Subgroups — D₃×#63469 #13149845

Order 1728.

860 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×#3697	C₂	1	1	yes	maximal, characteristic
2	#11721782	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×C₉×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63469	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₃×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#11720861	C₂	1	1	yes	maximal, characteristic, complemented
7	#11720859	C₂	1	1	yes	maximal, characteristic, complemented
8	#11720809	C₂	1	2	yes	maximal, complemented
9	#11720807	C₂	1	2	yes	maximal, complemented
10	D₃×#3663	C₂	1	2	yes	maximal, complemented
11	D₃×C₈×D₉	C₂	1	2	yes	maximal, complemented
12	D₃×#907	—	3	1	no	maximal
13	C₂×#63469	—	3	1	no	maximal
14	#88736	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
16	C₃×#3697	C₂²	1	1	yes	characteristic
17	D₃×#611	C₄	1	2	yes	—
18	#88658	C₄	1	2	yes	—
19	D₃×D₃₆	C₄	1	1	yes	characteristic
20	C₄×D₃×D₉	C₂²	1	2	yes	—
21	#88642	C₄	1	1	yes	characteristic
22	#88641	C₄	1	1	yes	characteristic
23	#88640	C₂²	1	2	yes	—
24	D₃×Dic₁₈	C₄	1	1	yes	characteristic
25	C₃×C₉×M₁₆	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃⋊(C₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
27	#88523	C₂²	1	2	yes	complemented
28	C₈×C₃⋊D₉	C₂²	1	2	yes	complemented
29	C₉×#208	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×C₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
31	C₉×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
32	D₃×C₈×C₉	C₂²	1	2	yes	—
33	C₃×#3663	C₂²	1	2	yes	complemented
34	C₃×C₈×D₉	C₂²	1	2	yes	complemented
35	D₃×C₉⋊C₈	C₂²	1	1	yes	characteristic
36	D₃×C₉⋊C₈	C₂²	1	1	yes	characteristic
37	D₃×C₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	D₃×C₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	#88414	C₂²	1	2	yes	complemented
40	#88413	C₂²	1	2	yes	complemented
41	(C₃⋊D₉)⋊C₈	C₂²	1	2	yes	complemented
42	D₉×C₃⋊C₈	C₂²	1	2	yes	complemented
43	D₃×#235	—	3	1	no	—
44	#64116	—	3	1	no	—
45	C₃×#907	—	3	1	no	—
46	C₃×D₃×M₁₆	D₃	1	1	yes	characteristic
47	#63817	—	3	1	no	—
48	#63815	—	3	1	no	—
49	C₂×D₃×C₃⋊C₈	—	3	1	no	—
50	#63805	—	3	2	no	—
51	#63804	—	3	2	no	—
52	D₃×ΓL(1,𝔽₂₅)	—	3	2	no	—
53	D₃²×C₈	—	3	2	no	—
54	C₂×#3697	—	3	1	no	—
55	C₂×C₉×M₁₆	—	3	1	no	—
56	C₂²×C₉⋊C₈	—	3	1	no	—
57	#63469	—	3	1	no	—
58	#63469	—	3	1	no	—
59	#63469	—	3	1	no	—
60	#63469	—	3	2	no	—
61	#63469	—	3	2	no	—
62	#63469	—	6	1	no	—
63	#63469	D₃	1	1	yes	characteristic, direct product factor
64	C₂×#3663	—	3	2	no	—
65	C₂×C₈×D₉	—	3	2	no	—
66	C₂²×D₃×C₉	C₂×C₄	1	1	yes	characteristic
67	C₂×D₃×D₉	C₂×C₄	1	2	yes	—
68	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
69	#6233	C₂×C₄	1	2	yes	—
70	C₄⋊(C₃⋊D₉)	C₂×C₄	1	1	yes	characteristic
71	C₄×C₃⋊D₉	C₂³	1	2	yes	—
72	#6226	C₂×C₄	1	1	yes	characteristic
73	C₃×#611	C₂×C₄	1	2	yes	—
74	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic
75	C₄×D₃×C₉	C₂×C₄	1	1	yes	characteristic
76	C₄×D₃×C₉	C₂×C₄	1	1	yes	characteristic
77	C₄×D₃×C₉	C₂³	1	1	yes	characteristic
78	C₄×D₃×C₉	C₂³	1	1	yes	characteristic
79	C₃×D₃₆	C₂×C₄	1	1	yes	characteristic
80	C₃×C₄×D₉	C₂³	1	2	yes	—
81	C₃×Dic₁₈	C₂×C₄	1	1	yes	characteristic
82	#6195	C₂×C₄	1	2	yes	—
83	#6194	C₂×C₄	1	2	yes	—
84	D₃×Dic₉	C₂×C₄	1	2	yes	—
85	#6192	C₂×C₄	1	2	yes	—
86	(C₃⋊D₉)⋊C₄	C₂×C₄	1	2	yes	—
87	Dic₃×D₉	C₂×C₄	1	2	yes	—
88	#6189	C₂×C₄	1	2	yes	—
89	C₃×C₈×C₉	C₂³	1	2	yes	—
90	C₃⋊(C₉⋊C₈)	C₂³	1	1	yes	characteristic
91	C₃⋊(C₉⋊C₈)	C₂³	1	1	yes	characteristic
92	C₉×C₃⋊C₈	C₂³	1	2	yes	—
93	C₃×C₉⋊C₈	C₂³	1	1	yes	characteristic
94	C₃×C₉⋊C₈	C₂³	1	1	yes	characteristic
95	D₃×#131	—	9	1	no	—
96	C₂×#907	—	9	1	no	—
97	#3828	—	3	1	no	—
98	C₃×#235	—	3	1	no	—
99	C₂×C₃×C₄×D₃	C₂×D₃	1	1	yes	characteristic
100	D₃×#67	—	3	2	no	—
101	#3804	—	3	2	no	—
102	D₃×D₁₂	—	3	1	no	—
103	C₄×D₃²	—	3	2	no	—
104	#3799	—	3	1	no	—
105	#3798	—	3	2	no	—
106	#3795	—	3	1	no	—
107	D₃×Dic₆	—	3	1	no	—
108	C₃²×M₁₆	C₂×D₃	1	1	yes	characteristic
109	C₂×C₃⋊(C₃⋊C₈)	—	3	1	no	—
110	#3743	—	3	2	no	—
111	C₈×C₃⋊D₃	—	3	2	no	—
112	C₃×#208	C₂×D₃	1	1	yes	characteristic
113	C₂×C₃×C₃⋊C₈	—	3	1	no	—
114	C₃×ΓL(1,𝔽₂₅)	—	3	2	no	—
115	C₃×ΓL(1,𝔽₂₅)	C₂×D₃	1	2	yes	—
116	C₃×D₃×C₈	—	3	2	no	—
117	C₃×D₃×C₈	C₂×D₃	1	2	yes	—
118	#3712	—	3	2	no	—
119	#3711	—	3	2	no	—
120	#3710	—	3	2	no	—
121	D₃×C₃⋊C₈	—	3	1	no	—
122	D₃×C₃⋊C₈	—	3	1	no	—
123	D₃×C₃⋊C₈	—	3	1	no	—
124	D₃×C₃⋊C₈	—	3	1	no	—
125	D₃×C₃⋊C₈	—	3	2	no	—
126	C₂²×C₄×C₉	—	3	1	no	—
127	C₂×#611	—	3	2	no	—
128	#3697	—	3	1	no	—
129	#3697	—	3	2	no	—
130	#3697	—	3	1	no	—
131	#3697	—	3	2	no	—
132	#3697	—	3	1	no	—
133	#3697	—	6	1	no	—
134	#3697	C₂×D₃	1	1	yes	characteristic
135	C₂×D₃₆	—	3	1	no	—
136	C₂×C₄×D₉	—	3	2	no	—
137	C₂×Dic₁₈	—	3	1	no	—
138	C₉×M₁₆	—	2	1	no	—
139	C₉×M₁₆	—	3	1	no	—
140	C₉×M₁₆	—	3	2	no	—
141	C₉×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
142	C₂×C₈×C₉	—	3	2	no	—
143	C₂×C₉⋊C₈	—	3	1	no	—
144	C₂×C₉⋊C₈	—	3	1	no	—
145	C₂×C₉⋊C₈	—	3	1	no	—
146	C₂×C₉⋊C₈	—	3	1	no	—
147	C₂×C₉⋊C₈	—	3	1	no	—
148	C₂×C₉⋊C₈	—	6	1	no	—
149	C₂×C₉⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
150	#3663	—	3	2	no	—
151	#3663	—	3	2	no	—
152	#3663	—	3	2	no	—
153	#3663	—	6	2	no	—
154	#3663	C₂×D₃	1	2	yes	complemented
155	C₈×D₉	—	3	2	no	—
156	C₈×D₉	—	3	2	no	—
157	C₈×D₉	—	3	2	no	—
158	C₈×D₉	—	6	2	no	—
159	C₈×D₉	C₂×D₃	1	2	yes	complemented
160	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₃⋊D₉	C₂²×C₄	1	2	yes	—
162	C₂×D₃×C₉	—	2	2	no	—
163	C₂×D₃×C₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×D₃×C₉	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₃×D₉	C₂²×C₄	1	2	yes	—
166	D₃×D₉	—	2	4	no	—
167	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
168	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
169	C₃⋊Dic₉	C₂²×C₄	1	2	yes	—
170	C₉×Dic₃	C₂²×C₄	1	1	yes	characteristic
171	C₉×Dic₃	C₂²×C₄	1	1	yes	characteristic
172	C₃×Dic₉	C₂²×C₄	1	2	yes	—
173	D₃×#41	—	9	1	no	—
174	C₂×#235	—	9	1	no	—
175	C₃×#131	—	9	1	no	—
176	C₂×C₃×M₁₆	—	3	1	no	—
177	#948	—	9	1	no	—
178	C₂²×C₃⋊C₈	—	9	1	no	—
179	#907	—	3	1	no	—
180	#907	—	9	2	no	—
181	#907	—	9	2	no	—
182	#907	—	9	1	no	—
183	#907	—	9	1	no	—
184	#907	—	9	1	no	—
185	#907	—	9	1	no	—
186	#907	—	9	2	no	—
187	#907	—	18	1	no	—
188	D₃×M₁₆	—	9	2	no	—
189	D₃×M₁₆	D₉	1	1	yes	characteristic, complemented
190	#901	—	9	1	no	—
191	#901	—	9	2	no	—
192	C₂×ΓL(1,𝔽₂₅)	—	9	2	no	—
193	C₂×D₃×C₈	—	9	2	no	—
194	C₂×D₃×C₈	—	9	1	no	—
195	C₂×D₃×C₈	—	9	2	no	—
196	C₂²×C₃×D₃	C₄×D₃	1	1	yes	characteristic
197	C₂×D₃²	—	3	2	no	—
198	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
199	#638	—	3	2	no	—
200	C₄⋊(C₃⋊D₃)	—	3	1	no	—
201	C₄×C₃⋊D₃	—	3	2	no	—
202	#634	—	3	1	no	—
203	C₃×#67	—	3	2	no	—
204	C₂×C₃×Dic₃	C₄×D₃	1	1	yes	characteristic
205	C₃×D₁₂	—	3	1	no	—
206	C₃×C₄×D₃	—	3	2	no	—
207	C₃×C₄×D₃	C₄×D₃	1	1	yes	characteristic
208	C₃×C₄×D₃	C₄×D₃	1	1	yes	characteristic
209	C₃×C₄×D₃	C₂²×D₃	1	1	yes	characteristic
210	C₃×C₄×D₃	C₂²×D₃	1	1	yes	characteristic
211	C₃×Dic₆	—	3	1	no	—
212	#627	—	3	2	no	—
213	#626	—	3	2	no	—
214	#626	—	3	2	no	—
215	#625	—	3	2	no	—
216	#624	—	3	2	no	—
217	D₃×Dic₃	—	3	2	no	—
218	D₃×Dic₃	—	3	2	no	—
219	C₂³×C₉	—	3	1	no	—
220	C₂²×D₉	—	3	2	no	—
221	C₃²×C₈	C₂²×D₃	1	2	yes	—
222	C₃⋊(C₃⋊C₈)	—	3	1	no	—
223	C₃⋊(C₃⋊C₈)	—	3	1	no	—
224	C₃×C₃⋊C₈	—	3	1	no	—
225	C₃×C₃⋊C₈	—	3	1	no	—
226	C₃×C₃⋊C₈	C₂²×D₃	1	2	yes	—
227	C₂×C₄×C₉	—	2	1	no	—
228	C₂×C₄×C₉	—	3	1	no	—
229	C₂×C₄×C₉	—	3	1	no	—
230	C₂×C₄×C₉	—	3	1	no	—
231	C₂×C₄×C₉	—	3	1	no	—
232	C₂×C₄×C₉	—	3	1	no	—
233	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
234	#611	—	3	2	no	—
235	#611	—	3	2	no	—
236	#611	—	3	2	no	—
237	#611	—	6	2	no	—
238	#611	C₄×D₃	1	2	yes	—
239	C₂×Dic₉	—	3	2	no	—
240	D₃₆	—	3	2	no	—
241	D₃₆	—	3	1	no	—
242	D₃₆	—	6	1	no	—
243	D₃₆	C₄×D₃	1	1	yes	characteristic
244	C₄×D₉	—	3	2	no	—
245	C₄×D₉	—	3	2	no	—
246	C₄×D₉	—	3	2	no	—
247	C₄×D₉	—	6	2	no	—
248	C₄×D₉	C₂²×D₃	1	2	yes	—
249	Dic₁₈	—	3	1	no	—
250	Dic₁₈	—	3	2	no	—
251	Dic₁₈	—	6	1	no	—
252	Dic₁₈	C₄×D₃	1	1	yes	characteristic
253	C₈×C₉	—	2	2	no	—
254	C₈×C₉	—	3	2	no	—
255	C₈×C₉	C₂²×D₃	1	2	yes	—
256	C₉⋊C₈	—	3	1	no	—
257	C₉⋊C₈	—	3	1	no	—
258	C₉⋊C₈	—	6	1	no	—
259	C₉⋊C₈	—	6	1	no	—
260	C₉⋊C₈	C₂²×D₃	1	1	yes	characteristic
261	C₉⋊C₈	C₂²×D₃	1	1	yes	characteristic
262	C₂×#131	—	27	1	no	Sylow
263	C₂×C₃×C₉	—	2	1	no	—
264	C₂×C₃×C₉	C₂³×C₄	1	1	yes	characteristic
265	C₃⋊D₉	—	2	2	no	—
266	D₃×C₉	—	2	1	no	—
267	D₃×C₉	#131	1	2	yes	complemented
268	C₃×D₉	—	2	2	no	—
269	C₃×#41	—	9	1	no	—
270	C₂²×C₃×C₄	—	3	1	no	—
271	C₂×#67	—	9	2	no	—
272	#239	—	9	1	no	—
273	D₃×Q₈	—	9	1	no	—
274	#237	—	9	2	no	—
275	#237	—	9	1	no	—
276	D₃×D₄	—	9	2	no	—
277	D₃×D₄	—	9	1	no	—
278	#235	—	3	1	no	—
279	#235	—	9	1	no	—
280	#235	—	9	2	no	—
281	#235	—	9	1	no	—
282	#235	—	9	2	no	—
283	#235	—	9	1	no	—
284	#235	—	9	1	no	—
285	#235	—	9	2	no	—
286	#235	—	18	1	no	—
287	C₂×D₁₂	—	9	1	no	—
288	C₂×C₄×D₃	—	9	2	no	—
289	C₂×C₄×D₃	—	9	2	no	—
290	C₂×C₄×D₃	C₂×D₉	1	1	yes	characteristic
291	C₂×Dic₆	—	9	1	no	—
292	C₃×M₁₆	—	2	1	no	—
293	C₃×M₁₆	—	3	1	no	—
294	C₃×M₁₆	—	3	2	no	—
295	C₃×M₁₆	—	9	2	no	—
296	C₃×M₁₆	C₂×D₉	1	1	yes	characteristic, complemented
297	C₃×M₁₆	D₃²	1	1	yes	characteristic
298	C₂×C₃×C₈	—	3	2	no	—
299	C₂×C₃×C₈	—	9	1	no	—
300	C₂×C₃×C₈	—	9	2	no	—
301	#208	—	9	2	no	—
302	#208	C₂×D₉	1	1	yes	characteristic, complemented
303	C₂×C₃⋊C₈	—	3	1	no	—
304	C₂×C₃⋊C₈	—	9	1	no	—
305	C₂×C₃⋊C₈	—	9	1	no	—
306	C₂×C₃⋊C₈	—	9	1	no	—
307	C₂×C₃⋊C₈	—	9	1	no	—
308	C₂×C₃⋊C₈	—	9	1	no	—
309	C₂×C₃⋊C₈	—	9	1	no	—
310	C₂×C₃⋊C₈	—	9	2	no	—
311	C₂×C₃⋊C₈	—	18	1	no	—
312	ΓL(1,𝔽₂₅)	—	3	2	no	—
313	ΓL(1,𝔽₂₅)	—	9	2	no	—
314	ΓL(1,𝔽₂₅)	—	9	2	no	—
315	ΓL(1,𝔽₂₅)	—	9	2	no	—
316	ΓL(1,𝔽₂₅)	—	9	2	no	—
317	ΓL(1,𝔽₂₅)	—	9	2	no	—
318	ΓL(1,𝔽₂₅)	—	18	2	no	—
319	ΓL(1,𝔽₂₅)	C₂×D₉	1	2	yes	complemented
320	D₃×C₈	—	3	2	no	—
321	D₃×C₈	—	9	2	no	—
322	D₃×C₈	—	9	2	no	—
323	D₃×C₈	—	9	1	no	—
324	D₃×C₈	—	9	1	no	—
325	D₃×C₈	—	9	1	no	—
326	D₃×C₈	—	9	1	no	—
327	D₃×C₈	—	9	2	no	—
328	D₃×C₈	—	9	2	no	—
329	D₃×C₈	—	9	2	no	—
330	D₃×C₈	—	18	2	no	—
331	D₃×C₈	C₂×D₉	1	2	yes	—
332	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
333	C₂×C₃⋊D₃	—	3	2	no	—
334	C₂×C₃×D₃	—	2	2	no	—
335	C₂×C₃×D₃	—	3	2	no	—
336	C₂×C₃×D₃	C₂×C₄×D₃	1	1	yes	characteristic
337	C₂×C₃×D₃	C₂×C₄×D₃	1	1	yes	characteristic
338	D₃²	—	6	4	no	—
339	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
340	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
341	C₃⋊Dic₃	—	3	2	no	—
342	C₃×Dic₃	—	3	2	no	—
343	C₃×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
344	C₃×Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
345	C₂²×C₉	—	2	1	no	—
346	C₂²×C₉	—	3	1	no	—
347	C₂²×C₉	—	3	1	no	—
348	C₂²×C₉	—	6	2	no	—
349	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
350	C₂×D₉	—	3	2	no	—
351	C₂×D₉	—	6	2	no	—
352	C₂×D₉	—	6	4	no	—
353	C₂×D₉	C₂×C₄×D₃	1	2	yes	—
354	C₄×C₉	—	2	1	no	—
355	C₄×C₉	—	2	1	no	—
356	C₄×C₉	—	3	1	no	—
357	C₄×C₉	—	3	1	no	—
358	C₄×C₉	C₂×C₄×D₃	1	1	yes	characteristic
359	C₄×C₉	C₂³×D₃	1	1	yes	characteristic
360	Dic₉	—	3	2	no	—
361	Dic₉	—	6	2	no	—
362	Dic₉	C₂×C₄×D₃	1	2	yes	—
363	C₂×#41	—	27	1	no	—
364	#131	—	9	1	no	—
365	#131	—	27	1	no	—
366	#131	—	27	2	no	—
367	#131	—	27	2	no	—
368	#131	—	27	1	no	—
369	#131	—	27	1	no	—
370	C₂×M₁₆	—	3	1	no	—
371	C₂×M₁₆	—	27	2	no	—
372	C₂²×C₈	—	27	2	no	—
373	C₂²×C₈	—	27	1	no	—
374	C₃×C₉	C₂×#131	1	1	yes	characteristic, complemented, Sylow
375	C₂³×C₃	—	3	1	no	—
376	C₂²×D₃	—	9	2	no	—
377	C₂²×D₃	—	9	2	no	—
378	C₂²×D₃	C₄×D₉	1	1	yes	characteristic
379	C₃×Q₈	—	9	1	no	—
380	C₃×D₄	—	9	2	no	—
381	C₃×D₄	—	9	1	no	—
382	C₂×C₃×C₄	—	2	1	no	—
383	C₂×C₃×C₄	—	3	1	no	—
384	C₂×C₃×C₄	—	3	1	no	—
385	C₂×C₃×C₄	—	3	1	no	—
386	C₂×C₃×C₄	—	3	1	no	—
387	C₂×C₃×C₄	—	3	1	no	—
388	C₂×C₃×C₄	—	9	2	no	—
389	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
391	#67	—	3	2	no	—
392	#67	—	9	2	no	—
393	#67	—	9	2	no	—
394	#67	—	9	2	no	—
395	#67	—	9	2	no	—
396	#67	—	9	2	no	—
397	#67	—	9	2	no	—
398	#67	—	18	2	no	—
399	C₂×Dic₃	—	9	2	no	—
400	C₂×Dic₃	—	9	2	no	—
401	C₂×Dic₃	C₄×D₉	1	1	yes	characteristic
402	D₁₂	—	3	1	no	—
403	D₁₂	—	9	2	no	—
404	D₁₂	—	9	2	no	—
405	D₁₂	—	9	1	no	—
406	D₁₂	—	9	1	no	—
407	D₁₂	—	18	1	no	—
408	C₄×D₃	—	3	2	no	—
409	C₄×D₃	—	9	2	no	—
410	C₄×D₃	—	9	2	no	—
411	C₄×D₃	—	9	2	no	—
412	C₄×D₃	—	9	2	no	—
413	C₄×D₃	—	9	2	no	—
414	C₄×D₃	—	9	2	no	—
415	C₄×D₃	—	18	2	no	—
416	C₄×D₃	C₄×D₉	1	1	yes	characteristic
417	C₄×D₃	C₄×D₉	1	1	yes	characteristic
418	C₄×D₃	C₂²×D₉	1	1	yes	characteristic
419	C₄×D₃	C₂²×D₉	1	1	yes	characteristic
420	Dic₆	—	3	1	no	—
421	Dic₆	—	9	2	no	—
422	Dic₆	—	9	1	no	—
423	Dic₆	—	9	1	no	—
424	Dic₆	—	9	2	no	—
425	Dic₆	—	18	1	no	—
426	C₃×C₈	—	2	2	no	—
427	C₃×C₈	—	3	2	no	—
428	C₃×C₈	—	9	1	no	—
429	C₃×C₈	—	9	1	no	—
430	C₃×C₈	C₂²×D₉	1	2	yes	—
431	C₃×C₈	C₂×D₃²	1	2	yes	—
432	C₃⋊C₈	—	3	1	no	—
433	C₃⋊C₈	—	3	1	no	—
434	C₃⋊C₈	—	9	1	no	—
435	C₃⋊C₈	—	9	1	no	—
436	C₃⋊C₈	—	9	1	no	—
437	C₃⋊C₈	—	9	1	no	—
438	C₃⋊C₈	—	18	1	no	—
439	C₃⋊C₈	—	18	1	no	—
440	C₃⋊C₈	C₂²×D₉	1	2	yes	—
441	C₂×C₃²	—	2	1	no	—
442	C₂×C₃²	C₂²×C₄×D₃	1	1	yes	characteristic
443	C₃⋊D₃	—	6	2	no	—
444	C₃×D₃	—	2	1	no	—
445	C₃×D₃	—	6	2	no	—
446	C₃×D₃	#907	1	2	yes	—
447	C₂×C₉	—	2	1	no	—
448	C₂×C₉	—	2	1	no	—
449	C₂×C₉	—	3	2	no	—
450	C₂×C₉	—	4	1	no	—
451	C₂×C₉	—	6	1	no	—
452	C₂×C₉	C₂²×C₄×D₃	1	1	yes	characteristic
453	D₉	—	2	2	no	—
454	D₉	—	6	2	no	—
455	D₉	—	12	2	no	—
456	#41	—	9	1	no	—
457	#41	—	27	2	no	—
458	#41	—	27	2	no	—
459	#41	—	27	1	no	—
460	#41	—	27	1	no	—
461	#41	—	27	1	no	—
462	C₂×Q₈	—	27	1	no	—
463	C₂×D₄	—	27	1	no	—
464	C₂×D₄	—	27	2	no	—
465	C₂²×C₄	—	3	1	no	—
466	C₂²×C₄	—	27	2	no	—
467	M₁₆	—	3	1	no	—
468	M₁₆	—	3	2	no	—
469	M₁₆	—	9	2	no	—
470	M₁₆	—	27	2	no	—
471	M₁₆	—	27	2	no	—
472	M₁₆	—	27	2	no	—
473	M₁₆	D₃×D₉	1	1	yes	characteristic, complemented
474	C₂×C₈	—	3	2	no	—
475	C₂×C₈	—	9	1	no	—
476	C₂×C₈	—	9	2	no	—
477	C₂×C₈	—	27	2	no	—
478	C₂×C₈	—	27	2	no	—
479	C₂×C₈	—	27	1	no	—
480	C₂×C₈	—	27	1	no	—
481	C₂×C₈	—	27	1	no	—
482	C₂×C₈	—	27	1	no	—
483	C₂×C₈	—	27	1	no	—
484	C₂×C₈	—	27	2	no	—
485	C₂²×C₃	—	2	1	no	—
486	C₂²×C₃	—	3	1	no	—
487	C₂²×C₃	—	3	1	no	—
488	C₂²×C₃	—	6	2	no	—
489	C₂²×C₃	—	9	2	no	—
490	C₂²×C₃	C₂×C₄×D₉	1	1	yes	characteristic
491	C₂²×C₃	C₄×D₃²	1	1	yes	characteristic
492	C₂×D₃	—	2	2	no	—
493	C₂×D₃	—	3	2	no	—
494	C₂×D₃	—	9	2	no	—
495	C₂×D₃	—	9	2	no	—
496	C₂×D₃	—	18	2	no	—
497	C₂×D₃	—	18	4	no	—
498	C₂×D₃	—	18	4	no	—
499	C₂×D₃	C₂×C₄×D₉	1	1	yes	characteristic
500	C₂×D₃	C₂×C₄×D₉	1	1	yes	characteristic
501	C₃×C₄	—	2	1	no	—
502	C₃×C₄	—	2	1	no	—
503	C₃×C₄	—	3	1	no	—
504	C₃×C₄	—	3	1	no	—
505	C₃×C₄	—	9	2	no	—
506	C₃×C₄	C₂×C₄×D₉	1	1	yes	characteristic
507	C₃×C₄	C₂³×D₉	1	1	yes	characteristic
508	C₃×C₄	C₄×D₃²	1	1	yes	characteristic
509	C₃×C₄	C₂²×D₃²	1	1	yes	characteristic
510	Dic₃	—	3	2	no	—
511	Dic₃	—	9	2	no	—
512	Dic₃	—	9	2	no	—
513	Dic₃	—	18	2	no	—
514	Dic₃	C₂×C₄×D₉	1	1	yes	characteristic
515	Dic₃	C₂×C₄×D₉	1	1	yes	characteristic
516	C₃²	C₂×#907	1	1	yes	characteristic
517	C₉	—	2	1	no	—
518	C₉	D₃×#131	1	1	yes	characteristic, complemented
519	C₂³	—	3	1	no	—
520	C₂³	—	27	2	no	—
521	Q₈	—	9	1	no	—
522	Q₈	—	27	2	no	—
523	Q₈	—	27	1	no	—
524	D₄	—	9	2	no	—
525	D₄	—	9	1	no	—
526	D₄	—	27	2	no	—
527	D₄	—	27	2	no	—
528	D₄	—	27	2	no	—
529	D₄	—	27	2	no	—
530	D₄	—	27	1	no	—
531	C₂×C₄	—	3	1	no	—
532	C₂×C₄	—	3	1	no	—
533	C₂×C₄	—	3	1	no	—
534	C₂×C₄	—	3	1	no	—
535	C₂×C₄	—	3	1	no	—
536	C₂×C₄	—	9	2	no	—
537	C₂×C₄	—	27	2	no	—
538	C₂×C₄	—	27	2	no	—
539	C₂×C₄	—	27	2	no	—
540	C₂×C₄	—	27	2	no	—
541	C₂×C₄	C₂×D₃×D₉	1	1	yes	characteristic
542	C₈	—	3	2	no	—
543	C₈	—	9	1	no	—
544	C₈	—	9	1	no	—
545	C₈	—	27	1	no	—
546	C₈	—	27	1	no	—
547	C₈	C₂×D₃×D₉	1	2	yes	—
548	C₂×C₃	—	2	1	no	—
549	C₂×C₃	—	2	1	no	—
550	C₂×C₃	—	2	1	no	—
551	C₂×C₃	—	3	2	no	—
552	C₂×C₃	—	4	1	no	—
553	C₂×C₃	—	6	1	no	—
554	C₂×C₃	—	18	2	no	—
555	C₂×C₃	C₂²×C₄×D₉	1	1	yes	characteristic
556	C₂×C₃	C₂×C₄×D₃²	1	1	yes	characteristic
557	D₃	—	2	1	no	—
558	D₃	—	6	2	no	—
559	D₃	—	18	2	no	—
560	D₃	—	18	2	no	—
561	D₃	—	36	2	no	—
562	D₃	#63469	1	2	yes	direct product factor
563	C₂²	—	3	1	no	—
564	C₂²	—	3	1	no	—
565	C₂²	—	6	2	no	—
566	C₂²	—	9	2	no	—
567	C₂²	—	27	2	no	—
568	C₂²	—	54	4	no	—
569	C₂²	C₄×D₃×D₉	1	1	yes	characteristic
570	C₄	—	3	1	no	—
571	C₄	—	3	1	no	—
572	C₄	—	9	2	no	—
573	C₄	—	27	2	no	—
574	C₄	C₄×D₃×D₉	1	1	yes	characteristic
575	C₄	C₂²×D₃×D₉	1	1	yes	characteristic
576	C₃	—	2	1	no	—
577	C₃	C₂×#63469	1	1	yes	characteristic, complemented
578	C₃	D₃×#907	1	1	yes	characteristic
579	C₂	—	2	1	no	—
580	C₂	—	3	2	no	—
581	C₂	—	6	1	no	—
582	C₂	—	18	2	no	—
583	C₂	—	54	2	no	—
584	C₂	C₂×C₄×D₃×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₃×D₉
commutator	C₂×C₃×C₉	C₂³×C₄
Frattini	C₃×C₄	C₂²×D₃²
Fitting	C₃×C₉×M₁₆	C₂²
socle	C₂×C₃²	C₂²×C₄×D₃
prime radical	D₃×#3697	C₂
cosocle	C₃×C₄×C₉	C₂⁴
hypercenter	M₁₆	D₃×D₉
hypocenter	C₃×C₉	C₂×#131
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. #11721782	C₂	semidirect
3. D₃×C₉×M₁₆	C₂	semidirect
4. C₃×#63469	C₂	semidirect
5. C₂×D₃×C₉⋊C₈	C₂	semidirect
6. #11720861	C₂	semidirect
7. #11720859	C₂	semidirect
8. #11720809	C₂	semidirect
9. #11720807	C₂	semidirect
10. D₃×#3663	C₂	semidirect
11. D₃×C₈×D₉	C₂	semidirect
25. C₃×C₉×M₁₆	C₂²	semidirect
26. C₂×C₃⋊(C₉⋊C₈)	C₂²	semidirect
27. #88523	C₂²	semidirect
28. C₈×C₃⋊D₉	C₂²	semidirect
29. C₉×#208	C₂²	semidirect
30. C₂×C₃×C₉⋊C₈	C₂²	semidirect
31. C₉×ΓL(1,𝔽₂₅)	C₂²	semidirect
33. C₃×#3663	C₂²	semidirect
34. C₃×C₈×D₉	C₂²	semidirect
37. D₃×C₉⋊C₈	C₂²	semidirect
38. D₃×C₉⋊C₈	C₂²	semidirect
39. #88414	C₂²	semidirect
40. #88413	C₂²	semidirect
41. (C₃⋊D₉)⋊C₈	C₂²	semidirect
42. D₉×C₃⋊C₈	C₂²	semidirect
63. #63469	D₃	direct (N × H)
141. C₉×M₁₆	C₂×D₃	semidirect
149. C₂×C₉⋊C₈	C₂×D₃	semidirect
154. #3663	C₂×D₃	semidirect
159. C₈×D₉	C₂×D₃	semidirect
189. D₃×M₁₆	D₉	semidirect
267. D₃×C₉	#131	semidirect
296. C₃×M₁₆	C₂×D₉	semidirect
302. #208	C₂×D₉	semidirect
319. ΓL(1,𝔽₂₅)	C₂×D₉	semidirect
374. C₃×C₉	C₂×#131	semidirect
473. M₁₆	D₃×D₉	semidirect
518. C₉	D₃×#131	semidirect
562. D₃	#63469	direct (N × H)
577. C₃	C₂×#63469	semidirect

Maximal subgroups

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

subgroup	index
D₃×#3697	2
#11721782	2
D₃×C₉×M₁₆	2
C₃×#63469	2
C₂×D₃×C₉⋊C₈	2
#11720861	2
#11720859	2
#11720809	2
#11720807	2
D₃×#3663	2
D₃×C₈×D₉	2
D₃×#907	3
C₂×#63469	3

Subgroups — D3×#63469 #13149845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#63469 #13149845