Subgroups — C₂²×D₃²×Dic₃ #13181308

Order 1728.

6210 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×D₃²	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6294	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×Dic₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₃×C₃⋊Dic₃	C₂	1	2	yes	maximal, complemented
5	C₂²×C₃×D₃×Dic₃	C₂	1	2	yes	maximal, complemented
6	C₂×D₃²×Dic₃	C₂	1	24	yes	maximal, direct product factor
7	C₂³×D₃×Dic₃	—	3	2	no	maximal
8	C₂²×C₄×D₃²	—	3	1	no	maximal
9	C₂³×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
10	C₂³×C₃²×D₃	C₂²	1	2	yes	—
11	C₂²×C₃×D₃²	C₄	1	16	yes	complemented
12	C₂²×C₃×D₃²	C₂²	1	12	yes	—
13	C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	complemented
15	C₂²×C₃²×Dic₃	C₂²	1	1	yes	characteristic, complemented
16	C₂×#6294	C₂²	1	12	yes	complemented
17	C₂×Dic₃×C₃⋊D₃	C₂²	1	12	yes	complemented
18	C₂×D₃×C₃⋊Dic₃	C₂²	1	24	yes	complemented
19	C₂×C₃×D₃×Dic₃	C₂²	1	24	yes	complemented
20	D₃²×Dic₃	C₂²	1	64	yes	direct product factor
21	C₂⁴×C₃×D₃	—	3	2	no	—
22	C₂³×D₃²	D₃	1	1	yes	characteristic
23	C₂³×C₃⋊Dic₃	—	3	2	no	—
24	C₂²×C₄×C₃⋊D₃	—	3	1	no	—
25	C₂³×C₃×Dic₃	—	3	2	no	—
26	C₂²×C₃×C₄×D₃	—	3	2	no	—
27	C₂²×#624	—	3	1	no	—
28	C₂²×D₃×Dic₃	—	3	2	no	—
29	C₂²×D₃×Dic₃	—	3	2	no	—
30	C₂²×D₃×Dic₃	—	3	48	no	—
31	C₂²×D₃×Dic₃	—	3	2	no	—
32	C₂²×D₃×Dic₃	—	3	2	no	—
33	C₂²×D₃×Dic₃	—	6	2	no	—
34	C₂²×D₃×Dic₃	—	6	1	no	—
35	C₂²×D₃×Dic₃	D₃	1	2	yes	direct product factor
36	C₂×C₄×D₃²	—	3	24	no	—
37	C₂³×C₃³	C₂³	1	1	yes	characteristic
38	C₂²×C₃×C₃⋊D₃	C₂×C₄	1	8	yes	complemented
39	C₂²×C₃×C₃⋊D₃	C₂³	1	6	yes	—
40	C₂²×C₃²×D₃	C₂×C₄	1	16	yes	complemented
41	C₂²×C₃²×D₃	C₂³	1	12	yes	—
42	C₂×C₃×D₃²	C₂×C₄	1	96	yes	complemented
43	C₂×C₃×D₃²	C₂³	1	16	yes	—
44	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	6	yes	complemented
45	C₂×C₃×C₃⋊Dic₃	C₂³	1	12	yes	complemented
46	C₂×C₃²×Dic₃	C₂³	1	6	yes	complemented
47	#6294	C₂³	1	16	yes	complemented
48	Dic₃×C₃⋊D₃	C₂³	1	16	yes	complemented
49	D₃×C₃⋊Dic₃	C₂³	1	32	yes	complemented
50	C₃×D₃×Dic₃	C₂³	1	32	yes	complemented
51	C₂⁴×Dic₃	—	9	1	no	—
52	C₂³×C₄×D₃	—	9	2	no	—
53	C₂⁴×C₃²	—	3	2	no	—
54	C₂³×C₃⋊D₃	C₂×D₃	1	1	yes	characteristic
55	C₂³×C₃×D₃	—	2	2	no	—
56	C₂³×C₃×D₃	—	3	2	no	—
57	C₂³×C₃×D₃	—	3	32	no	—
58	C₂³×C₃×D₃	—	3	24	no	—
59	C₂³×C₃×D₃	—	6	1	no	—
60	C₂³×C₃×D₃	C₂×D₃	1	2	yes	—
61	C₂³×C₃×D₃	C₂×D₃	1	2	yes	—
62	C₂²×D₃²	Dic₃	1	16	yes	direct product factor
63	C₂²×D₃²	C₂×D₃	1	12	yes	—
64	C₂²×C₃²×C₄	—	3	1	no	—
65	C₂²×C₃⋊Dic₃	—	3	1	no	—
66	C₂²×C₃⋊Dic₃	—	3	2	no	—
67	C₂²×C₃⋊Dic₃	—	3	24	no	—
68	C₂²×C₃⋊Dic₃	—	6	2	no	—
69	C₂²×C₃⋊Dic₃	—	6	1	no	—
70	C₂²×C₃⋊Dic₃	—	12	1	no	—
71	C₂²×C₃⋊Dic₃	C₂×D₃	1	2	yes	complemented
72	C₂×C₄×C₃⋊D₃	—	3	12	no	—
73	C₂²×C₃×Dic₃	—	2	1	no	—
74	C₂²×C₃×Dic₃	—	3	2	no	—
75	C₂²×C₃×Dic₃	—	3	2	no	—
76	C₂²×C₃×Dic₃	—	3	24	no	—
77	C₂²×C₃×Dic₃	—	6	2	no	—
78	C₂²×C₃×Dic₃	C₂×D₃	1	2	yes	complemented
79	C₂×C₃×C₄×D₃	—	3	24	no	—
80	C₂×#624	—	3	12	no	—
81	C₂×D₃×Dic₃	—	3	24	no	—
82	C₂×D₃×Dic₃	—	3	24	no	—
83	C₂×D₃×Dic₃	—	3	24	no	—
84	C₂×D₃×Dic₃	—	3	24	no	—
85	C₂×D₃×Dic₃	—	3	128	no	—
86	C₂×D₃×Dic₃	—	6	12	no	—
87	C₂×D₃×Dic₃	—	6	24	no	—
88	C₂×D₃×Dic₃	C₂×D₃	1	24	yes	direct product factor
89	C₄×D₃²	—	3	64	no	—
90	C₂²×C₃³	C₂²×C₄	1	4	yes	complemented
91	C₂²×C₃³	C₂⁴	1	3	yes	—
92	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	24	yes	complemented
93	C₂×C₃×C₃⋊D₃	C₂⁴	1	4	yes	—
94	C₂×C₃²×D₃	C₂²×C₄	1	48	yes	complemented
95	C₂×C₃²×D₃	C₂⁴	1	8	yes	—
96	C₃×D₃²	C₂²×C₄	1	64	yes	complemented
97	C₃⋊(C₃⋊Dic₃)	C₂⁴	1	4	yes	complemented
98	C₃×C₃⋊Dic₃	C₂⁴	1	8	yes	complemented
99	C₃²×Dic₃	C₂⁴	1	4	yes	complemented
100	C₂⁵×C₃	—	9	1	no	—
101	C₂⁴×D₃	—	3	2	no	—
102	C₂³×C₃×C₄	—	9	2	no	—
103	C₂³×Dic₃	—	3	2	no	—
104	C₂³×Dic₃	—	9	1	no	—
105	C₂³×Dic₃	—	9	24	no	—
106	C₂³×Dic₃	—	9	2	no	—
107	C₂³×Dic₃	—	9	2	no	—
108	C₂³×Dic₃	—	9	1	no	—
109	C₂³×Dic₃	—	18	2	no	—
110	C₂²×C₄×D₃	—	3	2	no	—
111	C₂²×C₄×D₃	—	9	48	no	—
112	C₂²×C₄×D₃	—	9	2	no	—
113	C₂²×C₄×D₃	—	9	2	no	—
114	C₂²×C₄×D₃	—	9	2	no	—
115	C₂²×C₄×D₃	—	18	1	no	—
116	C₂³×C₃²	—	2	2	no	—
117	C₂³×C₃²	—	2	1	no	—
118	C₂³×C₃²	—	3	16	no	—
119	C₂³×C₃²	—	3	12	no	—
120	C₂³×C₃²	—	4	1	no	—
121	C₂³×C₃²	C₂²×D₃	1	2	yes	—
122	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
123	C₂²×C₃⋊D₃	C₂×Dic₃	1	8	yes	complemented
124	C₂²×C₃⋊D₃	C₂²×D₃	1	6	yes	—
125	C₂²×C₃×D₃	—	2	16	no	—
126	C₂²×C₃×D₃	—	2	12	no	—
127	C₂²×C₃×D₃	—	3	16	no	—
128	C₂²×C₃×D₃	—	3	12	no	—
129	C₂²×C₃×D₃	—	3	192	no	—
130	C₂²×C₃×D₃	—	3	32	no	—
131	C₂²×C₃×D₃	—	6	8	no	—
132	C₂²×C₃×D₃	—	6	6	no	—
133	C₂²×C₃×D₃	C₄×D₃	1	16	yes	complemented
134	C₂²×C₃×D₃	C₂×Dic₃	1	16	yes	complemented
135	C₂²×C₃×D₃	C₂²×D₃	1	12	yes	—
136	C₂²×C₃×D₃	C₂²×D₃	1	12	yes	—
137	C₂×D₃²	C₂×Dic₃	1	96	yes	direct product factor
138	C₂×D₃²	C₂²×D₃	1	16	yes	—
139	C₂×C₃²×C₄	—	3	6	no	—
140	C₂×C₃⋊Dic₃	—	3	6	no	—
141	C₂×C₃⋊Dic₃	—	3	12	no	—
142	C₂×C₃⋊Dic₃	—	3	32	no	—
143	C₂×C₃⋊Dic₃	—	6	12	no	—
144	C₂×C₃⋊Dic₃	—	6	6	no	—
145	C₂×C₃⋊Dic₃	—	12	6	no	—
146	C₂×C₃⋊Dic₃	C₂²×D₃	1	12	yes	complemented
147	C₄×C₃⋊D₃	—	3	16	no	—
148	C₂×C₃×Dic₃	—	2	6	no	—
149	C₂×C₃×Dic₃	—	3	12	no	—
150	C₂×C₃×Dic₃	—	3	12	no	—
151	C₂×C₃×Dic₃	—	3	32	no	—
152	C₂×C₃×Dic₃	—	6	12	no	—
153	C₂×C₃×Dic₃	C₂²×D₃	1	12	yes	complemented
154	C₃×C₄×D₃	—	3	32	no	—
155	#624	—	3	16	no	—
156	D₃×Dic₃	—	3	32	no	—
157	D₃×Dic₃	—	3	32	no	—
158	D₃×Dic₃	—	3	32	no	—
159	D₃×Dic₃	—	3	32	no	—
160	D₃×Dic₃	—	6	32	no	—
161	D₃×Dic₃	—	6	16	no	—
162	D₃×Dic₃	C₂²×D₃	1	32	yes	direct product factor
163	C₂⁴×C₄	—	27	1	no	Sylow
164	C₂×C₃³	C₂³×C₄	1	6	yes	complemented
165	C₂×C₃³	C₂⁵	1	1	yes	characteristic
166	C₃×C₃⋊D₃	C₂³×C₄	1	8	yes	complemented
167	C₃²×D₃	C₂³×C₄	1	16	yes	complemented
168	C₂⁴×C₃	—	3	2	no	—
169	C₂⁴×C₃	—	3	2	no	—
170	C₂⁴×C₃	—	6	2	no	—
171	C₂⁴×C₃	—	9	16	no	—
172	C₂⁴×C₃	—	9	12	no	—
173	C₂⁴×C₃	—	9	1	no	—
174	C₂³×D₃	—	3	2	no	—
175	C₂³×D₃	—	3	32	no	—
176	C₂³×D₃	—	3	24	no	—
177	C₂³×D₃	—	6	1	no	—
178	C₂³×D₃	D₃²	1	2	yes	—
179	C₂²×C₃×C₄	—	3	2	no	—
180	C₂²×C₃×C₄	—	6	1	no	—
181	C₂²×C₃×C₄	—	9	24	no	—
182	C₂²×C₃×C₄	—	9	2	no	—
183	C₂²×Dic₃	—	3	2	no	—
184	C₂²×Dic₃	—	3	2	no	—
185	C₂²×Dic₃	—	3	24	no	—
186	C₂²×Dic₃	—	6	2	no	—
187	C₂²×Dic₃	—	9	12	no	—
188	C₂²×Dic₃	—	9	64	no	—
189	C₂²×Dic₃	—	9	24	no	—
190	C₂²×Dic₃	—	9	24	no	—
191	C₂²×Dic₃	—	9	2	no	—
192	C₂²×Dic₃	—	9	1	no	—
193	C₂²×Dic₃	—	9	12	no	—
194	C₂²×Dic₃	—	18	24	no	—
195	C₂²×Dic₃	—	18	1	no	—
196	C₂²×Dic₃	—	18	2	no	—
197	C₂²×Dic₃	—	36	1	no	—
198	C₂²×Dic₃	D₃²	1	1	yes	characteristic, direct product factor
199	C₂×C₄×D₃	—	3	24	no	—
200	C₂×C₄×D₃	—	9	128	no	—
201	C₂×C₄×D₃	—	9	24	no	—
202	C₂×C₄×D₃	—	9	24	no	—
203	C₂×C₄×D₃	—	9	24	no	—
204	C₂×C₄×D₃	—	18	12	no	—
205	C₂²×C₃²	—	2	3	no	—
206	C₂²×C₃²	—	2	6	no	—
207	C₂²×C₃²	—	2	4	no	—
208	C₂²×C₃²	—	2	8	no	—
209	C₂²×C₃²	—	3	48	no	—
210	C₂²×C₃²	—	3	8	no	—
211	C₂²×C₃²	—	4	4	no	—
212	C₂²×C₃²	—	4	3	no	—
213	C₂²×C₃²	C₂×C₄×D₃	1	8	yes	complemented
214	C₂²×C₃²	C₂²×Dic₃	1	4	yes	complemented
215	C₂²×C₃²	C₂³×D₃	1	6	yes	—
216	C₂²×C₃²	C₂³×D₃	1	3	yes	—
217	C₂×C₃⋊D₃	C₂²×Dic₃	1	24	yes	complemented
218	C₂×C₃⋊D₃	C₂³×D₃	1	4	yes	—
219	C₂×C₃×D₃	—	2	8	no	—
220	C₂×C₃×D₃	—	2	48	no	—
221	C₂×C₃×D₃	—	3	48	no	—
222	C₂×C₃×D₃	—	3	8	no	—
223	C₂×C₃×D₃	—	3	128	no	—
224	C₂×C₃×D₃	—	6	24	no	—
225	C₂×C₃×D₃	—	6	4	no	—
226	C₂×C₃×D₃	C₂×C₄×D₃	1	48	yes	complemented
227	C₂×C₃×D₃	C₂²×Dic₃	1	48	yes	complemented
228	C₂×C₃×D₃	C₂³×D₃	1	8	yes	—
229	C₂×C₃×D₃	C₂³×D₃	1	8	yes	—
230	D₃²	C₂²×Dic₃	1	64	yes	direct product factor
231	C₃²×C₄	—	3	4	no	—
232	C₃⋊Dic₃	—	3	4	no	—
233	C₃⋊Dic₃	—	3	8	no	—
234	C₃⋊Dic₃	—	6	8	no	—
235	C₃⋊Dic₃	—	6	4	no	—
236	C₃⋊Dic₃	—	12	4	no	—
237	C₃⋊Dic₃	C₂³×D₃	1	8	yes	complemented
238	C₃×Dic₃	—	2	4	no	—
239	C₃×Dic₃	—	3	8	no	—
240	C₃×Dic₃	—	3	8	no	—
241	C₃×Dic₃	—	6	8	no	—
242	C₃×Dic₃	C₂³×D₃	1	8	yes	complemented
243	C₂⁵	—	9	1	no	—
244	C₂³×C₄	—	9	2	no	—
245	C₂³×C₄	—	27	1	no	—
246	C₂³×C₄	—	27	24	no	—
247	C₂³×C₄	—	27	1	no	—
248	C₂³×C₄	—	27	2	no	—
249	C₃³	C₂⁴×C₄	1	1	yes	characteristic, complemented, Sylow
250	C₂³×C₃	—	2	2	no	—
251	C₂³×C₃	—	2	1	no	—
252	C₂³×C₃	—	3	12	no	—
253	C₂³×C₃	—	3	12	no	—
254	C₂³×C₃	—	3	16	no	—
255	C₂³×C₃	—	3	16	no	—
256	C₂³×C₃	—	4	1	no	—
257	C₂³×C₃	—	6	12	no	—
258	C₂³×C₃	—	6	16	no	—
259	C₂³×C₃	—	9	16	no	—
260	C₂³×C₃	—	9	96	no	—
261	C₂³×C₃	—	9	6	no	—
262	C₂³×C₃	—	9	8	no	—
263	C₂³×C₃	C₂×D₃²	1	1	yes	characteristic
264	C₂³×C₃	C₂×D₃²	1	2	yes	—
265	C₂²×D₃	—	3	12	no	—
266	C₂²×D₃	—	3	16	no	—
267	C₂²×D₃	—	3	32	no	—
268	C₂²×D₃	—	3	192	no	—
269	C₂²×D₃	—	6	8	no	—
270	C₂²×D₃	—	6	6	no	—
271	C₂²×D₃	D₃×Dic₃	1	16	yes	direct product factor
272	C₂²×D₃	C₂×D₃²	1	12	yes	—
273	C₂×C₃×C₄	—	3	12	no	—
274	C₂×C₃×C₄	—	6	6	no	—
275	C₂×C₃×C₄	—	9	32	no	—
276	C₂×C₃×C₄	—	9	12	no	—
277	C₂×Dic₃	—	3	12	no	—
278	C₂×Dic₃	—	3	12	no	—
279	C₂×Dic₃	—	3	32	no	—
280	C₂×Dic₃	—	6	12	no	—
281	C₂×Dic₃	—	9	16	no	—
282	C₂×Dic₃	—	9	32	no	—
283	C₂×Dic₃	—	9	32	no	—
284	C₂×Dic₃	—	9	12	no	—
285	C₂×Dic₃	—	9	6	no	—
286	C₂×Dic₃	—	9	16	no	—
287	C₂×Dic₃	—	18	32	no	—
288	C₂×Dic₃	—	18	6	no	—
289	C₂×Dic₃	—	18	12	no	—
290	C₂×Dic₃	—	36	6	no	—
291	C₂×Dic₃	C₂×D₃²	1	6	yes	direct product factor
292	C₄×D₃	—	3	32	no	—
293	C₄×D₃	—	9	32	no	—
294	C₄×D₃	—	9	32	no	—
295	C₄×D₃	—	9	32	no	—
296	C₄×D₃	—	18	16	no	—
297	C₂×C₃²	—	2	6	no	—
298	C₂×C₃²	—	2	12	no	—
299	C₂×C₃²	—	2	1	no	—
300	C₂×C₃²	—	2	2	no	—
301	C₂×C₃²	—	3	16	no	—
302	C₂×C₃²	—	4	6	no	—
303	C₂×C₃²	—	4	1	no	—
304	C₂×C₃²	C₂²×C₄×D₃	1	12	yes	complemented
305	C₂×C₃²	C₂³×Dic₃	1	6	yes	complemented
306	C₂×C₃²	C₂⁴×D₃	1	2	yes	—
307	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
308	C₃⋊D₃	C₂³×Dic₃	1	8	yes	complemented
309	C₃×D₃	—	2	16	no	—
310	C₃×D₃	—	3	16	no	—
311	C₃×D₃	—	6	8	no	—
312	C₃×D₃	C₂²×C₄×D₃	1	16	yes	complemented
313	C₃×D₃	C₂³×Dic₃	1	16	yes	complemented
314	C₂⁴	—	3	2	no	—
315	C₂⁴	—	9	12	no	—
316	C₂⁴	—	9	16	no	—
317	C₂⁴	—	9	1	no	—
318	C₂²×C₄	—	3	1	no	—
319	C₂²×C₄	—	9	24	no	—
320	C₂²×C₄	—	9	2	no	—
321	C₂²×C₄	—	27	12	no	—
322	C₂²×C₄	—	27	64	no	—
323	C₂²×C₄	—	27	12	no	—
324	C₂²×C₄	—	27	24	no	—
325	C₂²×C₄	—	27	1	no	—
326	C₂²×C₃	—	2	6	no	—
327	C₂²×C₃	—	2	3	no	—
328	C₂²×C₃	—	2	4	no	—
329	C₂²×C₃	—	2	8	no	—
330	C₂²×C₃	—	3	48	no	—
331	C₂²×C₃	—	3	48	no	—
332	C₂²×C₃	—	3	8	no	—
333	C₂²×C₃	—	3	8	no	—
334	C₂²×C₃	—	4	3	no	—
335	C₂²×C₃	—	4	4	no	—
336	C₂²×C₃	—	6	8	no	—
337	C₂²×C₃	—	6	48	no	—
338	C₂²×C₃	—	9	64	no	—
339	C₂²×C₃	—	9	24	no	—
340	C₂²×C₃	—	9	4	no	—
341	C₂²×C₃	C₄×D₃²	1	4	yes	complemented
342	C₂²×C₃	C₂×D₃×Dic₃	1	8	yes	complemented
343	C₂²×C₃	C₂²×D₃²	1	3	yes	—
344	C₂²×C₃	C₂²×D₃²	1	6	yes	—
345	C₂×D₃	—	3	48	no	—
346	C₂×D₃	—	3	8	no	—
347	C₂×D₃	—	3	128	no	—
348	C₂×D₃	—	6	4	no	—
349	C₂×D₃	—	6	24	no	—
350	C₂×D₃	C₂×D₃×Dic₃	1	48	yes	direct product factor
351	C₂×D₃	C₂²×D₃²	1	8	yes	—
352	C₃×C₄	—	3	8	no	—
353	C₃×C₄	—	6	4	no	—
354	C₃×C₄	—	9	8	no	—
355	Dic₃	—	3	8	no	—
356	Dic₃	—	3	8	no	—
357	Dic₃	—	6	8	no	—
358	Dic₃	—	9	8	no	—
359	Dic₃	—	9	4	no	—
360	Dic₃	—	18	4	no	—
361	Dic₃	—	18	8	no	—
362	Dic₃	—	36	4	no	—
363	Dic₃	C₂²×D₃²	1	4	yes	direct product factor
364	C₃²	—	2	1	no	—
365	C₃²	—	2	2	no	—
366	C₃²	—	4	1	no	—
367	C₃²	C₂³×C₄×D₃	1	2	yes	complemented
368	C₃²	C₂⁴×Dic₃	1	1	yes	characteristic, complemented
369	C₂³	—	3	12	no	—
370	C₂³	—	3	16	no	—
371	C₂³	—	9	16	no	—
372	C₂³	—	9	96	no	—
373	C₂³	—	9	6	no	—
374	C₂³	—	9	8	no	—
375	C₂³	D₃³	1	1	yes	characteristic
376	C₂×C₄	—	3	6	no	—
377	C₂×C₄	—	9	32	no	—
378	C₂×C₄	—	9	12	no	—
379	C₂×C₄	—	27	16	no	—
380	C₂×C₄	—	27	16	no	—
381	C₂×C₄	—	27	32	no	—
382	C₂×C₄	—	27	6	no	—
383	C₂×C₃	—	2	6	no	—
384	C₂×C₃	—	2	12	no	—
385	C₂×C₃	—	2	2	no	—
386	C₂×C₃	—	2	1	no	—
387	C₂×C₃	—	3	16	no	—
388	C₂×C₃	—	3	16	no	—
389	C₂×C₃	—	4	6	no	—
390	C₂×C₃	—	4	1	no	—
391	C₂×C₃	—	6	16	no	—
392	C₂×C₃	—	9	8	no	—
393	C₂×C₃	C₂×C₄×D₃²	1	6	yes	complemented
394	C₂×C₃	C₂²×D₃×Dic₃	1	12	yes	complemented
395	C₂×C₃	C₂³×D₃²	1	1	yes	characteristic
396	C₂×C₃	C₂³×D₃²	1	2	yes	—
397	D₃	—	3	16	no	—
398	D₃	—	6	8	no	—
399	D₃	C₂²×D₃×Dic₃	1	16	yes	direct product factor
400	C₂²	—	3	48	no	—
401	C₂²	—	3	8	no	—
402	C₂²	—	9	64	no	—
403	C₂²	—	9	24	no	—
404	C₂²	—	9	4	no	—
405	C₂²	D₃²×Dic₃	1	4	yes	direct product factor
406	C₂²	C₂×D₃³	1	3	yes	—
407	C₄	—	3	4	no	—
408	C₄	—	9	8	no	—
409	C₄	—	27	4	no	—
410	C₃	—	2	1	no	—
411	C₃	—	2	2	no	—
412	C₃	—	4	1	no	—
413	C₃	C₂²×C₄×D₃²	1	1	yes	characteristic, complemented
414	C₃	C₂³×D₃×Dic₃	1	2	yes	complemented
415	C₂	—	3	16	no	—
416	C₂	—	9	8	no	—
417	C₂	C₂×D₃²×Dic₃	1	6	yes	direct product factor
418	C₂	C₂²×D₃³	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³	D₃³
commutator, hypocenter	C₃³	C₂⁴×C₄
Frattini	C₂	C₂²×D₃³
Fitting, socle	C₂³×C₃³	C₂³
prime radical	C₂³×C₃×D₃²	C₂
cosocle	C₂×C₃³	C₂⁵
LCS	G ▷ C₃³
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
2. C₂²×#6294	C₂	semidirect
3. C₂²×Dic₃×C₃⋊D₃	C₂	semidirect
4. C₂²×D₃×C₃⋊Dic₃	C₂	semidirect
5. C₂²×C₃×D₃×Dic₃	C₂	semidirect
6. C₂×D₃²×Dic₃	C₂	direct (N × H)
11. C₂²×C₃×D₃²	C₄	semidirect
13. C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
14. C₂²×C₃×C₃⋊Dic₃	C₂²	semidirect
15. C₂²×C₃²×Dic₃	C₂²	semidirect
16. C₂×#6294	C₂²	semidirect
17. C₂×Dic₃×C₃⋊D₃	C₂²	semidirect
18. C₂×D₃×C₃⋊Dic₃	C₂²	semidirect
19. C₂×C₃×D₃×Dic₃	C₂²	semidirect
20. D₃²×Dic₃	C₂²	direct (N × H)
35. C₂²×D₃×Dic₃	D₃	direct (N × H)
38. C₂²×C₃×C₃⋊D₃	C₂×C₄	semidirect
40. C₂²×C₃²×D₃	C₂×C₄	semidirect
42. C₂×C₃×D₃²	C₂×C₄	semidirect
44. C₂×C₃⋊(C₃⋊Dic₃)	C₂³	semidirect
45. C₂×C₃×C₃⋊Dic₃	C₂³	semidirect
46. C₂×C₃²×Dic₃	C₂³	semidirect
47. #6294	C₂³	semidirect
48. Dic₃×C₃⋊D₃	C₂³	semidirect
49. D₃×C₃⋊Dic₃	C₂³	semidirect
50. C₃×D₃×Dic₃	C₂³	semidirect
62. C₂²×D₃²	Dic₃	direct (N × H)
71. C₂²×C₃⋊Dic₃	C₂×D₃	semidirect
78. C₂²×C₃×Dic₃	C₂×D₃	semidirect
88. C₂×D₃×Dic₃	C₂×D₃	direct (N × H)
90. C₂²×C₃³	C₂²×C₄	semidirect
92. C₂×C₃×C₃⋊D₃	C₂²×C₄	semidirect
94. C₂×C₃²×D₃	C₂²×C₄	semidirect
96. C₃×D₃²	C₂²×C₄	semidirect
97. C₃⋊(C₃⋊Dic₃)	C₂⁴	semidirect
98. C₃×C₃⋊Dic₃	C₂⁴	semidirect
99. C₃²×Dic₃	C₂⁴	semidirect
123. C₂²×C₃⋊D₃	C₂×Dic₃	semidirect
133. C₂²×C₃×D₃	C₄×D₃	semidirect
134. C₂²×C₃×D₃	C₂×Dic₃	semidirect
137. C₂×D₃²	C₂×Dic₃	direct (N × H)
146. C₂×C₃⋊Dic₃	C₂²×D₃	semidirect
153. C₂×C₃×Dic₃	C₂²×D₃	semidirect
162. D₃×Dic₃	C₂²×D₃	direct (N × H)
164. C₂×C₃³	C₂³×C₄	semidirect
166. C₃×C₃⋊D₃	C₂³×C₄	semidirect
167. C₃²×D₃	C₂³×C₄	semidirect
198. C₂²×Dic₃	D₃²	direct (N × H)
213. C₂²×C₃²	C₂×C₄×D₃	semidirect
214. C₂²×C₃²	C₂²×Dic₃	semidirect
217. C₂×C₃⋊D₃	C₂²×Dic₃	semidirect
226. C₂×C₃×D₃	C₂×C₄×D₃	semidirect
227. C₂×C₃×D₃	C₂²×Dic₃	semidirect
230. D₃²	C₂²×Dic₃	direct (N × H)
237. C₃⋊Dic₃	C₂³×D₃	semidirect
242. C₃×Dic₃	C₂³×D₃	semidirect
249. C₃³	C₂⁴×C₄	semidirect
271. C₂²×D₃	D₃×Dic₃	direct (N × H)
291. C₂×Dic₃	C₂×D₃²	direct (N × H)
304. C₂×C₃²	C₂²×C₄×D₃	semidirect
305. C₂×C₃²	C₂³×Dic₃	semidirect
308. C₃⋊D₃	C₂³×Dic₃	semidirect
312. C₃×D₃	C₂²×C₄×D₃	semidirect
313. C₃×D₃	C₂³×Dic₃	semidirect
341. C₂²×C₃	C₄×D₃²	semidirect
342. C₂²×C₃	C₂×D₃×Dic₃	semidirect
350. C₂×D₃	C₂×D₃×Dic₃	direct (N × H)
363. Dic₃	C₂²×D₃²	direct (N × H)
367. C₃²	C₂³×C₄×D₃	semidirect
368. C₃²	C₂⁴×Dic₃	semidirect
393. C₂×C₃	C₂×C₄×D₃²	semidirect
394. C₂×C₃	C₂²×D₃×Dic₃	semidirect
399. D₃	C₂²×D₃×Dic₃	direct (N × H)
405. C₂²	D₃²×Dic₃	direct (N × H)
413. C₃	C₂²×C₄×D₃²	semidirect
414. C₃	C₂³×D₃×Dic₃	semidirect
417. C₂	C₂×D₃²×Dic₃	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×C₃×D₃²	2
C₂²×#6294	2
C₂²×Dic₃×C₃⋊D₃	2
C₂²×D₃×C₃⋊Dic₃	2
C₂²×C₃×D₃×Dic₃	2
C₂×D₃²×Dic₃	2
C₂³×D₃×Dic₃	3
C₂²×C₄×D₃²	3

Subgroups — C22×D32×Dic3 #13181308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₃²×Dic₃ #13181308