Subgroups — D₃×C₉×#104 #13141972

Order 1728.

554 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₉×#41	C₂	1	1	yes	maximal, characteristic
2	D₃×C₉×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉×#104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#837	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#825	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#805	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×D₃×#104	C₃	1	1	yes	maximal, characteristic
9	C₂×C₉×#104	—	3	1	no	maximal
10	C₃×C₉×#41	C₂²	1	1	yes	characteristic
11	C₉×#239	C₄	1	1	yes	characteristic, complemented
12	D₃×Q₈×C₉	C₄	1	1	yes	characteristic, complemented
13	C₉×#237	—	2	1	no	—
14	C₉×#237	C₄	1	1	yes	characteristic, complemented
15	D₃×D₄×C₉	—	2	1	no	—
16	D₃×D₄×C₉	C₄	1	1	yes	characteristic, complemented
17	C₉×#235	—	2	1	no	—
18	C₉×#235	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₃×C₉	—	2	1	no	—
20	C₂×C₄×D₃×C₉	—	2	1	no	—
21	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
22	C₃×C₉×M₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
24	C₄×C₉×Dic₃	—	2	1	no	—
25	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
26	C₉×#208	C₂²	1	1	yes	characteristic, complemented
27	C₉×ΓL(1,𝔽₂₅)	—	2	1	no	—
28	D₃×C₈×C₉	—	2	1	no	—
29	C₃×D₃×#41	C₂×C₃	1	1	yes	characteristic
30	C₃×D₃×M₁₆	C₂×C₃	1	1	yes	characteristic
31	C₃×C₄²×D₃	C₂×C₃	1	1	yes	characteristic
32	C₂×C₉×#41	—	3	1	no	—
33	C₃²×#104	C₂×C₃	1	1	yes	characteristic
34	C₃×#837	C₂×C₃	1	1	yes	characteristic
35	C₃×#825	C₂×C₃	1	1	yes	characteristic
36	C₃×#805	C₂×C₃	1	1	yes	characteristic
37	C₂×C₉×M₁₆	—	3	1	no	—
38	C₂×C₄²×C₉	—	3	1	no	—
39	C₉×#104	—	2	1	no	—
40	C₉×#104	—	3	1	no	—
41	C₉×#104	—	3	1	no	—
42	C₉×#104	—	3	1	no	—
43	C₉×#104	D₃	1	1	yes	characteristic, direct product factor
44	C₂²×D₃×C₉	—	2	1	no	—
45	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
46	C₃×Q₈×C₉	C₂×C₄	1	1	yes	characteristic, complemented
47	C₃×D₄×C₉	—	2	1	no	—
48	C₃×D₄×C₉	C₂×C₄	1	1	yes	characteristic, complemented
49	C₂×C₃×C₄×C₉	—	2	1	no	—
50	C₂×C₃×C₄×C₉	—	2	1	no	—
51	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
52	C₉×#67	—	2	1	no	—
53	C₉×#67	—	2	1	no	—
54	C₉×#67	—	2	1	no	—
55	C₂×C₉×Dic₃	—	2	1	no	—
56	C₂×C₉×Dic₃	—	2	1	no	—
57	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
58	C₉×D₁₂	—	2	1	no	—
59	C₉×D₁₂	C₂×C₄	1	1	yes	characteristic, complemented
60	C₄×D₃×C₉	—	2	4	no	—
61	C₄×D₃×C₉	—	2	1	no	—
62	C₄×D₃×C₉	—	2	1	no	—
63	C₄×D₃×C₉	—	2	1	no	—
64	C₄×D₃×C₉	C₂×C₄	1	1	yes	characteristic
65	C₄×D₃×C₉	C₂×C₄	1	1	yes	characteristic
66	C₄×D₃×C₉	D₄	1	1	yes	characteristic
67	C₄×D₃×C₉	D₄	1	1	yes	characteristic
68	C₉×Dic₆	—	2	1	no	—
69	C₉×Dic₆	C₂×C₄	1	1	yes	characteristic, complemented
70	C₃×C₈×C₉	—	2	1	no	—
71	C₉×C₃⋊C₈	—	2	1	no	—
72	C₂×C₃×#104	—	3	1	no	—
73	D₃×#104	C₉	1	1	yes	characteristic, direct product factor
74	C₃²×#41	C₂²×C₃	1	1	yes	characteristic
75	C₃×#239	C₃×C₄	1	1	yes	characteristic
76	C₃×D₃×Q₈	C₃×C₄	1	1	yes	characteristic
77	C₃×#237	—	2	1	no	—
78	C₃×#237	C₃×C₄	1	1	yes	characteristic
79	C₃×D₃×D₄	—	2	1	no	—
80	C₃×D₃×D₄	C₃×C₄	1	1	yes	characteristic
81	C₃×#235	—	2	1	no	—
82	C₃×#235	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×C₄×D₃	—	2	1	no	—
84	C₂×C₃×C₄×D₃	—	2	1	no	—
85	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
86	C₃²×M₁₆	C₂²×C₃	1	1	yes	characteristic
87	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
88	C₃×C₄×Dic₃	—	2	1	no	—
89	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
90	C₃×#208	C₂²×C₃	1	1	yes	characteristic
91	C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
92	C₃×D₃×C₈	—	2	1	no	—
93	C₉×#41	—	2	1	no	—
94	C₉×#41	—	3	1	no	—
95	C₉×#41	—	3	1	no	—
96	C₉×#41	—	3	1	no	—
97	C₉×#41	—	6	1	no	—
98	C₉×#41	—	6	1	no	—
99	C₉×#41	C₂×D₃	1	1	yes	characteristic
100	C₂×Q₈×C₉	—	3	1	no	—
101	C₂×D₄×C₉	—	3	1	no	—
102	C₂×D₄×C₉	—	6	1	no	—
103	C₂²×C₄×C₉	—	3	1	no	—
104	C₂²×C₄×C₉	—	6	1	no	—
105	C₂²×C₄×C₉	—	6	1	no	—
106	C₉×M₁₆	—	2	1	no	—
107	C₉×M₁₆	—	3	1	no	—
108	C₉×M₁₆	—	6	1	no	—
109	C₉×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
110	C₂×C₈×C₉	—	6	1	no	—
111	C₄²×C₉	—	2	1	no	—
112	C₄²×C₉	—	3	1	no	—
113	C₄²×C₉	—	6	1	no	—
114	C₄²×C₉	C₂×D₃	1	1	yes	characteristic, complemented
115	C₂²×C₃×C₉	—	2	1	no	—
116	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
117	C₂×D₃×C₉	—	2	2	no	—
118	C₂×D₃×C₉	—	2	1	no	—
119	C₂×D₃×C₉	—	4	2	no	—
120	C₂×D₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₂×D₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
122	C₃×C₄×C₉	—	2	2	no	—
123	C₃×C₄×C₉	—	2	1	no	—
124	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
125	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
126	C₉×Dic₃	—	2	2	no	—
127	C₉×Dic₃	—	2	1	no	—
128	C₉×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
129	C₉×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₃×#41	—	3	1	no	—
131	D₃×#41	C₂×C₉	1	1	yes	characteristic
132	C₂×C₃×M₁₆	—	3	1	no	—
133	C₂×C₃×C₄²	—	3	1	no	—
134	D₃×M₁₆	C₂×C₉	1	1	yes	characteristic, complemented
135	C₄²×D₃	C₂×C₉	1	1	yes	characteristic, complemented
136	C₃×#104	—	2	1	no	—
137	C₃×#104	—	3	1	no	—
138	C₃×#104	—	3	1	no	—
139	C₃×#104	—	3	1	no	—
140	C₃×#104	C₂×C₉	1	1	yes	characteristic, complemented
141	C₃×#104	C₃×D₃	1	1	yes	characteristic
142	#837	C₂×C₉	1	1	yes	characteristic, complemented
143	#825	C₂×C₉	1	1	yes	characteristic, complemented
144	#805	C₂×C₉	1	1	yes	characteristic, complemented
145	C₂²×C₃×D₃	—	2	1	no	—
146	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
147	C₃²×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
148	C₃²×D₄	—	2	1	no	—
149	C₃²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
150	C₂×C₃²×C₄	—	2	1	no	—
151	C₂×C₃²×C₄	—	2	1	no	—
152	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
153	C₃×#67	—	2	1	no	—
154	C₃×#67	—	2	1	no	—
155	C₃×#67	—	2	1	no	—
156	C₂×C₃×Dic₃	—	2	1	no	—
157	C₂×C₃×Dic₃	—	2	1	no	—
158	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
159	C₃×D₁₂	—	2	1	no	—
160	C₃×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
161	C₃×C₄×D₃	—	2	4	no	—
162	C₃×C₄×D₃	—	2	1	no	—
163	C₃×C₄×D₃	—	2	1	no	—
164	C₃×C₄×D₃	—	2	1	no	—
165	C₃×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
166	C₃×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
167	C₃×C₄×D₃	C₃×D₄	1	1	yes	characteristic
168	C₃×C₄×D₃	C₃×D₄	1	1	yes	characteristic
169	C₃×Dic₆	—	2	1	no	—
170	C₃×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
171	C₂³×C₉	—	3	1	no	—
172	C₂³×C₉	—	6	1	no	—
173	C₃²×C₈	—	2	1	no	—
174	C₃×C₃⋊C₈	—	2	1	no	—
175	Q₈×C₉	—	2	1	no	—
176	Q₈×C₉	—	3	1	no	—
177	Q₈×C₉	—	6	1	no	—
178	Q₈×C₉	C₄×D₃	1	1	yes	characteristic, complemented
179	D₄×C₉	—	2	1	no	—
180	D₄×C₉	—	2	1	no	—
181	D₄×C₉	—	3	1	no	—
182	D₄×C₉	—	4	1	no	—
183	D₄×C₉	—	6	1	no	—
184	D₄×C₉	—	6	1	no	—
185	D₄×C₉	—	6	1	no	—
186	D₄×C₉	—	6	1	no	—
187	D₄×C₉	C₄×D₃	1	1	yes	characteristic, complemented
188	C₂×C₄×C₉	—	2	1	no	—
189	C₂×C₄×C₉	—	2	1	no	—
190	C₂×C₄×C₉	—	2	1	no	—
191	C₂×C₄×C₉	—	3	1	no	—
192	C₂×C₄×C₉	—	3	1	no	—
193	C₂×C₄×C₉	—	3	1	no	—
194	C₂×C₄×C₉	—	3	1	no	—
195	C₂×C₄×C₉	—	3	1	no	—
196	C₂×C₄×C₉	—	4	1	no	—
197	C₂×C₄×C₉	—	4	1	no	—
198	C₂×C₄×C₉	—	6	1	no	—
199	C₂×C₄×C₉	—	6	1	no	—
200	C₂×C₄×C₉	—	6	4	no	—
201	C₂×C₄×C₉	—	6	1	no	—
202	C₂×C₄×C₉	—	6	1	no	—
203	C₂×C₄×C₉	—	6	1	no	—
204	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
205	C₈×C₉	—	2	1	no	—
206	C₈×C₉	—	4	1	no	—
207	C₈×C₉	—	6	1	no	—
208	C₂×#104	—	3	1	no	Sylow
209	C₂×C₃×C₉	—	2	1	no	—
210	C₂×C₃×C₉	—	4	1	no	—
211	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	D₃×C₉	—	2	1	no	—
213	D₃×C₉	—	4	1	no	—
214	D₃×C₉	#104	1	2	yes	direct product factor
215	C₃×#41	—	2	1	no	—
216	C₃×#41	—	3	1	no	—
217	C₃×#41	—	3	1	no	—
218	C₃×#41	—	3	1	no	—
219	C₃×#41	—	6	1	no	—
220	C₃×#41	—	6	1	no	—
221	C₃×#41	C₂²×C₉	1	1	yes	characteristic
222	C₃×#41	C₂×C₃×D₃	1	1	yes	characteristic
223	C₂×C₃×Q₈	—	3	1	no	—
224	C₂×C₃×D₄	—	3	1	no	—
225	C₂×C₃×D₄	—	6	1	no	—
226	C₂²×C₃×C₄	—	3	1	no	—
227	C₂²×C₃×C₄	—	6	1	no	—
228	C₂²×C₃×C₄	—	6	1	no	—
229	#239	C₄×C₉	1	1	yes	characteristic, complemented
230	D₃×Q₈	C₄×C₉	1	1	yes	characteristic, complemented
231	#237	—	2	1	no	—
232	#237	C₄×C₉	1	1	yes	characteristic, complemented
233	D₃×D₄	—	2	1	no	—
234	D₃×D₄	C₄×C₉	1	1	yes	characteristic, complemented
235	#235	—	2	1	no	—
236	#235	C₂²×C₉	1	1	yes	characteristic
237	C₂×C₄×D₃	—	2	1	no	—
238	C₂×C₄×D₃	—	2	1	no	—
239	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
240	C₃×M₁₆	—	2	1	no	—
241	C₃×M₁₆	—	3	1	no	—
242	C₃×M₁₆	—	6	1	no	—
243	C₃×M₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
244	C₃×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
245	C₂×C₃×C₈	—	6	1	no	—
246	C₃×C₄²	—	2	1	no	—
247	C₃×C₄²	—	3	1	no	—
248	C₃×C₄²	—	6	1	no	—
249	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic, complemented
250	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
251	C₄×Dic₃	—	2	1	no	—
252	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
253	#208	C₂²×C₉	1	1	yes	characteristic, complemented
254	ΓL(1,𝔽₂₅)	—	2	1	no	—
255	D₃×C₈	—	2	1	no	—
256	C₂²×C₃²	—	2	1	no	—
257	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
258	C₂×C₃×D₃	—	2	2	no	—
259	C₂×C₃×D₃	—	2	1	no	—
260	C₂×C₃×D₃	—	4	2	no	—
261	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
263	C₃²×C₄	—	2	2	no	—
264	C₃²×C₄	—	2	1	no	—
265	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
266	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
267	C₃×Dic₃	—	2	2	no	—
268	C₃×Dic₃	—	2	1	no	—
269	C₃×Dic₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
270	C₃×Dic₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
271	C₂²×C₉	—	2	1	no	—
272	C₂²×C₉	—	2	1	no	—
273	C₂²×C₉	—	3	1	no	—
274	C₂²×C₉	—	3	1	no	—
275	C₂²×C₉	—	4	1	no	—
276	C₂²×C₉	—	6	2	no	—
277	C₂²×C₉	—	6	1	no	—
278	C₂²×C₉	—	12	2	no	—
279	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
280	C₄×C₉	—	2	2	no	—
281	C₄×C₉	—	2	1	no	—
282	C₄×C₉	—	2	1	no	—
283	C₄×C₉	—	2	1	no	—
284	C₄×C₉	—	3	1	no	—
285	C₄×C₉	—	3	1	no	—
286	C₄×C₉	—	4	1	no	—
287	C₄×C₉	—	4	2	no	—
288	C₄×C₉	—	6	2	no	—
289	C₄×C₉	—	6	1	no	—
290	C₄×C₉	C₂×C₄×D₃	1	1	yes	characteristic
291	C₄×C₉	D₃×D₄	1	1	yes	characteristic
292	C₂×#41	—	3	1	no	—
293	C₂×M₁₆	—	3	1	no	—
294	C₂×C₄²	—	3	1	no	—
295	#104	—	3	1	no	—
296	#104	—	3	1	no	—
297	#104	—	3	1	no	—
298	#104	D₃×C₉	1	1	yes	characteristic, direct product factor
299	C₃×C₉	C₂×#104	1	1	yes	characteristic, complemented, Sylow
300	C₂³×C₃	—	3	1	no	—
301	C₂³×C₃	—	6	1	no	—
302	C₂²×D₃	—	2	1	no	—
303	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
304	C₃×Q₈	—	2	1	no	—
305	C₃×Q₈	—	3	1	no	—
306	C₃×Q₈	—	6	1	no	—
307	C₃×Q₈	C₂×C₄×C₉	1	1	yes	characteristic, complemented
308	C₃×Q₈	C₃×C₄×D₃	1	1	yes	characteristic
309	C₃×D₄	—	2	1	no	—
310	C₃×D₄	—	2	1	no	—
311	C₃×D₄	—	2	1	no	—
312	C₃×D₄	—	3	1	no	—
313	C₃×D₄	—	4	1	no	—
314	C₃×D₄	—	6	1	no	—
315	C₃×D₄	—	6	1	no	—
316	C₃×D₄	—	6	1	no	—
317	C₃×D₄	—	6	1	no	—
318	C₃×D₄	C₂×C₄×C₉	1	1	yes	characteristic, complemented
319	C₃×D₄	C₃×C₄×D₃	1	1	yes	characteristic
320	C₂×C₃×C₄	—	2	1	no	—
321	C₂×C₃×C₄	—	2	1	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	2	1	no	—
324	C₂×C₃×C₄	—	2	1	no	—
325	C₂×C₃×C₄	—	3	1	no	—
326	C₂×C₃×C₄	—	3	1	no	—
327	C₂×C₃×C₄	—	3	1	no	—
328	C₂×C₃×C₄	—	3	1	no	—
329	C₂×C₃×C₄	—	3	1	no	—
330	C₂×C₃×C₄	—	4	1	no	—
331	C₂×C₃×C₄	—	4	1	no	—
332	C₂×C₃×C₄	—	6	1	no	—
333	C₂×C₃×C₄	—	6	1	no	—
334	C₂×C₃×C₄	—	6	4	no	—
335	C₂×C₃×C₄	—	6	1	no	—
336	C₂×C₃×C₄	—	6	1	no	—
337	C₂×C₃×C₄	—	6	1	no	—
338	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
340	#67	—	2	1	no	—
341	#67	—	2	1	no	—
342	#67	—	2	1	no	—
343	C₂×Dic₃	—	2	1	no	—
344	C₂×Dic₃	—	2	1	no	—
345	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
346	D₁₂	—	2	1	no	—
347	D₁₂	C₂×C₄×C₉	1	1	yes	characteristic, complemented
348	C₄×D₃	—	2	4	no	—
349	C₄×D₃	—	2	1	no	—
350	C₄×D₃	—	2	1	no	—
351	C₄×D₃	—	2	1	no	—
352	C₄×D₃	C₂×C₄×C₉	1	1	yes	characteristic
353	C₄×D₃	C₂×C₄×C₉	1	1	yes	characteristic
354	C₄×D₃	D₄×C₉	1	1	yes	characteristic
355	C₄×D₃	D₄×C₉	1	1	yes	characteristic
356	Dic₆	—	2	1	no	—
357	Dic₆	C₂×C₄×C₉	1	1	yes	characteristic, complemented
358	C₃×C₈	—	2	1	no	—
359	C₃×C₈	—	2	1	no	—
360	C₃×C₈	—	4	1	no	—
361	C₃×C₈	—	6	1	no	—
362	C₃⋊C₈	—	2	1	no	—
363	C₂×C₃²	—	2	1	no	—
364	C₂×C₃²	—	4	1	no	—
365	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
366	C₃×D₃	—	2	1	no	—
367	C₃×D₃	—	4	1	no	—
368	C₃×D₃	C₃×#104	1	2	yes	—
369	C₂×C₉	—	2	1	no	—
370	C₂×C₉	—	2	1	no	—
371	C₂×C₉	—	3	2	no	—
372	C₂×C₉	—	4	1	no	—
373	C₂×C₉	—	4	1	no	—
374	C₂×C₉	—	6	1	no	—
375	C₂×C₉	—	8	1	no	—
376	C₂×C₉	—	12	1	no	—
377	C₂×C₉	D₃×C₂²⋊C₄	1	1	yes	characteristic
378	#41	—	3	1	no	—
379	#41	—	3	1	no	—
380	#41	—	3	1	no	—
381	#41	—	6	1	no	—
382	#41	—	6	1	no	—
383	#41	C₂×D₃×C₉	1	1	yes	characteristic
384	C₂×Q₈	—	3	1	no	—
385	C₂×D₄	—	3	1	no	—
386	C₂×D₄	—	6	1	no	—
387	C₂²×C₄	—	3	1	no	—
388	C₂²×C₄	—	6	1	no	—
389	C₂²×C₄	—	6	1	no	—
390	M₁₆	—	3	1	no	—
391	M₁₆	—	6	1	no	—
392	M₁₆	C₂×D₃×C₉	1	1	yes	characteristic, complemented
393	C₂×C₈	—	6	1	no	—
394	C₄²	—	3	1	no	—
395	C₄²	—	6	1	no	—
396	C₄²	C₂×D₃×C₉	1	1	yes	characteristic, complemented
397	C₂²×C₃	—	2	1	no	—
398	C₂²×C₃	—	2	1	no	—
399	C₂²×C₃	—	2	1	no	—
400	C₂²×C₃	—	3	1	no	—
401	C₂²×C₃	—	3	1	no	—
402	C₂²×C₃	—	4	1	no	—
403	C₂²×C₃	—	6	2	no	—
404	C₂²×C₃	—	6	1	no	—
405	C₂²×C₃	—	12	2	no	—
406	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
407	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
408	C₂×D₃	—	2	2	no	—
409	C₂×D₃	—	2	1	no	—
410	C₂×D₃	—	4	2	no	—
411	C₂×D₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
412	C₂×D₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
413	C₃×C₄	—	2	2	no	—
414	C₃×C₄	—	2	2	no	—
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	2	1	no	—
417	C₃×C₄	—	2	1	no	—
418	C₃×C₄	—	2	1	no	—
419	C₃×C₄	—	3	1	no	—
420	C₃×C₄	—	3	1	no	—
421	C₃×C₄	—	4	1	no	—
422	C₃×C₄	—	4	2	no	—
423	C₃×C₄	—	6	2	no	—
424	C₃×C₄	—	6	1	no	—
425	C₃×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
426	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
427	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
428	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
429	Dic₃	—	2	2	no	—
430	Dic₃	—	2	1	no	—
431	Dic₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
432	Dic₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
433	C₃²	C₂×C₃×#104	1	1	yes	characteristic
434	C₉	—	2	1	no	—
435	C₉	D₃×#104	1	1	yes	characteristic, direct product factor
436	C₂³	—	3	1	no	—
437	C₂³	—	6	1	no	—
438	Q₈	—	3	1	no	—
439	Q₈	—	6	1	no	—
440	Q₈	C₄×D₃×C₉	1	1	yes	characteristic, complemented
441	D₄	—	2	1	no	—
442	D₄	—	3	1	no	—
443	D₄	—	6	1	no	—
444	D₄	—	6	1	no	—
445	D₄	—	6	1	no	—
446	D₄	—	6	1	no	—
447	D₄	C₄×D₃×C₉	1	1	yes	characteristic, complemented
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	3	1	no	—
451	C₂×C₄	—	3	1	no	—
452	C₂×C₄	—	3	1	no	—
453	C₂×C₄	—	3	1	no	—
454	C₂×C₄	—	3	1	no	—
455	C₂×C₄	—	6	1	no	—
456	C₂×C₄	—	6	1	no	—
457	C₂×C₄	—	6	4	no	—
458	C₂×C₄	—	6	1	no	—
459	C₂×C₄	—	6	1	no	—
460	C₂×C₄	—	6	1	no	—
461	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
462	C₈	—	2	1	no	—
463	C₈	—	6	1	no	—
464	C₂×C₃	—	2	1	no	—
465	C₂×C₃	—	2	1	no	—
466	C₂×C₃	—	2	1	no	—
467	C₂×C₃	—	3	2	no	—
468	C₂×C₃	—	4	1	no	—
469	C₂×C₃	—	4	1	no	—
470	C₂×C₃	—	4	1	no	—
471	C₂×C₃	—	6	1	no	—
472	C₂×C₃	—	8	1	no	—
473	C₂×C₃	—	12	1	no	—
474	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
475	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
476	D₃	—	2	1	no	—
477	D₃	—	4	1	no	—
478	D₃	C₉×#104	1	2	yes	direct product factor
479	C₂²	—	2	1	no	—
480	C₂²	—	3	1	no	—
481	C₂²	—	3	1	no	—
482	C₂²	—	6	2	no	—
483	C₂²	—	6	1	no	—
484	C₂²	—	12	2	no	—
485	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	2	1	no	—
488	C₄	—	3	1	no	—
489	C₄	—	3	1	no	—
490	C₄	—	6	2	no	—
491	C₄	—	6	1	no	—
492	C₄	C₂×C₄×D₃×C₉	1	1	yes	characteristic
493	C₄	D₃×D₄×C₉	1	1	yes	characteristic
494	C₃	—	2	1	no	—
495	C₃	C₂×C₉×#104	1	1	yes	characteristic, complemented
496	C₃	C₃×D₃×#104	1	1	yes	characteristic
497	C₂	—	2	1	no	—
498	C₂	—	3	2	no	—
499	C₂	—	4	1	no	—
500	C₂	—	6	1	no	—
501	C₂	—	12	1	no	—
502	C₂	D₃×C₉×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₉	D₃×D₄
commutator	C₃×C₄	C₂²×C₄×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×#104	C₂
socle	C₂×C₃²	C₂×C₃×C₂²⋊C₄
prime radical	C₃×D₃×#41	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#104	D₃
hypocenter	C₃	C₂×C₉×#104
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#104

Complements

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

N	H ≅ G/N	type
2. D₃×C₉×M₁₆	C₂	semidirect
3. C₄²×D₃×C₉	C₂	semidirect
4. C₃×C₉×#104	C₂	semidirect
5. C₉×#837	C₂	semidirect
6. C₉×#825	C₂	semidirect
7. C₉×#805	C₂	semidirect
11. C₉×#239	C₄	semidirect
12. D₃×Q₈×C₉	C₄	semidirect
14. C₉×#237	C₄	semidirect
16. D₃×D₄×C₉	C₄	semidirect
22. C₃×C₉×M₁₆	C₂²	semidirect
23. C₃×C₄²×C₉	C₂²	semidirect
25. C₄×C₉×Dic₃	C₂²	semidirect
26. C₉×#208	C₂²	semidirect
43. C₉×#104	D₃	direct (N × H)
46. C₃×Q₈×C₉	C₂×C₄	semidirect
48. C₃×D₄×C₉	C₂×C₄	semidirect
59. C₉×D₁₂	C₂×C₄	semidirect
69. C₉×Dic₆	C₂×C₄	semidirect
73. D₃×#104	C₉	direct (N × H)
109. C₉×M₁₆	C₂×D₃	semidirect
114. C₄²×C₉	C₂×D₃	semidirect
134. D₃×M₁₆	C₂×C₉	semidirect
135. C₄²×D₃	C₂×C₉	semidirect
140. C₃×#104	C₂×C₉	semidirect
142. #837	C₂×C₉	semidirect
143. #825	C₂×C₉	semidirect
144. #805	C₂×C₉	semidirect
178. Q₈×C₉	C₄×D₃	semidirect
187. D₄×C₉	C₄×D₃	semidirect
214. D₃×C₉	#104	direct (N × H)
229. #239	C₄×C₉	semidirect
230. D₃×Q₈	C₄×C₉	semidirect
232. #237	C₄×C₉	semidirect
234. D₃×D₄	C₄×C₉	semidirect
243. C₃×M₁₆	C₂²×C₉	semidirect
249. C₃×C₄²	C₂²×C₉	semidirect
252. C₄×Dic₃	C₂²×C₉	semidirect
253. #208	C₂²×C₉	semidirect
298. #104	D₃×C₉	direct (N × H)
299. C₃×C₉	C₂×#104	semidirect
307. C₃×Q₈	C₂×C₄×C₉	semidirect
318. C₃×D₄	C₂×C₄×C₉	semidirect
347. D₁₂	C₂×C₄×C₉	semidirect
357. Dic₆	C₂×C₄×C₉	semidirect
392. M₁₆	C₂×D₃×C₉	semidirect
396. C₄²	C₂×D₃×C₉	semidirect
435. C₉	D₃×#104	direct (N × H)
440. Q₈	C₄×D₃×C₉	semidirect
447. D₄	C₄×D₃×C₉	semidirect
478. D₃	C₉×#104	direct (N × H)
495. C₃	C₂×C₉×#104	semidirect

Maximal subgroups

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

subgroup	index
D₃×C₉×#41	2
D₃×C₉×M₁₆	2
C₄²×D₃×C₉	2
C₃×C₉×#104	2
C₉×#837	2
C₉×#825	2
C₉×#805	2
C₃×D₃×#104	3
C₂×C₉×#104	3

Subgroups — D3×C9×#104 #13141972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₉×#104 #13141972