Subgroups — C₃×#10589879 #13153508

Order 1728.

846 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41×D₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#3701	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63512	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#63505	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63481	C₂	1	2	yes	maximal, complemented
7	C₃×#63480	C₂	1	2	yes	maximal, complemented
8	C₃×#63478	C₂	1	2	yes	maximal, complemented
9	C₃×#63476	C₂	1	2	yes	maximal, complemented
10	C₃×#63470	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×M₁₆×D₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5777	—	3	1	no	maximal
13	#10589879	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₃×C₉×#41	C₂²	1	1	yes	characteristic
15	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
16	C₃×#3701	—	2	1	no	—
17	C₃×#3701	—	2	1	no	—
18	C₃×#3701	C₂²	1	2	yes	—
19	C₃×#3701	C₂²	1	2	yes	complemented
20	C₃×#3701	C₂²	1	1	yes	characteristic, complemented
21	C₃×Q₈×D₉	C₂²	1	1	yes	characteristic, complemented
22	C₃×#3699	—	2	1	no	—
23	C₃×#3699	C₂²	1	1	yes	characteristic, complemented
24	C₃×D₄×D₉	—	2	1	no	—
25	C₃×D₄×D₉	C₂²	1	1	yes	characteristic, complemented
26	C₃×#3697	—	2	1	no	—
27	C₃×#3697	C₂²	1	1	yes	characteristic
28	C₂×C₃×D₃₆	—	2	1	no	—
29	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×C₄×D₉	—	2	1	no	—
31	C₂×C₃×C₄×D₉	—	2	1	no	—
32	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
33	C₃×C₉×Q₁₆	C₂²	1	2	yes	complemented
34	C₃×C₉×SD₁₆	C₂²	1	2	yes	complemented
35	C₃×C₉×M₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3675	C₂²	1	2	yes	complemented
37	C₃×#3675	C₂²	1	2	yes	complemented
38	C₃×#3674	C₂²	1	2	yes	complemented
39	C₃×#3673	C₂²	1	2	yes	complemented
40	C₃×#3667	C₂²	1	1	yes	characteristic, complemented
41	C₃×D₇₂	C₂²	1	2	yes	complemented
42	C₃×#3664	C₂²	1	2	yes	complemented
43	C₃×#3663	C₂²	1	2	yes	complemented
44	C₃×C₈×D₉	C₂²	1	2	yes	complemented
45	C₃×D₃×#41	—	3	1	no	—
46	C₂×C₃×#239	—	3	1	no	—
47	C₃²×#137	D₃	1	1	yes	characteristic
48	C₃×#949	—	3	1	no	—
49	C₃×#942	—	3	1	no	—
50	C₃×#919	—	3	2	no	—
51	C₃×#918	—	3	2	no	—
52	C₃×#916	—	3	2	no	—
53	C₃×#914	—	3	2	no	—
54	C₃×#908	—	3	1	no	—
55	C₃×D₃×M₁₆	—	3	1	no	—
56	#41×D₉	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×#3701	C₂×C₃	1	1	yes	characteristic, complemented
58	C₉×#137	—	2	1	no	—
59	C₉×#137	C₂×C₃	1	1	yes	characteristic, complemented
60	#63512	C₂×C₃	1	1	yes	characteristic, complemented
61	#63505	C₂×C₃	1	1	yes	characteristic, complemented
62	#63481	C₂×C₃	1	2	yes	complemented
63	#63480	C₂×C₃	1	2	yes	complemented
64	#63478	C₂×C₃	1	2	yes	complemented
65	#63476	C₂×C₃	1	2	yes	complemented
66	#63470	C₂×C₃	1	1	yes	characteristic, complemented
67	M₁₆×D₉	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂²×C₃×D₉	—	2	1	no	—
69	C₂²×C₃×D₉	—	2	1	no	—
70	C₂²×C₃×D₉	D₄	1	1	yes	characteristic
71	C₃×Q₈×C₉	—	2	1	no	—
72	C₃×Q₈×C₉	C₂³	1	1	yes	characteristic
73	C₃×Q₈×C₉	C₂³	1	2	yes	—
74	C₃×D₄×C₉	—	2	1	no	—
75	C₃×D₄×C₉	C₂³	1	1	yes	characteristic
76	C₂×C₃×C₄×C₉	—	2	1	no	—
77	C₂×C₃×C₄×C₉	—	2	1	no	—
78	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
79	C₃×#611	—	2	1	no	—
80	C₃×#611	—	2	1	no	—
81	C₃×#611	—	2	1	no	—
82	C₂×C₃×Dic₉	—	2	1	no	—
83	C₂×C₃×Dic₉	D₄	1	1	yes	characteristic
84	C₃×D₃₆	—	2	2	no	—
85	C₃×D₃₆	—	2	2	no	—
86	C₃×D₃₆	—	2	1	no	—
87	C₃×D₃₆	—	2	1	no	—
88	C₃×D₃₆	C₂³	1	2	yes	—
89	C₃×D₃₆	C₂³	1	1	yes	characteristic
90	C₃×C₄×D₉	—	2	1	no	—
91	C₃×C₄×D₉	—	2	1	no	—
92	C₃×C₄×D₉	—	2	1	no	—
93	C₃×C₄×D₉	—	2	2	no	—
94	C₃×C₄×D₉	—	2	2	no	—
95	C₃×C₄×D₉	D₄	1	1	yes	characteristic
96	C₃×C₄×D₉	D₄	1	1	yes	characteristic
97	C₃×C₄×D₉	C₂³	1	1	yes	characteristic
98	C₃×C₄×D₉	C₂³	1	1	yes	characteristic
99	C₃×Dic₁₈	—	2	1	no	—
100	C₃×Dic₁₈	C₂³	1	1	yes	characteristic
101	C₃×C₈×C₉	C₂³	1	2	yes	—
102	C₃×C₉⋊C₈	C₂³	1	2	yes	—
103	C₃×#575	—	9	1	no	—
104	#5777	—	3	1	no	—
105	C₃²×#41	C₂×D₃	1	1	yes	characteristic
106	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
107	C₃×#239	—	3	2	no	—
108	C₃×#239	—	3	2	no	—
109	C₃×#239	—	3	1	no	—
110	C₃×#239	—	6	1	no	—
111	C₃×#239	—	6	1	no	—
112	C₃×D₃×Q₈	—	3	1	no	—
113	C₃×#237	—	3	1	no	—
114	C₃×#237	—	6	1	no	—
115	C₃×D₃×D₄	—	3	1	no	—
116	C₃×D₃×D₄	—	6	1	no	—
117	C₃×#235	—	3	1	no	—
118	C₃×#235	—	6	1	no	—
119	C₂×C₃×D₁₂	—	3	1	no	—
120	C₂×C₃×D₁₂	—	6	1	no	—
121	C₂×C₃×C₄×D₃	—	3	1	no	—
122	C₂×C₃×C₄×D₃	—	6	1	no	—
123	C₂×C₃×C₄×D₃	—	6	1	no	—
124	C₃²×Q₁₆	C₂×D₃	1	2	yes	—
125	C₃²×SD₁₆	C₂×D₃	1	2	yes	—
126	C₃²×M₁₆	C₂×D₃	1	1	yes	characteristic
127	C₃×#216	—	3	2	no	—
128	C₃×#215	—	3	2	no	—
129	C₃×#215	—	3	2	no	—
130	C₃×#213	—	3	2	no	—
131	C₃×#208	—	3	1	no	—
132	C₃×D₂₄	—	3	2	no	—
133	C₃×#204	—	3	2	no	—
134	C₃×ΓL(1,𝔽₂₅)	—	3	2	no	—
135	C₃×D₃×C₈	—	3	2	no	—
136	C₉×#41	—	2	1	no	—
137	C₉×#41	C₂²×C₃	1	1	yes	characteristic
138	C₂×Q₈×C₉	—	2	1	no	—
139	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
140	#3701	—	2	1	no	—
141	#3701	—	2	1	no	—
142	#3701	C₂²×C₃	1	2	yes	—
143	#3701	C₂²×C₃	1	2	yes	complemented
144	#3701	C₂²×C₃	1	1	yes	characteristic, complemented
145	Q₈×D₉	C₂²×C₃	1	1	yes	characteristic, complemented
146	#3699	—	2	1	no	—
147	#3699	C₂²×C₃	1	1	yes	characteristic, complemented
148	D₄×D₉	—	2	1	no	—
149	D₄×D₉	C₂²×C₃	1	1	yes	characteristic, complemented
150	#3697	—	2	1	no	—
151	#3697	C₂²×C₃	1	1	yes	characteristic
152	C₂×D₃₆	—	2	1	no	—
153	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic, complemented
154	C₂×C₄×D₉	—	2	1	no	—
155	C₂×C₄×D₉	—	2	1	no	—
156	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
157	C₉×Q₁₆	—	2	2	no	—
158	C₉×Q₁₆	C₂²×C₃	1	2	yes	complemented
159	C₉×SD₁₆	—	2	2	no	—
160	C₉×SD₁₆	C₂²×C₃	1	2	yes	complemented
161	C₉×M₁₆	—	2	1	no	—
162	C₉×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
163	#3675	C₂²×C₃	1	2	yes	complemented
164	#3675	C₂²×C₃	1	2	yes	complemented
165	#3674	C₂²×C₃	1	2	yes	complemented
166	#3673	C₂²×C₃	1	2	yes	complemented
167	#3667	C₂²×C₃	1	1	yes	characteristic, complemented
168	D₇₂	C₂²×C₃	1	2	yes	complemented
169	#3664	C₂²×C₃	1	2	yes	complemented
170	#3663	C₂²×C₃	1	2	yes	complemented
171	C₈×D₉	C₂²×C₃	1	2	yes	complemented
172	C₂²×C₃×C₉	—	2	1	no	—
173	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
174	C₂×C₃×D₉	—	2	2	no	—
175	C₂×C₃×D₉	—	2	1	no	—
176	C₂×C₃×D₉	—	4	1	no	—
177	C₂×C₃×D₉	—	4	2	no	—
178	C₂×C₃×D₉	—	4	2	no	—
179	C₂×C₃×D₉	C₂×D₄	1	1	yes	characteristic
180	C₂×C₃×D₉	C₂×D₄	1	1	yes	characteristic
181	C₃×C₄×C₉	—	2	1	no	—
182	C₃×C₄×C₉	—	2	2	no	—
183	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
184	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
185	C₃×Dic₉	—	2	1	no	—
186	C₃×Dic₉	C₂×D₄	1	1	yes	characteristic
187	C₃×Dic₉	C₂×D₄	1	1	yes	characteristic
188	C₂×C₃×#41	—	9	1	no	—
189	C₂×C₃×#41	—	9	1	no	—
190	D₃×#41	—	3	1	no	—
191	C₂×#239	—	3	1	no	—
192	C₃×#137	—	2	1	no	—
193	C₃×#137	—	9	1	no	—
194	C₃×#137	—	9	2	no	—
195	C₃×#137	D₉	1	1	yes	characteristic, complemented
196	C₃×#137	C₃×D₃	1	1	yes	characteristic
197	C₃×AGL(1,ℤ/8)	—	9	1	no	—
198	C₃×AGL(1,ℤ/8)	—	9	2	no	—
199	C₃×AGL(1,ℤ/8)	—	9	1	no	—
200	C₃×#135	—	9	2	no	—
201	C₃×#135	—	9	2	no	—
202	C₂×C₃×M₁₆	—	9	1	no	—
203	#949	—	3	1	no	—
204	#942	—	3	1	no	—
205	#919	—	3	2	no	—
206	#918	—	3	2	no	—
207	#916	—	3	2	no	—
208	#914	—	3	2	no	—
209	#908	—	3	1	no	—
210	D₃×M₁₆	—	3	1	no	—
211	C₂²×C₃×D₃	—	3	1	no	—
212	C₂²×C₃×D₃	—	6	1	no	—
213	C₂²×C₃×D₃	—	6	1	no	—
214	C₃²×Q₈	—	2	1	no	—
215	C₃²×Q₈	C₂²×D₃	1	1	yes	characteristic
216	C₃²×Q₈	C₂²×D₃	1	2	yes	—
217	C₃²×D₄	—	2	1	no	—
218	C₃²×D₄	C₂²×D₃	1	1	yes	characteristic
219	C₂×C₃²×C₄	—	2	1	no	—
220	C₂×C₃²×C₄	—	2	1	no	—
221	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
222	C₃×#67	—	6	1	no	—
223	C₃×#67	—	6	1	no	—
224	C₃×#67	—	6	1	no	—
225	C₂×C₃×Dic₃	—	3	1	no	—
226	C₂×C₃×Dic₃	—	6	1	no	—
227	C₃×D₁₂	—	3	2	no	—
228	C₃×D₁₂	—	3	1	no	—
229	C₃×D₁₂	—	6	2	no	—
230	C₃×D₁₂	—	6	2	no	—
231	C₃×D₁₂	—	6	1	no	—
232	C₃×D₁₂	—	6	1	no	—
233	C₃×C₄×D₃	—	3	1	no	—
234	C₃×C₄×D₃	—	3	1	no	—
235	C₃×C₄×D₃	—	3	1	no	—
236	C₃×C₄×D₃	—	3	1	no	—
237	C₃×C₄×D₃	—	6	1	no	—
238	C₃×C₄×D₃	—	6	2	no	—
239	C₃×C₄×D₃	—	6	2	no	—
240	C₃×C₄×D₃	—	6	1	no	—
241	C₃×C₄×D₃	—	6	1	no	—
242	C₃×Dic₆	—	3	1	no	—
243	C₃×Dic₆	—	6	1	no	—
244	C₂²×D₉	—	2	1	no	—
245	C₂²×D₉	—	2	1	no	—
246	C₂²×D₉	C₃×D₄	1	1	yes	characteristic
247	C₃²×C₈	C₂²×D₃	1	2	yes	—
248	C₃×C₃⋊C₈	—	3	2	no	—
249	Q₈×C₉	—	2	1	no	—
250	Q₈×C₉	—	2	2	no	—
251	Q₈×C₉	—	2	1	no	—
252	Q₈×C₉	—	4	1	no	—
253	Q₈×C₉	C₂³×C₃	1	2	yes	—
254	Q₈×C₉	C₂³×C₃	1	1	yes	characteristic
255	D₄×C₉	—	2	1	no	—
256	D₄×C₉	—	2	1	no	—
257	D₄×C₉	—	4	1	no	—
258	D₄×C₉	C₂³×C₃	1	1	yes	characteristic
259	C₂×C₄×C₉	—	2	1	no	—
260	C₂×C₄×C₉	—	2	1	no	—
261	C₂×C₄×C₉	—	2	1	no	—
262	C₂×C₄×C₉	—	4	1	no	—
263	C₂×C₄×C₉	—	4	1	no	—
264	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
265	#611	—	2	1	no	—
266	#611	—	2	1	no	—
267	#611	—	2	1	no	—
268	C₂×Dic₉	—	2	1	no	—
269	C₂×Dic₉	C₃×D₄	1	1	yes	characteristic
270	D₃₆	—	2	2	no	—
271	D₃₆	—	2	2	no	—
272	D₃₆	—	2	1	no	—
273	D₃₆	—	2	1	no	—
274	D₃₆	C₂³×C₃	1	2	yes	—
275	D₃₆	C₂³×C₃	1	1	yes	characteristic
276	C₄×D₉	—	2	1	no	—
277	C₄×D₉	—	2	1	no	—
278	C₄×D₉	—	2	1	no	—
279	C₄×D₉	—	2	2	no	—
280	C₄×D₉	—	2	2	no	—
281	C₄×D₉	C₃×D₄	1	1	yes	characteristic
282	C₄×D₉	C₃×D₄	1	1	yes	characteristic
283	C₄×D₉	C₂³×C₃	1	1	yes	characteristic
284	C₄×D₉	C₂³×C₃	1	1	yes	characteristic
285	Dic₁₈	—	2	1	no	—
286	Dic₁₈	C₂³×C₃	1	1	yes	characteristic
287	C₈×C₉	—	2	2	no	—
288	C₈×C₉	C₂³×C₃	1	2	yes	—
289	C₉⋊C₈	C₂³×C₃	1	2	yes	—
290	#575	—	9	1	no	Sylow
291	C₂×C₃×C₉	—	2	1	no	—
292	C₂×C₃×C₉	—	4	1	no	—
293	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
294	C₃×D₉	—	2	1	no	—
295	C₃×D₉	—	2	1	no	—
296	C₃×D₉	—	4	2	no	—
297	C₃×D₉	—	4	1	no	—
298	C₃×#41	—	2	1	no	—
299	C₃×#41	—	9	1	no	—
300	C₃×#41	—	9	2	no	—
301	C₃×#41	—	9	2	no	—
302	C₃×#41	—	9	1	no	—
303	C₃×#41	—	9	1	no	—
304	C₃×#41	—	18	1	no	—
305	C₃×#41	—	18	1	no	—
306	C₃×#41	—	18	1	no	—
307	C₃×#41	—	18	1	no	—
308	C₃×#41	C₂×D₉	1	1	yes	characteristic
309	C₃×#41	C₂×C₃×D₃	1	1	yes	characteristic
310	C₂×C₃×Q₈	—	2	1	no	—
311	C₂×C₃×Q₈	—	9	1	no	—
312	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic, complemented
313	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
314	C₂×C₃×D₄	—	9	1	no	—
315	C₂×C₃×D₄	—	9	1	no	—
316	C₂×C₃×D₄	—	18	1	no	—
317	C₂×C₃×D₄	—	18	1	no	—
318	C₂²×C₃×C₄	—	9	1	no	—
319	C₂²×C₃×C₄	—	18	1	no	—
320	C₂²×C₃×C₄	—	18	1	no	—
321	#239	—	3	2	no	—
322	#239	—	3	2	no	—
323	#239	—	3	1	no	—
324	#239	—	6	1	no	—
325	#239	—	6	1	no	—
326	D₃×Q₈	—	3	1	no	—
327	#237	—	3	1	no	—
328	#237	—	6	1	no	—
329	D₃×D₄	—	3	1	no	—
330	D₃×D₄	—	6	1	no	—
331	#235	—	3	1	no	—
332	#235	—	6	1	no	—
333	C₂×D₁₂	—	3	1	no	—
334	C₂×D₁₂	—	6	1	no	—
335	C₂×C₄×D₃	—	3	1	no	—
336	C₂×C₄×D₃	—	6	1	no	—
337	C₂×C₄×D₃	—	6	1	no	—
338	C₃×Q₁₆	—	2	2	no	—
339	C₃×Q₁₆	—	9	2	no	—
340	C₃×Q₁₆	C₂×D₉	1	2	yes	complemented
341	C₃×Q₁₆	C₂×C₃×D₃	1	2	yes	—
342	C₃×SD₁₆	—	2	2	no	—
343	C₃×SD₁₆	—	9	2	no	—
344	C₃×SD₁₆	—	9	2	no	—
345	C₃×SD₁₆	—	9	2	no	—
346	C₃×SD₁₆	C₂×D₉	1	2	yes	complemented
347	C₃×SD₁₆	C₂×C₃×D₃	1	2	yes	—
348	C₃×D₈	—	9	2	no	—
349	C₃×D₈	—	9	2	no	—
350	C₃×M₁₆	—	2	1	no	—
351	C₃×M₁₆	—	9	1	no	—
352	C₃×M₁₆	—	9	2	no	—
353	C₃×M₁₆	C₂×D₉	1	1	yes	characteristic, complemented
354	C₃×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
355	C₂×C₃×C₈	—	9	2	no	—
356	#216	—	3	2	no	—
357	#215	—	3	2	no	—
358	#215	—	3	2	no	—
359	#213	—	3	2	no	—
360	#208	—	3	1	no	—
361	D₂₄	—	3	2	no	—
362	#204	—	3	2	no	—
363	ΓL(1,𝔽₂₅)	—	3	2	no	—
364	D₃×C₈	—	3	2	no	—
365	C₂²×C₃²	—	2	1	no	—
366	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
367	C₂×C₃×D₃	—	3	1	no	—
368	C₂×C₃×D₃	—	3	1	no	—
369	C₂×C₃×D₃	—	6	2	no	—
370	C₂×C₃×D₃	—	6	1	no	—
371	C₂×C₃×D₃	—	12	1	no	—
372	C₂×C₃×D₃	—	12	2	no	—
373	C₂×C₃×D₃	—	12	2	no	—
374	C₃²×C₄	—	2	1	no	—
375	C₃²×C₄	—	2	2	no	—
376	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
377	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
378	C₃×Dic₃	—	3	1	no	—
379	C₃×Dic₃	—	3	1	no	—
380	C₃×Dic₃	—	6	1	no	—
381	C₂²×C₉	—	2	1	no	—
382	C₂²×C₉	—	2	1	no	—
383	C₂²×C₉	—	4	1	no	—
384	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
385	C₂×D₉	—	2	2	no	—
386	C₂×D₉	—	2	1	no	—
387	C₂×D₉	—	4	1	no	—
388	C₂×D₉	—	4	2	no	—
389	C₂×D₉	—	4	2	no	—
390	C₂×D₉	C₂×C₃×D₄	1	1	yes	characteristic
391	C₂×D₉	C₂×C₃×D₄	1	1	yes	characteristic
392	C₄×C₉	—	2	1	no	—
393	C₄×C₉	—	2	2	no	—
394	C₄×C₉	—	2	1	no	—
395	C₄×C₉	—	2	1	no	—
396	C₄×C₉	—	4	1	no	—
397	C₄×C₉	—	4	2	no	—
398	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
399	C₄×C₉	C₂⁴×C₃	1	1	yes	characteristic
400	Dic₉	—	2	1	no	—
401	Dic₉	C₂×C₃×D₄	1	1	yes	characteristic
402	Dic₉	C₂×C₃×D₄	1	1	yes	characteristic
403	C₂×#41	—	9	1	no	—
404	C₂×#41	—	9	1	no	—
405	#137	—	9	1	no	—
406	#137	—	9	2	no	—
407	#137	C₃×D₉	1	1	yes	characteristic, complemented
408	AGL(1,ℤ/8)	—	9	1	no	—
409	AGL(1,ℤ/8)	—	9	2	no	—
410	AGL(1,ℤ/8)	—	9	1	no	—
411	#135	—	9	2	no	—
412	#135	—	9	2	no	—
413	C₂×M₁₆	—	9	1	no	—
414	C₃×C₉	#575	1	1	yes	characteristic, complemented, Sylow
415	C₂³×C₃	—	9	1	no	—
416	C₂³×C₃	—	18	1	no	—
417	C₂³×C₃	—	18	1	no	—
418	C₂²×D₃	—	3	1	no	—
419	C₂²×D₃	—	6	1	no	—
420	C₂²×D₃	—	6	1	no	—
421	C₃×Q₈	—	2	1	no	—
422	C₃×Q₈	—	2	1	no	—
423	C₃×Q₈	—	2	2	no	—
424	C₃×Q₈	—	2	1	no	—
425	C₃×Q₈	—	4	1	no	—
426	C₃×Q₈	—	9	1	no	—
427	C₃×Q₈	—	18	1	no	—
428	C₃×Q₈	C₂²×D₉	1	1	yes	characteristic
429	C₃×Q₈	C₂²×D₉	1	2	yes	—
430	C₃×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
431	C₃×Q₈	C₂²×C₃×D₃	1	2	yes	—
432	C₃×D₄	—	2	1	no	—
433	C₃×D₄	—	2	1	no	—
434	C₃×D₄	—	2	1	no	—
435	C₃×D₄	—	4	1	no	—
436	C₃×D₄	—	9	2	no	—
437	C₃×D₄	—	9	1	no	—
438	C₃×D₄	—	18	1	no	—
439	C₃×D₄	—	18	2	no	—
440	C₃×D₄	—	18	2	no	—
441	C₃×D₄	—	18	1	no	—
442	C₃×D₄	—	18	1	no	—
443	C₃×D₄	—	18	1	no	—
444	C₃×D₄	—	18	1	no	—
445	C₃×D₄	C₂²×D₉	1	1	yes	characteristic
446	C₃×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
447	C₂×C₃×C₄	—	2	1	no	—
448	C₂×C₃×C₄	—	2	1	no	—
449	C₂×C₃×C₄	—	2	1	no	—
450	C₂×C₃×C₄	—	2	1	no	—
451	C₂×C₃×C₄	—	2	1	no	—
452	C₂×C₃×C₄	—	4	1	no	—
453	C₂×C₃×C₄	—	4	1	no	—
454	C₂×C₃×C₄	—	9	1	no	—
455	C₂×C₃×C₄	—	9	1	no	—
456	C₂×C₃×C₄	—	9	1	no	—
457	C₂×C₃×C₄	—	9	1	no	—
458	C₂×C₃×C₄	—	9	1	no	—
459	C₂×C₃×C₄	—	18	1	no	—
460	C₂×C₃×C₄	—	18	2	no	—
461	C₂×C₃×C₄	—	18	2	no	—
462	C₂×C₃×C₄	—	18	1	no	—
463	C₂×C₃×C₄	—	18	1	no	—
464	C₂×C₃×C₄	—	18	1	no	—
465	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
466	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
467	#67	—	6	1	no	—
468	#67	—	6	1	no	—
469	#67	—	6	1	no	—
470	C₂×Dic₃	—	3	1	no	—
471	C₂×Dic₃	—	6	1	no	—
472	D₁₂	—	3	2	no	—
473	D₁₂	—	3	1	no	—
474	D₁₂	—	6	2	no	—
475	D₁₂	—	6	2	no	—
476	D₁₂	—	6	1	no	—
477	D₁₂	—	6	1	no	—
478	C₄×D₃	—	3	1	no	—
479	C₄×D₃	—	3	1	no	—
480	C₄×D₃	—	3	1	no	—
481	C₄×D₃	—	3	1	no	—
482	C₄×D₃	—	6	1	no	—
483	C₄×D₃	—	6	2	no	—
484	C₄×D₃	—	6	2	no	—
485	C₄×D₃	—	6	1	no	—
486	C₄×D₃	—	6	1	no	—
487	Dic₆	—	3	1	no	—
488	Dic₆	—	6	1	no	—
489	C₃×C₈	—	2	2	no	—
490	C₃×C₈	—	9	2	no	—
491	C₃×C₈	C₂²×D₉	1	2	yes	—
492	C₃×C₈	C₂²×C₃×D₃	1	2	yes	—
493	C₃⋊C₈	—	3	2	no	—
494	C₂×C₃²	—	2	1	no	—
495	C₂×C₃²	—	4	1	no	—
496	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
497	C₃×D₃	—	6	1	no	—
498	C₃×D₃	—	6	1	no	—
499	C₃×D₃	—	12	2	no	—
500	C₃×D₃	—	12	1	no	—
501	C₂×C₉	—	2	1	no	—
502	C₂×C₉	—	2	1	no	—
503	C₂×C₉	—	4	1	no	—
504	C₂×C₉	—	4	1	no	—
505	C₂×C₉	—	8	1	no	—
506	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
507	D₉	—	2	1	no	—
508	D₉	—	2	1	no	—
509	D₉	—	4	2	no	—
510	D₉	—	4	1	no	—
511	#41	—	9	1	no	—
512	#41	—	9	2	no	—
513	#41	—	9	2	no	—
514	#41	—	9	1	no	—
515	#41	—	9	1	no	—
516	#41	—	18	1	no	—
517	#41	—	18	1	no	—
518	#41	—	18	1	no	—
519	#41	—	18	1	no	—
520	#41	C₂×C₃×D₉	1	1	yes	characteristic
521	C₂×Q₈	—	9	1	no	—
522	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic, complemented
523	C₂×D₄	—	9	1	no	—
524	C₂×D₄	—	9	1	no	—
525	C₂×D₄	—	18	1	no	—
526	C₂×D₄	—	18	1	no	—
527	C₂²×C₄	—	9	1	no	—
528	C₂²×C₄	—	18	1	no	—
529	C₂²×C₄	—	18	1	no	—
530	Q₁₆	—	9	2	no	—
531	Q₁₆	C₂×C₃×D₉	1	2	yes	complemented
532	SD₁₆	—	9	2	no	—
533	SD₁₆	—	9	2	no	—
534	SD₁₆	—	9	2	no	—
535	SD₁₆	C₂×C₃×D₉	1	2	yes	complemented
536	D₈	—	9	2	no	—
537	D₈	—	9	2	no	—
538	M₁₆	—	9	1	no	—
539	M₁₆	—	9	2	no	—
540	M₁₆	C₂×C₃×D₉	1	1	yes	characteristic, complemented
541	C₂×C₈	—	9	2	no	—
542	C₂²×C₃	—	2	1	no	—
543	C₂²×C₃	—	2	1	no	—
544	C₂²×C₃	—	2	1	no	—
545	C₂²×C₃	—	4	1	no	—
546	C₂²×C₃	—	9	1	no	—
547	C₂²×C₃	—	9	1	no	—
548	C₂²×C₃	—	18	2	no	—
549	C₂²×C₃	—	18	1	no	—
550	C₂²×C₃	—	36	1	no	—
551	C₂²×C₃	—	36	2	no	—
552	C₂²×C₃	—	36	2	no	—
553	C₂²×C₃	D₄×D₉	1	1	yes	characteristic
554	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
555	C₂×D₃	—	3	1	no	—
556	C₂×D₃	—	3	1	no	—
557	C₂×D₃	—	6	2	no	—
558	C₂×D₃	—	6	1	no	—
559	C₂×D₃	—	12	1	no	—
560	C₂×D₃	—	12	2	no	—
561	C₂×D₃	—	12	2	no	—
562	C₃×C₄	—	2	1	no	—
563	C₃×C₄	—	2	2	no	—
564	C₃×C₄	—	2	1	no	—
565	C₃×C₄	—	2	2	no	—
566	C₃×C₄	—	2	1	no	—
567	C₃×C₄	—	2	1	no	—
568	C₃×C₄	—	4	1	no	—
569	C₃×C₄	—	4	2	no	—
570	C₃×C₄	—	9	1	no	—
571	C₃×C₄	—	9	1	no	—
572	C₃×C₄	—	18	1	no	—
573	C₃×C₄	D₄×D₉	1	1	yes	characteristic
574	C₃×C₄	C₂³×D₉	1	1	yes	characteristic
575	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
576	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
577	Dic₃	—	3	1	no	—
578	Dic₃	—	3	1	no	—
579	Dic₃	—	6	1	no	—
580	C₃²	#5777	1	1	yes	characteristic
581	C₉	—	2	1	no	—
582	C₉	C₃×#575	1	1	yes	characteristic, complemented
583	C₂³	—	9	1	no	—
584	C₂³	—	18	1	no	—
585	C₂³	—	18	1	no	—
586	Q₈	—	2	1	no	—
587	Q₈	—	9	1	no	—
588	Q₈	—	18	1	no	—
589	Q₈	C₂²×C₃×D₉	1	1	yes	characteristic
590	Q₈	C₂²×C₃×D₉	1	2	yes	—
591	D₄	—	2	1	no	—
592	D₄	—	9	2	no	—
593	D₄	—	9	1	no	—
594	D₄	—	18	1	no	—
595	D₄	—	18	2	no	—
596	D₄	—	18	2	no	—
597	D₄	—	18	1	no	—
598	D₄	—	18	1	no	—
599	D₄	—	18	1	no	—
600	D₄	—	18	1	no	—
601	D₄	C₂²×C₃×D₉	1	1	yes	characteristic
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	9	1	no	—
605	C₂×C₄	—	9	1	no	—
606	C₂×C₄	—	9	1	no	—
607	C₂×C₄	—	9	1	no	—
608	C₂×C₄	—	9	1	no	—
609	C₂×C₄	—	18	1	no	—
610	C₂×C₄	—	18	2	no	—
611	C₂×C₄	—	18	2	no	—
612	C₂×C₄	—	18	1	no	—
613	C₂×C₄	—	18	1	no	—
614	C₂×C₄	—	18	1	no	—
615	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
616	C₈	—	9	2	no	—
617	C₈	C₂²×C₃×D₉	1	2	yes	—
618	C₂×C₃	—	2	1	no	—
619	C₂×C₃	—	2	1	no	—
620	C₂×C₃	—	2	1	no	—
621	C₂×C₃	—	4	1	no	—
622	C₂×C₃	—	4	1	no	—
623	C₂×C₃	—	4	1	no	—
624	C₂×C₃	—	8	1	no	—
625	C₂×C₃	—	18	1	no	—
626	C₂×C₃	—	18	1	no	—
627	C₂×C₃	—	36	2	no	—
628	C₂×C₃	—	36	1	no	—
629	C₂×C₃	C₂×D₄×D₉	1	1	yes	characteristic
630	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
631	D₃	—	6	1	no	—
632	D₃	—	6	1	no	—
633	D₃	—	12	2	no	—
634	D₃	—	12	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	9	1	no	—
637	C₂²	—	9	1	no	—
638	C₂²	—	18	2	no	—
639	C₂²	—	18	1	no	—
640	C₂²	—	36	1	no	—
641	C₂²	—	36	2	no	—
642	C₂²	—	36	2	no	—
643	C₂²	C₃×D₄×D₉	1	1	yes	characteristic
644	C₄	—	2	1	no	—
645	C₄	—	2	2	no	—
646	C₄	—	9	1	no	—
647	C₄	—	9	1	no	—
648	C₄	—	18	1	no	—
649	C₄	C₃×D₄×D₉	1	1	yes	characteristic
650	C₄	C₂³×C₃×D₉	1	1	yes	characteristic
651	C₃	—	2	1	no	—
652	C₃	#10589879	1	1	yes	characteristic, direct product factor
653	C₃	C₃×#5777	1	1	yes	characteristic
654	C₂	—	2	1	no	—
655	C₂	—	4	1	no	—
656	C₂	—	18	1	no	—
657	C₂	—	18	1	no	—
658	C₂	—	36	2	no	—
659	C₂	—	36	1	no	—
660	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×#137	C₂
socle	C₂×C₃²	C₂×D₃×D₄
hypercenter	C₃×#137	D₉
hypocenter	C₉	C₃×#575
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#137

Complements

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

N	H ≅ G/N	type
1. C₃×#41×D₉	C₂	semidirect
2. C₂×C₃×#3701	C₂	semidirect
3. C₃×C₉×#137	C₂	semidirect
4. C₃×#63512	C₂	semidirect
5. C₃×#63505	C₂	semidirect
6. C₃×#63481	C₂	semidirect
7. C₃×#63480	C₂	semidirect
8. C₃×#63478	C₂	semidirect
9. C₃×#63476	C₂	semidirect
10. C₃×#63470	C₂	semidirect
11. C₃×M₁₆×D₉	C₂	semidirect
13. #10589879	C₃	direct (N × H)
15. C₂×C₃×Q₈×C₉	C₂²	semidirect
19. C₃×#3701	C₂²	semidirect
20. C₃×#3701	C₂²	semidirect
21. C₃×Q₈×D₉	C₂²	semidirect
23. C₃×#3699	C₂²	semidirect
25. C₃×D₄×D₉	C₂²	semidirect
29. C₂×C₃×D₃₆	C₂²	semidirect
33. C₃×C₉×Q₁₆	C₂²	semidirect
34. C₃×C₉×SD₁₆	C₂²	semidirect
35. C₃×C₉×M₁₆	C₂²	semidirect
36. C₃×#3675	C₂²	semidirect
37. C₃×#3675	C₂²	semidirect
38. C₃×#3674	C₂²	semidirect
39. C₃×#3673	C₂²	semidirect
40. C₃×#3667	C₂²	semidirect
41. C₃×D₇₂	C₂²	semidirect
42. C₃×#3664	C₂²	semidirect
43. C₃×#3663	C₂²	semidirect
44. C₃×C₈×D₉	C₂²	semidirect
56. #41×D₉	C₂×C₃	semidirect
57. C₂×#3701	C₂×C₃	semidirect
59. C₉×#137	C₂×C₃	semidirect
60. #63512	C₂×C₃	semidirect
61. #63505	C₂×C₃	semidirect
62. #63481	C₂×C₃	semidirect
63. #63480	C₂×C₃	semidirect
64. #63478	C₂×C₃	semidirect
65. #63476	C₂×C₃	semidirect
66. #63470	C₂×C₃	semidirect
67. M₁₆×D₉	C₂×C₃	semidirect
139. C₂×Q₈×C₉	C₂²×C₃	semidirect
143. #3701	C₂²×C₃	semidirect
144. #3701	C₂²×C₃	semidirect
145. Q₈×D₉	C₂²×C₃	semidirect
147. #3699	C₂²×C₃	semidirect
149. D₄×D₉	C₂²×C₃	semidirect
153. C₂×D₃₆	C₂²×C₃	semidirect
158. C₉×Q₁₆	C₂²×C₃	semidirect
160. C₉×SD₁₆	C₂²×C₃	semidirect
162. C₉×M₁₆	C₂²×C₃	semidirect
163. #3675	C₂²×C₃	semidirect
164. #3675	C₂²×C₃	semidirect
165. #3674	C₂²×C₃	semidirect
166. #3673	C₂²×C₃	semidirect
167. #3667	C₂²×C₃	semidirect
168. D₇₂	C₂²×C₃	semidirect
169. #3664	C₂²×C₃	semidirect
170. #3663	C₂²×C₃	semidirect
171. C₈×D₉	C₂²×C₃	semidirect
195. C₃×#137	D₉	semidirect
312. C₂×C₃×Q₈	C₂×D₉	semidirect
340. C₃×Q₁₆	C₂×D₉	semidirect
346. C₃×SD₁₆	C₂×D₉	semidirect
353. C₃×M₁₆	C₂×D₉	semidirect
407. #137	C₃×D₉	semidirect
414. C₃×C₉	#575	semidirect
522. C₂×Q₈	C₂×C₃×D₉	semidirect
531. Q₁₆	C₂×C₃×D₉	semidirect
535. SD₁₆	C₂×C₃×D₉	semidirect
540. M₁₆	C₂×C₃×D₉	semidirect
582. C₉	C₃×#575	semidirect
652. C₃	#10589879	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×#41×D₉	2
C₂×C₃×#3701	2
C₃×C₉×#137	2
C₃×#63512	2
C₃×#63505	2
C₃×#63481	2
C₃×#63480	2
C₃×#63478	2
C₃×#63476	2
C₃×#63470	2
C₃×M₁₆×D₉	2
C₃×#5777	3
#10589879	3

Subgroups — C3×#10589879 #13153508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589879 #13153508