Subgroups — D₃×C₉×#121 #13152823

Order 1728.

1372 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×D₄×C₉	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#939	C₂	1	2	yes	maximal, complemented
6	C₉×#938	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#930	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#895	C₂	1	1	yes	maximal, characteristic, complemented
9	D₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#884	C₂	1	2	yes	maximal, complemented
11	D₃×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₃×D₃×#121	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#121	—	3	1	no	maximal
14	C₂³×D₃×C₉	C₂²	1	2	yes	—
15	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃×D₄×C₉	C₂²	1	2	yes	complemented
18	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₉×#67	C₂²	1	2	yes	complemented
20	C₂×C₉×#67	C₂²	1	2	yes	complemented
21	C₂×C₉×#67	C₂²	1	2	yes	complemented
22	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
23	D₃×D₄×C₉	—	2	8	no	—
24	D₃×D₄×C₉	—	2	4	no	—
25	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₉×D₁₂	C₂²	1	2	yes	complemented
27	C₂×C₄×D₃×C₉	—	2	4	no	—
28	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
30	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
35	C₉×#217	C₂²	1	2	yes	complemented
36	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
37	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
38	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
39	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
40	C₂×C₃×D₃×D₄	C₂×C₃	1	1	yes	characteristic
41	C₂×C₃×D₃×D₄	C₂×C₃	1	2	yes	—
42	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
43	C₃²×#121	C₂×C₃	1	1	yes	characteristic
44	C₃×#939	C₂×C₃	1	2	yes	—
45	C₃×#938	C₂×C₃	1	1	yes	characteristic
46	C₃×#930	C₂×C₃	1	1	yes	characteristic
47	C₃×#895	C₂×C₃	1	1	yes	characteristic
48	C₃×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
49	C₃×#884	C₂×C₃	1	2	yes	—
50	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	2	yes	—
51	C₂²×D₄×C₉	—	3	1	no	—
52	C₂²×D₄×C₉	—	3	2	no	—
53	C₂³×C₄×C₉	—	3	1	no	—
54	C₉×#121	—	2	1	no	—
55	C₉×#121	—	3	1	no	—
56	C₉×#121	—	3	2	no	—
57	C₉×#121	—	3	1	no	—
58	C₉×#121	—	3	1	no	—
59	C₉×#121	—	3	2	no	—
60	C₉×#121	D₃	1	1	yes	characteristic, direct product factor
61	C₂×C₉×C₄⋊C₄	—	3	1	no	—
62	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
63	C₂³×C₃×C₉	C₂³	1	2	yes	—
64	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
65	C₂²×D₃×C₉	—	2	2	no	—
66	C₂²×D₃×C₉	—	2	2	no	—
67	C₂²×D₃×C₉	—	2	4	no	—
68	C₂²×D₃×C₉	—	2	4	no	—
69	C₂²×D₃×C₉	—	2	4	no	—
70	C₂²×D₃×C₉	D₄	1	4	yes	complemented
71	C₂²×D₃×C₉	C₂³	1	2	yes	—
72	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
73	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
74	C₃×D₄×C₉	—	2	4	no	—
75	C₃×D₄×C₉	—	2	2	no	—
76	C₂×C₃×C₄×C₉	—	2	2	no	—
77	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
79	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
80	C₉×#67	—	2	4	no	—
81	C₉×#67	—	2	4	no	—
82	C₉×#67	—	2	4	no	—
83	C₂×C₉×Dic₃	—	2	2	no	—
84	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
85	C₂×C₉×Dic₃	C₂³	1	2	yes	—
86	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
87	C₉×D₁₂	—	2	4	no	—
88	C₉×D₁₂	—	2	2	no	—
89	C₄×D₃×C₉	—	2	2	no	—
90	C₄×D₃×C₉	—	2	4	no	—
91	C₄×D₃×C₉	—	2	2	no	—
92	C₄×D₃×C₉	—	2	2	no	—
93	C₄×D₃×C₉	D₄	1	4	yes	complemented
94	C₂×C₃×#121	—	3	1	no	—
95	D₃×#121	C₉	1	1	yes	characteristic, direct product factor
96	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	—
97	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
100	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
102	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
103	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
104	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
105	C₃×D₃×D₄	—	2	8	no	—
106	C₃×D₃×D₄	—	2	4	no	—
107	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
108	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₃×C₄×D₃	—	2	4	no	—
110	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
112	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
115	C₂⁴×C₉	—	3	1	no	—
116	C₂⁴×C₉	—	3	2	no	—
117	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
118	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
119	C₃×#217	C₂²×C₃	1	2	yes	—
120	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
121	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
122	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
123	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
124	C₂×D₄×C₉	—	2	1	no	—
125	C₂×D₄×C₉	—	2	2	no	—
126	C₂×D₄×C₉	—	3	2	no	—
127	C₂×D₄×C₉	—	3	2	no	—
128	C₂×D₄×C₉	—	3	2	no	—
129	C₂×D₄×C₉	—	3	2	no	—
130	C₂×D₄×C₉	—	3	1	no	—
131	C₂×D₄×C₉	—	6	4	no	—
132	C₂×D₄×C₉	—	6	8	no	—
133	C₂×D₄×C₉	C₂×D₃	1	2	yes	complemented
134	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
135	C₂²×C₄×C₉	—	2	1	no	—
136	C₂²×C₄×C₉	—	3	1	no	—
137	C₂²×C₄×C₉	—	3	1	no	—
138	C₂²×C₄×C₉	—	3	1	no	—
139	C₂²×C₄×C₉	—	3	2	no	—
140	C₂²×C₄×C₉	—	3	1	no	—
141	C₂²×C₄×C₉	—	3	1	no	—
142	C₂²×C₄×C₉	—	6	4	no	—
143	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
144	C₉×C₄⋊C₄	—	2	1	no	—
145	C₉×C₄⋊C₄	—	3	2	no	—
146	C₉×C₄⋊C₄	—	3	1	no	—
147	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
148	C₉×C₂²⋊C₄	—	2	2	no	—
149	C₉×C₂²⋊C₄	—	3	2	no	—
150	C₉×C₂²⋊C₄	—	3	2	no	—
151	C₉×C₂²⋊C₄	—	3	2	no	—
152	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
153	C₂²×C₃×C₉	—	2	1	no	—
154	C₂²×C₃×C₉	—	2	1	no	—
155	C₂²×C₃×C₉	—	2	2	no	—
156	C₂²×C₃×C₉	—	2	2	no	—
157	C₂²×C₃×C₉	—	2	2	no	—
158	C₂²×C₃×C₉	C₂×D₄	1	2	yes	complemented
159	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
160	C₂×D₃×C₉	—	2	1	no	—
161	C₂×D₃×C₉	—	2	1	no	—
162	C₂×D₃×C₉	—	2	8	no	—
163	C₂×D₃×C₉	—	2	2	no	—
164	C₂×D₃×C₉	—	2	2	no	—
165	C₂×D₃×C₉	—	2	2	no	—
166	C₂×D₃×C₉	—	4	8	no	—
167	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
168	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
169	C₂×D₃×C₉	C₂×D₄	1	2	yes	complemented
170	C₂×D₃×C₉	#41	1	2	yes	—
171	C₃×C₄×C₉	—	2	1	no	—
172	C₃×C₄×C₉	—	2	2	no	—
173	C₃×C₄×C₉	C₂×D₄	1	2	yes	complemented
174	C₉×Dic₃	—	2	1	no	—
175	C₉×Dic₃	—	2	2	no	—
176	C₉×Dic₃	C₂×D₄	1	2	yes	complemented
177	C₂²×C₃×D₄	—	3	1	no	—
178	C₂²×C₃×D₄	—	3	2	no	—
179	C₂³×C₃×C₄	—	3	1	no	—
180	C₂×D₃×D₄	C₂×C₉	1	2	yes	complemented
181	C₂×D₃×D₄	C₂×C₉	1	1	yes	characteristic, complemented
182	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic, complemented
183	C₃×#121	—	2	1	no	—
184	C₃×#121	—	3	1	no	—
185	C₃×#121	—	3	2	no	—
186	C₃×#121	—	3	1	no	—
187	C₃×#121	—	3	1	no	—
188	C₃×#121	—	3	2	no	—
189	C₃×#121	C₂×C₉	1	1	yes	characteristic, complemented
190	C₃×#121	C₃×D₃	1	1	yes	characteristic
191	C₂×C₃×C₄⋊C₄	—	3	1	no	—
192	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
193	#939	C₂×C₉	1	2	yes	complemented
194	#938	C₂×C₉	1	1	yes	characteristic, complemented
195	#930	C₂×C₉	1	1	yes	characteristic, complemented
196	#895	C₂×C₉	1	1	yes	characteristic, complemented
197	D₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
198	#884	C₂×C₉	1	2	yes	complemented
199	D₃×C₂²⋊C₄	C₂×C₉	1	2	yes	complemented
200	C₂³×C₃²	C₂³×C₃	1	2	yes	—
201	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
202	C₂²×C₃×D₃	—	2	2	no	—
203	C₂²×C₃×D₃	—	2	2	no	—
204	C₂²×C₃×D₃	—	2	4	no	—
205	C₂²×C₃×D₃	—	2	4	no	—
206	C₂²×C₃×D₃	—	2	4	no	—
207	C₂²×C₃×D₃	C₃×D₄	1	4	yes	—
208	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
209	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
210	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
211	C₃²×D₄	—	2	4	no	—
212	C₃²×D₄	—	2	2	no	—
213	C₂×C₃²×C₄	—	2	2	no	—
214	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
215	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
216	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
217	C₃×#67	—	2	4	no	—
218	C₃×#67	—	2	4	no	—
219	C₃×#67	—	2	4	no	—
220	C₂×C₃×Dic₃	—	2	2	no	—
221	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
222	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
223	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
224	C₃×D₁₂	—	2	4	no	—
225	C₃×D₁₂	—	2	2	no	—
226	C₃×C₄×D₃	—	2	2	no	—
227	C₃×C₄×D₃	—	2	4	no	—
228	C₃×C₄×D₃	—	2	2	no	—
229	C₃×C₄×D₃	—	2	2	no	—
230	C₃×C₄×D₃	C₃×D₄	1	4	yes	—
231	C₂³×C₉	—	2	1	no	—
232	C₂³×C₉	—	2	2	no	—
233	C₂³×C₉	—	3	1	no	—
234	C₂³×C₉	—	3	4	no	—
235	C₂³×C₉	—	3	1	no	—
236	C₂³×C₉	—	3	2	no	—
237	C₂³×C₉	—	6	2	no	—
238	C₂³×C₉	—	6	2	no	—
239	C₂³×C₉	—	6	4	no	—
240	C₂³×C₉	—	6	4	no	—
241	C₂³×C₉	—	6	4	no	—
242	C₂³×C₉	C₂²×D₃	1	2	yes	—
243	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
244	D₄×C₉	—	2	4	no	—
245	D₄×C₉	—	2	2	no	—
246	D₄×C₉	—	4	2	no	—
247	D₄×C₉	—	4	4	no	—
248	D₄×C₉	—	6	4	no	—
249	D₄×C₉	—	6	4	no	—
250	D₄×C₉	—	6	4	no	—
251	D₄×C₉	—	6	4	no	—
252	D₄×C₉	—	6	2	no	—
253	C₂×C₄×C₉	—	2	2	no	—
254	C₂×C₄×C₉	—	2	1	no	—
255	C₂×C₄×C₉	—	2	1	no	—
256	C₂×C₄×C₉	—	2	2	no	—
257	C₂×C₄×C₉	—	3	1	no	—
258	C₂×C₄×C₉	—	3	4	no	—
259	C₂×C₄×C₉	—	3	1	no	—
260	C₂×C₄×C₉	—	3	2	no	—
261	C₂×C₄×C₉	—	4	2	no	—
262	C₂×C₄×C₉	—	6	2	no	—
263	C₂×C₄×C₉	—	6	2	no	—
264	C₂×C₄×C₉	—	6	4	no	—
265	C₂×C₄×C₉	—	6	2	no	—
266	C₂×C₄×C₉	—	6	2	no	—
267	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
268	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
269	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
270	C₂×#121	—	3	1	no	Sylow
271	C₂×C₃×C₉	—	2	2	no	—
272	C₂×C₃×C₉	—	4	2	no	—
273	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
276	D₃×C₉	—	2	2	no	—
277	D₃×C₉	—	4	2	no	—
278	D₃×C₉	#121	1	4	yes	direct product factor
279	C₂⁴×C₃	—	3	1	no	—
280	C₂⁴×C₃	—	3	2	no	—
281	C₂³×D₃	C₂²×C₉	1	2	yes	—
282	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
283	C₂×C₃×D₄	—	2	1	no	—
284	C₂×C₃×D₄	—	2	2	no	—
285	C₂×C₃×D₄	—	3	2	no	—
286	C₂×C₃×D₄	—	3	2	no	—
287	C₂×C₃×D₄	—	3	2	no	—
288	C₂×C₃×D₄	—	3	2	no	—
289	C₂×C₃×D₄	—	3	1	no	—
290	C₂×C₃×D₄	—	6	4	no	—
291	C₂×C₃×D₄	—	6	8	no	—
292	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
293	C₂×C₃×D₄	C₂²×C₉	1	2	yes	complemented
294	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
295	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
296	C₂²×C₃×C₄	—	2	1	no	—
297	C₂²×C₃×C₄	—	3	1	no	—
298	C₂²×C₃×C₄	—	3	1	no	—
299	C₂²×C₃×C₄	—	3	1	no	—
300	C₂²×C₃×C₄	—	3	2	no	—
301	C₂²×C₃×C₄	—	3	1	no	—
302	C₂²×C₃×C₄	—	3	1	no	—
303	C₂²×C₃×C₄	—	6	4	no	—
304	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
305	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
306	C₂×#67	C₂²×C₉	1	2	yes	complemented
307	C₂×#67	C₂²×C₉	1	2	yes	complemented
308	C₂×#67	C₂²×C₉	1	2	yes	complemented
309	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
310	D₃×D₄	—	2	8	no	—
311	D₃×D₄	—	2	4	no	—
312	C₂×D₁₂	C₂²×C₉	1	2	yes	complemented
313	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
314	C₂×C₄×D₃	—	2	4	no	—
315	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
316	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
317	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
318	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
319	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
320	C₃×C₄⋊C₄	—	2	1	no	—
321	C₃×C₄⋊C₄	—	3	2	no	—
322	C₃×C₄⋊C₄	—	3	1	no	—
323	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
324	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
325	C₃×C₂²⋊C₄	—	2	2	no	—
326	C₃×C₂²⋊C₄	—	3	2	no	—
327	C₃×C₂²⋊C₄	—	3	2	no	—
328	C₃×C₂²⋊C₄	—	3	2	no	—
329	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
330	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
331	#217	C₂²×C₉	1	2	yes	complemented
332	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
333	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
334	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
335	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
336	C₂²×C₃²	—	2	1	no	—
337	C₂²×C₃²	—	2	1	no	—
338	C₂²×C₃²	—	2	2	no	—
339	C₂²×C₃²	—	2	2	no	—
340	C₂²×C₃²	—	2	2	no	—
341	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
342	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
343	C₂×C₃×D₃	—	2	1	no	—
344	C₂×C₃×D₃	—	2	1	no	—
345	C₂×C₃×D₃	—	2	8	no	—
346	C₂×C₃×D₃	—	2	2	no	—
347	C₂×C₃×D₃	—	2	2	no	—
348	C₂×C₃×D₃	—	2	2	no	—
349	C₂×C₃×D₃	—	4	8	no	—
350	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
351	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
352	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
353	C₂×C₃×D₃	C₃×#41	1	2	yes	—
354	C₃²×C₄	—	2	1	no	—
355	C₃²×C₄	—	2	2	no	—
356	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
357	C₃×Dic₃	—	2	1	no	—
358	C₃×Dic₃	—	2	2	no	—
359	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
360	C₂²×C₉	—	2	1	no	—
361	C₂²×C₉	—	2	1	no	—
362	C₂²×C₉	—	2	2	no	—
363	C₂²×C₉	—	2	2	no	—
364	C₂²×C₉	—	2	2	no	—
365	C₂²×C₉	—	2	1	no	—
366	C₂²×C₉	—	2	2	no	—
367	C₂²×C₉	—	3	2	no	—
368	C₂²×C₉	—	3	2	no	—
369	C₂²×C₉	—	3	2	no	—
370	C₂²×C₉	—	3	2	no	—
371	C₂²×C₉	—	4	1	no	—
372	C₂²×C₉	—	4	1	no	—
373	C₂²×C₉	—	4	2	no	—
374	C₂²×C₉	—	4	2	no	—
375	C₂²×C₉	—	4	2	no	—
376	C₂²×C₉	—	6	8	no	—
377	C₂²×C₉	—	6	1	no	—
378	C₂²×C₉	—	6	1	no	—
379	C₂²×C₉	—	6	2	no	—
380	C₂²×C₉	—	6	2	no	—
381	C₂²×C₉	—	6	2	no	—
382	C₂²×C₉	—	12	8	no	—
383	C₂²×C₉	D₃×D₄	1	2	yes	complemented
384	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
385	C₄×C₉	—	2	1	no	—
386	C₄×C₉	—	2	2	no	—
387	C₄×C₉	—	2	2	no	—
388	C₄×C₉	—	3	2	no	—
389	C₄×C₉	—	4	1	no	—
390	C₄×C₉	—	4	2	no	—
391	C₄×C₉	—	6	1	no	—
392	C₄×C₉	—	6	2	no	—
393	C₄×C₉	D₃×D₄	1	2	yes	complemented
394	C₂²×D₄	—	3	1	no	—
395	C₂²×D₄	—	3	2	no	—
396	C₂³×C₄	—	3	1	no	—
397	#121	—	3	1	no	—
398	#121	—	3	2	no	—
399	#121	—	3	1	no	—
400	#121	—	3	1	no	—
401	#121	—	3	2	no	—
402	#121	D₃×C₉	1	1	yes	characteristic, direct product factor
403	C₂×C₄⋊C₄	—	3	1	no	—
404	C₂×C₂²⋊C₄	—	3	2	no	—
405	C₃×C₉	C₂×#121	1	1	yes	characteristic, complemented, Sylow
406	C₂³×C₃	—	2	1	no	—
407	C₂³×C₃	—	2	2	no	—
408	C₂³×C₃	—	3	1	no	—
409	C₂³×C₃	—	3	1	no	—
410	C₂³×C₃	—	3	4	no	—
411	C₂³×C₃	—	3	2	no	—
412	C₂³×C₃	—	6	2	no	—
413	C₂³×C₃	—	6	2	no	—
414	C₂³×C₃	—	6	4	no	—
415	C₂³×C₃	—	6	4	no	—
416	C₂³×C₃	—	6	4	no	—
417	C₂³×C₃	C₂³×C₉	1	2	yes	—
418	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
419	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
420	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
421	C₂²×D₃	—	2	2	no	—
422	C₂²×D₃	—	2	2	no	—
423	C₂²×D₃	—	2	4	no	—
424	C₂²×D₃	—	2	4	no	—
425	C₂²×D₃	—	2	4	no	—
426	C₂²×D₃	D₄×C₉	1	4	yes	complemented
427	C₂²×D₃	C₂³×C₉	1	2	yes	—
428	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
429	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
430	C₃×D₄	—	2	4	no	—
431	C₃×D₄	—	2	4	no	—
432	C₃×D₄	—	2	2	no	—
433	C₃×D₄	—	2	2	no	—
434	C₃×D₄	—	4	2	no	—
435	C₃×D₄	—	4	4	no	—
436	C₃×D₄	—	6	4	no	—
437	C₃×D₄	—	6	4	no	—
438	C₃×D₄	—	6	4	no	—
439	C₃×D₄	—	6	4	no	—
440	C₃×D₄	—	6	2	no	—
441	C₂×C₃×C₄	—	2	2	no	—
442	C₂×C₃×C₄	—	2	2	no	—
443	C₂×C₃×C₄	—	2	1	no	—
444	C₂×C₃×C₄	—	2	1	no	—
445	C₂×C₃×C₄	—	2	2	no	—
446	C₂×C₃×C₄	—	3	1	no	—
447	C₂×C₃×C₄	—	3	4	no	—
448	C₂×C₃×C₄	—	3	1	no	—
449	C₂×C₃×C₄	—	3	2	no	—
450	C₂×C₃×C₄	—	4	2	no	—
451	C₂×C₃×C₄	—	6	2	no	—
452	C₂×C₃×C₄	—	6	2	no	—
453	C₂×C₃×C₄	—	6	4	no	—
454	C₂×C₃×C₄	—	6	2	no	—
455	C₂×C₃×C₄	—	6	2	no	—
456	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
457	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
458	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
459	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
460	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
461	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
462	#67	—	2	4	no	—
463	#67	—	2	4	no	—
464	#67	—	2	4	no	—
465	C₂×Dic₃	—	2	2	no	—
466	C₂×Dic₃	C₂³×C₉	1	2	yes	—
467	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
468	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
469	D₁₂	—	2	4	no	—
470	D₁₂	—	2	2	no	—
471	C₄×D₃	—	2	2	no	—
472	C₄×D₃	—	2	4	no	—
473	C₄×D₃	—	2	2	no	—
474	C₄×D₃	—	2	2	no	—
475	C₄×D₃	D₄×C₉	1	4	yes	complemented
476	C₂×C₃²	—	2	2	no	—
477	C₂×C₃²	—	4	2	no	—
478	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
479	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
480	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
481	C₃×D₃	—	2	2	no	—
482	C₃×D₃	—	4	2	no	—
483	C₃×D₃	C₃×#121	1	4	yes	—
484	C₂×C₉	—	2	2	no	—
485	C₂×C₉	—	2	1	no	—
486	C₂×C₉	—	2	1	no	—
487	C₂×C₉	—	2	1	no	—
488	C₂×C₉	—	3	4	no	—
489	C₂×C₉	—	4	2	no	—
490	C₂×C₉	—	4	2	no	—
491	C₂×C₉	—	6	2	no	—
492	C₂×C₉	—	8	2	no	—
493	C₂×C₉	—	12	2	no	—
494	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
495	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
496	C₂×C₉	D₃×#41	1	1	yes	characteristic
497	C₂⁴	—	3	1	no	—
498	C₂⁴	—	3	2	no	—
499	C₂×D₄	—	3	2	no	—
500	C₂×D₄	—	3	2	no	—
501	C₂×D₄	—	3	2	no	—
502	C₂×D₄	—	3	2	no	—
503	C₂×D₄	—	3	1	no	—
504	C₂×D₄	—	6	4	no	—
505	C₂×D₄	—	6	8	no	—
506	C₂×D₄	C₂×D₃×C₉	1	2	yes	complemented
507	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
508	C₂²×C₄	—	3	1	no	—
509	C₂²×C₄	—	3	1	no	—
510	C₂²×C₄	—	3	1	no	—
511	C₂²×C₄	—	3	2	no	—
512	C₂²×C₄	—	3	1	no	—
513	C₂²×C₄	—	3	1	no	—
514	C₂²×C₄	—	6	4	no	—
515	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
516	C₄⋊C₄	—	3	2	no	—
517	C₄⋊C₄	—	3	1	no	—
518	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
519	C₂²⋊C₄	—	3	2	no	—
520	C₂²⋊C₄	—	3	2	no	—
521	C₂²⋊C₄	—	3	2	no	—
522	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
523	C₂²×C₃	—	2	1	no	—
524	C₂²×C₃	—	2	1	no	—
525	C₂²×C₃	—	2	1	no	—
526	C₂²×C₃	—	2	1	no	—
527	C₂²×C₃	—	2	2	no	—
528	C₂²×C₃	—	2	2	no	—
529	C₂²×C₃	—	2	2	no	—
530	C₂²×C₃	—	2	2	no	—
531	C₂²×C₃	—	2	2	no	—
532	C₂²×C₃	—	2	2	no	—
533	C₂²×C₃	—	2	1	no	—
534	C₂²×C₃	—	2	2	no	—
535	C₂²×C₃	—	3	2	no	—
536	C₂²×C₃	—	3	2	no	—
537	C₂²×C₃	—	3	2	no	—
538	C₂²×C₃	—	3	2	no	—
539	C₂²×C₃	—	4	1	no	—
540	C₂²×C₃	—	4	1	no	—
541	C₂²×C₃	—	4	2	no	—
542	C₂²×C₃	—	4	2	no	—
543	C₂²×C₃	—	4	2	no	—
544	C₂²×C₃	—	6	8	no	—
545	C₂²×C₃	—	6	1	no	—
546	C₂²×C₃	—	6	1	no	—
547	C₂²×C₃	—	6	2	no	—
548	C₂²×C₃	—	6	2	no	—
549	C₂²×C₃	—	6	2	no	—
550	C₂²×C₃	—	12	8	no	—
551	C₂²×C₃	C₂×D₄×C₉	1	2	yes	complemented
552	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
553	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
554	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
555	C₂×D₃	—	2	1	no	—
556	C₂×D₃	—	2	1	no	—
557	C₂×D₃	—	2	8	no	—
558	C₂×D₃	—	2	2	no	—
559	C₂×D₃	—	2	2	no	—
560	C₂×D₃	—	2	2	no	—
561	C₂×D₃	—	4	8	no	—
562	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
563	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
564	C₂×D₃	C₂×D₄×C₉	1	2	yes	complemented
565	C₂×D₃	C₉×#41	1	2	yes	—
566	C₃×C₄	—	2	1	no	—
567	C₃×C₄	—	2	2	no	—
568	C₃×C₄	—	2	1	no	—
569	C₃×C₄	—	2	2	no	—
570	C₃×C₄	—	2	2	no	—
571	C₃×C₄	—	3	2	no	—
572	C₃×C₄	—	4	1	no	—
573	C₃×C₄	—	4	2	no	—
574	C₃×C₄	—	6	1	no	—
575	C₃×C₄	—	6	2	no	—
576	C₃×C₄	C₂×D₄×C₉	1	2	yes	complemented
577	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
578	Dic₃	—	2	1	no	—
579	Dic₃	—	2	2	no	—
580	Dic₃	C₂×D₄×C₉	1	2	yes	complemented
581	C₃²	C₂×C₃×#121	1	1	yes	characteristic
582	C₉	—	2	1	no	—
583	C₉	D₃×#121	1	1	yes	characteristic, direct product factor
584	C₂³	—	3	1	no	—
585	C₂³	—	3	1	no	—
586	C₂³	—	3	4	no	—
587	C₂³	—	3	2	no	—
588	C₂³	—	6	2	no	—
589	C₂³	—	6	2	no	—
590	C₂³	—	6	4	no	—
591	C₂³	—	6	4	no	—
592	C₂³	—	6	4	no	—
593	C₂³	C₂²×D₃×C₉	1	2	yes	—
594	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
595	D₄	—	2	4	no	—
596	D₄	—	2	2	no	—
597	D₄	—	6	4	no	—
598	D₄	—	6	4	no	—
599	D₄	—	6	4	no	—
600	D₄	—	6	4	no	—
601	D₄	—	6	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	3	1	no	—
604	C₂×C₄	—	3	4	no	—
605	C₂×C₄	—	3	1	no	—
606	C₂×C₄	—	3	2	no	—
607	C₂×C₄	—	6	2	no	—
608	C₂×C₄	—	6	2	no	—
609	C₂×C₄	—	6	4	no	—
610	C₂×C₄	—	6	2	no	—
611	C₂×C₄	—	6	2	no	—
612	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
613	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
614	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
615	C₂×C₃	—	2	2	no	—
616	C₂×C₃	—	2	2	no	—
617	C₂×C₃	—	2	1	no	—
618	C₂×C₃	—	2	1	no	—
619	C₂×C₃	—	2	1	no	—
620	C₂×C₃	—	3	4	no	—
621	C₂×C₃	—	4	2	no	—
622	C₂×C₃	—	4	2	no	—
623	C₂×C₃	—	4	2	no	—
624	C₂×C₃	—	6	2	no	—
625	C₂×C₃	—	8	2	no	—
626	C₂×C₃	—	12	2	no	—
627	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
628	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
629	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
630	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
631	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
632	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
633	D₃	—	2	2	no	—
634	D₃	—	4	2	no	—
635	D₃	C₉×#121	1	4	yes	direct product factor
636	C₂²	—	2	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	3	2	no	—
642	C₂²	—	3	2	no	—
643	C₂²	—	3	2	no	—
644	C₂²	—	3	2	no	—
645	C₂²	—	6	8	no	—
646	C₂²	—	6	1	no	—
647	C₂²	—	6	1	no	—
648	C₂²	—	6	2	no	—
649	C₂²	—	6	2	no	—
650	C₂²	—	6	2	no	—
651	C₂²	—	12	8	no	—
652	C₂²	D₃×D₄×C₉	1	2	yes	complemented
653	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
654	C₄	—	2	1	no	—
655	C₄	—	2	2	no	—
656	C₄	—	3	2	no	—
657	C₄	—	6	1	no	—
658	C₄	—	6	2	no	—
659	C₄	D₃×D₄×C₉	1	2	yes	complemented
660	C₃	—	2	1	no	—
661	C₃	C₂×C₉×#121	1	1	yes	characteristic, complemented
662	C₃	C₃×D₃×#121	1	1	yes	characteristic
663	C₂	—	2	2	no	—
664	C₂	—	3	4	no	—
665	C₂	—	4	2	no	—
666	C₂	—	6	2	no	—
667	C₂	—	12	2	no	—
668	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
669	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
670	C₂	D₃×C₉×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#121	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×D₃×#121	C₃
hypercenter	C₉×#121	D₃
hypocenter	C₃	C₂×C₉×#121
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#121

Complements

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

N	H ≅ G/N	type
1. C₂×D₃×D₄×C₉	C₂	semidirect
2. C₂×D₃×D₄×C₉	C₂	semidirect
3. C₂²×C₄×D₃×C₉	C₂	semidirect
4. C₃×C₉×#121	C₂	semidirect
5. C₉×#939	C₂	semidirect
6. C₉×#938	C₂	semidirect
7. C₉×#930	C₂	semidirect
8. C₉×#895	C₂	semidirect
9. D₃×C₉×C₄⋊C₄	C₂	semidirect
10. C₉×#884	C₂	semidirect
11. D₃×C₉×C₂²⋊C₄	C₂	semidirect
16. C₂×C₃×D₄×C₉	C₂²	semidirect
17. C₂×C₃×D₄×C₉	C₂²	semidirect
18. C₂²×C₃×C₄×C₉	C₂²	semidirect
19. C₂×C₉×#67	C₂²	semidirect
20. C₂×C₉×#67	C₂²	semidirect
21. C₂×C₉×#67	C₂²	semidirect
22. C₂²×C₉×Dic₃	C₂²	semidirect
25. C₂×C₉×D₁₂	C₂²	semidirect
26. C₂×C₉×D₁₂	C₂²	semidirect
31. C₂×C₄×D₃×C₉	C₂²	semidirect
32. C₂×C₄×D₃×C₉	C₂²	semidirect
33. C₃×C₉×C₄⋊C₄	C₂²	semidirect
34. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
35. C₉×#217	C₂²	semidirect
36. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
37. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
38. C₉×C₄⋊Dic₃	C₂²	semidirect
39. C₉×Dic₃⋊C₄	C₂²	semidirect
60. C₉×#121	D₃	direct (N × H)
70. C₂²×D₃×C₉	D₄	semidirect
93. C₄×D₃×C₉	D₄	semidirect
95. D₃×#121	C₉	direct (N × H)
133. C₂×D₄×C₉	C₂×D₃	semidirect
134. C₂×D₄×C₉	C₂×D₃	semidirect
143. C₂²×C₄×C₉	C₂×D₃	semidirect
147. C₉×C₄⋊C₄	C₂×D₃	semidirect
152. C₉×C₂²⋊C₄	C₂×D₃	semidirect
158. C₂²×C₃×C₉	C₂×D₄	semidirect
169. C₂×D₃×C₉	C₂×D₄	semidirect
173. C₃×C₄×C₉	C₂×D₄	semidirect
176. C₉×Dic₃	C₂×D₄	semidirect
180. C₂×D₃×D₄	C₂×C₉	semidirect
181. C₂×D₃×D₄	C₂×C₉	semidirect
182. C₂²×C₄×D₃	C₂×C₉	semidirect
189. C₃×#121	C₂×C₉	semidirect
193. #939	C₂×C₉	semidirect
194. #938	C₂×C₉	semidirect
195. #930	C₂×C₉	semidirect
196. #895	C₂×C₉	semidirect
197. D₃×C₄⋊C₄	C₂×C₉	semidirect
198. #884	C₂×C₉	semidirect
199. D₃×C₂²⋊C₄	C₂×C₉	semidirect
278. D₃×C₉	#121	direct (N × H)
292. C₂×C₃×D₄	C₂²×C₉	semidirect
293. C₂×C₃×D₄	C₂²×C₉	semidirect
304. C₂²×C₃×C₄	C₂²×C₉	semidirect
306. C₂×#67	C₂²×C₉	semidirect
307. C₂×#67	C₂²×C₉	semidirect
308. C₂×#67	C₂²×C₉	semidirect
309. C₂²×Dic₃	C₂²×C₉	semidirect
312. C₂×D₁₂	C₂²×C₉	semidirect
313. C₂×D₁₂	C₂²×C₉	semidirect
318. C₂×C₄×D₃	C₂²×C₉	semidirect
319. C₂×C₄×D₃	C₂²×C₉	semidirect
323. C₃×C₄⋊C₄	C₂²×C₉	semidirect
329. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
331. #217	C₂²×C₉	semidirect
332. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
333. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
334. C₄⋊Dic₃	C₂²×C₉	semidirect
335. Dic₃⋊C₄	C₂²×C₉	semidirect
383. C₂²×C₉	D₃×D₄	semidirect
393. C₄×C₉	D₃×D₄	semidirect
402. #121	D₃×C₉	direct (N × H)
405. C₃×C₉	C₂×#121	semidirect
426. C₂²×D₃	D₄×C₉	semidirect
475. C₄×D₃	D₄×C₉	semidirect
506. C₂×D₄	C₂×D₃×C₉	semidirect
507. C₂×D₄	C₂×D₃×C₉	semidirect
515. C₂²×C₄	C₂×D₃×C₉	semidirect
518. C₄⋊C₄	C₂×D₃×C₉	semidirect
522. C₂²⋊C₄	C₂×D₃×C₉	semidirect
551. C₂²×C₃	C₂×D₄×C₉	semidirect
564. C₂×D₃	C₂×D₄×C₉	semidirect
576. C₃×C₄	C₂×D₄×C₉	semidirect
580. Dic₃	C₂×D₄×C₉	semidirect
583. C₉	D₃×#121	direct (N × H)
635. D₃	C₉×#121	direct (N × H)
652. C₂²	D₃×D₄×C₉	semidirect
659. C₄	D₃×D₄×C₉	semidirect
661. C₃	C₂×C₉×#121	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×D₄×C₉	2
C₂²×C₄×D₃×C₉	2
C₃×C₉×#121	2
C₉×#939	2
C₉×#938	2
C₉×#930	2
C₉×#895	2
D₃×C₉×C₄⋊C₄	2
C₉×#884	2
D₃×C₉×C₂²⋊C₄	2
C₃×D₃×#121	3
C₂×C₉×#121	3

Subgroups — D3×C9×#121 #13152823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₉×#121 #13152823