Subgroups — C₃×#79282 #11858809

Order 1152.

1027 conjugacy classes of subgroups.

The subgroup lattice has 615 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#4925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4837	C₂	1	2	yes	maximal, complemented
5	C₃×#4835	C₂	1	2	yes	maximal, complemented
6	C₃×#4726	C₂	1	2	yes	maximal
7	C₃×#4719	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal, complemented
9	C₃×#4685	C₂	1	2	yes	maximal, complemented
10	C₃×#2920	—	3	1	no	maximal
11	#79282	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂²×C₃×C₄×D₃	C₄	1	1	yes	characteristic
13	C₂²×C₃×C₄×D₃	C₄	1	1	yes	characteristic
14	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
15	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×Dic₃	C₄	1	1	yes	characteristic
17	C₂×C₃×C₄×Dic₃	C₄	1	1	yes	characteristic
18	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
20	C₃×C₄²×D₃	C₄	1	1	yes	characteristic
21	C₃×C₄²×D₃	C₄	1	1	yes	characteristic
22	C₃×C₄²×D₃	C₄	1	1	yes	characteristic
23	C₃×C₄²×D₃	C₄	1	1	yes	characteristic
24	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
25	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
26	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
27	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
28	C₃²×C₄⋊C₈	C₂²	1	2	yes	complemented
29	C₃²×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₃²×C₄×C₈	C₂²	1	2	yes	complemented
31	C₃×#830	C₂²	1	2	yes	—
32	C₃×(C₂×D₃)⋊C₈	C₂²	1	4	yes	—
33	C₃×#815	C₂²	1	4	yes	complemented
34	C₃×Dic₃⋊C₈	C₂²	1	4	yes	complemented
35	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
36	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	complemented
37	C₂²×C₃×C₄²	—	3	1	no	—
38	C₂×C₄²×D₃	C₂×C₃	1	1	yes	characteristic
39	C₃×#432	—	3	2	no	—
40	C₃×#432	—	3	2	no	—
41	C₃×#431	—	2	1	no	—
42	C₃×#431	—	3	1	no	—
43	C₃×#431	—	3	2	no	—
44	C₃×#431	D₃	1	1	yes	characteristic, complemented
45	C₃×#431	C₂×C₃	1	1	yes	characteristic, complemented
46	C₃×#423	—	3	2	no	—
47	C₃×#407	—	3	2	no	—
48	C₃×C₄×M₁₆	—	3	2	no	—
49	#4925	C₂×C₃	1	1	yes	characteristic, complemented
50	#4837	C₂×C₃	1	2	yes	complemented
51	#4835	C₂×C₃	1	2	yes	complemented
52	#4726	C₂×C₃	1	2	yes	—
53	#4719	C₂×C₃	1	2	yes	complemented
54	C₄×ΓL(1,𝔽₂₅)	C₂×C₃	1	2	yes	complemented
55	#4685	C₂×C₃	1	2	yes	complemented
56	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
60	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×C₄×D₃	—	2	4	no	—
64	C₂×C₃×C₄×D₃	—	2	4	no	—
65	C₂×C₃×C₄×D₃	—	2	4	no	—
66	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
78	C₂×C₃²×C₈	C₂³	1	4	yes	—
79	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
80	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
81	C₃²×C₄²	C₂³	1	1	yes	characteristic
82	C₃²×C₄²	C₂³	1	1	yes	characteristic
83	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
84	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
85	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
86	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
87	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
88	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
89	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
90	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
91	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
92	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
93	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
94	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
96	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
97	#2920	—	3	1	no	Sylow
98	C₂³×C₃×C₄	—	3	1	no	—
99	C₂³×C₃×C₄	—	3	1	no	—
100	C₂³×C₃×C₄	—	3	1	no	—
101	C₂²×C₄×D₃	C₃×C₄	1	1	yes	characteristic
102	C₂²×C₄×D₃	C₃×C₄	1	1	yes	characteristic
103	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₃×M₁₆	—	3	4	no	—
105	C₂×C₃×C₄²	—	2	1	no	—
106	C₂×C₃×C₄²	—	3	1	no	—
107	C₂×C₃×C₄²	—	3	1	no	—
108	C₂×C₃×C₄²	—	3	1	no	—
109	C₂×C₃×C₄²	—	3	1	no	—
110	C₂×C₃×C₄²	—	3	1	no	—
111	C₂×C₃×C₄²	—	3	1	no	—
112	C₂×C₃×C₄²	—	3	1	no	—
113	C₂×C₃×C₄²	—	3	1	no	—
114	C₂×C₃×C₄²	—	3	1	no	—
115	C₂×C₃×C₄²	—	3	1	no	—
116	C₂×C₃×C₄²	—	3	1	no	—
117	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
118	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₄×Dic₃	C₃×C₄	1	1	yes	characteristic
120	C₂×C₄×Dic₃	C₃×C₄	1	1	yes	characteristic
121	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
122	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	4	yes	—
123	C₄²×D₃	C₃×C₄	1	1	yes	characteristic
124	C₄²×D₃	C₃×C₄	1	1	yes	characteristic
125	C₄²×D₃	C₃×C₄	1	1	yes	characteristic
126	C₄²×D₃	C₃×C₄	1	1	yes	characteristic
127	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
128	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
129	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
130	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
131	C₃×C₄⋊C₈	—	2	2	no	—
132	C₃×C₄⋊C₈	—	3	4	no	—
133	C₃×C₄⋊C₈	—	3	2	no	—
134	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	complemented
135	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
136	C₃×C₂²⋊C₈	—	2	2	no	—
137	C₃×C₂²⋊C₈	—	3	2	no	—
138	C₃×C₂²⋊C₈	—	3	4	no	—
139	C₃×C₂²⋊C₈	C₂×D₃	1	2	yes	—
140	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
141	C₃×#97	—	3	4	no	—
142	C₃×C₄×C₈	—	2	2	no	—
143	C₃×C₄×C₈	—	3	2	no	—
144	C₃×C₄×C₈	C₂×D₃	1	2	yes	complemented
145	C₃×C₄×C₈	C₂²×C₃	1	2	yes	complemented
146	#830	C₂²×C₃	1	2	yes	—
147	(C₂×D₃)⋊C₈	C₂²×C₃	1	4	yes	—
148	#815	C₂²×C₃	1	4	yes	complemented
149	Dic₃⋊C₈	C₂²×C₃	1	4	yes	complemented
150	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	complemented
151	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	complemented
152	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₃×D₃	—	2	2	no	—
154	C₂²×C₃×D₃	—	2	2	no	—
155	C₂²×C₃×D₃	—	2	2	no	—
156	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₃²×C₄	—	2	2	no	—
159	C₂×C₃²×C₄	—	2	2	no	—
160	C₂×C₃²×C₄	M₁₆	1	4	yes	complemented
161	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
167	C₂×C₃×Dic₃	—	2	2	no	—
168	C₂×C₃×Dic₃	—	2	2	no	—
169	C₂×C₃×Dic₃	—	2	2	no	—
170	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
176	C₃×C₄×D₃	—	2	2	no	—
177	C₃×C₄×D₃	—	2	2	no	—
178	C₃×C₄×D₃	—	2	2	no	—
179	C₃×C₄×D₃	—	2	2	no	—
180	C₃×C₄×D₃	—	2	2	no	—
181	C₃×C₄×D₃	—	2	2	no	—
182	C₃×C₄×D₃	—	2	2	no	—
183	C₃×C₄×D₃	—	2	2	no	—
184	C₃×C₄×D₃	—	2	2	no	—
185	C₃×C₄×D₃	—	2	2	no	—
186	C₃×C₄×D₃	M₁₆	1	4	yes	complemented
187	C₃×C₄×D₃	#41	1	4	yes	—
188	C₃²×C₈	—	2	4	no	—
189	C₃×C₃⋊C₈	—	2	4	no	—
190	C₂²×C₄²	—	3	1	no	—
191	#432	—	3	2	no	—
192	#432	—	3	2	no	—
193	#431	—	3	1	no	—
194	#431	—	3	2	no	—
195	#431	C₃×D₃	1	1	yes	characteristic, complemented
196	#423	—	3	2	no	—
197	#407	—	3	2	no	—
198	C₄×M₁₆	—	3	2	no	—
199	C₂⁴×C₃	—	3	1	no	—
200	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
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	—	3	1	no	—
205	C₂²×C₃×C₄	—	3	1	no	—
206	C₂²×C₃×C₄	—	3	1	no	—
207	C₂²×C₃×C₄	—	3	1	no	—
208	C₂²×C₃×C₄	—	3	1	no	—
209	C₂²×C₃×C₄	—	3	1	no	—
210	C₂²×C₃×C₄	—	3	1	no	—
211	C₂²×C₃×C₄	—	3	1	no	—
212	C₂²×C₃×C₄	—	3	1	no	—
213	C₂²×C₃×C₄	—	3	1	no	—
214	C₂²×C₃×C₄	—	3	1	no	—
215	C₂²×C₃×C₄	—	3	1	no	—
216	C₂²×C₃×C₄	—	3	1	no	—
217	C₂²×C₃×C₄	—	3	1	no	—
218	C₂²×C₃×C₄	—	3	1	no	—
219	C₂²×C₃×C₄	—	6	4	no	—
220	C₂²×C₃×C₄	—	6	4	no	—
221	C₂²×C₃×C₄	—	6	4	no	—
222	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
228	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
229	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
230	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
231	C₂×C₄×D₃	—	2	4	no	—
232	C₂×C₄×D₃	—	2	4	no	—
233	C₂×C₄×D₃	—	2	4	no	—
234	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
235	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
236	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
237	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
238	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
239	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
240	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
241	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
242	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
243	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
244	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
245	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
246	C₃×M₁₆	—	6	8	no	—
247	C₂×C₃×C₈	—	2	4	no	—
248	C₂×C₃×C₈	—	3	4	no	—
249	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
250	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
251	C₃×C₄²	—	2	1	no	—
252	C₃×C₄²	—	2	1	no	—
253	C₃×C₄²	—	2	1	no	—
254	C₃×C₄²	—	2	1	no	—
255	C₃×C₄²	—	3	1	no	—
256	C₃×C₄²	—	3	1	no	—
257	C₃×C₄²	—	3	1	no	—
258	C₃×C₄²	—	3	1	no	—
259	C₃×C₄²	—	3	1	no	—
260	C₃×C₄²	—	3	1	no	—
261	C₃×C₄²	—	3	1	no	—
262	C₃×C₄²	—	3	1	no	—
263	C₃×C₄²	—	3	1	no	—
264	C₃×C₄²	—	3	1	no	—
265	C₃×C₄²	—	3	1	no	—
266	C₃×C₄²	—	3	1	no	—
267	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
268	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
269	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
270	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
271	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
272	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
273	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
274	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
275	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
276	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
277	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
278	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
279	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
280	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
281	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
282	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
283	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
284	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
285	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
286	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
287	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
288	ΓL(1,𝔽₂₅)	—	2	8	no	—
289	C₂²×C₃²	—	2	1	no	—
290	C₂²×C₃²	—	2	1	no	—
291	C₂²×C₃²	C₂×M₁₆	1	2	yes	—
292	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
293	C₂×C₃×D₃	—	2	8	no	—
294	C₂×C₃×D₃	—	2	1	no	—
295	C₂×C₃×D₃	—	2	1	no	—
296	C₂×C₃×D₃	—	2	1	no	—
297	C₂×C₃×D₃	—	2	1	no	—
298	C₂×C₃×D₃	#117	1	2	yes	—
299	C₂×C₃×D₃	C₂×M₁₆	1	2	yes	—
300	C₃²×C₄	—	2	1	no	—
301	C₃²×C₄	—	2	1	no	—
302	C₃²×C₄	C₂×M₁₆	1	2	yes	—
303	C₃²×C₄	C₂×M₁₆	1	2	yes	—
304	C₃²×C₄	C₂×M₁₆	1	2	yes	—
305	C₃²×C₄	C₂×#41	1	2	yes	—
306	C₃×Dic₃	—	2	1	no	—
307	C₃×Dic₃	—	2	1	no	—
308	C₃×Dic₃	—	2	1	no	—
309	C₃×Dic₃	—	2	1	no	—
310	C₃×Dic₃	#117	1	2	yes	—
311	C₃×Dic₃	C₂×M₁₆	1	2	yes	—
312	C₂³×C₄	—	3	1	no	—
313	C₂³×C₄	—	3	1	no	—
314	C₂³×C₄	—	3	1	no	—
315	C₂×M₁₆	—	3	4	no	—
316	C₂×C₄²	—	3	1	no	—
317	C₂×C₄²	—	3	1	no	—
318	C₂×C₄²	—	3	1	no	—
319	C₂×C₄²	—	3	1	no	—
320	C₂×C₄²	—	3	1	no	—
321	C₂×C₄²	—	3	1	no	—
322	C₂×C₄²	—	3	1	no	—
323	C₂×C₄²	—	3	1	no	—
324	C₂×C₄²	—	3	1	no	—
325	C₂×C₄²	—	3	1	no	—
326	C₂×C₄²	—	3	1	no	—
327	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
328	C₄⋊C₈	—	3	4	no	—
329	C₄⋊C₈	—	3	2	no	—
330	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	complemented
331	C₂²⋊C₈	—	3	2	no	—
332	C₂²⋊C₈	—	3	4	no	—
333	C₂²⋊C₈	C₂×C₃×D₃	1	2	yes	—
334	#97	—	3	4	no	—
335	C₄×C₈	—	3	2	no	—
336	C₄×C₈	C₂×C₃×D₃	1	2	yes	complemented
337	C₂³×C₃	—	2	1	no	—
338	C₂³×C₃	—	3	1	no	—
339	C₂³×C₃	—	3	1	no	—
340	C₂³×C₃	—	6	2	no	—
341	C₂³×C₃	—	6	2	no	—
342	C₂³×C₃	—	6	2	no	—
343	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
344	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
345	C₂²×D₃	—	2	2	no	—
346	C₂²×D₃	—	2	2	no	—
347	C₂²×D₃	—	2	2	no	—
348	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
349	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	2	no	—
352	C₂×C₃×C₄	—	2	2	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	1	no	—
355	C₂×C₃×C₄	—	2	4	no	—
356	C₂×C₃×C₄	—	2	1	no	—
357	C₂×C₃×C₄	—	2	1	no	—
358	C₂×C₃×C₄	—	2	1	no	—
359	C₂×C₃×C₄	—	2	1	no	—
360	C₂×C₃×C₄	—	2	1	no	—
361	C₂×C₃×C₄	—	3	1	no	—
362	C₂×C₃×C₄	—	3	1	no	—
363	C₂×C₃×C₄	—	3	4	no	—
364	C₂×C₃×C₄	—	3	4	no	—
365	C₂×C₃×C₄	—	3	1	no	—
366	C₂×C₃×C₄	—	3	1	no	—
367	C₂×C₃×C₄	—	3	1	no	—
368	C₂×C₃×C₄	—	3	1	no	—
369	C₂×C₃×C₄	—	4	2	no	—
370	C₂×C₃×C₄	—	4	2	no	—
371	C₂×C₃×C₄	—	6	2	no	—
372	C₂×C₃×C₄	—	6	2	no	—
373	C₂×C₃×C₄	—	6	2	no	—
374	C₂×C₃×C₄	—	6	2	no	—
375	C₂×C₃×C₄	—	6	2	no	—
376	C₂×C₃×C₄	—	6	2	no	—
377	C₂×C₃×C₄	—	6	2	no	—
378	C₂×C₃×C₄	—	6	2	no	—
379	C₂×C₃×C₄	—	6	2	no	—
380	C₂×C₃×C₄	—	6	2	no	—
381	C₂×C₃×C₄	—	6	2	no	—
382	C₂×C₃×C₄	—	6	2	no	—
383	C₂×C₃×C₄	—	6	2	no	—
384	C₂×C₃×C₄	ΓL(1,𝔽₂₅)	1	4	yes	complemented
385	C₂×C₃×C₄	C₃×M₁₆	1	4	yes	complemented
386	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
392	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
393	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
394	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
395	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
396	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
397	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
398	C₂×Dic₃	—	2	2	no	—
399	C₂×Dic₃	—	2	2	no	—
400	C₂×Dic₃	—	2	2	no	—
401	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
402	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
403	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
404	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
405	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
406	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
407	C₄×D₃	—	2	2	no	—
408	C₄×D₃	—	2	2	no	—
409	C₄×D₃	—	2	2	no	—
410	C₄×D₃	—	2	2	no	—
411	C₄×D₃	—	2	2	no	—
412	C₄×D₃	—	2	2	no	—
413	C₄×D₃	—	2	2	no	—
414	C₄×D₃	—	2	2	no	—
415	C₄×D₃	—	2	2	no	—
416	C₄×D₃	—	2	2	no	—
417	C₄×D₃	C₃×M₁₆	1	4	yes	complemented
418	C₄×D₃	C₃×#41	1	4	yes	—
419	C₃×C₈	—	2	4	no	—
420	C₃×C₈	—	2	4	no	—
421	C₃×C₈	—	4	4	no	—
422	C₃×C₈	—	6	4	no	—
423	C₃⋊C₈	—	2	4	no	—
424	C₂×C₃²	—	2	2	no	—
425	C₂×C₃²	C₂×#117	1	1	yes	characteristic
426	C₂×C₃²	C₂²×M₁₆	1	1	yes	characteristic
427	C₂×C₃²	C₂²×M₁₆	1	1	yes	characteristic
428	C₃×D₃	—	2	2	no	—
429	C₃×D₃	—	2	2	no	—
430	C₂⁴	—	3	1	no	—
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	1	no	—
434	C₂²×C₄	—	3	1	no	—
435	C₂²×C₄	—	3	1	no	—
436	C₂²×C₄	—	3	1	no	—
437	C₂²×C₄	—	3	1	no	—
438	C₂²×C₄	—	3	1	no	—
439	C₂²×C₄	—	3	1	no	—
440	C₂²×C₄	—	3	1	no	—
441	C₂²×C₄	—	3	1	no	—
442	C₂²×C₄	—	3	1	no	—
443	C₂²×C₄	—	3	1	no	—
444	C₂²×C₄	—	3	1	no	—
445	C₂²×C₄	—	3	1	no	—
446	C₂²×C₄	—	6	4	no	—
447	C₂²×C₄	—	6	4	no	—
448	C₂²×C₄	—	6	4	no	—
449	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
450	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
451	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
452	M₁₆	—	6	8	no	—
453	C₂×C₈	—	3	4	no	—
454	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
455	C₄²	—	3	1	no	—
456	C₄²	—	3	1	no	—
457	C₄²	—	3	1	no	—
458	C₄²	—	3	1	no	—
459	C₄²	—	3	1	no	—
460	C₄²	—	3	1	no	—
461	C₄²	—	3	1	no	—
462	C₄²	—	3	1	no	—
463	C₄²	—	3	1	no	—
464	C₄²	—	3	1	no	—
465	C₄²	—	3	1	no	—
466	C₄²	—	3	1	no	—
467	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
468	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
469	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
470	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
471	C₂²×C₃	—	2	1	no	—
472	C₂²×C₃	—	2	1	no	—
473	C₂²×C₃	—	2	1	no	—
474	C₂²×C₃	—	2	1	no	—
475	C₂²×C₃	—	2	2	no	—
476	C₂²×C₃	—	2	1	no	—
477	C₂²×C₃	—	3	2	no	—
478	C₂²×C₃	—	3	2	no	—
479	C₂²×C₃	—	4	1	no	—
480	C₂²×C₃	—	4	1	no	—
481	C₂²×C₃	—	6	8	no	—
482	C₂²×C₃	—	6	1	no	—
483	C₂²×C₃	—	6	1	no	—
484	C₂²×C₃	—	6	1	no	—
485	C₂²×C₃	—	6	1	no	—
486	C₂²×C₃	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
487	C₂²×C₃	C₂×C₃×M₁₆	1	2	yes	—
488	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
489	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
490	C₂×D₃	—	2	8	no	—
491	C₂×D₃	—	2	1	no	—
492	C₂×D₃	—	2	1	no	—
493	C₂×D₃	—	2	1	no	—
494	C₂×D₃	—	2	1	no	—
495	C₂×D₃	C₃×#117	1	2	yes	—
496	C₂×D₃	C₂×C₃×M₁₆	1	2	yes	—
497	C₃×C₄	—	2	1	no	—
498	C₃×C₄	—	2	1	no	—
499	C₃×C₄	—	2	1	no	—
500	C₃×C₄	—	2	1	no	—
501	C₃×C₄	—	2	2	no	—
502	C₃×C₄	—	2	2	no	—
503	C₃×C₄	—	2	2	no	—
504	C₃×C₄	—	2	2	no	—
505	C₃×C₄	—	3	2	no	—
506	C₃×C₄	—	3	2	no	—
507	C₃×C₄	—	4	1	no	—
508	C₃×C₄	—	4	1	no	—
509	C₃×C₄	—	6	1	no	—
510	C₃×C₄	—	6	1	no	—
511	C₃×C₄	—	6	1	no	—
512	C₃×C₄	—	6	1	no	—
513	C₃×C₄	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
514	C₃×C₄	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
515	C₃×C₄	D₃×M₁₆	1	2	yes	—
516	C₃×C₄	C₂×C₃×M₁₆	1	2	yes	—
517	C₃×C₄	C₂×C₃×M₁₆	1	2	yes	—
518	C₃×C₄	C₂×C₃×M₁₆	1	2	yes	—
519	C₃×C₄	D₃×#41	1	2	yes	—
520	C₃×C₄	C₂×C₃×#41	1	2	yes	—
521	Dic₃	—	2	1	no	—
522	Dic₃	—	2	1	no	—
523	Dic₃	—	2	1	no	—
524	Dic₃	—	2	1	no	—
525	Dic₃	C₃×#117	1	2	yes	—
526	Dic₃	C₂×C₃×M₁₆	1	2	yes	—
527	C₃²	#2920	1	1	yes	characteristic, complemented, Sylow
528	C₂³	—	3	1	no	—
529	C₂³	—	3	1	no	—
530	C₂³	—	6	2	no	—
531	C₂³	—	6	2	no	—
532	C₂³	—	6	2	no	—
533	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	3	1	no	—
537	C₂×C₄	—	3	1	no	—
538	C₂×C₄	—	3	4	no	—
539	C₂×C₄	—	3	4	no	—
540	C₂×C₄	—	3	1	no	—
541	C₂×C₄	—	3	1	no	—
542	C₂×C₄	—	3	1	no	—
543	C₂×C₄	—	3	1	no	—
544	C₂×C₄	—	6	2	no	—
545	C₂×C₄	—	6	2	no	—
546	C₂×C₄	—	6	2	no	—
547	C₂×C₄	—	6	2	no	—
548	C₂×C₄	—	6	2	no	—
549	C₂×C₄	—	6	2	no	—
550	C₂×C₄	—	6	2	no	—
551	C₂×C₄	—	6	2	no	—
552	C₂×C₄	—	6	2	no	—
553	C₂×C₄	—	6	2	no	—
554	C₂×C₄	—	6	2	no	—
555	C₂×C₄	—	6	2	no	—
556	C₂×C₄	—	6	2	no	—
557	C₂×C₄	C₃×ΓL(1,𝔽₂₅)	1	4	yes	complemented
558	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
559	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
560	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
561	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
562	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
563	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
564	C₈	—	2	4	no	—
565	C₈	—	6	4	no	—
566	C₂×C₃	—	2	2	no	—
567	C₂×C₃	—	2	2	no	—
568	C₂×C₃	—	2	1	no	—
569	C₂×C₃	—	2	1	no	—
570	C₂×C₃	—	2	1	no	—
571	C₂×C₃	—	4	2	no	—
572	C₂×C₃	—	6	2	no	—
573	C₂×C₃	—	6	2	no	—
574	C₂×C₃	D₃×#117	1	1	yes	characteristic
575	C₂×C₃	C₂²×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
576	C₂×C₃	C₂×D₃×M₁₆	1	1	yes	characteristic
577	C₂×C₃	C₂×C₃×#117	1	1	yes	characteristic
578	C₂×C₃	C₂²×C₃×M₁₆	1	1	yes	characteristic
579	C₂×C₃	C₂²×C₃×M₁₆	1	1	yes	characteristic
580	D₃	—	2	2	no	—
581	D₃	—	2	2	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	3	2	no	—
585	C₂²	—	3	2	no	—
586	C₂²	—	6	8	no	—
587	C₂²	—	6	1	no	—
588	C₂²	—	6	1	no	—
589	C₂²	—	6	1	no	—
590	C₂²	—	6	1	no	—
591	C₂²	C₂×C₃×ΓL(1,𝔽₂₅)	1	2	yes	—
592	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	3	2	no	—
596	C₄	—	3	2	no	—
597	C₄	—	6	1	no	—
598	C₄	—	6	1	no	—
599	C₄	—	6	1	no	—
600	C₄	—	6	1	no	—
601	C₄	C₂×C₃×ΓL(1,𝔽₂₅)	1	2	yes	—
602	C₄	C₂×C₃×ΓL(1,𝔽₂₅)	1	2	yes	—
603	C₄	C₃×D₃×M₁₆	1	2	yes	—
604	C₄	C₃×D₃×#41	1	2	yes	—
605	C₃	—	2	1	no	—
606	C₃	#79282	1	1	yes	characteristic, direct product factor
607	C₃	C₃×#2920	1	1	yes	characteristic, complemented
608	C₂	—	2	2	no	—
609	C₂	—	6	2	no	—
610	C₂	—	6	2	no	—
611	C₂	C₃×D₃×#117	1	1	yes	characteristic
612	C₂	C₂²×C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
613	C₂	C₂×C₃×D₃×M₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄²	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#431	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#431	D₃
hypocenter	C₃	C₃×#2920
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄² ◁ C₃×#431

Complements

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

N	H ≅ G/N	type
2. C₃²×#431	C₂	semidirect
3. C₃×#4925	C₂	semidirect
4. C₃×#4837	C₂	semidirect
5. C₃×#4835	C₂	semidirect
7. C₃×#4719	C₂	semidirect
8. C₃×C₄×ΓL(1,𝔽₂₅)	C₂	semidirect
9. C₃×#4685	C₂	semidirect
11. #79282	C₃	direct (N × H)
28. C₃²×C₄⋊C₈	C₂²	semidirect
30. C₃²×C₄×C₈	C₂²	semidirect
33. C₃×#815	C₂²	semidirect
34. C₃×Dic₃⋊C₈	C₂²	semidirect
35. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
36. C₃×C₄×C₃⋊C₈	C₂²	semidirect
44. C₃×#431	D₃	semidirect
45. C₃×#431	C₂×C₃	semidirect
49. #4925	C₂×C₃	semidirect
50. #4837	C₂×C₃	semidirect
51. #4835	C₂×C₃	semidirect
53. #4719	C₂×C₃	semidirect
54. C₄×ΓL(1,𝔽₂₅)	C₂×C₃	semidirect
55. #4685	C₂×C₃	semidirect
134. C₃×C₄⋊C₈	C₂×D₃	semidirect
135. C₃×C₄⋊C₈	C₂²×C₃	semidirect
144. C₃×C₄×C₈	C₂×D₃	semidirect
145. C₃×C₄×C₈	C₂²×C₃	semidirect
148. #815	C₂²×C₃	semidirect
149. Dic₃⋊C₈	C₂²×C₃	semidirect
150. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
151. C₄×C₃⋊C₈	C₂²×C₃	semidirect
160. C₂×C₃²×C₄	M₁₆	semidirect
186. C₃×C₄×D₃	M₁₆	semidirect
195. #431	C₃×D₃	semidirect
330. C₄⋊C₈	C₂×C₃×D₃	semidirect
336. C₄×C₈	C₂×C₃×D₃	semidirect
384. C₂×C₃×C₄	ΓL(1,𝔽₂₅)	semidirect
385. C₂×C₃×C₄	C₃×M₁₆	semidirect
417. C₄×D₃	C₃×M₁₆	semidirect
527. C₃²	#2920	semidirect
557. C₂×C₄	C₃×ΓL(1,𝔽₂₅)	semidirect
606. C₃	#79282	direct (N × H)
607. C₃	C₃×#2920	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²×D₃	2
C₃²×#431	2
C₃×#4925	2
C₃×#4837	2
C₃×#4835	2
C₃×#4726	2
C₃×#4719	2
C₃×C₄×ΓL(1,𝔽₂₅)	2
C₃×#4685	2
C₃×#2920	3
#79282	3

Subgroups — C3×#79282 #11858809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79282 #11858809