Subgroups — C₂×C₉×#67⋊C₄ #13152345

Order 1728.

1410 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×#67	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×(C₂×D₃)⋊C₄	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×#67⋊C₄	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₃×#67⋊C₄	C₃	1	1	yes	maximal, characteristic
10	C₂×C₄×D₄×C₉	—	3	1	no	maximal
11	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
12	C₂³×D₃×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	C₂×C₉×#67	C₄	1	8	yes	complemented
16	C₂×C₉×#67	C₂²	1	4	yes	—
17	C₂²×C₉×Dic₃	—	2	4	no	—
18	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
19	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
20	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
21	C₂²×C₉×Dic₃	C₂²	1	4	yes	complemented
22	C₂×C₄×D₃×C₉	—	2	4	no	—
23	C₂×C₄×D₃×C₉	C₂²	1	4	yes	complemented
24	C₃×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
25	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
26	C₉×Dic₃⋊C₄	C₂²	1	4	yes	complemented
27	C₄×C₉×Dic₃	C₂²	1	4	yes	complemented
28	C₂²×C₃×#67	C₂×C₃	1	1	yes	characteristic
29	C₂³×C₃×Dic₃	C₂×C₃	1	1	yes	characteristic
30	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
31	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
32	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
33	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic
34	C₂×C₃×C₄×Dic₃	C₂×C₃	1	1	yes	characteristic
35	C₃×#67⋊C₄	C₂×C₃	1	8	yes	—
36	C₂²×D₄×C₉	—	3	1	no	—
37	C₂³×C₄×C₉	—	3	1	no	—
38	C₂³×C₄×C₉	—	3	1	no	—
39	C₄×D₄×C₉	—	3	8	no	—
40	C₂×C₉×C₄⋊C₄	—	3	1	no	—
41	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
42	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
43	C₂×C₉×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
44	C₂×C₄²×C₉	—	3	1	no	—
45	C₂³×C₃×C₉	—	2	2	no	—
46	C₂³×C₃×C₉	—	2	2	no	—
47	C₂³×C₃×C₉	C₂×C₄	1	4	yes	complemented
48	C₂³×C₃×C₉	C₂³	1	2	yes	—
49	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
50	C₂²×D₃×C₉	—	2	2	no	—
51	C₂²×D₃×C₉	—	2	2	no	—
52	C₂²×D₃×C₉	C₂×C₄	1	4	yes	complemented
53	C₂²×D₃×C₉	C₂³	1	2	yes	—
54	C₂×C₃×C₄×C₉	—	2	2	no	—
55	C₂×C₃×C₄×C₉	—	2	2	no	—
56	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
57	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
58	C₉×#67	C₂×C₄	1	16	yes	complemented
59	C₂×C₉×Dic₃	—	2	2	no	—
60	C₂×C₉×Dic₃	—	2	8	no	—
61	C₂×C₉×Dic₃	C₂×C₄	1	4	yes	complemented
62	C₂×C₉×Dic₃	D₄	1	4	yes	complemented
63	C₂×C₉×Dic₃	C₂³	1	2	yes	—
64	C₂×C₉×Dic₃	C₂³	1	2	yes	—
65	C₂×C₉×Dic₃	C₂³	1	2	yes	—
66	C₄×D₃×C₉	—	2	8	no	—
67	C₂×C₃×C₄×D₄	—	3	1	no	—
68	C₂×#67⋊C₄	C₉	1	1	yes	characteristic, direct product factor
69	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
70	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
71	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₃×#67	C₃×C₄	1	8	yes	—
74	C₂×C₃×#67	C₂²×C₃	1	4	yes	—
75	C₂²×C₃×Dic₃	—	2	4	no	—
76	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₃×Dic₃	C₂²×C₃	1	4	yes	—
78	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
79	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₃×C₄×D₃	—	2	4	no	—
81	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
82	C₂⁴×C₉	—	2	1	no	—
83	C₂⁴×C₉	—	3	1	no	—
84	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
85	C₃²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
86	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
87	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
88	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
89	C₂×D₄×C₉	—	3	8	no	—
90	C₂×D₄×C₉	—	3	4	no	—
91	C₂²×C₄×C₉	—	2	1	no	—
92	C₂²×C₄×C₉	—	2	1	no	—
93	C₂²×C₄×C₉	—	3	1	no	—
94	C₂²×C₄×C₉	—	3	1	no	—
95	C₂²×C₄×C₉	—	3	4	no	—
96	C₂²×C₄×C₉	—	3	1	no	—
97	C₂²×C₄×C₉	—	3	4	no	—
98	C₂²×C₄×C₉	—	6	4	no	—
99	C₂²×C₄×C₉	—	6	4	no	—
100	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
101	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
102	C₉×C₄⋊C₄	—	3	4	no	—
103	C₉×C₂²⋊C₄	—	2	4	no	—
104	C₉×C₂²⋊C₄	—	3	4	no	—
105	C₉×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
106	C₄²×C₉	—	3	4	no	—
107	C₂²×C₃×C₉	—	2	8	no	—
108	C₂²×C₃×C₉	—	2	2	no	—
109	C₂²×C₃×C₉	—	2	2	no	—
110	C₂²×C₃×C₉	C₂²×C₄	1	2	yes	—
111	C₂²×C₃×C₉	C₂²×C₄	1	4	yes	complemented
112	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
113	C₂²×C₃×C₉	#41	1	2	yes	—
114	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
115	C₂×D₃×C₉	—	2	8	no	—
116	C₂×D₃×C₉	—	2	2	no	—
117	C₂×D₃×C₉	—	2	2	no	—
118	C₂×D₃×C₉	C₂²×C₄	1	4	yes	complemented
119	C₃×C₄×C₉	—	2	2	no	—
120	C₃×C₄×C₉	—	2	2	no	—
121	C₉×Dic₃	—	2	2	no	—
122	C₉×Dic₃	C₂²×C₄	1	4	yes	complemented
123	C₉×Dic₃	C₂×D₄	1	4	yes	complemented
124	C₂²×C₃×D₄	—	3	1	no	—
125	C₂³×C₃×C₄	—	3	1	no	—
126	C₂³×C₃×C₄	—	3	1	no	—
127	C₂²×#67	C₂×C₉	1	1	yes	characteristic
128	C₂³×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
129	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic, complemented
130	C₃×C₄×D₄	—	3	8	no	—
131	C₂×C₃×C₄⋊C₄	—	3	1	no	—
132	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
133	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
134	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
135	C₂×C₃×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
136	C₂×C₃×C₄²	—	3	1	no	—
137	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
138	C₂×Dic₃⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
139	C₂×C₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
140	#67⋊C₄	C₂×C₉	1	8	yes	direct product factor
141	C₂³×C₃²	—	2	2	no	—
142	C₂³×C₃²	—	2	2	no	—
143	C₂³×C₃²	C₂×C₃×C₄	1	4	yes	—
144	C₂³×C₃²	C₂³×C₃	1	2	yes	—
145	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
146	C₂²×C₃×D₃	—	2	2	no	—
147	C₂²×C₃×D₃	—	2	2	no	—
148	C₂²×C₃×D₃	C₂×C₃×C₄	1	4	yes	—
149	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
150	C₂×C₃²×C₄	—	2	2	no	—
151	C₂×C₃²×C₄	—	2	2	no	—
152	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
153	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
154	C₃×#67	C₂×C₃×C₄	1	16	yes	—
155	C₂×C₃×Dic₃	—	2	2	no	—
156	C₂×C₃×Dic₃	—	2	8	no	—
157	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
158	C₂×C₃×Dic₃	C₃×D₄	1	4	yes	—
159	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
160	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
161	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
162	C₃×C₄×D₃	—	2	8	no	—
163	C₂³×C₉	—	2	2	no	—
164	C₂³×C₉	—	2	2	no	—
165	C₂³×C₉	—	2	4	no	—
166	C₂³×C₉	—	2	1	no	—
167	C₂³×C₉	—	2	2	no	—
168	C₂³×C₉	—	3	4	no	—
169	C₂³×C₉	—	3	2	no	—
170	C₂³×C₉	—	4	2	no	—
171	C₂³×C₉	—	4	2	no	—
172	C₂³×C₉	—	6	2	no	—
173	C₂³×C₉	—	6	2	no	—
174	C₂³×C₉	C₄×D₃	1	4	yes	complemented
175	C₂³×C₉	C₂²×D₃	1	2	yes	—
176	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
177	D₄×C₉	—	3	16	no	—
178	C₂×C₄×C₉	—	2	2	no	—
179	C₂×C₄×C₉	—	2	2	no	—
180	C₂×C₄×C₉	—	2	2	no	—
181	C₂×C₄×C₉	—	2	2	no	—
182	C₂×C₄×C₉	—	3	4	no	—
183	C₂×C₄×C₉	—	3	4	no	—
184	C₂×C₄×C₉	—	3	2	no	—
185	C₂×C₄×C₉	—	3	2	no	—
186	C₂×C₄×C₉	—	3	2	no	—
187	C₂×C₄×C₉	—	4	2	no	—
188	C₂×C₄×C₉	—	4	2	no	—
189	C₂×C₄×C₉	—	6	8	no	—
190	C₂×C₄×C₉	—	6	8	no	—
191	C₂×C₄×C₉	—	6	2	no	—
192	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
193	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
194	C₂×C₄×D₄	—	3	1	no	Sylow
195	C₂×C₃×C₉	—	2	4	no	—
196	C₂×C₃×C₉	C₄×D₄	1	4	yes	complemented
197	C₂×C₃×C₉	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
200	D₃×C₉	—	2	4	no	—
201	C₂⁴×C₃	—	2	1	no	—
202	C₂⁴×C₃	—	3	1	no	—
203	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
204	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
205	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
206	C₂×C₃×D₄	—	3	8	no	—
207	C₂×C₃×D₄	—	3	4	no	—
208	C₂²×C₃×C₄	—	2	1	no	—
209	C₂²×C₃×C₄	—	2	1	no	—
210	C₂²×C₃×C₄	—	3	1	no	—
211	C₂²×C₃×C₄	—	3	1	no	—
212	C₂²×C₃×C₄	—	3	1	no	—
213	C₂²×C₃×C₄	—	3	4	no	—
214	C₂²×C₃×C₄	—	3	4	no	—
215	C₂²×C₃×C₄	—	6	4	no	—
216	C₂²×C₃×C₄	—	6	4	no	—
217	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
221	C₂×#67	C₄×C₉	1	8	yes	complemented
222	C₂×#67	C₂²×C₉	1	4	yes	—
223	C₂²×Dic₃	—	2	4	no	—
224	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
225	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
226	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
227	C₂²×Dic₃	C₂²×C₉	1	4	yes	complemented
228	C₂×C₄×D₃	—	2	4	no	—
229	C₂×C₄×D₃	C₂²×C₉	1	4	yes	complemented
230	C₃×C₄⋊C₄	—	3	4	no	—
231	C₃×C₂²⋊C₄	—	2	4	no	—
232	C₃×C₂²⋊C₄	—	3	4	no	—
233	C₃×C₂²⋊C₄	C₂²×C₉	1	4	yes	complemented
234	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
235	C₃×C₄²	—	3	4	no	—
236	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	complemented
237	Dic₃⋊C₄	C₂²×C₉	1	4	yes	complemented
238	C₄×Dic₃	C₂²×C₉	1	4	yes	complemented
239	C₂²×C₃²	—	2	8	no	—
240	C₂²×C₃²	—	2	2	no	—
241	C₂²×C₃²	—	2	2	no	—
242	C₂²×C₃²	C₂²×C₃×C₄	1	2	yes	—
243	C₂²×C₃²	C₂²×C₃×C₄	1	4	yes	—
244	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
245	C₂²×C₃²	C₃×#41	1	2	yes	—
246	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
247	C₂×C₃×D₃	—	2	8	no	—
248	C₂×C₃×D₃	—	2	2	no	—
249	C₂×C₃×D₃	—	2	2	no	—
250	C₂×C₃×D₃	C₂²×C₃×C₄	1	4	yes	—
251	C₃²×C₄	—	2	2	no	—
252	C₃²×C₄	—	2	2	no	—
253	C₃×Dic₃	—	2	2	no	—
254	C₃×Dic₃	C₂²×C₃×C₄	1	4	yes	—
255	C₃×Dic₃	C₂×C₃×D₄	1	4	yes	—
256	C₂²×C₉	—	2	8	no	—
257	C₂²×C₉	—	2	2	no	—
258	C₂²×C₉	—	2	2	no	—
259	C₂²×C₉	—	2	1	no	—
260	C₂²×C₉	—	2	2	no	—
261	C₂²×C₉	—	2	4	no	—
262	C₂²×C₉	—	2	2	no	—
263	C₂²×C₉	—	2	2	no	—
264	C₂²×C₉	—	3	4	no	—
265	C₂²×C₉	—	4	8	no	—
266	C₂²×C₉	—	4	2	no	—
267	C₂²×C₉	—	4	2	no	—
268	C₂²×C₉	—	6	8	no	—
269	C₂²×C₉	—	6	2	no	—
270	C₂²×C₉	—	6	2	no	—
271	C₂²×C₉	C₂×C₄×D₃	1	2	yes	—
272	C₂²×C₉	C₂×C₄×D₃	1	4	yes	complemented
273	C₂²×C₉	D₃×D₄	1	2	yes	—
274	C₂²×C₉	#237	1	2	yes	—
275	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
276	C₄×C₉	—	2	2	no	—
277	C₄×C₉	—	2	2	no	—
278	C₄×C₉	—	3	4	no	—
279	C₄×C₉	—	3	4	no	—
280	C₄×C₉	—	4	2	no	—
281	C₄×C₉	—	4	2	no	—
282	C₄×C₉	—	6	2	no	—
283	C₂²×D₄	—	3	1	no	—
284	C₂³×C₄	—	3	1	no	—
285	C₂³×C₄	—	3	1	no	—
286	C₄×D₄	—	3	8	no	—
287	C₂×C₄⋊C₄	—	3	1	no	—
288	C₂×C₂²⋊C₄	—	3	1	no	—
289	C₂×C₂²⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
290	C₂×C₄²	—	3	1	no	—
291	C₃×C₉	C₂×C₄×D₄	1	1	yes	characteristic, complemented, Sylow
292	C₂³×C₃	—	2	2	no	—
293	C₂³×C₃	—	2	2	no	—
294	C₂³×C₃	—	2	2	no	—
295	C₂³×C₃	—	2	2	no	—
296	C₂³×C₃	—	2	4	no	—
297	C₂³×C₃	—	2	1	no	—
298	C₂³×C₃	—	2	2	no	—
299	C₂³×C₃	—	3	2	no	—
300	C₂³×C₃	—	3	4	no	—
301	C₂³×C₃	—	4	2	no	—
302	C₂³×C₃	—	4	2	no	—
303	C₂³×C₃	—	6	2	no	—
304	C₂³×C₃	—	6	2	no	—
305	C₂³×C₃	C₂×C₄×C₉	1	4	yes	complemented
306	C₂³×C₃	C₂³×C₉	1	2	yes	—
307	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
308	C₂³×C₃	C₃×C₄×D₃	1	4	yes	—
309	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
310	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
311	C₂²×D₃	—	2	2	no	—
312	C₂²×D₃	—	2	2	no	—
313	C₂²×D₃	C₂×C₄×C₉	1	4	yes	complemented
314	C₂²×D₃	C₂³×C₉	1	2	yes	—
315	C₃×D₄	—	3	16	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	3	2	no	—
323	C₂×C₃×C₄	—	3	2	no	—
324	C₂×C₃×C₄	—	3	4	no	—
325	C₂×C₃×C₄	—	3	4	no	—
326	C₂×C₃×C₄	—	3	2	no	—
327	C₂×C₃×C₄	—	4	2	no	—
328	C₂×C₃×C₄	—	4	2	no	—
329	C₂×C₃×C₄	—	6	8	no	—
330	C₂×C₃×C₄	—	6	8	no	—
331	C₂×C₃×C₄	—	6	2	no	—
332	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
333	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
334	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
335	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
336	#67	C₂×C₄×C₉	1	16	yes	complemented
337	C₂×Dic₃	—	2	2	no	—
338	C₂×Dic₃	—	2	8	no	—
339	C₂×Dic₃	C₂×C₄×C₉	1	4	yes	complemented
340	C₂×Dic₃	D₄×C₉	1	4	yes	complemented
341	C₂×Dic₃	C₂³×C₉	1	2	yes	—
342	C₂×Dic₃	C₂³×C₉	1	2	yes	—
343	C₂×Dic₃	C₂³×C₉	1	2	yes	—
344	C₄×D₃	—	2	8	no	—
345	C₂×C₃²	—	2	4	no	—
346	C₂×C₃²	C₃×C₄×D₄	1	4	yes	—
347	C₂×C₃²	C₂³×C₃×C₄	1	1	yes	characteristic
348	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
349	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
350	C₃×D₃	—	2	4	no	—
351	C₂×C₉	—	2	4	no	—
352	C₂×C₉	—	2	4	no	—
353	C₂×C₉	—	2	1	no	—
354	C₂×C₉	—	2	1	no	—
355	C₂×C₉	—	2	1	no	—
356	C₂×C₉	—	4	4	no	—
357	C₂×C₉	—	6	4	no	—
358	C₂×C₉	#67⋊C₄	1	4	yes	direct product factor
359	C₂×C₉	C₂²×C₄×D₃	1	1	yes	characteristic
360	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
361	C₂×C₉	C₂×#237	1	1	yes	characteristic
362	C₂⁴	—	3	1	no	—
363	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
364	C₂×D₄	—	3	8	no	—
365	C₂×D₄	—	3	4	no	—
366	C₂²×C₄	—	3	1	no	—
367	C₂²×C₄	—	3	1	no	—
368	C₂²×C₄	—	3	1	no	—
369	C₂²×C₄	—	3	4	no	—
370	C₂²×C₄	—	3	4	no	—
371	C₂²×C₄	—	6	4	no	—
372	C₂²×C₄	—	6	4	no	—
373	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
375	C₄⋊C₄	—	3	4	no	—
376	C₂²⋊C₄	—	3	4	no	—
377	C₂²⋊C₄	C₂×D₃×C₉	1	4	yes	complemented
378	C₄²	—	3	4	no	—
379	C₂²×C₃	—	2	8	no	—
380	C₂²×C₃	—	2	8	no	—
381	C₂²×C₃	—	2	2	no	—
382	C₂²×C₃	—	2	2	no	—
383	C₂²×C₃	—	2	2	no	—
384	C₂²×C₃	—	2	2	no	—
385	C₂²×C₃	—	2	1	no	—
386	C₂²×C₃	—	2	2	no	—
387	C₂²×C₃	—	2	4	no	—
388	C₂²×C₃	—	2	2	no	—
389	C₂²×C₃	—	2	2	no	—
390	C₂²×C₃	—	3	4	no	—
391	C₂²×C₃	—	4	2	no	—
392	C₂²×C₃	—	4	2	no	—
393	C₂²×C₃	—	4	8	no	—
394	C₂²×C₃	—	6	8	no	—
395	C₂²×C₃	—	6	2	no	—
396	C₂²×C₃	—	6	2	no	—
397	C₂²×C₃	C₂²×C₄×C₉	1	2	yes	—
398	C₂²×C₃	C₂²×C₄×C₉	1	4	yes	complemented
399	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
400	C₂²×C₃	C₉×#41	1	2	yes	—
401	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
402	C₂²×C₃	C₂×C₃×C₄×D₃	1	2	yes	—
403	C₂²×C₃	C₂×C₃×C₄×D₃	1	4	yes	—
404	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
405	C₂²×C₃	C₃×#237	1	2	yes	—
406	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
407	C₂×D₃	—	2	8	no	—
408	C₂×D₃	—	2	2	no	—
409	C₂×D₃	—	2	2	no	—
410	C₂×D₃	C₂²×C₄×C₉	1	4	yes	complemented
411	C₃×C₄	—	2	2	no	—
412	C₃×C₄	—	2	2	no	—
413	C₃×C₄	—	2	2	no	—
414	C₃×C₄	—	2	2	no	—
415	C₃×C₄	—	3	4	no	—
416	C₃×C₄	—	3	4	no	—
417	C₃×C₄	—	4	2	no	—
418	C₃×C₄	—	4	2	no	—
419	C₃×C₄	—	6	2	no	—
420	Dic₃	—	2	2	no	—
421	Dic₃	C₂²×C₄×C₉	1	4	yes	complemented
422	Dic₃	C₂×D₄×C₉	1	4	yes	complemented
423	C₃²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
424	C₉	—	2	1	no	—
425	C₉	C₂×#67⋊C₄	1	1	yes	characteristic, direct product factor
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	3	2	no	—
429	C₂³	—	3	4	no	—
430	C₂³	—	6	2	no	—
431	C₂³	—	6	2	no	—
432	C₂³	C₄×D₃×C₉	1	4	yes	complemented
433	C₂³	C₂²×D₃×C₉	1	2	yes	—
434	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
435	D₄	—	3	16	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	3	2	no	—
439	C₂×C₄	—	3	2	no	—
440	C₂×C₄	—	3	4	no	—
441	C₂×C₄	—	3	4	no	—
442	C₂×C₄	—	3	2	no	—
443	C₂×C₄	—	6	8	no	—
444	C₂×C₄	—	6	8	no	—
445	C₂×C₄	—	6	2	no	—
446	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
447	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
448	C₂×C₃	—	2	4	no	—
449	C₂×C₃	—	2	4	no	—
450	C₂×C₃	—	2	1	no	—
451	C₂×C₃	—	2	1	no	—
452	C₂×C₃	—	2	1	no	—
453	C₂×C₃	—	2	4	no	—
454	C₂×C₃	—	4	4	no	—
455	C₂×C₃	—	6	4	no	—
456	C₂×C₃	C₄×D₄×C₉	1	4	yes	complemented
457	C₂×C₃	C₂³×C₄×C₉	1	1	yes	characteristic
458	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
459	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
460	C₂×C₃	C₃×#67⋊C₄	1	4	yes	—
461	C₂×C₃	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
462	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
463	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
464	D₃	—	2	4	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	8	no	—
468	C₂²	—	3	4	no	—
469	C₂²	—	6	2	no	—
470	C₂²	—	6	2	no	—
471	C₂²	—	6	8	no	—
472	C₂²	C₂×C₄×D₃×C₉	1	2	yes	—
473	C₂²	C₂×C₄×D₃×C₉	1	4	yes	complemented
474	C₂²	D₃×D₄×C₉	1	2	yes	—
475	C₂²	C₉×#237	1	2	yes	—
476	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
477	C₄	—	2	2	no	—
478	C₄	—	2	2	no	—
479	C₄	—	3	4	no	—
480	C₄	—	3	4	no	—
481	C₄	—	6	2	no	—
482	C₃	—	2	1	no	—
483	C₃	C₂×C₄×D₄×C₉	1	1	yes	characteristic, complemented
484	C₃	C₂×C₃×#67⋊C₄	1	1	yes	characteristic
485	C₂	—	2	4	no	—
486	C₂	—	6	4	no	—
487	C₂	C₉×#67⋊C₄	1	4	yes	direct product factor
488	C₂	C₂²×C₄×D₃×C₉	1	1	yes	characteristic
489	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
490	C₂	C₂×C₉×#237	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂×C₃	C₂³×C₄×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×C₂²⋊C₄	C₂
socle	C₂³×C₃²	C₂³×C₃
prime radical	C₂²×C₃×#67	C₂×C₃
cosocle	C₂²×C₃²	C₂⁴×C₃
hypercenter	C₂×C₉×C₂²⋊C₄	D₃
hypocenter	C₃	C₂×C₄×D₄×C₉
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₉×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₉×Dic₃	C₂	semidirect
3. C₂²×C₄×D₃×C₉	C₂	semidirect
4. C₂×C₃×C₉×C₂²⋊C₄	C₂	semidirect
5. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
7. C₂×C₄×C₉×Dic₃	C₂	semidirect
8. C₉×#67⋊C₄	C₂	direct (N × H)
15. C₂×C₉×#67	C₄	semidirect
21. C₂²×C₉×Dic₃	C₂²	semidirect
23. C₂×C₄×D₃×C₉	C₂²	semidirect
24. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
25. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
26. C₉×Dic₃⋊C₄	C₂²	semidirect
27. C₄×C₉×Dic₃	C₂²	semidirect
43. C₂×C₉×C₂²⋊C₄	D₃	semidirect
47. C₂³×C₃×C₉	C₂×C₄	semidirect
52. C₂²×D₃×C₉	C₂×C₄	semidirect
58. C₉×#67	C₂×C₄	semidirect
61. C₂×C₉×Dic₃	C₂×C₄	semidirect
62. C₂×C₉×Dic₃	D₄	semidirect
68. C₂×#67⋊C₄	C₉	direct (N × H)
105. C₉×C₂²⋊C₄	C₂×D₃	semidirect
111. C₂²×C₃×C₉	C₂²×C₄	semidirect
118. C₂×D₃×C₉	C₂²×C₄	semidirect
122. C₉×Dic₃	C₂²×C₄	semidirect
123. C₉×Dic₃	C₂×D₄	semidirect
128. C₂³×Dic₃	C₂×C₉	semidirect
129. C₂²×C₄×D₃	C₂×C₉	semidirect
134. C₂×C₃×C₂²⋊C₄	C₂×C₉	semidirect
137. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
138. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
139. C₂×C₄×Dic₃	C₂×C₉	semidirect
140. #67⋊C₄	C₂×C₉	direct (N × H)
174. C₂³×C₉	C₄×D₃	semidirect
196. C₂×C₃×C₉	C₄×D₄	semidirect
221. C₂×#67	C₄×C₉	semidirect
227. C₂²×Dic₃	C₂²×C₉	semidirect
229. C₂×C₄×D₃	C₂²×C₉	semidirect
233. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
236. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
237. Dic₃⋊C₄	C₂²×C₉	semidirect
238. C₄×Dic₃	C₂²×C₉	semidirect
272. C₂²×C₉	C₂×C₄×D₃	semidirect
289. C₂×C₂²⋊C₄	D₃×C₉	semidirect
291. C₃×C₉	C₂×C₄×D₄	semidirect
305. C₂³×C₃	C₂×C₄×C₉	semidirect
313. C₂²×D₃	C₂×C₄×C₉	semidirect
336. #67	C₂×C₄×C₉	semidirect
339. C₂×Dic₃	C₂×C₄×C₉	semidirect
340. C₂×Dic₃	D₄×C₉	semidirect
358. C₂×C₉	#67⋊C₄	direct (N × H)
377. C₂²⋊C₄	C₂×D₃×C₉	semidirect
398. C₂²×C₃	C₂²×C₄×C₉	semidirect
410. C₂×D₃	C₂²×C₄×C₉	semidirect
421. Dic₃	C₂²×C₄×C₉	semidirect
422. Dic₃	C₂×D₄×C₉	semidirect
425. C₉	C₂×#67⋊C₄	direct (N × H)
432. C₂³	C₄×D₃×C₉	semidirect
456. C₂×C₃	C₄×D₄×C₉	semidirect
473. C₂²	C₂×C₄×D₃×C₉	semidirect
483. C₃	C₂×C₄×D₄×C₉	semidirect
487. C₂	C₉×#67⋊C₄	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×C₉×#67	2
C₂³×C₉×Dic₃	2
C₂²×C₄×D₃×C₉	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₂×C₉×Dic₃⋊C₄	2
C₂×C₄×C₉×Dic₃	2
C₉×#67⋊C₄	2
C₂×C₃×#67⋊C₄	3
C₂×C₄×D₄×C₉	3

Subgroups — C2×C9×#67⋊C4 #13152345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#67⋊C₄ #13152345