Subgroups — C₃×#10589680 #13152684

Order 1728.

736 conjugacy classes of subgroups.

The subgroup lattice has 470 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×#63459	C₂	1	1	yes	maximal, characteristic
5	C₃×#63458	C₂	1	2	yes	maximal
6	C₃×#63451	C₂	1	2	yes	maximal, complemented
7	C₃×#63450	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#63434	C₂	1	2	yes	maximal
9	C₃×C₄²×D₉	C₂	1	1	yes	maximal, characteristic
10	C₃×C₄×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×Dic₁₈	C₂	1	2	yes	maximal, complemented
12	C₃×#5578	—	3	1	no	maximal
13	#10589680	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×C₄×D₉	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
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	2	yes	—
22	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
23	C₃×C₄²×C₉	C₂²	1	2	yes	—
24	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
25	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
26	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
27	C₃×C₄⋊Dic₉	C₂²	1	2	yes	—
28	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
29	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
30	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
31	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
32	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
33	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
34	C₃×C₄×Dic₉	C₂²	1	2	yes	—
35	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
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×#897	—	3	1	no	—
41	C₃×#896	—	3	2	no	—
42	C₃×#889	—	3	2	no	—
43	C₃×#888	—	3	1	no	—
44	C₃×#872	—	3	2	no	—
45	C₃×C₄²×D₃	—	3	1	no	—
46	C₃×C₄×Dic₆	—	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	#63459	C₂×C₃	1	1	yes	characteristic
53	#63458	C₂×C₃	1	2	yes	—
54	#63451	C₂×C₃	1	2	yes	complemented
55	#63450	C₂×C₃	1	1	yes	characteristic, complemented
56	#63434	C₂×C₃	1	2	yes	—
57	C₄²×D₉	C₂×C₃	1	1	yes	characteristic
58	C₄×Dic₁₈	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	2	yes	—
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×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₃×Dic₉	C₂³	1	2	yes	—
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×C₄×D₉	—	2	2	no	—
73	C₃×C₄×D₉	—	2	2	no	—
74	C₃×C₄×D₉	Q₈	1	4	yes	complemented
75	C₃×Dic₁₈	—	2	2	no	—
76	C₃×Dic₁₈	—	2	4	no	—
77	C₃×#533	—	9	1	no	—
78	#5578	—	3	1	no	—
79	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
80	C₂×C₃×C₄×D₃	—	3	1	no	—
81	C₂×C₃×C₄×D₃	—	3	1	no	—
82	C₂×C₃×C₄×D₃	—	3	1	no	—
83	C₂×C₃×Dic₆	—	3	2	no	—
84	C₂×C₃×Dic₆	—	3	1	no	—
85	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
86	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
87	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
88	C₃²×C₄²	C₂×D₃	1	2	yes	—
89	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
90	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
91	C₃×C₄⋊Dic₃	—	3	1	no	—
92	C₃×C₄⋊Dic₃	—	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	2	no	—
97	C₃×Dic₃⋊C₄	—	3	2	no	—
98	C₃×C₄×Dic₃	—	3	1	no	—
99	C₃×C₄×Dic₃	—	3	1	no	—
100	C₃×C₄×Dic₃	—	3	1	no	—
101	C₃×C₄×Dic₃	—	3	2	no	—
102	C₂×Q₈×C₉	—	2	1	no	—
103	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
107	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
108	C₂×Dic₁₈	C₂²×C₃	1	2	yes	—
109	C₉×C₄⋊C₄	—	2	1	no	—
110	C₉×C₄⋊C₄	—	2	2	no	—
111	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
112	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
113	C₄²×C₉	—	2	1	no	—
114	C₄²×C₉	—	2	2	no	—
115	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
116	C₄²×C₉	C₂²×C₃	1	2	yes	—
117	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
118	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
119	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
120	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
121	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
122	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
123	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
124	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
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	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
130	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
131	C₂×C₃×D₉	—	2	1	no	—
132	C₂×C₃×D₉	—	2	1	no	—
133	C₂×C₃×D₉	C₂×Q₈	1	2	yes	—
134	C₃×C₄×C₉	—	2	2	no	—
135	C₃×C₄×C₉	—	2	2	no	—
136	C₃×C₄×C₉	—	2	1	no	—
137	C₃×C₄×C₉	C₂×Q₈	1	2	yes	—
138	C₃×C₄×C₉	#41	1	2	yes	—
139	C₃×Dic₉	—	2	2	no	—
140	C₃×Dic₉	—	2	2	no	—
141	C₃×Dic₉	—	2	1	no	—
142	C₃×Dic₉	C₂×Q₈	1	2	yes	—
143	C₃×Dic₉	#41	1	2	yes	—
144	C₃×C₄⋊Q₈	—	9	1	no	—
145	C₃×C₄⋊Q₈	—	9	1	no	—
146	C₃×#125	—	9	2	no	—
147	C₃×C₂²⋊Q₈	—	9	1	no	—
148	C₃×C₂²⋊Q₈	—	9	2	no	—
149	C₃×C₂²⋊Q₈	—	9	1	no	—
150	C₃×C₄×Q₈	—	2	1	no	—
151	C₃×C₄×Q₈	—	9	2	no	—
152	C₃×C₄×Q₈	—	9	1	no	—
153	C₃×C₄×Q₈	D₉	1	1	yes	characteristic, complemented
154	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
155	C₃×#117	—	9	2	no	—
156	C₂×C₃×C₄²	—	9	1	no	—
157	#946	—	3	1	no	—
158	#944	—	3	1	no	—
159	#897	—	3	1	no	—
160	#896	—	3	2	no	—
161	#889	—	3	2	no	—
162	#888	—	3	1	no	—
163	#872	—	3	2	no	—
164	C₄²×D₃	—	3	1	no	—
165	C₄×Dic₆	—	3	2	no	—
166	C₄×Dic₆	—	3	1	no	—
167	C₂²×C₃×D₃	—	3	1	no	—
168	C₃²×Q₈	—	2	2	no	—
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	2	yes	—
172	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
173	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
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	C₂×C₃×Dic₃	—	3	2	no	—
179	C₃×C₄×D₃	—	3	4	no	—
180	C₃×C₄×D₃	—	6	2	no	—
181	C₃×C₄×D₃	—	6	2	no	—
182	C₃×Dic₆	—	6	4	no	—
183	C₃×Dic₆	—	6	2	no	—
184	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
185	Q₈×C₉	—	2	4	no	—
186	Q₈×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	—	2	1	no	—
191	C₂×C₄×C₉	—	2	2	no	—
192	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
193	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
194	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
195	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₄×C₉	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	2	yes	—
200	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
201	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
202	C₄×D₉	—	2	2	no	—
203	C₄×D₉	—	2	2	no	—
204	C₄×D₉	C₃×Q₈	1	4	yes	complemented
205	Dic₁₈	—	2	2	no	—
206	Dic₁₈	—	2	4	no	—
207	#533	—	9	1	no	Sylow
208	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
209	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
210	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
211	C₃×D₉	—	2	2	no	—
212	C₂×C₃×Q₈	—	2	1	no	—
213	C₂×C₃×Q₈	—	9	2	no	—
214	C₂×C₃×Q₈	—	9	1	no	—
215	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic
216	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
217	C₂²×C₃×C₄	—	9	1	no	—
218	C₂²×C₃×C₄	—	9	1	no	—
219	C₂²×C₃×C₄	—	9	1	no	—
220	C₂×C₄×D₃	—	3	1	no	—
221	C₂×C₄×D₃	—	3	1	no	—
222	C₂×C₄×D₃	—	3	1	no	—
223	C₂×Dic₆	—	3	2	no	—
224	C₂×Dic₆	—	3	1	no	—
225	C₃×C₄⋊C₄	—	2	2	no	—
226	C₃×C₄⋊C₄	—	2	1	no	—
227	C₃×C₄⋊C₄	—	9	2	no	—
228	C₃×C₄⋊C₄	—	9	2	no	—
229	C₃×C₄⋊C₄	—	9	2	no	—
230	C₃×C₄⋊C₄	—	9	2	no	—
231	C₃×C₄⋊C₄	—	9	2	no	—
232	C₃×C₄⋊C₄	—	9	2	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×C₃×D₃	1	1	yes	characteristic
237	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
238	C₃×C₂²⋊C₄	—	9	2	no	—
239	C₃×C₂²⋊C₄	—	9	2	no	—
240	C₃×C₄²	—	2	1	no	—
241	C₃×C₄²	—	2	2	no	—
242	C₃×C₄²	—	9	1	no	—
243	C₃×C₄²	—	9	1	no	—
244	C₃×C₄²	—	9	1	no	—
245	C₃×C₄²	—	9	2	no	—
246	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
247	C₃×C₄²	C₂×D₉	1	2	yes	—
248	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
249	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
250	(C₂×D₃)⋊C₄	—	3	2	no	—
251	(C₂×D₃)⋊C₄	—	3	2	no	—
252	C₄⋊Dic₃	—	3	1	no	—
253	C₄⋊Dic₃	—	3	2	no	—
254	Dic₃⋊C₄	—	3	2	no	—
255	Dic₃⋊C₄	—	3	2	no	—
256	Dic₃⋊C₄	—	3	2	no	—
257	Dic₃⋊C₄	—	3	2	no	—
258	Dic₃⋊C₄	—	3	2	no	—
259	C₄×Dic₃	—	3	1	no	—
260	C₄×Dic₃	—	3	2	no	—
261	C₄×Dic₃	—	3	1	no	—
262	C₄×Dic₃	—	3	1	no	—
263	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
264	C₂×C₃×D₃	—	3	2	no	—
265	C₂×C₃×D₃	—	6	1	no	—
266	C₂×C₃×D₃	—	6	1	no	—
267	C₃²×C₄	—	2	2	no	—
268	C₃²×C₄	—	2	2	no	—
269	C₃²×C₄	—	2	1	no	—
270	C₃²×C₄	#235	1	2	yes	—
271	C₃²×C₄	D₃×Q₈	1	2	yes	—
272	C₃×Dic₃	—	3	2	no	—
273	C₃×Dic₃	—	3	2	no	—
274	C₃×Dic₃	—	6	2	no	—
275	C₃×Dic₃	—	6	1	no	—
276	C₃×Dic₃	—	6	2	no	—
277	C₂²×C₉	—	2	1	no	—
278	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
279	C₂×D₉	—	2	1	no	—
280	C₂×D₉	—	2	1	no	—
281	C₂×D₉	C₂×C₃×Q₈	1	2	yes	—
282	C₄×C₉	—	2	4	no	—
283	C₄×C₉	—	2	2	no	—
284	C₄×C₉	—	2	1	no	—
285	C₄×C₉	—	2	2	no	—
286	C₄×C₉	—	2	2	no	—
287	C₄×C₉	—	2	2	no	—
288	C₄×C₉	—	4	2	no	—
289	C₄×C₉	—	4	1	no	—
290	C₄×C₉	C₂×C₃×Q₈	1	2	yes	—
291	C₄×C₉	C₃×#41	1	2	yes	—
292	Dic₉	—	2	2	no	—
293	Dic₉	—	2	2	no	—
294	Dic₉	—	2	1	no	—
295	Dic₉	C₂×C₃×Q₈	1	2	yes	—
296	Dic₉	C₃×#41	1	2	yes	—
297	C₄⋊Q₈	—	9	1	no	—
298	C₄⋊Q₈	—	9	1	no	—
299	#125	—	9	2	no	—
300	C₂²⋊Q₈	—	9	1	no	—
301	C₂²⋊Q₈	—	9	2	no	—
302	C₂²⋊Q₈	—	9	1	no	—
303	C₄×Q₈	—	9	2	no	—
304	C₄×Q₈	—	9	1	no	—
305	C₄×Q₈	C₃×D₉	1	1	yes	characteristic, complemented
306	#117	—	9	2	no	—
307	C₂×C₄²	—	9	1	no	—
308	C₃×C₉	#533	1	1	yes	characteristic, complemented, Sylow
309	C₂³×C₃	—	9	1	no	—
310	C₂²×D₃	—	3	1	no	—
311	C₃×Q₈	—	2	4	no	—
312	C₃×Q₈	—	2	2	no	—
313	C₃×Q₈	—	2	2	no	—
314	C₃×Q₈	—	18	4	no	—
315	C₃×Q₈	—	18	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	—	2	1	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	9	1	no	—
322	C₂×C₃×C₄	—	9	1	no	—
323	C₂×C₃×C₄	—	9	4	no	—
324	C₂×C₃×C₄	—	9	1	no	—
325	C₂×C₃×C₄	—	9	2	no	—
326	C₂×C₃×C₄	—	9	2	no	—
327	C₂×C₃×C₄	—	18	2	no	—
328	C₂×C₃×C₄	—	18	2	no	—
329	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
331	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
332	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
336	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
337	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
338	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
339	C₂×Dic₃	—	3	1	no	—
340	C₂×Dic₃	—	3	1	no	—
341	C₂×Dic₃	—	3	1	no	—
342	C₂×Dic₃	—	3	2	no	—
343	C₂×Dic₃	—	3	2	no	—
344	C₄×D₃	—	3	4	no	—
345	C₄×D₃	—	6	2	no	—
346	C₄×D₃	—	6	2	no	—
347	Dic₆	—	6	4	no	—
348	Dic₆	—	6	2	no	—
349	C₂×C₃²	C₂×#235	1	1	yes	characteristic
350	C₂×C₃²	C₂×D₃×Q₈	1	1	yes	characteristic
351	C₂×C₃²	D₃×#41	1	1	yes	characteristic
352	C₃×D₃	—	6	2	no	—
353	C₂×C₉	—	2	1	no	—
354	C₂×C₉	—	2	1	no	—
355	C₂×C₉	—	2	1	no	—
356	C₂×C₉	C₂²×C₃×Q₈	1	1	yes	characteristic
357	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
358	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
359	D₉	—	2	2	no	—
360	C₂×Q₈	—	9	2	no	—
361	C₂×Q₈	—	9	1	no	—
362	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic
363	C₂²×C₄	—	9	1	no	—
364	C₂²×C₄	—	9	1	no	—
365	C₂²×C₄	—	9	1	no	—
366	C₄⋊C₄	—	9	2	no	—
367	C₄⋊C₄	—	9	2	no	—
368	C₄⋊C₄	—	9	2	no	—
369	C₄⋊C₄	—	9	2	no	—
370	C₄⋊C₄	—	9	2	no	—
371	C₄⋊C₄	—	9	2	no	—
372	C₄⋊C₄	—	9	1	no	—
373	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	—
374	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
375	C₂²⋊C₄	—	9	2	no	—
376	C₂²⋊C₄	—	9	2	no	—
377	C₄²	—	9	1	no	—
378	C₄²	—	9	1	no	—
379	C₄²	—	9	1	no	—
380	C₄²	—	9	2	no	—
381	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
382	C₄²	C₂×C₃×D₉	1	2	yes	—
383	C₂²×C₃	—	2	1	no	—
384	C₂²×C₃	—	9	2	no	—
385	C₂²×C₃	—	18	1	no	—
386	C₂²×C₃	—	18	1	no	—
387	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
388	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
389	C₂×D₃	—	3	2	no	—
390	C₂×D₃	—	6	1	no	—
391	C₂×D₃	—	6	1	no	—
392	C₃×C₄	—	2	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	1	no	—
398	C₃×C₄	—	2	2	no	—
399	C₃×C₄	—	2	2	no	—
400	C₃×C₄	—	2	2	no	—
401	C₃×C₄	—	4	1	no	—
402	C₃×C₄	—	4	2	no	—
403	C₃×C₄	—	9	2	no	—
404	C₃×C₄	—	9	2	no	—
405	C₃×C₄	—	18	1	no	—
406	C₃×C₄	—	18	2	no	—
407	C₃×C₄	—	18	2	no	—
408	C₃×C₄	#3697	1	2	yes	—
409	C₃×C₄	Q₈×D₉	1	2	yes	—
410	C₃×C₄	C₃×#235	1	2	yes	—
411	C₃×C₄	C₃×D₃×Q₈	1	2	yes	—
412	Dic₃	—	3	2	no	—
413	Dic₃	—	3	2	no	—
414	Dic₃	—	6	2	no	—
415	Dic₃	—	6	1	no	—
416	Dic₃	—	6	2	no	—
417	C₃²	#5578	1	1	yes	characteristic
418	C₉	—	2	1	no	—
419	C₉	C₃×#533	1	1	yes	characteristic, complemented
420	C₂³	—	9	1	no	—
421	Q₈	—	2	2	no	—
422	Q₈	—	18	4	no	—
423	Q₈	—	18	2	no	—
424	C₂×C₄	—	9	1	no	—
425	C₂×C₄	—	9	1	no	—
426	C₂×C₄	—	9	4	no	—
427	C₂×C₄	—	9	1	no	—
428	C₂×C₄	—	9	2	no	—
429	C₂×C₄	—	9	2	no	—
430	C₂×C₄	—	18	2	no	—
431	C₂×C₄	—	18	2	no	—
432	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
433	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
434	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
435	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
436	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
437	C₂×C₃	—	2	1	no	—
438	C₂×C₃	—	2	1	no	—
439	C₂×C₃	—	2	1	no	—
440	C₂×C₃	—	18	2	no	—
441	C₂×C₃	C₂×#3697	1	1	yes	characteristic
442	C₂×C₃	C₂×Q₈×D₉	1	1	yes	characteristic
443	C₂×C₃	#41×D₉	1	1	yes	characteristic
444	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
445	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
446	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
447	D₃	—	6	2	no	—
448	C₂²	—	9	2	no	—
449	C₂²	—	18	1	no	—
450	C₂²	—	18	1	no	—
451	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	2	no	—
455	C₄	—	9	2	no	—
456	C₄	—	9	2	no	—
457	C₄	—	18	1	no	—
458	C₄	—	18	2	no	—
459	C₄	—	18	2	no	—
460	C₄	C₃×#3697	1	2	yes	—
461	C₄	C₃×Q₈×D₉	1	2	yes	—
462	C₃	—	2	1	no	—
463	C₃	#10589680	1	1	yes	characteristic, direct product factor
464	C₃	C₃×#5578	1	1	yes	characteristic
465	C₂	—	18	2	no	—
466	C₂	C₂×C₃×#3697	1	1	yes	characteristic
467	C₂	C₂×C₃×Q₈×D₉	1	1	yes	characteristic
468	C₂	C₃×#41×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×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×#533
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃×C₄ ◁ 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×#63451	C₂	semidirect
7. C₃×#63450	C₂	semidirect
10. C₃×C₄×Dic₁₈	C₂	semidirect
11. C₃×C₄×Dic₁₈	C₂	semidirect
13. #10589680	C₃	direct (N × H)
49. C₄×Q₈×C₉	C₂×C₃	semidirect
51. #63506	C₂×C₃	semidirect
54. #63451	C₂×C₃	semidirect
55. #63450	C₂×C₃	semidirect
58. C₄×Dic₁₈	C₂×C₃	semidirect
59. C₄×Dic₁₈	C₂×C₃	semidirect
74. C₃×C₄×D₉	Q₈	semidirect
153. C₃×C₄×Q₈	D₉	semidirect
204. C₄×D₉	C₃×Q₈	semidirect
305. C₄×Q₈	C₃×D₉	semidirect
308. C₃×C₉	#533	semidirect
419. C₉	C₃×#533	semidirect
463. C₃	#10589680	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×#63459	2
C₃×#63458	2
C₃×#63451	2
C₃×#63450	2
C₃×#63434	2
C₃×C₄²×D₉	2
C₃×C₄×Dic₁₈	2
C₃×#5578	3
#10589680	3

Subgroups — C3×#10589680 #13152684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589680 #13152684