Subgroups — D₃×C₉×#102 #13141752

Order 1728.

656 conjugacy classes of subgroups.

The subgroup lattice has 434 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	C₂×D₃×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#832	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#821	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#809	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×D₃×#102	C₃	1	1	yes	maximal, characteristic
9	C₂×C₉×#102	—	3	1	no	maximal
10	C₂³×D₃×C₉	—	2	1	no	—
11	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₉×#67	—	2	1	no	—
13	D₃×D₄×C₉	—	2	2	no	—
14	D₃×D₄×C₉	C₄	1	4	yes	complemented
15	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₃×C₉	—	2	1	no	—
17	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
20	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
21	C₉×Dic₃⋊C₄	—	2	1	no	—
22	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
23	D₃×C₈×C₉	—	2	2	no	—
24	C₂×C₃×D₃×D₄	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×D₃×C₈	C₂×C₃	1	1	yes	characteristic
26	C₃×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
27	C₂²×D₄×C₉	—	3	1	no	—
28	C₃²×#102	C₂×C₃	1	1	yes	characteristic
29	C₃×#832	C₂×C₃	1	1	yes	characteristic
30	C₃×#821	C₂×C₃	1	1	yes	characteristic
31	C₃×#809	C₂×C₃	1	1	yes	characteristic
32	C₂²×C₈×C₉	—	3	1	no	—
33	C₂×C₉×C₄⋊C₄	—	3	1	no	—
34	C₉×#102	—	2	1	no	—
35	C₉×#102	—	3	1	no	—
36	C₉×#102	—	3	1	no	—
37	C₉×#102	—	3	1	no	—
38	C₉×#102	D₃	1	1	yes	characteristic, direct product factor
39	C₂³×C₃×C₉	—	2	1	no	—
40	C₂²×D₃×C₉	—	2	1	no	—
41	C₂²×D₃×C₉	—	2	4	no	—
42	C₂²×D₃×C₉	—	4	2	no	—
43	C₂²×D₃×C₉	—	4	2	no	—
44	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
45	C₃×D₄×C₉	—	2	1	no	—
46	C₃×D₄×C₉	C₂×C₄	1	2	yes	complemented
47	C₂×C₃×C₄×C₉	—	2	1	no	—
48	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
49	C₉×#67	—	2	4	no	—
50	C₂×C₉×Dic₃	—	2	1	no	—
51	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
52	C₉×D₁₂	—	2	1	no	—
53	C₉×D₁₂	C₂×C₄	1	2	yes	complemented
54	C₄×D₃×C₉	—	4	2	no	—
55	C₄×D₃×C₉	C₂×C₄	1	2	yes	—
56	C₄×D₃×C₉	D₄	1	2	yes	—
57	C₃×C₈×C₉	—	2	1	no	—
58	C₉×C₃⋊C₈	—	2	1	no	—
59	C₂×C₃×#102	—	3	1	no	—
60	D₃×#102	C₉	1	1	yes	characteristic, direct product factor
61	C₂³×C₃×D₃	—	2	1	no	—
62	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₃×#67	—	2	1	no	—
64	C₃×D₃×D₄	—	2	2	no	—
65	C₃×D₃×D₄	C₃×C₄	1	4	yes	—
66	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₃×C₄×D₃	—	2	1	no	—
68	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
69	C₂⁴×C₉	—	6	1	no	—
70	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
71	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
72	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
73	C₃×Dic₃⋊C₄	—	2	1	no	—
74	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
75	C₃×D₃×C₈	—	2	2	no	—
76	C₂×D₄×C₉	—	2	1	no	—
77	C₂×D₄×C₉	—	3	4	no	—
78	C₂×D₄×C₉	—	3	1	no	—
79	C₂×D₄×C₉	—	6	2	no	—
80	C₂×D₄×C₉	—	6	1	no	—
81	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
82	C₂²×C₄×C₉	—	3	1	no	—
83	C₂²×C₄×C₉	—	6	1	no	—
84	C₂×C₈×C₉	—	2	1	no	—
85	C₂×C₈×C₉	—	3	1	no	—
86	C₂×C₈×C₉	—	6	2	no	—
87	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
88	C₉×C₄⋊C₄	—	2	1	no	—
89	C₉×C₄⋊C₄	—	3	1	no	—
90	C₉×C₄⋊C₄	—	6	1	no	—
91	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
92	C₂²×C₃×C₉	—	2	2	no	—
93	C₂²×C₃×C₉	—	4	1	no	—
94	C₂²×C₃×C₉	—	4	1	no	—
95	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
96	C₂×D₃×C₉	—	2	2	no	—
97	C₂×D₃×C₉	—	4	1	no	—
98	C₂×D₃×C₉	—	4	1	no	—
99	C₂×D₃×C₉	—	4	8	no	—
100	C₂×D₃×C₉	C₂²⋊C₄	1	2	yes	—
101	C₂×D₃×C₉	D₈	1	2	yes	—
102	C₂×D₃×C₉	SD₁₆	1	2	yes	—
103	C₃×C₄×C₉	—	4	1	no	—
104	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
105	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
106	C₉×Dic₃	—	4	1	no	—
107	C₉×Dic₃	C₂²⋊C₄	1	2	yes	—
108	C₂²×C₃×D₄	—	3	1	no	—
109	C₂×D₃×D₄	C₂×C₉	1	1	yes	characteristic
110	C₂²×C₃×C₈	—	3	1	no	—
111	C₂×C₃×C₄⋊C₄	—	3	1	no	—
112	C₂×D₃×C₈	C₂×C₉	1	1	yes	characteristic, complemented
113	D₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
114	C₃×#102	—	2	1	no	—
115	C₃×#102	—	3	1	no	—
116	C₃×#102	—	3	1	no	—
117	C₃×#102	—	3	1	no	—
118	C₃×#102	C₂×C₉	1	1	yes	characteristic, complemented
119	C₃×#102	C₃×D₃	1	1	yes	characteristic
120	#832	C₂×C₉	1	1	yes	characteristic, complemented
121	#821	C₂×C₉	1	1	yes	characteristic, complemented
122	#809	C₂×C₉	1	1	yes	characteristic, complemented
123	C₂³×C₃²	—	2	1	no	—
124	C₂²×C₃×D₃	—	2	1	no	—
125	C₂²×C₃×D₃	—	2	4	no	—
126	C₂²×C₃×D₃	—	4	2	no	—
127	C₂²×C₃×D₃	—	4	2	no	—
128	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
129	C₃²×D₄	—	2	1	no	—
130	C₃²×D₄	C₂×C₃×C₄	1	2	yes	—
131	C₂×C₃²×C₄	—	2	1	no	—
132	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
133	C₃×#67	—	2	4	no	—
134	C₂×C₃×Dic₃	—	2	1	no	—
135	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
136	C₃×D₁₂	—	2	1	no	—
137	C₃×D₁₂	C₂×C₃×C₄	1	2	yes	—
138	C₃×C₄×D₃	—	4	2	no	—
139	C₃×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
140	C₃×C₄×D₃	C₃×D₄	1	2	yes	—
141	C₂³×C₉	—	2	1	no	—
142	C₂³×C₉	—	3	1	no	—
143	C₂³×C₉	—	4	1	no	—
144	C₂³×C₉	—	6	4	no	—
145	C₂³×C₉	—	6	1	no	—
146	C₂³×C₉	—	12	2	no	—
147	C₂³×C₉	—	12	2	no	—
148	C₃²×C₈	—	2	1	no	—
149	C₃×C₃⋊C₈	—	2	1	no	—
150	D₄×C₉	—	2	1	no	—
151	D₄×C₉	—	2	2	no	—
152	D₄×C₉	—	3	2	no	—
153	D₄×C₉	—	4	1	no	—
154	D₄×C₉	—	6	4	no	—
155	D₄×C₉	—	6	1	no	—
156	D₄×C₉	C₄×D₃	1	2	yes	complemented
157	C₂×C₄×C₉	—	2	1	no	—
158	C₂×C₄×C₉	—	2	1	no	—
159	C₂×C₄×C₉	—	3	1	no	—
160	C₂×C₄×C₉	—	3	2	no	—
161	C₂×C₄×C₉	—	3	2	no	—
162	C₂×C₄×C₉	—	4	1	no	—
163	C₂×C₄×C₉	—	6	1	no	—
164	C₂×C₄×C₉	—	12	2	no	—
165	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
166	C₈×C₉	—	2	1	no	—
167	C₈×C₉	—	4	1	no	—
168	C₈×C₉	—	6	1	no	—
169	C₂×#102	—	3	1	no	Sylow
170	C₂×C₃×C₉	—	4	2	no	—
171	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₃×C₉	C₂×D₈	1	1	yes	characteristic
173	C₂×C₃×C₉	C₂×SD₁₆	1	1	yes	characteristic
174	D₃×C₉	—	4	2	no	—
175	D₃×C₉	#102	1	4	yes	direct product factor
176	C₂⁴×C₃	—	6	1	no	—
177	C₂³×D₃	—	2	1	no	—
178	C₂×C₃×D₄	—	2	1	no	—
179	C₂×C₃×D₄	—	3	4	no	—
180	C₂×C₃×D₄	—	3	1	no	—
181	C₂×C₃×D₄	—	6	2	no	—
182	C₂×C₃×D₄	—	6	1	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	1	no	—
187	C₂×#67	—	2	1	no	—
188	D₃×D₄	—	2	2	no	—
189	D₃×D₄	C₄×C₉	1	4	yes	complemented
190	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
191	C₂×C₄×D₃	—	2	1	no	—
192	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
193	C₂×C₃×C₈	—	2	1	no	—
194	C₂×C₃×C₈	—	3	1	no	—
195	C₂×C₃×C₈	—	6	2	no	—
196	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic, complemented
197	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
198	C₃×C₄⋊C₄	—	2	1	no	—
199	C₃×C₄⋊C₄	—	3	1	no	—
200	C₃×C₄⋊C₄	—	6	1	no	—
201	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
202	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
203	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
204	Dic₃⋊C₄	—	2	1	no	—
205	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
206	D₃×C₈	—	2	2	no	—
207	C₂²×C₃²	—	2	2	no	—
208	C₂²×C₃²	—	4	1	no	—
209	C₂²×C₃²	—	4	1	no	—
210	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
211	C₂×C₃×D₃	—	2	2	no	—
212	C₂×C₃×D₃	—	4	1	no	—
213	C₂×C₃×D₃	—	4	1	no	—
214	C₂×C₃×D₃	—	4	8	no	—
215	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	2	yes	—
216	C₂×C₃×D₃	C₃×D₈	1	2	yes	—
217	C₂×C₃×D₃	C₃×SD₁₆	1	2	yes	—
218	C₃²×C₄	—	4	1	no	—
219	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
220	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
221	C₃×Dic₃	—	4	1	no	—
222	C₃×Dic₃	C₃×C₂²⋊C₄	1	2	yes	—
223	C₂²×C₉	—	2	2	no	—
224	C₂²×C₉	—	2	1	no	—
225	C₂²×C₉	—	3	2	no	—
226	C₂²×C₉	—	3	2	no	—
227	C₂²×C₉	—	3	2	no	—
228	C₂²×C₉	—	4	2	no	—
229	C₂²×C₉	—	4	1	no	—
230	C₂²×C₉	—	4	1	no	—
231	C₂²×C₉	—	6	2	no	—
232	C₂²×C₉	—	8	1	no	—
233	C₂²×C₉	—	8	1	no	—
234	C₂²×C₉	—	12	8	no	—
235	C₂²×C₉	—	12	1	no	—
236	C₂²×C₉	—	12	1	no	—
237	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
238	C₄×C₉	—	2	1	no	—
239	C₄×C₉	—	2	1	no	—
240	C₄×C₉	—	3	2	no	—
241	C₄×C₉	—	4	1	no	—
242	C₄×C₉	—	8	1	no	—
243	C₄×C₉	—	12	1	no	—
244	C₄×C₉	C₂×C₄×D₃	1	1	yes	characteristic
245	C₄×C₉	D₃×D₄	1	1	yes	characteristic
246	C₂²×D₄	—	3	1	no	—
247	C₂²×C₈	—	3	1	no	—
248	C₂×C₄⋊C₄	—	3	1	no	—
249	#102	—	3	1	no	—
250	#102	—	3	1	no	—
251	#102	—	3	1	no	—
252	#102	D₃×C₉	1	1	yes	characteristic, direct product factor
253	C₃×C₉	C₂×#102	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	—	4	1	no	—
258	C₂³×C₃	—	6	4	no	—
259	C₂³×C₃	—	6	1	no	—
260	C₂³×C₃	—	12	2	no	—
261	C₂³×C₃	—	12	2	no	—
262	C₂²×D₃	—	2	1	no	—
263	C₂²×D₃	—	2	4	no	—
264	C₂²×D₃	—	4	2	no	—
265	C₂²×D₃	—	4	2	no	—
266	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
267	C₃×D₄	—	2	1	no	—
268	C₃×D₄	—	2	1	no	—
269	C₃×D₄	—	2	2	no	—
270	C₃×D₄	—	3	2	no	—
271	C₃×D₄	—	4	1	no	—
272	C₃×D₄	—	6	4	no	—
273	C₃×D₄	—	6	1	no	—
274	C₃×D₄	C₂×C₄×C₉	1	2	yes	complemented
275	C₃×D₄	C₃×C₄×D₃	1	2	yes	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	3	1	no	—
280	C₂×C₃×C₄	—	3	2	no	—
281	C₂×C₃×C₄	—	3	2	no	—
282	C₂×C₃×C₄	—	4	1	no	—
283	C₂×C₃×C₄	—	6	1	no	—
284	C₂×C₃×C₄	—	12	2	no	—
285	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
287	#67	—	2	4	no	—
288	C₂×Dic₃	—	2	1	no	—
289	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
290	D₁₂	—	2	1	no	—
291	D₁₂	C₂×C₄×C₉	1	2	yes	complemented
292	C₄×D₃	—	4	2	no	—
293	C₄×D₃	C₂×C₄×C₉	1	2	yes	—
294	C₄×D₃	D₄×C₉	1	2	yes	—
295	C₃×C₈	—	2	1	no	—
296	C₃×C₈	—	2	1	no	—
297	C₃×C₈	—	4	1	no	—
298	C₃×C₈	—	6	1	no	—
299	C₃⋊C₈	—	2	1	no	—
300	C₂×C₃²	—	4	2	no	—
301	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
302	C₂×C₃²	C₂×C₃×D₈	1	1	yes	characteristic
303	C₂×C₃²	C₂×C₃×SD₁₆	1	1	yes	characteristic
304	C₃×D₃	—	4	2	no	—
305	C₃×D₃	C₃×#102	1	4	yes	—
306	C₂×C₉	—	2	1	no	—
307	C₂×C₉	—	2	1	no	—
308	C₂×C₉	—	2	1	no	—
309	C₂×C₉	—	3	4	no	—
310	C₂×C₉	—	4	2	no	—
311	C₂×C₉	—	8	2	no	—
312	C₂×C₉	—	12	2	no	—
313	C₂×C₉	D₃×C₂²⋊C₄	1	1	yes	characteristic
314	C₂×C₉	D₃×D₈	1	1	yes	characteristic
315	C₂×C₉	D₃×SD₁₆	1	1	yes	characteristic
316	C₂⁴	—	6	1	no	—
317	C₂×D₄	—	3	4	no	—
318	C₂×D₄	—	3	1	no	—
319	C₂×D₄	—	6	2	no	—
320	C₂×D₄	—	6	1	no	—
321	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
322	C₂²×C₄	—	3	1	no	—
323	C₂²×C₄	—	6	1	no	—
324	C₂×C₈	—	3	1	no	—
325	C₂×C₈	—	6	2	no	—
326	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
327	C₄⋊C₄	—	3	1	no	—
328	C₄⋊C₄	—	6	1	no	—
329	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
330	C₂²×C₃	—	2	2	no	—
331	C₂²×C₃	—	2	2	no	—
332	C₂²×C₃	—	2	1	no	—
333	C₂²×C₃	—	3	2	no	—
334	C₂²×C₃	—	3	2	no	—
335	C₂²×C₃	—	3	2	no	—
336	C₂²×C₃	—	4	2	no	—
337	C₂²×C₃	—	4	1	no	—
338	C₂²×C₃	—	4	1	no	—
339	C₂²×C₃	—	4	1	no	—
340	C₂²×C₃	—	4	1	no	—
341	C₂²×C₃	—	6	2	no	—
342	C₂²×C₃	—	8	1	no	—
343	C₂²×C₃	—	8	1	no	—
344	C₂²×C₃	—	12	8	no	—
345	C₂²×C₃	—	12	1	no	—
346	C₂²×C₃	—	12	1	no	—
347	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
348	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
349	C₂×D₃	—	2	2	no	—
350	C₂×D₃	—	4	1	no	—
351	C₂×D₃	—	4	1	no	—
352	C₂×D₃	—	4	8	no	—
353	C₂×D₃	C₉×C₂²⋊C₄	1	2	yes	—
354	C₂×D₃	C₉×D₈	1	2	yes	—
355	C₂×D₃	C₉×SD₁₆	1	2	yes	—
356	C₃×C₄	—	2	1	no	—
357	C₃×C₄	—	2	1	no	—
358	C₃×C₄	—	3	2	no	—
359	C₃×C₄	—	4	1	no	—
360	C₃×C₄	—	4	1	no	—
361	C₃×C₄	—	8	1	no	—
362	C₃×C₄	—	12	1	no	—
363	C₃×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
364	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
365	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
366	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
367	Dic₃	—	4	1	no	—
368	Dic₃	C₉×C₂²⋊C₄	1	2	yes	—
369	C₃²	C₂×C₃×#102	1	1	yes	characteristic
370	C₉	—	2	1	no	—
371	C₉	D₃×#102	1	1	yes	characteristic, direct product factor
372	C₂³	—	2	1	no	—
373	C₂³	—	3	1	no	—
374	C₂³	—	6	4	no	—
375	C₂³	—	6	1	no	—
376	C₂³	—	12	2	no	—
377	C₂³	—	12	2	no	—
378	D₄	—	2	1	no	—
379	D₄	—	3	2	no	—
380	D₄	—	6	4	no	—
381	D₄	—	6	1	no	—
382	D₄	C₄×D₃×C₉	1	2	yes	complemented
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	3	1	no	—
385	C₂×C₄	—	3	2	no	—
386	C₂×C₄	—	3	2	no	—
387	C₂×C₄	—	6	1	no	—
388	C₂×C₄	—	12	2	no	—
389	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
390	C₈	—	2	1	no	—
391	C₈	—	6	1	no	—
392	C₂×C₃	—	2	1	no	—
393	C₂×C₃	—	2	1	no	—
394	C₂×C₃	—	2	1	no	—
395	C₂×C₃	—	3	4	no	—
396	C₂×C₃	—	4	2	no	—
397	C₂×C₃	—	4	2	no	—
398	C₂×C₃	—	8	2	no	—
399	C₂×C₃	—	12	2	no	—
400	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
401	C₂×C₃	C₂×C₉×D₈	1	1	yes	characteristic
402	C₂×C₃	C₂×C₉×SD₁₆	1	1	yes	characteristic
403	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
404	C₂×C₃	C₃×D₃×D₈	1	1	yes	characteristic
405	C₂×C₃	C₃×D₃×SD₁₆	1	1	yes	characteristic
406	D₃	—	4	2	no	—
407	D₃	C₉×#102	1	4	yes	direct product factor
408	C₂²	—	2	2	no	—
409	C₂²	—	3	2	no	—
410	C₂²	—	3	2	no	—
411	C₂²	—	3	2	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	6	2	no	—
415	C₂²	—	12	8	no	—
416	C₂²	—	12	1	no	—
417	C₂²	—	12	1	no	—
418	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
419	C₄	—	3	2	no	—
420	C₄	—	4	1	no	—
421	C₄	—	12	1	no	—
422	C₄	C₂×C₄×D₃×C₉	1	1	yes	characteristic
423	C₄	D₃×D₄×C₉	1	1	yes	characteristic
424	C₃	—	2	1	no	—
425	C₃	C₂×C₉×#102	1	1	yes	characteristic, complemented
426	C₃	C₃×D₃×#102	1	1	yes	characteristic
427	C₂	—	3	4	no	—
428	C₂	—	4	2	no	—
429	C₂	—	12	2	no	—
430	C₂	D₃×C₉×C₂²⋊C₄	1	1	yes	characteristic
431	C₂	D₃×C₉×D₈	1	1	yes	characteristic
432	C₂	D₃×C₉×SD₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	D₃×D₄
commutator	C₃×C₄	C₂²×C₄×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×#102	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₂×C₃×D₃×D₄	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#102	D₃
hypocenter	C₃	C₂×C₉×#102
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#102

Complements

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

N	H ≅ G/N	type
2. C₂×D₃×C₈×C₉	C₂	semidirect
3. D₃×C₉×C₄⋊C₄	C₂	semidirect
4. C₃×C₉×#102	C₂	semidirect
5. C₉×#832	C₂	semidirect
6. C₉×#821	C₂	semidirect
7. C₉×#809	C₂	semidirect
14. D₃×D₄×C₉	C₄	semidirect
18. C₂×C₃×C₈×C₉	C₂²	semidirect
19. C₃×C₉×C₄⋊C₄	C₂²	semidirect
20. C₉×C₄⋊Dic₃	C₂²	semidirect
22. C₂×C₉×C₃⋊C₈	C₂²	semidirect
38. C₉×#102	D₃	direct (N × H)
46. C₃×D₄×C₉	C₂×C₄	semidirect
53. C₉×D₁₂	C₂×C₄	semidirect
60. D₃×#102	C₉	direct (N × H)
87. C₂×C₈×C₉	C₂×D₃	semidirect
91. C₉×C₄⋊C₄	C₂×D₃	semidirect
112. C₂×D₃×C₈	C₂×C₉	semidirect
113. D₃×C₄⋊C₄	C₂×C₉	semidirect
118. C₃×#102	C₂×C₉	semidirect
120. #832	C₂×C₉	semidirect
121. #821	C₂×C₉	semidirect
122. #809	C₂×C₉	semidirect
156. D₄×C₉	C₄×D₃	semidirect
175. D₃×C₉	#102	direct (N × H)
189. D₃×D₄	C₄×C₉	semidirect
196. C₂×C₃×C₈	C₂²×C₉	semidirect
201. C₃×C₄⋊C₄	C₂²×C₉	semidirect
203. C₄⋊Dic₃	C₂²×C₉	semidirect
205. C₂×C₃⋊C₈	C₂²×C₉	semidirect
252. #102	D₃×C₉	direct (N × H)
253. C₃×C₉	C₂×#102	semidirect
274. C₃×D₄	C₂×C₄×C₉	semidirect
291. D₁₂	C₂×C₄×C₉	semidirect
326. C₂×C₈	C₂×D₃×C₉	semidirect
329. C₄⋊C₄	C₂×D₃×C₉	semidirect
371. C₉	D₃×#102	direct (N × H)
382. D₄	C₄×D₃×C₉	semidirect
407. D₃	C₉×#102	direct (N × H)
425. C₃	C₂×C₉×#102	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
C₂×D₃×C₈×C₉	2
D₃×C₉×C₄⋊C₄	2
C₃×C₉×#102	2
C₉×#832	2
C₉×#821	2
C₉×#809	2
C₃×D₃×#102	3
C₂×C₉×#102	3

Subgroups — D3×C9×#102 #13141752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₉×#102 #13141752