Subgroups — C₉×#4771 #13141754

Order 1728.

536 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#237	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#832	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#816	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#810	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4771	C₃	1	1	yes	maximal, characteristic
9	C₉×#417	—	3	1	no	maximal
10	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₉×#67	—	2	1	no	—
12	C₂²×C₉×Dic₃	—	2	1	no	—
13	C₉×#237	—	2	2	no	—
14	C₉×#237	C₄	1	4	yes	complemented
15	C₂×C₄×D₃×C₉	—	2	1	no	—
16	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
19	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
21	C₉×Dic₃⋊C₄	—	2	1	no	—
22	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₉×ΓL(1,𝔽₂₅)	—	2	2	no	—
24	C₂×C₃×#237	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	1	1	yes	characteristic
26	C₃×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
27	C₂×C₉×#41	—	3	1	no	—
28	C₃²×#102	C₂×C₃	1	1	yes	characteristic
29	C₃×#832	C₂×C₃	1	1	yes	characteristic
30	C₃×#816	C₂×C₃	1	1	yes	characteristic
31	C₃×#810	C₂×C₃	1	1	yes	characteristic
32	C₂×C₉×M₁₆	—	3	1	no	—
33	C₂×C₉×C₄⋊C₄	—	3	1	no	—
34	C₉×#103	—	3	1	no	—
35	C₉×#103	—	3	1	no	—
36	C₉×#102	—	2	1	no	—
37	C₉×#102	—	3	1	no	—
38	C₉×#102	D₃	1	1	yes	characteristic, complemented
39	C₂³×C₃×C₉	—	2	1	no	—
40	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
41	C₃×D₄×C₉	—	2	1	no	—
42	C₃×D₄×C₉	C₂×C₄	1	2	yes	complemented
43	C₂×C₃×C₄×C₉	—	2	1	no	—
44	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
45	C₉×#67	—	2	4	no	—
46	C₂×C₉×Dic₃	—	2	1	no	—
47	C₂×C₉×Dic₃	—	2	4	no	—
48	C₂×C₉×Dic₃	—	2	1	no	—
49	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
50	C₄×D₃×C₉	—	4	2	no	—
51	C₄×D₃×C₉	C₂×C₄	1	2	yes	—
52	C₄×D₃×C₉	D₄	1	2	yes	—
53	C₉×Dic₆	—	2	1	no	—
54	C₉×Dic₆	C₂×C₄	1	2	yes	complemented
55	C₃×C₈×C₉	—	2	1	no	—
56	C₉×C₃⋊C₈	—	2	1	no	—
57	C₃×#417	—	3	1	no	—
58	#4771	C₉	1	1	yes	characteristic, direct product factor
59	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
60	C₂×C₃×#67	—	2	1	no	—
61	C₂²×C₃×Dic₃	—	2	1	no	—
62	C₃×#237	—	2	2	no	—
63	C₃×#237	C₃×C₄	1	4	yes	—
64	C₂×C₃×C₄×D₃	—	2	1	no	—
65	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
68	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
69	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
70	C₃×Dic₃⋊C₄	—	2	1	no	—
71	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
72	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
73	C₉×#41	—	3	4	no	—
74	C₉×#41	—	6	2	no	—
75	C₂×Q₈×C₉	—	3	1	no	—
76	C₂×D₄×C₉	—	2	1	no	—
77	C₂×D₄×C₉	—	6	1	no	—
78	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
79	C₂²×C₄×C₉	—	3	1	no	—
80	C₂²×C₄×C₉	—	6	1	no	—
81	C₂²×C₄×C₉	—	6	1	no	—
82	C₉×M₁₆	—	6	2	no	—
83	C₂×C₈×C₉	—	2	1	no	—
84	C₂×C₈×C₉	—	3	1	no	—
85	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
86	C₉×C₄⋊C₄	—	2	1	no	—
87	C₉×C₄⋊C₄	—	3	1	no	—
88	C₉×C₄⋊C₄	—	6	1	no	—
89	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
90	C₂²×C₃×C₉	—	2	2	no	—
91	C₂²×C₃×C₉	—	4	1	no	—
92	C₂²×C₃×C₉	—	4	1	no	—
93	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
94	C₂×D₃×C₉	—	2	1	no	—
95	C₂×D₃×C₉	—	2	1	no	—
96	C₂×D₃×C₉	C₂²⋊C₄	1	2	yes	—
97	C₃×C₄×C₉	—	4	1	no	—
98	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
99	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
100	C₉×Dic₃	—	2	2	no	—
101	C₉×Dic₃	—	4	1	no	—
102	C₉×Dic₃	C₂²⋊C₄	1	2	yes	—
103	C₂×C₃×#41	—	3	1	no	—
104	C₂×#237	C₂×C₉	1	1	yes	characteristic
105	C₂×C₃×M₁₆	—	3	1	no	—
106	C₂×C₃×C₄⋊C₄	—	3	1	no	—
107	C₂×ΓL(1,𝔽₂₅)	C₂×C₉	1	1	yes	characteristic, complemented
108	D₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
109	C₃×#103	—	3	1	no	—
110	C₃×#103	—	3	1	no	—
111	C₃×#102	—	2	1	no	—
112	C₃×#102	—	3	1	no	—
113	C₃×#102	C₂×C₉	1	1	yes	characteristic, complemented
114	C₃×#102	C₃×D₃	1	1	yes	characteristic
115	#832	C₂×C₉	1	1	yes	characteristic, complemented
116	#816	C₂×C₉	1	1	yes	characteristic, complemented
117	#810	C₂×C₉	1	1	yes	characteristic, complemented
118	C₂³×C₃²	—	2	1	no	—
119	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
120	C₃²×D₄	—	2	1	no	—
121	C₃²×D₄	C₂×C₃×C₄	1	2	yes	—
122	C₂×C₃²×C₄	—	2	1	no	—
123	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
124	C₃×#67	—	2	4	no	—
125	C₂×C₃×Dic₃	—	2	1	no	—
126	C₂×C₃×Dic₃	—	2	4	no	—
127	C₂×C₃×Dic₃	—	2	1	no	—
128	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
129	C₃×C₄×D₃	—	4	2	no	—
130	C₃×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
131	C₃×C₄×D₃	C₃×D₄	1	2	yes	—
132	C₃×Dic₆	—	2	1	no	—
133	C₃×Dic₆	C₂×C₃×C₄	1	2	yes	—
134	C₂³×C₉	—	2	1	no	—
135	C₂³×C₉	—	3	1	no	—
136	C₂³×C₉	—	4	1	no	—
137	C₃²×C₈	—	2	1	no	—
138	C₃×C₃⋊C₈	—	2	1	no	—
139	Q₈×C₉	—	3	2	no	—
140	Q₈×C₉	—	6	1	no	—
141	D₄×C₉	—	2	1	no	—
142	D₄×C₉	—	2	2	no	—
143	D₄×C₉	—	4	1	no	—
144	D₄×C₉	—	6	4	no	—
145	D₄×C₉	C₄×D₃	1	2	yes	complemented
146	C₂×C₄×C₉	—	2	1	no	—
147	C₂×C₄×C₉	—	2	1	no	—
148	C₂×C₄×C₉	—	3	1	no	—
149	C₂×C₄×C₉	—	3	2	no	—
150	C₂×C₄×C₉	—	3	2	no	—
151	C₂×C₄×C₉	—	4	1	no	—
152	C₂×C₄×C₉	—	6	4	no	—
153	C₂×C₄×C₉	—	6	1	no	—
154	C₂×C₄×C₉	—	6	1	no	—
155	C₂×C₄×C₉	—	12	2	no	—
156	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
157	C₈×C₉	—	2	1	no	—
158	C₈×C₉	—	4	1	no	—
159	C₈×C₉	—	6	1	no	—
160	#417	—	3	1	no	Sylow
161	C₂×C₃×C₉	—	4	2	no	—
162	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₃×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂×C₃×C₉	#137	1	1	yes	characteristic
165	D₃×C₉	—	2	2	no	—
166	C₃×#41	—	3	4	no	—
167	C₃×#41	—	6	2	no	—
168	C₂×C₃×Q₈	—	3	1	no	—
169	C₂×C₃×D₄	—	2	1	no	—
170	C₂×C₃×D₄	—	6	1	no	—
171	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
172	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
173	C₂²×C₃×C₄	—	3	1	no	—
174	C₂²×C₃×C₄	—	6	1	no	—
175	C₂²×C₃×C₄	—	6	1	no	—
176	C₂×#67	—	2	1	no	—
177	C₂²×Dic₃	—	2	1	no	—
178	#237	—	2	2	no	—
179	#237	C₄×C₉	1	4	yes	complemented
180	C₂×C₄×D₃	—	2	1	no	—
181	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
182	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
183	C₃×M₁₆	—	6	2	no	—
184	C₂×C₃×C₈	—	2	1	no	—
185	C₂×C₃×C₈	—	3	1	no	—
186	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
187	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
188	C₃×C₄⋊C₄	—	2	1	no	—
189	C₃×C₄⋊C₄	—	3	1	no	—
190	C₃×C₄⋊C₄	—	6	1	no	—
191	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
192	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
193	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
194	Dic₃⋊C₄	—	2	1	no	—
195	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
196	ΓL(1,𝔽₂₅)	—	2	2	no	—
197	C₂²×C₃²	—	2	2	no	—
198	C₂²×C₃²	—	4	1	no	—
199	C₂²×C₃²	—	4	1	no	—
200	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
201	C₂×C₃×D₃	—	2	1	no	—
202	C₂×C₃×D₃	—	2	1	no	—
203	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	2	yes	—
204	C₃²×C₄	—	4	1	no	—
205	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
206	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
207	C₃×Dic₃	—	2	2	no	—
208	C₃×Dic₃	—	4	1	no	—
209	C₃×Dic₃	C₃×C₂²⋊C₄	1	2	yes	—
210	C₂²×C₉	—	2	2	no	—
211	C₂²×C₉	—	2	1	no	—
212	C₂²×C₉	—	3	2	no	—
213	C₂²×C₉	—	4	2	no	—
214	C₂²×C₉	—	4	1	no	—
215	C₂²×C₉	—	4	1	no	—
216	C₂²×C₉	—	6	1	no	—
217	C₂²×C₉	—	6	1	no	—
218	C₂²×C₉	—	8	1	no	—
219	C₂²×C₉	—	8	1	no	—
220	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
221	C₄×C₉	—	2	1	no	—
222	C₄×C₉	—	2	1	no	—
223	C₄×C₉	—	3	2	no	—
224	C₄×C₉	—	4	1	no	—
225	C₄×C₉	—	6	2	no	—
226	C₄×C₉	—	8	1	no	—
227	C₄×C₉	—	12	1	no	—
228	C₄×C₉	C₂×C₄×D₃	1	1	yes	characteristic
229	C₄×C₉	D₃×D₄	1	1	yes	characteristic
230	C₂×#41	—	3	1	no	—
231	C₂×M₁₆	—	3	1	no	—
232	C₂×C₄⋊C₄	—	3	1	no	—
233	#103	—	3	1	no	—
234	#103	—	3	1	no	—
235	#102	—	3	1	no	—
236	#102	D₃×C₉	1	1	yes	characteristic, complemented
237	C₃×C₉	#417	1	1	yes	characteristic, complemented, Sylow
238	C₂³×C₃	—	2	1	no	—
239	C₂³×C₃	—	2	1	no	—
240	C₂³×C₃	—	3	1	no	—
241	C₂³×C₃	—	4	1	no	—
242	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
243	C₃×Q₈	—	3	2	no	—
244	C₃×Q₈	—	6	1	no	—
245	C₃×D₄	—	2	1	no	—
246	C₃×D₄	—	2	1	no	—
247	C₃×D₄	—	2	2	no	—
248	C₃×D₄	—	4	1	no	—
249	C₃×D₄	—	6	4	no	—
250	C₃×D₄	C₂×C₄×C₉	1	2	yes	complemented
251	C₃×D₄	C₃×C₄×D₃	1	2	yes	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	3	1	no	—
256	C₂×C₃×C₄	—	3	2	no	—
257	C₂×C₃×C₄	—	3	2	no	—
258	C₂×C₃×C₄	—	4	1	no	—
259	C₂×C₃×C₄	—	6	4	no	—
260	C₂×C₃×C₄	—	6	1	no	—
261	C₂×C₃×C₄	—	6	1	no	—
262	C₂×C₃×C₄	—	12	2	no	—
263	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
265	#67	—	2	4	no	—
266	C₂×Dic₃	—	2	1	no	—
267	C₂×Dic₃	—	2	4	no	—
268	C₂×Dic₃	—	2	1	no	—
269	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
270	C₄×D₃	—	4	2	no	—
271	C₄×D₃	C₂×C₄×C₉	1	2	yes	—
272	C₄×D₃	D₄×C₉	1	2	yes	—
273	Dic₆	—	2	1	no	—
274	Dic₆	C₂×C₄×C₉	1	2	yes	complemented
275	C₃×C₈	—	2	1	no	—
276	C₃×C₈	—	2	1	no	—
277	C₃×C₈	—	4	1	no	—
278	C₃×C₈	—	6	1	no	—
279	C₃⋊C₈	—	2	1	no	—
280	C₂×C₃²	—	4	2	no	—
281	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
282	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
283	C₂×C₃²	C₃×#137	1	1	yes	characteristic
284	C₃×D₃	—	2	2	no	—
285	C₂×C₉	—	2	1	no	—
286	C₂×C₉	—	2	1	no	—
287	C₂×C₉	—	2	1	no	—
288	C₂×C₉	—	4	2	no	—
289	C₂×C₉	—	6	2	no	—
290	C₂×C₉	—	8	2	no	—
291	C₂×C₉	D₃×C₂²⋊C₄	1	1	yes	characteristic
292	C₂×C₉	#911	1	1	yes	characteristic
293	C₂×C₉	#915	1	1	yes	characteristic
294	#41	—	3	4	no	—
295	#41	—	6	2	no	—
296	C₂×Q₈	—	3	1	no	—
297	C₂×D₄	—	6	1	no	—
298	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
299	C₂²×C₄	—	3	1	no	—
300	C₂²×C₄	—	6	1	no	—
301	C₂²×C₄	—	6	1	no	—
302	M₁₆	—	6	2	no	—
303	C₂×C₈	—	3	1	no	—
304	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
305	C₄⋊C₄	—	3	1	no	—
306	C₄⋊C₄	—	6	1	no	—
307	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
308	C₂²×C₃	—	2	2	no	—
309	C₂²×C₃	—	2	2	no	—
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	3	2	no	—
312	C₂²×C₃	—	4	2	no	—
313	C₂²×C₃	—	4	1	no	—
314	C₂²×C₃	—	4	1	no	—
315	C₂²×C₃	—	4	1	no	—
316	C₂²×C₃	—	4	1	no	—
317	C₂²×C₃	—	6	1	no	—
318	C₂²×C₃	—	6	1	no	—
319	C₂²×C₃	—	8	1	no	—
320	C₂²×C₃	—	8	1	no	—
321	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
322	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
323	C₂×D₃	—	2	1	no	—
324	C₂×D₃	—	2	1	no	—
325	C₂×D₃	C₉×C₂²⋊C₄	1	2	yes	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	3	2	no	—
329	C₃×C₄	—	4	1	no	—
330	C₃×C₄	—	4	1	no	—
331	C₃×C₄	—	6	2	no	—
332	C₃×C₄	—	8	1	no	—
333	C₃×C₄	—	12	1	no	—
334	C₃×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
335	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
336	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
337	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
338	Dic₃	—	2	2	no	—
339	Dic₃	—	4	1	no	—
340	Dic₃	C₉×C₂²⋊C₄	1	2	yes	—
341	C₃²	C₃×#417	1	1	yes	characteristic
342	C₉	—	2	1	no	—
343	C₉	#4771	1	1	yes	characteristic, direct product factor
344	C₂³	—	2	1	no	—
345	C₂³	—	3	1	no	—
346	Q₈	—	3	2	no	—
347	Q₈	—	6	1	no	—
348	D₄	—	2	1	no	—
349	D₄	—	6	4	no	—
350	D₄	C₄×D₃×C₉	1	2	yes	complemented
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	3	1	no	—
353	C₂×C₄	—	3	2	no	—
354	C₂×C₄	—	3	2	no	—
355	C₂×C₄	—	6	4	no	—
356	C₂×C₄	—	6	1	no	—
357	C₂×C₄	—	6	1	no	—
358	C₂×C₄	—	12	2	no	—
359	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
360	C₈	—	2	1	no	—
361	C₈	—	6	1	no	—
362	C₂×C₃	—	2	1	no	—
363	C₂×C₃	—	2	1	no	—
364	C₂×C₃	—	2	1	no	—
365	C₂×C₃	—	4	2	no	—
366	C₂×C₃	—	4	2	no	—
367	C₂×C₃	—	6	2	no	—
368	C₂×C₃	—	8	2	no	—
369	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
370	C₂×C₃	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
371	C₂×C₃	C₉×#137	1	1	yes	characteristic
372	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
373	C₂×C₃	C₃×#911	1	1	yes	characteristic
374	C₂×C₃	C₃×#915	1	1	yes	characteristic
375	D₃	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	3	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	6	1	no	—
381	C₂²	—	6	1	no	—
382	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
383	C₄	—	3	2	no	—
384	C₄	—	4	1	no	—
385	C₄	—	6	2	no	—
386	C₄	—	12	1	no	—
387	C₄	C₂×C₄×D₃×C₉	1	1	yes	characteristic
388	C₄	D₃×D₄×C₉	1	1	yes	characteristic
389	C₃	—	2	1	no	—
390	C₃	C₉×#417	1	1	yes	characteristic, complemented
391	C₃	C₃×#4771	1	1	yes	characteristic
392	C₂	—	4	2	no	—
393	C₂	—	6	2	no	—
394	C₂	D₃×C₉×C₂²⋊C₄	1	1	yes	characteristic
395	C₂	C₉×#911	1	1	yes	characteristic
396	C₂	C₉×#915	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	D₃×D₄
commutator	C₃×C₄	C₂²×C₄×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×#102	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₂×C₃×#237	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#102	D₃
hypocenter	C₃	C₉×#417
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#102

Complements

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

N	H ≅ G/N	type
2. C₂×C₉×ΓL(1,𝔽₂₅)	C₂	semidirect
3. D₃×C₉×C₄⋊C₄	C₂	semidirect
4. C₃×C₉×#102	C₂	semidirect
5. C₉×#832	C₂	semidirect
6. C₉×#816	C₂	semidirect
7. C₉×#810	C₂	semidirect
14. C₉×#237	C₄	semidirect
38. C₉×#102	D₃	semidirect
42. C₃×D₄×C₉	C₂×C₄	semidirect
54. C₉×Dic₆	C₂×C₄	semidirect
58. #4771	C₉	direct (N × H)
107. C₂×ΓL(1,𝔽₂₅)	C₂×C₉	semidirect
108. D₃×C₄⋊C₄	C₂×C₉	semidirect
113. C₃×#102	C₂×C₉	semidirect
115. #832	C₂×C₉	semidirect
116. #816	C₂×C₉	semidirect
117. #810	C₂×C₉	semidirect
145. D₄×C₉	C₄×D₃	semidirect
179. #237	C₄×C₉	semidirect
236. #102	D₃×C₉	semidirect
237. C₃×C₉	#417	semidirect
250. C₃×D₄	C₂×C₄×C₉	semidirect
274. Dic₆	C₂×C₄×C₉	semidirect
343. C₉	#4771	direct (N × H)
350. D₄	C₄×D₃×C₉	semidirect
390. C₃	C₉×#417	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#237	2
C₂×C₉×ΓL(1,𝔽₂₅)	2
D₃×C₉×C₄⋊C₄	2
C₃×C₉×#102	2
C₉×#832	2
C₉×#816	2
C₉×#810	2
C₃×#4771	3
C₉×#417	3

Subgroups — C9×#4771 #13141754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4771 #13141754