Subgroups — C₂×C₃×#64139 #13179541

Order 1728.

3500 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃³×C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#638	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64139	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3752	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#64139	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×#930	—	3	4	no	maximal
9	C₂⁴×C₃³	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₃⋊D₃	C₂²	1	2	yes	—
11	C₂²×C₃³×C₄	—	2	4	no	—
12	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
13	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
14	C₂²×C₃³×C₄	C₂²	1	4	yes	complemented
15	C₂×C₃×#638	—	2	8	no	—
16	C₂×C₃×#638	C₂²	1	8	yes	complemented
17	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	—
18	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
19	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	4	yes	complemented
20	C₃×#3752	C₂²	1	8	yes	complemented
21	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	4	yes	complemented
22	C₂³×C₃²×C₄	—	2	4	no	—
23	C₂³×C₃²×C₄	D₃	1	4	yes	complemented
24	C₂³×C₃²×C₄	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂²×#638	C₂×C₃	1	2	yes	complemented
26	C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂²×C₃×#67	—	3	8	no	—
28	C₂²×C₃×D₁₂	—	3	4	no	—
29	#64139	C₂×C₃	1	8	yes	direct product factor
30	C₂×#3752	C₂×C₃	1	2	yes	complemented
31	C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	1	1	yes	characteristic, complemented
32	C₃×#930	—	3	32	no	—
33	C₂×C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
34	C₂×C₃×C₄⋊Dic₃	—	3	4	no	—
35	C₂³×C₃³	—	2	2	no	—
36	C₂³×C₃³	—	2	2	no	—
37	C₂³×C₃³	D₄	1	4	yes	complemented
38	C₂³×C₃³	C₂³	1	2	yes	—
39	C₂³×C₃³	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
41	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
42	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
43	C₂²×C₃×C₃⋊D₃	C₂³	1	4	yes	—
44	C₂×C₃³×C₄	—	2	2	no	—
45	C₂×C₃³×C₄	—	2	8	no	—
46	C₂×C₃³×C₄	D₄	1	4	yes	complemented
47	C₂×C₃³×C₄	C₂³	1	2	yes	—
48	C₂×C₃³×C₄	C₂³	1	2	yes	—
49	C₃×#638	—	2	16	no	—
50	C₂×C₃×C₃⋊Dic₃	—	2	4	no	—
51	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	—
52	C₃×C₄⋊(C₃⋊D₃)	—	2	8	no	—
53	C₂×C₃×#121	—	9	1	no	—
54	C₂×#930	—	3	4	no	—
55	C₂⁴×C₃²	—	2	4	no	—
56	C₂⁴×C₃²	C₂×D₃	1	4	yes	—
57	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
58	C₂³×C₃⋊D₃	C₂²×C₃	1	2	yes	—
59	C₂³×C₃×D₃	—	3	8	no	—
60	C₂²×C₃²×C₄	—	2	32	no	—
61	C₂²×C₃²×C₄	—	2	4	no	—
62	C₂²×C₃²×C₄	—	2	4	no	—
63	C₂²×C₃²×C₄	—	2	16	no	—
64	C₂²×C₃²×C₄	—	2	16	no	—
65	C₂²×C₃²×C₄	—	2	4	no	—
66	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
67	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
68	C₂²×C₃²×C₄	C₂×D₃	1	16	yes	complemented
69	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
71	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	complemented
72	C₂×#638	—	2	8	no	—
73	C₂×#638	C₂²×C₃	1	8	yes	complemented
74	C₂²×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
75	C₂×C₄⋊(C₃⋊D₃)	—	2	4	no	—
76	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	4	yes	complemented
77	C₂×C₃×#67	—	3	32	no	—
78	C₂×C₃×#67	—	6	32	no	—
79	C₂²×C₃×Dic₃	—	3	8	no	—
80	C₂×C₃×D₁₂	—	3	16	no	—
81	C₂×C₃×D₁₂	—	6	16	no	—
82	#3752	C₂²×C₃	1	8	yes	complemented
83	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	4	yes	complemented
84	C₃×(C₂×D₃)⋊C₄	—	3	32	no	—
85	C₃×C₄⋊Dic₃	—	3	16	no	—
86	C₂²×C₃³	—	2	8	no	—
87	C₂²×C₃³	—	2	2	no	—
88	C₂²×C₃³	—	2	2	no	—
89	C₂²×C₃³	C₂×D₄	1	2	yes	—
90	C₂²×C₃³	C₂×D₄	1	2	yes	—
91	C₂²×C₃³	C₂×D₄	1	4	yes	complemented
92	C₂²×C₃³	#41	1	2	yes	—
93	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
94	C₂×C₃×C₃⋊D₃	—	2	4	no	—
95	C₂×C₃×C₃⋊D₃	—	2	4	no	—
96	C₂×C₃×C₃⋊D₃	—	2	4	no	—
97	C₂×C₃×C₃⋊D₃	—	4	8	no	—
98	C₃³×C₄	—	2	2	no	—
99	C₃³×C₄	C₂×D₄	1	4	yes	complemented
100	C₃×C₃⋊Dic₃	—	2	4	no	—
101	C₂²×C₃×D₄	—	9	2	no	—
102	C₂²×C₃×D₄	—	9	1	no	—
103	C₂³×C₃×C₄	—	2	4	no	—
104	C₂³×C₃×C₄	C₃×D₃	1	4	yes	complemented
105	C₂³×C₃×C₄	C₃⋊D₃	1	1	yes	characteristic, complemented
106	C₂²×#67	—	3	8	no	—
107	C₂²×D₁₂	—	3	4	no	—
108	C₃×#121	—	9	8	no	—
109	C₂×C₃×C₄⋊C₄	—	9	1	no	—
110	C₂×C₃×C₂²⋊C₄	—	9	2	no	—
111	#930	—	3	32	no	—
112	C₂×(C₂×D₃)⋊C₄	—	3	8	no	—
113	C₂×C₄⋊Dic₃	—	3	4	no	—
114	C₂³×C₃²	—	2	16	no	—
115	C₂³×C₃²	—	2	16	no	—
116	C₂³×C₃²	—	2	8	no	—
117	C₂³×C₃²	—	2	8	no	—
118	C₂³×C₃²	—	2	2	no	—
119	C₂³×C₃²	—	2	2	no	—
120	C₂³×C₃²	—	2	16	no	—
121	C₂³×C₃²	—	2	8	no	—
122	C₂³×C₃²	—	2	4	no	—
123	C₂³×C₃²	D₁₂	1	16	yes	complemented
124	C₂³×C₃²	C₃×D₄	1	4	yes	complemented
125	C₂³×C₃²	C₂²×D₃	1	8	yes	—
126	C₂³×C₃²	C₂²×D₃	1	4	yes	—
127	C₂³×C₃²	C₂³×C₃	1	2	yes	—
128	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
129	C₂²×C₃⋊D₃	—	2	4	no	—
130	C₂²×C₃⋊D₃	—	2	4	no	—
131	C₂²×C₃⋊D₃	—	2	4	no	—
132	C₂²×C₃⋊D₃	C₂³×C₃	1	4	yes	—
133	C₂²×C₃×D₃	—	3	16	no	—
134	C₂²×C₃×D₃	—	6	16	no	—
135	C₂²×C₃×D₃	—	6	16	no	—
136	C₂²×C₃×D₃	—	6	16	no	—
137	C₂×C₃²×C₄	—	2	16	no	—
138	C₂×C₃²×C₄	—	2	64	no	—
139	C₂×C₃²×C₄	—	2	8	no	—
140	C₂×C₃²×C₄	—	2	2	no	—
141	C₂×C₃²×C₄	—	2	32	no	—
142	C₂×C₃²×C₄	—	2	8	no	—
143	C₂×C₃²×C₄	—	2	16	no	—
144	C₂×C₃²×C₄	—	2	8	no	—
145	C₂×C₃²×C₄	—	2	8	no	—
146	C₂×C₃²×C₄	#67	1	16	yes	complemented
147	C₂×C₃²×C₄	C₃×D₄	1	4	yes	complemented
148	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
149	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
150	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
151	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
152	#638	—	2	16	no	—
153	C₂×C₃⋊Dic₃	—	2	4	no	—
154	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	—
155	C₄⋊(C₃⋊D₃)	—	2	8	no	—
156	C₃×#67	—	6	64	no	—
157	C₂×C₃×Dic₃	—	3	16	no	—
158	C₂×C₃×Dic₃	—	6	16	no	—
159	C₃×D₁₂	—	6	32	no	—
160	C₂×#121	—	9	1	no	Sylow
161	C₂×C₃³	—	2	4	no	—
162	C₂×C₃³	#121	1	4	yes	complemented
163	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₃³	C₂×#41	1	1	yes	characteristic
166	C₃×C₃⋊D₃	—	4	4	no	—
167	C₂⁴×C₃	—	2	4	no	—
168	C₂⁴×C₃	—	9	2	no	—
169	C₂⁴×C₃	C₂×C₃×D₃	1	4	yes	—
170	C₂⁴×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
171	C₂³×D₃	—	3	8	no	—
172	C₂×C₃×D₄	—	9	8	no	—
173	C₂×C₃×D₄	—	9	4	no	—
174	C₂×C₃×D₄	—	18	8	no	—
175	C₂×C₃×D₄	—	18	4	no	—
176	C₂²×C₃×C₄	—	2	32	no	—
177	C₂²×C₃×C₄	—	2	16	no	—
178	C₂²×C₃×C₄	—	2	4	no	—
179	C₂²×C₃×C₄	—	2	4	no	—
180	C₂²×C₃×C₄	—	2	4	no	—
181	C₂²×C₃×C₄	—	2	16	no	—
182	C₂²×C₃×C₄	—	9	2	no	—
183	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
184	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
185	C₂²×C₃×C₄	C₂×C₃×D₃	1	16	yes	complemented
186	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
187	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
188	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	4	yes	complemented
189	C₂×#67	—	3	32	no	—
190	C₂×#67	—	6	32	no	—
191	C₂²×Dic₃	—	3	8	no	—
192	C₂×D₁₂	—	3	16	no	—
193	C₂×D₁₂	—	6	16	no	—
194	C₃×C₄⋊C₄	—	9	4	no	—
195	C₃×C₂²⋊C₄	—	9	8	no	—
196	(C₂×D₃)⋊C₄	—	3	32	no	—
197	C₄⋊Dic₃	—	3	16	no	—
198	C₂²×C₃²	—	2	16	no	—
199	C₂²×C₃²	—	2	64	no	—
200	C₂²×C₃²	—	2	16	no	—
201	C₂²×C₃²	—	2	32	no	—
202	C₂²×C₃²	—	2	8	no	—
203	C₂²×C₃²	—	2	8	no	—
204	C₂²×C₃²	—	2	8	no	—
205	C₂²×C₃²	—	2	2	no	—
206	C₂²×C₃²	—	2	2	no	—
207	C₂²×C₃²	—	2	4	no	—
208	C₂²×C₃²	—	2	8	no	—
209	C₂²×C₃²	—	2	16	no	—
210	C₂²×C₃²	—	2	8	no	—
211	C₂²×C₃²	—	2	8	no	—
212	C₂²×C₃²	C₂×D₁₂	1	8	yes	—
213	C₂²×C₃²	C₂×D₁₂	1	16	yes	complemented
214	C₂²×C₃²	#235	1	8	yes	—
215	C₂²×C₃²	C₂×#67	1	8	yes	—
216	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
217	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
218	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	complemented
219	C₂²×C₃²	C₃×#41	1	2	yes	—
220	C₂²×C₃²	C₂³×D₃	1	4	yes	—
221	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
222	C₂×C₃⋊D₃	—	2	4	no	—
223	C₂×C₃⋊D₃	—	2	4	no	—
224	C₂×C₃⋊D₃	—	2	4	no	—
225	C₂×C₃⋊D₃	—	4	8	no	—
226	C₂×C₃×D₃	—	6	16	no	—
227	C₂×C₃×D₃	—	6	16	no	—
228	C₂×C₃×D₃	—	6	16	no	—
229	C₂×C₃×D₃	—	12	32	no	—
230	C₃²×C₄	—	2	16	no	—
231	C₃²×C₄	—	2	8	no	—
232	C₃²×C₄	—	2	2	no	—
233	C₃²×C₄	—	2	16	no	—
234	C₃²×C₄	C₂×#67	1	16	yes	complemented
235	C₃²×C₄	C₂×C₃×D₄	1	4	yes	complemented
236	C₃⋊Dic₃	—	2	4	no	—
237	C₃×Dic₃	—	6	16	no	—
238	C₂²×D₄	—	9	2	no	—
239	C₂²×D₄	—	9	1	no	—
240	C₂³×C₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
241	#121	—	9	8	no	—
242	C₂×C₄⋊C₄	—	9	1	no	—
243	C₂×C₂²⋊C₄	—	9	2	no	—
244	C₃³	C₂×#121	1	1	yes	characteristic, complemented, Sylow
245	C₂³×C₃	—	2	16	no	—
246	C₂³×C₃	—	2	16	no	—
247	C₂³×C₃	—	2	8	no	—
248	C₂³×C₃	—	2	8	no	—
249	C₂³×C₃	—	2	2	no	—
250	C₂³×C₃	—	2	2	no	—
251	C₂³×C₃	—	2	16	no	—
252	C₂³×C₃	—	2	8	no	—
253	C₂³×C₃	—	2	4	no	—
254	C₂³×C₃	—	9	4	no	—
255	C₂³×C₃	—	18	4	no	—
256	C₂³×C₃	—	18	4	no	—
257	C₂³×C₃	—	18	4	no	—
258	C₂³×C₃	C₃×D₁₂	1	16	yes	complemented
259	C₂³×C₃	C₄⋊(C₃⋊D₃)	1	4	yes	complemented
260	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
261	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
262	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
263	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
264	C₂²×D₃	—	3	16	no	—
265	C₂²×D₃	—	6	16	no	—
266	C₂²×D₃	—	6	16	no	—
267	C₂²×D₃	—	6	16	no	—
268	C₃×D₄	—	18	16	no	—
269	C₃×D₄	—	18	8	no	—
270	C₂×C₃×C₄	—	2	16	no	—
271	C₂×C₃×C₄	—	2	64	no	—
272	C₂×C₃×C₄	—	2	8	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	32	no	—
275	C₂×C₃×C₄	—	2	8	no	—
276	C₂×C₃×C₄	—	2	16	no	—
277	C₂×C₃×C₄	—	2	8	no	—
278	C₂×C₃×C₄	—	2	8	no	—
279	C₂×C₃×C₄	—	9	4	no	—
280	C₂×C₃×C₄	—	18	4	no	—
281	C₂×C₃×C₄	C₃×#67	1	16	yes	complemented
282	C₂×C₃×C₄	#638	1	4	yes	complemented
283	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
284	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
285	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
286	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
287	#67	—	6	64	no	—
288	C₂×Dic₃	—	3	16	no	—
289	C₂×Dic₃	—	6	16	no	—
290	D₁₂	—	6	32	no	—
291	C₂×C₃²	—	2	32	no	—
292	C₂×C₃²	—	2	16	no	—
293	C₂×C₃²	—	2	4	no	—
294	C₂×C₃²	—	2	16	no	—
295	C₂×C₃²	—	2	4	no	—
296	C₂×C₃²	—	2	4	no	—
297	C₂×C₃²	—	2	4	no	—
298	C₂×C₃²	#930	1	16	yes	complemented
299	C₂×C₃²	C₃×#121	1	4	yes	complemented
300	C₂×C₃²	C₂²×D₁₂	1	4	yes	—
301	C₂×C₃²	C₂×#235	1	4	yes	—
302	C₂×C₃²	C₂²×#67	1	4	yes	—
303	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
304	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
305	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
306	C₃⋊D₃	—	4	4	no	—
307	C₃×D₃	—	12	16	no	—
308	C₂⁴	—	9	2	no	—
309	C₂⁴	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
310	C₂×D₄	—	9	8	no	—
311	C₂×D₄	—	9	4	no	—
312	C₂×D₄	—	18	8	no	—
313	C₂×D₄	—	18	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	9	2	no	—
316	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	4	yes	complemented
319	C₄⋊C₄	—	9	4	no	—
320	C₂²⋊C₄	—	9	8	no	—
321	C₂²×C₃	—	2	16	no	—
322	C₂²×C₃	—	2	64	no	—
323	C₂²×C₃	—	2	16	no	—
324	C₂²×C₃	—	2	32	no	—
325	C₂²×C₃	—	2	8	no	—
326	C₂²×C₃	—	2	8	no	—
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	2	8	no	—
330	C₂²×C₃	—	2	4	no	—
331	C₂²×C₃	—	2	8	no	—
332	C₂²×C₃	—	2	16	no	—
333	C₂²×C₃	—	2	8	no	—
334	C₂²×C₃	—	2	8	no	—
335	C₂²×C₃	—	18	4	no	—
336	C₂²×C₃	—	18	4	no	—
337	C₂²×C₃	—	18	4	no	—
338	C₂²×C₃	—	36	8	no	—
339	C₂²×C₃	C₂×C₃×D₁₂	1	8	yes	—
340	C₂²×C₃	C₂×C₃×D₁₂	1	16	yes	complemented
341	C₂²×C₃	C₃×#235	1	8	yes	—
342	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
343	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
344	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	1	4	yes	complemented
345	C₂²×C₃	#3828	1	2	yes	—
346	C₂²×C₃	C₂×#638	1	2	yes	—
347	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
348	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
349	C₂×D₃	—	6	16	no	—
350	C₂×D₃	—	6	16	no	—
351	C₂×D₃	—	6	16	no	—
352	C₂×D₃	—	12	32	no	—
353	C₃×C₄	—	2	16	no	—
354	C₃×C₄	—	2	8	no	—
355	C₃×C₄	—	2	2	no	—
356	C₃×C₄	—	2	16	no	—
357	C₃×C₄	—	18	4	no	—
358	C₃×C₄	C₂×C₃×#67	1	16	yes	complemented
359	C₃×C₄	C₂×#638	1	4	yes	complemented
360	Dic₃	—	6	16	no	—
361	C₃²	—	2	4	no	—
362	C₃²	C₂×#930	1	4	yes	complemented
363	C₃²	C₂×C₃×#121	1	1	yes	characteristic, complemented
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	9	4	no	—
367	C₂³	—	18	4	no	—
368	C₂³	—	18	4	no	—
369	C₂³	—	18	4	no	—
370	C₂³	C₃×C₄⋊(C₃⋊D₃)	1	4	yes	complemented
371	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
372	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
373	D₄	—	18	16	no	—
374	D₄	—	18	8	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	9	4	no	—
378	C₂×C₄	—	18	4	no	—
379	C₂×C₄	C₃×#638	1	4	yes	complemented
380	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
381	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
382	C₂×C₃	—	2	32	no	—
383	C₂×C₃	—	2	16	no	—
384	C₂×C₃	—	2	4	no	—
385	C₂×C₃	—	2	16	no	—
386	C₂×C₃	—	2	4	no	—
387	C₂×C₃	—	2	4	no	—
388	C₂×C₃	—	2	4	no	—
389	C₂×C₃	—	36	4	no	—
390	C₂×C₃	C₃×#930	1	16	yes	complemented
391	C₂×C₃	#64139	1	4	yes	direct product factor
392	C₂×C₃	C₂²×C₃×D₁₂	1	4	yes	—
393	C₂×C₃	C₂×C₃×#235	1	4	yes	—
394	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
395	C₂×C₃	C₂²×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
396	C₂×C₃	C₂×#3828	1	1	yes	characteristic
397	C₂×C₃	C₂²×#638	1	1	yes	characteristic
398	D₃	—	12	16	no	—
399	C₂²	—	2	8	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	18	4	no	—
403	C₂²	—	18	4	no	—
404	C₂²	—	18	4	no	—
405	C₂²	—	36	8	no	—
406	C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
407	C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	1	4	yes	complemented
408	C₂²	C₃×#3828	1	2	yes	—
409	C₂²	C₂×C₃×#638	1	2	yes	—
410	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
411	C₄	—	2	2	no	—
412	C₄	—	18	4	no	—
413	C₄	C₂×C₃×#638	1	4	yes	complemented
414	C₃	—	2	4	no	—
415	C₃	C₂×C₃×#930	1	4	yes	complemented
416	C₃	C₂×#64139	1	1	yes	characteristic, direct product factor
417	C₂	—	2	4	no	—
418	C₂	—	36	4	no	—
419	C₂	C₃×#64139	1	4	yes	direct product factor
420	C₂	C₂²×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
421	C₂	C₂×C₃×#3828	1	1	yes	characteristic
422	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	C₂³×C₃³×C₄	C₂
socle	C₂³×C₃³	C₂³
hypercenter	C₂³×C₃×C₄	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×#121
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃³×C₄	C₂	semidirect
2. C₂²×C₃×#638	C₂	semidirect
3. C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	semidirect
4. C₃×#64139	C₂	direct (N × H)
5. C₂×C₃×#3752	C₂	semidirect
6. C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	semidirect
7. C₂×#64139	C₃	direct (N × H)
14. C₂²×C₃³×C₄	C₂²	semidirect
16. C₂×C₃×#638	C₂²	semidirect
19. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
20. C₃×#3752	C₂²	semidirect
21. C₃×C₄⋊(C₃⋊Dic₃)	C₂²	semidirect
23. C₂³×C₃²×C₄	D₃	semidirect
24. C₂³×C₃²×C₄	C₂×C₃	semidirect
25. C₂²×#638	C₂×C₃	semidirect
26. C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
29. #64139	C₂×C₃	direct (N × H)
30. C₂×#3752	C₂×C₃	semidirect
31. C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	semidirect
37. C₂³×C₃³	D₄	semidirect
46. C₂×C₃³×C₄	D₄	semidirect
68. C₂²×C₃²×C₄	C₂×D₃	semidirect
71. C₂²×C₃²×C₄	C₂²×C₃	semidirect
73. C₂×#638	C₂²×C₃	semidirect
76. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
82. #3752	C₂²×C₃	semidirect
83. C₄⋊(C₃⋊Dic₃)	C₂²×C₃	semidirect
91. C₂²×C₃³	C₂×D₄	semidirect
99. C₃³×C₄	C₂×D₄	semidirect
104. C₂³×C₃×C₄	C₃×D₃	semidirect
105. C₂³×C₃×C₄	C₃⋊D₃	semidirect
123. C₂³×C₃²	D₁₂	semidirect
124. C₂³×C₃²	C₃×D₄	semidirect
146. C₂×C₃²×C₄	#67	semidirect
147. C₂×C₃²×C₄	C₃×D₄	semidirect
162. C₂×C₃³	#121	semidirect
185. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
188. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
213. C₂²×C₃²	C₂×D₁₂	semidirect
218. C₂²×C₃²	C₂×C₃×D₄	semidirect
234. C₃²×C₄	C₂×#67	semidirect
235. C₃²×C₄	C₂×C₃×D₄	semidirect
240. C₂³×C₄	C₃×C₃⋊D₃	semidirect
244. C₃³	C₂×#121	semidirect
258. C₂³×C₃	C₃×D₁₂	semidirect
259. C₂³×C₃	C₄⋊(C₃⋊D₃)	semidirect
281. C₂×C₃×C₄	C₃×#67	semidirect
282. C₂×C₃×C₄	#638	semidirect
298. C₂×C₃²	#930	semidirect
299. C₂×C₃²	C₃×#121	semidirect
318. C₂²×C₄	C₂×C₃×C₃⋊D₃	semidirect
340. C₂²×C₃	C₂×C₃×D₁₂	semidirect
344. C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	semidirect
358. C₃×C₄	C₂×C₃×#67	semidirect
359. C₃×C₄	C₂×#638	semidirect
362. C₃²	C₂×#930	semidirect
363. C₃²	C₂×C₃×#121	semidirect
370. C₂³	C₃×C₄⋊(C₃⋊D₃)	semidirect
379. C₂×C₄	C₃×#638	semidirect
390. C₂×C₃	C₃×#930	semidirect
391. C₂×C₃	#64139	direct (N × H)
407. C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	semidirect
413. C₄	C₂×C₃×#638	semidirect
415. C₃	C₂×C₃×#930	semidirect
416. C₃	C₂×#64139	direct (N × H)
419. C₂	C₃×#64139	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃³×C₄	2
C₂²×C₃×#638	2
C₂²×C₃×C₄⋊(C₃⋊D₃)	2
C₃×#64139	2
C₂×C₃×#3752	2
C₂×C₃×C₄⋊(C₃⋊Dic₃)	2
C₂×#64139	3
C₂×C₃×#930	3

Subgroups — C2×C3×#64139 #13179541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64139 #13179541