Subgroups — C₂×D₃×C₄⋊#157 #13180970

Order 1728.

1416 conjugacy classes of subgroups.

The subgroup lattice has 426 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	D₃×C₄⋊#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	—	2	8	no	—
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	D₄	1	4	yes	—
36	C₂×D₃×C₃⋊D₃	Q₈	1	4	yes	—
37	C₂×D₃×C₃⋊D₃	C₂³	1	2	yes	—
38	C₂×C₃⋊#157	—	2	4	no	—
39	C₂×C₃⋊#157	C₂³	1	4	yes	—
40	C₂×C₃×#157	—	2	4	no	—
41	C₂×C₃×#157	C₂³	1	4	yes	—
42	D₃×#157	—	2	16	no	—
43	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic, complemented
44	C₂×C₃⋊(C₃⋊Dic₃)	C₂×C₄	1	1	yes	characteristic, complemented
45	C₄×C₃⋊(C₃⋊D₃)	C₂×C₄	1	4	yes	complemented
46	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic, complemented
47	C₃×C₄×C₃⋊D₃	C₂×C₄	1	2	yes	complemented
48	C₃×C₄×C₃⋊D₃	C₂³	1	2	yes	—
49	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic, complemented
50	C₃²×C₄×D₃	C₂×C₄	1	4	yes	complemented
51	#6289	C₂×C₄	1	4	yes	complemented
52	Dic₃×C₃⋊D₃	C₂×C₄	1	2	yes	complemented
53	Dic₃×C₃⋊D₃	C₂³	1	2	yes	—
54	D₃×C₃⋊Dic₃	C₂×C₄	1	4	yes	complemented
55	C₂×D₃×C₄⋊C₄	—	9	1	no	maximal
56	C₂³×C₃⋊D₃	—	3	1	no	—
57	C₂²×D₃²	—	6	2	no	—
58	C₂²×#157	—	3	2	no	—
59	C₂²×#157	—	3	8	no	—
60	C₂²×#157	—	6	8	no	—
61	C₂²×#157	C₂×D₃	1	2	yes	—
62	C₂²×C₃²×C₄	—	3	1	no	—
63	C₂²×C₃⋊Dic₃	—	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	1	no	—
67	C₂×C₄×C₃⋊D₃	—	3	4	no	—
68	C₂×C₄×C₃⋊D₃	—	3	4	no	—
69	C₂×C₄×C₃⋊D₃	—	6	2	no	—
70	C₂×C₄×C₃⋊D₃	—	12	2	no	—
71	C₂×C₄×C₃⋊D₃	C₂×D₃	1	1	yes	characteristic
72	C₂×C₃×C₄×D₃	—	2	2	no	—
73	C₂×C₃×C₄×D₃	—	6	2	no	—
74	C₂×#624	—	6	2	no	—
75	C₂×D₃×Dic₃	—	6	2	no	—
76	C₂×D₃×Dic₃	—	6	2	no	—
77	C₄×D₃²	—	6	8	no	—
78	C₄×D₃²	—	6	8	no	—
79	C₄⋊#157	—	3	8	no	—
80	C₄⋊#157	—	3	4	no	—
81	C₄⋊#157	C₂×D₃	1	4	yes	direct product factor
82	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₃⋊(C₃⋊D₃)	C₄⋊C₄	1	4	yes	complemented
84	C₂×C₃⋊(C₃⋊D₃)	C₂²×C₄	1	2	yes	—
85	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₃×C₃⋊D₃	C₂×D₄	1	2	yes	—
87	C₂×C₃×C₃⋊D₃	C₂×Q₈	1	2	yes	—
88	C₂×C₃×C₃⋊D₃	C₂⁴	1	1	yes	characteristic
89	C₂×C₃²×D₃	C₄⋊C₄	1	4	yes	complemented
90	C₂×C₃²×D₃	C₂²×C₄	1	2	yes	—
91	D₃×C₃⋊D₃	C₄⋊C₄	1	8	yes	complemented
92	D₃×C₃⋊D₃	C₂×D₄	1	4	yes	—
93	D₃×C₃⋊D₃	C₂×Q₈	1	4	yes	—
94	C₃⋊#157	—	2	4	no	—
95	C₃×#157	—	2	4	no	—
96	C₃³×C₄	C₂²×C₄	1	2	yes	complemented
97	C₃⋊(C₃⋊Dic₃)	C₂²×C₄	1	2	yes	complemented
98	C₃×C₃⋊Dic₃	C₂²×C₄	1	2	yes	complemented
99	C₃²×Dic₃	C₂²×C₄	1	2	yes	complemented
100	C₂²×C₄×D₃	—	9	1	no	—
101	C₂²×C₄×D₃	—	9	2	no	—
102	C₂²×C₄×D₃	—	18	2	no	—
103	C₂×C₃×C₄⋊C₄	—	9	1	no	—
104	C₂×C₄⋊Dic₃	—	9	1	no	—
105	C₂×Dic₃⋊C₄	—	9	2	no	—
106	D₃×C₄⋊C₄	—	9	8	no	—
107	C₂³×C₃²	—	3	1	no	—
108	C₂²×C₃⋊D₃	—	3	1	no	—
109	C₂²×C₃⋊D₃	—	3	2	no	—
110	C₂²×C₃⋊D₃	—	3	4	no	—
111	C₂²×C₃⋊D₃	—	3	4	no	—
112	C₂²×C₃⋊D₃	—	3	2	no	—
113	C₂²×C₃⋊D₃	—	6	2	no	—
114	C₂²×C₃⋊D₃	—	12	2	no	—
115	C₂²×C₃⋊D₃	C₂²×D₃	1	1	yes	characteristic
116	C₂²×C₃×D₃	—	2	2	no	—
117	C₂²×C₃×D₃	—	6	2	no	—
118	C₂×D₃²	—	6	4	no	—
119	C₂×D₃²	—	6	8	no	—
120	C₂×D₃²	—	6	8	no	—
121	C₂×D₃²	—	6	4	no	—
122	C₂×#157	—	2	4	no	—
123	C₂×#157	—	3	4	no	—
124	C₂×#157	—	6	16	no	—
125	C₂×#157	—	6	4	no	—
126	C₂×#157	C₂²×D₃	1	4	yes	—
127	C₂×C₃²×C₄	—	2	2	no	—
128	C₂×C₃²×C₄	—	3	1	no	—
129	C₂×C₃²×C₄	—	3	4	no	—
130	C₂×C₃²×C₄	—	4	2	no	—
131	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic, complemented
132	C₂×C₃⋊Dic₃	—	3	1	no	—
133	C₂×C₃⋊Dic₃	—	3	4	no	—
134	C₂×C₃⋊Dic₃	—	6	2	no	—
135	C₂×C₃⋊Dic₃	—	12	2	no	—
136	C₂×C₃⋊Dic₃	C₄×D₃	1	1	yes	characteristic, complemented
137	C₄×C₃⋊D₃	—	3	2	no	—
138	C₄×C₃⋊D₃	—	3	2	no	—
139	C₄×C₃⋊D₃	—	3	4	no	—
140	C₄×C₃⋊D₃	—	3	4	no	—
141	C₄×C₃⋊D₃	—	6	8	no	—
142	C₄×C₃⋊D₃	—	12	8	no	—
143	C₄×C₃⋊D₃	C₄×D₃	1	2	yes	complemented
144	C₄×C₃⋊D₃	C₂²×D₃	1	2	yes	—
145	C₂×C₃×Dic₃	—	2	2	no	—
146	C₂×C₃×Dic₃	—	6	2	no	—
147	C₃×C₄×D₃	—	2	8	no	—
148	C₃×C₄×D₃	—	6	4	no	—
149	C₃×C₄×D₃	—	6	4	no	—
150	#624	—	6	8	no	—
151	D₃×Dic₃	—	6	8	no	—
152	D₃×Dic₃	—	6	4	no	—
153	D₃×Dic₃	—	6	4	no	—
154	C₂²×C₄⋊C₄	—	27	1	no	Sylow
155	C₂×C₃³	C₂×C₄⋊C₄	1	2	yes	complemented
156	C₂×C₃³	C₂³×C₄	1	1	yes	characteristic
157	C₃⋊(C₃⋊D₃)	C₂×C₄⋊C₄	1	4	yes	complemented
158	C₃×C₃⋊D₃	C₂×C₄⋊C₄	1	2	yes	complemented
159	C₃×C₃⋊D₃	C₂²×D₄	1	1	yes	characteristic
160	C₃×C₃⋊D₃	C₂²×Q₈	1	1	yes	characteristic
161	C₃²×D₃	C₂×C₄⋊C₄	1	4	yes	complemented
162	C₂³×D₃	—	9	1	no	—
163	C₂³×D₃	—	18	2	no	—
164	C₂²×C₃×C₄	—	6	2	no	—
165	C₂²×C₃×C₄	—	9	1	no	—
166	C₂²×C₃×C₄	—	9	2	no	—
167	C₂²×Dic₃	—	9	1	no	—
168	C₂²×Dic₃	—	9	2	no	—
169	C₂²×Dic₃	—	18	2	no	—
170	C₂×C₄×D₃	—	6	2	no	—
171	C₂×C₄×D₃	—	9	1	no	—
172	C₂×C₄×D₃	—	9	1	no	—
173	C₂×C₄×D₃	—	9	1	no	—
174	C₂×C₄×D₃	—	9	4	no	—
175	C₂×C₄×D₃	—	9	4	no	—
176	C₂×C₄×D₃	—	9	8	no	—
177	C₂×C₄×D₃	—	18	8	no	—
178	C₂×C₄×D₃	—	18	8	no	—
179	C₂×C₄×D₃	—	18	2	no	—
180	C₂×C₄×D₃	—	18	2	no	—
181	C₂×C₄×D₃	—	18	2	no	—
182	C₂×C₄×D₃	—	18	8	no	—
183	C₂×C₄×D₃	—	36	2	no	—
184	C₂×C₄×D₃	#157	1	1	yes	characteristic, complemented
185	C₃×C₄⋊C₄	—	9	4	no	—
186	C₄⋊Dic₃	—	9	4	no	—
187	Dic₃⋊C₄	—	9	8	no	—
188	C₂²×C₃²	—	2	2	no	—
189	C₂²×C₃²	—	3	4	no	—
190	C₂²×C₃²	—	3	2	no	—
191	C₂²×C₃²	—	4	2	no	—
192	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
193	C₂×C₃⋊D₃	—	3	4	no	—
194	C₂×C₃⋊D₃	—	3	2	no	—
195	C₂×C₃⋊D₃	—	3	8	no	—
196	C₂×C₃⋊D₃	—	3	4	no	—
197	C₂×C₃⋊D₃	—	3	4	no	—
198	C₂×C₃⋊D₃	—	6	8	no	—
199	C₂×C₃⋊D₃	—	6	4	no	—
200	C₂×C₃⋊D₃	—	12	8	no	—
201	C₂×C₃⋊D₃	—	12	4	no	—
202	C₂×C₃⋊D₃	C₂×C₄×D₃	1	1	yes	characteristic
203	C₂×C₃⋊D₃	D₃×D₄	1	2	yes	—
204	C₂×C₃⋊D₃	D₃×Q₈	1	2	yes	—
205	C₂×C₃⋊D₃	C₂³×D₃	1	1	yes	characteristic
206	C₂×C₃×D₃	—	2	4	no	—
207	C₂×C₃×D₃	—	2	8	no	—
208	C₂×C₃×D₃	—	6	2	no	—
209	C₂×C₃×D₃	—	6	4	no	—
210	C₂×C₃×D₃	—	6	4	no	—
211	C₂×C₃×D₃	—	6	2	no	—
212	D₃²	—	6	16	no	—
213	D₃²	—	6	8	no	—
214	D₃²	—	6	8	no	—
215	#157	—	2	4	no	—
216	#157	—	6	4	no	—
217	C₃²×C₄	—	2	4	no	—
218	C₃²×C₄	—	3	2	no	—
219	C₃²×C₄	—	4	4	no	—
220	C₃²×C₄	C₂×C₄×D₃	1	2	yes	complemented
221	C₃⋊Dic₃	—	3	2	no	—
222	C₃⋊Dic₃	—	6	4	no	—
223	C₃⋊Dic₃	—	12	4	no	—
224	C₃⋊Dic₃	C₂×C₄×D₃	1	2	yes	complemented
225	C₃×Dic₃	—	2	4	no	—
226	C₃×Dic₃	—	6	4	no	—
227	C₂³×C₄	—	27	1	no	—
228	C₂³×C₄	—	27	2	no	—
229	C₂×C₄⋊C₄	—	9	1	no	—
230	C₂×C₄⋊C₄	—	27	8	no	—
231	C₂×C₄⋊C₄	—	27	2	no	—
232	C₂×C₄⋊C₄	—	27	1	no	—
233	C₃³	C₂²×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
234	C₂³×C₃	—	6	2	no	—
235	C₂³×C₃	—	9	1	no	—
236	C₂²×D₃	—	6	2	no	—
237	C₂²×D₃	—	9	1	no	—
238	C₂²×D₃	—	9	2	no	—
239	C₂²×D₃	—	9	2	no	—
240	C₂²×D₃	—	9	4	no	—
241	C₂²×D₃	—	9	4	no	—
242	C₂²×D₃	—	18	4	no	—
243	C₂²×D₃	—	18	4	no	—
244	C₂²×D₃	—	18	8	no	—
245	C₂²×D₃	—	18	8	no	—
246	C₂²×D₃	—	18	2	no	—
247	C₂²×D₃	—	36	2	no	—
248	C₂²×D₃	C₂×#157	1	1	yes	characteristic
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	4	2	no	—
251	C₂×C₃×C₄	—	6	8	no	—
252	C₂×C₃×C₄	—	6	2	no	—
253	C₂×C₃×C₄	—	9	1	no	—
254	C₂×C₃×C₄	—	9	2	no	—
255	C₂×C₃×C₄	—	9	2	no	—
256	C₂×C₃×C₄	—	9	4	no	—
257	C₂×C₃×C₄	—	18	4	no	—
258	C₂×C₃×C₄	C₂×#157	1	1	yes	characteristic, complemented
259	C₂×Dic₃	—	6	2	no	—
260	C₂×Dic₃	—	9	1	no	—
261	C₂×Dic₃	—	9	2	no	—
262	C₂×Dic₃	—	9	2	no	—
263	C₂×Dic₃	—	9	4	no	—
264	C₂×Dic₃	—	18	8	no	—
265	C₂×Dic₃	—	18	2	no	—
266	C₂×Dic₃	—	18	4	no	—
267	C₂×Dic₃	—	36	2	no	—
268	C₂×Dic₃	C₂×#157	1	1	yes	characteristic, complemented
269	C₄×D₃	—	6	4	no	—
270	C₄×D₃	—	6	4	no	—
271	C₄×D₃	—	9	4	no	—
272	C₄×D₃	—	9	4	no	—
273	C₄×D₃	—	9	4	no	—
274	C₄×D₃	—	18	8	no	—
275	C₄×D₃	—	18	8	no	—
276	C₄×D₃	—	18	4	no	—
277	C₄×D₃	—	18	4	no	—
278	C₄×D₃	—	18	16	no	—
279	C₄×D₃	—	36	8	no	—
280	C₄×D₃	C₂×#157	1	4	yes	complemented
281	C₂×C₃²	—	2	4	no	—
282	C₂×C₃²	—	2	2	no	—
283	C₂×C₃²	—	3	4	no	—
284	C₂×C₃²	—	4	4	no	—
285	C₂×C₃²	—	4	2	no	—
286	C₂×C₃²	D₃×C₄⋊C₄	1	2	yes	complemented
287	C₂×C₃²	C₂²×C₄×D₃	1	1	yes	characteristic
288	C₃⋊D₃	—	3	4	no	—
289	C₃⋊D₃	—	6	8	no	—
290	C₃⋊D₃	—	12	8	no	—
291	C₃⋊D₃	D₃×C₄⋊C₄	1	2	yes	complemented
292	C₃⋊D₃	C₂×D₃×D₄	1	1	yes	characteristic
293	C₃⋊D₃	C₂×D₃×Q₈	1	1	yes	characteristic
294	C₃×D₃	—	2	8	no	—
295	C₃×D₃	—	6	4	no	—
296	C₃×D₃	—	6	2	no	—
297	C₃×D₃	—	6	2	no	—
298	C₂⁴	—	27	1	no	—
299	C₂²×C₄	—	3	1	no	—
300	C₂²×C₄	—	9	1	no	—
301	C₂²×C₄	—	9	2	no	—
302	C₂²×C₄	—	27	4	no	—
303	C₂²×C₄	—	27	1	no	—
304	C₂²×C₄	—	27	4	no	—
305	C₂²×C₄	—	27	1	no	—
306	C₂²×C₄	—	27	1	no	—
307	C₂²×C₄	—	27	8	no	—
308	C₂²×C₄	—	27	1	no	—
309	C₂²×C₄	—	27	2	no	—
310	C₂²×C₄	—	54	8	no	—
311	C₄⋊C₄	—	9	4	no	—
312	C₄⋊C₄	—	27	8	no	—
313	C₄⋊C₄	—	27	4	no	—
314	C₂²×C₃	—	2	2	no	—
315	C₂²×C₃	—	4	2	no	—
316	C₂²×C₃	—	6	4	no	—
317	C₂²×C₃	—	6	8	no	—
318	C₂²×C₃	—	9	2	no	—
319	C₂²×C₃	—	9	2	no	—
320	C₂²×C₃	—	9	1	no	—
321	C₂²×C₃	—	9	1	no	—
322	C₂²×C₃	C₂²×#157	1	1	yes	characteristic
323	C₂×D₃	—	6	2	no	—
324	C₂×D₃	—	6	2	no	—
325	C₂×D₃	—	6	4	no	—
326	C₂×D₃	—	6	4	no	—
327	C₂×D₃	—	9	4	no	—
328	C₂×D₃	—	9	2	no	—
329	C₂×D₃	—	9	4	no	—
330	C₂×D₃	—	9	4	no	—
331	C₂×D₃	—	9	8	no	—
332	C₂×D₃	—	18	8	no	—
333	C₂×D₃	—	18	16	no	—
334	C₂×D₃	—	18	8	no	—
335	C₂×D₃	—	18	4	no	—
336	C₂×D₃	—	18	8	no	—
337	C₂×D₃	—	36	4	no	—
338	C₂×D₃	—	36	8	no	—
339	C₂×D₃	C₄⋊#157	1	4	yes	direct product factor
340	C₂×D₃	C₂²×#157	1	2	yes	—
341	C₃×C₄	—	2	4	no	—
342	C₃×C₄	—	4	4	no	—
343	C₃×C₄	—	6	4	no	—
344	C₃×C₄	—	9	2	no	—
345	C₃×C₄	—	18	4	no	—
346	C₃×C₄	C₂²×#157	1	2	yes	complemented
347	Dic₃	—	6	4	no	—
348	Dic₃	—	9	2	no	—
349	Dic₃	—	18	4	no	—
350	Dic₃	—	18	4	no	—
351	Dic₃	—	36	4	no	—
352	Dic₃	C₂²×#157	1	2	yes	complemented
353	C₃²	—	2	2	no	—
354	C₃²	—	4	2	no	—
355	C₃²	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic, complemented
356	C₂³	—	3	1	no	—
357	C₂³	—	9	1	no	—
358	C₂³	—	27	2	no	—
359	C₂³	—	27	2	no	—
360	C₂³	—	27	4	no	—
361	C₂³	—	27	4	no	—
362	C₂³	—	27	1	no	—
363	C₂×C₄	—	3	1	no	—
364	C₂×C₄	—	3	4	no	—
365	C₂×C₄	—	9	1	no	—
366	C₂×C₄	—	9	2	no	—
367	C₂×C₄	—	9	2	no	—
368	C₂×C₄	—	9	4	no	—
369	C₂×C₄	—	18	4	no	—
370	C₂×C₄	—	27	4	no	—
371	C₂×C₄	—	27	2	no	—
372	C₂×C₄	—	27	2	no	—
373	C₂×C₄	—	27	4	no	—
374	C₂×C₄	—	27	1	no	—
375	C₂×C₄	—	27	4	no	—
376	C₂×C₄	—	27	4	no	—
377	C₂×C₄	—	54	16	no	—
378	C₂×C₄	—	54	4	no	—
379	C₂×C₄	D₃×#157	1	1	yes	characteristic, complemented
380	C₂×C₃	—	2	2	no	—
381	C₂×C₃	—	2	4	no	—
382	C₂×C₃	—	4	2	no	—
383	C₂×C₃	—	4	4	no	—
384	C₂×C₃	—	6	8	no	—
385	C₂×C₃	—	9	1	no	—
386	C₂×C₃	—	9	2	no	—
387	C₂×C₃	—	9	1	no	—
388	C₂×C₃	C₂×C₄⋊#157	1	2	yes	complemented
389	C₂×C₃	C₂³×#157	1	1	yes	characteristic
390	D₃	—	6	4	no	—
391	D₃	—	6	2	no	—
392	D₃	—	6	2	no	—
393	D₃	—	9	4	no	—
394	D₃	—	18	8	no	—
395	D₃	—	36	8	no	—
396	D₃	C₂×C₄⋊#157	1	4	yes	direct product factor
397	C₂²	—	3	2	no	—
398	C₂²	—	3	4	no	—
399	C₂²	—	9	1	no	—
400	C₂²	—	9	1	no	—
401	C₂²	—	9	2	no	—
402	C₂²	—	9	2	no	—
403	C₂²	—	27	4	no	—
404	C₂²	—	27	4	no	—
405	C₂²	—	27	8	no	—
406	C₂²	—	27	2	no	—
407	C₂²	—	27	4	no	—
408	C₂²	C₂×D₃×#157	1	1	yes	characteristic
409	C₄	—	3	2	no	—
410	C₄	—	9	2	no	—
411	C₄	—	18	4	no	—
412	C₄	—	27	2	no	—
413	C₄	—	54	4	no	—
414	C₄	C₂×D₃×#157	1	2	yes	complemented
415	C₃	—	2	2	no	—
416	C₃	—	4	2	no	—
417	C₃	C₂²×C₄⋊#157	1	1	yes	characteristic, complemented
418	C₂	—	3	4	no	—
419	C₂	—	9	1	no	—
420	C₂	—	9	1	no	—
421	C₂	—	9	2	no	—
422	C₂	—	27	4	no	—
423	C₂	D₃×C₄⋊#157	1	2	yes	direct product factor
424	C₂	C₂²×D₃×#157	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₃×#157
commutator	C₂×C₃³	C₂³×C₄
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
hypercenter	C₂×C₄	D₃×#157
hypocenter	C₃³	C₂²×C₄⋊C₄
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂² ◁ 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. D₃×C₄⋊#157	C₂	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)
43. C₂×C₃³×C₄	C₂×C₄	semidirect
44. C₂×C₃⋊(C₃⋊Dic₃)	C₂×C₄	semidirect
45. C₄×C₃⋊(C₃⋊D₃)	C₂×C₄	semidirect
46. C₂×C₃×C₃⋊Dic₃	C₂×C₄	semidirect
47. C₃×C₄×C₃⋊D₃	C₂×C₄	semidirect
49. C₂×C₃²×Dic₃	C₂×C₄	semidirect
50. C₃²×C₄×D₃	C₂×C₄	semidirect
51. #6289	C₂×C₄	semidirect
52. Dic₃×C₃⋊D₃	C₂×C₄	semidirect
54. D₃×C₃⋊Dic₃	C₂×C₄	semidirect
81. C₄⋊#157	C₂×D₃	direct (N × H)
83. C₂×C₃⋊(C₃⋊D₃)	C₄⋊C₄	semidirect
89. C₂×C₃²×D₃	C₄⋊C₄	semidirect
91. D₃×C₃⋊D₃	C₄⋊C₄	semidirect
96. C₃³×C₄	C₂²×C₄	semidirect
97. C₃⋊(C₃⋊Dic₃)	C₂²×C₄	semidirect
98. C₃×C₃⋊Dic₃	C₂²×C₄	semidirect
99. C₃²×Dic₃	C₂²×C₄	semidirect
131. C₂×C₃²×C₄	C₄×D₃	semidirect
136. C₂×C₃⋊Dic₃	C₄×D₃	semidirect
143. C₄×C₃⋊D₃	C₄×D₃	semidirect
155. C₂×C₃³	C₂×C₄⋊C₄	semidirect
157. C₃⋊(C₃⋊D₃)	C₂×C₄⋊C₄	semidirect
158. C₃×C₃⋊D₃	C₂×C₄⋊C₄	semidirect
161. C₃²×D₃	C₂×C₄⋊C₄	semidirect
184. C₂×C₄×D₃	#157	semidirect
220. C₃²×C₄	C₂×C₄×D₃	semidirect
224. C₃⋊Dic₃	C₂×C₄×D₃	semidirect
233. C₃³	C₂²×C₄⋊C₄	semidirect
258. C₂×C₃×C₄	C₂×#157	semidirect
268. C₂×Dic₃	C₂×#157	semidirect
280. C₄×D₃	C₂×#157	semidirect
286. C₂×C₃²	D₃×C₄⋊C₄	semidirect
291. C₃⋊D₃	D₃×C₄⋊C₄	semidirect
339. C₂×D₃	C₄⋊#157	direct (N × H)
346. C₃×C₄	C₂²×#157	semidirect
352. Dic₃	C₂²×#157	semidirect
355. C₃²	C₂×D₃×C₄⋊C₄	semidirect
379. C₂×C₄	D₃×#157	semidirect
388. C₂×C₃	C₂×C₄⋊#157	semidirect
396. D₃	C₂×C₄⋊#157	direct (N × H)
414. C₄	C₂×D₃×#157	semidirect
417. C₃	C₂²×C₄⋊#157	semidirect
423. C₂	D₃×C₄⋊#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
D₃×C₄⋊#157	2
C₂²×C₄⋊#157	3
C₂×D₃×C₄⋊C₄	9

Subgroups — C2×D3×C4⋊#157 #13180970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₄⋊#157 #13180970