Subgroups — C₃×#10589831 #13153298

Order 1728.

686 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#63508	C₂	1	2	yes	maximal
3	C₃×#63506	C₂	1	2	yes	maximal, complemented
4	C₃×#63458	C₂	1	2	yes	maximal
5	C₃×#63454	C₂	1	1	yes	maximal, characteristic
6	C₃×C₄⋊C₄×D₉	C₂	1	1	yes	maximal, characteristic
7	C₃×#63452	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#63451	C₂	1	2	yes	maximal, complemented
9	C₃×#63450	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#63434	C₂	1	1	yes	maximal, characteristic
11	C₃×#63432	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5729	—	3	1	no	maximal
13	#10589831	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×Q₈×C₉	C₂²	1	2	yes	—
15	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
16	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
17	C₂×C₃×Dic₁₈	C₂²	1	2	yes	—
18	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
22	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
23	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
24	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
25	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
31	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
37	C₃²×C₄⋊Q₈	D₃	1	1	yes	characteristic
38	C₃×#946	—	3	2	no	—
39	C₃×#944	—	3	2	no	—
40	C₃×#896	—	3	2	no	—
41	C₃×#892	—	3	1	no	—
42	C₃×D₃×C₄⋊C₄	—	3	1	no	—
43	C₃×#890	—	3	1	no	—
44	C₃×#889	—	3	2	no	—
45	C₃×#888	—	3	1	no	—
46	C₃×#872	—	3	1	no	—
47	C₃×#870	—	3	1	no	—
48	C₉×C₄⋊Q₈	—	2	1	no	—
49	C₉×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
50	#63508	C₂×C₃	1	2	yes	—
51	#63506	C₂×C₃	1	2	yes	complemented
52	#63458	C₂×C₃	1	2	yes	—
53	#63454	C₂×C₃	1	1	yes	characteristic
54	C₄⋊C₄×D₉	C₂×C₃	1	1	yes	characteristic
55	#63452	C₂×C₃	1	1	yes	characteristic, complemented
56	#63451	C₂×C₃	1	2	yes	complemented
57	#63450	C₂×C₃	1	1	yes	characteristic, complemented
58	#63434	C₂×C₃	1	1	yes	characteristic
59	#63432	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂²×C₃×D₉	C₂³	1	1	yes	characteristic
61	C₃×Q₈×C₉	—	4	2	no	—
62	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
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	1	yes	characteristic
66	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
68	C₂×C₃×Dic₉	C₂³	1	2	yes	—
69	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
70	C₂×C₃×Dic₉	C₂³	1	2	yes	—
71	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
72	C₃×C₄×D₉	—	4	2	no	—
73	C₃×C₄×D₉	Q₈	1	4	yes	complemented
74	C₃×Dic₁₈	—	4	2	no	—
75	C₃×#544	—	9	1	no	—
76	#5729	—	3	1	no	—
77	C₂×C₃²×Q₈	C₂×D₃	1	2	yes	—
78	C₂×C₃×C₄×D₃	—	3	1	no	—
79	C₂×C₃×C₄×D₃	—	3	2	no	—
80	C₂×C₃×Dic₆	—	3	2	no	—
81	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
82	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
83	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
84	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
85	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
86	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
87	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
88	C₃×C₄⋊Dic₃	—	3	1	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	1	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	1	no	—
97	C₃×Dic₃⋊C₄	—	3	2	no	—
98	C₃×C₄×Dic₃	—	3	1	no	—
99	C₃×C₄×Dic₃	—	3	2	no	—
100	C₂×Q₈×C₉	—	2	2	no	—
101	C₂×Q₈×C₉	C₂²×C₃	1	2	yes	—
102	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
103	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
104	C₂×Dic₁₈	C₂²×C₃	1	2	yes	—
105	C₉×C₄⋊C₄	—	2	1	no	—
106	C₉×C₄⋊C₄	—	2	2	no	—
107	C₉×C₄⋊C₄	—	2	1	no	—
108	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
109	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
110	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
111	C₄²×C₉	—	2	1	no	—
112	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
113	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
115	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
117	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
118	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
119	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
125	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	C₄×Dic₉	C₂²×C₃	1	2	yes	—
127	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
128	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
129	C₂×C₃×D₉	—	2	1	no	—
130	C₂×C₃×D₉	—	2	1	no	—
131	C₂×C₃×D₉	C₂×Q₈	1	2	yes	—
132	C₃×C₄×C₉	—	2	1	no	—
133	C₃×C₄×C₉	—	2	2	no	—
134	C₃×C₄×C₉	—	2	2	no	—
135	C₃×C₄×C₉	—	2	1	no	—
136	C₃×C₄×C₉	C₂×Q₈	1	2	yes	—
137	C₃×Dic₉	—	2	1	no	—
138	C₃×Dic₉	—	2	2	no	—
139	C₃×Dic₉	—	2	1	no	—
140	C₃×Dic₉	—	2	2	no	—
141	C₃×Dic₉	C₂×Q₈	1	2	yes	—
142	C₃×C₄⋊Q₈	—	2	1	no	—
143	C₃×C₄⋊Q₈	—	9	2	no	—
144	C₃×C₄⋊Q₈	—	9	1	no	—
145	C₃×C₄⋊Q₈	D₉	1	1	yes	characteristic, complemented
146	C₃×C₄⋊Q₈	C₃×D₃	1	1	yes	characteristic
147	C₃×#125	—	9	2	no	—
148	C₃×#125	—	9	1	no	—
149	C₃×#125	—	9	1	no	—
150	C₃×C₂²⋊Q₈	—	9	2	no	—
151	C₃×C₂²⋊Q₈	—	9	2	no	—
152	C₃×#117	—	9	1	no	—
153	C₃×#117	—	9	1	no	—
154	C₂×C₃×C₄⋊C₄	—	9	1	no	—
155	#946	—	3	2	no	—
156	#944	—	3	2	no	—
157	#896	—	3	2	no	—
158	#892	—	3	1	no	—
159	D₃×C₄⋊C₄	—	3	1	no	—
160	#890	—	3	1	no	—
161	#889	—	3	2	no	—
162	#888	—	3	1	no	—
163	#872	—	3	1	no	—
164	#870	—	3	1	no	—
165	C₂²×C₃×D₃	—	3	1	no	—
166	C₃²×Q₈	—	4	2	no	—
167	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
168	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
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	1	yes	characteristic
172	C₂×C₃×Dic₃	—	3	1	no	—
173	C₂×C₃×Dic₃	—	3	1	no	—
174	C₂×C₃×Dic₃	—	3	2	no	—
175	C₂×C₃×Dic₃	—	3	1	no	—
176	C₂×C₃×Dic₃	—	3	2	no	—
177	C₃×C₄×D₃	—	3	4	no	—
178	C₃×C₄×D₃	—	12	2	no	—
179	C₃×Dic₆	—	12	2	no	—
180	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
181	Q₈×C₉	—	4	2	no	—
182	Q₈×C₉	—	4	4	no	—
183	C₂×C₄×C₉	—	2	1	no	—
184	C₂×C₄×C₉	—	2	1	no	—
185	C₂×C₄×C₉	—	2	1	no	—
186	C₂×C₄×C₉	—	2	2	no	—
187	C₂×C₄×C₉	—	2	2	no	—
188	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
189	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
193	C₂×Dic₉	C₂³×C₃	1	2	yes	—
194	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
195	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
196	C₂×Dic₉	C₂³×C₃	1	2	yes	—
197	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
198	C₄×D₉	—	4	2	no	—
199	C₄×D₉	C₃×Q₈	1	4	yes	complemented
200	Dic₁₈	—	4	2	no	—
201	#544	—	9	1	no	Sylow
202	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
203	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
205	C₃×D₉	—	2	2	no	—
206	C₂×C₃×Q₈	—	2	2	no	—
207	C₂×C₃×Q₈	—	9	2	no	—
208	C₂×C₃×Q₈	C₂×D₉	1	2	yes	—
209	C₂×C₃×Q₈	C₂×C₃×D₃	1	2	yes	—
210	C₂²×C₃×C₄	—	9	1	no	—
211	C₂²×C₃×C₄	—	9	2	no	—
212	C₂×C₄×D₃	—	3	1	no	—
213	C₂×C₄×D₃	—	3	2	no	—
214	C₂×Dic₆	—	3	2	no	—
215	C₃×C₄⋊C₄	—	2	1	no	—
216	C₃×C₄⋊C₄	—	2	1	no	—
217	C₃×C₄⋊C₄	—	2	2	no	—
218	C₃×C₄⋊C₄	—	9	2	no	—
219	C₃×C₄⋊C₄	—	9	1	no	—
220	C₃×C₄⋊C₄	—	9	1	no	—
221	C₃×C₄⋊C₄	—	9	2	no	—
222	C₃×C₄⋊C₄	—	9	2	no	—
223	C₃×C₄⋊C₄	—	9	2	no	—
224	C₃×C₄⋊C₄	—	9	2	no	—
225	C₃×C₄⋊C₄	—	9	1	no	—
226	C₃×C₄⋊C₄	—	9	1	no	—
227	C₃×C₄⋊C₄	—	9	2	no	—
228	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
229	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
230	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	—
231	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
232	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
233	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
234	C₃×C₂²⋊C₄	—	9	2	no	—
235	C₃×C₂²⋊C₄	—	9	1	no	—
236	C₃×C₂²⋊C₄	—	9	1	no	—
237	C₃×C₄²	—	2	1	no	—
238	C₃×C₄²	—	9	2	no	—
239	C₃×C₄²	—	9	1	no	—
240	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
241	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
242	(C₂×D₃)⋊C₄	—	3	1	no	—
243	(C₂×D₃)⋊C₄	—	3	1	no	—
244	(C₂×D₃)⋊C₄	—	3	2	no	—
245	C₄⋊Dic₃	—	3	1	no	—
246	C₄⋊Dic₃	—	3	1	no	—
247	C₄⋊Dic₃	—	3	2	no	—
248	Dic₃⋊C₄	—	3	2	no	—
249	Dic₃⋊C₄	—	3	2	no	—
250	Dic₃⋊C₄	—	3	1	no	—
251	Dic₃⋊C₄	—	3	1	no	—
252	Dic₃⋊C₄	—	3	2	no	—
253	Dic₃⋊C₄	—	3	2	no	—
254	Dic₃⋊C₄	—	3	2	no	—
255	C₄×Dic₃	—	3	1	no	—
256	C₄×Dic₃	—	3	2	no	—
257	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
258	C₂×C₃×D₃	—	3	2	no	—
259	C₂×C₃×D₃	—	6	1	no	—
260	C₂×C₃×D₃	—	6	1	no	—
261	C₃²×C₄	—	2	1	no	—
262	C₃²×C₄	—	2	1	no	—
263	C₃²×C₄	—	2	2	no	—
264	C₃²×C₄	—	2	2	no	—
265	C₃²×C₄	D₃×Q₈	1	2	yes	—
266	C₃×Dic₃	—	3	2	no	—
267	C₃×Dic₃	—	6	1	no	—
268	C₃×Dic₃	—	6	2	no	—
269	C₃×Dic₃	—	6	1	no	—
270	C₃×Dic₃	—	6	2	no	—
271	C₂²×C₉	—	2	1	no	—
272	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
273	C₂×D₉	—	2	1	no	—
274	C₂×D₉	—	2	1	no	—
275	C₂×D₉	C₂×C₃×Q₈	1	2	yes	—
276	C₄×C₉	—	2	2	no	—
277	C₄×C₉	—	2	2	no	—
278	C₄×C₉	—	2	2	no	—
279	C₄×C₉	—	2	2	no	—
280	C₄×C₉	—	2	1	no	—
281	C₄×C₉	—	2	1	no	—
282	C₄×C₉	—	2	2	no	—
283	C₄×C₉	—	4	2	no	—
284	C₄×C₉	—	4	2	no	—
285	C₄×C₉	C₂×C₃×Q₈	1	2	yes	—
286	Dic₉	—	2	1	no	—
287	Dic₉	—	2	2	no	—
288	Dic₉	—	2	2	no	—
289	Dic₉	—	2	1	no	—
290	Dic₉	C₂×C₃×Q₈	1	2	yes	—
291	C₄⋊Q₈	—	9	2	no	—
292	C₄⋊Q₈	—	9	1	no	—
293	C₄⋊Q₈	C₃×D₉	1	1	yes	characteristic, complemented
294	#125	—	9	2	no	—
295	#125	—	9	1	no	—
296	#125	—	9	1	no	—
297	C₂²⋊Q₈	—	9	2	no	—
298	C₂²⋊Q₈	—	9	2	no	—
299	#117	—	9	1	no	—
300	#117	—	9	1	no	—
301	C₂×C₄⋊C₄	—	9	1	no	—
302	C₃×C₉	#544	1	1	yes	characteristic, complemented, Sylow
303	C₂³×C₃	—	9	1	no	—
304	C₂²×D₃	—	3	1	no	—
305	C₃×Q₈	—	4	2	no	—
306	C₃×Q₈	—	4	2	no	—
307	C₃×Q₈	—	4	4	no	—
308	C₃×Q₈	—	36	2	no	—
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	—	2	1	no	—
311	C₂×C₃×C₄	—	2	1	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	9	1	no	—
315	C₂×C₃×C₄	—	9	4	no	—
316	C₂×C₃×C₄	—	9	1	no	—
317	C₂×C₃×C₄	—	9	2	no	—
318	C₂×C₃×C₄	—	9	1	no	—
319	C₂×C₃×C₄	—	9	2	no	—
320	C₂×C₃×C₄	—	36	2	no	—
321	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
322	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
325	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
327	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
330	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
331	C₂×Dic₃	—	3	1	no	—
332	C₂×Dic₃	—	3	1	no	—
333	C₂×Dic₃	—	3	2	no	—
334	C₂×Dic₃	—	3	1	no	—
335	C₂×Dic₃	—	3	2	no	—
336	C₄×D₃	—	3	4	no	—
337	C₄×D₃	—	12	2	no	—
338	Dic₆	—	12	2	no	—
339	C₂×C₃²	#1004	1	1	yes	characteristic
340	C₂×C₃²	C₂×D₃×Q₈	1	1	yes	characteristic
341	C₂×C₃²	#1007	1	1	yes	characteristic
342	C₃×D₃	—	6	2	no	—
343	C₂×C₉	—	2	1	no	—
344	C₂×C₉	—	2	1	no	—
345	C₂×C₉	—	2	1	no	—
346	C₂×C₉	C₂²×C₃×Q₈	1	1	yes	characteristic
347	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
349	D₉	—	2	2	no	—
350	C₂×Q₈	—	9	2	no	—
351	C₂×Q₈	C₂×C₃×D₉	1	2	yes	—
352	C₂²×C₄	—	9	1	no	—
353	C₂²×C₄	—	9	2	no	—
354	C₄⋊C₄	—	9	2	no	—
355	C₄⋊C₄	—	9	1	no	—
356	C₄⋊C₄	—	9	1	no	—
357	C₄⋊C₄	—	9	1	no	—
358	C₄⋊C₄	—	9	1	no	—
359	C₄⋊C₄	—	9	2	no	—
360	C₄⋊C₄	—	9	2	no	—
361	C₄⋊C₄	—	9	2	no	—
362	C₄⋊C₄	—	9	2	no	—
363	C₄⋊C₄	—	9	2	no	—
364	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
365	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
366	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	—
367	C₂²⋊C₄	—	9	2	no	—
368	C₂²⋊C₄	—	9	1	no	—
369	C₂²⋊C₄	—	9	1	no	—
370	C₄²	—	9	2	no	—
371	C₄²	—	9	1	no	—
372	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
373	C₂²×C₃	—	2	1	no	—
374	C₂²×C₃	—	9	2	no	—
375	C₂²×C₃	—	18	1	no	—
376	C₂²×C₃	—	18	1	no	—
377	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
378	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
379	C₂×D₃	—	3	2	no	—
380	C₂×D₃	—	6	1	no	—
381	C₂×D₃	—	6	1	no	—
382	C₃×C₄	—	2	2	no	—
383	C₃×C₄	—	2	2	no	—
384	C₃×C₄	—	2	2	no	—
385	C₃×C₄	—	2	2	no	—
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	—	2	1	no	—
388	C₃×C₄	—	2	2	no	—
389	C₃×C₄	—	2	1	no	—
390	C₃×C₄	—	2	2	no	—
391	C₃×C₄	—	2	1	no	—
392	C₃×C₄	—	2	2	no	—
393	C₃×C₄	—	4	2	no	—
394	C₃×C₄	—	4	2	no	—
395	C₃×C₄	—	9	2	no	—
396	C₃×C₄	—	18	2	no	—
397	C₃×C₄	—	18	1	no	—
398	C₃×C₄	—	18	1	no	—
399	C₃×C₄	—	18	2	no	—
400	C₃×C₄	Q₈×D₉	1	2	yes	—
401	C₃×C₄	C₃×D₃×Q₈	1	2	yes	—
402	Dic₃	—	3	2	no	—
403	Dic₃	—	6	1	no	—
404	Dic₃	—	6	2	no	—
405	Dic₃	—	6	1	no	—
406	Dic₃	—	6	2	no	—
407	C₃²	#5729	1	1	yes	characteristic
408	C₉	—	2	1	no	—
409	C₉	C₃×#544	1	1	yes	characteristic, complemented
410	C₂³	—	9	1	no	—
411	Q₈	—	4	2	no	—
412	Q₈	—	36	2	no	—
413	C₂×C₄	—	9	1	no	—
414	C₂×C₄	—	9	4	no	—
415	C₂×C₄	—	9	1	no	—
416	C₂×C₄	—	9	2	no	—
417	C₂×C₄	—	9	1	no	—
418	C₂×C₄	—	9	2	no	—
419	C₂×C₄	—	36	2	no	—
420	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
421	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
424	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
425	C₂×C₃	—	2	1	no	—
426	C₂×C₃	—	2	1	no	—
427	C₂×C₃	—	2	1	no	—
428	C₂×C₃	—	18	2	no	—
429	C₂×C₃	#63710	1	1	yes	characteristic
430	C₂×C₃	C₂×Q₈×D₉	1	1	yes	characteristic
431	C₂×C₃	#63713	1	1	yes	characteristic
432	C₂×C₃	C₃×#1004	1	1	yes	characteristic
433	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
434	C₂×C₃	C₃×#1007	1	1	yes	characteristic
435	D₃	—	6	2	no	—
436	C₂²	—	9	2	no	—
437	C₂²	—	18	1	no	—
438	C₂²	—	18	1	no	—
439	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
440	C₄	—	2	2	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	1	no	—
444	C₄	—	9	2	no	—
445	C₄	—	18	2	no	—
446	C₄	—	18	1	no	—
447	C₄	—	18	1	no	—
448	C₄	—	18	2	no	—
449	C₄	C₃×Q₈×D₉	1	2	yes	—
450	C₃	—	2	1	no	—
451	C₃	#10589831	1	1	yes	characteristic, direct product factor
452	C₃	C₃×#5729	1	1	yes	characteristic
453	C₂	—	18	2	no	—
454	C₂	C₃×#63710	1	1	yes	characteristic
455	C₂	C₂×C₃×Q₈×D₉	1	1	yes	characteristic
456	C₂	C₃×#63713	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×C₄⋊Q₈	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₂²×C₃×D₉	C₂³
hypercenter	C₃×C₄⋊Q₈	D₉
hypocenter	C₉	C₃×#544
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×C₄⋊Q₈	C₂	semidirect
3. C₃×#63506	C₂	semidirect
7. C₃×#63452	C₂	semidirect
8. C₃×#63451	C₂	semidirect
9. C₃×#63450	C₂	semidirect
11. C₃×#63432	C₂	semidirect
13. #10589831	C₃	direct (N × H)
49. C₉×C₄⋊Q₈	C₂×C₃	semidirect
51. #63506	C₂×C₃	semidirect
55. #63452	C₂×C₃	semidirect
56. #63451	C₂×C₃	semidirect
57. #63450	C₂×C₃	semidirect
59. #63432	C₂×C₃	semidirect
73. C₃×C₄×D₉	Q₈	semidirect
145. C₃×C₄⋊Q₈	D₉	semidirect
199. C₄×D₉	C₃×Q₈	semidirect
293. C₄⋊Q₈	C₃×D₉	semidirect
302. C₃×C₉	#544	semidirect
409. C₉	C₃×#544	semidirect
451. C₃	#10589831	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×C₄⋊Q₈	2
C₃×#63508	2
C₃×#63506	2
C₃×#63458	2
C₃×#63454	2
C₃×C₄⋊C₄×D₉	2
C₃×#63452	2
C₃×#63451	2
C₃×#63450	2
C₃×#63434	2
C₃×#63432	2
C₃×#5729	3
#10589831	3

Subgroups — C3×#10589831 #13153298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589831 #13153298