Subgroups — C₈×#6292 #13159606

Order 1728.

1108 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#6292	C₂	1	1	yes	maximal, characteristic
4	C₃²×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₃⋊(C₃⋊(C₃⋊C₈))	C₂	1	1	yes	maximal, characteristic, complemented
6	#11722024	C₂	1	1	yes	maximal, characteristic, complemented
7	#11722023	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×C₄⋊(C₃⋊D₃)	—	3	1	no	maximal
9	C₈×#626	—	3	4	no	maximal
10	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
12	C₂×#6292	C₄	1	1	yes	characteristic
13	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃⋊(C₃⋊(C₃⋊C₈))	C₂²	1	1	yes	characteristic
15	C₈×C₃⋊(C₃⋊D₃)	—	2	2	no	—
16	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
17	C₃×C₈×C₃⋊D₃	—	2	2	no	—
18	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	Dic₃⋊(C₃⋊Dic₃)	C₄	1	1	yes	characteristic
21	#88804	C₄	1	1	yes	characteristic
22	#88803	C₄	1	1	yes	characteristic
23	C₂×C₈×C₃⋊D₃	—	3	1	no	—
24	C₂×C₈×C₃⋊D₃	—	3	4	no	—
25	C₂×C₈×C₃⋊D₃	—	6	4	no	—
26	C₂×C₈×C₃⋊D₃	D₃	1	1	yes	characteristic, complemented
27	C₄×C₄⋊(C₃⋊D₃)	—	3	1	no	—
28	C₂×C₃×D₃×C₈	—	3	4	no	—
29	C₄×#626	—	3	4	no	—
30	C₃²×C₄×C₈	—	3	1	no	—
31	#63647	—	3	1	no	—
32	#63647	—	3	1	no	—
33	C₄⋊(C₃⋊(C₃⋊C₈))	—	3	1	no	—
34	C₃×C₈×Dic₃	D₃	1	4	yes	complemented
35	Dic₃⋊(C₃⋊C₈)	—	3	4	no	—
36	#63557	—	3	4	no	—
37	(C₂×D₃)⋊(C₃⋊C₈)	—	3	4	no	—
38	C₂²×C₃⋊(C₃⋊D₃)	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
41	C₂×C₃⋊(C₃⋊Dic₃)	C₂×C₄	1	1	yes	characteristic
42	C₄×C₃⋊(C₃⋊D₃)	—	2	1	no	—
43	C₄×C₃⋊(C₃⋊D₃)	—	2	1	no	—
44	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
45	C₃×C₄×C₃⋊D₃	—	2	1	no	—
46	C₃×C₄×C₃⋊D₃	—	2	1	no	—
47	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
49	#6292	C₈	1	4	yes	direct product factor
50	C₃³×C₈	D₄	1	2	yes	complemented
51	C₃⋊(C₃⋊(C₃⋊C₈))	—	2	1	no	—
52	C₃×C₃⋊(C₃⋊C₈)	—	2	1	no	—
53	C₃²×C₃⋊C₈	—	2	1	no	—
54	C₈×#67	—	9	1	no	—
55	C₈×D₁₂	—	9	4	no	—
56	C₂×C₄⋊(C₃⋊D₃)	—	3	1	no	—
57	C₂×C₄×C₃⋊D₃	—	3	1	no	—
58	C₂×C₄×C₃⋊D₃	—	3	4	no	—
59	C₂×C₄×C₃⋊D₃	—	6	4	no	—
60	C₂×C₄×C₃⋊D₃	C₂×D₃	1	1	yes	characteristic
61	C₂×C₃×C₄×D₃	—	3	4	no	—
62	C₂×#626	—	3	4	no	—
63	C₂×C₃²×C₈	—	2	4	no	—
64	C₂×C₃²×C₈	—	3	1	no	—
65	C₂×C₃²×C₈	C₂×D₃	1	4	yes	—
66	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
67	C₃²×C₄²	—	3	1	no	—
68	#3752	—	3	1	no	—
69	#3752	—	3	1	no	—
70	C₄⋊(C₃⋊Dic₃)	—	3	1	no	—
71	C₂×C₃⋊(C₃⋊C₈)	—	3	1	no	—
72	C₂×C₃⋊(C₃⋊C₈)	—	3	4	no	—
73	C₂×C₃⋊(C₃⋊C₈)	—	6	4	no	—
74	C₂×C₃⋊(C₃⋊C₈)	C₂×D₃	1	1	yes	characteristic
75	C₈×C₃⋊D₃	—	2	2	no	—
76	C₈×C₃⋊D₃	—	6	16	no	—
77	C₈×C₃⋊D₃	—	6	8	no	—
78	C₈×C₃⋊D₃	—	6	2	no	—
79	C₃×C₄×Dic₃	C₂×D₃	1	4	yes	—
80	C₂×C₃×C₃⋊C₈	—	3	4	no	—
81	C₂×C₃×C₃⋊C₈	C₂×D₃	1	4	yes	—
82	C₃×D₃×C₈	—	6	8	no	—
83	Dic₃⋊Dic₃	—	3	4	no	—
84	#3722	—	3	4	no	—
85	(C₂×D₃)⋊Dic₃	—	3	4	no	—
86	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
88	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
89	C₂×C₃⋊(C₃⋊D₃)	C₂×C₈	1	2	yes	complemented
90	C₂×C₃×C₃⋊D₃	—	2	1	no	—
91	C₂×C₃×C₃⋊D₃	—	2	1	no	—
92	C₂×C₃×C₃⋊D₃	C₂×C₈	1	2	yes	complemented
93	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
94	C₃³×C₄	#41	1	1	yes	characteristic
95	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
96	C₃×C₃⋊Dic₃	—	2	1	no	—
97	C₃²×Dic₃	—	2	1	no	—
98	C₃²×Dic₃	C₂×C₈	1	2	yes	complemented
99	C₂²×C₃×C₈	—	9	1	no	—
100	C₄×#67	—	9	1	no	—
101	C₂×D₃×C₈	—	3	4	no	—
102	C₂×D₃×C₈	—	9	4	no	—
103	C₂×D₃×C₈	—	9	1	no	—
104	C₂×D₃×C₈	—	18	4	no	—
105	C₄×D₁₂	—	9	4	no	—
106	C₃×C₄×C₈	—	3	4	no	—
107	#830	—	9	1	no	—
108	(C₂×D₃)⋊C₈	—	9	4	no	—
109	(C₂×D₃)⋊C₈	—	9	4	no	—
110	(C₂×D₃)⋊C₈	—	9	1	no	—
111	Dic₃⋊C₈	—	9	1	no	—
112	C₈×Dic₃	C₃⋊D₃	1	1	yes	characteristic, complemented
113	C₄⋊(C₃⋊C₈)	—	9	4	no	—
114	C₂²×C₃⋊D₃	—	3	1	no	—
115	C₂²×C₃⋊D₃	—	3	4	no	—
116	C₂²×C₃⋊D₃	—	6	4	no	—
117	C₂²×C₃⋊D₃	C₄×D₃	1	1	yes	characteristic
118	C₂²×C₃×D₃	—	3	4	no	—
119	C₂×C₃²×C₄	—	2	4	no	—
120	C₂×C₃²×C₄	—	3	1	no	—
121	C₂×C₃²×C₄	—	3	1	no	—
122	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
123	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
124	C₂×C₃⋊Dic₃	—	3	1	no	—
125	C₂×C₃⋊Dic₃	—	3	4	no	—
126	C₂×C₃⋊Dic₃	—	6	4	no	—
127	C₂×C₃⋊Dic₃	C₄×D₃	1	1	yes	characteristic
128	C₄⋊(C₃⋊D₃)	—	3	4	no	—
129	C₄×C₃⋊D₃	—	2	1	no	—
130	C₄×C₃⋊D₃	—	2	1	no	—
131	C₄×C₃⋊D₃	—	6	8	no	—
132	C₄×C₃⋊D₃	—	6	8	no	—
133	C₄×C₃⋊D₃	—	6	4	no	—
134	C₄×C₃⋊D₃	—	6	4	no	—
135	C₄×C₃⋊D₃	—	6	1	no	—
136	C₄×C₃⋊D₃	—	6	1	no	—
137	C₂×C₃×Dic₃	—	3	4	no	—
138	C₂×C₃×Dic₃	C₄×D₃	1	4	yes	—
139	C₂×C₃×Dic₃	C₄×D₃	1	4	yes	—
140	C₃×C₄×D₃	—	6	4	no	—
141	C₃×C₄×D₃	—	6	4	no	—
142	#626	—	3	16	no	—
143	C₃²×C₈	—	2	8	no	—
144	C₃²×C₈	—	6	1	no	—
145	C₃²×C₈	D₁₂	1	8	yes	complemented
146	C₃²×C₈	#67	1	2	yes	complemented
147	C₃⋊(C₃⋊C₈)	—	2	1	no	—
148	C₃⋊(C₃⋊C₈)	—	6	8	no	—
149	C₃⋊(C₃⋊C₈)	—	6	4	no	—
150	C₃⋊(C₃⋊C₈)	—	6	1	no	—
151	C₃×C₃⋊C₈	—	2	4	no	—
152	C₃×C₃⋊C₈	—	6	4	no	—
153	C₈×D₄	—	27	1	no	Sylow
154	C₂×C₃³	C₄×D₄	1	1	yes	characteristic
155	C₂×C₃³	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₃³	#131	1	1	yes	characteristic
157	C₃⋊(C₃⋊D₃)	—	2	2	no	—
158	C₃×C₃⋊D₃	—	2	2	no	—
159	C₂²×C₃×C₄	—	9	1	no	—
160	C₂×#67	—	9	1	no	—
161	C₂×D₁₂	—	9	4	no	—
162	C₂×C₄×D₃	—	3	4	no	—
163	C₂×C₄×D₃	—	9	4	no	—
164	C₂×C₄×D₃	—	9	1	no	—
165	C₂×C₄×D₃	—	18	4	no	—
166	C₂×C₃×C₈	—	2	4	no	—
167	C₂×C₃×C₈	—	3	4	no	—
168	C₂×C₃×C₈	—	9	1	no	—
169	C₂×C₃×C₈	—	18	2	no	—
170	C₂×C₃×C₈	D₃²	1	4	yes	—
171	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
172	C₃×C₄²	—	3	4	no	—
173	#217	—	9	1	no	—
174	(C₂×D₃)⋊C₄	—	9	4	no	—
175	(C₂×D₃)⋊C₄	—	9	4	no	—
176	(C₂×D₃)⋊C₄	—	9	1	no	—
177	C₄⋊Dic₃	—	9	4	no	—
178	Dic₃⋊C₄	—	9	1	no	—
179	C₄×Dic₃	C₂×C₃⋊D₃	1	1	yes	characteristic
180	C₂×C₃⋊C₈	—	3	4	no	—
181	C₂×C₃⋊C₈	—	9	4	no	—
182	C₂×C₃⋊C₈	—	9	1	no	—
183	C₂×C₃⋊C₈	—	18	4	no	—
184	C₂×C₃⋊C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
185	D₃×C₈	—	6	8	no	—
186	D₃×C₈	—	18	16	no	—
187	D₃×C₈	—	18	8	no	—
188	D₃×C₈	—	18	2	no	—
189	C₂²×C₃²	—	2	4	no	—
190	C₂²×C₃²	C₂×C₄×D₃	1	4	yes	—
191	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
192	C₂×C₃⋊D₃	—	2	1	no	—
193	C₂×C₃⋊D₃	—	2	1	no	—
194	C₂×C₃⋊D₃	—	3	2	no	—
195	C₂×C₃⋊D₃	—	3	8	no	—
196	C₂×C₃⋊D₃	—	6	8	no	—
197	C₂×C₃⋊D₃	—	6	8	no	—
198	C₂×C₃⋊D₃	—	6	8	no	—
199	C₂×C₃⋊D₃	—	6	4	no	—
200	C₂×C₃⋊D₃	—	6	4	no	—
201	C₂×C₃⋊D₃	—	6	1	no	—
202	C₂×C₃⋊D₃	—	6	1	no	—
203	C₂×C₃⋊D₃	D₃×C₈	1	2	yes	complemented
204	C₂×C₃×D₃	—	3	8	no	—
205	C₂×C₃×D₃	—	6	4	no	—
206	C₂×C₃×D₃	—	6	4	no	—
207	C₃²×C₄	—	2	4	no	—
208	C₃²×C₄	—	2	4	no	—
209	C₃²×C₄	—	3	2	no	—
210	C₃²×C₄	—	6	1	no	—
211	C₃²×C₄	C₂×D₁₂	1	4	yes	—
212	C₃²×C₄	#235	1	4	yes	—
213	C₃²×C₄	#235	1	1	yes	characteristic
214	C₃²×C₄	C₂×#67	1	1	yes	characteristic
215	C₃⋊Dic₃	—	2	1	no	—
216	C₃⋊Dic₃	—	6	8	no	—
217	C₃⋊Dic₃	—	6	4	no	—
218	C₃⋊Dic₃	—	6	1	no	—
219	C₃×Dic₃	—	2	4	no	—
220	C₃×Dic₃	—	6	4	no	—
221	C₃×Dic₃	D₃×C₈	1	8	yes	complemented
222	C₂²×C₈	—	9	1	no	—
223	C₂²×C₈	—	27	1	no	—
224	C₄×D₄	—	27	1	no	—
225	C₄⋊C₈	—	27	1	no	—
226	C₂²⋊C₈	—	27	1	no	—
227	C₂²⋊C₈	—	27	1	no	—
228	C₄×C₈	—	3	1	no	—
229	C₃³	C₈×D₄	1	1	yes	characteristic, complemented, Sylow
230	C₂³×C₃	—	9	1	no	—
231	C₂²×D₃	—	3	4	no	—
232	C₂²×D₃	—	9	4	no	—
233	C₂²×D₃	—	9	1	no	—
234	C₂²×D₃	—	18	4	no	—
235	C₂×C₃×C₄	—	2	4	no	—
236	C₂×C₃×C₄	—	3	4	no	—
237	C₂×C₃×C₄	—	3	4	no	—
238	C₂×C₃×C₄	—	9	1	no	—
239	C₂×C₃×C₄	—	18	1	no	—
240	C₂×C₃×C₄	—	18	1	no	—
241	C₂×C₃×C₄	C₂×D₃²	1	4	yes	—
242	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
243	#67	—	9	4	no	—
244	C₂×Dic₃	—	3	4	no	—
245	C₂×Dic₃	—	9	4	no	—
246	C₂×Dic₃	—	9	1	no	—
247	C₂×Dic₃	—	18	4	no	—
248	C₂×Dic₃	C₄×C₃⋊D₃	1	1	yes	characteristic
249	C₂×Dic₃	C₄×C₃⋊D₃	1	1	yes	characteristic
250	D₁₂	—	9	16	no	—
251	C₄×D₃	—	6	4	no	—
252	C₄×D₃	—	6	4	no	—
253	C₄×D₃	—	18	8	no	—
254	C₄×D₃	—	18	8	no	—
255	C₄×D₃	—	18	4	no	—
256	C₄×D₃	—	18	4	no	—
257	C₄×D₃	—	18	1	no	—
258	C₄×D₃	—	18	1	no	—
259	C₃×C₈	—	2	8	no	—
260	C₃×C₈	—	6	4	no	—
261	C₃×C₈	—	18	1	no	—
262	C₃×C₈	#626	1	8	yes	complemented
263	C₃×C₈	C₄⋊(C₃⋊D₃)	1	2	yes	complemented
264	C₃⋊C₈	—	2	1	no	—
265	C₃⋊C₈	—	6	4	no	—
266	C₃⋊C₈	—	18	8	no	—
267	C₃⋊C₈	—	18	4	no	—
268	C₃⋊C₈	—	18	1	no	—
269	C₂×C₃²	—	2	4	no	—
270	C₂×C₃²	—	2	4	no	—
271	C₂×C₃²	—	2	4	no	—
272	C₂×C₃²	C₄×D₁₂	1	4	yes	—
273	C₂×C₃²	C₂×D₃×C₈	1	4	yes	—
274	C₂×C₃²	C₂×D₃×C₈	1	1	yes	characteristic
275	C₂×C₃²	#901	1	4	yes	—
276	C₂×C₃²	#901	1	1	yes	characteristic
277	C₂×C₃²	C₄×#67	1	1	yes	characteristic
278	C₃⋊D₃	—	2	2	no	—
279	C₃⋊D₃	—	6	16	no	—
280	C₃⋊D₃	—	6	8	no	—
281	C₃⋊D₃	—	6	2	no	—
282	C₃×D₃	—	6	8	no	—
283	C₂×D₄	—	27	1	no	—
284	C₂²×C₄	—	9	1	no	—
285	C₂²×C₄	—	27	1	no	—
286	C₂×C₈	—	3	1	no	—
287	C₂×C₈	—	9	1	no	—
288	C₂×C₈	—	18	2	no	—
289	C₂×C₈	—	27	1	no	—
290	C₂×C₈	—	54	2	no	—
291	C₂×C₈	D₃×C₃⋊D₃	1	1	yes	characteristic
292	C₄⋊C₄	—	27	1	no	—
293	C₂²⋊C₄	—	27	1	no	—
294	C₂²⋊C₄	—	27	1	no	—
295	C₄²	—	3	1	no	—
296	C₂²×C₃	—	2	4	no	—
297	C₂²×C₃	—	9	2	no	—
298	C₂²×C₃	—	18	1	no	—
299	C₂²×C₃	—	18	1	no	—
300	C₂²×C₃	C₄×D₃²	1	4	yes	—
301	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
302	C₂×D₃	—	3	8	no	—
303	C₂×D₃	—	6	4	no	—
304	C₂×D₃	—	6	4	no	—
305	C₂×D₃	—	9	8	no	—
306	C₂×D₃	—	9	2	no	—
307	C₂×D₃	—	18	8	no	—
308	C₂×D₃	—	18	8	no	—
309	C₂×D₃	—	18	8	no	—
310	C₂×D₃	—	18	4	no	—
311	C₂×D₃	—	18	1	no	—
312	C₂×D₃	—	18	1	no	—
313	C₂×D₃	—	18	4	no	—
314	C₃×C₄	—	2	4	no	—
315	C₃×C₄	—	2	4	no	—
316	C₃×C₄	—	3	8	no	—
317	C₃×C₄	—	6	4	no	—
318	C₃×C₄	—	18	1	no	—
319	C₃×C₄	#3798	1	4	yes	—
320	C₃×C₄	C₂×#626	1	4	yes	—
321	C₃×C₄	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
322	C₃×C₄	#3828	1	1	yes	characteristic
323	Dic₃	—	2	1	no	—
324	Dic₃	—	6	4	no	—
325	Dic₃	—	18	8	no	—
326	Dic₃	—	18	1	no	—
327	Dic₃	—	18	4	no	—
328	Dic₃	C₈×C₃⋊D₃	1	2	yes	complemented
329	C₃²	—	2	4	no	—
330	C₃²	C₈×D₁₂	1	4	yes	complemented
331	C₃²	C₈×#67	1	1	yes	characteristic, complemented
332	C₂³	—	9	1	no	—
333	C₂³	—	27	1	no	—
334	D₄	—	27	4	no	—
335	C₂×C₄	—	3	1	no	—
336	C₂×C₄	—	3	1	no	—
337	C₂×C₄	—	9	1	no	—
338	C₂×C₄	—	18	1	no	—
339	C₂×C₄	—	18	1	no	—
340	C₂×C₄	—	27	1	no	—
341	C₂×C₄	—	54	1	no	—
342	C₂×C₄	—	54	1	no	—
343	C₂×C₄	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic
344	C₈	—	6	1	no	—
345	C₈	—	18	1	no	—
346	C₈	—	54	1	no	—
347	C₈	#6292	1	2	yes	direct product factor
348	C₂×C₃	—	2	4	no	—
349	C₂×C₃	—	2	4	no	—
350	C₂×C₃	—	2	4	no	—
351	C₂×C₃	—	18	2	no	—
352	C₂×C₃	D₃²×C₈	1	4	yes	—
353	C₂×C₃	#63803	1	4	yes	—
354	C₂×C₃	C₄×#626	1	4	yes	—
355	C₂×C₃	C₄×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
356	C₂×C₃	C₂×C₈×C₃⋊D₃	1	1	yes	characteristic
357	C₂×C₃	#64110	1	1	yes	characteristic
358	D₃	—	6	8	no	—
359	D₃	—	18	16	no	—
360	D₃	—	18	2	no	—
361	D₃	—	18	8	no	—
362	C₂²	—	9	2	no	—
363	C₂²	—	18	1	no	—
364	C₂²	—	18	1	no	—
365	C₂²	—	27	2	no	—
366	C₂²	—	54	1	no	—
367	C₂²	—	54	1	no	—
368	C₂²	C₄×D₃×C₃⋊D₃	1	1	yes	characteristic
369	C₄	—	3	2	no	—
370	C₄	—	6	1	no	—
371	C₄	—	18	1	no	—
372	C₄	—	54	1	no	—
373	C₄	#89020	1	1	yes	characteristic
374	C₄	C₂×#6292	1	1	yes	characteristic
375	C₃	—	2	4	no	—
376	C₃	C₈×#626	1	4	yes	complemented
377	C₃	C₈×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
378	C₂	—	18	2	no	—
379	C₂	—	54	2	no	—
380	C₂	D₃×C₈×C₃⋊D₃	1	1	yes	characteristic
381	C₂	#11723331	1	1	yes	characteristic
382	C₂	C₄×#6292	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₈	D₃×C₃⋊D₃
commutator	C₂×C₃³	C₂²×C₈
Frattini	C₂×C₄	C₂×D₃×C₃⋊D₃
Fitting	C₂×C₃³×C₈	C₂²
socle	C₂²×C₃³	C₂²×C₄
prime radical	C₂×#6292	C₄
cosocle	C₂×C₃³×C₄	C₂³
hypocenter	C₃³	C₈×D₄
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×C₃⋊(C₃⋊D₃)	C₂	semidirect
2. C₂×C₃×C₈×C₃⋊D₃	C₂	semidirect
4. C₃²×C₈×Dic₃	C₂	semidirect
5. Dic₃⋊(C₃⋊(C₃⋊C₈))	C₂	semidirect
6. #11722024	C₂	semidirect
7. #11722023	C₂	semidirect
26. C₂×C₈×C₃⋊D₃	D₃	semidirect
34. C₃×C₈×Dic₃	D₃	semidirect
49. #6292	C₈	direct (N × H)
50. C₃³×C₈	D₄	semidirect
89. C₂×C₃⋊(C₃⋊D₃)	C₂×C₈	semidirect
92. C₂×C₃×C₃⋊D₃	C₂×C₈	semidirect
98. C₃²×Dic₃	C₂×C₈	semidirect
112. C₈×Dic₃	C₃⋊D₃	semidirect
145. C₃²×C₈	D₁₂	semidirect
146. C₃²×C₈	#67	semidirect
203. C₂×C₃⋊D₃	D₃×C₈	semidirect
221. C₃×Dic₃	D₃×C₈	semidirect
229. C₃³	C₈×D₄	semidirect
262. C₃×C₈	#626	semidirect
263. C₃×C₈	C₄⋊(C₃⋊D₃)	semidirect
328. Dic₃	C₈×C₃⋊D₃	semidirect
330. C₃²	C₈×D₁₂	semidirect
331. C₃²	C₈×#67	semidirect
347. C₈	#6292	direct (N × H)
376. C₃	C₈×#626	semidirect
377. C₃	C₈×C₄⋊(C₃⋊D₃)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×C₃⋊(C₃⋊D₃)	2
C₂×C₃×C₈×C₃⋊D₃	2
C₄×#6292	2
C₃²×C₈×Dic₃	2
Dic₃⋊(C₃⋊(C₃⋊C₈))	2
#11722024	2
#11722023	2
C₈×C₄⋊(C₃⋊D₃)	3
C₈×#626	3

Subgroups — C8×#6292 #13159606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#6292 #13159606