Subgroups — C₉×#5778 #13153513

Order 1728.

834 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#1009	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#1007	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#950	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×#215	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#919	C₂	1	2	yes	maximal, complemented
7	C₉×#918	C₂	1	2	yes	maximal, complemented
8	C₉×#914	C₂	1	2	yes	maximal, complemented
9	D₃×C₉×SD₁₆	C₂	1	2	yes	maximal, complemented
10	C₉×#908	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#907	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5778	C₃	1	1	yes	maximal, characteristic
13	C₉×#577	—	3	1	no	maximal
14	C₃×C₉×#41	C₂²	1	1	yes	characteristic
15	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
16	C₉×#239	—	2	1	no	—
17	C₉×#239	C₂²	1	2	yes	—
18	C₉×#239	C₂²	1	2	yes	complemented
19	D₃×Q₈×C₉	—	2	1	no	—
20	D₃×Q₈×C₉	C₂²	1	2	yes	complemented
21	D₃×D₄×C₉	—	2	2	no	—
22	D₃×D₄×C₉	C₂²	1	2	yes	—
23	C₉×#235	—	2	2	no	—
24	C₉×#235	—	2	1	no	—
25	C₉×#235	C₂²	1	1	yes	characteristic
26	C₉×#235	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₉×D₁₂	—	2	1	no	—
28	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
29	C₃×C₉×Q₁₆	C₂²	1	2	yes	complemented
30	C₃×C₉×SD₁₆	C₂²	1	2	yes	complemented
31	C₃×C₉×M₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₉×#216	C₂²	1	1	yes	characteristic, complemented
33	C₉×#215	C₂²	1	2	yes	complemented
34	C₉×#215	C₂²	1	2	yes	complemented
35	C₉×#215	C₂²	1	1	yes	characteristic, complemented
36	C₉×#214	C₂²	1	1	yes	characteristic, complemented
37	C₉×#213	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	C₉×D₂₄	C₂²	1	2	yes	complemented
40	C₉×#204	C₂²	1	2	yes	complemented
41	C₉×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
42	D₃×C₈×C₉	C₂²	1	2	yes	complemented
43	C₃×#1009	C₂×C₃	1	1	yes	characteristic
44	C₃×#1007	C₂×C₃	1	1	yes	characteristic
45	C₃²×#137	C₂×C₃	1	1	yes	characteristic
46	C₃×#950	C₂×C₃	1	1	yes	characteristic
47	C₂×C₃×#215	C₂×C₃	1	1	yes	characteristic
48	C₃×#919	C₂×C₃	1	2	yes	—
49	C₃×#918	C₂×C₃	1	2	yes	—
50	C₃×#914	C₂×C₃	1	2	yes	—
51	C₃×D₃×SD₁₆	C₂×C₃	1	2	yes	—
52	C₃×#908	C₂×C₃	1	1	yes	characteristic
53	C₃×#907	C₂×C₃	1	1	yes	characteristic
54	C₉×2₋¹⁺⁴	—	3	1	no	—
55	C₉×H(5,𝔽₂)	—	3	1	no	—
56	C₉×#137	—	2	1	no	—
57	C₉×#137	—	3	2	no	—
58	C₉×#137	D₃	1	1	yes	characteristic, complemented
59	C₉×AGL(1,ℤ/8)	—	3	2	no	—
60	C₉×AGL(1,ℤ/8)	—	3	1	no	—
61	C₉×#135	—	3	1	no	—
62	C₉×#135	—	3	2	no	—
63	C₂×C₉×SD₁₆	—	3	1	no	—
64	C₂×C₉×SD₁₆	—	3	2	no	—
65	C₉×#131	—	3	1	no	—
66	C₂²×D₃×C₉	—	2	1	no	—
67	C₂²×D₃×C₉	—	2	2	no	—
68	C₃×Q₈×C₉	—	2	1	no	—
69	C₃×Q₈×C₉	C₂³	1	2	yes	—
70	C₃×Q₈×C₉	C₂³	1	1	yes	characteristic
71	C₃×D₄×C₉	—	2	1	no	—
72	C₃×D₄×C₉	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₄×C₉	—	2	1	no	—
74	C₂×C₃×C₄×C₉	—	2	1	no	—
75	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
76	C₉×#67	—	2	1	no	—
77	C₉×#67	—	2	2	no	—
78	C₉×#67	D₄	1	2	yes	—
79	C₉×D₁₂	—	2	2	no	—
80	C₉×D₁₂	—	2	2	no	—
81	C₉×D₁₂	—	2	1	no	—
82	C₉×D₁₂	D₄	1	1	yes	characteristic
83	C₉×D₁₂	C₂³	1	2	yes	—
84	C₉×D₁₂	C₂³	1	1	yes	characteristic
85	C₄×D₃×C₉	—	2	2	no	—
86	C₄×D₃×C₉	—	2	1	no	—
87	C₄×D₃×C₉	—	2	2	no	—
88	C₄×D₃×C₉	—	2	2	no	—
89	C₄×D₃×C₉	C₂³	1	2	yes	—
90	C₉×Dic₆	—	2	2	no	—
91	C₉×Dic₆	D₄	1	1	yes	characteristic
92	C₉×Dic₆	C₂³	1	1	yes	characteristic
93	C₃×C₈×C₉	C₂³	1	2	yes	—
94	C₉×C₃⋊C₈	C₂³	1	1	yes	characteristic
95	C₉×C₃⋊C₈	C₂³	1	1	yes	characteristic
96	C₃×#577	—	3	1	no	—
97	#5778	C₉	1	1	yes	characteristic, direct product factor
98	C₃²×#41	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
100	C₃×#239	—	2	1	no	—
101	C₃×#239	C₂²×C₃	1	2	yes	—
102	C₃×#239	C₂²×C₃	1	2	yes	—
103	C₃×D₃×Q₈	—	2	1	no	—
104	C₃×D₃×Q₈	C₂²×C₃	1	2	yes	—
105	C₃×D₃×D₄	—	2	2	no	—
106	C₃×D₃×D₄	C₂²×C₃	1	2	yes	—
107	C₃×#235	—	2	2	no	—
108	C₃×#235	—	2	1	no	—
109	C₃×#235	C₂²×C₃	1	1	yes	characteristic
110	C₃×#235	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₃×D₁₂	—	2	1	no	—
112	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
113	C₃²×Q₁₆	C₂²×C₃	1	2	yes	—
114	C₃²×SD₁₆	C₂²×C₃	1	2	yes	—
115	C₃²×M₁₆	C₂²×C₃	1	1	yes	characteristic
116	C₃×#216	C₂²×C₃	1	1	yes	characteristic
117	C₃×#215	C₂²×C₃	1	2	yes	—
118	C₃×#215	C₂²×C₃	1	2	yes	—
119	C₃×#215	C₂²×C₃	1	1	yes	characteristic
120	C₃×#214	C₂²×C₃	1	1	yes	characteristic
121	C₃×#213	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
123	C₃×D₂₄	C₂²×C₃	1	2	yes	—
124	C₃×#204	C₂²×C₃	1	2	yes	—
125	C₃×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
126	C₃×D₃×C₈	C₂²×C₃	1	2	yes	—
127	C₉×#41	—	2	1	no	—
128	C₉×#41	—	3	1	no	—
129	C₉×#41	—	3	2	no	—
130	C₉×#41	—	3	2	no	—
131	C₉×#41	—	3	1	no	—
132	C₉×#41	—	6	2	no	—
133	C₉×#41	—	6	1	no	—
134	C₉×#41	—	6	1	no	—
135	C₉×#41	C₂×D₃	1	1	yes	characteristic
136	C₂×Q₈×C₉	—	2	1	no	—
137	C₂×Q₈×C₉	—	3	2	no	—
138	C₂×Q₈×C₉	—	6	1	no	—
139	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
140	C₂×D₄×C₉	—	3	2	no	—
141	C₂×D₄×C₉	—	3	1	no	—
142	C₂×D₄×C₉	—	6	1	no	—
143	C₂×D₄×C₉	—	6	2	no	—
144	C₉×Q₁₆	—	2	2	no	—
145	C₉×Q₁₆	—	3	1	no	—
146	C₉×Q₁₆	C₂×D₃	1	2	yes	complemented
147	C₉×SD₁₆	—	2	2	no	—
148	C₉×SD₁₆	—	3	2	no	—
149	C₉×SD₁₆	—	3	2	no	—
150	C₉×SD₁₆	—	3	1	no	—
151	C₉×SD₁₆	—	3	1	no	—
152	C₉×SD₁₆	—	3	2	no	—
153	C₉×SD₁₆	C₂×D₃	1	2	yes	complemented
154	C₉×D₈	—	3	1	no	—
155	C₉×D₈	—	3	2	no	—
156	C₉×M₁₆	—	2	1	no	—
157	C₉×M₁₆	—	3	2	no	—
158	C₉×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
159	C₂×C₈×C₉	—	3	1	no	—
160	C₂×C₈×C₉	—	3	2	no	—
161	C₂²×C₃×C₉	—	2	1	no	—
162	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
163	C₂×D₃×C₉	—	2	1	no	—
164	C₂×D₃×C₉	—	2	2	no	—
165	C₂×D₃×C₉	—	8	2	no	—
166	C₂×D₃×C₉	—	8	1	no	—
167	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
168	C₃×C₄×C₉	—	2	2	no	—
169	C₃×C₄×C₉	—	2	1	no	—
170	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
171	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
172	C₉×Dic₃	—	2	1	no	—
173	C₉×Dic₃	C₂×D₄	1	2	yes	—
174	C₃×2₋¹⁺⁴	—	3	1	no	—
175	C₃×H(5,𝔽₂)	—	3	1	no	—
176	#1009	C₂×C₉	1	1	yes	characteristic, complemented
177	#1007	C₂×C₉	1	1	yes	characteristic, complemented
178	C₃×#137	—	2	1	no	—
179	C₃×#137	—	3	2	no	—
180	C₃×#137	C₂×C₉	1	1	yes	characteristic, complemented
181	C₃×#137	C₃×D₃	1	1	yes	characteristic
182	C₃×AGL(1,ℤ/8)	—	3	2	no	—
183	C₃×AGL(1,ℤ/8)	—	3	1	no	—
184	C₃×#135	—	3	1	no	—
185	C₃×#135	—	3	2	no	—
186	C₂×C₃×SD₁₆	—	3	1	no	—
187	C₂×C₃×SD₁₆	—	3	2	no	—
188	C₃×#131	—	3	1	no	—
189	#950	C₂×C₉	1	1	yes	characteristic, complemented
190	C₂×#215	C₂×C₉	1	1	yes	characteristic, complemented
191	#919	C₂×C₉	1	2	yes	complemented
192	#918	C₂×C₉	1	2	yes	complemented
193	#914	C₂×C₉	1	2	yes	complemented
194	D₃×SD₁₆	C₂×C₉	1	2	yes	complemented
195	#908	C₂×C₉	1	1	yes	characteristic, complemented
196	#907	C₂×C₉	1	1	yes	characteristic, complemented
197	C₂²×C₃×D₃	—	2	1	no	—
198	C₂²×C₃×D₃	—	2	2	no	—
199	C₃²×Q₈	—	2	1	no	—
200	C₃²×Q₈	C₂³×C₃	1	2	yes	—
201	C₃²×Q₈	C₂³×C₃	1	1	yes	characteristic
202	C₃²×D₄	—	2	1	no	—
203	C₃²×D₄	C₂³×C₃	1	1	yes	characteristic
204	C₂×C₃²×C₄	—	2	1	no	—
205	C₂×C₃²×C₄	—	2	1	no	—
206	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
207	C₃×#67	—	2	1	no	—
208	C₃×#67	—	2	2	no	—
209	C₃×#67	C₃×D₄	1	2	yes	—
210	C₃×D₁₂	—	2	2	no	—
211	C₃×D₁₂	—	2	2	no	—
212	C₃×D₁₂	—	2	1	no	—
213	C₃×D₁₂	C₃×D₄	1	1	yes	characteristic
214	C₃×D₁₂	C₂³×C₃	1	2	yes	—
215	C₃×D₁₂	C₂³×C₃	1	1	yes	characteristic
216	C₃×C₄×D₃	—	2	2	no	—
217	C₃×C₄×D₃	—	2	1	no	—
218	C₃×C₄×D₃	—	2	2	no	—
219	C₃×C₄×D₃	—	2	2	no	—
220	C₃×C₄×D₃	C₂³×C₃	1	2	yes	—
221	C₃×Dic₆	—	2	2	no	—
222	C₃×Dic₆	C₃×D₄	1	1	yes	characteristic
223	C₃×Dic₆	C₂³×C₃	1	1	yes	characteristic
224	C₂³×C₉	—	6	2	no	—
225	C₂³×C₉	—	6	1	no	—
226	C₃²×C₈	C₂³×C₃	1	2	yes	—
227	C₃×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
228	C₃×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
229	Q₈×C₉	—	2	1	no	—
230	Q₈×C₉	—	2	2	no	—
231	Q₈×C₉	—	2	1	no	—
232	Q₈×C₉	—	3	1	no	—
233	Q₈×C₉	—	3	1	no	—
234	Q₈×C₉	—	4	1	no	—
235	Q₈×C₉	—	6	2	no	—
236	Q₈×C₉	C₂²×D₃	1	2	yes	—
237	Q₈×C₉	C₂²×D₃	1	1	yes	characteristic
238	D₄×C₉	—	2	1	no	—
239	D₄×C₉	—	2	1	no	—
240	D₄×C₉	—	3	2	no	—
241	D₄×C₉	—	3	1	no	—
242	D₄×C₉	—	3	1	no	—
243	D₄×C₉	—	3	2	no	—
244	D₄×C₉	—	4	1	no	—
245	D₄×C₉	—	6	2	no	—
246	D₄×C₉	—	6	2	no	—
247	D₄×C₉	—	6	2	no	—
248	D₄×C₉	—	6	1	no	—
249	D₄×C₉	—	6	1	no	—
250	D₄×C₉	C₂²×D₃	1	1	yes	characteristic
251	C₂×C₄×C₉	—	2	1	no	—
252	C₂×C₄×C₉	—	2	1	no	—
253	C₂×C₄×C₉	—	2	1	no	—
254	C₂×C₄×C₉	—	3	2	no	—
255	C₂×C₄×C₉	—	4	1	no	—
256	C₂×C₄×C₉	—	4	1	no	—
257	C₂×C₄×C₉	—	6	2	no	—
258	C₂×C₄×C₉	—	6	2	no	—
259	C₂×C₄×C₉	—	6	2	no	—
260	C₂×C₄×C₉	—	6	1	no	—
261	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
262	C₈×C₉	—	2	2	no	—
263	C₈×C₉	—	3	1	no	—
264	C₈×C₉	—	3	1	no	—
265	C₈×C₉	C₂²×D₃	1	2	yes	—
266	#577	—	3	1	no	Sylow
267	C₂×C₃×C₉	—	2	1	no	—
268	C₂×C₃×C₉	—	4	1	no	—
269	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
270	D₃×C₉	—	2	2	no	—
271	D₃×C₉	—	4	1	no	—
272	D₃×C₉	—	4	2	no	—
273	C₃×#41	—	2	1	no	—
274	C₃×#41	—	3	1	no	—
275	C₃×#41	—	3	2	no	—
276	C₃×#41	—	3	2	no	—
277	C₃×#41	—	3	1	no	—
278	C₃×#41	—	6	2	no	—
279	C₃×#41	—	6	1	no	—
280	C₃×#41	—	6	1	no	—
281	C₃×#41	C₂²×C₉	1	1	yes	characteristic
282	C₃×#41	C₂×C₃×D₃	1	1	yes	characteristic
283	C₂×C₃×Q₈	—	2	1	no	—
284	C₂×C₃×Q₈	—	3	2	no	—
285	C₂×C₃×Q₈	—	6	1	no	—
286	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
287	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
288	C₂×C₃×D₄	—	3	2	no	—
289	C₂×C₃×D₄	—	3	1	no	—
290	C₂×C₃×D₄	—	6	1	no	—
291	C₂×C₃×D₄	—	6	2	no	—
292	#239	—	2	1	no	—
293	#239	C₂²×C₉	1	2	yes	—
294	#239	C₂²×C₉	1	2	yes	complemented
295	D₃×Q₈	—	2	1	no	—
296	D₃×Q₈	C₂²×C₉	1	2	yes	complemented
297	D₃×D₄	—	2	2	no	—
298	D₃×D₄	C₂²×C₉	1	2	yes	—
299	#235	—	2	2	no	—
300	#235	—	2	1	no	—
301	#235	C₂²×C₉	1	1	yes	characteristic
302	#235	C₂²×C₉	1	1	yes	characteristic, complemented
303	C₂×D₁₂	—	2	1	no	—
304	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
305	C₃×Q₁₆	—	2	2	no	—
306	C₃×Q₁₆	—	3	1	no	—
307	C₃×Q₁₆	C₂²×C₉	1	2	yes	complemented
308	C₃×Q₁₆	C₂×C₃×D₃	1	2	yes	—
309	C₃×SD₁₆	—	2	2	no	—
310	C₃×SD₁₆	—	3	2	no	—
311	C₃×SD₁₆	—	3	2	no	—
312	C₃×SD₁₆	—	3	1	no	—
313	C₃×SD₁₆	—	3	1	no	—
314	C₃×SD₁₆	—	3	2	no	—
315	C₃×SD₁₆	C₂²×C₉	1	2	yes	complemented
316	C₃×SD₁₆	C₂×C₃×D₃	1	2	yes	—
317	C₃×D₈	—	3	1	no	—
318	C₃×D₈	—	3	2	no	—
319	C₃×M₁₆	—	2	1	no	—
320	C₃×M₁₆	—	3	2	no	—
321	C₃×M₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
322	C₃×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
323	C₂×C₃×C₈	—	3	1	no	—
324	C₂×C₃×C₈	—	3	2	no	—
325	#216	C₂²×C₉	1	1	yes	characteristic, complemented
326	#215	C₂²×C₉	1	2	yes	complemented
327	#215	C₂²×C₉	1	2	yes	complemented
328	#215	C₂²×C₉	1	1	yes	characteristic, complemented
329	#214	C₂²×C₉	1	1	yes	characteristic, complemented
330	#213	C₂²×C₉	1	1	yes	characteristic, complemented
331	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
332	D₂₄	C₂²×C₉	1	2	yes	complemented
333	#204	C₂²×C₉	1	2	yes	complemented
334	ΓL(1,𝔽₂₅)	C₂²×C₉	1	2	yes	complemented
335	D₃×C₈	C₂²×C₉	1	2	yes	complemented
336	C₂²×C₃²	—	2	1	no	—
337	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
338	C₂×C₃×D₃	—	2	1	no	—
339	C₂×C₃×D₃	—	2	2	no	—
340	C₂×C₃×D₃	—	8	2	no	—
341	C₂×C₃×D₃	—	8	1	no	—
342	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
343	C₃²×C₄	—	2	2	no	—
344	C₃²×C₄	—	2	1	no	—
345	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
346	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
347	C₃×Dic₃	—	2	1	no	—
348	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
349	C₂²×C₉	—	2	1	no	—
350	C₂²×C₉	—	2	1	no	—
351	C₂²×C₉	—	3	2	no	—
352	C₂²×C₉	—	4	1	no	—
353	C₂²×C₉	—	6	1	no	—
354	C₂²×C₉	—	6	2	no	—
355	C₂²×C₉	—	24	1	no	—
356	C₂²×C₉	—	24	2	no	—
357	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
358	C₄×C₉	—	2	1	no	—
359	C₄×C₉	—	2	2	no	—
360	C₄×C₉	—	2	1	no	—
361	C₄×C₉	—	2	1	no	—
362	C₄×C₉	—	3	2	no	—
363	C₄×C₉	—	4	1	no	—
364	C₄×C₉	—	4	2	no	—
365	C₄×C₉	—	6	1	no	—
366	C₄×C₉	D₃×D₄	1	1	yes	characteristic
367	C₄×C₉	C₂³×D₃	1	1	yes	characteristic
368	2₋¹⁺⁴	—	3	1	no	—
369	H(5,𝔽₂)	—	3	1	no	—
370	#137	—	3	2	no	—
371	#137	D₃×C₉	1	1	yes	characteristic, complemented
372	AGL(1,ℤ/8)	—	3	2	no	—
373	AGL(1,ℤ/8)	—	3	1	no	—
374	#135	—	3	1	no	—
375	#135	—	3	2	no	—
376	C₂×SD₁₆	—	3	1	no	—
377	C₂×SD₁₆	—	3	2	no	—
378	#131	—	3	1	no	—
379	C₃×C₉	#577	1	1	yes	characteristic, complemented, Sylow
380	C₂³×C₃	—	6	2	no	—
381	C₂³×C₃	—	6	1	no	—
382	C₂²×D₃	—	2	1	no	—
383	C₂²×D₃	—	2	2	no	—
384	C₃×Q₈	—	2	1	no	—
385	C₃×Q₈	—	2	1	no	—
386	C₃×Q₈	—	2	2	no	—
387	C₃×Q₈	—	2	1	no	—
388	C₃×Q₈	—	3	1	no	—
389	C₃×Q₈	—	3	1	no	—
390	C₃×Q₈	—	4	1	no	—
391	C₃×Q₈	—	6	2	no	—
392	C₃×Q₈	C₂³×C₉	1	2	yes	—
393	C₃×Q₈	C₂³×C₉	1	1	yes	characteristic
394	C₃×Q₈	C₂²×C₃×D₃	1	2	yes	—
395	C₃×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
396	C₃×D₄	—	2	1	no	—
397	C₃×D₄	—	2	1	no	—
398	C₃×D₄	—	2	1	no	—
399	C₃×D₄	—	3	2	no	—
400	C₃×D₄	—	3	1	no	—
401	C₃×D₄	—	3	2	no	—
402	C₃×D₄	—	3	1	no	—
403	C₃×D₄	—	4	1	no	—
404	C₃×D₄	—	6	2	no	—
405	C₃×D₄	—	6	2	no	—
406	C₃×D₄	—	6	2	no	—
407	C₃×D₄	—	6	1	no	—
408	C₃×D₄	—	6	1	no	—
409	C₃×D₄	C₂³×C₉	1	1	yes	characteristic
410	C₃×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
411	C₂×C₃×C₄	—	2	1	no	—
412	C₂×C₃×C₄	—	2	1	no	—
413	C₂×C₃×C₄	—	2	1	no	—
414	C₂×C₃×C₄	—	2	1	no	—
415	C₂×C₃×C₄	—	2	1	no	—
416	C₂×C₃×C₄	—	3	2	no	—
417	C₂×C₃×C₄	—	4	1	no	—
418	C₂×C₃×C₄	—	4	1	no	—
419	C₂×C₃×C₄	—	6	2	no	—
420	C₂×C₃×C₄	—	6	2	no	—
421	C₂×C₃×C₄	—	6	2	no	—
422	C₂×C₃×C₄	—	6	1	no	—
423	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
424	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
425	#67	—	2	1	no	—
426	#67	—	2	2	no	—
427	#67	D₄×C₉	1	2	yes	—
428	D₁₂	—	2	2	no	—
429	D₁₂	—	2	2	no	—
430	D₁₂	—	2	1	no	—
431	D₁₂	D₄×C₉	1	1	yes	characteristic
432	D₁₂	C₂³×C₉	1	2	yes	—
433	D₁₂	C₂³×C₉	1	1	yes	characteristic
434	C₄×D₃	—	2	2	no	—
435	C₄×D₃	—	2	1	no	—
436	C₄×D₃	—	2	2	no	—
437	C₄×D₃	—	2	2	no	—
438	C₄×D₃	C₂³×C₉	1	2	yes	—
439	Dic₆	—	2	2	no	—
440	Dic₆	D₄×C₉	1	1	yes	characteristic
441	Dic₆	C₂³×C₉	1	1	yes	characteristic
442	C₃×C₈	—	2	2	no	—
443	C₃×C₈	—	3	1	no	—
444	C₃×C₈	—	3	1	no	—
445	C₃×C₈	C₂³×C₉	1	2	yes	—
446	C₃×C₈	C₂²×C₃×D₃	1	2	yes	—
447	C₃⋊C₈	C₂³×C₉	1	1	yes	characteristic
448	C₃⋊C₈	C₂³×C₉	1	1	yes	characteristic
449	C₂×C₃²	—	2	1	no	—
450	C₂×C₃²	—	4	1	no	—
451	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
452	C₃×D₃	—	2	2	no	—
453	C₃×D₃	—	4	1	no	—
454	C₃×D₃	—	4	2	no	—
455	C₂×C₉	—	2	1	no	—
456	C₂×C₉	—	2	1	no	—
457	C₂×C₉	—	4	1	no	—
458	C₂×C₉	—	4	1	no	—
459	C₂×C₉	—	6	2	no	—
460	C₂×C₉	—	8	1	no	—
461	C₂×C₉	—	12	1	no	—
462	C₂×C₉	—	12	2	no	—
463	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
464	#41	—	3	1	no	—
465	#41	—	3	2	no	—
466	#41	—	3	2	no	—
467	#41	—	3	1	no	—
468	#41	—	6	2	no	—
469	#41	—	6	1	no	—
470	#41	—	6	1	no	—
471	#41	C₂×D₃×C₉	1	1	yes	characteristic
472	C₂×Q₈	—	3	2	no	—
473	C₂×Q₈	—	6	1	no	—
474	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
475	C₂×D₄	—	3	2	no	—
476	C₂×D₄	—	3	1	no	—
477	C₂×D₄	—	6	1	no	—
478	C₂×D₄	—	6	2	no	—
479	Q₁₆	—	3	1	no	—
480	Q₁₆	C₂×D₃×C₉	1	2	yes	complemented
481	SD₁₆	—	3	2	no	—
482	SD₁₆	—	3	2	no	—
483	SD₁₆	—	3	1	no	—
484	SD₁₆	—	3	1	no	—
485	SD₁₆	—	3	2	no	—
486	SD₁₆	C₂×D₃×C₉	1	2	yes	complemented
487	D₈	—	3	1	no	—
488	D₈	—	3	2	no	—
489	M₁₆	—	3	2	no	—
490	M₁₆	C₂×D₃×C₉	1	1	yes	characteristic, complemented
491	C₂×C₈	—	3	1	no	—
492	C₂×C₈	—	3	2	no	—
493	C₂²×C₃	—	2	1	no	—
494	C₂²×C₃	—	2	1	no	—
495	C₂²×C₃	—	2	1	no	—
496	C₂²×C₃	—	3	2	no	—
497	C₂²×C₃	—	4	1	no	—
498	C₂²×C₃	—	6	1	no	—
499	C₂²×C₃	—	6	2	no	—
500	C₂²×C₃	—	24	1	no	—
501	C₂²×C₃	—	24	2	no	—
502	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
503	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
504	C₂×D₃	—	2	1	no	—
505	C₂×D₃	—	2	2	no	—
506	C₂×D₃	—	8	2	no	—
507	C₂×D₃	—	8	1	no	—
508	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
509	C₃×C₄	—	2	1	no	—
510	C₃×C₄	—	2	2	no	—
511	C₃×C₄	—	2	2	no	—
512	C₃×C₄	—	2	1	no	—
513	C₃×C₄	—	2	1	no	—
514	C₃×C₄	—	2	1	no	—
515	C₃×C₄	—	3	2	no	—
516	C₃×C₄	—	4	1	no	—
517	C₃×C₄	—	4	2	no	—
518	C₃×C₄	—	6	1	no	—
519	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
520	C₃×C₄	C₂⁴×C₉	1	1	yes	characteristic
521	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
522	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
523	Dic₃	—	2	1	no	—
524	Dic₃	C₂×D₄×C₉	1	2	yes	—
525	C₃²	C₃×#577	1	1	yes	characteristic
526	C₉	—	2	1	no	—
527	C₉	#5778	1	1	yes	characteristic, direct product factor
528	C₂³	—	6	2	no	—
529	C₂³	—	6	1	no	—
530	Q₈	—	2	1	no	—
531	Q₈	—	3	1	no	—
532	Q₈	—	3	1	no	—
533	Q₈	—	6	2	no	—
534	Q₈	C₂²×D₃×C₉	1	2	yes	—
535	Q₈	C₂²×D₃×C₉	1	1	yes	characteristic
536	D₄	—	2	1	no	—
537	D₄	—	3	2	no	—
538	D₄	—	3	1	no	—
539	D₄	—	3	2	no	—
540	D₄	—	3	1	no	—
541	D₄	—	6	2	no	—
542	D₄	—	6	2	no	—
543	D₄	—	6	2	no	—
544	D₄	—	6	1	no	—
545	D₄	—	6	1	no	—
546	D₄	C₂²×D₃×C₉	1	1	yes	characteristic
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	3	2	no	—
550	C₂×C₄	—	6	2	no	—
551	C₂×C₄	—	6	2	no	—
552	C₂×C₄	—	6	2	no	—
553	C₂×C₄	—	6	1	no	—
554	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
555	C₈	—	3	1	no	—
556	C₈	—	3	1	no	—
557	C₈	C₂²×D₃×C₉	1	2	yes	—
558	C₂×C₃	—	2	1	no	—
559	C₂×C₃	—	2	1	no	—
560	C₂×C₃	—	2	1	no	—
561	C₂×C₃	—	4	1	no	—
562	C₂×C₃	—	4	1	no	—
563	C₂×C₃	—	4	1	no	—
564	C₂×C₃	—	6	2	no	—
565	C₂×C₃	—	8	1	no	—
566	C₂×C₃	—	12	2	no	—
567	C₂×C₃	—	12	1	no	—
568	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
569	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
570	D₃	—	2	2	no	—
571	D₃	—	4	2	no	—
572	D₃	—	4	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	3	2	no	—
575	C₂²	—	6	1	no	—
576	C₂²	—	6	2	no	—
577	C₂²	—	24	1	no	—
578	C₂²	—	24	2	no	—
579	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
580	C₄	—	2	1	no	—
581	C₄	—	2	2	no	—
582	C₄	—	3	2	no	—
583	C₄	—	6	1	no	—
584	C₄	D₃×D₄×C₉	1	1	yes	characteristic
585	C₄	C₂³×D₃×C₉	1	1	yes	characteristic
586	C₃	—	2	1	no	—
587	C₃	C₉×#577	1	1	yes	characteristic, complemented
588	C₃	C₃×#5778	1	1	yes	characteristic
589	C₂	—	2	1	no	—
590	C₂	—	4	1	no	—
591	C₂	—	6	2	no	—
592	C₂	—	12	2	no	—
593	C₂	—	12	1	no	—
594	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	C₂×D₃×D₄
commutator	C₃×C₄	C₂⁴×C₉
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₃×C₉×#137	C₂
socle	C₂×C₃²	C₂²×C₃×D₄
prime radical	C₃×#5778	C₃
cosocle	C₃²×C₄	C₂⁴×C₃
hypercenter	C₉×#137	D₃
hypocenter	C₃	C₉×#577
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#137

Complements

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

N	H ≅ G/N	type
1. C₉×#1009	C₂	semidirect
2. C₉×#1007	C₂	semidirect
3. C₃×C₉×#137	C₂	semidirect
4. C₉×#950	C₂	semidirect
5. C₂×C₉×#215	C₂	semidirect
6. C₉×#919	C₂	semidirect
7. C₉×#918	C₂	semidirect
8. C₉×#914	C₂	semidirect
9. D₃×C₉×SD₁₆	C₂	semidirect
10. C₉×#908	C₂	semidirect
11. C₉×#907	C₂	semidirect
15. C₂×C₃×Q₈×C₉	C₂²	semidirect
18. C₉×#239	C₂²	semidirect
20. D₃×Q₈×C₉	C₂²	semidirect
26. C₉×#235	C₂²	semidirect
29. C₃×C₉×Q₁₆	C₂²	semidirect
30. C₃×C₉×SD₁₆	C₂²	semidirect
31. C₃×C₉×M₁₆	C₂²	semidirect
32. C₉×#216	C₂²	semidirect
33. C₉×#215	C₂²	semidirect
34. C₉×#215	C₂²	semidirect
35. C₉×#215	C₂²	semidirect
36. C₉×#214	C₂²	semidirect
37. C₉×#213	C₂²	semidirect
38. C₂×C₉×C₃⋊C₈	C₂²	semidirect
39. C₉×D₂₄	C₂²	semidirect
40. C₉×#204	C₂²	semidirect
41. C₉×ΓL(1,𝔽₂₅)	C₂²	semidirect
42. D₃×C₈×C₉	C₂²	semidirect
58. C₉×#137	D₃	semidirect
97. #5778	C₉	direct (N × H)
139. C₂×Q₈×C₉	C₂×D₃	semidirect
146. C₉×Q₁₆	C₂×D₃	semidirect
153. C₉×SD₁₆	C₂×D₃	semidirect
158. C₉×M₁₆	C₂×D₃	semidirect
176. #1009	C₂×C₉	semidirect
177. #1007	C₂×C₉	semidirect
180. C₃×#137	C₂×C₉	semidirect
189. #950	C₂×C₉	semidirect
190. C₂×#215	C₂×C₉	semidirect
191. #919	C₂×C₉	semidirect
192. #918	C₂×C₉	semidirect
193. #914	C₂×C₉	semidirect
194. D₃×SD₁₆	C₂×C₉	semidirect
195. #908	C₂×C₉	semidirect
196. #907	C₂×C₉	semidirect
286. C₂×C₃×Q₈	C₂²×C₉	semidirect
294. #239	C₂²×C₉	semidirect
296. D₃×Q₈	C₂²×C₉	semidirect
302. #235	C₂²×C₉	semidirect
307. C₃×Q₁₆	C₂²×C₉	semidirect
315. C₃×SD₁₆	C₂²×C₉	semidirect
321. C₃×M₁₆	C₂²×C₉	semidirect
325. #216	C₂²×C₉	semidirect
326. #215	C₂²×C₉	semidirect
327. #215	C₂²×C₉	semidirect
328. #215	C₂²×C₉	semidirect
329. #214	C₂²×C₉	semidirect
330. #213	C₂²×C₉	semidirect
331. C₂×C₃⋊C₈	C₂²×C₉	semidirect
332. D₂₄	C₂²×C₉	semidirect
333. #204	C₂²×C₉	semidirect
334. ΓL(1,𝔽₂₅)	C₂²×C₉	semidirect
335. D₃×C₈	C₂²×C₉	semidirect
371. #137	D₃×C₉	semidirect
379. C₃×C₉	#577	semidirect
474. C₂×Q₈	C₂×D₃×C₉	semidirect
480. Q₁₆	C₂×D₃×C₉	semidirect
486. SD₁₆	C₂×D₃×C₉	semidirect
490. M₁₆	C₂×D₃×C₉	semidirect
527. C₉	#5778	direct (N × H)
587. C₃	C₉×#577	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₉×#1009	2
C₉×#1007	2
C₃×C₉×#137	2
C₉×#950	2
C₂×C₉×#215	2
C₉×#919	2
C₉×#918	2
C₉×#914	2
D₃×C₉×SD₁₆	2
C₉×#908	2
C₉×#907	2
C₃×#5778	3
C₉×#577	3

Subgroups — C9×#5778 #13153513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5778 #13153513