Subgroups — C₂×C₃×#64146 #13179552

Order 1728.

4916 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃³×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#638	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#3757	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64146	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#3752	C₂	1	2	yes	maximal, complemented
7	C₂×#64146	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×#937	—	3	4	no	maximal
9	C₂⁴×C₃³	C₂²	1	1	yes	characteristic
10	C₂⁴×C₃³	C₂²	1	1	yes	characteristic, complemented
11	C₂³×C₃×C₃⋊D₃	—	2	4	no	—
12	C₂³×C₃×C₃⋊D₃	—	2	8	no	—
13	C₂³×C₃×C₃⋊D₃	C₂²	1	2	yes	—
14	C₂³×C₃×C₃⋊D₃	C₂²	1	4	yes	complemented
15	C₂×C₃³×D₄	—	2	4	no	—
16	C₂×C₃³×D₄	C₂²	1	4	yes	complemented
17	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×#638	—	2	8	no	—
19	C₂×C₃×#638	C₂²	1	8	yes	complemented
20	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	complemented
21	C₃×#3757	C₂²	1	4	yes	complemented
22	C₃×#3752	C₂²	1	8	yes	complemented
23	C₂⁴×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂⁴×C₃×D₃	—	3	4	no	—
25	C₂²×C₃²×D₄	—	2	4	no	—
26	C₂²×C₃²×D₄	D₃	1	4	yes	complemented
27	C₂²×C₃²×D₄	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂²×#638	C₂×C₃	1	2	yes	complemented
29	C₂²×C₃×#67	—	3	8	no	—
30	C₂×#3757	C₂×C₃	1	1	yes	characteristic, complemented
31	#64146	C₂×C₃	1	8	yes	direct product factor
32	C₂×#3752	C₂×C₃	1	2	yes	complemented
33	C₂×C₃×#217	—	3	4	no	—
34	C₃×#937	—	3	32	no	—
35	C₂×C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
36	C₂³×C₃³	—	2	4	no	—
37	C₂³×C₃³	—	2	2	no	—
38	C₂³×C₃³	—	2	4	no	—
39	C₂³×C₃³	D₄	1	4	yes	complemented
40	C₂³×C₃³	C₂³	1	2	yes	—
41	C₂³×C₃³	C₂³	1	1	yes	characteristic
42	C₂³×C₃³	C₂³	1	2	yes	complemented
43	C₂²×C₃×C₃⋊D₃	—	2	32	no	—
44	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
45	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
46	C₂²×C₃×C₃⋊D₃	—	2	8	no	—
47	C₂²×C₃×C₃⋊D₃	—	2	16	no	—
48	C₂²×C₃×C₃⋊D₃	D₄	1	8	yes	complemented
49	C₂²×C₃×C₃⋊D₃	C₂³	1	4	yes	—
50	C₃³×D₄	—	2	8	no	—
51	C₂×C₃³×C₄	—	2	2	no	—
52	C₂×C₃³×C₄	C₂³	1	2	yes	complemented
53	C₃×#638	—	2	16	no	—
54	C₂×C₃×C₃⋊Dic₃	—	2	4	no	—
55	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	complemented
56	C₂×C₃×#120	—	9	1	no	—
57	C₂×#937	—	3	4	no	—
58	C₂⁴×C₃²	—	2	4	no	—
59	C₂⁴×C₃²	—	2	4	no	—
60	C₂⁴×C₃²	C₂×D₃	1	4	yes	—
61	C₂⁴×C₃²	C₂×D₃	1	4	yes	complemented
62	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
63	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic, complemented
64	C₂³×C₃⋊D₃	—	2	4	no	—
65	C₂³×C₃⋊D₃	—	2	8	no	—
66	C₂³×C₃⋊D₃	C₂²×C₃	1	2	yes	—
67	C₂³×C₃⋊D₃	C₂²×C₃	1	4	yes	complemented
68	C₂³×C₃×D₃	—	3	8	no	—
69	C₂³×C₃×D₃	—	3	16	no	—
70	C₂³×C₃×D₃	—	6	32	no	—
71	C₂³×C₃×D₃	—	6	16	no	—
72	C₂×C₃²×D₄	—	2	32	no	—
73	C₂×C₃²×D₄	—	2	16	no	—
74	C₂×C₃²×D₄	—	2	16	no	—
75	C₂×C₃²×D₄	—	2	4	no	—
76	C₂×C₃²×D₄	C₂×D₃	1	16	yes	complemented
77	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	complemented
78	C₂²×C₃²×C₄	—	2	4	no	—
79	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	complemented
80	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
81	C₂×#638	—	2	8	no	—
82	C₂×#638	C₂²×C₃	1	8	yes	complemented
83	C₂²×C₃⋊Dic₃	C₂²×C₃	1	2	yes	complemented
84	C₂×C₃×#67	—	3	32	no	—
85	C₂×C₃×#67	—	6	32	no	—
86	C₂²×C₃×Dic₃	—	3	8	no	—
87	#3757	C₂²×C₃	1	4	yes	complemented
88	#3752	C₂²×C₃	1	8	yes	complemented
89	C₃×#217	—	3	16	no	—
90	C₃×(C₂×D₃)⋊C₄	—	3	32	no	—
91	C₂²×C₃³	—	2	8	no	—
92	C₂²×C₃³	—	2	4	no	—
93	C₂²×C₃³	—	2	2	no	—
94	C₂²×C₃³	—	2	4	no	—
95	C₂²×C₃³	—	4	4	no	—
96	C₂²×C₃³	C₂×D₄	1	4	yes	—
97	C₂²×C₃³	C₂×D₄	1	2	yes	—
98	C₂²×C₃³	C₂×D₄	1	4	yes	complemented
99	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
100	C₂×C₃×C₃⋊D₃	—	2	32	no	—
101	C₂×C₃×C₃⋊D₃	—	2	16	no	—
102	C₂×C₃×C₃⋊D₃	—	2	4	no	—
103	C₂×C₃×C₃⋊D₃	—	2	4	no	—
104	C₂×C₃×C₃⋊D₃	C₂×D₄	1	8	yes	complemented
105	C₃³×C₄	—	2	2	no	—
106	C₃×C₃⋊Dic₃	—	2	4	no	—
107	C₂⁵×C₃	—	9	1	no	—
108	C₂⁴×D₃	—	3	4	no	—
109	C₂²×C₃×D₄	—	2	4	no	—
110	C₂²×C₃×D₄	—	9	2	no	—
111	C₂²×C₃×D₄	C₃×D₃	1	4	yes	complemented
112	C₂²×C₃×D₄	C₃⋊D₃	1	1	yes	characteristic, complemented
113	C₂²×#67	—	3	8	no	—
114	C₃×#120	—	9	8	no	—
115	C₂×C₃×C₂²⋊C₄	—	9	1	no	—
116	C₂×C₃×C₂²⋊C₄	—	9	2	no	—
117	C₂×#217	—	3	4	no	—
118	#937	—	3	32	no	—
119	C₂×(C₂×D₃)⋊C₄	—	3	8	no	—
120	C₂³×C₃²	—	2	4	no	—
121	C₂³×C₃²	—	2	16	no	—
122	C₂³×C₃²	—	2	8	no	—
123	C₂³×C₃²	—	2	4	no	—
124	C₂³×C₃²	—	2	2	no	—
125	C₂³×C₃²	—	2	16	no	—
126	C₂³×C₃²	—	2	4	no	—
127	C₂³×C₃²	—	2	8	no	—
128	C₂³×C₃²	—	2	8	no	—
129	C₂³×C₃²	—	2	16	no	—
130	C₂³×C₃²	—	2	16	no	—
131	C₂³×C₃²	—	4	16	no	—
132	C₂³×C₃²	—	4	16	no	—
133	C₂³×C₃²	#67	1	16	yes	complemented
134	C₂³×C₃²	C₃×D₄	1	4	yes	complemented
135	C₂³×C₃²	C₂²×D₃	1	8	yes	—
136	C₂³×C₃²	C₂²×D₃	1	4	yes	—
137	C₂³×C₃²	C₂²×D₃	1	8	yes	complemented
138	C₂³×C₃²	C₂³×C₃	1	2	yes	—
139	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
140	C₂³×C₃²	C₂³×C₃	1	2	yes	complemented
141	C₂²×C₃⋊D₃	—	2	32	no	—
142	C₂²×C₃⋊D₃	—	2	4	no	—
143	C₂²×C₃⋊D₃	—	2	4	no	—
144	C₂²×C₃⋊D₃	—	2	8	no	—
145	C₂²×C₃⋊D₃	—	2	16	no	—
146	C₂²×C₃⋊D₃	C₃×D₄	1	8	yes	complemented
147	C₂²×C₃⋊D₃	C₂³×C₃	1	4	yes	—
148	C₂²×C₃×D₃	—	3	32	no	—
149	C₂²×C₃×D₃	—	3	16	no	—
150	C₂²×C₃×D₃	—	6	64	no	—
151	C₂²×C₃×D₃	—	6	128	no	—
152	C₂²×C₃×D₃	—	6	16	no	—
153	C₂²×C₃×D₃	—	6	16	no	—
154	C₂²×C₃×D₃	—	6	32	no	—
155	C₃²×D₄	—	2	64	no	—
156	C₃²×D₄	—	2	32	no	—
157	C₃²×D₄	—	2	8	no	—
158	C₂×C₃²×C₄	—	2	16	no	—
159	C₂×C₃²×C₄	—	2	8	no	—
160	C₂×C₃²×C₄	—	2	2	no	—
161	C₂×C₃²×C₄	—	2	8	no	—
162	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	complemented
163	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	complemented
164	#638	—	2	16	no	—
165	C₂×C₃⋊Dic₃	—	2	4	no	—
166	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	complemented
167	C₃×#67	—	6	64	no	—
168	C₂×C₃×Dic₃	—	3	16	no	—
169	C₂×C₃×Dic₃	—	6	16	no	—
170	C₂×#120	—	9	1	no	Sylow
171	C₂×C₃³	—	2	4	no	—
172	C₂×C₃³	—	4	2	no	—
173	C₂×C₃³	#120	1	4	yes	complemented
174	C₂×C₃³	C₂²×D₄	1	2	yes	—
175	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
176	C₃×C₃⋊D₃	—	2	8	no	—
177	C₂⁴×C₃	—	2	4	no	—
178	C₂⁴×C₃	—	2	4	no	—
179	C₂⁴×C₃	—	9	2	no	—
180	C₂⁴×C₃	—	9	4	no	—
181	C₂⁴×C₃	—	18	8	no	—
182	C₂⁴×C₃	—	18	4	no	—
183	C₂⁴×C₃	C₂×C₃×D₃	1	4	yes	—
184	C₂⁴×C₃	C₂×C₃×D₃	1	4	yes	complemented
185	C₂⁴×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
186	C₂⁴×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
187	C₂³×D₃	—	3	8	no	—
188	C₂³×D₃	—	3	16	no	—
189	C₂³×D₃	—	6	32	no	—
190	C₂³×D₃	—	6	16	no	—
191	C₂×C₃×D₄	—	2	32	no	—
192	C₂×C₃×D₄	—	2	16	no	—
193	C₂×C₃×D₄	—	2	4	no	—
194	C₂×C₃×D₄	—	2	16	no	—
195	C₂×C₃×D₄	—	9	8	no	—
196	C₂×C₃×D₄	—	18	8	no	—
197	C₂×C₃×D₄	C₂×C₃×D₃	1	16	yes	complemented
198	C₂×C₃×D₄	C₂×C₃⋊D₃	1	4	yes	complemented
199	C₂²×C₃×C₄	—	2	4	no	—
200	C₂²×C₃×C₄	—	9	2	no	—
201	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	complemented
202	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
203	C₂×#67	—	3	32	no	—
204	C₂×#67	—	6	32	no	—
205	C₂²×Dic₃	—	3	8	no	—
206	C₃×C₂²⋊C₄	—	9	4	no	—
207	C₃×C₂²⋊C₄	—	9	8	no	—
208	#217	—	3	16	no	—
209	(C₂×D₃)⋊C₄	—	3	32	no	—
210	C₂²×C₃²	—	2	8	no	—
211	C₂²×C₃²	—	2	4	no	—
212	C₂²×C₃²	—	2	16	no	—
213	C₂²×C₃²	—	2	8	no	—
214	C₂²×C₃²	—	2	4	no	—
215	C₂²×C₃²	—	2	2	no	—
216	C₂²×C₃²	—	2	4	no	—
217	C₂²×C₃²	—	2	16	no	—
218	C₂²×C₃²	—	2	8	no	—
219	C₂²×C₃²	—	2	16	no	—
220	C₂²×C₃²	—	2	32	no	—
221	C₂²×C₃²	—	2	16	no	—
222	C₂²×C₃²	—	2	16	no	—
223	C₂²×C₃²	—	4	32	no	—
224	C₂²×C₃²	—	4	16	no	—
225	C₂²×C₃²	—	4	16	no	—
226	C₂²×C₃²	—	4	32	no	—
227	C₂²×C₃²	—	4	16	no	—
228	C₂²×C₃²	—	4	4	no	—
229	C₂²×C₃²	D₃×D₄	1	16	yes	—
230	C₂²×C₃²	C₂×#67	1	8	yes	—
231	C₂²×C₃²	C₂×#67	1	16	yes	complemented
232	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
233	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
234	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	complemented
235	C₂²×C₃²	C₂³×D₃	1	4	yes	—
236	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
237	C₂×C₃⋊D₃	—	2	32	no	—
238	C₂×C₃⋊D₃	—	2	16	no	—
239	C₂×C₃⋊D₃	—	2	4	no	—
240	C₂×C₃⋊D₃	—	2	4	no	—
241	C₂×C₃⋊D₃	C₂×C₃×D₄	1	8	yes	complemented
242	C₂×C₃×D₃	—	3	32	no	—
243	C₂×C₃×D₃	—	6	128	no	—
244	C₂×C₃×D₃	—	6	64	no	—
245	C₂×C₃×D₃	—	6	16	no	—
246	C₂×C₃×D₃	—	6	16	no	—
247	C₃²×C₄	—	2	16	no	—
248	C₃²×C₄	—	2	8	no	—
249	C₃²×C₄	—	2	2	no	—
250	C₃⋊Dic₃	—	2	4	no	—
251	C₃×Dic₃	—	6	16	no	—
252	C₂⁵	—	9	1	no	—
253	C₂²×D₄	—	9	2	no	—
254	C₂²×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
255	#120	—	9	8	no	—
256	C₂×C₂²⋊C₄	—	9	1	no	—
257	C₂×C₂²⋊C₄	—	9	2	no	—
258	C₃³	C₂×#120	1	1	yes	characteristic, complemented, Sylow
259	C₂³×C₃	—	2	16	no	—
260	C₂³×C₃	—	2	4	no	—
261	C₂³×C₃	—	2	16	no	—
262	C₂³×C₃	—	2	16	no	—
263	C₂³×C₃	—	2	8	no	—
264	C₂³×C₃	—	2	4	no	—
265	C₂³×C₃	—	2	2	no	—
266	C₂³×C₃	—	2	16	no	—
267	C₂³×C₃	—	2	4	no	—
268	C₂³×C₃	—	2	8	no	—
269	C₂³×C₃	—	2	8	no	—
270	C₂³×C₃	—	4	16	no	—
271	C₂³×C₃	—	4	16	no	—
272	C₂³×C₃	—	9	4	no	—
273	C₂³×C₃	—	9	8	no	—
274	C₂³×C₃	—	18	16	no	—
275	C₂³×C₃	—	18	32	no	—
276	C₂³×C₃	—	18	4	no	—
277	C₂³×C₃	—	18	4	no	—
278	C₂³×C₃	—	18	8	no	—
279	C₂³×C₃	C₃×#67	1	16	yes	complemented
280	C₂³×C₃	#638	1	4	yes	complemented
281	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
282	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
283	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	complemented
284	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
285	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
286	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	complemented
287	C₂²×D₃	—	3	16	no	—
288	C₂²×D₃	—	3	32	no	—
289	C₂²×D₃	—	6	64	no	—
290	C₂²×D₃	—	6	128	no	—
291	C₂²×D₃	—	6	16	no	—
292	C₂²×D₃	—	6	16	no	—
293	C₂²×D₃	—	6	32	no	—
294	C₃×D₄	—	2	64	no	—
295	C₃×D₄	—	2	32	no	—
296	C₃×D₄	—	2	8	no	—
297	C₃×D₄	—	18	16	no	—
298	C₂×C₃×C₄	—	2	16	no	—
299	C₂×C₃×C₄	—	2	8	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	8	no	—
302	C₂×C₃×C₄	—	9	4	no	—
303	C₂×C₃×C₄	—	18	4	no	—
304	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	complemented
305	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	complemented
306	#67	—	6	64	no	—
307	C₂×Dic₃	—	3	16	no	—
308	C₂×Dic₃	—	6	16	no	—
309	C₂×C₃²	—	2	4	no	—
310	C₂×C₃²	—	2	16	no	—
311	C₂×C₃²	—	2	8	no	—
312	C₂×C₃²	—	2	4	no	—
313	C₂×C₃²	—	2	16	no	—
314	C₂×C₃²	—	4	16	no	—
315	C₂×C₃²	—	4	16	no	—
316	C₂×C₃²	—	4	8	no	—
317	C₂×C₃²	—	4	2	no	—
318	C₂×C₃²	#937	1	16	yes	complemented
319	C₂×C₃²	C₃×#120	1	4	yes	complemented
320	C₂×C₃²	C₂×D₃×D₄	1	8	yes	—
321	C₂×C₃²	C₂²×#67	1	4	yes	—
322	C₂×C₃²	C₂²×C₃×D₄	1	2	yes	—
323	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
324	C₃⋊D₃	—	2	8	no	—
325	C₃×D₃	—	6	32	no	—
326	C₂⁴	—	9	2	no	—
327	C₂⁴	—	9	4	no	—
328	C₂⁴	—	18	8	no	—
329	C₂⁴	—	18	4	no	—
330	C₂⁴	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
331	C₂⁴	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	9	8	no	—
334	C₂×D₄	—	18	8	no	—
335	C₂×D₄	C₂×C₃×C₃⋊D₃	1	4	yes	complemented
336	C₂²×C₄	—	9	2	no	—
337	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
338	C₂²⋊C₄	—	9	4	no	—
339	C₂²⋊C₄	—	9	8	no	—
340	C₂²×C₃	—	2	32	no	—
341	C₂²×C₃	—	2	16	no	—
342	C₂²×C₃	—	2	4	no	—
343	C₂²×C₃	—	2	8	no	—
344	C₂²×C₃	—	2	16	no	—
345	C₂²×C₃	—	2	16	no	—
346	C₂²×C₃	—	2	8	no	—
347	C₂²×C₃	—	2	4	no	—
348	C₂²×C₃	—	2	2	no	—
349	C₂²×C₃	—	2	4	no	—
350	C₂²×C₃	—	2	16	no	—
351	C₂²×C₃	—	2	8	no	—
352	C₂²×C₃	—	2	16	no	—
353	C₂²×C₃	—	4	32	no	—
354	C₂²×C₃	—	4	16	no	—
355	C₂²×C₃	—	4	16	no	—
356	C₂²×C₃	—	4	32	no	—
357	C₂²×C₃	—	4	16	no	—
358	C₂²×C₃	—	4	4	no	—
359	C₂²×C₃	—	9	8	no	—
360	C₂²×C₃	—	18	32	no	—
361	C₂²×C₃	—	18	4	no	—
362	C₂²×C₃	—	18	4	no	—
363	C₂²×C₃	—	18	16	no	—
364	C₂²×C₃	C₃×D₃×D₄	1	16	yes	—
365	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
366	C₂²×C₃	C₂×C₃×#67	1	16	yes	complemented
367	C₂²×C₃	D₄×C₃⋊D₃	1	4	yes	—
368	C₂²×C₃	C₂×#638	1	2	yes	—
369	C₂²×C₃	C₂×#638	1	4	yes	complemented
370	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
371	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
372	C₂×D₃	—	3	32	no	—
373	C₂×D₃	—	6	128	no	—
374	C₂×D₃	—	6	64	no	—
375	C₂×D₃	—	6	16	no	—
376	C₂×D₃	—	6	16	no	—
377	C₃×C₄	—	2	16	no	—
378	C₃×C₄	—	2	8	no	—
379	C₃×C₄	—	2	2	no	—
380	C₃×C₄	—	18	4	no	—
381	Dic₃	—	6	16	no	—
382	C₃²	—	2	4	no	—
383	C₃²	C₂×#937	1	4	yes	complemented
384	C₃²	C₂×C₃×#120	1	1	yes	characteristic, complemented
385	C₂³	—	2	4	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	9	4	no	—
389	C₂³	—	9	8	no	—
390	C₂³	—	18	16	no	—
391	C₂³	—	18	32	no	—
392	C₂³	—	18	4	no	—
393	C₂³	—	18	4	no	—
394	C₂³	—	18	8	no	—
395	C₂³	C₃×#638	1	4	yes	complemented
396	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
397	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
398	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	complemented
399	D₄	—	2	8	no	—
400	D₄	—	18	16	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	9	4	no	—
403	C₂×C₄	—	18	4	no	—
404	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	complemented
405	C₂×C₃	—	2	16	no	—
406	C₂×C₃	—	2	4	no	—
407	C₂×C₃	—	2	16	no	—
408	C₂×C₃	—	2	8	no	—
409	C₂×C₃	—	2	4	no	—
410	C₂×C₃	—	4	16	no	—
411	C₂×C₃	—	4	16	no	—
412	C₂×C₃	—	4	8	no	—
413	C₂×C₃	—	4	2	no	—
414	C₂×C₃	—	18	8	no	—
415	C₂×C₃	C₃×#937	1	16	yes	complemented
416	C₂×C₃	#64146	1	4	yes	direct product factor
417	C₂×C₃	C₂×C₃×D₃×D₄	1	8	yes	—
418	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
419	C₂×C₃	C₂×D₄×C₃⋊D₃	1	2	yes	—
420	C₂×C₃	C₂²×#638	1	1	yes	characteristic
421	D₃	—	6	32	no	—
422	C₂²	—	2	8	no	—
423	C₂²	—	2	4	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	9	8	no	—
428	C₂²	—	18	32	no	—
429	C₂²	—	18	16	no	—
430	C₂²	—	18	4	no	—
431	C₂²	—	18	4	no	—
432	C₂²	C₃×D₄×C₃⋊D₃	1	4	yes	—
433	C₂²	C₂×C₃×#638	1	2	yes	—
434	C₂²	C₂×C₃×#638	1	4	yes	complemented
435	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	18	4	no	—
438	C₃	—	2	4	no	—
439	C₃	C₂×C₃×#937	1	4	yes	complemented
440	C₃	C₂×#64146	1	1	yes	characteristic, direct product factor
441	C₂	—	2	4	no	—
442	C₂	—	4	2	no	—
443	C₂	—	18	8	no	—
444	C₂	C₃×#64146	1	4	yes	direct product factor
445	C₂	C₂×C₃×D₄×C₃⋊D₃	1	2	yes	—
446	C₂	C₂²×C₃×#638	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂²×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₂²×C₃³×D₄	C₂
socle	C₂³×C₃³	C₂³
hypercenter	C₂²×C₃×D₄	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×#120
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃×C₃⋊D₃	C₂	semidirect
2. C₂²×C₃³×D₄	C₂	semidirect
3. C₂²×C₃×#638	C₂	semidirect
4. C₂×C₃×#3757	C₂	semidirect
5. C₃×#64146	C₂	direct (N × H)
6. C₂×C₃×#3752	C₂	semidirect
7. C₂×#64146	C₃	direct (N × H)
10. C₂⁴×C₃³	C₂²	semidirect
14. C₂³×C₃×C₃⋊D₃	C₂²	semidirect
16. C₂×C₃³×D₄	C₂²	semidirect
17. C₂²×C₃³×C₄	C₂²	semidirect
19. C₂×C₃×#638	C₂²	semidirect
20. C₂²×C₃×C₃⋊Dic₃	C₂²	semidirect
21. C₃×#3757	C₂²	semidirect
22. C₃×#3752	C₂²	semidirect
23. C₂⁴×C₃⋊D₃	C₂×C₃	semidirect
26. C₂²×C₃²×D₄	D₃	semidirect
27. C₂²×C₃²×D₄	C₂×C₃	semidirect
28. C₂²×#638	C₂×C₃	semidirect
30. C₂×#3757	C₂×C₃	semidirect
31. #64146	C₂×C₃	direct (N × H)
32. C₂×#3752	C₂×C₃	semidirect
39. C₂³×C₃³	D₄	semidirect
42. C₂³×C₃³	C₂³	semidirect
48. C₂²×C₃×C₃⋊D₃	D₄	semidirect
52. C₂×C₃³×C₄	C₂³	semidirect
55. C₂×C₃×C₃⋊Dic₃	C₂³	semidirect
61. C₂⁴×C₃²	C₂×D₃	semidirect
63. C₂⁴×C₃²	C₂²×C₃	semidirect
67. C₂³×C₃⋊D₃	C₂²×C₃	semidirect
76. C₂×C₃²×D₄	C₂×D₃	semidirect
77. C₂×C₃²×D₄	C₂²×C₃	semidirect
79. C₂²×C₃²×C₄	C₂×D₃	semidirect
80. C₂²×C₃²×C₄	C₂²×C₃	semidirect
82. C₂×#638	C₂²×C₃	semidirect
83. C₂²×C₃⋊Dic₃	C₂²×C₃	semidirect
87. #3757	C₂²×C₃	semidirect
88. #3752	C₂²×C₃	semidirect
98. C₂²×C₃³	C₂×D₄	semidirect
104. C₂×C₃×C₃⋊D₃	C₂×D₄	semidirect
111. C₂²×C₃×D₄	C₃×D₃	semidirect
112. C₂²×C₃×D₄	C₃⋊D₃	semidirect
133. C₂³×C₃²	#67	semidirect
134. C₂³×C₃²	C₃×D₄	semidirect
137. C₂³×C₃²	C₂²×D₃	semidirect
140. C₂³×C₃²	C₂³×C₃	semidirect
146. C₂²×C₃⋊D₃	C₃×D₄	semidirect
162. C₂×C₃²×C₄	C₂²×D₃	semidirect
163. C₂×C₃²×C₄	C₂³×C₃	semidirect
166. C₂×C₃⋊Dic₃	C₂³×C₃	semidirect
173. C₂×C₃³	#120	semidirect
184. C₂⁴×C₃	C₂×C₃×D₃	semidirect
186. C₂⁴×C₃	C₂×C₃⋊D₃	semidirect
197. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
198. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
201. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
202. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
231. C₂²×C₃²	C₂×#67	semidirect
234. C₂²×C₃²	C₂×C₃×D₄	semidirect
241. C₂×C₃⋊D₃	C₂×C₃×D₄	semidirect
254. C₂²×D₄	C₃×C₃⋊D₃	semidirect
258. C₃³	C₂×#120	semidirect
279. C₂³×C₃	C₃×#67	semidirect
280. C₂³×C₃	#638	semidirect
283. C₂³×C₃	C₂²×C₃×D₃	semidirect
286. C₂³×C₃	C₂²×C₃⋊D₃	semidirect
304. C₂×C₃×C₄	C₂²×C₃×D₃	semidirect
305. C₂×C₃×C₄	C₂²×C₃⋊D₃	semidirect
318. C₂×C₃²	#937	semidirect
319. C₂×C₃²	C₃×#120	semidirect
331. C₂⁴	C₂×C₃×C₃⋊D₃	semidirect
335. C₂×D₄	C₂×C₃×C₃⋊D₃	semidirect
337. C₂²×C₄	C₂×C₃×C₃⋊D₃	semidirect
366. C₂²×C₃	C₂×C₃×#67	semidirect
369. C₂²×C₃	C₂×#638	semidirect
383. C₃²	C₂×#937	semidirect
384. C₃²	C₂×C₃×#120	semidirect
395. C₂³	C₃×#638	semidirect
398. C₂³	C₂²×C₃×C₃⋊D₃	semidirect
404. C₂×C₄	C₂²×C₃×C₃⋊D₃	semidirect
415. C₂×C₃	C₃×#937	semidirect
416. C₂×C₃	#64146	direct (N × H)
434. C₂²	C₂×C₃×#638	semidirect
439. C₃	C₂×C₃×#937	semidirect
440. C₃	C₂×#64146	direct (N × H)
444. C₂	C₃×#64146	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×C₃⋊D₃	2
C₂²×C₃³×D₄	2
C₂²×C₃×#638	2
C₂×C₃×#3757	2
C₃×#64146	2
C₂×C₃×#3752	2
C₂×#64146	3
C₂×C₃×#937	3

Subgroups — C2×C3×#64146 #13179552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64146 #13179552