Subgroups — C₂×C₃×D₄×C₃⋊Dic₃ #13179543

Order 1728.

3500 conjugacy classes of subgroups.

The subgroup lattice has 368 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
2	C₂³×C₃×C₃⋊Dic₃	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#3757	C₂	1	2	yes	maximal, complemented
4	C₃×D₄×C₃⋊Dic₃	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₄×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₄×C₃⋊Dic₃	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×D₄×Dic₃	—	3	4	no	maximal
9	C₂⁴×C₃³	C₂²	1	2	yes	—
10	C₂×C₃³×D₄	C₄	1	8	yes	complemented
11	C₂×C₃³×D₄	C₂²	1	4	yes	—
12	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₃⋊Dic₃	—	2	8	no	—
14	C₂²×C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	—
16	C₂²×C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₃⋊Dic₃	C₂²	1	8	yes	complemented
18	C₃×#3757	C₂²	1	8	yes	complemented
19	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	4	yes	complemented
20	C₃×C₄×C₃⋊Dic₃	C₂²	1	4	yes	complemented
21	C₂²×C₃²×D₄	—	2	4	no	—
22	C₂²×C₃²×D₄	D₃	1	4	yes	—
23	C₂²×C₃²×D₄	C₂×C₃	1	1	yes	characteristic
24	C₂³×C₃⋊Dic₃	C₂×C₃	1	2	yes	complemented
25	C₂³×C₃×Dic₃	—	3	8	no	—
26	C₂×#3757	C₂×C₃	1	2	yes	complemented
27	D₄×C₃⋊Dic₃	C₂×C₃	1	8	yes	direct product factor
28	C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×C₄×C₃⋊Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₃×#217	—	3	8	no	—
31	C₃×D₄×Dic₃	—	3	32	no	—
32	C₂×C₃×C₄⋊Dic₃	—	3	4	no	—
33	C₂×C₃×C₄×Dic₃	—	3	4	no	—
34	C₂³×C₃³	—	2	4	no	—
35	C₂³×C₃³	—	2	4	no	—
36	C₂³×C₃³	C₂×C₄	1	8	yes	complemented
37	C₂³×C₃³	C₂³	1	4	yes	—
38	C₂³×C₃³	C₂³	1	1	yes	characteristic
39	C₃³×D₄	C₂×C₄	1	16	yes	complemented
40	C₂×C₃³×C₄	C₂×C₄	1	4	yes	complemented
41	C₂×C₃³×C₄	C₂³	1	2	yes	—
42	C₂×C₃×C₃⋊Dic₃	—	2	4	no	—
43	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
44	C₂×C₃×C₃⋊Dic₃	—	2	16	no	—
45	C₂×C₃×C₃⋊Dic₃	D₄	1	4	yes	direct product factor
46	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
47	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	—
48	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
49	C₂×C₃×C₄×D₄	—	9	1	no	—
50	C₂×D₄×Dic₃	—	3	4	no	—
51	C₂⁴×C₃²	—	2	8	no	—
52	C₂⁴×C₃²	C₂×D₃	1	8	yes	—
53	C₂⁴×C₃²	C₂²×C₃	1	2	yes	—
54	C₂×C₃²×D₄	—	2	32	no	—
55	C₂×C₃²×D₄	—	2	16	no	—
56	C₂×C₃²×D₄	Dic₃	1	32	yes	complemented
57	C₂×C₃²×D₄	C₃×C₄	1	8	yes	complemented
58	C₂×C₃²×D₄	C₂×D₃	1	16	yes	—
59	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
60	C₂²×C₃²×C₄	—	2	4	no	—
61	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
62	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
63	C₂²×C₃⋊Dic₃	—	2	8	no	—
64	C₂²×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
65	C₂²×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
67	C₂²×C₃⋊Dic₃	C₂²×C₃	1	8	yes	complemented
68	C₂²×C₃×Dic₃	—	3	4	no	—
69	C₂²×C₃×Dic₃	—	3	4	no	—
70	C₂²×C₃×Dic₃	—	3	8	no	—
71	C₂²×C₃×Dic₃	—	3	32	no	—
72	C₂²×C₃×Dic₃	—	6	32	no	—
73	#3757	C₂²×C₃	1	8	yes	complemented
74	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	4	yes	complemented
75	C₄×C₃⋊Dic₃	C₂²×C₃	1	4	yes	complemented
76	C₃×#217	—	3	32	no	—
77	C₃×C₄⋊Dic₃	—	3	16	no	—
78	C₃×C₄×Dic₃	—	3	16	no	—
79	C₂²×C₃³	—	2	16	no	—
80	C₂²×C₃³	—	2	4	no	—
81	C₂²×C₃³	—	2	4	no	—
82	C₂²×C₃³	C₂²×C₄	1	2	yes	—
83	C₂²×C₃³	C₂²×C₄	1	8	yes	complemented
84	C₂²×C₃³	C₂×D₄	1	2	yes	—
85	C₂²×C₃³	#41	1	2	yes	—
86	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
87	C₃³×C₄	C₂²×C₄	1	4	yes	complemented
88	C₃×C₃⋊Dic₃	—	2	4	no	—
89	C₃×C₃⋊Dic₃	—	2	2	no	—
90	C₃×C₃⋊Dic₃	C₂×D₄	1	4	yes	direct product factor
91	C₂²×C₃×D₄	—	2	4	no	—
92	C₂²×C₃×D₄	C₃×D₃	1	4	yes	—
93	C₂²×C₃×D₄	C₃⋊D₃	1	1	yes	characteristic
94	C₂³×C₃×C₄	—	9	2	no	—
95	C₂³×Dic₃	—	3	8	no	—
96	C₃×C₄×D₄	—	9	8	no	—
97	C₂×C₃×C₄⋊C₄	—	9	1	no	—
98	C₂×C₃×C₂²⋊C₄	—	9	2	no	—
99	C₂×C₃×C₄²	—	9	1	no	—
100	C₂×#217	—	3	8	no	—
101	D₄×Dic₃	—	3	32	no	—
102	C₂×C₄⋊Dic₃	—	3	4	no	—
103	C₂×C₄×Dic₃	—	3	4	no	—
104	C₂³×C₃²	—	2	4	no	—
105	C₂³×C₃²	—	2	4	no	—
106	C₂³×C₃²	—	2	32	no	—
107	C₂³×C₃²	—	2	4	no	—
108	C₂³×C₃²	—	2	16	no	—
109	C₂³×C₃²	—	2	16	no	—
110	C₂³×C₃²	—	2	16	no	—
111	C₂³×C₃²	—	4	16	no	—
112	C₂³×C₃²	—	4	16	no	—
113	C₂³×C₃²	C₂×Dic₃	1	32	yes	complemented
114	C₂³×C₃²	C₂×C₃×C₄	1	8	yes	complemented
115	C₂³×C₃²	C₂²×D₃	1	16	yes	—
116	C₂³×C₃²	C₂²×D₃	1	4	yes	—
117	C₂³×C₃²	C₂³×C₃	1	4	yes	—
118	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
119	C₃²×D₄	—	2	64	no	—
120	C₃²×D₄	C₂×Dic₃	1	64	yes	complemented
121	C₃²×D₄	C₂×C₃×C₄	1	16	yes	complemented
122	C₂×C₃²×C₄	—	2	16	no	—
123	C₂×C₃²×C₄	—	2	8	no	—
124	C₂×C₃²×C₄	C₂×Dic₃	1	16	yes	complemented
125	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	complemented
126	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
127	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
128	C₂×C₃⋊Dic₃	—	2	4	no	—
129	C₂×C₃⋊Dic₃	—	2	2	no	—
130	C₂×C₃⋊Dic₃	—	2	16	no	—
131	C₂×C₃⋊Dic₃	C₃×D₄	1	4	yes	direct product factor
132	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
133	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	—
134	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
135	C₂×C₃×Dic₃	—	3	16	no	—
136	C₂×C₃×Dic₃	—	3	8	no	—
137	C₂×C₃×Dic₃	—	3	8	no	—
138	C₂×C₃×Dic₃	—	3	16	no	—
139	C₂×C₃×Dic₃	—	6	64	no	—
140	C₂×C₃×Dic₃	—	6	16	no	—
141	C₂×C₃×Dic₃	—	6	8	no	—
142	C₂×C₄×D₄	—	9	1	no	Sylow
143	C₂×C₃³	—	2	8	no	—
144	C₂×C₃³	C₄×D₄	1	4	yes	complemented
145	C₂×C₃³	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₃³	C₂×#41	1	1	yes	characteristic
148	C₂⁴×C₃	—	2	8	no	—
149	C₂⁴×C₃	C₂×C₃×D₃	1	8	yes	—
150	C₂⁴×C₃	C₂×C₃⋊D₃	1	2	yes	—
151	C₂×C₃×D₄	—	2	32	no	—
152	C₂×C₃×D₄	—	2	16	no	—
153	C₂×C₃×D₄	C₃×Dic₃	1	32	yes	complemented
154	C₂×C₃×D₄	C₃⋊Dic₃	1	8	yes	direct product factor
155	C₂×C₃×D₄	C₂×C₃×D₃	1	16	yes	—
156	C₂×C₃×D₄	C₂×C₃⋊D₃	1	4	yes	—
157	C₂²×C₃×C₄	—	2	4	no	—
158	C₂²×C₃×C₄	—	9	1	no	—
159	C₂²×C₃×C₄	—	9	8	no	—
160	C₂²×C₃×C₄	—	9	1	no	—
161	C₂²×C₃×C₄	—	9	2	no	—
162	C₂²×C₃×C₄	—	18	8	no	—
163	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
164	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
165	C₂²×Dic₃	—	3	4	no	—
166	C₂²×Dic₃	—	3	4	no	—
167	C₂²×Dic₃	—	3	8	no	—
168	C₂²×Dic₃	—	3	32	no	—
169	C₂²×Dic₃	—	6	32	no	—
170	C₃×C₄⋊C₄	—	9	4	no	—
171	C₃×C₂²⋊C₄	—	9	8	no	—
172	C₃×C₄²	—	9	4	no	—
173	#217	—	3	32	no	—
174	C₄⋊Dic₃	—	3	16	no	—
175	C₄×Dic₃	—	3	16	no	—
176	C₂²×C₃²	—	2	16	no	—
177	C₂²×C₃²	—	2	4	no	—
178	C₂²×C₃²	—	2	4	no	—
179	C₂²×C₃²	—	2	4	no	—
180	C₂²×C₃²	—	2	8	no	—
181	C₂²×C₃²	—	2	8	no	—
182	C₂²×C₃²	—	2	8	no	—
183	C₂²×C₃²	—	2	32	no	—
184	C₂²×C₃²	—	2	64	no	—
185	C₂²×C₃²	—	2	16	no	—
186	C₂²×C₃²	—	2	16	no	—
187	C₂²×C₃²	—	4	64	no	—
188	C₂²×C₃²	—	4	16	no	—
189	C₂²×C₃²	—	4	16	no	—
190	C₂²×C₃²	D₃×D₄	1	8	yes	—
191	C₂²×C₃²	#237	1	8	yes	—
192	C₂²×C₃²	C₂²×Dic₃	1	8	yes	—
193	C₂²×C₃²	C₂²×Dic₃	1	32	yes	complemented
194	C₂²×C₃²	C₂²×C₃×C₄	1	2	yes	—
195	C₂²×C₃²	C₂²×C₃×C₄	1	8	yes	complemented
196	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
197	C₂²×C₃²	C₃×#41	1	2	yes	—
198	C₂²×C₃²	C₂³×D₃	1	4	yes	—
199	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
200	C₃²×C₄	—	2	16	no	—
201	C₃²×C₄	C₂²×Dic₃	1	16	yes	complemented
202	C₃²×C₄	C₂²×C₃×C₄	1	4	yes	complemented
203	C₃⋊Dic₃	—	2	4	no	—
204	C₃⋊Dic₃	—	2	2	no	—
205	C₃⋊Dic₃	C₂×C₃×D₄	1	4	yes	direct product factor
206	C₃×Dic₃	—	3	16	no	—
207	C₃×Dic₃	—	6	16	no	—
208	C₃×Dic₃	—	6	8	no	—
209	C₂²×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic
210	C₂³×C₄	—	9	2	no	—
211	C₄×D₄	—	9	8	no	—
212	C₂×C₄⋊C₄	—	9	1	no	—
213	C₂×C₂²⋊C₄	—	9	2	no	—
214	C₂×C₄²	—	9	1	no	—
215	C₃³	C₂×C₄×D₄	1	1	yes	characteristic, complemented, Sylow
216	C₂³×C₃	—	2	16	no	—
217	C₂³×C₃	—	2	16	no	—
218	C₂³×C₃	—	2	4	no	—
219	C₂³×C₃	—	2	4	no	—
220	C₂³×C₃	—	2	32	no	—
221	C₂³×C₃	—	2	4	no	—
222	C₂³×C₃	—	2	16	no	—
223	C₂³×C₃	—	4	16	no	—
224	C₂³×C₃	—	4	16	no	—
225	C₂³×C₃	C₂×C₃×Dic₃	1	32	yes	complemented
226	C₂³×C₃	C₂×C₃⋊Dic₃	1	8	yes	complemented
227	C₂³×C₃	C₂²×C₃×D₃	1	16	yes	—
228	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
229	C₂³×C₃	C₂²×C₃⋊D₃	1	4	yes	—
230	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
231	C₃×D₄	—	2	64	no	—
232	C₃×D₄	C₂×C₃×Dic₃	1	64	yes	complemented
233	C₃×D₄	C₂×C₃⋊Dic₃	1	16	yes	direct product factor
234	C₂×C₃×C₄	—	2	16	no	—
235	C₂×C₃×C₄	—	2	8	no	—
236	C₂×C₃×C₄	—	9	2	no	—
237	C₂×C₃×C₄	—	9	4	no	—
238	C₂×C₃×C₄	—	9	2	no	—
239	C₂×C₃×C₄	—	9	4	no	—
240	C₂×C₃×C₄	—	18	16	no	—
241	C₂×C₃×C₄	—	18	4	no	—
242	C₂×C₃×C₄	—	18	2	no	—
243	C₂×C₃×C₄	C₂×C₃×Dic₃	1	16	yes	complemented
244	C₂×C₃×C₄	C₂×C₃⋊Dic₃	1	4	yes	complemented
245	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
246	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
247	C₂×Dic₃	—	3	8	no	—
248	C₂×Dic₃	—	3	16	no	—
249	C₂×Dic₃	—	3	8	no	—
250	C₂×Dic₃	—	3	16	no	—
251	C₂×Dic₃	—	6	64	no	—
252	C₂×Dic₃	—	6	16	no	—
253	C₂×Dic₃	—	6	8	no	—
254	C₂×C₃²	—	2	8	no	—
255	C₂×C₃²	—	2	16	no	—
256	C₂×C₃²	—	2	4	no	—
257	C₂×C₃²	—	2	4	no	—
258	C₂×C₃²	—	2	4	no	—
259	C₂×C₃²	—	2	32	no	—
260	C₂×C₃²	—	4	32	no	—
261	C₂×C₃²	D₄×Dic₃	1	16	yes	complemented
262	C₂×C₃²	C₃×C₄×D₄	1	4	yes	complemented
263	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
264	C₂×C₃²	C₂×#237	1	4	yes	—
265	C₂×C₃²	C₂³×Dic₃	1	4	yes	—
266	C₂×C₃²	C₂³×C₃×C₄	1	1	yes	characteristic
267	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
268	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
269	C₂⁴	C₂×C₃×C₃⋊D₃	1	2	yes	—
270	C₂×D₄	C₃×C₃⋊Dic₃	1	8	yes	direct product factor
271	C₂×D₄	C₂×C₃×C₃⋊D₃	1	4	yes	—
272	C₂²×C₄	—	9	1	no	—
273	C₂²×C₄	—	9	1	no	—
274	C₂²×C₄	—	9	2	no	—
275	C₂²×C₄	—	9	8	no	—
276	C₂²×C₄	—	18	8	no	—
277	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
278	C₄⋊C₄	—	9	4	no	—
279	C₂²⋊C₄	—	9	8	no	—
280	C₄²	—	9	4	no	—
281	C₂²×C₃	—	2	64	no	—
282	C₂²×C₃	—	2	16	no	—
283	C₂²×C₃	—	2	16	no	—
284	C₂²×C₃	—	2	4	no	—
285	C₂²×C₃	—	2	4	no	—
286	C₂²×C₃	—	2	16	no	—
287	C₂²×C₃	—	2	4	no	—
288	C₂²×C₃	—	2	8	no	—
289	C₂²×C₃	—	2	8	no	—
290	C₂²×C₃	—	2	8	no	—
291	C₂²×C₃	—	2	32	no	—
292	C₂²×C₃	—	4	64	no	—
293	C₂²×C₃	—	4	16	no	—
294	C₂²×C₃	—	4	16	no	—
295	C₂²×C₃	C₃×D₃×D₄	1	8	yes	—
296	C₂²×C₃	C₃×#237	1	8	yes	—
297	C₂²×C₃	C₂²×C₃×Dic₃	1	8	yes	—
298	C₂²×C₃	C₂²×C₃×Dic₃	1	32	yes	complemented
299	C₂²×C₃	D₄×C₃⋊D₃	1	2	yes	—
300	C₂²×C₃	#3830	1	2	yes	—
301	C₂²×C₃	C₂²×C₃⋊Dic₃	1	2	yes	—
302	C₂²×C₃	C₂²×C₃⋊Dic₃	1	8	yes	complemented
303	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
304	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
305	C₃×C₄	—	2	16	no	—
306	C₃×C₄	—	9	4	no	—
307	C₃×C₄	—	18	4	no	—
308	C₃×C₄	—	18	2	no	—
309	C₃×C₄	C₂²×C₃×Dic₃	1	16	yes	complemented
310	C₃×C₄	C₂²×C₃⋊Dic₃	1	4	yes	complemented
311	Dic₃	—	3	16	no	—
312	Dic₃	—	6	16	no	—
313	Dic₃	—	6	8	no	—
314	C₃²	—	2	4	no	—
315	C₃²	C₂×D₄×Dic₃	1	4	yes	complemented
316	C₃²	C₂×C₃×C₄×D₄	1	1	yes	characteristic, complemented
317	C₂³	—	2	4	no	—
318	C₂³	—	2	4	no	—
319	C₂³	C₂×C₃×C₃⋊Dic₃	1	8	yes	complemented
320	C₂³	C₂²×C₃×C₃⋊D₃	1	4	yes	—
321	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
322	D₄	C₂×C₃×C₃⋊Dic₃	1	16	yes	direct product factor
323	C₂×C₄	—	9	2	no	—
324	C₂×C₄	—	9	4	no	—
325	C₂×C₄	—	9	2	no	—
326	C₂×C₄	—	9	4	no	—
327	C₂×C₄	—	18	16	no	—
328	C₂×C₄	—	18	4	no	—
329	C₂×C₄	—	18	2	no	—
330	C₂×C₄	C₂×C₃×C₃⋊Dic₃	1	4	yes	complemented
331	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
332	C₂×C₃	—	2	32	no	—
333	C₂×C₃	—	2	8	no	—
334	C₂×C₃	—	2	16	no	—
335	C₂×C₃	—	2	4	no	—
336	C₂×C₃	—	2	4	no	—
337	C₂×C₃	—	2	4	no	—
338	C₂×C₃	—	4	32	no	—
339	C₂×C₃	C₃×D₄×Dic₃	1	16	yes	complemented
340	C₂×C₃	D₄×C₃⋊Dic₃	1	4	yes	direct product factor
341	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
342	C₂×C₃	C₂×C₃×#237	1	4	yes	—
343	C₂×C₃	C₂³×C₃×Dic₃	1	4	yes	—
344	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
345	C₂×C₃	C₂×#3830	1	1	yes	characteristic
346	C₂×C₃	C₂³×C₃⋊Dic₃	1	1	yes	characteristic
347	C₂²	—	2	16	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	4	no	—
350	C₂²	C₃×D₄×C₃⋊D₃	1	2	yes	—
351	C₂²	C₃×#3830	1	2	yes	—
352	C₂²	C₂²×C₃×C₃⋊Dic₃	1	2	yes	—
353	C₂²	C₂²×C₃×C₃⋊Dic₃	1	8	yes	complemented
354	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
355	C₄	—	9	4	no	—
356	C₄	—	18	4	no	—
357	C₄	—	18	2	no	—
358	C₄	C₂²×C₃×C₃⋊Dic₃	1	4	yes	complemented
359	C₃	—	2	4	no	—
360	C₃	C₂×C₃×D₄×Dic₃	1	4	yes	complemented
361	C₃	C₂×D₄×C₃⋊Dic₃	1	1	yes	characteristic, direct product factor
362	C₂	—	2	8	no	—
363	C₂	C₃×D₄×C₃⋊Dic₃	1	4	yes	direct product factor
364	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
365	C₂	C₂×C₃×#3830	1	1	yes	characteristic
366	C₂	C₂³×C₃×C₃⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂²×C₃⋊D₃
commutator	C₂×C₃²	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting, prime radical	C₂²×C₃³×D₄	C₂
socle	C₂³×C₃³	C₂³
cosocle	C₂²×C₃²	C₂⁴×C₃
hypercenter	C₂²×C₃×D₄	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×C₄×D₄
LCS	G ▷ C₂×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
2. C₂³×C₃×C₃⋊Dic₃	C₂	semidirect
3. C₂×C₃×#3757	C₂	semidirect
4. C₃×D₄×C₃⋊Dic₃	C₂	direct (N × H)
5. C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	semidirect
6. C₂×C₃×C₄×C₃⋊Dic₃	C₂	semidirect
7. C₂×D₄×C₃⋊Dic₃	C₃	direct (N × H)
10. C₂×C₃³×D₄	C₄	semidirect
17. C₂²×C₃×C₃⋊Dic₃	C₂²	semidirect
18. C₃×#3757	C₂²	semidirect
19. C₃×C₄⋊(C₃⋊Dic₃)	C₂²	semidirect
20. C₃×C₄×C₃⋊Dic₃	C₂²	semidirect
24. C₂³×C₃⋊Dic₃	C₂×C₃	semidirect
26. C₂×#3757	C₂×C₃	semidirect
27. D₄×C₃⋊Dic₃	C₂×C₃	direct (N × H)
28. C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	semidirect
29. C₂×C₄×C₃⋊Dic₃	C₂×C₃	semidirect
36. C₂³×C₃³	C₂×C₄	semidirect
39. C₃³×D₄	C₂×C₄	semidirect
40. C₂×C₃³×C₄	C₂×C₄	semidirect
45. C₂×C₃×C₃⋊Dic₃	D₄	direct (N × H)
56. C₂×C₃²×D₄	Dic₃	semidirect
57. C₂×C₃²×D₄	C₃×C₄	semidirect
67. C₂²×C₃⋊Dic₃	C₂²×C₃	semidirect
73. #3757	C₂²×C₃	semidirect
74. C₄⋊(C₃⋊Dic₃)	C₂²×C₃	semidirect
75. C₄×C₃⋊Dic₃	C₂²×C₃	semidirect
83. C₂²×C₃³	C₂²×C₄	semidirect
87. C₃³×C₄	C₂²×C₄	semidirect
90. C₃×C₃⋊Dic₃	C₂×D₄	direct (N × H)
113. C₂³×C₃²	C₂×Dic₃	semidirect
114. C₂³×C₃²	C₂×C₃×C₄	semidirect
120. C₃²×D₄	C₂×Dic₃	semidirect
121. C₃²×D₄	C₂×C₃×C₄	semidirect
124. C₂×C₃²×C₄	C₂×Dic₃	semidirect
125. C₂×C₃²×C₄	C₂×C₃×C₄	semidirect
131. C₂×C₃⋊Dic₃	C₃×D₄	direct (N × H)
144. C₂×C₃³	C₄×D₄	semidirect
153. C₂×C₃×D₄	C₃×Dic₃	semidirect
154. C₂×C₃×D₄	C₃⋊Dic₃	direct (N × H)
193. C₂²×C₃²	C₂²×Dic₃	semidirect
195. C₂²×C₃²	C₂²×C₃×C₄	semidirect
201. C₃²×C₄	C₂²×Dic₃	semidirect
202. C₃²×C₄	C₂²×C₃×C₄	semidirect
205. C₃⋊Dic₃	C₂×C₃×D₄	direct (N × H)
215. C₃³	C₂×C₄×D₄	semidirect
225. C₂³×C₃	C₂×C₃×Dic₃	semidirect
226. C₂³×C₃	C₂×C₃⋊Dic₃	semidirect
232. C₃×D₄	C₂×C₃×Dic₃	semidirect
233. C₃×D₄	C₂×C₃⋊Dic₃	direct (N × H)
243. C₂×C₃×C₄	C₂×C₃×Dic₃	semidirect
244. C₂×C₃×C₄	C₂×C₃⋊Dic₃	semidirect
261. C₂×C₃²	D₄×Dic₃	semidirect
262. C₂×C₃²	C₃×C₄×D₄	semidirect
270. C₂×D₄	C₃×C₃⋊Dic₃	direct (N × H)
298. C₂²×C₃	C₂²×C₃×Dic₃	semidirect
302. C₂²×C₃	C₂²×C₃⋊Dic₃	semidirect
309. C₃×C₄	C₂²×C₃×Dic₃	semidirect
310. C₃×C₄	C₂²×C₃⋊Dic₃	semidirect
315. C₃²	C₂×D₄×Dic₃	semidirect
316. C₃²	C₂×C₃×C₄×D₄	semidirect
319. C₂³	C₂×C₃×C₃⋊Dic₃	semidirect
322. D₄	C₂×C₃×C₃⋊Dic₃	direct (N × H)
330. C₂×C₄	C₂×C₃×C₃⋊Dic₃	semidirect
339. C₂×C₃	C₃×D₄×Dic₃	semidirect
340. C₂×C₃	D₄×C₃⋊Dic₃	direct (N × H)
353. C₂²	C₂²×C₃×C₃⋊Dic₃	semidirect
358. C₄	C₂²×C₃×C₃⋊Dic₃	semidirect
360. C₃	C₂×C₃×D₄×Dic₃	semidirect
361. C₃	C₂×D₄×C₃⋊Dic₃	direct (N × H)
363. C₂	C₃×D₄×C₃⋊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
C₂²×C₃³×D₄	2
C₂³×C₃×C₃⋊Dic₃	2
C₂×C₃×#3757	2
C₃×D₄×C₃⋊Dic₃	2
C₂×C₃×C₄⋊(C₃⋊Dic₃)	2
C₂×C₃×C₄×C₃⋊Dic₃	2
C₂×D₄×C₃⋊Dic₃	3
C₂×C₃×D₄×Dic₃	3

Subgroups — C2×C3×D4×C3⋊Dic3 #13179543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₄×C₃⋊Dic₃ #13179543