Subgroups — C₂×C₃×C₉×#121 #13154548

Order 1728.

2130 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³×C₃×C₉	C₂³
commutator	C₂²	C₂⁴×C₃×C₉
Frattini, cosocle	C₂²×C₃	C₂⁴×C₃²
socle	C₂³×C₃²	C₂³×C₃
prime radical	C₂×C₃²×#121	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. C₂²×C₃×D₄×C₉	C₂	semidirect
2. C₂²×C₃×D₄×C₉	C₂	semidirect
3. C₂³×C₃×C₄×C₉	C₂	semidirect
4. C₃×C₉×#121	C₂	direct (N × H)
5. C₂×C₃×C₉×C₄⋊C₄	C₂	semidirect
6. C₂×C₃×C₉×C₂²⋊C₄	C₂	semidirect
8. C₂×C₉×#121	C₃	direct (N × H)
13. C₂×C₃×D₄×C₉	C₂²	semidirect
14. C₂×C₃×D₄×C₉	C₂²	semidirect
19. C₂²×C₃×C₄×C₉	C₂²	semidirect
20. C₃×C₉×C₄⋊C₄	C₂²	semidirect
21. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
28. C₂²×D₄×C₉	C₂×C₃	semidirect
29. C₂²×D₄×C₉	C₂×C₃	semidirect
30. C₂³×C₄×C₉	C₂×C₃	semidirect
31. C₉×#121	C₂×C₃	direct (N × H)
32. C₂×C₉×C₄⋊C₄	C₂×C₃	semidirect
33. C₂×C₉×C₂²⋊C₄	C₂×C₃	semidirect
39. C₂³×C₃×C₉	D₄	semidirect
48. C₂×C₃×C₄×C₉	D₄	semidirect
52. C₂×C₃×#121	C₉	direct (N × H)
71. C₂×D₄×C₉	C₂²×C₃	semidirect
72. C₂×D₄×C₉	C₂²×C₃	semidirect
77. C₂²×C₄×C₉	C₂²×C₃	semidirect
78. C₉×C₄⋊C₄	C₂²×C₃	semidirect
79. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
89. C₂²×C₃×C₉	C₂×D₄	semidirect
94. C₃×C₄×C₉	C₂×D₄	semidirect
95. C₂²×C₃×D₄	C₂×C₉	semidirect
96. C₂²×C₃×D₄	C₂×C₉	semidirect
99. C₂³×C₃×C₄	C₂×C₉	semidirect
101. C₃×#121	C₂×C₉	direct (N × H)
103. C₂×C₃×C₄⋊C₄	C₂×C₉	semidirect
105. C₂×C₃×C₂²⋊C₄	C₂×C₉	semidirect
130. C₂³×C₉	C₃×D₄	semidirect
139. C₂×C₄×C₉	C₃×D₄	semidirect
143. C₂×#121	C₃×C₉	direct (N × H)
146. C₂×C₃×C₉	#121	direct (N × H)
158. C₂×C₃×D₄	C₂²×C₉	semidirect
159. C₂×C₃×D₄	C₂²×C₉	semidirect
167. C₂²×C₃×C₄	C₂²×C₉	semidirect
172. C₃×C₄⋊C₄	C₂²×C₉	semidirect
174. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
200. C₂²×C₉	C₂×C₃×D₄	semidirect
205. C₄×C₉	C₂×C₃×D₄	semidirect
206. C₂²×D₄	C₂×C₃×C₉	semidirect
207. C₂²×D₄	C₂×C₃×C₉	semidirect
208. C₂³×C₄	C₂×C₃×C₉	semidirect
209. #121	C₂×C₃×C₉	direct (N × H)
210. C₂×C₄⋊C₄	C₂×C₃×C₉	semidirect
211. C₂×C₂²⋊C₄	C₂×C₃×C₉	semidirect
212. C₃×C₉	C₂×#121	direct (N × H)
223. C₂³×C₃	D₄×C₉	semidirect
241. C₂×C₃×C₄	D₄×C₉	semidirect
257. C₂×C₉	C₃×#121	direct (N × H)
265. C₂×D₄	C₂²×C₃×C₉	semidirect
266. C₂×D₄	C₂²×C₃×C₉	semidirect
271. C₂²×C₄	C₂²×C₃×C₉	semidirect
272. C₄⋊C₄	C₂²×C₃×C₉	semidirect
273. C₂²⋊C₄	C₂²×C₃×C₉	semidirect
290. C₂²×C₃	C₂×D₄×C₉	semidirect
302. C₃×C₄	C₂×D₄×C₉	semidirect
305. C₉	C₂×C₃×#121	direct (N × H)
311. C₂³	C₃×D₄×C₉	semidirect
320. C₂×C₄	C₃×D₄×C₉	semidirect
328. C₂×C₃	C₉×#121	direct (N × H)
345. C₂²	C₂×C₃×D₄×C₉	semidirect
350. C₄	C₂×C₃×D₄×C₉	semidirect
351. C₃	C₂×C₉×#121	direct (N × H)
355. C₂	C₃×C₉×#121	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₄×C₉	2
C₂³×C₃×C₄×C₉	2
C₃×C₉×#121	2
C₂×C₃×C₉×C₄⋊C₄	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₂×C₃²×#121	3
C₂×C₉×#121	3

Subgroups — C2×C3×C9×#121 #13154548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₉×#121 #13154548