Subgroups — C₂×D₃×C₈×Dic₃ #11857107

Order 1152.

1601 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₃×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×D₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#63553	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×Dic₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	D₃×C₈×Dic₃	C₂	1	8	yes	maximal, direct product factor
9	C₂²×C₈×Dic₃	—	3	1	no	maximal
10	C₂×C₄×D₃×C₈	—	3	1	no	maximal
11	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
12	C₂²×D₃×Dic₃	C₄	1	2	yes	—
13	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×D₃×C₈	C₄	1	8	yes	complemented
20	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
21	C₂×Dic₃²	C₄	1	2	yes	—
22	C₄×D₃×Dic₃	C₄	1	4	yes	—
23	C₄×D₃×Dic₃	C₂²	1	4	yes	—
24	C₂×D₃×C₃⋊C₈	C₄	1	8	yes	complemented
25	C₂×D₃×C₃⋊C₈	C₂²	1	4	yes	—
26	C₈×C₃⋊Dic₃	C₂²	1	4	yes	complemented
27	C₃×C₈×Dic₃	C₂²	1	4	yes	complemented
28	#63553	C₂²	1	4	yes	complemented
29	Dic₃×C₃⋊C₈	C₂²	1	4	yes	complemented
30	C₂³×C₃×C₈	—	3	1	no	—
31	C₂²×C₄×Dic₃	—	3	1	no	—
32	C₂³×C₃⋊C₈	—	3	1	no	—
33	C₂²×D₃×C₈	—	3	1	no	—
34	C₂²×D₃×C₈	D₃	1	1	yes	characteristic
35	C₂×C₄²×D₃	—	3	1	no	—
36	C₂×C₃×C₄×C₈	—	3	1	no	—
37	C₂×C₈×Dic₃	—	3	1	no	—
38	C₂×C₈×Dic₃	—	3	1	no	—
39	C₂×C₈×Dic₃	—	3	1	no	—
40	C₂×C₈×Dic₃	—	3	1	no	—
41	C₂×C₈×Dic₃	—	3	1	no	—
42	C₂×C₈×Dic₃	—	3	8	no	—
43	C₂×C₈×Dic₃	—	6	1	no	—
44	C₂×C₈×Dic₃	D₃	1	1	yes	characteristic, direct product factor
45	C₂×C₄×C₃⋊C₈	—	3	1	no	—
46	C₄×D₃×C₈	—	3	8	no	—
47	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
49	C₂²×C₃⋊Dic₃	C₂×C₄	1	2	yes	—
50	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
52	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
53	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
54	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
55	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
56	C₂×D₃×Dic₃	C₈	1	16	yes	direct product factor
57	C₂×D₃×Dic₃	C₂×C₄	1	8	yes	—
58	C₂×C₃²×C₈	C₂×C₄	1	4	yes	complemented
59	C₂×C₃²×C₈	C₂³	1	2	yes	—
60	C₄×C₃⋊Dic₃	C₂×C₄	1	2	yes	—
61	C₄×C₃⋊Dic₃	C₂³	1	2	yes	—
62	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	4	yes	complemented
63	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	—
64	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
65	C₃×C₄×Dic₃	C₂³	1	2	yes	—
66	C₂×C₃×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
67	C₂×C₃×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
68	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
69	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
70	C₃×D₃×C₈	C₂×C₄	1	16	yes	complemented
71	Dic₃²	C₂×C₄	1	8	yes	—
72	D₃×C₃⋊C₈	C₂×C₄	1	16	yes	complemented
73	C₂²×C₄×C₈	—	9	1	no	Sylow
74	C₂³×C₃×C₄	—	3	1	no	—
75	C₂³×Dic₃	—	3	2	no	—
76	C₂²×C₄×D₃	—	3	2	no	—
77	C₂²×C₄×D₃	C₂×D₃	1	1	yes	characteristic
78	C₂²×C₃×C₈	—	2	1	no	—
79	C₂²×C₃×C₈	—	3	1	no	—
80	C₂²×C₃×C₈	—	3	1	no	—
81	C₂²×C₃×C₈	—	3	8	no	—
82	C₂²×C₃×C₈	—	3	4	no	—
83	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
84	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
85	C₂×C₃×C₄²	—	3	1	no	—
86	C₂×C₄×Dic₃	—	3	1	no	—
87	C₂×C₄×Dic₃	—	3	1	no	—
88	C₂×C₄×Dic₃	—	3	2	no	—
89	C₂×C₄×Dic₃	—	3	2	no	—
90	C₂×C₄×Dic₃	—	3	4	no	—
91	C₂×C₄×Dic₃	—	3	4	no	—
92	C₂×C₄×Dic₃	—	6	1	no	—
93	C₂×C₄×Dic₃	C₂×D₃	1	1	yes	characteristic
94	C₂²×C₃⋊C₈	—	3	1	no	—
95	C₂²×C₃⋊C₈	—	3	1	no	—
96	C₂²×C₃⋊C₈	—	3	8	no	—
97	C₂²×C₃⋊C₈	—	3	4	no	—
98	C₂²×C₃⋊C₈	—	6	1	no	—
99	C₂²×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
100	C₂²×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
101	C₂×D₃×C₈	—	3	8	no	—
102	C₂×D₃×C₈	—	3	4	no	—
103	C₂×D₃×C₈	Dic₃	1	8	yes	direct product factor
104	C₂×D₃×C₈	C₂×D₃	1	4	yes	—
105	C₄²×D₃	—	3	4	no	—
106	C₄²×D₃	—	3	4	no	—
107	C₃×C₄×C₈	—	3	4	no	—
108	C₈×Dic₃	—	3	4	no	—
109	C₈×Dic₃	—	3	4	no	—
110	C₈×Dic₃	—	3	4	no	—
111	C₈×Dic₃	—	3	4	no	—
112	C₈×Dic₃	—	3	4	no	—
113	C₈×Dic₃	—	6	4	no	—
114	C₈×Dic₃	C₂×D₃	1	4	yes	direct product factor
115	C₄×C₃⋊C₈	—	3	4	no	—
116	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₃×D₃	C₄²	1	4	yes	—
118	C₂²×C₃×D₃	C₂×C₈	1	8	yes	—
119	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
120	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
122	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
123	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
124	C₂×C₃⋊Dic₃	C₂×C₈	1	8	yes	complemented
125	C₂×C₃⋊Dic₃	C₂²×C₄	1	4	yes	—
126	C₂×C₃×Dic₃	C₄²	1	4	yes	—
127	C₂×C₃×Dic₃	C₂×C₈	1	8	yes	complemented
128	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
129	C₂×C₃×Dic₃	C₂²×C₄	1	4	yes	—
130	C₃×C₄×D₃	C₄²	1	8	yes	—
131	C₃×C₄×D₃	C₂²×C₄	1	4	yes	—
132	C₃×C₄×D₃	C₂²×C₄	1	4	yes	—
133	D₃×Dic₃	C₂×C₈	1	32	yes	direct product factor
134	C₃²×C₈	C₂²×C₄	1	4	yes	complemented
135	C₃⋊(C₃⋊C₈)	C₂²×C₄	1	4	yes	complemented
136	C₃×C₃⋊C₈	C₂²×C₄	1	4	yes	complemented
137	C₃×C₃⋊C₈	C₂²×C₄	1	4	yes	complemented
138	C₂³×C₈	—	3	1	no	—
139	C₂³×C₈	—	9	1	no	—
140	C₂²×C₄²	—	9	1	no	—
141	C₂×C₄×C₈	—	3	1	no	—
142	C₂×C₄×C₈	—	9	8	no	—
143	C₂×C₄×C₈	—	9	1	no	—
144	C₂×C₄×C₈	—	9	1	no	—
145	C₂×C₄×C₈	—	9	1	no	—
146	C₂⁴×C₃	—	3	1	no	—
147	C₂³×D₃	C₄×D₃	1	1	yes	characteristic
148	C₂²×C₃×C₄	—	2	1	no	—
149	C₂²×C₃×C₄	—	3	1	no	—
150	C₂²×C₃×C₄	—	3	2	no	—
151	C₂²×C₃×C₄	—	3	4	no	—
152	C₂²×C₃×C₄	—	3	2	no	—
153	C₂²×C₃×C₄	—	3	4	no	—
154	C₂²×C₃×C₄	—	3	2	no	—
155	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
157	C₂²×Dic₃	—	3	2	no	—
158	C₂²×Dic₃	—	3	2	no	—
159	C₂²×Dic₃	—	3	16	no	—
160	C₂²×Dic₃	—	3	8	no	—
161	C₂²×Dic₃	—	6	2	no	—
162	C₂²×Dic₃	C₄×D₃	1	2	yes	—
163	C₂²×Dic₃	C₄×D₃	1	1	yes	characteristic
164	C₂×C₄×D₃	—	3	16	no	—
165	C₂×C₄×D₃	—	3	8	no	—
166	C₂×C₄×D₃	C₄×D₃	1	2	yes	—
167	C₂×C₄×D₃	C₄×D₃	1	4	yes	—
168	C₂×C₄×D₃	C₂×Dic₃	1	4	yes	—
169	C₂×C₄×D₃	C₂²×D₃	1	2	yes	—
170	C₂×C₃×C₈	—	2	4	no	—
171	C₂×C₃×C₈	—	2	2	no	—
172	C₂×C₃×C₈	—	3	4	no	—
173	C₂×C₃×C₈	—	3	4	no	—
174	C₂×C₃×C₈	—	3	2	no	—
175	C₂×C₃×C₈	—	3	2	no	—
176	C₂×C₃×C₈	—	3	16	no	—
177	C₂×C₃×C₈	C₄×D₃	1	4	yes	complemented
178	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	complemented
179	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
180	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
181	C₃×C₄²	—	3	2	no	—
182	C₃×C₄²	—	3	2	no	—
183	C₄×Dic₃	—	3	2	no	—
184	C₄×Dic₃	—	3	2	no	—
185	C₄×Dic₃	—	3	2	no	—
186	C₄×Dic₃	—	3	2	no	—
187	C₄×Dic₃	—	3	8	no	—
188	C₄×Dic₃	—	3	8	no	—
189	C₄×Dic₃	—	6	2	no	—
190	C₄×Dic₃	—	6	2	no	—
191	C₄×Dic₃	C₄×D₃	1	2	yes	—
192	C₄×Dic₃	C₂²×D₃	1	2	yes	—
193	C₂×C₃⋊C₈	—	3	4	no	—
194	C₂×C₃⋊C₈	—	3	4	no	—
195	C₂×C₃⋊C₈	—	3	2	no	—
196	C₂×C₃⋊C₈	—	3	2	no	—
197	C₂×C₃⋊C₈	—	3	16	no	—
198	C₂×C₃⋊C₈	—	6	2	no	—
199	C₂×C₃⋊C₈	—	6	4	no	—
200	C₂×C₃⋊C₈	C₄×D₃	1	4	yes	complemented
201	C₂×C₃⋊C₈	C₂×Dic₃	1	4	yes	complemented
202	C₂×C₃⋊C₈	C₂²×D₃	1	2	yes	—
203	C₂×C₃⋊C₈	C₂²×D₃	1	2	yes	—
204	D₃×C₈	—	3	16	no	—
205	D₃×C₈	C₂×Dic₃	1	16	yes	direct product factor
206	C₂²×C₃²	C₂×C₄²	1	2	yes	—
207	C₂²×C₃²	C₂²×C₈	1	4	yes	—
208	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₃×D₃	C₄×C₈	1	16	yes	complemented
210	C₂×C₃×D₃	C₂×C₄²	1	4	yes	—
211	C₂×C₃×D₃	C₂²×C₈	1	8	yes	—
212	C₃²×C₄	C₂×C₄²	1	2	yes	—
213	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
214	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
215	C₃⋊Dic₃	C₂²×C₈	1	8	yes	complemented
216	C₃×Dic₃	C₂×C₄²	1	4	yes	—
217	C₃×Dic₃	C₂²×C₈	1	8	yes	complemented
218	C₂³×C₄	—	3	1	no	—
219	C₂³×C₄	—	9	2	no	—
220	C₂²×C₈	—	3	1	no	—
221	C₂²×C₈	—	3	1	no	—
222	C₂²×C₈	—	3	8	no	—
223	C₂²×C₈	—	3	4	no	—
224	C₂²×C₈	—	9	4	no	—
225	C₂²×C₈	—	9	8	no	—
226	C₂²×C₈	—	9	1	no	—
227	C₂²×C₈	D₃²	1	1	yes	characteristic
228	C₂×C₄²	—	3	1	no	—
229	C₂×C₄²	—	9	4	no	—
230	C₂×C₄²	—	9	4	no	—
231	C₂×C₄²	—	9	2	no	—
232	C₂×C₄²	—	9	1	no	—
233	C₄×C₈	—	3	4	no	—
234	C₄×C₈	—	9	4	no	—
235	C₄×C₈	—	9	4	no	—
236	C₄×C₈	—	9	4	no	—
237	C₂³×C₃	—	2	1	no	—
238	C₂³×C₃	—	3	4	no	—
239	C₂³×C₃	—	3	8	no	—
240	C₂³×C₃	—	3	2	no	—
241	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
242	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
243	C₂²×D₃	D₃×C₈	1	8	yes	—
244	C₂²×D₃	C₄×Dic₃	1	4	yes	—
245	C₂²×D₃	C₂×C₄×D₃	1	2	yes	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	3	4	no	—
251	C₂×C₃×C₄	—	3	8	no	—
252	C₂×C₃×C₄	—	3	2	no	—
253	C₂×C₃×C₄	—	3	4	no	—
254	C₂×C₃×C₄	—	3	8	no	—
255	C₂×C₃×C₄	—	3	4	no	—
256	C₂×C₃×C₄	—	3	4	no	—
257	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
259	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
261	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
262	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
263	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
265	C₂×Dic₃	—	3	8	no	—
266	C₂×Dic₃	—	3	8	no	—
267	C₂×Dic₃	—	3	4	no	—
268	C₂×Dic₃	—	3	4	no	—
269	C₂×Dic₃	—	3	32	no	—
270	C₂×Dic₃	—	6	8	no	—
271	C₂×Dic₃	—	6	4	no	—
272	C₂×Dic₃	D₃×C₈	1	8	yes	direct product factor
273	C₂×Dic₃	C₄×Dic₃	1	4	yes	—
274	C₂×Dic₃	C₂×C₄×D₃	1	4	yes	—
275	C₂×Dic₃	C₂×C₄×D₃	1	2	yes	—
276	C₄×D₃	—	3	32	no	—
277	C₄×D₃	C₄×Dic₃	1	8	yes	—
278	C₄×D₃	C₂×C₄×D₃	1	4	yes	—
279	C₄×D₃	C₂²×Dic₃	1	4	yes	—
280	C₃×C₈	—	2	4	no	—
281	C₃×C₈	—	3	4	no	—
282	C₃×C₈	—	3	4	no	—
283	C₃×C₈	C₂×C₄×D₃	1	4	yes	complemented
284	C₃×C₈	C₂²×Dic₃	1	4	yes	complemented
285	C₃⋊C₈	—	3	4	no	—
286	C₃⋊C₈	—	3	4	no	—
287	C₃⋊C₈	—	6	4	no	—
288	C₃⋊C₈	C₂×C₄×D₃	1	4	yes	complemented
289	C₃⋊C₈	C₂²×Dic₃	1	4	yes	complemented
290	C₂×C₃²	C₂×C₄×C₈	1	4	yes	complemented
291	C₂×C₃²	C₂²×C₄²	1	1	yes	characteristic
292	C₂×C₃²	C₂³×C₈	1	2	yes	—
293	C₃×D₃	C₂×C₄×C₈	1	8	yes	complemented
294	C₂⁴	—	3	1	no	—
295	C₂²×C₄	—	3	2	no	—
296	C₂²×C₄	—	3	1	no	—
297	C₂²×C₄	—	3	2	no	—
298	C₂²×C₄	—	3	2	no	—
299	C₂²×C₄	—	3	4	no	—
300	C₂²×C₄	—	3	4	no	—
301	C₂²×C₄	—	9	8	no	—
302	C₂²×C₄	—	9	16	no	—
303	C₂²×C₄	—	9	2	no	—
304	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
305	C₂×C₈	—	3	2	no	—
306	C₂×C₈	—	3	2	no	—
307	C₂×C₈	—	3	4	no	—
308	C₂×C₈	—	3	4	no	—
309	C₂×C₈	—	3	16	no	—
310	C₂×C₈	—	9	16	no	—
311	C₂×C₈	—	9	2	no	—
312	C₂×C₈	—	9	4	no	—
313	C₂×C₈	D₃×Dic₃	1	4	yes	direct product factor
314	C₂×C₈	C₂×D₃²	1	2	yes	—
315	C₄²	—	3	2	no	—
316	C₄²	—	3	2	no	—
317	C₄²	—	9	8	no	—
318	C₄²	—	9	2	no	—
319	C₄²	—	9	2	no	—
320	C₂²×C₃	—	2	4	no	—
321	C₂²×C₃	—	2	1	no	—
322	C₂²×C₃	—	2	2	no	—
323	C₂²×C₃	—	3	16	no	—
324	C₂²×C₃	—	3	4	no	—
325	C₂²×C₃	—	3	8	no	—
326	C₂²×C₃	C₄²×D₃	1	2	yes	—
327	C₂²×C₃	C₂×D₃×C₈	1	4	yes	—
328	C₂²×C₃	C₂×D₃×C₈	1	4	yes	—
329	C₂²×C₃	C₂×C₄×Dic₃	1	2	yes	—
330	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
331	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
332	C₂×D₃	C₈×Dic₃	1	16	yes	direct product factor
333	C₂×D₃	C₂×D₃×C₈	1	8	yes	—
334	C₂×D₃	C₂×C₄×Dic₃	1	4	yes	—
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	—	3	4	no	—
339	C₃×C₄	—	3	8	no	—
340	C₃×C₄	C₄²×D₃	1	2	yes	—
341	C₃×C₄	C₂×C₄×Dic₃	1	2	yes	—
342	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
343	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
344	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
345	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
346	Dic₃	—	3	8	no	—
347	Dic₃	—	3	8	no	—
348	Dic₃	—	6	8	no	—
349	Dic₃	C₂×D₃×C₈	1	8	yes	direct product factor
350	Dic₃	C₂×C₄×Dic₃	1	4	yes	—
351	C₃²	C₂²×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
352	C₂³	—	3	8	no	—
353	C₂³	—	3	2	no	—
354	C₂³	—	3	4	no	—
355	C₂³	C₄×D₃²	1	1	yes	characteristic
356	C₂×C₄	—	3	8	no	—
357	C₂×C₄	—	3	4	no	—
358	C₂×C₄	—	3	2	no	—
359	C₂×C₄	—	3	4	no	—
360	C₂×C₄	—	3	4	no	—
361	C₂×C₄	—	3	4	no	—
362	C₂×C₄	—	3	8	no	—
363	C₂×C₄	—	9	32	no	—
364	C₂×C₄	—	9	8	no	—
365	C₂×C₄	—	9	4	no	—
366	C₂×C₄	C₄×D₃²	1	2	yes	—
367	C₂×C₄	C₄×D₃²	1	1	yes	characteristic
368	C₂×C₄	C₂×D₃×Dic₃	1	2	yes	—
369	C₂×C₄	C₂²×D₃²	1	1	yes	characteristic
370	C₈	—	3	4	no	—
371	C₈	—	3	4	no	—
372	C₈	—	9	4	no	—
373	C₈	C₂×D₃×Dic₃	1	4	yes	direct product factor
374	C₂×C₃	—	2	1	no	—
375	C₂×C₃	—	2	2	no	—
376	C₂×C₃	—	2	4	no	—
377	C₂×C₃	—	3	8	no	—
378	C₂×C₃	C₄×D₃×C₈	1	4	yes	complemented
379	C₂×C₃	C₂×C₈×Dic₃	1	4	yes	complemented
380	C₂×C₃	C₂×C₄²×D₃	1	1	yes	characteristic
381	C₂×C₃	C₂²×D₃×C₈	1	2	yes	—
382	C₂×C₃	C₂²×D₃×C₈	1	2	yes	—
383	C₂×C₃	C₂²×C₄×Dic₃	1	1	yes	characteristic
384	D₃	C₂×C₈×Dic₃	1	8	yes	direct product factor
385	C₂²	—	3	4	no	—
386	C₂²	—	3	8	no	—
387	C₂²	—	3	16	no	—
388	C₂²	D₃²×C₈	1	4	yes	—
389	C₂²	C₄×D₃×Dic₃	1	2	yes	—
390	C₂²	C₂×C₄×D₃²	1	1	yes	characteristic
391	C₄	—	3	4	no	—
392	C₄	—	3	8	no	—
393	C₄	—	9	8	no	—
394	C₄	C₄×D₃×Dic₃	1	2	yes	—
395	C₄	C₂×C₄×D₃²	1	1	yes	characteristic
396	C₄	C₂²×D₃×Dic₃	1	1	yes	characteristic
397	C₃	—	2	1	no	—
398	C₃	C₂×C₄×D₃×C₈	1	1	yes	characteristic, complemented
399	C₃	C₂²×C₈×Dic₃	1	1	yes	characteristic, complemented
400	C₂	—	3	8	no	—
401	C₂	D₃×C₈×Dic₃	1	4	yes	direct product factor
402	C₂	C₂×D₃²×C₈	1	2	yes	—
403	C₂	C₂×C₄×D₃×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₈	D₃²
commutator, hypocenter	C₃²	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂²×D₃²
Fitting	C₂²×C₃²×C₈	C₂²
socle	C₂³×C₃²	C₂²×C₄
prime radical	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂×C₃²×C₄	C₂⁴
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. C₂×C₈×C₃⋊Dic₃	C₂	semidirect
5. C₂×C₃×C₈×Dic₃	C₂	semidirect
6. C₂×#63553	C₂	semidirect
7. C₂×Dic₃×C₃⋊C₈	C₂	semidirect
8. D₃×C₈×Dic₃	C₂	direct (N × H)
19. C₂×C₃×D₃×C₈	C₄	semidirect
24. C₂×D₃×C₃⋊C₈	C₄	semidirect
26. C₈×C₃⋊Dic₃	C₂²	semidirect
27. C₃×C₈×Dic₃	C₂²	semidirect
28. #63553	C₂²	semidirect
29. Dic₃×C₃⋊C₈	C₂²	semidirect
44. C₂×C₈×Dic₃	D₃	direct (N × H)
56. C₂×D₃×Dic₃	C₈	direct (N × H)
58. C₂×C₃²×C₈	C₂×C₄	semidirect
62. C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	semidirect
66. C₂×C₃×C₃⋊C₈	C₂×C₄	semidirect
67. C₂×C₃×C₃⋊C₈	C₂×C₄	semidirect
70. C₃×D₃×C₈	C₂×C₄	semidirect
72. D₃×C₃⋊C₈	C₂×C₄	semidirect
103. C₂×D₃×C₈	Dic₃	direct (N × H)
114. C₈×Dic₃	C₂×D₃	direct (N × H)
124. C₂×C₃⋊Dic₃	C₂×C₈	semidirect
127. C₂×C₃×Dic₃	C₂×C₈	semidirect
133. D₃×Dic₃	C₂×C₈	direct (N × H)
134. C₃²×C₈	C₂²×C₄	semidirect
135. C₃⋊(C₃⋊C₈)	C₂²×C₄	semidirect
136. C₃×C₃⋊C₈	C₂²×C₄	semidirect
137. C₃×C₃⋊C₈	C₂²×C₄	semidirect
177. C₂×C₃×C₈	C₄×D₃	semidirect
178. C₂×C₃×C₈	C₂×Dic₃	semidirect
200. C₂×C₃⋊C₈	C₄×D₃	semidirect
201. C₂×C₃⋊C₈	C₂×Dic₃	semidirect
205. D₃×C₈	C₂×Dic₃	direct (N × H)
209. C₂×C₃×D₃	C₄×C₈	semidirect
215. C₃⋊Dic₃	C₂²×C₈	semidirect
217. C₃×Dic₃	C₂²×C₈	semidirect
272. C₂×Dic₃	D₃×C₈	direct (N × H)
283. C₃×C₈	C₂×C₄×D₃	semidirect
284. C₃×C₈	C₂²×Dic₃	semidirect
288. C₃⋊C₈	C₂×C₄×D₃	semidirect
289. C₃⋊C₈	C₂²×Dic₃	semidirect
290. C₂×C₃²	C₂×C₄×C₈	semidirect
293. C₃×D₃	C₂×C₄×C₈	semidirect
313. C₂×C₈	D₃×Dic₃	direct (N × H)
332. C₂×D₃	C₈×Dic₃	direct (N × H)
349. Dic₃	C₂×D₃×C₈	direct (N × H)
351. C₃²	C₂²×C₄×C₈	semidirect
373. C₈	C₂×D₃×Dic₃	direct (N × H)
378. C₂×C₃	C₄×D₃×C₈	semidirect
379. C₂×C₃	C₂×C₈×Dic₃	semidirect
384. D₃	C₂×C₈×Dic₃	direct (N × H)
398. C₃	C₂×C₄×D₃×C₈	semidirect
399. C₃	C₂²×C₈×Dic₃	semidirect
401. C₂	D₃×C₈×Dic₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₃×C₈	2
C₂×C₄×D₃×Dic₃	2
C₂²×D₃×C₃⋊C₈	2
C₂×C₈×C₃⋊Dic₃	2
C₂×C₃×C₈×Dic₃	2
C₂×#63553	2
C₂×Dic₃×C₃⋊C₈	2
D₃×C₈×Dic₃	2
C₂²×C₈×Dic₃	3
C₂×C₄×D₃×C₈	3

Subgroups — C2×D3×C8×Dic3 #11857107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₈×Dic₃ #11857107