Subgroups — C₉×#5768 #13153477

Order 1728.

848 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₉×#41	C₂	1	2	yes	maximal, complemented
2	C₃×C₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#950	C₂	1	2	yes	maximal, complemented
4	C₉×#918	C₂	1	2	yes	maximal, complemented
5	C₉×#915	C₂	1	2	yes	maximal, complemented
6	C₉×#914	C₂	1	2	yes	maximal, complemented
7	C₉×#911	C₂	1	2	yes	maximal, complemented
8	C₉×#904	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₉×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5768	C₃	1	1	yes	maximal, characteristic
11	C₉×#575	—	3	1	no	maximal
12	C₃×C₉×#41	C₂²	1	2	yes	complemented
13	C₉×#239	C₂²	1	2	yes	—
14	D₃×Q₈×C₉	C₂²	1	2	yes	complemented
15	C₉×#237	—	2	2	no	—
16	C₉×#237	C₂²	1	2	yes	—
17	D₃×D₄×C₉	—	2	2	no	—
18	D₃×D₄×C₉	C₂²	1	2	yes	complemented
19	C₉×#235	—	2	2	no	—
20	C₉×#235	C₂²	1	2	yes	complemented
21	C₂×C₄×D₃×C₉	—	2	2	no	—
22	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
23	C₃×C₉×Q₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₉×SD₁₆	C₂²	1	2	yes	complemented
25	C₃×C₉×D₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
27	C₉×#216	C₂²	1	2	yes	complemented
28	C₉×#215	C₂²	1	2	yes	complemented
29	C₉×#214	C₂²	1	2	yes	complemented
30	C₉×#213	C₂²	1	2	yes	complemented
31	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
32	C₉×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
33	C₉×D₂₄	C₂²	1	1	yes	characteristic, complemented
34	C₉×#204	C₂²	1	2	yes	complemented
35	C₉×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
36	C₉×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
37	C₃×D₃×#41	C₂×C₃	1	2	yes	—
38	C₃²×#135	C₂×C₃	1	1	yes	characteristic
39	C₃×#950	C₂×C₃	1	2	yes	—
40	C₃×#918	C₂×C₃	1	2	yes	—
41	C₃×#915	C₂×C₃	1	2	yes	—
42	C₃×#914	C₂×C₃	1	2	yes	—
43	C₃×#911	C₂×C₃	1	2	yes	—
44	C₃×#904	C₂×C₃	1	1	yes	characteristic
45	C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	1	1	yes	characteristic
46	C₂×C₉×#41	—	3	2	no	—
47	C₉×#137	—	3	2	no	—
48	C₉×#137	—	3	2	no	—
49	C₉×AGL(1,ℤ/8)	—	3	2	no	—
50	C₉×AGL(1,ℤ/8)	—	3	2	no	—
51	C₉×#135	—	2	1	no	—
52	C₉×#135	—	3	2	no	—
53	C₉×#135	—	3	1	no	—
54	C₉×#135	D₃	1	1	yes	characteristic, complemented
55	C₂×C₉×M₁₆	—	3	1	no	—
56	C₂²×D₃×C₉	—	2	2	no	—
57	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
58	C₃×Q₈×C₉	C₂³	1	2	yes	—
59	C₃×D₄×C₉	—	2	2	no	—
60	C₃×D₄×C₉	C₂³	1	2	yes	—
61	C₂×C₃×C₄×C₉	—	2	2	no	—
62	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
63	C₉×#67	—	2	2	no	—
64	C₉×#67	—	2	2	no	—
65	C₉×#67	—	2	2	no	—
66	C₂×C₉×Dic₃	—	2	2	no	—
67	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
68	C₉×D₁₂	—	2	2	no	—
69	C₉×D₁₂	C₂³	1	2	yes	—
70	C₄×D₃×C₉	—	2	2	no	—
71	C₄×D₃×C₉	—	2	2	no	—
72	C₄×D₃×C₉	—	2	2	no	—
73	C₄×D₃×C₉	D₄	1	2	yes	—
74	C₄×D₃×C₉	C₂³	1	2	yes	—
75	C₉×Dic₆	—	2	2	no	—
76	C₉×Dic₆	C₂³	1	2	yes	—
77	C₃×C₈×C₉	C₂³	1	1	yes	characteristic
78	C₃×C₈×C₉	C₂³	1	1	yes	characteristic
79	C₉×C₃⋊C₈	C₂³	1	2	yes	—
80	C₃×#575	—	3	1	no	—
81	#5768	C₉	1	1	yes	characteristic, direct product factor
82	C₃²×#41	C₂²×C₃	1	2	yes	—
83	C₃×#239	C₂²×C₃	1	2	yes	—
84	C₃×D₃×Q₈	C₂²×C₃	1	2	yes	—
85	C₃×#237	—	2	2	no	—
86	C₃×#237	C₂²×C₃	1	2	yes	—
87	C₃×D₃×D₄	—	2	2	no	—
88	C₃×D₃×D₄	C₂²×C₃	1	2	yes	—
89	C₃×#235	—	2	2	no	—
90	C₃×#235	C₂²×C₃	1	2	yes	—
91	C₂×C₃×C₄×D₃	—	2	2	no	—
92	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
93	C₃²×Q₁₆	C₂²×C₃	1	1	yes	characteristic
94	C₃²×SD₁₆	C₂²×C₃	1	2	yes	—
95	C₃²×D₈	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
97	C₃×#216	C₂²×C₃	1	2	yes	—
98	C₃×#215	C₂²×C₃	1	2	yes	—
99	C₃×#214	C₂²×C₃	1	2	yes	—
100	C₃×#213	C₂²×C₃	1	2	yes	—
101	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
102	C₃×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
103	C₃×D₂₄	C₂²×C₃	1	1	yes	characteristic
104	C₃×#204	C₂²×C₃	1	2	yes	—
105	C₃×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
106	C₃×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
107	C₉×#41	—	2	2	no	—
108	C₉×#41	—	3	2	no	—
109	C₉×#41	—	3	2	no	—
110	C₉×#41	—	3	2	no	—
111	C₉×#41	—	6	2	no	—
112	C₉×#41	—	6	2	no	—
113	C₉×#41	C₂×D₃	1	2	yes	complemented
114	C₂×Q₈×C₉	—	3	2	no	—
115	C₂×D₄×C₉	—	3	2	no	—
116	C₂×D₄×C₉	—	6	2	no	—
117	C₂²×C₄×C₉	—	3	1	no	—
118	C₂²×C₄×C₉	—	6	2	no	—
119	C₉×Q₁₆	—	2	1	no	—
120	C₉×Q₁₆	—	3	2	no	—
121	C₉×Q₁₆	—	3	1	no	—
122	C₉×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
123	C₉×SD₁₆	—	2	2	no	—
124	C₉×SD₁₆	—	3	2	no	—
125	C₉×SD₁₆	—	3	2	no	—
126	C₉×SD₁₆	—	3	2	no	—
127	C₉×SD₁₆	C₂×D₃	1	2	yes	complemented
128	C₉×D₈	—	2	1	no	—
129	C₉×D₈	—	3	2	no	—
130	C₉×D₈	—	3	1	no	—
131	C₉×D₈	C₂×D₃	1	1	yes	characteristic, complemented
132	C₉×M₁₆	—	3	2	no	—
133	C₉×M₁₆	—	3	2	no	—
134	C₂×C₈×C₉	—	2	1	no	—
135	C₂×C₈×C₉	—	3	1	no	—
136	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
137	C₂²×C₃×C₉	—	2	2	no	—
138	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
139	C₂×D₃×C₉	—	2	2	no	—
140	C₂×D₃×C₉	—	4	1	no	—
141	C₂×D₃×C₉	—	4	4	no	—
142	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
143	C₃×C₄×C₉	—	2	2	no	—
144	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
145	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
146	C₉×Dic₃	—	2	2	no	—
147	C₉×Dic₃	C₂×D₄	1	2	yes	—
148	C₂×C₃×#41	—	3	2	no	—
149	D₃×#41	C₂×C₉	1	2	yes	complemented
150	C₃×#137	—	3	2	no	—
151	C₃×#137	—	3	2	no	—
152	C₃×AGL(1,ℤ/8)	—	3	2	no	—
153	C₃×AGL(1,ℤ/8)	—	3	2	no	—
154	C₃×#135	—	2	1	no	—
155	C₃×#135	—	3	2	no	—
156	C₃×#135	—	3	1	no	—
157	C₃×#135	C₂×C₉	1	1	yes	characteristic, complemented
158	C₃×#135	C₃×D₃	1	1	yes	characteristic
159	C₂×C₃×M₁₆	—	3	1	no	—
160	#950	C₂×C₉	1	2	yes	complemented
161	#918	C₂×C₉	1	2	yes	complemented
162	#915	C₂×C₉	1	2	yes	complemented
163	#914	C₂×C₉	1	2	yes	complemented
164	#911	C₂×C₉	1	2	yes	complemented
165	#904	C₂×C₉	1	1	yes	characteristic, complemented
166	C₂×ΓL(1,𝔽₂₅)	C₂×C₉	1	1	yes	characteristic, complemented
167	C₂²×C₃×D₃	—	2	2	no	—
168	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
169	C₃²×Q₈	C₂³×C₃	1	2	yes	—
170	C₃²×D₄	—	2	2	no	—
171	C₃²×D₄	C₂³×C₃	1	2	yes	—
172	C₂×C₃²×C₄	—	2	2	no	—
173	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
174	C₃×#67	—	2	2	no	—
175	C₃×#67	—	2	2	no	—
176	C₃×#67	—	2	2	no	—
177	C₂×C₃×Dic₃	—	2	2	no	—
178	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
179	C₃×D₁₂	—	2	2	no	—
180	C₃×D₁₂	C₂³×C₃	1	2	yes	—
181	C₃×C₄×D₃	—	2	2	no	—
182	C₃×C₄×D₃	—	2	2	no	—
183	C₃×C₄×D₃	—	2	2	no	—
184	C₃×C₄×D₃	C₃×D₄	1	2	yes	—
185	C₃×C₄×D₃	C₂³×C₃	1	2	yes	—
186	C₃×Dic₆	—	2	2	no	—
187	C₃×Dic₆	C₂³×C₃	1	2	yes	—
188	C₂³×C₉	—	3	1	no	—
189	C₂³×C₉	—	6	2	no	—
190	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
191	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
192	C₃×C₃⋊C₈	C₂³×C₃	1	2	yes	—
193	Q₈×C₉	—	2	2	no	—
194	Q₈×C₉	—	3	2	no	—
195	Q₈×C₉	—	6	2	no	—
196	Q₈×C₉	C₂²×D₃	1	2	yes	—
197	D₄×C₉	—	2	2	no	—
198	D₄×C₉	—	2	2	no	—
199	D₄×C₉	—	3	2	no	—
200	D₄×C₉	—	4	2	no	—
201	D₄×C₉	—	6	2	no	—
202	D₄×C₉	—	6	2	no	—
203	D₄×C₉	—	6	2	no	—
204	D₄×C₉	—	6	2	no	—
205	D₄×C₉	C₂²×D₃	1	2	yes	—
206	C₂×C₄×C₉	—	2	2	no	—
207	C₂×C₄×C₉	—	2	1	no	—
208	C₂×C₄×C₉	—	3	1	no	—
209	C₂×C₄×C₉	—	3	2	no	—
210	C₂×C₄×C₉	—	3	2	no	—
211	C₂×C₄×C₉	—	4	2	no	—
212	C₂×C₄×C₉	—	6	2	no	—
213	C₂×C₄×C₉	—	6	2	no	—
214	C₂×C₄×C₉	—	6	2	no	—
215	C₂×C₄×C₉	—	6	2	no	—
216	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
217	C₈×C₉	—	2	1	no	—
218	C₈×C₉	—	2	1	no	—
219	C₈×C₉	—	3	2	no	—
220	C₈×C₉	C₂²×D₃	1	1	yes	characteristic
221	C₈×C₉	C₂²×D₃	1	1	yes	characteristic
222	#575	—	3	1	no	Sylow
223	C₂×C₃×C₉	—	2	1	no	—
224	C₂×C₃×C₉	—	4	2	no	—
225	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
226	D₃×C₉	—	2	2	no	—
227	D₃×C₉	—	4	2	no	—
228	C₃×#41	—	2	2	no	—
229	C₃×#41	—	3	2	no	—
230	C₃×#41	—	3	2	no	—
231	C₃×#41	—	3	2	no	—
232	C₃×#41	—	6	2	no	—
233	C₃×#41	—	6	2	no	—
234	C₃×#41	C₂²×C₉	1	2	yes	complemented
235	C₃×#41	C₂×C₃×D₃	1	2	yes	—
236	C₂×C₃×Q₈	—	3	2	no	—
237	C₂×C₃×D₄	—	3	2	no	—
238	C₂×C₃×D₄	—	6	2	no	—
239	C₂²×C₃×C₄	—	3	1	no	—
240	C₂²×C₃×C₄	—	6	2	no	—
241	#239	C₂²×C₉	1	2	yes	—
242	D₃×Q₈	C₂²×C₉	1	2	yes	complemented
243	#237	—	2	2	no	—
244	#237	C₂²×C₉	1	2	yes	—
245	D₃×D₄	—	2	2	no	—
246	D₃×D₄	C₂²×C₉	1	2	yes	complemented
247	#235	—	2	2	no	—
248	#235	C₂²×C₉	1	2	yes	complemented
249	C₂×C₄×D₃	—	2	2	no	—
250	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
251	C₃×Q₁₆	—	2	1	no	—
252	C₃×Q₁₆	—	3	2	no	—
253	C₃×Q₁₆	—	3	1	no	—
254	C₃×Q₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
255	C₃×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
256	C₃×SD₁₆	—	2	2	no	—
257	C₃×SD₁₆	—	3	2	no	—
258	C₃×SD₁₆	—	3	2	no	—
259	C₃×SD₁₆	—	3	2	no	—
260	C₃×SD₁₆	C₂²×C₉	1	2	yes	complemented
261	C₃×SD₁₆	C₂×C₃×D₃	1	2	yes	—
262	C₃×D₈	—	2	1	no	—
263	C₃×D₈	—	3	2	no	—
264	C₃×D₈	—	3	1	no	—
265	C₃×D₈	C₂²×C₉	1	1	yes	characteristic, complemented
266	C₃×D₈	C₂×C₃×D₃	1	1	yes	characteristic
267	C₃×M₁₆	—	3	2	no	—
268	C₃×M₁₆	—	3	2	no	—
269	C₂×C₃×C₈	—	2	1	no	—
270	C₂×C₃×C₈	—	3	1	no	—
271	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic, complemented
272	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
273	#216	C₂²×C₉	1	2	yes	complemented
274	#215	C₂²×C₉	1	2	yes	complemented
275	#214	C₂²×C₉	1	2	yes	complemented
276	#213	C₂²×C₉	1	2	yes	complemented
277	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
278	Dic₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
279	D₂₄	C₂²×C₉	1	1	yes	characteristic, complemented
280	#204	C₂²×C₉	1	2	yes	complemented
281	ΓL(1,𝔽₂₅)	C₂²×C₉	1	2	yes	complemented
282	ΓL(1,𝔽₂₅)	C₂²×C₉	1	2	yes	complemented
283	C₂²×C₃²	—	2	2	no	—
284	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂×C₃×D₃	—	2	2	no	—
286	C₂×C₃×D₃	—	4	1	no	—
287	C₂×C₃×D₃	—	4	4	no	—
288	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
289	C₃²×C₄	—	2	2	no	—
290	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
291	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
292	C₃×Dic₃	—	2	2	no	—
293	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
294	C₂²×C₉	—	2	2	no	—
295	C₂²×C₉	—	2	1	no	—
296	C₂²×C₉	—	3	2	no	—
297	C₂²×C₉	—	4	2	no	—
298	C₂²×C₉	—	6	2	no	—
299	C₂²×C₉	—	12	1	no	—
300	C₂²×C₉	—	12	4	no	—
301	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
302	C₄×C₉	—	2	2	no	—
303	C₄×C₉	—	2	1	no	—
304	C₄×C₉	—	2	1	no	—
305	C₄×C₉	—	3	2	no	—
306	C₄×C₉	—	4	2	no	—
307	C₄×C₉	—	6	2	no	—
308	C₄×C₉	D₃×D₄	1	1	yes	characteristic
309	C₄×C₉	C₂³×D₃	1	1	yes	characteristic
310	C₂×#41	—	3	2	no	—
311	#137	—	3	2	no	—
312	#137	—	3	2	no	—
313	AGL(1,ℤ/8)	—	3	2	no	—
314	AGL(1,ℤ/8)	—	3	2	no	—
315	#135	—	3	2	no	—
316	#135	—	3	1	no	—
317	#135	D₃×C₉	1	1	yes	characteristic, complemented
318	C₂×M₁₆	—	3	1	no	—
319	C₃×C₉	#575	1	1	yes	characteristic, complemented, Sylow
320	C₂³×C₃	—	3	1	no	—
321	C₂³×C₃	—	6	2	no	—
322	C₂²×D₃	—	2	2	no	—
323	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
324	C₃×Q₈	—	2	2	no	—
325	C₃×Q₈	—	3	2	no	—
326	C₃×Q₈	—	6	2	no	—
327	C₃×Q₈	C₂³×C₉	1	2	yes	—
328	C₃×Q₈	C₂²×C₃×D₃	1	2	yes	—
329	C₃×D₄	—	2	2	no	—
330	C₃×D₄	—	2	2	no	—
331	C₃×D₄	—	2	2	no	—
332	C₃×D₄	—	3	2	no	—
333	C₃×D₄	—	4	2	no	—
334	C₃×D₄	—	6	2	no	—
335	C₃×D₄	—	6	2	no	—
336	C₃×D₄	—	6	2	no	—
337	C₃×D₄	—	6	2	no	—
338	C₃×D₄	C₂³×C₉	1	2	yes	—
339	C₃×D₄	C₂²×C₃×D₃	1	2	yes	—
340	C₂×C₃×C₄	—	2	2	no	—
341	C₂×C₃×C₄	—	2	2	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	3	1	no	—
344	C₂×C₃×C₄	—	3	2	no	—
345	C₂×C₃×C₄	—	3	2	no	—
346	C₂×C₃×C₄	—	4	2	no	—
347	C₂×C₃×C₄	—	6	2	no	—
348	C₂×C₃×C₄	—	6	2	no	—
349	C₂×C₃×C₄	—	6	2	no	—
350	C₂×C₃×C₄	—	6	2	no	—
351	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
353	#67	—	2	2	no	—
354	#67	—	2	2	no	—
355	#67	—	2	2	no	—
356	C₂×Dic₃	—	2	2	no	—
357	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
358	D₁₂	—	2	2	no	—
359	D₁₂	C₂³×C₉	1	2	yes	—
360	C₄×D₃	—	2	2	no	—
361	C₄×D₃	—	2	2	no	—
362	C₄×D₃	—	2	2	no	—
363	C₄×D₃	D₄×C₉	1	2	yes	—
364	C₄×D₃	C₂³×C₉	1	2	yes	—
365	Dic₆	—	2	2	no	—
366	Dic₆	C₂³×C₉	1	2	yes	—
367	C₃×C₈	—	2	1	no	—
368	C₃×C₈	—	2	1	no	—
369	C₃×C₈	—	3	2	no	—
370	C₃×C₈	C₂³×C₉	1	1	yes	characteristic
371	C₃×C₈	C₂³×C₉	1	1	yes	characteristic
372	C₃×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
373	C₃×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
374	C₃⋊C₈	C₂³×C₉	1	2	yes	—
375	C₂×C₃²	—	2	1	no	—
376	C₂×C₃²	—	4	2	no	—
377	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
378	C₃×D₃	—	2	2	no	—
379	C₃×D₃	—	4	2	no	—
380	C₂×C₉	—	2	1	no	—
381	C₂×C₉	—	2	1	no	—
382	C₂×C₉	—	4	1	no	—
383	C₂×C₉	—	4	2	no	—
384	C₂×C₉	—	6	2	no	—
385	C₂×C₉	—	8	2	no	—
386	C₂×C₉	—	12	2	no	—
387	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
388	#41	—	3	2	no	—
389	#41	—	3	2	no	—
390	#41	—	3	2	no	—
391	#41	—	6	2	no	—
392	#41	—	6	2	no	—
393	#41	C₂×D₃×C₉	1	2	yes	complemented
394	C₂×Q₈	—	3	2	no	—
395	C₂×D₄	—	3	2	no	—
396	C₂×D₄	—	6	2	no	—
397	C₂²×C₄	—	3	1	no	—
398	C₂²×C₄	—	6	2	no	—
399	Q₁₆	—	3	2	no	—
400	Q₁₆	—	3	1	no	—
401	Q₁₆	C₂×D₃×C₉	1	1	yes	characteristic, complemented
402	SD₁₆	—	3	2	no	—
403	SD₁₆	—	3	2	no	—
404	SD₁₆	—	3	2	no	—
405	SD₁₆	C₂×D₃×C₉	1	2	yes	complemented
406	D₈	—	3	2	no	—
407	D₈	—	3	1	no	—
408	D₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
409	M₁₆	—	3	2	no	—
410	M₁₆	—	3	2	no	—
411	C₂×C₈	—	3	1	no	—
412	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
413	C₂²×C₃	—	2	2	no	—
414	C₂²×C₃	—	2	2	no	—
415	C₂²×C₃	—	2	1	no	—
416	C₂²×C₃	—	3	2	no	—
417	C₂²×C₃	—	4	2	no	—
418	C₂²×C₃	—	6	2	no	—
419	C₂²×C₃	—	12	1	no	—
420	C₂²×C₃	—	12	4	no	—
421	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
422	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
423	C₂×D₃	—	2	2	no	—
424	C₂×D₃	—	4	1	no	—
425	C₂×D₃	—	4	4	no	—
426	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
427	C₃×C₄	—	2	2	no	—
428	C₃×C₄	—	2	2	no	—
429	C₃×C₄	—	2	1	no	—
430	C₃×C₄	—	2	1	no	—
431	C₃×C₄	—	3	2	no	—
432	C₃×C₄	—	4	2	no	—
433	C₃×C₄	—	6	2	no	—
434	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
435	C₃×C₄	C₂⁴×C₉	1	1	yes	characteristic
436	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
437	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
438	Dic₃	—	2	2	no	—
439	Dic₃	C₂×D₄×C₉	1	2	yes	—
440	C₃²	C₃×#575	1	1	yes	characteristic
441	C₉	—	2	1	no	—
442	C₉	#5768	1	1	yes	characteristic, direct product factor
443	C₂³	—	3	1	no	—
444	C₂³	—	6	2	no	—
445	Q₈	—	3	2	no	—
446	Q₈	—	6	2	no	—
447	Q₈	C₂²×D₃×C₉	1	2	yes	—
448	D₄	—	2	2	no	—
449	D₄	—	3	2	no	—
450	D₄	—	6	2	no	—
451	D₄	—	6	2	no	—
452	D₄	—	6	2	no	—
453	D₄	—	6	2	no	—
454	D₄	C₂²×D₃×C₉	1	2	yes	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	3	1	no	—
457	C₂×C₄	—	3	2	no	—
458	C₂×C₄	—	3	2	no	—
459	C₂×C₄	—	6	2	no	—
460	C₂×C₄	—	6	2	no	—
461	C₂×C₄	—	6	2	no	—
462	C₂×C₄	—	6	2	no	—
463	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
464	C₈	—	3	2	no	—
465	C₈	C₂²×D₃×C₉	1	1	yes	characteristic
466	C₈	C₂²×D₃×C₉	1	1	yes	characteristic
467	C₂×C₃	—	2	1	no	—
468	C₂×C₃	—	2	1	no	—
469	C₂×C₃	—	2	1	no	—
470	C₂×C₃	—	4	1	no	—
471	C₂×C₃	—	4	2	no	—
472	C₂×C₃	—	4	2	no	—
473	C₂×C₃	—	6	2	no	—
474	C₂×C₃	—	8	2	no	—
475	C₂×C₃	—	12	2	no	—
476	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
477	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
478	D₃	—	2	2	no	—
479	D₃	—	4	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	3	2	no	—
482	C₂²	—	6	2	no	—
483	C₂²	—	12	1	no	—
484	C₂²	—	12	4	no	—
485	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	3	2	no	—
488	C₄	—	6	2	no	—
489	C₄	D₃×D₄×C₉	1	1	yes	characteristic
490	C₄	C₂³×D₃×C₉	1	1	yes	characteristic
491	C₃	—	2	1	no	—
492	C₃	C₉×#575	1	1	yes	characteristic, complemented
493	C₃	C₃×#5768	1	1	yes	characteristic
494	C₂	—	2	1	no	—
495	C₂	—	4	2	no	—
496	C₂	—	6	2	no	—
497	C₂	—	12	2	no	—
498	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₉	D₃×D₄
commutator	C₃×C₄	C₂⁴×C₉
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₃×C₉×#135	C₂
socle	C₂×C₃²	C₂²×C₃×D₄
prime radical	C₃×#5768	C₃
cosocle	C₃²×C₄	C₂⁴×C₃
hypercenter	C₉×#135	D₃
hypocenter	C₃	C₉×#575
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#135

Complements

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

N	H ≅ G/N	type
1. D₃×C₉×#41	C₂	semidirect
2. C₃×C₉×#135	C₂	semidirect
3. C₉×#950	C₂	semidirect
4. C₉×#918	C₂	semidirect
5. C₉×#915	C₂	semidirect
6. C₉×#914	C₂	semidirect
7. C₉×#911	C₂	semidirect
8. C₉×#904	C₂	semidirect
9. C₂×C₉×ΓL(1,𝔽₂₅)	C₂	semidirect
12. C₃×C₉×#41	C₂²	semidirect
14. D₃×Q₈×C₉	C₂²	semidirect
18. D₃×D₄×C₉	C₂²	semidirect
20. C₉×#235	C₂²	semidirect
23. C₃×C₉×Q₁₆	C₂²	semidirect
24. C₃×C₉×SD₁₆	C₂²	semidirect
25. C₃×C₉×D₈	C₂²	semidirect
26. C₂×C₃×C₈×C₉	C₂²	semidirect
27. C₉×#216	C₂²	semidirect
28. C₉×#215	C₂²	semidirect
29. C₉×#214	C₂²	semidirect
30. C₉×#213	C₂²	semidirect
31. C₂×C₉×C₃⋊C₈	C₂²	semidirect
32. C₉×Dic₁₂	C₂²	semidirect
33. C₉×D₂₄	C₂²	semidirect
34. C₉×#204	C₂²	semidirect
35. C₉×ΓL(1,𝔽₂₅)	C₂²	semidirect
36. C₉×ΓL(1,𝔽₂₅)	C₂²	semidirect
54. C₉×#135	D₃	semidirect
81. #5768	C₉	direct (N × H)
113. C₉×#41	C₂×D₃	semidirect
122. C₉×Q₁₆	C₂×D₃	semidirect
127. C₉×SD₁₆	C₂×D₃	semidirect
131. C₉×D₈	C₂×D₃	semidirect
136. C₂×C₈×C₉	C₂×D₃	semidirect
149. D₃×#41	C₂×C₉	semidirect
157. C₃×#135	C₂×C₉	semidirect
160. #950	C₂×C₉	semidirect
161. #918	C₂×C₉	semidirect
162. #915	C₂×C₉	semidirect
163. #914	C₂×C₉	semidirect
164. #911	C₂×C₉	semidirect
165. #904	C₂×C₉	semidirect
166. C₂×ΓL(1,𝔽₂₅)	C₂×C₉	semidirect
234. C₃×#41	C₂²×C₉	semidirect
242. D₃×Q₈	C₂²×C₉	semidirect
246. D₃×D₄	C₂²×C₉	semidirect
248. #235	C₂²×C₉	semidirect
254. C₃×Q₁₆	C₂²×C₉	semidirect
260. C₃×SD₁₆	C₂²×C₉	semidirect
265. C₃×D₈	C₂²×C₉	semidirect
271. C₂×C₃×C₈	C₂²×C₉	semidirect
273. #216	C₂²×C₉	semidirect
274. #215	C₂²×C₉	semidirect
275. #214	C₂²×C₉	semidirect
276. #213	C₂²×C₉	semidirect
277. C₂×C₃⋊C₈	C₂²×C₉	semidirect
278. Dic₁₂	C₂²×C₉	semidirect
279. D₂₄	C₂²×C₉	semidirect
280. #204	C₂²×C₉	semidirect
281. ΓL(1,𝔽₂₅)	C₂²×C₉	semidirect
282. ΓL(1,𝔽₂₅)	C₂²×C₉	semidirect
317. #135	D₃×C₉	semidirect
319. C₃×C₉	#575	semidirect
393. #41	C₂×D₃×C₉	semidirect
401. Q₁₆	C₂×D₃×C₉	semidirect
405. SD₁₆	C₂×D₃×C₉	semidirect
408. D₈	C₂×D₃×C₉	semidirect
412. C₂×C₈	C₂×D₃×C₉	semidirect
442. C₉	#5768	direct (N × H)
492. C₃	C₉×#575	semidirect

Maximal subgroups

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

subgroup	index
D₃×C₉×#41	2
C₃×C₉×#135	2
C₉×#950	2
C₉×#918	2
C₉×#915	2
C₉×#914	2
C₉×#911	2
C₉×#904	2
C₂×C₉×ΓL(1,𝔽₂₅)	2
C₃×#5768	3
C₉×#575	3

Subgroups — C9×#5768 #13153477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5768 #13153477