Subgroups — C₉×#5771 #13153480

Order 1728.

806 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#1010	C₂	1	2	yes	maximal, complemented
2	C₃×C₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#951	C₂	1	2	yes	maximal, complemented
4	D₃×C₉×Q₁₆	C₂	1	2	yes	maximal, complemented
5	C₉×#915	C₂	1	4	yes	maximal, complemented
6	C₉×#912	C₂	1	2	yes	maximal, complemented
7	C₂×C₉×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#901	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5771	C₃	1	1	yes	maximal, characteristic
10	C₉×#578	—	3	1	no	maximal
11	C₃×C₉×#41	C₂²	1	2	yes	—
12	D₃×Q₈×C₉	C₂²	1	4	yes	—
13	C₉×#237	—	2	4	no	—
14	C₉×#237	C₂²	1	4	yes	—
15	C₉×#235	—	2	2	no	—
16	C₉×#235	C₂²	1	1	yes	characteristic
17	C₂×C₉×Dic₆	—	2	2	no	—
18	C₂×C₉×Dic₆	C₂²	1	2	yes	—
19	C₃×C₉×Q₁₆	C₂²	1	1	yes	characteristic
20	C₃×C₉×SD₁₆	C₂²	1	2	yes	—
21	C₃×C₉×D₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
23	C₉×#216	C₂²	1	4	yes	—
24	C₉×#214	C₂²	1	4	yes	—
25	C₉×#208	C₂²	1	1	yes	characteristic
26	C₉×Dic₁₂	C₂²	1	2	yes	—
27	C₉×Dic₁₂	C₂²	1	2	yes	—
28	C₉×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
29	D₃×C₈×C₉	C₂²	1	2	yes	—
30	C₃×#1010	C₂×C₃	1	2	yes	—
31	C₃²×#135	C₂×C₃	1	1	yes	characteristic
32	C₃×#951	C₂×C₃	1	2	yes	—
33	C₃×D₃×Q₁₆	C₂×C₃	1	2	yes	—
34	C₃×#915	C₂×C₃	1	4	yes	—
35	C₃×#912	C₂×C₃	1	2	yes	—
36	C₂×C₃×Dic₁₂	C₂×C₃	1	1	yes	characteristic
37	C₃×#901	C₂×C₃	1	1	yes	characteristic
38	C₉×2₋¹⁺⁴	—	3	2	no	—
39	C₉×#137	—	3	2	no	—
40	C₉×#137	—	3	4	no	—
41	C₉×#135	—	2	1	no	—
42	C₉×#135	—	3	2	no	—
43	C₉×#135	D₃	1	1	yes	characteristic, complemented
44	C₂×C₉×Q₁₆	—	3	2	no	—
45	C₂×C₉×Q₁₆	—	3	1	no	—
46	C₉×#131	—	3	1	no	—
47	C₃×Q₈×C₉	C₂³	1	2	yes	—
48	C₃×D₄×C₉	—	2	2	no	—
49	C₃×D₄×C₉	C₂³	1	2	yes	—
50	C₂×C₃×C₄×C₉	—	2	2	no	—
51	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
52	C₉×#67	—	2	4	no	—
53	C₉×#67	D₄	1	2	yes	—
54	C₂×C₉×Dic₃	—	2	2	no	—
55	C₂×C₉×Dic₃	—	2	4	no	—
56	C₉×D₁₂	D₄	1	1	yes	characteristic
57	C₄×D₃×C₉	—	2	4	no	—
58	C₄×D₃×C₉	C₂³	1	2	yes	—
59	C₉×Dic₆	—	2	2	no	—
60	C₉×Dic₆	—	2	4	no	—
61	C₉×Dic₆	D₄	1	1	yes	characteristic
62	C₉×Dic₆	C₂³	1	4	yes	—
63	C₃×C₈×C₉	C₂³	1	1	yes	characteristic
64	C₃×C₈×C₉	C₂³	1	1	yes	characteristic
65	C₉×C₃⋊C₈	C₂³	1	2	yes	—
66	C₃×#578	—	3	1	no	—
67	#5771	C₉	1	1	yes	characteristic, direct product factor
68	C₃²×#41	C₂²×C₃	1	2	yes	—
69	C₃×D₃×Q₈	C₂²×C₃	1	4	yes	—
70	C₃×#237	—	2	4	no	—
71	C₃×#237	C₂²×C₃	1	4	yes	—
72	C₃×#235	—	2	2	no	—
73	C₃×#235	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃×Dic₆	—	2	2	no	—
75	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
76	C₃²×Q₁₆	C₂²×C₃	1	1	yes	characteristic
77	C₃²×SD₁₆	C₂²×C₃	1	2	yes	—
78	C₃²×D₈	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
80	C₃×#216	C₂²×C₃	1	4	yes	—
81	C₃×#214	C₂²×C₃	1	4	yes	—
82	C₃×#208	C₂²×C₃	1	1	yes	characteristic
83	C₃×Dic₁₂	C₂²×C₃	1	2	yes	—
84	C₃×Dic₁₂	C₂²×C₃	1	2	yes	—
85	C₃×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
86	C₃×D₃×C₈	C₂²×C₃	1	2	yes	—
87	C₉×#41	—	2	2	no	—
88	C₉×#41	—	3	1	no	—
89	C₉×#41	—	3	4	no	—
90	C₉×#41	—	6	2	no	—
91	C₉×#41	—	6	4	no	—
92	C₉×#41	C₂×D₃	1	2	yes	—
93	C₂×Q₈×C₉	—	3	4	no	—
94	C₂×Q₈×C₉	—	3	2	no	—
95	C₂×Q₈×C₉	—	6	2	no	—
96	C₉×Q₁₆	—	2	1	no	—
97	C₉×Q₁₆	—	3	4	no	—
98	C₉×Q₁₆	—	3	2	no	—
99	C₉×Q₁₆	—	3	2	no	—
100	C₉×Q₁₆	C₂×D₃	1	1	yes	characteristic
101	C₉×SD₁₆	—	2	2	no	—
102	C₉×SD₁₆	—	3	4	no	—
103	C₉×SD₁₆	C₂×D₃	1	2	yes	—
104	C₉×D₈	—	2	1	no	—
105	C₉×D₈	C₂×D₃	1	1	yes	characteristic
106	C₉×M₁₆	—	3	1	no	—
107	C₉×M₁₆	—	3	2	no	—
108	C₂×C₈×C₉	—	2	1	no	—
109	C₂×C₈×C₉	—	3	2	no	—
110	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
111	C₂²×C₃×C₉	—	2	2	no	—
112	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
113	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
114	C₃×C₄×C₉	—	2	2	no	—
115	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
116	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
117	C₉×Dic₃	—	2	4	no	—
118	C₉×Dic₃	C₂×D₄	1	2	yes	—
119	C₃×2₋¹⁺⁴	—	3	2	no	—
120	#1010	C₂×C₉	1	2	yes	complemented
121	C₃×#137	—	3	2	no	—
122	C₃×#137	—	3	4	no	—
123	C₃×#135	—	2	1	no	—
124	C₃×#135	—	3	2	no	—
125	C₃×#135	C₂×C₉	1	1	yes	characteristic, complemented
126	C₃×#135	C₃×D₃	1	1	yes	characteristic
127	C₂×C₃×Q₁₆	—	3	2	no	—
128	C₂×C₃×Q₁₆	—	3	1	no	—
129	C₃×#131	—	3	1	no	—
130	#951	C₂×C₉	1	2	yes	complemented
131	D₃×Q₁₆	C₂×C₉	1	2	yes	complemented
132	#915	C₂×C₉	1	4	yes	complemented
133	#912	C₂×C₉	1	2	yes	complemented
134	C₂×Dic₁₂	C₂×C₉	1	1	yes	characteristic, complemented
135	#901	C₂×C₉	1	1	yes	characteristic, complemented
136	C₃²×Q₈	C₂³×C₃	1	2	yes	—
137	C₃²×D₄	—	2	2	no	—
138	C₃²×D₄	C₂³×C₃	1	2	yes	—
139	C₂×C₃²×C₄	—	2	2	no	—
140	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
141	C₃×#67	—	2	4	no	—
142	C₃×#67	C₃×D₄	1	2	yes	—
143	C₂×C₃×Dic₃	—	2	2	no	—
144	C₂×C₃×Dic₃	—	2	4	no	—
145	C₃×D₁₂	C₃×D₄	1	1	yes	characteristic
146	C₃×C₄×D₃	—	2	4	no	—
147	C₃×C₄×D₃	C₂³×C₃	1	2	yes	—
148	C₃×Dic₆	—	2	2	no	—
149	C₃×Dic₆	—	2	4	no	—
150	C₃×Dic₆	C₃×D₄	1	1	yes	characteristic
151	C₃×Dic₆	C₂³×C₃	1	4	yes	—
152	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
153	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
154	C₃×C₃⋊C₈	C₂³×C₃	1	2	yes	—
155	Q₈×C₉	—	2	2	no	—
156	Q₈×C₉	—	3	1	no	—
157	Q₈×C₉	—	3	4	no	—
158	Q₈×C₉	—	6	4	no	—
159	Q₈×C₉	—	6	2	no	—
160	Q₈×C₉	C₂²×D₃	1	2	yes	—
161	D₄×C₉	—	2	2	no	—
162	D₄×C₉	—	2	2	no	—
163	D₄×C₉	—	3	2	no	—
164	D₄×C₉	—	3	1	no	—
165	D₄×C₉	—	4	2	no	—
166	D₄×C₉	—	6	4	no	—
167	D₄×C₉	C₂²×D₃	1	2	yes	—
168	C₂×C₄×C₉	—	2	2	no	—
169	C₂×C₄×C₉	—	2	1	no	—
170	C₂×C₄×C₉	—	3	2	no	—
171	C₂×C₄×C₉	—	4	2	no	—
172	C₂×C₄×C₉	—	6	4	no	—
173	C₂×C₄×C₉	—	6	4	no	—
174	C₂×C₄×C₉	—	6	2	no	—
175	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
176	C₈×C₉	—	2	1	no	—
177	C₈×C₉	—	2	1	no	—
178	C₈×C₉	—	3	2	no	—
179	C₈×C₉	C₂²×D₃	1	1	yes	characteristic
180	C₈×C₉	C₂²×D₃	1	1	yes	characteristic
181	#578	—	3	1	no	Sylow
182	C₂×C₃×C₉	—	2	1	no	—
183	C₂×C₃×C₉	—	4	2	no	—
184	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
185	D₃×C₉	—	2	2	no	—
186	C₃×#41	—	2	2	no	—
187	C₃×#41	—	3	1	no	—
188	C₃×#41	—	3	4	no	—
189	C₃×#41	—	6	2	no	—
190	C₃×#41	—	6	4	no	—
191	C₃×#41	C₂²×C₉	1	2	yes	—
192	C₃×#41	C₂×C₃×D₃	1	2	yes	—
193	C₂×C₃×Q₈	—	3	4	no	—
194	C₂×C₃×Q₈	—	3	2	no	—
195	C₂×C₃×Q₈	—	6	2	no	—
196	D₃×Q₈	C₂²×C₉	1	4	yes	—
197	#237	—	2	4	no	—
198	#237	C₂²×C₉	1	4	yes	—
199	#235	—	2	2	no	—
200	#235	C₂²×C₉	1	1	yes	characteristic
201	C₂×Dic₆	—	2	2	no	—
202	C₂×Dic₆	C₂²×C₉	1	2	yes	—
203	C₃×Q₁₆	—	2	1	no	—
204	C₃×Q₁₆	—	3	4	no	—
205	C₃×Q₁₆	—	3	2	no	—
206	C₃×Q₁₆	—	3	2	no	—
207	C₃×Q₁₆	C₂²×C₉	1	1	yes	characteristic
208	C₃×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
209	C₃×SD₁₆	—	2	2	no	—
210	C₃×SD₁₆	—	3	4	no	—
211	C₃×SD₁₆	C₂²×C₉	1	2	yes	—
212	C₃×SD₁₆	C₂×C₃×D₃	1	2	yes	—
213	C₃×D₈	—	2	1	no	—
214	C₃×D₈	C₂²×C₉	1	1	yes	characteristic
215	C₃×D₈	C₂×C₃×D₃	1	1	yes	characteristic
216	C₃×M₁₆	—	3	1	no	—
217	C₃×M₁₆	—	3	2	no	—
218	C₂×C₃×C₈	—	2	1	no	—
219	C₂×C₃×C₈	—	3	2	no	—
220	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
221	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
222	#216	C₂²×C₉	1	4	yes	—
223	#214	C₂²×C₉	1	4	yes	—
224	#208	C₂²×C₉	1	1	yes	characteristic
225	Dic₁₂	C₂²×C₉	1	2	yes	—
226	Dic₁₂	C₂²×C₉	1	2	yes	—
227	ΓL(1,𝔽₂₅)	C₂²×C₉	1	2	yes	—
228	D₃×C₈	C₂²×C₉	1	2	yes	—
229	C₂²×C₃²	—	2	2	no	—
230	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
231	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
232	C₃²×C₄	—	2	2	no	—
233	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
234	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
235	C₃×Dic₃	—	2	4	no	—
236	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
237	C₂²×C₉	—	2	2	no	—
238	C₂²×C₉	—	2	1	no	—
239	C₂²×C₉	—	3	2	no	—
240	C₂²×C₉	—	4	2	no	—
241	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
242	C₄×C₉	—	2	2	no	—
243	C₄×C₉	—	2	1	no	—
244	C₄×C₉	—	2	1	no	—
245	C₄×C₉	—	3	2	no	—
246	C₄×C₉	—	4	2	no	—
247	C₄×C₉	—	6	4	no	—
248	C₄×C₉	D₃×D₄	1	1	yes	characteristic
249	C₄×C₉	C₂³×D₃	1	1	yes	characteristic
250	2₋¹⁺⁴	—	3	2	no	—
251	#137	—	3	2	no	—
252	#137	—	3	4	no	—
253	#135	—	3	2	no	—
254	#135	D₃×C₉	1	1	yes	characteristic, complemented
255	C₂×Q₁₆	—	3	2	no	—
256	C₂×Q₁₆	—	3	1	no	—
257	#131	—	3	1	no	—
258	C₃×C₉	#578	1	1	yes	characteristic, complemented, Sylow
259	C₃×Q₈	—	2	2	no	—
260	C₃×Q₈	—	3	1	no	—
261	C₃×Q₈	—	3	4	no	—
262	C₃×Q₈	—	6	4	no	—
263	C₃×Q₈	—	6	2	no	—
264	C₃×Q₈	C₂³×C₉	1	2	yes	—
265	C₃×Q₈	C₂²×C₃×D₃	1	2	yes	—
266	C₃×D₄	—	2	2	no	—
267	C₃×D₄	—	2	2	no	—
268	C₃×D₄	—	2	2	no	—
269	C₃×D₄	—	3	2	no	—
270	C₃×D₄	—	3	1	no	—
271	C₃×D₄	—	4	2	no	—
272	C₃×D₄	—	6	4	no	—
273	C₃×D₄	C₂³×C₉	1	2	yes	—
274	C₃×D₄	C₂²×C₃×D₃	1	2	yes	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	3	2	no	—
279	C₂×C₃×C₄	—	4	2	no	—
280	C₂×C₃×C₄	—	6	4	no	—
281	C₂×C₃×C₄	—	6	4	no	—
282	C₂×C₃×C₄	—	6	2	no	—
283	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
285	#67	—	2	4	no	—
286	#67	D₄×C₉	1	2	yes	—
287	C₂×Dic₃	—	2	2	no	—
288	C₂×Dic₃	—	2	4	no	—
289	D₁₂	D₄×C₉	1	1	yes	characteristic
290	C₄×D₃	—	2	4	no	—
291	C₄×D₃	C₂³×C₉	1	2	yes	—
292	Dic₆	—	2	2	no	—
293	Dic₆	—	2	4	no	—
294	Dic₆	D₄×C₉	1	1	yes	characteristic
295	Dic₆	C₂³×C₉	1	4	yes	—
296	C₃×C₈	—	2	1	no	—
297	C₃×C₈	—	2	1	no	—
298	C₃×C₈	—	3	2	no	—
299	C₃×C₈	C₂³×C₉	1	1	yes	characteristic
300	C₃×C₈	C₂³×C₉	1	1	yes	characteristic
301	C₃×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
302	C₃×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
303	C₃⋊C₈	C₂³×C₉	1	2	yes	—
304	C₂×C₃²	—	2	1	no	—
305	C₂×C₃²	—	4	2	no	—
306	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
307	C₃×D₃	—	2	2	no	—
308	C₂×C₉	—	2	1	no	—
309	C₂×C₉	—	2	1	no	—
310	C₂×C₉	—	4	1	no	—
311	C₂×C₉	—	4	2	no	—
312	C₂×C₉	—	6	2	no	—
313	C₂×C₉	—	8	2	no	—
314	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
315	#41	—	3	1	no	—
316	#41	—	3	4	no	—
317	#41	—	6	2	no	—
318	#41	—	6	4	no	—
319	#41	C₂×D₃×C₉	1	2	yes	—
320	C₂×Q₈	—	3	4	no	—
321	C₂×Q₈	—	3	2	no	—
322	C₂×Q₈	—	6	2	no	—
323	Q₁₆	—	3	4	no	—
324	Q₁₆	—	3	2	no	—
325	Q₁₆	—	3	2	no	—
326	Q₁₆	C₂×D₃×C₉	1	1	yes	characteristic
327	SD₁₆	—	3	4	no	—
328	SD₁₆	C₂×D₃×C₉	1	2	yes	—
329	D₈	C₂×D₃×C₉	1	1	yes	characteristic
330	M₁₆	—	3	1	no	—
331	M₁₆	—	3	2	no	—
332	C₂×C₈	—	3	2	no	—
333	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
334	C₂²×C₃	—	2	2	no	—
335	C₂²×C₃	—	2	2	no	—
336	C₂²×C₃	—	2	1	no	—
337	C₂²×C₃	—	3	2	no	—
338	C₂²×C₃	—	4	2	no	—
339	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
340	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
341	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
342	C₃×C₄	—	2	2	no	—
343	C₃×C₄	—	2	2	no	—
344	C₃×C₄	—	2	1	no	—
345	C₃×C₄	—	2	1	no	—
346	C₃×C₄	—	3	2	no	—
347	C₃×C₄	—	4	2	no	—
348	C₃×C₄	—	6	4	no	—
349	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
350	C₃×C₄	C₂⁴×C₉	1	1	yes	characteristic
351	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
352	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
353	Dic₃	—	2	4	no	—
354	Dic₃	C₂×D₄×C₉	1	2	yes	—
355	C₃²	C₃×#578	1	1	yes	characteristic
356	C₉	—	2	1	no	—
357	C₉	#5771	1	1	yes	characteristic, direct product factor
358	Q₈	—	3	1	no	—
359	Q₈	—	3	4	no	—
360	Q₈	—	6	4	no	—
361	Q₈	—	6	2	no	—
362	Q₈	C₂²×D₃×C₉	1	2	yes	—
363	D₄	—	2	2	no	—
364	D₄	—	3	2	no	—
365	D₄	—	3	1	no	—
366	D₄	—	6	4	no	—
367	D₄	C₂²×D₃×C₉	1	2	yes	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	3	2	no	—
370	C₂×C₄	—	6	4	no	—
371	C₂×C₄	—	6	4	no	—
372	C₂×C₄	—	6	2	no	—
373	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
374	C₈	—	3	2	no	—
375	C₈	C₂²×D₃×C₉	1	1	yes	characteristic
376	C₈	C₂²×D₃×C₉	1	1	yes	characteristic
377	C₂×C₃	—	2	1	no	—
378	C₂×C₃	—	2	1	no	—
379	C₂×C₃	—	2	1	no	—
380	C₂×C₃	—	4	1	no	—
381	C₂×C₃	—	4	2	no	—
382	C₂×C₃	—	4	2	no	—
383	C₂×C₃	—	6	2	no	—
384	C₂×C₃	—	8	2	no	—
385	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
386	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
387	D₃	—	2	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	3	2	no	—
390	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	3	2	no	—
393	C₄	—	6	4	no	—
394	C₄	D₃×D₄×C₉	1	1	yes	characteristic
395	C₄	C₂³×D₃×C₉	1	1	yes	characteristic
396	C₃	—	2	1	no	—
397	C₃	C₉×#578	1	1	yes	characteristic, complemented
398	C₃	C₃×#5771	1	1	yes	characteristic
399	C₂	—	2	1	no	—
400	C₂	—	4	2	no	—
401	C₂	—	6	2	no	—
402	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×#135	C₂
socle	C₂×C₃²	C₂²×C₃×D₄
prime radical	C₃×#5771	C₃
cosocle	C₃²×C₄	C₂⁴×C₃
hypercenter	C₉×#135	D₃
hypocenter	C₃	C₉×#578
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#135

Complements

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

N	H ≅ G/N	type
1. C₉×#1010	C₂	semidirect
2. C₃×C₉×#135	C₂	semidirect
3. C₉×#951	C₂	semidirect
4. D₃×C₉×Q₁₆	C₂	semidirect
5. C₉×#915	C₂	semidirect
6. C₉×#912	C₂	semidirect
7. C₂×C₉×Dic₁₂	C₂	semidirect
8. C₉×#901	C₂	semidirect
43. C₉×#135	D₃	semidirect
67. #5771	C₉	direct (N × H)
120. #1010	C₂×C₉	semidirect
125. C₃×#135	C₂×C₉	semidirect
130. #951	C₂×C₉	semidirect
131. D₃×Q₁₆	C₂×C₉	semidirect
132. #915	C₂×C₉	semidirect
133. #912	C₂×C₉	semidirect
134. C₂×Dic₁₂	C₂×C₉	semidirect
135. #901	C₂×C₉	semidirect
254. #135	D₃×C₉	semidirect
258. C₃×C₉	#578	semidirect
357. C₉	#5771	direct (N × H)
397. C₃	C₉×#578	semidirect

Maximal subgroups

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

subgroup	index
C₉×#1010	2
C₃×C₉×#135	2
C₉×#951	2
D₃×C₉×Q₁₆	2
C₉×#915	2
C₉×#912	2
C₂×C₉×Dic₁₂	2
C₉×#901	2
C₃×#5771	3
C₉×#578	3

Subgroups — C9×#5771 #13153480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5771 #13153480