Subgroups — C₂²×C₄×D₃×C₃⋊D₃ #13181597

Order 1728.

9116 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×D₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃²×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#6289	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×Dic₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×D₃×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₃×C₃⋊D₃	C₂	1	24	yes	maximal, direct product factor
9	C₂³×C₄×C₃⋊D₃	—	3	1	no	maximal
10	C₂²×C₄×D₃²	—	3	4	no	maximal
11	C₂³×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
13	C₂³×C₃²×D₃	C₂²	1	1	yes	characteristic
14	C₂²×D₃×C₃⋊D₃	C₄	1	16	yes	direct product factor
15	C₂²×D₃×C₃⋊D₃	C₂²	1	12	yes	—
16	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	12	yes	complemented
19	C₂²×C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	12	yes	complemented
21	C₂²×C₃²×Dic₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃²×C₄×D₃	C₂²	1	12	yes	complemented
23	C₂×#6289	C₂²	1	12	yes	complemented
24	C₂×Dic₃×C₃⋊D₃	C₂²	1	12	yes	complemented
25	C₂×D₃×C₃⋊Dic₃	C₂²	1	12	yes	complemented
26	C₄×D₃×C₃⋊D₃	C₂²	1	64	yes	direct product factor
27	C₂⁴×C₃⋊D₃	—	3	1	no	—
28	C₂³×D₃²	—	3	4	no	—
29	C₂³×C₃²×C₄	—	3	1	no	—
30	C₂³×C₃⋊Dic₃	—	3	1	no	—
31	C₂²×C₄×C₃⋊D₃	—	3	1	no	—
32	C₂²×C₄×C₃⋊D₃	—	3	1	no	—
33	C₂²×C₄×C₃⋊D₃	—	3	24	no	—
34	C₂²×C₄×C₃⋊D₃	—	3	4	no	—
35	C₂²×C₄×C₃⋊D₃	—	3	1	no	—
36	C₂²×C₄×C₃⋊D₃	—	6	4	no	—
37	C₂²×C₄×C₃⋊D₃	D₃	1	1	yes	characteristic, direct product factor
38	C₂²×C₃×C₄×D₃	—	3	4	no	—
39	C₂²×C₃×C₄×D₃	D₃	1	4	yes	complemented
40	C₂²×#624	—	3	4	no	—
41	C₂²×D₃×Dic₃	—	3	4	no	—
42	C₂²×D₃×Dic₃	—	3	4	no	—
43	C₂×C₄×D₃²	—	3	96	no	—
44	C₂³×C₃³	C₂³	1	1	yes	characteristic
45	C₂²×C₃⋊(C₃⋊D₃)	C₂×C₄	1	8	yes	complemented
46	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	6	yes	—
47	C₂²×C₃×C₃⋊D₃	C₂×C₄	1	8	yes	complemented
48	C₂²×C₃×C₃⋊D₃	C₂³	1	6	yes	—
49	C₂²×C₃²×D₃	C₂×C₄	1	8	yes	complemented
50	C₂²×C₃²×D₃	C₂³	1	6	yes	—
51	C₂×D₃×C₃⋊D₃	C₂×C₄	1	96	yes	direct product factor
52	C₂×D₃×C₃⋊D₃	C₂³	1	16	yes	—
53	C₂×C₃³×C₄	C₂³	1	6	yes	complemented
54	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	6	yes	complemented
55	C₄×C₃⋊(C₃⋊D₃)	C₂³	1	16	yes	complemented
56	C₂×C₃×C₃⋊Dic₃	C₂³	1	6	yes	complemented
57	C₃×C₄×C₃⋊D₃	C₂³	1	16	yes	complemented
58	C₂×C₃²×Dic₃	C₂³	1	6	yes	complemented
59	C₃²×C₄×D₃	C₂³	1	16	yes	complemented
60	#6289	C₂³	1	16	yes	complemented
61	Dic₃×C₃⋊D₃	C₂³	1	16	yes	complemented
62	D₃×C₃⋊Dic₃	C₂³	1	16	yes	complemented
63	C₂³×C₄×D₃	—	9	4	no	—
64	C₂³×C₄×D₃	—	9	1	no	—
65	C₂⁴×C₃²	—	3	1	no	—
66	C₂³×C₃⋊D₃	—	3	1	no	—
67	C₂³×C₃⋊D₃	—	3	4	no	—
68	C₂³×C₃⋊D₃	—	3	16	no	—
69	C₂³×C₃⋊D₃	—	3	12	no	—
70	C₂³×C₃⋊D₃	—	6	4	no	—
71	C₂³×C₃⋊D₃	C₂×D₃	1	1	yes	characteristic
72	C₂³×C₃×D₃	—	3	4	no	—
73	C₂³×C₃×D₃	C₂×D₃	1	4	yes	—
74	C₂²×D₃²	—	3	64	no	—
75	C₂²×D₃²	—	3	48	no	—
76	C₂²×C₃²×C₄	—	2	4	no	—
77	C₂²×C₃²×C₄	—	3	1	no	—
78	C₂²×C₃²×C₄	—	3	12	no	—
79	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	complemented
80	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic, complemented
81	C₂²×C₃⋊Dic₃	—	3	1	no	—
82	C₂²×C₃⋊Dic₃	—	3	4	no	—
83	C₂²×C₃⋊Dic₃	—	3	12	no	—
84	C₂²×C₃⋊Dic₃	—	6	4	no	—
85	C₂²×C₃⋊Dic₃	C₂×D₃	1	1	yes	characteristic, complemented
86	C₂×C₄×C₃⋊D₃	—	3	12	no	—
87	C₂×C₄×C₃⋊D₃	—	3	12	no	—
88	C₂×C₄×C₃⋊D₃	—	3	48	no	—
89	C₂×C₄×C₃⋊D₃	—	3	12	no	—
90	C₂×C₄×C₃⋊D₃	—	3	64	no	—
91	C₂×C₄×C₃⋊D₃	—	6	48	no	—
92	C₂×C₄×C₃⋊D₃	C₂×D₃	1	12	yes	direct product factor
93	C₂²×C₃×Dic₃	—	3	4	no	—
94	C₂²×C₃×Dic₃	C₂×D₃	1	4	yes	complemented
95	C₂×C₃×C₄×D₃	—	3	48	no	—
96	C₂×C₃×C₄×D₃	C₂×D₃	1	48	yes	complemented
97	C₂×#624	—	3	48	no	—
98	C₂×D₃×Dic₃	—	3	48	no	—
99	C₂×D₃×Dic₃	—	3	48	no	—
100	C₄×D₃²	—	3	256	no	—
101	C₂²×C₃³	C₂²×C₄	1	4	yes	complemented
102	C₂²×C₃³	C₂⁴	1	3	yes	—
103	C₂×C₃⋊(C₃⋊D₃)	C₂²×C₄	1	24	yes	complemented
104	C₂×C₃⋊(C₃⋊D₃)	C₂⁴	1	4	yes	—
105	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	24	yes	complemented
106	C₂×C₃×C₃⋊D₃	C₂⁴	1	4	yes	—
107	C₂×C₃²×D₃	C₂²×C₄	1	24	yes	complemented
108	C₂×C₃²×D₃	C₂⁴	1	4	yes	—
109	D₃×C₃⋊D₃	C₂²×C₄	1	64	yes	direct product factor
110	C₃³×C₄	C₂⁴	1	4	yes	complemented
111	C₃⋊(C₃⋊Dic₃)	C₂⁴	1	4	yes	complemented
112	C₃×C₃⋊Dic₃	C₂⁴	1	4	yes	complemented
113	C₃²×Dic₃	C₂⁴	1	4	yes	complemented
114	C₂⁴×D₃	—	9	4	no	—
115	C₂⁴×D₃	—	9	1	no	—
116	C₂³×C₃×C₄	—	3	4	no	—
117	C₂³×C₃×C₄	—	9	1	no	—
118	C₂³×Dic₃	—	9	4	no	—
119	C₂³×Dic₃	—	9	1	no	—
120	C₂²×C₄×D₃	—	3	4	no	—
121	C₂²×C₄×D₃	—	9	96	no	—
122	C₂²×C₄×D₃	—	9	4	no	—
123	C₂²×C₄×D₃	—	9	4	no	—
124	C₂²×C₄×D₃	—	9	1	no	—
125	C₂²×C₄×D₃	—	9	4	no	—
126	C₂²×C₄×D₃	—	9	1	no	—
127	C₂²×C₄×D₃	—	9	1	no	—
128	C₂²×C₄×D₃	—	9	24	no	—
129	C₂²×C₄×D₃	—	18	4	no	—
130	C₂²×C₄×D₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
131	C₂³×C₃²	—	2	4	no	—
132	C₂³×C₃²	—	3	8	no	—
133	C₂³×C₃²	—	3	6	no	—
134	C₂³×C₃²	C₂²×D₃	1	4	yes	—
135	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
136	C₂²×C₃⋊D₃	—	3	8	no	—
137	C₂²×C₃⋊D₃	—	3	6	no	—
138	C₂²×C₃⋊D₃	—	3	96	no	—
139	C₂²×C₃⋊D₃	—	3	16	no	—
140	C₂²×C₃⋊D₃	—	3	32	no	—
141	C₂²×C₃⋊D₃	—	3	24	no	—
142	C₂²×C₃⋊D₃	—	6	32	no	—
143	C₂²×C₃⋊D₃	—	6	24	no	—
144	C₂²×C₃⋊D₃	C₄×D₃	1	8	yes	direct product factor
145	C₂²×C₃⋊D₃	C₂²×D₃	1	6	yes	—
146	C₂²×C₃×D₃	—	3	32	no	—
147	C₂²×C₃×D₃	—	3	24	no	—
148	C₂²×C₃×D₃	C₄×D₃	1	32	yes	complemented
149	C₂²×C₃×D₃	C₂²×D₃	1	24	yes	—
150	C₂×D₃²	—	3	384	no	—
151	C₂×D₃²	—	3	64	no	—
152	C₂×C₃²×C₄	—	2	24	no	—
153	C₂×C₃²×C₄	—	3	6	no	—
154	C₂×C₃²×C₄	—	3	16	no	—
155	C₂×C₃²×C₄	C₂²×D₃	1	24	yes	complemented
156	C₂×C₃²×C₄	C₂²×D₃	1	6	yes	complemented
157	C₂×C₃⋊Dic₃	—	3	6	no	—
158	C₂×C₃⋊Dic₃	—	3	16	no	—
159	C₂×C₃⋊Dic₃	—	3	24	no	—
160	C₂×C₃⋊Dic₃	—	6	24	no	—
161	C₂×C₃⋊Dic₃	C₂²×D₃	1	6	yes	complemented
162	C₄×C₃⋊D₃	—	3	16	no	—
163	C₄×C₃⋊D₃	—	3	16	no	—
164	C₄×C₃⋊D₃	—	3	16	no	—
165	C₄×C₃⋊D₃	—	3	64	no	—
166	C₄×C₃⋊D₃	—	6	64	no	—
167	C₄×C₃⋊D₃	C₂²×D₃	1	16	yes	direct product factor
168	C₂×C₃×Dic₃	—	3	24	no	—
169	C₂×C₃×Dic₃	C₂²×D₃	1	24	yes	complemented
170	C₃×C₄×D₃	—	3	64	no	—
171	C₃×C₄×D₃	C₂²×D₃	1	64	yes	complemented
172	#624	—	3	64	no	—
173	D₃×Dic₃	—	3	64	no	—
174	D₃×Dic₃	—	3	64	no	—
175	C₂⁴×C₄	—	27	1	no	Sylow
176	C₂×C₃³	C₂³×C₄	1	6	yes	complemented
177	C₂×C₃³	C₂⁵	1	1	yes	characteristic
178	C₃⋊(C₃⋊D₃)	C₂³×C₄	1	8	yes	complemented
179	C₃×C₃⋊D₃	C₂³×C₄	1	8	yes	complemented
180	C₃²×D₃	C₂³×C₄	1	8	yes	complemented
181	C₂⁴×C₃	—	3	4	no	—
182	C₂⁴×C₃	—	9	1	no	—
183	C₂³×D₃	—	3	4	no	—
184	C₂³×D₃	—	9	48	no	—
185	C₂³×D₃	—	9	64	no	—
186	C₂³×D₃	—	9	4	no	—
187	C₂³×D₃	—	9	1	no	—
188	C₂³×D₃	—	9	16	no	—
189	C₂³×D₃	—	9	12	no	—
190	C₂³×D₃	—	18	4	no	—
191	C₂³×D₃	C₂×C₃⋊D₃	1	1	yes	characteristic
192	C₂²×C₃×C₄	—	2	4	no	—
193	C₂²×C₃×C₄	—	3	4	no	—
194	C₂²×C₃×C₄	—	3	48	no	—
195	C₂²×C₃×C₄	—	9	1	no	—
196	C₂²×C₃×C₄	—	9	12	no	—
197	C₂²×C₃×C₄	D₃²	1	4	yes	complemented
198	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
199	C₂²×Dic₃	—	3	4	no	—
200	C₂²×Dic₃	—	9	48	no	—
201	C₂²×Dic₃	—	9	4	no	—
202	C₂²×Dic₃	—	9	1	no	—
203	C₂²×Dic₃	—	9	12	no	—
204	C₂²×Dic₃	—	18	4	no	—
205	C₂²×Dic₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
206	C₂×C₄×D₃	—	3	48	no	—
207	C₂×C₄×D₃	—	9	256	no	—
208	C₂×C₄×D₃	—	9	48	no	—
209	C₂×C₄×D₃	—	9	48	no	—
210	C₂×C₄×D₃	—	9	12	no	—
211	C₂×C₄×D₃	—	9	48	no	—
212	C₂×C₄×D₃	—	9	12	no	—
213	C₂×C₄×D₃	—	9	12	no	—
214	C₂×C₄×D₃	—	9	64	no	—
215	C₂×C₄×D₃	—	18	48	no	—
216	C₂×C₄×D₃	C₂×C₃⋊D₃	1	12	yes	direct product factor
217	C₂²×C₃²	—	2	12	no	—
218	C₂²×C₃²	—	2	16	no	—
219	C₂²×C₃²	—	3	24	no	—
220	C₂²×C₃²	—	3	4	no	—
221	C₂²×C₃²	C₂×C₄×D₃	1	16	yes	complemented
222	C₂²×C₃²	C₂×C₄×D₃	1	4	yes	complemented
223	C₂²×C₃²	C₂³×D₃	1	12	yes	—
224	C₂²×C₃²	C₂³×D₃	1	3	yes	—
225	C₂×C₃⋊D₃	—	3	24	no	—
226	C₂×C₃⋊D₃	—	3	4	no	—
227	C₂×C₃⋊D₃	—	3	64	no	—
228	C₂×C₃⋊D₃	—	3	96	no	—
229	C₂×C₃⋊D₃	—	3	16	no	—
230	C₂×C₃⋊D₃	—	6	96	no	—
231	C₂×C₃⋊D₃	—	6	16	no	—
232	C₂×C₃⋊D₃	C₂×C₄×D₃	1	24	yes	direct product factor
233	C₂×C₃⋊D₃	C₂³×D₃	1	4	yes	—
234	C₂×C₃×D₃	—	3	96	no	—
235	C₂×C₃×D₃	—	3	16	no	—
236	C₂×C₃×D₃	C₂×C₄×D₃	1	96	yes	complemented
237	C₂×C₃×D₃	C₂³×D₃	1	16	yes	—
238	D₃²	—	3	256	no	—
239	C₃²×C₄	—	2	16	no	—
240	C₃²×C₄	—	3	4	no	—
241	C₃²×C₄	C₂³×D₃	1	16	yes	complemented
242	C₃²×C₄	C₂³×D₃	1	4	yes	complemented
243	C₃⋊Dic₃	—	3	4	no	—
244	C₃⋊Dic₃	—	3	16	no	—
245	C₃⋊Dic₃	—	6	16	no	—
246	C₃⋊Dic₃	C₂³×D₃	1	4	yes	complemented
247	C₃×Dic₃	—	3	16	no	—
248	C₃×Dic₃	C₂³×D₃	1	16	yes	complemented
249	C₂⁵	—	27	1	no	—
250	C₂³×C₄	—	3	1	no	—
251	C₂³×C₄	—	9	1	no	—
252	C₂³×C₄	—	27	1	no	—
253	C₂³×C₄	—	27	24	no	—
254	C₂³×C₄	—	27	1	no	—
255	C₂³×C₄	—	27	1	no	—
256	C₂³×C₄	—	27	1	no	—
257	C₃³	C₂⁴×C₄	1	1	yes	characteristic, complemented, Sylow
258	C₂³×C₃	—	2	4	no	—
259	C₂³×C₃	—	3	24	no	—
260	C₂³×C₃	—	3	32	no	—
261	C₂³×C₃	—	9	6	no	—
262	C₂³×C₃	—	9	8	no	—
263	C₂³×C₃	C₂×D₃²	1	4	yes	—
264	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
265	C₂²×D₃	—	3	24	no	—
266	C₂²×D₃	—	3	32	no	—
267	C₂²×D₃	—	9	64	no	—
268	C₂²×D₃	—	9	384	no	—
269	C₂²×D₃	—	9	24	no	—
270	C₂²×D₃	—	9	6	no	—
271	C₂²×D₃	—	9	32	no	—
272	C₂²×D₃	—	9	8	no	—
273	C₂²×D₃	—	9	16	no	—
274	C₂²×D₃	—	9	96	no	—
275	C₂²×D₃	—	18	24	no	—
276	C₂²×D₃	—	18	32	no	—
277	C₂²×D₃	C₄×C₃⋊D₃	1	8	yes	direct product factor
278	C₂²×D₃	C₂²×C₃⋊D₃	1	6	yes	—
279	C₂×C₃×C₄	—	2	24	no	—
280	C₂×C₃×C₄	—	3	24	no	—
281	C₂×C₃×C₄	—	3	64	no	—
282	C₂×C₃×C₄	—	9	6	no	—
283	C₂×C₃×C₄	—	9	16	no	—
284	C₂×C₃×C₄	C₂×D₃²	1	24	yes	complemented
285	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	6	yes	complemented
286	C₂×Dic₃	—	3	24	no	—
287	C₂×Dic₃	—	9	64	no	—
288	C₂×Dic₃	—	9	24	no	—
289	C₂×Dic₃	—	9	6	no	—
290	C₂×Dic₃	—	9	16	no	—
291	C₂×Dic₃	—	18	24	no	—
292	C₂×Dic₃	C₂²×C₃⋊D₃	1	6	yes	complemented
293	C₄×D₃	—	3	64	no	—
294	C₄×D₃	—	9	64	no	—
295	C₄×D₃	—	9	64	no	—
296	C₄×D₃	—	9	16	no	—
297	C₄×D₃	—	9	64	no	—
298	C₄×D₃	—	9	16	no	—
299	C₄×D₃	—	9	16	no	—
300	C₄×D₃	—	18	64	no	—
301	C₄×D₃	C₂²×C₃⋊D₃	1	16	yes	direct product factor
302	C₂×C₃²	—	2	24	no	—
303	C₂×C₃²	—	2	4	no	—
304	C₂×C₃²	—	3	8	no	—
305	C₂×C₃²	C₂²×C₄×D₃	1	24	yes	complemented
306	C₂×C₃²	C₂²×C₄×D₃	1	6	yes	complemented
307	C₂×C₃²	C₂⁴×D₃	1	4	yes	—
308	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
309	C₃⋊D₃	—	3	8	no	—
310	C₃⋊D₃	—	3	32	no	—
311	C₃⋊D₃	—	6	32	no	—
312	C₃⋊D₃	C₂²×C₄×D₃	1	8	yes	direct product factor
313	C₃×D₃	—	3	32	no	—
314	C₃×D₃	C₂²×C₄×D₃	1	32	yes	complemented
315	C₂⁴	—	3	1	no	—
316	C₂⁴	—	9	1	no	—
317	C₂⁴	—	27	12	no	—
318	C₂⁴	—	27	16	no	—
319	C₂⁴	—	27	1	no	—
320	C₂²×C₄	—	3	1	no	—
321	C₂²×C₄	—	3	12	no	—
322	C₂²×C₄	—	9	1	no	—
323	C₂²×C₄	—	9	12	no	—
324	C₂²×C₄	—	27	12	no	—
325	C₂²×C₄	—	27	64	no	—
326	C₂²×C₄	—	27	12	no	—
327	C₂²×C₄	—	27	12	no	—
328	C₂²×C₄	—	27	1	no	—
329	C₂²×C₄	—	27	12	no	—
330	C₂²×C₄	D₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
331	C₂²×C₃	—	2	12	no	—
332	C₂²×C₃	—	2	16	no	—
333	C₂²×C₃	—	3	96	no	—
334	C₂²×C₃	—	3	16	no	—
335	C₂²×C₃	—	9	24	no	—
336	C₂²×C₃	—	9	4	no	—
337	C₂²×C₃	C₄×D₃²	1	16	yes	complemented
338	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	4	yes	complemented
339	C₂²×C₃	C₂²×D₃²	1	12	yes	—
340	C₂²×C₃	C₂³×C₃⋊D₃	1	3	yes	—
341	C₂×D₃	—	3	96	no	—
342	C₂×D₃	—	3	16	no	—
343	C₂×D₃	—	9	256	no	—
344	C₂×D₃	—	9	96	no	—
345	C₂×D₃	—	9	24	no	—
346	C₂×D₃	—	9	16	no	—
347	C₂×D₃	—	9	4	no	—
348	C₂×D₃	—	9	64	no	—
349	C₂×D₃	—	18	16	no	—
350	C₂×D₃	—	18	96	no	—
351	C₂×D₃	C₂×C₄×C₃⋊D₃	1	24	yes	direct product factor
352	C₂×D₃	C₂³×C₃⋊D₃	1	4	yes	—
353	C₃×C₄	—	2	16	no	—
354	C₃×C₄	—	3	16	no	—
355	C₃×C₄	—	9	4	no	—
356	C₃×C₄	C₂²×D₃²	1	16	yes	complemented
357	C₃×C₄	C₂³×C₃⋊D₃	1	4	yes	complemented
358	Dic₃	—	3	16	no	—
359	Dic₃	—	9	16	no	—
360	Dic₃	—	9	4	no	—
361	Dic₃	—	18	16	no	—
362	Dic₃	C₂³×C₃⋊D₃	1	4	yes	complemented
363	C₃²	—	2	4	no	—
364	C₃²	C₂³×C₄×D₃	1	4	yes	complemented
365	C₃²	C₂³×C₄×D₃	1	1	yes	characteristic, complemented
366	C₂³	—	3	6	no	—
367	C₂³	—	3	8	no	—
368	C₂³	—	9	6	no	—
369	C₂³	—	9	8	no	—
370	C₂³	—	27	16	no	—
371	C₂³	—	27	96	no	—
372	C₂³	—	27	6	no	—
373	C₂³	—	27	8	no	—
374	C₂³	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic
375	C₂×C₄	—	3	6	no	—
376	C₂×C₄	—	3	16	no	—
377	C₂×C₄	—	9	6	no	—
378	C₂×C₄	—	9	16	no	—
379	C₂×C₄	—	27	16	no	—
380	C₂×C₄	—	27	16	no	—
381	C₂×C₄	—	27	16	no	—
382	C₂×C₄	—	27	6	no	—
383	C₂×C₄	—	27	16	no	—
384	C₂×C₄	C₂×D₃×C₃⋊D₃	1	6	yes	direct product factor
385	C₂×C₃	—	2	24	no	—
386	C₂×C₃	—	2	4	no	—
387	C₂×C₃	—	3	32	no	—
388	C₂×C₃	—	9	8	no	—
389	C₂×C₃	C₂×C₄×D₃²	1	24	yes	complemented
390	C₂×C₃	C₂²×C₄×C₃⋊D₃	1	6	yes	complemented
391	C₂×C₃	C₂³×D₃²	1	4	yes	—
392	C₂×C₃	C₂⁴×C₃⋊D₃	1	1	yes	characteristic
393	D₃	—	3	32	no	—
394	D₃	—	9	32	no	—
395	D₃	—	9	8	no	—
396	D₃	—	18	32	no	—
397	D₃	C₂²×C₄×C₃⋊D₃	1	8	yes	direct product factor
398	C₂²	—	3	24	no	—
399	C₂²	—	3	4	no	—
400	C₂²	—	9	24	no	—
401	C₂²	—	9	4	no	—
402	C₂²	—	27	64	no	—
403	C₂²	—	27	24	no	—
404	C₂²	—	27	4	no	—
405	C₂²	C₄×D₃×C₃⋊D₃	1	4	yes	direct product factor
406	C₂²	C₂²×D₃×C₃⋊D₃	1	3	yes	—
407	C₄	—	3	4	no	—
408	C₄	—	9	4	no	—
409	C₄	—	27	4	no	—
410	C₄	C₂²×D₃×C₃⋊D₃	1	4	yes	direct product factor
411	C₃	—	2	4	no	—
412	C₃	C₂²×C₄×D₃²	1	4	yes	complemented
413	C₃	C₂³×C₄×C₃⋊D₃	1	1	yes	characteristic, complemented
414	C₂	—	3	8	no	—
415	C₂	—	9	8	no	—
416	C₂	—	27	8	no	—
417	C₂	C₂×C₄×D₃×C₃⋊D₃	1	6	yes	direct product factor
418	C₂	C₂³×D₃×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄	D₃×C₃⋊D₃
commutator, hypocenter	C₃³	C₂⁴×C₄
Frattini	C₂	C₂³×D₃×C₃⋊D₃
Fitting	C₂²×C₃³×C₄	C₂²
socle	C₂³×C₃³	C₂³
prime radical	C₂³×D₃×C₃⋊D₃	C₂
cosocle	C₂×C₃³	C₂⁵
LCS	G ▷ C₃³
UCS	C₁ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₃⋊(C₃⋊D₃)	C₂	semidirect
3. C₂²×C₃×C₄×C₃⋊D₃	C₂	semidirect
4. C₂²×C₃²×C₄×D₃	C₂	semidirect
5. C₂²×#6289	C₂	semidirect
6. C₂²×Dic₃×C₃⋊D₃	C₂	semidirect
7. C₂²×D₃×C₃⋊Dic₃	C₂	semidirect
8. C₂×C₄×D₃×C₃⋊D₃	C₂	direct (N × H)
14. C₂²×D₃×C₃⋊D₃	C₄	direct (N × H)
16. C₂²×C₃³×C₄	C₂²	semidirect
17. C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
18. C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	semidirect
19. C₂²×C₃×C₃⋊Dic₃	C₂²	semidirect
20. C₂×C₃×C₄×C₃⋊D₃	C₂²	semidirect
21. C₂²×C₃²×Dic₃	C₂²	semidirect
22. C₂×C₃²×C₄×D₃	C₂²	semidirect
23. C₂×#6289	C₂²	semidirect
24. C₂×Dic₃×C₃⋊D₃	C₂²	semidirect
25. C₂×D₃×C₃⋊Dic₃	C₂²	semidirect
26. C₄×D₃×C₃⋊D₃	C₂²	direct (N × H)
37. C₂²×C₄×C₃⋊D₃	D₃	direct (N × H)
39. C₂²×C₃×C₄×D₃	D₃	semidirect
45. C₂²×C₃⋊(C₃⋊D₃)	C₂×C₄	semidirect
47. C₂²×C₃×C₃⋊D₃	C₂×C₄	semidirect
49. C₂²×C₃²×D₃	C₂×C₄	semidirect
51. C₂×D₃×C₃⋊D₃	C₂×C₄	direct (N × H)
53. C₂×C₃³×C₄	C₂³	semidirect
54. C₂×C₃⋊(C₃⋊Dic₃)	C₂³	semidirect
55. C₄×C₃⋊(C₃⋊D₃)	C₂³	semidirect
56. C₂×C₃×C₃⋊Dic₃	C₂³	semidirect
57. C₃×C₄×C₃⋊D₃	C₂³	semidirect
58. C₂×C₃²×Dic₃	C₂³	semidirect
59. C₃²×C₄×D₃	C₂³	semidirect
60. #6289	C₂³	semidirect
61. Dic₃×C₃⋊D₃	C₂³	semidirect
62. D₃×C₃⋊Dic₃	C₂³	semidirect
79. C₂²×C₃²×C₄	C₂×D₃	semidirect
80. C₂²×C₃²×C₄	C₂×D₃	semidirect
85. C₂²×C₃⋊Dic₃	C₂×D₃	semidirect
92. C₂×C₄×C₃⋊D₃	C₂×D₃	direct (N × H)
94. C₂²×C₃×Dic₃	C₂×D₃	semidirect
96. C₂×C₃×C₄×D₃	C₂×D₃	semidirect
101. C₂²×C₃³	C₂²×C₄	semidirect
103. C₂×C₃⋊(C₃⋊D₃)	C₂²×C₄	semidirect
105. C₂×C₃×C₃⋊D₃	C₂²×C₄	semidirect
107. C₂×C₃²×D₃	C₂²×C₄	semidirect
109. D₃×C₃⋊D₃	C₂²×C₄	direct (N × H)
110. C₃³×C₄	C₂⁴	semidirect
111. C₃⋊(C₃⋊Dic₃)	C₂⁴	semidirect
112. C₃×C₃⋊Dic₃	C₂⁴	semidirect
113. C₃²×Dic₃	C₂⁴	semidirect
130. C₂²×C₄×D₃	C₃⋊D₃	direct (N × H)
144. C₂²×C₃⋊D₃	C₄×D₃	direct (N × H)
148. C₂²×C₃×D₃	C₄×D₃	semidirect
155. C₂×C₃²×C₄	C₂²×D₃	semidirect
156. C₂×C₃²×C₄	C₂²×D₃	semidirect
161. C₂×C₃⋊Dic₃	C₂²×D₃	semidirect
167. C₄×C₃⋊D₃	C₂²×D₃	direct (N × H)
169. C₂×C₃×Dic₃	C₂²×D₃	semidirect
171. C₃×C₄×D₃	C₂²×D₃	semidirect
176. C₂×C₃³	C₂³×C₄	semidirect
178. C₃⋊(C₃⋊D₃)	C₂³×C₄	semidirect
179. C₃×C₃⋊D₃	C₂³×C₄	semidirect
180. C₃²×D₃	C₂³×C₄	semidirect
197. C₂²×C₃×C₄	D₃²	semidirect
198. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
205. C₂²×Dic₃	C₂×C₃⋊D₃	semidirect
216. C₂×C₄×D₃	C₂×C₃⋊D₃	direct (N × H)
221. C₂²×C₃²	C₂×C₄×D₃	semidirect
222. C₂²×C₃²	C₂×C₄×D₃	semidirect
232. C₂×C₃⋊D₃	C₂×C₄×D₃	direct (N × H)
236. C₂×C₃×D₃	C₂×C₄×D₃	semidirect
241. C₃²×C₄	C₂³×D₃	semidirect
242. C₃²×C₄	C₂³×D₃	semidirect
246. C₃⋊Dic₃	C₂³×D₃	semidirect
248. C₃×Dic₃	C₂³×D₃	semidirect
257. C₃³	C₂⁴×C₄	semidirect
277. C₂²×D₃	C₄×C₃⋊D₃	direct (N × H)
284. C₂×C₃×C₄	C₂×D₃²	semidirect
285. C₂×C₃×C₄	C₂²×C₃⋊D₃	semidirect
292. C₂×Dic₃	C₂²×C₃⋊D₃	semidirect
301. C₄×D₃	C₂²×C₃⋊D₃	direct (N × H)
305. C₂×C₃²	C₂²×C₄×D₃	semidirect
306. C₂×C₃²	C₂²×C₄×D₃	semidirect
312. C₃⋊D₃	C₂²×C₄×D₃	direct (N × H)
314. C₃×D₃	C₂²×C₄×D₃	semidirect
330. C₂²×C₄	D₃×C₃⋊D₃	direct (N × H)
337. C₂²×C₃	C₄×D₃²	semidirect
338. C₂²×C₃	C₂×C₄×C₃⋊D₃	semidirect
351. C₂×D₃	C₂×C₄×C₃⋊D₃	direct (N × H)
356. C₃×C₄	C₂²×D₃²	semidirect
357. C₃×C₄	C₂³×C₃⋊D₃	semidirect
362. Dic₃	C₂³×C₃⋊D₃	semidirect
364. C₃²	C₂³×C₄×D₃	semidirect
365. C₃²	C₂³×C₄×D₃	semidirect
384. C₂×C₄	C₂×D₃×C₃⋊D₃	direct (N × H)
389. C₂×C₃	C₂×C₄×D₃²	semidirect
390. C₂×C₃	C₂²×C₄×C₃⋊D₃	semidirect
397. D₃	C₂²×C₄×C₃⋊D₃	direct (N × H)
405. C₂²	C₄×D₃×C₃⋊D₃	direct (N × H)
410. C₄	C₂²×D₃×C₃⋊D₃	direct (N × H)
412. C₃	C₂²×C₄×D₃²	semidirect
413. C₃	C₂³×C₄×C₃⋊D₃	semidirect
417. C₂	C₂×C₄×D₃×C₃⋊D₃	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×D₃×C₃⋊D₃	2
C₂²×C₄×C₃⋊(C₃⋊D₃)	2
C₂²×C₃×C₄×C₃⋊D₃	2
C₂²×C₃²×C₄×D₃	2
C₂²×#6289	2
C₂²×Dic₃×C₃⋊D₃	2
C₂²×D₃×C₃⋊Dic₃	2
C₂×C₄×D₃×C₃⋊D₃	2
C₂³×C₄×C₃⋊D₃	3
C₂²×C₄×D₃²	3

Subgroups — C22×C4×D3×C3⋊D3 #13181597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×D₃×C₃⋊D₃ #13181597