Subgroups — C₉×#5668 #13153101

Order 1728.

1006 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×C₉×#239	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#944	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#884	C₂	1	4	yes	maximal, complemented
7	C₉×#67⋊C₄	C₂	1	4	yes	maximal, complemented
8	C₉×#875	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄²×D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5668	C₃	1	1	yes	maximal, characteristic
11	C₉×#532	—	3	1	no	maximal
12	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₉×#67	C₂²	1	2	yes	—
15	C₂×C₉×#67	C₂²	1	4	yes	—
16	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
17	C₉×#239	—	2	4	no	—
18	C₉×#237	—	2	4	no	—
19	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
20	C₂×C₉×D₁₂	C₂²	1	2	yes	—
21	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
22	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
23	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
24	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
25	C₃×C₉×C₂²⋊C₄	C₂²	1	4	yes	—
26	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
28	C₉×Dic₃⋊C₄	C₂²	1	4	yes	—
29	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
30	C₄×C₉×Dic₃	C₂²	1	2	yes	—
31	C₂×C₃×#239	C₂×C₃	1	1	yes	characteristic
32	C₂×C₃×#237	C₂×C₃	1	1	yes	characteristic
33	C₃²×#124	C₂×C₃	1	1	yes	characteristic
34	C₃×#944	C₂×C₃	1	1	yes	characteristic
35	C₃×#940	C₂×C₃	1	1	yes	characteristic
36	C₃×#884	C₂×C₃	1	4	yes	—
37	C₃×#67⋊C₄	C₂×C₃	1	4	yes	—
38	C₃×#875	C₂×C₃	1	1	yes	characteristic
39	C₃×C₄²×D₃	C₂×C₃	1	1	yes	characteristic
40	C₂×C₉×#41	—	3	1	no	—
41	C₂×C₉×#41	—	3	1	no	—
42	C₉×C₄⋊Q₈	—	3	1	no	—
43	C₉×#127	—	3	1	no	—
44	C₉×#124	—	2	1	no	—
45	C₉×#124	—	3	1	no	—
46	C₉×#124	D₃	1	1	yes	characteristic, complemented
47	C₉×#121	—	3	4	no	—
48	C₄×D₄×C₉	—	3	4	no	—
49	C₂×C₄²×C₉	—	3	1	no	—
50	C₂³×C₃×C₉	C₂³	1	2	yes	—
51	C₂²×D₃×C₉	C₂³	1	2	yes	—
52	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
53	C₃×Q₈×C₉	—	2	2	no	—
54	C₃×D₄×C₉	—	2	2	no	—
55	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
56	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
57	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
58	C₉×#67	—	2	4	no	—
59	C₉×#67	—	2	8	no	—
60	C₂×C₉×Dic₃	—	2	4	no	—
61	C₂×C₉×Dic₃	C₂³	1	2	yes	—
62	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
63	C₂×C₉×Dic₃	C₂³	1	2	yes	—
64	C₉×D₁₂	—	2	4	no	—
65	C₉×D₁₂	—	2	2	no	—
66	C₄×D₃×C₉	—	2	4	no	—
67	C₄×D₃×C₉	—	2	4	no	—
68	C₄×D₃×C₉	D₄	1	4	yes	complemented
69	C₉×Dic₆	—	2	2	no	—
70	C₃×#532	—	3	1	no	—
71	#5668	C₉	1	1	yes	characteristic, direct product factor
72	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃×#67	C₂²×C₃	1	4	yes	—
75	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
76	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
77	C₃×#239	—	2	4	no	—
78	C₃×#237	—	2	4	no	—
79	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
80	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
82	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
83	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
85	C₃²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
86	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
87	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
88	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
89	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
90	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
91	C₉×#41	—	6	4	no	—
92	C₉×#41	—	6	4	no	—
93	C₂×Q₈×C₉	—	2	1	no	—
94	C₂×Q₈×C₉	—	3	1	no	—
95	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
96	C₂×D₄×C₉	—	2	1	no	—
97	C₂×D₄×C₉	—	3	4	no	—
98	C₂×D₄×C₉	—	3	2	no	—
99	C₂×D₄×C₉	—	3	2	no	—
100	C₂×D₄×C₉	—	3	1	no	—
101	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
102	C₂²×C₄×C₉	—	3	1	no	—
103	C₂²×C₄×C₉	—	3	2	no	—
104	C₂²×C₄×C₉	—	3	2	no	—
105	C₂²×C₄×C₉	—	3	2	no	—
106	C₉×C₄⋊C₄	—	3	4	no	—
107	C₉×C₂²⋊C₄	—	2	4	no	—
108	C₉×C₂²⋊C₄	—	3	4	no	—
109	C₉×C₂²⋊C₄	C₂×D₃	1	4	yes	—
110	C₄²×C₉	—	2	1	no	—
111	C₄²×C₉	—	3	2	no	—
112	C₄²×C₉	—	3	1	no	—
113	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
114	C₂²×C₃×C₉	—	2	2	no	—
115	C₂²×C₃×C₉	—	2	4	no	—
116	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
117	C₂×D₃×C₉	—	2	2	no	—
118	C₂×D₃×C₉	—	2	2	no	—
119	C₂×D₃×C₉	—	2	4	no	—
120	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
121	C₃×C₄×C₉	—	2	2	no	—
122	C₃×C₄×C₉	—	2	2	no	—
123	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
124	C₉×Dic₃	—	2	2	no	—
125	C₉×Dic₃	C₂×D₄	1	2	yes	—
126	C₉×Dic₃	#41	1	4	yes	complemented
127	C₂×C₃×#41	—	3	1	no	—
128	C₂×C₃×#41	—	3	1	no	—
129	C₂×#239	C₂×C₉	1	1	yes	characteristic, complemented
130	C₂×#237	C₂×C₉	1	1	yes	characteristic, complemented
131	C₃×C₄⋊Q₈	—	3	1	no	—
132	C₃×#127	—	3	1	no	—
133	C₃×#124	—	2	1	no	—
134	C₃×#124	—	3	1	no	—
135	C₃×#124	C₂×C₉	1	1	yes	characteristic, complemented
136	C₃×#124	C₃×D₃	1	1	yes	characteristic
137	C₃×#121	—	3	4	no	—
138	C₃×C₄×D₄	—	3	4	no	—
139	C₂×C₃×C₄²	—	3	1	no	—
140	#944	C₂×C₉	1	1	yes	characteristic, complemented
141	#940	C₂×C₉	1	1	yes	characteristic, complemented
142	#884	C₂×C₉	1	4	yes	complemented
143	#67⋊C₄	C₂×C₉	1	4	yes	complemented
144	#875	C₂×C₉	1	1	yes	characteristic, complemented
145	C₄²×D₃	C₂×C₉	1	1	yes	characteristic, complemented
146	C₂³×C₃²	C₂³×C₃	1	2	yes	—
147	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
148	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
149	C₃²×Q₈	—	2	2	no	—
150	C₃²×D₄	—	2	2	no	—
151	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
152	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
153	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
154	C₃×#67	—	2	4	no	—
155	C₃×#67	—	2	8	no	—
156	C₂×C₃×Dic₃	—	2	4	no	—
157	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
158	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
159	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
160	C₃×D₁₂	—	2	4	no	—
161	C₃×D₁₂	—	2	2	no	—
162	C₃×C₄×D₃	—	2	4	no	—
163	C₃×C₄×D₃	—	2	4	no	—
164	C₃×C₄×D₃	C₃×D₄	1	4	yes	—
165	C₃×Dic₆	—	2	2	no	—
166	C₂³×C₉	—	2	2	no	—
167	C₂³×C₉	—	3	1	no	—
168	C₂³×C₉	—	3	2	no	—
169	C₂³×C₉	C₂²×D₃	1	2	yes	—
170	Q₈×C₉	—	2	2	no	—
171	Q₈×C₉	—	4	2	no	—
172	Q₈×C₉	—	6	2	no	—
173	D₄×C₉	—	2	2	no	—
174	D₄×C₉	—	4	2	no	—
175	D₄×C₉	—	6	4	no	—
176	D₄×C₉	—	6	8	no	—
177	D₄×C₉	—	6	4	no	—
178	D₄×C₉	—	6	2	no	—
179	C₂×C₄×C₉	—	2	1	no	—
180	C₂×C₄×C₉	—	2	2	no	—
181	C₂×C₄×C₉	—	2	2	no	—
182	C₂×C₄×C₉	—	3	2	no	—
183	C₂×C₄×C₉	—	3	1	no	—
184	C₂×C₄×C₉	—	3	4	no	—
185	C₂×C₄×C₉	—	3	2	no	—
186	C₂×C₄×C₉	—	6	4	no	—
187	C₂×C₄×C₉	—	6	4	no	—
188	C₂×C₄×C₉	—	6	4	no	—
189	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
190	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
191	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
192	#532	—	3	1	no	Sylow
193	C₂×C₃×C₉	—	4	2	no	—
194	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₃×C₉	C₂×#41	1	2	yes	—
196	D₃×C₉	—	2	2	no	—
197	D₃×C₉	—	4	2	no	—
198	C₃×#41	—	6	4	no	—
199	C₃×#41	—	6	4	no	—
200	C₂×C₃×Q₈	—	2	1	no	—
201	C₂×C₃×Q₈	—	3	1	no	—
202	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
203	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
204	C₂×C₃×D₄	—	2	1	no	—
205	C₂×C₃×D₄	—	3	4	no	—
206	C₂×C₃×D₄	—	3	2	no	—
207	C₂×C₃×D₄	—	3	2	no	—
208	C₂×C₃×D₄	—	3	1	no	—
209	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
210	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
211	C₂²×C₃×C₄	—	3	1	no	—
212	C₂²×C₃×C₄	—	3	2	no	—
213	C₂²×C₃×C₄	—	3	2	no	—
214	C₂²×C₃×C₄	—	3	2	no	—
215	C₂×#67	C₂²×C₉	1	4	yes	—
216	C₂×#67	C₂²×C₉	1	2	yes	—
217	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
218	#239	—	2	4	no	—
219	#237	—	2	4	no	—
220	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
221	C₂×D₁₂	C₂²×C₉	1	2	yes	—
222	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
223	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
224	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
225	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
226	C₃×C₄⋊C₄	—	3	4	no	—
227	C₃×C₂²⋊C₄	—	2	4	no	—
228	C₃×C₂²⋊C₄	—	3	4	no	—
229	C₃×C₂²⋊C₄	C₂²×C₉	1	4	yes	—
230	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
231	C₃×C₄²	—	2	1	no	—
232	C₃×C₄²	—	3	2	no	—
233	C₃×C₄²	—	3	1	no	—
234	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
235	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
236	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
237	Dic₃⋊C₄	C₂²×C₉	1	4	yes	—
238	C₄×Dic₃	C₂²×C₉	1	2	yes	—
239	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
240	C₂²×C₃²	—	2	2	no	—
241	C₂²×C₃²	—	2	4	no	—
242	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
243	C₂×C₃×D₃	—	2	2	no	—
244	C₂×C₃×D₃	—	2	2	no	—
245	C₂×C₃×D₃	—	2	4	no	—
246	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
247	C₃²×C₄	—	2	2	no	—
248	C₃²×C₄	—	2	2	no	—
249	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
250	C₃×Dic₃	—	2	2	no	—
251	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
252	C₃×Dic₃	C₃×#41	1	4	yes	—
253	C₂²×C₉	—	2	2	no	—
254	C₂²×C₉	—	2	4	no	—
255	C₂²×C₉	—	2	1	no	—
256	C₂²×C₉	—	3	2	no	—
257	C₂²×C₉	—	4	2	no	—
258	C₂²×C₉	—	4	4	no	—
259	C₂²×C₉	—	6	2	no	—
260	C₂²×C₉	—	6	2	no	—
261	C₂²×C₉	—	6	4	no	—
262	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
263	C₄×C₉	—	2	2	no	—
264	C₄×C₉	—	2	2	no	—
265	C₄×C₉	—	2	2	no	—
266	C₄×C₉	—	3	2	no	—
267	C₄×C₉	—	3	4	no	—
268	C₄×C₉	—	4	2	no	—
269	C₄×C₉	—	4	2	no	—
270	C₄×C₉	—	6	2	no	—
271	C₄×C₉	D₃×D₄	1	2	yes	—
272	C₂×#41	—	3	1	no	—
273	C₂×#41	—	3	1	no	—
274	C₄⋊Q₈	—	3	1	no	—
275	#127	—	3	1	no	—
276	#124	—	3	1	no	—
277	#124	D₃×C₉	1	1	yes	characteristic, complemented
278	#121	—	3	4	no	—
279	C₄×D₄	—	3	4	no	—
280	C₂×C₄²	—	3	1	no	—
281	C₃×C₉	#532	1	1	yes	characteristic, complemented, Sylow
282	C₂³×C₃	—	2	2	no	—
283	C₂³×C₃	—	3	1	no	—
284	C₂³×C₃	—	3	2	no	—
285	C₂³×C₃	C₂³×C₉	1	2	yes	—
286	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
287	C₂²×D₃	C₂³×C₉	1	2	yes	—
288	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
289	C₃×Q₈	—	2	2	no	—
290	C₃×Q₈	—	2	2	no	—
291	C₃×Q₈	—	4	2	no	—
292	C₃×Q₈	—	6	2	no	—
293	C₃×D₄	—	2	2	no	—
294	C₃×D₄	—	2	2	no	—
295	C₃×D₄	—	4	2	no	—
296	C₃×D₄	—	6	4	no	—
297	C₃×D₄	—	6	8	no	—
298	C₃×D₄	—	6	4	no	—
299	C₃×D₄	—	6	2	no	—
300	C₂×C₃×C₄	—	2	1	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	3	2	no	—
304	C₂×C₃×C₄	—	3	1	no	—
305	C₂×C₃×C₄	—	3	4	no	—
306	C₂×C₃×C₄	—	3	2	no	—
307	C₂×C₃×C₄	—	6	4	no	—
308	C₂×C₃×C₄	—	6	4	no	—
309	C₂×C₃×C₄	—	6	4	no	—
310	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
311	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
312	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
314	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
315	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
316	#67	—	2	4	no	—
317	#67	—	2	8	no	—
318	C₂×Dic₃	—	2	4	no	—
319	C₂×Dic₃	C₂³×C₉	1	2	yes	—
320	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
321	C₂×Dic₃	C₂³×C₉	1	2	yes	—
322	D₁₂	—	2	4	no	—
323	D₁₂	—	2	2	no	—
324	C₄×D₃	—	2	4	no	—
325	C₄×D₃	—	2	4	no	—
326	C₄×D₃	D₄×C₉	1	4	yes	complemented
327	Dic₆	—	2	2	no	—
328	C₂×C₃²	—	4	2	no	—
329	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
330	C₂×C₃²	C₂×C₃×#41	1	2	yes	—
331	C₃×D₃	—	2	2	no	—
332	C₃×D₃	—	4	2	no	—
333	C₂×C₉	—	2	1	no	—
334	C₂×C₉	—	2	2	no	—
335	C₂×C₉	—	4	2	no	—
336	C₂×C₉	—	6	2	no	—
337	C₂×C₉	—	8	2	no	—
338	C₂×C₉	—	12	2	no	—
339	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
340	C₂×C₉	D₃×#41	1	2	yes	—
341	#41	—	6	4	no	—
342	#41	—	6	4	no	—
343	C₂×Q₈	—	3	1	no	—
344	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
345	C₂×D₄	—	3	4	no	—
346	C₂×D₄	—	3	2	no	—
347	C₂×D₄	—	3	2	no	—
348	C₂×D₄	—	3	1	no	—
349	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
350	C₂²×C₄	—	3	1	no	—
351	C₂²×C₄	—	3	2	no	—
352	C₂²×C₄	—	3	2	no	—
353	C₂²×C₄	—	3	2	no	—
354	C₄⋊C₄	—	3	4	no	—
355	C₂²⋊C₄	—	3	4	no	—
356	C₂²⋊C₄	C₂×D₃×C₉	1	4	yes	—
357	C₄²	—	3	2	no	—
358	C₄²	—	3	1	no	—
359	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
360	C₂²×C₃	—	2	2	no	—
361	C₂²×C₃	—	2	4	no	—
362	C₂²×C₃	—	2	2	no	—
363	C₂²×C₃	—	2	4	no	—
364	C₂²×C₃	—	2	1	no	—
365	C₂²×C₃	—	3	2	no	—
366	C₂²×C₃	—	4	2	no	—
367	C₂²×C₃	—	4	4	no	—
368	C₂²×C₃	—	6	2	no	—
369	C₂²×C₃	—	6	2	no	—
370	C₂²×C₃	—	6	4	no	—
371	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
372	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
373	C₂×D₃	—	2	2	no	—
374	C₂×D₃	—	2	2	no	—
375	C₂×D₃	—	2	4	no	—
376	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
377	C₃×C₄	—	2	2	no	—
378	C₃×C₄	—	2	2	no	—
379	C₃×C₄	—	2	2	no	—
380	C₃×C₄	—	2	2	no	—
381	C₃×C₄	—	2	2	no	—
382	C₃×C₄	—	3	2	no	—
383	C₃×C₄	—	3	4	no	—
384	C₃×C₄	—	4	2	no	—
385	C₃×C₄	—	4	2	no	—
386	C₃×C₄	—	6	2	no	—
387	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
388	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
389	Dic₃	—	2	2	no	—
390	Dic₃	C₂×D₄×C₉	1	2	yes	—
391	Dic₃	C₉×#41	1	4	yes	complemented
392	C₃²	C₃×#532	1	1	yes	characteristic
393	C₉	—	2	1	no	—
394	C₉	#5668	1	1	yes	characteristic, direct product factor
395	C₂³	—	3	1	no	—
396	C₂³	—	3	2	no	—
397	C₂³	C₂²×D₃×C₉	1	2	yes	—
398	Q₈	—	2	2	no	—
399	Q₈	—	6	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	6	4	no	—
402	D₄	—	6	8	no	—
403	D₄	—	6	4	no	—
404	D₄	—	6	2	no	—
405	C₂×C₄	—	3	2	no	—
406	C₂×C₄	—	3	1	no	—
407	C₂×C₄	—	3	4	no	—
408	C₂×C₄	—	3	2	no	—
409	C₂×C₄	—	6	4	no	—
410	C₂×C₄	—	6	4	no	—
411	C₂×C₄	—	6	4	no	—
412	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
413	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
414	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
415	C₂×C₃	—	2	1	no	—
416	C₂×C₃	—	2	2	no	—
417	C₂×C₃	—	4	2	no	—
418	C₂×C₃	—	4	2	no	—
419	C₂×C₃	—	6	2	no	—
420	C₂×C₃	—	8	2	no	—
421	C₂×C₃	—	12	2	no	—
422	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
423	C₂×C₃	C₂×C₉×#41	1	2	yes	—
424	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
425	C₂×C₃	C₃×D₃×#41	1	2	yes	—
426	D₃	—	2	2	no	—
427	D₃	—	4	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	3	2	no	—
431	C₂²	—	6	2	no	—
432	C₂²	—	6	2	no	—
433	C₂²	—	6	4	no	—
434	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
435	C₄	—	2	2	no	—
436	C₄	—	2	2	no	—
437	C₄	—	3	2	no	—
438	C₄	—	3	4	no	—
439	C₄	—	6	2	no	—
440	C₄	D₃×D₄×C₉	1	2	yes	—
441	C₃	—	2	1	no	—
442	C₃	C₉×#532	1	1	yes	characteristic, complemented
443	C₃	C₃×#5668	1	1	yes	characteristic
444	C₂	—	4	2	no	—
445	C₂	—	6	2	no	—
446	C₂	—	12	2	no	—
447	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
448	C₂	D₃×C₉×#41	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#124	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5668	C₃
hypercenter	C₉×#124	D₃
hypocenter	C₃	C₉×#532
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#239	C₂	semidirect
2. C₂×C₉×#237	C₂	semidirect
3. C₃×C₉×#124	C₂	semidirect
4. C₉×#944	C₂	semidirect
5. C₉×#940	C₂	semidirect
6. C₉×#884	C₂	semidirect
7. C₉×#67⋊C₄	C₂	semidirect
8. C₉×#875	C₂	semidirect
9. C₄²×D₃×C₉	C₂	semidirect
46. C₉×#124	D₃	semidirect
68. C₄×D₃×C₉	D₄	semidirect
71. #5668	C₉	direct (N × H)
126. C₉×Dic₃	#41	semidirect
129. C₂×#239	C₂×C₉	semidirect
130. C₂×#237	C₂×C₉	semidirect
135. C₃×#124	C₂×C₉	semidirect
140. #944	C₂×C₉	semidirect
141. #940	C₂×C₉	semidirect
142. #884	C₂×C₉	semidirect
143. #67⋊C₄	C₂×C₉	semidirect
144. #875	C₂×C₉	semidirect
145. C₄²×D₃	C₂×C₉	semidirect
277. #124	D₃×C₉	semidirect
281. C₃×C₉	#532	semidirect
326. C₄×D₃	D₄×C₉	semidirect
391. Dic₃	C₉×#41	semidirect
394. C₉	#5668	direct (N × H)
442. C₃	C₉×#532	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#239	2
C₂×C₉×#237	2
C₃×C₉×#124	2
C₉×#944	2
C₉×#940	2
C₉×#884	2
C₉×#67⋊C₄	2
C₉×#875	2
C₄²×D₃×C₉	2
C₃×#5668	3
C₉×#532	3

Subgroups — C9×#5668 #13153101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5668 #13153101