Subgroups — C₃×#20559 #10639166

Order 768.

1118 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#435	C₂	1	2	yes	maximal
2	C₃×C₄²×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃×#1771	C₂	1	2	yes	maximal, complemented
4	C₃×C₄×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#1753	C₂	1	2	yes	maximal, complemented
6	C₃×C₈×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#1745	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#1728	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#336	C₂	1	1	yes	maximal, characteristic, complemented
12	#20559	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
14	C₂³×C₃×C₈	C₂²	1	2	yes	—
15	C₂×C₃×C₄×D₄	C₄	1	2	yes	—
16	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
19	C₃×#435	C₄	1	16	yes	complemented
20	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₃×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₃×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₃×#97	C₂²	1	2	yes	—
24	C₂×C₃×#97	C₂²	1	2	yes	—
25	C₂×C₃×C₄×C₈	C₂²	1	2	yes	—
26	C₂×C₃×C₄×C₈	C₂²	1	2	yes	—
27	C₃×C₄×C₄⋊C₄	C₄	1	2	yes	—
28	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₂²⋊C₄	C₄	1	2	yes	—
30	C₃×C₄×C₂²⋊C₄	C₄	1	2	yes	—
31	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₃×C₄³	C₂²	1	1	yes	characteristic
34	C₃×#336	C₂²	1	1	yes	characteristic
35	C₃×#336	C₂²	1	2	yes	—
36	C₃×#336	C₂²	1	1	yes	characteristic
37	C₃×#336	C₂²	1	1	yes	characteristic
38	C₃×#336	C₂²	1	1	yes	characteristic
39	C₃×#336	C₂²	1	2	yes	—
40	C₃×#336	C₂²	1	2	yes	—
41	C₂×#435	C₂×C₃	1	2	yes	—
42	C₄²×D₄	C₂×C₃	1	1	yes	characteristic
43	#1771	C₂×C₃	1	2	yes	complemented
44	C₄×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
45	#1753	C₂×C₃	1	2	yes	complemented
46	C₈×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
47	#1749	C₂×C₃	1	1	yes	characteristic, complemented
48	C₄×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
49	#1745	C₂×C₃	1	1	yes	characteristic, complemented
50	#1728	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂×#336	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₃×C₄	C₂×C₄	1	2	yes	—
54	C₂³×C₃×C₄	C₂×C₄	1	2	yes	—
55	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
56	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
57	C₂×C₃×M₁₆	—	4	2	no	—
58	C₂×C₃×M₁₆	—	4	2	no	—
59	C₂×C₃×M₁₆	C₂×C₄	1	8	yes	complemented
60	C₂²×C₃×C₈	—	4	2	no	—
61	C₂²×C₃×C₈	—	4	2	no	—
62	C₂²×C₃×C₈	C₂×C₄	1	8	yes	complemented
63	C₂²×C₃×C₈	C₂³	1	2	yes	—
64	C₂²×C₃×C₈	C₂³	1	2	yes	—
65	C₂²×C₃×C₈	C₂³	1	2	yes	—
66	C₂²×C₃×C₈	C₂³	1	2	yes	—
67	C₃×C₄×D₄	—	2	8	no	—
68	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
69	C₂×C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
70	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
75	C₂×C₃×C₄²	—	4	2	no	—
76	C₂×C₃×C₄²	—	4	2	no	—
77	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
78	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
79	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
80	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
81	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
86	C₃×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
87	C₃×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
88	C₃×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
89	C₃×#97	—	4	2	no	—
90	C₃×#97	C₂×C₄	1	8	yes	complemented
91	C₃×C₄×C₈	—	4	2	no	—
92	C₃×C₄×C₈	—	4	2	no	—
93	C₃×#95	C₂×C₄	1	2	yes	—
94	C₃×#95	C₂×C₄	1	2	yes	—
95	C₃×#95	C₂×C₄	1	2	yes	—
96	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
97	C₂³×C₈	C₂²×C₃	1	2	yes	—
98	C₂×C₄×D₄	C₃×C₄	1	2	yes	—
99	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
100	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
101	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
102	#435	C₃×C₄	1	16	yes	complemented
103	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	—
104	C₂×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
105	C₂×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
106	C₂×#97	C₂²×C₃	1	2	yes	—
107	C₂×#97	C₂²×C₃	1	2	yes	—
108	C₂×C₄×C₈	C₂²×C₃	1	2	yes	—
109	C₂×C₄×C₈	C₂²×C₃	1	2	yes	—
110	C₄×C₄⋊C₄	C₃×C₄	1	2	yes	—
111	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
112	C₄×C₂²⋊C₄	C₃×C₄	1	2	yes	—
113	C₄×C₂²⋊C₄	C₃×C₄	1	2	yes	—
114	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
115	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₄³	C₂²×C₃	1	1	yes	characteristic
117	#336	C₂²×C₃	1	1	yes	characteristic
118	#336	C₂²×C₃	1	1	yes	characteristic
119	#336	C₂²×C₃	1	2	yes	—
120	#336	C₂²×C₃	1	1	yes	characteristic
121	#336	C₂²×C₃	1	2	yes	—
122	#336	C₂²×C₃	1	1	yes	characteristic
123	#336	C₂²×C₃	1	2	yes	—
124	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
125	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₃×D₄	—	2	4	no	—
127	C₂×C₃×D₄	C₄²	1	4	yes	—
128	C₂²×C₃×C₄	—	2	2	no	—
129	C₂²×C₃×C₄	—	2	2	no	—
130	C₂²×C₃×C₄	—	2	1	no	—
131	C₂²×C₃×C₄	—	2	1	no	—
132	C₂²×C₃×C₄	—	2	1	no	—
133	C₂²×C₃×C₄	—	2	1	no	—
134	C₂²×C₃×C₄	—	2	4	no	—
135	C₂²×C₃×C₄	—	2	4	no	—
136	C₂²×C₃×C₄	—	2	4	no	—
137	C₂²×C₃×C₄	—	2	4	no	—
138	C₂²×C₃×C₄	—	4	2	no	—
139	C₂²×C₃×C₄	—	4	2	no	—
140	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
141	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
146	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
147	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
148	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
149	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
150	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
151	C₃×M₁₆	—	4	8	no	—
152	C₂×C₃×C₈	—	2	2	no	—
153	C₂×C₃×C₈	—	2	2	no	—
154	C₂×C₃×C₈	—	2	2	no	—
155	C₂×C₃×C₈	—	2	2	no	—
156	C₂×C₃×C₈	—	2	2	no	—
157	C₂×C₃×C₈	—	2	2	no	—
158	C₂×C₃×C₈	—	2	2	no	—
159	C₂×C₃×C₈	—	2	2	no	—
160	C₂×C₃×C₈	—	4	8	no	—
161	C₂×C₃×C₈	C₂²×C₄	1	4	yes	—
162	C₂×C₃×C₈	C₂²×C₄	1	4	yes	—
163	C₂×C₃×C₈	C₂²×C₄	1	4	yes	—
164	C₂×C₃×C₈	C₂²×C₄	1	4	yes	—
165	C₃×C₄⋊C₄	—	2	4	no	—
166	C₃×C₄⋊C₄	C₄²	1	4	yes	—
167	C₃×C₂²⋊C₄	—	2	4	no	—
168	C₃×C₂²⋊C₄	C₄²	1	4	yes	—
169	C₃×C₂²⋊C₄	C₄²	1	4	yes	—
170	C₃×C₂²⋊C₄	M₁₆	1	8	yes	complemented
171	C₃×C₄²	—	2	4	no	—
172	C₃×C₄²	—	2	4	no	—
173	C₃×C₄²	—	2	1	no	—
174	C₃×C₄²	—	2	2	no	—
175	C₃×C₄²	—	2	2	no	—
176	C₃×C₄²	—	2	2	no	—
177	C₃×C₄²	—	2	1	no	—
178	C₃×C₄²	—	4	2	no	—
179	C₃×C₄²	—	4	2	no	—
180	C₃×C₄²	C₂²×C₄	1	4	yes	—
181	C₂²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
182	C₂³×C₄	C₂×C₃×C₄	1	2	yes	—
183	C₂³×C₄	C₂×C₃×C₄	1	2	yes	—
184	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
185	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
186	C₂×M₁₆	—	4	2	no	—
187	C₂×M₁₆	—	4	2	no	—
188	C₂×M₁₆	C₂×C₃×C₄	1	8	yes	complemented
189	C₂²×C₈	—	4	2	no	—
190	C₂²×C₈	—	4	2	no	—
191	C₂²×C₈	C₂×C₃×C₄	1	8	yes	complemented
192	C₂²×C₈	C₂³×C₃	1	2	yes	—
193	C₂²×C₈	C₂³×C₃	1	2	yes	—
194	C₂²×C₈	C₂³×C₃	1	2	yes	—
195	C₂²×C₈	C₂³×C₃	1	2	yes	—
196	C₄×D₄	—	2	8	no	—
197	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
198	C₂×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
199	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
200	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
201	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
202	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
203	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
204	C₂×C₄²	—	4	2	no	—
205	C₂×C₄²	—	4	2	no	—
206	C₂×C₄²	C₂×C₃×C₄	1	2	yes	—
207	C₂×C₄²	C₂×C₃×C₄	1	2	yes	—
208	C₂×C₄²	C₂×C₃×C₄	1	2	yes	—
209	C₂×C₄²	C₂×C₃×C₄	1	2	yes	—
210	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
211	C₂×C₄²	C₂³×C₃	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	C₄⋊C₈	C₂×C₃×C₄	1	8	yes	complemented
216	C₂²⋊C₈	C₂×C₃×C₄	1	8	yes	complemented
217	C₂²⋊C₈	C₂×C₃×C₄	1	8	yes	complemented
218	#97	—	4	2	no	—
219	#97	C₂×C₃×C₄	1	8	yes	complemented
220	C₄×C₈	—	4	2	no	—
221	C₄×C₈	—	4	2	no	—
222	#95	C₂×C₃×C₄	1	2	yes	—
223	#95	C₂×C₃×C₄	1	2	yes	—
224	#95	C₂×C₃×C₄	1	2	yes	—
225	C₂³×C₃	—	2	1	no	—
226	C₂³×C₃	—	2	1	no	—
227	C₂³×C₃	—	2	2	no	—
228	C₂³×C₃	—	2	1	no	—
229	C₂³×C₃	—	2	1	no	—
230	C₂³×C₃	—	2	2	no	—
231	C₂³×C₃	—	2	2	no	—
232	C₂³×C₃	C₂×C₄²	1	2	yes	—
233	C₂³×C₃	C₂×C₄²	1	2	yes	—
234	C₂³×C₃	C₂×M₁₆	1	4	yes	—
235	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
236	C₃×D₄	—	2	8	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	2	4	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	4	8	no	—
257	C₂×C₃×C₄	—	4	8	no	—
258	C₂×C₃×C₄	C₂×C₄²	1	2	yes	—
259	C₂×C₃×C₄	C₂×C₄²	1	2	yes	—
260	C₂×C₃×C₄	C₂×C₄²	1	2	yes	—
261	C₂×C₃×C₄	C₂×C₄²	1	2	yes	—
262	C₂×C₃×C₄	C₂×M₁₆	1	4	yes	—
263	C₂×C₃×C₄	C₂×M₁₆	1	4	yes	—
264	C₂×C₃×C₄	#131	1	4	yes	—
265	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
266	C₂×C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
267	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
268	C₂×C₃×C₄	2₋¹⁺⁴	1	1	yes	characteristic
269	C₃×C₈	—	2	4	no	—
270	C₃×C₈	—	2	4	no	—
271	C₃×C₈	—	2	4	no	—
272	C₃×C₈	—	2	4	no	—
273	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
274	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	C₃×C₄²	1	4	yes	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
290	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
292	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
295	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
296	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
297	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
298	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
299	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
300	M₁₆	—	4	8	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	4	8	no	—
310	C₂×C₈	C₂²×C₃×C₄	1	4	yes	—
311	C₂×C₈	C₂²×C₃×C₄	1	4	yes	—
312	C₂×C₈	C₂²×C₃×C₄	1	4	yes	—
313	C₂×C₈	C₂²×C₃×C₄	1	4	yes	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	C₃×C₄²	1	4	yes	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	C₃×C₄²	1	4	yes	—
318	C₂²⋊C₄	C₃×C₄²	1	4	yes	—
319	C₂²⋊C₄	C₃×M₁₆	1	8	yes	complemented
320	C₄²	—	2	4	no	—
321	C₄²	—	2	4	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	4	2	no	—
328	C₄²	—	4	2	no	—
329	C₄²	C₂²×C₃×C₄	1	4	yes	—
330	C₂²×C₃	—	2	2	no	—
331	C₂²×C₃	—	2	4	no	—
332	C₂²×C₃	—	2	4	no	—
333	C₂²×C₃	—	2	2	no	—
334	C₂²×C₃	—	2	2	no	—
335	C₂²×C₃	—	2	2	no	—
336	C₂²×C₃	—	2	2	no	—
337	C₂²×C₃	—	4	2	no	—
338	C₂²×C₃	—	4	2	no	—
339	C₂²×C₃	C₄×M₁₆	1	4	yes	—
340	C₂²×C₃	C₂²×C₄²	1	1	yes	characteristic
341	C₂²×C₃	#518	1	1	yes	characteristic
342	C₂²×C₃	#520	1	1	yes	characteristic
343	C₂²×C₃	C₂²×M₁₆	1	2	yes	—
344	C₂²×C₃	C₂×#131	1	2	yes	—
345	C₃×C₄	—	2	2	no	—
346	C₃×C₄	—	2	2	no	—
347	C₃×C₄	—	2	4	no	—
348	C₃×C₄	—	2	4	no	—
349	C₃×C₄	—	2	4	no	—
350	C₃×C₄	—	2	2	no	—
351	C₃×C₄	—	2	2	no	—
352	C₃×C₄	—	4	2	no	—
353	C₃×C₄	#518	1	2	yes	—
354	C₃×C₄	#520	1	2	yes	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	C₂×C₃×C₄²	1	2	yes	—
363	C₂³	C₂×C₃×C₄²	1	2	yes	—
364	C₂³	C₂×C₃×M₁₆	1	4	yes	—
365	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
366	D₄	—	2	8	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	8	no	—
387	C₂×C₄	—	4	8	no	—
388	C₂×C₄	C₂×C₃×C₄²	1	2	yes	—
389	C₂×C₄	C₂×C₃×C₄²	1	2	yes	—
390	C₂×C₄	C₂×C₃×C₄²	1	2	yes	—
391	C₂×C₄	C₂×C₃×C₄²	1	2	yes	—
392	C₂×C₄	C₂×C₃×M₁₆	1	4	yes	—
393	C₂×C₄	C₂×C₃×M₁₆	1	4	yes	—
394	C₂×C₄	C₃×#131	1	4	yes	—
395	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
396	C₂×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
397	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
398	C₂×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
399	C₈	—	2	4	no	—
400	C₈	—	2	4	no	—
401	C₈	—	2	4	no	—
402	C₈	—	2	4	no	—
403	C₂×C₃	—	2	4	no	—
404	C₂×C₃	—	4	2	no	—
405	C₂×C₃	#2275	1	1	yes	characteristic
406	C₂×C₃	C₂×C₄×M₁₆	1	1	yes	characteristic
407	C₂×C₃	C₄×#131	1	1	yes	characteristic
408	C₂×C₃	#2974	1	2	yes	—
409	C₂×C₃	#2990	1	2	yes	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	C₃×C₄×M₁₆	1	4	yes	—
420	C₂²	C₂²×C₃×C₄²	1	1	yes	characteristic
421	C₂²	C₃×#518	1	1	yes	characteristic
422	C₂²	C₃×#520	1	1	yes	characteristic
423	C₂²	C₂²×C₃×M₁₆	1	2	yes	—
424	C₂²	C₂×C₃×#131	1	2	yes	—
425	C₄	—	2	2	no	—
426	C₄	—	2	4	no	—
427	C₄	—	2	4	no	—
428	C₄	—	2	4	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	2	no	—
432	C₄	—	4	2	no	—
433	C₄	C₃×#518	1	2	yes	—
434	C₄	C₃×#520	1	2	yes	—
435	C₃	#20559	1	1	yes	characteristic, direct product factor, Sylow
436	C₂	—	2	4	no	—
437	C₂	—	4	2	no	—
438	C₂	C₃×#2275	1	1	yes	characteristic
439	C₂	C₂×C₃×C₄×M₁₆	1	1	yes	characteristic
440	C₂	C₃×C₄×#131	1	1	yes	characteristic
441	C₂	C₃×#2974	1	2	yes	—
442	C₂	C₃×#2990	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂⁴
commutator	C₂²	C₂²×C₃×C₄²
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
socle	C₂³×C₃	C₂³×C₄
prime radical	C₂²×C₃×D₄	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×#1771	C₂	semidirect
4. C₃×C₄×C₄⋊C₈	C₂	semidirect
5. C₃×#1753	C₂	semidirect
6. C₃×C₈×C₂²⋊C₄	C₂	semidirect
7. C₃×#1749	C₂	semidirect
8. C₃×C₄×C₂²⋊C₈	C₂	semidirect
9. C₃×#1745	C₂	semidirect
10. C₃×#1728	C₂	semidirect
11. C₂×C₃×#336	C₂	semidirect
12. #20559	C₃	direct (N × H)
19. C₃×#435	C₄	semidirect
43. #1771	C₂×C₃	semidirect
44. C₄×C₄⋊C₈	C₂×C₃	semidirect
45. #1753	C₂×C₃	semidirect
46. C₈×C₂²⋊C₄	C₂×C₃	semidirect
47. #1749	C₂×C₃	semidirect
48. C₄×C₂²⋊C₈	C₂×C₃	semidirect
49. #1745	C₂×C₃	semidirect
50. #1728	C₂×C₃	semidirect
51. C₂×#336	C₂×C₃	semidirect
59. C₂×C₃×M₁₆	C₂×C₄	semidirect
62. C₂²×C₃×C₈	C₂×C₄	semidirect
86. C₃×C₄⋊C₈	C₂×C₄	semidirect
87. C₃×C₂²⋊C₈	C₂×C₄	semidirect
88. C₃×C₂²⋊C₈	C₂×C₄	semidirect
90. C₃×#97	C₂×C₄	semidirect
102. #435	C₃×C₄	semidirect
170. C₃×C₂²⋊C₄	M₁₆	semidirect
188. C₂×M₁₆	C₂×C₃×C₄	semidirect
191. C₂²×C₈	C₂×C₃×C₄	semidirect
215. C₄⋊C₈	C₂×C₃×C₄	semidirect
216. C₂²⋊C₈	C₂×C₃×C₄	semidirect
217. C₂²⋊C₈	C₂×C₃×C₄	semidirect
219. #97	C₂×C₃×C₄	semidirect
319. C₂²⋊C₄	C₃×M₁₆	semidirect
435. C₃	#20559	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×#435	2
C₃×C₄²×D₄	2
C₃×#1771	2
C₃×C₄×C₄⋊C₈	2
C₃×#1753	2
C₃×C₈×C₂²⋊C₄	2
C₃×#1749	2
C₃×C₄×C₂²⋊C₈	2
C₃×#1745	2
C₃×#1728	2
C₂×C₃×#336	2
#20559	3

Subgroups — C3×#20559 #10639166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#20559 #10639166