Subgroups — C₂×C₃×D₃²×D₄ #13181546

Order 1728.

6210 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×D₃²	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×D₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×D₃×D₄	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#3811	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×D₃×#67	C₂	1	4	yes	maximal, complemented
6	C₃×D₃²×D₄	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#3802	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×D₃×D₁₂	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×C₄×D₃²	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₃×D₃×D₄	—	3	2	no	maximal
11	C₂×D₃²×D₄	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂³×C₃×C₃⋊D₃	C₂²	1	2	yes	complemented
13	C₂³×C₃²×D₃	C₂²	1	4	yes	complemented
14	C₂²×C₃×D₃²	—	2	16	no	—
15	C₂²×C₃×D₃²	C₂²	1	1	yes	characteristic
16	C₂²×C₃×D₃²	C₂²	1	16	yes	complemented
17	C₂²×C₃×D₃²	C₂²	1	4	yes	complemented
18	C₂²×C₃×D₃²	C₂²	1	2	yes	complemented
19	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×#638	C₂²	1	2	yes	complemented
21	C₃×D₄×C₃⋊D₃	C₂²	1	8	yes	complemented
22	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃²×#67	C₂²	1	4	yes	complemented
25	C₃²×D₃×D₄	C₂²	1	16	yes	complemented
26	C₂×C₃²×D₁₂	C₂²	1	2	yes	complemented
27	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	complemented
28	C₃×#3811	C₂²	1	16	yes	complemented
29	C₃×D₃×#67	C₂²	1	32	yes	complemented
30	C₂×C₃×#626	C₂²	1	4	yes	complemented
31	C₂×C₃×#625	C₂²	1	2	yes	complemented
32	C₂×C₃×#624	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×D₃×Dic₃	C₂²	1	2	yes	complemented
34	C₃×#3802	C₂²	1	8	yes	complemented
35	C₃×D₃×D₁₂	C₂²	1	16	yes	complemented
36	C₃×C₄×D₃²	C₂²	1	8	yes	complemented
37	C₂⁴×C₃×D₃	—	3	4	no	—
38	C₂³×D₃²	C₂×C₃	1	2	yes	complemented
39	C₂²×C₃²×D₄	—	3	2	no	—
40	C₂×D₄×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂²×C₃×#67	—	3	4	no	—
42	C₂×C₃×D₃×D₄	—	2	2	no	—
43	C₂×C₃×D₃×D₄	—	3	2	no	—
44	C₂×C₃×D₃×D₄	—	3	4	no	—
45	C₂×C₃×D₃×D₄	—	3	32	no	—
46	C₂×C₃×D₃×D₄	—	3	2	no	—
47	C₂×C₃×D₃×D₄	—	3	2	no	—
48	C₂×C₃×D₃×D₄	—	3	4	no	—
49	C₂×C₃×D₃×D₄	—	6	1	no	—
50	C₂×C₃×D₃×D₄	D₃	1	2	yes	direct product factor
51	C₂×C₃×D₃×D₄	C₂×C₃	1	2	yes	complemented
52	C₂²×C₃×D₁₂	—	3	2	no	—
53	C₂²×C₃×C₄×D₃	—	3	2	no	—
54	C₂×#3811	C₂×C₃	1	2	yes	complemented
55	C₂×D₃×#67	C₂×C₃	1	4	yes	complemented
56	D₃²×D₄	C₂×C₃	1	16	yes	direct product factor
57	C₂×#3802	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂×D₃×D₁₂	C₂×C₃	1	2	yes	complemented
59	C₂×C₄×D₃²	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂³×C₃³	C₂³	1	2	yes	complemented
61	C₂²×C₃×C₃⋊D₃	—	2	8	no	—
62	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₃⋊D₃	C₂³	1	8	yes	complemented
64	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	complemented
65	C₂²×C₃²×D₃	—	2	16	no	—
66	C₂²×C₃²×D₃	C₂³	1	2	yes	—
67	C₂²×C₃²×D₃	C₂³	1	16	yes	complemented
68	C₂²×C₃²×D₃	C₂³	1	4	yes	complemented
69	C₂×C₃×D₃²	—	2	8	no	—
70	C₂×C₃×D₃²	—	2	16	no	—
71	C₂×C₃×D₃²	—	2	64	no	—
72	C₂×C₃×D₃²	D₄	1	8	yes	direct product factor
73	C₂×C₃×D₃²	C₂³	1	4	yes	—
74	C₂×C₃×D₃²	C₂³	1	16	yes	complemented
75	C₂×C₃×D₃²	C₂³	1	8	yes	complemented
76	C₃³×D₄	C₂³	1	4	yes	complemented
77	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic, complemented
78	C₃×#638	C₂³	1	8	yes	complemented
79	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic, complemented
80	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	4	yes	complemented
81	C₃×C₄×C₃⋊D₃	C₂³	1	4	yes	complemented
82	C₃²×#67	C₂³	1	16	yes	complemented
83	C₂×C₃²×Dic₃	C₂³	1	2	yes	complemented
84	C₃²×D₁₂	C₂³	1	8	yes	complemented
85	C₃²×C₄×D₃	C₂³	1	8	yes	complemented
86	C₃×#626	C₂³	1	16	yes	complemented
87	C₃×#625	C₂³	1	8	yes	complemented
88	C₃×#624	C₂³	1	4	yes	complemented
89	C₃×D₃×Dic₃	C₂³	1	8	yes	complemented
90	C₂³×C₃×D₄	—	9	1	no	—
91	C₂²×D₃×D₄	—	3	2	no	—
92	C₂⁴×C₃²	—	3	4	no	—
93	C₂³×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
94	C₂³×C₃×D₃	—	2	4	no	—
95	C₂³×C₃×D₃	—	3	2	no	—
96	C₂³×C₃×D₃	—	3	4	no	—
97	C₂³×C₃×D₃	—	3	4	no	—
98	C₂³×C₃×D₃	—	3	4	no	—
99	C₂³×C₃×D₃	—	3	4	no	—
100	C₂³×C₃×D₃	—	3	32	no	—
101	C₂³×C₃×D₃	—	6	32	no	—
102	C₂³×C₃×D₃	—	6	2	no	—
103	C₂³×C₃×D₃	C₂×D₃	1	4	yes	complemented
104	C₂³×C₃×D₃	C₂²×C₃	1	4	yes	complemented
105	C₂²×D₃²	—	2	16	no	—
106	C₂²×D₃²	C₂²×C₃	1	1	yes	characteristic
107	C₂²×D₃²	C₂²×C₃	1	16	yes	complemented
108	C₂²×D₃²	C₂²×C₃	1	4	yes	complemented
109	C₂²×D₃²	C₂²×C₃	1	2	yes	complemented
110	C₂×C₃²×D₄	—	2	1	no	—
111	C₂×C₃²×D₄	—	2	2	no	—
112	C₂×C₃²×D₄	—	3	4	no	—
113	C₂×C₃²×D₄	—	3	16	no	—
114	C₂×C₃²×D₄	—	3	2	no	—
115	C₂×C₃²×D₄	—	4	1	no	—
116	C₂×C₃²×D₄	C₂×D₃	1	2	yes	complemented
117	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
118	C₂²×C₃²×C₄	—	3	2	no	—
119	C₂×#638	C₂²×C₃	1	2	yes	complemented
120	D₄×C₃⋊D₃	C₂²×C₃	1	8	yes	complemented
121	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic, complemented
122	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic, complemented
123	C₂×C₃×#67	—	2	4	no	—
124	C₂×C₃×#67	—	3	4	no	—
125	C₂×C₃×#67	—	3	4	no	—
126	C₂×C₃×#67	—	3	32	no	—
127	C₂×C₃×#67	—	3	4	no	—
128	C₂×C₃×#67	—	6	2	no	—
129	C₂×C₃×#67	C₂×D₃	1	4	yes	complemented
130	C₂×C₃×#67	C₂²×C₃	1	4	yes	complemented
131	C₂²×C₃×Dic₃	—	3	2	no	—
132	C₃×D₃×D₄	—	2	16	no	—
133	C₃×D₃×D₄	—	3	32	no	—
134	C₃×D₃×D₄	—	3	16	no	—
135	C₃×D₃×D₄	—	3	32	no	—
136	C₃×D₃×D₄	—	3	16	no	—
137	C₃×D₃×D₄	—	3	16	no	—
138	C₃×D₃×D₄	—	6	8	no	—
139	C₃×D₃×D₄	C₂×D₃	1	16	yes	direct product factor
140	C₃×D₃×D₄	C₂²×C₃	1	16	yes	complemented
141	C₂×C₃×D₁₂	—	2	2	no	—
142	C₂×C₃×D₁₂	—	3	4	no	—
143	C₂×C₃×D₁₂	—	3	2	no	—
144	C₂×C₃×D₁₂	—	3	16	no	—
145	C₂×C₃×D₁₂	—	6	1	no	—
146	C₂×C₃×D₁₂	C₂×D₃	1	2	yes	complemented
147	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	complemented
148	C₂×C₃×C₄×D₃	—	2	2	no	—
149	C₂×C₃×C₄×D₃	—	3	2	no	—
150	C₂×C₃×C₄×D₃	—	3	2	no	—
151	C₂×C₃×C₄×D₃	—	3	2	no	—
152	C₂×C₃×C₄×D₃	—	3	16	no	—
153	C₂×C₃×C₄×D₃	—	6	1	no	—
154	C₂×C₃×C₄×D₃	C₂×D₃	1	2	yes	complemented
155	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	complemented
156	#3811	C₂²×C₃	1	16	yes	complemented
157	D₃×#67	C₂²×C₃	1	32	yes	complemented
158	C₂×#626	C₂²×C₃	1	4	yes	complemented
159	C₂×#625	C₂²×C₃	1	2	yes	complemented
160	C₂×#624	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₂×D₃×Dic₃	C₂²×C₃	1	2	yes	complemented
162	#3802	C₂²×C₃	1	8	yes	complemented
163	D₃×D₁₂	C₂²×C₃	1	16	yes	complemented
164	C₄×D₃²	C₂²×C₃	1	8	yes	complemented
165	C₂²×C₃³	—	2	4	no	—
166	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
167	C₂²×C₃³	C₂⁴	1	4	yes	complemented
168	C₂×C₃×C₃⋊D₃	—	2	4	no	—
169	C₂×C₃×C₃⋊D₃	—	2	16	no	—
170	C₂×C₃×C₃⋊D₃	C₂×D₄	1	4	yes	complemented
171	C₂×C₃×C₃⋊D₃	C₂⁴	1	2	yes	—
172	C₂×C₃×C₃⋊D₃	C₂⁴	1	4	yes	complemented
173	C₂×C₃²×D₃	—	2	8	no	—
174	C₂×C₃²×D₃	—	2	32	no	—
175	C₂×C₃²×D₃	C₂×D₄	1	8	yes	complemented
176	C₂×C₃²×D₃	C₂⁴	1	4	yes	—
177	C₂×C₃²×D₃	C₂⁴	1	8	yes	complemented
178	C₃×D₃²	—	2	16	no	—
179	C₃×D₃²	—	2	32	no	—
180	C₃×D₃²	C₂×D₄	1	16	yes	direct product factor
181	C₃³×C₄	C₂⁴	1	2	yes	complemented
182	C₃×C₃⋊Dic₃	C₂⁴	1	2	yes	complemented
183	C₃²×Dic₃	C₂⁴	1	4	yes	complemented
184	C₂⁵×C₃	—	9	2	no	—
185	C₂⁴×D₃	—	3	4	no	—
186	C₂²×C₃×D₄	—	3	2	no	—
187	C₂²×C₃×D₄	—	3	2	no	—
188	C₂²×C₃×D₄	—	6	2	no	—
189	C₂²×C₃×D₄	—	9	2	no	—
190	C₂²×C₃×D₄	—	9	2	no	—
191	C₂²×C₃×D₄	—	9	16	no	—
192	C₂²×C₃×D₄	—	9	1	no	—
193	C₂²×C₃×D₄	—	9	4	no	—
194	C₂²×C₃×D₄	—	9	1	no	—
195	C₂³×C₃×C₄	—	9	1	no	—
196	C₂²×#67	—	3	4	no	—
197	C₂×D₃×D₄	—	3	4	no	—
198	C₂×D₃×D₄	—	3	2	no	—
199	C₂×D₃×D₄	—	3	4	no	—
200	C₂×D₃×D₄	—	3	32	no	—
201	C₂×D₃×D₄	—	3	2	no	—
202	C₂×D₃×D₄	—	3	2	no	—
203	C₂×D₃×D₄	—	6	1	no	—
204	C₂×D₃×D₄	C₃×D₃	1	2	yes	direct product factor
205	C₂²×D₁₂	—	3	2	no	—
206	C₂²×C₄×D₃	—	3	2	no	—
207	C₂³×C₃²	—	2	2	no	—
208	C₂³×C₃²	—	2	4	no	—
209	C₂³×C₃²	—	3	2	no	—
210	C₂³×C₃²	—	3	4	no	—
211	C₂³×C₃²	—	3	16	no	—
212	C₂³×C₃²	—	4	2	no	—
213	C₂³×C₃²	—	6	16	no	—
214	C₂³×C₃²	C₂²×D₃	1	4	yes	complemented
215	C₂³×C₃²	C₂³×C₃	1	2	yes	complemented
216	C₂²×C₃⋊D₃	—	2	8	no	—
217	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
218	C₂²×C₃⋊D₃	C₂³×C₃	1	8	yes	complemented
219	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	complemented
220	C₂²×C₃×D₃	—	2	16	no	—
221	C₂²×C₃×D₃	—	2	16	no	—
222	C₂²×C₃×D₃	—	2	2	no	—
223	C₂²×C₃×D₃	—	2	4	no	—
224	C₂²×C₃×D₃	—	2	16	no	—
225	C₂²×C₃×D₃	—	3	2	no	—
226	C₂²×C₃×D₃	—	3	16	no	—
227	C₂²×C₃×D₃	—	3	8	no	—
228	C₂²×C₃×D₃	—	3	4	no	—
229	C₂²×C₃×D₃	—	3	16	no	—
230	C₂²×C₃×D₃	—	3	16	no	—
231	C₂²×C₃×D₃	—	3	16	no	—
232	C₂²×C₃×D₃	—	3	16	no	—
233	C₂²×C₃×D₃	—	4	16	no	—
234	C₂²×C₃×D₃	—	6	1	no	—
235	C₂²×C₃×D₃	—	6	2	no	—
236	C₂²×C₃×D₃	—	6	8	no	—
237	C₂²×C₃×D₃	—	6	16	no	—
238	C₂²×C₃×D₃	—	6	128	no	—
239	C₂²×C₃×D₃	—	6	16	no	—
240	C₂²×C₃×D₃	—	6	16	no	—
241	C₂²×C₃×D₃	—	6	16	no	—
242	C₂²×C₃×D₃	—	12	8	no	—
243	C₂²×C₃×D₃	C₂²×D₃	1	2	yes	—
244	C₂²×C₃×D₃	C₂²×D₃	1	16	yes	complemented
245	C₂²×C₃×D₃	C₂²×D₃	1	4	yes	complemented
246	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
247	C₂²×C₃×D₃	C₂³×C₃	1	16	yes	complemented
248	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	complemented
249	C₂×D₃²	—	2	8	no	—
250	C₂×D₃²	—	2	16	no	—
251	C₂×D₃²	—	2	64	no	—
252	C₂×D₃²	C₃×D₄	1	8	yes	direct product factor
253	C₂×D₃²	C₂³×C₃	1	4	yes	—
254	C₂×D₃²	C₂³×C₃	1	16	yes	complemented
255	C₂×D₃²	C₂³×C₃	1	8	yes	complemented
256	C₃²×D₄	—	2	4	no	—
257	C₃²×D₄	—	2	8	no	—
258	C₃²×D₄	—	3	16	no	—
259	C₃²×D₄	—	3	8	no	—
260	C₃²×D₄	—	4	4	no	—
261	C₃²×D₄	C₂²×D₃	1	8	yes	complemented
262	C₃²×D₄	C₂³×C₃	1	4	yes	complemented
263	C₂×C₃²×C₄	—	2	1	no	—
264	C₂×C₃²×C₄	—	2	2	no	—
265	C₂×C₃²×C₄	—	3	2	no	—
266	C₂×C₃²×C₄	—	3	8	no	—
267	C₂×C₃²×C₄	—	4	1	no	—
268	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	complemented
269	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic, complemented
270	#638	C₂³×C₃	1	8	yes	complemented
271	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic, complemented
272	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	4	yes	complemented
273	C₄×C₃⋊D₃	C₂³×C₃	1	4	yes	complemented
274	C₃×#67	—	2	16	no	—
275	C₃×#67	—	3	16	no	—
276	C₃×#67	—	3	16	no	—
277	C₃×#67	—	3	16	no	—
278	C₃×#67	—	6	8	no	—
279	C₃×#67	C₂²×D₃	1	16	yes	complemented
280	C₃×#67	C₂³×C₃	1	16	yes	complemented
281	C₂×C₃×Dic₃	—	2	2	no	—
282	C₂×C₃×Dic₃	—	3	2	no	—
283	C₂×C₃×Dic₃	—	3	8	no	—
284	C₂×C₃×Dic₃	—	6	1	no	—
285	C₂×C₃×Dic₃	C₂²×D₃	1	2	yes	complemented
286	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	complemented
287	C₃×D₁₂	—	2	8	no	—
288	C₃×D₁₂	—	3	16	no	—
289	C₃×D₁₂	—	3	8	no	—
290	C₃×D₁₂	—	6	4	no	—
291	C₃×D₁₂	C₂²×D₃	1	8	yes	complemented
292	C₃×D₁₂	C₂³×C₃	1	8	yes	complemented
293	C₃×C₄×D₃	—	2	8	no	—
294	C₃×C₄×D₃	—	3	8	no	—
295	C₃×C₄×D₃	—	3	8	no	—
296	C₃×C₄×D₃	—	3	8	no	—
297	C₃×C₄×D₃	—	6	4	no	—
298	C₃×C₄×D₃	C₂²×D₃	1	8	yes	complemented
299	C₃×C₄×D₃	C₂³×C₃	1	8	yes	complemented
300	#626	C₂³×C₃	1	16	yes	complemented
301	#625	C₂³×C₃	1	8	yes	complemented
302	#624	C₂³×C₃	1	4	yes	complemented
303	D₃×Dic₃	C₂³×C₃	1	8	yes	complemented
304	C₂³×D₄	—	9	1	no	Sylow
305	C₂×C₃³	—	2	4	no	—
306	C₂×C₃³	C₂²×D₄	1	2	yes	complemented
307	C₂×C₃³	C₂⁵	1	1	yes	characteristic
308	C₃×C₃⋊D₃	—	2	4	no	—
309	C₃×C₃⋊D₃	C₂²×D₄	1	4	yes	complemented
310	C₃²×D₃	—	2	8	no	—
311	C₃²×D₃	C₂²×D₄	1	8	yes	complemented
312	C₂⁴×C₃	—	3	4	no	—
313	C₂⁴×C₃	—	3	4	no	—
314	C₂⁴×C₃	—	6	4	no	—
315	C₂⁴×C₃	—	9	1	no	—
316	C₂⁴×C₃	—	9	4	no	—
317	C₂⁴×C₃	—	9	2	no	—
318	C₂⁴×C₃	—	9	16	no	—
319	C₂⁴×C₃	—	9	2	no	—
320	C₂⁴×C₃	—	18	16	no	—
321	C₂³×D₃	—	3	2	no	—
322	C₂³×D₃	—	3	4	no	—
323	C₂³×D₃	—	3	4	no	—
324	C₂³×D₃	—	3	4	no	—
325	C₂³×D₃	—	3	4	no	—
326	C₂³×D₃	—	3	32	no	—
327	C₂³×D₃	—	6	2	no	—
328	C₂³×D₃	—	6	32	no	—
329	C₂³×D₃	C₂×C₃×D₃	1	4	yes	complemented
330	C₂×C₃×D₄	—	2	1	no	—
331	C₂×C₃×D₄	—	2	2	no	—
332	C₂×C₃×D₄	—	3	4	no	—
333	C₂×C₃×D₄	—	3	4	no	—
334	C₂×C₃×D₄	—	3	16	no	—
335	C₂×C₃×D₄	—	3	16	no	—
336	C₂×C₃×D₄	—	3	2	no	—
337	C₂×C₃×D₄	—	3	2	no	—
338	C₂×C₃×D₄	—	4	1	no	—
339	C₂×C₃×D₄	—	6	2	no	—
340	C₂×C₃×D₄	—	6	16	no	—
341	C₂×C₃×D₄	—	6	4	no	—
342	C₂×C₃×D₄	—	9	16	no	—
343	C₂×C₃×D₄	—	9	4	no	—
344	C₂×C₃×D₄	—	9	16	no	—
345	C₂×C₃×D₄	—	9	8	no	—
346	C₂×C₃×D₄	—	9	32	no	—
347	C₂×C₃×D₄	—	9	2	no	—
348	C₂×C₃×D₄	—	9	2	no	—
349	C₂×C₃×D₄	—	9	8	no	—
350	C₂×C₃×D₄	—	9	1	no	—
351	C₂×C₃×D₄	D₃²	1	1	yes	characteristic, direct product factor
352	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	complemented
353	C₂²×C₃×C₄	—	3	2	no	—
354	C₂²×C₃×C₄	—	3	2	no	—
355	C₂²×C₃×C₄	—	6	2	no	—
356	C₂²×C₃×C₄	—	9	1	no	—
357	C₂²×C₃×C₄	—	9	8	no	—
358	C₂²×C₃×C₄	—	9	2	no	—
359	C₂²×C₃×C₄	—	9	1	no	—
360	C₂×#67	—	3	4	no	—
361	C₂×#67	—	3	4	no	—
362	C₂×#67	—	3	32	no	—
363	C₂×#67	—	3	4	no	—
364	C₂×#67	—	6	2	no	—
365	C₂×#67	C₂×C₃×D₃	1	4	yes	complemented
366	C₂²×Dic₃	—	3	2	no	—
367	D₃×D₄	—	3	32	no	—
368	D₃×D₄	—	3	16	no	—
369	D₃×D₄	—	3	32	no	—
370	D₃×D₄	—	3	16	no	—
371	D₃×D₄	—	3	16	no	—
372	D₃×D₄	—	6	8	no	—
373	D₃×D₄	C₂×C₃×D₃	1	16	yes	direct product factor
374	C₂×D₁₂	—	3	4	no	—
375	C₂×D₁₂	—	3	2	no	—
376	C₂×D₁₂	—	3	16	no	—
377	C₂×D₁₂	—	6	1	no	—
378	C₂×D₁₂	C₂×C₃×D₃	1	2	yes	complemented
379	C₂×C₄×D₃	—	3	2	no	—
380	C₂×C₄×D₃	—	3	2	no	—
381	C₂×C₄×D₃	—	3	2	no	—
382	C₂×C₄×D₃	—	3	16	no	—
383	C₂×C₄×D₃	—	6	1	no	—
384	C₂×C₄×D₃	C₂×C₃×D₃	1	2	yes	complemented
385	C₂²×C₃²	—	2	8	no	—
386	C₂²×C₃²	—	2	4	no	—
387	C₂²×C₃²	—	2	1	no	—
388	C₂²×C₃²	—	2	4	no	—
389	C₂²×C₃²	—	2	2	no	—
390	C₂²×C₃²	—	2	8	no	—
391	C₂²×C₃²	—	3	8	no	—
392	C₂²×C₃²	—	3	4	no	—
393	C₂²×C₃²	—	3	8	no	—
394	C₂²×C₃²	—	4	1	no	—
395	C₂²×C₃²	—	4	4	no	—
396	C₂²×C₃²	—	4	8	no	—
397	C₂²×C₃²	—	4	4	no	—
398	C₂²×C₃²	—	6	32	no	—
399	C₂²×C₃²	—	6	8	no	—
400	C₂²×C₃²	—	8	4	no	—
401	C₂²×C₃²	C₂³×D₃	1	2	yes	—
402	C₂²×C₃²	C₂³×D₃	1	8	yes	complemented
403	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
404	C₂²×C₃²	C₂⁴×C₃	1	4	yes	complemented
405	C₂×C₃⋊D₃	—	2	4	no	—
406	C₂×C₃⋊D₃	—	2	16	no	—
407	C₂×C₃⋊D₃	C₂×C₃×D₄	1	4	yes	complemented
408	C₂×C₃⋊D₃	C₂⁴×C₃	1	2	yes	—
409	C₂×C₃⋊D₃	C₂⁴×C₃	1	4	yes	complemented
410	C₂×C₃×D₃	—	2	8	no	—
411	C₂×C₃×D₃	—	2	8	no	—
412	C₂×C₃×D₃	—	2	32	no	—
413	C₂×C₃×D₃	—	2	32	no	—
414	C₂×C₃×D₃	—	2	4	no	—
415	C₂×C₃×D₃	—	2	8	no	—
416	C₂×C₃×D₃	—	2	8	no	—
417	C₂×C₃×D₃	—	3	8	no	—
418	C₂×C₃×D₃	—	3	4	no	—
419	C₂×C₃×D₃	—	3	32	no	—
420	C₂×C₃×D₃	—	3	8	no	—
421	C₂×C₃×D₃	—	4	32	no	—
422	C₂×C₃×D₃	—	4	8	no	—
423	C₂×C₃×D₃	—	6	4	no	—
424	C₂×C₃×D₃	—	6	2	no	—
425	C₂×C₃×D₃	—	6	4	no	—
426	C₂×C₃×D₃	—	6	32	no	—
427	C₂×C₃×D₃	—	6	32	no	—
428	C₂×C₃×D₃	—	6	32	no	—
429	C₂×C₃×D₃	—	6	8	no	—
430	C₂×C₃×D₃	—	6	32	no	—
431	C₂×C₃×D₃	—	12	16	no	—
432	C₂×C₃×D₃	—	12	4	no	—
433	C₂×C₃×D₃	D₃×D₄	1	8	yes	direct product factor
434	C₂×C₃×D₃	C₂×C₃×D₄	1	8	yes	complemented
435	C₂×C₃×D₃	C₂³×D₃	1	4	yes	—
436	C₂×C₃×D₃	C₂³×D₃	1	8	yes	complemented
437	C₂×C₃×D₃	C₂⁴×C₃	1	4	yes	—
438	C₂×C₃×D₃	C₂⁴×C₃	1	8	yes	complemented
439	D₃²	—	2	16	no	—
440	D₃²	—	2	32	no	—
441	D₃²	C₂×C₃×D₄	1	16	yes	direct product factor
442	C₃²×C₄	—	2	2	no	—
443	C₃²×C₄	—	2	4	no	—
444	C₃²×C₄	—	3	4	no	—
445	C₃²×C₄	—	4	2	no	—
446	C₃²×C₄	C₂³×D₃	1	4	yes	complemented
447	C₃²×C₄	C₂⁴×C₃	1	2	yes	complemented
448	C₃⋊Dic₃	C₂⁴×C₃	1	2	yes	complemented
449	C₃×Dic₃	—	2	4	no	—
450	C₃×Dic₃	—	3	4	no	—
451	C₃×Dic₃	—	6	2	no	—
452	C₃×Dic₃	C₂³×D₃	1	4	yes	complemented
453	C₃×Dic₃	C₂⁴×C₃	1	4	yes	complemented
454	C₂⁵	—	9	2	no	—
455	C₂²×D₄	—	3	2	no	—
456	C₂²×D₄	—	9	2	no	—
457	C₂²×D₄	—	9	2	no	—
458	C₂²×D₄	—	9	16	no	—
459	C₂²×D₄	—	9	1	no	—
460	C₂²×D₄	—	9	4	no	—
461	C₂²×D₄	—	9	1	no	—
462	C₂³×C₄	—	9	1	no	—
463	C₃³	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
464	C₂³×C₃	—	2	4	no	—
465	C₂³×C₃	—	2	2	no	—
466	C₂³×C₃	—	3	2	no	—
467	C₂³×C₃	—	3	2	no	—
468	C₂³×C₃	—	3	4	no	—
469	C₂³×C₃	—	3	16	no	—
470	C₂³×C₃	—	3	4	no	—
471	C₂³×C₃	—	3	16	no	—
472	C₂³×C₃	—	4	2	no	—
473	C₂³×C₃	—	6	2	no	—
474	C₂³×C₃	—	6	4	no	—
475	C₂³×C₃	—	6	16	no	—
476	C₂³×C₃	—	6	16	no	—
477	C₂³×C₃	—	6	16	no	—
478	C₂³×C₃	—	9	4	no	—
479	C₂³×C₃	—	9	8	no	—
480	C₂³×C₃	—	9	16	no	—
481	C₂³×C₃	—	9	8	no	—
482	C₂³×C₃	—	9	1	no	—
483	C₂³×C₃	—	9	2	no	—
484	C₂³×C₃	—	9	8	no	—
485	C₂³×C₃	—	12	16	no	—
486	C₂³×C₃	—	18	8	no	—
487	C₂³×C₃	—	18	16	no	—
488	C₂³×C₃	—	18	64	no	—
489	C₂³×C₃	—	18	8	no	—
490	C₂³×C₃	C₂×D₃²	1	2	yes	complemented
491	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	complemented
492	C₂²×D₃	—	2	16	no	—
493	C₂²×D₃	—	3	2	no	—
494	C₂²×D₃	—	3	8	no	—
495	C₂²×D₃	—	3	16	no	—
496	C₂²×D₃	—	3	4	no	—
497	C₂²×D₃	—	3	16	no	—
498	C₂²×D₃	—	3	16	no	—
499	C₂²×D₃	—	3	16	no	—
500	C₂²×D₃	—	3	16	no	—
501	C₂²×D₃	—	6	1	no	—
502	C₂²×D₃	—	6	2	no	—
503	C₂²×D₃	—	6	8	no	—
504	C₂²×D₃	—	6	16	no	—
505	C₂²×D₃	—	6	128	no	—
506	C₂²×D₃	—	6	16	no	—
507	C₂²×D₃	—	6	16	no	—
508	C₂²×D₃	—	6	16	no	—
509	C₂²×D₃	—	12	8	no	—
510	C₂²×D₃	C₂²×C₃×D₃	1	2	yes	—
511	C₂²×D₃	C₂²×C₃×D₃	1	16	yes	complemented
512	C₂²×D₃	C₂²×C₃×D₃	1	4	yes	complemented
513	C₃×D₄	—	2	8	no	—
514	C₃×D₄	—	2	4	no	—
515	C₃×D₄	—	3	16	no	—
516	C₃×D₄	—	3	16	no	—
517	C₃×D₄	—	3	8	no	—
518	C₃×D₄	—	3	8	no	—
519	C₃×D₄	—	4	4	no	—
520	C₃×D₄	—	6	8	no	—
521	C₃×D₄	—	6	16	no	—
522	C₃×D₄	—	9	16	no	—
523	C₃×D₄	—	9	8	no	—
524	C₃×D₄	—	9	8	no	—
525	C₃×D₄	—	9	4	no	—
526	C₃×D₄	C₂×D₃²	1	4	yes	direct product factor
527	C₃×D₄	C₂²×C₃×D₃	1	8	yes	complemented
528	C₂×C₃×C₄	—	2	2	no	—
529	C₂×C₃×C₄	—	2	1	no	—
530	C₂×C₃×C₄	—	3	2	no	—
531	C₂×C₃×C₄	—	3	2	no	—
532	C₂×C₃×C₄	—	3	8	no	—
533	C₂×C₃×C₄	—	3	8	no	—
534	C₂×C₃×C₄	—	4	1	no	—
535	C₂×C₃×C₄	—	6	8	no	—
536	C₂×C₃×C₄	—	6	2	no	—
537	C₂×C₃×C₄	—	9	4	no	—
538	C₂×C₃×C₄	—	9	8	no	—
539	C₂×C₃×C₄	—	9	1	no	—
540	C₂×C₃×C₄	—	9	4	no	—
541	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic, complemented
542	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	complemented
543	#67	—	3	16	no	—
544	#67	—	3	16	no	—
545	#67	—	3	16	no	—
546	#67	—	6	8	no	—
547	#67	C₂²×C₃×D₃	1	16	yes	complemented
548	C₂×Dic₃	—	3	2	no	—
549	C₂×Dic₃	—	3	8	no	—
550	C₂×Dic₃	—	6	1	no	—
551	C₂×Dic₃	C₂²×C₃×D₃	1	2	yes	complemented
552	D₁₂	—	3	16	no	—
553	D₁₂	—	3	8	no	—
554	D₁₂	—	6	4	no	—
555	D₁₂	C₂²×C₃×D₃	1	8	yes	complemented
556	C₄×D₃	—	3	8	no	—
557	C₄×D₃	—	3	8	no	—
558	C₄×D₃	—	3	8	no	—
559	C₄×D₃	—	6	4	no	—
560	C₄×D₃	C₂²×C₃×D₃	1	8	yes	complemented
561	C₂×C₃²	—	2	8	no	—
562	C₂×C₃²	—	2	4	no	—
563	C₂×C₃²	—	2	2	no	—
564	C₂×C₃²	—	2	4	no	—
565	C₂×C₃²	—	2	1	no	—
566	C₂×C₃²	—	2	2	no	—
567	C₂×C₃²	—	3	8	no	—
568	C₂×C₃²	—	4	2	no	—
569	C₂×C₃²	—	4	1	no	—
570	C₂×C₃²	—	4	8	no	—
571	C₂×C₃²	—	4	4	no	—
572	C₂×C₃²	—	6	8	no	—
573	C₂×C₃²	—	8	4	no	—
574	C₂×C₃²	C₂×D₃×D₄	1	4	yes	complemented
575	C₂×C₃²	C₂²×C₃×D₄	1	2	yes	complemented
576	C₂×C₃²	C₂⁴×D₃	1	2	yes	—
577	C₂×C₃²	C₂⁵×C₃	1	1	yes	characteristic
578	C₃⋊D₃	—	2	4	no	—
579	C₃⋊D₃	C₂²×C₃×D₄	1	4	yes	complemented
580	C₃×D₃	—	2	8	no	—
581	C₃×D₃	—	2	8	no	—
582	C₃×D₃	—	2	8	no	—
583	C₃×D₃	—	3	8	no	—
584	C₃×D₃	—	4	8	no	—
585	C₃×D₃	—	6	4	no	—
586	C₃×D₃	—	6	8	no	—
587	C₃×D₃	—	12	4	no	—
588	C₃×D₃	C₂×D₃×D₄	1	8	yes	direct product factor
589	C₃×D₃	C₂²×C₃×D₄	1	8	yes	complemented
590	C₂⁴	—	3	4	no	—
591	C₂⁴	—	9	1	no	—
592	C₂⁴	—	9	4	no	—
593	C₂⁴	—	9	2	no	—
594	C₂⁴	—	9	16	no	—
595	C₂⁴	—	9	2	no	—
596	C₂⁴	—	18	16	no	—
597	C₂×D₄	—	3	4	no	—
598	C₂×D₄	—	3	16	no	—
599	C₂×D₄	—	3	2	no	—
600	C₂×D₄	—	9	16	no	—
601	C₂×D₄	—	9	4	no	—
602	C₂×D₄	—	9	16	no	—
603	C₂×D₄	—	9	8	no	—
604	C₂×D₄	—	9	32	no	—
605	C₂×D₄	—	9	2	no	—
606	C₂×D₄	—	9	2	no	—
607	C₂×D₄	—	9	8	no	—
608	C₂×D₄	—	9	1	no	—
609	C₂×D₄	C₃×D₃²	1	1	yes	characteristic, direct product factor
610	C₂²×C₄	—	3	2	no	—
611	C₂²×C₄	—	9	1	no	—
612	C₂²×C₄	—	9	8	no	—
613	C₂²×C₄	—	9	2	no	—
614	C₂²×C₄	—	9	1	no	—
615	C₂²×C₃	—	2	4	no	—
616	C₂²×C₃	—	2	8	no	—
617	C₂²×C₃	—	2	1	no	—
618	C₂²×C₃	—	2	2	no	—
619	C₂²×C₃	—	2	4	no	—
620	C₂²×C₃	—	2	8	no	—
621	C₂²×C₃	—	3	8	no	—
622	C₂²×C₃	—	3	8	no	—
623	C₂²×C₃	—	3	4	no	—
624	C₂²×C₃	—	3	4	no	—
625	C₂²×C₃	—	3	8	no	—
626	C₂²×C₃	—	3	8	no	—
627	C₂²×C₃	—	4	4	no	—
628	C₂²×C₃	—	4	8	no	—
629	C₂²×C₃	—	4	1	no	—
630	C₂²×C₃	—	4	4	no	—
631	C₂²×C₃	—	6	4	no	—
632	C₂²×C₃	—	6	8	no	—
633	C₂²×C₃	—	6	8	no	—
634	C₂²×C₃	—	6	32	no	—
635	C₂²×C₃	—	6	32	no	—
636	C₂²×C₃	—	6	8	no	—
637	C₂²×C₃	—	6	8	no	—
638	C₂²×C₃	—	8	4	no	—
639	C₂²×C₃	—	9	16	no	—
640	C₂²×C₃	—	9	4	no	—
641	C₂²×C₃	—	9	2	no	—
642	C₂²×C₃	—	9	4	no	—
643	C₂²×C₃	—	12	8	no	—
644	C₂²×C₃	—	12	32	no	—
645	C₂²×C₃	—	18	16	no	—
646	C₂²×C₃	—	18	32	no	—
647	C₂²×C₃	—	18	16	no	—
648	C₂²×C₃	—	18	4	no	—
649	C₂²×C₃	C₂²×D₃²	1	1	yes	characteristic
650	C₂²×C₃	C₂²×D₃²	1	4	yes	complemented
651	C₂²×C₃	C₂³×C₃×D₃	1	2	yes	—
652	C₂²×C₃	C₂³×C₃×D₃	1	8	yes	complemented
653	C₂×D₃	—	2	8	no	—
654	C₂×D₃	—	2	32	no	—
655	C₂×D₃	—	3	8	no	—
656	C₂×D₃	—	3	4	no	—
657	C₂×D₃	—	3	32	no	—
658	C₂×D₃	—	3	8	no	—
659	C₂×D₃	—	6	2	no	—
660	C₂×D₃	—	6	4	no	—
661	C₂×D₃	—	6	4	no	—
662	C₂×D₃	—	6	32	no	—
663	C₂×D₃	—	6	32	no	—
664	C₂×D₃	—	6	32	no	—
665	C₂×D₃	—	6	8	no	—
666	C₂×D₃	—	6	32	no	—
667	C₂×D₃	—	12	16	no	—
668	C₂×D₃	—	12	4	no	—
669	C₂×D₃	C₃×D₃×D₄	1	8	yes	direct product factor
670	C₂×D₃	C₂³×C₃×D₃	1	4	yes	—
671	C₂×D₃	C₂³×C₃×D₃	1	8	yes	complemented
672	C₃×C₄	—	2	2	no	—
673	C₃×C₄	—	2	4	no	—
674	C₃×C₄	—	3	4	no	—
675	C₃×C₄	—	3	4	no	—
676	C₃×C₄	—	4	2	no	—
677	C₃×C₄	—	6	4	no	—
678	C₃×C₄	—	9	2	no	—
679	C₃×C₄	C₂²×D₃²	1	2	yes	complemented
680	C₃×C₄	C₂³×C₃×D₃	1	4	yes	complemented
681	Dic₃	—	3	4	no	—
682	Dic₃	—	6	2	no	—
683	Dic₃	C₂³×C₃×D₃	1	4	yes	complemented
684	C₃²	—	2	1	no	—
685	C₃²	—	2	2	no	—
686	C₃²	—	4	1	no	—
687	C₃²	C₂²×D₃×D₄	1	2	yes	complemented
688	C₃²	C₂³×C₃×D₄	1	1	yes	characteristic, complemented
689	C₂³	—	3	2	no	—
690	C₂³	—	3	4	no	—
691	C₂³	—	3	16	no	—
692	C₂³	—	6	16	no	—
693	C₂³	—	9	4	no	—
694	C₂³	—	9	8	no	—
695	C₂³	—	9	16	no	—
696	C₂³	—	9	8	no	—
697	C₂³	—	9	1	no	—
698	C₂³	—	9	2	no	—
699	C₂³	—	9	8	no	—
700	C₂³	—	18	8	no	—
701	C₂³	—	18	16	no	—
702	C₂³	—	18	64	no	—
703	C₂³	—	18	8	no	—
704	C₂³	C₂×C₃×D₃²	1	2	yes	complemented
705	D₄	—	3	16	no	—
706	D₄	—	3	8	no	—
707	D₄	—	9	16	no	—
708	D₄	—	9	8	no	—
709	D₄	—	9	8	no	—
710	D₄	—	9	4	no	—
711	D₄	C₂×C₃×D₃²	1	4	yes	direct product factor
712	C₂×C₄	—	3	2	no	—
713	C₂×C₄	—	3	8	no	—
714	C₂×C₄	—	9	4	no	—
715	C₂×C₄	—	9	8	no	—
716	C₂×C₄	—	9	1	no	—
717	C₂×C₄	—	9	4	no	—
718	C₂×C₄	C₂×C₃×D₃²	1	1	yes	characteristic, complemented
719	C₂×C₃	—	2	4	no	—
720	C₂×C₃	—	2	8	no	—
721	C₂×C₃	—	2	1	no	—
722	C₂×C₃	—	2	2	no	—
723	C₂×C₃	—	2	2	no	—
724	C₂×C₃	—	2	4	no	—
725	C₂×C₃	—	3	8	no	—
726	C₂×C₃	—	3	8	no	—
727	C₂×C₃	—	4	4	no	—
728	C₂×C₃	—	4	8	no	—
729	C₂×C₃	—	4	1	no	—
730	C₂×C₃	—	4	2	no	—
731	C₂×C₃	—	6	8	no	—
732	C₂×C₃	—	6	8	no	—
733	C₂×C₃	—	6	8	no	—
734	C₂×C₃	—	8	4	no	—
735	C₂×C₃	—	9	4	no	—
736	C₂×C₃	—	12	8	no	—
737	C₂×C₃	—	18	4	no	—
738	C₂×C₃	D₃²×D₄	1	2	yes	direct product factor
739	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	complemented
740	C₂×C₃	C₂³×D₃²	1	1	yes	characteristic
741	C₂×C₃	C₂⁴×C₃×D₃	1	2	yes	—
742	D₃	—	2	8	no	—
743	D₃	—	3	8	no	—
744	D₃	—	6	4	no	—
745	D₃	—	6	8	no	—
746	D₃	—	12	4	no	—
747	D₃	C₂×C₃×D₃×D₄	1	8	yes	direct product factor
748	C₂²	—	2	4	no	—
749	C₂²	—	3	4	no	—
750	C₂²	—	3	8	no	—
751	C₂²	—	3	8	no	—
752	C₂²	—	6	32	no	—
753	C₂²	—	6	8	no	—
754	C₂²	—	9	16	no	—
755	C₂²	—	9	2	no	—
756	C₂²	—	9	4	no	—
757	C₂²	—	9	4	no	—
758	C₂²	—	18	16	no	—
759	C₂²	—	18	32	no	—
760	C₂²	—	18	16	no	—
761	C₂²	—	18	4	no	—
762	C₂²	C₂²×C₃×D₃²	1	1	yes	characteristic
763	C₂²	C₂²×C₃×D₃²	1	4	yes	complemented
764	C₄	—	3	4	no	—
765	C₄	—	9	2	no	—
766	C₄	C₂²×C₃×D₃²	1	2	yes	complemented
767	C₃	—	2	1	no	—
768	C₃	—	2	2	no	—
769	C₃	—	4	1	no	—
770	C₃	C₂×D₃²×D₄	1	1	yes	characteristic, direct product factor
771	C₃	C₂²×C₃×D₃×D₄	1	2	yes	complemented
772	C₂	—	2	4	no	—
773	C₂	—	3	8	no	—
774	C₂	—	6	8	no	—
775	C₂	—	9	4	no	—
776	C₂	—	18	4	no	—
777	C₂	C₃×D₃²×D₄	1	2	yes	direct product factor
778	C₂	C₂³×C₃×D₃²	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₃²
commutator, cosocle	C₂×C₃²	C₂⁵×C₃
Frattini	C₂	C₂³×C₃×D₃²
Fitting	C₂×C₃³×D₄	C₂²
socle	C₂²×C₃³	C₂⁴
hypercenter	C₂×C₃×D₄	D₃²
hypocenter	C₃²	C₂³×C₃×D₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×D₃²	C₂	semidirect
2. C₂×C₃×D₄×C₃⋊D₃	C₂	semidirect
3. C₂×C₃²×D₃×D₄	C₂	semidirect
4. C₂×C₃×#3811	C₂	semidirect
5. C₂×C₃×D₃×#67	C₂	semidirect
6. C₃×D₃²×D₄	C₂	direct (N × H)
7. C₂×C₃×#3802	C₂	semidirect
8. C₂×C₃×D₃×D₁₂	C₂	semidirect
9. C₂×C₃×C₄×D₃²	C₂	semidirect
11. C₂×D₃²×D₄	C₃	direct (N × H)
12. C₂³×C₃×C₃⋊D₃	C₂²	semidirect
13. C₂³×C₃²×D₃	C₂²	semidirect
16. C₂²×C₃×D₃²	C₂²	semidirect
17. C₂²×C₃×D₃²	C₂²	semidirect
18. C₂²×C₃×D₃²	C₂²	semidirect
19. C₂×C₃³×D₄	C₂²	semidirect
20. C₂×C₃×#638	C₂²	semidirect
21. C₃×D₄×C₃⋊D₃	C₂²	semidirect
22. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
23. C₂×C₃×C₄×C₃⋊D₃	C₂²	semidirect
24. C₂×C₃²×#67	C₂²	semidirect
25. C₃²×D₃×D₄	C₂²	semidirect
26. C₂×C₃²×D₁₂	C₂²	semidirect
27. C₂×C₃²×C₄×D₃	C₂²	semidirect
28. C₃×#3811	C₂²	semidirect
29. C₃×D₃×#67	C₂²	semidirect
30. C₂×C₃×#626	C₂²	semidirect
31. C₂×C₃×#625	C₂²	semidirect
32. C₂×C₃×#624	C₂²	semidirect
33. C₂×C₃×D₃×Dic₃	C₂²	semidirect
34. C₃×#3802	C₂²	semidirect
35. C₃×D₃×D₁₂	C₂²	semidirect
36. C₃×C₄×D₃²	C₂²	semidirect
38. C₂³×D₃²	C₂×C₃	semidirect
40. C₂×D₄×C₃⋊D₃	C₂×C₃	semidirect
50. C₂×C₃×D₃×D₄	D₃	direct (N × H)
51. C₂×C₃×D₃×D₄	C₂×C₃	semidirect
54. C₂×#3811	C₂×C₃	semidirect
55. C₂×D₃×#67	C₂×C₃	semidirect
56. D₃²×D₄	C₂×C₃	direct (N × H)
57. C₂×#3802	C₂×C₃	semidirect
58. C₂×D₃×D₁₂	C₂×C₃	semidirect
59. C₂×C₄×D₃²	C₂×C₃	semidirect
60. C₂³×C₃³	C₂³	semidirect
63. C₂²×C₃×C₃⋊D₃	C₂³	semidirect
64. C₂²×C₃×C₃⋊D₃	C₂³	semidirect
67. C₂²×C₃²×D₃	C₂³	semidirect
68. C₂²×C₃²×D₃	C₂³	semidirect
72. C₂×C₃×D₃²	D₄	direct (N × H)
74. C₂×C₃×D₃²	C₂³	semidirect
75. C₂×C₃×D₃²	C₂³	semidirect
76. C₃³×D₄	C₂³	semidirect
77. C₂×C₃³×C₄	C₂³	semidirect
78. C₃×#638	C₂³	semidirect
79. C₂×C₃×C₃⋊Dic₃	C₂³	semidirect
80. C₃×C₄⋊(C₃⋊D₃)	C₂³	semidirect
81. C₃×C₄×C₃⋊D₃	C₂³	semidirect
82. C₃²×#67	C₂³	semidirect
83. C₂×C₃²×Dic₃	C₂³	semidirect
84. C₃²×D₁₂	C₂³	semidirect
85. C₃²×C₄×D₃	C₂³	semidirect
86. C₃×#626	C₂³	semidirect
87. C₃×#625	C₂³	semidirect
88. C₃×#624	C₂³	semidirect
89. C₃×D₃×Dic₃	C₂³	semidirect
93. C₂³×C₃⋊D₃	C₂²×C₃	semidirect
103. C₂³×C₃×D₃	C₂×D₃	semidirect
104. C₂³×C₃×D₃	C₂²×C₃	semidirect
107. C₂²×D₃²	C₂²×C₃	semidirect
108. C₂²×D₃²	C₂²×C₃	semidirect
109. C₂²×D₃²	C₂²×C₃	semidirect
116. C₂×C₃²×D₄	C₂×D₃	semidirect
117. C₂×C₃²×D₄	C₂²×C₃	semidirect
119. C₂×#638	C₂²×C₃	semidirect
120. D₄×C₃⋊D₃	C₂²×C₃	semidirect
121. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
122. C₂×C₄×C₃⋊D₃	C₂²×C₃	semidirect
129. C₂×C₃×#67	C₂×D₃	semidirect
130. C₂×C₃×#67	C₂²×C₃	semidirect
139. C₃×D₃×D₄	C₂×D₃	direct (N × H)
140. C₃×D₃×D₄	C₂²×C₃	semidirect
146. C₂×C₃×D₁₂	C₂×D₃	semidirect
147. C₂×C₃×D₁₂	C₂²×C₃	semidirect
154. C₂×C₃×C₄×D₃	C₂×D₃	semidirect
155. C₂×C₃×C₄×D₃	C₂²×C₃	semidirect
156. #3811	C₂²×C₃	semidirect
157. D₃×#67	C₂²×C₃	semidirect
158. C₂×#626	C₂²×C₃	semidirect
159. C₂×#625	C₂²×C₃	semidirect
160. C₂×#624	C₂²×C₃	semidirect
161. C₂×D₃×Dic₃	C₂²×C₃	semidirect
162. #3802	C₂²×C₃	semidirect
163. D₃×D₁₂	C₂²×C₃	semidirect
164. C₄×D₃²	C₂²×C₃	semidirect
167. C₂²×C₃³	C₂⁴	semidirect
170. C₂×C₃×C₃⋊D₃	C₂×D₄	semidirect
172. C₂×C₃×C₃⋊D₃	C₂⁴	semidirect
175. C₂×C₃²×D₃	C₂×D₄	semidirect
177. C₂×C₃²×D₃	C₂⁴	semidirect
180. C₃×D₃²	C₂×D₄	direct (N × H)
181. C₃³×C₄	C₂⁴	semidirect
182. C₃×C₃⋊Dic₃	C₂⁴	semidirect
183. C₃²×Dic₃	C₂⁴	semidirect
204. C₂×D₃×D₄	C₃×D₃	direct (N × H)
214. C₂³×C₃²	C₂²×D₃	semidirect
215. C₂³×C₃²	C₂³×C₃	semidirect
218. C₂²×C₃⋊D₃	C₂³×C₃	semidirect
219. C₂²×C₃⋊D₃	C₂³×C₃	semidirect
244. C₂²×C₃×D₃	C₂²×D₃	semidirect
245. C₂²×C₃×D₃	C₂²×D₃	semidirect
247. C₂²×C₃×D₃	C₂³×C₃	semidirect
248. C₂²×C₃×D₃	C₂³×C₃	semidirect
252. C₂×D₃²	C₃×D₄	direct (N × H)
254. C₂×D₃²	C₂³×C₃	semidirect
255. C₂×D₃²	C₂³×C₃	semidirect
261. C₃²×D₄	C₂²×D₃	semidirect
262. C₃²×D₄	C₂³×C₃	semidirect
268. C₂×C₃²×C₄	C₂²×D₃	semidirect
269. C₂×C₃²×C₄	C₂³×C₃	semidirect
270. #638	C₂³×C₃	semidirect
271. C₂×C₃⋊Dic₃	C₂³×C₃	semidirect
272. C₄⋊(C₃⋊D₃)	C₂³×C₃	semidirect
273. C₄×C₃⋊D₃	C₂³×C₃	semidirect
279. C₃×#67	C₂²×D₃	semidirect
280. C₃×#67	C₂³×C₃	semidirect
285. C₂×C₃×Dic₃	C₂²×D₃	semidirect
286. C₂×C₃×Dic₃	C₂³×C₃	semidirect
291. C₃×D₁₂	C₂²×D₃	semidirect
292. C₃×D₁₂	C₂³×C₃	semidirect
298. C₃×C₄×D₃	C₂²×D₃	semidirect
299. C₃×C₄×D₃	C₂³×C₃	semidirect
300. #626	C₂³×C₃	semidirect
301. #625	C₂³×C₃	semidirect
302. #624	C₂³×C₃	semidirect
303. D₃×Dic₃	C₂³×C₃	semidirect
306. C₂×C₃³	C₂²×D₄	semidirect
309. C₃×C₃⋊D₃	C₂²×D₄	semidirect
311. C₃²×D₃	C₂²×D₄	semidirect
329. C₂³×D₃	C₂×C₃×D₃	semidirect
351. C₂×C₃×D₄	D₃²	direct (N × H)
352. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
365. C₂×#67	C₂×C₃×D₃	semidirect
373. D₃×D₄	C₂×C₃×D₃	direct (N × H)
378. C₂×D₁₂	C₂×C₃×D₃	semidirect
384. C₂×C₄×D₃	C₂×C₃×D₃	semidirect
402. C₂²×C₃²	C₂³×D₃	semidirect
404. C₂²×C₃²	C₂⁴×C₃	semidirect
407. C₂×C₃⋊D₃	C₂×C₃×D₄	semidirect
409. C₂×C₃⋊D₃	C₂⁴×C₃	semidirect
433. C₂×C₃×D₃	D₃×D₄	direct (N × H)
434. C₂×C₃×D₃	C₂×C₃×D₄	semidirect
436. C₂×C₃×D₃	C₂³×D₃	semidirect
438. C₂×C₃×D₃	C₂⁴×C₃	semidirect
441. D₃²	C₂×C₃×D₄	direct (N × H)
446. C₃²×C₄	C₂³×D₃	semidirect
447. C₃²×C₄	C₂⁴×C₃	semidirect
448. C₃⋊Dic₃	C₂⁴×C₃	semidirect
452. C₃×Dic₃	C₂³×D₃	semidirect
453. C₃×Dic₃	C₂⁴×C₃	semidirect
463. C₃³	C₂³×D₄	semidirect
490. C₂³×C₃	C₂×D₃²	semidirect
491. C₂³×C₃	C₂²×C₃×D₃	semidirect
511. C₂²×D₃	C₂²×C₃×D₃	semidirect
512. C₂²×D₃	C₂²×C₃×D₃	semidirect
526. C₃×D₄	C₂×D₃²	direct (N × H)
527. C₃×D₄	C₂²×C₃×D₃	semidirect
541. C₂×C₃×C₄	C₂×D₃²	semidirect
542. C₂×C₃×C₄	C₂²×C₃×D₃	semidirect
547. #67	C₂²×C₃×D₃	semidirect
551. C₂×Dic₃	C₂²×C₃×D₃	semidirect
555. D₁₂	C₂²×C₃×D₃	semidirect
560. C₄×D₃	C₂²×C₃×D₃	semidirect
574. C₂×C₃²	C₂×D₃×D₄	semidirect
575. C₂×C₃²	C₂²×C₃×D₄	semidirect
579. C₃⋊D₃	C₂²×C₃×D₄	semidirect
588. C₃×D₃	C₂×D₃×D₄	direct (N × H)
589. C₃×D₃	C₂²×C₃×D₄	semidirect
609. C₂×D₄	C₃×D₃²	direct (N × H)
650. C₂²×C₃	C₂²×D₃²	semidirect
652. C₂²×C₃	C₂³×C₃×D₃	semidirect
669. C₂×D₃	C₃×D₃×D₄	direct (N × H)
671. C₂×D₃	C₂³×C₃×D₃	semidirect
679. C₃×C₄	C₂²×D₃²	semidirect
680. C₃×C₄	C₂³×C₃×D₃	semidirect
683. Dic₃	C₂³×C₃×D₃	semidirect
687. C₃²	C₂²×D₃×D₄	semidirect
688. C₃²	C₂³×C₃×D₄	semidirect
704. C₂³	C₂×C₃×D₃²	semidirect
711. D₄	C₂×C₃×D₃²	direct (N × H)
718. C₂×C₄	C₂×C₃×D₃²	semidirect
738. C₂×C₃	D₃²×D₄	direct (N × H)
739. C₂×C₃	C₂×C₃×D₃×D₄	semidirect
747. D₃	C₂×C₃×D₃×D₄	direct (N × H)
763. C₂²	C₂²×C₃×D₃²	semidirect
766. C₄	C₂²×C₃×D₃²	semidirect
770. C₃	C₂×D₃²×D₄	direct (N × H)
771. C₃	C₂²×C₃×D₃×D₄	semidirect
777. C₂	C₃×D₃²×D₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×D₃²	2
C₂×C₃×D₄×C₃⋊D₃	2
C₂×C₃²×D₃×D₄	2
C₂×C₃×#3811	2
C₂×C₃×D₃×#67	2
C₃×D₃²×D₄	2
C₂×C₃×#3802	2
C₂×C₃×D₃×D₁₂	2
C₂×C₃×C₄×D₃²	2
C₂²×C₃×D₃×D₄	3
C₂×D₃²×D₄	3

Subgroups — C2×C3×D32×D4 #13181546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₃²×D₄ #13181546