Subgroups — D₃×C₉×#120 #13152760

Order 1728.

2116 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×D₄×C₉	C₂	1	3	yes	maximal, complemented
3	C₃×C₉×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#953	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#937	C₂	1	3	yes	maximal, complemented
6	C₉×#882	C₂	1	3	yes	maximal, complemented
7	D₃×C₉×C₂²⋊C₄	C₂	1	3	yes	maximal, complemented
8	C₃×D₃×#120	C₃	1	1	yes	maximal, characteristic
9	C₂×C₉×#120	—	3	1	no	maximal
10	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic, complemented
11	C₂³×D₃×C₉	—	2	12	no	—
12	C₂³×D₃×C₉	C₂²	1	3	yes	—
13	C₂³×D₃×C₉	C₂²	1	3	yes	complemented
14	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₃×D₄×C₉	C₂²	1	3	yes	complemented
16	C₂×C₉×#67	C₂²	1	3	yes	complemented
17	C₂×C₉×#67	C₂²	1	3	yes	complemented
18	D₃×D₄×C₉	—	2	12	no	—
19	C₂×C₉×D₁₂	C₂²	1	3	yes	complemented
20	C₂×C₄×D₃×C₉	C₂²	1	3	yes	complemented
21	C₃×C₉×C₂²⋊C₄	C₂²	1	3	yes	complemented
22	C₉×#217	C₂²	1	3	yes	complemented
23	C₉×(C₂×D₃)⋊C₄	C₂²	1	6	yes	complemented
24	C₂⁴×C₃×D₃	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×D₃×D₄	C₂×C₃	1	3	yes	—
26	C₂⁵×C₉	—	3	1	no	—
27	C₃²×#120	C₂×C₃	1	1	yes	characteristic
28	C₃×#953	C₂×C₃	1	1	yes	characteristic
29	C₃×#937	C₂×C₃	1	3	yes	—
30	C₃×#882	C₂×C₃	1	3	yes	—
31	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	3	yes	—
32	C₂²×D₄×C₉	—	3	3	no	—
33	C₉×#120	—	2	1	no	—
34	C₉×#120	—	3	1	no	—
35	C₉×#120	—	3	3	no	—
36	C₉×#120	—	3	3	no	—
37	C₉×#120	D₃	1	1	yes	characteristic, direct product factor
38	C₂×C₉×C₂²⋊C₄	—	3	3	no	—
39	C₂³×C₃×C₉	—	2	6	no	—
40	C₂³×C₃×C₉	C₂³	1	3	yes	—
41	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic, complemented
42	C₂²×D₃×C₉	—	2	32	no	—
43	C₂²×D₃×C₉	—	2	6	no	—
44	C₂²×D₃×C₉	—	2	12	no	—
45	C₂²×D₃×C₉	—	2	12	no	—
46	C₂²×D₃×C₉	—	2	6	no	—
47	C₂²×D₃×C₉	D₄	1	12	yes	complemented
48	C₂²×D₃×C₉	C₂³	1	3	yes	—
49	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
50	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic, complemented
51	C₃×D₄×C₉	—	2	6	no	—
52	C₂×C₃×C₄×C₉	C₂³	1	3	yes	complemented
53	C₉×#67	—	2	6	no	—
54	C₉×#67	—	2	6	no	—
55	C₂×C₉×Dic₃	C₂³	1	3	yes	complemented
56	C₉×D₁₂	—	2	6	no	—
57	C₄×D₃×C₉	—	2	6	no	—
58	C₂×C₃×#120	—	3	1	no	—
59	D₃×#120	C₉	1	1	yes	characteristic, direct product factor
60	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
61	C₂³×C₃×D₃	—	2	12	no	—
62	C₂³×C₃×D₃	C₂²×C₃	1	3	yes	—
63	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
64	C₂³×C₃×D₃	C₂²×C₃	1	3	yes	—
65	C₂×C₃²×D₄	C₂²×C₃	1	3	yes	—
66	C₂×C₃×#67	C₂²×C₃	1	3	yes	—
67	C₂×C₃×#67	C₂²×C₃	1	3	yes	—
68	C₃×D₃×D₄	—	2	12	no	—
69	C₂×C₃×D₁₂	C₂²×C₃	1	3	yes	—
70	C₂×C₃×C₄×D₃	C₂²×C₃	1	3	yes	—
71	C₂⁴×C₉	—	2	1	no	—
72	C₂⁴×C₉	—	3	3	no	—
73	C₂⁴×C₉	—	3	3	no	—
74	C₂⁴×C₉	—	3	1	no	—
75	C₂⁴×C₉	—	6	12	no	—
76	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic, complemented
77	C₃²×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
78	C₃×#217	C₂²×C₃	1	3	yes	—
79	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	6	yes	—
80	C₂×D₄×C₉	—	2	3	no	—
81	C₂×D₄×C₉	—	3	3	no	—
82	C₂×D₄×C₉	—	3	3	no	—
83	C₂×D₄×C₉	—	3	3	no	—
84	C₂×D₄×C₉	—	6	12	no	—
85	C₂×D₄×C₉	C₂×D₃	1	3	yes	complemented
86	C₂²×C₄×C₉	—	3	3	no	—
87	C₉×C₂²⋊C₄	—	2	3	no	—
88	C₉×C₂²⋊C₄	—	3	3	no	—
89	C₉×C₂²⋊C₄	—	3	6	no	—
90	C₉×C₂²⋊C₄	C₂×D₃	1	3	yes	complemented
91	C₂²×C₃×C₉	—	2	8	no	—
92	C₂²×C₃×C₉	—	2	6	no	—
93	C₂²×C₃×C₉	—	2	3	no	—
94	C₂²×C₃×C₉	C₂×D₄	1	6	yes	complemented
95	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
96	C₂×D₃×C₉	—	2	24	no	—
97	C₂×D₃×C₉	—	2	6	no	—
98	C₂×D₃×C₉	—	2	24	no	—
99	C₂×D₃×C₉	—	2	3	no	—
100	C₂×D₃×C₉	—	4	4	no	—
101	C₂×D₃×C₉	C₂×D₄	1	6	yes	—
102	C₂×D₃×C₉	C₂×D₄	1	6	yes	complemented
103	C₃×C₄×C₉	—	2	3	no	—
104	C₉×Dic₃	—	2	3	no	—
105	C₂⁵×C₃	—	3	1	no	—
106	C₂⁴×D₃	C₂×C₉	1	1	yes	characteristic, complemented
107	C₂²×C₃×D₄	—	3	3	no	—
108	C₂×D₃×D₄	C₂×C₉	1	3	yes	complemented
109	C₃×#120	—	2	1	no	—
110	C₃×#120	—	3	1	no	—
111	C₃×#120	—	3	3	no	—
112	C₃×#120	—	3	3	no	—
113	C₃×#120	C₂×C₉	1	1	yes	characteristic, complemented
114	C₃×#120	C₃×D₃	1	1	yes	characteristic
115	C₂×C₃×C₂²⋊C₄	—	3	3	no	—
116	#953	C₂×C₉	1	1	yes	characteristic, complemented
117	#937	C₂×C₉	1	3	yes	complemented
118	#882	C₂×C₉	1	3	yes	complemented
119	D₃×C₂²⋊C₄	C₂×C₉	1	3	yes	complemented
120	C₂³×C₃²	—	2	6	no	—
121	C₂³×C₃²	C₂³×C₃	1	3	yes	—
122	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
123	C₂²×C₃×D₃	—	2	32	no	—
124	C₂²×C₃×D₃	—	2	6	no	—
125	C₂²×C₃×D₃	—	2	12	no	—
126	C₂²×C₃×D₃	—	2	12	no	—
127	C₂²×C₃×D₃	—	2	6	no	—
128	C₂²×C₃×D₃	C₃×D₄	1	12	yes	—
129	C₂²×C₃×D₃	C₂³×C₃	1	3	yes	—
130	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
131	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
132	C₃²×D₄	—	2	6	no	—
133	C₂×C₃²×C₄	C₂³×C₃	1	3	yes	—
134	C₃×#67	—	2	6	no	—
135	C₃×#67	—	2	6	no	—
136	C₂×C₃×Dic₃	C₂³×C₃	1	3	yes	—
137	C₃×D₁₂	—	2	6	no	—
138	C₃×C₄×D₃	—	2	6	no	—
139	C₂³×C₉	—	2	6	no	—
140	C₂³×C₉	—	2	3	no	—
141	C₂³×C₉	—	2	1	no	—
142	C₂³×C₉	—	3	1	no	—
143	C₂³×C₉	—	3	12	no	—
144	C₂³×C₉	—	3	3	no	—
145	C₂³×C₉	—	3	1	no	—
146	C₂³×C₉	—	4	6	no	—
147	C₂³×C₉	—	6	12	no	—
148	C₂³×C₉	—	6	12	no	—
149	C₂³×C₉	—	6	6	no	—
150	C₂³×C₉	—	6	32	no	—
151	C₂³×C₉	—	6	6	no	—
152	C₂³×C₉	C₂²×D₃	1	3	yes	—
153	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic, complemented
154	D₄×C₉	—	2	6	no	—
155	D₄×C₉	—	4	6	no	—
156	D₄×C₉	—	6	6	no	—
157	D₄×C₉	—	6	6	no	—
158	D₄×C₉	—	6	6	no	—
159	C₂×C₄×C₉	—	2	3	no	—
160	C₂×C₄×C₉	—	3	3	no	—
161	C₂×C₄×C₉	—	6	6	no	—
162	C₂×C₄×C₉	C₂²×D₃	1	3	yes	complemented
163	C₂×#120	—	3	1	no	Sylow
164	C₂×C₃×C₉	—	2	6	no	—
165	C₂×C₃×C₉	—	4	1	no	—
166	C₂×C₃×C₉	C₂²×D₄	1	3	yes	—
167	D₃×C₉	—	2	6	no	—
168	D₃×C₉	—	4	1	no	—
169	D₃×C₉	#120	1	4	yes	direct product factor
170	C₂⁴×C₃	—	2	1	no	—
171	C₂⁴×C₃	—	3	3	no	—
172	C₂⁴×C₃	—	3	3	no	—
173	C₂⁴×C₃	—	3	1	no	—
174	C₂⁴×C₃	—	6	12	no	—
175	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic, complemented
176	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
177	C₂³×D₃	—	2	12	no	—
178	C₂³×D₃	C₂²×C₉	1	3	yes	—
179	C₂³×D₃	C₂²×C₉	1	3	yes	complemented
180	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
181	C₂×C₃×D₄	—	2	3	no	—
182	C₂×C₃×D₄	—	3	3	no	—
183	C₂×C₃×D₄	—	3	3	no	—
184	C₂×C₃×D₄	—	3	3	no	—
185	C₂×C₃×D₄	—	6	12	no	—
186	C₂×C₃×D₄	C₂²×C₉	1	3	yes	complemented
187	C₂×C₃×D₄	C₂×C₃×D₃	1	3	yes	—
188	C₂²×C₃×C₄	—	3	3	no	—
189	C₂×#67	C₂²×C₉	1	3	yes	complemented
190	C₂×#67	C₂²×C₉	1	3	yes	complemented
191	D₃×D₄	—	2	12	no	—
192	C₂×D₁₂	C₂²×C₉	1	3	yes	complemented
193	C₂×C₄×D₃	C₂²×C₉	1	3	yes	complemented
194	C₃×C₂²⋊C₄	—	2	3	no	—
195	C₃×C₂²⋊C₄	—	3	3	no	—
196	C₃×C₂²⋊C₄	—	3	6	no	—
197	C₃×C₂²⋊C₄	C₂²×C₉	1	3	yes	complemented
198	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	3	yes	—
199	#217	C₂²×C₉	1	3	yes	complemented
200	(C₂×D₃)⋊C₄	C₂²×C₉	1	6	yes	complemented
201	C₂²×C₃²	—	2	8	no	—
202	C₂²×C₃²	—	2	6	no	—
203	C₂²×C₃²	—	2	3	no	—
204	C₂²×C₃²	C₂×C₃×D₄	1	6	yes	—
205	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
206	C₂×C₃×D₃	—	2	24	no	—
207	C₂×C₃×D₃	—	2	6	no	—
208	C₂×C₃×D₃	—	2	24	no	—
209	C₂×C₃×D₃	—	2	3	no	—
210	C₂×C₃×D₃	—	4	4	no	—
211	C₂×C₃×D₃	C₂×C₃×D₄	1	6	yes	—
212	C₂×C₃×D₃	C₂×C₃×D₄	1	6	yes	—
213	C₃²×C₄	—	2	3	no	—
214	C₃×Dic₃	—	2	3	no	—
215	C₂²×C₉	—	2	8	no	—
216	C₂²×C₉	—	2	6	no	—
217	C₂²×C₉	—	2	3	no	—
218	C₂²×C₉	—	2	1	no	—
219	C₂²×C₉	—	2	6	no	—
220	C₂²×C₉	—	3	6	no	—
221	C₂²×C₉	—	3	6	no	—
222	C₂²×C₉	—	4	6	no	—
223	C₂²×C₉	—	4	3	no	—
224	C₂²×C₉	—	4	8	no	—
225	C₂²×C₉	—	6	24	no	—
226	C₂²×C₉	—	6	24	no	—
227	C₂²×C₉	—	6	6	no	—
228	C₂²×C₉	—	6	3	no	—
229	C₂²×C₉	—	12	4	no	—
230	C₂²×C₉	D₃×D₄	1	6	yes	complemented
231	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
232	C₄×C₉	—	2	3	no	—
233	C₄×C₉	—	4	3	no	—
234	C₄×C₉	—	6	3	no	—
235	C₂⁵	—	3	1	no	—
236	C₂²×D₄	—	3	3	no	—
237	#120	—	3	1	no	—
238	#120	—	3	3	no	—
239	#120	—	3	3	no	—
240	#120	D₃×C₉	1	1	yes	characteristic, direct product factor
241	C₂×C₂²⋊C₄	—	3	3	no	—
242	C₃×C₉	C₂×#120	1	1	yes	characteristic, complemented, Sylow
243	C₂³×C₃	—	2	6	no	—
244	C₂³×C₃	—	2	6	no	—
245	C₂³×C₃	—	2	3	no	—
246	C₂³×C₃	—	2	1	no	—
247	C₂³×C₃	—	3	1	no	—
248	C₂³×C₃	—	3	3	no	—
249	C₂³×C₃	—	3	12	no	—
250	C₂³×C₃	—	3	1	no	—
251	C₂³×C₃	—	4	6	no	—
252	C₂³×C₃	—	6	12	no	—
253	C₂³×C₃	—	6	12	no	—
254	C₂³×C₃	—	6	6	no	—
255	C₂³×C₃	—	6	32	no	—
256	C₂³×C₃	—	6	6	no	—
257	C₂³×C₃	C₂³×C₉	1	3	yes	—
258	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic, complemented
259	C₂³×C₃	C₂²×C₃×D₃	1	3	yes	—
260	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
261	C₂²×D₃	—	2	32	no	—
262	C₂²×D₃	—	2	6	no	—
263	C₂²×D₃	—	2	12	no	—
264	C₂²×D₃	—	2	12	no	—
265	C₂²×D₃	—	2	6	no	—
266	C₂²×D₃	D₄×C₉	1	12	yes	complemented
267	C₂²×D₃	C₂³×C₉	1	3	yes	—
268	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
269	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic, complemented
270	C₃×D₄	—	2	6	no	—
271	C₃×D₄	—	2	6	no	—
272	C₃×D₄	—	4	6	no	—
273	C₃×D₄	—	6	6	no	—
274	C₃×D₄	—	6	6	no	—
275	C₃×D₄	—	6	6	no	—
276	C₂×C₃×C₄	—	2	3	no	—
277	C₂×C₃×C₄	—	3	3	no	—
278	C₂×C₃×C₄	—	6	6	no	—
279	C₂×C₃×C₄	C₂³×C₉	1	3	yes	complemented
280	C₂×C₃×C₄	C₂²×C₃×D₃	1	3	yes	—
281	#67	—	2	6	no	—
282	#67	—	2	6	no	—
283	C₂×Dic₃	C₂³×C₉	1	3	yes	complemented
284	D₁₂	—	2	6	no	—
285	C₄×D₃	—	2	6	no	—
286	C₂×C₃²	—	2	6	no	—
287	C₂×C₃²	—	4	1	no	—
288	C₂×C₃²	C₂²×C₃×D₄	1	3	yes	—
289	C₃×D₃	—	2	6	no	—
290	C₃×D₃	—	4	1	no	—
291	C₃×D₃	C₃×#120	1	4	yes	—
292	C₂×C₉	—	2	6	no	—
293	C₂×C₉	—	2	3	no	—
294	C₂×C₉	—	3	4	no	—
295	C₂×C₉	—	4	6	no	—
296	C₂×C₉	—	4	1	no	—
297	C₂×C₉	—	6	6	no	—
298	C₂×C₉	—	8	1	no	—
299	C₂×C₉	—	12	1	no	—
300	C₂×C₉	C₂×D₃×D₄	1	3	yes	—
301	C₂⁴	—	3	3	no	—
302	C₂⁴	—	3	3	no	—
303	C₂⁴	—	3	1	no	—
304	C₂⁴	—	6	12	no	—
305	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic, complemented
306	C₂×D₄	—	3	3	no	—
307	C₂×D₄	—	3	3	no	—
308	C₂×D₄	—	3	3	no	—
309	C₂×D₄	—	6	12	no	—
310	C₂×D₄	C₂×D₃×C₉	1	3	yes	complemented
311	C₂²×C₄	—	3	3	no	—
312	C₂²⋊C₄	—	3	3	no	—
313	C₂²⋊C₄	—	3	6	no	—
314	C₂²⋊C₄	C₂×D₃×C₉	1	3	yes	complemented
315	C₂²×C₃	—	2	8	no	—
316	C₂²×C₃	—	2	8	no	—
317	C₂²×C₃	—	2	6	no	—
318	C₂²×C₃	—	2	6	no	—
319	C₂²×C₃	—	2	3	no	—
320	C₂²×C₃	—	2	3	no	—
321	C₂²×C₃	—	2	1	no	—
322	C₂²×C₃	—	2	6	no	—
323	C₂²×C₃	—	3	6	no	—
324	C₂²×C₃	—	3	6	no	—
325	C₂²×C₃	—	4	6	no	—
326	C₂²×C₃	—	4	3	no	—
327	C₂²×C₃	—	4	8	no	—
328	C₂²×C₃	—	6	24	no	—
329	C₂²×C₃	—	6	24	no	—
330	C₂²×C₃	—	6	6	no	—
331	C₂²×C₃	—	6	3	no	—
332	C₂²×C₃	—	12	4	no	—
333	C₂²×C₃	C₂×D₄×C₉	1	6	yes	complemented
334	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
335	C₂²×C₃	C₃×D₃×D₄	1	6	yes	—
336	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
337	C₂×D₃	—	2	24	no	—
338	C₂×D₃	—	2	6	no	—
339	C₂×D₃	—	2	24	no	—
340	C₂×D₃	—	2	3	no	—
341	C₂×D₃	—	4	4	no	—
342	C₂×D₃	C₂×D₄×C₉	1	6	yes	—
343	C₂×D₃	C₂×D₄×C₉	1	6	yes	complemented
344	C₃×C₄	—	2	3	no	—
345	C₃×C₄	—	2	3	no	—
346	C₃×C₄	—	4	3	no	—
347	C₃×C₄	—	6	3	no	—
348	Dic₃	—	2	3	no	—
349	C₃²	C₂×C₃×#120	1	1	yes	characteristic
350	C₉	—	2	1	no	—
351	C₉	D₃×#120	1	1	yes	characteristic, direct product factor
352	C₂³	—	2	6	no	—
353	C₂³	—	3	1	no	—
354	C₂³	—	3	3	no	—
355	C₂³	—	3	12	no	—
356	C₂³	—	3	1	no	—
357	C₂³	—	6	12	no	—
358	C₂³	—	6	12	no	—
359	C₂³	—	6	6	no	—
360	C₂³	—	6	32	no	—
361	C₂³	—	6	6	no	—
362	C₂³	C₂²×D₃×C₉	1	3	yes	—
363	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic, complemented
364	D₄	—	2	6	no	—
365	D₄	—	6	6	no	—
366	D₄	—	6	6	no	—
367	D₄	—	6	6	no	—
368	C₂×C₄	—	3	3	no	—
369	C₂×C₄	—	6	6	no	—
370	C₂×C₄	C₂²×D₃×C₉	1	3	yes	complemented
371	C₂×C₃	—	2	6	no	—
372	C₂×C₃	—	2	6	no	—
373	C₂×C₃	—	2	3	no	—
374	C₂×C₃	—	3	4	no	—
375	C₂×C₃	—	4	6	no	—
376	C₂×C₃	—	4	1	no	—
377	C₂×C₃	—	4	1	no	—
378	C₂×C₃	—	6	6	no	—
379	C₂×C₃	—	8	1	no	—
380	C₂×C₃	—	12	1	no	—
381	C₂×C₃	C₂²×D₄×C₉	1	3	yes	—
382	C₂×C₃	C₂×C₃×D₃×D₄	1	3	yes	—
383	D₃	—	2	6	no	—
384	D₃	—	4	1	no	—
385	D₃	C₉×#120	1	4	yes	direct product factor
386	C₂²	—	2	8	no	—
387	C₂²	—	2	6	no	—
388	C₂²	—	2	3	no	—
389	C₂²	—	3	6	no	—
390	C₂²	—	3	6	no	—
391	C₂²	—	6	24	no	—
392	C₂²	—	6	24	no	—
393	C₂²	—	6	6	no	—
394	C₂²	—	6	3	no	—
395	C₂²	—	12	4	no	—
396	C₂²	D₃×D₄×C₉	1	6	yes	complemented
397	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
398	C₄	—	2	3	no	—
399	C₄	—	6	3	no	—
400	C₃	—	2	1	no	—
401	C₃	C₂×C₉×#120	1	1	yes	characteristic, complemented
402	C₃	C₃×D₃×#120	1	1	yes	characteristic
403	C₂	—	2	6	no	—
404	C₂	—	3	4	no	—
405	C₂	—	4	1	no	—
406	C₂	—	6	6	no	—
407	C₂	—	12	1	no	—
408	C₂	C₂×D₃×D₄×C₉	1	3	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#120	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×D₃×#120	C₃
hypercenter	C₉×#120	D₃
hypocenter	C₃	C₂×C₉×#120
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#120

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₃×C₉	C₂	semidirect
2. C₂×D₃×D₄×C₉	C₂	semidirect
3. C₃×C₉×#120	C₂	semidirect
4. C₉×#953	C₂	semidirect
5. C₉×#937	C₂	semidirect
6. C₉×#882	C₂	semidirect
7. D₃×C₉×C₂²⋊C₄	C₂	semidirect
10. C₂⁴×C₃×C₉	C₂²	semidirect
13. C₂³×D₃×C₉	C₂²	semidirect
14. C₂³×D₃×C₉	C₂²	semidirect
15. C₂×C₃×D₄×C₉	C₂²	semidirect
16. C₂×C₉×#67	C₂²	semidirect
17. C₂×C₉×#67	C₂²	semidirect
19. C₂×C₉×D₁₂	C₂²	semidirect
20. C₂×C₄×D₃×C₉	C₂²	semidirect
21. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
22. C₉×#217	C₂²	semidirect
23. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
37. C₉×#120	D₃	direct (N × H)
41. C₂³×C₃×C₉	C₂³	semidirect
47. C₂²×D₃×C₉	D₄	semidirect
50. C₂²×D₃×C₉	C₂³	semidirect
52. C₂×C₃×C₄×C₉	C₂³	semidirect
55. C₂×C₉×Dic₃	C₂³	semidirect
59. D₃×#120	C₉	direct (N × H)
76. C₂⁴×C₉	C₂×D₃	semidirect
85. C₂×D₄×C₉	C₂×D₃	semidirect
90. C₉×C₂²⋊C₄	C₂×D₃	semidirect
94. C₂²×C₃×C₉	C₂×D₄	semidirect
102. C₂×D₃×C₉	C₂×D₄	semidirect
106. C₂⁴×D₃	C₂×C₉	semidirect
108. C₂×D₃×D₄	C₂×C₉	semidirect
113. C₃×#120	C₂×C₉	semidirect
116. #953	C₂×C₉	semidirect
117. #937	C₂×C₉	semidirect
118. #882	C₂×C₉	semidirect
119. D₃×C₂²⋊C₄	C₂×C₉	semidirect
153. C₂³×C₉	C₂²×D₃	semidirect
162. C₂×C₄×C₉	C₂²×D₃	semidirect
169. D₃×C₉	#120	direct (N × H)
175. C₂⁴×C₃	C₂²×C₉	semidirect
179. C₂³×D₃	C₂²×C₉	semidirect
180. C₂³×D₃	C₂²×C₉	semidirect
186. C₂×C₃×D₄	C₂²×C₉	semidirect
189. C₂×#67	C₂²×C₉	semidirect
190. C₂×#67	C₂²×C₉	semidirect
192. C₂×D₁₂	C₂²×C₉	semidirect
193. C₂×C₄×D₃	C₂²×C₉	semidirect
197. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
199. #217	C₂²×C₉	semidirect
200. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
230. C₂²×C₉	D₃×D₄	semidirect
240. #120	D₃×C₉	direct (N × H)
242. C₃×C₉	C₂×#120	semidirect
258. C₂³×C₃	C₂³×C₉	semidirect
266. C₂²×D₃	D₄×C₉	semidirect
269. C₂²×D₃	C₂³×C₉	semidirect
279. C₂×C₃×C₄	C₂³×C₉	semidirect
283. C₂×Dic₃	C₂³×C₉	semidirect
305. C₂⁴	C₂×D₃×C₉	semidirect
310. C₂×D₄	C₂×D₃×C₉	semidirect
314. C₂²⋊C₄	C₂×D₃×C₉	semidirect
333. C₂²×C₃	C₂×D₄×C₉	semidirect
343. C₂×D₃	C₂×D₄×C₉	semidirect
351. C₉	D₃×#120	direct (N × H)
363. C₂³	C₂²×D₃×C₉	semidirect
370. C₂×C₄	C₂²×D₃×C₉	semidirect
385. D₃	C₉×#120	direct (N × H)
396. C₂²	D₃×D₄×C₉	semidirect
401. C₃	C₂×C₉×#120	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×D₃×C₉	2
C₂×D₃×D₄×C₉	2
C₃×C₉×#120	2
C₉×#953	2
C₉×#937	2
C₉×#882	2
D₃×C₉×C₂²⋊C₄	2
C₃×D₃×#120	3
C₂×C₉×#120	3

Subgroups — D3×C9×#120 #13152760

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₉×#120 #13152760