Subgroups — C₂×C₃×#64117 #13179497

Order 1728.

2060 conjugacy classes of subgroups.

The subgroup lattice has 406 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, complemented
2	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃³×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64117	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3745	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#3744	C₂	1	2	yes	maximal, complemented
7	C₂×#64117	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×#908	—	3	4	no	maximal
9	C₂³×C₃×C₃⋊D₃	—	2	1	no	—
10	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
11	C₂×C₃×#638	—	2	1	no	—
12	C₃×#3828	—	2	2	no	—
13	C₃×#3828	C₂²	1	4	yes	complemented
14	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
15	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
16	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	—
17	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	4	yes	complemented
18	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×C₄×C₃⋊D₃	—	2	1	no	—
20	C₂×C₃×#634	C₂²	1	1	yes	characteristic, complemented
21	C₃³×M₁₆	C₂²	1	4	yes	complemented
22	C₂×C₃³×C₈	C₂²	1	2	yes	complemented
23	C₃×#3745	C₂²	1	8	yes	complemented
24	C₃×#3744	C₂²	1	8	yes	complemented
25	C₂×#3828	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×C₃×#235	—	3	4	no	—
28	C₂²×C₃×D₁₂	—	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	#64117	C₂×C₃	1	8	yes	direct product factor
33	C₂×#3745	C₂×C₃	1	2	yes	complemented
34	C₂×#3744	C₂×C₃	1	2	yes	complemented
35	C₃×#908	—	3	32	no	—
36	C₂×C₃×D₂₄	—	3	8	no	—
37	C₂×C₃×#204	—	3	8	no	—
38	C₂³×C₃³	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
40	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
41	C₂²×C₃×C₃⋊D₃	—	2	1	no	—
42	C₂²×C₃×C₃⋊D₃	—	4	4	no	—
43	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
44	C₂×C₃³×C₄	D₄	1	2	yes	—
45	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
46	C₂×C₃³×C₄	C₂³	1	2	yes	—
47	C₃×#638	—	2	4	no	—
48	C₂×C₃×C₃⋊Dic₃	—	2	1	no	—
49	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
50	C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
51	C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
52	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	4	yes	—
53	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	2	yes	complemented
54	C₃×C₄×C₃⋊D₃	—	2	4	no	—
55	C₃×#634	—	2	1	no	—
56	C₃×#634	C₂³	1	2	yes	complemented
57	C₃³×C₈	C₂³	1	4	yes	complemented
58	C₂×C₃×AGL(1,ℤ/8)	—	9	1	no	—
59	C₂×#908	—	3	4	no	—
60	C₂³×C₃⋊D₃	—	2	1	no	—
61	C₂³×C₃×D₃	—	6	4	no	—
62	C₂²×C₃²×C₄	—	2	4	no	—
63	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
64	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
65	C₂×#638	—	2	1	no	—
66	#3828	—	2	2	no	—
67	#3828	C₂²×C₃	1	4	yes	complemented
68	C₂×C₄⋊(C₃⋊D₃)	—	2	2	no	—
69	C₂×C₄⋊(C₃⋊D₃)	—	2	1	no	—
70	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	—
71	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	4	yes	complemented
72	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic, complemented
73	C₂×C₄×C₃⋊D₃	—	2	1	no	—
74	C₂×#634	C₂²×C₃	1	1	yes	characteristic, complemented
75	C₂×C₃×#67	—	6	4	no	—
76	C₃×#235	—	3	16	no	—
77	C₃×#235	—	6	8	no	—
78	C₂×C₃×D₁₂	—	3	8	no	—
79	C₂×C₃×D₁₂	—	3	4	no	—
80	C₂×C₃×D₁₂	—	3	16	no	—
81	C₂×C₃×D₁₂	—	6	4	no	—
82	C₂×C₃×D₁₂	—	6	8	no	—
83	C₂×C₃×C₄×D₃	—	6	4	no	—
84	C₂×C₃×Dic₆	—	3	4	no	—
85	C₃²×M₁₆	—	2	16	no	—
86	C₃²×M₁₆	C₂×D₃	1	16	yes	complemented
87	C₃²×M₁₆	C₂²×C₃	1	4	yes	complemented
88	C₂×C₃²×C₈	—	2	8	no	—
89	C₂×C₃²×C₈	C₂×D₃	1	8	yes	complemented
90	C₂×C₃²×C₈	C₂²×C₃	1	2	yes	complemented
91	#3745	C₂²×C₃	1	8	yes	complemented
92	#3744	C₂²×C₃	1	8	yes	complemented
93	C₃×D₂₄	—	3	32	no	—
94	C₃×#204	—	3	32	no	—
95	C₂²×C₃³	—	2	2	no	—
96	C₂²×C₃³	C₂×D₄	1	2	yes	—
97	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃×C₃⋊D₃	—	2	2	no	—
99	C₂×C₃×C₃⋊D₃	—	2	4	no	—
100	C₂×C₃×C₃⋊D₃	—	4	8	no	—
101	C₂×C₃×C₃⋊D₃	—	4	2	no	—
102	C₂×C₃×C₃⋊D₃	—	4	4	no	—
103	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
104	C₃³×C₄	C₂×D₄	1	2	yes	—
105	C₃³×C₄	C₂⁴	1	1	yes	characteristic
106	C₃×C₃⋊Dic₃	—	2	2	no	—
107	C₂×C₃×#41	—	9	1	no	—
108	C₂²×C₃×D₄	—	9	1	no	—
109	C₂×#235	—	3	4	no	—
110	C₂²×D₁₂	—	3	4	no	—
111	C₃×AGL(1,ℤ/8)	—	9	8	no	—
112	C₂×C₃×SD₁₆	—	9	2	no	—
113	C₂×C₃×D₈	—	9	2	no	—
114	C₂×C₃×M₁₆	—	2	4	no	—
115	C₂×C₃×M₁₆	C₃×D₃	1	4	yes	complemented
116	C₂×C₃×M₁₆	C₃⋊D₃	1	1	yes	characteristic, complemented
117	#908	—	3	32	no	—
118	C₂×D₂₄	—	3	8	no	—
119	C₂×#204	—	3	8	no	—
120	C₂³×C₃²	—	2	4	no	—
121	C₂³×C₃²	D₁₂	1	4	yes	—
122	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
123	C₂²×C₃⋊D₃	—	2	2	no	—
124	C₂²×C₃⋊D₃	—	2	4	no	—
125	C₂²×C₃⋊D₃	—	2	1	no	—
126	C₂²×C₃⋊D₃	—	4	4	no	—
127	C₂²×C₃×D₃	—	6	16	no	—
128	C₂²×C₃×D₃	—	6	8	no	—
129	C₂²×C₃×D₃	—	6	4	no	—
130	C₂²×C₃×D₃	—	12	16	no	—
131	C₂×C₃²×C₄	—	2	4	no	—
132	C₂×C₃²×C₄	—	2	8	no	—
133	C₂×C₃²×C₄	—	2	4	no	—
134	C₂×C₃²×C₄	—	2	8	no	—
135	C₂×C₃²×C₄	D₁₂	1	4	yes	—
136	C₂×C₃²×C₄	D₁₂	1	8	yes	—
137	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
138	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
139	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
140	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
141	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
142	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
143	#638	—	2	4	no	—
144	C₂×C₃⋊Dic₃	—	2	1	no	—
145	C₄⋊(C₃⋊D₃)	—	2	2	no	—
146	C₄⋊(C₃⋊D₃)	—	2	4	no	—
147	C₄⋊(C₃⋊D₃)	—	2	1	no	—
148	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	4	yes	—
149	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	2	yes	complemented
150	C₄×C₃⋊D₃	—	2	4	no	—
151	#634	—	2	1	no	—
152	#634	C₂³×C₃	1	2	yes	complemented
153	C₃×#67	—	6	16	no	—
154	C₂×C₃×Dic₃	—	6	4	no	—
155	C₃×D₁₂	—	3	16	no	—
156	C₃×D₁₂	—	3	8	no	—
157	C₃×D₁₂	—	6	8	no	—
158	C₃×D₁₂	—	6	16	no	—
159	C₃×D₁₂	—	6	4	no	—
160	C₃×C₄×D₃	—	6	16	no	—
161	C₃×Dic₆	—	3	8	no	—
162	C₃×Dic₆	—	6	4	no	—
163	C₃²×C₈	—	2	16	no	—
164	C₃²×C₈	C₂²×D₃	1	16	yes	complemented
165	C₃²×C₈	C₂³×C₃	1	4	yes	complemented
166	C₂×AGL(1,ℤ/8)	—	9	1	no	Sylow
167	C₂×C₃³	—	2	2	no	—
168	C₂×C₃³	AGL(1,ℤ/8)	1	2	yes	complemented
169	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
170	C₃×C₃⋊D₃	—	4	2	no	—
171	C₃×C₃⋊D₃	—	4	4	no	—
172	C₂⁴×C₃	—	18	1	no	—
173	C₂³×D₃	—	6	4	no	—
174	C₃×#41	—	9	4	no	—
175	C₃×#41	—	18	2	no	—
176	C₂×C₃×Q₈	—	9	1	no	—
177	C₂×C₃×D₄	—	9	1	no	—
178	C₂×C₃×D₄	—	9	2	no	—
179	C₂×C₃×D₄	—	9	4	no	—
180	C₂×C₃×D₄	—	18	1	no	—
181	C₂×C₃×D₄	—	18	2	no	—
182	C₂×C₃×D₄	—	18	1	no	—
183	C₂²×C₃×C₄	—	2	4	no	—
184	C₂²×C₃×C₄	—	18	1	no	—
185	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
186	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
187	C₂×#67	—	6	4	no	—
188	#235	—	3	16	no	—
189	#235	—	6	8	no	—
190	C₂×D₁₂	—	3	8	no	—
191	C₂×D₁₂	—	3	4	no	—
192	C₂×D₁₂	—	3	16	no	—
193	C₂×D₁₂	—	6	4	no	—
194	C₂×D₁₂	—	6	8	no	—
195	C₂×C₄×D₃	—	6	4	no	—
196	C₂×Dic₆	—	3	4	no	—
197	C₃×SD₁₆	—	9	8	no	—
198	C₃×D₈	—	9	8	no	—
199	C₃×M₁₆	—	2	16	no	—
200	C₃×M₁₆	C₂×C₃×D₃	1	16	yes	complemented
201	C₃×M₁₆	C₂×C₃⋊D₃	1	4	yes	complemented
202	C₂×C₃×C₈	—	2	8	no	—
203	C₂×C₃×C₈	C₂×C₃×D₃	1	8	yes	complemented
204	C₂×C₃×C₈	C₂×C₃⋊D₃	1	2	yes	complemented
205	D₂₄	—	3	32	no	—
206	#204	—	3	32	no	—
207	C₂²×C₃²	—	2	2	no	—
208	C₂²×C₃²	—	2	4	no	—
209	C₂²×C₃²	—	2	8	no	—
210	C₂²×C₃²	—	2	8	no	—
211	C₂²×C₃²	—	4	8	no	—
212	C₂²×C₃²	C₂×D₁₂	1	8	yes	—
213	C₂²×C₃²	C₂×D₁₂	1	4	yes	—
214	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
215	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
216	C₂×C₃⋊D₃	—	2	2	no	—
217	C₂×C₃⋊D₃	—	2	4	no	—
218	C₂×C₃⋊D₃	—	4	8	no	—
219	C₂×C₃⋊D₃	—	4	2	no	—
220	C₂×C₃⋊D₃	—	4	4	no	—
221	C₂×C₃×D₃	—	6	8	no	—
222	C₂×C₃×D₃	—	6	16	no	—
223	C₂×C₃×D₃	—	12	32	no	—
224	C₂×C₃×D₃	—	12	8	no	—
225	C₂×C₃×D₃	—	12	16	no	—
226	C₃²×C₄	—	2	4	no	—
227	C₃²×C₄	—	2	4	no	—
228	C₃²×C₄	—	2	8	no	—
229	C₃²×C₄	C₂×D₁₂	1	4	yes	—
230	C₃²×C₄	C₂×D₁₂	1	8	yes	—
231	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
232	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
233	C₃²×C₄	C₂³×D₃	1	4	yes	—
234	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
235	C₃⋊Dic₃	—	2	2	no	—
236	C₃×Dic₃	—	6	8	no	—
237	C₂×#41	—	9	1	no	—
238	C₂²×D₄	—	9	1	no	—
239	AGL(1,ℤ/8)	—	9	8	no	—
240	C₂×SD₁₆	—	9	2	no	—
241	C₂×D₈	—	9	2	no	—
242	C₂×M₁₆	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
243	C₃³	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
244	C₂³×C₃	—	2	4	no	—
245	C₂³×C₃	—	18	4	no	—
246	C₂³×C₃	—	18	1	no	—
247	C₂³×C₃	—	18	2	no	—
248	C₂³×C₃	—	36	4	no	—
249	C₂³×C₃	C₃×D₁₂	1	4	yes	—
250	C₂³×C₃	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
251	C₂²×D₃	—	6	4	no	—
252	C₂²×D₃	—	6	16	no	—
253	C₂²×D₃	—	6	8	no	—
254	C₂²×D₃	—	12	16	no	—
255	C₃×Q₈	—	9	2	no	—
256	C₃×Q₈	—	18	1	no	—
257	C₃×D₄	—	9	2	no	—
258	C₃×D₄	—	9	4	no	—
259	C₃×D₄	—	18	4	no	—
260	C₃×D₄	—	18	4	no	—
261	C₃×D₄	—	18	2	no	—
262	C₃×D₄	—	18	1	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	2	8	no	—
265	C₂×C₃×C₄	—	2	4	no	—
266	C₂×C₃×C₄	—	2	8	no	—
267	C₂×C₃×C₄	—	18	1	no	—
268	C₂×C₃×C₄	—	18	4	no	—
269	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
270	C₂×C₃×C₄	C₃×D₁₂	1	8	yes	—
271	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	1	2	yes	—
272	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
274	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
275	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
276	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
277	#67	—	6	16	no	—
278	C₂×Dic₃	—	6	4	no	—
279	D₁₂	—	3	16	no	—
280	D₁₂	—	3	8	no	—
281	D₁₂	—	6	8	no	—
282	D₁₂	—	6	16	no	—
283	D₁₂	—	6	4	no	—
284	C₄×D₃	—	6	16	no	—
285	Dic₆	—	3	8	no	—
286	Dic₆	—	6	4	no	—
287	C₃×C₈	—	2	16	no	—
288	C₃×C₈	C₂²×C₃×D₃	1	16	yes	complemented
289	C₃×C₈	C₂²×C₃⋊D₃	1	4	yes	complemented
290	C₂×C₃²	—	2	2	no	—
291	C₂×C₃²	—	2	8	no	—
292	C₂×C₃²	—	2	4	no	—
293	C₂×C₃²	—	2	8	no	—
294	C₂×C₃²	—	4	8	no	—
295	C₂×C₃²	#908	1	8	yes	complemented
296	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	2	yes	complemented
297	C₂×C₃²	C₂²×D₁₂	1	4	yes	—
298	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
299	C₃⋊D₃	—	4	2	no	—
300	C₃⋊D₃	—	4	4	no	—
301	C₃×D₃	—	12	8	no	—
302	C₃×D₃	—	12	16	no	—
303	C₂⁴	—	18	1	no	—
304	#41	—	9	4	no	—
305	#41	—	18	2	no	—
306	C₂×Q₈	—	9	1	no	—
307	C₂×D₄	—	9	1	no	—
308	C₂×D₄	—	9	2	no	—
309	C₂×D₄	—	9	4	no	—
310	C₂×D₄	—	18	1	no	—
311	C₂×D₄	—	18	1	no	—
312	C₂×D₄	—	18	2	no	—
313	C₂²×C₄	—	18	1	no	—
314	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
315	SD₁₆	—	9	8	no	—
316	D₈	—	9	8	no	—
317	M₁₆	C₂×C₃×C₃⋊D₃	1	4	yes	complemented
318	C₂×C₈	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
319	C₂²×C₃	—	2	8	no	—
320	C₂²×C₃	—	2	2	no	—
321	C₂²×C₃	—	2	4	no	—
322	C₂²×C₃	—	2	8	no	—
323	C₂²×C₃	—	4	8	no	—
324	C₂²×C₃	—	18	2	no	—
325	C₂²×C₃	—	18	4	no	—
326	C₂²×C₃	—	36	8	no	—
327	C₂²×C₃	—	36	4	no	—
328	C₂²×C₃	—	36	2	no	—
329	C₂²×C₃	C₂×C₃×D₁₂	1	8	yes	—
330	C₂²×C₃	C₂×C₃×D₁₂	1	4	yes	—
331	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
332	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
333	C₂×D₃	—	6	8	no	—
334	C₂×D₃	—	6	16	no	—
335	C₂×D₃	—	12	32	no	—
336	C₂×D₃	—	12	16	no	—
337	C₂×D₃	—	12	8	no	—
338	C₃×C₄	—	2	4	no	—
339	C₃×C₄	—	2	8	no	—
340	C₃×C₄	—	2	4	no	—
341	C₃×C₄	—	18	2	no	—
342	C₃×C₄	C₂×C₃×D₁₂	1	4	yes	—
343	C₃×C₄	C₂×C₃×D₁₂	1	8	yes	—
344	C₃×C₄	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
345	C₃×C₄	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
346	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
347	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
348	Dic₃	—	6	8	no	—
349	C₃²	—	2	4	no	—
350	C₃²	C₂×#908	1	4	yes	complemented
351	C₃²	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented
352	C₂³	—	18	1	no	—
353	C₂³	—	18	4	no	—
354	C₂³	—	18	2	no	—
355	C₂³	—	36	4	no	—
356	C₂³	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
357	Q₈	—	9	2	no	—
358	Q₈	—	18	1	no	—
359	D₄	—	9	2	no	—
360	D₄	—	9	4	no	—
361	D₄	—	18	4	no	—
362	D₄	—	18	4	no	—
363	D₄	—	18	2	no	—
364	D₄	—	18	1	no	—
365	C₂×C₄	—	18	1	no	—
366	C₂×C₄	—	18	4	no	—
367	C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
368	C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
369	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
371	C₈	C₂²×C₃×C₃⋊D₃	1	4	yes	complemented
372	C₂×C₃	—	2	8	no	—
373	C₂×C₃	—	2	2	no	—
374	C₂×C₃	—	2	8	no	—
375	C₂×C₃	—	2	4	no	—
376	C₂×C₃	—	4	8	no	—
377	C₂×C₃	—	36	4	no	—
378	C₂×C₃	—	36	2	no	—
379	C₂×C₃	C₃×#908	1	8	yes	complemented
380	C₂×C₃	#64117	1	2	yes	direct product factor
381	C₂×C₃	C₂²×C₃×D₁₂	1	4	yes	—
382	C₂×C₃	C₂²×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
383	D₃	—	12	16	no	—
384	D₃	—	12	8	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	18	2	no	—
387	C₂²	—	18	4	no	—
388	C₂²	—	36	8	no	—
389	C₂²	—	36	4	no	—
390	C₂²	—	36	2	no	—
391	C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
392	C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
393	C₄	—	18	2	no	—
394	C₄	C₂×C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
395	C₄	C₂×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
396	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
397	C₃	—	2	4	no	—
398	C₃	C₂×C₃×#908	1	4	yes	complemented
399	C₃	C₂×#64117	1	1	yes	characteristic, direct product factor
400	C₂	—	2	2	no	—
401	C₂	—	36	4	no	—
402	C₂	—	36	2	no	—
403	C₂	C₃×#64117	1	2	yes	direct product factor
404	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
hypercenter	C₂×C₃×M₁₆	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×AGL(1,ℤ/8)
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
1. C₂×C₃×#3828	C₂	semidirect
2. C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	semidirect
3. C₂×C₃³×M₁₆	C₂	semidirect
4. C₃×#64117	C₂	direct (N × H)
5. C₂×C₃×#3745	C₂	semidirect
6. C₂×C₃×#3744	C₂	semidirect
7. C₂×#64117	C₃	direct (N × H)
13. C₃×#3828	C₂²	semidirect
17. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
18. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
20. C₂×C₃×#634	C₂²	semidirect
21. C₃³×M₁₆	C₂²	semidirect
22. C₂×C₃³×C₈	C₂²	semidirect
23. C₃×#3745	C₂²	semidirect
24. C₃×#3744	C₂²	semidirect
25. C₂×#3828	C₂×C₃	semidirect
26. C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
30. C₂×C₃²×M₁₆	D₃	semidirect
31. C₂×C₃²×M₁₆	C₂×C₃	semidirect
32. #64117	C₂×C₃	direct (N × H)
33. C₂×#3745	C₂×C₃	semidirect
34. C₂×#3744	C₂×C₃	semidirect
53. C₃×C₄⋊(C₃⋊D₃)	C₂³	semidirect
56. C₃×#634	C₂³	semidirect
57. C₃³×C₈	C₂³	semidirect
67. #3828	C₂²×C₃	semidirect
71. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
72. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
74. C₂×#634	C₂²×C₃	semidirect
86. C₃²×M₁₆	C₂×D₃	semidirect
87. C₃²×M₁₆	C₂²×C₃	semidirect
89. C₂×C₃²×C₈	C₂×D₃	semidirect
90. C₂×C₃²×C₈	C₂²×C₃	semidirect
91. #3745	C₂²×C₃	semidirect
92. #3744	C₂²×C₃	semidirect
115. C₂×C₃×M₁₆	C₃×D₃	semidirect
116. C₂×C₃×M₁₆	C₃⋊D₃	semidirect
149. C₄⋊(C₃⋊D₃)	C₂³×C₃	semidirect
152. #634	C₂³×C₃	semidirect
164. C₃²×C₈	C₂²×D₃	semidirect
165. C₃²×C₈	C₂³×C₃	semidirect
168. C₂×C₃³	AGL(1,ℤ/8)	semidirect
200. C₃×M₁₆	C₂×C₃×D₃	semidirect
201. C₃×M₁₆	C₂×C₃⋊D₃	semidirect
203. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
204. C₂×C₃×C₈	C₂×C₃⋊D₃	semidirect
242. C₂×M₁₆	C₃×C₃⋊D₃	semidirect
243. C₃³	C₂×AGL(1,ℤ/8)	semidirect
288. C₃×C₈	C₂²×C₃×D₃	semidirect
289. C₃×C₈	C₂²×C₃⋊D₃	semidirect
295. C₂×C₃²	#908	semidirect
296. C₂×C₃²	C₃×AGL(1,ℤ/8)	semidirect
317. M₁₆	C₂×C₃×C₃⋊D₃	semidirect
318. C₂×C₈	C₂×C₃×C₃⋊D₃	semidirect
350. C₃²	C₂×#908	semidirect
351. C₃²	C₂×C₃×AGL(1,ℤ/8)	semidirect
371. C₈	C₂²×C₃×C₃⋊D₃	semidirect
379. C₂×C₃	C₃×#908	semidirect
380. C₂×C₃	#64117	direct (N × H)
398. C₃	C₂×C₃×#908	semidirect
399. C₃	C₂×#64117	direct (N × H)
403. C₂	C₃×#64117	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×C₄⋊(C₃⋊D₃)	2
C₂×C₃³×M₁₆	2
C₃×#64117	2
C₂×C₃×#3745	2
C₂×C₃×#3744	2
C₂×#64117	3
C₂×C₃×#908	3

Subgroups — C2×C3×#64117 #13179497

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64117 #13179497