Subgroups — C₂×C₃²×C₄×#67 #13179165

Order 1728.

3500 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃³×C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃²×#67	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃²×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃²×#217	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×C₄×#67	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃²×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃²×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃²×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃²×C₄×D₄	—	3	1	no	maximal
10	C₂×C₃×C₄×#67	C₃	1	4	yes	maximal, direct product factor
11	C₂⁴×C₃³	C₂²	1	1	yes	characteristic
12	C₂³×C₃²×D₃	C₂²	1	1	yes	characteristic
13	C₂²×C₃³×C₄	—	2	4	no	—
14	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃³×C₄	C₂²	1	4	yes	complemented
17	C₂×C₃²×#67	C₄	1	8	yes	direct product factor
18	C₂×C₃²×#67	C₂²	1	4	yes	—
19	C₂²×C₃²×Dic₃	C₂²	1	1	yes	characteristic
20	C₂²×C₃²×Dic₃	C₂²	1	1	yes	characteristic
21	C₂²×C₃²×Dic₃	C₂²	1	1	yes	characteristic
22	C₂×C₃²×C₄×D₃	—	2	4	no	—
23	C₂×C₃²×C₄×D₃	C₂²	1	4	yes	complemented
24	C₃²×#217	C₂²	1	4	yes	complemented
25	C₃²×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
26	C₃²×Dic₃⋊C₄	C₂²	1	4	yes	complemented
27	C₃²×C₄×Dic₃	C₂²	1	4	yes	complemented
28	C₂²×C₃²×D₄	—	3	1	no	—
29	C₂³×C₃²×C₄	—	2	4	no	—
30	C₂³×C₃²×C₄	—	3	1	no	—
31	C₂³×C₃²×C₄	D₃	1	1	yes	characteristic, complemented
32	C₂³×C₃²×C₄	C₂×C₃	1	4	yes	complemented
33	C₂²×C₃×#67	C₂×C₃	1	4	yes	—
34	C₂²×C₃×C₄×D₃	C₂×C₃	1	4	yes	complemented
35	C₃²×C₄×D₄	—	3	8	no	—
36	C₂×C₃²×C₄⋊C₄	—	3	1	no	—
37	C₂×C₃²×C₂²⋊C₄	—	3	1	no	—
38	C₂×C₃²×C₂²⋊C₄	—	3	1	no	—
39	C₂×C₃²×C₄²	—	3	1	no	—
40	C₂×C₃×#217	C₂×C₃	1	4	yes	complemented
41	C₃×C₄×#67	C₂×C₃	1	32	yes	direct product factor
42	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	4	yes	complemented
43	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	4	yes	complemented
44	C₂×C₃×C₄×Dic₃	C₂×C₃	1	4	yes	complemented
45	C₂³×C₃³	—	2	2	no	—
46	C₂³×C₃³	—	2	2	no	—
47	C₂³×C₃³	C₂×C₄	1	4	yes	complemented
48	C₂³×C₃³	C₂³	1	2	yes	—
49	C₂³×C₃³	C₂³	1	1	yes	characteristic
50	C₂²×C₃²×D₃	—	2	2	no	—
51	C₂²×C₃²×D₃	—	2	2	no	—
52	C₂²×C₃²×D₃	C₂×C₄	1	4	yes	complemented
53	C₂²×C₃²×D₃	C₂³	1	2	yes	—
54	C₂×C₃³×C₄	—	2	2	no	—
55	C₂×C₃³×C₄	—	2	8	no	—
56	C₂×C₃³×C₄	D₄	1	4	yes	complemented
57	C₂×C₃³×C₄	C₂³	1	2	yes	—
58	C₂×C₃³×C₄	C₂³	1	2	yes	—
59	C₃²×#67	C₂×C₄	1	16	yes	direct product factor
60	C₂×C₃²×Dic₃	—	2	2	no	—
61	C₂×C₃²×Dic₃	—	2	2	no	—
62	C₂×C₃²×Dic₃	C₂×C₄	1	4	yes	complemented
63	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
64	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
65	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
66	C₃²×C₄×D₃	—	2	8	no	—
67	C₂×C₃×C₄×D₄	—	3	4	no	—
68	C₂×C₄×#67	C₃²	1	1	yes	characteristic, direct product factor
69	C₂⁴×C₃²	—	2	4	no	—
70	C₂⁴×C₃²	—	3	1	no	—
71	C₂⁴×C₃²	C₂×D₃	1	1	yes	characteristic
72	C₂⁴×C₃²	C₂²×C₃	1	4	yes	—
73	C₂³×C₃×D₃	C₂²×C₃	1	4	yes	—
74	C₂×C₃²×D₄	—	3	8	no	—
75	C₂×C₃²×D₄	—	3	4	no	—
76	C₂²×C₃²×C₄	—	2	32	no	—
77	C₂²×C₃²×C₄	—	2	4	no	—
78	C₂²×C₃²×C₄	—	2	4	no	—
79	C₂²×C₃²×C₄	—	2	16	no	—
80	C₂²×C₃²×C₄	—	2	4	no	—
81	C₂²×C₃²×C₄	—	2	16	no	—
82	C₂²×C₃²×C₄	—	3	1	no	—
83	C₂²×C₃²×C₄	—	3	1	no	—
84	C₂²×C₃²×C₄	—	3	1	no	—
85	C₂²×C₃²×C₄	—	3	4	no	—
86	C₂²×C₃²×C₄	—	6	4	no	—
87	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
88	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
89	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	complemented
90	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
91	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
92	C₂²×C₃²×C₄	C₂²×C₃	1	16	yes	complemented
93	C₂×C₃×#67	C₃×C₄	1	32	yes	direct product factor
94	C₂×C₃×#67	C₂²×C₃	1	16	yes	—
95	C₂²×C₃×Dic₃	C₂²×C₃	1	4	yes	—
96	C₂²×C₃×Dic₃	C₂²×C₃	1	4	yes	—
97	C₂²×C₃×Dic₃	C₂²×C₃	1	4	yes	—
98	C₂×C₃×C₄×D₃	—	2	16	no	—
99	C₂×C₃×C₄×D₃	C₂²×C₃	1	16	yes	complemented
100	C₃²×C₄⋊C₄	—	3	4	no	—
101	C₃²×C₂²⋊C₄	—	3	4	no	—
102	C₃²×C₂²⋊C₄	—	3	4	no	—
103	C₃²×C₄²	—	3	4	no	—
104	C₃×#217	C₂²×C₃	1	16	yes	complemented
105	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	16	yes	complemented
106	C₃×Dic₃⋊C₄	C₂²×C₃	1	16	yes	complemented
107	C₃×C₄×Dic₃	C₂²×C₃	1	16	yes	complemented
108	C₂²×C₃³	—	2	8	no	—
109	C₂²×C₃³	—	2	2	no	—
110	C₂²×C₃³	—	2	2	no	—
111	C₂²×C₃³	C₂²×C₄	1	2	yes	—
112	C₂²×C₃³	C₂²×C₄	1	4	yes	complemented
113	C₂²×C₃³	C₂×D₄	1	2	yes	—
114	C₂²×C₃³	#41	1	2	yes	—
115	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
116	C₂×C₃²×D₃	—	2	8	no	—
117	C₂×C₃²×D₃	—	2	2	no	—
118	C₂×C₃²×D₃	—	2	2	no	—
119	C₂×C₃²×D₃	C₂²×C₄	1	4	yes	complemented
120	C₃³×C₄	—	2	2	no	—
121	C₃³×C₄	C₂×D₄	1	4	yes	complemented
122	C₃²×Dic₃	—	2	2	no	—
123	C₃²×Dic₃	—	2	2	no	—
124	C₃²×Dic₃	C₂²×C₄	1	4	yes	complemented
125	C₂²×C₃×D₄	—	3	4	no	—
126	C₂³×C₃×C₄	—	2	4	no	—
127	C₂³×C₃×C₄	—	3	4	no	—
128	C₂³×C₃×C₄	C₃×D₃	1	4	yes	complemented
129	C₂³×C₃×C₄	C₂×C₃²	1	1	yes	characteristic, complemented
130	C₂²×#67	C₂×C₃²	1	1	yes	characteristic
131	C₂²×C₄×D₃	C₂×C₃²	1	1	yes	characteristic, complemented
132	C₃×C₄×D₄	—	3	32	no	—
133	C₂×C₃×C₄⋊C₄	—	3	4	no	—
134	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
135	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
136	C₂×C₃×C₄²	—	3	4	no	—
137	C₂×#217	C₂×C₃²	1	1	yes	characteristic, complemented
138	C₄×#67	C₂×C₃²	1	8	yes	direct product factor
139	C₂×(C₂×D₃)⋊C₄	C₂×C₃²	1	1	yes	characteristic, complemented
140	C₂×Dic₃⋊C₄	C₂×C₃²	1	1	yes	characteristic, complemented
141	C₂×C₄×Dic₃	C₂×C₃²	1	1	yes	characteristic, complemented
142	C₂³×C₃²	—	2	16	no	—
143	C₂³×C₃²	—	2	16	no	—
144	C₂³×C₃²	—	2	2	no	—
145	C₂³×C₃²	—	2	2	no	—
146	C₂³×C₃²	—	2	8	no	—
147	C₂³×C₃²	—	2	8	no	—
148	C₂³×C₃²	—	2	16	no	—
149	C₂³×C₃²	—	2	8	no	—
150	C₂³×C₃²	—	2	4	no	—
151	C₂³×C₃²	—	3	4	no	—
152	C₂³×C₃²	—	3	2	no	—
153	C₂³×C₃²	—	6	2	no	—
154	C₂³×C₃²	—	6	2	no	—
155	C₂³×C₃²	C₄×D₃	1	4	yes	complemented
156	C₂³×C₃²	C₂×C₃×C₄	1	16	yes	complemented
157	C₂³×C₃²	C₂²×D₃	1	2	yes	—
158	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
159	C₂³×C₃²	C₂³×C₃	1	8	yes	—
160	C₂³×C₃²	C₂³×C₃	1	4	yes	—
161	C₂²×C₃×D₃	—	2	8	no	—
162	C₂²×C₃×D₃	—	2	8	no	—
163	C₂²×C₃×D₃	C₂×C₃×C₄	1	16	yes	complemented
164	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
165	C₃²×D₄	—	3	16	no	—
166	C₂×C₃²×C₄	—	2	16	no	—
167	C₂×C₃²×C₄	—	2	64	no	—
168	C₂×C₃²×C₄	—	2	2	no	—
169	C₂×C₃²×C₄	—	2	8	no	—
170	C₂×C₃²×C₄	—	2	8	no	—
171	C₂×C₃²×C₄	—	2	32	no	—
172	C₂×C₃²×C₄	—	2	16	no	—
173	C₂×C₃²×C₄	—	2	8	no	—
174	C₂×C₃²×C₄	—	2	8	no	—
175	C₂×C₃²×C₄	—	3	4	no	—
176	C₂×C₃²×C₄	—	3	2	no	—
177	C₂×C₃²×C₄	—	3	2	no	—
178	C₂×C₃²×C₄	—	3	2	no	—
179	C₂×C₃²×C₄	—	6	2	no	—
180	C₂×C₃²×C₄	—	6	2	no	—
181	C₂×C₃²×C₄	—	6	8	no	—
182	C₂×C₃²×C₄	#67	1	4	yes	direct product factor
183	C₂×C₃²×C₄	C₃×D₄	1	16	yes	complemented
184	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
185	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
186	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
187	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
188	C₃×#67	C₂×C₃×C₄	1	64	yes	direct product factor
189	C₂×C₃×Dic₃	—	2	8	no	—
190	C₂×C₃×Dic₃	—	2	8	no	—
191	C₂×C₃×Dic₃	C₂×C₃×C₄	1	16	yes	complemented
192	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
193	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
194	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
195	C₃×C₄×D₃	—	2	32	no	—
196	C₂×C₄×D₄	—	3	1	no	Sylow
197	C₂×C₃³	—	2	4	no	—
198	C₂×C₃³	C₄×D₄	1	4	yes	complemented
199	C₂×C₃³	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₃³	C₂×#41	1	1	yes	characteristic
202	C₃²×D₃	—	2	4	no	—
203	C₂⁴×C₃	—	2	4	no	—
204	C₂⁴×C₃	—	3	4	no	—
205	C₂⁴×C₃	C₂×C₃×D₃	1	4	yes	—
206	C₂⁴×C₃	C₂²×C₃²	1	1	yes	characteristic
207	C₂³×D₃	C₂²×C₃²	1	1	yes	characteristic
208	C₂×C₃×D₄	—	3	32	no	—
209	C₂×C₃×D₄	—	3	16	no	—
210	C₂²×C₃×C₄	—	2	32	no	—
211	C₂²×C₃×C₄	—	2	16	no	—
212	C₂²×C₃×C₄	—	2	4	no	—
213	C₂²×C₃×C₄	—	2	4	no	—
214	C₂²×C₃×C₄	—	2	4	no	—
215	C₂²×C₃×C₄	—	2	16	no	—
216	C₂²×C₃×C₄	—	3	4	no	—
217	C₂²×C₃×C₄	—	3	4	no	—
218	C₂²×C₃×C₄	—	3	4	no	—
219	C₂²×C₃×C₄	—	3	16	no	—
220	C₂²×C₃×C₄	—	6	16	no	—
221	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
222	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
223	C₂²×C₃×C₄	C₂×C₃×D₃	1	16	yes	complemented
224	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂²×C₃²	1	4	yes	complemented
227	C₂×#67	C₃²×C₄	1	8	yes	direct product factor
228	C₂×#67	C₂²×C₃²	1	4	yes	—
229	C₂²×Dic₃	C₂²×C₃²	1	1	yes	characteristic
230	C₂²×Dic₃	C₂²×C₃²	1	1	yes	characteristic
231	C₂²×Dic₃	C₂²×C₃²	1	1	yes	characteristic
232	C₂×C₄×D₃	—	2	4	no	—
233	C₂×C₄×D₃	C₂²×C₃²	1	4	yes	complemented
234	C₃×C₄⋊C₄	—	3	16	no	—
235	C₃×C₂²⋊C₄	—	3	16	no	—
236	C₃×C₂²⋊C₄	—	3	16	no	—
237	C₃×C₄²	—	3	16	no	—
238	#217	C₂²×C₃²	1	4	yes	complemented
239	(C₂×D₃)⋊C₄	C₂²×C₃²	1	4	yes	complemented
240	Dic₃⋊C₄	C₂²×C₃²	1	4	yes	complemented
241	C₄×Dic₃	C₂²×C₃²	1	4	yes	complemented
242	C₂²×C₃²	—	2	16	no	—
243	C₂²×C₃²	—	2	64	no	—
244	C₂²×C₃²	—	2	16	no	—
245	C₂²×C₃²	—	2	8	no	—
246	C₂²×C₃²	—	2	32	no	—
247	C₂²×C₃²	—	2	2	no	—
248	C₂²×C₃²	—	2	2	no	—
249	C₂²×C₃²	—	2	8	no	—
250	C₂²×C₃²	—	2	8	no	—
251	C₂²×C₃²	—	2	4	no	—
252	C₂²×C₃²	—	2	8	no	—
253	C₂²×C₃²	—	2	16	no	—
254	C₂²×C₃²	—	2	8	no	—
255	C₂²×C₃²	—	2	8	no	—
256	C₂²×C₃²	—	3	4	no	—
257	C₂²×C₃²	—	6	8	no	—
258	C₂²×C₃²	—	6	2	no	—
259	C₂²×C₃²	—	6	2	no	—
260	C₂²×C₃²	C₂×C₄×D₃	1	2	yes	—
261	C₂²×C₃²	C₂×C₄×D₃	1	4	yes	complemented
262	C₂²×C₃²	#235	1	2	yes	—
263	C₂²×C₃²	C₂×#67	1	2	yes	—
264	C₂²×C₃²	C₂²×C₃×C₄	1	8	yes	—
265	C₂²×C₃²	C₂²×C₃×C₄	1	16	yes	complemented
266	C₂²×C₃²	C₂×C₃×D₄	1	8	yes	—
267	C₂²×C₃²	C₃×#41	1	8	yes	—
268	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
269	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
270	C₂×C₃×D₃	—	2	32	no	—
271	C₂×C₃×D₃	—	2	8	no	—
272	C₂×C₃×D₃	—	2	8	no	—
273	C₂×C₃×D₃	C₂²×C₃×C₄	1	16	yes	complemented
274	C₃²×C₄	—	2	16	no	—
275	C₃²×C₄	—	2	2	no	—
276	C₃²×C₄	—	2	8	no	—
277	C₃²×C₄	—	2	16	no	—
278	C₃²×C₄	—	3	4	no	—
279	C₃²×C₄	—	6	2	no	—
280	C₃²×C₄	—	6	2	no	—
281	C₃²×C₄	C₂×#67	1	4	yes	direct product factor
282	C₃²×C₄	C₂×C₃×D₄	1	16	yes	complemented
283	C₃×Dic₃	—	2	8	no	—
284	C₃×Dic₃	—	2	8	no	—
285	C₃×Dic₃	C₂²×C₃×C₄	1	16	yes	complemented
286	C₂²×D₄	—	3	1	no	—
287	C₂³×C₄	—	3	1	no	—
288	C₂³×C₄	C₃²×D₃	1	1	yes	characteristic, complemented
289	C₄×D₄	—	3	8	no	—
290	C₂×C₄⋊C₄	—	3	1	no	—
291	C₂×C₂²⋊C₄	—	3	1	no	—
292	C₂×C₂²⋊C₄	—	3	1	no	—
293	C₂×C₄²	—	3	1	no	—
294	C₃³	C₂×C₄×D₄	1	1	yes	characteristic, complemented, Sylow
295	C₂³×C₃	—	2	16	no	—
296	C₂³×C₃	—	2	16	no	—
297	C₂³×C₃	—	2	8	no	—
298	C₂³×C₃	—	2	8	no	—
299	C₂³×C₃	—	2	2	no	—
300	C₂³×C₃	—	2	2	no	—
301	C₂³×C₃	—	2	16	no	—
302	C₂³×C₃	—	2	8	no	—
303	C₂³×C₃	—	2	4	no	—
304	C₂³×C₃	—	3	8	no	—
305	C₂³×C₃	—	3	16	no	—
306	C₂³×C₃	—	6	8	no	—
307	C₂³×C₃	—	6	8	no	—
308	C₂³×C₃	C₃×C₄×D₃	1	16	yes	complemented
309	C₂³×C₃	C₂×C₃²×C₄	1	4	yes	complemented
310	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
311	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
312	C₂³×C₃	C₂³×C₃²	1	2	yes	—
313	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
314	C₂²×D₃	—	2	2	no	—
315	C₂²×D₃	—	2	2	no	—
316	C₂²×D₃	C₂×C₃²×C₄	1	4	yes	complemented
317	C₂²×D₃	C₂³×C₃²	1	2	yes	—
318	C₃×D₄	—	3	64	no	—
319	C₂×C₃×C₄	—	2	16	no	—
320	C₂×C₃×C₄	—	2	64	no	—
321	C₂×C₃×C₄	—	2	8	no	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	—	2	32	no	—
324	C₂×C₃×C₄	—	2	8	no	—
325	C₂×C₃×C₄	—	2	16	no	—
326	C₂×C₃×C₄	—	2	8	no	—
327	C₂×C₃×C₄	—	2	8	no	—
328	C₂×C₃×C₄	—	3	8	no	—
329	C₂×C₃×C₄	—	3	16	no	—
330	C₂×C₃×C₄	—	3	8	no	—
331	C₂×C₃×C₄	—	3	8	no	—
332	C₂×C₃×C₄	—	6	8	no	—
333	C₂×C₃×C₄	—	6	8	no	—
334	C₂×C₃×C₄	—	6	32	no	—
335	C₂×C₃×C₄	C₃×#67	1	16	yes	direct product factor
336	C₂×C₃×C₄	C₃²×D₄	1	4	yes	complemented
337	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
338	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
339	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
340	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
341	#67	C₂×C₃²×C₄	1	16	yes	direct product factor
342	C₂×Dic₃	—	2	2	no	—
343	C₂×Dic₃	—	2	2	no	—
344	C₂×Dic₃	C₂×C₃²×C₄	1	4	yes	complemented
345	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
346	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
347	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
348	C₄×D₃	—	2	8	no	—
349	C₂×C₃²	—	2	32	no	—
350	C₂×C₃²	—	2	4	no	—
351	C₂×C₃²	—	2	16	no	—
352	C₂×C₃²	—	2	16	no	—
353	C₂×C₃²	—	2	4	no	—
354	C₂×C₃²	—	2	4	no	—
355	C₂×C₃²	—	2	4	no	—
356	C₂×C₃²	—	6	4	no	—
357	C₂×C₃²	C₄×#67	1	4	yes	direct product factor
358	C₂×C₃²	C₃×C₄×D₄	1	16	yes	complemented
359	C₂×C₃²	C₂²×C₄×D₃	1	1	yes	characteristic
360	C₂×C₃²	C₂×#235	1	1	yes	characteristic
361	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
362	C₂×C₃²	C₂³×C₃×C₄	1	4	yes	—
363	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
364	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
365	C₃×D₃	—	2	16	no	—
366	C₂⁴	—	3	1	no	—
367	C₂⁴	C₂×C₃²×D₃	1	1	yes	characteristic
368	C₂×D₄	—	3	8	no	—
369	C₂×D₄	—	3	4	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	3	1	no	—
372	C₂²×C₄	—	3	1	no	—
373	C₂²×C₄	—	3	1	no	—
374	C₂²×C₄	—	3	4	no	—
375	C₂²×C₄	—	6	4	no	—
376	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
378	C₂²×C₄	C₂×C₃²×D₃	1	4	yes	complemented
379	C₄⋊C₄	—	3	4	no	—
380	C₂²⋊C₄	—	3	4	no	—
381	C₂²⋊C₄	—	3	4	no	—
382	C₄²	—	3	4	no	—
383	C₂²×C₃	—	2	16	no	—
384	C₂²×C₃	—	2	64	no	—
385	C₂²×C₃	—	2	16	no	—
386	C₂²×C₃	—	2	32	no	—
387	C₂²×C₃	—	2	8	no	—
388	C₂²×C₃	—	2	8	no	—
389	C₂²×C₃	—	2	2	no	—
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	—	2	8	no	—
392	C₂²×C₃	—	2	4	no	—
393	C₂²×C₃	—	2	8	no	—
394	C₂²×C₃	—	2	16	no	—
395	C₂²×C₃	—	2	8	no	—
396	C₂²×C₃	—	2	8	no	—
397	C₂²×C₃	—	3	16	no	—
398	C₂²×C₃	—	6	32	no	—
399	C₂²×C₃	—	6	8	no	—
400	C₂²×C₃	—	6	8	no	—
401	C₂²×C₃	C₂×C₃×C₄×D₃	1	8	yes	—
402	C₂²×C₃	C₂×C₃×C₄×D₃	1	16	yes	complemented
403	C₂²×C₃	C₃×#235	1	8	yes	—
404	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
405	C₂²×C₃	C₂²×C₃²×C₄	1	2	yes	—
406	C₂²×C₃	C₂²×C₃²×C₄	1	4	yes	complemented
407	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	—
408	C₂²×C₃	C₃²×#41	1	2	yes	—
409	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
410	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
411	C₂×D₃	—	2	2	no	—
412	C₂×D₃	—	2	2	no	—
413	C₂×D₃	—	2	8	no	—
414	C₂×D₃	C₂²×C₃²×C₄	1	4	yes	complemented
415	C₃×C₄	—	2	16	no	—
416	C₃×C₄	—	2	8	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	2	16	no	—
419	C₃×C₄	—	3	16	no	—
420	C₃×C₄	—	6	8	no	—
421	C₃×C₄	—	6	8	no	—
422	C₃×C₄	C₂×C₃×#67	1	16	yes	direct product factor
423	C₃×C₄	C₂×C₃²×D₄	1	4	yes	complemented
424	Dic₃	—	2	2	no	—
425	Dic₃	—	2	2	no	—
426	Dic₃	C₂²×C₃²×C₄	1	4	yes	complemented
427	C₃²	—	2	4	no	—
428	C₃²	C₂×C₄×#67	1	1	yes	characteristic, direct product factor
429	C₃²	C₂×C₃×C₄×D₄	1	4	yes	complemented
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	3	2	no	—
433	C₂³	—	3	4	no	—
434	C₂³	—	6	2	no	—
435	C₂³	—	6	2	no	—
436	C₂³	C₃²×C₄×D₃	1	4	yes	complemented
437	C₂³	C₂²×C₃²×D₃	1	2	yes	—
438	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
439	D₄	—	3	16	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	3	2	no	—
443	C₂×C₄	—	3	4	no	—
444	C₂×C₄	—	3	2	no	—
445	C₂×C₄	—	3	2	no	—
446	C₂×C₄	—	6	2	no	—
447	C₂×C₄	—	6	2	no	—
448	C₂×C₄	—	6	8	no	—
449	C₂×C₄	C₃²×#67	1	4	yes	direct product factor
450	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
451	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
452	C₂×C₃	—	2	32	no	—
453	C₂×C₃	—	2	16	no	—
454	C₂×C₃	—	2	4	no	—
455	C₂×C₃	—	2	16	no	—
456	C₂×C₃	—	2	4	no	—
457	C₂×C₃	—	2	4	no	—
458	C₂×C₃	—	2	4	no	—
459	C₂×C₃	—	6	16	no	—
460	C₂×C₃	C₃×C₄×#67	1	16	yes	direct product factor
461	C₂×C₃	C₃²×C₄×D₄	1	4	yes	complemented
462	C₂×C₃	C₂²×C₃×C₄×D₃	1	4	yes	—
463	C₂×C₃	C₂×C₃×#235	1	4	yes	—
464	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
465	C₂×C₃	C₂³×C₃²×C₄	1	1	yes	characteristic
466	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
467	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
468	D₃	—	2	4	no	—
469	C₂²	—	2	8	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	3	4	no	—
473	C₂²	—	6	8	no	—
474	C₂²	—	6	2	no	—
475	C₂²	—	6	2	no	—
476	C₂²	C₂×C₃²×C₄×D₃	1	2	yes	—
477	C₂²	C₂×C₃²×C₄×D₃	1	4	yes	complemented
478	C₂²	C₃²×#235	1	2	yes	—
479	C₂²	C₂×C₃²×#67	1	2	yes	—
480	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
481	C₄	—	2	2	no	—
482	C₄	—	3	4	no	—
483	C₄	—	6	2	no	—
484	C₄	—	6	2	no	—
485	C₄	C₂×C₃²×#67	1	4	yes	direct product factor
486	C₃	—	2	4	no	—
487	C₃	C₂×C₃×C₄×#67	1	4	yes	direct product factor
488	C₃	C₂×C₃²×C₄×D₄	1	1	yes	characteristic, complemented
489	C₂	—	2	4	no	—
490	C₂	—	6	4	no	—
491	C₂	C₃²×C₄×#67	1	4	yes	direct product factor
492	C₂	C₂²×C₃²×C₄×D₃	1	1	yes	characteristic
493	C₂	C₂×C₃²×#235	1	1	yes	characteristic
494	C₂	C₂²×C₃²×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²×C₄	C₂×D₃
commutator	C₂×C₃	C₂³×C₃²×C₄
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₂³×C₃³×C₄	C₂
socle	C₂³×C₃³	C₂³
prime radical	C₂²×C₃²×#67	C₂
cosocle	C₂²×C₃	C₂⁴×C₃²
hypercenter	C₂³×C₃²×C₄	D₃
hypocenter	C₃	C₂×C₃²×C₄×D₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃²×C₄ ◁ C₂³×C₃²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃³×C₄	C₂	semidirect
3. C₂²×C₃²×C₄×D₃	C₂	semidirect
4. C₂×C₃²×#217	C₂	semidirect
5. C₃²×C₄×#67	C₂	direct (N × H)
6. C₂×C₃²×(C₂×D₃)⋊C₄	C₂	semidirect
7. C₂×C₃²×Dic₃⋊C₄	C₂	semidirect
8. C₂×C₃²×C₄×Dic₃	C₂	semidirect
10. C₂×C₃×C₄×#67	C₃	direct (N × H)
16. C₂²×C₃³×C₄	C₂²	semidirect
17. C₂×C₃²×#67	C₄	direct (N × H)
23. C₂×C₃²×C₄×D₃	C₂²	semidirect
24. C₃²×#217	C₂²	semidirect
25. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
26. C₃²×Dic₃⋊C₄	C₂²	semidirect
27. C₃²×C₄×Dic₃	C₂²	semidirect
31. C₂³×C₃²×C₄	D₃	semidirect
32. C₂³×C₃²×C₄	C₂×C₃	semidirect
34. C₂²×C₃×C₄×D₃	C₂×C₃	semidirect
40. C₂×C₃×#217	C₂×C₃	semidirect
41. C₃×C₄×#67	C₂×C₃	direct (N × H)
42. C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	semidirect
43. C₂×C₃×Dic₃⋊C₄	C₂×C₃	semidirect
44. C₂×C₃×C₄×Dic₃	C₂×C₃	semidirect
47. C₂³×C₃³	C₂×C₄	semidirect
52. C₂²×C₃²×D₃	C₂×C₄	semidirect
56. C₂×C₃³×C₄	D₄	semidirect
59. C₃²×#67	C₂×C₄	direct (N × H)
62. C₂×C₃²×Dic₃	C₂×C₄	semidirect
68. C₂×C₄×#67	C₃²	direct (N × H)
89. C₂²×C₃²×C₄	C₂×D₃	semidirect
92. C₂²×C₃²×C₄	C₂²×C₃	semidirect
93. C₂×C₃×#67	C₃×C₄	direct (N × H)
99. C₂×C₃×C₄×D₃	C₂²×C₃	semidirect
104. C₃×#217	C₂²×C₃	semidirect
105. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
106. C₃×Dic₃⋊C₄	C₂²×C₃	semidirect
107. C₃×C₄×Dic₃	C₂²×C₃	semidirect
112. C₂²×C₃³	C₂²×C₄	semidirect
119. C₂×C₃²×D₃	C₂²×C₄	semidirect
121. C₃³×C₄	C₂×D₄	semidirect
124. C₃²×Dic₃	C₂²×C₄	semidirect
128. C₂³×C₃×C₄	C₃×D₃	semidirect
129. C₂³×C₃×C₄	C₂×C₃²	semidirect
131. C₂²×C₄×D₃	C₂×C₃²	semidirect
137. C₂×#217	C₂×C₃²	semidirect
138. C₄×#67	C₂×C₃²	direct (N × H)
139. C₂×(C₂×D₃)⋊C₄	C₂×C₃²	semidirect
140. C₂×Dic₃⋊C₄	C₂×C₃²	semidirect
141. C₂×C₄×Dic₃	C₂×C₃²	semidirect
155. C₂³×C₃²	C₄×D₃	semidirect
156. C₂³×C₃²	C₂×C₃×C₄	semidirect
163. C₂²×C₃×D₃	C₂×C₃×C₄	semidirect
182. C₂×C₃²×C₄	#67	direct (N × H)
183. C₂×C₃²×C₄	C₃×D₄	semidirect
188. C₃×#67	C₂×C₃×C₄	direct (N × H)
191. C₂×C₃×Dic₃	C₂×C₃×C₄	semidirect
198. C₂×C₃³	C₄×D₄	semidirect
223. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
226. C₂²×C₃×C₄	C₂²×C₃²	semidirect
227. C₂×#67	C₃²×C₄	direct (N × H)
233. C₂×C₄×D₃	C₂²×C₃²	semidirect
238. #217	C₂²×C₃²	semidirect
239. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
240. Dic₃⋊C₄	C₂²×C₃²	semidirect
241. C₄×Dic₃	C₂²×C₃²	semidirect
261. C₂²×C₃²	C₂×C₄×D₃	semidirect
265. C₂²×C₃²	C₂²×C₃×C₄	semidirect
273. C₂×C₃×D₃	C₂²×C₃×C₄	semidirect
281. C₃²×C₄	C₂×#67	direct (N × H)
282. C₃²×C₄	C₂×C₃×D₄	semidirect
285. C₃×Dic₃	C₂²×C₃×C₄	semidirect
288. C₂³×C₄	C₃²×D₃	semidirect
294. C₃³	C₂×C₄×D₄	semidirect
308. C₂³×C₃	C₃×C₄×D₃	semidirect
309. C₂³×C₃	C₂×C₃²×C₄	semidirect
316. C₂²×D₃	C₂×C₃²×C₄	semidirect
335. C₂×C₃×C₄	C₃×#67	direct (N × H)
336. C₂×C₃×C₄	C₃²×D₄	semidirect
341. #67	C₂×C₃²×C₄	direct (N × H)
344. C₂×Dic₃	C₂×C₃²×C₄	semidirect
357. C₂×C₃²	C₄×#67	direct (N × H)
358. C₂×C₃²	C₃×C₄×D₄	semidirect
378. C₂²×C₄	C₂×C₃²×D₃	semidirect
402. C₂²×C₃	C₂×C₃×C₄×D₃	semidirect
406. C₂²×C₃	C₂²×C₃²×C₄	semidirect
414. C₂×D₃	C₂²×C₃²×C₄	semidirect
422. C₃×C₄	C₂×C₃×#67	direct (N × H)
423. C₃×C₄	C₂×C₃²×D₄	semidirect
426. Dic₃	C₂²×C₃²×C₄	semidirect
428. C₃²	C₂×C₄×#67	direct (N × H)
429. C₃²	C₂×C₃×C₄×D₄	semidirect
436. C₂³	C₃²×C₄×D₃	semidirect
449. C₂×C₄	C₃²×#67	direct (N × H)
460. C₂×C₃	C₃×C₄×#67	direct (N × H)
461. C₂×C₃	C₃²×C₄×D₄	semidirect
477. C₂²	C₂×C₃²×C₄×D₃	semidirect
485. C₄	C₂×C₃²×#67	direct (N × H)
487. C₃	C₂×C₃×C₄×#67	direct (N × H)
488. C₃	C₂×C₃²×C₄×D₄	semidirect
491. C₂	C₃²×C₄×#67	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×C₃³×C₄	2
C₂²×C₃²×#67	2
C₂²×C₃²×C₄×D₃	2
C₂×C₃²×#217	2
C₃²×C₄×#67	2
C₂×C₃²×(C₂×D₃)⋊C₄	2
C₂×C₃²×Dic₃⋊C₄	2
C₂×C₃²×C₄×Dic₃	2
C₂×C₃²×C₄×D₄	3
C₂×C₃×C₄×#67	3

Subgroups — C2×C32×C4×#67 #13179165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₄×#67 #13179165