Subgroups — C₃×#10589724 #13152893

Order 1728.

740 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×Q₈×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63506	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63486	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×C₄×Dic₉	C₂	1	1	yes	maximal, characteristic
6	C₃×#63451	C₂	1	2	yes	maximal, complemented
7	C₃×#63450	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#63449	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#63449	C₂	1	2	yes	maximal, complemented
10	C₃×#63440	C₂	1	2	yes	maximal
11	C₃×#63439	C₂	1	2	yes	maximal
12	C₃×#5622	—	3	1	no	maximal
13	#10589724	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
17	C₂²×C₃×Dic₉	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×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₃×#3676	C₂²	1	2	yes	—
24	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
25	C₃×C₄⋊Dic₉	C₂²	1	2	yes	—
26	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
27	C₃×Dic₉⋊C₄	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×C₄×Dic₉	C₂²	1	1	yes	characteristic
32	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
33	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
34	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
35	C₃×C₄×Dic₉	C₂²	1	2	yes	—
36	C₃×C₄×Dic₉	C₂²	1	2	yes	—
37	C₃²×C₂²⋊Q₈	D₃	1	1	yes	characteristic
38	C₃×Q₈×Dic₃	—	3	1	no	—
39	C₃×#944	—	3	1	no	—
40	C₃×#924	—	3	1	no	—
41	C₂×C₃×C₄×Dic₃	—	3	1	no	—
42	C₃×#889	—	3	2	no	—
43	C₃×#888	—	3	1	no	—
44	C₃×#887	—	3	1	no	—
45	C₃×#887	—	3	2	no	—
46	C₃×#878	—	3	2	no	—
47	C₃×#877	—	3	2	no	—
48	C₉×C₂²⋊Q₈	—	2	1	no	—
49	C₉×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
50	Q₈×Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
51	#63506	C₂×C₃	1	1	yes	characteristic, complemented
52	#63486	C₂×C₃	1	1	yes	characteristic
53	C₂×C₄×Dic₉	C₂×C₃	1	1	yes	characteristic
54	#63451	C₂×C₃	1	2	yes	complemented
55	#63450	C₂×C₃	1	1	yes	characteristic, complemented
56	#63449	C₂×C₃	1	2	yes	complemented
57	#63449	C₂×C₃	1	1	yes	characteristic, complemented
58	#63440	C₂×C₃	1	2	yes	—
59	#63439	C₂×C₃	1	2	yes	—
60	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
61	C₃×Q₈×C₉	—	2	2	no	—
62	C₂×C₃×C₄×C₉	—	2	2	no	—
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	—	2	2	no	—
68	C₂×C₃×Dic₉	Q₈	1	4	yes	complemented
69	C₂×C₃×Dic₉	C₂³	1	2	yes	—
70	C₂×C₃×Dic₉	C₂³	1	2	yes	—
71	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
72	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
73	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
74	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
75	C₃×Dic₁₈	—	2	2	no	—
76	C₃×Dic₁₈	—	2	4	no	—
77	C₃×#533	—	9	1	no	—
78	#5622	—	3	1	no	—
79	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
80	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
81	C₂²×C₃×Dic₃	—	3	1	no	—
82	C₂²×C₃×Dic₃	—	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×C₂²⋊C₄	C₂×D₃	1	2	yes	—
88	C₃×#217	—	3	2	no	—
89	C₃×C₄⋊Dic₃	—	3	2	no	—
90	C₃×C₄⋊Dic₃	—	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×C₄×Dic₃	—	3	2	no	—
97	C₃×C₄×Dic₃	—	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	1	no	—
102	C₂×Q₈×C₉	—	2	1	no	—
103	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
104	C₂²×C₄×C₉	—	2	1	no	—
105	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
106	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
107	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
108	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
109	C₂×Dic₁₈	C₂²×C₃	1	2	yes	—
110	C₉×C₄⋊C₄	—	2	1	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	2	yes	—
114	C₉×C₂²⋊C₄	—	2	2	no	—
115	C₉×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
116	#3676	C₂²×C₃	1	2	yes	—
117	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
118	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
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	2	yes	—
123	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
124	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
125	C₄×Dic₉	C₂²×C₃	1	2	yes	—
126	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
127	C₄×Dic₉	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	—	2	1	no	—
131	C₂²×C₃×C₉	—	2	1	no	—
132	C₂²×C₃×C₉	C₂×Q₈	1	2	yes	—
133	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
134	C₃×C₄×C₉	—	2	2	no	—
135	C₃×C₄×C₉	—	2	1	no	—
136	C₃×C₄×C₉	—	2	2	no	—
137	C₃×C₄×C₉	#41	1	2	yes	—
138	C₃×Dic₉	—	2	2	no	—
139	C₃×Dic₉	—	2	2	no	—
140	C₃×Dic₉	—	2	1	no	—
141	C₃×Dic₉	C₂×Q₈	1	2	yes	—
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	—	2	1	no	—
148	C₃×C₂²⋊Q₈	—	9	1	no	—
149	C₃×C₂²⋊Q₈	—	9	2	no	—
150	C₃×C₂²⋊Q₈	D₉	1	1	yes	characteristic
151	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
152	C₃×C₄×Q₈	—	9	1	no	—
153	C₃×C₄×Q₈	—	9	1	no	—
154	C₃×C₄×Q₈	—	9	2	no	—
155	C₃×#117	—	9	2	no	—
156	C₂×C₃×C₄²	—	9	1	no	—
157	Q₈×Dic₃	—	3	1	no	—
158	#944	—	3	1	no	—
159	#924	—	3	1	no	—
160	C₂×C₄×Dic₃	—	3	1	no	—
161	#889	—	3	2	no	—
162	#888	—	3	1	no	—
163	#887	—	3	1	no	—
164	#887	—	3	2	no	—
165	#878	—	3	2	no	—
166	#877	—	3	2	no	—
167	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
168	C₃²×Q₈	—	2	2	no	—
169	C₂×C₃²×C₄	—	2	2	no	—
170	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
171	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
172	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
173	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
174	C₂×C₃×Dic₃	—	3	4	no	—
175	C₂×C₃×Dic₃	—	3	1	no	—
176	C₂×C₃×Dic₃	—	3	1	no	—
177	C₂×C₃×Dic₃	—	3	1	no	—
178	C₂×C₃×Dic₃	—	3	1	no	—
179	C₂×C₃×Dic₃	—	3	2	no	—
180	C₂×C₃×Dic₃	—	3	2	no	—
181	C₂×C₃×Dic₃	—	6	2	no	—
182	C₃×Dic₆	—	6	4	no	—
183	C₃×Dic₆	—	6	2	no	—
184	C₂³×C₉	—	2	1	no	—
185	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
186	Q₈×C₉	—	2	2	no	—
187	Q₈×C₉	—	4	2	no	—
188	C₂×C₄×C₉	—	2	2	no	—
189	C₂×C₄×C₉	—	2	1	no	—
190	C₂×C₄×C₉	—	2	2	no	—
191	C₂×C₄×C₉	—	2	2	no	—
192	C₂×C₄×C₉	—	2	1	no	—
193	C₂×C₄×C₉	—	4	2	no	—
194	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
195	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
196	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
197	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
198	C₂×Dic₉	—	2	2	no	—
199	C₂×Dic₉	C₃×Q₈	1	4	yes	complemented
200	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
201	C₂×Dic₉	C₂³×C₃	1	2	yes	—
202	C₂×Dic₉	C₂³×C₃	1	2	yes	—
203	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
204	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
205	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
206	Dic₁₈	—	2	2	no	—
207	Dic₁₈	—	2	4	no	—
208	#533	—	9	1	no	Sylow
209	C₂×C₃×C₉	—	2	2	no	—
210	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
211	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
212	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
213	C₂×C₃×Q₈	—	2	1	no	—
214	C₂×C₃×Q₈	—	9	2	no	—
215	C₂×C₃×Q₈	—	9	1	no	—
216	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic
217	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
218	C₂²×C₃×C₄	—	2	1	no	—
219	C₂²×C₃×C₄	—	9	1	no	—
220	C₂²×C₃×C₄	—	9	1	no	—
221	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
223	C₂²×Dic₃	—	3	1	no	—
224	C₂²×Dic₃	—	3	1	no	—
225	C₂×Dic₆	—	3	2	no	—
226	C₂×Dic₆	—	3	1	no	—
227	C₃×C₄⋊C₄	—	2	2	no	—
228	C₃×C₄⋊C₄	—	2	1	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	2	no	—
234	C₃×C₄⋊C₄	—	9	2	no	—
235	C₃×C₄⋊C₄	—	9	1	no	—
236	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	—
237	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
238	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
239	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
240	C₃×C₂²⋊C₄	—	2	2	no	—
241	C₃×C₂²⋊C₄	—	9	2	no	—
242	C₃×C₂²⋊C₄	C₂×D₉	1	2	yes	—
243	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
244	C₃×C₄²	—	9	1	no	—
245	C₃×C₄²	—	9	1	no	—
246	C₃×C₄²	—	9	1	no	—
247	C₃×C₄²	—	9	1	no	—
248	C₃×C₄²	—	9	2	no	—
249	C₃×C₄²	—	9	2	no	—
250	#217	—	3	2	no	—
251	C₄⋊Dic₃	—	3	2	no	—
252	C₄⋊Dic₃	—	3	1	no	—
253	Dic₃⋊C₄	—	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	C₄×Dic₃	—	3	2	no	—
259	C₄×Dic₃	—	3	2	no	—
260	C₄×Dic₃	—	3	1	no	—
261	C₄×Dic₃	—	3	1	no	—
262	C₄×Dic₃	—	3	1	no	—
263	C₄×Dic₃	—	3	1	no	—
264	C₂²×C₃²	—	2	1	no	—
265	C₂²×C₃²	—	2	1	no	—
266	C₂²×C₃²	D₃×Q₈	1	2	yes	—
267	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
268	C₃²×C₄	—	2	1	no	—
269	C₃²×C₄	—	2	2	no	—
270	C₃²×C₄	—	2	2	no	—
271	C₃²×C₄	#237	1	2	yes	—
272	C₃×Dic₃	—	3	2	no	—
273	C₃×Dic₃	—	3	2	no	—
274	C₃×Dic₃	—	3	2	no	—
275	C₃×Dic₃	—	6	2	no	—
276	C₃×Dic₃	—	6	2	no	—
277	C₃×Dic₃	—	6	1	no	—
278	C₂²×C₉	—	2	1	no	—
279	C₂²×C₉	—	2	1	no	—
280	C₂²×C₉	—	2	1	no	—
281	C₂²×C₉	—	2	2	no	—
282	C₂²×C₉	—	4	1	no	—
283	C₂²×C₉	—	4	1	no	—
284	C₂²×C₉	C₂×C₃×Q₈	1	2	yes	—
285	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
286	C₄×C₉	—	2	2	no	—
287	C₄×C₉	—	2	1	no	—
288	C₄×C₉	—	2	2	no	—
289	C₄×C₉	—	2	2	no	—
290	C₄×C₉	—	4	2	no	—
291	C₄×C₉	—	4	1	no	—
292	C₄×C₉	—	4	2	no	—
293	C₄×C₉	C₃×#41	1	2	yes	—
294	Dic₉	—	2	2	no	—
295	Dic₉	—	2	2	no	—
296	Dic₉	—	2	1	no	—
297	Dic₉	C₂×C₃×Q₈	1	2	yes	—
298	Dic₉	C₂×C₃×Q₈	1	2	yes	—
299	Dic₉	C₃×#41	1	2	yes	—
300	C₄⋊Q₈	—	9	1	no	—
301	C₄⋊Q₈	—	9	1	no	—
302	#125	—	9	2	no	—
303	C₂²⋊Q₈	—	9	1	no	—
304	C₂²⋊Q₈	—	9	2	no	—
305	C₂²⋊Q₈	C₃×D₉	1	1	yes	characteristic
306	C₄×Q₈	—	9	1	no	—
307	C₄×Q₈	—	9	1	no	—
308	C₄×Q₈	—	9	2	no	—
309	#117	—	9	2	no	—
310	C₂×C₄²	—	9	1	no	—
311	C₃×C₉	#533	1	1	yes	characteristic, complemented, Sylow
312	C₂³×C₃	—	2	1	no	—
313	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
314	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
315	C₃×Q₈	—	2	2	no	—
316	C₃×Q₈	—	2	2	no	—
317	C₃×Q₈	—	4	2	no	—
318	C₃×Q₈	—	18	4	no	—
319	C₃×Q₈	—	18	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	2	2	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	4	2	no	—
327	C₂×C₃×C₄	—	9	4	no	—
328	C₂×C₃×C₄	—	9	1	no	—
329	C₂×C₃×C₄	—	9	1	no	—
330	C₂×C₃×C₄	—	9	1	no	—
331	C₂×C₃×C₄	—	9	1	no	—
332	C₂×C₃×C₄	—	9	2	no	—
333	C₂×C₃×C₄	—	9	2	no	—
334	C₂×C₃×C₄	—	18	2	no	—
335	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
336	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
337	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
338	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
341	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
342	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
343	C₂×Dic₃	—	3	1	no	—
344	C₂×Dic₃	—	3	1	no	—
345	C₂×Dic₃	—	3	1	no	—
346	C₂×Dic₃	—	3	4	no	—
347	C₂×Dic₃	—	3	1	no	—
348	C₂×Dic₃	—	3	2	no	—
349	C₂×Dic₃	—	3	2	no	—
350	C₂×Dic₃	—	6	2	no	—
351	Dic₆	—	6	4	no	—
352	Dic₆	—	6	2	no	—
353	C₂×C₃²	—	2	2	no	—
354	C₂×C₃²	C₂×#237	1	1	yes	characteristic
355	C₂×C₃²	C₂×D₃×Q₈	1	1	yes	characteristic
356	C₂×C₃²	D₃×#41	1	1	yes	characteristic
357	C₂×C₉	—	2	2	no	—
358	C₂×C₉	—	2	1	no	—
359	C₂×C₉	—	2	1	no	—
360	C₂×C₉	—	2	1	no	—
361	C₂×C₉	—	4	2	no	—
362	C₂×C₉	C₂²×C₃×Q₈	1	1	yes	characteristic
363	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
364	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
365	C₂×Q₈	—	9	2	no	—
366	C₂×Q₈	—	9	1	no	—
367	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic
368	C₂²×C₄	—	9	1	no	—
369	C₂²×C₄	—	9	1	no	—
370	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
371	C₄⋊C₄	—	9	2	no	—
372	C₄⋊C₄	—	9	2	no	—
373	C₄⋊C₄	—	9	2	no	—
374	C₄⋊C₄	—	9	2	no	—
375	C₄⋊C₄	—	9	2	no	—
376	C₄⋊C₄	—	9	2	no	—
377	C₄⋊C₄	—	9	1	no	—
378	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	—
379	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
380	C₂²⋊C₄	—	9	2	no	—
381	C₂²⋊C₄	C₂×C₃×D₉	1	2	yes	—
382	C₄²	—	9	1	no	—
383	C₄²	—	9	1	no	—
384	C₄²	—	9	1	no	—
385	C₄²	—	9	1	no	—
386	C₄²	—	9	2	no	—
387	C₄²	—	9	2	no	—
388	C₂²×C₃	—	2	1	no	—
389	C₂²×C₃	—	2	1	no	—
390	C₂²×C₃	—	2	1	no	—
391	C₂²×C₃	—	2	1	no	—
392	C₂²×C₃	—	2	1	no	—
393	C₂²×C₃	—	2	2	no	—
394	C₂²×C₃	—	4	1	no	—
395	C₂²×C₃	—	4	1	no	—
396	C₂²×C₃	Q₈×D₉	1	2	yes	—
397	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
398	C₂²×C₃	C₃×D₃×Q₈	1	2	yes	—
399	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
400	C₃×C₄	—	2	1	no	—
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	2	2	no	—
403	C₃×C₄	—	2	1	no	—
404	C₃×C₄	—	2	2	no	—
405	C₃×C₄	—	2	2	no	—
406	C₃×C₄	—	2	2	no	—
407	C₃×C₄	—	4	1	no	—
408	C₃×C₄	—	4	2	no	—
409	C₃×C₄	—	4	2	no	—
410	C₃×C₄	—	9	2	no	—
411	C₃×C₄	—	9	2	no	—
412	C₃×C₄	—	9	2	no	—
413	C₃×C₄	—	18	2	no	—
414	C₃×C₄	—	18	1	no	—
415	C₃×C₄	—	18	2	no	—
416	C₃×C₄	#3699	1	2	yes	—
417	C₃×C₄	C₃×#237	1	2	yes	—
418	Dic₃	—	3	2	no	—
419	Dic₃	—	3	2	no	—
420	Dic₃	—	3	2	no	—
421	Dic₃	—	6	2	no	—
422	Dic₃	—	6	2	no	—
423	Dic₃	—	6	1	no	—
424	C₃²	#5622	1	1	yes	characteristic
425	C₉	—	2	1	no	—
426	C₉	C₃×#533	1	1	yes	characteristic, complemented
427	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
428	Q₈	—	2	2	no	—
429	Q₈	—	18	4	no	—
430	Q₈	—	18	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	9	1	no	—
433	C₂×C₄	—	9	1	no	—
434	C₂×C₄	—	9	1	no	—
435	C₂×C₄	—	9	4	no	—
436	C₂×C₄	—	9	1	no	—
437	C₂×C₄	—	9	2	no	—
438	C₂×C₄	—	9	2	no	—
439	C₂×C₄	—	18	2	no	—
440	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
441	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
442	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
443	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
444	C₂×C₃	—	2	2	no	—
445	C₂×C₃	—	2	2	no	—
446	C₂×C₃	—	2	1	no	—
447	C₂×C₃	—	2	1	no	—
448	C₂×C₃	—	2	1	no	—
449	C₂×C₃	—	4	2	no	—
450	C₂×C₃	C₂×#3699	1	1	yes	characteristic
451	C₂×C₃	C₂×Q₈×D₉	1	1	yes	characteristic
452	C₂×C₃	#41×D₉	1	1	yes	characteristic
453	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
454	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
455	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	C₃×Q₈×D₉	1	2	yes	—
459	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	9	2	no	—
464	C₄	—	9	2	no	—
465	C₄	—	9	2	no	—
466	C₄	—	18	2	no	—
467	C₄	—	18	1	no	—
468	C₄	—	18	2	no	—
469	C₄	C₃×#3699	1	2	yes	—
470	C₃	—	2	1	no	—
471	C₃	#10589724	1	1	yes	characteristic, direct product factor
472	C₃	C₃×#5622	1	1	yes	characteristic
473	C₂	—	2	2	no	—
474	C₂	C₂×C₃×#3699	1	1	yes	characteristic
475	C₂	C₂×C₃×Q₈×D₉	1	1	yes	characteristic
476	C₂	C₃×#41×D₉	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×C₂²⋊Q₈	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₂³×C₃²	C₂²×D₃
hypercenter	C₃×C₂²⋊Q₈	D₉
hypocenter	C₉	C₃×#533
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₃×Q₈×Dic₉	C₂	semidirect
3. C₃×#63506	C₂	semidirect
6. C₃×#63451	C₂	semidirect
7. C₃×#63450	C₂	semidirect
8. C₃×#63449	C₂	semidirect
9. C₃×#63449	C₂	semidirect
13. #10589724	C₃	direct (N × H)
50. Q₈×Dic₉	C₂×C₃	semidirect
51. #63506	C₂×C₃	semidirect
54. #63451	C₂×C₃	semidirect
55. #63450	C₂×C₃	semidirect
56. #63449	C₂×C₃	semidirect
57. #63449	C₂×C₃	semidirect
68. C₂×C₃×Dic₉	Q₈	semidirect
199. C₂×Dic₉	C₃×Q₈	semidirect
311. C₃×C₉	#533	semidirect
426. C₉	C₃×#533	semidirect
471. C₃	#10589724	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×C₂²⋊Q₈	2
C₃×Q₈×Dic₉	2
C₃×#63506	2
C₃×#63486	2
C₂×C₃×C₄×Dic₉	2
C₃×#63451	2
C₃×#63450	2
C₃×#63449	2
C₃×#63440	2
C₃×#63439	2
C₃×#5622	3
#10589724	3

Subgroups — C3×#10589724 #13152893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589724 #13152893