Subgroups — C₃²×C₄×#237 #13178925

Order 1728.

2236 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#237	C₂	1	1	yes	maximal, characteristic
2	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₄×#67	C₂	1	2	yes	maximal, complemented
5	C₂×C₃²×C₄×Dic₃	C₂	1	2	yes	maximal, complemented
6	C₃²×#892	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#887	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#67⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₃²×#877	C₂	1	2	yes	maximal, complemented
10	C₃²×C₄²×D₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×C₄×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃²×C₄×#41	—	3	1	no	maximal
13	C₃×C₄×#237	C₃	1	4	yes	maximal, direct product factor
14	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃³×C₄	C₂²	1	2	yes	—
16	C₂×C₃²×#67	C₂²	1	2	yes	—
17	C₂²×C₃²×Dic₃	C₂²	1	2	yes	—
18	C₂²×C₃²×Dic₃	C₂²	1	2	yes	—
19	C₃²×#237	C₄	1	8	yes	direct product factor
20	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
21	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
22	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
23	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic
24	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₃³×C₄²	C₂²	1	1	yes	characteristic
27	C₃²×#217	C₂²	1	2	yes	—
28	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
29	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
30	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
31	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
32	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
33	C₃²×C₄×Dic₃	C₂²	1	2	yes	—
34	C₃²×C₄×Dic₃	C₂²	1	2	yes	—
35	C₃²×C₄×Dic₃	C₂²	1	2	yes	—
36	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
37	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
38	C₂×C₃²×#41	—	3	1	no	—
39	C₂×C₃×#237	C₂×C₃	1	4	yes	—
40	C₃²×C₄×Q₈	—	3	1	no	—
41	C₃²×C₄×Q₈	—	3	1	no	—
42	C₃²×C₄×D₄	—	2	4	no	—
43	C₃²×C₄×D₄	—	3	1	no	—
44	C₃²×C₄×D₄	—	3	2	no	—
45	C₃²×C₄×D₄	—	3	2	no	—
46	C₃²×C₄×D₄	D₃	1	1	yes	characteristic, complemented
47	C₃²×C₄×D₄	C₂×C₃	1	4	yes	complemented
48	C₃²×#117	—	3	1	no	—
49	C₃²×#117	—	3	2	no	—
50	C₂×C₃²×C₄²	—	3	2	no	—
51	C₂×C₃²×C₄²	—	3	1	no	—
52	C₃×D₄×Dic₃	C₂×C₃	1	4	yes	complemented
53	C₃×C₄×#67	C₂×C₃	1	8	yes	complemented
54	C₂×C₃×C₄×Dic₃	C₂×C₃	1	8	yes	complemented
55	C₃×#892	C₂×C₃	1	4	yes	complemented
56	C₃×#887	C₂×C₃	1	4	yes	complemented
57	C₃×#67⋊C₄	C₂×C₃	1	8	yes	complemented
58	C₃×#877	C₂×C₃	1	8	yes	complemented
59	C₃×C₄²×D₃	C₂×C₃	1	4	yes	complemented
60	C₃×C₄×Dic₆	C₂×C₃	1	4	yes	complemented
61	C₂³×C₃³	C₂³	1	2	yes	—
62	C₂²×C₃²×D₃	C₂³	1	1	yes	characteristic
63	C₃³×D₄	C₂×C₄	1	4	yes	complemented
64	C₂×C₃³×C₄	—	2	4	no	—
65	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
66	C₂×C₃³×C₄	C₂³	1	2	yes	—
67	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
68	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
69	C₃²×#67	C₂×C₄	1	8	yes	complemented
70	C₂×C₃²×Dic₃	—	2	4	no	—
71	C₂×C₃²×Dic₃	C₂×C₄	1	8	yes	complemented
72	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
73	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
74	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
75	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
76	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
77	C₃²×C₄×D₃	—	2	2	no	—
78	C₃²×C₄×D₃	—	2	2	no	—
79	C₃²×C₄×D₃	C₂×C₄	1	4	yes	complemented
80	C₃²×Dic₆	C₂×C₄	1	4	yes	complemented
81	C₃×C₄×#41	—	3	4	no	—
82	C₄×#237	C₃²	1	1	yes	characteristic, direct product factor
83	C₃²×#41	—	3	8	no	—
84	C₂×C₃²×Q₈	—	3	1	no	—
85	C₂×C₃²×D₄	—	2	4	no	—
86	C₂×C₃²×D₄	—	3	2	no	—
87	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
88	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
89	C₂²×C₃²×C₄	—	2	8	no	—
90	C₂²×C₃²×C₄	—	3	2	no	—
91	C₂²×C₃²×C₄	—	3	1	no	—
92	C₂²×C₃²×C₄	—	3	2	no	—
93	C₂²×C₃²×C₄	—	3	1	no	—
94	C₂²×C₃²×C₄	—	3	1	no	—
95	C₂²×C₃²×C₄	C₂×D₃	1	2	yes	—
96	C₂²×C₃²×C₄	C₂²×C₃	1	8	yes	—
97	C₂×C₃×#67	C₂²×C₃	1	8	yes	—
98	C₂²×C₃×Dic₃	C₂²×C₃	1	8	yes	—
99	C₂²×C₃×Dic₃	C₂²×C₃	1	8	yes	—
100	C₃×#237	C₃×C₄	1	32	yes	direct product factor
101	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
102	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
103	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
104	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	—
105	C₃²×C₄⋊C₄	—	2	4	no	—
106	C₃²×C₄⋊C₄	—	3	2	no	—
107	C₃²×C₄⋊C₄	—	3	2	no	—
108	C₃²×C₄⋊C₄	—	3	1	no	—
109	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
110	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
111	C₃²×C₂²⋊C₄	—	2	8	no	—
112	C₃²×C₂²⋊C₄	—	3	2	no	—
113	C₃²×C₂²⋊C₄	—	3	2	no	—
114	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
115	C₃²×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
116	C₃²×C₄²	—	2	4	no	—
117	C₃²×C₄²	—	3	2	no	—
118	C₃²×C₄²	—	3	1	no	—
119	C₃²×C₄²	—	3	2	no	—
120	C₃²×C₄²	—	3	1	no	—
121	C₃²×C₄²	—	3	1	no	—
122	C₃²×C₄²	—	3	2	no	—
123	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
124	C₃²×C₄²	C₂²×C₃	1	4	yes	—
125	C₃×#217	C₂²×C₃	1	8	yes	—
126	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
127	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
128	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
129	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
130	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
131	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	—
132	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	—
133	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
134	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
135	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	—
136	C₂²×C₃³	—	2	2	no	—
137	C₂²×C₃³	—	2	2	no	—
138	C₂²×C₃³	C₂²×C₄	1	4	yes	—
139	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
140	C₂×C₃²×D₃	—	2	1	no	—
141	C₂×C₃²×D₃	—	2	1	no	—
142	C₂×C₃²×D₃	C₂²×C₄	1	2	yes	—
143	C₃³×C₄	—	2	1	no	—
144	C₃³×C₄	—	2	2	no	—
145	C₃³×C₄	C₂²×C₄	1	2	yes	—
146	C₃³×C₄	#41	1	2	yes	complemented
147	C₃²×Dic₃	—	2	1	no	—
148	C₃²×Dic₃	—	2	2	no	—
149	C₃²×Dic₃	C₂²×C₄	1	4	yes	—
150	C₃²×Dic₃	C₂²×C₄	1	2	yes	—
151	C₃²×Dic₃	#41	1	2	yes	complemented
152	C₂×C₃×#41	—	3	4	no	—
153	C₂×#237	C₂×C₃²	1	1	yes	characteristic
154	C₃×C₄×Q₈	—	3	4	no	—
155	C₃×C₄×Q₈	—	3	4	no	—
156	C₃×C₄×D₄	—	2	4	no	—
157	C₃×C₄×D₄	—	3	4	no	—
158	C₃×C₄×D₄	—	3	8	no	—
159	C₃×C₄×D₄	—	3	8	no	—
160	C₃×C₄×D₄	C₃×D₃	1	4	yes	complemented
161	C₃×C₄×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
162	C₃×#117	—	3	4	no	—
163	C₃×#117	—	3	8	no	—
164	C₂×C₃×C₄²	—	3	8	no	—
165	C₂×C₃×C₄²	—	3	4	no	—
166	D₄×Dic₃	C₂×C₃²	1	1	yes	characteristic, complemented
167	C₄×#67	C₂×C₃²	1	2	yes	complemented
168	C₂×C₄×Dic₃	C₂×C₃²	1	2	yes	complemented
169	#892	C₂×C₃²	1	1	yes	characteristic, complemented
170	#887	C₂×C₃²	1	1	yes	characteristic, complemented
171	#67⋊C₄	C₂×C₃²	1	2	yes	complemented
172	#877	C₂×C₃²	1	2	yes	complemented
173	C₄²×D₃	C₂×C₃²	1	1	yes	characteristic, complemented
174	C₄×Dic₆	C₂×C₃²	1	1	yes	characteristic, complemented
175	C₂³×C₃²	—	2	8	no	—
176	C₂³×C₃²	—	3	1	no	—
177	C₂³×C₃²	C₂²×D₃	1	2	yes	—
178	C₂³×C₃²	C₂³×C₃	1	8	yes	—
179	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
180	C₃²×Q₈	—	3	4	no	—
181	C₃²×D₄	—	2	16	no	—
182	C₃²×D₄	—	3	8	no	—
183	C₃²×D₄	C₄×D₃	1	4	yes	complemented
184	C₃²×D₄	C₂×C₃×C₄	1	16	yes	complemented
185	C₂×C₃²×C₄	—	2	4	no	—
186	C₂×C₃²×C₄	—	2	4	no	—
187	C₂×C₃²×C₄	—	2	4	no	—
188	C₂×C₃²×C₄	—	2	4	no	—
189	C₂×C₃²×C₄	—	2	8	no	—
190	C₂×C₃²×C₄	—	2	16	no	—
191	C₂×C₃²×C₄	—	3	8	no	—
192	C₂×C₃²×C₄	—	3	1	no	—
193	C₂×C₃²×C₄	—	3	1	no	—
194	C₂×C₃²×C₄	—	3	2	no	—
195	C₂×C₃²×C₄	—	3	4	no	—
196	C₂×C₃²×C₄	—	3	1	no	—
197	C₂×C₃²×C₄	—	3	2	no	—
198	C₂×C₃²×C₄	—	4	16	no	—
199	C₂×C₃²×C₄	—	6	2	no	—
200	C₂×C₃²×C₄	—	6	4	no	—
201	C₂×C₃²×C₄	—	6	2	no	—
202	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
203	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
204	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
205	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
206	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
207	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
208	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
209	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
210	C₃×#67	C₂×C₃×C₄	1	32	yes	complemented
211	C₂×C₃×Dic₃	—	2	16	no	—
212	C₂×C₃×Dic₃	C₂×C₃×C₄	1	32	yes	complemented
213	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
214	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
215	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
216	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
217	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
218	C₃×C₄×D₃	—	2	8	no	—
219	C₃×C₄×D₃	—	2	8	no	—
220	C₃×C₄×D₃	C₂×C₃×C₄	1	16	yes	complemented
221	C₃×Dic₆	C₂×C₃×C₄	1	16	yes	complemented
222	C₄×#41	—	3	1	no	Sylow
223	C₂×C₃³	—	2	4	no	—
224	C₂×C₃³	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₃³	C₂×#41	1	1	yes	characteristic
226	C₂×C₃³	C₂×#41	1	1	yes	characteristic
227	C₃²×D₃	—	2	2	no	—
228	C₃×#41	—	3	32	no	—
229	C₂×C₃×Q₈	—	3	4	no	—
230	C₂×C₃×D₄	—	2	4	no	—
231	C₂×C₃×D₄	—	3	8	no	—
232	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
233	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
234	C₂²×C₃×C₄	—	2	8	no	—
235	C₂²×C₃×C₄	—	3	8	no	—
236	C₂²×C₃×C₄	—	3	4	no	—
237	C₂²×C₃×C₄	—	3	8	no	—
238	C₂²×C₃×C₄	—	3	4	no	—
239	C₂²×C₃×C₄	—	3	4	no	—
240	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	—
241	C₂²×C₃×C₄	C₂²×C₃²	1	2	yes	—
242	C₂×#67	C₂²×C₃²	1	2	yes	—
243	C₂²×Dic₃	C₂²×C₃²	1	2	yes	—
244	C₂²×Dic₃	C₂²×C₃²	1	2	yes	—
245	#237	C₃²×C₄	1	8	yes	direct product factor
246	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
247	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
248	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
249	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic
250	C₃×C₄⋊C₄	—	2	4	no	—
251	C₃×C₄⋊C₄	—	3	8	no	—
252	C₃×C₄⋊C₄	—	3	8	no	—
253	C₃×C₄⋊C₄	—	3	4	no	—
254	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
255	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
256	C₃×C₂²⋊C₄	—	2	8	no	—
257	C₃×C₂²⋊C₄	—	3	8	no	—
258	C₃×C₂²⋊C₄	—	3	8	no	—
259	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
260	C₃×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
261	C₃×C₄²	—	2	4	no	—
262	C₃×C₄²	—	3	4	no	—
263	C₃×C₄²	—	3	8	no	—
264	C₃×C₄²	—	3	4	no	—
265	C₃×C₄²	—	3	8	no	—
266	C₃×C₄²	—	3	4	no	—
267	C₃×C₄²	—	3	8	no	—
268	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
269	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic
270	#217	C₂²×C₃²	1	2	yes	—
271	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
272	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
273	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
274	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
275	C₄×Dic₃	C₂²×C₃²	1	2	yes	—
276	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
277	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
278	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
279	C₄×Dic₃	C₂²×C₃²	1	2	yes	—
280	C₄×Dic₃	C₂²×C₃²	1	2	yes	—
281	C₂²×C₃²	—	2	2	no	—
282	C₂²×C₃²	—	2	2	no	—
283	C₂²×C₃²	—	2	4	no	—
284	C₂²×C₃²	—	2	16	no	—
285	C₂²×C₃²	—	2	8	no	—
286	C₂²×C₃²	—	2	8	no	—
287	C₂²×C₃²	—	3	2	no	—
288	C₂²×C₃²	—	4	8	no	—
289	C₂²×C₃²	—	4	8	no	—
290	C₂²×C₃²	—	6	1	no	—
291	C₂²×C₃²	—	6	1	no	—
292	C₂²×C₃²	C₂×C₄×D₃	1	4	yes	—
293	C₂²×C₃²	C₂²×C₃×C₄	1	16	yes	—
294	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
295	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
296	C₂×C₃×D₃	—	2	4	no	—
297	C₂×C₃×D₃	—	2	4	no	—
298	C₂×C₃×D₃	C₂²×C₃×C₄	1	8	yes	—
299	C₃²×C₄	—	2	2	no	—
300	C₃²×C₄	—	2	1	no	—
301	C₃²×C₄	—	2	8	no	—
302	C₃²×C₄	—	2	8	no	—
303	C₃²×C₄	—	2	4	no	—
304	C₃²×C₄	—	2	8	no	—
305	C₃²×C₄	—	3	2	no	—
306	C₃²×C₄	—	3	4	no	—
307	C₃²×C₄	—	3	2	no	—
308	C₃²×C₄	—	4	4	no	—
309	C₃²×C₄	—	4	8	no	—
310	C₃²×C₄	—	6	1	no	—
311	C₃²×C₄	—	6	2	no	—
312	C₃²×C₄	C₂×C₄×D₃	1	2	yes	—
313	C₃²×C₄	#237	1	2	yes	direct product factor
314	C₃²×C₄	C₂²×C₃×C₄	1	8	yes	—
315	C₃²×C₄	C₃×#41	1	8	yes	complemented
316	C₃×Dic₃	—	2	4	no	—
317	C₃×Dic₃	—	2	8	no	—
318	C₃×Dic₃	C₂²×C₃×C₄	1	16	yes	—
319	C₃×Dic₃	C₂²×C₃×C₄	1	8	yes	—
320	C₃×Dic₃	C₃×#41	1	8	yes	complemented
321	C₂×#41	—	3	1	no	—
322	C₄×Q₈	—	3	1	no	—
323	C₄×Q₈	—	3	1	no	—
324	C₄×D₄	—	3	1	no	—
325	C₄×D₄	—	3	2	no	—
326	C₄×D₄	—	3	2	no	—
327	C₄×D₄	C₃²×D₃	1	1	yes	characteristic, complemented
328	#117	—	3	1	no	—
329	#117	—	3	2	no	—
330	C₂×C₄²	—	3	2	no	—
331	C₂×C₄²	—	3	1	no	—
332	C₃³	C₄×#41	1	1	yes	characteristic, complemented, Sylow
333	C₂³×C₃	—	2	8	no	—
334	C₂³×C₃	—	3	4	no	—
335	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
336	C₂³×C₃	C₂³×C₃²	1	2	yes	—
337	C₂²×D₃	C₂³×C₃²	1	1	yes	characteristic
338	C₃×Q₈	—	3	16	no	—
339	C₃×D₄	—	2	16	no	—
340	C₃×D₄	—	3	32	no	—
341	C₃×D₄	C₃×C₄×D₃	1	16	yes	complemented
342	C₃×D₄	C₂×C₃²×C₄	1	4	yes	complemented
343	C₂×C₃×C₄	—	2	16	no	—
344	C₂×C₃×C₄	—	2	4	no	—
345	C₂×C₃×C₄	—	2	4	no	—
346	C₂×C₃×C₄	—	2	4	no	—
347	C₂×C₃×C₄	—	2	4	no	—
348	C₂×C₃×C₄	—	2	8	no	—
349	C₂×C₃×C₄	—	3	4	no	—
350	C₂×C₃×C₄	—	3	4	no	—
351	C₂×C₃×C₄	—	3	8	no	—
352	C₂×C₃×C₄	—	3	32	no	—
353	C₂×C₃×C₄	—	3	16	no	—
354	C₂×C₃×C₄	—	3	4	no	—
355	C₂×C₃×C₄	—	3	8	no	—
356	C₂×C₃×C₄	—	4	16	no	—
357	C₂×C₃×C₄	—	6	8	no	—
358	C₂×C₃×C₄	—	6	16	no	—
359	C₂×C₃×C₄	—	6	8	no	—
360	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
361	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
362	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
363	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
364	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
365	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
366	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
367	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
368	#67	C₂×C₃²×C₄	1	8	yes	complemented
369	C₂×Dic₃	—	2	4	no	—
370	C₂×Dic₃	C₂×C₃²×C₄	1	8	yes	complemented
371	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
372	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
373	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
374	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
375	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
376	C₄×D₃	—	2	2	no	—
377	C₄×D₃	—	2	2	no	—
378	C₄×D₃	C₂×C₃²×C₄	1	4	yes	complemented
379	Dic₆	C₂×C₃²×C₄	1	4	yes	complemented
380	C₂×C₃²	—	2	4	no	—
381	C₂×C₃²	—	2	4	no	—
382	C₂×C₃²	—	2	4	no	—
383	C₂×C₃²	—	2	4	no	—
384	C₂×C₃²	—	2	16	no	—
385	C₂×C₃²	—	4	16	no	—
386	C₂×C₃²	—	6	2	no	—
387	C₂×C₃²	C₂²×C₄×D₃	1	1	yes	characteristic
388	C₂×C₃²	C₂×#237	1	1	yes	characteristic
389	C₂×C₃²	D₃×#41	1	1	yes	characteristic
390	C₂×C₃²	C₂³×C₃×C₄	1	4	yes	—
391	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
392	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
393	C₃×D₃	—	2	8	no	—
394	#41	—	3	8	no	—
395	C₂×Q₈	—	3	1	no	—
396	C₂×D₄	—	3	2	no	—
397	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic
398	C₂²×C₄	—	3	2	no	—
399	C₂²×C₄	—	3	1	no	—
400	C₂²×C₄	—	3	2	no	—
401	C₂²×C₄	—	3	1	no	—
402	C₂²×C₄	—	3	1	no	—
403	C₂²×C₄	C₂×C₃²×D₃	1	2	yes	—
404	C₄⋊C₄	—	3	2	no	—
405	C₄⋊C₄	—	3	2	no	—
406	C₄⋊C₄	—	3	1	no	—
407	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic
408	C₂²⋊C₄	—	3	2	no	—
409	C₂²⋊C₄	—	3	2	no	—
410	C₂²⋊C₄	C₂×C₃²×D₃	1	2	yes	—
411	C₄²	—	3	1	no	—
412	C₄²	—	3	2	no	—
413	C₄²	—	3	1	no	—
414	C₄²	—	3	2	no	—
415	C₄²	—	3	1	no	—
416	C₄²	—	3	2	no	—
417	C₄²	C₂×C₃²×D₃	1	1	yes	characteristic
418	C₂²×C₃	—	2	8	no	—
419	C₂²×C₃	—	2	8	no	—
420	C₂²×C₃	—	2	2	no	—
421	C₂²×C₃	—	2	2	no	—
422	C₂²×C₃	—	2	4	no	—
423	C₂²×C₃	—	2	16	no	—
424	C₂²×C₃	—	3	8	no	—
425	C₂²×C₃	—	4	8	no	—
426	C₂²×C₃	—	4	8	no	—
427	C₂²×C₃	—	6	4	no	—
428	C₂²×C₃	—	6	4	no	—
429	C₂²×C₃	C₂×C₃×C₄×D₃	1	16	yes	—
430	C₂²×C₃	C₂²×C₃²×C₄	1	4	yes	—
431	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
432	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
433	C₂×D₃	—	2	1	no	—
434	C₂×D₃	—	2	1	no	—
435	C₂×D₃	C₂²×C₃²×C₄	1	2	yes	—
436	C₃×C₄	—	2	8	no	—
437	C₃×C₄	—	2	4	no	—
438	C₃×C₄	—	2	1	no	—
439	C₃×C₄	—	2	2	no	—
440	C₃×C₄	—	2	8	no	—
441	C₃×C₄	—	2	8	no	—
442	C₃×C₄	—	3	8	no	—
443	C₃×C₄	—	3	16	no	—
444	C₃×C₄	—	3	8	no	—
445	C₃×C₄	—	4	8	no	—
446	C₃×C₄	—	4	4	no	—
447	C₃×C₄	—	6	4	no	—
448	C₃×C₄	—	6	8	no	—
449	C₃×C₄	C₂×C₃×C₄×D₃	1	8	yes	—
450	C₃×C₄	C₃×#237	1	8	yes	direct product factor
451	C₃×C₄	C₂²×C₃²×C₄	1	2	yes	—
452	C₃×C₄	C₃²×#41	1	2	yes	complemented
453	Dic₃	—	2	1	no	—
454	Dic₃	—	2	2	no	—
455	Dic₃	C₂²×C₃²×C₄	1	4	yes	—
456	Dic₃	C₂²×C₃²×C₄	1	2	yes	—
457	Dic₃	C₃²×#41	1	2	yes	complemented
458	C₃²	—	2	4	no	—
459	C₃²	C₄×#237	1	1	yes	characteristic, direct product factor
460	C₃²	C₃×C₄×#41	1	4	yes	complemented
461	C₂³	—	3	1	no	—
462	C₂³	C₂²×C₃²×D₃	1	2	yes	—
463	Q₈	—	3	4	no	—
464	D₄	—	3	8	no	—
465	D₄	C₃²×C₄×D₃	1	4	yes	complemented
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	3	1	no	—
468	C₂×C₄	—	3	1	no	—
469	C₂×C₄	—	3	2	no	—
470	C₂×C₄	—	3	8	no	—
471	C₂×C₄	—	3	4	no	—
472	C₂×C₄	—	3	1	no	—
473	C₂×C₄	—	3	2	no	—
474	C₂×C₄	—	6	2	no	—
475	C₂×C₄	—	6	4	no	—
476	C₂×C₄	—	6	2	no	—
477	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
478	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
479	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
480	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
481	C₂×C₃	—	2	16	no	—
482	C₂×C₃	—	2	4	no	—
483	C₂×C₃	—	2	4	no	—
484	C₂×C₃	—	2	4	no	—
485	C₂×C₃	—	2	4	no	—
486	C₂×C₃	—	4	16	no	—
487	C₂×C₃	—	6	8	no	—
488	C₂×C₃	C₂²×C₃×C₄×D₃	1	4	yes	—
489	C₂×C₃	C₂×C₃×#237	1	4	yes	—
490	C₂×C₃	C₃×D₃×#41	1	4	yes	—
491	C₂×C₃	C₂³×C₃²×C₄	1	1	yes	characteristic
492	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
493	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
494	D₃	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	3	2	no	—
498	C₂²	—	6	1	no	—
499	C₂²	—	6	1	no	—
500	C₂²	C₂×C₃²×C₄×D₃	1	4	yes	—
501	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
502	C₄	—	2	2	no	—
503	C₄	—	2	1	no	—
504	C₄	—	3	2	no	—
505	C₄	—	3	4	no	—
506	C₄	—	3	2	no	—
507	C₄	—	6	1	no	—
508	C₄	—	6	2	no	—
509	C₄	C₂×C₃²×C₄×D₃	1	2	yes	—
510	C₄	C₃²×#237	1	2	yes	direct product factor
511	C₃	—	2	4	no	—
512	C₃	C₃×C₄×#237	1	4	yes	direct product factor
513	C₃	C₃²×C₄×#41	1	1	yes	characteristic, complemented
514	C₂	—	2	4	no	—
515	C₂	—	6	2	no	—
516	C₂	C₂²×C₃²×C₄×D₃	1	1	yes	characteristic
517	C₂	C₂×C₃²×#237	1	1	yes	characteristic
518	C₂	C₃²×D₃×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₄	C₂²×D₃
commutator	C₂×C₃	C₂³×C₃²×C₄
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₃³×C₄×D₄	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₂×C₃²×#237	C₂
cosocle	C₂²×C₃	C₂⁴×C₃²
hypercenter	C₃²×C₄×D₄	D₃
hypocenter	C₃	C₃²×C₄×#41
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₃²×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₃³×C₄×D₄	C₂	semidirect
3. C₃²×D₄×Dic₃	C₂	semidirect
4. C₃²×C₄×#67	C₂	semidirect
5. C₂×C₃²×C₄×Dic₃	C₂	semidirect
6. C₃²×#892	C₂	semidirect
7. C₃²×#887	C₂	semidirect
8. C₃²×#67⋊C₄	C₂	semidirect
9. C₃²×#877	C₂	semidirect
10. C₃²×C₄²×D₃	C₂	semidirect
11. C₃²×C₄×Dic₆	C₂	semidirect
13. C₃×C₄×#237	C₃	direct (N × H)
19. C₃²×#237	C₄	direct (N × H)
46. C₃²×C₄×D₄	D₃	semidirect
47. C₃²×C₄×D₄	C₂×C₃	semidirect
52. C₃×D₄×Dic₃	C₂×C₃	semidirect
53. C₃×C₄×#67	C₂×C₃	semidirect
54. C₂×C₃×C₄×Dic₃	C₂×C₃	semidirect
55. C₃×#892	C₂×C₃	semidirect
56. C₃×#887	C₂×C₃	semidirect
57. C₃×#67⋊C₄	C₂×C₃	semidirect
58. C₃×#877	C₂×C₃	semidirect
59. C₃×C₄²×D₃	C₂×C₃	semidirect
60. C₃×C₄×Dic₆	C₂×C₃	semidirect
63. C₃³×D₄	C₂×C₄	semidirect
69. C₃²×#67	C₂×C₄	semidirect
71. C₂×C₃²×Dic₃	C₂×C₄	semidirect
79. C₃²×C₄×D₃	C₂×C₄	semidirect
80. C₃²×Dic₆	C₂×C₄	semidirect
82. C₄×#237	C₃²	direct (N × H)
100. C₃×#237	C₃×C₄	direct (N × H)
146. C₃³×C₄	#41	semidirect
151. C₃²×Dic₃	#41	semidirect
160. C₃×C₄×D₄	C₃×D₃	semidirect
161. C₃×C₄×D₄	C₂×C₃²	semidirect
166. D₄×Dic₃	C₂×C₃²	semidirect
167. C₄×#67	C₂×C₃²	semidirect
168. C₂×C₄×Dic₃	C₂×C₃²	semidirect
169. #892	C₂×C₃²	semidirect
170. #887	C₂×C₃²	semidirect
171. #67⋊C₄	C₂×C₃²	semidirect
172. #877	C₂×C₃²	semidirect
173. C₄²×D₃	C₂×C₃²	semidirect
174. C₄×Dic₆	C₂×C₃²	semidirect
183. C₃²×D₄	C₄×D₃	semidirect
184. C₃²×D₄	C₂×C₃×C₄	semidirect
210. C₃×#67	C₂×C₃×C₄	semidirect
212. C₂×C₃×Dic₃	C₂×C₃×C₄	semidirect
220. C₃×C₄×D₃	C₂×C₃×C₄	semidirect
221. C₃×Dic₆	C₂×C₃×C₄	semidirect
245. #237	C₃²×C₄	direct (N × H)
313. C₃²×C₄	#237	direct (N × H)
315. C₃²×C₄	C₃×#41	semidirect
320. C₃×Dic₃	C₃×#41	semidirect
327. C₄×D₄	C₃²×D₃	semidirect
332. C₃³	C₄×#41	semidirect
341. C₃×D₄	C₃×C₄×D₃	semidirect
342. C₃×D₄	C₂×C₃²×C₄	semidirect
368. #67	C₂×C₃²×C₄	semidirect
370. C₂×Dic₃	C₂×C₃²×C₄	semidirect
378. C₄×D₃	C₂×C₃²×C₄	semidirect
379. Dic₆	C₂×C₃²×C₄	semidirect
450. C₃×C₄	C₃×#237	direct (N × H)
452. C₃×C₄	C₃²×#41	semidirect
457. Dic₃	C₃²×#41	semidirect
459. C₃²	C₄×#237	direct (N × H)
460. C₃²	C₃×C₄×#41	semidirect
465. D₄	C₃²×C₄×D₃	semidirect
510. C₄	C₃²×#237	direct (N × H)
512. C₃	C₃×C₄×#237	direct (N × H)
513. C₃	C₃²×C₄×#41	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#237	2
C₃³×C₄×D₄	2
C₃²×D₄×Dic₃	2
C₃²×C₄×#67	2
C₂×C₃²×C₄×Dic₃	2
C₃²×#892	2
C₃²×#887	2
C₃²×#67⋊C₄	2
C₃²×#877	2
C₃²×C₄²×D₃	2
C₃²×C₄×Dic₆	2
C₃²×C₄×#41	3
C₃×C₄×#237	3

Subgroups — C32×C4×#237 #13178925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₄×#237 #13178925