Subgroups — C₂×C₃×#63513 #13153681

Order 1728.

962 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#3697	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63513	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×#3675	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3674	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#3673	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#3672	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₃×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#950	—	3	1	no	maximal
10	C₂×#63513	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₃×C₉×#41	—	2	2	no	—
12	C₃×C₉×#41	C₂²	1	4	yes	complemented
13	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₃×D₄×C₉	—	2	1	no	—
15	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₄×C₉	—	2	1	no	—
17	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
18	C₂×C₃×#611	—	2	1	no	—
19	C₃×#3697	—	2	2	no	—
20	C₃×#3697	C₂²	1	4	yes	complemented
21	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄×D₉	—	2	1	no	—
23	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
24	C₃×#3675	C₂²	1	4	yes	complemented
25	C₃×#3674	C₂²	1	4	yes	complemented
26	C₃×#3673	C₂²	1	4	yes	complemented
27	C₃×#3672	C₂²	1	4	yes	complemented
28	C₂×C₃×C₉⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₉⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₉⋊C₈	C₂²	1	4	yes	complemented
31	C₂×C₃²×#41	D₃	1	1	yes	characteristic
32	C₂×C₃×#235	—	3	1	no	—
33	C₃×#950	—	3	8	no	—
34	C₂×C₃×#216	—	3	1	no	—
35	C₂×C₃×#215	—	3	1	no	—
36	C₂×C₃×#214	—	3	1	no	—
37	C₂×C₃×#213	—	3	1	no	—
38	C₂²×C₃×C₃⋊C₈	—	3	1	no	—
39	C₂×C₉×#41	—	2	1	no	—
40	C₂×C₉×#41	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×#3697	C₂×C₃	1	1	yes	characteristic, complemented
42	#63513	C₂×C₃	1	8	yes	direct product factor
43	C₂×#3675	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×#3674	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×#3673	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×#3672	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂²×C₉⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂³×C₃×C₉	—	2	1	no	—
49	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
50	C₂²×C₃×D₉	—	2	1	no	—
51	C₃×Q₈×C₉	—	2	1	no	—
52	C₃×Q₈×C₉	C₂³	1	2	yes	—
53	C₃×D₄×C₉	—	2	4	no	—
54	C₃×D₄×C₉	—	2	1	no	—
55	C₃×D₄×C₉	C₂³	1	2	yes	—
56	C₂×C₃×C₄×C₉	—	2	1	no	—
57	C₂×C₃×C₄×C₉	—	2	4	no	—
58	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
59	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
60	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
62	C₃×#611	—	2	4	no	—
63	C₂×C₃×Dic₉	—	2	1	no	—
64	C₃×D₃₆	—	2	1	no	—
65	C₃×D₃₆	C₂³	1	2	yes	—
66	C₃×C₄×D₉	—	2	4	no	—
67	C₃×Dic₁₈	—	2	1	no	—
68	C₃×Dic₁₈	C₂³	1	2	yes	—
69	C₃×C₉⋊C₈	C₂³	1	2	yes	—
70	C₃×C₉⋊C₈	C₂³	1	2	yes	—
71	C₂×C₃×#135	—	9	1	no	—
72	C₂×#950	—	3	1	no	—
73	C₃²×#41	—	2	2	no	—
74	C₃²×#41	C₂×D₃	1	4	yes	—
75	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
76	C₂×C₃²×D₄	—	2	1	no	—
77	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
78	C₂²×C₃²×C₄	—	2	1	no	—
79	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
80	C₂×C₃×#67	—	6	1	no	—
81	C₃×#235	—	3	4	no	—
82	C₃×#235	—	6	2	no	—
83	C₂×C₃×D₁₂	—	3	1	no	—
84	C₂×C₃×C₄×D₃	—	6	1	no	—
85	C₂×C₃×Dic₆	—	3	1	no	—
86	C₃×#216	—	3	4	no	—
87	C₃×#215	—	3	4	no	—
88	C₃×#214	—	3	4	no	—
89	C₃×#213	—	3	4	no	—
90	C₂×C₃×C₃⋊C₈	—	3	1	no	—
91	C₂×C₃×C₃⋊C₈	—	3	1	no	—
92	C₂×C₃×C₃⋊C₈	—	3	4	no	—
93	C₉×#41	—	2	4	no	—
94	C₉×#41	—	2	4	no	—
95	C₉×#41	—	2	2	no	—
96	C₉×#41	C₂²×C₃	1	4	yes	complemented
97	C₂×Q₈×C₉	—	2	1	no	—
98	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
99	C₂×D₄×C₉	—	2	2	no	—
100	C₂×D₄×C₉	—	2	1	no	—
101	C₂×D₄×C₉	—	2	1	no	—
102	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
103	C₂²×C₄×C₉	—	2	2	no	—
104	C₂²×C₄×C₉	—	2	1	no	—
105	C₂²×C₄×C₉	—	2	1	no	—
106	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
107	C₂×#611	—	2	1	no	—
108	#3697	—	2	2	no	—
109	#3697	C₂²×C₃	1	4	yes	complemented
110	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₄×D₉	—	2	1	no	—
112	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
113	#3675	C₂²×C₃	1	4	yes	complemented
114	#3674	C₂²×C₃	1	4	yes	complemented
115	#3673	C₂²×C₃	1	4	yes	complemented
116	#3672	C₂²×C₃	1	4	yes	complemented
117	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₉⋊C₈	C₂²×C₃	1	4	yes	complemented
120	C₂²×C₃×C₉	—	2	2	no	—
121	C₂²×C₃×C₉	—	2	2	no	—
122	C₂²×C₃×C₉	—	4	2	no	—
123	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
124	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
125	C₂×C₃×D₉	—	2	2	no	—
126	C₂×C₃×D₉	—	4	2	no	—
127	C₃×C₄×C₉	—	2	2	no	—
128	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
129	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
130	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
131	C₃×Dic₉	—	2	2	no	—
132	C₂×C₃×#41	—	2	1	no	—
133	C₂×C₃×#41	—	9	1	no	—
134	C₂×C₃×#41	D₉	1	1	yes	characteristic, complemented
135	C₂×C₃×#41	C₃×D₃	1	1	yes	characteristic
136	C₂×#235	—	3	1	no	—
137	C₃×#135	—	9	8	no	—
138	C₂×C₃×Q₁₆	—	9	1	no	—
139	C₂×C₃×SD₁₆	—	9	1	no	—
140	C₂×C₃×SD₁₆	—	9	1	no	—
141	C₂×C₃×D₈	—	9	1	no	—
142	C₂²×C₃×C₈	—	9	1	no	—
143	#950	—	3	8	no	—
144	C₂×#216	—	3	1	no	—
145	C₂×#215	—	3	1	no	—
146	C₂×#214	—	3	1	no	—
147	C₂×#213	—	3	1	no	—
148	C₂²×C₃⋊C₈	—	3	1	no	—
149	C₂³×C₃²	—	2	1	no	—
150	C₂³×C₃²	#67	1	1	yes	characteristic
151	C₂²×C₃×D₃	—	6	1	no	—
152	C₃²×Q₈	—	2	1	no	—
153	C₃²×Q₈	C₂²×D₃	1	2	yes	—
154	C₃²×D₄	—	2	4	no	—
155	C₃²×D₄	—	2	1	no	—
156	C₃²×D₄	C₂²×D₃	1	2	yes	—
157	C₂×C₃²×C₄	—	2	1	no	—
158	C₂×C₃²×C₄	—	2	4	no	—
159	C₂×C₃²×C₄	#67	1	2	yes	—
160	C₂×C₃²×C₄	#67	1	1	yes	characteristic
161	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
162	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
163	C₃×#67	—	6	4	no	—
164	C₂×C₃×Dic₃	—	6	1	no	—
165	C₃×D₁₂	—	3	2	no	—
166	C₃×D₁₂	—	6	1	no	—
167	C₃×C₄×D₃	—	6	4	no	—
168	C₃×Dic₆	—	3	2	no	—
169	C₃×Dic₆	—	6	1	no	—
170	C₂³×C₉	—	2	2	no	—
171	C₂³×C₉	—	2	1	no	—
172	C₂³×C₉	—	2	1	no	—
173	C₂³×C₉	C₃×D₄	1	1	yes	characteristic
174	C₂²×D₉	—	2	1	no	—
175	C₃×C₃⋊C₈	—	3	2	no	—
176	C₃×C₃⋊C₈	—	3	2	no	—
177	Q₈×C₉	—	2	2	no	—
178	Q₈×C₉	—	2	1	no	—
179	Q₈×C₉	—	2	2	no	—
180	Q₈×C₉	C₂³×C₃	1	2	yes	—
181	D₄×C₉	—	2	8	no	—
182	D₄×C₉	—	2	2	no	—
183	D₄×C₉	—	2	4	no	—
184	D₄×C₉	—	2	1	no	—
185	D₄×C₉	—	2	2	no	—
186	D₄×C₉	C₂³×C₃	1	2	yes	—
187	C₂×C₄×C₉	—	2	2	no	—
188	C₂×C₄×C₉	—	2	8	no	—
189	C₂×C₄×C₉	—	2	1	no	—
190	C₂×C₄×C₉	—	2	4	no	—
191	C₂×C₄×C₉	—	2	1	no	—
192	C₂×C₄×C₉	—	2	2	no	—
193	C₂×C₄×C₉	—	2	1	no	—
194	C₂×C₄×C₉	—	2	2	no	—
195	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
196	C₂×C₄×C₉	C₃×D₄	1	2	yes	—
197	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
199	#611	—	2	4	no	—
200	C₂×Dic₉	—	2	1	no	—
201	D₃₆	—	2	1	no	—
202	D₃₆	C₂³×C₃	1	2	yes	—
203	C₄×D₉	—	2	4	no	—
204	Dic₁₈	—	2	1	no	—
205	Dic₁₈	C₂³×C₃	1	2	yes	—
206	C₉⋊C₈	C₂³×C₃	1	2	yes	—
207	C₉⋊C₈	C₂³×C₃	1	2	yes	—
208	C₂×#135	—	9	1	no	Sylow
209	C₂×C₃×C₉	—	2	2	no	—
210	C₂×C₃×C₉	—	4	2	no	—
211	C₂×C₃×C₉	#135	1	2	yes	complemented
212	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
213	C₃×D₉	—	4	2	no	—
214	C₃×#41	—	2	4	no	—
215	C₃×#41	—	2	2	no	—
216	C₃×#41	—	2	2	no	—
217	C₃×#41	—	2	4	no	—
218	C₃×#41	—	9	4	no	—
219	C₃×#41	—	18	2	no	—
220	C₃×#41	C₂×D₉	1	4	yes	complemented
221	C₃×#41	C₂×C₃×D₃	1	4	yes	—
222	C₂×C₃×Q₈	—	2	1	no	—
223	C₂×C₃×Q₈	—	9	1	no	—
224	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic
225	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
226	C₂×C₃×D₄	—	2	2	no	—
227	C₂×C₃×D₄	—	2	1	no	—
228	C₂×C₃×D₄	—	2	1	no	—
229	C₂×C₃×D₄	—	2	1	no	—
230	C₂×C₃×D₄	—	9	1	no	—
231	C₂×C₃×D₄	—	18	1	no	—
232	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic
233	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
234	C₂²×C₃×C₄	—	2	2	no	—
235	C₂²×C₃×C₄	—	2	1	no	—
236	C₂²×C₃×C₄	—	2	1	no	—
237	C₂²×C₃×C₄	—	2	1	no	—
238	C₂²×C₃×C₄	—	18	1	no	—
239	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
240	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
241	C₂×#67	—	6	1	no	—
242	#235	—	3	4	no	—
243	#235	—	6	2	no	—
244	C₂×D₁₂	—	3	1	no	—
245	C₂×C₄×D₃	—	6	1	no	—
246	C₂×Dic₆	—	3	1	no	—
247	C₃×Q₁₆	—	9	4	no	—
248	C₃×SD₁₆	—	9	4	no	—
249	C₃×SD₁₆	—	9	4	no	—
250	C₃×D₈	—	9	4	no	—
251	C₂×C₃×C₈	—	9	1	no	—
252	C₂×C₃×C₈	—	9	1	no	—
253	C₂×C₃×C₈	—	9	4	no	—
254	#216	—	3	4	no	—
255	#215	—	3	4	no	—
256	#214	—	3	4	no	—
257	#213	—	3	4	no	—
258	C₂×C₃⋊C₈	—	3	1	no	—
259	C₂×C₃⋊C₈	—	3	1	no	—
260	C₂×C₃⋊C₈	—	3	4	no	—
261	C₂²×C₃²	—	2	2	no	—
262	C₂²×C₃²	—	2	2	no	—
263	C₂²×C₃²	—	4	2	no	—
264	C₂²×C₃²	C₂×#67	1	2	yes	—
265	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
266	C₂×C₃×D₃	—	6	2	no	—
267	C₂×C₃×D₃	—	12	2	no	—
268	C₃²×C₄	—	2	2	no	—
269	C₃²×C₄	C₂×#67	1	1	yes	characteristic
270	C₃²×C₄	C₂×#67	1	2	yes	—
271	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
272	C₃×Dic₃	—	6	2	no	—
273	C₂²×C₉	—	2	2	no	—
274	C₂²×C₉	—	2	4	no	—
275	C₂²×C₉	—	2	2	no	—
276	C₂²×C₉	—	2	1	no	—
277	C₂²×C₉	—	2	2	no	—
278	C₂²×C₉	—	4	2	no	—
279	C₂²×C₉	—	4	4	no	—
280	C₂²×C₉	—	4	2	no	—
281	C₂²×C₉	C₂×C₃×D₄	1	2	yes	—
282	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
283	C₂×D₉	—	2	2	no	—
284	C₂×D₉	—	4	2	no	—
285	C₄×C₉	—	2	4	no	—
286	C₄×C₉	—	2	2	no	—
287	C₄×C₉	—	2	1	no	—
288	C₄×C₉	—	2	2	no	—
289	C₄×C₉	—	2	1	no	—
290	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
291	C₄×C₉	C₂×C₃×D₄	1	2	yes	—
292	C₄×C₉	C₂⁴×C₃	1	1	yes	characteristic
293	Dic₉	—	2	2	no	—
294	C₂×#41	—	9	1	no	—
295	C₂×#41	C₃×D₉	1	1	yes	characteristic, complemented
296	#135	—	9	8	no	—
297	C₂×Q₁₆	—	9	1	no	—
298	C₂×SD₁₆	—	9	1	no	—
299	C₂×SD₁₆	—	9	1	no	—
300	C₂×D₈	—	9	1	no	—
301	C₂²×C₈	—	9	1	no	—
302	C₃×C₉	C₂×#135	1	1	yes	characteristic, complemented, Sylow
303	C₂³×C₃	—	2	2	no	—
304	C₂³×C₃	—	2	1	no	—
305	C₂³×C₃	—	2	1	no	—
306	C₂³×C₃	—	2	1	no	—
307	C₂³×C₃	—	18	1	no	—
308	C₂³×C₃	#611	1	1	yes	characteristic
309	C₂³×C₃	C₃×#67	1	1	yes	characteristic
310	C₂²×D₃	—	6	1	no	—
311	C₃×Q₈	—	2	2	no	—
312	C₃×Q₈	—	2	1	no	—
313	C₃×Q₈	—	2	1	no	—
314	C₃×Q₈	—	2	2	no	—
315	C₃×Q₈	—	9	2	no	—
316	C₃×Q₈	—	18	1	no	—
317	C₃×Q₈	C₂²×D₉	1	2	yes	—
318	C₃×Q₈	C₂²×C₃×D₃	1	2	yes	—
319	C₃×D₄	—	2	8	no	—
320	C₃×D₄	—	2	2	no	—
321	C₃×D₄	—	2	4	no	—
322	C₃×D₄	—	2	4	no	—
323	C₃×D₄	—	2	1	no	—
324	C₃×D₄	—	2	1	no	—
325	C₃×D₄	—	2	2	no	—
326	C₃×D₄	—	9	2	no	—
327	C₃×D₄	—	18	4	no	—
328	C₃×D₄	—	18	1	no	—
329	C₃×D₄	C₂²×D₉	1	2	yes	—
330	C₃×D₄	C₂²×C₃×D₃	1	2	yes	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	2	8	no	—
333	C₂×C₃×C₄	—	2	1	no	—
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	2	4	no	—
336	C₂×C₃×C₄	—	2	4	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	2	2	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	2	no	—
341	C₂×C₃×C₄	—	18	1	no	—
342	C₂×C₃×C₄	—	18	4	no	—
343	C₂×C₃×C₄	#611	1	2	yes	—
344	C₂×C₃×C₄	#611	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
347	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
348	C₂×C₃×C₄	C₃×#67	1	2	yes	—
349	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
350	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
351	#67	—	6	4	no	—
352	C₂×Dic₃	—	6	1	no	—
353	D₁₂	—	3	2	no	—
354	D₁₂	—	6	1	no	—
355	C₄×D₃	—	6	4	no	—
356	Dic₆	—	3	2	no	—
357	Dic₆	—	6	1	no	—
358	C₃×C₈	—	9	2	no	—
359	C₃×C₈	—	9	2	no	—
360	C₃⋊C₈	—	3	2	no	—
361	C₃⋊C₈	—	3	2	no	—
362	C₂×C₃²	—	2	2	no	—
363	C₂×C₃²	—	4	2	no	—
364	C₂×C₃²	#950	1	2	yes	—
365	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
366	C₃×D₃	—	12	2	no	—
367	C₂×C₉	—	2	2	no	—
368	C₂×C₉	—	2	2	no	—
369	C₂×C₉	—	2	1	no	—
370	C₂×C₉	—	4	2	no	—
371	C₂×C₉	—	4	4	no	—
372	C₂×C₉	—	4	2	no	—
373	C₂×C₉	C₃×#135	1	2	yes	complemented
374	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
375	D₉	—	4	2	no	—
376	#41	—	2	2	no	—
377	#41	—	9	4	no	—
378	#41	—	18	2	no	—
379	#41	C₂×C₃×D₉	1	4	yes	complemented
380	C₂×Q₈	—	9	1	no	—
381	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	9	1	no	—
384	C₂×D₄	—	18	1	no	—
385	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	18	1	no	—
388	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
389	Q₁₆	—	9	4	no	—
390	SD₁₆	—	9	4	no	—
391	SD₁₆	—	9	4	no	—
392	D₈	—	9	4	no	—
393	C₂×C₈	—	9	1	no	—
394	C₂×C₈	—	9	1	no	—
395	C₂×C₈	—	9	4	no	—
396	C₂²×C₃	—	2	2	no	—
397	C₂²×C₃	—	2	2	no	—
398	C₂²×C₃	—	2	4	no	—
399	C₂²×C₃	—	2	2	no	—
400	C₂²×C₃	—	2	2	no	—
401	C₂²×C₃	—	2	1	no	—
402	C₂²×C₃	—	2	2	no	—
403	C₂²×C₃	—	4	2	no	—
404	C₂²×C₃	—	4	4	no	—
405	C₂²×C₃	—	4	2	no	—
406	C₂²×C₃	—	4	2	no	—
407	C₂²×C₃	—	18	2	no	—
408	C₂²×C₃	—	36	2	no	—
409	C₂²×C₃	C₂×#611	1	2	yes	—
410	C₂²×C₃	C₂×#611	1	1	yes	characteristic
411	C₂²×C₃	C₂×C₃×#67	1	2	yes	—
412	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
413	C₂×D₃	—	6	2	no	—
414	C₂×D₃	—	12	2	no	—
415	C₃×C₄	—	2	4	no	—
416	C₃×C₄	—	2	2	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	2	1	no	—
419	C₃×C₄	—	2	2	no	—
420	C₃×C₄	—	2	1	no	—
421	C₃×C₄	—	18	2	no	—
422	C₃×C₄	C₂×#611	1	2	yes	—
423	C₃×C₄	C₂×#611	1	1	yes	characteristic
424	C₃×C₄	C₂³×D₉	1	1	yes	characteristic
425	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
426	C₃×C₄	C₂×C₃×#67	1	2	yes	—
427	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
428	Dic₃	—	6	2	no	—
429	C₃²	C₂×#950	1	1	yes	characteristic
430	C₉	—	2	1	no	—
431	C₉	C₂×C₃×#135	1	1	yes	characteristic, complemented
432	C₂³	—	2	1	no	—
433	C₂³	—	18	1	no	—
434	C₂³	C₃×#611	1	1	yes	characteristic
435	Q₈	—	2	1	no	—
436	Q₈	—	9	2	no	—
437	Q₈	—	18	1	no	—
438	Q₈	C₂²×C₃×D₉	1	2	yes	—
439	D₄	—	2	4	no	—
440	D₄	—	2	1	no	—
441	D₄	—	9	2	no	—
442	D₄	—	18	4	no	—
443	D₄	—	18	1	no	—
444	D₄	C₂²×C₃×D₉	1	2	yes	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	18	1	no	—
448	C₂×C₄	—	18	4	no	—
449	C₂×C₄	C₃×#611	1	1	yes	characteristic
450	C₂×C₄	C₃×#611	1	2	yes	—
451	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
452	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
453	C₈	—	9	2	no	—
454	C₈	—	9	2	no	—
455	C₂×C₃	—	2	2	no	—
456	C₂×C₃	—	2	2	no	—
457	C₂×C₃	—	2	1	no	—
458	C₂×C₃	—	2	2	no	—
459	C₂×C₃	—	4	2	no	—
460	C₂×C₃	—	4	4	no	—
461	C₂×C₃	—	4	2	no	—
462	C₂×C₃	—	4	2	no	—
463	C₂×C₃	—	36	2	no	—
464	C₂×C₃	#63513	1	2	yes	direct product factor
465	C₂×C₃	C₂²×#611	1	1	yes	characteristic
466	C₂×C₃	C₃×#950	1	2	yes	—
467	C₂×C₃	C₂²×C₃×#67	1	1	yes	characteristic
468	D₃	—	12	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	18	2	no	—
473	C₂²	—	36	2	no	—
474	C₂²	C₂×C₃×#611	1	2	yes	—
475	C₂²	C₂×C₃×#611	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	18	2	no	—
478	C₄	C₂×C₃×#611	1	2	yes	—
479	C₄	C₂×C₃×#611	1	1	yes	characteristic
480	C₄	C₂³×C₃×D₉	1	1	yes	characteristic
481	C₃	—	2	1	no	—
482	C₃	C₂×#63513	1	1	yes	characteristic, direct product factor
483	C₃	C₂×C₃×#950	1	1	yes	characteristic
484	C₂	—	2	2	no	—
485	C₂	—	4	2	no	—
486	C₂	—	36	2	no	—
487	C₂	C₃×#63513	1	2	yes	direct product factor
488	C₂	C₂²×C₃×#611	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	#611
commutator, cosocle	C₄×C₉	C₂⁴×C₃
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×#41	C₂
socle	C₂²×C₃²	C₂×#67
hypercenter	C₂×C₃×#41	D₉
hypocenter	C₉	C₂×C₃×#135
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₉×#41	C₂	semidirect
2. C₂×C₃×#3697	C₂	semidirect
3. C₃×#63513	C₂	direct (N × H)
4. C₂×C₃×#3675	C₂	semidirect
5. C₂×C₃×#3674	C₂	semidirect
6. C₂×C₃×#3673	C₂	semidirect
7. C₂×C₃×#3672	C₂	semidirect
8. C₂²×C₃×C₉⋊C₈	C₂	semidirect
10. C₂×#63513	C₃	direct (N × H)
12. C₃×C₉×#41	C₂²	semidirect
20. C₃×#3697	C₂²	semidirect
24. C₃×#3675	C₂²	semidirect
25. C₃×#3674	C₂²	semidirect
26. C₃×#3673	C₂²	semidirect
27. C₃×#3672	C₂²	semidirect
30. C₂×C₃×C₉⋊C₈	C₂²	semidirect
40. C₂×C₉×#41	C₂×C₃	semidirect
41. C₂×#3697	C₂×C₃	semidirect
42. #63513	C₂×C₃	direct (N × H)
43. C₂×#3675	C₂×C₃	semidirect
44. C₂×#3674	C₂×C₃	semidirect
45. C₂×#3673	C₂×C₃	semidirect
46. C₂×#3672	C₂×C₃	semidirect
47. C₂²×C₉⋊C₈	C₂×C₃	semidirect
96. C₉×#41	C₂²×C₃	semidirect
109. #3697	C₂²×C₃	semidirect
113. #3675	C₂²×C₃	semidirect
114. #3674	C₂²×C₃	semidirect
115. #3673	C₂²×C₃	semidirect
116. #3672	C₂²×C₃	semidirect
119. C₂×C₉⋊C₈	C₂²×C₃	semidirect
134. C₂×C₃×#41	D₉	semidirect
211. C₂×C₃×C₉	#135	semidirect
220. C₃×#41	C₂×D₉	semidirect
295. C₂×#41	C₃×D₉	semidirect
302. C₃×C₉	C₂×#135	semidirect
373. C₂×C₉	C₃×#135	semidirect
379. #41	C₂×C₃×D₉	semidirect
431. C₉	C₂×C₃×#135	semidirect
464. C₂×C₃	#63513	direct (N × H)
482. C₃	C₂×#63513	direct (N × H)
487. C₂	C₃×#63513	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×C₉×#41	2
C₂×C₃×#3697	2
C₃×#63513	2
C₂×C₃×#3675	2
C₂×C₃×#3674	2
C₂×C₃×#3673	2
C₂×C₃×#3672	2
C₂²×C₃×C₉⋊C₈	2
C₂×C₃×#950	3
C₂×#63513	3

Subgroups — C2×C3×#63513 #13153681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#63513 #13153681