Subgroups — C₂×C₃×#64118 #13179498

Order 1728.

1820 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×#3828	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×#634	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃³×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64118	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3746	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#3744	C₂	1	2	yes	maximal, complemented
7	C₂×#64118	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×#909	—	3	4	no	maximal
9	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
10	C₂×C₃×#638	—	2	1	no	—
11	C₂²×C₃×C₃⋊Dic₃	—	2	1	no	—
12	C₃×#3828	—	2	2	no	—
13	C₃×#3828	C₂²	1	4	yes	—
14	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄×C₃⋊D₃	—	2	1	no	—
16	C₂×C₃×#634	—	2	2	no	—
17	C₂×C₃×#634	—	2	1	no	—
18	C₂×C₃×#634	C₂²	1	2	yes	—
19	C₂×C₃×#634	C₂²	1	1	yes	characteristic
20	C₂×C₃×#634	C₂²	1	4	yes	complemented
21	C₃³×M₁₆	C₂²	1	4	yes	complemented
22	C₂×C₃³×C₈	C₂²	1	2	yes	—
23	C₃×#3746	C₂²	1	8	yes	complemented
24	C₃×#3744	C₂²	1	8	yes	complemented
25	C₂×#3828	C₂×C₃	1	1	yes	characteristic
26	C₂²×#634	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×C₃×#235	—	3	4	no	—
28	C₂²×C₃×Dic₆	—	3	4	no	—
29	C₂×C₃²×M₁₆	—	2	4	no	—
30	C₂×C₃²×M₁₆	D₃	1	4	yes	complemented
31	C₂×C₃²×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
32	#64118	C₂×C₃	1	8	yes	direct product factor
33	C₂×#3746	C₂×C₃	1	2	yes	complemented
34	C₂×#3744	C₂×C₃	1	2	yes	complemented
35	C₃×#909	—	3	32	no	—
36	C₂×C₃×Dic₁₂	—	3	8	no	—
37	C₂×C₃×#204	—	3	8	no	—
38	C₂³×C₃³	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₃⋊D₃	—	2	1	no	—
40	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
41	C₂×C₃³×C₄	D₄	1	2	yes	—
42	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
43	C₂×C₃³×C₄	C₂³	1	2	yes	—
44	C₃×#638	—	2	4	no	—
45	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
46	C₂×C₃×C₃⋊Dic₃	—	2	4	no	—
47	C₂×C₃×C₃⋊Dic₃	—	2	1	no	—
48	C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
49	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	2	yes	—
50	C₃×C₄×C₃⋊D₃	—	2	4	no	—
51	C₃×#634	—	2	2	no	—
52	C₃×#634	—	2	4	no	—
53	C₃×#634	—	2	1	no	—
54	C₃×#634	C₂³	1	4	yes	—
55	C₃×#634	C₂³	1	2	yes	—
56	C₃³×C₈	C₂³	1	4	yes	—
57	C₂×C₃×#137	—	9	1	no	—
58	C₂×#909	—	3	4	no	—
59	C₂²×C₃²×C₄	—	2	4	no	—
60	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
61	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
62	C₂×#638	—	2	1	no	—
63	C₂²×C₃⋊Dic₃	—	2	1	no	—
64	#3828	—	2	2	no	—
65	#3828	C₂²×C₃	1	4	yes	—
66	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₄×C₃⋊D₃	—	2	1	no	—
68	C₂×#634	—	2	2	no	—
69	C₂×#634	—	2	1	no	—
70	C₂×#634	C₂²×C₃	1	2	yes	—
71	C₂×#634	C₂²×C₃	1	1	yes	characteristic
72	C₂×#634	C₂²×C₃	1	4	yes	complemented
73	C₂×C₃×#67	—	6	4	no	—
74	C₂²×C₃×Dic₃	—	6	4	no	—
75	C₃×#235	—	3	16	no	—
76	C₃×#235	—	6	8	no	—
77	C₂×C₃×D₁₂	—	3	4	no	—
78	C₂×C₃×C₄×D₃	—	6	4	no	—
79	C₂×C₃×Dic₆	—	3	8	no	—
80	C₂×C₃×Dic₆	—	3	4	no	—
81	C₂×C₃×Dic₆	—	3	16	no	—
82	C₂×C₃×Dic₆	—	6	4	no	—
83	C₂×C₃×Dic₆	—	6	8	no	—
84	C₃²×M₁₆	—	2	16	no	—
85	C₃²×M₁₆	C₂×D₃	1	16	yes	complemented
86	C₃²×M₁₆	C₂²×C₃	1	4	yes	complemented
87	C₂×C₃²×C₈	—	2	8	no	—
88	C₂×C₃²×C₈	C₂×D₃	1	8	yes	—
89	C₂×C₃²×C₈	C₂²×C₃	1	2	yes	—
90	#3746	C₂²×C₃	1	8	yes	complemented
91	#3744	C₂²×C₃	1	8	yes	complemented
92	C₃×Dic₁₂	—	3	32	no	—
93	C₃×#204	—	3	32	no	—
94	C₂²×C₃³	—	2	2	no	—
95	C₂²×C₃³	C₂×D₄	1	2	yes	—
96	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₃⋊D₃	—	2	2	no	—
98	C₂×C₃×C₃⋊D₃	—	4	2	no	—
99	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
100	C₃³×C₄	C₂×D₄	1	2	yes	—
101	C₃³×C₄	C₂⁴	1	1	yes	characteristic
102	C₃×C₃⋊Dic₃	—	2	4	no	—
103	C₃×C₃⋊Dic₃	—	2	2	no	—
104	C₂×C₃×#41	—	9	1	no	—
105	C₂²×C₃×Q₈	—	9	1	no	—
106	C₂×#235	—	3	4	no	—
107	C₂²×Dic₆	—	3	4	no	—
108	C₃×#137	—	9	8	no	—
109	C₂×C₃×Q₁₆	—	9	2	no	—
110	C₂×C₃×SD₁₆	—	9	2	no	—
111	C₂×C₃×M₁₆	—	2	4	no	—
112	C₂×C₃×M₁₆	C₃×D₃	1	4	yes	complemented
113	C₂×C₃×M₁₆	C₃⋊D₃	1	1	yes	characteristic, complemented
114	#909	—	3	32	no	—
115	C₂×Dic₁₂	—	3	8	no	—
116	C₂×#204	—	3	8	no	—
117	C₂³×C₃²	—	2	4	no	—
118	C₂³×C₃²	D₁₂	1	4	yes	—
119	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
120	C₂²×C₃⋊D₃	—	2	1	no	—
121	C₂²×C₃×D₃	—	6	4	no	—
122	C₂×C₃²×C₄	—	2	4	no	—
123	C₂×C₃²×C₄	—	2	8	no	—
124	C₂×C₃²×C₄	—	2	4	no	—
125	C₂×C₃²×C₄	—	2	8	no	—
126	C₂×C₃²×C₄	D₁₂	1	4	yes	—
127	C₂×C₃²×C₄	D₁₂	1	8	yes	—
128	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
130	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
131	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
132	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
133	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
134	#638	—	2	4	no	—
135	C₂×C₃⋊Dic₃	—	2	2	no	—
136	C₂×C₃⋊Dic₃	—	2	4	no	—
137	C₂×C₃⋊Dic₃	—	2	1	no	—
138	C₄⋊(C₃⋊D₃)	—	2	1	no	—
139	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	2	yes	—
140	C₄×C₃⋊D₃	—	2	4	no	—
141	#634	—	2	2	no	—
142	#634	—	2	4	no	—
143	#634	—	2	1	no	—
144	#634	C₂³×C₃	1	4	yes	—
145	#634	C₂³×C₃	1	2	yes	—
146	C₃×#67	—	6	16	no	—
147	C₂×C₃×Dic₃	—	6	16	no	—
148	C₂×C₃×Dic₃	—	6	8	no	—
149	C₂×C₃×Dic₃	—	6	4	no	—
150	C₃×D₁₂	—	3	8	no	—
151	C₃×D₁₂	—	6	4	no	—
152	C₃×C₄×D₃	—	6	16	no	—
153	C₃×Dic₆	—	3	16	no	—
154	C₃×Dic₆	—	3	8	no	—
155	C₃×Dic₆	—	6	8	no	—
156	C₃×Dic₆	—	6	16	no	—
157	C₃×Dic₆	—	6	4	no	—
158	C₃²×C₈	—	2	16	no	—
159	C₃²×C₈	C₂²×D₃	1	16	yes	—
160	C₃²×C₈	C₂³×C₃	1	4	yes	—
161	C₂×#137	—	9	1	no	Sylow
162	C₂×C₃³	—	2	2	no	—
163	C₂×C₃³	#137	1	2	yes	complemented
164	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
165	C₃×C₃⋊D₃	—	4	2	no	—
166	C₃×#41	—	9	4	no	—
167	C₃×#41	—	18	2	no	—
168	C₂×C₃×Q₈	—	9	2	no	—
169	C₂×C₃×Q₈	—	9	1	no	—
170	C₂×C₃×Q₈	—	9	4	no	—
171	C₂×C₃×Q₈	—	18	2	no	—
172	C₂×C₃×Q₈	—	18	1	no	—
173	C₂×C₃×D₄	—	9	1	no	—
174	C₂×C₃×D₄	—	18	1	no	—
175	C₂²×C₃×C₄	—	2	4	no	—
176	C₂²×C₃×C₄	—	18	1	no	—
177	C₂²×C₃×C₄	—	18	1	no	—
178	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
179	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
180	C₂×#67	—	6	4	no	—
181	C₂²×Dic₃	—	6	4	no	—
182	#235	—	3	16	no	—
183	#235	—	6	8	no	—
184	C₂×D₁₂	—	3	4	no	—
185	C₂×C₄×D₃	—	6	4	no	—
186	C₂×Dic₆	—	3	8	no	—
187	C₂×Dic₆	—	3	4	no	—
188	C₂×Dic₆	—	3	16	no	—
189	C₂×Dic₆	—	6	4	no	—
190	C₂×Dic₆	—	6	8	no	—
191	C₃×Q₁₆	—	9	8	no	—
192	C₃×SD₁₆	—	9	8	no	—
193	C₃×M₁₆	—	2	16	no	—
194	C₃×M₁₆	C₂×C₃×D₃	1	16	yes	complemented
195	C₃×M₁₆	C₂×C₃⋊D₃	1	4	yes	complemented
196	C₂×C₃×C₈	—	2	8	no	—
197	C₂×C₃×C₈	C₂×C₃×D₃	1	8	yes	—
198	C₂×C₃×C₈	C₂×C₃⋊D₃	1	2	yes	—
199	Dic₁₂	—	3	32	no	—
200	#204	—	3	32	no	—
201	C₂²×C₃²	—	2	2	no	—
202	C₂²×C₃²	—	2	4	no	—
203	C₂²×C₃²	—	2	8	no	—
204	C₂²×C₃²	—	2	8	no	—
205	C₂²×C₃²	—	4	8	no	—
206	C₂²×C₃²	C₂×D₁₂	1	8	yes	—
207	C₂²×C₃²	C₂×D₁₂	1	4	yes	—
208	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
209	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
210	C₂×C₃⋊D₃	—	2	2	no	—
211	C₂×C₃⋊D₃	—	4	2	no	—
212	C₂×C₃×D₃	—	6	8	no	—
213	C₂×C₃×D₃	—	12	8	no	—
214	C₃²×C₄	—	2	4	no	—
215	C₃²×C₄	—	2	4	no	—
216	C₃²×C₄	—	2	8	no	—
217	C₃²×C₄	C₂×D₁₂	1	4	yes	—
218	C₃²×C₄	C₂×D₁₂	1	8	yes	—
219	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
220	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
221	C₃²×C₄	C₂³×D₃	1	4	yes	—
222	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
223	C₃⋊Dic₃	—	2	4	no	—
224	C₃⋊Dic₃	—	2	2	no	—
225	C₃×Dic₃	—	6	16	no	—
226	C₃×Dic₃	—	6	8	no	—
227	C₂×#41	—	9	1	no	—
228	C₂²×Q₈	—	9	1	no	—
229	#137	—	9	8	no	—
230	C₂×Q₁₆	—	9	2	no	—
231	C₂×SD₁₆	—	9	2	no	—
232	C₂×M₁₆	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
233	C₃³	C₂×#137	1	1	yes	characteristic, complemented, Sylow
234	C₂³×C₃	—	2	4	no	—
235	C₂³×C₃	—	18	1	no	—
236	C₂³×C₃	C₃×D₁₂	1	4	yes	—
237	C₂³×C₃	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
238	C₂²×D₃	—	6	4	no	—
239	C₃×Q₈	—	9	4	no	—
240	C₃×Q₈	—	9	2	no	—
241	C₃×Q₈	—	18	4	no	—
242	C₃×Q₈	—	18	2	no	—
243	C₃×Q₈	—	18	1	no	—
244	C₃×D₄	—	9	2	no	—
245	C₃×D₄	—	18	4	no	—
246	C₃×D₄	—	18	1	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	8	no	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	2	8	no	—
251	C₂×C₃×C₄	—	18	4	no	—
252	C₂×C₃×C₄	—	18	1	no	—
253	C₂×C₃×C₄	—	18	2	no	—
254	C₂×C₃×C₄	—	18	4	no	—
255	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
256	C₂×C₃×C₄	C₃×D₁₂	1	8	yes	—
257	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	1	2	yes	—
258	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
260	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
261	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
262	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
263	#67	—	6	16	no	—
264	C₂×Dic₃	—	6	16	no	—
265	C₂×Dic₃	—	6	8	no	—
266	C₂×Dic₃	—	6	4	no	—
267	D₁₂	—	3	8	no	—
268	D₁₂	—	6	4	no	—
269	C₄×D₃	—	6	16	no	—
270	Dic₆	—	3	16	no	—
271	Dic₆	—	3	8	no	—
272	Dic₆	—	6	8	no	—
273	Dic₆	—	6	16	no	—
274	Dic₆	—	6	4	no	—
275	C₃×C₈	—	2	16	no	—
276	C₃×C₈	C₂²×C₃×D₃	1	16	yes	—
277	C₃×C₈	C₂²×C₃⋊D₃	1	4	yes	—
278	C₂×C₃²	—	2	2	no	—
279	C₂×C₃²	—	2	8	no	—
280	C₂×C₃²	—	2	4	no	—
281	C₂×C₃²	—	2	8	no	—
282	C₂×C₃²	—	4	8	no	—
283	C₂×C₃²	#909	1	8	yes	complemented
284	C₂×C₃²	C₃×#137	1	2	yes	complemented
285	C₂×C₃²	C₂²×D₁₂	1	4	yes	—
286	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
287	C₃⋊D₃	—	4	2	no	—
288	C₃×D₃	—	12	8	no	—
289	#41	—	9	4	no	—
290	#41	—	18	2	no	—
291	C₂×Q₈	—	9	2	no	—
292	C₂×Q₈	—	9	1	no	—
293	C₂×Q₈	—	9	4	no	—
294	C₂×Q₈	—	18	1	no	—
295	C₂×Q₈	—	18	2	no	—
296	C₂×D₄	—	9	1	no	—
297	C₂×D₄	—	18	1	no	—
298	C₂²×C₄	—	18	1	no	—
299	C₂²×C₄	—	18	1	no	—
300	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
301	Q₁₆	—	9	8	no	—
302	SD₁₆	—	9	8	no	—
303	M₁₆	C₂×C₃×C₃⋊D₃	1	4	yes	complemented
304	C₂×C₈	C₂×C₃×C₃⋊D₃	1	2	yes	—
305	C₂²×C₃	—	2	8	no	—
306	C₂²×C₃	—	2	2	no	—
307	C₂²×C₃	—	2	4	no	—
308	C₂²×C₃	—	2	8	no	—
309	C₂²×C₃	—	4	8	no	—
310	C₂²×C₃	—	18	2	no	—
311	C₂²×C₃	—	36	2	no	—
312	C₂²×C₃	C₂×C₃×D₁₂	1	8	yes	—
313	C₂²×C₃	C₂×C₃×D₁₂	1	4	yes	—
314	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
315	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
316	C₂×D₃	—	6	8	no	—
317	C₂×D₃	—	12	8	no	—
318	C₃×C₄	—	2	4	no	—
319	C₃×C₄	—	2	8	no	—
320	C₃×C₄	—	2	4	no	—
321	C₃×C₄	—	18	2	no	—
322	C₃×C₄	—	18	4	no	—
323	C₃×C₄	C₂×C₃×D₁₂	1	4	yes	—
324	C₃×C₄	C₂×C₃×D₁₂	1	8	yes	—
325	C₃×C₄	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
326	C₃×C₄	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
327	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
328	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
329	Dic₃	—	6	16	no	—
330	Dic₃	—	6	8	no	—
331	C₃²	—	2	4	no	—
332	C₃²	C₂×#909	1	4	yes	complemented
333	C₃²	C₂×C₃×#137	1	1	yes	characteristic, complemented
334	C₂³	—	18	1	no	—
335	C₂³	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
336	Q₈	—	9	4	no	—
337	Q₈	—	9	2	no	—
338	Q₈	—	18	4	no	—
339	Q₈	—	18	2	no	—
340	Q₈	—	18	1	no	—
341	D₄	—	9	2	no	—
342	D₄	—	18	4	no	—
343	D₄	—	18	1	no	—
344	C₂×C₄	—	18	1	no	—
345	C₂×C₄	—	18	4	no	—
346	C₂×C₄	—	18	2	no	—
347	C₂×C₄	—	18	4	no	—
348	C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
349	C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
350	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
351	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
352	C₈	C₂²×C₃×C₃⋊D₃	1	4	yes	—
353	C₂×C₃	—	2	8	no	—
354	C₂×C₃	—	2	2	no	—
355	C₂×C₃	—	2	8	no	—
356	C₂×C₃	—	2	4	no	—
357	C₂×C₃	—	4	8	no	—
358	C₂×C₃	—	36	2	no	—
359	C₂×C₃	C₃×#909	1	8	yes	complemented
360	C₂×C₃	#64118	1	2	yes	direct product factor
361	C₂×C₃	C₂²×C₃×D₁₂	1	4	yes	—
362	C₂×C₃	C₂²×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
363	D₃	—	12	8	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	18	2	no	—
366	C₂²	—	36	2	no	—
367	C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
368	C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
369	C₄	—	18	2	no	—
370	C₄	—	18	4	no	—
371	C₄	C₂×C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
372	C₄	C₂×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
373	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
374	C₃	—	2	4	no	—
375	C₃	C₂×C₃×#909	1	4	yes	complemented
376	C₃	C₂×#64118	1	1	yes	characteristic, direct product factor
377	C₂	—	2	2	no	—
378	C₂	—	36	2	no	—
379	C₂	C₃×#64118	1	2	yes	direct product factor
380	C₂	C₂²×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)
commutator, cosocle	C₃²×C₄	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₂×C₃³×M₁₆	C₂
socle	C₂²×C₃³	C₂×D₄
prime radical	C₂×C₃×#3828	C₂
hypercenter	C₂×C₃×M₁₆	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×#137
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×#634	C₂	semidirect
3. C₂×C₃³×M₁₆	C₂	semidirect
4. C₃×#64118	C₂	direct (N × H)
5. C₂×C₃×#3746	C₂	semidirect
6. C₂×C₃×#3744	C₂	semidirect
7. C₂×#64118	C₃	direct (N × H)
20. C₂×C₃×#634	C₂²	semidirect
21. C₃³×M₁₆	C₂²	semidirect
23. C₃×#3746	C₂²	semidirect
24. C₃×#3744	C₂²	semidirect
26. C₂²×#634	C₂×C₃	semidirect
30. C₂×C₃²×M₁₆	D₃	semidirect
31. C₂×C₃²×M₁₆	C₂×C₃	semidirect
32. #64118	C₂×C₃	direct (N × H)
33. C₂×#3746	C₂×C₃	semidirect
34. C₂×#3744	C₂×C₃	semidirect
72. C₂×#634	C₂²×C₃	semidirect
85. C₃²×M₁₆	C₂×D₃	semidirect
86. C₃²×M₁₆	C₂²×C₃	semidirect
90. #3746	C₂²×C₃	semidirect
91. #3744	C₂²×C₃	semidirect
112. C₂×C₃×M₁₆	C₃×D₃	semidirect
113. C₂×C₃×M₁₆	C₃⋊D₃	semidirect
163. C₂×C₃³	#137	semidirect
194. C₃×M₁₆	C₂×C₃×D₃	semidirect
195. C₃×M₁₆	C₂×C₃⋊D₃	semidirect
232. C₂×M₁₆	C₃×C₃⋊D₃	semidirect
233. C₃³	C₂×#137	semidirect
283. C₂×C₃²	#909	semidirect
284. C₂×C₃²	C₃×#137	semidirect
303. M₁₆	C₂×C₃×C₃⋊D₃	semidirect
332. C₃²	C₂×#909	semidirect
333. C₃²	C₂×C₃×#137	semidirect
359. C₂×C₃	C₃×#909	semidirect
360. C₂×C₃	#64118	direct (N × H)
375. C₃	C₂×C₃×#909	semidirect
376. C₃	C₂×#64118	direct (N × H)
379. C₂	C₃×#64118	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×#3828	2
C₂²×C₃×#634	2
C₂×C₃³×M₁₆	2
C₃×#64118	2
C₂×C₃×#3746	2
C₂×C₃×#3744	2
C₂×#64118	3
C₂×C₃×#909	3

Subgroups — C2×C3×#64118 #13179498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64118 #13179498