Subgroups — C₂×C₉×#898 #13152423

Order 1728.

830 conjugacy classes of subgroups.

The subgroup lattice has 408 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×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₂×C₉×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₉×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#898	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₃×#898	C₃	1	1	yes	maximal, characteristic
10	C₂×C₉×#126	—	3	1	no	maximal
11	C₂³×D₃×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×C₉×Dic₃	C₂²	1	1	yes	characteristic
16	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
17	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
18	C₃×C₉×C₄⋊C₄	C₂²	1	4	yes	complemented
19	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
20	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
21	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
22	C₉×C₄⋊Dic₃	C₂²	1	4	yes	complemented
23	C₉×Dic₃⋊C₄	C₂²	1	4	yes	complemented
24	C₄×C₉×Dic₃	C₂²	1	4	yes	complemented
25	C₂×C₃²×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
27	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
28	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic
30	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic
31	C₂×C₃×C₄×Dic₃	C₂×C₃	1	1	yes	characteristic
32	C₃×#898	C₂×C₃	1	8	yes	—
33	C₉×#126	—	3	8	no	—
34	C₂×C₉×C₄⋊C₄	—	2	1	no	—
35	C₂×C₉×C₄⋊C₄	—	3	1	no	—
36	C₂×C₉×C₄⋊C₄	—	3	1	no	—
37	C₂×C₉×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
38	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
39	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
40	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
41	C₂×C₄²×C₉	—	3	1	no	—
42	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
43	C₂²×D₃×C₉	—	2	2	no	—
44	C₂²×D₃×C₉	—	2	2	no	—
45	C₂²×D₃×C₉	—	2	2	no	—
46	C₂²×D₃×C₉	C₂³	1	2	yes	—
47	C₂×C₃×C₄×C₉	—	2	2	no	—
48	C₂×C₃×C₄×C₉	—	2	2	no	—
49	C₂×C₃×C₄×C₉	—	2	2	no	—
50	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
51	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
52	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
53	C₂×C₉×Dic₃	—	2	2	no	—
54	C₂×C₉×Dic₃	—	2	2	no	—
55	C₂×C₉×Dic₃	—	2	2	no	—
56	C₂×C₉×Dic₃	C₂³	1	2	yes	—
57	C₂×C₉×Dic₃	C₂³	1	2	yes	—
58	C₂×C₉×Dic₃	C₂³	1	2	yes	—
59	C₂×C₃×#126	—	3	1	no	—
60	C₂×#898	C₉	1	1	yes	characteristic, direct product factor
61	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
62	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
63	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
64	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
65	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
67	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
68	C₂⁴×C₉	—	3	1	no	—
69	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
70	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
71	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
72	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
73	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
74	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
75	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
76	C₂²×C₄×C₉	—	2	1	no	—
77	C₂²×C₄×C₉	—	2	1	no	—
78	C₂²×C₄×C₉	—	2	1	no	—
79	C₂²×C₄×C₉	—	3	1	no	—
80	C₂²×C₄×C₉	—	3	1	no	—
81	C₂²×C₄×C₉	—	3	1	no	—
82	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
83	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
84	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
85	C₉×C₄⋊C₄	—	2	4	no	—
86	C₉×C₄⋊C₄	—	3	4	no	—
87	C₉×C₄⋊C₄	—	3	4	no	—
88	C₉×C₄⋊C₄	C₂×D₃	1	4	yes	complemented
89	C₉×C₂²⋊C₄	—	3	4	no	—
90	C₉×C₂²⋊C₄	—	3	4	no	—
91	C₉×C₂²⋊C₄	—	3	4	no	—
92	C₄²×C₉	—	3	4	no	—
93	C₂²×C₃×C₉	#41	1	2	yes	—
94	C₂²×C₃×C₉	#41	1	2	yes	—
95	C₂²×C₃×C₉	#41	1	2	yes	—
96	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
97	C₂×D₃×C₉	—	2	2	no	—
98	C₂×D₃×C₉	—	2	2	no	—
99	C₂×D₃×C₉	—	2	2	no	—
100	C₂×D₃×C₉	—	4	4	no	—
101	C₃×C₄×C₉	—	2	2	no	—
102	C₃×C₄×C₉	—	2	2	no	—
103	C₃×C₄×C₉	—	2	2	no	—
104	C₉×Dic₃	—	2	2	no	—
105	C₉×Dic₃	—	2	2	no	—
106	C₉×Dic₃	—	2	2	no	—
107	C₃×#126	—	3	8	no	—
108	C₂×C₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₃×C₄⋊C₄	—	3	1	no	—
110	C₂×C₃×C₄⋊C₄	—	3	1	no	—
111	C₂×C₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
112	C₂×C₃×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic
113	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
114	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
115	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
116	C₂×C₃×C₄²	—	3	1	no	—
117	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic
118	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic
119	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic
120	C₂×C₄⋊Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
121	C₂×Dic₃⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
122	C₂×C₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
123	#898	C₂×C₉	1	8	yes	direct product factor
124	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
125	C₂²×C₃×D₃	—	2	2	no	—
126	C₂²×C₃×D₃	—	2	2	no	—
127	C₂²×C₃×D₃	—	2	2	no	—
128	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
129	C₂×C₃²×C₄	—	2	2	no	—
130	C₂×C₃²×C₄	—	2	2	no	—
131	C₂×C₃²×C₄	—	2	2	no	—
132	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
133	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
134	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
135	C₂×C₃×Dic₃	—	2	2	no	—
136	C₂×C₃×Dic₃	—	2	2	no	—
137	C₂×C₃×Dic₃	—	2	2	no	—
138	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
139	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
140	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
141	C₂³×C₉	—	2	1	no	—
142	C₂³×C₉	—	3	2	no	—
143	C₂³×C₉	—	6	2	no	—
144	C₂³×C₉	—	6	2	no	—
145	C₂³×C₉	—	6	2	no	—
146	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
147	C₂×C₄×C₉	—	2	4	no	—
148	C₂×C₄×C₉	—	2	2	no	—
149	C₂×C₄×C₉	—	2	2	no	—
150	C₂×C₄×C₉	—	2	2	no	—
151	C₂×C₄×C₉	—	2	2	no	—
152	C₂×C₄×C₉	—	2	2	no	—
153	C₂×C₄×C₉	—	2	2	no	—
154	C₂×C₄×C₉	—	3	2	no	—
155	C₂×C₄×C₉	—	3	2	no	—
156	C₂×C₄×C₉	—	3	2	no	—
157	C₂×C₄×C₉	—	4	2	no	—
158	C₂×C₄×C₉	—	4	2	no	—
159	C₂×C₄×C₉	—	6	2	no	—
160	C₂×C₄×C₉	—	6	2	no	—
161	C₂×C₄×C₉	—	6	2	no	—
162	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
163	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
164	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
165	C₂×#126	—	3	1	no	Sylow
166	C₂×C₃×C₉	#126	1	4	yes	complemented
167	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
168	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
169	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
170	D₃×C₉	—	4	2	no	—
171	C₂⁴×C₃	—	3	1	no	—
172	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
173	C₂²×C₃×C₄	—	2	1	no	—
174	C₂²×C₃×C₄	—	2	1	no	—
175	C₂²×C₃×C₄	—	2	1	no	—
176	C₂²×C₃×C₄	—	3	1	no	—
177	C₂²×C₃×C₄	—	3	1	no	—
178	C₂²×C₃×C₄	—	3	1	no	—
179	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
181	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
185	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
186	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
187	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
188	C₃×C₄⋊C₄	—	2	4	no	—
189	C₃×C₄⋊C₄	—	3	4	no	—
190	C₃×C₄⋊C₄	—	3	4	no	—
191	C₃×C₄⋊C₄	C₂²×C₉	1	4	yes	complemented
192	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
193	C₃×C₂²⋊C₄	—	3	4	no	—
194	C₃×C₂²⋊C₄	—	3	4	no	—
195	C₃×C₂²⋊C₄	—	3	4	no	—
196	C₃×C₄²	—	3	4	no	—
197	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
198	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
199	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
200	C₄⋊Dic₃	C₂²×C₉	1	4	yes	complemented
201	Dic₃⋊C₄	C₂²×C₉	1	4	yes	complemented
202	C₄×Dic₃	C₂²×C₉	1	4	yes	complemented
203	C₂²×C₃²	C₃×#41	1	2	yes	—
204	C₂²×C₃²	C₃×#41	1	2	yes	—
205	C₂²×C₃²	C₃×#41	1	2	yes	—
206	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
207	C₂×C₃×D₃	—	2	2	no	—
208	C₂×C₃×D₃	—	2	2	no	—
209	C₂×C₃×D₃	—	2	2	no	—
210	C₂×C₃×D₃	—	4	4	no	—
211	C₃²×C₄	—	2	2	no	—
212	C₃²×C₄	—	2	2	no	—
213	C₃²×C₄	—	2	2	no	—
214	C₃×Dic₃	—	2	2	no	—
215	C₃×Dic₃	—	2	2	no	—
216	C₃×Dic₃	—	2	2	no	—
217	C₂²×C₉	—	2	1	no	—
218	C₂²×C₉	—	2	2	no	—
219	C₂²×C₉	—	2	2	no	—
220	C₂²×C₉	—	2	2	no	—
221	C₂²×C₉	—	6	2	no	—
222	C₂²×C₉	—	6	2	no	—
223	C₂²×C₉	—	6	2	no	—
224	C₂²×C₉	—	12	4	no	—
225	C₂²×C₉	#235	1	2	yes	—
226	C₂²×C₉	#237	1	2	yes	—
227	C₂²×C₉	#239	1	2	yes	—
228	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
229	C₄×C₉	—	2	4	no	—
230	C₄×C₉	—	2	2	no	—
231	C₄×C₉	—	2	2	no	—
232	C₄×C₉	—	2	2	no	—
233	C₄×C₉	—	4	2	no	—
234	C₄×C₉	—	4	2	no	—
235	C₄×C₉	—	6	2	no	—
236	C₄×C₉	—	6	2	no	—
237	C₄×C₉	—	6	2	no	—
238	#126	—	3	8	no	—
239	C₂×C₄⋊C₄	—	3	1	no	—
240	C₂×C₄⋊C₄	—	3	1	no	—
241	C₂×C₄⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
242	C₂×C₂²⋊C₄	—	3	1	no	—
243	C₂×C₂²⋊C₄	—	3	1	no	—
244	C₂×C₂²⋊C₄	—	3	1	no	—
245	C₂×C₄²	—	3	1	no	—
246	C₃×C₉	C₂×#126	1	1	yes	characteristic, complemented, Sylow
247	C₂³×C₃	—	2	1	no	—
248	C₂³×C₃	—	3	2	no	—
249	C₂³×C₃	—	6	2	no	—
250	C₂³×C₃	—	6	2	no	—
251	C₂³×C₃	—	6	2	no	—
252	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
253	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
254	C₂²×D₃	—	2	2	no	—
255	C₂²×D₃	—	2	2	no	—
256	C₂²×D₃	—	2	2	no	—
257	C₂²×D₃	C₂³×C₉	1	2	yes	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	3	2	no	—
269	C₂×C₃×C₄	—	3	2	no	—
270	C₂×C₃×C₄	—	3	2	no	—
271	C₂×C₃×C₄	—	4	2	no	—
272	C₂×C₃×C₄	—	4	2	no	—
273	C₂×C₃×C₄	—	6	2	no	—
274	C₂×C₃×C₄	—	6	2	no	—
275	C₂×C₃×C₄	—	6	2	no	—
276	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
277	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
278	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
279	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
280	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
281	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
282	C₂×Dic₃	—	2	2	no	—
283	C₂×Dic₃	—	2	2	no	—
284	C₂×Dic₃	—	2	2	no	—
285	C₂×Dic₃	C₂³×C₉	1	2	yes	—
286	C₂×Dic₃	C₂³×C₉	1	2	yes	—
287	C₂×Dic₃	C₂³×C₉	1	2	yes	—
288	C₂×C₃²	C₃×#126	1	4	yes	—
289	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
290	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
291	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
292	C₃×D₃	—	4	2	no	—
293	C₂×C₉	—	2	4	no	—
294	C₂×C₉	—	2	1	no	—
295	C₂×C₉	—	2	1	no	—
296	C₂×C₉	—	2	1	no	—
297	C₂×C₉	—	12	2	no	—
298	C₂×C₉	#898	1	4	yes	direct product factor
299	C₂×C₉	C₂×#235	1	1	yes	characteristic
300	C₂×C₉	C₂×#237	1	1	yes	characteristic
301	C₂×C₉	C₂×#239	1	1	yes	characteristic
302	C₂⁴	—	3	1	no	—
303	C₂²×C₄	—	3	1	no	—
304	C₂²×C₄	—	3	1	no	—
305	C₂²×C₄	—	3	1	no	—
306	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
309	C₄⋊C₄	—	3	4	no	—
310	C₄⋊C₄	—	3	4	no	—
311	C₄⋊C₄	C₂×D₃×C₉	1	4	yes	complemented
312	C₂²⋊C₄	—	3	4	no	—
313	C₂²⋊C₄	—	3	4	no	—
314	C₂²⋊C₄	—	3	4	no	—
315	C₄²	—	3	4	no	—
316	C₂²×C₃	—	2	1	no	—
317	C₂²×C₃	—	2	2	no	—
318	C₂²×C₃	—	2	2	no	—
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	6	2	no	—
321	C₂²×C₃	—	6	2	no	—
322	C₂²×C₃	—	6	2	no	—
323	C₂²×C₃	—	12	4	no	—
324	C₂²×C₃	C₉×#41	1	2	yes	—
325	C₂²×C₃	C₉×#41	1	2	yes	—
326	C₂²×C₃	C₉×#41	1	2	yes	—
327	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
328	C₂²×C₃	C₃×#235	1	2	yes	—
329	C₂²×C₃	C₃×#237	1	2	yes	—
330	C₂²×C₃	C₃×#239	1	2	yes	—
331	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
332	C₂×D₃	—	2	2	no	—
333	C₂×D₃	—	2	2	no	—
334	C₂×D₃	—	2	2	no	—
335	C₂×D₃	—	4	4	no	—
336	C₃×C₄	—	2	4	no	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	—	2	2	no	—
339	C₃×C₄	—	2	2	no	—
340	C₃×C₄	—	2	2	no	—
341	C₃×C₄	—	2	2	no	—
342	C₃×C₄	—	2	2	no	—
343	C₃×C₄	—	4	2	no	—
344	C₃×C₄	—	4	2	no	—
345	C₃×C₄	—	6	2	no	—
346	C₃×C₄	—	6	2	no	—
347	C₃×C₄	—	6	2	no	—
348	Dic₃	—	2	2	no	—
349	Dic₃	—	2	2	no	—
350	Dic₃	—	2	2	no	—
351	C₃²	C₂×C₃×#126	1	1	yes	characteristic
352	C₉	—	2	1	no	—
353	C₉	C₂×#898	1	1	yes	characteristic, direct product factor
354	C₂³	—	3	2	no	—
355	C₂³	—	6	2	no	—
356	C₂³	—	6	2	no	—
357	C₂³	—	6	2	no	—
358	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	3	2	no	—
363	C₂×C₄	—	3	2	no	—
364	C₂×C₄	—	3	2	no	—
365	C₂×C₄	—	6	2	no	—
366	C₂×C₄	—	6	2	no	—
367	C₂×C₄	—	6	2	no	—
368	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
369	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
370	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
371	C₂×C₃	—	2	1	no	—
372	C₂×C₃	—	2	1	no	—
373	C₂×C₃	—	2	1	no	—
374	C₂×C₃	—	2	4	no	—
375	C₂×C₃	—	12	2	no	—
376	C₂×C₃	C₉×#126	1	4	yes	complemented
377	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
378	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
379	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
380	C₂×C₃	C₃×#898	1	4	yes	—
381	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
382	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
383	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
384	D₃	—	4	2	no	—
385	C₂²	—	6	2	no	—
386	C₂²	—	6	2	no	—
387	C₂²	—	6	2	no	—
388	C₂²	—	12	4	no	—
389	C₂²	C₉×#235	1	2	yes	—
390	C₂²	C₉×#237	1	2	yes	—
391	C₂²	C₉×#239	1	2	yes	—
392	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	6	2	no	—
397	C₄	—	6	2	no	—
398	C₄	—	6	2	no	—
399	C₃	—	2	1	no	—
400	C₃	C₂×C₉×#126	1	1	yes	characteristic, complemented
401	C₃	C₂×C₃×#898	1	1	yes	characteristic
402	C₂	—	12	2	no	—
403	C₂	C₉×#898	1	4	yes	direct product factor
404	C₂	C₂×C₉×#235	1	1	yes	characteristic
405	C₂	C₂×C₉×#237	1	1	yes	characteristic
406	C₂	C₂×C₉×#239	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×C₄⋊C₄	C₂
socle	C₂³×C₃²	C₂³×C₃
prime radical	C₂³×C₃×D₃	C₂²×C₃
cosocle	C₂²×C₃²	C₂⁴×C₃
hypercenter	C₂×C₉×C₄⋊C₄	D₃
hypocenter	C₃	C₂×C₉×#126
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₉×C₄⋊C₄

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×C₉×C₄⋊Dic₃	C₂	semidirect
6. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
7. C₂×C₄×C₉×Dic₃	C₂	semidirect
8. C₉×#898	C₂	direct (N × H)
18. C₃×C₉×C₄⋊C₄	C₂²	semidirect
22. C₉×C₄⋊Dic₃	C₂²	semidirect
23. C₉×Dic₃⋊C₄	C₂²	semidirect
24. C₄×C₉×Dic₃	C₂²	semidirect
37. C₂×C₉×C₄⋊C₄	D₃	semidirect
60. C₂×#898	C₉	direct (N × H)
88. C₉×C₄⋊C₄	C₂×D₃	semidirect
111. C₂×C₃×C₄⋊C₄	C₂×C₉	semidirect
120. C₂×C₄⋊Dic₃	C₂×C₉	semidirect
121. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
122. C₂×C₄×Dic₃	C₂×C₉	semidirect
123. #898	C₂×C₉	direct (N × H)
166. C₂×C₃×C₉	#126	semidirect
191. C₃×C₄⋊C₄	C₂²×C₉	semidirect
200. C₄⋊Dic₃	C₂²×C₉	semidirect
201. Dic₃⋊C₄	C₂²×C₉	semidirect
202. C₄×Dic₃	C₂²×C₉	semidirect
241. C₂×C₄⋊C₄	D₃×C₉	semidirect
246. C₃×C₉	C₂×#126	semidirect
298. C₂×C₉	#898	direct (N × H)
311. C₄⋊C₄	C₂×D₃×C₉	semidirect
353. C₉	C₂×#898	direct (N × H)
376. C₂×C₃	C₉×#126	semidirect
400. C₃	C₂×C₉×#126	semidirect
403. C₂	C₉×#898	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×C₉×(C₂×D₃)⋊C₄	2
C₂×C₉×C₄⋊Dic₃	2
C₂×C₉×Dic₃⋊C₄	2
C₂×C₄×C₉×Dic₃	2
C₉×#898	2
C₂×C₃×#898	3
C₂×C₉×#126	3

Subgroups — C2×C9×#898 #13152423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#898 #13152423