Subgroups — C₃×#10589781 #13153093

Order 1728.

820 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#63508	C₂	1	2	yes	maximal, complemented
3	C₃×#63499	C₂	1	1	yes	maximal, characteristic
4	C₃×#63497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#63445	C₂	1	2	yes	maximal, complemented
6	C₃×#611⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₃×C₂²⋊C₄×D₉	C₂	1	2	yes	maximal, complemented
8	C₃×#63441	C₂	1	2	yes	maximal, complemented
9	C₃×#63434	C₂	1	2	yes	maximal, complemented
10	C₃×#5679	—	3	1	no	maximal
11	#10589781	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂³×C₃×D₉	C₂²	1	1	yes	characteristic
13	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×#611	C₂²	1	2	yes	—
16	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
18	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
19	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
21	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
22	C₃×#3676	C₂²	1	2	yes	—
23	C₃×#3676	C₂²	1	1	yes	characteristic
24	C₃×#3676	C₂²	1	1	yes	characteristic, complemented
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	2	yes	complemented
29	C₃×Dic₉⋊C₄	C₂²	1	2	yes	complemented
30	C₃×Dic₉⋊C₄	C₂²	1	2	yes	complemented
31	C₃×Dic₉⋊C₄	C₂²	1	2	yes	complemented
32	C₃×C₄×Dic₉	C₂²	1	2	yes	complemented
33	C₃²×#124	D₃	1	1	yes	characteristic
34	C₃×#946	—	3	2	no	—
35	C₃×#937	—	3	1	no	—
36	C₃×#935	—	3	1	no	—
37	C₃×#883	—	3	2	no	—
38	C₃×#67⋊C₄	—	3	2	no	—
39	C₃×D₃×C₂²⋊C₄	—	3	2	no	—
40	C₃×#879	—	3	2	no	—
41	C₃×#872	—	3	2	no	—
42	C₉×#124	—	2	1	no	—
43	C₉×#124	C₂×C₃	1	1	yes	characteristic, complemented
44	#63508	C₂×C₃	1	2	yes	complemented
45	#63499	C₂×C₃	1	1	yes	characteristic
46	#63497	C₂×C₃	1	1	yes	characteristic, complemented
47	#63445	C₂×C₃	1	2	yes	complemented
48	#611⋊C₄	C₂×C₃	1	2	yes	complemented
49	C₂²⋊C₄×D₉	C₂×C₃	1	2	yes	complemented
50	#63441	C₂×C₃	1	2	yes	complemented
51	#63434	C₂×C₃	1	2	yes	complemented
52	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
53	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
54	C₂²×C₃×D₉	—	2	4	no	—
55	C₂²×C₃×D₉	—	4	1	no	—
56	C₂²×C₃×D₉	C₂³	1	2	yes	—
57	C₃×Q₈×C₉	—	4	1	no	—
58	C₃×D₄×C₉	—	4	1	no	—
59	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
60	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
61	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
62	C₃×#611	—	2	4	no	—
63	C₂×C₃×Dic₉	—	4	1	no	—
64	C₂×C₃×Dic₉	C₂³	1	2	yes	—
65	C₂×C₃×Dic₉	C₂³	1	2	yes	—
66	C₂×C₃×Dic₉	C₂³	1	2	yes	—
67	C₃×C₄×D₉	—	2	4	no	—
68	C₃×C₄×D₉	—	4	2	no	—
69	C₃×#551	—	9	1	no	—
70	#5679	—	3	1	no	—
71	C₂³×C₃×D₃	—	3	1	no	—
72	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
73	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
74	C₂×C₃×#67	—	3	2	no	—
75	C₂²×C₃×Dic₃	—	3	1	no	—
76	C₂×C₃×C₄×D₃	—	3	2	no	—
77	C₂×C₃×C₄×D₃	—	3	2	no	—
78	C₂³×D₉	C₂²×C₃	1	1	yes	characteristic
79	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
80	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
81	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
82	C₃×#217	—	3	1	no	—
83	C₃×#217	—	3	2	no	—
84	C₃×#217	—	3	1	no	—
85	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
86	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
87	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
88	C₃×C₄⋊Dic₃	—	3	2	no	—
89	C₃×Dic₃⋊C₄	—	3	2	no	—
90	C₃×Dic₃⋊C₄	—	3	2	no	—
91	C₃×Dic₃⋊C₄	—	3	2	no	—
92	C₃×C₄×Dic₃	—	3	2	no	—
93	C₂×Q₈×C₉	—	2	1	no	—
94	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
95	C₂×D₄×C₉	—	2	1	no	—
96	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
97	C₂×#611	C₂²×C₃	1	2	yes	—
98	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
99	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
100	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
101	C₉×C₂²⋊C₄	—	2	2	no	—
102	C₉×C₂²⋊C₄	—	2	2	no	—
103	C₉×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
104	C₉×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
105	C₄²×C₉	—	2	1	no	—
106	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
107	#3676	C₂²×C₃	1	2	yes	—
108	#3676	C₂²×C₃	1	1	yes	characteristic
109	#3676	C₂²×C₃	1	1	yes	characteristic, complemented
110	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
111	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
112	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
113	C₄⋊Dic₉	C₂²×C₃	1	2	yes	complemented
114	Dic₉⋊C₄	C₂²×C₃	1	2	yes	complemented
115	Dic₉⋊C₄	C₂²×C₃	1	2	yes	complemented
116	Dic₉⋊C₄	C₂²×C₃	1	2	yes	complemented
117	C₄×Dic₉	C₂²×C₃	1	2	yes	complemented
118	C₂²×C₃×C₉	—	2	2	no	—
119	C₂²×C₃×C₉	—	2	2	no	—
120	C₂²×C₃×C₉	—	2	1	no	—
121	C₂²×C₃×C₉	—	2	1	no	—
122	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
123	C₂×C₃×D₉	—	2	2	no	—
124	C₂×C₃×D₉	—	2	2	no	—
125	C₂×C₃×D₉	—	4	4	no	—
126	C₂×C₃×D₉	#41	1	4	yes	—
127	C₃×C₄×C₉	—	2	2	no	—
128	C₃×C₄×C₉	—	2	1	no	—
129	C₃×C₄×C₉	—	2	2	no	—
130	C₃×Dic₉	—	2	2	no	—
131	C₃×Dic₉	—	2	2	no	—
132	C₃×Dic₉	—	2	2	no	—
133	C₃×#126	—	9	2	no	—
134	C₃×#124	—	2	1	no	—
135	C₃×#124	D₉	1	1	yes	characteristic, complemented
136	C₃×#124	C₃×D₃	1	1	yes	characteristic
137	C₃×#123	—	9	1	no	—
138	C₃×#123	—	9	2	no	—
139	C₃×C₂²⋊Q₈	—	9	2	no	—
140	C₃×#120	—	9	1	no	—
141	C₃×C₄×D₄	—	9	2	no	—
142	C₃×#117	—	9	2	no	—
143	C₂×C₃×C₂²⋊C₄	—	9	2	no	—
144	#946	—	3	2	no	—
145	#937	—	3	1	no	—
146	#935	—	3	1	no	—
147	#883	—	3	2	no	—
148	#67⋊C₄	—	3	2	no	—
149	D₃×C₂²⋊C₄	—	3	2	no	—
150	#879	—	3	2	no	—
151	#872	—	3	2	no	—
152	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
153	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
154	C₂²×C₃×D₃	—	3	2	no	—
155	C₂²×C₃×D₃	—	6	4	no	—
156	C₂²×C₃×D₃	—	12	1	no	—
157	C₃²×Q₈	—	4	1	no	—
158	C₃²×D₄	—	4	1	no	—
159	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
160	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
161	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
162	C₃×#67	—	6	4	no	—
163	C₂×C₃×Dic₃	—	3	2	no	—
164	C₂×C₃×Dic₃	—	3	2	no	—
165	C₂×C₃×Dic₃	—	3	2	no	—
166	C₂×C₃×Dic₃	—	12	1	no	—
167	C₃×C₄×D₃	—	6	4	no	—
168	C₃×C₄×D₃	—	12	2	no	—
169	C₂³×C₉	—	2	1	no	—
170	C₂³×C₉	—	2	1	no	—
171	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
172	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
173	C₂²×D₉	—	2	4	no	—
174	C₂²×D₉	—	4	1	no	—
175	C₂²×D₉	C₂³×C₃	1	2	yes	—
176	Q₈×C₉	—	4	1	no	—
177	Q₈×C₉	—	4	2	no	—
178	D₄×C₉	—	4	1	no	—
179	D₄×C₉	—	4	2	no	—
180	C₂×C₄×C₉	—	2	1	no	—
181	C₂×C₄×C₉	—	2	2	no	—
182	C₂×C₄×C₉	—	2	2	no	—
183	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
184	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
185	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
186	#611	—	2	4	no	—
187	C₂×Dic₉	—	4	1	no	—
188	C₂×Dic₉	C₂³×C₃	1	2	yes	—
189	C₂×Dic₉	C₂³×C₃	1	2	yes	—
190	C₂×Dic₉	C₂³×C₃	1	2	yes	—
191	C₄×D₉	—	2	4	no	—
192	C₄×D₉	—	4	2	no	—
193	#551	—	9	1	no	Sylow
194	C₂×C₃×C₉	—	4	1	no	—
195	C₂×C₃×C₉	—	4	1	no	—
196	C₂×C₃×C₉	C₂×#41	1	2	yes	—
197	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
198	C₃×D₉	—	2	4	no	—
199	C₂⁴×C₃	—	9	1	no	—
200	C₂³×D₃	—	3	1	no	—
201	C₂×C₃×Q₈	—	2	1	no	—
202	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic, complemented
203	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
204	C₂×C₃×D₄	—	2	1	no	—
205	C₂×C₃×D₄	—	9	2	no	—
206	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic
207	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
208	C₂²×C₃×C₄	—	9	1	no	—
209	C₂²×C₃×C₄	—	9	2	no	—
210	C₂²×C₃×C₄	—	9	2	no	—
211	C₂×#67	—	3	2	no	—
212	C₂²×Dic₃	—	3	1	no	—
213	C₂×C₄×D₃	—	3	2	no	—
214	C₂×C₄×D₃	—	3	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×C₂²⋊C₄	—	2	2	no	—
220	C₃×C₂²⋊C₄	—	2	2	no	—
221	C₃×C₂²⋊C₄	—	9	2	no	—
222	C₃×C₂²⋊C₄	—	9	1	no	—
223	C₃×C₂²⋊C₄	—	9	1	no	—
224	C₃×C₂²⋊C₄	—	9	2	no	—
225	C₃×C₂²⋊C₄	—	9	2	no	—
226	C₃×C₂²⋊C₄	—	9	2	no	—
227	C₃×C₂²⋊C₄	C₂×D₉	1	2	yes	—
228	C₃×C₂²⋊C₄	C₂×D₉	1	2	yes	complemented
229	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
230	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
231	C₃×C₄²	—	2	1	no	—
232	C₃×C₄²	—	9	2	no	—
233	C₃×C₄²	C₂×D₉	1	1	yes	characteristic, complemented
234	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
235	#217	—	3	1	no	—
236	#217	—	3	2	no	—
237	#217	—	3	1	no	—
238	(C₂×D₃)⋊C₄	—	3	2	no	—
239	(C₂×D₃)⋊C₄	—	3	2	no	—
240	(C₂×D₃)⋊C₄	—	3	2	no	—
241	C₄⋊Dic₃	—	3	2	no	—
242	Dic₃⋊C₄	—	3	2	no	—
243	Dic₃⋊C₄	—	3	2	no	—
244	Dic₃⋊C₄	—	3	2	no	—
245	C₄×Dic₃	—	3	2	no	—
246	C₂²×C₃²	—	2	1	no	—
247	C₂²×C₃²	—	2	1	no	—
248	C₂²×C₃²	—	2	2	no	—
249	C₂²×C₃²	—	2	2	no	—
250	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
251	C₂×C₃×D₃	—	3	4	no	—
252	C₂×C₃×D₃	—	6	2	no	—
253	C₂×C₃×D₃	—	6	2	no	—
254	C₂×C₃×D₃	—	12	4	no	—
255	C₃²×C₄	—	2	1	no	—
256	C₃²×C₄	—	2	2	no	—
257	C₃²×C₄	—	2	2	no	—
258	C₃×Dic₃	—	6	2	no	—
259	C₃×Dic₃	—	6	2	no	—
260	C₃×Dic₃	—	6	2	no	—
261	C₂²×C₉	—	2	2	no	—
262	C₂²×C₉	—	2	2	no	—
263	C₂²×C₉	—	2	1	no	—
264	C₂²×C₉	—	2	1	no	—
265	C₂²×C₉	—	2	1	no	—
266	C₂²×C₉	—	4	1	no	—
267	C₂²×C₉	—	4	1	no	—
268	C₂²×C₉	—	4	2	no	—
269	C₂²×C₉	—	4	2	no	—
270	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
271	C₂×D₉	—	2	2	no	—
272	C₂×D₉	—	2	2	no	—
273	C₂×D₉	—	4	4	no	—
274	C₂×D₉	C₃×#41	1	4	yes	—
275	C₄×C₉	—	2	2	no	—
276	C₄×C₉	—	2	2	no	—
277	C₄×C₉	—	2	2	no	—
278	C₄×C₉	—	2	1	no	—
279	C₄×C₉	—	4	2	no	—
280	C₄×C₉	—	4	2	no	—
281	Dic₉	—	2	2	no	—
282	Dic₉	—	2	2	no	—
283	Dic₉	—	2	2	no	—
284	#126	—	9	2	no	—
285	#124	C₃×D₉	1	1	yes	characteristic, complemented
286	#123	—	9	1	no	—
287	#123	—	9	2	no	—
288	C₂²⋊Q₈	—	9	2	no	—
289	#120	—	9	1	no	—
290	C₄×D₄	—	9	2	no	—
291	#117	—	9	2	no	—
292	C₂×C₂²⋊C₄	—	9	2	no	—
293	C₃×C₉	#551	1	1	yes	characteristic, complemented, Sylow
294	C₂³×C₃	—	2	1	no	—
295	C₂³×C₃	—	2	1	no	—
296	C₂³×C₃	—	9	2	no	—
297	C₂³×C₃	—	18	4	no	—
298	C₂³×C₃	—	36	1	no	—
299	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
300	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
301	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
302	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
303	C₂²×D₃	—	3	2	no	—
304	C₂²×D₃	—	6	4	no	—
305	C₂²×D₃	—	12	1	no	—
306	C₃×Q₈	—	4	1	no	—
307	C₃×Q₈	—	4	1	no	—
308	C₃×Q₈	—	4	2	no	—
309	C₃×D₄	—	4	1	no	—
310	C₃×D₄	—	4	1	no	—
311	C₃×D₄	—	4	2	no	—
312	C₃×D₄	—	18	4	no	—
313	C₂×C₃×C₄	—	2	1	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	9	2	no	—
317	C₂×C₃×C₄	—	9	2	no	—
318	C₂×C₃×C₄	—	9	2	no	—
319	C₂×C₃×C₄	—	18	4	no	—
320	C₂×C₃×C₄	—	36	2	no	—
321	C₂×C₃×C₄	—	36	1	no	—
322	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
323	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂²×D₉	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×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
328	#67	—	6	4	no	—
329	C₂×Dic₃	—	3	2	no	—
330	C₂×Dic₃	—	3	2	no	—
331	C₂×Dic₃	—	3	2	no	—
332	C₂×Dic₃	—	12	1	no	—
333	C₄×D₃	—	6	4	no	—
334	C₄×D₃	—	12	2	no	—
335	C₂×C₃²	—	4	1	no	—
336	C₂×C₃²	—	4	1	no	—
337	C₂×C₃²	#1004	1	1	yes	characteristic
338	C₂×C₃²	D₃×#41	1	2	yes	—
339	C₃×D₃	—	6	4	no	—
340	C₂×C₉	—	2	1	no	—
341	C₂×C₉	—	2	2	no	—
342	C₂×C₉	—	4	1	no	—
343	C₂×C₉	—	4	1	no	—
344	C₂×C₉	—	8	1	no	—
345	C₂×C₉	—	8	1	no	—
346	C₂×C₉	C₂×C₃×#41	1	2	yes	—
347	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
348	D₉	—	2	4	no	—
349	C₂⁴	—	9	1	no	—
350	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic, complemented
351	C₂×D₄	—	9	2	no	—
352	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic
353	C₂²×C₄	—	9	1	no	—
354	C₂²×C₄	—	9	2	no	—
355	C₂²×C₄	—	9	2	no	—
356	C₄⋊C₄	—	9	2	no	—
357	C₄⋊C₄	—	9	2	no	—
358	C₄⋊C₄	—	9	2	no	—
359	C₄⋊C₄	—	9	2	no	—
360	C₂²⋊C₄	—	9	2	no	—
361	C₂²⋊C₄	—	9	1	no	—
362	C₂²⋊C₄	—	9	1	no	—
363	C₂²⋊C₄	—	9	2	no	—
364	C₂²⋊C₄	—	9	2	no	—
365	C₂²⋊C₄	—	9	2	no	—
366	C₂²⋊C₄	C₂×C₃×D₉	1	2	yes	—
367	C₂²⋊C₄	C₂×C₃×D₉	1	2	yes	complemented
368	C₄²	—	9	2	no	—
369	C₄²	C₂×C₃×D₉	1	1	yes	characteristic, complemented
370	C₂²×C₃	—	2	1	no	—
371	C₂²×C₃	—	2	1	no	—
372	C₂²×C₃	—	2	2	no	—
373	C₂²×C₃	—	2	2	no	—
374	C₂²×C₃	—	2	1	no	—
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	2	2	no	—
377	C₂²×C₃	—	2	2	no	—
378	C₂²×C₃	—	2	1	no	—
379	C₂²×C₃	—	4	1	no	—
380	C₂²×C₃	—	4	1	no	—
381	C₂²×C₃	—	4	2	no	—
382	C₂²×C₃	—	4	2	no	—
383	C₂²×C₃	—	9	4	no	—
384	C₂²×C₃	—	18	2	no	—
385	C₂²×C₃	—	18	2	no	—
386	C₂²×C₃	—	36	4	no	—
387	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
388	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
389	C₂×D₃	—	3	4	no	—
390	C₂×D₃	—	6	2	no	—
391	C₂×D₃	—	6	2	no	—
392	C₂×D₃	—	12	4	no	—
393	C₃×C₄	—	2	2	no	—
394	C₃×C₄	—	2	2	no	—
395	C₃×C₄	—	2	1	no	—
396	C₃×C₄	—	2	2	no	—
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	—	2	1	no	—
399	C₃×C₄	—	2	2	no	—
400	C₃×C₄	—	4	2	no	—
401	C₃×C₄	—	4	2	no	—
402	C₃×C₄	—	18	2	no	—
403	C₃×C₄	—	18	2	no	—
404	C₃×C₄	—	18	2	no	—
405	Dic₃	—	6	2	no	—
406	Dic₃	—	6	2	no	—
407	Dic₃	—	6	2	no	—
408	C₃²	#5679	1	1	yes	characteristic
409	C₉	—	2	1	no	—
410	C₉	C₃×#551	1	1	yes	characteristic, complemented
411	C₂³	—	9	2	no	—
412	C₂³	—	18	4	no	—
413	C₂³	—	36	1	no	—
414	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
415	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
416	Q₈	—	4	1	no	—
417	D₄	—	4	1	no	—
418	D₄	—	18	4	no	—
419	C₂×C₄	—	9	2	no	—
420	C₂×C₄	—	9	2	no	—
421	C₂×C₄	—	9	2	no	—
422	C₂×C₄	—	18	4	no	—
423	C₂×C₄	—	36	2	no	—
424	C₂×C₄	—	36	1	no	—
425	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
426	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
427	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
428	C₂×C₃	—	2	1	no	—
429	C₂×C₃	—	2	2	no	—
430	C₂×C₃	—	4	1	no	—
431	C₂×C₃	—	4	1	no	—
432	C₂×C₃	—	4	1	no	—
433	C₂×C₃	—	4	1	no	—
434	C₂×C₃	—	8	1	no	—
435	C₂×C₃	—	8	1	no	—
436	C₂×C₃	—	18	4	no	—
437	C₂×C₃	#63710	1	1	yes	characteristic
438	C₂×C₃	#41×D₉	1	2	yes	—
439	C₂×C₃	C₃×#1004	1	1	yes	characteristic
440	C₂×C₃	C₃×D₃×#41	1	2	yes	—
441	D₃	—	6	4	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	9	4	no	—
447	C₂²	—	18	2	no	—
448	C₂²	—	18	2	no	—
449	C₂²	—	36	4	no	—
450	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
451	C₄	—	2	2	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	2	no	—
454	C₄	—	18	2	no	—
455	C₄	—	18	2	no	—
456	C₄	—	18	2	no	—
457	C₃	—	2	1	no	—
458	C₃	#10589781	1	1	yes	characteristic, direct product factor
459	C₃	C₃×#5679	1	1	yes	characteristic
460	C₂	—	4	1	no	—
461	C₂	—	4	1	no	—
462	C₂	—	18	4	no	—
463	C₂	C₃×#63710	1	1	yes	characteristic
464	C₂	C₃×#41×D₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂³×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#124	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₃×#63499	C₂
hypercenter	C₃×#124	D₉
hypocenter	C₉	C₃×#551
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#124

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#124	C₂	semidirect
2. C₃×#63508	C₂	semidirect
4. C₃×#63497	C₂	semidirect
5. C₃×#63445	C₂	semidirect
6. C₃×#611⋊C₄	C₂	semidirect
7. C₃×C₂²⋊C₄×D₉	C₂	semidirect
8. C₃×#63441	C₂	semidirect
9. C₃×#63434	C₂	semidirect
11. #10589781	C₃	direct (N × H)
13. C₂×C₃×Q₈×C₉	C₂²	semidirect
16. C₂²×C₃×Dic₉	C₂²	semidirect
20. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
21. C₃×C₄²×C₉	C₂²	semidirect
24. C₃×#3676	C₂²	semidirect
28. C₃×C₄⋊Dic₉	C₂²	semidirect
29. C₃×Dic₉⋊C₄	C₂²	semidirect
30. C₃×Dic₉⋊C₄	C₂²	semidirect
31. C₃×Dic₉⋊C₄	C₂²	semidirect
32. C₃×C₄×Dic₉	C₂²	semidirect
43. C₉×#124	C₂×C₃	semidirect
44. #63508	C₂×C₃	semidirect
46. #63497	C₂×C₃	semidirect
47. #63445	C₂×C₃	semidirect
48. #611⋊C₄	C₂×C₃	semidirect
49. C₂²⋊C₄×D₉	C₂×C₃	semidirect
50. #63441	C₂×C₃	semidirect
51. #63434	C₂×C₃	semidirect
94. C₂×Q₈×C₉	C₂²×C₃	semidirect
98. C₂²×Dic₉	C₂²×C₃	semidirect
104. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
106. C₄²×C₉	C₂²×C₃	semidirect
109. #3676	C₂²×C₃	semidirect
113. C₄⋊Dic₉	C₂²×C₃	semidirect
114. Dic₉⋊C₄	C₂²×C₃	semidirect
115. Dic₉⋊C₄	C₂²×C₃	semidirect
116. Dic₉⋊C₄	C₂²×C₃	semidirect
117. C₄×Dic₉	C₂²×C₃	semidirect
135. C₃×#124	D₉	semidirect
202. C₂×C₃×Q₈	C₂×D₉	semidirect
228. C₃×C₂²⋊C₄	C₂×D₉	semidirect
233. C₃×C₄²	C₂×D₉	semidirect
285. #124	C₃×D₉	semidirect
293. C₃×C₉	#551	semidirect
350. C₂×Q₈	C₂×C₃×D₉	semidirect
367. C₂²⋊C₄	C₂×C₃×D₉	semidirect
369. C₄²	C₂×C₃×D₉	semidirect
410. C₉	C₃×#551	semidirect
458. C₃	#10589781	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×C₉×#124	2
C₃×#63508	2
C₃×#63499	2
C₃×#63497	2
C₃×#63445	2
C₃×#611⋊C₄	2
C₃×C₂²⋊C₄×D₉	2
C₃×#63441	2
C₃×#63434	2
C₃×#5679	3
#10589781	3

Subgroups — C3×#10589781 #13153093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589781 #13153093