Subgroups — C₃×#10588486 #13141867

Order 1728.

516 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×D₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#3675	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3664	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63457	C₂	1	1	yes	maximal, characteristic
5	C₃×C₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×(C₂×D₉)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#63368	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4806	—	3	1	no	maximal
9	#10588486	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
11	C₃×Q₈×D₉	—	2	2	no	—
12	C₃×Q₈×D₉	—	2	2	no	—
13	C₂×C₃×D₃₆	—	2	1	no	—
14	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄×D₉	—	2	1	no	—
16	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
17	C₂×C₃×Dic₁₈	—	2	1	no	—
18	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×#3675	—	2	2	no	—
22	C₃×(C₂×D₉)⋊C₄	—	2	1	no	—
23	C₂×C₃×C₉⋊C₈	C₂²	1	1	yes	characteristic
24	C₃×#3664	—	2	2	no	—
25	C₂×C₃×D₃×Q₈	—	3	1	no	—
26	C₂×C₃×#215	—	3	1	no	—
27	C₂×C₃×#204	—	3	1	no	—
28	C₃×#895	—	3	1	no	—
29	C₂×Q₈×D₉	C₂×C₃	1	1	yes	characteristic, complemented
30	C₃²×#103	D₃	1	1	yes	characteristic
31	C₃×(C₂×D₃)⋊C₈	—	3	1	no	—
32	C₃×#810	—	3	1	no	—
33	C₂×#3675	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#3664	C₂×C₃	1	1	yes	characteristic, complemented
35	#63457	C₂×C₃	1	1	yes	characteristic
36	C₉×#103	—	2	1	no	—
37	C₉×#103	C₂×C₃	1	1	yes	characteristic, complemented
38	(C₂×D₉)⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
39	#63368	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂²×C₃×D₉	—	2	1	no	—
41	C₂²×C₃×D₉	D₄	1	1	yes	characteristic
42	C₃×Q₈×C₉	—	2	1	no	—
43	C₃×Q₈×C₉	D₄	1	2	yes	complemented
44	C₂×C₃×C₄×C₉	—	2	1	no	—
45	C₂×C₃×C₄×C₉	—	2	1	no	—
46	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
47	C₂×C₃×Dic₉	—	2	1	no	—
48	C₂×C₃×Dic₉	D₄	1	1	yes	characteristic
49	C₃×D₃₆	—	2	1	no	—
50	C₃×D₃₆	—	2	1	no	—
51	C₃×D₃₆	—	4	2	no	—
52	C₃×C₄×D₉	—	2	4	no	—
53	C₃×C₄×D₉	—	2	1	no	—
54	C₃×C₄×D₉	—	2	1	no	—
55	C₃×Dic₁₈	—	2	4	no	—
56	C₃×Dic₁₈	—	2	1	no	—
57	C₃×Dic₁₈	D₄	1	2	yes	complemented
58	C₃×C₈×C₉	—	2	1	no	—
59	C₃×C₉⋊C₈	—	2	1	no	—
60	C₃×#448	—	9	1	no	—
61	#4806	—	3	1	no	—
62	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
63	C₃×D₃×Q₈	—	6	2	no	—
64	C₃×D₃×Q₈	—	6	2	no	—
65	C₂×C₃×D₁₂	—	3	1	no	—
66	C₂×C₃×D₁₂	—	6	1	no	—
67	C₂×C₃×C₄×D₃	—	3	1	no	—
68	C₂×C₃×C₄×D₃	—	6	1	no	—
69	C₂×C₃×Dic₆	—	3	1	no	—
70	C₂×C₃×Dic₆	—	6	1	no	—
71	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
72	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
73	C₃×#215	—	6	2	no	—
74	C₃×(C₂×D₃)⋊C₄	—	6	1	no	—
75	C₂×C₃×C₃⋊C₈	—	3	1	no	—
76	C₃×#204	—	6	2	no	—
77	C₂×Q₈×C₉	—	2	1	no	—
78	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
79	Q₈×D₉	—	2	2	no	—
80	Q₈×D₉	—	2	2	no	—
81	C₂×D₃₆	—	2	1	no	—
82	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₄×D₉	—	2	1	no	—
84	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
85	C₂×Dic₁₈	—	2	1	no	—
86	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₈×C₉	—	2	1	no	—
88	C₂×C₈×C₉	C₂²×C₃	1	1	yes	characteristic
89	C₉×C₄⋊C₄	—	2	1	no	—
90	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	#3675	—	2	2	no	—
92	(C₂×D₉)⋊C₄	—	2	1	no	—
93	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
94	#3664	—	2	2	no	—
95	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×D₉	—	2	1	no	—
97	C₂×C₃×D₉	—	2	1	no	—
98	C₂×C₃×D₉	—	4	1	no	—
99	C₂×C₃×D₉	—	4	1	no	—
100	C₂×C₃×D₉	—	4	1	no	—
101	C₂×C₃×D₉	SD₁₆	1	2	yes	complemented
102	C₃×C₄×C₉	—	2	2	no	—
103	C₃×C₄×C₉	—	4	1	no	—
104	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
105	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
106	C₃×Dic₉	—	2	1	no	—
107	C₃×Dic₉	—	2	2	no	—
108	C₂²×C₃×Q₈	—	9	1	no	—
109	C₂×D₃×Q₈	—	3	1	no	—
110	C₂×C₃×SD₁₆	—	9	1	no	—
111	C₂×C₃×SD₁₆	—	9	1	no	—
112	C₃×#121	—	9	1	no	—
113	C₂×#215	—	3	1	no	—
114	C₂×#204	—	3	1	no	—
115	#895	—	3	1	no	—
116	C₃×#103	—	2	1	no	—
117	C₃×#103	—	9	1	no	—
118	C₃×#103	D₉	1	1	yes	characteristic, complemented
119	C₃×#103	C₃×D₃	1	1	yes	characteristic
120	C₃×C₂²⋊C₈	—	9	1	no	—
121	(C₂×D₃)⋊C₈	—	3	1	no	—
122	#810	—	3	1	no	—
123	C₂²×C₃×D₃	—	3	1	no	—
124	C₂²×C₃×D₃	—	6	1	no	—
125	C₃²×Q₈	—	2	1	no	—
126	C₃²×Q₈	D₁₂	1	2	yes	—
127	C₂×C₃²×C₄	—	2	1	no	—
128	C₂×C₃²×C₄	—	2	1	no	—
129	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
130	C₂×C₃×Dic₃	—	3	1	no	—
131	C₂×C₃×Dic₃	—	6	1	no	—
132	C₃×D₁₂	—	6	1	no	—
133	C₃×D₁₂	—	6	1	no	—
134	C₃×D₁₂	—	12	2	no	—
135	C₃×C₄×D₃	—	6	4	no	—
136	C₃×C₄×D₃	—	6	1	no	—
137	C₃×C₄×D₃	—	6	1	no	—
138	C₃×Dic₆	—	3	2	no	—
139	C₃×Dic₆	—	6	4	no	—
140	C₃×Dic₆	—	6	1	no	—
141	C₂²×D₉	—	2	1	no	—
142	C₂²×D₉	C₃×D₄	1	1	yes	characteristic
143	C₃²×C₈	—	2	1	no	—
144	C₃×C₃⋊C₈	—	6	1	no	—
145	Q₈×C₉	—	2	1	no	—
146	Q₈×C₉	—	2	2	no	—
147	Q₈×C₉	—	4	1	no	—
148	Q₈×C₉	C₃×D₄	1	2	yes	complemented
149	C₂×C₄×C₉	—	2	1	no	—
150	C₂×C₄×C₉	—	2	1	no	—
151	C₂×C₄×C₉	—	2	1	no	—
152	C₂×C₄×C₉	—	4	1	no	—
153	C₂×C₄×C₉	—	4	1	no	—
154	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
155	C₂×Dic₉	—	2	1	no	—
156	C₂×Dic₉	C₃×D₄	1	1	yes	characteristic
157	D₃₆	—	2	1	no	—
158	D₃₆	—	2	1	no	—
159	D₃₆	—	4	2	no	—
160	C₄×D₉	—	2	4	no	—
161	C₄×D₉	—	2	1	no	—
162	C₄×D₉	—	2	1	no	—
163	Dic₁₈	—	2	4	no	—
164	Dic₁₈	—	2	1	no	—
165	Dic₁₈	C₃×D₄	1	2	yes	complemented
166	C₈×C₉	—	2	1	no	—
167	C₈×C₉	—	4	1	no	—
168	C₉⋊C₈	—	2	1	no	—
169	#448	—	9	1	no	Sylow
170	C₂×C₃×C₉	#120	1	1	yes	characteristic
171	C₂×C₃×C₉	C₂×SD₁₆	1	1	yes	characteristic
172	C₂×C₃×C₉	#137	1	1	yes	characteristic
173	C₃×D₉	—	2	2	no	—
174	C₃×D₉	—	8	1	no	—
175	C₂×C₃×Q₈	—	2	1	no	—
176	C₂×C₃×Q₈	—	9	1	no	—
177	C₂×C₃×Q₈	—	18	1	no	—
178	C₂×C₃×Q₈	—	18	2	no	—
179	C₂×C₃×Q₈	—	18	2	no	—
180	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic
181	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
182	C₂×C₃×D₄	—	9	1	no	—
183	C₂×C₃×D₄	—	18	1	no	—
184	C₂²×C₃×C₄	—	9	1	no	—
185	C₂²×C₃×C₄	—	18	1	no	—
186	D₃×Q₈	—	6	2	no	—
187	D₃×Q₈	—	6	2	no	—
188	C₂×D₁₂	—	3	1	no	—
189	C₂×D₁₂	—	6	1	no	—
190	C₂×C₄×D₃	—	3	1	no	—
191	C₂×C₄×D₃	—	6	1	no	—
192	C₂×Dic₆	—	3	1	no	—
193	C₂×Dic₆	—	6	1	no	—
194	C₃×SD₁₆	—	18	2	no	—
195	C₃×SD₁₆	—	18	2	no	—
196	C₂×C₃×C₈	—	2	1	no	—
197	C₂×C₃×C₈	—	9	1	no	—
198	C₂×C₃×C₈	C₂×D₉	1	1	yes	characteristic
199	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
200	C₃×C₄⋊C₄	—	2	1	no	—
201	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
202	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
203	C₃×C₂²⋊C₄	—	18	1	no	—
204	#215	—	6	2	no	—
205	(C₂×D₃)⋊C₄	—	6	1	no	—
206	C₂×C₃⋊C₈	—	3	1	no	—
207	#204	—	6	2	no	—
208	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
209	C₂×C₃×D₃	—	3	2	no	—
210	C₂×C₃×D₃	—	6	1	no	—
211	C₂×C₃×D₃	—	6	1	no	—
212	C₂×C₃×D₃	—	12	1	no	—
213	C₂×C₃×D₃	—	12	1	no	—
214	C₂×C₃×D₃	—	12	1	no	—
215	C₃²×C₄	—	2	2	no	—
216	C₃²×C₄	—	4	1	no	—
217	C₃²×C₄	C₂×D₁₂	1	1	yes	characteristic
218	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
219	C₃×Dic₃	—	6	2	no	—
220	C₃×Dic₃	—	6	1	no	—
221	C₂²×C₉	—	2	1	no	—
222	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
223	C₂×D₉	—	2	1	no	—
224	C₂×D₉	—	2	1	no	—
225	C₂×D₉	—	4	1	no	—
226	C₂×D₉	—	4	1	no	—
227	C₂×D₉	—	4	1	no	—
228	C₂×D₉	C₃×SD₁₆	1	2	yes	complemented
229	C₄×C₉	—	2	2	no	—
230	C₄×C₉	—	2	1	no	—
231	C₄×C₉	—	2	1	no	—
232	C₄×C₉	—	4	2	no	—
233	C₄×C₉	—	4	1	no	—
234	C₄×C₉	—	8	1	no	—
235	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
236	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
237	Dic₉	—	2	1	no	—
238	Dic₉	—	2	2	no	—
239	C₂²×Q₈	—	9	1	no	—
240	C₂×SD₁₆	—	9	1	no	—
241	C₂×SD₁₆	—	9	1	no	—
242	#121	—	9	1	no	—
243	#103	—	9	1	no	—
244	#103	C₃×D₉	1	1	yes	characteristic, complemented
245	C₂²⋊C₈	—	9	1	no	—
246	C₃×C₉	#448	1	1	yes	characteristic, complemented, Sylow
247	C₂³×C₃	—	9	1	no	—
248	C₂³×C₃	—	18	1	no	—
249	C₂²×D₃	—	3	1	no	—
250	C₂²×D₃	—	6	1	no	—
251	C₃×Q₈	—	2	1	no	—
252	C₃×Q₈	—	2	1	no	—
253	C₃×Q₈	—	2	2	no	—
254	C₃×Q₈	—	4	1	no	—
255	C₃×Q₈	—	9	2	no	—
256	C₃×Q₈	—	18	4	no	—
257	C₃×Q₈	—	18	1	no	—
258	C₃×Q₈	D₃₆	1	2	yes	complemented
259	C₃×Q₈	C₃×D₁₂	1	2	yes	—
260	C₃×D₄	—	18	1	no	—
261	C₃×D₄	—	18	1	no	—
262	C₃×D₄	—	36	2	no	—
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	4	1	no	—
269	C₂×C₃×C₄	—	4	1	no	—
270	C₂×C₃×C₄	—	9	1	no	—
271	C₂×C₃×C₄	—	18	4	no	—
272	C₂×C₃×C₄	—	18	1	no	—
273	C₂×C₃×C₄	—	18	1	no	—
274	C₂×C₃×C₄	—	18	1	no	—
275	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
277	C₂×Dic₃	—	3	1	no	—
278	C₂×Dic₃	—	6	1	no	—
279	D₁₂	—	6	1	no	—
280	D₁₂	—	6	1	no	—
281	D₁₂	—	12	2	no	—
282	C₄×D₃	—	6	4	no	—
283	C₄×D₃	—	6	1	no	—
284	C₄×D₃	—	6	1	no	—
285	Dic₆	—	3	2	no	—
286	Dic₆	—	6	4	no	—
287	Dic₆	—	6	1	no	—
288	C₃×C₈	—	2	1	no	—
289	C₃×C₈	—	2	1	no	—
290	C₃×C₈	—	4	1	no	—
291	C₃×C₈	—	18	1	no	—
292	C₃⋊C₈	—	6	1	no	—
293	C₂×C₃²	#882	1	1	yes	characteristic
294	C₂×C₃²	D₃×SD₁₆	1	1	yes	characteristic
295	C₂×C₃²	#918	1	1	yes	characteristic
296	C₃×D₃	—	6	2	no	—
297	C₃×D₃	—	24	1	no	—
298	C₂×C₉	—	2	1	no	—
299	C₂×C₉	—	2	1	no	—
300	C₂×C₉	—	2	1	no	—
301	C₂×C₉	C₃×#120	1	1	yes	characteristic
302	C₂×C₉	C₂×C₃×SD₁₆	1	1	yes	characteristic
303	C₂×C₉	C₃×#137	1	1	yes	characteristic
304	D₉	—	2	2	no	—
305	D₉	—	8	1	no	—
306	C₂×Q₈	—	9	1	no	—
307	C₂×Q₈	—	18	1	no	—
308	C₂×Q₈	—	18	2	no	—
309	C₂×Q₈	—	18	2	no	—
310	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic
311	C₂×D₄	—	9	1	no	—
312	C₂×D₄	—	18	1	no	—
313	C₂²×C₄	—	9	1	no	—
314	C₂²×C₄	—	18	1	no	—
315	SD₁₆	—	18	2	no	—
316	SD₁₆	—	18	2	no	—
317	C₂×C₈	—	9	1	no	—
318	C₂×C₈	C₂×C₃×D₉	1	1	yes	characteristic
319	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
320	C₂²⋊C₄	—	18	1	no	—
321	C₂²×C₃	—	2	1	no	—
322	C₂²×C₃	—	9	2	no	—
323	C₂²×C₃	—	18	1	no	—
324	C₂²×C₃	—	18	1	no	—
325	C₂²×C₃	—	36	1	no	—
326	C₂²×C₃	—	36	1	no	—
327	C₂²×C₃	—	36	1	no	—
328	C₂²×C₃	D₄×D₉	1	1	yes	characteristic
329	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
330	C₂×D₃	—	3	2	no	—
331	C₂×D₃	—	6	1	no	—
332	C₂×D₃	—	6	1	no	—
333	C₂×D₃	—	12	1	no	—
334	C₂×D₃	—	12	1	no	—
335	C₂×D₃	—	12	1	no	—
336	C₃×C₄	—	2	2	no	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	2	1	no	—
340	C₃×C₄	—	4	2	no	—
341	C₃×C₄	—	4	1	no	—
342	C₃×C₄	—	4	1	no	—
343	C₃×C₄	—	8	1	no	—
344	C₃×C₄	—	18	1	no	—
345	C₃×C₄	—	18	2	no	—
346	C₃×C₄	C₂×D₃₆	1	1	yes	characteristic
347	C₃×C₄	D₄×D₉	1	1	yes	characteristic
348	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
349	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
350	Dic₃	—	6	2	no	—
351	Dic₃	—	6	1	no	—
352	C₃²	#4806	1	1	yes	characteristic
353	C₉	—	2	1	no	—
354	C₉	C₃×#448	1	1	yes	characteristic, complemented
355	C₂³	—	9	1	no	—
356	C₂³	—	18	1	no	—
357	Q₈	—	2	1	no	—
358	Q₈	—	9	2	no	—
359	Q₈	—	18	4	no	—
360	Q₈	—	18	1	no	—
361	Q₈	C₃×D₃₆	1	2	yes	complemented
362	D₄	—	18	1	no	—
363	D₄	—	18	1	no	—
364	D₄	—	36	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	9	1	no	—
368	C₂×C₄	—	18	4	no	—
369	C₂×C₄	—	18	1	no	—
370	C₂×C₄	—	18	1	no	—
371	C₂×C₄	—	18	1	no	—
372	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
373	C₈	—	2	1	no	—
374	C₈	—	18	1	no	—
375	C₂×C₃	—	2	1	no	—
376	C₂×C₃	—	2	1	no	—
377	C₂×C₃	—	2	1	no	—
378	C₂×C₃	—	18	2	no	—
379	C₂×C₃	—	72	1	no	—
380	C₂×C₃	#63444	1	1	yes	characteristic
381	C₂×C₃	SD₁₆×D₉	1	1	yes	characteristic
382	C₂×C₃	#63480	1	1	yes	characteristic
383	C₂×C₃	C₃×#882	1	1	yes	characteristic
384	C₂×C₃	C₃×D₃×SD₁₆	1	1	yes	characteristic
385	C₂×C₃	C₃×#918	1	1	yes	characteristic
386	D₃	—	6	2	no	—
387	D₃	—	24	1	no	—
388	C₂²	—	9	2	no	—
389	C₂²	—	18	1	no	—
390	C₂²	—	18	1	no	—
391	C₂²	—	36	1	no	—
392	C₂²	—	36	1	no	—
393	C₂²	—	36	1	no	—
394	C₂²	C₃×D₄×D₉	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	4	1	no	—
397	C₄	—	18	1	no	—
398	C₄	—	18	2	no	—
399	C₄	C₂×C₃×D₃₆	1	1	yes	characteristic
400	C₄	C₃×D₄×D₉	1	1	yes	characteristic
401	C₃	—	2	1	no	—
402	C₃	#10588486	1	1	yes	characteristic, direct product factor
403	C₃	C₃×#4806	1	1	yes	characteristic
404	C₂	—	18	2	no	—
405	C₂	—	72	1	no	—
406	C₂	C₃×#63444	1	1	yes	characteristic
407	C₂	C₃×SD₁₆×D₉	1	1	yes	characteristic
408	C₂	C₃×#63480	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₄×D₉
commutator, cosocle	C₂×C₄×C₉	C₂³×C₃
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×#103	C₂
socle	C₂²×C₃²	D₃×D₄
prime radical	C₃×#63457	C₂
hypercenter	C₃×#103	D₉
hypocenter	C₉	C₃×#448
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#103

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×Q₈×D₉	C₂	semidirect
2. C₂×C₃×#3675	C₂	semidirect
3. C₂×C₃×#3664	C₂	semidirect
5. C₃×C₉×#103	C₂	semidirect
6. C₃×(C₂×D₉)⋊C₈	C₂	semidirect
7. C₃×#63368	C₂	semidirect
9. #10588486	C₃	direct (N × H)
29. C₂×Q₈×D₉	C₂×C₃	semidirect
33. C₂×#3675	C₂×C₃	semidirect
34. C₂×#3664	C₂×C₃	semidirect
37. C₉×#103	C₂×C₃	semidirect
38. (C₂×D₉)⋊C₈	C₂×C₃	semidirect
39. #63368	C₂×C₃	semidirect
43. C₃×Q₈×C₉	D₄	semidirect
57. C₃×Dic₁₈	D₄	semidirect
101. C₂×C₃×D₉	SD₁₆	semidirect
118. C₃×#103	D₉	semidirect
148. Q₈×C₉	C₃×D₄	semidirect
165. Dic₁₈	C₃×D₄	semidirect
228. C₂×D₉	C₃×SD₁₆	semidirect
244. #103	C₃×D₉	semidirect
246. C₃×C₉	#448	semidirect
258. C₃×Q₈	D₃₆	semidirect
354. C₉	C₃×#448	semidirect
361. Q₈	C₃×D₃₆	semidirect
402. C₃	#10588486	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×Q₈×D₉	2
C₂×C₃×#3675	2
C₂×C₃×#3664	2
C₃×#63457	2
C₃×C₉×#103	2
C₃×(C₂×D₉)⋊C₈	2
C₃×#63368	2
C₃×#4806	3
#10588486	3

Subgroups — C3×#10588486 #13141867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10588486 #13141867