Subgroups — C₃×#10588688 #13142713

Order 1728.

466 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#3667	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#63389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₄⋊(C₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#63362	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5011	—	3	1	no	maximal
9	#10588688	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃×D₄×C₉	C₄	1	1	yes	characteristic
11	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₃×C₉×C₄⋊C₄	C₄	1	1	yes	characteristic
14	C₃×C₉×C₂²⋊C₄	C₄	1	1	yes	characteristic
15	C₃×C₉×C₂²⋊C₄	C₄	1	1	yes	characteristic
16	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
17	C₃×#3667	—	2	2	no	—
18	C₂×C₃×C₉⋊C₈	—	2	2	no	—
19	C₂×C₃×C₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₉⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₉⋊C₈	C₂²	1	1	yes	characteristic
23	C₃²×C₄×D₄	D₃	1	1	yes	characteristic
24	C₂×C₃×#208	—	3	1	no	—
25	C₂²×C₃×C₃⋊C₈	—	3	1	no	—
26	C₃×#830	—	3	1	no	—
27	C₃×#830	—	3	1	no	—
28	C₃×C₄⋊(C₃⋊C₈)	—	3	1	no	—
29	C₃×#803	—	3	1	no	—
30	C₄×D₄×C₉	—	2	1	no	—
31	C₄×D₄×C₉	C₂×C₃	1	1	yes	characteristic
32	C₂×#3667	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂²×C₉⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
34	#63389	C₂×C₃	1	1	yes	characteristic, complemented
35	#63389	C₂×C₃	1	1	yes	characteristic, complemented
36	C₄⋊(C₉⋊C₈)	C₂×C₃	1	1	yes	characteristic, complemented
37	#63362	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂³×C₃×C₉	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₃×C₉	C₂×C₄	1	1	yes	characteristic
40	C₃×D₄×C₉	—	2	2	no	—
41	C₂×C₃×C₄×C₉	—	2	1	no	—
42	C₂×C₃×C₄×C₉	—	2	1	no	—
43	C₂×C₃×C₄×C₉	—	2	1	no	—
44	C₂×C₃×C₄×C₉	—	2	1	no	—
45	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
50	C₃×C₉⋊C₈	—	2	1	no	—
51	C₃×C₉⋊C₈	—	2	1	no	—
52	C₃×C₉⋊C₈	—	2	1	no	—
53	C₃×C₉⋊C₈	D₄	1	2	yes	complemented
54	C₃×#435	—	9	1	no	—
55	#5011	—	3	1	no	—
56	C₂×C₃²×D₄	Dic₃	1	1	yes	characteristic
57	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
58	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
59	C₃²×C₄⋊C₄	Dic₃	1	1	yes	characteristic
60	C₃²×C₂²⋊C₄	Dic₃	1	1	yes	characteristic
61	C₃²×C₂²⋊C₄	Dic₃	1	1	yes	characteristic
62	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
63	C₃×#208	—	6	2	no	—
64	C₂×C₃×C₃⋊C₈	—	3	1	no	—
65	C₂×C₃×C₃⋊C₈	—	3	1	no	—
66	C₂×C₃×C₃⋊C₈	—	3	1	no	—
67	C₂×C₃×C₃⋊C₈	—	3	1	no	—
68	C₂×C₃×C₃⋊C₈	—	6	2	no	—
69	C₂×D₄×C₉	—	2	1	no	—
70	C₂×D₄×C₉	C₃×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₉	—	2	1	no	—
72	C₂²×C₄×C₉	—	2	1	no	—
73	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
74	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
75	C₉×C₄⋊C₄	—	2	1	no	—
76	C₉×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
77	C₉×C₂²⋊C₄	—	2	1	no	—
78	C₉×C₂²⋊C₄	—	2	1	no	—
79	C₉×C₂²⋊C₄	C₃×C₄	1	1	yes	characteristic
80	C₉×C₂²⋊C₄	C₃×C₄	1	1	yes	characteristic
81	C₄²×C₉	—	2	1	no	—
82	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
83	#3667	—	2	2	no	—
84	C₂×C₉⋊C₈	—	2	2	no	—
85	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₃×C₉	—	2	1	no	—
90	C₂²×C₃×C₉	—	2	1	no	—
91	C₂²×C₃×C₉	—	2	1	no	—
92	C₂²×C₃×C₉	—	2	1	no	—
93	C₂²×C₃×C₉	—	2	1	no	—
94	C₂²×C₃×C₉	M₁₆	1	2	yes	complemented
95	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
96	C₃×C₄×C₉	—	2	1	no	—
97	C₃×C₄×C₉	—	2	1	no	—
98	C₃×C₄×C₉	—	2	1	no	—
99	C₃×C₄×C₉	—	2	1	no	—
100	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
101	C₃×C₄×C₉	#41	1	1	yes	characteristic
102	C₂×C₃×M₁₆	—	9	1	no	—
103	C₂²×C₃×C₈	—	9	1	no	—
104	C₃×C₄×D₄	—	2	1	no	—
105	C₃×C₄×D₄	D₉	1	1	yes	characteristic
106	C₃×C₄×D₄	C₃×D₃	1	1	yes	characteristic
107	C₂×#208	—	3	1	no	—
108	C₂²×C₃⋊C₈	—	3	1	no	—
109	C₃×C₄⋊C₈	—	9	1	no	—
110	C₃×C₂²⋊C₈	—	9	1	no	—
111	C₃×C₂²⋊C₈	—	9	1	no	—
112	C₃×#97	—	9	1	no	—
113	#830	—	3	1	no	—
114	#830	—	3	1	no	—
115	C₄⋊(C₃⋊C₈)	—	3	1	no	—
116	#803	—	3	1	no	—
117	C₂³×C₃²	C₂×Dic₃	1	1	yes	characteristic
118	C₂³×C₃²	C₂×Dic₃	1	1	yes	characteristic
119	C₃²×D₄	—	2	2	no	—
120	C₂×C₃²×C₄	—	2	1	no	—
121	C₂×C₃²×C₄	—	2	1	no	—
122	C₂×C₃²×C₄	—	2	1	no	—
123	C₂×C₃²×C₄	—	2	1	no	—
124	C₂×C₃²×C₄	C₂×Dic₃	1	1	yes	characteristic
125	C₂×C₃²×C₄	C₂×Dic₃	1	1	yes	characteristic
126	C₂×C₃²×C₄	C₂×Dic₃	1	1	yes	characteristic
127	C₂×C₃²×C₄	C₂×Dic₃	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
129	C₂³×C₉	—	2	1	no	—
130	C₂³×C₉	—	2	1	no	—
131	C₂³×C₉	C₂×C₃×C₄	1	1	yes	characteristic
132	C₂³×C₉	C₂×C₃×C₄	1	1	yes	characteristic
133	C₃×C₃⋊C₈	—	3	2	no	—
134	C₃×C₃⋊C₈	—	6	1	no	—
135	C₃×C₃⋊C₈	—	6	1	no	—
136	C₃×C₃⋊C₈	—	6	1	no	—
137	D₄×C₉	—	2	4	no	—
138	D₄×C₉	—	2	2	no	—
139	C₂×C₄×C₉	—	2	1	no	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	1	no	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	2	1	no	—
146	C₂×C₄×C₉	—	2	1	no	—
147	C₂×C₄×C₉	—	2	1	no	—
148	C₂×C₄×C₉	—	4	1	no	—
149	C₂×C₄×C₉	—	4	1	no	—
150	C₂×C₄×C₉	—	4	1	no	—
151	C₂×C₄×C₉	—	4	1	no	—
152	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
153	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
154	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
155	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
156	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
157	C₉⋊C₈	—	2	1	no	—
158	C₉⋊C₈	—	2	1	no	—
159	C₉⋊C₈	—	2	1	no	—
160	C₉⋊C₈	C₃×D₄	1	2	yes	complemented
161	#435	—	9	1	no	Sylow
162	C₂×C₃×C₉	—	2	2	no	—
163	C₂×C₃×C₉	—	4	1	no	—
164	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
165	C₂×C₃×C₉	C₂×M₁₆	1	1	yes	characteristic
166	C₂×C₃×C₉	#131	1	1	yes	characteristic
167	C₂×C₃×D₄	—	2	1	no	—
168	C₂×C₃×D₄	Dic₉	1	1	yes	characteristic
169	C₂×C₃×D₄	C₃×Dic₃	1	1	yes	characteristic
170	C₂²×C₃×C₄	—	2	1	no	—
171	C₂²×C₃×C₄	—	2	1	no	—
172	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
176	C₃×M₁₆	—	18	2	no	—
177	C₂×C₃×C₈	—	9	1	no	—
178	C₂×C₃×C₈	—	9	1	no	—
179	C₂×C₃×C₈	—	9	1	no	—
180	C₂×C₃×C₈	—	9	1	no	—
181	C₂×C₃×C₈	—	18	2	no	—
182	C₃×C₄⋊C₄	—	2	1	no	—
183	C₃×C₄⋊C₄	Dic₉	1	1	yes	characteristic
184	C₃×C₄⋊C₄	C₃×Dic₃	1	1	yes	characteristic
185	C₃×C₂²⋊C₄	—	2	1	no	—
186	C₃×C₂²⋊C₄	—	2	1	no	—
187	C₃×C₂²⋊C₄	Dic₉	1	1	yes	characteristic
188	C₃×C₂²⋊C₄	Dic₉	1	1	yes	characteristic
189	C₃×C₂²⋊C₄	C₃×Dic₃	1	1	yes	characteristic
190	C₃×C₂²⋊C₄	C₃×Dic₃	1	1	yes	characteristic
191	C₃×C₄²	—	2	1	no	—
192	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
193	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
194	#208	—	6	2	no	—
195	C₂×C₃⋊C₈	—	3	1	no	—
196	C₂×C₃⋊C₈	—	3	1	no	—
197	C₂×C₃⋊C₈	—	3	1	no	—
198	C₂×C₃⋊C₈	—	3	1	no	—
199	C₂×C₃⋊C₈	—	6	2	no	—
200	C₂²×C₃²	—	2	1	no	—
201	C₂²×C₃²	—	2	1	no	—
202	C₂²×C₃²	—	2	1	no	—
203	C₂²×C₃²	—	2	1	no	—
204	C₂²×C₃²	—	2	1	no	—
205	C₂²×C₃²	#208	1	2	yes	—
206	C₂²×C₃²	C₂²×Dic₃	1	1	yes	characteristic
207	C₃²×C₄	—	2	1	no	—
208	C₃²×C₄	—	2	1	no	—
209	C₃²×C₄	—	2	1	no	—
210	C₃²×C₄	—	2	1	no	—
211	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
212	C₃²×C₄	#237	1	1	yes	characteristic
213	C₂²×C₉	—	2	1	no	—
214	C₂²×C₉	—	2	1	no	—
215	C₂²×C₉	—	2	2	no	—
216	C₂²×C₉	—	2	1	no	—
217	C₂²×C₉	—	2	1	no	—
218	C₂²×C₉	—	2	1	no	—
219	C₂²×C₉	—	2	2	no	—
220	C₂²×C₉	—	2	1	no	—
221	C₂²×C₉	—	4	1	no	—
222	C₂²×C₉	—	4	1	no	—
223	C₂²×C₉	—	4	1	no	—
224	C₂²×C₉	—	4	1	no	—
225	C₂²×C₉	C₃×M₁₆	1	2	yes	complemented
226	C₂²×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
227	C₄×C₉	—	2	2	no	—
228	C₄×C₉	—	2	1	no	—
229	C₄×C₉	—	2	1	no	—
230	C₄×C₉	—	2	1	no	—
231	C₄×C₉	—	2	1	no	—
232	C₄×C₉	—	2	1	no	—
233	C₄×C₉	—	2	1	no	—
234	C₄×C₉	—	4	1	no	—
235	C₄×C₉	—	4	1	no	—
236	C₄×C₉	—	4	1	no	—
237	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
238	C₄×C₉	C₃×#41	1	1	yes	characteristic
239	C₂×M₁₆	—	9	1	no	—
240	C₂²×C₈	—	9	1	no	—
241	C₄×D₄	C₃×D₉	1	1	yes	characteristic
242	C₄⋊C₈	—	9	1	no	—
243	C₂²⋊C₈	—	9	1	no	—
244	C₂²⋊C₈	—	9	1	no	—
245	#97	—	9	1	no	—
246	C₃×C₉	#435	1	1	yes	characteristic, complemented, Sylow
247	C₂³×C₃	—	2	1	no	—
248	C₂³×C₃	—	2	1	no	—
249	C₂³×C₃	C₂×Dic₉	1	1	yes	characteristic
250	C₂³×C₃	C₂×Dic₉	1	1	yes	characteristic
251	C₂³×C₃	C₂×C₃×Dic₃	1	1	yes	characteristic
252	C₂³×C₃	C₂×C₃×Dic₃	1	1	yes	characteristic
253	C₃×D₄	—	2	4	no	—
254	C₃×D₄	—	2	2	no	—
255	C₃×D₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	1	no	—
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	4	1	no	—
270	C₂×C₃×C₄	—	4	1	no	—
271	C₂×C₃×C₄	—	4	1	no	—
272	C₂×C₃×C₄	—	4	1	no	—
273	C₂×C₃×C₄	C₂×Dic₉	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂×Dic₉	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂×Dic₉	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂×Dic₉	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
283	C₃×C₈	—	9	2	no	—
284	C₃×C₈	—	18	1	no	—
285	C₃×C₈	—	18	1	no	—
286	C₃×C₈	—	18	1	no	—
287	C₃⋊C₈	—	3	2	no	—
288	C₃⋊C₈	—	6	1	no	—
289	C₃⋊C₈	—	6	1	no	—
290	C₃⋊C₈	—	6	1	no	—
291	C₂×C₃²	—	2	2	no	—
292	C₂×C₃²	—	4	1	no	—
293	C₂×C₃²	C₂×#208	1	1	yes	characteristic
294	C₂×C₃²	D₄×Dic₃	1	1	yes	characteristic
295	C₂×C₃²	#948	1	1	yes	characteristic
296	C₂×C₉	—	2	2	no	—
297	C₂×C₉	—	2	1	no	—
298	C₂×C₉	—	2	1	no	—
299	C₂×C₉	—	2	1	no	—
300	C₂×C₉	—	4	2	no	—
301	C₂×C₉	—	4	2	no	—
302	C₂×C₉	—	4	1	no	—
303	C₂×C₉	C₃×C₄×D₄	1	1	yes	characteristic
304	C₂×C₉	C₂×C₃×M₁₆	1	1	yes	characteristic
305	C₂×C₉	C₃×#131	1	1	yes	characteristic
306	C₂×D₄	C₃×Dic₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
309	M₁₆	—	18	2	no	—
310	C₂×C₈	—	9	1	no	—
311	C₂×C₈	—	9	1	no	—
312	C₂×C₈	—	9	1	no	—
313	C₂×C₈	—	9	1	no	—
314	C₂×C₈	—	18	2	no	—
315	C₄⋊C₄	C₃×Dic₉	1	1	yes	characteristic
316	C₂²⋊C₄	C₃×Dic₉	1	1	yes	characteristic
317	C₂²⋊C₄	C₃×Dic₉	1	1	yes	characteristic
318	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
319	C₂²×C₃	—	2	1	no	—
320	C₂²×C₃	—	2	1	no	—
321	C₂²×C₃	—	2	1	no	—
322	C₂²×C₃	—	2	1	no	—
323	C₂²×C₃	—	2	2	no	—
324	C₂²×C₃	—	2	1	no	—
325	C₂²×C₃	—	2	1	no	—
326	C₂²×C₃	—	2	1	no	—
327	C₂²×C₃	—	2	1	no	—
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	—	2	1	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	—	2	2	no	—
332	C₂²×C₃	—	4	1	no	—
333	C₂²×C₃	—	4	1	no	—
334	C₂²×C₃	—	4	1	no	—
335	C₂²×C₃	—	4	1	no	—
336	C₂²×C₃	#3667	1	2	yes	complemented
337	C₂²×C₃	C₂²×Dic₉	1	1	yes	characteristic
338	C₂²×C₃	C₃×#208	1	2	yes	—
339	C₂²×C₃	C₂²×C₃×Dic₃	1	1	yes	characteristic
340	C₃×C₄	—	2	2	no	—
341	C₃×C₄	—	2	1	no	—
342	C₃×C₄	—	2	1	no	—
343	C₃×C₄	—	2	1	no	—
344	C₃×C₄	—	2	1	no	—
345	C₃×C₄	—	2	1	no	—
346	C₃×C₄	—	2	1	no	—
347	C₃×C₄	—	2	1	no	—
348	C₃×C₄	—	2	1	no	—
349	C₃×C₄	—	2	1	no	—
350	C₃×C₄	—	2	1	no	—
351	C₃×C₄	—	4	1	no	—
352	C₃×C₄	—	4	1	no	—
353	C₃×C₄	—	4	1	no	—
354	C₃×C₄	D₄×D₉	1	1	yes	characteristic
355	C₃×C₄	#3699	1	1	yes	characteristic
356	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
357	C₃×C₄	C₃×#237	1	1	yes	characteristic
358	C₃²	#5011	1	1	yes	characteristic
359	C₉	—	2	1	no	—
360	C₉	C₃×#435	1	1	yes	characteristic, complemented
361	C₂³	C₂×C₃×Dic₉	1	1	yes	characteristic
362	C₂³	C₂×C₃×Dic₉	1	1	yes	characteristic
363	D₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	C₂×C₃×Dic₉	1	1	yes	characteristic
369	C₂×C₄	C₂×C₃×Dic₉	1	1	yes	characteristic
370	C₂×C₄	C₂×C₃×Dic₉	1	1	yes	characteristic
371	C₂×C₄	C₂×C₃×Dic₉	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
373	C₈	—	9	2	no	—
374	C₈	—	18	1	no	—
375	C₈	—	18	1	no	—
376	C₈	—	18	1	no	—
377	C₂×C₃	—	2	2	no	—
378	C₂×C₃	—	2	2	no	—
379	C₂×C₃	—	2	1	no	—
380	C₂×C₃	—	2	1	no	—
381	C₂×C₃	—	2	1	no	—
382	C₂×C₃	—	4	2	no	—
383	C₂×C₃	—	4	2	no	—
384	C₂×C₃	—	4	1	no	—
385	C₂×C₃	—	4	1	no	—
386	C₂×C₃	C₂×#3667	1	1	yes	characteristic
387	C₂×C₃	D₄×Dic₉	1	1	yes	characteristic
388	C₂×C₃	#63510	1	1	yes	characteristic
389	C₂×C₃	C₂×C₃×#208	1	1	yes	characteristic
390	C₂×C₃	C₃×D₄×Dic₃	1	1	yes	characteristic
391	C₂×C₃	C₃×#948	1	1	yes	characteristic
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	C₃×#3667	1	2	yes	complemented
398	C₂²	C₂²×C₃×Dic₉	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	C₃×D₄×D₉	1	1	yes	characteristic
404	C₄	C₃×#3699	1	1	yes	characteristic
405	C₃	—	2	1	no	—
406	C₃	#10588688	1	1	yes	characteristic, direct product factor
407	C₃	C₃×#5011	1	1	yes	characteristic
408	C₂	—	2	2	no	—
409	C₂	—	4	1	no	—
410	C₂	C₂×C₃×#3667	1	1	yes	characteristic
411	C₂	C₃×D₄×Dic₉	1	1	yes	characteristic
412	C₂	C₃×#63510	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₉
commutator	C₂²×C₉	C₂²×C₃×C₄
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₄×D₄×C₉	C₂
socle	C₂²×C₃²	C₂²×Dic₃
prime radical	C₂×C₃²×D₄	Dic₃
cosocle	C₂×C₄×C₉	C₂³×C₃
hypercenter	C₃×C₄×D₄	D₉
hypocenter	C₉	C₃×#435
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#3667	C₂	semidirect
3. C₂²×C₃×C₉⋊C₈	C₂	semidirect
4. C₃×#63389	C₂	semidirect
5. C₃×#63389	C₂	semidirect
6. C₃×C₄⋊(C₉⋊C₈)	C₂	semidirect
7. C₃×#63362	C₂	semidirect
9. #10588688	C₃	direct (N × H)
32. C₂×#3667	C₂×C₃	semidirect
33. C₂²×C₉⋊C₈	C₂×C₃	semidirect
34. #63389	C₂×C₃	semidirect
35. #63389	C₂×C₃	semidirect
36. C₄⋊(C₉⋊C₈)	C₂×C₃	semidirect
37. #63362	C₂×C₃	semidirect
53. C₃×C₉⋊C₈	D₄	semidirect
94. C₂²×C₃×C₉	M₁₆	semidirect
160. C₉⋊C₈	C₃×D₄	semidirect
225. C₂²×C₉	C₃×M₁₆	semidirect
246. C₃×C₉	#435	semidirect
336. C₂²×C₃	#3667	semidirect
360. C₉	C₃×#435	semidirect
397. C₂²	C₃×#3667	semidirect
406. C₃	#10588688	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×D₄×C₉	2
C₂×C₃×#3667	2
C₂²×C₃×C₉⋊C₈	2
C₃×#63389	2
C₃×C₄⋊(C₉⋊C₈)	2
C₃×#63362	2
C₃×#5011	3
#10588688	3

Subgroups — C3×#10588688 #13142713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10588688 #13142713