Subgroups — D₃×C₉×#99 #13141651

Order 1728.

682 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×D₄×C₉	C₂	1	1	yes	maximal, characteristic
2	D₃×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
3	C₃×C₉×#99	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#834	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#806	C₂	1	2	yes	maximal, complemented
6	C₃×D₃×#99	C₃	1	1	yes	maximal, characteristic
7	C₂×C₉×#99	—	3	1	no	maximal
8	C₂³×D₃×C₉	C₄	1	1	yes	characteristic, complemented
9	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
10	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₉×#67	C₄	1	1	yes	characteristic, complemented
12	C₂×C₉×#67	C₂²	1	1	yes	characteristic
13	D₃×D₄×C₉	—	2	2	no	—
14	D₃×D₄×C₉	—	2	2	no	—
15	C₂×C₉×D₁₂	C₄	1	1	yes	characteristic, complemented
16	C₂×C₄×D₃×C₉	—	2	2	no	—
17	C₂×C₄×D₃×C₉	C₄	1	1	yes	characteristic, complemented
18	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
19	C₉×#217	C₂²	1	2	yes	complemented
20	C₉×(C₂×D₃)⋊C₄	—	2	2	no	—
21	C₂×C₃×D₃×D₄	C₂×C₃	1	1	yes	characteristic
22	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	2	yes	—
23	C₂²×D₄×C₉	—	3	1	no	—
24	C₃²×#99	C₂×C₃	1	1	yes	characteristic
25	C₃×#834	C₂×C₃	1	1	yes	characteristic
26	C₃×#806	C₂×C₃	1	2	yes	—
27	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
28	C₉×#99	—	2	1	no	—
29	C₉×#99	—	3	1	no	—
30	C₉×#99	—	3	2	no	—
31	C₉×#99	D₃	1	1	yes	characteristic, direct product factor
32	C₂³×C₃×C₉	C₂×C₄	1	1	yes	characteristic, complemented
33	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
34	C₂²×D₃×C₉	—	2	1	no	—
35	C₂²×D₃×C₉	—	2	1	no	—
36	C₂²×D₃×C₉	—	4	2	no	—
37	C₂²×D₃×C₉	—	4	2	no	—
38	C₂²×D₃×C₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×D₃×C₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×D₃×C₉	C₂×C₄	1	1	yes	characteristic, complemented
41	C₂²×D₃×C₉	D₄	1	2	yes	—
42	C₂²×D₃×C₉	D₄	1	2	yes	—
43	C₃×D₄×C₉	—	2	2	no	—
44	C₂×C₃×C₄×C₉	—	2	2	no	—
45	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic, complemented
46	C₉×#67	—	2	2	no	—
47	C₉×#67	—	2	2	no	—
48	C₂×C₉×Dic₃	—	2	2	no	—
49	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic, complemented
50	C₉×D₁₂	—	2	2	no	—
51	C₄×D₃×C₉	—	2	1	no	—
52	C₄×D₃×C₉	—	2	1	no	—
53	C₄×D₃×C₉	—	4	4	no	—
54	C₂×C₃×#99	—	3	1	no	—
55	D₃×#99	C₉	1	1	yes	characteristic, direct product factor
56	C₂³×C₃×D₃	C₃×C₄	1	1	yes	characteristic
57	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
58	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₃×#67	C₃×C₄	1	1	yes	characteristic
60	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
61	C₃×D₃×D₄	—	2	2	no	—
62	C₃×D₃×D₄	—	2	2	no	—
63	C₂×C₃×D₁₂	C₃×C₄	1	1	yes	characteristic
64	C₂×C₃×C₄×D₃	—	2	2	no	—
65	C₂×C₃×C₄×D₃	C₃×C₄	1	1	yes	characteristic
66	C₂⁴×C₉	—	3	1	no	—
67	C₂⁴×C₉	—	3	1	no	—
68	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
69	C₃×#217	C₂²×C₃	1	2	yes	—
70	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
71	C₂×D₄×C₉	—	2	1	no	—
72	C₂×D₄×C₉	—	3	1	no	—
73	C₂×D₄×C₉	—	3	1	no	—
74	C₂×D₄×C₉	—	3	1	no	—
75	C₂×D₄×C₉	—	6	2	no	—
76	C₂×D₄×C₉	—	6	2	no	—
77	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
78	C₂²×C₄×C₉	—	3	1	no	—
79	C₂²×C₄×C₉	—	6	2	no	—
80	C₉×C₂²⋊C₄	—	2	2	no	—
81	C₉×C₂²⋊C₄	—	3	2	no	—
82	C₉×C₂²⋊C₄	—	6	2	no	—
83	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
84	C₂²×C₃×C₉	—	2	1	no	—
85	C₂²×C₃×C₉	—	4	1	no	—
86	C₂²×C₃×C₉	—	4	1	no	—
87	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
89	C₂×D₃×C₉	—	2	4	no	—
90	C₂×D₃×C₉	—	2	2	no	—
91	C₂×D₃×C₉	—	2	1	no	—
92	C₂×D₃×C₉	—	4	1	no	—
93	C₂×D₃×C₉	—	4	2	no	—
94	C₂×D₃×C₉	—	4	2	no	—
95	C₂×D₃×C₉	—	4	2	no	—
96	C₂×D₃×C₉	—	4	1	no	—
97	C₂×D₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×D₃×C₉	C₂²⋊C₄	1	2	yes	—
99	C₂×D₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₃×C₄×C₉	—	2	1	no	—
101	C₃×C₄×C₉	—	4	2	no	—
102	C₉×Dic₃	—	2	1	no	—
103	C₉×Dic₃	—	4	2	no	—
104	C₂²×C₃×D₄	—	3	1	no	—
105	C₂×D₃×D₄	C₂×C₉	1	1	yes	characteristic
106	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
107	D₃×C₂²⋊C₄	C₂×C₉	1	2	yes	complemented
108	C₃×#99	—	2	1	no	—
109	C₃×#99	—	3	1	no	—
110	C₃×#99	—	3	2	no	—
111	C₃×#99	C₂×C₉	1	1	yes	characteristic, complemented
112	C₃×#99	C₃×D₃	1	1	yes	characteristic
113	#834	C₂×C₉	1	1	yes	characteristic, complemented
114	#806	C₂×C₉	1	2	yes	complemented
115	C₂³×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
116	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
117	C₂²×C₃×D₃	—	2	1	no	—
118	C₂²×C₃×D₃	—	2	1	no	—
119	C₂²×C₃×D₃	—	4	2	no	—
120	C₂²×C₃×D₃	—	4	2	no	—
121	C₂²×C₃×D₃	C₂×C₃×C₄	1	1	yes	characteristic
122	C₂²×C₃×D₃	C₂×C₃×C₄	1	1	yes	characteristic
123	C₂²×C₃×D₃	C₂×C₃×C₄	1	1	yes	characteristic
124	C₂²×C₃×D₃	C₃×D₄	1	2	yes	—
125	C₂²×C₃×D₃	C₃×D₄	1	2	yes	—
126	C₃²×D₄	—	2	2	no	—
127	C₂×C₃²×C₄	—	2	2	no	—
128	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
129	C₃×#67	—	2	2	no	—
130	C₃×#67	—	2	2	no	—
131	C₂×C₃×Dic₃	—	2	2	no	—
132	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
133	C₃×D₁₂	—	2	2	no	—
134	C₃×C₄×D₃	—	2	1	no	—
135	C₃×C₄×D₃	—	2	1	no	—
136	C₃×C₄×D₃	—	4	4	no	—
137	C₂³×C₉	—	2	1	no	—
138	C₂³×C₉	—	2	1	no	—
139	C₂³×C₉	—	3	1	no	—
140	C₂³×C₉	—	3	2	no	—
141	C₂³×C₉	—	3	1	no	—
142	C₂³×C₉	—	3	2	no	—
143	C₂³×C₉	—	3	1	no	—
144	C₂³×C₉	—	6	1	no	—
145	C₂³×C₉	—	6	1	no	—
146	C₂³×C₉	—	12	2	no	—
147	C₂³×C₉	—	12	2	no	—
148	C₂³×C₉	C₄×D₃	1	1	yes	characteristic, complemented
149	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
150	D₄×C₉	—	2	2	no	—
151	D₄×C₉	—	4	2	no	—
152	D₄×C₉	—	6	2	no	—
153	D₄×C₉	—	6	2	no	—
154	D₄×C₉	—	6	2	no	—
155	C₂×C₄×C₉	—	2	2	no	—
156	C₂×C₄×C₉	—	2	1	no	—
157	C₂×C₄×C₉	—	3	1	no	—
158	C₂×C₄×C₉	—	4	2	no	—
159	C₂×C₄×C₉	—	6	1	no	—
160	C₂×C₄×C₉	—	6	1	no	—
161	C₂×C₄×C₉	—	6	2	no	—
162	C₂×C₄×C₉	—	12	4	no	—
163	C₂×C₄×C₉	C₄×D₃	1	1	yes	characteristic, complemented
164	C₂×#99	—	3	1	no	Sylow
165	C₂×C₃×C₉	—	2	2	no	—
166	C₂×C₃×C₉	—	2	1	no	—
167	C₂×C₃×C₉	—	4	1	no	—
168	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	D₃×C₉	—	2	1	no	—
170	D₃×C₉	—	2	2	no	—
171	D₃×C₉	—	4	1	no	—
172	D₃×C₉	#99	1	2	yes	direct product factor
173	C₂⁴×C₃	—	3	1	no	—
174	C₂⁴×C₃	—	3	1	no	—
175	C₂³×D₃	C₄×C₉	1	1	yes	characteristic, complemented
176	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
177	C₂×C₃×D₄	—	2	1	no	—
178	C₂×C₃×D₄	—	3	1	no	—
179	C₂×C₃×D₄	—	3	1	no	—
180	C₂×C₃×D₄	—	3	1	no	—
181	C₂×C₃×D₄	—	6	2	no	—
182	C₂×C₃×D₄	—	6	2	no	—
183	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
184	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
185	C₂²×C₃×C₄	—	3	1	no	—
186	C₂²×C₃×C₄	—	6	2	no	—
187	C₂×#67	C₄×C₉	1	1	yes	characteristic, complemented
188	C₂×#67	C₂²×C₉	1	1	yes	characteristic
189	D₃×D₄	—	2	2	no	—
190	D₃×D₄	—	2	2	no	—
191	C₂×D₁₂	C₄×C₉	1	1	yes	characteristic, complemented
192	C₂×C₄×D₃	—	2	2	no	—
193	C₂×C₄×D₃	C₄×C₉	1	1	yes	characteristic, complemented
194	C₃×C₂²⋊C₄	—	2	2	no	—
195	C₃×C₂²⋊C₄	—	3	2	no	—
196	C₃×C₂²⋊C₄	—	6	2	no	—
197	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
198	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
199	#217	C₂²×C₉	1	2	yes	complemented
200	(C₂×D₃)⋊C₄	—	2	2	no	—
201	C₂²×C₃²	—	2	1	no	—
202	C₂²×C₃²	—	4	1	no	—
203	C₂²×C₃²	—	4	1	no	—
204	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
205	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
206	C₂×C₃×D₃	—	2	4	no	—
207	C₂×C₃×D₃	—	2	2	no	—
208	C₂×C₃×D₃	—	2	1	no	—
209	C₂×C₃×D₃	—	4	1	no	—
210	C₂×C₃×D₃	—	4	2	no	—
211	C₂×C₃×D₃	—	4	2	no	—
212	C₂×C₃×D₃	—	4	2	no	—
213	C₂×C₃×D₃	—	4	1	no	—
214	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	2	yes	—
216	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
217	C₃²×C₄	—	2	1	no	—
218	C₃²×C₄	—	4	2	no	—
219	C₃×Dic₃	—	2	1	no	—
220	C₃×Dic₃	—	4	2	no	—
221	C₂²×C₉	—	2	1	no	—
222	C₂²×C₉	—	2	1	no	—
223	C₂²×C₉	—	2	2	no	—
224	C₂²×C₉	—	3	1	no	—
225	C₂²×C₉	—	3	1	no	—
226	C₂²×C₉	—	3	2	no	—
227	C₂²×C₉	—	4	1	no	—
228	C₂²×C₉	—	4	1	no	—
229	C₂²×C₉	—	4	1	no	—
230	C₂²×C₉	—	6	4	no	—
231	C₂²×C₉	—	6	2	no	—
232	C₂²×C₉	—	6	1	no	—
233	C₂²×C₉	—	8	1	no	—
234	C₂²×C₉	—	8	1	no	—
235	C₂²×C₉	—	12	2	no	—
236	C₂²×C₉	—	12	1	no	—
237	C₂²×C₉	—	12	1	no	—
238	C₂²×C₉	—	12	2	no	—
239	C₂²×C₉	—	12	2	no	—
240	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
241	C₂²×C₉	D₃×D₄	1	2	yes	—
242	C₄×C₉	—	2	1	no	—
243	C₄×C₉	—	4	1	no	—
244	C₄×C₉	—	4	2	no	—
245	C₄×C₉	—	6	1	no	—
246	C₄×C₉	—	8	2	no	—
247	C₄×C₉	—	12	2	no	—
248	C₂²×D₄	—	3	1	no	—
249	C₂×C₂²⋊C₄	—	3	2	no	—
250	#99	—	3	1	no	—
251	#99	—	3	2	no	—
252	#99	D₃×C₉	1	1	yes	characteristic, direct product factor
253	C₃×C₉	C₂×#99	1	1	yes	characteristic, complemented, Sylow
254	C₂³×C₃	—	2	1	no	—
255	C₂³×C₃	—	2	1	no	—
256	C₂³×C₃	—	3	1	no	—
257	C₂³×C₃	—	3	2	no	—
258	C₂³×C₃	—	3	1	no	—
259	C₂³×C₃	—	3	2	no	—
260	C₂³×C₃	—	3	1	no	—
261	C₂³×C₃	—	6	1	no	—
262	C₂³×C₃	—	6	1	no	—
263	C₂³×C₃	—	12	2	no	—
264	C₂³×C₃	—	12	2	no	—
265	C₂³×C₃	C₂×C₄×C₉	1	1	yes	characteristic, complemented
266	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
267	C₂³×C₃	C₃×C₄×D₃	1	1	yes	characteristic
268	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
269	C₂²×D₃	—	2	1	no	—
270	C₂²×D₃	—	2	1	no	—
271	C₂²×D₃	—	4	2	no	—
272	C₂²×D₃	—	4	2	no	—
273	C₂²×D₃	C₂×C₄×C₉	1	1	yes	characteristic
274	C₂²×D₃	C₂×C₄×C₉	1	1	yes	characteristic
275	C₂²×D₃	C₂×C₄×C₉	1	1	yes	characteristic, complemented
276	C₂²×D₃	D₄×C₉	1	2	yes	—
277	C₂²×D₃	D₄×C₉	1	2	yes	—
278	C₃×D₄	—	2	2	no	—
279	C₃×D₄	—	2	2	no	—
280	C₃×D₄	—	4	2	no	—
281	C₃×D₄	—	6	2	no	—
282	C₃×D₄	—	6	2	no	—
283	C₃×D₄	—	6	2	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	3	1	no	—
288	C₂×C₃×C₄	—	4	2	no	—
289	C₂×C₃×C₄	—	6	1	no	—
290	C₂×C₃×C₄	—	6	1	no	—
291	C₂×C₃×C₄	—	6	2	no	—
292	C₂×C₃×C₄	—	12	4	no	—
293	C₂×C₃×C₄	C₂×C₄×C₉	1	1	yes	characteristic, complemented
294	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
295	#67	—	2	2	no	—
296	#67	—	2	2	no	—
297	C₂×Dic₃	—	2	2	no	—
298	C₂×Dic₃	C₂×C₄×C₉	1	1	yes	characteristic, complemented
299	D₁₂	—	2	2	no	—
300	C₄×D₃	—	2	1	no	—
301	C₄×D₃	—	2	1	no	—
302	C₄×D₃	—	4	4	no	—
303	C₂×C₃²	—	2	2	no	—
304	C₂×C₃²	—	2	1	no	—
305	C₂×C₃²	—	4	1	no	—
306	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
307	C₃×D₃	—	2	1	no	—
308	C₃×D₃	—	2	2	no	—
309	C₃×D₃	—	4	1	no	—
310	C₃×D₃	C₃×#99	1	2	yes	—
311	C₂×C₉	—	2	2	no	—
312	C₂×C₉	—	2	1	no	—
313	C₂×C₉	—	2	1	no	—
314	C₂×C₉	—	3	2	no	—
315	C₂×C₉	—	4	2	no	—
316	C₂×C₉	—	4	1	no	—
317	C₂×C₉	—	4	1	no	—
318	C₂×C₉	—	6	2	no	—
319	C₂×C₉	—	6	1	no	—
320	C₂×C₉	—	8	1	no	—
321	C₂×C₉	—	12	1	no	—
322	C₂×C₉	D₃×C₂²⋊C₄	1	1	yes	characteristic
323	C₂⁴	—	3	1	no	—
324	C₂⁴	—	3	1	no	—
325	C₂×D₄	—	3	1	no	—
326	C₂×D₄	—	3	1	no	—
327	C₂×D₄	—	3	1	no	—
328	C₂×D₄	—	6	2	no	—
329	C₂×D₄	—	6	2	no	—
330	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
331	C₂²×C₄	—	3	1	no	—
332	C₂²×C₄	—	6	2	no	—
333	C₂²⋊C₄	—	3	2	no	—
334	C₂²⋊C₄	—	6	2	no	—
335	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
336	C₂²×C₃	—	2	1	no	—
337	C₂²×C₃	—	2	1	no	—
338	C₂²×C₃	—	2	1	no	—
339	C₂²×C₃	—	2	2	no	—
340	C₂²×C₃	—	3	1	no	—
341	C₂²×C₃	—	3	1	no	—
342	C₂²×C₃	—	3	2	no	—
343	C₂²×C₃	—	4	1	no	—
344	C₂²×C₃	—	4	1	no	—
345	C₂²×C₃	—	4	1	no	—
346	C₂²×C₃	—	4	1	no	—
347	C₂²×C₃	—	4	1	no	—
348	C₂²×C₃	—	6	4	no	—
349	C₂²×C₃	—	6	2	no	—
350	C₂²×C₃	—	6	1	no	—
351	C₂²×C₃	—	8	1	no	—
352	C₂²×C₃	—	8	1	no	—
353	C₂²×C₃	—	12	2	no	—
354	C₂²×C₃	—	12	1	no	—
355	C₂²×C₃	—	12	1	no	—
356	C₂²×C₃	—	12	2	no	—
357	C₂²×C₃	—	12	2	no	—
358	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
359	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
360	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
361	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
362	C₂×D₃	—	2	4	no	—
363	C₂×D₃	—	2	2	no	—
364	C₂×D₃	—	2	1	no	—
365	C₂×D₃	—	4	1	no	—
366	C₂×D₃	—	4	2	no	—
367	C₂×D₃	—	4	2	no	—
368	C₂×D₃	—	4	2	no	—
369	C₂×D₃	—	4	1	no	—
370	C₂×D₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
371	C₂×D₃	C₉×C₂²⋊C₄	1	2	yes	—
372	C₂×D₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
373	C₃×C₄	—	2	1	no	—
374	C₃×C₄	—	2	1	no	—
375	C₃×C₄	—	4	1	no	—
376	C₃×C₄	—	4	2	no	—
377	C₃×C₄	—	4	2	no	—
378	C₃×C₄	—	6	1	no	—
379	C₃×C₄	—	8	2	no	—
380	C₃×C₄	—	12	2	no	—
381	Dic₃	—	2	1	no	—
382	Dic₃	—	4	2	no	—
383	C₃²	C₂×C₃×#99	1	1	yes	characteristic
384	C₉	—	2	1	no	—
385	C₉	D₃×#99	1	1	yes	characteristic, direct product factor
386	C₂³	—	3	1	no	—
387	C₂³	—	3	2	no	—
388	C₂³	—	3	1	no	—
389	C₂³	—	3	2	no	—
390	C₂³	—	3	1	no	—
391	C₂³	—	6	1	no	—
392	C₂³	—	6	1	no	—
393	C₂³	—	12	2	no	—
394	C₂³	—	12	2	no	—
395	C₂³	C₄×D₃×C₉	1	1	yes	characteristic, complemented
396	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
397	D₄	—	2	2	no	—
398	D₄	—	6	2	no	—
399	D₄	—	6	2	no	—
400	D₄	—	6	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	3	1	no	—
403	C₂×C₄	—	6	1	no	—
404	C₂×C₄	—	6	1	no	—
405	C₂×C₄	—	6	2	no	—
406	C₂×C₄	—	12	4	no	—
407	C₂×C₄	C₄×D₃×C₉	1	1	yes	characteristic, complemented
408	C₂×C₃	—	2	2	no	—
409	C₂×C₃	—	2	1	no	—
410	C₂×C₃	—	2	2	no	—
411	C₂×C₃	—	2	1	no	—
412	C₂×C₃	—	2	1	no	—
413	C₂×C₃	—	3	2	no	—
414	C₂×C₃	—	4	2	no	—
415	C₂×C₃	—	4	1	no	—
416	C₂×C₃	—	4	1	no	—
417	C₂×C₃	—	4	1	no	—
418	C₂×C₃	—	6	1	no	—
419	C₂×C₃	—	6	2	no	—
420	C₂×C₃	—	8	1	no	—
421	C₂×C₃	—	12	1	no	—
422	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
423	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
424	D₃	—	2	1	no	—
425	D₃	—	2	2	no	—
426	D₃	—	4	1	no	—
427	D₃	C₉×#99	1	2	yes	direct product factor
428	C₂²	—	2	1	no	—
429	C₂²	—	3	1	no	—
430	C₂²	—	3	1	no	—
431	C₂²	—	3	2	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	6	4	no	—
435	C₂²	—	6	2	no	—
436	C₂²	—	6	1	no	—
437	C₂²	—	12	2	no	—
438	C₂²	—	12	1	no	—
439	C₂²	—	12	1	no	—
440	C₂²	—	12	2	no	—
441	C₂²	—	12	2	no	—
442	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
443	C₂²	D₃×D₄×C₉	1	2	yes	—
444	C₄	—	2	1	no	—
445	C₄	—	4	2	no	—
446	C₄	—	6	1	no	—
447	C₄	—	12	2	no	—
448	C₃	—	2	1	no	—
449	C₃	C₂×C₉×#99	1	1	yes	characteristic, complemented
450	C₃	C₃×D₃×#99	1	1	yes	characteristic
451	C₂	—	2	2	no	—
452	C₂	—	2	1	no	—
453	C₂	—	3	2	no	—
454	C₂	—	4	1	no	—
455	C₂	—	6	1	no	—
456	C₂	—	6	2	no	—
457	C₂	—	12	1	no	—
458	C₂	D₃×C₉×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	D₃×C₂²⋊C₄
commutator	C₂²×C₃	C₂²×C₄×C₉
Frattini	C₂³×C₃	C₂²×C₃×D₃
Fitting	C₃×C₉×#99	C₂
socle	C₂×C₃²	C₂×C₃×C₂²⋊C₄
prime radical	C₂×C₃×D₃×D₄	C₂×C₃
cosocle	C₂³×C₃²	C₂³×C₃
hypercenter	C₉×#99	D₃
hypocenter	C₃	C₂×C₉×#99
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₉ ◁ C₂³×C₉ ◁ C₉×#99

Complements

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

N	H ≅ G/N	type
2. D₃×C₉×C₂²⋊C₄	C₂	semidirect
3. C₃×C₉×#99	C₂	semidirect
4. C₉×#834	C₂	semidirect
5. C₉×#806	C₂	semidirect
8. C₂³×D₃×C₉	C₄	semidirect
11. C₂×C₉×#67	C₄	semidirect
15. C₂×C₉×D₁₂	C₄	semidirect
17. C₂×C₄×D₃×C₉	C₄	semidirect
18. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
19. C₉×#217	C₂²	semidirect
31. C₉×#99	D₃	direct (N × H)
32. C₂³×C₃×C₉	C₂×C₄	semidirect
40. C₂²×D₃×C₉	C₂×C₄	semidirect
45. C₂×C₃×C₄×C₉	C₂×C₄	semidirect
49. C₂×C₉×Dic₃	C₂×C₄	semidirect
55. D₃×#99	C₉	direct (N × H)
83. C₉×C₂²⋊C₄	C₂×D₃	semidirect
107. D₃×C₂²⋊C₄	C₂×C₉	semidirect
111. C₃×#99	C₂×C₉	semidirect
113. #834	C₂×C₉	semidirect
114. #806	C₂×C₉	semidirect
148. C₂³×C₉	C₄×D₃	semidirect
163. C₂×C₄×C₉	C₄×D₃	semidirect
172. D₃×C₉	#99	direct (N × H)
175. C₂³×D₃	C₄×C₉	semidirect
187. C₂×#67	C₄×C₉	semidirect
191. C₂×D₁₂	C₄×C₉	semidirect
193. C₂×C₄×D₃	C₄×C₉	semidirect
197. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
199. #217	C₂²×C₉	semidirect
252. #99	D₃×C₉	direct (N × H)
253. C₃×C₉	C₂×#99	semidirect
265. C₂³×C₃	C₂×C₄×C₉	semidirect
275. C₂²×D₃	C₂×C₄×C₉	semidirect
293. C₂×C₃×C₄	C₂×C₄×C₉	semidirect
298. C₂×Dic₃	C₂×C₄×C₉	semidirect
335. C₂²⋊C₄	C₂×D₃×C₉	semidirect
385. C₉	D₃×#99	direct (N × H)
395. C₂³	C₄×D₃×C₉	semidirect
407. C₂×C₄	C₄×D₃×C₉	semidirect
427. D₃	C₉×#99	direct (N × H)
449. C₃	C₂×C₉×#99	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×D₄×C₉	2
D₃×C₉×C₂²⋊C₄	2
C₃×C₉×#99	2
C₉×#834	2
C₉×#806	2
C₃×D₃×#99	3
C₂×C₉×#99	3

Subgroups — D3×C9×#99 #13141651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₉×#99 #13141651