Subgroups — C₃×#21568 #10640175

Order 768.

878 conjugacy classes of subgroups.

The subgroup lattice has 674 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×#405	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2395	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×#1869	C₂	1	1	yes	maximal, characteristic
9	C₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#1818	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	#21568	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
19	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×#117	C₂²	1	1	yes	characteristic
22	C₃×#435	—	2	4	no	—
23	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₂²⋊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	C₃×#405	—	2	4	no	—
32	C₂×C₃×#97	C₂²	1	1	yes	characteristic
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×C₄×C₈	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	C₃×#400	C₄	1	1	yes	characteristic
40	C₃×#399	C₄	1	1	yes	characteristic
41	C₃×#398	C₄	1	1	yes	characteristic
42	C₃×#397	C₄	1	1	yes	characteristic
43	C₃×#397	C₄	1	1	yes	characteristic
44	C₃×#397	C₄	1	1	yes	characteristic
45	C₃×#394	C₄	1	1	yes	characteristic
46	C₃×#394	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×#405	C₂×C₃	1	1	yes	characteristic, complemented
64	#2395	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	#1869	C₂×C₃	1	1	yes	characteristic
70	#1850	C₂×C₃	1	1	yes	characteristic, complemented
71	#1818	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	C₂³	1	1	yes	characteristic
79	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
80	C₂×C₃×M₁₆	—	2	2	no	—
81	C₂×C₃×M₁₆	—	2	2	no	—
82	C₂×C₃×M₁₆	D₄	1	4	yes	—
83	C₂²×C₃×C₈	—	2	2	no	—
84	C₂²×C₃×C₈	—	2	2	no	—
85	C₂²×C₃×C₈	—	2	2	no	—
86	C₂²×C₃×C₈	—	2	2	no	—
87	C₂²×C₃×C₈	—	2	2	no	—
88	C₂²×C₃×C₈	—	2	2	no	—
89	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
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	C₃×C₄×D₄	—	2	2	no	—
98	C₃×C₄×D₄	—	2	2	no	—
99	C₃×#117	—	2	2	no	—
100	C₃×#117	—	2	2	no	—
101	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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×C₄⋊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×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
118	C₂×C₃×C₄²	C₂³	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	C₃×C₄⋊C₈	—	2	2	no	—
124	C₃×C₄⋊C₈	—	2	2	no	—
125	C₃×C₄⋊C₈	—	2	2	no	—
126	C₃×C₂²⋊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×#97	—	2	2	no	—
132	C₃×#97	—	2	2	no	—
133	C₃×#97	—	2	2	no	—
134	C₃×#97	—	2	2	no	—
135	C₃×C₄×C₈	—	2	2	no	—
136	C₃×C₄×C₈	—	2	2	no	—
137	C₃×C₄×C₈	—	2	2	no	—
138	C₃×#95	C₂×C₄	1	1	yes	characteristic
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	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
149	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
150	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
152	C₂×#117	C₂²×C₃	1	1	yes	characteristic
153	#435	—	2	4	no	—
154	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
158	C₂×C₂²⋊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	#405	—	2	4	no	—
163	C₂×#97	C₂²×C₃	1	1	yes	characteristic
164	C₂×#97	C₂²×C₃	1	1	yes	characteristic
165	C₂×#97	C₂²×C₃	1	1	yes	characteristic
166	C₂×#97	C₂²×C₃	1	1	yes	characteristic
167	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
168	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
169	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
170	#400	C₃×C₄	1	1	yes	characteristic
171	#399	C₃×C₄	1	1	yes	characteristic
172	#398	C₃×C₄	1	1	yes	characteristic
173	#397	C₃×C₄	1	1	yes	characteristic
174	#397	C₃×C₄	1	1	yes	characteristic
175	#397	C₃×C₄	1	1	yes	characteristic
176	#394	C₃×C₄	1	1	yes	characteristic
177	#394	C₃×C₄	1	1	yes	characteristic
178	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
179	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
180	C₄×C₂²⋊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	#336	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	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
194	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₃×D₄	—	2	2	no	—
196	C₂×C₃×D₄	—	2	2	no	—
197	C₂×C₃×D₄	—	4	1	no	—
198	C₂²×C₃×C₄	—	2	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	1	no	—
204	C₂²×C₃×C₄	—	2	1	no	—
205	C₂²×C₃×C₄	—	2	1	no	—
206	C₂²×C₃×C₄	—	2	1	no	—
207	C₂²×C₃×C₄	—	2	1	no	—
208	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
210	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
211	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
213	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
214	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
221	C₂²×C₃×C₄	#41	1	2	yes	—
222	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
223	C₃×M₁₆	—	2	8	no	—
224	C₂×C₃×C₈	—	2	8	no	—
225	C₂×C₃×C₈	—	2	1	no	—
226	C₂×C₃×C₈	—	2	1	no	—
227	C₂×C₃×C₈	—	2	1	no	—
228	C₂×C₃×C₈	—	2	1	no	—
229	C₂×C₃×C₈	—	2	1	no	—
230	C₂×C₃×C₈	—	2	1	no	—
231	C₂×C₃×C₈	—	2	1	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	—	4	4	no	—
244	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
245	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
246	C₂×C₃×C₈	#41	1	2	yes	—
247	C₂×C₃×C₈	#41	1	2	yes	—
248	C₂×C₃×C₈	#41	1	2	yes	—
249	C₂×C₃×C₈	#41	1	2	yes	—
250	C₃×C₄⋊C₄	—	2	2	no	—
251	C₃×C₄⋊C₄	—	2	2	no	—
252	C₃×C₄⋊C₄	—	2	2	no	—
253	C₃×C₄⋊C₄	—	2	2	no	—
254	C₃×C₄⋊C₄	—	4	1	no	—
255	C₃×C₄⋊C₄	—	4	1	no	—
256	C₃×C₄⋊C₄	—	4	1	no	—
257	C₃×C₂²⋊C₄	—	2	2	no	—
258	C₃×C₂²⋊C₄	—	2	2	no	—
259	C₃×C₂²⋊C₄	—	2	2	no	—
260	C₃×C₂²⋊C₄	—	2	2	no	—
261	C₃×C₂²⋊C₄	—	2	2	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	—	4	1	no	—
266	C₃×C₂²⋊C₄	—	4	1	no	—
267	C₃×C₄²	—	2	1	no	—
268	C₃×C₄²	—	2	1	no	—
269	C₃×C₄²	—	2	1	no	—
270	C₃×C₄²	—	2	1	no	—
271	C₃×C₄²	—	2	1	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	C₂²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
279	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	C₃×D₄	1	4	yes	—
283	C₂²×C₈	—	2	2	no	—
284	C₂²×C₈	—	2	2	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	—	2	2	no	—
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	—	2	2	no	—
299	#117	—	2	2	no	—
300	#117	—	2	2	no	—
301	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
311	C₂×C₂²⋊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×C₄²	C₂³×C₃	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
323	C₄⋊C₈	—	2	2	no	—
324	C₄⋊C₈	—	2	2	no	—
325	C₄⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	2	2	no	—
328	C₂²⋊C₈	—	2	2	no	—
329	C₂²⋊C₈	—	2	2	no	—
330	C₂²⋊C₈	—	2	2	no	—
331	#97	—	2	2	no	—
332	#97	—	2	2	no	—
333	#97	—	2	2	no	—
334	#97	—	2	2	no	—
335	C₄×C₈	—	2	2	no	—
336	C₄×C₈	—	2	2	no	—
337	C₄×C₈	—	2	2	no	—
338	#95	C₂×C₃×C₄	1	1	yes	characteristic
339	#95	C₂×C₃×C₄	1	1	yes	characteristic
340	#95	C₂×C₃×C₄	1	1	yes	characteristic
341	#95	C₂×C₃×C₄	1	1	yes	characteristic
342	#95	C₂×C₃×C₄	1	1	yes	characteristic
343	#95	C₂×C₃×C₄	1	1	yes	characteristic
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	C₂³×C₃	—	2	1	no	—
349	C₂³×C₃	—	2	1	no	—
350	C₂³×C₃	—	2	1	no	—
351	C₂³×C₃	—	2	1	no	—
352	C₂³×C₃	—	2	1	no	—
353	C₂³×C₃	—	2	1	no	—
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	C₄×D₄	1	2	yes	—
361	C₂³×C₃	#131	1	2	yes	—
362	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
363	C₃×D₄	—	4	4	no	—
364	C₂×C₃×C₄	—	2	1	no	—
365	C₂×C₃×C₄	—	2	1	no	—
366	C₂×C₃×C₄	—	2	1	no	—
367	C₂×C₃×C₄	—	2	1	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	2	2	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	2	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	1	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	1	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	—	4	1	no	—
403	C₂×C₃×C₄	—	4	1	no	—
404	C₂×C₃×C₄	—	4	1	no	—
405	C₂×C₃×C₄	—	4	1	no	—
406	C₂×C₃×C₄	C₄×D₄	1	2	yes	—
407	C₂×C₃×C₄	#131	1	2	yes	—
408	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
410	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
411	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
412	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
413	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
414	C₃×C₈	—	2	2	no	—
415	C₃×C₈	—	2	2	no	—
416	C₃×C₈	—	2	2	no	—
417	C₃×C₈	—	4	1	no	—
418	C₃×C₈	—	4	1	no	—
419	C₃×C₈	—	4	1	no	—
420	C₃×C₈	—	4	1	no	—
421	C₃×C₈	#123	1	4	yes	—
422	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
423	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	4	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
438	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
439	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
440	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
441	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
442	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
443	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
444	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
445	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
446	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
447	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
448	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
449	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
450	C₂²×C₄	C₃×#41	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
452	M₁₆	—	2	8	no	—
453	C₂×C₈	—	2	8	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	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	—	4	4	no	—
473	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
474	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
475	C₂×C₈	C₃×#41	1	2	yes	—
476	C₂×C₈	C₃×#41	1	2	yes	—
477	C₂×C₈	C₃×#41	1	2	yes	—
478	C₂×C₈	C₃×#41	1	2	yes	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	4	1	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₂²×C₃	—	2	2	no	—
507	C₂²×C₃	—	2	2	no	—
508	C₂²×C₃	—	2	2	no	—
509	C₂²×C₃	—	2	2	no	—
510	C₂²×C₃	—	2	2	no	—
511	C₂²×C₃	—	2	2	no	—
512	C₂²×C₃	—	4	1	no	—
513	C₂²×C₃	—	4	1	no	—
514	C₂²×C₃	—	4	1	no	—
515	C₂²×C₃	—	4	1	no	—
516	C₂²×C₃	—	4	1	no	—
517	C₂²×C₃	—	4	1	no	—
518	C₂²×C₃	—	4	1	no	—
519	C₂²×C₃	—	4	1	no	—
520	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
521	C₂²×C₃	C₄×#41	1	1	yes	characteristic
522	C₂²×C₃	C₄×#41	1	1	yes	characteristic
523	C₂²×C₃	C₂×#131	1	1	yes	characteristic
524	C₂²×C₃	C₂×#131	1	1	yes	characteristic
525	C₂²×C₃	#568	1	1	yes	characteristic
526	C₂²×C₃	#568	1	1	yes	characteristic
527	C₃×C₄	—	2	2	no	—
528	C₃×C₄	—	2	2	no	—
529	C₃×C₄	—	4	1	no	—
530	C₃×C₄	—	4	1	no	—
531	C₃×C₄	—	4	1	no	—
532	C₃×C₄	—	4	1	no	—
533	C₃×C₄	—	4	1	no	—
534	C₃×C₄	—	4	1	no	—
535	C₃×C₄	—	4	1	no	—
536	C₃×C₄	—	4	1	no	—
537	C₃×C₄	—	4	1	no	—
538	C₃×C₄	—	4	1	no	—
539	C₃×C₄	C₂×#123	1	1	yes	characteristic
540	C₃×C₄	#525	1	1	yes	characteristic
541	C₃×C₄	#529	1	1	yes	characteristic
542	C₃×C₄	#529	1	1	yes	characteristic
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	C₃×C₄×D₄	1	2	yes	—
556	C₂³	C₃×#131	1	2	yes	—
557	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
558	D₄	—	4	4	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	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	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	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	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	C₃×C₄×D₄	1	2	yes	—
602	C₂×C₄	C₃×#131	1	2	yes	—
603	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
604	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
605	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
606	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
607	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
608	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
609	C₈	—	2	2	no	—
610	C₈	—	2	2	no	—
611	C₈	—	2	2	no	—
612	C₈	—	4	1	no	—
613	C₈	—	4	1	no	—
614	C₈	—	4	1	no	—
615	C₈	—	4	1	no	—
616	C₈	C₃×#123	1	4	yes	—
617	C₂×C₃	—	4	2	no	—
618	C₂×C₃	—	4	2	no	—
619	C₂×C₃	C₄×#123	1	1	yes	characteristic
620	C₂×C₃	#2933	1	1	yes	characteristic
621	C₂×C₃	#2935	1	1	yes	characteristic
622	C₂×C₃	#2966	1	1	yes	characteristic
623	C₂×C₃	#2967	1	1	yes	characteristic
624	C₂×C₃	#2968	1	1	yes	characteristic
625	C₂×C₃	#2968	1	1	yes	characteristic
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
641	C₂²	C₃×C₄×#41	1	1	yes	characteristic
642	C₂²	C₃×C₄×#41	1	1	yes	characteristic
643	C₂²	C₂×C₃×#131	1	1	yes	characteristic
644	C₂²	C₂×C₃×#131	1	1	yes	characteristic
645	C₂²	C₃×#568	1	1	yes	characteristic
646	C₂²	C₃×#568	1	1	yes	characteristic
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	C₂×C₃×#123	1	1	yes	characteristic
660	C₄	C₃×#525	1	1	yes	characteristic
661	C₄	C₃×#529	1	1	yes	characteristic
662	C₄	C₃×#529	1	1	yes	characteristic
663	C₃	#21568	1	1	yes	characteristic, direct product factor, Sylow
664	C₂	—	4	2	no	—
665	C₂	—	4	2	no	—
666	C₂	C₃×C₄×#123	1	1	yes	characteristic
667	C₂	C₃×#2933	1	1	yes	characteristic
668	C₂	C₃×#2935	1	1	yes	characteristic
669	C₂	C₃×#2966	1	1	yes	characteristic
670	C₂	C₃×#2967	1	1	yes	characteristic
671	C₂	C₃×#2968	1	1	yes	characteristic
672	C₂	C₃×#2968	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×#405	C₂	semidirect
4. C₃×#1924	C₂	semidirect
5. C₃×#1923	C₂	semidirect
6. C₃×#1917	C₂	semidirect
7. C₃×#1916	C₂	semidirect
9. C₃×#1850	C₂	semidirect
10. C₃×#1818	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. #21568	C₃	direct (N × H)
63. C₂×#405	C₂×C₃	semidirect
65. #1924	C₂×C₃	semidirect
66. #1923	C₂×C₃	semidirect
67. #1917	C₂×C₃	semidirect
68. #1916	C₂×C₃	semidirect
70. #1850	C₂×C₃	semidirect
71. #1818	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
663. C₃	#21568	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×#405	2
C₃×#2395	2
C₃×#1924	2
C₃×#1923	2
C₃×#1917	2
C₃×#1916	2
C₃×#1869	2
C₃×#1850	2
C₃×#1818	2
C₃×#1771	2
C₃×#1770	2
C₃×#1753	2
C₃×#1752	2
C₃×C₈×C₂²⋊C₄	2
#21568	3

Subgroups — C3×#21568 #10640175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#21568 #10640175