Subgroups — C₃×#10589670 #13152669

Order 1728.

706 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#63509	C₂	1	1	yes	maximal, characteristic
3	C₃×#63506	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63460	C₂	1	2	yes	maximal, complemented
5	C₃×#63458	C₂	1	2	yes	maximal, complemented
6	C₃×#63455	C₂	1	1	yes	maximal, characteristic
7	C₃×#63449	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#63438	C₂	1	2	yes	maximal, complemented
9	C₃×#63437	C₂	1	1	yes	maximal, characteristic
10	C₃×#63434	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5568	—	3	1	no	maximal
13	#10589670	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
17	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
18	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
19	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
21	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
22	C₃×C₄²×C₉	C₂²	1	2	yes	—
23	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
24	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
25	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
26	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
27	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
28	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
29	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
32	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
33	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
34	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
35	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
36	C₃×C₄×Dic₉	C₂²	1	2	yes	—
37	C₃²×C₄×Q₈	D₃	1	1	yes	characteristic
38	C₃×#947	—	3	1	no	—
39	C₃×#944	—	3	1	no	—
40	C₃×#898	—	3	2	no	—
41	C₃×#896	—	3	2	no	—
42	C₃×#893	—	3	1	no	—
43	C₃×#887	—	3	1	no	—
44	C₃×#876	—	3	2	no	—
45	C₃×#875	—	3	1	no	—
46	C₃×#872	—	3	2	no	—
47	C₃×C₄×Dic₆	—	3	1	no	—
48	C₄×Q₈×C₉	—	2	1	no	—
49	C₄×Q₈×C₉	C₂×C₃	1	1	yes	characteristic, complemented
50	#63509	C₂×C₃	1	1	yes	characteristic
51	#63506	C₂×C₃	1	1	yes	characteristic, complemented
52	#63460	C₂×C₃	1	2	yes	complemented
53	#63458	C₂×C₃	1	2	yes	complemented
54	#63455	C₂×C₃	1	1	yes	characteristic
55	#63449	C₂×C₃	1	1	yes	characteristic, complemented
56	#63438	C₂×C₃	1	2	yes	complemented
57	#63437	C₂×C₃	1	1	yes	characteristic
58	#63434	C₂×C₃	1	2	yes	complemented
59	C₄×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂²×C₃×D₉	C₂³	1	2	yes	—
61	C₃×Q₈×C₉	—	2	2	no	—
62	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
64	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
65	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
68	C₂×C₃×Dic₉	C₂³	1	2	yes	—
69	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
70	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
71	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
72	C₃×D₃₆	—	2	2	no	—
73	C₃×C₄×D₉	—	2	4	no	—
74	C₃×Dic₁₈	—	2	2	no	—
75	C₃×Dic₁₈	—	2	2	no	—
76	C₃×#556	—	9	1	no	—
77	#5568	—	3	1	no	—
78	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
79	C₂×C₃×D₁₂	—	3	1	no	—
80	C₂×C₃×C₄×D₃	—	3	2	no	—
81	C₂×C₃×Dic₆	—	3	1	no	—
82	C₂×C₃×Dic₆	—	3	1	no	—
83	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
84	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
85	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
86	C₃²×C₄²	C₂×D₃	1	2	yes	—
87	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
88	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
89	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
90	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
91	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
92	C₃×C₄⋊Dic₃	—	3	1	no	—
93	C₃×Dic₃⋊C₄	—	3	2	no	—
94	C₃×Dic₃⋊C₄	—	3	2	no	—
95	C₃×Dic₃⋊C₄	—	3	2	no	—
96	C₃×Dic₃⋊C₄	—	3	1	no	—
97	C₃×Dic₃⋊C₄	—	3	1	no	—
98	C₃×C₄×Dic₃	—	3	2	no	—
99	C₃×C₄×Dic₃	—	3	1	no	—
100	C₃×C₄×Dic₃	—	3	1	no	—
101	C₂×Q₈×C₉	—	2	1	no	—
102	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
103	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
105	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
106	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
107	C₉×C₄⋊C₄	—	2	1	no	—
108	C₉×C₄⋊C₄	—	2	2	no	—
109	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
110	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
111	C₄²×C₉	—	2	1	no	—
112	C₄²×C₉	—	2	2	no	—
113	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
114	C₄²×C₉	C₂²×C₃	1	2	yes	—
115	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
116	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
117	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
118	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
119	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
120	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
121	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
122	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
123	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
126	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
127	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
128	C₄×Dic₉	C₂²×C₃	1	2	yes	—
129	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
130	C₂×C₃×D₉	—	2	2	no	—
131	C₂×C₃×D₉	—	2	2	no	—
132	C₂×C₃×D₉	—	2	2	no	—
133	C₃×C₄×C₉	—	2	2	no	—
134	C₃×C₄×C₉	—	2	1	no	—
135	C₃×C₄×C₉	—	2	2	no	—
136	C₃×C₄×C₉	—	2	1	no	—
137	C₃×C₄×C₉	#41	1	2	yes	—
138	C₃×Dic₉	—	2	2	no	—
139	C₃×Dic₉	—	2	1	no	—
140	C₃×Dic₉	—	2	1	no	—
141	C₃×Dic₉	—	2	1	no	—
142	C₃×Dic₉	#41	1	2	yes	—
143	C₃×C₄⋊Q₈	—	9	1	no	—
144	C₃×#126	—	9	2	no	—
145	C₃×#126	—	9	2	no	—
146	C₃×#124	—	9	1	no	—
147	C₃×#124	—	9	1	no	—
148	C₃×C₂²⋊Q₈	—	9	2	no	—
149	C₃×C₄×Q₈	—	2	1	no	—
150	C₃×C₄×Q₈	—	9	1	no	—
151	C₃×C₄×Q₈	—	9	1	no	—
152	C₃×C₄×Q₈	D₉	1	1	yes	characteristic, complemented
153	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
154	C₃×C₄×D₄	—	9	1	no	—
155	C₃×#117	—	9	2	no	—
156	#947	—	3	1	no	—
157	#944	—	3	1	no	—
158	#898	—	3	2	no	—
159	#896	—	3	2	no	—
160	#893	—	3	1	no	—
161	#887	—	3	1	no	—
162	#876	—	3	2	no	—
163	#875	—	3	1	no	—
164	#872	—	3	2	no	—
165	C₄×Dic₆	—	3	1	no	—
166	C₂²×C₃×D₃	—	3	2	no	—
167	C₃²×Q₈	—	2	2	no	—
168	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
169	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
170	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
171	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
172	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
173	C₂×C₃×Dic₃	—	3	1	no	—
174	C₂×C₃×Dic₃	—	3	1	no	—
175	C₂×C₃×Dic₃	—	3	1	no	—
176	C₂×C₃×Dic₃	—	3	2	no	—
177	C₂×C₃×Dic₃	—	3	1	no	—
178	C₃×D₁₂	—	6	2	no	—
179	C₃×C₄×D₃	—	6	4	no	—
180	C₃×Dic₆	—	6	2	no	—
181	C₃×Dic₆	—	6	2	no	—
182	C₂²×D₉	C₂³×C₃	1	2	yes	—
183	Q₈×C₉	—	2	4	no	—
184	Q₈×C₉	—	2	2	no	—
185	C₂×C₄×C₉	—	2	1	no	—
186	C₂×C₄×C₉	—	2	2	no	—
187	C₂×C₄×C₉	—	2	1	no	—
188	C₂×C₄×C₉	—	2	2	no	—
189	C₂×C₄×C₉	—	2	1	no	—
190	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
191	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
192	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
193	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
194	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
195	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
196	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
197	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
198	C₂×Dic₉	C₂³×C₃	1	2	yes	—
199	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
200	D₃₆	—	2	2	no	—
201	C₄×D₉	—	2	4	no	—
202	Dic₁₈	—	2	2	no	—
203	Dic₁₈	—	2	2	no	—
204	#556	—	9	1	no	Sylow
205	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
206	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
207	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
208	C₃×D₉	—	4	2	no	—
209	C₂×C₃×Q₈	—	2	1	no	—
210	C₂×C₃×Q₈	—	9	1	no	—
211	C₂×C₃×Q₈	—	9	1	no	—
212	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic
213	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
214	C₂×C₃×D₄	—	9	1	no	—
215	C₂²×C₃×C₄	—	9	2	no	—
216	C₂×D₁₂	—	3	1	no	—
217	C₂×C₄×D₃	—	3	2	no	—
218	C₂×Dic₆	—	3	1	no	—
219	C₂×Dic₆	—	3	1	no	—
220	C₃×C₄⋊C₄	—	2	1	no	—
221	C₃×C₄⋊C₄	—	2	2	no	—
222	C₃×C₄⋊C₄	—	9	1	no	—
223	C₃×C₄⋊C₄	—	9	2	no	—
224	C₃×C₄⋊C₄	—	9	2	no	—
225	C₃×C₄⋊C₄	—	9	1	no	—
226	C₃×C₄⋊C₄	—	9	2	no	—
227	C₃×C₄⋊C₄	—	9	1	no	—
228	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
229	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	—
230	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
231	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
232	C₃×C₂²⋊C₄	—	9	2	no	—
233	C₃×C₂²⋊C₄	—	9	2	no	—
234	C₃×C₂²⋊C₄	—	9	2	no	—
235	C₃×C₂²⋊C₄	—	9	2	no	—
236	C₃×C₂²⋊C₄	—	9	2	no	—
237	C₃×C₄²	—	2	2	no	—
238	C₃×C₄²	—	2	1	no	—
239	C₃×C₄²	—	9	2	no	—
240	C₃×C₄²	—	9	1	no	—
241	C₃×C₄²	—	9	1	no	—
242	C₃×C₄²	C₂×D₉	1	2	yes	—
243	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
244	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
245	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
246	(C₂×D₃)⋊C₄	—	3	2	no	—
247	(C₂×D₃)⋊C₄	—	3	2	no	—
248	(C₂×D₃)⋊C₄	—	3	2	no	—
249	(C₂×D₃)⋊C₄	—	3	2	no	—
250	(C₂×D₃)⋊C₄	—	3	2	no	—
251	C₄⋊Dic₃	—	3	1	no	—
252	Dic₃⋊C₄	—	3	1	no	—
253	Dic₃⋊C₄	—	3	1	no	—
254	Dic₃⋊C₄	—	3	2	no	—
255	Dic₃⋊C₄	—	3	2	no	—
256	Dic₃⋊C₄	—	3	2	no	—
257	C₄×Dic₃	—	3	1	no	—
258	C₄×Dic₃	—	3	1	no	—
259	C₄×Dic₃	—	3	2	no	—
260	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
261	C₂×C₃×D₃	—	6	2	no	—
262	C₂×C₃×D₃	—	6	2	no	—
263	C₂×C₃×D₃	—	6	2	no	—
264	C₃²×C₄	—	2	2	no	—
265	C₃²×C₄	—	2	1	no	—
266	C₃²×C₄	—	2	1	no	—
267	C₃²×C₄	—	2	2	no	—
268	C₃²×C₄	#235	1	2	yes	—
269	C₃×Dic₃	—	3	2	no	—
270	C₃×Dic₃	—	6	2	no	—
271	C₃×Dic₃	—	6	1	no	—
272	C₃×Dic₃	—	6	1	no	—
273	C₃×Dic₃	—	6	1	no	—
274	C₂²×C₉	—	2	1	no	—
275	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
276	C₂×D₉	—	2	2	no	—
277	C₂×D₉	—	2	2	no	—
278	C₂×D₉	—	2	2	no	—
279	C₄×C₉	—	2	2	no	—
280	C₄×C₉	—	2	4	no	—
281	C₄×C₉	—	2	1	no	—
282	C₄×C₉	—	2	2	no	—
283	C₄×C₉	—	2	2	no	—
284	C₄×C₉	—	2	1	no	—
285	C₄×C₉	—	2	2	no	—
286	C₄×C₉	—	4	1	no	—
287	C₄×C₉	—	4	2	no	—
288	C₄×C₉	C₃×#41	1	2	yes	—
289	Dic₉	—	2	2	no	—
290	Dic₉	—	2	1	no	—
291	Dic₉	—	2	1	no	—
292	Dic₉	—	2	1	no	—
293	Dic₉	C₃×#41	1	2	yes	—
294	C₄⋊Q₈	—	9	1	no	—
295	#126	—	9	2	no	—
296	#126	—	9	2	no	—
297	#124	—	9	1	no	—
298	#124	—	9	1	no	—
299	C₂²⋊Q₈	—	9	2	no	—
300	C₄×Q₈	—	9	1	no	—
301	C₄×Q₈	—	9	1	no	—
302	C₄×Q₈	C₃×D₉	1	1	yes	characteristic, complemented
303	C₄×D₄	—	9	1	no	—
304	#117	—	9	2	no	—
305	C₃×C₉	#556	1	1	yes	characteristic, complemented, Sylow
306	C₂³×C₃	—	9	2	no	—
307	C₂²×D₃	—	3	2	no	—
308	C₃×Q₈	—	2	4	no	—
309	C₃×Q₈	—	2	2	no	—
310	C₃×Q₈	—	2	2	no	—
311	C₃×Q₈	—	18	2	no	—
312	C₃×Q₈	—	18	2	no	—
313	C₃×D₄	—	18	2	no	—
314	C₂×C₃×C₄	—	2	1	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	1	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	1	no	—
319	C₂×C₃×C₄	—	9	1	no	—
320	C₂×C₃×C₄	—	9	1	no	—
321	C₂×C₃×C₄	—	9	1	no	—
322	C₂×C₃×C₄	—	9	2	no	—
323	C₂×C₃×C₄	—	9	1	no	—
324	C₂×C₃×C₄	—	18	4	no	—
325	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
326	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
328	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
331	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
333	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
335	C₂×Dic₃	—	3	1	no	—
336	C₂×Dic₃	—	3	1	no	—
337	C₂×Dic₃	—	3	1	no	—
338	C₂×Dic₃	—	3	2	no	—
339	C₂×Dic₃	—	3	1	no	—
340	D₁₂	—	6	2	no	—
341	C₄×D₃	—	6	4	no	—
342	Dic₆	—	6	2	no	—
343	Dic₆	—	6	2	no	—
344	C₂×C₃²	C₂×#235	1	1	yes	characteristic
345	C₂×C₃²	#1007	1	1	yes	characteristic
346	C₂×C₃²	D₃×#41	1	1	yes	characteristic
347	C₃×D₃	—	12	2	no	—
348	C₂×C₉	—	2	1	no	—
349	C₂×C₉	—	2	1	no	—
350	C₂×C₉	—	2	1	no	—
351	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
352	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
353	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
354	D₉	—	4	2	no	—
355	C₂×Q₈	—	9	1	no	—
356	C₂×Q₈	—	9	1	no	—
357	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic
358	C₂×D₄	—	9	1	no	—
359	C₂²×C₄	—	9	2	no	—
360	C₄⋊C₄	—	9	1	no	—
361	C₄⋊C₄	—	9	2	no	—
362	C₄⋊C₄	—	9	2	no	—
363	C₄⋊C₄	—	9	1	no	—
364	C₄⋊C₄	—	9	1	no	—
365	C₄⋊C₄	—	9	2	no	—
366	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
367	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	—
368	C₂²⋊C₄	—	9	2	no	—
369	C₂²⋊C₄	—	9	2	no	—
370	C₂²⋊C₄	—	9	2	no	—
371	C₂²⋊C₄	—	9	2	no	—
372	C₂²⋊C₄	—	9	2	no	—
373	C₄²	—	9	2	no	—
374	C₄²	—	9	1	no	—
375	C₄²	—	9	1	no	—
376	C₄²	C₂×C₃×D₉	1	2	yes	—
377	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
378	C₂²×C₃	—	2	1	no	—
379	C₂²×C₃	—	18	2	no	—
380	C₂²×C₃	—	18	2	no	—
381	C₂²×C₃	—	18	2	no	—
382	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
383	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
384	C₂×D₃	—	6	2	no	—
385	C₂×D₃	—	6	2	no	—
386	C₂×D₃	—	6	2	no	—
387	C₃×C₄	—	2	4	no	—
388	C₃×C₄	—	2	2	no	—
389	C₃×C₄	—	2	2	no	—
390	C₃×C₄	—	2	1	no	—
391	C₃×C₄	—	2	1	no	—
392	C₃×C₄	—	2	2	no	—
393	C₃×C₄	—	2	2	no	—
394	C₃×C₄	—	2	1	no	—
395	C₃×C₄	—	2	2	no	—
396	C₃×C₄	—	2	1	no	—
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	—	4	2	no	—
399	C₃×C₄	—	4	1	no	—
400	C₃×C₄	—	9	2	no	—
401	C₃×C₄	—	18	2	no	—
402	C₃×C₄	—	18	1	no	—
403	C₃×C₄	—	18	1	no	—
404	C₃×C₄	—	18	1	no	—
405	C₃×C₄	#3697	1	2	yes	—
406	C₃×C₄	C₃×#235	1	2	yes	—
407	Dic₃	—	3	2	no	—
408	Dic₃	—	6	2	no	—
409	Dic₃	—	6	1	no	—
410	Dic₃	—	6	1	no	—
411	Dic₃	—	6	1	no	—
412	C₃²	#5568	1	1	yes	characteristic
413	C₉	—	2	1	no	—
414	C₉	C₃×#556	1	1	yes	characteristic, complemented
415	C₂³	—	9	2	no	—
416	Q₈	—	2	2	no	—
417	Q₈	—	18	2	no	—
418	Q₈	—	18	2	no	—
419	D₄	—	18	2	no	—
420	C₂×C₄	—	9	1	no	—
421	C₂×C₄	—	9	1	no	—
422	C₂×C₄	—	9	1	no	—
423	C₂×C₄	—	9	2	no	—
424	C₂×C₄	—	9	1	no	—
425	C₂×C₄	—	18	4	no	—
426	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
427	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
429	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
431	C₂×C₃	—	2	1	no	—
432	C₂×C₃	—	2	1	no	—
433	C₂×C₃	—	2	1	no	—
434	C₂×C₃	—	36	2	no	—
435	C₂×C₃	C₂×#3697	1	1	yes	characteristic
436	C₂×C₃	#63713	1	1	yes	characteristic
437	C₂×C₃	#41×D₉	1	1	yes	characteristic
438	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
439	C₂×C₃	C₃×#1007	1	1	yes	characteristic
440	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
441	D₃	—	12	2	no	—
442	C₂²	—	18	2	no	—
443	C₂²	—	18	2	no	—
444	C₂²	—	18	2	no	—
445	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	1	no	—
450	C₄	—	9	2	no	—
451	C₄	—	18	2	no	—
452	C₄	—	18	1	no	—
453	C₄	—	18	1	no	—
454	C₄	—	18	1	no	—
455	C₄	C₃×#3697	1	2	yes	—
456	C₃	—	2	1	no	—
457	C₃	#10589670	1	1	yes	characteristic, direct product factor
458	C₃	C₃×#5568	1	1	yes	characteristic
459	C₂	—	36	2	no	—
460	C₂	C₂×C₃×#3697	1	1	yes	characteristic
461	C₂	C₃×#63713	1	1	yes	characteristic
462	C₂	C₃×#41×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₄×Q₈×C₉	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₂×C₃×D₃₆	C₂²
hypercenter	C₃×C₄×Q₈	D₉
hypocenter	C₉	C₃×#556
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×Q₈×C₉	C₂	semidirect
3. C₃×#63506	C₂	semidirect
4. C₃×#63460	C₂	semidirect
5. C₃×#63458	C₂	semidirect
7. C₃×#63449	C₂	semidirect
8. C₃×#63438	C₂	semidirect
10. C₃×#63434	C₂	semidirect
11. C₃×C₄×Dic₁₈	C₂	semidirect
13. #10589670	C₃	direct (N × H)
49. C₄×Q₈×C₉	C₂×C₃	semidirect
51. #63506	C₂×C₃	semidirect
52. #63460	C₂×C₃	semidirect
53. #63458	C₂×C₃	semidirect
55. #63449	C₂×C₃	semidirect
56. #63438	C₂×C₃	semidirect
58. #63434	C₂×C₃	semidirect
59. C₄×Dic₁₈	C₂×C₃	semidirect
152. C₃×C₄×Q₈	D₉	semidirect
302. C₄×Q₈	C₃×D₉	semidirect
305. C₃×C₉	#556	semidirect
414. C₉	C₃×#556	semidirect
457. C₃	#10589670	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×Q₈×C₉	2
C₃×#63509	2
C₃×#63506	2
C₃×#63460	2
C₃×#63458	2
C₃×#63455	2
C₃×#63449	2
C₃×#63438	2
C₃×#63437	2
C₃×#63434	2
C₃×C₄×Dic₁₈	2
C₃×#5568	3
#10589670	3

Subgroups — C3×#10589670 #13152669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589670 #13152669