Subgroups — C₃×#10592428 #13162758

Order 1728.

932 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	C₃×C₄×#638	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#3748	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3743	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃³×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#63647	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63641	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₈×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#10592428	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₃×#4729	—	3	4	no	maximal
10	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
11	C₂×C₃×#638	C₄	1	1	yes	characteristic
12	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
13	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
15	C₃×#3757	C₄	1	1	yes	characteristic
16	C₃×#3752	C₄	1	1	yes	characteristic
17	C₃×#3750	C₄	1	1	yes	characteristic
18	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₃×#3748	—	2	2	no	—
20	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
22	C₃×#3743	—	2	2	no	—
23	C₄×#638	C₂×C₃	1	1	yes	characteristic
24	C₂×#3748	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂×#3743	C₂×C₃	1	1	yes	characteristic, complemented
26	C₃×C₄×#67	—	3	4	no	—
27	C₂×C₃×#208	—	3	4	no	—
28	C₂×C₃×ΓL(1,𝔽₂₅)	—	3	4	no	—
29	C₃²×C₂²⋊C₈	—	2	4	no	—
30	C₃²×C₂²⋊C₈	D₃	1	4	yes	complemented
31	C₃²×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
32	#63647	C₂×C₃	1	1	yes	characteristic, complemented
33	#63641	C₂×C₃	1	1	yes	characteristic, complemented
34	C₈×C₃⋊Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
35	C₃×(C₂×D₃)⋊C₈	—	3	4	no	—
36	C₃×Dic₃⋊C₈	—	3	4	no	—
37	C₃×C₈×Dic₃	—	3	4	no	—
38	C₂³×C₃³	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃³×C₄	—	2	1	no	—
41	C₂×C₃³×C₄	—	2	1	no	—
42	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
44	C₃×#638	—	2	2	no	—
45	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
48	C₃×C₄×C₃⋊D₃	—	2	1	no	—
49	C₃×C₄×C₃⋊D₃	—	2	1	no	—
50	C₃³×C₈	—	2	1	no	—
51	C₃³×C₈	—	2	1	no	—
52	C₃×C₃⋊(C₃⋊C₈)	—	2	1	no	—
53	C₃×C₃⋊(C₃⋊C₈)	D₄	1	2	yes	complemented
54	C₃×#436	—	9	1	no	—
55	#4729	—	3	4	no	—
56	C₂²×C₃²×C₄	—	2	4	no	—
57	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
58	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
59	C₂×#638	C₃×C₄	1	1	yes	characteristic
60	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
61	C₂×C₃×#67	—	3	4	no	—
62	C₂×C₃×C₄×D₃	—	3	4	no	—
63	C₂×C₃²×C₈	—	2	4	no	—
64	C₂×C₃²×C₈	—	2	4	no	—
65	C₂×C₃²×C₈	C₂×D₃	1	4	yes	—
66	C₂×C₃²×C₈	C₂×D₃	1	4	yes	—
67	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
69	#3757	C₃×C₄	1	1	yes	characteristic
70	#3752	C₃×C₄	1	1	yes	characteristic
71	#3750	C₃×C₄	1	1	yes	characteristic
72	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
73	#3748	—	2	2	no	—
74	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
76	#3743	—	2	2	no	—
77	C₃×#217	—	3	4	no	—
78	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
79	C₃×Dic₃⋊C₄	—	3	4	no	—
80	C₃×C₄×Dic₃	—	3	4	no	—
81	C₃×#208	—	6	8	no	—
82	C₂×C₃×C₃⋊C₈	—	3	4	no	—
83	C₂×C₃×C₃⋊C₈	—	3	4	no	—
84	C₃×ΓL(1,𝔽₂₅)	—	6	8	no	—
85	C₂²×C₃³	—	2	1	no	—
86	C₂²×C₃³	—	2	1	no	—
87	C₂²×C₃³	—	2	1	no	—
88	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₃×C₃⋊D₃	—	2	1	no	—
90	C₂×C₃×C₃⋊D₃	—	2	1	no	—
91	C₂×C₃×C₃⋊D₃	—	2	1	no	—
92	C₃³×C₄	—	2	1	no	—
93	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
94	C₃³×C₄	#41	1	1	yes	characteristic
95	C₃×C₃⋊Dic₃	—	2	1	no	—
96	C₃×C₃⋊Dic₃	—	2	1	no	—
97	C₃×C₃⋊Dic₃	M₁₆	1	2	yes	complemented
98	C₂×C₃×M₁₆	—	9	1	no	—
99	C₂×C₃×M₁₆	—	9	1	no	—
100	C₃×C₄×D₄	—	9	1	no	—
101	C₄×#67	—	3	4	no	—
102	C₂×#208	—	3	4	no	—
103	C₂×ΓL(1,𝔽₂₅)	—	3	4	no	—
104	C₃×C₄⋊C₈	—	9	1	no	—
105	C₃×C₂²⋊C₈	—	2	4	no	—
106	C₃×C₂²⋊C₈	—	9	1	no	—
107	C₃×C₂²⋊C₈	C₃×D₃	1	4	yes	complemented
108	C₃×C₂²⋊C₈	C₃⋊D₃	1	1	yes	characteristic, complemented
109	C₃×C₄×C₈	—	9	1	no	—
110	(C₂×D₃)⋊C₈	—	3	4	no	—
111	Dic₃⋊C₈	—	3	4	no	—
112	C₈×Dic₃	—	3	4	no	—
113	C₂³×C₃²	—	2	4	no	—
114	C₂³×C₃²	C₄×D₃	1	4	yes	—
115	C₂³×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
116	C₂²×C₃⋊D₃	C₂×C₃×C₄	1	1	yes	characteristic
117	C₂²×C₃×D₃	—	3	4	no	—
118	C₂×C₃²×C₄	—	2	1	no	—
119	C₂×C₃²×C₄	—	2	1	no	—
120	C₂×C₃²×C₄	—	2	4	no	—
121	C₂×C₃²×C₄	—	2	4	no	—
122	C₂×C₃²×C₄	—	2	4	no	—
123	C₂×C₃²×C₄	—	2	4	no	—
124	C₂×C₃²×C₄	—	4	4	no	—
125	C₂×C₃²×C₄	—	4	4	no	—
126	C₂×C₃²×C₄	C₄×D₃	1	4	yes	—
127	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
129	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
130	#638	—	2	2	no	—
131	C₂×C₃⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
132	C₂×C₃⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
133	C₂×C₃⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
134	C₄×C₃⋊D₃	—	2	1	no	—
135	C₄×C₃⋊D₃	—	2	1	no	—
136	C₃×#67	—	6	8	no	—
137	C₂×C₃×Dic₃	—	3	4	no	—
138	C₂×C₃×Dic₃	—	3	4	no	—
139	C₂×C₃×Dic₃	—	3	4	no	—
140	C₃×C₄×D₃	—	6	4	no	—
141	C₃×C₄×D₃	—	6	4	no	—
142	C₃²×C₈	—	2	1	no	—
143	C₃²×C₈	—	2	1	no	—
144	C₃²×C₈	—	2	4	no	—
145	C₃²×C₈	—	2	4	no	—
146	C₃²×C₈	—	4	4	no	—
147	C₃²×C₈	—	4	4	no	—
148	C₃⋊(C₃⋊C₈)	—	2	1	no	—
149	C₃⋊(C₃⋊C₈)	C₃×D₄	1	2	yes	complemented
150	C₃×C₃⋊C₈	—	3	8	no	—
151	C₃×C₃⋊C₈	—	6	4	no	—
152	#436	—	9	1	no	Sylow
153	C₂×C₃³	—	4	1	no	—
154	C₂×C₃³	C₄×D₄	1	1	yes	characteristic
155	C₂×C₃³	C₂×M₁₆	1	1	yes	characteristic
156	C₂×C₃³	#131	1	1	yes	characteristic
157	C₃×C₃⋊D₃	—	4	1	no	—
158	C₂×C₃×D₄	—	9	1	no	—
159	C₂²×C₃×C₄	—	2	4	no	—
160	C₂²×C₃×C₄	—	9	1	no	—
161	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
162	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
163	C₂×#67	—	3	4	no	—
164	C₂×C₄×D₃	—	3	4	no	—
165	C₃×M₁₆	—	18	2	no	—
166	C₃×M₁₆	—	18	2	no	—
167	C₂×C₃×C₈	—	2	4	no	—
168	C₂×C₃×C₈	—	2	4	no	—
169	C₂×C₃×C₈	—	9	1	no	—
170	C₂×C₃×C₈	—	9	1	no	—
171	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
172	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
173	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
174	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
175	C₃×C₄⋊C₄	—	9	1	no	—
176	C₃×C₂²⋊C₄	—	9	1	no	—
177	C₃×C₂²⋊C₄	—	9	1	no	—
178	C₃×C₄²	—	9	1	no	—
179	#217	—	3	4	no	—
180	(C₂×D₃)⋊C₄	—	3	4	no	—
181	Dic₃⋊C₄	—	3	4	no	—
182	C₄×Dic₃	—	3	4	no	—
183	#208	—	6	8	no	—
184	C₂×C₃⋊C₈	—	3	4	no	—
185	C₂×C₃⋊C₈	—	3	4	no	—
186	ΓL(1,𝔽₂₅)	—	6	8	no	—
187	C₂²×C₃²	—	2	8	no	—
188	C₂²×C₃²	—	2	4	no	—
189	C₂²×C₃²	—	2	1	no	—
190	C₂²×C₃²	—	2	1	no	—
191	C₂²×C₃²	—	2	1	no	—
192	C₂²×C₃²	—	2	4	no	—
193	C₂²×C₃²	—	2	4	no	—
194	C₂²×C₃²	—	2	4	no	—
195	C₂²×C₃²	—	4	4	no	—
196	C₂²×C₃²	—	4	4	no	—
197	C₂²×C₃²	C₂×C₄×D₃	1	4	yes	—
198	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
199	C₂×C₃⋊D₃	—	2	1	no	—
200	C₂×C₃⋊D₃	—	2	1	no	—
201	C₂×C₃⋊D₃	—	2	1	no	—
202	C₂×C₃×D₃	—	6	4	no	—
203	C₂×C₃×D₃	—	6	4	no	—
204	C₂×C₃×D₃	—	6	4	no	—
205	C₃²×C₄	—	2	1	no	—
206	C₃²×C₄	—	2	4	no	—
207	C₃²×C₄	—	2	4	no	—
208	C₃²×C₄	—	2	4	no	—
209	C₃²×C₄	—	4	4	no	—
210	C₃²×C₄	D₃×D₄	1	4	yes	—
211	C₃²×C₄	#237	1	4	yes	—
212	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
213	C₃²×C₄	C₃×#41	1	1	yes	characteristic
214	C₃⋊Dic₃	—	2	1	no	—
215	C₃⋊Dic₃	—	2	1	no	—
216	C₃⋊Dic₃	C₃×M₁₆	1	2	yes	complemented
217	C₃×Dic₃	—	3	8	no	—
218	C₃×Dic₃	—	6	4	no	—
219	C₃×Dic₃	—	6	4	no	—
220	C₂×M₁₆	—	9	1	no	—
221	C₂×M₁₆	—	9	1	no	—
222	C₄×D₄	—	9	1	no	—
223	C₄⋊C₈	—	9	1	no	—
224	C₂²⋊C₈	—	9	1	no	—
225	C₂²⋊C₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
226	C₄×C₈	—	9	1	no	—
227	C₃³	#436	1	1	yes	characteristic, complemented, Sylow
228	C₂³×C₃	—	2	4	no	—
229	C₂³×C₃	—	9	1	no	—
230	C₂³×C₃	C₃×C₄×D₃	1	4	yes	—
231	C₂³×C₃	C₄×C₃⋊D₃	1	1	yes	characteristic
232	C₂²×D₃	—	3	4	no	—
233	C₃×D₄	—	18	2	no	—
234	C₂×C₃×C₄	—	2	4	no	—
235	C₂×C₃×C₄	—	2	4	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	4	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	4	4	no	—
241	C₂×C₃×C₄	—	4	4	no	—
242	C₂×C₃×C₄	—	9	1	no	—
243	C₂×C₃×C₄	—	9	1	no	—
244	C₂×C₃×C₄	—	9	1	no	—
245	C₂×C₃×C₄	—	18	1	no	—
246	C₂×C₃×C₄	—	18	1	no	—
247	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
248	C₂×C₃×C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
250	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
251	#67	—	6	8	no	—
252	C₂×Dic₃	—	3	4	no	—
253	C₂×Dic₃	—	3	4	no	—
254	C₂×Dic₃	—	3	4	no	—
255	C₄×D₃	—	6	4	no	—
256	C₄×D₃	—	6	4	no	—
257	C₃×C₈	—	2	4	no	—
258	C₃×C₈	—	2	4	no	—
259	C₃×C₈	—	2	1	no	—
260	C₃×C₈	—	2	1	no	—
261	C₃×C₈	—	4	4	no	—
262	C₃×C₈	—	4	4	no	—
263	C₃×C₈	—	9	2	no	—
264	C₃×C₈	—	18	1	no	—
265	C₃⋊C₈	—	3	8	no	—
266	C₃⋊C₈	—	6	4	no	—
267	C₂×C₃²	—	2	4	no	—
268	C₂×C₃²	—	2	4	no	—
269	C₂×C₃²	—	2	4	no	—
270	C₂×C₃²	—	4	8	no	—
271	C₂×C₃²	—	4	4	no	—
272	C₂×C₃²	—	4	1	no	—
273	C₂×C₃²	#67⋊C₄	1	4	yes	—
274	C₂×C₃²	#901	1	4	yes	—
275	C₂×C₃²	D₃×M₁₆	1	4	yes	—
276	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
277	C₂×C₃²	C₂×C₃×M₁₆	1	1	yes	characteristic
278	C₂×C₃²	C₃×#131	1	1	yes	characteristic
279	C₃⋊D₃	—	4	1	no	—
280	C₃×D₃	—	12	4	no	—
281	C₂×D₄	—	9	1	no	—
282	C₂²×C₄	—	9	1	no	—
283	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
284	M₁₆	—	18	2	no	—
285	M₁₆	—	18	2	no	—
286	C₂×C₈	—	9	1	no	—
287	C₂×C₈	—	9	1	no	—
288	C₂×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
289	C₂×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
290	C₄⋊C₄	—	9	1	no	—
291	C₂²⋊C₄	—	9	1	no	—
292	C₂²⋊C₄	—	9	1	no	—
293	C₄²	—	9	1	no	—
294	C₂²×C₃	—	2	8	no	—
295	C₂²×C₃	—	2	4	no	—
296	C₂²×C₃	—	2	4	no	—
297	C₂²×C₃	—	2	4	no	—
298	C₂²×C₃	—	2	1	no	—
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	2	4	no	—
302	C₂²×C₃	—	4	4	no	—
303	C₂²×C₃	—	4	4	no	—
304	C₂²×C₃	—	18	1	no	—
305	C₂²×C₃	—	18	1	no	—
306	C₂²×C₃	—	18	1	no	—
307	C₂²×C₃	C₂×C₃×C₄×D₃	1	4	yes	—
308	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
309	C₂×D₃	—	6	4	no	—
310	C₂×D₃	—	6	4	no	—
311	C₂×D₃	—	6	4	no	—
312	C₃×C₄	—	2	4	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	2	4	no	—
315	C₃×C₄	—	2	4	no	—
316	C₃×C₄	—	4	4	no	—
317	C₃×C₄	—	9	2	no	—
318	C₃×C₄	—	18	1	no	—
319	C₃×C₄	—	18	1	no	—
320	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
321	C₃×C₄	C₃×#237	1	4	yes	—
322	C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
323	C₃×C₄	#3830	1	1	yes	characteristic
324	Dic₃	—	3	8	no	—
325	Dic₃	—	6	4	no	—
326	Dic₃	—	6	4	no	—
327	C₃²	—	2	4	no	—
328	C₃²	#4729	1	4	yes	complemented
329	C₃²	C₃×#436	1	1	yes	characteristic, complemented
330	C₂³	—	9	1	no	—
331	C₂³	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
332	D₄	—	18	2	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	9	1	no	—
336	C₂×C₄	—	9	1	no	—
337	C₂×C₄	—	9	1	no	—
338	C₂×C₄	—	18	1	no	—
339	C₂×C₄	—	18	1	no	—
340	C₂×C₄	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
341	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
342	C₈	—	2	1	no	—
343	C₈	—	2	1	no	—
344	C₈	—	9	2	no	—
345	C₈	—	18	1	no	—
346	C₂×C₃	—	2	4	no	—
347	C₂×C₃	—	2	4	no	—
348	C₂×C₃	—	2	4	no	—
349	C₂×C₃	—	4	8	no	—
350	C₂×C₃	—	4	4	no	—
351	C₂×C₃	—	4	1	no	—
352	C₂×C₃	—	36	1	no	—
353	C₂×C₃	C₃×#67⋊C₄	1	4	yes	—
354	C₂×C₃	C₃×#901	1	4	yes	—
355	C₂×C₃	C₃×D₃×M₁₆	1	4	yes	—
356	C₂×C₃	#64090	1	1	yes	characteristic
357	C₂×C₃	#64110	1	1	yes	characteristic
358	C₂×C₃	M₁₆×C₃⋊D₃	1	1	yes	characteristic
359	D₃	—	12	4	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	18	1	no	—
364	C₂²	—	18	1	no	—
365	C₂²	—	18	1	no	—
366	C₂²	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
367	C₄	—	2	1	no	—
368	C₄	—	9	2	no	—
369	C₄	—	18	1	no	—
370	C₄	—	18	1	no	—
371	C₄	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
372	C₄	C₃×#3830	1	1	yes	characteristic
373	C₃	—	2	4	no	—
374	C₃	C₃×#4729	1	4	yes	complemented
375	C₃	#10592428	1	1	yes	characteristic, direct product factor
376	C₂	—	4	1	no	—
377	C₂	—	36	1	no	—
378	C₂	C₃×#64090	1	1	yes	characteristic
379	C₂	C₃×#64110	1	1	yes	characteristic
380	C₂	C₃×M₁₆×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×C₃⋊D₃
commutator	C₂²×C₃²	C₂²×C₃×C₄
Frattini	C₂×C₄	C₂²×C₃×C₃⋊D₃
Fitting	C₃³×C₂²⋊C₈	C₂
socle	C₂²×C₃³	C₂²×C₄
prime radical	C₂×C₃×#638	C₄
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₃×C₂²⋊C₈	C₃⋊D₃
hypocenter	C₃²	C₃×#436
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#3748	C₂	semidirect
3. C₂×C₃×#3743	C₂	semidirect
4. C₃³×C₂²⋊C₈	C₂	semidirect
5. C₃×#63647	C₂	semidirect
6. C₃×#63641	C₂	semidirect
7. C₃×C₈×C₃⋊Dic₃	C₂	semidirect
8. #10592428	C₃	direct (N × H)
24. C₂×#3748	C₂×C₃	semidirect
25. C₂×#3743	C₂×C₃	semidirect
30. C₃²×C₂²⋊C₈	D₃	semidirect
31. C₃²×C₂²⋊C₈	C₂×C₃	semidirect
32. #63647	C₂×C₃	semidirect
33. #63641	C₂×C₃	semidirect
34. C₈×C₃⋊Dic₃	C₂×C₃	semidirect
53. C₃×C₃⋊(C₃⋊C₈)	D₄	semidirect
97. C₃×C₃⋊Dic₃	M₁₆	semidirect
107. C₃×C₂²⋊C₈	C₃×D₃	semidirect
108. C₃×C₂²⋊C₈	C₃⋊D₃	semidirect
149. C₃⋊(C₃⋊C₈)	C₃×D₄	semidirect
216. C₃⋊Dic₃	C₃×M₁₆	semidirect
225. C₂²⋊C₈	C₃×C₃⋊D₃	semidirect
227. C₃³	#436	semidirect
328. C₃²	#4729	semidirect
329. C₃²	C₃×#436	semidirect
374. C₃	C₃×#4729	semidirect
375. C₃	#10592428	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×#638	2
C₂×C₃×#3748	2
C₂×C₃×#3743	2
C₃³×C₂²⋊C₈	2
C₃×#63647	2
C₃×#63641	2
C₃×C₈×C₃⋊Dic₃	2
#10592428	3
C₃×#4729	3

Subgroups — C3×#10592428 #13162758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10592428 #13162758