	3	32	no	—
153	C₂×D₃²	—	3	16	no	—
154	C₂×C₃²×C₄	—	2	4	no	—
155	C₂×C₃²×C₄	—	3	1	no	—
156	C₂×C₃²×C₄	—	3	2	no	—
157	C₂×C₃²×C₄	—	3	2	no	—
158	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
159	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
160	C₂×C₃⋊Dic₃	—	3	1	no	—
161	C₂×C₃⋊Dic₃	—	3	4	no	—
162	C₂×C₃⋊Dic₃	—	3	4	no	—
163	C₂×C₃⋊Dic₃	—	6	4	no	—
164	C₂×C₃⋊Dic₃	C₄×D₃	1	1	yes	characteristic
165	C₄×C₃⋊D₃	—	3	4	no	—
166	C₄×C₃⋊D₃	—	3	2	no	—
167	C₄×C₃⋊D₃	—	3	2	no	—
168	C₄×C₃⋊D₃	—	3	4	no	—
169	C₄×C₃⋊D₃	—	3	8	no	—
170	C₄×C₃⋊D₃	—	3	8	no	—
171	C₄×C₃⋊D₃	—	6	8	no	—
172	C₄×C₃⋊D₃	—	6	8	no	—
173	C₄×C₃⋊D₃	C₄×D₃	1	2	yes	—
174	C₄×C₃⋊D₃	C₂²×D₃	1	2	yes	—
175	C₂×C₃×Dic₃	—	3	4	no	—
176	C₂×C₃×Dic₃	C₄×D₃	1	4	yes	—
177	C₃×C₄×D₃	—	3	8	no	—
178	C₃×C₄×D₃	—	3	8	no	—
179	C₃×C₄×D₃	C₄×D₃	1	8	yes	—
180	C₃×C₄×D₃	C₂²×D₃	1	8	yes	—
181	#624	—	3	16	no	—
182	D₃×Dic₃	—	3	16	no	—
183	D₃×Dic₃	—	3	16	no	—
184	C₃²×C₈	—	2	8	no	—
185	C₃²×C₈	—	3	2	no	—
186	C₃²×C₈	C₂²×D₃	1	8	yes	complemented
187	C₃²×C₈	C₂²×D₃	1	2	yes	complemented
188	C₃⋊(C₃⋊C₈)	—	3	2	no	—
189	C₃⋊(C₃⋊C₈)	—	3	8	no	—
190	C₃⋊(C₃⋊C₈)	—	6	8	no	—
191	C₃⋊(C₃⋊C₈)	C₂²×D₃	1	2	yes	complemented
192	C₃×C₃⋊C₈	—	3	8	no	—
193	C₃×C₃⋊C₈	C₂²×D₃	1	8	yes	complemented
194	C₂³×C₈	—	27	1	no	Sylow
195	C₂×C₃³	C₂²×C₈	1	2	yes	complemented
196	C₂×C₃³	C₂³×C₄	1	1	yes	characteristic
197	C₃⋊(C₃⋊D₃)	C₂²×C₈	1	4	yes	complemented
198	C₃×C₃⋊D₃	C₂²×C₈	1	4	yes	complemented
199	C₃²×D₃	C₂²×C₈	1	4	yes	complemented
200	C₂³×D₃	—	9	4	no	—
201	C₂³×D₃	—	9	1	no	—
202	C₂²×C₃×C₄	—	3	4	no	—
203	C₂²×C₃×C₄	—	9	1	no	—
204	C₂²×Dic₃	—	9	4	no	—
205	C₂²×Dic₃	—	9	1	no	—
206	C₂×C₄×D₃	—	3	4	no	—
207	C₂×C₄×D₃	—	9	16	no	—
208	C₂×C₄×D₃	—	9	16	no	—
209	C₂×C₄×D₃	—	9	4	no	—
210	C₂×C₄×D₃	—	9	4	no	—
211	C₂×C₄×D₃	—	9	1	no	—
212	C₂×C₄×D₃	—	9	4	no	—
213	C₂×C₄×D₃	—	9	1	no	—
214	C₂×C₄×D₃	—	9	1	no	—
215	C₂×C₄×D₃	—	9	4	no	—
216	C₂×C₄×D₃	—	9	4	no	—
217	C₂×C₄×D₃	—	18	4	no	—
218	C₂×C₄×D₃	C₂×C₃⋊D₃	1	1	yes	characteristic
219	C₂×C₃×C₈	—	2	4	no	—
220	C₂×C₃×C₈	—	3	4	no	—
221	C₂×C₃×C₈	—	3	16	no	—
222	C₂×C₃×C₈	—	9	1	no	—
223	C₂×C₃×C₈	—	9	4	no	—
224	C₂×C₃×C₈	D₃²	1	4	yes	complemented
225	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
226	C₂×C₃⋊C₈	—	3	4	no	—
227	C₂×C₃⋊C₈	—	9	16	no	—
228	C₂×C₃⋊C₈	—	9	4	no	—
229	C₂×C₃⋊C₈	—	9	1	no	—
230	C₂×C₃⋊C₈	—	9	4	no	—
231	C₂×C₃⋊C₈	—	18	4	no	—
232	C₂×C₃⋊C₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
233	D₃×C₈	—	3	16	no	—
234	D₃×C₈	—	9	16	no	—
235	D₃×C₈	—	9	16	no	—
236	D₃×C₈	—	9	4	no	—
237	D₃×C₈	—	9	16	no	—
238	D₃×C₈	—	9	4	no	—
239	D₃×C₈	—	9	4	no	—
240	D₃×C₈	—	18	16	no	—
241	D₃×C₈	C₂×C₃⋊D₃	1	4	yes	direct product factor
242	C₂²×C₃²	—	2	4	no	—
243	C₂²×C₃²	—	3	4	no	—
244	C₂²×C₃²	—	3	2	no	—
245	C₂²×C₃²	C₂×C₄×D₃	1	4	yes	—
246	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂×C₃⋊D₃	—	3	4	no	—
248	C₂×C₃⋊D₃	—	3	2	no	—
249	C₂×C₃⋊D₃	—	3	16	no	—
250	C₂×C₃⋊D₃	—	3	16	no	—
251	C₂×C₃⋊D₃	—	3	8	no	—
252	C₂×C₃⋊D₃	—	6	16	no	—
253	C₂×C₃⋊D₃	—	6	8	no	—
254	C₂×C₃⋊D₃	D₃×C₈	1	4	yes	direct product factor
255	C₂×C₃⋊D₃	C₂×C₄×D₃	1	2	yes	—
256	C₂×C₃×D₃	—	3	16	no	—
257	C₂×C₃×D₃	—	3	8	no	—
258	C₂×C₃×D₃	D₃×C₈	1	16	yes	complemented
259	C₂×C₃×D₃	C₂×C₄×D₃	1	8	yes	—
260	D₃²	—	3	64	no	—
261	C₃²×C₄	—	2	4	no	—
262	C₃²×C₄	—	2	4	no	—
263	C₃²×C₄	—	3	2	no	—
264	C₃²×C₄	C₂×C₄×D₃	1	4	yes	—
265	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
266	C₃²×C₄	C₂³×D₃	1	4	yes	—
267	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
268	C₃⋊Dic₃	—	3	2	no	—
269	C₃⋊Dic₃	—	3	8	no	—
270	C₃⋊Dic₃	—	6	8	no	—
271	C₃⋊Dic₃	C₂×C₄×D₃	1	2	yes	—
272	C₃×Dic₃	—	3	8	no	—
273	C₃×Dic₃	C₂×C₄×D₃	1	8	yes	—
274	C₂³×C₄	—	27	1	no	—
275	C₂²×C₈	—	3	1	no	—
276	C₂²×C₈	—	9	1	no	—
277	C₂²×C₈	—	27	1	no	—
278	C₂²×C₈	—	27	8	no	—
279	C₂²×C₈	—	27	1	no	—
280	C₂²×C₈	—	27	1	no	—
281	C₂²×C₈	—	27	1	no	—
282	C₃³	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
283	C₂³×C₃	—	3	4	no	—
284	C₂³×C₃	—	9	1	no	—
285	C₂²×D₃	—	3	4	no	—
286	C₂²×D₃	—	9	16	no	—
287	C₂²×D₃	—	9	32	no	—
288	C₂²×D₃	—	9	4	no	—
289	C₂²×D₃	—	9	1	no	—
290	C₂²×D₃	—	9	8	no	—
291	C₂²×D₃	—	9	4	no	—
292	C₂²×D₃	—	18	4	no	—
293	C₂²×D₃	C₄×C₃⋊D₃	1	1	yes	characteristic
294	C₂×C₃×C₄	—	2	4	no	—
295	C₂×C₃×C₄	—	3	4	no	—
296	C₂×C₃×C₄	—	3	8	no	—
297	C₂×C₃×C₄	—	3	8	no	—
298	C₂×C₃×C₄	—	9	1	no	—
299	C₂×C₃×C₄	—	9	2	no	—
300	C₂×C₃×C₄	—	9	2	no	—
301	C₂×C₃×C₄	C₂×D₃²	1	4	yes	—
302	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
303	C₂×Dic₃	—	3	4	no	—
304	C₂×Dic₃	—	9	16	no	—
305	C₂×Dic₃	—	9	4	no	—
306	C₂×Dic₃	—	9	1	no	—
307	C₂×Dic₃	—	9	4	no	—
308	C₂×Dic₃	—	18	4	no	—
309	C₂×Dic₃	C₄×C₃⋊D₃	1	1	yes	characteristic
310	C₄×D₃	—	3	8	no	—
311	C₄×D₃	—	3	8	no	—
312	C₄×D₃	—	9	16	no	—
313	C₄×D₃	—	9	16	no	—
314	C₄×D₃	—	9	4	no	—
315	C₄×D₃	—	9	8	no	—
316	C₄×D₃	—	9	2	no	—
317	C₄×D₃	—	9	8	no	—
318	C₄×D₃	—	9	2	no	—
319	C₄×D₃	—	9	4	no	—
320	C₄×D₃	—	18	8	no	—
321	C₄×D₃	—	18	8	no	—
322	C₄×D₃	C₄×C₃⋊D₃	1	2	yes	—
323	C₄×D₃	C₂²×C₃⋊D₃	1	2	yes	—
324	C₃×C₈	—	2	8	no	—
325	C₃×C₈	—	3	8	no	—
326	C₃×C₈	—	9	2	no	—
327	C₃×C₈	C₂×D₃²	1	8	yes	complemented
328	C₃×C₈	C₂²×C₃⋊D₃	1	2	yes	complemented
329	C₃⋊C₈	—	3	8	no	—
330	C₃⋊C₈	—	9	8	no	—
331	C₃⋊C₈	—	9	2	no	—
332	C₃⋊C₈	—	18	8	no	—
333	C₃⋊C₈	C₂²×C₃⋊D₃	1	2	yes	complemented
334	C₂×C₃²	—	2	8	no	—
335	C₂×C₃²	—	2	4	no	—
336	C₂×C₃²	—	3	4	no	—
337	C₂×C₃²	C₂×D₃×C₈	1	8	yes	complemented
338	C₂×C₃²	C₂×D₃×C₈	1	2	yes	complemented
339	C₂×C₃²	C₂²×C₄×D₃	1	4	yes	—
340	C₂×C₃²	C₂²×C₄×D₃	1	1	yes	characteristic
341	C₃⋊D₃	—	3	4	no	—
342	C₃⋊D₃	—	3	16	no	—
343	C₃⋊D₃	—	6	16	no	—
344	C₃⋊D₃	C₂×D₃×C₈	1	4	yes	direct product factor
345	C₃×D₃	—	3	16	no	—
346	C₃×D₃	C₂×D₃×C₈	1	16	yes	complemented
347	C₂⁴	—	27	1	no	—
348	C₂²×C₄	—	3	1	no	—
349	C₂²×C₄	—	9	1	no	—
350	C₂²×C₄	—	27	4	no	—
351	C₂²×C₄	—	27	1	no	—
352	C₂²×C₄	—	27	4	no	—
353	C₂²×C₄	—	27	1	no	—
354	C₂²×C₄	—	27	1	no	—
355	C₂²×C₄	—	27	1	no	—
356	C₂×C₈	—	3	1	no	—
357	C₂×C₈	—	3	4	no	—
358	C₂×C₈	—	9	1	no	—
359	C₂×C₈	—	9	4	no	—
360	C₂×C₈	—	27	4	no	—
361	C₂×C₈	—	27	4	no	—
362	C₂×C₈	—	27	4	no	—
363	C₂×C₈	—	27	1	no	—
364	C₂×C₈	—	27	4	no	—
365	C₂×C₈	D₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
366	C₂²×C₃	—	2	4	no	—
367	C₂²×C₃	—	3	16	no	—
368	C₂²×C₃	—	3	8	no	—
369	C₂²×C₃	—	9	2	no	—
370	C₂²×C₃	—	9	4	no	—
371	C₂²×C₃	C₄×D₃²	1	4	yes	—
372	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
373	C₂×D₃	—	3	16	no	—
374	C₂×D₃	—	3	8	no	—
375	C₂×D₃	—	9	64	no	—
376	C₂×D₃	—	9	16	no	—
377	C₂×D₃	—	9	8	no	—
378	C₂×D₃	—	9	2	no	—
379	C₂×D₃	—	9	4	no	—
380	C₂×D₃	—	9	16	no	—
381	C₂×D₃	—	18	8	no	—
382	C₂×D₃	—	18	16	no	—
383	C₂×D₃	C₈×C₃⋊D₃	1	4	yes	direct product factor
384	C₂×D₃	C₂×C₄×C₃⋊D₃	1	2	yes	—
385	C₃×C₄	—	2	4	no	—
386	C₃×C₄	—	2	4	no	—
387	C₃×C₄	—	3	8	no	—
388	C₃×C₄	—	9	2	no	—
389	C₃×C₄	C₄×D₃²	1	4	yes	—
390	C₃×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
391	C₃×C₄	C₂²×D₃²	1	4	yes	—
392	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
393	Dic₃	—	3	8	no	—
394	Dic₃	—	9	8	no	—
395	Dic₃	—	9	2	no	—
396	Dic₃	—	18	8	no	—
397	Dic₃	C₂×C₄×C₃⋊D₃	1	2	yes	—
398	C₃²	—	2	4	no	—
399	C₃²	C₂²×D₃×C₈	1	4	yes	complemented
400	C₃²	C₂²×D₃×C₈	1	1	yes	characteristic, complemented
401	C₂³	—	3	1	no	—
402	C₂³	—	9	1	no	—
403	C₂³	—	27	4	no	—
404	C₂³	—	27	8	no	—
405	C₂³	—	27	1	no	—
406	C₂×C₄	—	3	1	no	—
407	C₂×C₄	—	3	2	no	—
408	C₂×C₄	—	3	2	no	—
409	C₂×C₄	—	9	1	no	—
410	C₂×C₄	—	9	2	no	—
411	C₂×C₄	—	9	2	no	—
412	C₂×C₄	—	27	4	no	—
413	C₂×C₄	—	27	4	no	—
414	C₂×C₄	—	27	4	no	—
415	C₂×C₄	—	27	1	no	—
416	C₂×C₄	—	27	2	no	—
417	C₂×C₄	—	27	2	no	—
418	C₂×C₄	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic
419	C₈	—	3	2	no	—
420	C₈	—	9	2	no	—
421	C₈	—	27	2	no	—
422	C₈	C₂×D₃×C₃⋊D₃	1	2	yes	direct product factor
423	C₂×C₃	—	2	4	no	—
424	C₂×C₃	—	2	8	no	—
425	C₂×C₃	—	3	16	no	—
426	C₂×C₃	—	9	4	no	—
427	C₂×C₃	D₃²×C₈	1	8	yes	complemented
428	C₂×C₃	C₂×C₈×C₃⋊D₃	1	2	yes	complemented
429	C₂×C₃	C₂×C₄×D₃²	1	4	yes	—
430	C₂×C₃	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
431	D₃	—	3	16	no	—
432	D₃	—	9	16	no	—
433	D₃	—	9	4	no	—
434	D₃	—	18	16	no	—
435	D₃	C₂×C₈×C₃⋊D₃	1	4	yes	direct product factor
436	C₂²	—	3	2	no	—
437	C₂²	—	3	4	no	—
438	C₂²	—	9	2	no	—
439	C₂²	—	9	4	no	—
440	C₂²	—	27	16	no	—
441	C₂²	—	27	2	no	—
442	C₂²	—	27	4	no	—
443	C₂²	C₄×D₃×C₃⋊D₃	1	1	yes	characteristic
444	C₄	—	3	2	no	—
445	C₄	—	9	2	no	—
446	C₄	—	27	2	no	—
447	C₄	C₄×D₃×C₃⋊D₃	1	1	yes	characteristic
448	C₄	C₂²×D₃×C₃⋊D₃	1	1	yes	characteristic
449	C₃	—	2	4	no	—
450	C₃	C₂×D₃²×C₈	1	4	yes	complemented
451	C₃	C₂²×C₈×C₃⋊D₃	1	1	yes	characteristic, complemented
452	C₂	—	3	4	no	—
453	C₂	—	9	4	no	—
454	C₂	—	27	4	no	—
455	C₂	D₃×C₈×C₃⋊D₃	1	2	yes	direct product factor
456	C₂	C₂×C₄×D₃×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₈	D₃×C₃⋊D₃
commutator, hypocenter	C₃³	C₂³×C₈
Frattini	C₄	C₂²×D₃×C₃⋊D₃
Fitting	C₂×C₃³×C₈	C₂²
socle	C₂²×C₃³	C₂²×C₄
prime radical	C₂²×D₃×C₃⋊D₃	C₄
cosocle	C₃³×C₄	C₂⁴
LCS	G ▷ C₃³
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×C₃⋊(C₃⋊D₃)	C₂	semidirect
3. C₂×C₃×C₈×C₃⋊D₃	C₂	semidirect
4. C₂×C₃²×D₃×C₈	C₂	semidirect
5. C₂×#88785	C₂	semidirect
6. C₂×C₃⋊D₃×C₃⋊C₈	C₂	semidirect
7. C₂×D₃×C₃⋊(C₃⋊C₈)	C₂	semidirect
8. D₃×C₈×C₃⋊D₃	C₂	direct (N × H)
20. C₂×C₃³×C₈	C₂²	semidirect
21. C₂×C₃⋊(C₃⋊(C₃⋊C₈))	C₂²	semidirect
22. C₈×C₃⋊(C₃⋊D₃)	C₂²	semidirect
23. C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	semidirect
24. C₃×C₈×C₃⋊D₃	C₂²	semidirect
25. C₂×C₃²×C₃⋊C₈	C₂²	semidirect
26. C₃²×D₃×C₈	C₂²	semidirect
27. #88785	C₂²	semidirect
28. C₃⋊D₃×C₃⋊C₈	C₂²	semidirect
29. D₃×C₃⋊(C₃⋊C₈)	C₂²	semidirect
40. C₂×C₈×C₃⋊D₃	D₃	direct (N × H)
42. C₂×C₃×D₃×C₈	D₃	semidirect
50. C₂×D₃×C₃⋊D₃	C₈	direct (N × H)
65. C₃³×C₈	C₂³	semidirect
66. C₃⋊(C₃⋊(C₃⋊C₈))	C₂³	semidirect
67. C₃×C₃⋊(C₃⋊C₈)	C₂³	semidirect
68. C₃²×C₃⋊C₈	C₂³	semidirect
93. C₂×C₃²×C₈	C₂×D₃	semidirect
94. C₂×C₃²×C₈	C₂×D₃	semidirect
99. C₂×C₃⋊(C₃⋊C₈)	C₂×D₃	semidirect
105. C₈×C₃⋊D₃	C₂×D₃	direct (N × H)
107. C₂×C₃×C₃⋊C₈	C₂×D₃	semidirect
109. C₃×D₃×C₈	C₂×D₃	semidirect
114. C₂×C₃⋊(C₃⋊D₃)	C₂×C₈	semidirect
116. C₂×C₃×C₃⋊D₃	C₂×C₈	semidirect
118. C₂×C₃²×D₃	C₂×C₈	semidirect
120. D₃×C₃⋊D₃	C₂×C₈	direct (N × H)
142. C₂×D₃×C₈	C₃⋊D₃	direct (N × H)
186. C₃²×C₈	C₂²×D₃	semidirect
187. C₃²×C₈	C₂²×D₃	semidirect
191. C₃⋊(C₃⋊C₈)	C₂²×D₃	semidirect
193. C₃×C₃⋊C₈	C₂²×D₃	semidirect
195. C₂×C₃³	C₂²×C₈	semidirect
197. C₃⋊(C₃⋊D₃)	C₂²×C₈	semidirect
198. C₃×C₃⋊D₃	C₂²×C₈	semidirect
199. C₃²×D₃	C₂²×C₈	semidirect
224. C₂×C₃×C₈	D₃²	semidirect
225. C₂×C₃×C₈	C₂×C₃⋊D₃	semidirect
232. C₂×C₃⋊C₈	C₂×C₃⋊D₃	semidirect
241. D₃×C₈	C₂×C₃⋊D₃	direct (N × H)
254. C₂×C₃⋊D₃	D₃×C₈	direct (N × H)
258. C₂×C₃×D₃	D₃×C₈	semidirect
282. C₃³	C₂³×C₈	semidirect
327. C₃×C₈	C₂×D₃²	semidirect
328. C₃×C₈	C₂²×C₃⋊D₃	semidirect
333. C₃⋊C₈	C₂²×C₃⋊D₃	semidirect
337. C₂×C₃²	C₂×D₃×C₈	semidirect
338. C₂×C₃²	C₂×D₃×C₈	semidirect
344. C₃⋊D₃	C₂×D₃×C₈	direct (N × H)
346. C₃×D₃	C₂×D₃×C₈	semidirect
365. C₂×C₈	D₃×C₃⋊D₃	direct (N × H)
383. C₂×D₃	C₈×C₃⋊D₃	direct (N × H)
399. C₃²	C₂²×D₃×C₈	semidirect
400. C₃²	C₂²×D₃×C₈	semidirect
422. C₈	C₂×D₃×C₃⋊D₃	direct (N × H)
427. C₂×C₃	D₃²×C₈	semidirect
428. C₂×C₃	C₂×C₈×C₃⋊D₃	semidirect
435. D₃	C₂×C₈×C₃⋊D₃	direct (N × H)
450. C₃	C₂×D₃²×C₈	semidirect
451. C₃	C₂²×C₈×C₃⋊D₃	semidirect
455. C₂	D₃×C₈×C₃⋊D₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×D₃×C₃⋊D₃	2
C₂×C₈×C₃⋊(C₃⋊D₃)	2
C₂×C₃×C₈×C₃⋊D₃	2
C₂×C₃²×D₃×C₈	2
C₂×#88785	2
C₂×C₃⋊D₃×C₃⋊C₈	2
C₂×D₃×C₃⋊(C₃⋊C₈)	2
D₃×C₈×C₃⋊D₃	2
C₂²×C₈×C₃⋊D₃	3
C₂×D₃²×C₈	3

Subgroups — C2×D3×C8×C3⋊D3 #13176611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₈×C₃⋊D₃ #13176611