Subgroups — C₉×#5733 #13153314

Order 1728.

716 conjugacy classes of subgroups.

The subgroup lattice has 488 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	C₉×#947	C₂	1	2	yes	maximal, complemented
3	C₉×#946	C₂	1	2	yes	maximal, complemented
4	C₉×#898	C₂	1	2	yes	maximal, complemented
5	C₉×#897	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#895	C₂	1	1	yes	maximal, characteristic
7	C₉×#894	C₂	1	2	yes	maximal, complemented
8	C₉×#893	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#887	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#872	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5733	C₃	1	1	yes	maximal, characteristic
13	C₉×#542	—	3	1	no	maximal
14	C₂×C₃×Q₈×C₉	C₂²	1	2	yes	—
15	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
16	C₂×C₉×D₁₂	C₂²	1	2	yes	—
17	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
19	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
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×C₄²×C₉	C₂²	1	1	yes	characteristic
24	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
25	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
26	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
29	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
30	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
31	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
32	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
33	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
34	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
35	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
36	C₄×C₉×Dic₃	C₂²	1	2	yes	—
37	C₃²×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
38	C₃×#947	C₂×C₃	1	2	yes	—
39	C₃×#946	C₂×C₃	1	2	yes	—
40	C₃×#898	C₂×C₃	1	2	yes	—
41	C₃×#897	C₂×C₃	1	1	yes	characteristic
42	C₃×#895	C₂×C₃	1	1	yes	characteristic
43	C₃×#894	C₂×C₃	1	2	yes	—
44	C₃×#893	C₂×C₃	1	1	yes	characteristic
45	C₃×#887	C₂×C₃	1	1	yes	characteristic
46	C₃×#875	C₂×C₃	1	1	yes	characteristic
47	C₃×#872	C₂×C₃	1	1	yes	characteristic
48	C₉×C₄⋊Q₈	—	2	1	no	—
49	C₉×C₄⋊Q₈	D₃	1	1	yes	characteristic, complemented
50	C₉×#126	—	3	2	no	—
51	C₉×#124	—	3	2	no	—
52	C₉×#124	—	3	1	no	—
53	C₉×#123	—	3	2	no	—
54	C₉×C₂²⋊Q₈	—	3	2	no	—
55	C₉×C₂²⋊Q₈	—	3	1	no	—
56	C₉×#121	—	3	1	no	—
57	C₄×Q₈×C₉	—	3	1	no	—
58	C₄×D₄×C₉	—	3	1	no	—
59	C₉×#117	—	3	1	no	—
60	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
61	C₂²×D₃×C₉	C₂³	1	2	yes	—
62	C₃×Q₈×C₉	—	4	2	no	—
63	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
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×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₂×C₉×Dic₃	C₂³	1	2	yes	—
69	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
72	C₉×D₁₂	—	2	2	no	—
73	C₉×D₁₂	—	4	2	no	—
74	C₄×D₃×C₉	—	2	2	no	—
75	C₄×D₃×C₉	—	4	2	no	—
76	C₉×Dic₆	—	2	2	no	—
77	C₃×#542	—	3	1	no	—
78	#5733	C₉	1	1	yes	characteristic, direct product factor
79	C₂×C₃²×Q₈	C₂²×C₃	1	2	yes	—
80	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
82	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
84	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
85	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
88	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
89	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
90	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
92	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
93	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
94	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
95	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
97	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
98	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
99	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
100	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
101	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
102	C₂×Q₈×C₉	—	2	2	no	—
103	C₂×Q₈×C₉	—	3	1	no	—
104	C₂×Q₈×C₉	C₂×D₃	1	2	yes	—
105	C₂×D₄×C₉	—	3	1	no	—
106	C₂×D₄×C₉	—	3	2	no	—
107	C₂²×C₄×C₉	—	3	1	no	—
108	C₂²×C₄×C₉	—	3	2	no	—
109	C₉×C₄⋊C₄	—	2	1	no	—
110	C₉×C₄⋊C₄	—	2	1	no	—
111	C₉×C₄⋊C₄	—	2	2	no	—
112	C₉×C₄⋊C₄	—	3	1	no	—
113	C₉×C₄⋊C₄	—	3	1	no	—
114	C₉×C₄⋊C₄	—	3	2	no	—
115	C₉×C₄⋊C₄	—	3	2	no	—
116	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
117	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
118	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
119	C₉×C₂²⋊C₄	—	3	1	no	—
120	C₉×C₂²⋊C₄	—	3	1	no	—
121	C₉×C₂²⋊C₄	—	3	2	no	—
122	C₉×C₂²⋊C₄	—	3	2	no	—
123	C₉×C₂²⋊C₄	—	3	2	no	—
124	C₉×C₂²⋊C₄	—	3	2	no	—
125	C₉×C₂²⋊C₄	—	3	2	no	—
126	C₄²×C₉	—	2	1	no	—
127	C₄²×C₉	—	3	1	no	—
128	C₄²×C₉	—	3	2	no	—
129	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
130	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
131	C₂×D₃×C₉	—	2	1	no	—
132	C₂×D₃×C₉	—	2	2	no	—
133	C₂×D₃×C₉	—	2	2	no	—
134	C₂×D₃×C₉	—	2	1	no	—
135	C₂×D₃×C₉	—	2	1	no	—
136	C₂×D₃×C₉	—	2	2	no	—
137	C₃×C₄×C₉	—	2	1	no	—
138	C₃×C₄×C₉	—	2	2	no	—
139	C₃×C₄×C₉	—	2	2	no	—
140	C₃×C₄×C₉	—	2	1	no	—
141	C₃×C₄×C₉	#41	1	2	yes	—
142	C₉×Dic₃	—	2	2	no	—
143	C₉×Dic₃	—	2	1	no	—
144	C₉×Dic₃	—	2	1	no	—
145	C₉×Dic₃	—	2	1	no	—
146	C₃×C₄⋊Q₈	—	2	1	no	—
147	C₃×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
148	C₃×C₄⋊Q₈	C₃×D₃	1	1	yes	characteristic
149	C₃×#126	—	3	2	no	—
150	C₃×#124	—	3	2	no	—
151	C₃×#124	—	3	1	no	—
152	C₃×#123	—	3	2	no	—
153	C₃×C₂²⋊Q₈	—	3	2	no	—
154	C₃×C₂²⋊Q₈	—	3	1	no	—
155	C₃×#121	—	3	1	no	—
156	C₃×C₄×Q₈	—	3	1	no	—
157	C₃×C₄×D₄	—	3	1	no	—
158	C₃×#117	—	3	1	no	—
159	#947	C₂×C₉	1	2	yes	complemented
160	#946	C₂×C₉	1	2	yes	complemented
161	#898	C₂×C₉	1	2	yes	complemented
162	#897	C₂×C₉	1	1	yes	characteristic, complemented
163	#895	C₂×C₉	1	1	yes	characteristic
164	#894	C₂×C₉	1	2	yes	complemented
165	#893	C₂×C₉	1	1	yes	characteristic, complemented
166	#887	C₂×C₉	1	1	yes	characteristic, complemented
167	#875	C₂×C₉	1	1	yes	characteristic, complemented
168	#872	C₂×C₉	1	1	yes	characteristic, complemented
169	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
170	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
171	C₃²×Q₈	—	4	2	no	—
172	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
173	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
174	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
175	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
176	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
177	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
178	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
179	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
180	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
181	C₃×D₁₂	—	2	2	no	—
182	C₃×D₁₂	—	4	2	no	—
183	C₃×C₄×D₃	—	2	2	no	—
184	C₃×C₄×D₃	—	4	2	no	—
185	C₃×Dic₆	—	2	2	no	—
186	C₂³×C₉	—	3	2	no	—
187	C₂³×C₉	—	3	1	no	—
188	Q₈×C₉	—	4	2	no	—
189	Q₈×C₉	—	4	4	no	—
190	Q₈×C₉	—	6	2	no	—
191	D₄×C₉	—	6	2	no	—
192	D₄×C₉	—	12	2	no	—
193	C₂×C₄×C₉	—	2	1	no	—
194	C₂×C₄×C₉	—	2	1	no	—
195	C₂×C₄×C₉	—	2	1	no	—
196	C₂×C₄×C₉	—	2	2	no	—
197	C₂×C₄×C₉	—	2	2	no	—
198	C₂×C₄×C₉	—	3	1	no	—
199	C₂×C₄×C₉	—	3	2	no	—
200	C₂×C₄×C₉	—	3	1	no	—
201	C₂×C₄×C₉	—	3	1	no	—
202	C₂×C₄×C₉	—	6	2	no	—
203	C₂×C₄×C₉	—	12	2	no	—
204	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
205	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
206	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
207	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
208	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
209	#542	—	3	1	no	Sylow
210	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
211	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
213	D₃×C₉	—	4	1	no	—
214	D₃×C₉	—	4	2	no	—
215	C₂×C₃×Q₈	—	2	2	no	—
216	C₂×C₃×Q₈	—	3	1	no	—
217	C₂×C₃×Q₈	C₂²×C₉	1	2	yes	—
218	C₂×C₃×Q₈	C₂×C₃×D₃	1	2	yes	—
219	C₂×C₃×D₄	—	3	1	no	—
220	C₂×C₃×D₄	—	3	2	no	—
221	C₂²×C₃×C₄	—	3	1	no	—
222	C₂²×C₃×C₄	—	3	2	no	—
223	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
224	C₂×D₁₂	C₂²×C₉	1	2	yes	—
225	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
226	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
227	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
228	C₃×C₄⋊C₄	—	2	1	no	—
229	C₃×C₄⋊C₄	—	2	1	no	—
230	C₃×C₄⋊C₄	—	2	2	no	—
231	C₃×C₄⋊C₄	—	3	1	no	—
232	C₃×C₄⋊C₄	—	3	1	no	—
233	C₃×C₄⋊C₄	—	3	2	no	—
234	C₃×C₄⋊C₄	—	3	2	no	—
235	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
236	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
237	C₃×C₄⋊C₄	C₂²×C₉	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×C₂²⋊C₄	—	3	1	no	—
242	C₃×C₂²⋊C₄	—	3	1	no	—
243	C₃×C₂²⋊C₄	—	3	2	no	—
244	C₃×C₂²⋊C₄	—	3	2	no	—
245	C₃×C₂²⋊C₄	—	3	2	no	—
246	C₃×C₂²⋊C₄	—	3	2	no	—
247	C₃×C₂²⋊C₄	—	3	2	no	—
248	C₃×C₄²	—	2	1	no	—
249	C₃×C₄²	—	3	1	no	—
250	C₃×C₄²	—	3	2	no	—
251	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
252	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
253	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
254	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
255	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
256	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
257	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
258	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
259	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
260	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
261	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
262	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
263	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
264	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
265	C₄×Dic₃	C₂²×C₉	1	2	yes	—
266	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
267	C₂×C₃×D₃	—	2	1	no	—
268	C₂×C₃×D₃	—	2	2	no	—
269	C₂×C₃×D₃	—	2	2	no	—
270	C₂×C₃×D₃	—	2	1	no	—
271	C₂×C₃×D₃	—	2	1	no	—
272	C₂×C₃×D₃	—	2	2	no	—
273	C₃²×C₄	—	2	1	no	—
274	C₃²×C₄	—	2	1	no	—
275	C₃²×C₄	—	2	2	no	—
276	C₃²×C₄	—	2	2	no	—
277	C₃²×C₄	C₃×#41	1	2	yes	—
278	C₃×Dic₃	—	2	2	no	—
279	C₃×Dic₃	—	2	1	no	—
280	C₃×Dic₃	—	2	1	no	—
281	C₃×Dic₃	—	2	1	no	—
282	C₂²×C₉	—	2	1	no	—
283	C₂²×C₉	—	6	2	no	—
284	C₂²×C₉	—	6	1	no	—
285	C₂²×C₉	—	6	1	no	—
286	C₂²×C₉	—	6	2	no	—
287	C₂²×C₉	—	6	2	no	—
288	C₂²×C₉	—	6	1	no	—
289	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
290	C₄×C₉	—	2	2	no	—
291	C₄×C₉	—	2	2	no	—
292	C₄×C₉	—	2	2	no	—
293	C₄×C₉	—	2	2	no	—
294	C₄×C₉	—	2	1	no	—
295	C₄×C₉	—	2	1	no	—
296	C₄×C₉	—	2	2	no	—
297	C₄×C₉	—	4	2	no	—
298	C₄×C₉	—	4	2	no	—
299	C₄×C₉	—	6	1	no	—
300	C₄×C₉	—	6	1	no	—
301	C₄×C₉	—	6	2	no	—
302	C₄×C₉	—	6	1	no	—
303	C₄×C₉	#239	1	2	yes	—
304	C₄⋊Q₈	D₃×C₉	1	1	yes	characteristic, complemented
305	#126	—	3	2	no	—
306	#124	—	3	2	no	—
307	#124	—	3	1	no	—
308	#123	—	3	2	no	—
309	C₂²⋊Q₈	—	3	2	no	—
310	C₂²⋊Q₈	—	3	1	no	—
311	#121	—	3	1	no	—
312	C₄×Q₈	—	3	1	no	—
313	C₄×D₄	—	3	1	no	—
314	#117	—	3	1	no	—
315	C₃×C₉	#542	1	1	yes	characteristic, complemented, Sylow
316	C₂³×C₃	—	3	2	no	—
317	C₂³×C₃	—	3	1	no	—
318	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
319	C₂²×D₃	C₂³×C₉	1	2	yes	—
320	C₃×Q₈	—	4	2	no	—
321	C₃×Q₈	—	4	2	no	—
322	C₃×Q₈	—	4	4	no	—
323	C₃×Q₈	—	6	2	no	—
324	C₃×D₄	—	6	2	no	—
325	C₃×D₄	—	12	2	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	2	1	no	—
328	C₂×C₃×C₄	—	2	1	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	3	1	no	—
332	C₂×C₃×C₄	—	3	2	no	—
333	C₂×C₃×C₄	—	3	1	no	—
334	C₂×C₃×C₄	—	3	1	no	—
335	C₂×C₃×C₄	—	6	2	no	—
336	C₂×C₃×C₄	—	12	2	no	—
337	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
338	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
341	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
343	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
344	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
346	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
347	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
348	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
349	C₂×Dic₃	C₂³×C₉	1	2	yes	—
350	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
351	D₁₂	—	2	2	no	—
352	D₁₂	—	4	2	no	—
353	C₄×D₃	—	2	2	no	—
354	C₄×D₃	—	4	2	no	—
355	Dic₆	—	2	2	no	—
356	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
357	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
358	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
359	C₃×D₃	—	4	1	no	—
360	C₃×D₃	—	4	2	no	—
361	C₂×C₉	—	2	1	no	—
362	C₂×C₉	—	2	1	no	—
363	C₂×C₉	—	2	1	no	—
364	C₂×C₉	—	12	2	no	—
365	C₂×C₉	—	12	1	no	—
366	C₂×C₉	#1004	1	1	yes	characteristic
367	C₂×C₉	C₂×#239	1	1	yes	characteristic
368	C₂×C₉	#1007	1	1	yes	characteristic
369	C₂×Q₈	—	3	1	no	—
370	C₂×Q₈	C₂×D₃×C₉	1	2	yes	—
371	C₂×D₄	—	3	1	no	—
372	C₂×D₄	—	3	2	no	—
373	C₂²×C₄	—	3	1	no	—
374	C₂²×C₄	—	3	2	no	—
375	C₄⋊C₄	—	3	1	no	—
376	C₄⋊C₄	—	3	1	no	—
377	C₄⋊C₄	—	3	2	no	—
378	C₄⋊C₄	—	3	2	no	—
379	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
380	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
381	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
382	C₂²⋊C₄	—	3	1	no	—
383	C₂²⋊C₄	—	3	1	no	—
384	C₂²⋊C₄	—	3	2	no	—
385	C₂²⋊C₄	—	3	2	no	—
386	C₂²⋊C₄	—	3	2	no	—
387	C₂²⋊C₄	—	3	2	no	—
388	C₂²⋊C₄	—	3	2	no	—
389	C₄²	—	3	1	no	—
390	C₄²	—	3	2	no	—
391	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
392	C₂²×C₃	—	2	1	no	—
393	C₂²×C₃	—	6	2	no	—
394	C₂²×C₃	—	6	1	no	—
395	C₂²×C₃	—	6	1	no	—
396	C₂²×C₃	—	6	2	no	—
397	C₂²×C₃	—	6	2	no	—
398	C₂²×C₃	—	6	1	no	—
399	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
400	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
401	C₂×D₃	—	2	1	no	—
402	C₂×D₃	—	2	2	no	—
403	C₂×D₃	—	2	2	no	—
404	C₂×D₃	—	2	1	no	—
405	C₂×D₃	—	2	1	no	—
406	C₂×D₃	—	2	2	no	—
407	C₃×C₄	—	2	2	no	—
408	C₃×C₄	—	2	2	no	—
409	C₃×C₄	—	2	2	no	—
410	C₃×C₄	—	2	2	no	—
411	C₃×C₄	—	2	1	no	—
412	C₃×C₄	—	2	1	no	—
413	C₃×C₄	—	2	2	no	—
414	C₃×C₄	—	2	2	no	—
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	2	1	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	4	2	no	—
419	C₃×C₄	—	4	2	no	—
420	C₃×C₄	—	6	1	no	—
421	C₃×C₄	—	6	1	no	—
422	C₃×C₄	—	6	2	no	—
423	C₃×C₄	—	6	1	no	—
424	C₃×C₄	C₉×#41	1	2	yes	—
425	C₃×C₄	C₃×#239	1	2	yes	—
426	Dic₃	—	2	2	no	—
427	Dic₃	—	2	1	no	—
428	Dic₃	—	2	1	no	—
429	Dic₃	—	2	1	no	—
430	C₃²	C₃×#542	1	1	yes	characteristic
431	C₉	—	2	1	no	—
432	C₉	#5733	1	1	yes	characteristic, direct product factor
433	C₂³	—	3	2	no	—
434	C₂³	—	3	1	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	6	2	no	—
437	D₄	—	6	2	no	—
438	D₄	—	12	2	no	—
439	C₂×C₄	—	3	1	no	—
440	C₂×C₄	—	3	2	no	—
441	C₂×C₄	—	3	1	no	—
442	C₂×C₄	—	3	1	no	—
443	C₂×C₄	—	6	2	no	—
444	C₂×C₄	—	12	2	no	—
445	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
446	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
449	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
450	C₂×C₃	—	2	1	no	—
451	C₂×C₃	—	2	1	no	—
452	C₂×C₃	—	2	1	no	—
453	C₂×C₃	—	12	2	no	—
454	C₂×C₃	—	12	1	no	—
455	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
456	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
458	C₂×C₃	C₃×#1004	1	1	yes	characteristic
459	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
460	C₂×C₃	C₃×#1007	1	1	yes	characteristic
461	D₃	—	4	1	no	—
462	D₃	—	4	2	no	—
463	C₂²	—	6	2	no	—
464	C₂²	—	6	1	no	—
465	C₂²	—	6	1	no	—
466	C₂²	—	6	2	no	—
467	C₂²	—	6	2	no	—
468	C₂²	—	6	1	no	—
469	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	6	1	no	—
475	C₄	—	6	1	no	—
476	C₄	—	6	2	no	—
477	C₄	—	6	1	no	—
478	C₄	C₉×#239	1	2	yes	—
479	C₃	—	2	1	no	—
480	C₃	C₉×#542	1	1	yes	characteristic, complemented
481	C₃	C₃×#5733	1	1	yes	characteristic
482	C₂	—	12	2	no	—
483	C₂	—	12	1	no	—
484	C₂	C₉×#1004	1	1	yes	characteristic
485	C₂	C₂×C₉×#239	1	1	yes	characteristic
486	C₂	C₉×#1007	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×C₄⋊Q₈	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#895	C₂×C₃
hypercenter	C₉×C₄⋊Q₈	D₃
hypocenter	C₃	C₉×#542
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×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
2. C₉×#947	C₂	semidirect
3. C₉×#946	C₂	semidirect
4. C₉×#898	C₂	semidirect
5. C₉×#897	C₂	semidirect
7. C₉×#894	C₂	semidirect
8. C₉×#893	C₂	semidirect
9. C₉×#887	C₂	semidirect
10. C₉×#875	C₂	semidirect
11. C₉×#872	C₂	semidirect
49. C₉×C₄⋊Q₈	D₃	semidirect
78. #5733	C₉	direct (N × H)
147. C₃×C₄⋊Q₈	C₂×C₉	semidirect
159. #947	C₂×C₉	semidirect
160. #946	C₂×C₉	semidirect
161. #898	C₂×C₉	semidirect
162. #897	C₂×C₉	semidirect
164. #894	C₂×C₉	semidirect
165. #893	C₂×C₉	semidirect
166. #887	C₂×C₉	semidirect
167. #875	C₂×C₉	semidirect
168. #872	C₂×C₉	semidirect
304. C₄⋊Q₈	D₃×C₉	semidirect
315. C₃×C₉	#542	semidirect
432. C₉	#5733	direct (N × H)
480. C₃	C₉×#542	semidirect

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
C₉×#947	2
C₉×#946	2
C₉×#898	2
C₉×#897	2
C₉×#895	2
C₉×#894	2
C₉×#893	2
C₉×#887	2
C₉×#875	2
C₉×#872	2
C₃×#5733	3
C₉×#542	3

Subgroups — C9×#5733 #13153314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5733 #13153314