Subgroups — C₃×#10589685 #13152689

Order 1728.

646 conjugacy classes of subgroups.

The subgroup lattice has 452 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×#63508	C₂	1	1	yes	maximal, characteristic
3	C₃×#63506	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63460	C₂	1	2	yes	maximal
5	C₃×#63459	C₂	1	1	yes	maximal, characteristic
6	C₃×#63452	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#63451	C₂	1	2	yes	maximal, complemented
8	C₃×#63438	C₂	1	2	yes	maximal
9	C₃×#63434	C₂	1	1	yes	maximal, characteristic
10	C₃×#63432	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5583	—	3	1	no	maximal
13	#10589685	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
16	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
17	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
18	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
20	C₃×C₄²×C₉	C₂²	1	2	yes	—
21	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
22	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
23	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
24	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
25	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
26	C₃×C₄⋊Dic₉	C₂²	1	2	yes	—
27	C₃×C₄⋊Dic₉	C₂²	1	2	yes	—
28	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
29	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
31	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
32	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
33	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
34	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
35	C₃×C₄×Dic₉	C₂²	1	2	yes	—
36	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
37	C₃²×C₄×Q₈	D₃	1	1	yes	characteristic
38	C₃×#946	—	3	1	no	—
39	C₃×#944	—	3	1	no	—
40	C₃×#898	—	3	2	no	—
41	C₃×#897	—	3	1	no	—
42	C₃×#890	—	3	1	no	—
43	C₃×#889	—	3	2	no	—
44	C₃×#876	—	3	2	no	—
45	C₃×#872	—	3	1	no	—
46	C₃×#870	—	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	#63508	C₂×C₃	1	1	yes	characteristic
51	#63506	C₂×C₃	1	1	yes	characteristic, complemented
52	#63460	C₂×C₃	1	2	yes	—
53	#63459	C₂×C₃	1	1	yes	characteristic
54	#63452	C₂×C₃	1	1	yes	characteristic, complemented
55	#63451	C₂×C₃	1	2	yes	complemented
56	#63438	C₂×C₃	1	2	yes	—
57	#63434	C₂×C₃	1	1	yes	characteristic
58	#63432	C₂×C₃	1	2	yes	complemented
59	C₄×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂²×C₃×D₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
65	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
66	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₃×Dic₉	C₂³	1	2	yes	—
68	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
69	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
70	C₂×C₃×Dic₉	C₂³	1	2	yes	—
71	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
72	C₃×C₄×D₉	—	2	2	no	—
73	C₃×Dic₁₈	—	2	2	no	—
74	C₃×#541	—	9	1	no	—
75	#5583	—	3	1	no	—
76	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
77	C₂×C₃×C₄×D₃	—	3	1	no	—
78	C₂×C₃×Dic₆	—	3	1	no	—
79	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
80	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
81	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
82	C₃²×C₄²	C₂×D₃	1	2	yes	—
83	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
84	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
85	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
86	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
87	C₃×C₄⋊Dic₃	—	3	2	no	—
88	C₃×C₄⋊Dic₃	—	3	2	no	—
89	C₃×C₄⋊Dic₃	—	3	1	no	—
90	C₃×Dic₃⋊C₄	—	3	1	no	—
91	C₃×Dic₃⋊C₄	—	3	2	no	—
92	C₃×Dic₃⋊C₄	—	3	2	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×C₄×Dic₃	—	3	2	no	—
98	C₃×C₄×Dic₃	—	3	1	no	—
99	C₂×Q₈×C₉	—	2	1	no	—
100	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
102	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
103	C₉×C₄⋊C₄	—	2	2	no	—
104	C₉×C₄⋊C₄	—	2	1	no	—
105	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
106	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	C₄²×C₉	—	2	1	no	—
108	C₄²×C₉	—	2	2	no	—
109	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
110	C₄²×C₉	C₂²×C₃	1	2	yes	—
111	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
112	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
115	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
116	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
117	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
118	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
119	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
120	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
121	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
122	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
125	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
126	C₄×Dic₉	C₂²×C₃	1	2	yes	—
127	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
128	C₂×C₃×D₉	—	2	1	no	—
129	C₂×C₃×D₉	—	2	1	no	—
130	C₂×C₃×D₉	—	2	1	no	—
131	C₃×C₄×C₉	—	2	2	no	—
132	C₃×C₄×C₉	—	2	1	no	—
133	C₃×C₄×C₉	—	2	1	no	—
134	C₃×C₄×C₉	—	2	2	no	—
135	C₃×C₄×C₉	#41	1	2	yes	—
136	C₃×Dic₉	—	2	2	no	—
137	C₃×Dic₉	—	2	1	no	—
138	C₃×Dic₉	—	2	2	no	—
139	C₃×Dic₉	—	2	1	no	—
140	C₃×Dic₉	—	2	1	no	—
141	C₃×C₄⋊Q₈	—	9	1	no	—
142	C₃×#126	—	9	2	no	—
143	C₃×#126	—	9	2	no	—
144	C₃×#125	—	9	2	no	—
145	C₃×#125	—	9	1	no	—
146	C₃×#125	—	9	2	no	—
147	C₃×C₂²⋊Q₈	—	9	1	no	—
148	C₃×C₂²⋊Q₈	—	9	1	no	—
149	C₃×C₄×Q₈	—	2	1	no	—
150	C₃×C₄×Q₈	—	9	1	no	—
151	C₃×C₄×Q₈	D₉	1	1	yes	characteristic, complemented
152	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
153	C₃×#117	—	9	1	no	—
154	#946	—	3	1	no	—
155	#944	—	3	1	no	—
156	#898	—	3	2	no	—
157	#897	—	3	1	no	—
158	#890	—	3	1	no	—
159	#889	—	3	2	no	—
160	#876	—	3	2	no	—
161	#872	—	3	1	no	—
162	#870	—	3	2	no	—
163	C₄×Dic₆	—	3	1	no	—
164	C₂²×C₃×D₃	—	3	1	no	—
165	C₃²×Q₈	—	2	2	no	—
166	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
167	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
168	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
169	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
170	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
171	C₂×C₃×Dic₃	—	3	1	no	—
172	C₂×C₃×Dic₃	—	3	2	no	—
173	C₂×C₃×Dic₃	—	3	1	no	—
174	C₂×C₃×Dic₃	—	3	2	no	—
175	C₂×C₃×Dic₃	—	3	1	no	—
176	C₃×C₄×D₃	—	6	2	no	—
177	C₃×Dic₆	—	6	2	no	—
178	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
179	Q₈×C₉	—	2	4	no	—
180	Q₈×C₉	—	2	2	no	—
181	C₂×C₄×C₉	—	2	1	no	—
182	C₂×C₄×C₉	—	2	2	no	—
183	C₂×C₄×C₉	—	2	1	no	—
184	C₂×C₄×C₉	—	2	1	no	—
185	C₂×C₄×C₉	—	2	2	no	—
186	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
187	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
188	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
189	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
190	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
191	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
192	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
193	C₂×Dic₉	C₂³×C₃	1	2	yes	—
194	C₂×Dic₉	C₂³×C₃	1	2	yes	—
195	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
196	C₄×D₉	—	2	2	no	—
197	Dic₁₈	—	2	2	no	—
198	#541	—	9	1	no	Sylow
199	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
200	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
201	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
202	C₃×D₉	—	4	1	no	—
203	C₂×C₃×Q₈	—	2	1	no	—
204	C₂×C₃×Q₈	—	9	1	no	—
205	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic
206	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
207	C₂²×C₃×C₄	—	9	1	no	—
208	C₂×C₄×D₃	—	3	1	no	—
209	C₂×Dic₆	—	3	1	no	—
210	C₃×C₄⋊C₄	—	2	1	no	—
211	C₃×C₄⋊C₄	—	2	2	no	—
212	C₃×C₄⋊C₄	—	9	1	no	—
213	C₃×C₄⋊C₄	—	9	1	no	—
214	C₃×C₄⋊C₄	—	9	2	no	—
215	C₃×C₄⋊C₄	—	9	2	no	—
216	C₃×C₄⋊C₄	—	9	2	no	—
217	C₃×C₄⋊C₄	—	9	2	no	—
218	C₃×C₄⋊C₄	—	9	2	no	—
219	C₃×C₄⋊C₄	—	9	1	no	—
220	C₃×C₄⋊C₄	—	9	2	no	—
221	C₃×C₄⋊C₄	—	9	2	no	—
222	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
223	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	—
224	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
225	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
226	C₃×C₂²⋊C₄	—	9	1	no	—
227	C₃×C₂²⋊C₄	—	9	1	no	—
228	C₃×C₂²⋊C₄	—	9	2	no	—
229	C₃×C₂²⋊C₄	—	9	2	no	—
230	C₃×C₄²	—	2	1	no	—
231	C₃×C₄²	—	2	2	no	—
232	C₃×C₄²	—	9	1	no	—
233	C₃×C₄²	—	9	2	no	—
234	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
235	C₃×C₄²	C₂×D₉	1	2	yes	—
236	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
237	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
238	(C₂×D₃)⋊C₄	—	3	1	no	—
239	(C₂×D₃)⋊C₄	—	3	1	no	—
240	(C₂×D₃)⋊C₄	—	3	2	no	—
241	(C₂×D₃)⋊C₄	—	3	2	no	—
242	C₄⋊Dic₃	—	3	1	no	—
243	C₄⋊Dic₃	—	3	2	no	—
244	C₄⋊Dic₃	—	3	2	no	—
245	Dic₃⋊C₄	—	3	2	no	—
246	Dic₃⋊C₄	—	3	1	no	—
247	Dic₃⋊C₄	—	3	2	no	—
248	Dic₃⋊C₄	—	3	2	no	—
249	Dic₃⋊C₄	—	3	1	no	—
250	Dic₃⋊C₄	—	3	2	no	—
251	Dic₃⋊C₄	—	3	2	no	—
252	C₄×Dic₃	—	3	2	no	—
253	C₄×Dic₃	—	3	1	no	—
254	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
255	C₂×C₃×D₃	—	6	1	no	—
256	C₂×C₃×D₃	—	6	1	no	—
257	C₂×C₃×D₃	—	6	1	no	—
258	C₃²×C₄	—	2	2	no	—
259	C₃²×C₄	—	2	1	no	—
260	C₃²×C₄	—	2	1	no	—
261	C₃²×C₄	—	2	2	no	—
262	C₃²×C₄	#235	1	2	yes	—
263	C₃×Dic₃	—	6	2	no	—
264	C₃×Dic₃	—	6	1	no	—
265	C₃×Dic₃	—	6	2	no	—
266	C₃×Dic₃	—	6	1	no	—
267	C₃×Dic₃	—	6	1	no	—
268	C₂²×C₉	—	2	1	no	—
269	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
270	C₂×D₉	—	2	1	no	—
271	C₂×D₉	—	2	1	no	—
272	C₂×D₉	—	2	1	no	—
273	C₄×C₉	—	2	2	no	—
274	C₄×C₉	—	2	4	no	—
275	C₄×C₉	—	2	2	no	—
276	C₄×C₉	—	2	1	no	—
277	C₄×C₉	—	2	1	no	—
278	C₄×C₉	—	2	2	no	—
279	C₄×C₉	—	2	2	no	—
280	C₄×C₉	—	4	1	no	—
281	C₄×C₉	—	4	2	no	—
282	C₄×C₉	C₃×#41	1	2	yes	—
283	Dic₉	—	2	2	no	—
284	Dic₉	—	2	1	no	—
285	Dic₉	—	2	1	no	—
286	Dic₉	—	2	2	no	—
287	Dic₉	—	2	1	no	—
288	C₄⋊Q₈	—	9	1	no	—
289	#126	—	9	2	no	—
290	#126	—	9	2	no	—
291	#125	—	9	2	no	—
292	#125	—	9	1	no	—
293	#125	—	9	2	no	—
294	C₂²⋊Q₈	—	9	1	no	—
295	C₂²⋊Q₈	—	9	1	no	—
296	C₄×Q₈	—	9	1	no	—
297	C₄×Q₈	C₃×D₉	1	1	yes	characteristic, complemented
298	#117	—	9	1	no	—
299	C₃×C₉	#541	1	1	yes	characteristic, complemented, Sylow
300	C₂³×C₃	—	9	1	no	—
301	C₂²×D₃	—	3	1	no	—
302	C₃×Q₈	—	2	4	no	—
303	C₃×Q₈	—	2	2	no	—
304	C₃×Q₈	—	2	2	no	—
305	C₃×Q₈	—	18	2	no	—
306	C₂×C₃×C₄	—	2	1	no	—
307	C₂×C₃×C₄	—	2	2	no	—
308	C₂×C₃×C₄	—	2	1	no	—
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	9	1	no	—
312	C₂×C₃×C₄	—	9	2	no	—
313	C₂×C₃×C₄	—	9	1	no	—
314	C₂×C₃×C₄	—	9	2	no	—
315	C₂×C₃×C₄	—	9	1	no	—
316	C₂×C₃×C₄	—	18	2	no	—
317	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
319	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
320	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
321	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
325	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
326	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
327	C₂×Dic₃	—	3	1	no	—
328	C₂×Dic₃	—	3	2	no	—
329	C₂×Dic₃	—	3	1	no	—
330	C₂×Dic₃	—	3	2	no	—
331	C₂×Dic₃	—	3	1	no	—
332	C₄×D₃	—	6	2	no	—
333	Dic₆	—	6	2	no	—
334	C₂×C₃²	C₂×#235	1	1	yes	characteristic
335	C₂×C₃²	#1007	1	1	yes	characteristic
336	C₂×C₃²	#1010	1	1	yes	characteristic
337	C₃×D₃	—	12	1	no	—
338	C₂×C₉	—	2	1	no	—
339	C₂×C₉	—	2	1	no	—
340	C₂×C₉	—	2	1	no	—
341	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
342	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
343	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
344	D₉	—	4	1	no	—
345	C₂×Q₈	—	9	1	no	—
346	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic
347	C₂²×C₄	—	9	1	no	—
348	C₄⋊C₄	—	9	1	no	—
349	C₄⋊C₄	—	9	1	no	—
350	C₄⋊C₄	—	9	1	no	—
351	C₄⋊C₄	—	9	2	no	—
352	C₄⋊C₄	—	9	2	no	—
353	C₄⋊C₄	—	9	2	no	—
354	C₄⋊C₄	—	9	2	no	—
355	C₄⋊C₄	—	9	2	no	—
356	C₄⋊C₄	—	9	2	no	—
357	C₄⋊C₄	—	9	2	no	—
358	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
359	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	—
360	C₂²⋊C₄	—	9	1	no	—
361	C₂²⋊C₄	—	9	1	no	—
362	C₂²⋊C₄	—	9	2	no	—
363	C₂²⋊C₄	—	9	2	no	—
364	C₄²	—	9	1	no	—
365	C₄²	—	9	2	no	—
366	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
367	C₄²	C₂×C₃×D₉	1	2	yes	—
368	C₂²×C₃	—	2	1	no	—
369	C₂²×C₃	—	18	1	no	—
370	C₂²×C₃	—	18	1	no	—
371	C₂²×C₃	—	18	1	no	—
372	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
373	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
374	C₂×D₃	—	6	1	no	—
375	C₂×D₃	—	6	1	no	—
376	C₂×D₃	—	6	1	no	—
377	C₃×C₄	—	2	4	no	—
378	C₃×C₄	—	2	2	no	—
379	C₃×C₄	—	2	2	no	—
380	C₃×C₄	—	2	1	no	—
381	C₃×C₄	—	2	1	no	—
382	C₃×C₄	—	2	2	no	—
383	C₃×C₄	—	2	2	no	—
384	C₃×C₄	—	2	1	no	—
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	2	2	no	—
387	C₃×C₄	—	2	2	no	—
388	C₃×C₄	—	4	1	no	—
389	C₃×C₄	—	4	2	no	—
390	C₃×C₄	—	18	1	no	—
391	C₃×C₄	—	18	2	no	—
392	C₃×C₄	—	18	1	no	—
393	C₃×C₄	—	18	2	no	—
394	C₃×C₄	—	18	1	no	—
395	C₃×C₄	#3697	1	2	yes	—
396	C₃×C₄	C₃×#235	1	2	yes	—
397	Dic₃	—	6	2	no	—
398	Dic₃	—	6	1	no	—
399	Dic₃	—	6	2	no	—
400	Dic₃	—	6	1	no	—
401	Dic₃	—	6	1	no	—
402	C₃²	#5583	1	1	yes	characteristic
403	C₉	—	2	1	no	—
404	C₉	C₃×#541	1	1	yes	characteristic, complemented
405	C₂³	—	9	1	no	—
406	Q₈	—	2	2	no	—
407	Q₈	—	18	2	no	—
408	C₂×C₄	—	9	1	no	—
409	C₂×C₄	—	9	2	no	—
410	C₂×C₄	—	9	1	no	—
411	C₂×C₄	—	9	2	no	—
412	C₂×C₄	—	9	1	no	—
413	C₂×C₄	—	18	2	no	—
414	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
417	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
418	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
419	C₂×C₃	—	2	1	no	—
420	C₂×C₃	—	2	1	no	—
421	C₂×C₃	—	2	1	no	—
422	C₂×C₃	—	36	1	no	—
423	C₂×C₃	C₂×#3697	1	1	yes	characteristic
424	C₂×C₃	#63713	1	1	yes	characteristic
425	C₂×C₃	#63716	1	1	yes	characteristic
426	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
427	C₂×C₃	C₃×#1007	1	1	yes	characteristic
428	C₂×C₃	C₃×#1010	1	1	yes	characteristic
429	D₃	—	12	1	no	—
430	C₂²	—	18	1	no	—
431	C₂²	—	18	1	no	—
432	C₂²	—	18	1	no	—
433	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	2	no	—
438	C₄	—	18	1	no	—
439	C₄	—	18	2	no	—
440	C₄	—	18	1	no	—
441	C₄	—	18	2	no	—
442	C₄	—	18	1	no	—
443	C₄	C₃×#3697	1	2	yes	—
444	C₃	—	2	1	no	—
445	C₃	#10589685	1	1	yes	characteristic, direct product factor
446	C₃	C₃×#5583	1	1	yes	characteristic
447	C₂	—	36	1	no	—
448	C₂	C₂×C₃×#3697	1	1	yes	characteristic
449	C₂	C₃×#63713	1	1	yes	characteristic
450	C₂	C₃×#63716	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	C₂²×C₃×D₉	C₂³
hypercenter	C₃×C₄×Q₈	D₉
hypocenter	C₉	C₃×#541
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
6. C₃×#63452	C₂	semidirect
7. C₃×#63451	C₂	semidirect
10. C₃×#63432	C₂	semidirect
11. C₃×C₄×Dic₁₈	C₂	semidirect
13. #10589685	C₃	direct (N × H)
49. C₄×Q₈×C₉	C₂×C₃	semidirect
51. #63506	C₂×C₃	semidirect
54. #63452	C₂×C₃	semidirect
55. #63451	C₂×C₃	semidirect
58. #63432	C₂×C₃	semidirect
59. C₄×Dic₁₈	C₂×C₃	semidirect
151. C₃×C₄×Q₈	D₉	semidirect
297. C₄×Q₈	C₃×D₉	semidirect
299. C₃×C₉	#541	semidirect
404. C₉	C₃×#541	semidirect
445. C₃	#10589685	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×#63508	2
C₃×#63506	2
C₃×#63460	2
C₃×#63459	2
C₃×#63452	2
C₃×#63451	2
C₃×#63438	2
C₃×#63434	2
C₃×#63432	2
C₃×C₄×Dic₁₈	2
C₃×#5583	3
#10589685	3

Subgroups — C3×#10589685 #13152689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589685 #13152689