Subgroups — C₃×#78657 #11859458

Order 1152.

1079 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5832	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#907	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#408	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5118	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5110	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4729	C₂	1	4	yes	maximal, complemented
9	C₃×#67⋊C₈	C₂	1	4	yes	maximal, complemented
10	C₃×#2931	—	3	1	no	maximal
11	#78657	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
13	C₂×C₃×#235	C₂²	1	1	yes	characteristic
14	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
16	C₃×#948	—	2	4	no	—
17	C₃×#947	C₄	1	1	yes	characteristic
18	C₃×#944	C₄	1	1	yes	characteristic
19	C₃×#940	C₄	1	1	yes	characteristic
20	C₃×#939	C₄	1	4	yes	—
21	C₃×#936	C₄	1	1	yes	characteristic
22	C₃×C₄×#67	C₂²	1	4	yes	—
23	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
24	C₂×C₃×#208	C₂²	1	2	yes	—
25	C₂×C₃×#208	C₂²	1	1	yes	characteristic
26	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
27	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₃×#907	—	2	4	no	—
29	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
30	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
31	C₃²×C₂²⋊C₈	C₂²	1	4	yes	—
32	C₃×(C₂×D₃)⋊C₈	C₂²	1	4	yes	—
33	C₃×Dic₃⋊C₈	C₂²	1	4	yes	—
34	C₃×C₈×Dic₃	C₂²	1	2	yes	—
35	C₃×C₈×Dic₃	C₂²	1	2	yes	—
36	C₂×C₃×#131	—	3	1	no	—
37	C₂×C₃×#131	—	3	1	no	—
38	C₃×#532	—	3	1	no	—
39	#5832	C₂×C₃	1	1	yes	characteristic
40	C₂×#948	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×#907	C₂×C₃	1	1	yes	characteristic, complemented
42	C₃×#436	—	3	4	no	—
43	C₃×C₈×D₄	—	3	4	no	—
44	C₃×#423	—	3	1	no	—
45	C₃×#408	—	2	1	no	—
46	C₃×#408	—	3	1	no	—
47	C₃×#408	D₃	1	1	yes	characteristic, complemented
48	C₃×#408	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×C₃×C₄×C₈	—	3	1	no	—
50	#5118	C₂×C₃	1	1	yes	characteristic, complemented
51	#5110	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×C₈×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
53	#4729	C₂×C₃	1	4	yes	complemented
54	#67⋊C₈	C₂×C₃	1	4	yes	complemented
55	C₃²×#41	—	2	2	no	—
56	C₃²×#41	—	2	2	no	—
57	C₂×C₃²×Q₈	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃²×D₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃²×D₄	C₂×C₄	1	2	yes	—
60	C₂²×C₃²×C₄	C₂³	1	2	yes	—
61	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
62	C₂×C₃×#67	C₂×C₄	1	4	yes	—
63	C₂×C₃×#67	C₂×C₄	1	2	yes	—
64	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
65	C₃×#235	—	2	2	no	—
66	C₃×#235	—	2	2	no	—
67	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
68	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
69	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
70	C₃²×M₁₆	—	2	2	no	—
71	C₂×C₃²×C₈	—	2	2	no	—
72	C₂×C₃²×C₈	C₂³	1	2	yes	—
73	C₂×C₃²×C₈	C₂³	1	2	yes	—
74	C₃×#217	C₂×C₄	1	4	yes	—
75	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
76	C₃×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
77	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
78	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
79	C₃×C₄×Dic₃	C₂³	1	2	yes	—
80	C₃×#208	—	2	2	no	—
81	C₃×#208	—	2	4	no	—
82	C₂×C₃×C₃⋊C₈	—	2	4	no	—
83	C₂×C₃×C₃⋊C₈	D₄	1	4	yes	complemented
84	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
85	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
87	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
88	C₃×D₃×C₈	—	2	4	no	—
89	#2931	—	3	1	no	Sylow
90	C₂×C₃×#41	—	2	1	no	—
91	C₂×C₃×#41	—	3	1	no	—
92	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
93	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
94	C₂×#235	C₂²×C₃	1	1	yes	characteristic
95	C₃×#131	—	6	4	no	—
96	C₃×#131	—	6	4	no	—
97	C₂×C₃×M₁₆	—	2	1	no	—
98	C₂×C₃×M₁₆	—	3	1	no	—
99	C₂×C₃×M₁₆	—	3	2	no	—
100	C₂×C₃×M₁₆	—	3	2	no	—
101	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
102	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
103	C₂²×C₃×C₈	—	2	1	no	—
104	C₂²×C₃×C₈	—	3	1	no	—
105	C₂²×C₃×C₈	—	3	2	no	—
106	C₂²×C₃×C₈	—	3	2	no	—
107	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
108	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
109	C₃×C₄⋊Q₈	—	3	1	no	—
110	C₃×#127	—	3	1	no	—
111	C₃×#124	—	3	1	no	—
112	C₃×#124	—	3	1	no	—
113	C₃×#121	—	3	4	no	—
114	C₃×C₄×D₄	—	3	4	no	—
115	C₂×C₃×C₄²	—	3	1	no	—
116	#948	—	2	4	no	—
117	#947	C₃×C₄	1	1	yes	characteristic
118	#944	C₃×C₄	1	1	yes	characteristic
119	#940	C₃×C₄	1	1	yes	characteristic
120	#939	C₃×C₄	1	4	yes	—
121	#936	C₃×C₄	1	1	yes	characteristic
122	C₄×#67	C₂²×C₃	1	4	yes	—
123	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
124	C₂×#208	C₂²×C₃	1	2	yes	—
125	C₂×#208	C₂²×C₃	1	1	yes	characteristic
126	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
127	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
128	#907	—	2	4	no	—
129	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
130	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
131	C₃×C₄⋊C₈	—	3	4	no	—
132	C₃×C₂²⋊C₈	—	2	4	no	—
133	C₃×C₂²⋊C₈	—	3	4	no	—
134	C₃×C₂²⋊C₈	C₂×D₃	1	4	yes	—
135	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
136	C₃×C₄×C₈	—	3	2	no	—
137	C₃×C₄×C₈	—	3	2	no	—
138	(C₂×D₃)⋊C₈	C₂²×C₃	1	4	yes	—
139	Dic₃⋊C₈	C₂²×C₃	1	4	yes	—
140	C₈×Dic₃	C₂²×C₃	1	2	yes	—
141	C₈×Dic₃	C₂²×C₃	1	2	yes	—
142	C₂³×C₃²	C₂²×C₄	1	2	yes	—
143	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
145	C₃²×Q₈	—	2	2	no	—
146	C₃²×D₄	—	2	4	no	—
147	C₃²×D₄	—	2	2	no	—
148	C₂×C₃²×C₄	—	2	2	no	—
149	C₂×C₃²×C₄	—	2	2	no	—
150	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
151	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
153	C₂×C₃²×C₄	#41	1	2	yes	—
154	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
155	C₃×#67	—	2	4	no	—
156	C₃×#67	—	2	8	no	—
157	C₂×C₃×Dic₃	—	2	4	no	—
158	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
159	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
160	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
161	C₃×D₁₂	—	2	2	no	—
162	C₃×C₄×D₃	—	2	2	no	—
163	C₃×C₄×D₃	—	2	2	no	—
164	C₃×Dic₆	—	2	2	no	—
165	C₃²×C₈	—	2	2	no	—
166	C₃²×C₈	—	2	2	no	—
167	C₃×C₃⋊C₈	—	2	2	no	—
168	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
169	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
170	C₂×#131	—	3	1	no	—
171	C₂×#131	—	3	1	no	—
172	#532	—	3	1	no	—
173	#436	—	3	4	no	—
174	C₈×D₄	—	3	4	no	—
175	#423	—	3	1	no	—
176	#408	—	3	1	no	—
177	#408	C₃×D₃	1	1	yes	characteristic, complemented
178	C₂×C₄×C₈	—	3	1	no	—
179	C₃×#41	—	2	2	no	—
180	C₃×#41	—	2	2	no	—
181	C₃×#41	—	2	2	no	—
182	C₃×#41	—	2	2	no	—
183	C₃×#41	—	4	2	no	—
184	C₃×#41	—	4	2	no	—
185	C₃×#41	—	6	2	no	—
186	C₃×#41	—	6	2	no	—
187	C₂×C₃×Q₈	—	2	1	no	—
188	C₂×C₃×Q₈	—	3	1	no	—
189	C₂×C₃×Q₈	C₄×D₃	1	1	yes	characteristic
190	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
191	C₂×C₃×D₄	—	2	2	no	—
192	C₂×C₃×D₄	—	2	1	no	—
193	C₂×C₃×D₄	—	3	4	no	—
194	C₂×C₃×D₄	—	3	2	no	—
195	C₂×C₃×D₄	—	3	1	no	—
196	C₂×C₃×D₄	C₄×D₃	1	2	yes	—
197	C₂×C₃×D₄	C₄×D₃	1	1	yes	characteristic
198	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
199	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
200	C₂²×C₃×C₄	—	2	1	no	—
201	C₂²×C₃×C₄	—	2	2	no	—
202	C₂²×C₃×C₄	—	3	2	no	—
203	C₂²×C₃×C₄	—	3	2	no	—
204	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
205	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
207	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
208	C₂×#67	C₂×C₃×C₄	1	4	yes	—
209	C₂×#67	C₂×C₃×C₄	1	2	yes	—
210	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
211	#235	—	2	2	no	—
212	#235	—	2	2	no	—
213	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
214	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
215	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
216	C₃×M₁₆	—	2	2	no	—
217	C₃×M₁₆	—	2	2	no	—
218	C₃×M₁₆	—	4	2	no	—
219	C₃×M₁₆	—	6	4	no	—
220	C₃×M₁₆	—	6	4	no	—
221	C₃×M₁₆	—	6	2	no	—
222	C₂×C₃×C₈	—	2	2	no	—
223	C₂×C₃×C₈	—	2	2	no	—
224	C₂×C₃×C₈	—	2	2	no	—
225	C₂×C₃×C₈	—	2	2	no	—
226	C₂×C₃×C₈	—	3	4	no	—
227	C₂×C₃×C₈	—	3	1	no	—
228	C₂×C₃×C₈	—	3	1	no	—
229	C₂×C₃×C₈	—	3	2	no	—
230	C₂×C₃×C₈	—	4	2	no	—
231	C₂×C₃×C₈	—	6	4	no	—
232	C₂×C₃×C₈	—	6	4	no	—
233	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
234	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
235	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
236	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
237	C₃×C₄⋊C₄	—	3	4	no	—
238	C₃×C₂²⋊C₄	—	3	4	no	—
239	C₃×C₂²⋊C₄	—	3	4	no	—
240	C₃×C₄²	—	3	1	no	—
241	C₃×C₄²	—	3	1	no	—
242	C₃×C₄²	—	3	2	no	—
243	#217	C₂×C₃×C₄	1	4	yes	—
244	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	4	yes	—
245	Dic₃⋊C₄	C₂×C₃×C₄	1	4	yes	—
246	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
247	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
248	C₄×Dic₃	C₂³×C₃	1	2	yes	—
249	#208	—	2	2	no	—
250	#208	—	2	4	no	—
251	C₂×C₃⋊C₈	—	2	4	no	—
252	C₂×C₃⋊C₈	C₃×D₄	1	4	yes	complemented
253	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
254	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
255	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
256	ΓL(1,𝔽₂₅)	—	2	4	no	—
257	D₃×C₈	—	2	4	no	—
258	C₂²×C₃²	—	2	2	no	—
259	C₂²×C₃²	—	2	2	no	—
260	C₂²×C₃²	—	2	4	no	—
261	C₂²×C₃²	C₄×D₄	1	2	yes	—
262	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₃×D₃	—	2	2	no	—
264	C₂×C₃×D₃	—	2	4	no	—
265	C₃²×C₄	—	2	2	no	—
266	C₃²×C₄	C₄×D₄	1	2	yes	—
267	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
268	C₃²×C₄	C₂×#41	1	1	yes	characteristic
269	C₃×Dic₃	—	2	2	no	—
270	C₃×Dic₃	—	2	2	no	—
271	C₃×Dic₃	#131	1	4	yes	complemented
272	C₂×#41	—	3	1	no	—
273	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
274	#131	—	6	4	no	—
275	#131	—	6	4	no	—
276	C₂×M₁₆	—	3	1	no	—
277	C₂×M₁₆	—	3	2	no	—
278	C₂×M₁₆	—	3	2	no	—
279	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
280	C₂²×C₈	—	3	1	no	—
281	C₂²×C₈	—	3	2	no	—
282	C₂²×C₈	—	3	2	no	—
283	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
284	C₄⋊Q₈	—	3	1	no	—
285	#127	—	3	1	no	—
286	#124	—	3	1	no	—
287	#124	—	3	1	no	—
288	#121	—	3	4	no	—
289	C₄×D₄	—	3	4	no	—
290	C₂×C₄²	—	3	1	no	—
291	C₄⋊C₈	—	3	4	no	—
292	C₂²⋊C₈	—	3	4	no	—
293	C₂²⋊C₈	C₂×C₃×D₃	1	4	yes	—
294	C₄×C₈	—	3	2	no	—
295	C₄×C₈	—	3	2	no	—
296	C₂³×C₃	—	2	1	no	—
297	C₂³×C₃	—	2	2	no	—
298	C₂³×C₃	—	3	2	no	—
299	C₂³×C₃	C₂×C₄×D₃	1	2	yes	—
300	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
301	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
302	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
303	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
304	C₃×Q₈	—	2	2	no	—
305	C₃×Q₈	—	2	2	no	—
306	C₃×Q₈	—	4	2	no	—
307	C₃×Q₈	—	6	2	no	—
308	C₃×D₄	—	2	4	no	—
309	C₃×D₄	—	2	4	no	—
310	C₃×D₄	—	2	2	no	—
311	C₃×D₄	—	2	2	no	—
312	C₃×D₄	—	4	2	no	—
313	C₃×D₄	—	4	4	no	—
314	C₃×D₄	—	6	8	no	—
315	C₃×D₄	—	6	4	no	—
316	C₃×D₄	—	6	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	1	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	2	2	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	2	2	no	—
326	C₂×C₃×C₄	—	3	2	no	—
327	C₂×C₃×C₄	—	3	2	no	—
328	C₂×C₃×C₄	—	3	2	no	—
329	C₂×C₃×C₄	—	4	2	no	—
330	C₂×C₃×C₄	—	4	2	no	—
331	C₂×C₃×C₄	—	6	4	no	—
332	C₂×C₃×C₄	—	6	2	no	—
333	C₂×C₃×C₄	—	6	2	no	—
334	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
335	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
336	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
337	C₂×C₃×C₄	#237	1	2	yes	—
338	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
339	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
341	C₂×C₃×C₄	C₃×#41	1	2	yes	—
342	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
344	#67	—	2	4	no	—
345	#67	—	2	8	no	—
346	C₂×Dic₃	—	2	4	no	—
347	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
348	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
349	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
350	D₁₂	—	2	2	no	—
351	C₄×D₃	—	2	2	no	—
352	C₄×D₃	—	2	2	no	—
353	Dic₆	—	2	2	no	—
354	C₃×C₈	—	2	2	no	—
355	C₃×C₈	—	2	2	no	—
356	C₃×C₈	—	2	2	no	—
357	C₃×C₈	—	2	2	no	—
358	C₃×C₈	—	3	2	no	—
359	C₃×C₈	—	3	2	no	—
360	C₃×C₈	—	4	2	no	—
361	C₃×C₈	—	4	2	no	—
362	C₃×C₈	—	6	2	no	—
363	C₃⋊C₈	—	2	2	no	—
364	C₃⋊C₈	C₂×C₃×D₄	1	2	yes	—
365	C₃⋊C₈	C₂×C₃×D₄	1	2	yes	—
366	C₂×C₃²	—	2	2	no	—
367	C₂×C₃²	—	4	2	no	—
368	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
369	C₂×C₃²	C₂×#131	1	2	yes	—
370	C₃×D₃	—	4	2	no	—
371	#41	—	2	2	no	—
372	#41	—	2	2	no	—
373	#41	—	6	2	no	—
374	#41	—	6	2	no	—
375	C₂×Q₈	—	3	1	no	—
376	C₂×Q₈	C₃×C₄×D₃	1	1	yes	characteristic
377	C₂×D₄	—	3	4	no	—
378	C₂×D₄	—	3	2	no	—
379	C₂×D₄	—	3	1	no	—
380	C₂×D₄	C₃×C₄×D₃	1	2	yes	—
381	C₂×D₄	C₃×C₄×D₃	1	1	yes	characteristic
382	C₂²×C₄	—	3	2	no	—
383	C₂²×C₄	—	3	2	no	—
384	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
385	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
386	M₁₆	—	2	2	no	—
387	M₁₆	—	6	4	no	—
388	M₁₆	—	6	4	no	—
389	M₁₆	—	6	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	3	1	no	—
392	C₂×C₈	—	3	1	no	—
393	C₂×C₈	—	3	4	no	—
394	C₂×C₈	—	3	2	no	—
395	C₂×C₈	—	6	4	no	—
396	C₂×C₈	—	6	4	no	—
397	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
398	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
399	C₄⋊C₄	—	3	4	no	—
400	C₂²⋊C₄	—	3	4	no	—
401	C₂²⋊C₄	—	3	4	no	—
402	C₄²	—	3	2	no	—
403	C₄²	—	3	1	no	—
404	C₄²	—	3	1	no	—
405	C₂²×C₃	—	2	2	no	—
406	C₂²×C₃	—	2	2	no	—
407	C₂²×C₃	—	2	4	no	—
408	C₂²×C₃	—	2	2	no	—
409	C₂²×C₃	—	2	4	no	—
410	C₂²×C₃	—	2	2	no	—
411	C₂²×C₃	—	2	2	no	—
412	C₂²×C₃	—	2	1	no	—
413	C₂²×C₃	—	4	2	no	—
414	C₂²×C₃	—	4	2	no	—
415	C₂²×C₃	—	4	4	no	—
416	C₂²×C₃	—	6	2	no	—
417	C₂²×C₃	—	6	4	no	—
418	C₂²×C₃	#67⋊C₄	1	2	yes	—
419	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
420	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
421	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
422	C₂×D₃	—	2	4	no	—
423	C₂×D₃	—	2	2	no	—
424	C₃×C₄	—	2	2	no	—
425	C₃×C₄	—	2	2	no	—
426	C₃×C₄	—	2	2	no	—
427	C₃×C₄	—	2	1	no	—
428	C₃×C₄	—	2	1	no	—
429	C₃×C₄	—	3	4	no	—
430	C₃×C₄	—	4	2	no	—
431	C₃×C₄	—	6	2	no	—
432	C₃×C₄	—	6	2	no	—
433	C₃×C₄	#67⋊C₄	1	2	yes	—
434	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
435	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
436	C₃×C₄	C₂×#237	1	1	yes	characteristic
437	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
438	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
439	Dic₃	—	2	2	no	—
440	Dic₃	—	2	2	no	—
441	Dic₃	C₃×#131	1	4	yes	complemented
442	C₃²	#2931	1	1	yes	characteristic, complemented, Sylow
443	C₂³	—	3	2	no	—
444	C₂³	C₂×C₃×C₄×D₃	1	2	yes	—
445	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
446	Q₈	—	2	2	no	—
447	Q₈	—	6	2	no	—
448	D₄	—	2	4	no	—
449	D₄	—	2	2	no	—
450	D₄	—	6	8	no	—
451	D₄	—	6	4	no	—
452	D₄	—	6	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	3	2	no	—
456	C₂×C₄	—	3	2	no	—
457	C₂×C₄	—	3	2	no	—
458	C₂×C₄	—	6	4	no	—
459	C₂×C₄	—	6	2	no	—
460	C₂×C₄	—	6	2	no	—
461	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
462	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
463	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
464	C₂×C₄	C₃×#237	1	2	yes	—
465	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
466	C₈	—	2	2	no	—
467	C₈	—	2	2	no	—
468	C₈	—	3	2	no	—
469	C₈	—	3	2	no	—
470	C₈	—	6	2	no	—
471	C₂×C₃	—	2	2	no	—
472	C₂×C₃	—	2	2	no	—
473	C₂×C₃	—	2	2	no	—
474	C₂×C₃	—	2	1	no	—
475	C₂×C₃	—	4	2	no	—
476	C₂×C₃	—	4	2	no	—
477	C₂×C₃	—	4	2	no	—
478	C₂×C₃	—	8	2	no	—
479	C₂×C₃	—	12	2	no	—
480	C₂×C₃	C₂×#67⋊C₄	1	1	yes	characteristic
481	C₂×C₃	D₃×#131	1	2	yes	—
482	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
483	C₂×C₃	C₂×C₃×#131	1	2	yes	—
484	D₃	—	4	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	4	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	6	4	no	—
489	C₂²	—	6	2	no	—
490	C₂²	C₃×#67⋊C₄	1	2	yes	—
491	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
492	C₄	—	2	2	no	—
493	C₄	—	3	4	no	—
494	C₄	—	6	2	no	—
495	C₄	—	6	2	no	—
496	C₄	C₃×#67⋊C₄	1	2	yes	—
497	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
498	C₄	C₂×C₃×#237	1	1	yes	characteristic
499	C₃	—	2	1	no	—
500	C₃	#78657	1	1	yes	characteristic, direct product factor
501	C₃	C₃×#2931	1	1	yes	characteristic, complemented
502	C₂	—	2	2	no	—
503	C₂	—	4	2	no	—
504	C₂	—	12	2	no	—
505	C₂	C₂×C₃×#67⋊C₄	1	1	yes	characteristic
506	C₂	C₃×D₃×#131	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#408	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₃×#5832	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#408	D₃
hypocenter	C₃	C₃×#2931
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#408

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#948	C₂	semidirect
3. C₂×C₃×#907	C₂	semidirect
4. C₃²×#408	C₂	semidirect
5. C₃×#5118	C₂	semidirect
6. C₃×#5110	C₂	semidirect
7. C₂×C₃×C₈×Dic₃	C₂	semidirect
8. C₃×#4729	C₂	semidirect
9. C₃×#67⋊C₈	C₂	semidirect
11. #78657	C₃	direct (N × H)
40. C₂×#948	C₂×C₃	semidirect
41. C₂×#907	C₂×C₃	semidirect
47. C₃×#408	D₃	semidirect
48. C₃×#408	C₂×C₃	semidirect
50. #5118	C₂×C₃	semidirect
51. #5110	C₂×C₃	semidirect
52. C₂×C₈×Dic₃	C₂×C₃	semidirect
53. #4729	C₂×C₃	semidirect
54. #67⋊C₈	C₂×C₃	semidirect
83. C₂×C₃×C₃⋊C₈	D₄	semidirect
177. #408	C₃×D₃	semidirect
252. C₂×C₃⋊C₈	C₃×D₄	semidirect
271. C₃×Dic₃	#131	semidirect
441. Dic₃	C₃×#131	semidirect
442. C₃²	#2931	semidirect
500. C₃	#78657	direct (N × H)
501. C₃	C₃×#2931	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5832	2
C₂×C₃×#948	2
C₂×C₃×#907	2
C₃²×#408	2
C₃×#5118	2
C₃×#5110	2
C₂×C₃×C₈×Dic₃	2
C₃×#4729	2
C₃×#67⋊C₈	2
C₃×#2931	3
#78657	3

Subgroups — C3×#78657 #11859458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#78657 #11859458