Subgroups — C₉×#5486 #13152346

Order 1728.

1146 conjugacy classes of subgroups.

The subgroup lattice has 426 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	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#217	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₉×#67	C₂	1	4	yes	maximal, complemented
5	C₉×#67⋊C₄	C₂	1	4	yes	maximal, complemented
6	D₃×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₉×#877	C₂	1	2	yes	maximal, complemented
8	C₃×#5486	C₃	1	1	yes	maximal, characteristic
9	C₉×#518	—	3	1	no	maximal
10	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
11	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	complemented
13	C₂×C₉×#67	C₄	1	8	yes	complemented
14	C₂×C₉×#67	C₂²	1	2	yes	—
15	C₂×C₉×#67	C₂²	1	2	yes	—
16	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
17	C₂²×C₉×Dic₃	C₂²	1	2	yes	complemented
18	C₂×C₄×D₃×C₉	C₂²	1	4	yes	complemented
19	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
21	C₉×#217	C₂²	1	2	yes	—
22	C₉×#217	C₂²	1	2	yes	complemented
23	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
24	C₉×Dic₃⋊C₄	C₂²	1	4	yes	complemented
25	C₄×C₉×Dic₃	C₂²	1	4	yes	complemented
26	C₂²×C₃×#67	C₂×C₃	1	1	yes	characteristic
27	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
28	C₂×C₃×#217	C₂×C₃	1	1	yes	characteristic
29	C₃×C₄×#67	C₂×C₃	1	4	yes	—
30	C₃×#67⋊C₄	C₂×C₃	1	4	yes	—
31	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	2	yes	—
32	C₃×#877	C₂×C₃	1	2	yes	—
33	C₂²×D₄×C₉	—	3	1	no	—
34	C₄×D₄×C₉	—	3	4	no	—
35	C₄×D₄×C₉	—	3	4	no	—
36	C₉×#117	—	3	2	no	—
37	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
38	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
39	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
40	C₂×C₉×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
41	C₂³×C₃×C₉	—	4	2	no	—
42	C₂³×C₃×C₉	C₂×C₄	1	4	yes	complemented
43	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
44	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
45	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
46	C₂²×D₃×C₉	—	4	2	no	—
47	C₂²×D₃×C₉	C₂×C₄	1	4	yes	complemented
48	C₂²×D₃×C₉	C₂³	1	2	yes	—
49	C₂×C₃×C₄×C₉	—	4	2	no	—
50	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
51	C₉×#67	C₂×C₄	1	8	yes	complemented
52	C₉×#67	C₂×C₄	1	8	yes	complemented
53	C₂×C₉×Dic₃	—	4	2	no	—
54	C₂×C₉×Dic₃	C₂×C₄	1	4	yes	complemented
55	C₂×C₉×Dic₃	C₂³	1	4	yes	—
56	C₂×C₉×Dic₃	C₂³	1	2	yes	—
57	C₄×D₃×C₉	—	4	4	no	—
58	C₃×#518	—	3	1	no	—
59	#5486	C₉	1	1	yes	characteristic, direct product factor
60	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
61	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
62	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
63	C₂×C₃×#67	C₃×C₄	1	8	yes	—
64	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
65	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
66	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
67	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
69	C₂⁴×C₉	—	2	1	no	—
70	C₂⁴×C₉	—	3	1	no	—
71	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
72	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
73	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
74	C₃×#217	C₂²×C₃	1	2	yes	—
75	C₃×#217	C₂²×C₃	1	2	yes	—
76	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
77	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
78	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
79	C₂×D₄×C₉	—	3	8	no	—
80	C₂×D₄×C₉	—	3	2	no	—
81	C₂×D₄×C₉	—	3	2	no	—
82	C₂²×C₄×C₉	—	2	2	no	—
83	C₂²×C₄×C₉	—	3	1	no	—
84	C₂²×C₄×C₉	—	3	2	no	—
85	C₂²×C₄×C₉	—	3	4	no	—
86	C₂²×C₄×C₉	C₂×D₃	1	2	yes	complemented
87	C₉×C₄⋊C₄	—	3	4	no	—
88	C₉×C₂²⋊C₄	—	2	2	no	—
89	C₉×C₂²⋊C₄	—	2	2	no	—
90	C₉×C₂²⋊C₄	—	3	2	no	—
91	C₉×C₂²⋊C₄	—	3	2	no	—
92	C₉×C₂²⋊C₄	—	3	4	no	—
93	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
94	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
95	C₄²×C₉	—	3	4	no	—
96	C₂²×C₃×C₉	—	2	2	no	—
97	C₂²×C₃×C₉	—	2	2	no	—
98	C₂²×C₃×C₉	—	2	2	no	—
99	C₂²×C₃×C₉	—	4	4	no	—
100	C₂²×C₃×C₉	C₂²×C₄	1	2	yes	—
101	C₂²×C₃×C₉	C₂²×C₄	1	2	yes	—
102	C₂²×C₃×C₉	C₂²×C₄	1	2	yes	—
103	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
104	C₂×D₃×C₉	—	2	4	no	—
105	C₂×D₃×C₉	—	4	4	no	—
106	C₂×D₃×C₉	C₂²×C₄	1	4	yes	—
107	C₃×C₄×C₉	—	2	4	no	—
108	C₉×Dic₃	—	2	4	no	—
109	C₉×Dic₃	C₂²×C₄	1	4	yes	—
110	C₂²×C₃×D₄	—	3	1	no	—
111	C₂²×#67	C₂×C₉	1	1	yes	characteristic
112	C₃×C₄×D₄	—	3	4	no	—
113	C₃×C₄×D₄	—	3	4	no	—
114	C₃×#117	—	3	2	no	—
115	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
117	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
118	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
119	C₂×C₃×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
120	C₂×#217	C₂×C₉	1	1	yes	characteristic, complemented
121	C₄×#67	C₂×C₉	1	4	yes	complemented
122	#67⋊C₄	C₂×C₉	1	4	yes	complemented
123	D₃×C₂²⋊C₄	C₂×C₉	1	2	yes	complemented
124	#877	C₂×C₉	1	2	yes	complemented
125	C₂³×C₃²	—	4	2	no	—
126	C₂³×C₃²	C₂×C₃×C₄	1	4	yes	—
127	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
128	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
129	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
130	C₂²×C₃×D₃	—	4	2	no	—
131	C₂²×C₃×D₃	C₂×C₃×C₄	1	4	yes	—
132	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
133	C₂×C₃²×C₄	—	4	2	no	—
134	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
135	C₃×#67	C₂×C₃×C₄	1	8	yes	—
136	C₃×#67	C₂×C₃×C₄	1	8	yes	—
137	C₂×C₃×Dic₃	—	4	2	no	—
138	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
139	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
140	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
141	C₃×C₄×D₃	—	4	4	no	—
142	C₂³×C₉	—	2	4	no	—
143	C₂³×C₉	—	2	1	no	—
144	C₂³×C₉	—	2	1	no	—
145	C₂³×C₉	—	2	1	no	—
146	C₂³×C₉	—	3	2	no	—
147	C₂³×C₉	—	3	4	no	—
148	C₂³×C₉	—	4	2	no	—
149	C₂³×C₉	—	4	4	no	—
150	C₂³×C₉	—	12	2	no	—
151	C₂³×C₉	C₄×D₃	1	4	yes	complemented
152	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
153	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
154	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
155	D₄×C₉	—	3	8	no	—
156	D₄×C₉	—	3	8	no	—
157	C₂×C₄×C₉	—	2	4	no	—
158	C₂×C₄×C₉	—	3	4	no	—
159	C₂×C₄×C₉	—	3	2	no	—
160	C₂×C₄×C₉	—	3	4	no	—
161	C₂×C₄×C₉	—	4	2	no	—
162	C₂×C₄×C₉	—	4	4	no	—
163	C₂×C₄×C₉	—	12	4	no	—
164	C₂×C₄×C₉	—	12	2	no	—
165	C₂×C₄×C₉	C₂²×D₃	1	4	yes	—
166	#518	—	3	1	no	Sylow
167	C₂×C₃×C₉	—	2	2	no	—
168	C₂×C₃×C₉	—	2	2	no	—
169	C₂×C₃×C₉	—	2	2	no	—
170	C₂×C₃×C₉	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₃×C₉	H(5,𝔽₂)	1	2	yes	—
172	D₃×C₉	—	2	4	no	—
173	C₂⁴×C₃	—	2	1	no	—
174	C₂⁴×C₃	—	3	1	no	—
175	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
176	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
177	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
178	C₂×C₃×D₄	—	3	8	no	—
179	C₂×C₃×D₄	—	3	2	no	—
180	C₂×C₃×D₄	—	3	2	no	—
181	C₂²×C₃×C₄	—	2	2	no	—
182	C₂²×C₃×C₄	—	3	1	no	—
183	C₂²×C₃×C₄	—	3	2	no	—
184	C₂²×C₃×C₄	—	3	4	no	—
185	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	complemented
186	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
187	C₂×#67	C₄×C₉	1	8	yes	complemented
188	C₂×#67	C₂²×C₉	1	2	yes	—
189	C₂×#67	C₂²×C₉	1	2	yes	—
190	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
191	C₂²×Dic₃	C₂²×C₉	1	2	yes	complemented
192	C₂×C₄×D₃	C₂²×C₉	1	4	yes	complemented
193	C₃×C₄⋊C₄	—	3	4	no	—
194	C₃×C₂²⋊C₄	—	2	2	no	—
195	C₃×C₂²⋊C₄	—	2	2	no	—
196	C₃×C₂²⋊C₄	—	3	2	no	—
197	C₃×C₂²⋊C₄	—	3	2	no	—
198	C₃×C₂²⋊C₄	—	3	4	no	—
199	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
200	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
201	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
202	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
203	C₃×C₄²	—	3	4	no	—
204	#217	C₂²×C₉	1	2	yes	—
205	#217	C₂²×C₉	1	2	yes	complemented
206	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	complemented
207	Dic₃⋊C₄	C₂²×C₉	1	4	yes	complemented
208	C₄×Dic₃	C₂²×C₉	1	4	yes	complemented
209	C₂²×C₃²	—	2	2	no	—
210	C₂²×C₃²	—	2	2	no	—
211	C₂²×C₃²	—	2	2	no	—
212	C₂²×C₃²	—	4	4	no	—
213	C₂²×C₃²	C₂²×C₃×C₄	1	2	yes	—
214	C₂²×C₃²	C₂²×C₃×C₄	1	2	yes	—
215	C₂²×C₃²	C₂²×C₃×C₄	1	2	yes	—
216	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
217	C₂×C₃×D₃	—	2	4	no	—
218	C₂×C₃×D₃	—	4	4	no	—
219	C₂×C₃×D₃	C₂²×C₃×C₄	1	4	yes	—
220	C₃²×C₄	—	2	4	no	—
221	C₃×Dic₃	—	2	4	no	—
222	C₃×Dic₃	C₂²×C₃×C₄	1	4	yes	—
223	C₂²×C₉	—	2	4	no	—
224	C₂²×C₉	—	2	2	no	—
225	C₂²×C₉	—	2	2	no	—
226	C₂²×C₉	—	2	2	no	—
227	C₂²×C₉	—	2	1	no	—
228	C₂²×C₉	—	2	2	no	—
229	C₂²×C₉	—	2	2	no	—
230	C₂²×C₉	—	2	2	no	—
231	C₂²×C₉	—	3	4	no	—
232	C₂²×C₉	—	4	2	no	—
233	C₂²×C₉	—	4	2	no	—
234	C₂²×C₉	—	4	4	no	—
235	C₂²×C₉	—	4	8	no	—
236	C₂²×C₉	—	6	4	no	—
237	C₂²×C₉	—	12	4	no	—
238	C₂²×C₉	C₂×C₄×D₃	1	2	yes	—
239	C₂²×C₉	C₂×C₄×D₃	1	2	yes	—
240	C₂²×C₉	C₂×C₄×D₃	1	2	yes	—
241	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
242	C₄×C₉	—	2	4	no	—
243	C₄×C₉	—	3	4	no	—
244	C₄×C₉	—	4	4	no	—
245	C₄×C₉	—	6	4	no	—
246	C₂²×D₄	—	3	1	no	—
247	C₄×D₄	—	3	4	no	—
248	C₄×D₄	—	3	4	no	—
249	#117	—	3	2	no	—
250	C₂×C₂²⋊C₄	—	3	1	no	—
251	C₂×C₂²⋊C₄	—	3	2	no	—
252	C₂×C₂²⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
253	C₃×C₉	#518	1	1	yes	characteristic, complemented, Sylow
254	C₂³×C₃	—	2	4	no	—
255	C₂³×C₃	—	2	1	no	—
256	C₂³×C₃	—	2	1	no	—
257	C₂³×C₃	—	2	1	no	—
258	C₂³×C₃	—	3	2	no	—
259	C₂³×C₃	—	3	4	no	—
260	C₂³×C₃	—	4	2	no	—
261	C₂³×C₃	—	4	2	no	—
262	C₂³×C₃	—	4	4	no	—
263	C₂³×C₃	—	12	2	no	—
264	C₂³×C₃	C₂×C₄×C₉	1	4	yes	complemented
265	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
266	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
267	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
268	C₂³×C₃	C₃×C₄×D₃	1	4	yes	—
269	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
270	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
271	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
272	C₂²×D₃	—	4	2	no	—
273	C₂²×D₃	C₂×C₄×C₉	1	4	yes	complemented
274	C₂²×D₃	C₂³×C₉	1	2	yes	—
275	C₃×D₄	—	3	8	no	—
276	C₃×D₄	—	3	8	no	—
277	C₂×C₃×C₄	—	2	4	no	—
278	C₂×C₃×C₄	—	3	2	no	—
279	C₂×C₃×C₄	—	3	4	no	—
280	C₂×C₃×C₄	—	3	4	no	—
281	C₂×C₃×C₄	—	4	2	no	—
282	C₂×C₃×C₄	—	4	2	no	—
283	C₂×C₃×C₄	—	4	4	no	—
284	C₂×C₃×C₄	—	12	4	no	—
285	C₂×C₃×C₄	—	12	2	no	—
286	C₂×C₃×C₄	C₂³×C₉	1	4	yes	—
287	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
288	#67	C₂×C₄×C₉	1	8	yes	complemented
289	#67	C₂×C₄×C₉	1	8	yes	complemented
290	C₂×Dic₃	—	4	2	no	—
291	C₂×Dic₃	C₂×C₄×C₉	1	4	yes	complemented
292	C₂×Dic₃	C₂³×C₉	1	4	yes	—
293	C₂×Dic₃	C₂³×C₉	1	2	yes	—
294	C₄×D₃	—	4	4	no	—
295	C₂×C₃²	—	2	2	no	—
296	C₂×C₃²	—	2	2	no	—
297	C₂×C₃²	—	2	2	no	—
298	C₂×C₃²	C₂³×C₃×C₄	1	1	yes	characteristic
299	C₂×C₃²	C₃×H(5,𝔽₂)	1	2	yes	—
300	C₃×D₃	—	2	4	no	—
301	C₂×C₉	—	2	4	no	—
302	C₂×C₉	—	2	2	no	—
303	C₂×C₉	—	2	2	no	—
304	C₂×C₉	—	2	2	no	—
305	C₂×C₉	—	2	1	no	—
306	C₂×C₉	—	2	2	no	—
307	C₂×C₉	—	4	2	no	—
308	C₂×C₉	—	4	2	no	—
309	C₂×C₉	—	6	4	no	—
310	C₂×C₉	C₂²×C₄×D₃	1	1	yes	characteristic
311	C₂×C₉	#1004	1	2	yes	—
312	C₂⁴	—	3	1	no	—
313	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
314	C₂×D₄	—	3	8	no	—
315	C₂×D₄	—	3	2	no	—
316	C₂×D₄	—	3	2	no	—
317	C₂²×C₄	—	3	1	no	—
318	C₂²×C₄	—	3	2	no	—
319	C₂²×C₄	—	3	4	no	—
320	C₂²×C₄	C₂×D₃×C₉	1	2	yes	complemented
321	C₄⋊C₄	—	3	4	no	—
322	C₂²⋊C₄	—	3	2	no	—
323	C₂²⋊C₄	—	3	2	no	—
324	C₂²⋊C₄	—	3	4	no	—
325	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
326	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
327	C₄²	—	3	4	no	—
328	C₂²×C₃	—	2	4	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	2	2	no	—
331	C₂²×C₃	—	2	2	no	—
332	C₂²×C₃	—	2	2	no	—
333	C₂²×C₃	—	2	2	no	—
334	C₂²×C₃	—	2	2	no	—
335	C₂²×C₃	—	2	1	no	—
336	C₂²×C₃	—	2	2	no	—
337	C₂²×C₃	—	2	2	no	—
338	C₂²×C₃	—	2	2	no	—
339	C₂²×C₃	—	3	4	no	—
340	C₂²×C₃	—	4	2	no	—
341	C₂²×C₃	—	4	2	no	—
342	C₂²×C₃	—	4	4	no	—
343	C₂²×C₃	—	4	4	no	—
344	C₂²×C₃	—	4	8	no	—
345	C₂²×C₃	—	6	4	no	—
346	C₂²×C₃	—	12	4	no	—
347	C₂²×C₃	C₂²×C₄×C₉	1	2	yes	—
348	C₂²×C₃	C₂²×C₄×C₉	1	2	yes	—
349	C₂²×C₃	C₂²×C₄×C₉	1	2	yes	—
350	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
351	C₂²×C₃	C₂×C₃×C₄×D₃	1	2	yes	—
352	C₂²×C₃	C₂×C₃×C₄×D₃	1	2	yes	—
353	C₂²×C₃	C₂×C₃×C₄×D₃	1	2	yes	—
354	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
355	C₂×D₃	—	2	4	no	—
356	C₂×D₃	—	4	4	no	—
357	C₂×D₃	C₂²×C₄×C₉	1	4	yes	—
358	C₃×C₄	—	2	4	no	—
359	C₃×C₄	—	2	4	no	—
360	C₃×C₄	—	3	4	no	—
361	C₃×C₄	—	4	4	no	—
362	C₃×C₄	—	6	4	no	—
363	Dic₃	—	2	4	no	—
364	Dic₃	C₂²×C₄×C₉	1	4	yes	—
365	C₃²	C₃×#518	1	1	yes	characteristic
366	C₉	—	2	1	no	—
367	C₉	#5486	1	1	yes	characteristic, direct product factor
368	C₂³	—	3	2	no	—
369	C₂³	—	3	4	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	12	2	no	—
372	C₂³	C₄×D₃×C₉	1	4	yes	complemented
373	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
374	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
375	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
376	D₄	—	3	8	no	—
377	D₄	—	3	8	no	—
378	C₂×C₄	—	3	2	no	—
379	C₂×C₄	—	3	4	no	—
380	C₂×C₄	—	3	4	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	12	4	no	—
383	C₂×C₄	—	12	2	no	—
384	C₂×C₄	C₂²×D₃×C₉	1	4	yes	—
385	C₂×C₃	—	2	4	no	—
386	C₂×C₃	—	2	2	no	—
387	C₂×C₃	—	2	2	no	—
388	C₂×C₃	—	2	2	no	—
389	C₂×C₃	—	2	2	no	—
390	C₂×C₃	—	2	2	no	—
391	C₂×C₃	—	2	2	no	—
392	C₂×C₃	—	2	1	no	—
393	C₂×C₃	—	2	2	no	—
394	C₂×C₃	—	4	2	no	—
395	C₂×C₃	—	4	2	no	—
396	C₂×C₃	—	6	4	no	—
397	C₂×C₃	C₂³×C₄×C₉	1	1	yes	characteristic
398	C₂×C₃	C₉×H(5,𝔽₂)	1	2	yes	—
399	C₂×C₃	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
400	C₂×C₃	C₃×#1004	1	2	yes	—
401	D₃	—	2	4	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	3	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	6	4	no	—
408	C₂²	—	12	4	no	—
409	C₂²	C₂×C₄×D₃×C₉	1	2	yes	—
410	C₂²	C₂×C₄×D₃×C₉	1	2	yes	—
411	C₂²	C₂×C₄×D₃×C₉	1	2	yes	—
412	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
413	C₄	—	2	4	no	—
414	C₄	—	3	4	no	—
415	C₄	—	6	4	no	—
416	C₃	—	2	1	no	—
417	C₃	C₉×#518	1	1	yes	characteristic, complemented
418	C₃	C₃×#5486	1	1	yes	characteristic
419	C₂	—	2	2	no	—
420	C₂	—	2	2	no	—
421	C₂	—	2	2	no	—
422	C₂	—	6	4	no	—
423	C₂	C₂²×C₄×D₃×C₉	1	1	yes	characteristic
424	C₂	C₉×#1004	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂×C₃	C₂³×C₄×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×C₂²⋊C₄	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂²×C₃×#67	C₂×C₃
hypercenter	C₂×C₉×C₂²⋊C₄	D₃
hypocenter	C₃	C₉×#518
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₉×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₉×C₂²⋊C₄	C₂	semidirect
3. C₂×C₉×#217	C₂	semidirect
4. C₄×C₉×#67	C₂	semidirect
5. C₉×#67⋊C₄	C₂	semidirect
6. D₃×C₉×C₂²⋊C₄	C₂	semidirect
7. C₉×#877	C₂	semidirect
12. C₂²×C₃×C₄×C₉	C₂²	semidirect
13. C₂×C₉×#67	C₄	semidirect
17. C₂²×C₉×Dic₃	C₂²	semidirect
18. C₂×C₄×D₃×C₉	C₂²	semidirect
20. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
22. C₉×#217	C₂²	semidirect
23. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
24. C₉×Dic₃⋊C₄	C₂²	semidirect
25. C₄×C₉×Dic₃	C₂²	semidirect
40. C₂×C₉×C₂²⋊C₄	D₃	semidirect
42. C₂³×C₃×C₉	C₂×C₄	semidirect
47. C₂²×D₃×C₉	C₂×C₄	semidirect
51. C₉×#67	C₂×C₄	semidirect
52. C₉×#67	C₂×C₄	semidirect
54. C₂×C₉×Dic₃	C₂×C₄	semidirect
59. #5486	C₉	direct (N × H)
86. C₂²×C₄×C₉	C₂×D₃	semidirect
94. C₉×C₂²⋊C₄	C₂×D₃	semidirect
118. C₂×C₃×C₂²⋊C₄	C₂×C₉	semidirect
120. C₂×#217	C₂×C₉	semidirect
121. C₄×#67	C₂×C₉	semidirect
122. #67⋊C₄	C₂×C₉	semidirect
123. D₃×C₂²⋊C₄	C₂×C₉	semidirect
124. #877	C₂×C₉	semidirect
151. C₂³×C₉	C₄×D₃	semidirect
185. C₂²×C₃×C₄	C₂²×C₉	semidirect
187. C₂×#67	C₄×C₉	semidirect
191. C₂²×Dic₃	C₂²×C₉	semidirect
192. C₂×C₄×D₃	C₂²×C₉	semidirect
200. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
205. #217	C₂²×C₉	semidirect
206. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
207. Dic₃⋊C₄	C₂²×C₉	semidirect
208. C₄×Dic₃	C₂²×C₉	semidirect
252. C₂×C₂²⋊C₄	D₃×C₉	semidirect
253. C₃×C₉	#518	semidirect
264. C₂³×C₃	C₂×C₄×C₉	semidirect
273. C₂²×D₃	C₂×C₄×C₉	semidirect
288. #67	C₂×C₄×C₉	semidirect
289. #67	C₂×C₄×C₉	semidirect
291. C₂×Dic₃	C₂×C₄×C₉	semidirect
320. C₂²×C₄	C₂×D₃×C₉	semidirect
326. C₂²⋊C₄	C₂×D₃×C₉	semidirect
367. C₉	#5486	direct (N × H)
372. C₂³	C₄×D₃×C₉	semidirect
417. C₃	C₉×#518	semidirect

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
C₂×C₃×C₉×C₂²⋊C₄	2
C₂×C₉×#217	2
C₄×C₉×#67	2
C₉×#67⋊C₄	2
D₃×C₉×C₂²⋊C₄	2
C₉×#877	2
C₃×#5486	3
C₉×#518	3

Subgroups — C9×#5486 #13152346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5486 #13152346