Subgroups — C₂×C₃×#64147 #13179553

Order 1728.

3500 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×D₄	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	C₂×C₃×#3757	C₂	1	2	yes	maximal, complemented
5	C₃×#64147	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#64147	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×#938	—	3	4	no	maximal
9	C₂⁴×C₃³	C₂²	1	2	yes	—
10	C₂³×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃³×D₄	—	2	4	no	—
12	C₂×C₃³×D₄	C₂²	1	4	yes	complemented
13	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×#638	—	2	8	no	—
15	C₂×C₃×#638	C₂²	1	8	yes	complemented
16	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	—
17	C₂²×C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄×C₃⋊D₃	—	2	4	no	—
19	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	4	yes	complemented
20	C₃×#3757	C₂²	1	8	yes	complemented
21	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	4	yes	complemented
22	C₂²×C₃²×D₄	—	2	4	no	—
23	C₂²×C₃²×D₄	D₃	1	4	yes	complemented
24	C₂²×C₃²×D₄	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×C₄×D₃	—	3	4	no	—
29	C₂×#3757	C₂×C₃	1	2	yes	complemented
30	#64147	C₂×C₃	1	8	yes	direct product factor
31	C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×C₃×#217	—	3	8	no	—
33	C₃×#938	—	3	32	no	—
34	C₂×C₃×C₄⋊Dic₃	—	3	4	no	—
35	C₂³×C₃³	—	2	4	no	—
36	C₂³×C₃³	—	2	4	no	—
37	C₂³×C₃³	—	2	4	no	—
38	C₂³×C₃³	C₂³	1	4	yes	—
39	C₂³×C₃³	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
41	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
42	C₂²×C₃×C₃⋊D₃	D₄	1	4	yes	complemented
43	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
44	C₃³×D₄	—	2	8	no	—
45	C₂×C₃³×C₄	D₄	1	4	yes	complemented
46	C₂×C₃³×C₄	C₂³	1	2	yes	—
47	C₃×#638	—	2	16	no	—
48	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
49	C₂×C₃×C₃⋊Dic₃	—	2	4	no	—
50	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	—
51	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
52	C₃×C₄×C₃⋊D₃	—	2	8	no	—
53	C₂×C₃×#121	—	9	1	no	—
54	C₂×#938	—	3	4	no	—
55	C₂⁴×C₃²	—	2	8	no	—
56	C₂⁴×C₃²	C₂×D₃	1	8	yes	—
57	C₂⁴×C₃²	C₂²×C₃	1	2	yes	—
58	C₂³×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
59	C₂³×C₃×D₃	—	3	4	no	—
60	C₂×C₃²×D₄	—	2	32	no	—
61	C₂×C₃²×D₄	—	2	16	no	—
62	C₂×C₃²×D₄	—	2	16	no	—
63	C₂×C₃²×D₄	—	2	4	no	—
64	C₂×C₃²×D₄	C₂×D₃	1	16	yes	complemented
65	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	complemented
66	C₂²×C₃²×C₄	—	2	4	no	—
67	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
68	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
69	C₂×#638	—	2	8	no	—
70	C₂×#638	C₂²×C₃	1	8	yes	complemented
71	C₂²×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
73	C₂×C₄×C₃⋊D₃	—	2	4	no	—
74	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	4	yes	complemented
75	C₂×C₃×#67	—	3	32	no	—
76	C₂×C₃×#67	—	6	32	no	—
77	C₂²×C₃×Dic₃	—	3	8	no	—
78	C₂²×C₃×Dic₃	—	3	4	no	—
79	C₂×C₃×C₄×D₃	—	3	16	no	—
80	C₂×C₃×C₄×D₃	—	6	16	no	—
81	#3757	C₂²×C₃	1	8	yes	complemented
82	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	4	yes	complemented
83	C₃×#217	—	3	32	no	—
84	C₃×C₄⋊Dic₃	—	3	16	no	—
85	C₂²×C₃³	—	2	4	no	—
86	C₂²×C₃³	—	2	4	no	—
87	C₂²×C₃³	—	2	4	no	—
88	C₂²×C₃³	—	4	8	no	—
89	C₂²×C₃³	C₂×D₄	1	2	yes	—
90	C₂²×C₃³	C₂×D₄	1	2	yes	—
91	C₂²×C₃³	#41	1	2	yes	—
92	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
93	C₂×C₃×C₃⋊D₃	—	2	8	no	—
94	C₂×C₃×C₃⋊D₃	—	2	2	no	—
95	C₂×C₃×C₃⋊D₃	—	2	2	no	—
96	C₂×C₃×C₃⋊D₃	C₂×D₄	1	4	yes	complemented
97	C₃³×C₄	C₂×D₄	1	4	yes	complemented
98	C₃×C₃⋊Dic₃	—	2	2	no	—
99	C₃×C₃⋊Dic₃	—	2	4	no	—
100	C₂²×C₃×D₄	—	2	4	no	—
101	C₂²×C₃×D₄	—	9	2	no	—
102	C₂²×C₃×D₄	C₃×D₃	1	4	yes	complemented
103	C₂²×C₃×D₄	C₃⋊D₃	1	1	yes	characteristic, complemented
104	C₂³×C₃×C₄	—	9	1	no	—
105	C₂²×#67	—	3	8	no	—
106	C₂²×C₄×D₃	—	3	4	no	—
107	C₃×#121	—	9	8	no	—
108	C₂×C₃×C₄⋊C₄	—	9	1	no	—
109	C₂×C₃×C₂²⋊C₄	—	9	2	no	—
110	C₂×#217	—	3	8	no	—
111	#938	—	3	32	no	—
112	C₂×C₄⋊Dic₃	—	3	4	no	—
113	C₂³×C₃²	—	2	32	no	—
114	C₂³×C₃²	—	2	16	no	—
115	C₂³×C₃²	—	2	4	no	—
116	C₂³×C₃²	—	2	4	no	—
117	C₂³×C₃²	—	2	4	no	—
118	C₂³×C₃²	—	2	4	no	—
119	C₂³×C₃²	—	2	16	no	—
120	C₂³×C₃²	—	2	16	no	—
121	C₂³×C₃²	—	2	16	no	—
122	C₂³×C₃²	—	4	16	no	—
123	C₂³×C₃²	—	4	16	no	—
124	C₂³×C₃²	C₂²×D₃	1	16	yes	—
125	C₂³×C₃²	C₂²×D₃	1	4	yes	—
126	C₂³×C₃²	C₂³×C₃	1	4	yes	—
127	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
128	C₂²×C₃⋊D₃	—	2	2	no	—
129	C₂²×C₃⋊D₃	—	2	2	no	—
130	C₂²×C₃⋊D₃	C₃×D₄	1	4	yes	complemented
131	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
132	C₂²×C₃×D₃	—	3	16	no	—
133	C₂²×C₃×D₃	—	3	8	no	—
134	C₂²×C₃×D₃	—	6	8	no	—
135	C₂²×C₃×D₃	—	6	8	no	—
136	C₃²×D₄	—	2	64	no	—
137	C₃²×D₄	—	2	32	no	—
138	C₃²×D₄	—	2	8	no	—
139	C₂×C₃²×C₄	—	2	16	no	—
140	C₂×C₃²×C₄	—	2	8	no	—
141	C₂×C₃²×C₄	#67	1	16	yes	complemented
142	C₂×C₃²×C₄	C₃×D₄	1	4	yes	complemented
143	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
144	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
145	#638	—	2	16	no	—
146	C₂×C₃⋊Dic₃	—	2	2	no	—
147	C₂×C₃⋊Dic₃	—	2	4	no	—
148	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	—
149	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
150	C₄×C₃⋊D₃	—	2	8	no	—
151	C₃×#67	—	6	64	no	—
152	C₂×C₃×Dic₃	—	3	16	no	—
153	C₂×C₃×Dic₃	—	3	8	no	—
154	C₂×C₃×Dic₃	—	6	16	no	—
155	C₂×C₃×Dic₃	—	6	8	no	—
156	C₃×C₄×D₃	—	6	32	no	—
157	C₂×#121	—	9	1	no	Sylow
158	C₂×C₃³	—	4	4	no	—
159	C₂×C₃³	#121	1	4	yes	complemented
160	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₃³	C₂×#41	1	1	yes	characteristic
163	C₃×C₃⋊D₃	—	2	4	no	—
164	C₂⁴×C₃	—	2	8	no	—
165	C₂⁴×C₃	—	9	1	no	—
166	C₂⁴×C₃	C₂×C₃×D₃	1	8	yes	—
167	C₂⁴×C₃	C₂×C₃⋊D₃	1	2	yes	—
168	C₂³×D₃	—	3	4	no	—
169	C₂×C₃×D₄	—	2	32	no	—
170	C₂×C₃×D₄	—	2	16	no	—
171	C₂×C₃×D₄	—	2	4	no	—
172	C₂×C₃×D₄	—	2	16	no	—
173	C₂×C₃×D₄	—	9	8	no	—
174	C₂×C₃×D₄	—	18	8	no	—
175	C₂×C₃×D₄	C₂×C₃×D₃	1	16	yes	complemented
176	C₂×C₃×D₄	C₂×C₃⋊D₃	1	4	yes	complemented
177	C₂²×C₃×C₄	—	2	4	no	—
178	C₂²×C₃×C₄	—	9	1	no	—
179	C₂²×C₃×C₄	—	9	2	no	—
180	C₂²×C₃×C₄	—	9	4	no	—
181	C₂²×C₃×C₄	—	18	4	no	—
182	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
183	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
184	C₂×#67	—	3	32	no	—
185	C₂×#67	—	6	32	no	—
186	C₂²×Dic₃	—	3	8	no	—
187	C₂²×Dic₃	—	3	4	no	—
188	C₂×C₄×D₃	—	3	16	no	—
189	C₂×C₄×D₃	—	6	16	no	—
190	C₃×C₄⋊C₄	—	9	4	no	—
191	C₃×C₂²⋊C₄	—	9	8	no	—
192	#217	—	3	32	no	—
193	C₄⋊Dic₃	—	3	16	no	—
194	C₂²×C₃²	—	2	32	no	—
195	C₂²×C₃²	—	2	16	no	—
196	C₂²×C₃²	—	2	4	no	—
197	C₂²×C₃²	—	2	4	no	—
198	C₂²×C₃²	—	2	4	no	—
199	C₂²×C₃²	—	2	4	no	—
200	C₂²×C₃²	—	2	8	no	—
201	C₂²×C₃²	—	2	8	no	—
202	C₂²×C₃²	—	2	8	no	—
203	C₂²×C₃²	—	2	16	no	—
204	C₂²×C₃²	—	2	16	no	—
205	C₂²×C₃²	—	4	16	no	—
206	C₂²×C₃²	—	4	16	no	—
207	C₂²×C₃²	—	4	64	no	—
208	C₂²×C₃²	—	4	32	no	—
209	C₂²×C₃²	—	4	8	no	—
210	C₂²×C₃²	D₃×D₄	1	8	yes	—
211	C₂²×C₃²	#237	1	8	yes	—
212	C₂²×C₃²	C₂×#67	1	8	yes	—
213	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
214	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
215	C₂²×C₃²	C₃×#41	1	2	yes	—
216	C₂²×C₃²	C₂³×D₃	1	4	yes	—
217	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
218	C₂×C₃⋊D₃	—	2	8	no	—
219	C₂×C₃⋊D₃	—	2	2	no	—
220	C₂×C₃⋊D₃	—	2	2	no	—
221	C₂×C₃⋊D₃	C₂×C₃×D₄	1	4	yes	complemented
222	C₂×C₃×D₃	—	3	16	no	—
223	C₂×C₃×D₃	—	6	32	no	—
224	C₂×C₃×D₃	—	6	8	no	—
225	C₂×C₃×D₃	—	6	8	no	—
226	C₃²×C₄	—	2	16	no	—
227	C₃²×C₄	C₂×#67	1	16	yes	complemented
228	C₃²×C₄	C₂×C₃×D₄	1	4	yes	complemented
229	C₃⋊Dic₃	—	2	2	no	—
230	C₃⋊Dic₃	—	2	4	no	—
231	C₃×Dic₃	—	6	16	no	—
232	C₃×Dic₃	—	6	8	no	—
233	C₂²×D₄	—	9	2	no	—
234	C₂²×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
235	C₂³×C₄	—	9	1	no	—
236	#121	—	9	8	no	—
237	C₂×C₄⋊C₄	—	9	1	no	—
238	C₂×C₂²⋊C₄	—	9	2	no	—
239	C₃³	C₂×#121	1	1	yes	characteristic, complemented, Sylow
240	C₂³×C₃	—	2	32	no	—
241	C₂³×C₃	—	2	16	no	—
242	C₂³×C₃	—	2	16	no	—
243	C₂³×C₃	—	2	16	no	—
244	C₂³×C₃	—	2	4	no	—
245	C₂³×C₃	—	2	4	no	—
246	C₂³×C₃	—	2	4	no	—
247	C₂³×C₃	—	2	4	no	—
248	C₂³×C₃	—	2	16	no	—
249	C₂³×C₃	—	4	16	no	—
250	C₂³×C₃	—	4	16	no	—
251	C₂³×C₃	—	9	2	no	—
252	C₂³×C₃	—	9	4	no	—
253	C₂³×C₃	—	18	2	no	—
254	C₂³×C₃	—	18	2	no	—
255	C₂³×C₃	C₂²×C₃×D₃	1	16	yes	—
256	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
257	C₂³×C₃	C₂²×C₃⋊D₃	1	4	yes	—
258	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
259	C₂²×D₃	—	3	8	no	—
260	C₂²×D₃	—	3	16	no	—
261	C₂²×D₃	—	6	8	no	—
262	C₂²×D₃	—	6	8	no	—
263	C₃×D₄	—	2	64	no	—
264	C₃×D₄	—	2	32	no	—
265	C₃×D₄	—	2	8	no	—
266	C₃×D₄	—	18	16	no	—
267	C₂×C₃×C₄	—	2	16	no	—
268	C₂×C₃×C₄	—	2	8	no	—
269	C₂×C₃×C₄	—	9	2	no	—
270	C₂×C₃×C₄	—	9	4	no	—
271	C₂×C₃×C₄	—	18	4	no	—
272	C₂×C₃×C₄	—	18	2	no	—
273	C₂×C₃×C₄	—	18	8	no	—
274	C₂×C₃×C₄	C₃×#67	1	16	yes	complemented
275	C₂×C₃×C₄	#638	1	4	yes	complemented
276	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
277	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
278	#67	—	6	64	no	—
279	C₂×Dic₃	—	3	16	no	—
280	C₂×Dic₃	—	3	8	no	—
281	C₂×Dic₃	—	6	16	no	—
282	C₂×Dic₃	—	6	8	no	—
283	C₄×D₃	—	6	32	no	—
284	C₂×C₃²	—	2	16	no	—
285	C₂×C₃²	—	2	4	no	—
286	C₂×C₃²	—	2	4	no	—
287	C₂×C₃²	—	2	4	no	—
288	C₂×C₃²	—	4	32	no	—
289	C₂×C₃²	—	4	16	no	—
290	C₂×C₃²	—	4	4	no	—
291	C₂×C₃²	#938	1	16	yes	complemented
292	C₂×C₃²	C₃×#121	1	4	yes	complemented
293	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
294	C₂×C₃²	C₂×#237	1	4	yes	—
295	C₂×C₃²	C₂²×#67	1	4	yes	—
296	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
297	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
298	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
299	C₃⋊D₃	—	2	4	no	—
300	C₃×D₃	—	6	16	no	—
301	C₂⁴	—	9	1	no	—
302	C₂⁴	C₂×C₃×C₃⋊D₃	1	2	yes	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	9	8	no	—
305	C₂×D₄	—	18	8	no	—
306	C₂×D₄	C₂×C₃×C₃⋊D₃	1	4	yes	complemented
307	C₂²×C₄	—	9	1	no	—
308	C₂²×C₄	—	9	2	no	—
309	C₂²×C₄	—	9	4	no	—
310	C₂²×C₄	—	18	4	no	—
311	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
312	C₄⋊C₄	—	9	4	no	—
313	C₂²⋊C₄	—	9	8	no	—
314	C₂²×C₃	—	2	32	no	—
315	C₂²×C₃	—	2	16	no	—
316	C₂²×C₃	—	2	16	no	—
317	C₂²×C₃	—	2	16	no	—
318	C₂²×C₃	—	2	4	no	—
319	C₂²×C₃	—	2	4	no	—
320	C₂²×C₃	—	2	4	no	—
321	C₂²×C₃	—	2	4	no	—
322	C₂²×C₃	—	2	8	no	—
323	C₂²×C₃	—	2	8	no	—
324	C₂²×C₃	—	2	8	no	—
325	C₂²×C₃	—	4	16	no	—
326	C₂²×C₃	—	4	16	no	—
327	C₂²×C₃	—	4	64	no	—
328	C₂²×C₃	—	4	32	no	—
329	C₂²×C₃	—	4	8	no	—
330	C₂²×C₃	—	9	4	no	—
331	C₂²×C₃	—	18	2	no	—
332	C₂²×C₃	—	18	2	no	—
333	C₂²×C₃	—	18	8	no	—
334	C₂²×C₃	C₃×D₃×D₄	1	8	yes	—
335	C₂²×C₃	C₃×#237	1	8	yes	—
336	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
337	C₂²×C₃	D₄×C₃⋊D₃	1	2	yes	—
338	C₂²×C₃	#3830	1	2	yes	—
339	C₂²×C₃	C₂×#638	1	2	yes	—
340	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
341	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
342	C₂×D₃	—	3	16	no	—
343	C₂×D₃	—	6	32	no	—
344	C₂×D₃	—	6	8	no	—
345	C₂×D₃	—	6	8	no	—
346	C₃×C₄	—	2	16	no	—
347	C₃×C₄	—	18	4	no	—
348	C₃×C₄	—	18	2	no	—
349	C₃×C₄	C₂×C₃×#67	1	16	yes	complemented
350	C₃×C₄	C₂×#638	1	4	yes	complemented
351	Dic₃	—	6	16	no	—
352	Dic₃	—	6	8	no	—
353	C₃²	—	2	4	no	—
354	C₃²	C₂×#938	1	4	yes	complemented
355	C₃²	C₂×C₃×#121	1	1	yes	characteristic, complemented
356	C₂³	—	2	4	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	9	2	no	—
360	C₂³	—	9	4	no	—
361	C₂³	—	18	2	no	—
362	C₂³	—	18	2	no	—
363	C₂³	C₂²×C₃×C₃⋊D₃	1	4	yes	—
364	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
365	D₄	—	2	8	no	—
366	D₄	—	18	16	no	—
367	C₂×C₄	—	9	2	no	—
368	C₂×C₄	—	9	4	no	—
369	C₂×C₄	—	18	4	no	—
370	C₂×C₄	—	18	2	no	—
371	C₂×C₄	—	18	8	no	—
372	C₂×C₄	C₃×#638	1	4	yes	complemented
373	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
374	C₂×C₃	—	2	16	no	—
375	C₂×C₃	—	2	4	no	—
376	C₂×C₃	—	2	4	no	—
377	C₂×C₃	—	2	4	no	—
378	C₂×C₃	—	4	32	no	—
379	C₂×C₃	—	4	16	no	—
380	C₂×C₃	—	4	4	no	—
381	C₂×C₃	—	18	4	no	—
382	C₂×C₃	C₃×#938	1	16	yes	complemented
383	C₂×C₃	#64147	1	4	yes	direct product factor
384	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
385	C₂×C₃	C₂×C₃×#237	1	4	yes	—
386	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
387	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
388	C₂×C₃	C₂×#3830	1	1	yes	characteristic
389	C₂×C₃	C₂²×#638	1	1	yes	characteristic
390	D₃	—	6	16	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	2	4	no	—
394	C₂²	—	4	8	no	—
395	C₂²	—	9	4	no	—
396	C₂²	—	18	8	no	—
397	C₂²	—	18	2	no	—
398	C₂²	—	18	2	no	—
399	C₂²	C₃×D₄×C₃⋊D₃	1	2	yes	—
400	C₂²	C₃×#3830	1	2	yes	—
401	C₂²	C₂×C₃×#638	1	2	yes	—
402	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
403	C₄	—	18	4	no	—
404	C₄	—	18	2	no	—
405	C₄	C₂×C₃×#638	1	4	yes	complemented
406	C₃	—	2	4	no	—
407	C₃	C₂×C₃×#938	1	4	yes	complemented
408	C₃	C₂×#64147	1	1	yes	characteristic, direct product factor
409	C₂	—	4	4	no	—
410	C₂	—	18	4	no	—
411	C₂	C₃×#64147	1	4	yes	direct product factor
412	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
413	C₂	C₂×C₃×#3830	1	1	yes	characteristic
414	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×#121
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. C₂²×C₃³×D₄	C₂	semidirect
2. C₂²×C₃×#638	C₂	semidirect
3. C₂²×C₃×C₄×C₃⋊D₃	C₂	semidirect
4. C₂×C₃×#3757	C₂	semidirect
5. C₃×#64147	C₂	direct (N × H)
6. C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	semidirect
7. C₂×#64147	C₃	direct (N × H)
12. C₂×C₃³×D₄	C₂²	semidirect
15. C₂×C₃×#638	C₂²	semidirect
19. C₂×C₃×C₄×C₃⋊D₃	C₂²	semidirect
20. C₃×#3757	C₂²	semidirect
21. C₃×C₄⋊(C₃⋊Dic₃)	C₂²	semidirect
23. C₂²×C₃²×D₄	D₃	semidirect
24. C₂²×C₃²×D₄	C₂×C₃	semidirect
25. C₂²×#638	C₂×C₃	semidirect
26. C₂²×C₄×C₃⋊D₃	C₂×C₃	semidirect
29. C₂×#3757	C₂×C₃	semidirect
30. #64147	C₂×C₃	direct (N × H)
31. C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	semidirect
42. C₂²×C₃×C₃⋊D₃	D₄	semidirect
45. C₂×C₃³×C₄	D₄	semidirect
64. C₂×C₃²×D₄	C₂×D₃	semidirect
65. C₂×C₃²×D₄	C₂²×C₃	semidirect
70. C₂×#638	C₂²×C₃	semidirect
74. C₂×C₄×C₃⋊D₃	C₂²×C₃	semidirect
81. #3757	C₂²×C₃	semidirect
82. C₄⋊(C₃⋊Dic₃)	C₂²×C₃	semidirect
96. C₂×C₃×C₃⋊D₃	C₂×D₄	semidirect
97. C₃³×C₄	C₂×D₄	semidirect
102. C₂²×C₃×D₄	C₃×D₃	semidirect
103. C₂²×C₃×D₄	C₃⋊D₃	semidirect
130. C₂²×C₃⋊D₃	C₃×D₄	semidirect
141. C₂×C₃²×C₄	#67	semidirect
142. C₂×C₃²×C₄	C₃×D₄	semidirect
159. C₂×C₃³	#121	semidirect
175. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
176. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
221. C₂×C₃⋊D₃	C₂×C₃×D₄	semidirect
227. C₃²×C₄	C₂×#67	semidirect
228. C₃²×C₄	C₂×C₃×D₄	semidirect
234. C₂²×D₄	C₃×C₃⋊D₃	semidirect
239. C₃³	C₂×#121	semidirect
274. C₂×C₃×C₄	C₃×#67	semidirect
275. C₂×C₃×C₄	#638	semidirect
291. C₂×C₃²	#938	semidirect
292. C₂×C₃²	C₃×#121	semidirect
306. C₂×D₄	C₂×C₃×C₃⋊D₃	semidirect
349. C₃×C₄	C₂×C₃×#67	semidirect
350. C₃×C₄	C₂×#638	semidirect
354. C₃²	C₂×#938	semidirect
355. C₃²	C₂×C₃×#121	semidirect
372. C₂×C₄	C₃×#638	semidirect
382. C₂×C₃	C₃×#938	semidirect
383. C₂×C₃	#64147	direct (N × H)
405. C₄	C₂×C₃×#638	semidirect
407. C₃	C₂×C₃×#938	semidirect
408. C₃	C₂×#64147	direct (N × H)
411. C₂	C₃×#64147	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×C₃³×D₄	2
C₂²×C₃×#638	2
C₂²×C₃×C₄×C₃⋊D₃	2
C₂×C₃×#3757	2
C₃×#64147	2
C₂×C₃×C₄⋊(C₃⋊Dic₃)	2
C₂×#64147	3
C₂×C₃×#938	3

Subgroups — C2×C3×#64147 #13179553

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64147 #13179553