Subgroups — C₃×D₃×C₈×D₄ #11859143

Order 1152.

1299 conjugacy classes of subgroups.

The subgroup lattice has 608 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	2	yes	maximal, complemented
2	C₃×C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃²×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₈×#67	C₂	1	2	yes	maximal, complemented
5	C₃×D₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4834	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#67⋊C₈	C₂	1	2	yes	maximal, complemented
9	C₃×D₃×C₂²⋊C₈	C₂	1	2	yes	maximal, complemented
10	C₃×C₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×C₈×D₄	—	3	1	no	maximal
13	D₃×C₈×D₄	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×D₃×D₄	C₄	1	1	yes	characteristic
15	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
16	C₂²×C₃²×C₈	C₂²	1	2	yes	complemented
17	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
18	C₃×D₄×Dic₃	C₄	1	1	yes	characteristic
19	C₃×C₄×#67	C₂²	1	2	yes	—
20	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	complemented
21	C₂×C₃×D₃×C₈	—	2	8	no	—
22	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
23	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
24	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
25	C₂×C₃×D₃×C₈	C₂²	1	2	yes	complemented
26	C₂×C₃×D₃×C₈	C₂²	1	2	yes	complemented
27	C₃×#893	C₄	1	1	yes	characteristic
28	C₃×D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
29	C₃×#67⋊C₄	C₄	1	2	yes	—
30	C₃×D₃×C₂²⋊C₄	C₄	1	2	yes	—
31	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
32	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
33	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
34	C₃²×C₂²⋊C₈	C₂²	1	2	yes	complemented
35	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
36	C₃×#830	C₂²	1	2	yes	complemented
37	C₃×(C₂×D₃)⋊C₈	C₂²	1	2	yes	complemented
38	C₃×(C₂×D₃)⋊C₈	C₂²	1	2	yes	complemented
39	C₃×Dic₃⋊C₈	C₂²	1	2	yes	complemented
40	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
43	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	C₂³×C₃×C₈	—	3	2	no	—
45	C₂×C₃×C₄×D₄	—	3	1	no	—
46	C₂²×D₃×C₈	C₂×C₃	1	2	yes	complemented
47	C₄×D₃×D₄	C₂×C₃	1	1	yes	characteristic
48	C₃×C₈×D₄	—	2	1	no	—
49	C₃×C₈×D₄	—	3	2	no	—
50	C₃×C₈×D₄	—	3	1	no	—
51	C₃×C₈×D₄	—	3	1	no	—
52	C₃×C₈×D₄	—	3	2	no	—
53	C₃×C₈×D₄	—	3	1	no	—
54	C₃×C₈×D₄	D₃	1	1	yes	characteristic, direct product factor
55	C₃×C₈×D₄	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×C₃×C₄⋊C₈	—	3	1	no	—
57	C₂×C₃×C₂²⋊C₈	—	3	2	no	—
58	C₂×C₃×C₄×C₈	—	3	1	no	—
59	C₈×#67	C₂×C₃	1	2	yes	complemented
60	D₄×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
61	#4834	C₂×C₃	1	1	yes	characteristic, complemented
62	D₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
63	#67⋊C₈	C₂×C₃	1	2	yes	complemented
64	D₃×C₂²⋊C₈	C₂×C₃	1	2	yes	complemented
65	C₈×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
66	C₄×D₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
67	C₂³×C₃×D₃	C₂×C₄	1	2	yes	—
68	C₂×C₃²×D₄	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₃²×C₄	C₂³	1	2	yes	—
70	C₂×C₃×#67	C₂×C₄	1	2	yes	—
71	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
72	C₃×D₃×D₄	C₈	1	8	yes	direct product factor
73	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
74	C₂×C₃×C₄×D₃	—	2	4	no	—
75	C₂×C₃×C₄×D₃	—	2	4	no	—
76	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
78	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
79	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
81	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
82	C₂×C₃²×C₈	—	2	4	no	—
83	C₂×C₃²×C₈	C₂³	1	2	yes	—
84	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
85	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
86	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₃²×C₂²⋊C₄	C₂×C₄	1	2	yes	—
88	C₃²×C₄²	C₂³	1	1	yes	characteristic
89	C₃×#217	C₂×C₄	1	2	yes	—
90	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
91	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
92	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
93	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
94	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
95	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
96	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₃⋊C₈	—	2	4	no	—
98	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
99	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
101	C₃×D₃×C₈	—	2	4	no	—
102	C₃×D₃×C₈	—	2	2	no	—
103	C₃×D₃×C₈	—	2	4	no	—
104	C₃×D₃×C₈	—	2	4	no	—
105	C₃×D₃×C₈	D₄	1	4	yes	direct product factor
106	C₂×C₈×D₄	—	3	1	no	Sylow
107	C₂²×C₃×D₄	—	3	1	no	—
108	C₂³×C₃×C₄	—	3	2	no	—
109	C₂×D₃×D₄	C₃×C₄	1	1	yes	characteristic
110	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
111	C₂²×C₃×C₈	—	2	2	no	—
112	C₂²×C₃×C₈	—	3	1	no	—
113	C₂²×C₃×C₈	—	3	2	no	—
114	C₂²×C₃×C₈	—	3	2	no	—
115	C₂²×C₃×C₈	—	3	2	no	—
116	C₂²×C₃×C₈	—	3	1	no	—
117	C₂²×C₃×C₈	—	3	2	no	—
118	C₂²×C₃×C₈	—	6	8	no	—
119	C₂²×C₃×C₈	C₂×D₃	1	2	yes	complemented
120	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	complemented
121	C₃×C₄×D₄	—	2	1	no	—
122	C₃×C₄×D₄	—	3	1	no	—
123	C₃×C₄×D₄	—	3	2	no	—
124	C₃×C₄×D₄	—	3	1	no	—
125	C₃×C₄×D₄	—	3	2	no	—
126	C₃×C₄×D₄	—	3	1	no	—
127	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
128	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	—	3	1	no	—
130	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
131	C₂×C₃×C₄²	—	3	1	no	—
132	D₄×Dic₃	C₃×C₄	1	1	yes	characteristic
133	C₄×#67	C₂²×C₃	1	2	yes	—
134	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	complemented
135	C₂×D₃×C₈	—	2	8	no	—
136	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
137	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
138	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
139	C₂×D₃×C₈	C₂²×C₃	1	2	yes	complemented
140	C₂×D₃×C₈	C₂²×C₃	1	2	yes	complemented
141	#893	C₃×C₄	1	1	yes	characteristic
142	D₃×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
143	#67⋊C₄	C₃×C₄	1	2	yes	—
144	D₃×C₂²⋊C₄	C₃×C₄	1	2	yes	—
145	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
146	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
147	C₃×C₄⋊C₈	—	2	1	no	—
148	C₃×C₄⋊C₈	—	3	2	no	—
149	C₃×C₄⋊C₈	—	3	1	no	—
150	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
151	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
152	C₃×C₂²⋊C₈	—	2	2	no	—
153	C₃×C₂²⋊C₈	—	3	2	no	—
154	C₃×C₂²⋊C₈	—	3	2	no	—
155	C₃×C₂²⋊C₈	—	3	2	no	—
156	C₃×C₂²⋊C₈	C₂×D₃	1	2	yes	complemented
157	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	complemented
158	C₃×C₄×C₈	—	2	1	no	—
159	C₃×C₄×C₈	—	3	1	no	—
160	C₃×C₄×C₈	—	3	1	no	—
161	C₃×C₄×C₈	—	3	1	no	—
162	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
163	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
164	#830	C₂²×C₃	1	2	yes	complemented
165	(C₂×D₃)⋊C₈	C₂²×C₃	1	2	yes	complemented
166	(C₂×D₃)⋊C₈	C₂²×C₃	1	2	yes	complemented
167	Dic₃⋊C₈	C₂²×C₃	1	2	yes	complemented
168	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
170	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₂³×C₃²	C₂²×C₄	1	2	yes	—
173	C₂²×C₃×D₃	—	2	4	no	—
174	C₂²×C₃×D₃	—	2	4	no	—
175	C₂²×C₃×D₃	C₂×C₈	1	8	yes	complemented
176	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
177	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
178	C₃²×D₄	C₂×C₈	1	4	yes	complemented
179	C₂×C₃²×C₄	—	2	2	no	—
180	C₂×C₃²×C₄	—	2	2	no	—
181	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
183	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
185	C₃×#67	C₂×C₈	1	8	yes	complemented
186	C₂×C₃×Dic₃	—	2	4	no	—
187	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
189	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
191	C₃×D₁₂	C₂×C₈	1	4	yes	complemented
192	C₃×C₄×D₃	—	2	4	no	—
193	C₃×C₄×D₃	—	2	2	no	—
194	C₃×C₄×D₃	—	2	2	no	—
195	C₃×C₄×D₃	—	2	2	no	—
196	C₃×C₄×D₃	—	2	4	no	—
197	C₃×C₄×D₃	C₂×C₈	1	4	yes	complemented
198	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
199	C₃×C₄×D₃	#41	1	2	yes	—
200	C₃²×C₈	—	2	2	no	—
201	C₃²×C₈	—	2	1	no	—
202	C₃²×C₈	C₂×D₄	1	2	yes	complemented
203	C₃×C₃⋊C₈	—	2	2	no	—
204	C₃×C₃⋊C₈	—	2	1	no	—
205	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	complemented
206	C₂³×C₈	—	3	2	no	—
207	C₂×C₄×D₄	—	3	1	no	—
208	C₈×D₄	—	3	2	no	—
209	C₈×D₄	—	3	1	no	—
210	C₈×D₄	—	3	1	no	—
211	C₈×D₄	—	3	2	no	—
212	C₈×D₄	—	3	1	no	—
213	C₈×D₄	C₃×D₃	1	1	yes	characteristic, direct product factor
214	C₂×C₄⋊C₈	—	3	1	no	—
215	C₂×C₂²⋊C₈	—	3	2	no	—
216	C₂×C₄×C₈	—	3	1	no	—
217	C₂⁴×C₃	—	3	2	no	—
218	C₂³×D₃	C₂×C₃×C₄	1	2	yes	—
219	C₂×C₃×D₄	—	2	1	no	—
220	C₂×C₃×D₄	—	3	2	no	—
221	C₂×C₃×D₄	—	3	8	no	—
222	C₂×C₃×D₄	—	3	1	no	—
223	C₂×C₃×D₄	C₄×D₃	1	1	yes	characteristic
224	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
225	C₂²×C₃×C₄	—	2	2	no	—
226	C₂²×C₃×C₄	—	3	1	no	—
227	C₂²×C₃×C₄	—	3	1	no	—
228	C₂²×C₃×C₄	—	3	2	no	—
229	C₂²×C₃×C₄	—	3	1	no	—
230	C₂²×C₃×C₄	—	3	2	no	—
231	C₂²×C₃×C₄	—	3	2	no	—
232	C₂²×C₃×C₄	—	3	2	no	—
233	C₂²×C₃×C₄	—	6	4	no	—
234	C₂²×C₃×C₄	—	6	4	no	—
235	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
236	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
237	C₂×#67	C₂×C₃×C₄	1	2	yes	—
238	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
239	D₃×D₄	C₃×C₈	1	8	yes	direct product factor
240	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
241	C₂×C₄×D₃	—	2	4	no	—
242	C₂×C₄×D₃	—	2	4	no	—
243	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
244	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
245	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
246	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
247	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
248	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
249	C₂×C₃×C₈	—	2	4	no	—
250	C₂×C₃×C₈	—	2	4	no	—
251	C₂×C₃×C₈	—	2	1	no	—
252	C₂×C₃×C₈	—	2	1	no	—
253	C₂×C₃×C₈	—	2	2	no	—
254	C₂×C₃×C₈	—	3	1	no	—
255	C₂×C₃×C₈	—	3	4	no	—
256	C₂×C₃×C₈	—	3	1	no	—
257	C₂×C₃×C₈	—	3	2	no	—
258	C₂×C₃×C₈	—	4	4	no	—
259	C₂×C₃×C₈	—	6	4	no	—
260	C₂×C₃×C₈	—	6	2	no	—
261	C₂×C₃×C₈	—	6	4	no	—
262	C₂×C₃×C₈	—	6	4	no	—
263	C₂×C₃×C₈	—	6	4	no	—
264	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
265	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
266	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
267	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
268	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
269	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
270	C₃×C₄⋊C₄	—	2	1	no	—
271	C₃×C₄⋊C₄	—	3	2	no	—
272	C₃×C₄⋊C₄	—	3	1	no	—
273	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
274	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
275	C₃×C₂²⋊C₄	—	2	2	no	—
276	C₃×C₂²⋊C₄	—	3	2	no	—
277	C₃×C₂²⋊C₄	—	3	2	no	—
278	C₃×C₂²⋊C₄	—	3	2	no	—
279	C₃×C₂²⋊C₄	C₄×D₃	1	2	yes	—
280	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
281	C₃×C₄²	—	2	1	no	—
282	C₃×C₄²	—	3	1	no	—
283	C₃×C₄²	—	3	1	no	—
284	C₃×C₄²	—	3	1	no	—
285	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
286	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
287	#217	C₂×C₃×C₄	1	2	yes	—
288	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
289	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
290	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
291	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
292	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
293	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
294	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
295	C₂×C₃⋊C₈	—	2	4	no	—
296	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
297	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
298	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
299	D₃×C₈	—	2	4	no	—
300	D₃×C₈	—	2	2	no	—
301	D₃×C₈	—	2	4	no	—
302	D₃×C₈	—	2	4	no	—
303	D₃×C₈	C₃×D₄	1	4	yes	direct product factor
304	C₂²×C₃²	—	2	2	no	—
305	C₂²×C₃²	—	2	2	no	—
306	C₂²×C₃²	C₂²×C₈	1	4	yes	complemented
307	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
308	C₂×C₃×D₃	—	2	2	no	—
309	C₂×C₃×D₃	—	2	2	no	—
310	C₂×C₃×D₃	—	2	16	no	—
311	C₂×C₃×D₃	C₄×D₄	1	2	yes	—
312	C₂×C₃×D₃	C₂²×C₈	1	2	yes	—
313	C₂×C₃×D₃	C₂²×C₈	1	4	yes	complemented
314	C₂×C₃×D₃	#131	1	2	yes	—
315	C₃²×C₄	—	2	2	no	—
316	C₃²×C₄	—	2	1	no	—
317	C₃²×C₄	C₂²×C₈	1	2	yes	complemented
318	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
319	C₃²×C₄	C₂×#41	1	1	yes	characteristic
320	C₃×Dic₃	—	2	2	no	—
321	C₃×Dic₃	—	2	1	no	—
322	C₃×Dic₃	C₄×D₄	1	2	yes	—
323	C₃×Dic₃	C₂²×C₈	1	2	yes	complemented
324	C₂²×D₄	—	3	1	no	—
325	C₂³×C₄	—	3	2	no	—
326	C₂²×C₈	—	3	1	no	—
327	C₂²×C₈	—	3	2	no	—
328	C₂²×C₈	—	3	2	no	—
329	C₂²×C₈	—	3	2	no	—
330	C₂²×C₈	—	3	2	no	—
331	C₂²×C₈	—	3	1	no	—
332	C₂²×C₈	—	6	8	no	—
333	C₂²×C₈	C₂×C₃×D₃	1	2	yes	complemented
334	C₄×D₄	—	3	1	no	—
335	C₄×D₄	—	3	2	no	—
336	C₄×D₄	—	3	1	no	—
337	C₄×D₄	—	3	2	no	—
338	C₄×D₄	—	3	1	no	—
339	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
340	C₂×C₄⋊C₄	—	3	1	no	—
341	C₂×C₂²⋊C₄	—	3	2	no	—
342	C₂×C₄²	—	3	1	no	—
343	C₄⋊C₈	—	3	2	no	—
344	C₄⋊C₈	—	3	1	no	—
345	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
346	C₂²⋊C₈	—	3	2	no	—
347	C₂²⋊C₈	—	3	2	no	—
348	C₂²⋊C₈	—	3	2	no	—
349	C₂²⋊C₈	C₂×C₃×D₃	1	2	yes	complemented
350	C₄×C₈	—	3	1	no	—
351	C₄×C₈	—	3	1	no	—
352	C₄×C₈	—	3	1	no	—
353	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
354	C₂³×C₃	—	2	2	no	—
355	C₂³×C₃	—	3	1	no	—
356	C₂³×C₃	—	3	8	no	—
357	C₂³×C₃	—	3	2	no	—
358	C₂³×C₃	—	6	4	no	—
359	C₂³×C₃	—	6	4	no	—
360	C₂³×C₃	C₂×C₄×D₃	1	2	yes	—
361	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
362	C₂²×D₃	—	2	4	no	—
363	C₂²×D₃	—	2	4	no	—
364	C₂²×D₃	C₂×C₃×C₈	1	8	yes	complemented
365	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
366	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
367	C₃×D₄	—	2	4	no	—
368	C₃×D₄	—	3	8	no	—
369	C₃×D₄	—	3	4	no	—
370	C₃×D₄	D₃×C₈	1	4	yes	direct product factor
371	C₃×D₄	C₂×C₃×C₈	1	4	yes	complemented
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	1	no	—
379	C₂×C₃×C₄	—	2	2	no	—
380	C₂×C₃×C₄	—	3	1	no	—
381	C₂×C₃×C₄	—	3	1	no	—
382	C₂×C₃×C₄	—	3	4	no	—
383	C₂×C₃×C₄	—	3	2	no	—
384	C₂×C₃×C₄	—	3	2	no	—
385	C₂×C₃×C₄	—	3	1	no	—
386	C₂×C₃×C₄	—	3	2	no	—
387	C₂×C₃×C₄	—	4	2	no	—
388	C₂×C₃×C₄	—	4	2	no	—
389	C₂×C₃×C₄	—	6	4	no	—
390	C₂×C₃×C₄	—	6	2	no	—
391	C₂×C₃×C₄	—	6	4	no	—
392	C₂×C₃×C₄	—	6	4	no	—
393	C₂×C₃×C₄	—	6	2	no	—
394	C₂×C₃×C₄	—	6	2	no	—
395	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
396	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
397	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
398	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
399	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
400	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
401	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
402	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
403	#67	C₂×C₃×C₈	1	8	yes	complemented
404	C₂×Dic₃	—	2	4	no	—
405	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
406	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
407	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
408	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
409	D₁₂	C₂×C₃×C₈	1	4	yes	complemented
410	C₄×D₃	—	2	4	no	—
411	C₄×D₃	—	2	2	no	—
412	C₄×D₃	—	2	2	no	—
413	C₄×D₃	—	2	2	no	—
414	C₄×D₃	—	2	4	no	—
415	C₄×D₃	C₂×C₃×C₈	1	4	yes	complemented
416	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
417	C₄×D₃	C₃×#41	1	2	yes	—
418	C₃×C₈	—	2	2	no	—
419	C₃×C₈	—	2	1	no	—
420	C₃×C₈	—	2	2	no	—
421	C₃×C₈	—	2	1	no	—
422	C₃×C₈	—	2	2	no	—
423	C₃×C₈	—	3	2	no	—
424	C₃×C₈	—	4	1	no	—
425	C₃×C₈	—	4	2	no	—
426	C₃×C₈	—	6	2	no	—
427	C₃×C₈	—	6	1	no	—
428	C₃×C₈	D₃×D₄	1	2	yes	direct product factor
429	C₃×C₈	C₂×C₃×D₄	1	2	yes	complemented
430	C₃⋊C₈	—	2	2	no	—
431	C₃⋊C₈	—	2	1	no	—
432	C₃⋊C₈	C₂×C₃×D₄	1	2	yes	complemented
433	C₂×C₃²	—	2	4	no	—
434	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
435	C₂×C₃²	C₂³×C₈	1	1	yes	characteristic
436	C₂×C₃²	C₂×#131	1	1	yes	characteristic
437	C₃×D₃	—	2	4	no	—
438	C₃×D₃	C₈×D₄	1	4	yes	direct product factor
439	C₂⁴	—	3	2	no	—
440	C₂×D₄	—	3	2	no	—
441	C₂×D₄	—	3	8	no	—
442	C₂×D₄	—	3	1	no	—
443	C₂×D₄	C₃×C₄×D₃	1	1	yes	characteristic
444	C₂²×C₄	—	3	1	no	—
445	C₂²×C₄	—	3	1	no	—
446	C₂²×C₄	—	3	2	no	—
447	C₂²×C₄	—	3	2	no	—
448	C₂²×C₄	—	3	1	no	—
449	C₂²×C₄	—	3	2	no	—
450	C₂²×C₄	—	3	2	no	—
451	C₂²×C₄	—	6	4	no	—
452	C₂²×C₄	—	6	4	no	—
453	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
454	C₂×C₈	—	2	4	no	—
455	C₂×C₈	—	3	1	no	—
456	C₂×C₈	—	3	4	no	—
457	C₂×C₈	—	3	1	no	—
458	C₂×C₈	—	3	2	no	—
459	C₂×C₈	—	6	4	no	—
460	C₂×C₈	—	6	4	no	—
461	C₂×C₈	—	6	2	no	—
462	C₂×C₈	—	6	4	no	—
463	C₂×C₈	—	6	4	no	—
464	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
465	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
466	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
467	C₄⋊C₄	—	3	2	no	—
468	C₄⋊C₄	—	3	1	no	—
469	C₄⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
470	C₂²⋊C₄	—	3	2	no	—
471	C₂²⋊C₄	—	3	2	no	—
472	C₂²⋊C₄	—	3	2	no	—
473	C₂²⋊C₄	C₃×C₄×D₃	1	2	yes	—
474	C₄²	—	3	1	no	—
475	C₄²	—	3	1	no	—
476	C₄²	—	3	1	no	—
477	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
478	C₂²×C₃	—	2	2	no	—
479	C₂²×C₃	—	2	2	no	—
480	C₂²×C₃	—	2	2	no	—
481	C₂²×C₃	—	2	2	no	—
482	C₂²×C₃	—	2	4	no	—
483	C₂²×C₃	—	2	1	no	—
484	C₂²×C₃	—	3	2	no	—
485	C₂²×C₃	—	3	2	no	—
486	C₂²×C₃	—	3	2	no	—
487	C₂²×C₃	—	3	4	no	—
488	C₂²×C₃	—	4	2	no	—
489	C₂²×C₃	—	4	2	no	—
490	C₂²×C₃	—	6	16	no	—
491	C₂²×C₃	—	6	2	no	—
492	C₂²×C₃	—	6	2	no	—
493	C₂²×C₃	C₂×D₃×C₈	1	4	yes	complemented
494	C₂²×C₃	C₂²×C₃×C₈	1	4	yes	complemented
495	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
496	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
497	C₂×D₃	—	2	2	no	—
498	C₂×D₃	—	2	2	no	—
499	C₂×D₃	—	2	16	no	—
500	C₂×D₃	C₃×C₄×D₄	1	2	yes	—
501	C₂×D₃	C₂²×C₃×C₈	1	2	yes	—
502	C₂×D₃	C₂²×C₃×C₈	1	4	yes	complemented
503	C₂×D₃	C₃×#131	1	2	yes	—
504	C₃×C₄	—	2	1	no	—
505	C₃×C₄	—	2	1	no	—
506	C₃×C₄	—	2	2	no	—
507	C₃×C₄	—	2	2	no	—
508	C₃×C₄	—	2	2	no	—
509	C₃×C₄	—	2	1	no	—
510	C₃×C₄	—	2	1	no	—
511	C₃×C₄	—	3	2	no	—
512	C₃×C₄	—	3	2	no	—
513	C₃×C₄	—	4	2	no	—
514	C₃×C₄	—	4	1	no	—
515	C₃×C₄	—	6	1	no	—
516	C₃×C₄	—	6	2	no	—
517	C₃×C₄	C₂×D₃×C₈	1	2	yes	complemented
518	C₃×C₄	C₂²×C₃×C₈	1	2	yes	complemented
519	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
520	C₃×C₄	D₃×#41	1	1	yes	characteristic
521	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
522	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
523	Dic₃	—	2	1	no	—
524	Dic₃	—	2	2	no	—
525	Dic₃	C₃×C₄×D₄	1	2	yes	—
526	Dic₃	C₂²×C₃×C₈	1	2	yes	complemented
527	C₃²	C₂×C₈×D₄	1	1	yes	characteristic, complemented, Sylow
528	C₂³	—	3	1	no	—
529	C₂³	—	3	8	no	—
530	C₂³	—	3	2	no	—
531	C₂³	—	6	4	no	—
532	C₂³	—	6	4	no	—
533	C₂³	C₂×C₃×C₄×D₃	1	2	yes	—
534	D₄	—	3	8	no	—
535	D₄	—	3	4	no	—
536	D₄	C₃×D₃×C₈	1	4	yes	direct product factor
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	3	1	no	—
540	C₂×C₄	—	3	1	no	—
541	C₂×C₄	—	3	4	no	—
542	C₂×C₄	—	3	2	no	—
543	C₂×C₄	—	3	2	no	—
544	C₂×C₄	—	3	1	no	—
545	C₂×C₄	—	3	2	no	—
546	C₂×C₄	—	6	4	no	—
547	C₂×C₄	—	6	4	no	—
548	C₂×C₄	—	6	2	no	—
549	C₂×C₄	—	6	4	no	—
550	C₂×C₄	—	6	2	no	—
551	C₂×C₄	—	6	2	no	—
552	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
553	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
554	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
555	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
556	C₈	—	2	2	no	—
557	C₈	—	2	1	no	—
558	C₈	—	3	2	no	—
559	C₈	—	6	2	no	—
560	C₈	—	6	1	no	—
561	C₈	C₃×D₃×D₄	1	2	yes	direct product factor
562	C₂×C₃	—	2	4	no	—
563	C₂×C₃	—	2	4	no	—
564	C₂×C₃	—	2	1	no	—
565	C₂×C₃	—	2	1	no	—
566	C₂×C₃	—	2	1	no	—
567	C₂×C₃	—	3	4	no	—
568	C₂×C₃	—	4	4	no	—
569	C₂×C₃	—	6	4	no	—
570	C₂×C₃	C₄×D₃×D₄	1	1	yes	characteristic
571	C₂×C₃	C₂²×D₃×C₈	1	1	yes	characteristic
572	C₂×C₃	D₃×#131	1	1	yes	characteristic
573	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
574	C₂×C₃	C₂³×C₃×C₈	1	1	yes	characteristic
575	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
576	D₃	—	2	4	no	—
577	D₃	C₃×C₈×D₄	1	4	yes	direct product factor
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	3	2	no	—
581	C₂²	—	3	2	no	—
582	C₂²	—	3	2	no	—
583	C₂²	—	3	4	no	—
584	C₂²	—	6	16	no	—
585	C₂²	—	6	2	no	—
586	C₂²	—	6	2	no	—
587	C₂²	C₂×C₃×D₃×C₈	1	4	yes	complemented
588	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	2	no	—
591	C₄	—	3	2	no	—
592	C₄	—	3	2	no	—
593	C₄	—	6	1	no	—
594	C₄	—	6	2	no	—
595	C₄	C₂×C₃×D₃×C₈	1	2	yes	complemented
596	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
597	C₄	C₃×D₃×#41	1	1	yes	characteristic
598	C₃	—	2	1	no	—
599	C₃	D₃×C₈×D₄	1	1	yes	characteristic, direct product factor
600	C₃	C₂×C₃×C₈×D₄	1	1	yes	characteristic, complemented
601	C₂	—	2	4	no	—
602	C₂	—	3	4	no	—
603	C₂	—	6	4	no	—
604	C₂	C₃×C₄×D₃×D₄	1	1	yes	characteristic
605	C₂	C₂²×C₃×D₃×C₈	1	1	yes	characteristic
606	C₂	C₃×D₃×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₈	C₂²×D₃
commutator	C₂×C₃	C₂³×C₃×C₈
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₈×D₄	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂×C₃×D₃×D₄	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×C₈×D₄	D₃
hypocenter	C₃	C₂×C₃×C₈×D₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₃×C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₃×C₈	C₂	semidirect
3. C₃²×C₈×D₄	C₂	semidirect
4. C₃×C₈×#67	C₂	semidirect
5. C₃×D₄×C₃⋊C₈	C₂	semidirect
6. C₃×#4834	C₂	semidirect
7. C₃×D₃×C₄⋊C₈	C₂	semidirect
8. C₃×#67⋊C₈	C₂	semidirect
9. C₃×D₃×C₂²⋊C₈	C₂	semidirect
10. C₃×C₈×D₁₂	C₂	semidirect
11. C₃×C₄×D₃×C₈	C₂	semidirect
13. D₃×C₈×D₄	C₃	direct (N × H)
16. C₂²×C₃²×C₈	C₂²	semidirect
20. C₂²×C₃×C₃⋊C₈	C₂²	semidirect
25. C₂×C₃×D₃×C₈	C₂²	semidirect
26. C₂×C₃×D₃×C₈	C₂²	semidirect
33. C₃²×C₄⋊C₈	C₂²	semidirect
34. C₃²×C₂²⋊C₈	C₂²	semidirect
35. C₃²×C₄×C₈	C₂²	semidirect
36. C₃×#830	C₂²	semidirect
37. C₃×(C₂×D₃)⋊C₈	C₂²	semidirect
38. C₃×(C₂×D₃)⋊C₈	C₂²	semidirect
39. C₃×Dic₃⋊C₈	C₂²	semidirect
40. C₃×C₈×Dic₃	C₂²	semidirect
41. C₃×C₈×Dic₃	C₂²	semidirect
42. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
43. C₃×C₄×C₃⋊C₈	C₂²	semidirect
46. C₂²×D₃×C₈	C₂×C₃	semidirect
54. C₃×C₈×D₄	D₃	direct (N × H)
55. C₃×C₈×D₄	C₂×C₃	semidirect
59. C₈×#67	C₂×C₃	semidirect
60. D₄×C₃⋊C₈	C₂×C₃	semidirect
61. #4834	C₂×C₃	semidirect
62. D₃×C₄⋊C₈	C₂×C₃	semidirect
63. #67⋊C₈	C₂×C₃	semidirect
64. D₃×C₂²⋊C₈	C₂×C₃	semidirect
65. C₈×D₁₂	C₂×C₃	semidirect
66. C₄×D₃×C₈	C₂×C₃	semidirect
72. C₃×D₃×D₄	C₈	direct (N × H)
105. C₃×D₃×C₈	D₄	direct (N × H)
119. C₂²×C₃×C₈	C₂×D₃	semidirect
120. C₂²×C₃×C₈	C₂²×C₃	semidirect
134. C₂²×C₃⋊C₈	C₂²×C₃	semidirect
139. C₂×D₃×C₈	C₂²×C₃	semidirect
140. C₂×D₃×C₈	C₂²×C₃	semidirect
150. C₃×C₄⋊C₈	C₂×D₃	semidirect
151. C₃×C₄⋊C₈	C₂²×C₃	semidirect
156. C₃×C₂²⋊C₈	C₂×D₃	semidirect
157. C₃×C₂²⋊C₈	C₂²×C₃	semidirect
162. C₃×C₄×C₈	C₂×D₃	semidirect
163. C₃×C₄×C₈	C₂²×C₃	semidirect
164. #830	C₂²×C₃	semidirect
165. (C₂×D₃)⋊C₈	C₂²×C₃	semidirect
166. (C₂×D₃)⋊C₈	C₂²×C₃	semidirect
167. Dic₃⋊C₈	C₂²×C₃	semidirect
168. C₈×Dic₃	C₂²×C₃	semidirect
169. C₈×Dic₃	C₂²×C₃	semidirect
170. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
171. C₄×C₃⋊C₈	C₂²×C₃	semidirect
175. C₂²×C₃×D₃	C₂×C₈	semidirect
178. C₃²×D₄	C₂×C₈	semidirect
185. C₃×#67	C₂×C₈	semidirect
191. C₃×D₁₂	C₂×C₈	semidirect
197. C₃×C₄×D₃	C₂×C₈	semidirect
202. C₃²×C₈	C₂×D₄	semidirect
205. C₃×C₃⋊C₈	C₂×D₄	semidirect
213. C₈×D₄	C₃×D₃	direct (N × H)
239. D₃×D₄	C₃×C₈	direct (N × H)
303. D₃×C₈	C₃×D₄	direct (N × H)
306. C₂²×C₃²	C₂²×C₈	semidirect
313. C₂×C₃×D₃	C₂²×C₈	semidirect
317. C₃²×C₄	C₂²×C₈	semidirect
323. C₃×Dic₃	C₂²×C₈	semidirect
333. C₂²×C₈	C₂×C₃×D₃	semidirect
345. C₄⋊C₈	C₂×C₃×D₃	semidirect
349. C₂²⋊C₈	C₂×C₃×D₃	semidirect
353. C₄×C₈	C₂×C₃×D₃	semidirect
364. C₂²×D₃	C₂×C₃×C₈	semidirect
370. C₃×D₄	D₃×C₈	direct (N × H)
371. C₃×D₄	C₂×C₃×C₈	semidirect
403. #67	C₂×C₃×C₈	semidirect
409. D₁₂	C₂×C₃×C₈	semidirect
415. C₄×D₃	C₂×C₃×C₈	semidirect
428. C₃×C₈	D₃×D₄	direct (N × H)
429. C₃×C₈	C₂×C₃×D₄	semidirect
432. C₃⋊C₈	C₂×C₃×D₄	semidirect
438. C₃×D₃	C₈×D₄	direct (N × H)
493. C₂²×C₃	C₂×D₃×C₈	semidirect
494. C₂²×C₃	C₂²×C₃×C₈	semidirect
502. C₂×D₃	C₂²×C₃×C₈	semidirect
517. C₃×C₄	C₂×D₃×C₈	semidirect
518. C₃×C₄	C₂²×C₃×C₈	semidirect
526. Dic₃	C₂²×C₃×C₈	semidirect
527. C₃²	C₂×C₈×D₄	semidirect
536. D₄	C₃×D₃×C₈	direct (N × H)
561. C₈	C₃×D₃×D₄	direct (N × H)
577. D₃	C₃×C₈×D₄	direct (N × H)
587. C₂²	C₂×C₃×D₃×C₈	semidirect
595. C₄	C₂×C₃×D₃×C₈	semidirect
599. C₃	D₃×C₈×D₄	direct (N × H)
600. C₃	C₂×C₃×C₈×D₄	semidirect

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
C₃×C₄×D₃×D₄	2
C₃²×C₈×D₄	2
C₃×C₈×#67	2
C₃×D₄×C₃⋊C₈	2
C₃×#4834	2
C₃×D₃×C₄⋊C₈	2
C₃×#67⋊C₈	2
C₃×D₃×C₂²⋊C₈	2
C₃×C₈×D₁₂	2
C₃×C₄×D₃×C₈	2
C₂×C₃×C₈×D₄	3
D₃×C₈×D₄	3

Subgroups — C3×D3×C8×D4 #11859143

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×C₈×D₄ #11859143