Subgroups — C₉×#5524 #13152498

Order 1728.

1066 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#897	C₂	1	2	yes	maximal, complemented
5	C₉×#895	C₂	1	2	yes	maximal, complemented
6	C₉×#886	C₂	1	2	yes	maximal, complemented
7	C₉×#882	C₂	1	2	yes	maximal, complemented
8	C₄×C₉×D₁₂	C₂	1	4	yes	maximal, complemented
9	C₃×#5524	C₃	1	1	yes	maximal, characteristic
10	C₉×#525	—	3	1	no	maximal
11	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₉×#67	C₂²	1	2	yes	—
14	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
15	C₉×#235	—	2	4	no	—
16	C₂×C₉×D₁₂	C₂²	1	4	yes	—
17	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₄×D₃×C₉	—	2	4	no	—
19	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
20	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
21	C₂×C₄×D₃×C₉	C₂²	1	2	yes	complemented
22	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
24	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₃×C₄²×C₉	C₂²	1	2	yes	complemented
26	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
28	C₉×C₄⋊Dic₃	C₂²	1	4	yes	complemented
29	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
30	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
31	C₃²×#117	C₂×C₃	1	1	yes	characteristic
32	C₃×#897	C₂×C₃	1	2	yes	—
33	C₃×#895	C₂×C₃	1	2	yes	—
34	C₃×#886	C₂×C₃	1	2	yes	—
35	C₃×#882	C₂×C₃	1	2	yes	—
36	C₃×C₄×D₁₂	C₂×C₃	1	4	yes	—
37	C₂×C₉×#41	—	3	1	no	—
38	C₂³×C₄×C₉	—	3	1	no	—
39	C₉×#123	—	3	2	no	—
40	C₉×C₂²⋊Q₈	—	3	2	no	—
41	C₉×#121	—	3	2	no	—
42	C₉×#120	—	3	2	no	—
43	C₄×D₄×C₉	—	3	4	no	—
44	C₉×#117	—	2	1	no	—
45	C₉×#117	D₃	1	1	yes	characteristic, complemented
46	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
47	C₂²×D₃×C₉	—	2	2	no	—
48	C₂²×D₃×C₉	—	2	4	no	—
49	C₂²×D₃×C₉	C₂³	1	2	yes	—
50	C₂²×D₃×C₉	C₂³	1	2	yes	—
51	C₂×C₃×C₄×C₉	D₄	1	4	yes	complemented
52	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
53	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
54	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
55	C₉×#67	—	2	4	no	—
56	C₂×C₉×Dic₃	—	2	2	no	—
57	C₂×C₉×Dic₃	C₂³	1	2	yes	—
58	C₂×C₉×Dic₃	C₂³	1	2	yes	—
59	C₉×D₁₂	—	2	8	no	—
60	C₉×D₁₂	—	2	2	no	—
61	C₄×D₃×C₉	—	2	4	no	—
62	C₄×D₃×C₉	—	2	4	no	—
63	C₄×D₃×C₉	—	2	4	no	—
64	C₉×Dic₆	—	2	2	no	—
65	C₃×#525	—	3	1	no	—
66	#5524	C₉	1	1	yes	characteristic, direct product factor
67	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
70	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
71	C₃×#235	—	2	4	no	—
72	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
73	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃×C₄×D₃	—	2	4	no	—
75	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
76	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
77	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
78	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
79	C₂⁴×C₉	—	3	1	no	—
80	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
81	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
82	C₃²×C₄²	C₂²×C₃	1	2	yes	—
83	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
84	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
85	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
86	C₉×#41	—	6	4	no	—
87	C₂×Q₈×C₉	—	3	1	no	—
88	C₂×D₄×C₉	—	3	2	no	—
89	C₂×D₄×C₉	—	3	4	no	—
90	C₂×D₄×C₉	—	3	1	no	—
91	C₂²×C₄×C₉	—	2	1	no	—
92	C₂²×C₄×C₉	—	3	1	no	—
93	C₂²×C₄×C₉	—	3	2	no	—
94	C₂²×C₄×C₉	—	3	2	no	—
95	C₂²×C₄×C₉	—	3	2	no	—
96	C₂²×C₄×C₉	—	6	4	no	—
97	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
98	C₉×C₄⋊C₄	—	2	2	no	—
99	C₉×C₄⋊C₄	—	3	4	no	—
100	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
101	C₉×C₂²⋊C₄	—	2	2	no	—
102	C₉×C₂²⋊C₄	—	3	4	no	—
103	C₉×C₂²⋊C₄	—	3	4	no	—
104	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
105	C₄²×C₉	—	2	2	no	—
106	C₄²×C₉	C₂×D₃	1	2	yes	complemented
107	C₂²×C₃×C₉	—	2	2	no	—
108	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
109	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
110	C₂×D₃×C₉	—	2	8	no	—
111	C₂×D₃×C₉	—	2	2	no	—
112	C₂×D₃×C₉	—	2	2	no	—
113	C₂×D₃×C₉	—	2	2	no	—
114	C₂×D₃×C₉	—	2	4	no	—
115	C₂×D₃×C₉	#41	1	4	yes	complemented
116	C₃×C₄×C₉	—	2	4	no	—
117	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
118	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
119	C₉×Dic₃	—	2	2	no	—
120	C₉×Dic₃	—	2	2	no	—
121	C₂×C₃×#41	—	3	1	no	—
122	C₂³×C₃×C₄	—	3	1	no	—
123	C₂×#235	C₂×C₉	1	1	yes	characteristic, complemented
124	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic, complemented
125	C₃×#123	—	3	2	no	—
126	C₃×C₂²⋊Q₈	—	3	2	no	—
127	C₃×#121	—	3	2	no	—
128	C₃×#120	—	3	2	no	—
129	C₃×C₄×D₄	—	3	4	no	—
130	C₃×#117	—	2	1	no	—
131	C₃×#117	C₂×C₉	1	1	yes	characteristic, complemented
132	C₃×#117	C₃×D₃	1	1	yes	characteristic
133	#897	C₂×C₉	1	2	yes	complemented
134	#895	C₂×C₉	1	2	yes	complemented
135	#886	C₂×C₉	1	2	yes	complemented
136	#882	C₂×C₉	1	2	yes	complemented
137	C₄×D₁₂	C₂×C₉	1	4	yes	complemented
138	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
139	C₂²×C₃×D₃	—	2	2	no	—
140	C₂²×C₃×D₃	—	2	4	no	—
141	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
142	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
143	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
144	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
145	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
146	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
147	C₃×#67	—	2	4	no	—
148	C₂×C₃×Dic₃	—	2	2	no	—
149	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
150	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
151	C₃×D₁₂	—	2	8	no	—
152	C₃×D₁₂	—	2	2	no	—
153	C₃×C₄×D₃	—	2	4	no	—
154	C₃×C₄×D₃	—	2	4	no	—
155	C₃×C₄×D₃	—	2	4	no	—
156	C₃×Dic₆	—	2	2	no	—
157	C₂³×C₉	—	2	1	no	—
158	C₂³×C₉	—	3	2	no	—
159	C₂³×C₉	—	3	2	no	—
160	C₂³×C₉	—	6	4	no	—
161	C₂³×C₉	—	6	2	no	—
162	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
163	Q₈×C₉	—	6	2	no	—
164	D₄×C₉	—	6	8	no	—
165	D₄×C₉	—	6	4	no	—
166	D₄×C₉	—	6	2	no	—
167	C₂×C₄×C₉	—	2	4	no	—
168	C₂×C₄×C₉	—	2	1	no	—
169	C₂×C₄×C₉	—	2	1	no	—
170	C₂×C₄×C₉	—	2	4	no	—
171	C₂×C₄×C₉	—	3	2	no	—
172	C₂×C₄×C₉	—	3	2	no	—
173	C₂×C₄×C₉	—	6	2	no	—
174	C₂×C₄×C₉	—	6	4	no	—
175	C₂×C₄×C₉	—	6	4	no	—
176	C₂×C₄×C₉	—	6	4	no	—
177	C₂×C₄×C₉	D₁₂	1	4	yes	complemented
178	C₂×C₄×C₉	C₂²×D₃	1	4	yes	—
179	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
180	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
181	#525	—	3	1	no	Sylow
182	C₂×C₃×C₉	—	2	2	no	—
183	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₃×C₉	C₂×#41	1	2	yes	—
185	D₃×C₉	—	2	4	no	—
186	D₃×C₉	—	4	2	no	—
187	C₂⁴×C₃	—	3	1	no	—
188	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
189	C₃×#41	—	6	4	no	—
190	C₂×C₃×Q₈	—	3	1	no	—
191	C₂×C₃×D₄	—	3	2	no	—
192	C₂×C₃×D₄	—	3	4	no	—
193	C₂×C₃×D₄	—	3	1	no	—
194	C₂²×C₃×C₄	—	2	1	no	—
195	C₂²×C₃×C₄	—	3	1	no	—
196	C₂²×C₃×C₄	—	3	2	no	—
197	C₂²×C₃×C₄	—	3	2	no	—
198	C₂²×C₃×C₄	—	3	2	no	—
199	C₂²×C₃×C₄	—	6	4	no	—
200	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
202	C₂×#67	C₂²×C₉	1	2	yes	—
203	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
204	#235	—	2	4	no	—
205	C₂×D₁₂	C₂²×C₉	1	4	yes	—
206	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
207	C₂×C₄×D₃	—	2	4	no	—
208	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
209	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
210	C₂×C₄×D₃	C₂²×C₉	1	2	yes	complemented
211	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
212	C₃×C₄⋊C₄	—	2	2	no	—
213	C₃×C₄⋊C₄	—	3	4	no	—
214	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
215	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
216	C₃×C₂²⋊C₄	—	2	2	no	—
217	C₃×C₂²⋊C₄	—	3	4	no	—
218	C₃×C₂²⋊C₄	—	3	4	no	—
219	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
220	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
221	C₃×C₄²	—	2	2	no	—
222	C₃×C₄²	C₂²×C₉	1	2	yes	complemented
223	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
224	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
225	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	complemented
226	C₄⋊Dic₃	C₂²×C₉	1	4	yes	complemented
227	C₂²×C₃²	—	2	2	no	—
228	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
229	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
230	C₂×C₃×D₃	—	2	8	no	—
231	C₂×C₃×D₃	—	2	2	no	—
232	C₂×C₃×D₃	—	2	2	no	—
233	C₂×C₃×D₃	—	2	2	no	—
234	C₂×C₃×D₃	—	2	4	no	—
235	C₂×C₃×D₃	C₃×#41	1	4	yes	—
236	C₃²×C₄	—	2	4	no	—
237	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
238	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
239	C₃×Dic₃	—	2	2	no	—
240	C₃×Dic₃	—	2	2	no	—
241	C₂²×C₉	—	2	2	no	—
242	C₂²×C₉	—	2	1	no	—
243	C₂²×C₉	—	2	2	no	—
244	C₂²×C₉	—	3	4	no	—
245	C₂²×C₉	—	4	2	no	—
246	C₂²×C₉	—	6	8	no	—
247	C₂²×C₉	—	6	2	no	—
248	C₂²×C₉	—	6	2	no	—
249	C₂²×C₉	—	6	2	no	—
250	C₂²×C₉	—	6	4	no	—
251	C₂²×C₉	C₂×D₁₂	1	2	yes	—
252	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
253	C₄×C₉	—	2	4	no	—
254	C₄×C₉	—	2	2	no	—
255	C₄×C₉	—	2	2	no	—
256	C₄×C₉	—	4	4	no	—
257	C₄×C₉	—	6	2	no	—
258	C₄×C₉	—	6	2	no	—
259	C₄×C₉	C₂×D₁₂	1	2	yes	—
260	C₄×C₉	C₂×D₁₂	1	2	yes	—
261	C₂×#41	—	3	1	no	—
262	C₂³×C₄	—	3	1	no	—
263	#123	—	3	2	no	—
264	C₂²⋊Q₈	—	3	2	no	—
265	#121	—	3	2	no	—
266	#120	—	3	2	no	—
267	C₄×D₄	—	3	4	no	—
268	#117	D₃×C₉	1	1	yes	characteristic, complemented
269	C₃×C₉	#525	1	1	yes	characteristic, complemented, Sylow
270	C₂³×C₃	—	2	1	no	—
271	C₂³×C₃	—	3	2	no	—
272	C₂³×C₃	—	3	2	no	—
273	C₂³×C₃	—	6	4	no	—
274	C₂³×C₃	—	6	2	no	—
275	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
276	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
277	C₂²×D₃	—	2	2	no	—
278	C₂²×D₃	—	2	4	no	—
279	C₂²×D₃	C₂³×C₉	1	2	yes	—
280	C₂²×D₃	C₂³×C₉	1	2	yes	—
281	C₃×Q₈	—	6	2	no	—
282	C₃×D₄	—	6	8	no	—
283	C₃×D₄	—	6	4	no	—
284	C₃×D₄	—	6	2	no	—
285	C₂×C₃×C₄	—	2	4	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	4	no	—
289	C₂×C₃×C₄	—	3	2	no	—
290	C₂×C₃×C₄	—	3	2	no	—
291	C₂×C₃×C₄	—	6	2	no	—
292	C₂×C₃×C₄	—	6	4	no	—
293	C₂×C₃×C₄	—	6	4	no	—
294	C₂×C₃×C₄	—	6	4	no	—
295	C₂×C₃×C₄	D₄×C₉	1	4	yes	complemented
296	C₂×C₃×C₄	C₂³×C₉	1	4	yes	—
297	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
299	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
300	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
301	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
303	#67	—	2	4	no	—
304	C₂×Dic₃	—	2	2	no	—
305	C₂×Dic₃	C₂³×C₉	1	2	yes	—
306	C₂×Dic₃	C₂³×C₉	1	2	yes	—
307	D₁₂	—	2	8	no	—
308	D₁₂	—	2	2	no	—
309	C₄×D₃	—	2	4	no	—
310	C₄×D₃	—	2	4	no	—
311	C₄×D₃	—	2	4	no	—
312	Dic₆	—	2	2	no	—
313	C₂×C₃²	—	2	2	no	—
314	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
315	C₂×C₃²	C₂×C₃×#41	1	2	yes	—
316	C₃×D₃	—	2	4	no	—
317	C₃×D₃	—	4	2	no	—
318	C₂×C₉	—	2	2	no	—
319	C₂×C₉	—	2	1	no	—
320	C₂×C₉	—	2	2	no	—
321	C₂×C₉	—	4	2	no	—
322	C₂×C₉	—	6	4	no	—
323	C₂×C₉	—	12	2	no	—
324	C₂×C₉	C₂²×D₁₂	1	1	yes	characteristic
325	C₂×C₉	D₃×#41	1	2	yes	—
326	C₂⁴	—	3	1	no	—
327	#41	—	6	4	no	—
328	C₂×Q₈	—	3	1	no	—
329	C₂×D₄	—	3	2	no	—
330	C₂×D₄	—	3	4	no	—
331	C₂×D₄	—	3	1	no	—
332	C₂²×C₄	—	3	1	no	—
333	C₂²×C₄	—	3	2	no	—
334	C₂²×C₄	—	3	2	no	—
335	C₂²×C₄	—	3	2	no	—
336	C₂²×C₄	—	6	4	no	—
337	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
338	C₄⋊C₄	—	3	4	no	—
339	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
340	C₂²⋊C₄	—	3	4	no	—
341	C₂²⋊C₄	—	3	4	no	—
342	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
343	C₄²	C₂×D₃×C₉	1	2	yes	complemented
344	C₂²×C₃	—	2	2	no	—
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	—	2	1	no	—
347	C₂²×C₃	—	2	2	no	—
348	C₂²×C₃	—	3	4	no	—
349	C₂²×C₃	—	4	2	no	—
350	C₂²×C₃	—	6	8	no	—
351	C₂²×C₃	—	6	2	no	—
352	C₂²×C₃	—	6	2	no	—
353	C₂²×C₃	—	6	2	no	—
354	C₂²×C₃	—	6	4	no	—
355	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
356	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
357	C₂²×C₃	C₂×C₃×D₁₂	1	2	yes	—
358	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
359	C₂×D₃	—	2	8	no	—
360	C₂×D₃	—	2	2	no	—
361	C₂×D₃	—	2	2	no	—
362	C₂×D₃	—	2	2	no	—
363	C₂×D₃	—	2	4	no	—
364	C₂×D₃	C₉×#41	1	4	yes	complemented
365	C₃×C₄	—	2	4	no	—
366	C₃×C₄	—	2	4	no	—
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	2	2	no	—
369	C₃×C₄	—	4	4	no	—
370	C₃×C₄	—	6	2	no	—
371	C₃×C₄	—	6	2	no	—
372	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
373	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
374	C₃×C₄	C₂×C₃×D₁₂	1	2	yes	—
375	C₃×C₄	C₂×C₃×D₁₂	1	2	yes	—
376	Dic₃	—	2	2	no	—
377	Dic₃	—	2	2	no	—
378	C₃²	C₃×#525	1	1	yes	characteristic
379	C₉	—	2	1	no	—
380	C₉	#5524	1	1	yes	characteristic, direct product factor
381	C₂³	—	3	2	no	—
382	C₂³	—	3	2	no	—
383	C₂³	—	6	4	no	—
384	C₂³	—	6	2	no	—
385	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
386	Q₈	—	6	2	no	—
387	D₄	—	6	8	no	—
388	D₄	—	6	4	no	—
389	D₄	—	6	2	no	—
390	C₂×C₄	—	3	2	no	—
391	C₂×C₄	—	3	2	no	—
392	C₂×C₄	—	6	2	no	—
393	C₂×C₄	—	6	4	no	—
394	C₂×C₄	—	6	4	no	—
395	C₂×C₄	—	6	4	no	—
396	C₂×C₄	C₉×D₁₂	1	4	yes	complemented
397	C₂×C₄	C₂²×D₃×C₉	1	4	yes	—
398	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
400	C₂×C₃	—	2	2	no	—
401	C₂×C₃	—	2	2	no	—
402	C₂×C₃	—	2	1	no	—
403	C₂×C₃	—	2	2	no	—
404	C₂×C₃	—	4	2	no	—
405	C₂×C₃	—	6	4	no	—
406	C₂×C₃	—	12	2	no	—
407	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
408	C₂×C₃	C₂×C₉×#41	1	2	yes	—
409	C₂×C₃	C₂²×C₃×D₁₂	1	1	yes	characteristic
410	C₂×C₃	C₃×D₃×#41	1	2	yes	—
411	D₃	—	2	4	no	—
412	D₃	—	4	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	3	4	no	—
415	C₂²	—	6	8	no	—
416	C₂²	—	6	2	no	—
417	C₂²	—	6	2	no	—
418	C₂²	—	6	2	no	—
419	C₂²	—	6	4	no	—
420	C₂²	C₂×C₉×D₁₂	1	2	yes	—
421	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
422	C₄	—	2	4	no	—
423	C₄	—	6	2	no	—
424	C₄	—	6	2	no	—
425	C₄	C₂×C₉×D₁₂	1	2	yes	—
426	C₄	C₂×C₉×D₁₂	1	2	yes	—
427	C₃	—	2	1	no	—
428	C₃	C₉×#525	1	1	yes	characteristic, complemented
429	C₃	C₃×#5524	1	1	yes	characteristic
430	C₂	—	2	2	no	—
431	C₂	—	6	4	no	—
432	C₂	—	12	2	no	—
433	C₂	C₂²×C₉×D₁₂	1	1	yes	characteristic
434	C₂	D₃×C₉×#41	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#117	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5524	C₃
hypercenter	C₉×#117	D₃
hypocenter	C₃	C₉×#525
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₉×#117

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#235	C₂	semidirect
2. C₂²×C₄×D₃×C₉	C₂	semidirect
3. C₃×C₉×#117	C₂	semidirect
4. C₉×#897	C₂	semidirect
5. C₉×#895	C₂	semidirect
6. C₉×#886	C₂	semidirect
7. C₉×#882	C₂	semidirect
8. C₄×C₉×D₁₂	C₂	semidirect
17. C₂×C₉×D₁₂	C₂²	semidirect
21. C₂×C₄×D₃×C₉	C₂²	semidirect
22. C₂×C₉×Dic₆	C₂²	semidirect
23. C₃×C₉×C₄⋊C₄	C₂²	semidirect
25. C₃×C₄²×C₉	C₂²	semidirect
27. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
28. C₉×C₄⋊Dic₃	C₂²	semidirect
45. C₉×#117	D₃	semidirect
51. C₂×C₃×C₄×C₉	D₄	semidirect
66. #5524	C₉	direct (N × H)
100. C₉×C₄⋊C₄	C₂×D₃	semidirect
106. C₄²×C₉	C₂×D₃	semidirect
115. C₂×D₃×C₉	#41	semidirect
123. C₂×#235	C₂×C₉	semidirect
124. C₂²×C₄×D₃	C₂×C₉	semidirect
131. C₃×#117	C₂×C₉	semidirect
133. #897	C₂×C₉	semidirect
134. #895	C₂×C₉	semidirect
135. #886	C₂×C₉	semidirect
136. #882	C₂×C₉	semidirect
137. C₄×D₁₂	C₂×C₉	semidirect
177. C₂×C₄×C₉	D₁₂	semidirect
206. C₂×D₁₂	C₂²×C₉	semidirect
210. C₂×C₄×D₃	C₂²×C₉	semidirect
211. C₂×Dic₆	C₂²×C₉	semidirect
214. C₃×C₄⋊C₄	C₂²×C₉	semidirect
222. C₃×C₄²	C₂²×C₉	semidirect
225. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
226. C₄⋊Dic₃	C₂²×C₉	semidirect
268. #117	D₃×C₉	semidirect
269. C₃×C₉	#525	semidirect
295. C₂×C₃×C₄	D₄×C₉	semidirect
339. C₄⋊C₄	C₂×D₃×C₉	semidirect
343. C₄²	C₂×D₃×C₉	semidirect
364. C₂×D₃	C₉×#41	semidirect
380. C₉	#5524	direct (N × H)
396. C₂×C₄	C₉×D₁₂	semidirect
428. C₃	C₉×#525	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#235	2
C₂²×C₄×D₃×C₉	2
C₃×C₉×#117	2
C₉×#897	2
C₉×#895	2
C₉×#886	2
C₉×#882	2
C₄×C₉×D₁₂	2
C₃×#5524	3
C₉×#525	3

Subgroups — C9×#5524 #13152498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5524 #13152498