Subgroups — C₃×#10589776 #13153088

Order 1728.

1078 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3701	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄×D₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63509	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#63502	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63446	C₂	1	4	yes	maximal, complemented
7	C₃×#63444	C₂	1	4	yes	maximal, complemented
8	C₃×#63436	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#63434	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5674	—	3	1	no	maximal
11	#10589776	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂³×C₃×D₉	C₂²	1	2	yes	—
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	C₂×C₃×#611	C₂²	1	4	yes	complemented
17	C₃×#3701	—	2	4	no	—
18	C₃×D₄×D₉	—	2	4	no	—
19	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
20	C₂×C₃×D₃₆	C₂²	1	2	yes	—
21	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×D₃₆	C₂²	1	4	yes	complemented
23	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×D₉	C₂²	1	2	yes	complemented
25	C₃×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
26	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
27	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
28	C₃×(C₂×D₉)⋊C₄	C₂²	1	4	yes	complemented
29	C₃×Dic₉⋊C₄	C₂²	1	2	yes	complemented
30	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×#239	—	3	1	no	—
32	C₂×C₃×D₃×D₄	—	3	1	no	—
33	C₃²×#124	D₃	1	1	yes	characteristic
34	C₃×#947	—	3	1	no	—
35	C₃×#940	—	3	1	no	—
36	C₃×#884	—	3	4	no	—
37	C₃×#882	—	3	4	no	—
38	C₃×#874	—	3	1	no	—
39	C₃×#872	—	3	1	no	—
40	C₂×#3701	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×D₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
42	C₉×#124	—	2	1	no	—
43	C₉×#124	C₂×C₃	1	1	yes	characteristic, complemented
44	#63509	C₂×C₃	1	1	yes	characteristic, complemented
45	#63502	C₂×C₃	1	1	yes	characteristic, complemented
46	#63446	C₂×C₃	1	4	yes	complemented
47	#63444	C₂×C₃	1	4	yes	complemented
48	#63436	C₂×C₃	1	1	yes	characteristic, complemented
49	#63434	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂³×C₃×C₉	C₂³	1	2	yes	—
51	C₂²×C₃×D₉	—	2	4	no	—
52	C₂²×C₃×D₉	—	4	4	no	—
53	C₂²×C₃×D₉	C₂³	1	2	yes	—
54	C₂²×C₃×D₉	C₂³	1	2	yes	—
55	C₂²×C₃×D₉	C₂³	1	1	yes	characteristic
56	C₃×Q₈×C₉	—	2	2	no	—
57	C₃×D₄×C₉	—	2	2	no	—
58	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
59	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
60	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₃×#611	—	2	4	no	—
62	C₃×#611	—	4	4	no	—
63	C₂×C₃×Dic₉	C₂³	1	2	yes	—
64	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
65	C₃×D₃₆	—	2	4	no	—
66	C₃×D₃₆	—	2	2	no	—
67	C₃×D₃₆	—	2	2	no	—
68	C₃×D₃₆	—	4	4	no	—
69	C₃×C₄×D₉	—	2	4	no	—
70	C₃×C₄×D₉	D₄	1	4	yes	complemented
71	C₃×#535	—	9	1	no	—
72	#5674	—	3	1	no	—
73	C₂³×C₃×D₃	—	3	2	no	—
74	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
75	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
76	C₂×C₃×#67	—	3	2	no	—
77	C₂×C₃×#67	—	3	4	no	—
78	C₃×#239	—	6	4	no	—
79	C₃×D₃×D₄	—	6	4	no	—
80	C₂×C₃×D₁₂	—	3	2	no	—
81	C₂×C₃×D₁₂	—	3	1	no	—
82	C₂×C₃×D₁₂	—	3	1	no	—
83	C₂×C₃×D₁₂	—	3	4	no	—
84	C₂×C₃×C₄×D₃	—	3	1	no	—
85	C₂×C₃×C₄×D₃	—	3	2	no	—
86	C₂³×D₉	C₂²×C₃	1	2	yes	—
87	C₃²×C₂²⋊C₄	C₂×D₃	1	4	yes	—
88	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
89	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
90	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
91	C₃×Dic₃⋊C₄	—	3	2	no	—
92	C₃×C₄×Dic₃	—	3	1	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	C₂×#611	C₂²×C₃	1	4	yes	complemented
99	#3701	—	2	4	no	—
100	D₄×D₉	—	2	4	no	—
101	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
102	C₂×D₃₆	C₂²×C₃	1	2	yes	—
103	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₂×D₃₆	C₂²×C₃	1	4	yes	complemented
105	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₄×D₉	C₂²×C₃	1	2	yes	complemented
107	C₉×C₂²⋊C₄	—	2	4	no	—
108	C₉×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
109	C₄²×C₉	—	2	1	no	—
110	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
111	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
112	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	complemented
113	Dic₉⋊C₄	C₂²×C₃	1	2	yes	complemented
114	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
115	C₂²×C₃×C₉	—	2	2	no	—
116	C₂²×C₃×C₉	—	2	4	no	—
117	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
118	C₂×C₃×D₉	—	2	2	no	—
119	C₂×C₃×D₉	—	2	2	no	—
120	C₂×C₃×D₉	—	2	2	no	—
121	C₂×C₃×D₉	—	2	4	no	—
122	C₂×C₃×D₉	—	2	4	no	—
123	C₂×C₃×D₉	—	4	8	no	—
124	C₂×C₃×D₉	C₂×D₄	1	2	yes	—
125	C₃×C₄×C₉	—	2	2	no	—
126	C₃×C₄×C₉	—	2	2	no	—
127	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
128	C₃×Dic₉	—	2	2	no	—
129	C₃×Dic₉	C₂×D₄	1	2	yes	—
130	C₂×C₃×#41	—	9	1	no	—
131	C₂²×C₃×D₄	—	9	1	no	—
132	C₂×#239	—	3	1	no	—
133	C₂×D₃×D₄	—	3	1	no	—
134	C₃×#127	—	9	1	no	—
135	C₃×#127	—	9	1	no	—
136	C₃×#124	—	2	1	no	—
137	C₃×#124	—	9	1	no	—
138	C₃×#124	D₉	1	1	yes	characteristic, complemented
139	C₃×#124	C₃×D₃	1	1	yes	characteristic
140	C₃×#121	—	9	4	no	—
141	C₃×#120	—	9	4	no	—
142	C₃×#117	—	9	1	no	—
143	#947	—	3	1	no	—
144	#940	—	3	1	no	—
145	#884	—	3	4	no	—
146	#882	—	3	4	no	—
147	#874	—	3	1	no	—
148	#872	—	3	1	no	—
149	C₂³×C₃²	C₂²×D₃	1	2	yes	—
150	C₂²×C₃×D₃	—	3	1	no	—
151	C₂²×C₃×D₃	—	3	2	no	—
152	C₂²×C₃×D₃	—	3	2	no	—
153	C₂²×C₃×D₃	—	6	4	no	—
154	C₂²×C₃×D₃	—	12	4	no	—
155	C₃²×Q₈	—	2	2	no	—
156	C₃²×D₄	—	2	2	no	—
157	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
158	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
159	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
160	C₃×#67	—	6	4	no	—
161	C₃×#67	—	12	4	no	—
162	C₂×C₃×Dic₃	—	3	1	no	—
163	C₂×C₃×Dic₃	—	3	2	no	—
164	C₃×D₁₂	—	6	4	no	—
165	C₃×D₁₂	—	6	2	no	—
166	C₃×D₁₂	—	6	2	no	—
167	C₃×D₁₂	—	12	4	no	—
168	C₃×C₄×D₃	—	3	4	no	—
169	C₃×C₄×D₃	—	6	4	no	—
170	C₂³×C₉	—	2	2	no	—
171	C₂³×C₉	C₂³×C₃	1	2	yes	—
172	C₂²×D₉	—	2	4	no	—
173	C₂²×D₉	—	4	4	no	—
174	C₂²×D₉	C₂³×C₃	1	2	yes	—
175	C₂²×D₉	C₂³×C₃	1	2	yes	—
176	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
177	Q₈×C₉	—	2	2	no	—
178	Q₈×C₉	—	4	2	no	—
179	D₄×C₉	—	2	2	no	—
180	D₄×C₉	—	4	2	no	—
181	C₂×C₄×C₉	—	2	1	no	—
182	C₂×C₄×C₉	—	2	2	no	—
183	C₂×C₄×C₉	—	2	2	no	—
184	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
185	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
186	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
187	#611	—	2	4	no	—
188	#611	—	4	4	no	—
189	C₂×Dic₉	C₂³×C₃	1	2	yes	—
190	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
191	D₃₆	—	2	4	no	—
192	D₃₆	—	2	2	no	—
193	D₃₆	—	2	2	no	—
194	D₃₆	—	4	4	no	—
195	C₄×D₉	—	2	4	no	—
196	C₄×D₉	C₃×D₄	1	4	yes	complemented
197	#535	—	9	1	no	Sylow
198	C₂×C₃×C₉	—	4	2	no	—
199	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₃×C₉	H(5,𝔽₂)	1	2	yes	—
201	C₃×D₉	—	2	2	no	—
202	C₃×D₉	—	4	2	no	—
203	C₃×D₉	—	4	2	no	—
204	C₂⁴×C₃	—	9	2	no	—
205	C₂³×D₃	—	3	2	no	—
206	C₃×#41	—	18	4	no	—
207	C₂×C₃×Q₈	—	2	1	no	—
208	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic, complemented
209	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
210	C₂×C₃×D₄	—	2	1	no	—
211	C₂×C₃×D₄	—	9	2	no	—
212	C₂×C₃×D₄	—	9	4	no	—
213	C₂×C₃×D₄	—	9	2	no	—
214	C₂×C₃×D₄	—	9	1	no	—
215	C₂×C₃×D₄	—	9	1	no	—
216	C₂×C₃×D₄	—	9	4	no	—
217	C₂×C₃×D₄	—	18	4	no	—
218	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic
219	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
220	C₂²×C₃×C₄	—	9	1	no	—
221	C₂²×C₃×C₄	—	9	2	no	—
222	C₂×#67	—	3	2	no	—
223	C₂×#67	—	3	4	no	—
224	#239	—	6	4	no	—
225	D₃×D₄	—	6	4	no	—
226	C₂×D₁₂	—	3	1	no	—
227	C₂×D₁₂	—	3	1	no	—
228	C₂×D₁₂	—	3	2	no	—
229	C₂×D₁₂	—	3	4	no	—
230	C₂×C₄×D₃	—	3	1	no	—
231	C₂×C₄×D₃	—	3	2	no	—
232	C₃×C₄⋊C₄	—	9	2	no	—
233	C₃×C₂²⋊C₄	—	2	4	no	—
234	C₃×C₂²⋊C₄	—	9	2	no	—
235	C₃×C₂²⋊C₄	—	9	4	no	—
236	C₃×C₂²⋊C₄	C₂×D₉	1	4	yes	complemented
237	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
238	C₃×C₄²	—	2	1	no	—
239	C₃×C₄²	—	9	1	no	—
240	C₃×C₄²	C₂×D₉	1	1	yes	characteristic, complemented
241	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
242	(C₂×D₃)⋊C₄	—	3	2	no	—
243	(C₂×D₃)⋊C₄	—	3	4	no	—
244	Dic₃⋊C₄	—	3	2	no	—
245	C₄×Dic₃	—	3	1	no	—
246	C₂²×C₃²	—	2	2	no	—
247	C₂²×C₃²	—	2	4	no	—
248	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
249	C₂×C₃×D₃	—	3	2	no	—
250	C₂×C₃×D₃	—	6	2	no	—
251	C₂×C₃×D₃	—	6	2	no	—
252	C₂×C₃×D₃	—	6	2	no	—
253	C₂×C₃×D₃	—	6	4	no	—
254	C₂×C₃×D₃	—	6	4	no	—
255	C₂×C₃×D₃	—	12	8	no	—
256	C₃²×C₄	—	2	2	no	—
257	C₃²×C₄	—	2	2	no	—
258	C₃²×C₄	D₃×D₄	1	2	yes	—
259	C₃×Dic₃	—	3	2	no	—
260	C₃×Dic₃	—	6	2	no	—
261	C₂²×C₉	—	2	2	no	—
262	C₂²×C₉	—	2	4	no	—
263	C₂²×C₉	—	2	1	no	—
264	C₂²×C₉	—	4	2	no	—
265	C₂²×C₉	—	4	4	no	—
266	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
267	C₂×D₉	—	2	2	no	—
268	C₂×D₉	—	2	2	no	—
269	C₂×D₉	—	2	2	no	—
270	C₂×D₉	—	2	4	no	—
271	C₂×D₉	—	2	4	no	—
272	C₂×D₉	—	4	8	no	—
273	C₂×D₉	C₂×C₃×D₄	1	2	yes	—
274	C₄×C₉	—	2	2	no	—
275	C₄×C₉	—	2	2	no	—
276	C₄×C₉	—	2	2	no	—
277	C₄×C₉	—	4	2	no	—
278	C₄×C₉	—	4	2	no	—
279	C₄×C₉	C₂×C₃×D₄	1	2	yes	—
280	Dic₉	—	2	2	no	—
281	Dic₉	C₂×C₃×D₄	1	2	yes	—
282	C₂×#41	—	9	1	no	—
283	C₂²×D₄	—	9	1	no	—
284	#127	—	9	1	no	—
285	#127	—	9	1	no	—
286	#124	—	9	1	no	—
287	#124	C₃×D₉	1	1	yes	characteristic, complemented
288	#121	—	9	4	no	—
289	#120	—	9	4	no	—
290	#117	—	9	1	no	—
291	C₃×C₉	#535	1	1	yes	characteristic, complemented, Sylow
292	C₂³×C₃	—	2	2	no	—
293	C₂³×C₃	—	9	1	no	—
294	C₂³×C₃	—	9	2	no	—
295	C₂³×C₃	—	9	2	no	—
296	C₂³×C₃	—	18	4	no	—
297	C₂³×C₃	—	36	4	no	—
298	C₂³×C₃	C₂²×D₉	1	2	yes	—
299	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
300	C₂²×D₃	—	3	1	no	—
301	C₂²×D₃	—	3	2	no	—
302	C₂²×D₃	—	3	2	no	—
303	C₂²×D₃	—	6	4	no	—
304	C₂²×D₃	—	12	4	no	—
305	C₃×Q₈	—	2	2	no	—
306	C₃×Q₈	—	2	2	no	—
307	C₃×Q₈	—	4	2	no	—
308	C₃×D₄	—	2	2	no	—
309	C₃×D₄	—	2	2	no	—
310	C₃×D₄	—	4	2	no	—
311	C₃×D₄	—	18	4	no	—
312	C₃×D₄	—	18	4	no	—
313	C₃×D₄	—	18	2	no	—
314	C₃×D₄	—	18	2	no	—
315	C₃×D₄	—	36	4	no	—
316	C₃×D₄	—	36	4	no	—
317	C₂×C₃×C₄	—	2	1	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	9	1	no	—
321	C₂×C₃×C₄	—	9	4	no	—
322	C₂×C₃×C₄	—	9	2	no	—
323	C₂×C₃×C₄	—	18	4	no	—
324	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
325	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
326	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
328	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
329	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
330	#67	—	6	4	no	—
331	#67	—	12	4	no	—
332	C₂×Dic₃	—	3	1	no	—
333	C₂×Dic₃	—	3	2	no	—
334	D₁₂	—	6	4	no	—
335	D₁₂	—	6	2	no	—
336	D₁₂	—	6	2	no	—
337	D₁₂	—	12	4	no	—
338	C₄×D₃	—	3	4	no	—
339	C₄×D₃	—	6	4	no	—
340	C₂×C₃²	—	4	2	no	—
341	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
342	C₂×C₃²	#1009	1	2	yes	—
343	C₃×D₃	—	6	2	no	—
344	C₃×D₃	—	12	2	no	—
345	C₃×D₃	—	12	2	no	—
346	C₂×C₉	—	2	1	no	—
347	C₂×C₉	—	2	2	no	—
348	C₂×C₉	—	4	2	no	—
349	C₂×C₉	—	8	2	no	—
350	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
351	C₂×C₉	C₃×H(5,𝔽₂)	1	2	yes	—
352	D₉	—	2	2	no	—
353	D₉	—	4	2	no	—
354	D₉	—	4	2	no	—
355	C₂⁴	—	9	2	no	—
356	#41	—	18	4	no	—
357	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic, complemented
358	C₂×D₄	—	9	2	no	—
359	C₂×D₄	—	9	4	no	—
360	C₂×D₄	—	9	2	no	—
361	C₂×D₄	—	9	1	no	—
362	C₂×D₄	—	9	1	no	—
363	C₂×D₄	—	9	4	no	—
364	C₂×D₄	—	18	4	no	—
365	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic
366	C₂²×C₄	—	9	1	no	—
367	C₂²×C₄	—	9	2	no	—
368	C₄⋊C₄	—	9	2	no	—
369	C₂²⋊C₄	—	9	2	no	—
370	C₂²⋊C₄	—	9	4	no	—
371	C₂²⋊C₄	C₂×C₃×D₉	1	4	yes	complemented
372	C₄²	—	9	1	no	—
373	C₄²	C₂×C₃×D₉	1	1	yes	characteristic, complemented
374	C₂²×C₃	—	2	2	no	—
375	C₂²×C₃	—	2	4	no	—
376	C₂²×C₃	—	2	2	no	—
377	C₂²×C₃	—	2	4	no	—
378	C₂²×C₃	—	2	1	no	—
379	C₂²×C₃	—	4	2	no	—
380	C₂²×C₃	—	4	4	no	—
381	C₂²×C₃	—	9	2	no	—
382	C₂²×C₃	—	18	2	no	—
383	C₂²×C₃	—	18	2	no	—
384	C₂²×C₃	—	18	2	no	—
385	C₂²×C₃	—	18	4	no	—
386	C₂²×C₃	—	18	4	no	—
387	C₂²×C₃	—	36	8	no	—
388	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
389	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
390	C₂×D₃	—	3	2	no	—
391	C₂×D₃	—	6	2	no	—
392	C₂×D₃	—	6	2	no	—
393	C₂×D₃	—	6	2	no	—
394	C₂×D₃	—	6	4	no	—
395	C₂×D₃	—	6	4	no	—
396	C₂×D₃	—	12	8	no	—
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	—	2	2	no	—
399	C₃×C₄	—	2	2	no	—
400	C₃×C₄	—	2	2	no	—
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	4	2	no	—
403	C₃×C₄	—	4	2	no	—
404	C₃×C₄	—	9	2	no	—
405	C₃×C₄	—	18	2	no	—
406	C₃×C₄	D₄×D₉	1	2	yes	—
407	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
408	Dic₃	—	3	2	no	—
409	Dic₃	—	6	2	no	—
410	C₃²	#5674	1	1	yes	characteristic
411	C₉	—	2	1	no	—
412	C₉	C₃×#535	1	1	yes	characteristic, complemented
413	C₂³	—	9	1	no	—
414	C₂³	—	9	2	no	—
415	C₂³	—	9	2	no	—
416	C₂³	—	18	4	no	—
417	C₂³	—	36	4	no	—
418	C₂³	C₂²×C₃×D₉	1	2	yes	—
419	Q₈	—	2	2	no	—
420	D₄	—	2	2	no	—
421	D₄	—	18	4	no	—
422	D₄	—	18	4	no	—
423	D₄	—	18	2	no	—
424	D₄	—	18	2	no	—
425	D₄	—	36	4	no	—
426	D₄	—	36	4	no	—
427	C₂×C₄	—	9	1	no	—
428	C₂×C₄	—	9	4	no	—
429	C₂×C₄	—	9	2	no	—
430	C₂×C₄	—	18	4	no	—
431	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
432	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
433	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
434	C₂×C₃	—	2	1	no	—
435	C₂×C₃	—	2	2	no	—
436	C₂×C₃	—	4	2	no	—
437	C₂×C₃	—	4	2	no	—
438	C₂×C₃	—	8	2	no	—
439	C₂×C₃	—	18	2	no	—
440	C₂×C₃	—	36	2	no	—
441	C₂×C₃	—	36	2	no	—
442	C₂×C₃	C₂×D₄×D₉	1	1	yes	characteristic
443	C₂×C₃	#63715	1	2	yes	—
444	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
445	C₂×C₃	C₃×#1009	1	2	yes	—
446	D₃	—	6	2	no	—
447	D₃	—	12	2	no	—
448	D₃	—	12	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	9	2	no	—
452	C₂²	—	18	2	no	—
453	C₂²	—	18	2	no	—
454	C₂²	—	18	2	no	—
455	C₂²	—	18	4	no	—
456	C₂²	—	18	4	no	—
457	C₂²	—	36	8	no	—
458	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	9	2	no	—
462	C₄	—	18	2	no	—
463	C₄	C₃×D₄×D₉	1	2	yes	—
464	C₃	—	2	1	no	—
465	C₃	#10589776	1	1	yes	characteristic, direct product factor
466	C₃	C₃×#5674	1	1	yes	characteristic
467	C₂	—	4	2	no	—
468	C₂	—	18	2	no	—
469	C₂	—	36	2	no	—
470	C₂	—	36	2	no	—
471	C₂	C₂×C₃×D₄×D₉	1	1	yes	characteristic
472	C₂	C₃×#63715	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
hypercenter	C₃×#124	D₉
hypocenter	C₉	C₃×#535
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. C₂×C₃×#3701	C₂	semidirect
2. C₂×C₃×D₄×D₉	C₂	semidirect
3. C₃×C₉×#124	C₂	semidirect
4. C₃×#63509	C₂	semidirect
5. C₃×#63502	C₂	semidirect
6. C₃×#63446	C₂	semidirect
7. C₃×#63444	C₂	semidirect
8. C₃×#63436	C₂	semidirect
9. C₃×#63434	C₂	semidirect
11. #10589776	C₃	direct (N × H)
13. C₂×C₃×Q₈×C₉	C₂²	semidirect
16. C₂×C₃×#611	C₂²	semidirect
21. C₂×C₃×D₃₆	C₂²	semidirect
22. C₂×C₃×D₃₆	C₂²	semidirect
24. C₂×C₃×C₄×D₉	C₂²	semidirect
25. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
26. C₃×C₄²×C₉	C₂²	semidirect
28. C₃×(C₂×D₉)⋊C₄	C₂²	semidirect
29. C₃×Dic₉⋊C₄	C₂²	semidirect
30. C₃×C₄×Dic₉	C₂²	semidirect
40. C₂×#3701	C₂×C₃	semidirect
41. C₂×D₄×D₉	C₂×C₃	semidirect
43. C₉×#124	C₂×C₃	semidirect
44. #63509	C₂×C₃	semidirect
45. #63502	C₂×C₃	semidirect
46. #63446	C₂×C₃	semidirect
47. #63444	C₂×C₃	semidirect
48. #63436	C₂×C₃	semidirect
49. #63434	C₂×C₃	semidirect
70. C₃×C₄×D₉	D₄	semidirect
94. C₂×Q₈×C₉	C₂²×C₃	semidirect
98. C₂×#611	C₂²×C₃	semidirect
103. C₂×D₃₆	C₂²×C₃	semidirect
104. C₂×D₃₆	C₂²×C₃	semidirect
106. C₂×C₄×D₉	C₂²×C₃	semidirect
108. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
110. C₄²×C₉	C₂²×C₃	semidirect
112. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
113. Dic₉⋊C₄	C₂²×C₃	semidirect
114. C₄×Dic₉	C₂²×C₃	semidirect
138. C₃×#124	D₉	semidirect
196. C₄×D₉	C₃×D₄	semidirect
208. C₂×C₃×Q₈	C₂×D₉	semidirect
236. C₃×C₂²⋊C₄	C₂×D₉	semidirect
240. C₃×C₄²	C₂×D₉	semidirect
287. #124	C₃×D₉	semidirect
291. C₃×C₉	#535	semidirect
357. C₂×Q₈	C₂×C₃×D₉	semidirect
371. C₂²⋊C₄	C₂×C₃×D₉	semidirect
373. C₄²	C₂×C₃×D₉	semidirect
412. C₉	C₃×#535	semidirect
465. C₃	#10589776	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#3701	2
C₂×C₃×D₄×D₉	2
C₃×C₉×#124	2
C₃×#63509	2
C₃×#63502	2
C₃×#63446	2
C₃×#63444	2
C₃×#63436	2
C₃×#63434	2
C₃×#5674	3
#10589776	3

Subgroups — C3×#10589776 #13153088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589776 #13153088