Subgroups — C₃×#10589624 #13152483

Order 1728.

1006 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3697	C₂	1	1	yes	maximal, characteristic
2	C₃×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63455	C₂	1	2	yes	maximal, complemented
5	C₃×#63449	C₂	1	2	yes	maximal, complemented
6	C₃×#611⋊C₄	C₂	1	4	yes	maximal, complemented
7	C₃×#63434	C₂	1	2	yes	maximal, complemented
8	C₃×C₄²×D₉	C₂	1	2	yes	maximal, complemented
9	C₃×#5522	—	3	1	no	maximal
10	#10589624	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₃×#611	C₂²	1	2	yes	—
13	C₂²×C₃×Dic₉	C₂²	1	2	yes	—
14	C₃×#3697	C₄	1	8	yes	complemented
15	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×D₉	C₂²	1	4	yes	—
17	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
18	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
19	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
20	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₃×C₄²×C₉	C₂²	1	2	yes	—
22	C₃×(C₂×D₉)⋊C₄	C₂²	1	4	yes	—
23	C₃×Dic₉⋊C₄	C₂²	1	4	yes	—
24	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
25	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
26	C₃×C₄×Dic₉	C₂²	1	2	yes	—
27	C₃×C₄×Dic₉	C₂²	1	4	yes	—
28	C₂×C₃×#235	—	3	1	no	—
29	C₃²×#117	D₃	1	1	yes	characteristic
30	C₂×C₃×C₄×Dic₃	—	3	1	no	—
31	C₃×#893	—	3	2	no	—
32	C₃×#887	—	3	2	no	—
33	C₃×#67⋊C₄	—	3	4	no	—
34	C₃×#872	—	3	2	no	—
35	C₃×C₄²×D₃	—	3	2	no	—
36	C₂×#3697	C₂×C₃	1	1	yes	characteristic
37	C₉×#117	—	2	1	no	—
38	C₉×#117	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×C₄×Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
40	#63455	C₂×C₃	1	2	yes	complemented
41	#63449	C₂×C₃	1	2	yes	complemented
42	#611⋊C₄	C₂×C₃	1	4	yes	complemented
43	#63434	C₂×C₃	1	2	yes	complemented
44	C₄²×D₉	C₂×C₃	1	2	yes	complemented
45	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
46	C₂²×C₃×D₉	C₂³	1	2	yes	—
47	C₂×C₃×C₄×C₉	C₂×C₄	1	4	yes	complemented
48	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
49	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₃×#611	C₂×C₄	1	8	yes	complemented
52	C₂×C₃×Dic₉	—	2	4	no	—
53	C₂×C₃×Dic₉	C₂³	1	2	yes	—
54	C₂×C₃×Dic₉	C₂³	1	2	yes	—
55	C₂×C₃×Dic₉	C₂³	1	2	yes	—
56	C₃×D₃₆	C₂×C₄	1	4	yes	complemented
57	C₃×C₄×D₉	—	2	8	no	—
58	C₃×C₄×D₉	C₂×C₄	1	8	yes	complemented
59	C₃×Dic₁₈	C₂×C₄	1	4	yes	complemented
60	C₃×C₄×#41	—	9	1	no	—
61	#5522	—	3	1	no	—
62	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
63	C₂×C₃×#67	—	3	2	no	—
64	C₂²×C₃×Dic₃	—	3	2	no	—
65	C₃×#235	—	3	8	no	—
66	C₂×C₃×D₁₂	—	3	1	no	—
67	C₂×C₃×C₄×D₃	—	3	2	no	—
68	C₂×C₃×C₄×D₃	—	3	4	no	—
69	C₂×C₃×Dic₆	—	3	1	no	—
70	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
71	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
72	C₃²×C₄²	C₂×D₃	1	2	yes	—
73	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
74	C₃×Dic₃⋊C₄	—	3	4	no	—
75	C₃×C₄×Dic₃	—	3	4	no	—
76	C₃×C₄×Dic₃	—	3	2	no	—
77	C₃×C₄×Dic₃	—	3	1	no	—
78	C₃×C₄×Dic₃	—	3	1	no	—
79	C₂²×C₄×C₉	—	2	1	no	—
80	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
81	C₂×#611	C₂²×C₃	1	2	yes	—
82	C₂²×Dic₉	C₂²×C₃	1	2	yes	—
83	#3697	C₃×C₄	1	8	yes	complemented
84	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₄×D₉	C₂²×C₃	1	4	yes	—
86	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
87	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
88	C₉×C₄⋊C₄	—	2	2	no	—
89	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
90	C₉×C₂²⋊C₄	—	2	2	no	—
91	C₉×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
92	C₄²×C₉	—	2	2	no	—
93	C₄²×C₉	C₂²×C₃	1	2	yes	—
94	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	—
95	Dic₉⋊C₄	C₂²×C₃	1	4	yes	—
96	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
97	C₄×Dic₉	C₂²×C₃	1	4	yes	—
98	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
99	C₄×Dic₉	C₂²×C₃	1	2	yes	—
100	C₂²×C₃×C₉	—	2	2	no	—
101	C₂²×C₃×C₉	C₂²×C₄	1	2	yes	—
102	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
103	C₂×C₃×D₉	—	2	4	no	—
104	C₂×C₃×D₉	C₂²×C₄	1	4	yes	—
105	C₃×C₄×C₉	—	2	4	no	—
106	C₃×C₄×C₉	C₂²×C₄	1	2	yes	—
107	C₃×C₄×C₉	C₂²×C₄	1	2	yes	—
108	C₃×Dic₉	—	2	2	no	—
109	C₃×Dic₉	C₂²×C₄	1	4	yes	—
110	C₃×Dic₉	#41	1	4	yes	complemented
111	C₂×C₃×#41	—	9	1	no	—
112	C₂×#235	—	3	1	no	—
113	C₃×C₄×Q₈	—	9	2	no	—
114	C₃×C₄×D₄	—	9	2	no	—
115	C₃×C₄×D₄	—	9	4	no	—
116	C₃×#117	—	2	1	no	—
117	C₃×#117	—	9	2	no	—
118	C₃×#117	D₉	1	1	yes	characteristic, complemented
119	C₃×#117	C₃×D₃	1	1	yes	characteristic
120	C₂×C₃×C₄²	—	9	1	no	—
121	C₂×C₃×C₄²	—	9	2	no	—
122	C₂×C₄×Dic₃	—	3	1	no	—
123	#893	—	3	2	no	—
124	#887	—	3	2	no	—
125	#67⋊C₄	—	3	4	no	—
126	#872	—	3	2	no	—
127	C₄²×D₃	—	3	2	no	—
128	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
129	C₂²×C₃×D₃	—	3	2	no	—
130	C₂×C₃²×C₄	C₄×D₃	1	4	yes	—
131	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
132	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
133	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
134	C₃×#67	—	3	8	no	—
135	C₂×C₃×Dic₃	—	3	2	no	—
136	C₂×C₃×Dic₃	—	3	2	no	—
137	C₂×C₃×Dic₃	—	3	2	no	—
138	C₂×C₃×Dic₃	—	6	4	no	—
139	C₃×D₁₂	—	3	4	no	—
140	C₃×C₄×D₃	—	3	8	no	—
141	C₃×C₄×D₃	—	6	8	no	—
142	C₃×Dic₆	—	3	4	no	—
143	C₂³×C₉	—	2	1	no	—
144	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
145	C₂²×D₉	C₂³×C₃	1	2	yes	—
146	C₂×C₄×C₉	—	2	4	no	—
147	C₂×C₄×C₉	—	2	1	no	—
148	C₂×C₄×C₉	—	2	1	no	—
149	C₂×C₄×C₉	—	2	4	no	—
150	C₂×C₄×C₉	C₂×C₃×C₄	1	4	yes	complemented
151	C₂×C₄×C₉	C₂³×C₃	1	4	yes	—
152	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
153	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
154	#611	C₂×C₃×C₄	1	8	yes	complemented
155	C₂×Dic₉	—	2	4	no	—
156	C₂×Dic₉	C₂³×C₃	1	2	yes	—
157	C₂×Dic₉	C₂³×C₃	1	2	yes	—
158	C₂×Dic₉	C₂³×C₃	1	2	yes	—
159	D₃₆	C₂×C₃×C₄	1	4	yes	complemented
160	C₄×D₉	—	2	8	no	—
161	C₄×D₉	C₂×C₃×C₄	1	8	yes	complemented
162	Dic₁₈	C₂×C₃×C₄	1	4	yes	complemented
163	C₄×#41	—	9	1	no	Sylow
164	C₂×C₃×C₉	—	2	2	no	—
165	C₂×C₃×C₉	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₃×C₉	C₂×#41	1	2	yes	—
167	C₃×D₉	—	2	4	no	—
168	C₃×#41	—	9	8	no	—
169	C₂×C₃×Q₈	—	9	1	no	—
170	C₂×C₃×D₄	—	9	2	no	—
171	C₂×C₃×D₄	—	9	1	no	—
172	C₂²×C₃×C₄	—	2	1	no	—
173	C₂²×C₃×C₄	—	9	2	no	—
174	C₂²×C₃×C₄	—	9	2	no	—
175	C₂²×C₃×C₄	—	9	4	no	—
176	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
178	C₂×#67	—	3	2	no	—
179	C₂²×Dic₃	—	3	2	no	—
180	#235	—	3	8	no	—
181	C₂×D₁₂	—	3	1	no	—
182	C₂×C₄×D₃	—	3	2	no	—
183	C₂×C₄×D₃	—	3	4	no	—
184	C₂×Dic₆	—	3	1	no	—
185	C₃×C₄⋊C₄	—	2	2	no	—
186	C₃×C₄⋊C₄	—	9	4	no	—
187	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	—
188	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
189	C₃×C₂²⋊C₄	—	2	2	no	—
190	C₃×C₂²⋊C₄	—	9	4	no	—
191	C₃×C₂²⋊C₄	C₂×D₉	1	2	yes	—
192	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
193	C₃×C₄²	—	2	2	no	—
194	C₃×C₄²	—	9	4	no	—
195	C₃×C₄²	—	9	2	no	—
196	C₃×C₄²	—	9	1	no	—
197	C₃×C₄²	—	9	1	no	—
198	C₃×C₄²	C₂×D₉	1	2	yes	—
199	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
200	(C₂×D₃)⋊C₄	—	3	4	no	—
201	Dic₃⋊C₄	—	3	4	no	—
202	C₄×Dic₃	—	3	1	no	—
203	C₄×Dic₃	—	3	4	no	—
204	C₄×Dic₃	—	3	1	no	—
205	C₄×Dic₃	—	3	2	no	—
206	C₂²×C₃²	—	2	2	no	—
207	C₂²×C₃²	C₂×C₄×D₃	1	2	yes	—
208	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
209	C₂×C₃×D₃	—	3	4	no	—
210	C₂×C₃×D₃	—	6	4	no	—
211	C₃²×C₄	—	2	4	no	—
212	C₃²×C₄	C₂×C₄×D₃	1	2	yes	—
213	C₃²×C₄	C₂×C₄×D₃	1	2	yes	—
214	C₃×Dic₃	—	3	4	no	—
215	C₃×Dic₃	—	3	4	no	—
216	C₃×Dic₃	—	6	2	no	—
217	C₂²×C₉	—	2	2	no	—
218	C₂²×C₉	—	2	1	no	—
219	C₂²×C₉	—	2	2	no	—
220	C₂²×C₉	—	4	2	no	—
221	C₂²×C₉	C₂²×C₃×C₄	1	2	yes	—
222	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
223	C₂×D₉	—	2	4	no	—
224	C₂×D₉	C₂²×C₃×C₄	1	4	yes	—
225	C₄×C₉	—	2	4	no	—
226	C₄×C₉	—	2	2	no	—
227	C₄×C₉	—	2	2	no	—
228	C₄×C₉	—	4	4	no	—
229	C₄×C₉	C₂²×C₃×C₄	1	2	yes	—
230	C₄×C₉	C₂²×C₃×C₄	1	2	yes	—
231	Dic₉	—	2	2	no	—
232	Dic₉	C₂²×C₃×C₄	1	4	yes	—
233	Dic₉	C₃×#41	1	4	yes	complemented
234	C₂×#41	—	9	1	no	—
235	C₄×Q₈	—	9	2	no	—
236	C₄×D₄	—	9	2	no	—
237	C₄×D₄	—	9	4	no	—
238	#117	—	9	2	no	—
239	#117	C₃×D₉	1	1	yes	characteristic, complemented
240	C₂×C₄²	—	9	1	no	—
241	C₂×C₄²	—	9	2	no	—
242	C₃×C₉	C₄×#41	1	1	yes	characteristic, complemented, Sylow
243	C₂³×C₃	—	2	1	no	—
244	C₂³×C₃	—	9	2	no	—
245	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
246	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
247	C₂²×D₃	—	3	2	no	—
248	C₃×Q₈	—	9	4	no	—
249	C₃×D₄	—	9	8	no	—
250	C₃×D₄	—	9	4	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	9	2	no	—
256	C₂×C₃×C₄	—	9	2	no	—
257	C₂×C₃×C₄	—	9	8	no	—
258	C₂×C₃×C₄	—	9	2	no	—
259	C₂×C₃×C₄	—	18	8	no	—
260	C₂×C₃×C₄	—	18	4	no	—
261	C₂×C₃×C₄	C₄×D₉	1	4	yes	complemented
262	C₂×C₃×C₄	C₂²×D₉	1	4	yes	—
263	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
265	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
266	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
267	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
269	#67	—	3	8	no	—
270	C₂×Dic₃	—	3	2	no	—
271	C₂×Dic₃	—	3	2	no	—
272	C₂×Dic₃	—	3	2	no	—
273	C₂×Dic₃	—	6	4	no	—
274	D₁₂	—	3	4	no	—
275	C₄×D₃	—	3	8	no	—
276	C₄×D₃	—	6	8	no	—
277	Dic₆	—	3	4	no	—
278	C₂×C₃²	—	2	2	no	—
279	C₂×C₃²	C₂²×C₄×D₃	1	1	yes	characteristic
280	C₂×C₃²	D₃×#41	1	2	yes	—
281	C₃×D₃	—	6	4	no	—
282	C₂×C₉	—	2	2	no	—
283	C₂×C₉	—	2	1	no	—
284	C₂×C₉	—	2	2	no	—
285	C₂×C₉	—	4	2	no	—
286	C₂×C₉	C₂³×C₃×C₄	1	1	yes	characteristic
287	C₂×C₉	C₂×C₃×#41	1	2	yes	—
288	D₉	—	2	4	no	—
289	#41	—	9	8	no	—
290	C₂×Q₈	—	9	1	no	—
291	C₂×D₄	—	9	2	no	—
292	C₂×D₄	—	9	1	no	—
293	C₂²×C₄	—	9	2	no	—
294	C₂²×C₄	—	9	2	no	—
295	C₂²×C₄	—	9	4	no	—
296	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
297	C₄⋊C₄	—	9	4	no	—
298	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	—
299	C₂²⋊C₄	—	9	4	no	—
300	C₂²⋊C₄	C₂×C₃×D₉	1	2	yes	—
301	C₄²	—	9	1	no	—
302	C₄²	—	9	1	no	—
303	C₄²	—	9	4	no	—
304	C₄²	—	9	2	no	—
305	C₄²	C₂×C₃×D₉	1	2	yes	—
306	C₂²×C₃	—	2	2	no	—
307	C₂²×C₃	—	2	2	no	—
308	C₂²×C₃	—	2	1	no	—
309	C₂²×C₃	—	2	2	no	—
310	C₂²×C₃	—	4	2	no	—
311	C₂²×C₃	—	9	4	no	—
312	C₂²×C₃	—	18	4	no	—
313	C₂²×C₃	C₂×C₄×D₉	1	2	yes	—
314	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
315	C₂²×C₃	C₂×C₃×C₄×D₃	1	2	yes	—
316	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
317	C₂×D₃	—	3	4	no	—
318	C₂×D₃	—	6	4	no	—
319	C₃×C₄	—	2	4	no	—
320	C₃×C₄	—	2	4	no	—
321	C₃×C₄	—	2	2	no	—
322	C₃×C₄	—	2	2	no	—
323	C₃×C₄	—	4	4	no	—
324	C₃×C₄	—	9	4	no	—
325	C₃×C₄	—	9	4	no	—
326	C₃×C₄	—	18	2	no	—
327	C₃×C₄	C₂×C₄×D₉	1	2	yes	—
328	C₃×C₄	C₂×C₄×D₉	1	2	yes	—
329	C₃×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
330	C₃×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
331	Dic₃	—	3	4	no	—
332	Dic₃	—	3	4	no	—
333	Dic₃	—	6	2	no	—
334	C₃²	#5522	1	1	yes	characteristic
335	C₉	—	2	1	no	—
336	C₉	C₃×C₄×#41	1	1	yes	characteristic, complemented
337	C₂³	—	9	2	no	—
338	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
339	Q₈	—	9	4	no	—
340	D₄	—	9	8	no	—
341	D₄	—	9	4	no	—
342	C₂×C₄	—	9	2	no	—
343	C₂×C₄	—	9	2	no	—
344	C₂×C₄	—	9	8	no	—
345	C₂×C₄	—	9	2	no	—
346	C₂×C₄	—	18	8	no	—
347	C₂×C₄	—	18	4	no	—
348	C₂×C₄	C₃×C₄×D₉	1	4	yes	complemented
349	C₂×C₄	C₂²×C₃×D₉	1	4	yes	—
350	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
351	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
352	C₂×C₃	—	2	2	no	—
353	C₂×C₃	—	2	2	no	—
354	C₂×C₃	—	2	1	no	—
355	C₂×C₃	—	2	2	no	—
356	C₂×C₃	—	4	2	no	—
357	C₂×C₃	—	18	4	no	—
358	C₂×C₃	C₂²×C₄×D₉	1	1	yes	characteristic
359	C₂×C₃	#41×D₉	1	2	yes	—
360	C₂×C₃	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
361	C₂×C₃	C₃×D₃×#41	1	2	yes	—
362	D₃	—	6	4	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	9	4	no	—
365	C₂²	—	18	4	no	—
366	C₂²	C₂×C₃×C₄×D₉	1	2	yes	—
367	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
368	C₄	—	2	4	no	—
369	C₄	—	9	4	no	—
370	C₄	—	9	4	no	—
371	C₄	—	18	2	no	—
372	C₄	C₂×C₃×C₄×D₉	1	2	yes	—
373	C₄	C₂×C₃×C₄×D₉	1	2	yes	—
374	C₃	—	2	1	no	—
375	C₃	#10589624	1	1	yes	characteristic, direct product factor
376	C₃	C₃×#5522	1	1	yes	characteristic
377	C₂	—	2	2	no	—
378	C₂	—	18	4	no	—
379	C₂	C₂²×C₃×C₄×D₉	1	1	yes	characteristic
380	C₂	C₃×#41×D₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₉
commutator	C₂×C₉	C₂³×C₃×C₄
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#117	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₂×C₃×#3697	C₂
cosocle	C₂²×C₉	C₂⁴×C₃
hypercenter	C₃×#117	D₉
hypocenter	C₉	C₃×C₄×#41
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
2. C₃×C₉×#117	C₂	semidirect
3. C₂×C₃×C₄×Dic₉	C₂	semidirect
4. C₃×#63455	C₂	semidirect
5. C₃×#63449	C₂	semidirect
6. C₃×#611⋊C₄	C₂	semidirect
7. C₃×#63434	C₂	semidirect
8. C₃×C₄²×D₉	C₂	semidirect
10. #10589624	C₃	direct (N × H)
14. C₃×#3697	C₄	semidirect
38. C₉×#117	C₂×C₃	semidirect
39. C₂×C₄×Dic₉	C₂×C₃	semidirect
40. #63455	C₂×C₃	semidirect
41. #63449	C₂×C₃	semidirect
42. #611⋊C₄	C₂×C₃	semidirect
43. #63434	C₂×C₃	semidirect
44. C₄²×D₉	C₂×C₃	semidirect
47. C₂×C₃×C₄×C₉	C₂×C₄	semidirect
51. C₃×#611	C₂×C₄	semidirect
56. C₃×D₃₆	C₂×C₄	semidirect
58. C₃×C₄×D₉	C₂×C₄	semidirect
59. C₃×Dic₁₈	C₂×C₄	semidirect
83. #3697	C₃×C₄	semidirect
110. C₃×Dic₉	#41	semidirect
118. C₃×#117	D₉	semidirect
150. C₂×C₄×C₉	C₂×C₃×C₄	semidirect
154. #611	C₂×C₃×C₄	semidirect
159. D₃₆	C₂×C₃×C₄	semidirect
161. C₄×D₉	C₂×C₃×C₄	semidirect
162. Dic₁₈	C₂×C₃×C₄	semidirect
233. Dic₉	C₃×#41	semidirect
239. #117	C₃×D₉	semidirect
242. C₃×C₉	C₄×#41	semidirect
261. C₂×C₃×C₄	C₄×D₉	semidirect
336. C₉	C₃×C₄×#41	semidirect
348. C₂×C₄	C₃×C₄×D₉	semidirect
375. C₃	#10589624	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#3697	2
C₃×C₉×#117	2
C₂×C₃×C₄×Dic₉	2
C₃×#63455	2
C₃×#63449	2
C₃×#611⋊C₄	2
C₃×#63434	2
C₃×C₄²×D₉	2
C₃×#5522	3
#10589624	3

Subgroups — C3×#10589624 #13152483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589624 #13152483