Subgroups — C₃×#20777 #10639384

Order 768.

1062 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄³	C₂	1	1	yes	maximal, characteristic
2	C₃×#1839	C₂	1	2	yes	maximal, complemented
3	C₃×#1831	C₂	1	2	yes	maximal, complemented
4	C₃×#1817	C₂	1	2	yes	maximal
5	C₃×#1797	C₂	1	2	yes	maximal
6	C₃×C₄×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₂²⋊C₈	C₂	1	2	yes	maximal
8	C₃×#1744	C₂	1	2	yes	maximal, complemented
9	#20777	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂²×C₃×C₄²	C₄	1	1	yes	characteristic
11	C₂²×C₃×C₄²	C₄	1	1	yes	characteristic
12	C₂²×C₃×C₄²	C₄	1	1	yes	characteristic
13	C₂²×C₃×C₄²	C₄	1	1	yes	characteristic
14	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄⋊C₈	C₂²	1	4	yes	—
18	C₂×C₃×C₂²⋊C₈	C₂²	1	4	yes	—
19	C₂×C₃×C₄×C₈	C₂²	1	4	yes	—
20	C₃×C₄³	C₄	1	1	yes	characteristic
21	C₃×C₄³	C₄	1	1	yes	characteristic
22	C₃×C₄³	C₄	1	1	yes	characteristic
23	C₃×C₄³	C₄	1	1	yes	characteristic
24	C₃×C₄³	C₂²	1	1	yes	characteristic
25	C₃×C₄³	C₂²	1	1	yes	characteristic
26	C₃×C₄³	C₂²	1	1	yes	characteristic
27	C₃×C₄³	C₂²	1	1	yes	characteristic
28	C₃×#336	C₂²	1	4	yes	—
29	C₃×#336	C₂²	1	4	yes	—
30	C₃×#336	C₂²	1	4	yes	—
31	C₃×#336	C₂²	1	4	yes	—
32	C₂×C₄³	C₂×C₃	1	1	yes	characteristic
33	#1839	C₂×C₃	1	2	yes	complemented
34	#1831	C₂×C₃	1	2	yes	complemented
35	#1817	C₂×C₃	1	2	yes	—
36	#1797	C₂×C₃	1	2	yes	—
37	C₄×C₄⋊C₈	C₂×C₃	1	2	yes	complemented
38	C₄×C₂²⋊C₈	C₂×C₃	1	2	yes	—
39	#1744	C₂×C₃	1	2	yes	complemented
40	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
47	C₂²×C₃×C₈	C₂³	1	8	yes	—
48	C₂×C₃×C₄²	—	2	4	no	—
49	C₂×C₃×C₄²	—	2	4	no	—
50	C₂×C₃×C₄²	—	2	4	no	—
51	C₂×C₃×C₄²	—	2	4	no	—
52	C₂×C₃×C₄²	—	2	4	no	—
53	C₂×C₃×C₄²	—	2	4	no	—
54	C₂×C₃×C₄²	C₈	1	8	yes	complemented
55	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
56	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
57	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
64	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
65	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
66	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
67	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
68	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
69	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
70	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
71	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
72	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
73	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
74	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
75	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
76	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
77	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
83	C₃×C₄⋊C₈	—	2	8	no	—
84	C₃×C₂²⋊C₈	—	2	8	no	—
85	C₃×C₄×C₈	—	2	8	no	—
86	C₂²×C₄²	C₃×C₄	1	1	yes	characteristic
87	C₂²×C₄²	C₃×C₄	1	1	yes	characteristic
88	C₂²×C₄²	C₃×C₄	1	1	yes	characteristic
89	C₂²×C₄²	C₃×C₄	1	1	yes	characteristic
90	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
92	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₄⋊C₈	C₂²×C₃	1	4	yes	—
94	C₂×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
95	C₂×C₄×C₈	C₂²×C₃	1	4	yes	—
96	C₄³	C₃×C₄	1	1	yes	characteristic
97	C₄³	C₃×C₄	1	1	yes	characteristic
98	C₄³	C₃×C₄	1	1	yes	characteristic
99	C₄³	C₃×C₄	1	1	yes	characteristic
100	C₄³	C₂²×C₃	1	1	yes	characteristic
101	C₄³	C₂²×C₃	1	1	yes	characteristic
102	C₄³	C₂²×C₃	1	1	yes	characteristic
103	C₄³	C₂²×C₃	1	1	yes	characteristic
104	#336	C₂²×C₃	1	4	yes	—
105	#336	C₂²×C₃	1	4	yes	—
106	#336	C₂²×C₃	1	4	yes	—
107	#336	C₂²×C₃	1	4	yes	—
108	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₃×C₄	—	2	2	no	—
110	C₂²×C₃×C₄	—	2	2	no	—
111	C₂²×C₃×C₄	—	2	2	no	—
112	C₂²×C₃×C₄	—	2	2	no	—
113	C₂²×C₃×C₄	—	2	2	no	—
114	C₂²×C₃×C₄	—	2	2	no	—
115	C₂²×C₃×C₄	—	2	2	no	—
116	C₂²×C₃×C₄	—	2	2	no	—
117	C₂²×C₃×C₄	—	2	2	no	—
118	C₂²×C₃×C₄	—	2	2	no	—
119	C₂²×C₃×C₄	—	2	2	no	—
120	C₂²×C₃×C₄	—	2	2	no	—
121	C₂²×C₃×C₄	—	2	2	no	—
122	C₂²×C₃×C₄	—	2	2	no	—
123	C₂²×C₃×C₄	—	2	2	no	—
124	C₂²×C₃×C₄	—	2	2	no	—
125	C₂²×C₃×C₄	C₂×C₈	1	4	yes	—
126	C₂²×C₃×C₄	C₂×C₈	1	4	yes	—
127	C₂²×C₃×C₄	C₂×C₈	1	4	yes	—
128	C₂²×C₃×C₄	M₁₆	1	4	yes	—
129	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₃×C₄	#41	1	4	yes	—
143	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
144	C₂×C₃×C₈	—	2	8	no	—
145	C₂×C₃×C₈	—	2	8	no	—
146	C₂×C₃×C₈	—	2	8	no	—
147	C₃×C₄²	—	2	2	no	—
148	C₃×C₄²	—	2	2	no	—
149	C₃×C₄²	—	2	2	no	—
150	C₃×C₄²	—	2	2	no	—
151	C₃×C₄²	—	2	2	no	—
152	C₃×C₄²	—	2	2	no	—
153	C₃×C₄²	—	2	2	no	—
154	C₃×C₄²	—	2	2	no	—
155	C₃×C₄²	—	2	2	no	—
156	C₃×C₄²	—	2	2	no	—
157	C₃×C₄²	—	2	2	no	—
158	C₃×C₄²	—	2	2	no	—
159	C₃×C₄²	—	2	2	no	—
160	C₃×C₄²	—	2	2	no	—
161	C₃×C₄²	—	2	2	no	—
162	C₃×C₄²	—	2	2	no	—
163	C₃×C₄²	—	2	2	no	—
164	C₃×C₄²	—	2	2	no	—
165	C₃×C₄²	—	2	2	no	—
166	C₃×C₄²	—	2	2	no	—
167	C₃×C₄²	C₂×C₈	1	4	yes	—
168	C₃×C₄²	C₂×C₈	1	4	yes	—
169	C₃×C₄²	C₂×C₈	1	4	yes	—
170	C₃×C₄²	C₂×C₈	1	4	yes	—
171	C₃×C₄²	M₁₆	1	4	yes	—
172	C₃×C₄²	M₁₆	1	4	yes	—
173	C₃×C₄²	#41	1	4	yes	—
174	C₃×C₄²	#41	1	4	yes	—
175	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
176	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
177	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
178	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
179	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
180	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
181	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
182	C₂²×C₈	C₂³×C₃	1	8	yes	—
183	C₂×C₄²	—	2	4	no	—
184	C₂×C₄²	—	2	4	no	—
185	C₂×C₄²	—	2	4	no	—
186	C₂×C₄²	—	2	4	no	—
187	C₂×C₄²	—	2	4	no	—
188	C₂×C₄²	—	2	4	no	—
189	C₂×C₄²	C₃×C₈	1	8	yes	complemented
190	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
191	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
192	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
193	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
194	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
195	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
196	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
197	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
198	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
199	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
200	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
201	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
202	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
203	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
204	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
205	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
206	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
207	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
208	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
209	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
210	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
211	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
212	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
213	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
214	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
215	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
216	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
218	C₄⋊C₈	—	2	8	no	—
219	C₂²⋊C₈	—	2	8	no	—
220	C₄×C₈	—	2	8	no	—
221	C₂³×C₃	—	2	1	no	—
222	C₂³×C₃	—	2	1	no	—
223	C₂³×C₃	—	2	1	no	—
224	C₂³×C₃	—	2	1	no	—
225	C₂³×C₃	#117	1	2	yes	—
226	C₂³×C₃	C₂²×C₈	1	2	yes	—
227	C₂³×C₃	C₂×M₁₆	1	2	yes	—
228	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₃×C₄	—	2	8	no	—
230	C₂×C₃×C₄	—	2	8	no	—
231	C₂×C₃×C₄	—	2	1	no	—
232	C₂×C₃×C₄	—	2	1	no	—
233	C₂×C₃×C₄	—	2	1	no	—
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	8	no	—
252	C₂×C₃×C₄	—	2	8	no	—
253	C₂×C₃×C₄	—	2	8	no	—
254	C₂×C₃×C₄	—	2	8	no	—
255	C₂×C₃×C₄	—	2	8	no	—
256	C₂×C₃×C₄	#117	1	2	yes	—
257	C₂×C₃×C₄	#117	1	2	yes	—
258	C₂×C₃×C₄	#117	1	2	yes	—
259	C₂×C₃×C₄	#117	1	2	yes	—
260	C₂×C₃×C₄	#117	1	2	yes	—
261	C₂×C₃×C₄	C₂²×C₈	1	2	yes	—
262	C₂×C₃×C₄	C₂²×C₈	1	2	yes	—
263	C₂×C₃×C₄	C₂²×C₈	1	2	yes	—
264	C₂×C₃×C₄	C₂²×C₈	1	2	yes	—
265	C₂×C₃×C₄	C₂²×C₈	1	2	yes	—
266	C₂×C₃×C₄	C₂²×C₈	1	2	yes	—
267	C₂×C₃×C₄	C₂×M₁₆	1	2	yes	—
268	C₂×C₃×C₄	C₂×M₁₆	1	2	yes	—
269	C₂×C₃×C₄	C₂×M₁₆	1	2	yes	—
270	C₂×C₃×C₄	C₂×M₁₆	1	2	yes	—
271	C₂×C₃×C₄	C₂×M₁₆	1	2	yes	—
272	C₂×C₃×C₄	C₂×M₁₆	1	2	yes	—
273	C₂×C₃×C₄	C₂×M₁₆	1	2	yes	—
274	C₂×C₃×C₄	C₂×M₁₆	1	2	yes	—
275	C₂×C₃×C₄	C₂×#41	1	2	yes	—
276	C₂×C₃×C₄	C₂×#41	1	2	yes	—
277	C₂×C₃×C₄	C₂×#41	1	2	yes	—
278	C₃×C₈	—	4	8	no	—
279	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	C₂×C₃×C₈	1	4	yes	—
297	C₂²×C₄	C₂×C₃×C₈	1	4	yes	—
298	C₂²×C₄	C₂×C₃×C₈	1	4	yes	—
299	C₂²×C₄	C₃×M₁₆	1	4	yes	—
300	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
301	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
306	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
308	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
309	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
311	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
312	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
313	C₂²×C₄	C₃×#41	1	4	yes	—
314	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
315	C₂×C₈	—	2	8	no	—
316	C₂×C₈	—	2	8	no	—
317	C₂×C₈	—	2	8	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	C₂×C₃×C₈	1	4	yes	—
339	C₄²	C₂×C₃×C₈	1	4	yes	—
340	C₄²	C₂×C₃×C₈	1	4	yes	—
341	C₄²	C₂×C₃×C₈	1	4	yes	—
342	C₄²	C₃×M₁₆	1	4	yes	—
343	C₄²	C₃×M₁₆	1	4	yes	—
344	C₄²	C₃×#41	1	4	yes	—
345	C₄²	C₃×#41	1	4	yes	—
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	2	2	no	—
348	C₂²×C₃	—	2	2	no	—
349	C₂²×C₃	—	2	2	no	—
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	2	2	no	—
352	C₂²×C₃	#431	1	4	yes	—
353	C₂²×C₃	C₂×#117	1	1	yes	characteristic
354	C₂²×C₃	C₂×#117	1	1	yes	characteristic
355	C₂²×C₃	C₂×#117	1	1	yes	characteristic
356	C₂²×C₃	C₂³×C₈	1	1	yes	characteristic
357	C₂²×C₃	C₂²×M₁₆	1	1	yes	characteristic
358	C₂²×C₃	C₂²×M₁₆	1	1	yes	characteristic
359	C₂²×C₃	C₂²×M₁₆	1	1	yes	characteristic
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	2	2	no	—
362	C₃×C₄	—	2	2	no	—
363	C₃×C₄	—	2	2	no	—
364	C₃×C₄	—	2	2	no	—
365	C₃×C₄	—	2	2	no	—
366	C₃×C₄	—	2	2	no	—
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	2	2	no	—
369	C₃×C₄	—	2	2	no	—
370	C₃×C₄	#431	1	4	yes	—
371	C₃×C₄	#431	1	4	yes	—
372	C₃×C₄	#432	1	4	yes	—
373	C₃×C₄	#529	1	4	yes	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	C₃×#117	1	2	yes	—
379	C₂³	C₂²×C₃×C₈	1	2	yes	—
380	C₂³	C₂×C₃×M₁₆	1	2	yes	—
381	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	2	8	no	—
408	C₂×C₄	—	2	8	no	—
409	C₂×C₄	C₃×#117	1	2	yes	—
410	C₂×C₄	C₃×#117	1	2	yes	—
411	C₂×C₄	C₃×#117	1	2	yes	—
412	C₂×C₄	C₃×#117	1	2	yes	—
413	C₂×C₄	C₃×#117	1	2	yes	—
414	C₂×C₄	C₂²×C₃×C₈	1	2	yes	—
415	C₂×C₄	C₂²×C₃×C₈	1	2	yes	—
416	C₂×C₄	C₂²×C₃×C₈	1	2	yes	—
417	C₂×C₄	C₂²×C₃×C₈	1	2	yes	—
418	C₂×C₄	C₂²×C₃×C₈	1	2	yes	—
419	C₂×C₄	C₂²×C₃×C₈	1	2	yes	—
420	C₂×C₄	C₂×C₃×M₁₆	1	2	yes	—
421	C₂×C₄	C₂×C₃×M₁₆	1	2	yes	—
422	C₂×C₄	C₂×C₃×M₁₆	1	2	yes	—
423	C₂×C₄	C₂×C₃×M₁₆	1	2	yes	—
424	C₂×C₄	C₂×C₃×M₁₆	1	2	yes	—
425	C₂×C₄	C₂×C₃×M₁₆	1	2	yes	—
426	C₂×C₄	C₂×C₃×M₁₆	1	2	yes	—
427	C₂×C₄	C₂×C₃×M₁₆	1	2	yes	—
428	C₂×C₄	C₂×C₃×#41	1	2	yes	—
429	C₂×C₄	C₂×C₃×#41	1	2	yes	—
430	C₂×C₄	C₂×C₃×#41	1	2	yes	—
431	C₈	—	4	8	no	—
432	C₂×C₃	—	2	4	no	—
433	C₂×C₃	#2283	1	1	yes	characteristic
434	C₂×C₃	C₂×#431	1	1	yes	characteristic
435	C₂×C₃	C₂×#431	1	1	yes	characteristic
436	C₂×C₃	C₂×#431	1	1	yes	characteristic
437	C₂×C₃	C₂×#432	1	1	yes	characteristic
438	C₂×C₃	#2920	1	1	yes	characteristic
439	C₂×C₃	#2920	1	1	yes	characteristic
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	C₃×#431	1	4	yes	—
447	C₂²	C₂×C₃×#117	1	1	yes	characteristic
448	C₂²	C₂×C₃×#117	1	1	yes	characteristic
449	C₂²	C₂×C₃×#117	1	1	yes	characteristic
450	C₂²	C₂³×C₃×C₈	1	1	yes	characteristic
451	C₂²	C₂²×C₃×M₁₆	1	1	yes	characteristic
452	C₂²	C₂²×C₃×M₁₆	1	1	yes	characteristic
453	C₂²	C₂²×C₃×M₁₆	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	C₃×#431	1	4	yes	—
465	C₄	C₃×#431	1	4	yes	—
466	C₄	C₃×#432	1	4	yes	—
467	C₄	C₃×#529	1	4	yes	—
468	C₃	#20777	1	1	yes	characteristic, direct product factor, Sylow
469	C₂	—	2	4	no	—
470	C₂	C₃×#2283	1	1	yes	characteristic
471	C₂	C₂×C₃×#431	1	1	yes	characteristic
472	C₂	C₂×C₃×#431	1	1	yes	characteristic
473	C₂	C₂×C₃×#431	1	1	yes	characteristic
474	C₂	C₂×C₃×#432	1	1	yes	characteristic
475	C₂	C₃×#2920	1	1	yes	characteristic
476	C₂	C₃×#2920	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄²	C₂³
commutator	C₂²	C₂³×C₃×C₈
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
socle	C₂³×C₃	C₂³×C₄
prime radical	C₂⁴×C₃	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#1839	C₂	semidirect
3. C₃×#1831	C₂	semidirect
6. C₃×C₄×C₄⋊C₈	C₂	semidirect
8. C₃×#1744	C₂	semidirect
9. #20777	C₃	direct (N × H)
33. #1839	C₂×C₃	semidirect
34. #1831	C₂×C₃	semidirect
37. C₄×C₄⋊C₈	C₂×C₃	semidirect
39. #1744	C₂×C₃	semidirect
54. C₂×C₃×C₄²	C₈	semidirect
189. C₂×C₄²	C₃×C₈	semidirect
468. C₃	#20777	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄³	2
C₃×#1839	2
C₃×#1831	2
C₃×#1817	2
C₃×#1797	2
C₃×C₄×C₄⋊C₈	2
C₃×C₄×C₂²⋊C₈	2
C₃×#1744	2
#20777	3

Subgroups — C3×#20777 #10639384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#20777 #10639384