Subgroups — C₃×#10589792 #13153152

Order 1728.

740 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#63459	C₂	1	2	yes	maximal, complemented
3	C₃×#63458	C₂	1	2	yes	maximal, complemented
4	C₃×#63458	C₂	1	2	yes	maximal, complemented
5	C₃×#63455	C₂	1	1	yes	maximal, characteristic
6	C₃×#63455	C₂	1	1	yes	maximal, characteristic
7	C₃×C₄⋊C₄×D₉	C₂	1	2	yes	maximal, complemented
8	C₃×#63452	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#63450	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×D₃₆	C₂	1	1	yes	maximal, characteristic
11	C₃×C₄×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5690	—	3	1	no	maximal
13	#10589792	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
16	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
17	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
18	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×Dic₁₈	C₂²	1	2	yes	—
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
23	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
24	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
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×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
30	C₃×C₄⋊Dic₉	C₂²	1	2	yes	—
31	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
36	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
37	C₃²×#125	D₃	1	1	yes	characteristic
38	C₃×#897	—	3	2	no	—
39	C₃×#896	—	3	2	no	—
40	C₃×#896	—	3	2	no	—
41	C₃×#893	—	3	1	no	—
42	C₃×#893	—	3	1	no	—
43	C₃×D₃×C₄⋊C₄	—	3	2	no	—
44	C₃×#890	—	3	1	no	—
45	C₃×#888	—	3	1	no	—
46	C₃×C₄×D₁₂	—	3	1	no	—
47	C₃×C₄×Dic₆	—	3	1	no	—
48	C₉×#125	—	2	1	no	—
49	C₉×#125	C₂×C₃	1	1	yes	characteristic, complemented
50	#63459	C₂×C₃	1	2	yes	complemented
51	#63458	C₂×C₃	1	2	yes	complemented
52	#63458	C₂×C₃	1	2	yes	complemented
53	#63455	C₂×C₃	1	1	yes	characteristic
54	#63455	C₂×C₃	1	1	yes	characteristic
55	C₄⋊C₄×D₉	C₂×C₃	1	2	yes	complemented
56	#63452	C₂×C₃	1	1	yes	characteristic, complemented
57	#63450	C₂×C₃	1	1	yes	characteristic, complemented
58	C₄×D₃₆	C₂×C₃	1	1	yes	characteristic
59	C₄×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂²×C₃×D₉	C₂³	1	2	yes	—
61	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
62	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
65	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₂×C₃×Dic₉	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	1	yes	characteristic
71	C₃×D₃₆	Q₈	1	4	yes	complemented
72	C₃×C₄×D₉	—	2	4	no	—
73	C₃×C₄×D₉	—	4	2	no	—
74	C₃×C₄×D₉	—	4	2	no	—
75	C₃×Dic₁₈	—	2	2	no	—
76	C₃×Dic₁₈	—	4	2	no	—
77	C₃×#554	—	9	1	no	—
78	#5690	—	3	1	no	—
79	C₂×C₃×D₁₂	—	3	1	no	—
80	C₂×C₃×C₄×D₃	—	3	2	no	—
81	C₂×C₃×C₄×D₃	—	3	2	no	—
82	C₂×C₃×C₄×D₃	—	3	2	no	—
83	C₂×C₃×Dic₆	—	3	1	no	—
84	C₂×C₃×Dic₆	—	3	2	no	—
85	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
86	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
87	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
88	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
89	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
90	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
91	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
92	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
93	C₃×C₄⋊Dic₃	—	3	1	no	—
94	C₃×C₄⋊Dic₃	—	3	2	no	—
95	C₃×C₄⋊Dic₃	—	3	1	no	—
96	C₃×Dic₃⋊C₄	—	3	2	no	—
97	C₃×Dic₃⋊C₄	—	3	2	no	—
98	C₃×Dic₃⋊C₄	—	3	1	no	—
99	C₃×Dic₃⋊C₄	—	3	1	no	—
100	C₃×C₄×Dic₃	—	3	1	no	—
101	C₃×C₄×Dic₃	—	3	1	no	—
102	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
104	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
105	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
106	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
107	C₂×Dic₁₈	C₂²×C₃	1	2	yes	—
108	C₉×C₄⋊C₄	—	2	1	no	—
109	C₉×C₄⋊C₄	—	2	1	no	—
110	C₉×C₄⋊C₄	—	2	2	no	—
111	C₉×C₄⋊C₄	—	2	2	no	—
112	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
115	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
116	C₄²×C₉	—	2	1	no	—
117	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
118	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
119	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
120	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
121	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
122	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
123	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
124	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
127	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
128	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
129	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
130	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
131	C₂×C₃×D₉	—	2	2	no	—
132	C₂×C₃×D₉	—	2	2	no	—
133	C₂×C₃×D₉	C₂×Q₈	1	4	yes	—
134	C₃×C₄×C₉	—	2	1	no	—
135	C₃×C₄×C₉	—	2	2	no	—
136	C₃×C₄×C₉	—	2	2	no	—
137	C₃×C₄×C₉	—	2	1	no	—
138	C₃×C₄×C₉	C₂×Q₈	1	2	yes	—
139	C₃×Dic₉	—	2	1	no	—
140	C₃×Dic₉	—	2	1	no	—
141	C₃×Dic₉	—	2	2	no	—
142	C₃×Dic₉	—	2	1	no	—
143	C₃×Dic₉	#41	1	2	yes	—
144	C₃×C₄⋊Q₈	—	9	1	no	—
145	C₃×#125	—	2	1	no	—
146	C₃×#125	—	9	1	no	—
147	C₃×#125	D₉	1	1	yes	characteristic, complemented
148	C₃×#125	C₃×D₃	1	1	yes	characteristic
149	C₃×C₂²⋊Q₈	—	9	2	no	—
150	C₃×C₂²⋊Q₈	—	9	2	no	—
151	C₃×C₂²⋊Q₈	—	9	2	no	—
152	C₃×C₄×Q₈	—	9	1	no	—
153	C₃×C₄×D₄	—	9	1	no	—
154	C₃×C₄×D₄	—	9	1	no	—
155	C₃×C₄×D₄	—	9	1	no	—
156	C₂×C₃×C₄⋊C₄	—	9	2	no	—
157	#897	—	3	2	no	—
158	#896	—	3	2	no	—
159	#896	—	3	2	no	—
160	#893	—	3	1	no	—
161	#893	—	3	1	no	—
162	D₃×C₄⋊C₄	—	3	2	no	—
163	#890	—	3	1	no	—
164	#888	—	3	1	no	—
165	C₄×D₁₂	—	3	1	no	—
166	C₄×Dic₆	—	3	1	no	—
167	C₂²×C₃×D₃	—	3	2	no	—
168	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
169	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
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	1	no	—
177	C₂×C₃×Dic₃	—	3	2	no	—
178	C₃×D₁₂	—	3	4	no	—
179	C₃×C₄×D₃	—	6	4	no	—
180	C₃×C₄×D₃	—	12	2	no	—
181	C₃×C₄×D₃	—	12	2	no	—
182	C₃×Dic₆	—	6	2	no	—
183	C₃×Dic₆	—	12	2	no	—
184	C₂²×D₉	C₂³×C₃	1	2	yes	—
185	C₂×C₄×C₉	—	2	1	no	—
186	C₂×C₄×C₉	—	2	1	no	—
187	C₂×C₄×C₉	—	2	1	no	—
188	C₂×C₄×C₉	—	2	2	no	—
189	C₂×C₄×C₉	—	2	2	no	—
190	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
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	C₃×Q₈	1	4	yes	complemented
201	C₄×D₉	—	2	4	no	—
202	C₄×D₉	—	4	2	no	—
203	C₄×D₉	—	4	2	no	—
204	Dic₁₈	—	2	2	no	—
205	Dic₁₈	—	4	2	no	—
206	#554	—	9	1	no	Sylow
207	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
208	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
209	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
210	C₃×D₉	—	2	4	no	—
211	C₂×C₃×Q₈	—	9	1	no	—
212	C₂×C₃×Q₈	—	9	2	no	—
213	C₂×C₃×D₄	—	9	1	no	—
214	C₂²×C₃×C₄	—	9	2	no	—
215	C₂²×C₃×C₄	—	9	2	no	—
216	C₂²×C₃×C₄	—	9	2	no	—
217	C₂×D₁₂	—	3	1	no	—
218	C₂×C₄×D₃	—	3	2	no	—
219	C₂×C₄×D₃	—	3	2	no	—
220	C₂×C₄×D₃	—	3	2	no	—
221	C₂×Dic₆	—	3	1	no	—
222	C₂×Dic₆	—	3	2	no	—
223	C₃×C₄⋊C₄	—	2	2	no	—
224	C₃×C₄⋊C₄	—	2	1	no	—
225	C₃×C₄⋊C₄	—	2	1	no	—
226	C₃×C₄⋊C₄	—	2	2	no	—
227	C₃×C₄⋊C₄	—	9	1	no	—
228	C₃×C₄⋊C₄	—	9	2	no	—
229	C₃×C₄⋊C₄	—	9	1	no	—
230	C₃×C₄⋊C₄	—	9	2	no	—
231	C₃×C₄⋊C₄	—	9	2	no	—
232	C₃×C₄⋊C₄	—	9	1	no	—
233	C₃×C₄⋊C₄	—	9	1	no	—
234	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	—
235	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
236	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
237	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	—
238	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
239	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
240	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
241	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
242	C₃×C₂²⋊C₄	—	9	2	no	—
243	C₃×C₂²⋊C₄	—	9	2	no	—
244	C₃×C₂²⋊C₄	—	9	2	no	—
245	C₃×C₄²	—	2	1	no	—
246	C₃×C₄²	—	9	1	no	—
247	C₃×C₄²	—	9	1	no	—
248	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
249	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
250	(C₂×D₃)⋊C₄	—	3	2	no	—
251	(C₂×D₃)⋊C₄	—	3	2	no	—
252	(C₂×D₃)⋊C₄	—	3	2	no	—
253	C₄⋊Dic₃	—	3	1	no	—
254	C₄⋊Dic₃	—	3	1	no	—
255	C₄⋊Dic₃	—	3	2	no	—
256	Dic₃⋊C₄	—	3	1	no	—
257	Dic₃⋊C₄	—	3	1	no	—
258	Dic₃⋊C₄	—	3	2	no	—
259	Dic₃⋊C₄	—	3	2	no	—
260	C₄×Dic₃	—	3	1	no	—
261	C₄×Dic₃	—	3	1	no	—
262	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
263	C₂×C₃×D₃	—	3	4	no	—
264	C₂×C₃×D₃	—	6	2	no	—
265	C₂×C₃×D₃	—	6	2	no	—
266	C₃²×C₄	—	2	1	no	—
267	C₃²×C₄	—	2	2	no	—
268	C₃²×C₄	—	2	2	no	—
269	C₃²×C₄	—	2	1	no	—
270	C₃²×C₄	D₃×Q₈	1	2	yes	—
271	C₃×Dic₃	—	3	2	no	—
272	C₃×Dic₃	—	6	1	no	—
273	C₃×Dic₃	—	6	1	no	—
274	C₃×Dic₃	—	6	2	no	—
275	C₃×Dic₃	—	6	1	no	—
276	C₂²×C₉	—	2	1	no	—
277	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
278	C₂×D₉	—	2	2	no	—
279	C₂×D₉	—	2	2	no	—
280	C₂×D₉	C₂×C₃×Q₈	1	4	yes	—
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	—	4	2	no	—
289	C₄×C₉	—	4	1	no	—
290	C₄×C₉	C₂×C₃×Q₈	1	2	yes	—
291	Dic₉	—	2	1	no	—
292	Dic₉	—	2	1	no	—
293	Dic₉	—	2	2	no	—
294	Dic₉	—	2	1	no	—
295	Dic₉	C₃×#41	1	2	yes	—
296	C₄⋊Q₈	—	9	1	no	—
297	#125	—	9	1	no	—
298	#125	C₃×D₉	1	1	yes	characteristic, complemented
299	C₂²⋊Q₈	—	9	2	no	—
300	C₂²⋊Q₈	—	9	2	no	—
301	C₂²⋊Q₈	—	9	2	no	—
302	C₄×Q₈	—	9	1	no	—
303	C₄×D₄	—	9	1	no	—
304	C₄×D₄	—	9	1	no	—
305	C₄×D₄	—	9	1	no	—
306	C₂×C₄⋊C₄	—	9	2	no	—
307	C₃×C₉	#554	1	1	yes	characteristic, complemented, Sylow
308	C₂³×C₃	—	9	2	no	—
309	C₂²×D₃	—	3	2	no	—
310	C₃×Q₈	—	18	2	no	—
311	C₃×Q₈	—	36	2	no	—
312	C₃×D₄	—	9	4	no	—
313	C₂×C₃×C₄	—	2	1	no	—
314	C₂×C₃×C₄	—	2	1	no	—
315	C₂×C₃×C₄	—	2	1	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	9	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	—	18	4	no	—
324	C₂×C₃×C₄	—	36	2	no	—
325	C₂×C₃×C₄	—	36	2	no	—
326	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
329	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
330	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
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	2	yes	—
334	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
336	C₂×Dic₃	—	3	1	no	—
337	C₂×Dic₃	—	3	1	no	—
338	C₂×Dic₃	—	3	1	no	—
339	C₂×Dic₃	—	3	1	no	—
340	C₂×Dic₃	—	3	2	no	—
341	D₁₂	—	3	4	no	—
342	C₄×D₃	—	6	4	no	—
343	C₄×D₃	—	12	2	no	—
344	C₄×D₃	—	12	2	no	—
345	Dic₆	—	6	2	no	—
346	Dic₆	—	12	2	no	—
347	C₂×C₃²	C₂×D₃×Q₈	1	1	yes	characteristic
348	C₂×C₃²	D₃×#41	1	1	yes	characteristic
349	C₂×C₃²	#1009	1	1	yes	characteristic
350	C₃×D₃	—	6	4	no	—
351	C₂×C₉	—	2	1	no	—
352	C₂×C₉	—	2	1	no	—
353	C₂×C₉	—	2	1	no	—
354	C₂×C₉	C₂²×C₃×Q₈	1	1	yes	characteristic
355	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
356	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
357	D₉	—	2	4	no	—
358	C₂×Q₈	—	9	1	no	—
359	C₂×Q₈	—	9	2	no	—
360	C₂×D₄	—	9	1	no	—
361	C₂²×C₄	—	9	2	no	—
362	C₂²×C₄	—	9	2	no	—
363	C₂²×C₄	—	9	2	no	—
364	C₄⋊C₄	—	9	1	no	—
365	C₄⋊C₄	—	9	2	no	—
366	C₄⋊C₄	—	9	2	no	—
367	C₄⋊C₄	—	9	1	no	—
368	C₄⋊C₄	—	9	1	no	—
369	C₄⋊C₄	—	9	1	no	—
370	C₄⋊C₄	—	9	2	no	—
371	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	—
372	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
373	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
374	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	—
375	C₂²⋊C₄	—	9	2	no	—
376	C₂²⋊C₄	—	9	2	no	—
377	C₂²⋊C₄	—	9	2	no	—
378	C₄²	—	9	1	no	—
379	C₄²	—	9	1	no	—
380	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
381	C₂²×C₃	—	2	1	no	—
382	C₂²×C₃	—	9	4	no	—
383	C₂²×C₃	—	18	2	no	—
384	C₂²×C₃	—	18	2	no	—
385	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
386	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
387	C₂×D₃	—	3	4	no	—
388	C₂×D₃	—	6	2	no	—
389	C₂×D₃	—	6	2	no	—
390	C₃×C₄	—	2	1	no	—
391	C₃×C₄	—	2	2	no	—
392	C₃×C₄	—	2	2	no	—
393	C₃×C₄	—	2	1	no	—
394	C₃×C₄	—	2	2	no	—
395	C₃×C₄	—	2	1	no	—
396	C₃×C₄	—	2	1	no	—
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	—	2	2	no	—
399	C₃×C₄	—	4	2	no	—
400	C₃×C₄	—	4	1	no	—
401	C₃×C₄	—	4	1	no	—
402	C₃×C₄	—	4	2	no	—
403	C₃×C₄	—	9	2	no	—
404	C₃×C₄	—	18	1	no	—
405	C₃×C₄	—	18	1	no	—
406	C₃×C₄	—	18	2	no	—
407	C₃×C₄	—	18	1	no	—
408	C₃×C₄	Q₈×D₉	1	2	yes	—
409	C₃×C₄	C₃×D₃×Q₈	1	2	yes	—
410	Dic₃	—	3	2	no	—
411	Dic₃	—	6	1	no	—
412	Dic₃	—	6	1	no	—
413	Dic₃	—	6	2	no	—
414	Dic₃	—	6	1	no	—
415	C₃²	#5690	1	1	yes	characteristic
416	C₉	—	2	1	no	—
417	C₉	C₃×#554	1	1	yes	characteristic, complemented
418	C₂³	—	9	2	no	—
419	Q₈	—	18	2	no	—
420	Q₈	—	36	2	no	—
421	D₄	—	9	4	no	—
422	C₂×C₄	—	9	1	no	—
423	C₂×C₄	—	9	1	no	—
424	C₂×C₄	—	9	1	no	—
425	C₂×C₄	—	9	1	no	—
426	C₂×C₄	—	9	2	no	—
427	C₂×C₄	—	18	4	no	—
428	C₂×C₄	—	36	2	no	—
429	C₂×C₄	—	36	2	no	—
430	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
431	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
432	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
433	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
434	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
435	C₂×C₃	—	2	1	no	—
436	C₂×C₃	—	2	1	no	—
437	C₂×C₃	—	2	1	no	—
438	C₂×C₃	—	18	4	no	—
439	C₂×C₃	C₂×Q₈×D₉	1	1	yes	characteristic
440	C₂×C₃	#41×D₉	1	1	yes	characteristic
441	C₂×C₃	#63715	1	1	yes	characteristic
442	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
443	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
444	C₂×C₃	C₃×#1009	1	1	yes	characteristic
445	D₃	—	6	4	no	—
446	C₂²	—	9	4	no	—
447	C₂²	—	18	2	no	—
448	C₂²	—	18	2	no	—
449	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
450	C₄	—	2	2	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	2	no	—
454	C₄	—	9	2	no	—
455	C₄	—	18	1	no	—
456	C₄	—	18	1	no	—
457	C₄	—	18	2	no	—
458	C₄	—	18	1	no	—
459	C₄	C₃×Q₈×D₉	1	2	yes	—
460	C₃	—	2	1	no	—
461	C₃	#10589792	1	1	yes	characteristic, direct product factor
462	C₃	C₃×#5690	1	1	yes	characteristic
463	C₂	—	18	4	no	—
464	C₂	C₂×C₃×Q₈×D₉	1	1	yes	characteristic
465	C₂	C₃×#41×D₉	1	1	yes	characteristic
466	C₂	C₃×#63715	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×C₉×#125	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₂×C₃×D₃₆	C₂²
hypercenter	C₃×#125	D₉
hypocenter	C₉	C₃×#554
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#125

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#125	C₂	semidirect
2. C₃×#63459	C₂	semidirect
3. C₃×#63458	C₂	semidirect
4. C₃×#63458	C₂	semidirect
7. C₃×C₄⋊C₄×D₉	C₂	semidirect
8. C₃×#63452	C₂	semidirect
9. C₃×#63450	C₂	semidirect
11. C₃×C₄×Dic₁₈	C₂	semidirect
13. #10589792	C₃	direct (N × H)
49. C₉×#125	C₂×C₃	semidirect
50. #63459	C₂×C₃	semidirect
51. #63458	C₂×C₃	semidirect
52. #63458	C₂×C₃	semidirect
55. C₄⋊C₄×D₉	C₂×C₃	semidirect
56. #63452	C₂×C₃	semidirect
57. #63450	C₂×C₃	semidirect
59. C₄×Dic₁₈	C₂×C₃	semidirect
71. C₃×D₃₆	Q₈	semidirect
147. C₃×#125	D₉	semidirect
200. D₃₆	C₃×Q₈	semidirect
298. #125	C₃×D₉	semidirect
307. C₃×C₉	#554	semidirect
417. C₉	C₃×#554	semidirect
461. C₃	#10589792	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×#125	2
C₃×#63459	2
C₃×#63458	2
C₃×#63455	2
C₃×C₄⋊C₄×D₉	2
C₃×#63452	2
C₃×#63450	2
C₃×C₄×D₃₆	2
C₃×C₄×Dic₁₈	2
C₃×#5690	3
#10589792	3

Subgroups — C3×#10589792 #13153152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589792 #13153152