Subgroups — C₂×C₃⋊D₃×#217 #13178040

Order 1728.

4572 conjugacy classes of subgroups.

The subgroup lattice has 404 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
2	C₂²×Dic₃×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
3	C₂×#88864	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃²×#217	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃⋊D₃×#217	C₂	1	8	yes	maximal, direct product factor
6	C₂×#88803	C₂	1	2	yes	maximal, complemented
7	C₂×C₂²⋊C₄×C₃⋊D₃	—	3	1	no	maximal
8	C₂×D₃×#217	—	3	4	no	maximal
9	C₂⁴×C₃³	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₃⋊D₃	—	2	8	no	—
11	C₂³×C₃×C₃⋊D₃	C₄	1	8	yes	complemented
12	C₂³×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₃⋊D₃	C₂²	1	4	yes	—
14	C₂³×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
15	C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	1	2	yes	complemented
16	C₂²×C₃²×Dic₃	C₂²	1	2	yes	complemented
17	C₂×Dic₃×C₃⋊D₃	—	2	8	no	—
18	C₂×Dic₃×C₃⋊D₃	C₂²	1	8	yes	complemented
19	#88864	C₂²	1	4	yes	complemented
20	C₃²×#217	C₂²	1	4	yes	complemented
21	#88803	C₂²	1	8	yes	complemented
22	C₂⁴×C₃⋊D₃	D₃	1	1	yes	characteristic
23	C₂⁴×C₃×D₃	—	3	4	no	—
24	C₂²×C₄×C₃⋊D₃	—	3	2	no	—
25	C₂²×D₃×Dic₃	—	3	8	no	—
26	C₂×C₃²×C₂²⋊C₄	—	3	1	no	—
27	C₂×#3757	—	3	1	no	—
28	C₂×#3757	—	3	4	no	—
29	C₂×#3757	—	6	4	no	—
30	C₂×#3752	—	3	2	no	—
31	C₂²⋊C₄×C₃⋊D₃	—	3	8	no	—
32	C₂×C₃×#217	D₃	1	4	yes	complemented
33	D₃×#217	—	3	32	no	—
34	C₂×(C₂×D₃)⋊Dic₃	—	3	8	no	—
35	C₂³×C₃³	—	2	4	no	—
36	C₂³×C₃³	C₂×C₄	1	4	yes	complemented
37	C₂³×C₃³	C₂³	1	2	yes	—
38	C₂³×C₃³	C₂³	1	1	yes	characteristic
39	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
40	C₂²×C₃×C₃⋊D₃	—	2	32	no	—
41	C₂²×C₃×C₃⋊D₃	—	2	16	no	—
42	C₂²×C₃×C₃⋊D₃	C₂×C₄	1	4	yes	—
43	C₂²×C₃×C₃⋊D₃	C₂×C₄	1	16	yes	complemented
44	C₂²×C₃×C₃⋊D₃	C₂×C₄	1	4	yes	complemented
45	C₂²×C₃×C₃⋊D₃	D₄	1	8	yes	—
46	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
47	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
48	C₂×C₃⋊(C₃⋊Dic₃)	—	2	4	no	—
49	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	4	yes	complemented
50	C₂×C₃²×Dic₃	—	2	4	no	—
51	C₂×C₃²×Dic₃	C₂³	1	4	yes	complemented
52	Dic₃×C₃⋊D₃	—	2	16	no	—
53	C₂²×#217	—	9	1	no	—
54	C₂×D₃×C₂²⋊C₄	—	9	4	no	—
55	C₂⁴×C₃²	—	2	4	no	—
56	C₂⁴×C₃²	C₂×D₃	1	4	yes	—
57	C₂⁴×C₃²	C₂×D₃	1	1	yes	characteristic
58	C₂³×C₃⋊D₃	—	2	8	no	—
59	C₂³×C₃⋊D₃	Dic₃	1	8	yes	complemented
60	C₂³×C₃⋊D₃	C₂×D₃	1	4	yes	—
61	C₂³×C₃⋊D₃	C₂×D₃	1	1	yes	characteristic
62	C₂³×C₃⋊D₃	C₂×D₃	1	1	yes	characteristic
63	C₂³×C₃×D₃	—	3	4	no	—
64	C₂³×C₃×D₃	—	3	32	no	—
65	C₂³×C₃×D₃	—	3	4	no	—
66	C₂³×C₃×D₃	—	3	16	no	—
67	C₂³×C₃×D₃	—	6	32	no	—
68	C₂²×C₃²×C₄	—	3	2	no	—
69	C₂²×C₃⋊Dic₃	—	3	2	no	—
70	C₂²×C₃⋊Dic₃	—	3	8	no	—
71	C₂²×C₃⋊Dic₃	—	6	8	no	—
72	C₂×C₄×C₃⋊D₃	—	3	8	no	—
73	C₂×C₄×C₃⋊D₃	—	6	8	no	—
74	C₂²×C₃×Dic₃	C₂×D₃	1	8	yes	complemented
75	C₂×D₃×Dic₃	—	3	32	no	—
76	C₂×D₃×Dic₃	—	6	32	no	—
77	C₃²×C₂²⋊C₄	—	3	4	no	—
78	#3757	—	3	4	no	—
79	#3757	—	3	16	no	—
80	#3757	—	6	16	no	—
81	#3752	—	3	8	no	—
82	C₃×#217	C₂×D₃	1	16	yes	complemented
83	(C₂×D₃)⋊Dic₃	—	3	32	no	—
84	C₂²×C₃³	—	2	8	no	—
85	C₂²×C₃³	—	2	4	no	—
86	C₂²×C₃³	C₂²×C₄	1	2	yes	—
87	C₂²×C₃³	C₂²×C₄	1	4	yes	complemented
88	C₂²×C₃³	C₂×D₄	1	4	yes	—
89	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
90	C₂×C₃×C₃⋊D₃	—	2	8	no	—
91	C₂×C₃×C₃⋊D₃	—	2	4	no	—
92	C₂×C₃×C₃⋊D₃	—	2	32	no	—
93	C₂×C₃×C₃⋊D₃	C₂²⋊C₄	1	16	yes	complemented
94	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	4	yes	—
95	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	4	yes	complemented
96	C₂×C₃×C₃⋊D₃	C₂×D₄	1	8	yes	—
97	C₃⋊(C₃⋊Dic₃)	—	2	4	no	—
98	C₃²×Dic₃	—	2	4	no	—
99	C₂⁵×C₃	—	9	1	no	—
100	C₂⁴×D₃	—	3	4	no	—
101	C₂³×Dic₃	—	9	2	no	—
102	C₂²×C₄×D₃	—	9	8	no	—
103	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
104	C₂×#217	—	9	4	no	—
105	C₂×#217	—	9	1	no	—
106	C₂×#217	—	9	2	no	—
107	C₂×#217	—	9	8	no	—
108	C₂×#217	—	18	4	no	—
109	C₂×#217	C₃⋊D₃	1	1	yes	characteristic, direct product factor
110	C₂×(C₂×D₃)⋊C₄	—	9	8	no	—
111	D₃×C₂²⋊C₄	—	9	32	no	—
112	C₂³×C₃²	—	2	4	no	—
113	C₂³×C₃²	—	2	16	no	—
114	C₂³×C₃²	—	2	4	no	—
115	C₂³×C₃²	—	2	8	no	—
116	C₂³×C₃²	—	2	16	no	—
117	C₂³×C₃²	—	4	16	no	—
118	C₂³×C₃²	C₄×D₃	1	16	yes	complemented
119	C₂³×C₃²	C₂×Dic₃	1	4	yes	complemented
120	C₂³×C₃²	C₂²×D₃	1	8	yes	—
121	C₂³×C₃²	C₂²×D₃	1	4	yes	—
122	C₂³×C₃²	C₂²×D₃	1	2	yes	—
123	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
124	C₂²×C₃⋊D₃	—	2	4	no	—
125	C₂²×C₃⋊D₃	—	2	32	no	—
126	C₂²×C₃⋊D₃	—	2	16	no	—
127	C₂²×C₃⋊D₃	C₂×Dic₃	1	4	yes	—
128	C₂²×C₃⋊D₃	C₂×Dic₃	1	16	yes	complemented
129	C₂²×C₃⋊D₃	C₂×Dic₃	1	4	yes	complemented
130	C₂²×C₃⋊D₃	#67	1	8	yes	—
131	C₂²×C₃⋊D₃	C₂²×D₃	1	2	yes	—
132	C₂²×C₃⋊D₃	C₂²×D₃	1	2	yes	—
133	C₂²×C₃×D₃	—	3	16	no	—
134	C₂²×C₃×D₃	—	3	32	no	—
135	C₂²×C₃×D₃	—	3	8	no	—
136	C₂²×C₃×D₃	—	3	16	no	—
137	C₂²×C₃×D₃	—	3	64	no	—
138	C₂²×C₃×D₃	—	3	8	no	—
139	C₂²×C₃×D₃	—	6	128	no	—
140	C₂²×C₃×D₃	—	6	64	no	—
141	C₂²×C₃×D₃	—	6	16	no	—
142	C₂×C₃²×C₄	—	3	4	no	—
143	C₂×C₃²×C₄	—	6	4	no	—
144	C₂×C₃⋊Dic₃	—	3	4	no	—
145	C₂×C₃⋊Dic₃	—	3	16	no	—
146	C₂×C₃⋊Dic₃	—	6	16	no	—
147	C₂×C₃⋊Dic₃	—	6	4	no	—
148	C₂×C₃⋊Dic₃	—	6	16	no	—
149	C₂×C₃⋊Dic₃	—	12	16	no	—
150	C₄×C₃⋊D₃	—	6	16	no	—
151	C₂×C₃×Dic₃	—	2	16	no	—
152	C₂×C₃×Dic₃	C₂²×D₃	1	16	yes	complemented
153	D₃×Dic₃	—	6	64	no	—
154	C₂²×C₂²⋊C₄	—	27	1	no	Sylow
155	C₂×C₃³	—	2	4	no	—
156	C₂×C₃³	C₂×C₂²⋊C₄	1	4	yes	complemented
157	C₂×C₃³	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₃³	C₂²×D₄	1	2	yes	—
159	C₃×C₃⋊D₃	—	2	4	no	—
160	C₃×C₃⋊D₃	C₂×C₂²⋊C₄	1	8	yes	complemented
161	C₂⁴×C₃	—	2	4	no	—
162	C₂⁴×C₃	—	9	1	no	—
163	C₂⁴×C₃	—	9	8	no	—
164	C₂⁴×C₃	—	9	4	no	—
165	C₂⁴×C₃	—	9	1	no	—
166	C₂⁴×C₃	—	18	8	no	—
167	C₂⁴×C₃	D₃²	1	4	yes	—
168	C₂⁴×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
169	C₂³×D₃	—	3	4	no	—
170	C₂³×D₃	—	3	32	no	—
171	C₂³×D₃	—	3	16	no	—
172	C₂³×D₃	—	3	4	no	—
173	C₂³×D₃	—	6	32	no	—
174	C₂²×C₃×C₄	—	3	8	no	—
175	C₂²×Dic₃	—	9	8	no	—
176	C₂²×Dic₃	—	9	2	no	—
177	C₂²×Dic₃	—	9	8	no	—
178	C₂²×Dic₃	—	18	8	no	—
179	C₂²×Dic₃	—	18	8	no	—
180	C₂²×Dic₃	C₂×C₃⋊D₃	1	2	yes	complemented
181	C₂×C₄×D₃	—	9	32	no	—
182	C₂×C₄×D₃	—	18	32	no	—
183	C₃×C₂²⋊C₄	—	3	16	no	—
184	#217	—	9	16	no	—
185	#217	—	9	4	no	—
186	#217	—	9	8	no	—
187	#217	—	18	16	no	—
188	#217	C₂×C₃⋊D₃	1	4	yes	direct product factor
189	(C₂×D₃)⋊C₄	—	9	32	no	—
190	C₂²×C₃²	—	2	8	no	—
191	C₂²×C₃²	—	2	4	no	—
192	C₂²×C₃²	—	2	4	no	—
193	C₂²×C₃²	—	2	8	no	—
194	C₂²×C₃²	—	2	16	no	—
195	C₂²×C₃²	—	2	16	no	—
196	C₂²×C₃²	—	2	32	no	—
197	C₂²×C₃²	—	2	16	no	—
198	C₂²×C₃²	—	4	16	no	—
199	C₂²×C₃²	—	4	32	no	—
200	C₂²×C₃²	C₂×C₄×D₃	1	8	yes	—
201	C₂²×C₃²	C₂×C₄×D₃	1	16	yes	complemented
202	C₂²×C₃²	D₃×D₄	1	16	yes	—
203	C₂²×C₃²	C₂²×Dic₃	1	2	yes	—
204	C₂²×C₃²	C₂²×Dic₃	1	4	yes	complemented
205	C₂²×C₃²	C₂×#67	1	4	yes	—
206	C₂²×C₃²	C₂³×D₃	1	4	yes	—
207	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
208	C₂×C₃⋊D₃	—	2	8	no	—
209	C₂×C₃⋊D₃	—	2	4	no	—
210	C₂×C₃⋊D₃	—	2	32	no	—
211	C₂×C₃⋊D₃	#217	1	16	yes	direct product factor
212	C₂×C₃⋊D₃	C₂²×Dic₃	1	4	yes	—
213	C₂×C₃⋊D₃	C₂²×Dic₃	1	4	yes	complemented
214	C₂×C₃⋊D₃	C₂×#67	1	8	yes	—
215	C₂×C₃×D₃	—	3	64	no	—
216	C₂×C₃×D₃	—	3	16	no	—
217	C₂×C₃×D₃	—	3	32	no	—
218	C₂×C₃×D₃	—	3	16	no	—
219	C₂×C₃×D₃	—	6	128	no	—
220	C₂×C₃×D₃	—	6	32	no	—
221	C₂×C₃×D₃	—	6	16	no	—
222	C₃²×C₄	—	6	4	no	—
223	C₃⋊Dic₃	—	6	4	no	—
224	C₃⋊Dic₃	—	6	16	no	—
225	C₃⋊Dic₃	—	12	16	no	—
226	C₃×Dic₃	—	2	16	no	—
227	C₂⁵	—	9	1	no	—
228	C₂³×C₄	—	27	2	no	—
229	C₂×C₂²⋊C₄	—	3	1	no	—
230	C₂×C₂²⋊C₄	—	27	8	no	—
231	C₂×C₂²⋊C₄	—	27	2	no	—
232	C₂×C₂²⋊C₄	—	27	1	no	—
233	C₃³	C₂²×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
234	C₂³×C₃	—	2	16	no	—
235	C₂³×C₃	—	2	4	no	—
236	C₂³×C₃	—	2	16	no	—
237	C₂³×C₃	—	2	8	no	—
238	C₂³×C₃	—	2	4	no	—
239	C₂³×C₃	—	4	16	no	—
240	C₂³×C₃	—	9	2	no	—
241	C₂³×C₃	—	9	4	no	—
242	C₂³×C₃	—	9	8	no	—
243	C₂³×C₃	—	9	2	no	—
244	C₂³×C₃	—	9	4	no	—
245	C₂³×C₃	—	9	16	no	—
246	C₂³×C₃	—	18	32	no	—
247	C₂³×C₃	—	18	16	no	—
248	C₂³×C₃	—	18	4	no	—
249	C₂³×C₃	D₃×Dic₃	1	16	yes	complemented
250	C₂³×C₃	C₄×C₃⋊D₃	1	4	yes	complemented
251	C₂³×C₃	C₂×D₃²	1	8	yes	—
252	C₂³×C₃	C₂×D₃²	1	4	yes	—
253	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
254	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
255	C₂²×D₃	—	3	8	no	—
256	C₂²×D₃	—	3	16	no	—
257	C₂²×D₃	—	3	32	no	—
258	C₂²×D₃	—	3	8	no	—
259	C₂²×D₃	—	3	16	no	—
260	C₂²×D₃	—	3	64	no	—
261	C₂²×D₃	—	6	64	no	—
262	C₂²×D₃	—	6	128	no	—
263	C₂²×D₃	—	6	16	no	—
264	C₂×C₃×C₄	—	3	16	no	—
265	C₂×C₃×C₄	—	6	16	no	—
266	C₂×Dic₃	—	2	4	no	—
267	C₂×Dic₃	—	9	16	no	—
268	C₂×Dic₃	—	9	4	no	—
269	C₂×Dic₃	—	18	16	no	—
270	C₂×Dic₃	—	18	16	no	—
271	C₂×Dic₃	—	18	16	no	—
272	C₂×Dic₃	—	18	4	no	—
273	C₂×Dic₃	—	36	16	no	—
274	C₂×Dic₃	C₂²×C₃⋊D₃	1	4	yes	complemented
275	C₄×D₃	—	18	64	no	—
276	C₂×C₃²	—	2	4	no	—
277	C₂×C₃²	—	2	4	no	—
278	C₂×C₃²	—	2	8	no	—
279	C₂×C₃²	—	2	16	no	—
280	C₂×C₃²	—	2	16	no	—
281	C₂×C₃²	—	4	16	no	—
282	C₂×C₃²	D₃×C₂²⋊C₄	1	16	yes	complemented
283	C₂×C₃²	C₂×#217	1	4	yes	complemented
284	C₂×C₃²	C₂²×C₄×D₃	1	4	yes	—
285	C₂×C₃²	C₂×D₃×D₄	1	8	yes	—
286	C₂×C₃²	C₂³×Dic₃	1	1	yes	characteristic
287	C₂×C₃²	C₂²×#67	1	2	yes	—
288	C₃⋊D₃	—	2	4	no	—
289	C₃⋊D₃	C₂×#217	1	8	yes	direct product factor
290	C₃×D₃	—	3	32	no	—
291	C₃×D₃	—	6	16	no	—
292	C₂⁴	—	9	1	no	—
293	C₂⁴	—	9	8	no	—
294	C₂⁴	—	9	4	no	—
295	C₂⁴	—	9	1	no	—
296	C₂⁴	—	18	8	no	—
297	C₂⁴	D₃×C₃⋊D₃	1	1	yes	characteristic
298	C₂²×C₄	—	3	2	no	—
299	C₂²×C₄	—	27	8	no	—
300	C₂²×C₄	—	27	2	no	—
301	C₂²×C₄	—	54	8	no	—
302	C₂²⋊C₄	—	3	4	no	—
303	C₂²⋊C₄	—	27	8	no	—
304	C₂²⋊C₄	—	27	4	no	—
305	C₂²×C₃	—	2	16	no	—
306	C₂²×C₃	—	2	8	no	—
307	C₂²×C₃	—	2	4	no	—
308	C₂²×C₃	—	2	32	no	—
309	C₂²×C₃	—	2	4	no	—
310	C₂²×C₃	—	2	8	no	—
311	C₂²×C₃	—	2	16	no	—
312	C₂²×C₃	—	2	16	no	—
313	C₂²×C₃	—	4	16	no	—
314	C₂²×C₃	—	4	32	no	—
315	C₂²×C₃	—	9	16	no	—
316	C₂²×C₃	—	9	4	no	—
317	C₂²×C₃	—	9	8	no	—
318	C₂²×C₃	—	9	4	no	—
319	C₂²×C₃	—	18	32	no	—
320	C₂²×C₃	—	18	8	no	—
321	C₂²×C₃	—	18	4	no	—
322	C₂²×C₃	C₂×D₃×Dic₃	1	8	yes	—
323	C₂²×C₃	C₂×D₃×Dic₃	1	16	yes	complemented
324	C₂²×C₃	D₃×#67	1	16	yes	—
325	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	2	yes	—
326	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	4	yes	complemented
327	C₂²×C₃	D₄×C₃⋊D₃	1	4	yes	—
328	C₂²×C₃	C₂²×D₃²	1	4	yes	—
329	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
330	C₂×D₃	—	3	16	no	—
331	C₂×D₃	—	3	32	no	—
332	C₂×D₃	—	3	64	no	—
333	C₂×D₃	—	3	16	no	—
334	C₂×D₃	—	6	128	no	—
335	C₂×D₃	—	6	16	no	—
336	C₂×D₃	—	6	32	no	—
337	C₃×C₄	—	6	16	no	—
338	Dic₃	—	2	4	no	—
339	Dic₃	—	18	16	no	—
340	Dic₃	—	18	4	no	—
341	Dic₃	—	36	16	no	—
342	C₃²	—	2	4	no	—
343	C₃²	C₂×D₃×C₂²⋊C₄	1	4	yes	complemented
344	C₃²	C₂²×#217	1	1	yes	characteristic, complemented
345	C₂³	—	2	4	no	—
346	C₂³	—	9	2	no	—
347	C₂³	—	9	4	no	—
348	C₂³	—	9	8	no	—
349	C₂³	—	9	2	no	—
350	C₂³	—	9	4	no	—
351	C₂³	—	9	16	no	—
352	C₂³	—	18	16	no	—
353	C₂³	—	18	32	no	—
354	C₂³	—	18	4	no	—
355	C₂³	Dic₃×C₃⋊D₃	1	4	yes	complemented
356	C₂³	C₂×D₃×C₃⋊D₃	1	2	yes	—
357	C₂³	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic
358	C₂×C₄	—	3	4	no	—
359	C₂×C₄	—	6	4	no	—
360	C₂×C₄	—	27	4	no	—
361	C₂×C₄	—	54	16	no	—
362	C₂×C₄	—	54	4	no	—
363	C₂×C₃	—	2	4	no	—
364	C₂×C₃	—	2	16	no	—
365	C₂×C₃	—	2	4	no	—
366	C₂×C₃	—	2	8	no	—
367	C₂×C₃	—	2	16	no	—
368	C₂×C₃	—	4	16	no	—
369	C₂×C₃	—	9	8	no	—
370	C₂×C₃	—	18	4	no	—
371	C₂×C₃	D₃×#217	1	16	yes	complemented
372	C₂×C₃	C₂²⋊C₄×C₃⋊D₃	1	4	yes	complemented
373	C₂×C₃	C₂²×D₃×Dic₃	1	4	yes	—
374	C₂×C₃	C₂×D₃×#67	1	8	yes	—
375	C₂×C₃	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
376	C₂×C₃	C₂×D₄×C₃⋊D₃	1	2	yes	—
377	D₃	—	3	32	no	—
378	D₃	—	6	16	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	8	no	—
381	C₂²	—	9	4	no	—
382	C₂²	—	9	8	no	—
383	C₂²	—	9	16	no	—
384	C₂²	—	9	4	no	—
385	C₂²	—	18	32	no	—
386	C₂²	—	18	4	no	—
387	C₂²	—	18	8	no	—
388	C₂²	C₂×Dic₃×C₃⋊D₃	1	2	yes	—
389	C₂²	C₂×Dic₃×C₃⋊D₃	1	4	yes	complemented
390	C₂²	C₃⋊D₃×#67	1	4	yes	—
391	C₂²	C₂²×D₃×C₃⋊D₃	1	1	yes	characteristic
392	C₄	—	6	4	no	—
393	C₄	—	54	4	no	—
394	C₃	—	2	4	no	—
395	C₃	C₂×D₃×#217	1	4	yes	complemented
396	C₃	C₂×C₂²⋊C₄×C₃⋊D₃	1	1	yes	characteristic, complemented
397	C₂	—	2	4	no	—
398	C₂	—	9	8	no	—
399	C₂	—	18	4	no	—
400	C₂	C₃⋊D₃×#217	1	4	yes	direct product factor
401	C₂	C₂²×Dic₃×C₃⋊D₃	1	1	yes	characteristic
402	C₂	C₂×C₃⋊D₃×#67	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₃×C₃⋊D₃	C₂	semidirect
3. C₂×#88864	C₂	semidirect
4. C₂×C₃²×#217	C₂	semidirect
5. C₃⋊D₃×#217	C₂	direct (N × H)
6. C₂×#88803	C₂	semidirect
11. C₂³×C₃×C₃⋊D₃	C₄	semidirect
15. C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
16. C₂²×C₃²×Dic₃	C₂²	semidirect
18. C₂×Dic₃×C₃⋊D₃	C₂²	semidirect
19. #88864	C₂²	semidirect
20. C₃²×#217	C₂²	semidirect
21. #88803	C₂²	semidirect
32. C₂×C₃×#217	D₃	semidirect
36. C₂³×C₃³	C₂×C₄	semidirect
43. C₂²×C₃×C₃⋊D₃	C₂×C₄	semidirect
44. C₂²×C₃×C₃⋊D₃	C₂×C₄	semidirect
49. C₂×C₃⋊(C₃⋊Dic₃)	C₂³	semidirect
51. C₂×C₃²×Dic₃	C₂³	semidirect
59. C₂³×C₃⋊D₃	Dic₃	semidirect
74. C₂²×C₃×Dic₃	C₂×D₃	semidirect
82. C₃×#217	C₂×D₃	semidirect
87. C₂²×C₃³	C₂²×C₄	semidirect
93. C₂×C₃×C₃⋊D₃	C₂²⋊C₄	semidirect
95. C₂×C₃×C₃⋊D₃	C₂²×C₄	semidirect
109. C₂×#217	C₃⋊D₃	direct (N × H)
118. C₂³×C₃²	C₄×D₃	semidirect
119. C₂³×C₃²	C₂×Dic₃	semidirect
128. C₂²×C₃⋊D₃	C₂×Dic₃	semidirect
129. C₂²×C₃⋊D₃	C₂×Dic₃	semidirect
152. C₂×C₃×Dic₃	C₂²×D₃	semidirect
156. C₂×C₃³	C₂×C₂²⋊C₄	semidirect
160. C₃×C₃⋊D₃	C₂×C₂²⋊C₄	semidirect
180. C₂²×Dic₃	C₂×C₃⋊D₃	semidirect
188. #217	C₂×C₃⋊D₃	direct (N × H)
201. C₂²×C₃²	C₂×C₄×D₃	semidirect
204. C₂²×C₃²	C₂²×Dic₃	semidirect
211. C₂×C₃⋊D₃	#217	direct (N × H)
213. C₂×C₃⋊D₃	C₂²×Dic₃	semidirect
233. C₃³	C₂²×C₂²⋊C₄	semidirect
249. C₂³×C₃	D₃×Dic₃	semidirect
250. C₂³×C₃	C₄×C₃⋊D₃	semidirect
274. C₂×Dic₃	C₂²×C₃⋊D₃	semidirect
282. C₂×C₃²	D₃×C₂²⋊C₄	semidirect
283. C₂×C₃²	C₂×#217	semidirect
289. C₃⋊D₃	C₂×#217	direct (N × H)
323. C₂²×C₃	C₂×D₃×Dic₃	semidirect
326. C₂²×C₃	C₂×C₄×C₃⋊D₃	semidirect
343. C₃²	C₂×D₃×C₂²⋊C₄	semidirect
344. C₃²	C₂²×#217	semidirect
355. C₂³	Dic₃×C₃⋊D₃	semidirect
371. C₂×C₃	D₃×#217	semidirect
372. C₂×C₃	C₂²⋊C₄×C₃⋊D₃	semidirect
389. C₂²	C₂×Dic₃×C₃⋊D₃	semidirect
395. C₃	C₂×D₃×#217	semidirect
396. C₃	C₂×C₂²⋊C₄×C₃⋊D₃	semidirect
400. C₂	C₃⋊D₃×#217	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×Dic₃×C₃⋊D₃	2
C₂×#88864	2
C₂×C₃²×#217	2
C₃⋊D₃×#217	2
C₂×#88803	2
C₂×C₂²⋊C₄×C₃⋊D₃	3
C₂×D₃×#217	3

Subgroups — C2×C3⋊D3×#217 #13178040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊D₃×#217 #13178040