Subgroups — C₃×#10589872 #13153474

Order 1728.

836 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#63716	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#63715	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63512	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#63511	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63480	C₂	1	2	yes	maximal, complemented
7	C₃×#63478	C₂	1	2	yes	maximal, complemented
8	C₃×SD₁₆×D₉	C₂	1	2	yes	maximal, complemented
9	C₃×#63473	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#3664	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#63464	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5770	—	3	1	no	maximal
13	#10589872	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₃×C₉×#41	C₂²	1	1	yes	characteristic
15	C₃×C₉×#41	C₂²	1	1	yes	characteristic, complemented
16	C₃×#3701	C₂²	1	2	yes	—
17	C₃×Q₈×D₉	C₂²	1	2	yes	complemented
18	C₃×#3699	—	2	2	no	—
19	C₃×#3699	C₂²	1	2	yes	complemented
20	C₃×D₄×D₉	—	2	2	no	—
21	C₃×D₄×D₉	C₂²	1	2	yes	—
22	C₃×#3697	—	2	1	no	—
23	C₃×#3697	—	2	1	no	—
24	C₃×#3697	C₂²	1	1	yes	characteristic
25	C₂×C₃×D₃₆	—	2	1	no	—
26	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
27	C₂×C₃×Dic₁₈	—	2	1	no	—
28	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₉×Q₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₉×SD₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₉×SD₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₉×D₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
34	C₃×#3675	C₂²	1	2	yes	complemented
35	C₃×#3674	C₂²	1	2	yes	complemented
36	C₃×#3673	C₂²	1	2	yes	complemented
37	C₃×#3672	C₂²	1	2	yes	complemented
38	C₃×#3667	C₂²	1	1	yes	characteristic, complemented
39	C₃×#3664	C₂²	1	2	yes	complemented
40	C₃×#3664	C₂²	1	2	yes	complemented
41	C₃×#3663	C₂²	1	2	yes	complemented
42	C₃×C₈×D₉	C₂²	1	2	yes	complemented
43	C₃×#1010	—	3	1	no	—
44	C₃×#1009	—	3	1	no	—
45	C₃²×#135	D₃	1	1	yes	characteristic
46	C₃×#951	—	3	1	no	—
47	C₃×#949	—	3	1	no	—
48	C₃×#918	—	3	2	no	—
49	C₃×#916	—	3	2	no	—
50	C₃×D₃×SD₁₆	—	3	2	no	—
51	C₃×#911	—	3	2	no	—
52	C₂×C₃×#204	—	3	1	no	—
53	C₃×#901	—	3	1	no	—
54	#63716	C₂×C₃	1	1	yes	characteristic, complemented
55	#63715	C₂×C₃	1	1	yes	characteristic, complemented
56	C₉×#135	—	2	1	no	—
57	C₉×#135	C₂×C₃	1	1	yes	characteristic, complemented
58	#63512	C₂×C₃	1	1	yes	characteristic, complemented
59	#63511	C₂×C₃	1	1	yes	characteristic, complemented
60	#63480	C₂×C₃	1	2	yes	complemented
61	#63478	C₂×C₃	1	2	yes	complemented
62	SD₁₆×D₉	C₂×C₃	1	2	yes	complemented
63	#63473	C₂×C₃	1	2	yes	complemented
64	C₂×#3664	C₂×C₃	1	1	yes	characteristic, complemented
65	#63464	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂²×C₃×D₉	—	2	1	no	—
67	C₂²×C₃×D₉	—	2	2	no	—
68	C₃×Q₈×C₉	C₂³	1	1	yes	characteristic
69	C₃×Q₈×C₉	C₂³	1	1	yes	characteristic
70	C₃×D₄×C₉	—	2	1	no	—
71	C₃×D₄×C₉	—	2	1	no	—
72	C₃×D₄×C₉	C₂³	1	1	yes	characteristic
73	C₃×D₄×C₉	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×C₉	—	2	1	no	—
75	C₂×C₃×C₄×C₉	—	2	1	no	—
76	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
77	C₃×#611	—	2	2	no	—
78	C₃×#611	—	2	2	no	—
79	C₃×#611	D₄	1	2	yes	—
80	C₂×C₃×Dic₉	—	2	1	no	—
81	C₂×C₃×Dic₉	—	2	2	no	—
82	C₃×D₃₆	—	2	2	no	—
83	C₃×D₃₆	—	2	1	no	—
84	C₃×D₃₆	D₄	1	1	yes	characteristic
85	C₃×D₃₆	C₂³	1	2	yes	—
86	C₃×C₄×D₉	—	2	2	no	—
87	C₃×C₄×D₉	—	2	2	no	—
88	C₃×C₄×D₉	C₂³	1	2	yes	—
89	C₃×Dic₁₈	—	2	1	no	—
90	C₃×Dic₁₈	—	2	2	no	—
91	C₃×Dic₁₈	D₄	1	1	yes	characteristic
92	C₃×Dic₁₈	C₂³	1	2	yes	—
93	C₃×C₈×C₉	C₂³	1	1	yes	characteristic
94	C₃×C₈×C₉	C₂³	1	1	yes	characteristic
95	C₃×C₉⋊C₈	C₂³	1	2	yes	—
96	C₃×#577	—	9	1	no	—
97	#5770	—	3	1	no	—
98	C₃²×#41	C₂×D₃	1	1	yes	characteristic
99	C₃²×#41	C₂×D₃	1	1	yes	characteristic
100	C₃×#239	—	3	2	no	—
101	C₃×D₃×Q₈	—	3	2	no	—
102	C₃×#237	—	3	2	no	—
103	C₃×#237	—	6	2	no	—
104	C₃×D₃×D₄	—	3	2	no	—
105	C₃×D₃×D₄	—	6	2	no	—
106	C₃×#235	—	3	1	no	—
107	C₃×#235	—	6	1	no	—
108	C₃×#235	—	6	1	no	—
109	C₂×C₃×D₁₂	—	3	1	no	—
110	C₂×C₃×D₁₂	—	6	1	no	—
111	C₂×C₃×Dic₆	—	3	1	no	—
112	C₂×C₃×Dic₆	—	6	1	no	—
113	C₃²×Q₁₆	C₂×D₃	1	1	yes	characteristic
114	C₃²×SD₁₆	C₂×D₃	1	1	yes	characteristic
115	C₃²×SD₁₆	C₂×D₃	1	1	yes	characteristic
116	C₃²×D₈	C₂×D₃	1	1	yes	characteristic
117	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
118	C₃×#216	—	3	2	no	—
119	C₃×#215	—	3	2	no	—
120	C₃×#214	—	3	2	no	—
121	C₃×#213	—	3	2	no	—
122	C₃×#208	—	3	1	no	—
123	C₃×#204	—	3	2	no	—
124	C₃×#204	—	3	2	no	—
125	C₃×ΓL(1,𝔽₂₅)	—	3	2	no	—
126	C₃×D₃×C₈	—	3	2	no	—
127	C₉×#41	—	2	1	no	—
128	C₉×#41	—	2	1	no	—
129	C₉×#41	C₂²×C₃	1	1	yes	characteristic
130	C₉×#41	C₂²×C₃	1	1	yes	characteristic, complemented
131	#3701	C₂²×C₃	1	2	yes	—
132	Q₈×D₉	C₂²×C₃	1	2	yes	complemented
133	#3699	—	2	2	no	—
134	#3699	C₂²×C₃	1	2	yes	complemented
135	D₄×D₉	—	2	2	no	—
136	D₄×D₉	C₂²×C₃	1	2	yes	—
137	#3697	—	2	1	no	—
138	#3697	—	2	1	no	—
139	#3697	C₂²×C₃	1	1	yes	characteristic
140	C₂×D₃₆	—	2	1	no	—
141	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
142	C₂×Dic₁₈	—	2	1	no	—
143	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic, complemented
144	C₉×Q₁₆	—	2	1	no	—
145	C₉×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
146	C₉×SD₁₆	—	2	1	no	—
147	C₉×SD₁₆	—	2	1	no	—
148	C₉×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
149	C₉×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
150	C₉×D₈	—	2	1	no	—
151	C₉×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
152	C₂×C₈×C₉	—	2	1	no	—
153	C₂×C₈×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
154	#3675	C₂²×C₃	1	2	yes	complemented
155	#3674	C₂²×C₃	1	2	yes	complemented
156	#3673	C₂²×C₃	1	2	yes	complemented
157	#3672	C₂²×C₃	1	2	yes	complemented
158	#3667	C₂²×C₃	1	1	yes	characteristic, complemented
159	#3664	C₂²×C₃	1	2	yes	complemented
160	#3664	C₂²×C₃	1	2	yes	complemented
161	#3663	C₂²×C₃	1	2	yes	complemented
162	C₈×D₉	C₂²×C₃	1	2	yes	complemented
163	C₂²×C₃×C₉	—	2	1	no	—
164	C₂²×C₃×C₉	—	2	1	no	—
165	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
166	C₂×C₃×D₉	—	2	2	no	—
167	C₂×C₃×D₉	—	8	2	no	—
168	C₂×C₃×D₉	—	8	1	no	—
169	C₂×C₃×D₉	C₂×D₄	1	2	yes	—
170	C₃×C₄×C₉	—	2	1	no	—
171	C₃×C₄×C₉	—	2	1	no	—
172	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
173	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
174	C₃×Dic₉	—	2	2	no	—
175	C₃×Dic₉	C₂×D₄	1	2	yes	—
176	C₃×2₋¹⁺⁴	—	9	1	no	—
177	C₃×H(5,𝔽₂)	—	9	1	no	—
178	#1010	—	3	1	no	—
179	#1009	—	3	1	no	—
180	C₃×#137	—	9	1	no	—
181	C₃×#137	—	9	2	no	—
182	C₃×AGL(1,ℤ/8)	—	9	1	no	—
183	C₃×AGL(1,ℤ/8)	—	9	2	no	—
184	C₃×#135	—	2	1	no	—
185	C₃×#135	—	9	2	no	—
186	C₃×#135	D₉	1	1	yes	characteristic, complemented
187	C₃×#135	C₃×D₃	1	1	yes	characteristic
188	C₂×C₃×SD₁₆	—	9	2	no	—
189	C₂×C₃×SD₁₆	—	9	1	no	—
190	C₃×#131	—	9	1	no	—
191	#951	—	3	1	no	—
192	#949	—	3	1	no	—
193	#918	—	3	2	no	—
194	#916	—	3	2	no	—
195	D₃×SD₁₆	—	3	2	no	—
196	#911	—	3	2	no	—
197	C₂×#204	—	3	1	no	—
198	#901	—	3	1	no	—
199	C₂²×C₃×D₃	—	6	2	no	—
200	C₂²×C₃×D₃	—	6	1	no	—
201	C₃²×Q₈	C₂²×D₃	1	1	yes	characteristic
202	C₃²×Q₈	C₂²×D₃	1	1	yes	characteristic
203	C₃²×D₄	—	2	1	no	—
204	C₃²×D₄	—	2	1	no	—
205	C₃²×D₄	C₂²×D₃	1	1	yes	characteristic
206	C₃²×D₄	C₂²×D₃	1	1	yes	characteristic
207	C₂×C₃²×C₄	—	2	1	no	—
208	C₂×C₃²×C₄	—	2	1	no	—
209	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
210	C₃×#67	—	3	2	no	—
211	C₃×#67	—	6	2	no	—
212	C₃×#67	—	6	2	no	—
213	C₂×C₃×Dic₃	—	6	2	no	—
214	C₂×C₃×Dic₃	—	6	1	no	—
215	C₃×D₁₂	—	3	1	no	—
216	C₃×D₁₂	—	3	2	no	—
217	C₃×D₁₂	—	6	2	no	—
218	C₃×D₁₂	—	6	1	no	—
219	C₃×C₄×D₃	—	3	2	no	—
220	C₃×C₄×D₃	—	6	2	no	—
221	C₃×C₄×D₃	—	6	2	no	—
222	C₃×Dic₆	—	3	1	no	—
223	C₃×Dic₆	—	3	2	no	—
224	C₃×Dic₆	—	6	2	no	—
225	C₃×Dic₆	—	6	1	no	—
226	C₂²×D₉	—	2	1	no	—
227	C₂²×D₉	—	2	2	no	—
228	C₃²×C₈	C₂²×D₃	1	1	yes	characteristic
229	C₃²×C₈	C₂²×D₃	1	1	yes	characteristic
230	C₃×C₃⋊C₈	—	3	2	no	—
231	Q₈×C₉	—	2	1	no	—
232	Q₈×C₉	—	2	1	no	—
233	Q₈×C₉	C₂³×C₃	1	1	yes	characteristic
234	Q₈×C₉	C₂³×C₃	1	1	yes	characteristic
235	D₄×C₉	—	2	1	no	—
236	D₄×C₉	—	2	1	no	—
237	D₄×C₉	—	2	1	no	—
238	D₄×C₉	—	2	1	no	—
239	D₄×C₉	—	4	1	no	—
240	D₄×C₉	—	4	1	no	—
241	D₄×C₉	C₂³×C₃	1	1	yes	characteristic
242	D₄×C₉	C₂³×C₃	1	1	yes	characteristic
243	C₂×C₄×C₉	—	2	1	no	—
244	C₂×C₄×C₉	—	2	1	no	—
245	C₂×C₄×C₉	—	2	1	no	—
246	C₂×C₄×C₉	—	4	1	no	—
247	C₂×C₄×C₉	—	4	1	no	—
248	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
249	#611	—	2	2	no	—
250	#611	—	2	2	no	—
251	#611	C₃×D₄	1	2	yes	—
252	C₂×Dic₉	—	2	1	no	—
253	C₂×Dic₉	—	2	2	no	—
254	D₃₆	—	2	2	no	—
255	D₃₆	—	2	1	no	—
256	D₃₆	C₃×D₄	1	1	yes	characteristic
257	D₃₆	C₂³×C₃	1	2	yes	—
258	C₄×D₉	—	2	2	no	—
259	C₄×D₉	—	2	2	no	—
260	C₄×D₉	C₂³×C₃	1	2	yes	—
261	Dic₁₈	—	2	1	no	—
262	Dic₁₈	—	2	2	no	—
263	Dic₁₈	C₃×D₄	1	1	yes	characteristic
264	Dic₁₈	C₂³×C₃	1	2	yes	—
265	C₈×C₉	—	2	1	no	—
266	C₈×C₉	—	2	1	no	—
267	C₈×C₉	C₂³×C₃	1	1	yes	characteristic
268	C₈×C₉	C₂³×C₃	1	1	yes	characteristic
269	C₉⋊C₈	C₂³×C₃	1	2	yes	—
270	#577	—	9	1	no	Sylow
271	C₂×C₃×C₉	—	2	1	no	—
272	C₂×C₃×C₉	—	4	1	no	—
273	C₂×C₃×C₉	—	4	1	no	—
274	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
275	C₃×D₉	—	2	2	no	—
276	C₃×D₉	—	4	2	no	—
277	C₃×#41	—	2	1	no	—
278	C₃×#41	—	2	1	no	—
279	C₃×#41	—	9	1	no	—
280	C₃×#41	—	9	2	no	—
281	C₃×#41	—	9	2	no	—
282	C₃×#41	—	18	1	no	—
283	C₃×#41	—	18	1	no	—
284	C₃×#41	—	18	2	no	—
285	C₃×#41	C₂×D₉	1	1	yes	characteristic
286	C₃×#41	C₂×D₉	1	1	yes	characteristic, complemented
287	C₃×#41	C₂×C₃×D₃	1	1	yes	characteristic
288	C₃×#41	C₂×C₃×D₃	1	1	yes	characteristic
289	C₂×C₃×Q₈	—	9	2	no	—
290	C₂×C₃×Q₈	—	9	1	no	—
291	C₂×C₃×Q₈	—	18	1	no	—
292	C₂×C₃×D₄	—	9	2	no	—
293	C₂×C₃×D₄	—	9	1	no	—
294	C₂×C₃×D₄	—	18	1	no	—
295	C₂×C₃×D₄	—	18	2	no	—
296	#239	—	3	2	no	—
297	D₃×Q₈	—	3	2	no	—
298	#237	—	3	2	no	—
299	#237	—	6	2	no	—
300	D₃×D₄	—	3	2	no	—
301	D₃×D₄	—	6	2	no	—
302	#235	—	3	1	no	—
303	#235	—	6	1	no	—
304	#235	—	6	1	no	—
305	C₂×D₁₂	—	3	1	no	—
306	C₂×D₁₂	—	6	1	no	—
307	C₂×Dic₆	—	3	1	no	—
308	C₂×Dic₆	—	6	1	no	—
309	C₃×Q₁₆	—	2	1	no	—
310	C₃×Q₁₆	—	9	2	no	—
311	C₃×Q₁₆	C₂×D₉	1	1	yes	characteristic, complemented
312	C₃×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
313	C₃×SD₁₆	—	2	1	no	—
314	C₃×SD₁₆	—	2	1	no	—
315	C₃×SD₁₆	—	9	2	no	—
316	C₃×SD₁₆	—	9	2	no	—
317	C₃×SD₁₆	—	9	2	no	—
318	C₃×SD₁₆	—	9	2	no	—
319	C₃×SD₁₆	C₂×D₉	1	1	yes	characteristic, complemented
320	C₃×SD₁₆	C₂×D₉	1	1	yes	characteristic, complemented
321	C₃×SD₁₆	C₂×C₃×D₃	1	1	yes	characteristic
322	C₃×SD₁₆	C₂×C₃×D₃	1	1	yes	characteristic
323	C₃×D₈	—	2	1	no	—
324	C₃×D₈	—	9	2	no	—
325	C₃×D₈	C₂×D₉	1	1	yes	characteristic, complemented
326	C₃×D₈	C₂×C₃×D₃	1	1	yes	characteristic
327	C₃×M₁₆	—	9	1	no	—
328	C₃×M₁₆	—	9	2	no	—
329	C₂×C₃×C₈	—	2	1	no	—
330	C₂×C₃×C₈	—	9	2	no	—
331	C₂×C₃×C₈	C₂×D₉	1	1	yes	characteristic, complemented
332	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
333	#216	—	3	2	no	—
334	#215	—	3	2	no	—
335	#214	—	3	2	no	—
336	#213	—	3	2	no	—
337	#208	—	3	1	no	—
338	#204	—	3	2	no	—
339	#204	—	3	2	no	—
340	ΓL(1,𝔽₂₅)	—	3	2	no	—
341	D₃×C₈	—	3	2	no	—
342	C₂²×C₃²	—	2	1	no	—
343	C₂²×C₃²	—	2	1	no	—
344	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
345	C₂×C₃×D₃	—	3	2	no	—
346	C₂×C₃×D₃	—	6	2	no	—
347	C₂×C₃×D₃	—	24	2	no	—
348	C₂×C₃×D₃	—	24	1	no	—
349	C₃²×C₄	—	2	1	no	—
350	C₃²×C₄	—	2	1	no	—
351	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
352	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
353	C₃×Dic₃	—	3	2	no	—
354	C₃×Dic₃	—	6	2	no	—
355	C₂²×C₉	—	2	1	no	—
356	C₂²×C₉	—	2	1	no	—
357	C₂²×C₉	—	2	1	no	—
358	C₂²×C₉	—	4	1	no	—
359	C₂²×C₉	—	4	1	no	—
360	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
361	C₂×D₉	—	2	2	no	—
362	C₂×D₉	—	8	2	no	—
363	C₂×D₉	—	8	1	no	—
364	C₂×D₉	C₂×C₃×D₄	1	2	yes	—
365	C₄×C₉	—	2	1	no	—
366	C₄×C₉	—	2	1	no	—
367	C₄×C₉	—	2	1	no	—
368	C₄×C₉	—	2	1	no	—
369	C₄×C₉	—	4	1	no	—
370	C₄×C₉	—	4	1	no	—
371	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
372	C₄×C₉	C₂⁴×C₃	1	1	yes	characteristic
373	Dic₉	—	2	2	no	—
374	Dic₉	C₂×C₃×D₄	1	2	yes	—
375	2₋¹⁺⁴	—	9	1	no	—
376	H(5,𝔽₂)	—	9	1	no	—
377	#137	—	9	1	no	—
378	#137	—	9	2	no	—
379	AGL(1,ℤ/8)	—	9	1	no	—
380	AGL(1,ℤ/8)	—	9	2	no	—
381	#135	—	9	2	no	—
382	#135	C₃×D₉	1	1	yes	characteristic, complemented
383	C₂×SD₁₆	—	9	2	no	—
384	C₂×SD₁₆	—	9	1	no	—
385	#131	—	9	1	no	—
386	C₃×C₉	#577	1	1	yes	characteristic, complemented, Sylow
387	C₂³×C₃	—	18	2	no	—
388	C₂³×C₃	—	18	1	no	—
389	C₂²×D₃	—	6	2	no	—
390	C₂²×D₃	—	6	1	no	—
391	C₃×Q₈	—	2	1	no	—
392	C₃×Q₈	—	2	1	no	—
393	C₃×Q₈	—	9	1	no	—
394	C₃×Q₈	—	9	2	no	—
395	C₃×Q₈	—	18	2	no	—
396	C₃×Q₈	—	18	1	no	—
397	C₃×Q₈	C₂²×D₉	1	1	yes	characteristic
398	C₃×Q₈	C₂²×D₉	1	1	yes	characteristic
399	C₃×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
400	C₃×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
401	C₃×D₄	—	2	1	no	—
402	C₃×D₄	—	2	1	no	—
403	C₃×D₄	—	2	1	no	—
404	C₃×D₄	—	2	1	no	—
405	C₃×D₄	—	2	1	no	—
406	C₃×D₄	—	2	1	no	—
407	C₃×D₄	—	4	1	no	—
408	C₃×D₄	—	4	1	no	—
409	C₃×D₄	—	9	2	no	—
410	C₃×D₄	—	9	1	no	—
411	C₃×D₄	—	9	2	no	—
412	C₃×D₄	—	18	2	no	—
413	C₃×D₄	—	18	2	no	—
414	C₃×D₄	—	18	2	no	—
415	C₃×D₄	—	18	1	no	—
416	C₃×D₄	C₂²×D₉	1	1	yes	characteristic
417	C₃×D₄	C₂²×D₉	1	1	yes	characteristic
418	C₃×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
419	C₃×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
420	C₂×C₃×C₄	—	2	1	no	—
421	C₂×C₃×C₄	—	2	1	no	—
422	C₂×C₃×C₄	—	2	1	no	—
423	C₂×C₃×C₄	—	2	1	no	—
424	C₂×C₃×C₄	—	2	1	no	—
425	C₂×C₃×C₄	—	4	1	no	—
426	C₂×C₃×C₄	—	4	1	no	—
427	C₂×C₃×C₄	—	9	2	no	—
428	C₂×C₃×C₄	—	18	2	no	—
429	C₂×C₃×C₄	—	18	2	no	—
430	C₂×C₃×C₄	—	18	2	no	—
431	C₂×C₃×C₄	—	18	1	no	—
432	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
433	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
434	#67	—	3	2	no	—
435	#67	—	6	2	no	—
436	#67	—	6	2	no	—
437	C₂×Dic₃	—	6	2	no	—
438	C₂×Dic₃	—	6	1	no	—
439	D₁₂	—	3	2	no	—
440	D₁₂	—	3	1	no	—
441	D₁₂	—	6	2	no	—
442	D₁₂	—	6	1	no	—
443	C₄×D₃	—	3	2	no	—
444	C₄×D₃	—	6	2	no	—
445	C₄×D₃	—	6	2	no	—
446	Dic₆	—	3	1	no	—
447	Dic₆	—	3	2	no	—
448	Dic₆	—	6	2	no	—
449	Dic₆	—	6	1	no	—
450	C₃×C₈	—	2	1	no	—
451	C₃×C₈	—	2	1	no	—
452	C₃×C₈	—	9	2	no	—
453	C₃×C₈	C₂²×D₉	1	1	yes	characteristic
454	C₃×C₈	C₂²×D₉	1	1	yes	characteristic
455	C₃×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
456	C₃×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
457	C₃⋊C₈	—	3	2	no	—
458	C₂×C₃²	—	2	1	no	—
459	C₂×C₃²	—	4	1	no	—
460	C₂×C₃²	—	4	1	no	—
461	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
462	C₃×D₃	—	6	2	no	—
463	C₃×D₃	—	12	2	no	—
464	C₂×C₉	—	2	1	no	—
465	C₂×C₉	—	2	1	no	—
466	C₂×C₉	—	4	1	no	—
467	C₂×C₉	—	4	1	no	—
468	C₂×C₉	—	4	1	no	—
469	C₂×C₉	—	8	1	no	—
470	C₂×C₉	—	8	1	no	—
471	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
472	D₉	—	2	2	no	—
473	D₉	—	4	2	no	—
474	#41	—	9	1	no	—
475	#41	—	9	2	no	—
476	#41	—	9	2	no	—
477	#41	—	18	1	no	—
478	#41	—	18	1	no	—
479	#41	—	18	2	no	—
480	#41	C₂×C₃×D₉	1	1	yes	characteristic
481	#41	C₂×C₃×D₉	1	1	yes	characteristic, complemented
482	C₂×Q₈	—	9	2	no	—
483	C₂×Q₈	—	9	1	no	—
484	C₂×Q₈	—	18	1	no	—
485	C₂×D₄	—	9	2	no	—
486	C₂×D₄	—	9	1	no	—
487	C₂×D₄	—	18	1	no	—
488	C₂×D₄	—	18	2	no	—
489	Q₁₆	—	9	2	no	—
490	Q₁₆	C₂×C₃×D₉	1	1	yes	characteristic, complemented
491	SD₁₆	—	9	2	no	—
492	SD₁₆	—	9	2	no	—
493	SD₁₆	—	9	2	no	—
494	SD₁₆	—	9	2	no	—
495	SD₁₆	C₂×C₃×D₉	1	1	yes	characteristic, complemented
496	SD₁₆	C₂×C₃×D₉	1	1	yes	characteristic, complemented
497	D₈	—	9	2	no	—
498	D₈	C₂×C₃×D₉	1	1	yes	characteristic, complemented
499	M₁₆	—	9	1	no	—
500	M₁₆	—	9	2	no	—
501	C₂×C₈	—	9	2	no	—
502	C₂×C₈	C₂×C₃×D₉	1	1	yes	characteristic, complemented
503	C₂²×C₃	—	2	1	no	—
504	C₂²×C₃	—	2	1	no	—
505	C₂²×C₃	—	2	1	no	—
506	C₂²×C₃	—	2	1	no	—
507	C₂²×C₃	—	2	1	no	—
508	C₂²×C₃	—	4	1	no	—
509	C₂²×C₃	—	4	1	no	—
510	C₂²×C₃	—	9	2	no	—
511	C₂²×C₃	—	18	2	no	—
512	C₂²×C₃	—	72	1	no	—
513	C₂²×C₃	—	72	2	no	—
514	C₂²×C₃	D₄×D₉	1	1	yes	characteristic
515	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
516	C₂×D₃	—	3	2	no	—
517	C₂×D₃	—	6	2	no	—
518	C₂×D₃	—	24	2	no	—
519	C₂×D₃	—	24	1	no	—
520	C₃×C₄	—	2	1	no	—
521	C₃×C₄	—	2	1	no	—
522	C₃×C₄	—	2	1	no	—
523	C₃×C₄	—	2	1	no	—
524	C₃×C₄	—	2	1	no	—
525	C₃×C₄	—	2	1	no	—
526	C₃×C₄	—	4	1	no	—
527	C₃×C₄	—	4	1	no	—
528	C₃×C₄	—	9	2	no	—
529	C₃×C₄	—	18	2	no	—
530	C₃×C₄	D₄×D₉	1	1	yes	characteristic
531	C₃×C₄	C₂³×D₉	1	1	yes	characteristic
532	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
533	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
534	Dic₃	—	3	2	no	—
535	Dic₃	—	6	2	no	—
536	C₃²	#5770	1	1	yes	characteristic
537	C₉	—	2	1	no	—
538	C₉	C₃×#577	1	1	yes	characteristic, complemented
539	C₂³	—	18	2	no	—
540	C₂³	—	18	1	no	—
541	Q₈	—	9	1	no	—
542	Q₈	—	9	2	no	—
543	Q₈	—	18	2	no	—
544	Q₈	—	18	1	no	—
545	Q₈	C₂²×C₃×D₉	1	1	yes	characteristic
546	Q₈	C₂²×C₃×D₉	1	1	yes	characteristic
547	D₄	—	2	1	no	—
548	D₄	—	2	1	no	—
549	D₄	—	9	2	no	—
550	D₄	—	9	2	no	—
551	D₄	—	9	1	no	—
552	D₄	—	18	2	no	—
553	D₄	—	18	2	no	—
554	D₄	—	18	2	no	—
555	D₄	—	18	1	no	—
556	D₄	C₂²×C₃×D₉	1	1	yes	characteristic
557	D₄	C₂²×C₃×D₉	1	1	yes	characteristic
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	9	2	no	—
561	C₂×C₄	—	18	2	no	—
562	C₂×C₄	—	18	2	no	—
563	C₂×C₄	—	18	2	no	—
564	C₂×C₄	—	18	1	no	—
565	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
566	C₈	—	9	2	no	—
567	C₈	C₂²×C₃×D₉	1	1	yes	characteristic
568	C₈	C₂²×C₃×D₉	1	1	yes	characteristic
569	C₂×C₃	—	2	1	no	—
570	C₂×C₃	—	2	1	no	—
571	C₂×C₃	—	2	1	no	—
572	C₂×C₃	—	4	1	no	—
573	C₂×C₃	—	4	1	no	—
574	C₂×C₃	—	4	1	no	—
575	C₂×C₃	—	4	1	no	—
576	C₂×C₃	—	4	1	no	—
577	C₂×C₃	—	8	1	no	—
578	C₂×C₃	—	8	1	no	—
579	C₂×C₃	—	18	2	no	—
580	C₂×C₃	—	36	2	no	—
581	C₂×C₃	C₂×D₄×D₉	1	1	yes	characteristic
582	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
583	D₃	—	6	2	no	—
584	D₃	—	12	2	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	9	2	no	—
588	C₂²	—	18	2	no	—
589	C₂²	—	72	1	no	—
590	C₂²	—	72	2	no	—
591	C₂²	C₃×D₄×D₉	1	1	yes	characteristic
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	9	2	no	—
595	C₄	—	18	2	no	—
596	C₄	C₃×D₄×D₉	1	1	yes	characteristic
597	C₄	C₂³×C₃×D₉	1	1	yes	characteristic
598	C₃	—	2	1	no	—
599	C₃	#10589872	1	1	yes	characteristic, direct product factor
600	C₃	C₃×#5770	1	1	yes	characteristic
601	C₂	—	2	1	no	—
602	C₂	—	4	1	no	—
603	C₂	—	4	1	no	—
604	C₂	—	18	2	no	—
605	C₂	—	36	2	no	—
606	C₂	C₂×C₃×D₄×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₄×D₉
commutator, cosocle	C₄×C₉	C₂⁴×C₃
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₃×C₉×#135	C₂
socle	C₂×C₃²	C₂×D₃×D₄
hypercenter	C₃×#135	D₉
hypocenter	C₉	C₃×#577
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#135

Complements

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

N	H ≅ G/N	type
1. C₃×#63716	C₂	semidirect
2. C₃×#63715	C₂	semidirect
3. C₃×C₉×#135	C₂	semidirect
4. C₃×#63512	C₂	semidirect
5. C₃×#63511	C₂	semidirect
6. C₃×#63480	C₂	semidirect
7. C₃×#63478	C₂	semidirect
8. C₃×SD₁₆×D₉	C₂	semidirect
9. C₃×#63473	C₂	semidirect
10. C₂×C₃×#3664	C₂	semidirect
11. C₃×#63464	C₂	semidirect
13. #10589872	C₃	direct (N × H)
15. C₃×C₉×#41	C₂²	semidirect
17. C₃×Q₈×D₉	C₂²	semidirect
19. C₃×#3699	C₂²	semidirect
28. C₂×C₃×Dic₁₈	C₂²	semidirect
29. C₃×C₉×Q₁₆	C₂²	semidirect
30. C₃×C₉×SD₁₆	C₂²	semidirect
31. C₃×C₉×SD₁₆	C₂²	semidirect
32. C₃×C₉×D₈	C₂²	semidirect
33. C₂×C₃×C₈×C₉	C₂²	semidirect
34. C₃×#3675	C₂²	semidirect
35. C₃×#3674	C₂²	semidirect
36. C₃×#3673	C₂²	semidirect
37. C₃×#3672	C₂²	semidirect
38. C₃×#3667	C₂²	semidirect
39. C₃×#3664	C₂²	semidirect
40. C₃×#3664	C₂²	semidirect
41. C₃×#3663	C₂²	semidirect
42. C₃×C₈×D₉	C₂²	semidirect
54. #63716	C₂×C₃	semidirect
55. #63715	C₂×C₃	semidirect
57. C₉×#135	C₂×C₃	semidirect
58. #63512	C₂×C₃	semidirect
59. #63511	C₂×C₃	semidirect
60. #63480	C₂×C₃	semidirect
61. #63478	C₂×C₃	semidirect
62. SD₁₆×D₉	C₂×C₃	semidirect
63. #63473	C₂×C₃	semidirect
64. C₂×#3664	C₂×C₃	semidirect
65. #63464	C₂×C₃	semidirect
130. C₉×#41	C₂²×C₃	semidirect
132. Q₈×D₉	C₂²×C₃	semidirect
134. #3699	C₂²×C₃	semidirect
143. C₂×Dic₁₈	C₂²×C₃	semidirect
145. C₉×Q₁₆	C₂²×C₃	semidirect
148. C₉×SD₁₆	C₂²×C₃	semidirect
149. C₉×SD₁₆	C₂²×C₃	semidirect
151. C₉×D₈	C₂²×C₃	semidirect
153. C₂×C₈×C₉	C₂²×C₃	semidirect
154. #3675	C₂²×C₃	semidirect
155. #3674	C₂²×C₃	semidirect
156. #3673	C₂²×C₃	semidirect
157. #3672	C₂²×C₃	semidirect
158. #3667	C₂²×C₃	semidirect
159. #3664	C₂²×C₃	semidirect
160. #3664	C₂²×C₃	semidirect
161. #3663	C₂²×C₃	semidirect
162. C₈×D₉	C₂²×C₃	semidirect
186. C₃×#135	D₉	semidirect
286. C₃×#41	C₂×D₉	semidirect
311. C₃×Q₁₆	C₂×D₉	semidirect
319. C₃×SD₁₆	C₂×D₉	semidirect
320. C₃×SD₁₆	C₂×D₉	semidirect
325. C₃×D₈	C₂×D₉	semidirect
331. C₂×C₃×C₈	C₂×D₉	semidirect
382. #135	C₃×D₉	semidirect
386. C₃×C₉	#577	semidirect
481. #41	C₂×C₃×D₉	semidirect
490. Q₁₆	C₂×C₃×D₉	semidirect
495. SD₁₆	C₂×C₃×D₉	semidirect
496. SD₁₆	C₂×C₃×D₉	semidirect
498. D₈	C₂×C₃×D₉	semidirect
502. C₂×C₈	C₂×C₃×D₉	semidirect
538. C₉	C₃×#577	semidirect
599. C₃	#10589872	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#63716	2
C₃×#63715	2
C₃×C₉×#135	2
C₃×#63512	2
C₃×#63511	2
C₃×#63480	2
C₃×#63478	2
C₃×SD₁₆×D₉	2
C₃×#63473	2
C₂×C₃×#3664	2
C₃×#63464	2
C₃×#5770	3
#10589872	3

Subgroups — C3×#10589872 #13153474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589872 #13153474