Subgroups — C₃×#21562 #10640169

Order 768.

930 conjugacy classes of subgroups.

The subgroup lattice has 688 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	1	yes	maximal, characteristic
2	C₂×C₃×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×#123	C₂	1	1	yes	maximal, characteristic
4	C₃×#1924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#1917	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#1916	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1870	C₂	1	1	yes	maximal, characteristic
9	C₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#1817	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#1770	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#1753	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#1752	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	#21562	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×#123	C₄	1	1	yes	characteristic
21	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
23	C₃×#435	—	2	4	no	—
24	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₃×C₄×M₁₆	—	2	4	no	—
33	C₂×C₃×#97	C₂²	1	1	yes	characteristic
34	C₂×C₃×#97	C₂²	1	1	yes	characteristic
35	C₂×C₃×#97	C₂²	1	1	yes	characteristic
36	C₂×C₃×#97	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
40	C₃×#388	C₄	1	1	yes	characteristic
41	C₃×#388	C₄	1	1	yes	characteristic
42	C₃×#387	C₄	1	1	yes	characteristic
43	C₃×#387	C₄	1	1	yes	characteristic
44	C₃×#386	C₄	1	1	yes	characteristic
45	C₃×#385	C₄	1	1	yes	characteristic
46	C₃×#381	C₄	1	1	yes	characteristic
47	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
51	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
52	C₃×#336	C₂²	1	1	yes	characteristic
53	C₃×#336	C₂²	1	1	yes	characteristic
54	C₃×#336	C₂²	1	1	yes	characteristic
55	C₃×#336	C₂²	1	1	yes	characteristic
56	C₃×#336	C₂²	1	1	yes	characteristic
57	C₃×#336	C₂²	1	1	yes	characteristic
58	C₃×#336	C₂²	1	1	yes	characteristic
59	C₃×#336	C₂²	1	1	yes	characteristic
60	C₃×#336	C₂²	1	1	yes	characteristic
61	C₃×#336	C₂²	1	1	yes	characteristic
62	C₂×#435	C₂×C₃	1	1	yes	characteristic
63	C₂×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
64	C₄×#123	C₂×C₃	1	1	yes	characteristic
65	#1924	C₂×C₃	1	1	yes	characteristic, complemented
66	#1923	C₂×C₃	1	1	yes	characteristic, complemented
67	#1917	C₂×C₃	1	1	yes	characteristic, complemented
68	#1916	C₂×C₃	1	1	yes	characteristic, complemented
69	#1870	C₂×C₃	1	1	yes	characteristic
70	#1851	C₂×C₃	1	1	yes	characteristic, complemented
71	#1817	C₂×C₃	1	1	yes	characteristic, complemented
72	#1771	C₂×C₃	1	1	yes	characteristic, complemented
73	#1770	C₂×C₃	1	1	yes	characteristic, complemented
74	#1753	C₂×C₃	1	1	yes	characteristic, complemented
75	#1752	C₂×C₃	1	1	yes	characteristic, complemented
76	C₈×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
77	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
78	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
80	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
81	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
82	C₂×C₃×M₁₆	—	2	2	no	—
83	C₂×C₃×M₁₆	—	2	2	no	—
84	C₂×C₃×M₁₆	—	2	2	no	—
85	C₂×C₃×M₁₆	—	2	2	no	—
86	C₂×C₃×M₁₆	—	2	2	no	—
87	C₂×C₃×M₁₆	D₄	1	4	yes	—
88	C₂²×C₃×C₈	—	2	2	no	—
89	C₂²×C₃×C₈	—	2	2	no	—
90	C₂²×C₃×C₈	—	2	2	no	—
91	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
92	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
93	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
94	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
95	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
96	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
97	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
98	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
99	C₃×#123	—	2	4	no	—
100	C₃×C₄×D₄	—	2	2	no	—
101	C₃×C₄×D₄	—	2	2	no	—
102	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
113	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
115	C₂×C₃×C₄²	—	2	2	no	—
116	C₂×C₃×C₄²	—	2	2	no	—
117	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
118	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
119	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
120	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
121	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
122	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
123	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
124	C₃×C₄⋊C₈	—	2	2	no	—
125	C₃×C₄⋊C₈	—	2	2	no	—
126	C₃×C₄⋊C₈	—	2	2	no	—
127	C₃×C₂²⋊C₈	—	2	2	no	—
128	C₃×C₂²⋊C₈	—	2	2	no	—
129	C₃×C₂²⋊C₈	—	2	2	no	—
130	C₃×C₂²⋊C₈	—	2	2	no	—
131	C₃×C₂²⋊C₈	—	2	2	no	—
132	C₃×#97	—	2	2	no	—
133	C₃×#97	—	2	2	no	—
134	C₃×#97	—	2	2	no	—
135	C₃×#97	—	2	2	no	—
136	C₃×C₄×C₈	—	2	2	no	—
137	C₃×C₄×C₈	—	2	2	no	—
138	C₃×C₄×C₈	—	2	2	no	—
139	C₃×#95	C₂×C₄	1	1	yes	characteristic
140	C₃×#95	C₂×C₄	1	1	yes	characteristic
141	C₃×#95	C₂×C₄	1	1	yes	characteristic
142	C₃×#95	C₂×C₄	1	1	yes	characteristic
143	C₃×#95	C₂×C₄	1	1	yes	characteristic
144	C₃×#95	C₂×C₄	1	1	yes	characteristic
145	C₃×#95	C₂×C₄	1	1	yes	characteristic
146	C₃×#95	C₂×C₄	1	1	yes	characteristic
147	C₃×#95	C₂×C₄	1	1	yes	characteristic
148	C₃×#95	C₂×C₄	1	1	yes	characteristic
149	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
150	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
151	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
152	C₂×#123	C₃×C₄	1	1	yes	characteristic
153	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
154	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
155	#435	—	2	4	no	—
156	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
158	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
159	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
160	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
161	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
162	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
163	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
164	C₄×M₁₆	—	2	4	no	—
165	C₂×#97	C₂²×C₃	1	1	yes	characteristic
166	C₂×#97	C₂²×C₃	1	1	yes	characteristic
167	C₂×#97	C₂²×C₃	1	1	yes	characteristic
168	C₂×#97	C₂²×C₃	1	1	yes	characteristic
169	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
170	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
171	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
172	#388	C₃×C₄	1	1	yes	characteristic
173	#388	C₃×C₄	1	1	yes	characteristic
174	#387	C₃×C₄	1	1	yes	characteristic
175	#387	C₃×C₄	1	1	yes	characteristic
176	#386	C₃×C₄	1	1	yes	characteristic
177	#385	C₃×C₄	1	1	yes	characteristic
178	#381	C₃×C₄	1	1	yes	characteristic
179	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
180	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
181	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
182	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
183	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
184	#336	C₂²×C₃	1	1	yes	characteristic
185	#336	C₂²×C₃	1	1	yes	characteristic
186	#336	C₂²×C₃	1	1	yes	characteristic
187	#336	C₂²×C₃	1	1	yes	characteristic
188	#336	C₂²×C₃	1	1	yes	characteristic
189	#336	C₂²×C₃	1	1	yes	characteristic
190	#336	C₂²×C₃	1	1	yes	characteristic
191	#336	C₂²×C₃	1	1	yes	characteristic
192	#336	C₂²×C₃	1	1	yes	characteristic
193	#336	C₂²×C₃	1	1	yes	characteristic
194	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
195	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₃×D₄	—	2	2	no	—
197	C₂×C₃×D₄	—	2	2	no	—
198	C₂×C₃×D₄	—	4	1	no	—
199	C₂²×C₃×C₄	—	2	1	no	—
200	C₂²×C₃×C₄	—	2	1	no	—
201	C₂²×C₃×C₄	—	2	1	no	—
202	C₂²×C₃×C₄	—	2	1	no	—
203	C₂²×C₃×C₄	—	2	2	no	—
204	C₂²×C₃×C₄	—	2	2	no	—
205	C₂²×C₃×C₄	—	2	2	no	—
206	C₂²×C₃×C₄	—	2	2	no	—
207	C₂²×C₃×C₄	—	2	1	no	—
208	C₂²×C₃×C₄	—	2	1	no	—
209	C₂²×C₃×C₄	—	2	1	no	—
210	C₂²×C₃×C₄	—	2	1	no	—
211	C₂²×C₃×C₄	—	2	1	no	—
212	C₂²×C₃×C₄	—	2	1	no	—
213	C₂²×C₃×C₄	—	4	1	no	—
214	C₂²×C₃×C₄	—	4	1	no	—
215	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
217	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
228	C₂²×C₃×C₄	#41	1	2	yes	—
229	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
230	C₃×M₁₆	—	2	8	no	—
231	C₃×M₁₆	—	2	8	no	—
232	C₂×C₃×C₈	—	2	1	no	—
233	C₂×C₃×C₈	—	2	1	no	—
234	C₂×C₃×C₈	—	2	1	no	—
235	C₂×C₃×C₈	—	2	1	no	—
236	C₂×C₃×C₈	—	2	1	no	—
237	C₂×C₃×C₈	—	2	1	no	—
238	C₂×C₃×C₈	—	2	1	no	—
239	C₂×C₃×C₈	—	2	1	no	—
240	C₂×C₃×C₈	—	2	1	no	—
241	C₂×C₃×C₈	—	2	1	no	—
242	C₂×C₃×C₈	—	2	1	no	—
243	C₂×C₃×C₈	—	2	1	no	—
244	C₂×C₃×C₈	—	2	1	no	—
245	C₂×C₃×C₈	—	2	1	no	—
246	C₂×C₃×C₈	—	2	1	no	—
247	C₂×C₃×C₈	—	2	1	no	—
248	C₂×C₃×C₈	—	2	1	no	—
249	C₂×C₃×C₈	—	2	1	no	—
250	C₂×C₃×C₈	—	4	4	no	—
251	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
252	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
253	C₂×C₃×C₈	#41	1	2	yes	—
254	C₂×C₃×C₈	#41	1	2	yes	—
255	C₂×C₃×C₈	#41	1	2	yes	—
256	C₂×C₃×C₈	#41	1	2	yes	—
257	C₃×C₄⋊C₄	—	2	2	no	—
258	C₃×C₄⋊C₄	—	2	2	no	—
259	C₃×C₄⋊C₄	—	2	2	no	—
260	C₃×C₄⋊C₄	—	2	2	no	—
261	C₃×C₄⋊C₄	—	4	1	no	—
262	C₃×C₂²⋊C₄	—	2	2	no	—
263	C₃×C₂²⋊C₄	—	2	2	no	—
264	C₃×C₂²⋊C₄	—	2	2	no	—
265	C₃×C₂²⋊C₄	—	2	2	no	—
266	C₃×C₂²⋊C₄	—	2	2	no	—
267	C₃×C₂²⋊C₄	—	4	1	no	—
268	C₃×C₂²⋊C₄	—	4	1	no	—
269	C₃×C₂²⋊C₄	M₁₆	1	4	yes	complemented
270	C₃×C₄²	—	2	2	no	—
271	C₃×C₄²	—	2	2	no	—
272	C₃×C₄²	—	2	1	no	—
273	C₃×C₄²	—	2	1	no	—
274	C₃×C₄²	—	2	1	no	—
275	C₃×C₄²	—	2	1	no	—
276	C₃×C₄²	—	2	1	no	—
277	C₃×C₄²	—	2	1	no	—
278	C₃×C₄²	—	2	1	no	—
279	C₃×C₄²	—	2	1	no	—
280	C₃×C₄²	—	2	1	no	—
281	C₃×C₄²	—	2	1	no	—
282	C₂²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
283	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
284	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
287	C₂×M₁₆	—	2	2	no	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	—	2	2	no	—
292	C₂×M₁₆	C₃×D₄	1	4	yes	—
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	—	2	2	no	—
295	C₂²×C₈	—	2	2	no	—
296	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
302	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
304	#123	—	2	4	no	—
305	C₄×D₄	—	2	2	no	—
306	C₄×D₄	—	2	2	no	—
307	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
319	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
323	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
329	C₄⋊C₈	—	2	2	no	—
330	C₄⋊C₈	—	2	2	no	—
331	C₄⋊C₈	—	2	2	no	—
332	C₂²⋊C₈	—	2	2	no	—
333	C₂²⋊C₈	—	2	2	no	—
334	C₂²⋊C₈	—	2	2	no	—
335	C₂²⋊C₈	—	2	2	no	—
336	C₂²⋊C₈	—	2	2	no	—
337	#97	—	2	2	no	—
338	#97	—	2	2	no	—
339	#97	—	2	2	no	—
340	#97	—	2	2	no	—
341	C₄×C₈	—	2	2	no	—
342	C₄×C₈	—	2	2	no	—
343	C₄×C₈	—	2	2	no	—
344	#95	C₂×C₃×C₄	1	1	yes	characteristic
345	#95	C₂×C₃×C₄	1	1	yes	characteristic
346	#95	C₂×C₃×C₄	1	1	yes	characteristic
347	#95	C₂×C₃×C₄	1	1	yes	characteristic
348	#95	C₂×C₃×C₄	1	1	yes	characteristic
349	#95	C₂×C₃×C₄	1	1	yes	characteristic
350	#95	C₂×C₃×C₄	1	1	yes	characteristic
351	#95	C₂×C₃×C₄	1	1	yes	characteristic
352	#95	C₂×C₃×C₄	1	1	yes	characteristic
353	#95	C₂×C₃×C₄	1	1	yes	characteristic
354	C₂³×C₃	—	2	1	no	—
355	C₂³×C₃	—	2	1	no	—
356	C₂³×C₃	—	2	1	no	—
357	C₂³×C₃	—	2	1	no	—
358	C₂³×C₃	—	2	1	no	—
359	C₂³×C₃	—	2	1	no	—
360	C₂³×C₃	—	2	1	no	—
361	C₂³×C₃	—	2	1	no	—
362	C₂³×C₃	—	2	1	no	—
363	C₂³×C₃	—	2	1	no	—
364	C₂³×C₃	—	2	1	no	—
365	C₂³×C₃	—	2	1	no	—
366	C₂³×C₃	C₄×D₄	1	2	yes	—
367	C₂³×C₃	C₂×M₁₆	1	2	yes	—
368	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
369	C₃×D₄	—	4	4	no	—
370	C₂×C₃×C₄	—	2	1	no	—
371	C₂×C₃×C₄	—	2	1	no	—
372	C₂×C₃×C₄	—	2	1	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	2	2	no	—
380	C₂×C₃×C₄	—	2	2	no	—
381	C₂×C₃×C₄	—	2	2	no	—
382	C₂×C₃×C₄	—	2	1	no	—
383	C₂×C₃×C₄	—	2	1	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	2	1	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	2	1	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	1	no	—
400	C₂×C₃×C₄	—	2	1	no	—
401	C₂×C₃×C₄	—	2	1	no	—
402	C₂×C₃×C₄	—	2	1	no	—
403	C₂×C₃×C₄	—	2	1	no	—
404	C₂×C₃×C₄	—	2	1	no	—
405	C₂×C₃×C₄	—	2	1	no	—
406	C₂×C₃×C₄	—	4	4	no	—
407	C₂×C₃×C₄	—	4	4	no	—
408	C₂×C₃×C₄	—	4	1	no	—
409	C₂×C₃×C₄	—	4	1	no	—
410	C₂×C₃×C₄	—	4	1	no	—
411	C₂×C₃×C₄	—	4	1	no	—
412	C₂×C₃×C₄	C₄×D₄	1	2	yes	—
413	C₂×C₃×C₄	C₂×M₁₆	1	2	yes	—
414	C₂×C₃×C₄	C₂×M₁₆	1	2	yes	—
415	C₂×C₃×C₄	#131	1	2	yes	—
416	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
418	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
419	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
420	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
421	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
422	C₃×C₈	—	2	2	no	—
423	C₃×C₈	—	2	2	no	—
424	C₃×C₈	—	2	2	no	—
425	C₃×C₈	—	4	1	no	—
426	C₃×C₈	—	4	1	no	—
427	C₃×C₈	—	4	1	no	—
428	C₃×C₈	—	4	1	no	—
429	C₃×C₈	#123	1	4	yes	complemented
430	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
431	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	4	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	—	4	1	no	—
451	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
452	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
453	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
454	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
455	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
456	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
457	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
458	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
459	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
460	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
461	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
462	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
463	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
464	C₂²×C₄	C₃×#41	1	2	yes	—
465	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
466	M₁₆	—	2	8	no	—
467	M₁₆	—	2	8	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	4	4	no	—
487	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
488	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
489	C₂×C₈	C₃×#41	1	2	yes	—
490	C₂×C₈	C₃×#41	1	2	yes	—
491	C₂×C₈	C₃×#41	1	2	yes	—
492	C₂×C₈	C₃×#41	1	2	yes	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	4	1	no	—
504	C₂²⋊C₄	—	4	1	no	—
505	C₂²⋊C₄	C₃×M₁₆	1	4	yes	complemented
506	C₄²	—	2	2	no	—
507	C₄²	—	2	2	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₂²×C₃	—	2	2	no	—
519	C₂²×C₃	—	2	2	no	—
520	C₂²×C₃	—	2	2	no	—
521	C₂²×C₃	—	2	2	no	—
522	C₂²×C₃	—	2	2	no	—
523	C₂²×C₃	—	2	2	no	—
524	C₂²×C₃	—	4	1	no	—
525	C₂²×C₃	—	4	1	no	—
526	C₂²×C₃	—	4	1	no	—
527	C₂²×C₃	—	4	1	no	—
528	C₂²×C₃	—	4	1	no	—
529	C₂²×C₃	—	4	1	no	—
530	C₂²×C₃	—	4	1	no	—
531	C₂²×C₃	—	4	1	no	—
532	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
533	C₂²×C₃	C₄×#41	1	1	yes	characteristic
534	C₂²×C₃	C₄×#41	1	1	yes	characteristic
535	C₂²×C₃	C₂²×M₁₆	1	1	yes	characteristic
536	C₂²×C₃	C₂×#131	1	1	yes	characteristic
537	C₂²×C₃	#568	1	1	yes	characteristic
538	C₂²×C₃	#568	1	1	yes	characteristic
539	C₃×C₄	—	2	2	no	—
540	C₃×C₄	—	2	2	no	—
541	C₃×C₄	—	2	2	no	—
542	C₃×C₄	—	2	2	no	—
543	C₃×C₄	—	4	1	no	—
544	C₃×C₄	—	4	1	no	—
545	C₃×C₄	—	4	1	no	—
546	C₃×C₄	—	4	1	no	—
547	C₃×C₄	—	4	1	no	—
548	C₃×C₄	—	4	1	no	—
549	C₃×C₄	—	4	1	no	—
550	C₃×C₄	—	4	1	no	—
551	C₃×C₄	C₂×#123	1	1	yes	characteristic
552	C₃×C₄	#525	1	1	yes	characteristic
553	C₃×C₄	#529	1	1	yes	characteristic
554	C₃×C₄	#529	1	1	yes	characteristic
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	C₃×C₄×D₄	1	2	yes	—
568	C₂³	C₂×C₃×M₁₆	1	2	yes	—
569	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
570	D₄	—	4	4	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	4	4	no	—
608	C₂×C₄	—	4	4	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	C₃×C₄×D₄	1	2	yes	—
614	C₂×C₄	C₂×C₃×M₁₆	1	2	yes	—
615	C₂×C₄	C₂×C₃×M₁₆	1	2	yes	—
616	C₂×C₄	C₃×#131	1	2	yes	—
617	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
618	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
619	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
620	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
621	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
622	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
623	C₈	—	2	2	no	—
624	C₈	—	2	2	no	—
625	C₈	—	2	2	no	—
626	C₈	—	4	1	no	—
627	C₈	—	4	1	no	—
628	C₈	—	4	1	no	—
629	C₈	—	4	1	no	—
630	C₈	C₃×#123	1	4	yes	complemented
631	C₂×C₃	—	4	2	no	—
632	C₂×C₃	—	4	2	no	—
633	C₂×C₃	C₄×#123	1	1	yes	characteristic
634	C₂×C₃	#2933	1	1	yes	characteristic
635	C₂×C₃	D₄×M₁₆	1	1	yes	characteristic
636	C₂×C₃	#2965	1	1	yes	characteristic
637	C₂×C₃	#2967	1	1	yes	characteristic
638	C₂×C₃	#2969	1	1	yes	characteristic
639	C₂×C₃	#2970	1	1	yes	characteristic
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	1	no	—
654	C₂²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
655	C₂²	C₃×C₄×#41	1	1	yes	characteristic
656	C₂²	C₃×C₄×#41	1	1	yes	characteristic
657	C₂²	C₂²×C₃×M₁₆	1	1	yes	characteristic
658	C₂²	C₂×C₃×#131	1	1	yes	characteristic
659	C₂²	C₃×#568	1	1	yes	characteristic
660	C₂²	C₃×#568	1	1	yes	characteristic
661	C₄	—	2	2	no	—
662	C₄	—	2	2	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	1	no	—
672	C₄	—	4	1	no	—
673	C₄	C₂×C₃×#123	1	1	yes	characteristic
674	C₄	C₃×#525	1	1	yes	characteristic
675	C₄	C₃×#529	1	1	yes	characteristic
676	C₄	C₃×#529	1	1	yes	characteristic
677	C₃	#21562	1	1	yes	characteristic, direct product factor, Sylow
678	C₂	—	4	2	no	—
679	C₂	—	4	2	no	—
680	C₂	C₃×C₄×#123	1	1	yes	characteristic
681	C₂	C₃×#2933	1	1	yes	characteristic
682	C₂	C₃×D₄×M₁₆	1	1	yes	characteristic
683	C₂	C₃×#2965	1	1	yes	characteristic
684	C₂	C₃×#2967	1	1	yes	characteristic
685	C₂	C₃×#2969	1	1	yes	characteristic
686	C₂	C₃×#2970	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×M₁₆	C₂	semidirect
4. C₃×#1924	C₂	semidirect
5. C₃×#1923	C₂	semidirect
6. C₃×#1917	C₂	semidirect
7. C₃×#1916	C₂	semidirect
9. C₃×#1851	C₂	semidirect
10. C₃×#1817	C₂	semidirect
11. C₃×#1771	C₂	semidirect
12. C₃×#1770	C₂	semidirect
13. C₃×#1753	C₂	semidirect
14. C₃×#1752	C₂	semidirect
15. C₃×C₈×C₂²⋊C₄	C₂	semidirect
16. #21562	C₃	direct (N × H)
63. C₂×C₄×M₁₆	C₂×C₃	semidirect
65. #1924	C₂×C₃	semidirect
66. #1923	C₂×C₃	semidirect
67. #1917	C₂×C₃	semidirect
68. #1916	C₂×C₃	semidirect
70. #1851	C₂×C₃	semidirect
71. #1817	C₂×C₃	semidirect
72. #1771	C₂×C₃	semidirect
73. #1770	C₂×C₃	semidirect
74. #1753	C₂×C₃	semidirect
75. #1752	C₂×C₃	semidirect
76. C₈×C₂²⋊C₄	C₂×C₃	semidirect
269. C₃×C₂²⋊C₄	M₁₆	semidirect
429. C₃×C₈	#123	semidirect
505. C₂²⋊C₄	C₃×M₁₆	semidirect
630. C₈	C₃×#123	semidirect
677. C₃	#21562	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
C₂×C₃×C₄×M₁₆	2
C₃×C₄×#123	2
C₃×#1924	2
C₃×#1923	2
C₃×#1917	2
C₃×#1916	2
C₃×#1870	2
C₃×#1851	2
C₃×#1817	2
C₃×#1771	2
C₃×#1770	2
C₃×#1753	2
C₃×#1752	2
C₃×C₈×C₂²⋊C₄	2
#21562	3

Subgroups — C3×#21562 #10640169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#21562 #10640169