Subgroups — C₃×#60142 #10678749

Order 768.

2714 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3449	C₂	1	1	yes	maximal, characteristic
4	C₃×#2935	C₂	1	8	yes	maximal, complemented
5	C₃×#2933	C₂	1	8	yes	maximal, complemented
6	C₃×#2930	C₂	1	4	yes	maximal, complemented
7	C₃×#2929	C₂	1	4	yes	maximal, complemented
8	C₂×C₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2879	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2873	C₂	1	1	yes	maximal, characteristic, complemented
12	#60142	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
15	C₃×#568	—	2	8	no	—
16	C₂×C₃×#131	—	2	8	no	—
17	C₂×C₃×#131	C₂²	1	4	yes	—
18	C₂×C₃×#131	C₂²	1	4	yes	—
19	C₂×C₃×#131	C₂²	1	4	yes	complemented
20	C₂×C₃×#131	C₂²	1	4	yes	complemented
21	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₃×M₁₆	C₂²	1	2	yes	complemented
25	C₂²×C₃×M₁₆	C₂²	1	4	yes	complemented
26	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
27	C₂³×C₃×C₈	C₂²	1	2	yes	complemented
28	C₃×#537	C₄	1	4	yes	—
29	C₃×#536	C₄	1	2	yes	—
30	C₃×#536	C₄	1	2	yes	—
31	C₃×#535	C₄	1	2	yes	—
32	C₃×#535	C₄	1	2	yes	—
33	C₃×#534	C₄	1	4	yes	—
34	C₃×#532	C₂²	1	4	yes	—
35	C₃×#525	C₂²	1	4	yes	—
36	C₃×#525	C₂²	1	4	yes	—
37	C₂×C₃×#117	C₂²	1	1	yes	characteristic
38	C₃×#436	C₂²	1	16	yes	complemented
39	C₃×#435	C₂²	1	16	yes	complemented
40	C₃×#435	C₂²	1	16	yes	complemented
41	C₃×C₈×D₄	C₂²	1	16	yes	complemented
42	C₃×#424	C₂²	1	2	yes	complemented
43	C₃×#424	C₂²	1	2	yes	complemented
44	C₃×#424	C₂²	1	4	yes	complemented
45	C₂×C₃×C₄⋊C₈	C₂²	1	4	yes	complemented
46	C₃×#408	C₂²	1	2	yes	—
47	C₃×#408	C₂²	1	2	yes	—
48	C₃×#408	C₂²	1	4	yes	—
49	C₃×#408	C₂²	1	4	yes	complemented
50	C₃×#408	C₂²	1	4	yes	complemented
51	C₃×#407	C₂²	1	4	yes	complemented
52	C₂×C₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
53	C₃×#405	C₂²	1	4	yes	complemented
54	C₃×#405	C₂²	1	4	yes	complemented
55	C₃×C₄×M₁₆	C₂²	1	4	yes	complemented
56	C₂×#568	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂²×#131	C₂×C₃	1	1	yes	characteristic, complemented
58	#3449	C₂×C₃	1	1	yes	characteristic
59	#2935	C₂×C₃	1	8	yes	complemented
60	#2933	C₂×C₃	1	8	yes	complemented
61	#2930	C₂×C₃	1	4	yes	complemented
62	#2929	C₂×C₃	1	4	yes	complemented
63	C₂×#424	C₂×C₃	1	1	yes	characteristic, complemented
64	#2879	C₂×C₃	1	1	yes	characteristic, complemented
65	C₂×#408	C₂×C₃	1	1	yes	characteristic, complemented
66	#2873	C₂×C₃	1	1	yes	characteristic, complemented
67	C₂×C₃×#41	—	2	4	no	—
68	C₂×C₃×#41	—	2	4	no	—
69	C₂×C₃×#41	—	2	4	no	—
70	C₂×C₃×#41	—	2	4	no	—
71	C₂×C₃×#41	C₂×C₄	1	2	yes	—
72	C₂×C₃×#41	C₂×C₄	1	2	yes	—
73	C₂×C₃×#41	C₂×C₄	1	2	yes	—
74	C₂×C₃×#41	C₂×C₄	1	2	yes	—
75	C₂×C₃×#41	C₂³	1	2	yes	—
76	C₂×C₃×#41	C₂³	1	2	yes	—
77	C₂×C₃×#41	C₂³	1	2	yes	—
78	C₂×C₃×#41	C₂³	1	2	yes	—
79	C₂²×C₃×Q₈	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₃×Q₈	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₃×D₄	C₂×C₄	1	2	yes	—
82	C₂²×C₃×D₄	C₂×C₄	1	2	yes	—
83	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
85	C₂³×C₃×C₄	C₂³	1	2	yes	—
86	C₂³×C₃×C₄	C₂³	1	2	yes	—
87	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
88	C₃×#131	—	2	16	no	—
89	C₃×#131	—	2	16	no	—
90	C₃×#131	—	2	16	no	—
91	C₃×#131	—	2	16	no	—
92	C₂×C₃×M₁₆	—	2	4	no	—
93	C₂×C₃×M₁₆	—	2	4	no	—
94	C₂×C₃×M₁₆	—	2	16	no	—
95	C₂×C₃×M₁₆	—	2	8	no	—
96	C₂×C₃×M₁₆	D₄	1	8	yes	complemented
97	C₂×C₃×M₁₆	C₂³	1	2	yes	—
98	C₂×C₃×M₁₆	C₂³	1	2	yes	—
99	C₂×C₃×M₁₆	C₂³	1	2	yes	—
100	C₂×C₃×M₁₆	C₂³	1	2	yes	—
101	C₂×C₃×M₁₆	C₂³	1	8	yes	—
102	C₂×C₃×M₁₆	C₂³	1	8	yes	—
103	C₂×C₃×M₁₆	C₂³	1	2	yes	—
104	C₂×C₃×M₁₆	C₂³	1	2	yes	—
105	C₂²×C₃×C₈	—	2	4	no	—
106	C₂²×C₃×C₈	—	2	8	no	—
107	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
108	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
109	C₂²×C₃×C₈	C₂³	1	2	yes	—
110	C₂²×C₃×C₈	C₂³	1	2	yes	—
111	C₂²×C₃×C₈	C₂³	1	8	yes	—
112	C₂²×C₃×C₈	C₂³	1	2	yes	—
113	C₂²×C₃×C₈	C₂³	1	2	yes	—
114	C₂²×C₃×C₈	C₂³	1	8	yes	—
115	C₂²×C₃×C₈	C₂³	1	2	yes	—
116	C₃×C₄⋊Q₈	C₂×C₄	1	4	yes	—
117	C₃×#127	C₂×C₄	1	4	yes	—
118	C₃×#124	C₂×C₄	1	4	yes	—
119	C₃×#124	C₂×C₄	1	4	yes	—
120	C₃×#123	C₂×C₄	1	8	yes	—
121	C₃×#123	C₂×C₄	1	8	yes	—
122	C₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
123	C₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
124	C₃×#121	C₂×C₄	1	8	yes	—
125	C₃×#121	C₂×C₄	1	8	yes	—
126	C₃×#121	C₂×C₄	1	16	yes	—
127	C₃×#120	C₂×C₄	1	8	yes	—
128	C₃×#120	C₂×C₄	1	8	yes	—
129	C₃×C₄×D₄	C₂³	1	16	yes	—
130	C₃×#117	C₂×C₄	1	2	yes	—
131	C₃×#117	C₂×C₄	1	2	yes	—
132	C₃×#117	C₂³	1	2	yes	—
133	C₃×#117	C₂³	1	2	yes	—
134	C₂×C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
135	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
136	C₂×C₃×C₄²	C₂³	1	2	yes	—
137	C₃×C₄⋊C₈	C₂³	1	8	yes	—
138	C₃×C₄⋊C₈	C₂³	1	8	yes	—
139	C₃×C₂²⋊C₈	C₂³	1	8	yes	—
140	C₃×C₂²⋊C₈	C₂³	1	8	yes	—
141	C₃×C₂²⋊C₈	C₂³	1	16	yes	—
142	C₃×#97	C₂³	1	8	yes	—
143	C₃×C₄×C₈	C₂³	1	8	yes	—
144	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
145	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
146	#568	—	2	8	no	—
147	C₂×#131	—	2	8	no	—
148	C₂×#131	C₂²×C₃	1	4	yes	—
149	C₂×#131	C₂²×C₃	1	4	yes	—
150	C₂×#131	C₂²×C₃	1	4	yes	complemented
151	C₂×#131	C₂²×C₃	1	4	yes	complemented
152	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
153	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
154	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
155	C₂²×M₁₆	C₂²×C₃	1	2	yes	complemented
156	C₂²×M₁₆	C₂²×C₃	1	4	yes	complemented
157	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
158	C₂³×C₈	C₂²×C₃	1	2	yes	complemented
159	#537	C₃×C₄	1	4	yes	—
160	#536	C₃×C₄	1	2	yes	—
161	#536	C₃×C₄	1	2	yes	—
162	#535	C₃×C₄	1	2	yes	—
163	#535	C₃×C₄	1	2	yes	—
164	#534	C₃×C₄	1	4	yes	—
165	#532	C₂²×C₃	1	4	yes	—
166	#525	C₂²×C₃	1	4	yes	—
167	#525	C₂²×C₃	1	4	yes	—
168	C₂×#117	C₂²×C₃	1	1	yes	characteristic
169	#436	C₂²×C₃	1	16	yes	complemented
170	#435	C₂²×C₃	1	16	yes	complemented
171	#435	C₂²×C₃	1	16	yes	complemented
172	C₈×D₄	C₂²×C₃	1	16	yes	complemented
173	#424	C₂²×C₃	1	2	yes	complemented
174	#424	C₂²×C₃	1	2	yes	complemented
175	#424	C₂²×C₃	1	4	yes	complemented
176	C₂×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
177	#408	C₂²×C₃	1	2	yes	—
178	#408	C₂²×C₃	1	2	yes	—
179	#408	C₂²×C₃	1	4	yes	—
180	#408	C₂²×C₃	1	4	yes	complemented
181	#408	C₂²×C₃	1	4	yes	complemented
182	#407	C₂²×C₃	1	4	yes	complemented
183	C₂×C₂²⋊C₈	C₂²×C₃	1	4	yes	complemented
184	#405	C₂²×C₃	1	4	yes	complemented
185	#405	C₂²×C₃	1	4	yes	complemented
186	C₄×M₁₆	C₂²×C₃	1	4	yes	complemented
187	C₂⁴×C₃	C₂²×C₄	1	2	yes	—
188	C₂⁴×C₃	C₂²×C₄	1	2	yes	—
189	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
190	C₃×#41	—	2	8	no	—
191	C₃×#41	—	2	8	no	—
192	C₃×#41	—	2	8	no	—
193	C₃×#41	—	2	8	no	—
194	C₃×#41	—	2	4	no	—
195	C₃×#41	—	2	4	no	—
196	C₃×#41	—	2	4	no	—
197	C₃×#41	—	2	4	no	—
198	C₃×#41	—	2	4	no	—
199	C₃×#41	—	2	4	no	—
200	C₃×#41	—	2	4	no	—
201	C₃×#41	—	2	4	no	—
202	C₂×C₃×Q₈	—	2	4	no	—
203	C₂×C₃×Q₈	—	2	4	no	—
204	C₂×C₃×Q₈	C₂²×C₄	1	2	yes	—
205	C₂×C₃×Q₈	C₂²×C₄	1	2	yes	—
206	C₂×C₃×Q₈	C₂²×C₄	1	2	yes	—
207	C₂×C₃×Q₈	C₂²×C₄	1	2	yes	—
208	C₂×C₃×D₄	—	2	8	no	—
209	C₂×C₃×D₄	—	2	8	no	—
210	C₂×C₃×D₄	—	2	4	no	—
211	C₂×C₃×D₄	—	2	4	no	—
212	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
213	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
214	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
215	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
216	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
217	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
218	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
219	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
220	C₂×C₃×D₄	C₂²×C₄	1	16	yes	—
221	C₂²×C₃×C₄	—	2	4	no	—
222	C₂²×C₃×C₄	—	2	4	no	—
223	C₂²×C₃×C₄	—	2	4	no	—
224	C₂²×C₃×C₄	—	2	4	no	—
225	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
226	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
227	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
228	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
229	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
230	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
233	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
234	C₂²×C₃×C₄	#41	1	4	yes	—
235	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
236	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
237	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
238	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
240	C₃×M₁₆	—	2	4	no	—
241	C₃×M₁₆	—	2	4	no	—
242	C₃×M₁₆	—	2	4	no	—
243	C₃×M₁₆	—	2	4	no	—
244	C₃×M₁₆	—	2	16	no	—
245	C₃×M₁₆	—	2	16	no	—
246	C₃×M₁₆	C₂×D₄	1	8	yes	—
247	C₃×M₁₆	C₂×D₄	1	8	yes	—
248	C₂×C₃×C₈	—	2	2	no	—
249	C₂×C₃×C₈	—	2	2	no	—
250	C₂×C₃×C₈	—	2	4	no	—
251	C₂×C₃×C₈	—	2	4	no	—
252	C₂×C₃×C₈	—	2	4	no	—
253	C₂×C₃×C₈	—	2	4	no	—
254	C₂×C₃×C₈	—	2	16	no	—
255	C₂×C₃×C₈	—	2	16	no	—
256	C₂×C₃×C₈	C₂×D₄	1	8	yes	—
257	C₂×C₃×C₈	C₂⁴	1	4	yes	—
258	C₂×C₃×C₈	C₂⁴	1	2	yes	—
259	C₂×C₃×C₈	C₂⁴	1	2	yes	—
260	C₂×C₃×C₈	C₂⁴	1	4	yes	—
261	C₂×C₃×C₈	C₂⁴	1	4	yes	—
262	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
263	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
264	C₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
265	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
266	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
267	C₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
268	C₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
269	C₃×C₄²	C₂²×C₄	1	4	yes	—
270	C₃×C₄²	C₂⁴	1	4	yes	—
271	C₂×#41	—	2	4	no	—
272	C₂×#41	—	2	4	no	—
273	C₂×#41	—	2	4	no	—
274	C₂×#41	—	2	4	no	—
275	C₂×#41	C₂×C₃×C₄	1	2	yes	—
276	C₂×#41	C₂×C₃×C₄	1	2	yes	—
277	C₂×#41	C₂×C₃×C₄	1	2	yes	—
278	C₂×#41	C₂×C₃×C₄	1	2	yes	—
279	C₂×#41	C₂³×C₃	1	2	yes	—
280	C₂×#41	C₂³×C₃	1	2	yes	—
281	C₂×#41	C₂³×C₃	1	2	yes	—
282	C₂×#41	C₂³×C₃	1	2	yes	—
283	C₂²×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
284	C₂²×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
285	C₂²×D₄	C₂×C₃×C₄	1	2	yes	—
286	C₂²×D₄	C₂×C₃×C₄	1	2	yes	—
287	C₂²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
288	C₂²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
289	C₂³×C₄	C₂³×C₃	1	2	yes	—
290	C₂³×C₄	C₂³×C₃	1	2	yes	—
291	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
292	#131	—	2	16	no	—
293	#131	—	2	16	no	—
294	#131	—	2	16	no	—
295	#131	—	2	16	no	—
296	C₂×M₁₆	—	2	4	no	—
297	C₂×M₁₆	—	2	4	no	—
298	C₂×M₁₆	—	2	16	no	—
299	C₂×M₁₆	—	2	8	no	—
300	C₂×M₁₆	C₃×D₄	1	8	yes	complemented
301	C₂×M₁₆	C₂³×C₃	1	2	yes	—
302	C₂×M₁₆	C₂³×C₃	1	2	yes	—
303	C₂×M₁₆	C₂³×C₃	1	2	yes	—
304	C₂×M₁₆	C₂³×C₃	1	2	yes	—
305	C₂×M₁₆	C₂³×C₃	1	8	yes	—
306	C₂×M₁₆	C₂³×C₃	1	8	yes	—
307	C₂×M₁₆	C₂³×C₃	1	2	yes	—
308	C₂×M₁₆	C₂³×C₃	1	2	yes	—
309	C₂²×C₈	—	2	4	no	—
310	C₂²×C₈	—	2	8	no	—
311	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₃	1	2	yes	—
314	C₂²×C₈	C₂³×C₃	1	2	yes	—
315	C₂²×C₈	C₂³×C₃	1	8	yes	—
316	C₂²×C₈	C₂³×C₃	1	2	yes	—
317	C₂²×C₈	C₂³×C₃	1	2	yes	—
318	C₂²×C₈	C₂³×C₃	1	8	yes	—
319	C₂²×C₈	C₂³×C₃	1	2	yes	—
320	C₄⋊Q₈	C₂×C₃×C₄	1	4	yes	—
321	#127	C₂×C₃×C₄	1	4	yes	—
322	#124	C₂×C₃×C₄	1	4	yes	—
323	#124	C₂×C₃×C₄	1	4	yes	—
324	#123	C₂×C₃×C₄	1	8	yes	—
325	#123	C₂×C₃×C₄	1	8	yes	—
326	C₂²⋊Q₈	C₂×C₃×C₄	1	8	yes	—
327	C₂²⋊Q₈	C₂×C₃×C₄	1	8	yes	—
328	#121	C₂×C₃×C₄	1	8	yes	—
329	#121	C₂×C₃×C₄	1	8	yes	—
330	#121	C₂×C₃×C₄	1	16	yes	—
331	#120	C₂×C₃×C₄	1	8	yes	—
332	#120	C₂×C₃×C₄	1	8	yes	—
333	C₄×D₄	C₂³×C₃	1	16	yes	—
334	#117	C₂×C₃×C₄	1	2	yes	—
335	#117	C₂×C₃×C₄	1	2	yes	—
336	#117	C₂³×C₃	1	2	yes	—
337	#117	C₂³×C₃	1	2	yes	—
338	C₂×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
339	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
340	C₂×C₄²	C₂³×C₃	1	2	yes	—
341	C₄⋊C₈	C₂³×C₃	1	8	yes	—
342	C₄⋊C₈	C₂³×C₃	1	8	yes	—
343	C₂²⋊C₈	C₂³×C₃	1	8	yes	—
344	C₂²⋊C₈	C₂³×C₃	1	8	yes	—
345	C₂²⋊C₈	C₂³×C₃	1	16	yes	—
346	#97	C₂³×C₃	1	8	yes	—
347	C₄×C₈	C₂³×C₃	1	8	yes	—
348	C₂³×C₃	—	2	4	no	—
349	C₂³×C₃	—	2	4	no	—
350	C₂³×C₃	—	4	2	no	—
351	C₂³×C₃	—	4	4	no	—
352	C₂³×C₃	—	4	4	no	—
353	C₂³×C₃	C₄×D₄	1	4	yes	—
354	C₂³×C₃	C₂³×C₄	1	4	yes	—
355	C₂³×C₃	C₂³×C₄	1	4	yes	—
356	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
357	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
358	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
359	C₃×Q₈	—	2	4	no	—
360	C₃×Q₈	—	2	4	no	—
361	C₃×Q₈	—	2	4	no	—
362	C₃×Q₈	—	2	4	no	—
363	C₃×D₄	—	2	8	no	—
364	C₃×D₄	—	2	8	no	—
365	C₃×D₄	—	2	8	no	—
366	C₃×D₄	—	2	8	no	—
367	C₃×D₄	—	2	4	no	—
368	C₃×D₄	—	2	4	no	—
369	C₃×D₄	—	2	4	no	—
370	C₃×D₄	—	2	4	no	—
371	C₃×D₄	—	4	16	no	—
372	C₂×C₃×C₄	—	2	4	no	—
373	C₂×C₃×C₄	—	2	4	no	—
374	C₂×C₃×C₄	—	2	8	no	—
375	C₂×C₃×C₄	—	2	8	no	—
376	C₂×C₃×C₄	—	2	4	no	—
377	C₂×C₃×C₄	—	2	4	no	—
378	C₂×C₃×C₄	—	2	4	no	—
379	C₂×C₃×C₄	—	2	4	no	—
380	C₂×C₃×C₄	—	4	4	no	—
381	C₂×C₃×C₄	C₄×D₄	1	4	yes	—
382	C₂×C₃×C₄	C₄×D₄	1	4	yes	—
383	C₂×C₃×C₄	C₄×D₄	1	4	yes	—
384	C₂×C₃×C₄	C₂³×C₄	1	8	yes	—
385	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
386	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
387	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
391	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
392	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
393	C₂×C₃×C₄	C₂×#41	1	2	yes	—
394	C₂×C₃×C₄	C₂×#41	1	2	yes	—
395	C₂×C₃×C₄	C₂×#41	1	2	yes	—
396	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
397	C₃×C₈	—	2	2	no	—
398	C₃×C₈	—	2	2	no	—
399	C₃×C₈	—	2	4	no	—
400	C₃×C₈	—	2	4	no	—
401	C₃×C₈	C₂²×D₄	1	8	yes	—
402	C₂⁴	C₂²×C₃×C₄	1	2	yes	—
403	C₂⁴	C₂²×C₃×C₄	1	2	yes	—
404	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
405	#41	—	2	8	no	—
406	#41	—	2	8	no	—
407	#41	—	2	8	no	—
408	#41	—	2	8	no	—
409	#41	—	2	4	no	—
410	#41	—	2	4	no	—
411	#41	—	2	4	no	—
412	#41	—	2	4	no	—
413	#41	—	2	4	no	—
414	#41	—	2	4	no	—
415	#41	—	2	4	no	—
416	#41	—	2	4	no	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	—	2	4	no	—
419	C₂×Q₈	C₂²×C₃×C₄	1	2	yes	—
420	C₂×Q₈	C₂²×C₃×C₄	1	2	yes	—
421	C₂×Q₈	C₂²×C₃×C₄	1	2	yes	—
422	C₂×Q₈	C₂²×C₃×C₄	1	2	yes	—
423	C₂×D₄	—	2	8	no	—
424	C₂×D₄	—	2	8	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
428	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
429	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
430	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
431	C₂×D₄	C₂²×C₃×C₄	1	2	yes	—
432	C₂×D₄	C₂²×C₃×C₄	1	2	yes	—
433	C₂×D₄	C₂²×C₃×C₄	1	2	yes	—
434	C₂×D₄	C₂²×C₃×C₄	1	2	yes	—
435	C₂×D₄	C₂²×C₃×C₄	1	16	yes	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
441	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
442	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
443	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
444	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
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	C₂×C₃×D₄	1	4	yes	—
449	C₂²×C₄	C₃×#41	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
451	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
453	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
454	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
455	M₁₆	—	2	4	no	—
456	M₁₆	—	2	4	no	—
457	M₁₆	—	2	4	no	—
458	M₁₆	—	2	4	no	—
459	M₁₆	—	2	16	no	—
460	M₁₆	—	2	16	no	—
461	M₁₆	C₂×C₃×D₄	1	8	yes	—
462	M₁₆	C₂×C₃×D₄	1	8	yes	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	4	no	—
466	C₂×C₈	—	2	4	no	—
467	C₂×C₈	—	2	4	no	—
468	C₂×C₈	—	2	4	no	—
469	C₂×C₈	—	2	16	no	—
470	C₂×C₈	—	2	16	no	—
471	C₂×C₈	C₂×C₃×D₄	1	8	yes	—
472	C₂×C₈	C₂⁴×C₃	1	4	yes	—
473	C₂×C₈	C₂⁴×C₃	1	2	yes	—
474	C₂×C₈	C₂⁴×C₃	1	2	yes	—
475	C₂×C₈	C₂⁴×C₃	1	4	yes	—
476	C₂×C₈	C₂⁴×C₃	1	4	yes	—
477	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
478	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
479	C₄⋊C₄	C₂²×C₃×C₄	1	16	yes	—
480	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
481	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
482	C₂²⋊C₄	C₂²×C₃×C₄	1	16	yes	—
483	C₂²⋊C₄	C₂²×C₃×C₄	1	16	yes	—
484	C₄²	C₂²×C₃×C₄	1	4	yes	—
485	C₄²	C₂⁴×C₃	1	4	yes	—
486	C₂²×C₃	—	2	2	no	—
487	C₂²×C₃	—	2	2	no	—
488	C₂²×C₃	—	2	2	no	—
489	C₂²×C₃	—	2	4	no	—
490	C₂²×C₃	—	2	4	no	—
491	C₂²×C₃	—	2	8	no	—
492	C₂²×C₃	—	2	8	no	—
493	C₂²×C₃	—	4	4	no	—
494	C₂²×C₃	—	4	8	no	—
495	C₂²×C₃	—	8	4	no	—
496	C₂²×C₃	C₂×C₄×D₄	1	2	yes	—
497	C₂²×C₃	C₂×C₄×D₄	1	2	yes	—
498	C₂²×C₃	C₂×C₄×D₄	1	2	yes	—
499	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
500	C₃×C₄	—	2	4	no	—
501	C₃×C₄	—	2	4	no	—
502	C₃×C₄	—	2	8	no	—
503	C₃×C₄	C₂×C₄×D₄	1	2	yes	—
504	C₃×C₄	C₂×C₄×D₄	1	2	yes	—
505	C₃×C₄	C₂×C₄×D₄	1	2	yes	—
506	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
507	C₃×C₄	C₂²×#41	1	1	yes	characteristic
508	C₂³	—	2	4	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	4	2	no	—
511	C₂³	—	4	4	no	—
512	C₂³	—	4	4	no	—
513	C₂³	C₃×C₄×D₄	1	4	yes	—
514	C₂³	C₂³×C₃×C₄	1	4	yes	—
515	C₂³	C₂³×C₃×C₄	1	4	yes	—
516	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
517	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
518	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
519	Q₈	—	2	4	no	—
520	Q₈	—	2	4	no	—
521	Q₈	—	2	4	no	—
522	Q₈	—	2	4	no	—
523	D₄	—	2	8	no	—
524	D₄	—	2	8	no	—
525	D₄	—	2	8	no	—
526	D₄	—	2	8	no	—
527	D₄	—	2	4	no	—
528	D₄	—	2	4	no	—
529	D₄	—	2	4	no	—
530	D₄	—	2	4	no	—
531	D₄	—	4	16	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	8	no	—
539	C₂×C₄	—	2	8	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	C₃×C₄×D₄	1	4	yes	—
542	C₂×C₄	C₃×C₄×D₄	1	4	yes	—
543	C₂×C₄	C₃×C₄×D₄	1	4	yes	—
544	C₂×C₄	C₂³×C₃×C₄	1	8	yes	—
545	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
546	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
547	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
548	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
549	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
550	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
551	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
552	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
553	C₂×C₄	C₂×C₃×#41	1	2	yes	—
554	C₂×C₄	C₂×C₃×#41	1	2	yes	—
555	C₂×C₄	C₂×C₃×#41	1	2	yes	—
556	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
557	C₈	—	2	2	no	—
558	C₈	—	2	2	no	—
559	C₈	—	2	4	no	—
560	C₈	—	2	4	no	—
561	C₈	C₂²×C₃×D₄	1	8	yes	—
562	C₂×C₃	—	2	2	no	—
563	C₂×C₃	—	2	2	no	—
564	C₂×C₃	—	2	2	no	—
565	C₂×C₃	—	4	4	no	—
566	C₂×C₃	—	4	4	no	—
567	C₂×C₃	C₂²×C₄×D₄	1	1	yes	characteristic
568	C₂×C₃	#3573	1	2	yes	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	4	no	—
573	C₂²	—	2	4	no	—
574	C₂²	—	2	8	no	—
575	C₂²	—	2	8	no	—
576	C₂²	—	4	4	no	—
577	C₂²	—	4	8	no	—
578	C₂²	—	8	4	no	—
579	C₂²	C₂×C₃×C₄×D₄	1	2	yes	—
580	C₂²	C₂×C₃×C₄×D₄	1	2	yes	—
581	C₂²	C₂×C₃×C₄×D₄	1	2	yes	—
582	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
583	C₄	—	2	4	no	—
584	C₄	—	2	4	no	—
585	C₄	—	2	8	no	—
586	C₄	C₂×C₃×C₄×D₄	1	2	yes	—
587	C₄	C₂×C₃×C₄×D₄	1	2	yes	—
588	C₄	C₂×C₃×C₄×D₄	1	2	yes	—
589	C₄	C₂³×C₃×D₄	1	1	yes	characteristic
590	C₄	C₂²×C₃×#41	1	1	yes	characteristic
591	C₃	#60142	1	1	yes	characteristic, direct product factor, Sylow
592	C₂	—	2	2	no	—
593	C₂	—	2	2	no	—
594	C₂	—	2	2	no	—
595	C₂	—	4	4	no	—
596	C₂	—	4	4	no	—
597	C₂	C₂²×C₃×C₄×D₄	1	1	yes	characteristic
598	C₂	C₃×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂²×C₃	C₂⁴×C₄
prime radical	C₃×#3449	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#568	C₂	semidirect
2. C₂²×C₃×#131	C₂	semidirect
4. C₃×#2935	C₂	semidirect
5. C₃×#2933	C₂	semidirect
6. C₃×#2930	C₂	semidirect
7. C₃×#2929	C₂	semidirect
8. C₂×C₃×#424	C₂	semidirect
9. C₃×#2879	C₂	semidirect
10. C₂×C₃×#408	C₂	semidirect
11. C₃×#2873	C₂	semidirect
12. #60142	C₃	direct (N × H)
19. C₂×C₃×#131	C₂²	semidirect
20. C₂×C₃×#131	C₂²	semidirect
24. C₂²×C₃×M₁₆	C₂²	semidirect
25. C₂²×C₃×M₁₆	C₂²	semidirect
27. C₂³×C₃×C₈	C₂²	semidirect
38. C₃×#436	C₂²	semidirect
39. C₃×#435	C₂²	semidirect
40. C₃×#435	C₂²	semidirect
41. C₃×C₈×D₄	C₂²	semidirect
42. C₃×#424	C₂²	semidirect
43. C₃×#424	C₂²	semidirect
44. C₃×#424	C₂²	semidirect
45. C₂×C₃×C₄⋊C₈	C₂²	semidirect
49. C₃×#408	C₂²	semidirect
50. C₃×#408	C₂²	semidirect
51. C₃×#407	C₂²	semidirect
52. C₂×C₃×C₂²⋊C₈	C₂²	semidirect
53. C₃×#405	C₂²	semidirect
54. C₃×#405	C₂²	semidirect
55. C₃×C₄×M₁₆	C₂²	semidirect
56. C₂×#568	C₂×C₃	semidirect
57. C₂²×#131	C₂×C₃	semidirect
59. #2935	C₂×C₃	semidirect
60. #2933	C₂×C₃	semidirect
61. #2930	C₂×C₃	semidirect
62. #2929	C₂×C₃	semidirect
63. C₂×#424	C₂×C₃	semidirect
64. #2879	C₂×C₃	semidirect
65. C₂×#408	C₂×C₃	semidirect
66. #2873	C₂×C₃	semidirect
96. C₂×C₃×M₁₆	D₄	semidirect
150. C₂×#131	C₂²×C₃	semidirect
151. C₂×#131	C₂²×C₃	semidirect
155. C₂²×M₁₆	C₂²×C₃	semidirect
156. C₂²×M₁₆	C₂²×C₃	semidirect
158. C₂³×C₈	C₂²×C₃	semidirect
169. #436	C₂²×C₃	semidirect
170. #435	C₂²×C₃	semidirect
171. #435	C₂²×C₃	semidirect
172. C₈×D₄	C₂²×C₃	semidirect
173. #424	C₂²×C₃	semidirect
174. #424	C₂²×C₃	semidirect
175. #424	C₂²×C₃	semidirect
176. C₂×C₄⋊C₈	C₂²×C₃	semidirect
180. #408	C₂²×C₃	semidirect
181. #408	C₂²×C₃	semidirect
182. #407	C₂²×C₃	semidirect
183. C₂×C₂²⋊C₈	C₂²×C₃	semidirect
184. #405	C₂²×C₃	semidirect
185. #405	C₂²×C₃	semidirect
186. C₄×M₁₆	C₂²×C₃	semidirect
300. C₂×M₁₆	C₃×D₄	semidirect
591. C₃	#60142	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×#568	2
C₂²×C₃×#131	2
C₃×#3449	2
C₃×#2935	2
C₃×#2933	2
C₃×#2930	2
C₃×#2929	2
C₂×C₃×#424	2
C₃×#2879	2
C₂×C₃×#408	2
C₃×#2873	2
#60142	3

Subgroups — C3×#60142 #10678749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60142 #10678749