Subgroups — C₃×C₉×#388 #13144922

Order 1728.

950 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×C₄²×C₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₉×#95	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₉×#95	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#388	C₃	1	1	yes	maximal, characteristic
9	C₉×#388	C₃	1	3	yes	maximal, direct product factor
10	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₃×C₉×C₄⋊C₄	—	2	2	no	—
18	C₃×C₉×C₂²⋊C₄	—	2	2	no	—
19	C₃×C₉×C₂²⋊C₄	—	2	2	no	—
20	C₃×C₉×C₂²⋊C₄	C₄	1	4	yes	complemented
21	C₃×C₄²×C₉	—	2	2	no	—
22	C₂×C₃²×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
23	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃²×C₄²	C₂×C₃	1	1	yes	characteristic
27	C₃²×#95	C₂×C₃	1	1	yes	characteristic
28	C₃²×#95	C₂×C₃	1	1	yes	characteristic
29	C₂×C₉×C₄⋊C₄	C₂×C₃	1	3	yes	complemented
30	C₂×C₉×C₂²⋊C₄	C₂×C₃	1	3	yes	—
31	C₂×C₉×C₂²⋊C₄	C₂×C₃	1	3	yes	—
32	C₂×C₉×C₂²⋊C₄	C₂×C₃	1	3	yes	—
33	C₂×C₄²×C₉	C₂×C₃	1	3	yes	complemented
34	C₉×#95	C₂×C₃	1	3	yes	complemented
35	C₉×#95	C₂×C₃	1	3	yes	complemented
36	C₂³×C₃×C₉	—	2	1	no	—
37	C₂³×C₃×C₉	—	2	1	no	—
38	C₂³×C₃×C₉	—	2	1	no	—
39	C₂³×C₃×C₉	—	2	1	no	—
40	C₂³×C₃×C₉	—	2	1	no	—
41	C₂³×C₃×C₉	—	2	1	no	—
42	C₂³×C₃×C₉	C₂×C₄	1	2	yes	—
43	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
44	C₂×C₃×C₄×C₉	—	2	1	no	—
45	C₂×C₃×C₄×C₉	—	2	1	no	—
46	C₂×C₃×C₄×C₉	—	2	1	no	—
47	C₂×C₃×C₄×C₉	—	2	1	no	—
48	C₂×C₃×C₄×C₉	—	2	1	no	—
49	C₂×C₃×C₄×C₉	—	2	1	no	—
50	C₂×C₃×C₄×C₉	—	2	1	no	—
51	C₂×C₃×C₄×C₉	—	2	1	no	—
52	C₂×C₃×C₄×C₉	—	2	1	no	—
53	C₂×C₃×C₄×C₉	—	2	1	no	—
54	C₂×C₃×C₄×C₉	—	2	1	no	—
55	C₂×C₃×C₄×C₉	—	2	1	no	—
56	C₂×C₃×C₄×C₉	—	2	1	no	—
57	C₂×C₃×C₄×C₉	—	2	1	no	—
58	C₂×C₃×C₄×C₉	C₂×C₄	1	2	yes	—
59	C₂×C₃×C₄×C₉	C₂×C₄	1	2	yes	—
60	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
61	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
62	C₃×#388	C₉	1	3	yes	direct product factor
63	C₃×#388	C₃²	1	1	yes	characteristic
64	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
65	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
67	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
69	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
71	C₂⁴×C₉	C₂²×C₃	1	3	yes	—
72	C₃²×C₄⋊C₄	—	2	2	no	—
73	C₃²×C₂²⋊C₄	—	2	2	no	—
74	C₃²×C₂²⋊C₄	—	2	2	no	—
75	C₃²×C₂²⋊C₄	C₃×C₄	1	4	yes	—
76	C₃²×C₄²	—	2	2	no	—
77	C₂²×C₄×C₉	C₂²×C₃	1	3	yes	—
78	C₂²×C₄×C₉	C₂²×C₃	1	3	yes	—
79	C₂²×C₄×C₉	C₂²×C₃	1	3	yes	—
80	C₂²×C₄×C₉	C₂²×C₃	1	3	yes	—
81	C₂²×C₄×C₉	C₂²×C₃	1	3	yes	—
82	C₂²×C₄×C₉	C₂²×C₃	1	3	yes	—
83	C₉×C₄⋊C₄	—	2	6	no	—
84	C₉×C₂²⋊C₄	—	2	6	no	—
85	C₉×C₂²⋊C₄	—	2	6	no	—
86	C₉×C₂²⋊C₄	C₃×C₄	1	12	yes	complemented
87	C₄²×C₉	—	2	6	no	—
88	C₂²×C₃×C₉	—	2	2	no	—
89	C₂²×C₃×C₉	—	2	2	no	—
90	C₂²×C₃×C₉	—	2	2	no	—
91	C₂²×C₃×C₉	—	4	1	no	—
92	C₂²×C₃×C₉	—	4	1	no	—
93	C₂²×C₃×C₉	—	4	1	no	—
94	C₂²×C₃×C₉	—	4	1	no	—
95	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₃×C₉	#41	1	1	yes	characteristic
99	C₂²×C₃×C₉	#41	1	1	yes	characteristic
100	C₂²×C₃×C₉	#41	1	1	yes	characteristic
101	C₂²×C₃×C₉	#41	1	1	yes	characteristic
102	C₃×C₄×C₉	—	2	2	no	—
103	C₃×C₄×C₉	—	2	2	no	—
104	C₃×C₄×C₉	—	2	2	no	—
105	C₃×C₄×C₉	—	2	2	no	—
106	C₃×C₄×C₉	—	4	1	no	—
107	C₃×C₄×C₉	—	4	1	no	—
108	C₂×C₃×C₄⋊C₄	C₂×C₉	1	3	yes	complemented
109	C₂×C₃×C₄⋊C₄	C₂×C₃²	1	1	yes	characteristic
110	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	3	yes	—
111	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	3	yes	—
112	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	3	yes	—
113	C₂×C₃×C₂²⋊C₄	C₂×C₃²	1	1	yes	characteristic
114	C₂×C₃×C₂²⋊C₄	C₂×C₃²	1	1	yes	characteristic
115	C₂×C₃×C₂²⋊C₄	C₂×C₃²	1	1	yes	characteristic
116	C₂×C₃×C₄²	C₂×C₉	1	3	yes	complemented
117	C₂×C₃×C₄²	C₂×C₃²	1	1	yes	characteristic
118	C₃×#95	C₂×C₉	1	3	yes	complemented
119	C₃×#95	C₂×C₉	1	3	yes	complemented
120	C₃×#95	C₂×C₃²	1	1	yes	characteristic
121	C₃×#95	C₂×C₃²	1	1	yes	characteristic
122	C₂³×C₃²	—	2	1	no	—
123	C₂³×C₃²	—	2	1	no	—
124	C₂³×C₃²	—	2	1	no	—
125	C₂³×C₃²	—	2	1	no	—
126	C₂³×C₃²	—	2	1	no	—
127	C₂³×C₃²	—	2	1	no	—
128	C₂³×C₃²	C₂×C₃×C₄	1	2	yes	—
129	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
130	C₂×C₃²×C₄	—	2	1	no	—
131	C₂×C₃²×C₄	—	2	1	no	—
132	C₂×C₃²×C₄	—	2	1	no	—
133	C₂×C₃²×C₄	—	2	1	no	—
134	C₂×C₃²×C₄	—	2	1	no	—
135	C₂×C₃²×C₄	—	2	1	no	—
136	C₂×C₃²×C₄	—	2	1	no	—
137	C₂×C₃²×C₄	—	2	1	no	—
138	C₂×C₃²×C₄	—	2	1	no	—
139	C₂×C₃²×C₄	—	2	1	no	—
140	C₂×C₃²×C₄	—	2	1	no	—
141	C₂×C₃²×C₄	—	2	1	no	—
142	C₂×C₃²×C₄	—	2	1	no	—
143	C₂×C₃²×C₄	—	2	1	no	—
144	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
145	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
146	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
147	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
148	C₂³×C₉	—	2	3	no	—
149	C₂³×C₉	—	2	3	no	—
150	C₂³×C₉	—	2	3	no	—
151	C₂³×C₉	—	2	3	no	—
152	C₂³×C₉	—	2	3	no	—
153	C₂³×C₉	—	2	3	no	—
154	C₂³×C₉	C₂×C₃×C₄	1	6	yes	—
155	C₂³×C₉	C₂³×C₃	1	3	yes	—
156	C₂×C₄×C₉	—	2	3	no	—
157	C₂×C₄×C₉	—	2	3	no	—
158	C₂×C₄×C₉	—	2	3	no	—
159	C₂×C₄×C₉	—	2	3	no	—
160	C₂×C₄×C₉	—	2	3	no	—
161	C₂×C₄×C₉	—	2	3	no	—
162	C₂×C₄×C₉	—	2	3	no	—
163	C₂×C₄×C₉	—	2	3	no	—
164	C₂×C₄×C₉	—	2	3	no	—
165	C₂×C₄×C₉	—	2	3	no	—
166	C₂×C₄×C₉	—	2	3	no	—
167	C₂×C₄×C₉	—	2	3	no	—
168	C₂×C₄×C₉	—	2	3	no	—
169	C₂×C₄×C₉	—	2	3	no	—
170	C₂×C₄×C₉	C₂×C₃×C₄	1	6	yes	—
171	C₂×C₄×C₉	C₂×C₃×C₄	1	6	yes	—
172	C₂×C₄×C₉	C₃×D₄	1	6	yes	—
173	C₂×C₄×C₉	C₃×D₄	1	6	yes	—
174	#388	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
175	C₂×C₃×C₉	—	4	2	no	—
176	C₂×C₃×C₉	#117	1	1	yes	characteristic
177	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
178	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
179	C₂×C₃×C₉	#121	1	1	yes	characteristic
180	C₂×C₃×C₉	#123	1	1	yes	characteristic
181	C₂×C₃×C₉	#124	1	1	yes	characteristic
182	C₂×C₃×C₉	#126	1	1	yes	characteristic
183	C₂⁴×C₃	C₂²×C₉	1	3	yes	—
184	C₂⁴×C₃	C₂²×C₃²	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂²×C₉	1	3	yes	—
186	C₂²×C₃×C₄	C₂²×C₉	1	3	yes	—
187	C₂²×C₃×C₄	C₂²×C₉	1	3	yes	—
188	C₂²×C₃×C₄	C₂²×C₉	1	3	yes	—
189	C₂²×C₃×C₄	C₂²×C₉	1	3	yes	—
190	C₂²×C₃×C₄	C₂²×C₉	1	3	yes	—
191	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
195	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
196	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
197	C₃×C₄⋊C₄	—	2	6	no	—
198	C₃×C₄⋊C₄	—	2	2	no	—
199	C₃×C₂²⋊C₄	—	2	6	no	—
200	C₃×C₂²⋊C₄	—	2	6	no	—
201	C₃×C₂²⋊C₄	—	2	2	no	—
202	C₃×C₂²⋊C₄	—	2	2	no	—
203	C₃×C₂²⋊C₄	C₄×C₉	1	12	yes	complemented
204	C₃×C₂²⋊C₄	C₃²×C₄	1	4	yes	—
205	C₃×C₄²	—	2	6	no	—
206	C₃×C₄²	—	2	2	no	—
207	C₂²×C₃²	—	2	2	no	—
208	C₂²×C₃²	—	2	2	no	—
209	C₂²×C₃²	—	2	2	no	—
210	C₂²×C₃²	—	4	1	no	—
211	C₂²×C₃²	—	4	1	no	—
212	C₂²×C₃²	—	4	1	no	—
213	C₂²×C₃²	—	4	1	no	—
214	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
215	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
216	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
217	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
218	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
219	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
220	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
221	C₃²×C₄	—	2	2	no	—
222	C₃²×C₄	—	2	2	no	—
223	C₃²×C₄	—	2	2	no	—
224	C₃²×C₄	—	2	2	no	—
225	C₃²×C₄	—	4	1	no	—
226	C₃²×C₄	—	4	1	no	—
227	C₂²×C₉	—	2	6	no	—
228	C₂²×C₉	—	2	6	no	—
229	C₂²×C₉	—	2	6	no	—
230	C₂²×C₉	—	4	3	no	—
231	C₂²×C₉	—	4	3	no	—
232	C₂²×C₉	—	4	3	no	—
233	C₂²×C₉	—	4	3	no	—
234	C₂²×C₉	C₂²×C₃×C₄	1	3	yes	—
235	C₂²×C₉	C₂×C₃×D₄	1	3	yes	—
236	C₂²×C₉	C₂×C₃×D₄	1	3	yes	—
237	C₂²×C₉	C₃×#41	1	3	yes	—
238	C₂²×C₉	C₃×#41	1	3	yes	—
239	C₂²×C₉	C₃×#41	1	3	yes	—
240	C₂²×C₉	C₃×#41	1	3	yes	—
241	C₄×C₉	—	2	6	no	—
242	C₄×C₉	—	2	6	no	—
243	C₄×C₉	—	2	6	no	—
244	C₄×C₉	—	2	6	no	—
245	C₄×C₉	—	4	3	no	—
246	C₄×C₉	—	4	3	no	—
247	C₂×C₄⋊C₄	C₂×C₃×C₉	1	1	yes	characteristic, complemented
248	C₂×C₂²⋊C₄	C₂×C₃×C₉	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	C₂×C₃×C₉	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	C₂×C₃×C₉	1	1	yes	characteristic
251	C₂×C₄²	C₂×C₃×C₉	1	1	yes	characteristic, complemented
252	#95	C₂×C₃×C₉	1	1	yes	characteristic, complemented
253	#95	C₂×C₃×C₉	1	1	yes	characteristic, complemented
254	C₃×C₉	#388	1	1	yes	characteristic, direct product factor, Sylow
255	C₂³×C₃	—	2	3	no	—
256	C₂³×C₃	—	2	3	no	—
257	C₂³×C₃	—	2	3	no	—
258	C₂³×C₃	—	2	3	no	—
259	C₂³×C₃	—	2	3	no	—
260	C₂³×C₃	—	2	3	no	—
261	C₂³×C₃	—	2	1	no	—
262	C₂³×C₃	—	2	1	no	—
263	C₂³×C₃	—	2	1	no	—
264	C₂³×C₃	—	2	1	no	—
265	C₂³×C₃	—	2	1	no	—
266	C₂³×C₃	—	2	1	no	—
267	C₂³×C₃	C₂×C₄×C₉	1	6	yes	—
268	C₂³×C₃	C₂³×C₉	1	3	yes	—
269	C₂³×C₃	C₂×C₃²×C₄	1	2	yes	—
270	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
271	C₂×C₃×C₄	—	2	3	no	—
272	C₂×C₃×C₄	—	2	3	no	—
273	C₂×C₃×C₄	—	2	3	no	—
274	C₂×C₃×C₄	—	2	3	no	—
275	C₂×C₃×C₄	—	2	3	no	—
276	C₂×C₃×C₄	—	2	3	no	—
277	C₂×C₃×C₄	—	2	3	no	—
278	C₂×C₃×C₄	—	2	3	no	—
279	C₂×C₃×C₄	—	2	1	no	—
280	C₂×C₃×C₄	—	2	1	no	—
281	C₂×C₃×C₄	—	2	1	no	—
282	C₂×C₃×C₄	—	2	1	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	3	no	—
288	C₂×C₃×C₄	—	2	3	no	—
289	C₂×C₃×C₄	—	2	3	no	—
290	C₂×C₃×C₄	—	2	3	no	—
291	C₂×C₃×C₄	—	2	3	no	—
292	C₂×C₃×C₄	—	2	3	no	—
293	C₂×C₃×C₄	—	2	1	no	—
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	1	no	—
297	C₂×C₃×C₄	—	2	1	no	—
298	C₂×C₃×C₄	—	2	1	no	—
299	C₂×C₃×C₄	C₂×C₄×C₉	1	6	yes	—
300	C₂×C₃×C₄	C₂×C₄×C₉	1	6	yes	—
301	C₂×C₃×C₄	D₄×C₉	1	6	yes	—
302	C₂×C₃×C₄	D₄×C₉	1	6	yes	—
303	C₂×C₃×C₄	C₂×C₃²×C₄	1	2	yes	—
304	C₂×C₃×C₄	C₂×C₃²×C₄	1	2	yes	—
305	C₂×C₃×C₄	C₃²×D₄	1	2	yes	—
306	C₂×C₃×C₄	C₃²×D₄	1	2	yes	—
307	C₂×C₃²	—	4	2	no	—
308	C₂×C₃²	C₃×#117	1	1	yes	characteristic
309	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
310	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
311	C₂×C₃²	C₃×#121	1	1	yes	characteristic
312	C₂×C₃²	C₃×#123	1	1	yes	characteristic
313	C₂×C₃²	C₃×#124	1	1	yes	characteristic
314	C₂×C₃²	C₃×#126	1	1	yes	characteristic
315	C₂×C₉	—	4	6	no	—
316	C₂×C₉	C₃×#117	1	3	yes	—
317	C₂×C₉	C₃×C₄×D₄	1	3	yes	—
318	C₂×C₉	C₃×C₄×D₄	1	3	yes	—
319	C₂×C₉	C₃×#121	1	3	yes	—
320	C₂×C₉	C₃×#123	1	3	yes	—
321	C₂×C₉	C₃×#124	1	3	yes	—
322	C₂×C₉	C₃×#126	1	3	yes	—
323	C₂⁴	C₂²×C₃×C₉	1	1	yes	characteristic
324	C₂²×C₄	C₂²×C₃×C₉	1	1	yes	characteristic
325	C₂²×C₄	C₂²×C₃×C₉	1	1	yes	characteristic
326	C₂²×C₄	C₂²×C₃×C₉	1	1	yes	characteristic
327	C₂²×C₄	C₂²×C₃×C₉	1	1	yes	characteristic
328	C₂²×C₄	C₂²×C₃×C₉	1	1	yes	characteristic
329	C₂²×C₄	C₂²×C₃×C₉	1	1	yes	characteristic
330	C₄⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₂²⋊C₄	C₃×C₄×C₉	1	4	yes	complemented
334	C₄²	—	2	2	no	—
335	C₂²×C₃	—	2	6	no	—
336	C₂²×C₃	—	2	6	no	—
337	C₂²×C₃	—	2	6	no	—
338	C₂²×C₃	—	2	2	no	—
339	C₂²×C₃	—	2	2	no	—
340	C₂²×C₃	—	2	2	no	—
341	C₂²×C₃	—	4	3	no	—
342	C₂²×C₃	—	4	3	no	—
343	C₂²×C₃	—	4	3	no	—
344	C₂²×C₃	—	4	3	no	—
345	C₂²×C₃	—	4	1	no	—
346	C₂²×C₃	—	4	1	no	—
347	C₂²×C₃	—	4	1	no	—
348	C₂²×C₃	—	4	1	no	—
349	C₂²×C₃	C₂²×C₄×C₉	1	3	yes	—
350	C₂²×C₃	C₂×D₄×C₉	1	3	yes	—
351	C₂²×C₃	C₂×D₄×C₉	1	3	yes	—
352	C₂²×C₃	C₉×#41	1	3	yes	—
353	C₂²×C₃	C₉×#41	1	3	yes	—
354	C₂²×C₃	C₉×#41	1	3	yes	—
355	C₂²×C₃	C₉×#41	1	3	yes	—
356	C₂²×C₃	C₂²×C₃²×C₄	1	1	yes	characteristic
357	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
358	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
359	C₂²×C₃	C₃²×#41	1	1	yes	characteristic
360	C₂²×C₃	C₃²×#41	1	1	yes	characteristic
361	C₂²×C₃	C₃²×#41	1	1	yes	characteristic
362	C₂²×C₃	C₃²×#41	1	1	yes	characteristic
363	C₃×C₄	—	2	6	no	—
364	C₃×C₄	—	2	6	no	—
365	C₃×C₄	—	2	6	no	—
366	C₃×C₄	—	2	6	no	—
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	2	2	no	—
369	C₃×C₄	—	2	2	no	—
370	C₃×C₄	—	2	2	no	—
371	C₃×C₄	—	4	3	no	—
372	C₃×C₄	—	4	3	no	—
373	C₃×C₄	—	4	1	no	—
374	C₃×C₄	—	4	1	no	—
375	C₃²	C₃×#388	1	1	yes	characteristic
376	C₉	C₃×#388	1	3	yes	direct product factor
377	C₂³	—	2	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	C₂×C₃×C₄×C₉	1	2	yes	—
384	C₂³	C₂³×C₃×C₉	1	1	yes	characteristic
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	C₂×C₃×C₄×C₉	1	2	yes	—
400	C₂×C₄	C₂×C₃×C₄×C₉	1	2	yes	—
401	C₂×C₄	C₃×D₄×C₉	1	2	yes	—
402	C₂×C₄	C₃×D₄×C₉	1	2	yes	—
403	C₂×C₃	—	4	6	no	—
404	C₂×C₃	—	4	2	no	—
405	C₂×C₃	C₉×#117	1	3	yes	—
406	C₂×C₃	C₄×D₄×C₉	1	3	yes	—
407	C₂×C₃	C₄×D₄×C₉	1	3	yes	—
408	C₂×C₃	C₉×#121	1	3	yes	—
409	C₂×C₃	C₉×#123	1	3	yes	—
410	C₂×C₃	C₉×#124	1	3	yes	—
411	C₂×C₃	C₉×#126	1	3	yes	—
412	C₂×C₃	C₃²×#117	1	1	yes	characteristic
413	C₂×C₃	C₃²×C₄×D₄	1	1	yes	characteristic
414	C₂×C₃	C₃²×C₄×D₄	1	1	yes	characteristic
415	C₂×C₃	C₃²×#121	1	1	yes	characteristic
416	C₂×C₃	C₃²×#123	1	1	yes	characteristic
417	C₂×C₃	C₃²×#124	1	1	yes	characteristic
418	C₂×C₃	C₃²×#126	1	1	yes	characteristic
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	1	no	—
426	C₂²	C₂²×C₃×C₄×C₉	1	1	yes	characteristic
427	C₂²	C₂×C₃×D₄×C₉	1	1	yes	characteristic
428	C₂²	C₂×C₃×D₄×C₉	1	1	yes	characteristic
429	C₂²	C₃×C₉×#41	1	1	yes	characteristic
430	C₂²	C₃×C₉×#41	1	1	yes	characteristic
431	C₂²	C₃×C₉×#41	1	1	yes	characteristic
432	C₂²	C₃×C₉×#41	1	1	yes	characteristic
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	2	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₃	C₉×#388	1	3	yes	direct product factor
440	C₃	C₃²×#388	1	1	yes	characteristic
441	C₂	—	4	2	no	—
442	C₂	C₃×C₉×#117	1	1	yes	characteristic
443	C₂	C₃×C₄×D₄×C₉	1	1	yes	characteristic
444	C₂	C₃×C₄×D₄×C₉	1	1	yes	characteristic
445	C₂	C₃×C₉×#121	1	1	yes	characteristic
446	C₂	C₃×C₉×#123	1	1	yes	characteristic
447	C₂	C₃×C₉×#124	1	1	yes	characteristic
448	C₂	C₃×C₉×#126	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃×C₉	C₂³
commutator	C₂²	C₂²×C₃×C₄×C₉
Frattini, cosocle	C₂³×C₃	C₂³×C₃²
socle	C₂³×C₃²	C₂³×C₃
prime radical	C₂⁴×C₃²	C₂²×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₉×C₄⋊C₄	C₂	semidirect
5. C₂×C₃×C₄²×C₉	C₂	semidirect
6. C₃×C₉×#95	C₂	semidirect
7. C₃×C₉×#95	C₂	semidirect
9. C₉×#388	C₃	direct (N × H)
20. C₃×C₉×C₂²⋊C₄	C₄	semidirect
29. C₂×C₉×C₄⋊C₄	C₂×C₃	semidirect
33. C₂×C₄²×C₉	C₂×C₃	semidirect
34. C₉×#95	C₂×C₃	semidirect
35. C₉×#95	C₂×C₃	semidirect
62. C₃×#388	C₉	direct (N × H)
86. C₉×C₂²⋊C₄	C₃×C₄	semidirect
108. C₂×C₃×C₄⋊C₄	C₂×C₉	semidirect
116. C₂×C₃×C₄²	C₂×C₉	semidirect
118. C₃×#95	C₂×C₉	semidirect
119. C₃×#95	C₂×C₉	semidirect
174. #388	C₃×C₉	direct (N × H)
203. C₃×C₂²⋊C₄	C₄×C₉	semidirect
247. C₂×C₄⋊C₄	C₂×C₃×C₉	semidirect
251. C₂×C₄²	C₂×C₃×C₉	semidirect
252. #95	C₂×C₃×C₉	semidirect
253. #95	C₂×C₃×C₉	semidirect
254. C₃×C₉	#388	direct (N × H)
333. C₂²⋊C₄	C₃×C₄×C₉	semidirect
376. C₉	C₃×#388	direct (N × H)
439. C₃	C₉×#388	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×C₄⋊C₄	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₂×C₃×C₄²×C₉	2
C₃×C₉×#95	2
C₃²×#388	3
C₉×#388	3

Subgroups — C3×C9×#388 #13144922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×#388 #13144922