Subgroups — C₂×C₄×D₃×#157 #13180968

Order 1728.

1576 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₃×#157	C₂	1	2	yes	maximal
2	C₂×C₄×D₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₃⋊#157	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₄×#157	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₃×#157	C₂	1	2	yes	maximal, complemented
6	C₄×D₃×#157	C₂	1	8	yes	maximal, direct product factor
7	C₂²×C₄×#157	—	3	1	no	maximal
8	C₂²×D₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
9	C₂²×C₃⋊#157	C₂²	1	2	yes	—
10	C₂²×C₃×#157	C₂²	1	2	yes	—
11	C₂×D₃×#157	C₄	1	16	yes	direct product factor
12	C₂×D₃×#157	C₂²	1	8	yes	—
13	C₂×C₄×C₃⋊(C₃⋊D₃)	C₄	1	1	yes	characteristic, complemented
14	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
15	C₂×C₃²×C₄×D₃	C₄	1	1	yes	characteristic, complemented
16	C₂×#6289	C₄	1	1	yes	characteristic, complemented
17	C₂×Dic₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
18	C₂×D₃×C₃⋊Dic₃	C₄	1	1	yes	characteristic, complemented
19	C₄×D₃×C₃⋊D₃	C₄	1	4	yes	complemented
20	C₄×D₃×C₃⋊D₃	C₂²	1	4	yes	—
21	C₄×C₃⋊#157	C₂²	1	4	yes	complemented
22	C₃×C₄×#157	C₂²	1	4	yes	complemented
23	Dic₃×#157	C₂²	1	8	yes	complemented
24	C₂³×#157	—	3	2	no	—
25	C₂²×C₄×C₃⋊D₃	—	3	1	no	—
26	C₂×C₄×D₃²	—	6	2	no	—
27	C₂×C₄×#157	—	3	1	no	—
28	C₂×C₄×#157	—	3	8	no	—
29	C₂×C₄×#157	—	3	2	no	—
30	C₂×C₄×#157	D₃	1	1	yes	characteristic, direct product factor
31	C₂²×C₃⋊(C₃⋊D₃)	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
33	C₂²×C₃²×D₃	C₂×C₄	1	1	yes	characteristic
34	C₂×D₃×C₃⋊D₃	C₂×C₄	1	2	yes	—
35	C₂×D₃×C₃⋊D₃	C₂×C₄	1	8	yes	—
36	C₂×D₃×C₃⋊D₃	C₂³	1	2	yes	—
37	C₂×C₃⋊#157	C₂×C₄	1	8	yes	complemented
38	C₂×C₃⋊#157	C₂³	1	4	yes	—
39	C₂×C₃×#157	C₂×C₄	1	8	yes	complemented
40	C₂×C₃×#157	C₂³	1	4	yes	—
41	D₃×#157	C₂×C₄	1	32	yes	direct product factor
42	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic, complemented
43	C₂×C₃⋊(C₃⋊Dic₃)	C₂×C₄	1	1	yes	characteristic, complemented
44	C₄×C₃⋊(C₃⋊D₃)	C₂×C₄	1	4	yes	complemented
45	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic, complemented
46	C₃×C₄×C₃⋊D₃	C₂×C₄	1	2	yes	complemented
47	C₃×C₄×C₃⋊D₃	C₂³	1	2	yes	—
48	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic, complemented
49	C₃²×C₄×D₃	C₂×C₄	1	4	yes	complemented
50	#6289	C₂×C₄	1	4	yes	complemented
51	Dic₃×C₃⋊D₃	C₂×C₄	1	2	yes	complemented
52	Dic₃×C₃⋊D₃	C₂³	1	2	yes	—
53	D₃×C₃⋊Dic₃	C₂×C₄	1	4	yes	complemented
54	C₂×C₄²×D₃	—	9	1	no	maximal
55	C₂³×C₃⋊D₃	—	3	1	no	—
56	C₂²×D₃²	—	6	2	no	—
57	C₂²×#157	—	3	2	no	—
58	C₂²×#157	—	3	16	no	—
59	C₂²×#157	—	3	8	no	—
60	C₂²×#157	C₂×D₃	1	2	yes	—
61	C₂²×C₃²×C₄	—	3	1	no	—
62	C₂²×C₃⋊Dic₃	—	3	1	no	—
63	C₂×C₄×C₃⋊D₃	—	3	1	no	—
64	C₂×C₄×C₃⋊D₃	—	3	1	no	—
65	C₂×C₄×C₃⋊D₃	—	3	1	no	—
66	C₂×C₄×C₃⋊D₃	—	3	4	no	—
67	C₂×C₄×C₃⋊D₃	—	3	4	no	—
68	C₂×C₄×C₃⋊D₃	—	6	2	no	—
69	C₂×C₄×C₃⋊D₃	—	12	2	no	—
70	C₂×C₄×C₃⋊D₃	C₂×D₃	1	1	yes	characteristic
71	C₂×C₃×C₄×D₃	—	2	2	no	—
72	C₂×C₃×C₄×D₃	—	6	2	no	—
73	C₂×#624	—	6	2	no	—
74	C₂×D₃×Dic₃	—	6	2	no	—
75	C₂×D₃×Dic₃	—	6	2	no	—
76	C₄×D₃²	—	6	8	no	—
77	C₄×D₃²	—	6	8	no	—
78	C₄×#157	—	3	8	no	—
79	C₄×#157	—	3	4	no	—
80	C₄×#157	C₂×D₃	1	4	yes	direct product factor
81	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₃⋊(C₃⋊D₃)	C₄²	1	4	yes	complemented
83	C₂×C₃⋊(C₃⋊D₃)	C₂²×C₄	1	2	yes	—
84	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	4	yes	—
86	C₂×C₃×C₃⋊D₃	C₂⁴	1	1	yes	characteristic
87	C₂×C₃²×D₃	C₄²	1	4	yes	complemented
88	C₂×C₃²×D₃	C₂²×C₄	1	2	yes	—
89	D₃×C₃⋊D₃	C₄²	1	8	yes	complemented
90	D₃×C₃⋊D₃	C₂²×C₄	1	8	yes	—
91	C₃⋊#157	C₂²×C₄	1	8	yes	complemented
92	C₃×#157	C₂²×C₄	1	8	yes	complemented
93	C₃³×C₄	C₂²×C₄	1	2	yes	complemented
94	C₃⋊(C₃⋊Dic₃)	C₂²×C₄	1	2	yes	complemented
95	C₃×C₃⋊Dic₃	C₂²×C₄	1	2	yes	complemented
96	C₃²×Dic₃	C₂²×C₄	1	2	yes	complemented
97	C₂²×C₄×D₃	—	9	2	no	—
98	C₂²×C₄×D₃	—	9	1	no	—
99	C₂²×C₄×D₃	—	18	2	no	—
100	C₂×C₃×C₄²	—	9	1	no	—
101	C₂×C₄×Dic₃	—	9	1	no	—
102	C₂×C₄×Dic₃	—	9	2	no	—
103	C₄²×D₃	—	9	8	no	—
104	C₂³×C₃²	—	3	1	no	—
105	C₂²×C₃⋊D₃	—	3	1	no	—
106	C₂²×C₃⋊D₃	—	3	8	no	—
107	C₂²×C₃⋊D₃	—	3	2	no	—
108	C₂²×C₃⋊D₃	—	3	2	no	—
109	C₂²×C₃⋊D₃	—	6	2	no	—
110	C₂²×C₃⋊D₃	—	12	2	no	—
111	C₂²×C₃⋊D₃	C₂²×D₃	1	1	yes	characteristic
112	C₂²×C₃×D₃	—	2	2	no	—
113	C₂²×C₃×D₃	—	6	2	no	—
114	C₂×D₃²	—	6	16	no	—
115	C₂×D₃²	—	6	4	no	—
116	C₂×D₃²	—	6	4	no	—
117	C₂×#157	—	3	8	no	—
118	C₂×#157	—	3	4	no	—
119	C₂×#157	—	3	32	no	—
120	C₂×#157	C₄×D₃	1	8	yes	direct product factor
121	C₂×#157	C₂²×D₃	1	4	yes	—
122	C₂×C₃²×C₄	—	2	2	no	—
123	C₂×C₃²×C₄	—	3	1	no	—
124	C₂×C₃²×C₄	—	3	4	no	—
125	C₂×C₃²×C₄	—	4	2	no	—
126	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic, complemented
127	C₂×C₃⋊Dic₃	—	3	1	no	—
128	C₂×C₃⋊Dic₃	—	3	4	no	—
129	C₂×C₃⋊Dic₃	—	6	2	no	—
130	C₂×C₃⋊Dic₃	—	12	2	no	—
131	C₂×C₃⋊Dic₃	C₄×D₃	1	1	yes	characteristic, complemented
132	C₄×C₃⋊D₃	—	3	2	no	—
133	C₄×C₃⋊D₃	—	3	2	no	—
134	C₄×C₃⋊D₃	—	3	4	no	—
135	C₄×C₃⋊D₃	—	3	4	no	—
136	C₄×C₃⋊D₃	—	6	8	no	—
137	C₄×C₃⋊D₃	—	12	8	no	—
138	C₄×C₃⋊D₃	C₄×D₃	1	2	yes	complemented
139	C₄×C₃⋊D₃	C₂²×D₃	1	2	yes	—
140	C₂×C₃×Dic₃	—	2	2	no	—
141	C₂×C₃×Dic₃	—	6	2	no	—
142	C₃×C₄×D₃	—	2	8	no	—
143	C₃×C₄×D₃	—	6	4	no	—
144	C₃×C₄×D₃	—	6	4	no	—
145	#624	—	6	8	no	—
146	D₃×Dic₃	—	6	8	no	—
147	D₃×Dic₃	—	6	4	no	—
148	D₃×Dic₃	—	6	4	no	—
149	C₂²×C₄²	—	27	1	no	Sylow
150	C₂×C₃³	C₂×C₄²	1	2	yes	complemented
151	C₂×C₃³	C₂³×C₄	1	1	yes	characteristic
152	C₃⋊(C₃⋊D₃)	C₂×C₄²	1	4	yes	complemented
153	C₃×C₃⋊D₃	C₂×C₄²	1	2	yes	complemented
154	C₃×C₃⋊D₃	C₂³×C₄	1	2	yes	—
155	C₃²×D₃	C₂×C₄²	1	4	yes	complemented
156	C₂³×D₃	—	9	1	no	—
157	C₂³×D₃	—	18	2	no	—
158	C₂²×C₃×C₄	—	6	2	no	—
159	C₂²×C₃×C₄	—	9	2	no	—
160	C₂²×C₃×C₄	—	9	1	no	—
161	C₂²×Dic₃	—	9	2	no	—
162	C₂²×Dic₃	—	9	1	no	—
163	C₂²×Dic₃	—	18	2	no	—
164	C₂×C₄×D₃	—	6	2	no	—
165	C₂×C₄×D₃	—	9	16	no	—
166	C₂×C₄×D₃	—	9	8	no	—
167	C₂×C₄×D₃	—	9	1	no	—
168	C₂×C₄×D₃	—	9	1	no	—
169	C₂×C₄×D₃	—	9	1	no	—
170	C₂×C₄×D₃	—	9	4	no	—
171	C₂×C₄×D₃	—	9	4	no	—
172	C₂×C₄×D₃	—	18	8	no	—
173	C₂×C₄×D₃	—	18	8	no	—
174	C₂×C₄×D₃	—	18	2	no	—
175	C₂×C₄×D₃	—	18	2	no	—
176	C₂×C₄×D₃	—	18	2	no	—
177	C₂×C₄×D₃	—	36	2	no	—
178	C₂×C₄×D₃	#157	1	1	yes	characteristic, direct product factor
179	C₃×C₄²	—	9	4	no	—
180	C₄×Dic₃	—	9	8	no	—
181	C₄×Dic₃	—	9	4	no	—
182	C₂²×C₃²	—	2	2	no	—
183	C₂²×C₃²	—	3	4	no	—
184	C₂²×C₃²	—	3	2	no	—
185	C₂²×C₃²	—	4	2	no	—
186	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
187	C₂×C₃⋊D₃	—	3	4	no	—
188	C₂×C₃⋊D₃	—	3	2	no	—
189	C₂×C₃⋊D₃	—	3	8	no	—
190	C₂×C₃⋊D₃	—	3	8	no	—
191	C₂×C₃⋊D₃	—	6	8	no	—
192	C₂×C₃⋊D₃	—	6	4	no	—
193	C₂×C₃⋊D₃	—	12	8	no	—
194	C₂×C₃⋊D₃	—	12	4	no	—
195	C₂×C₃⋊D₃	C₂×C₄×D₃	1	1	yes	characteristic
196	C₂×C₃⋊D₃	C₂×C₄×D₃	1	4	yes	—
197	C₂×C₃⋊D₃	C₂³×D₃	1	1	yes	characteristic
198	C₂×C₃×D₃	—	2	4	no	—
199	C₂×C₃×D₃	—	2	8	no	—
200	C₂×C₃×D₃	—	6	2	no	—
201	C₂×C₃×D₃	—	6	8	no	—
202	C₂×C₃×D₃	—	6	2	no	—
203	D₃²	—	6	16	no	—
204	D₃²	—	6	16	no	—
205	#157	—	3	8	no	—
206	#157	C₂×C₄×D₃	1	8	yes	direct product factor
207	C₃²×C₄	—	2	4	no	—
208	C₃²×C₄	—	3	2	no	—
209	C₃²×C₄	—	4	4	no	—
210	C₃²×C₄	C₂×C₄×D₃	1	2	yes	complemented
211	C₃⋊Dic₃	—	3	2	no	—
212	C₃⋊Dic₃	—	6	4	no	—
213	C₃⋊Dic₃	—	12	4	no	—
214	C₃⋊Dic₃	C₂×C₄×D₃	1	2	yes	complemented
215	C₃×Dic₃	—	2	4	no	—
216	C₃×Dic₃	—	6	4	no	—
217	C₂³×C₄	—	27	1	no	—
218	C₂³×C₄	—	27	2	no	—
219	C₂×C₄²	—	9	1	no	—
220	C₂×C₄²	—	27	8	no	—
221	C₂×C₄²	—	27	2	no	—
222	C₂×C₄²	—	27	1	no	—
223	C₃³	C₂²×C₄²	1	1	yes	characteristic, complemented, Sylow
224	C₂³×C₃	—	6	2	no	—
225	C₂³×C₃	—	9	1	no	—
226	C₂²×D₃	—	6	2	no	—
227	C₂²×D₃	—	9	1	no	—
228	C₂²×D₃	—	9	2	no	—
229	C₂²×D₃	—	9	2	no	—
230	C₂²×D₃	—	9	8	no	—
231	C₂²×D₃	—	18	4	no	—
232	C₂²×D₃	—	18	4	no	—
233	C₂²×D₃	—	18	16	no	—
234	C₂²×D₃	—	18	2	no	—
235	C₂²×D₃	—	36	2	no	—
236	C₂²×D₃	C₂×#157	1	1	yes	characteristic
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	4	2	no	—
239	C₂×C₃×C₄	—	6	8	no	—
240	C₂×C₃×C₄	—	6	2	no	—
241	C₂×C₃×C₄	—	9	8	no	—
242	C₂×C₃×C₄	—	9	4	no	—
243	C₂×C₃×C₄	—	9	1	no	—
244	C₂×C₃×C₄	—	9	2	no	—
245	C₂×C₃×C₄	—	9	2	no	—
246	C₂×C₃×C₄	C₂×#157	1	1	yes	characteristic, complemented
247	C₂×Dic₃	—	6	2	no	—
248	C₂×Dic₃	—	9	8	no	—
249	C₂×Dic₃	—	9	4	no	—
250	C₂×Dic₃	—	9	1	no	—
251	C₂×Dic₃	—	9	2	no	—
252	C₂×Dic₃	—	9	2	no	—
253	C₂×Dic₃	—	18	8	no	—
254	C₂×Dic₃	—	18	2	no	—
255	C₂×Dic₃	—	36	2	no	—
256	C₂×Dic₃	C₂×#157	1	1	yes	characteristic, complemented
257	C₄×D₃	—	6	4	no	—
258	C₄×D₃	—	6	4	no	—
259	C₄×D₃	—	9	32	no	—
260	C₄×D₃	—	9	4	no	—
261	C₄×D₃	—	9	4	no	—
262	C₄×D₃	—	9	4	no	—
263	C₄×D₃	—	18	8	no	—
264	C₄×D₃	—	18	8	no	—
265	C₄×D₃	—	18	4	no	—
266	C₄×D₃	—	18	4	no	—
267	C₄×D₃	—	36	8	no	—
268	C₄×D₃	C₂×#157	1	4	yes	direct product factor
269	C₂×C₃²	—	2	4	no	—
270	C₂×C₃²	—	2	2	no	—
271	C₂×C₃²	—	3	4	no	—
272	C₂×C₃²	—	4	4	no	—
273	C₂×C₃²	—	4	2	no	—
274	C₂×C₃²	C₄²×D₃	1	2	yes	complemented
275	C₂×C₃²	C₂²×C₄×D₃	1	1	yes	characteristic
276	C₃⋊D₃	—	3	4	no	—
277	C₃⋊D₃	—	6	8	no	—
278	C₃⋊D₃	—	12	8	no	—
279	C₃⋊D₃	C₄²×D₃	1	2	yes	complemented
280	C₃⋊D₃	C₂²×C₄×D₃	1	2	yes	—
281	C₃×D₃	—	2	8	no	—
282	C₃×D₃	—	6	4	no	—
283	C₃×D₃	—	6	4	no	—
284	C₂⁴	—	27	1	no	—
285	C₂²×C₄	—	3	1	no	—
286	C₂²×C₄	—	9	2	no	—
287	C₂²×C₄	—	9	1	no	—
288	C₂²×C₄	—	27	4	no	—
289	C₂²×C₄	—	27	1	no	—
290	C₂²×C₄	—	27	4	no	—
291	C₂²×C₄	—	27	1	no	—
292	C₂²×C₄	—	27	1	no	—
293	C₂²×C₄	—	27	8	no	—
294	C₂²×C₄	—	27	16	no	—
295	C₂²×C₄	—	27	2	no	—
296	C₂²×C₄	—	27	1	no	—
297	C₄²	—	9	4	no	—
298	C₄²	—	27	8	no	—
299	C₄²	—	27	4	no	—
300	C₂²×C₃	—	2	2	no	—
301	C₂²×C₃	—	4	2	no	—
302	C₂²×C₃	—	6	4	no	—
303	C₂²×C₃	—	6	8	no	—
304	C₂²×C₃	—	9	4	no	—
305	C₂²×C₃	—	9	1	no	—
306	C₂²×C₃	—	9	1	no	—
307	C₂²×C₃	C₂²×#157	1	1	yes	characteristic
308	C₂×D₃	—	6	2	no	—
309	C₂×D₃	—	6	2	no	—
310	C₂×D₃	—	6	8	no	—
311	C₂×D₃	—	9	4	no	—
312	C₂×D₃	—	9	2	no	—
313	C₂×D₃	—	9	8	no	—
314	C₂×D₃	—	9	8	no	—
315	C₂×D₃	—	18	16	no	—
316	C₂×D₃	—	18	16	no	—
317	C₂×D₃	—	18	4	no	—
318	C₂×D₃	—	18	8	no	—
319	C₂×D₃	—	36	4	no	—
320	C₂×D₃	—	36	8	no	—
321	C₂×D₃	C₄×#157	1	4	yes	direct product factor
322	C₂×D₃	C₂²×#157	1	2	yes	—
323	C₃×C₄	—	2	4	no	—
324	C₃×C₄	—	4	4	no	—
325	C₃×C₄	—	6	4	no	—
326	C₃×C₄	—	9	8	no	—
327	C₃×C₄	—	9	2	no	—
328	C₃×C₄	C₂²×#157	1	2	yes	complemented
329	Dic₃	—	6	4	no	—
330	Dic₃	—	9	8	no	—
331	Dic₃	—	9	2	no	—
332	Dic₃	—	18	4	no	—
333	Dic₃	—	36	4	no	—
334	Dic₃	C₂²×#157	1	2	yes	complemented
335	C₃²	—	2	2	no	—
336	C₃²	—	4	2	no	—
337	C₃²	C₂×C₄²×D₃	1	1	yes	characteristic, complemented
338	C₂³	—	3	1	no	—
339	C₂³	—	9	1	no	—
340	C₂³	—	27	2	no	—
341	C₂³	—	27	2	no	—
342	C₂³	—	27	8	no	—
343	C₂³	—	27	1	no	—
344	C₂×C₄	—	3	1	no	—
345	C₂×C₄	—	3	4	no	—
346	C₂×C₄	—	9	4	no	—
347	C₂×C₄	—	9	8	no	—
348	C₂×C₄	—	9	1	no	—
349	C₂×C₄	—	9	2	no	—
350	C₂×C₄	—	9	2	no	—
351	C₂×C₄	—	27	4	no	—
352	C₂×C₄	—	27	2	no	—
353	C₂×C₄	—	27	2	no	—
354	C₂×C₄	—	27	4	no	—
355	C₂×C₄	—	27	32	no	—
356	C₂×C₄	—	27	4	no	—
357	C₂×C₄	—	27	8	no	—
358	C₂×C₄	—	27	1	no	—
359	C₂×C₄	—	27	4	no	—
360	C₂×C₄	D₃×#157	1	1	yes	characteristic, direct product factor
361	C₂×C₃	—	2	2	no	—
362	C₂×C₃	—	2	4	no	—
363	C₂×C₃	—	4	2	no	—
364	C₂×C₃	—	4	4	no	—
365	C₂×C₃	—	6	8	no	—
366	C₂×C₃	—	9	2	no	—
367	C₂×C₃	—	9	2	no	—
368	C₂×C₃	C₂×C₄×#157	1	2	yes	complemented
369	C₂×C₃	C₂³×#157	1	1	yes	characteristic
370	D₃	—	6	4	no	—
371	D₃	—	6	4	no	—
372	D₃	—	9	4	no	—
373	D₃	—	18	8	no	—
374	D₃	—	36	8	no	—
375	D₃	C₂×C₄×#157	1	4	yes	direct product factor
376	C₂²	—	3	2	no	—
377	C₂²	—	3	4	no	—
378	C₂²	—	9	1	no	—
379	C₂²	—	9	1	no	—
380	C₂²	—	9	4	no	—
381	C₂²	—	27	8	no	—
382	C₂²	—	27	8	no	—
383	C₂²	—	27	2	no	—
384	C₂²	—	27	4	no	—
385	C₂²	C₂×D₃×#157	1	1	yes	characteristic
386	C₄	—	3	2	no	—
387	C₄	—	9	8	no	—
388	C₄	—	9	2	no	—
389	C₄	—	27	8	no	—
390	C₄	—	27	2	no	—
391	C₄	C₂×D₃×#157	1	2	yes	direct product factor
392	C₃	—	2	2	no	—
393	C₃	—	4	2	no	—
394	C₃	C₂²×C₄×#157	1	1	yes	characteristic, complemented
395	C₂	—	3	4	no	—
396	C₂	—	9	2	no	—
397	C₂	—	9	2	no	—
398	C₂	—	27	4	no	—
399	C₂	C₄×D₃×#157	1	2	yes	direct product factor
400	C₂	C₂²×D₃×#157	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₃×#157
commutator, hypocenter	C₃³	C₂²×C₄²
Frattini	C₂	C₂²×D₃×#157
Fitting	C₂×C₃³×C₄	C₂×C₄
socle	C₂²×C₃³	C₂²×C₄
prime radical	C₂²×D₃×C₃⋊D₃	C₂²
cosocle	C₂×C₃×C₃⋊D₃	C₂⁴
LCS	G ▷ C₃³
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₃⋊#157	C₂	semidirect
4. C₂×C₃×C₄×#157	C₂	semidirect
5. C₂×Dic₃×#157	C₂	semidirect
6. C₄×D₃×#157	C₂	direct (N × H)
11. C₂×D₃×#157	C₄	direct (N × H)
13. C₂×C₄×C₃⋊(C₃⋊D₃)	C₄	semidirect
15. C₂×C₃²×C₄×D₃	C₄	semidirect
16. C₂×#6289	C₄	semidirect
18. C₂×D₃×C₃⋊Dic₃	C₄	semidirect
19. C₄×D₃×C₃⋊D₃	C₄	semidirect
21. C₄×C₃⋊#157	C₂²	semidirect
22. C₃×C₄×#157	C₂²	semidirect
23. Dic₃×#157	C₂²	semidirect
30. C₂×C₄×#157	D₃	direct (N × H)
37. C₂×C₃⋊#157	C₂×C₄	semidirect
39. C₂×C₃×#157	C₂×C₄	semidirect
41. D₃×#157	C₂×C₄	direct (N × H)
42. C₂×C₃³×C₄	C₂×C₄	semidirect
43. C₂×C₃⋊(C₃⋊Dic₃)	C₂×C₄	semidirect
44. C₄×C₃⋊(C₃⋊D₃)	C₂×C₄	semidirect
45. C₂×C₃×C₃⋊Dic₃	C₂×C₄	semidirect
46. C₃×C₄×C₃⋊D₃	C₂×C₄	semidirect
48. C₂×C₃²×Dic₃	C₂×C₄	semidirect
49. C₃²×C₄×D₃	C₂×C₄	semidirect
50. #6289	C₂×C₄	semidirect
51. Dic₃×C₃⋊D₃	C₂×C₄	semidirect
53. D₃×C₃⋊Dic₃	C₂×C₄	semidirect
80. C₄×#157	C₂×D₃	direct (N × H)
82. C₂×C₃⋊(C₃⋊D₃)	C₄²	semidirect
87. C₂×C₃²×D₃	C₄²	semidirect
89. D₃×C₃⋊D₃	C₄²	semidirect
91. C₃⋊#157	C₂²×C₄	semidirect
92. C₃×#157	C₂²×C₄	semidirect
93. C₃³×C₄	C₂²×C₄	semidirect
94. C₃⋊(C₃⋊Dic₃)	C₂²×C₄	semidirect
95. C₃×C₃⋊Dic₃	C₂²×C₄	semidirect
96. C₃²×Dic₃	C₂²×C₄	semidirect
120. C₂×#157	C₄×D₃	direct (N × H)
126. C₂×C₃²×C₄	C₄×D₃	semidirect
131. C₂×C₃⋊Dic₃	C₄×D₃	semidirect
138. C₄×C₃⋊D₃	C₄×D₃	semidirect
150. C₂×C₃³	C₂×C₄²	semidirect
152. C₃⋊(C₃⋊D₃)	C₂×C₄²	semidirect
153. C₃×C₃⋊D₃	C₂×C₄²	semidirect
155. C₃²×D₃	C₂×C₄²	semidirect
178. C₂×C₄×D₃	#157	direct (N × H)
206. #157	C₂×C₄×D₃	direct (N × H)
210. C₃²×C₄	C₂×C₄×D₃	semidirect
214. C₃⋊Dic₃	C₂×C₄×D₃	semidirect
223. C₃³	C₂²×C₄²	semidirect
246. C₂×C₃×C₄	C₂×#157	semidirect
256. C₂×Dic₃	C₂×#157	semidirect
268. C₄×D₃	C₂×#157	direct (N × H)
274. C₂×C₃²	C₄²×D₃	semidirect
279. C₃⋊D₃	C₄²×D₃	semidirect
321. C₂×D₃	C₄×#157	direct (N × H)
328. C₃×C₄	C₂²×#157	semidirect
334. Dic₃	C₂²×#157	semidirect
337. C₃²	C₂×C₄²×D₃	semidirect
360. C₂×C₄	D₃×#157	direct (N × H)
368. C₂×C₃	C₂×C₄×#157	semidirect
375. D₃	C₂×C₄×#157	direct (N × H)
391. C₄	C₂×D₃×#157	direct (N × H)
394. C₃	C₂²×C₄×#157	semidirect
399. C₂	C₄×D₃×#157	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₃×#157	2
C₂×C₄×D₃×C₃⋊D₃	2
C₂×C₄×C₃⋊#157	2
C₂×C₃×C₄×#157	2
C₂×Dic₃×#157	2
C₄×D₃×#157	2
C₂²×C₄×#157	3
C₂×C₄²×D₃	9

Subgroups — C2×C4×D3×#157 #13180968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×D₃×#157 #13180968