Subgroups — C₂×C₃×D₃×2₋¹⁺⁴ #11919230

Order 1152.

12141 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃×2₋¹⁺⁴	C₂	1	32	yes	maximal, direct product factor
3	C₂×C₃×#1010	C₂	1	10	yes	maximal, complemented
4	C₂×C₃×D₃×#41	C₂	1	10	yes	maximal, complemented
5	C₂×C₃×#1007	C₂	1	5	yes	maximal, complemented
6	C₂²×C₃×D₃×Q₈	C₂	1	5	yes	maximal, complemented
7	C₂²×C₃×2₋¹⁺⁴	—	3	1	no	maximal
8	C₂×D₃×2₋¹⁺⁴	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₃²×2₋¹⁺⁴	C₂²	1	16	yes	complemented
10	C₂×C₃²×#41	C₂²	1	10	yes	complemented
11	C₂²×C₃²×Q₈	C₂²	1	5	yes	complemented
12	C₃×#1010	C₂²	1	160	yes	complemented
13	C₃×D₃×#41	C₂²	1	160	yes	complemented
14	C₃×#1007	C₂²	1	80	yes	complemented
15	C₂×C₃×#239	C₂²	1	10	yes	complemented
16	C₂×C₃×D₃×Q₈	C₂²	1	10	yes	—
17	C₂×C₃×D₃×Q₈	C₂²	1	20	yes	complemented
18	C₂×C₃×D₃×Q₈	C₂²	1	80	yes	complemented
19	C₂×C₃×#237	C₂²	1	30	yes	complemented
20	C₂×C₃×D₃×D₄	C₂²	1	10	yes	—
21	C₂×C₃×#235	C₂²	1	30	yes	complemented
22	C₂²×C₃×C₄×D₃	C₂²	1	15	yes	—
23	C₂²×C₃×Dic₆	C₂²	1	15	yes	complemented
24	C₂×C₃×2₋¹⁺⁴	—	2	1	no	—
25	C₂×C₃×2₋¹⁺⁴	—	3	32	no	—
26	C₂×C₃×2₋¹⁺⁴	—	3	10	no	—
27	C₂×C₃×2₋¹⁺⁴	—	3	5	no	—
28	C₂×C₃×2₋¹⁺⁴	D₃	1	1	yes	characteristic, direct product factor
29	C₂×C₃×2₋¹⁺⁴	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂²×C₃×#41	—	3	10	no	—
31	C₂³×C₃×Q₈	—	3	5	no	—
32	D₃×2₋¹⁺⁴	C₂×C₃	1	32	yes	direct product factor
33	C₂×#1010	C₂×C₃	1	10	yes	complemented
34	C₂×D₃×#41	C₂×C₃	1	10	yes	complemented
35	C₂×#1007	C₂×C₃	1	5	yes	complemented
36	C₂²×D₃×Q₈	C₂×C₃	1	5	yes	complemented
37	C₂³×C₃×D₃	C₂³	1	5	yes	—
38	C₃²×#41	C₂³	1	80	yes	complemented
39	C₂×C₃²×Q₈	C₂³	1	10	yes	—
40	C₂×C₃²×Q₈	C₂³	1	40	yes	complemented
41	C₂×C₃²×D₄	C₂³	1	10	yes	—
42	C₂²×C₃²×C₄	C₂³	1	15	yes	—
43	C₂×C₃×#67	C₂³	1	20	yes	—
44	C₂²×C₃×Dic₃	C₂³	1	15	yes	—
45	C₃×#239	C₂³	1	80	yes	complemented
46	C₃×D₃×Q₈	C₂³	1	80	yes	—
47	C₃×D₃×Q₈	C₂³	1	160	yes	complemented
48	C₃×#237	C₂³	1	240	yes	complemented
49	C₃×D₃×D₄	C₂³	1	80	yes	—
50	C₃×#235	C₂³	1	240	yes	complemented
51	C₂×C₃×D₁₂	C₂³	1	10	yes	—
52	C₂×C₃×C₄×D₃	C₂³	1	10	yes	—
53	C₂×C₃×C₄×D₃	C₂³	1	30	yes	—
54	C₂×C₃×C₄×D₃	C₂³	1	120	yes	—
55	C₂×C₃×Dic₆	C₂³	1	30	yes	—
56	C₂×C₃×Dic₆	C₂³	1	120	yes	complemented
57	C₂²×2₋¹⁺⁴	—	3	1	no	Sylow
58	C₃×2₋¹⁺⁴	—	2	16	no	—
59	C₃×2₋¹⁺⁴	—	3	160	no	—
60	C₃×2₋¹⁺⁴	—	3	80	no	—
61	C₃×2₋¹⁺⁴	C₂×D₃	1	16	yes	direct product factor
62	C₃×2₋¹⁺⁴	C₂²×C₃	1	16	yes	complemented
63	C₂×C₃×#41	—	2	10	no	—
64	C₂×C₃×#41	—	3	160	no	—
65	C₂×C₃×#41	—	3	10	no	—
66	C₂×C₃×#41	—	3	30	no	—
67	C₂×C₃×#41	—	3	30	no	—
68	C₂×C₃×#41	C₂×D₃	1	10	yes	complemented
69	C₂×C₃×#41	C₂²×C₃	1	10	yes	complemented
70	C₂²×C₃×Q₈	—	2	5	no	—
71	C₂²×C₃×Q₈	—	3	10	no	—
72	C₂²×C₃×Q₈	—	3	20	no	—
73	C₂²×C₃×Q₈	—	3	80	no	—
74	C₂²×C₃×Q₈	—	3	15	no	—
75	C₂²×C₃×Q₈	C₂×D₃	1	5	yes	complemented
76	C₂²×C₃×Q₈	C₂²×C₃	1	5	yes	complemented
77	C₂²×C₃×D₄	—	3	10	no	—
78	C₂³×C₃×C₄	—	3	15	no	—
79	#1010	C₂²×C₃	1	160	yes	complemented
80	D₃×#41	C₂²×C₃	1	160	yes	complemented
81	#1007	C₂²×C₃	1	80	yes	complemented
82	C₂×#239	C₂²×C₃	1	10	yes	complemented
83	C₂×D₃×Q₈	C₂²×C₃	1	10	yes	—
84	C₂×D₃×Q₈	C₂²×C₃	1	20	yes	complemented
85	C₂×D₃×Q₈	C₂²×C₃	1	80	yes	complemented
86	C₂×#237	C₂²×C₃	1	30	yes	complemented
87	C₂×D₃×D₄	C₂²×C₃	1	10	yes	—
88	C₂×#235	C₂²×C₃	1	30	yes	complemented
89	C₂²×C₄×D₃	C₂²×C₃	1	15	yes	—
90	C₂²×Dic₆	C₂²×C₃	1	15	yes	complemented
91	C₂³×C₃²	C₂⁴	1	5	yes	—
92	C₂²×C₃×D₃	—	2	20	no	—
93	C₂²×C₃×D₃	C₂⁴	1	5	yes	—
94	C₂²×C₃×D₃	C₂⁴	1	20	yes	—
95	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
96	C₃²×Q₈	C₂⁴	1	40	yes	—
97	C₃²×D₄	C₂⁴	1	40	yes	—
98	C₂×C₃²×C₄	C₂⁴	1	10	yes	—
99	C₂×C₃²×C₄	C₂⁴	1	60	yes	—
100	C₃×#67	C₂⁴	1	80	yes	—
101	C₂×C₃×Dic₃	C₂⁴	1	10	yes	—
102	C₂×C₃×Dic₃	C₂⁴	1	60	yes	—
103	C₃×D₁₂	C₂⁴	1	40	yes	—
104	C₃×C₄×D₃	C₂⁴	1	40	yes	—
105	C₃×C₄×D₃	C₂⁴	1	120	yes	—
106	C₃×Dic₆	C₂⁴	1	120	yes	—
107	C₂×2₋¹⁺⁴	—	3	32	no	—
108	C₂×2₋¹⁺⁴	—	3	10	no	—
109	C₂×2₋¹⁺⁴	—	3	5	no	—
110	C₂×2₋¹⁺⁴	C₃×D₃	1	1	yes	characteristic, direct product factor
111	C₂²×#41	—	3	10	no	—
112	C₂³×Q₈	—	3	5	no	—
113	C₂⁴×C₃	—	3	5	no	—
114	C₂³×D₃	C₂³×C₃	1	5	yes	—
115	C₃×#41	—	2	80	no	—
116	C₃×#41	—	3	80	no	—
117	C₃×#41	—	3	240	no	—
118	C₃×#41	—	3	240	no	—
119	C₃×#41	C₂²×D₃	1	80	yes	complemented
120	C₃×#41	C₂³×C₃	1	80	yes	complemented
121	C₂×C₃×Q₈	—	2	10	no	—
122	C₂×C₃×Q₈	—	2	40	no	—
123	C₂×C₃×Q₈	—	3	80	no	—
124	C₂×C₃×Q₈	—	3	160	no	—
125	C₂×C₃×Q₈	—	3	30	no	—
126	C₂×C₃×Q₈	—	3	120	no	—
127	C₂×C₃×Q₈	C₂²×D₃	1	10	yes	—
128	C₂×C₃×Q₈	C₂²×D₃	1	40	yes	complemented
129	C₂×C₃×Q₈	C₂³×C₃	1	10	yes	—
130	C₂×C₃×Q₈	C₂³×C₃	1	40	yes	complemented
131	C₂×C₃×D₄	—	2	10	no	—
132	C₂×C₃×D₄	—	3	20	no	—
133	C₂×C₃×D₄	—	3	80	no	—
134	C₂×C₃×D₄	—	3	10	no	—
135	C₂×C₃×D₄	C₂²×D₃	1	10	yes	—
136	C₂×C₃×D₄	C₂³×C₃	1	10	yes	—
137	C₂²×C₃×C₄	—	2	15	no	—
138	C₂²×C₃×C₄	—	3	15	no	—
139	C₂²×C₃×C₄	—	3	10	no	—
140	C₂²×C₃×C₄	—	3	120	no	—
141	C₂²×C₃×C₄	—	3	30	no	—
142	C₂²×C₃×C₄	C₂²×D₃	1	15	yes	—
143	C₂²×C₃×C₄	C₂³×C₃	1	15	yes	—
144	C₂×#67	C₂³×C₃	1	20	yes	—
145	C₂²×Dic₃	C₂³×C₃	1	15	yes	—
146	#239	C₂³×C₃	1	80	yes	complemented
147	D₃×Q₈	C₂³×C₃	1	80	yes	—
148	D₃×Q₈	C₂³×C₃	1	160	yes	complemented
149	#237	C₂³×C₃	1	240	yes	complemented
150	D₃×D₄	C₂³×C₃	1	80	yes	—
151	#235	C₂³×C₃	1	240	yes	complemented
152	C₂×D₁₂	C₂³×C₃	1	10	yes	—
153	C₂×C₄×D₃	C₂³×C₃	1	10	yes	—
154	C₂×C₄×D₃	C₂³×C₃	1	30	yes	—
155	C₂×C₄×D₃	C₂³×C₃	1	120	yes	—
156	C₂×Dic₆	C₂³×C₃	1	30	yes	—
157	C₂×Dic₆	C₂³×C₃	1	120	yes	complemented
158	C₂²×C₃²	—	2	10	no	—
159	C₂²×C₃²	C₂⁵	1	10	yes	—
160	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
161	C₂×C₃×D₃	—	2	10	no	—
162	C₂×C₃×D₃	—	2	40	no	—
163	C₂×C₃×D₃	2₋¹⁺⁴	1	4	yes	direct product factor
164	C₂×C₃×D₃	C₂⁵	1	10	yes	—
165	C₂×C₃×D₃	C₂⁵	1	2	yes	—
166	C₃²×C₄	C₂⁵	1	20	yes	—
167	C₃×Dic₃	C₂⁵	1	20	yes	—
168	2₋¹⁺⁴	—	3	160	no	—
169	2₋¹⁺⁴	—	3	80	no	—
170	2₋¹⁺⁴	C₂×C₃×D₃	1	16	yes	direct product factor
171	C₂×#41	—	3	160	no	—
172	C₂×#41	—	3	10	no	—
173	C₂×#41	—	3	30	no	—
174	C₂×#41	—	3	30	no	—
175	C₂×#41	C₂×C₃×D₃	1	10	yes	complemented
176	C₂²×Q₈	—	3	10	no	—
177	C₂²×Q₈	—	3	20	no	—
178	C₂²×Q₈	—	3	80	no	—
179	C₂²×Q₈	—	3	15	no	—
180	C₂²×Q₈	C₂×C₃×D₃	1	5	yes	complemented
181	C₂²×D₄	—	3	10	no	—
182	C₂³×C₄	—	3	15	no	—
183	C₂³×C₃	—	2	5	no	—
184	C₂³×C₃	—	3	1	no	—
185	C₂³×C₃	—	3	20	no	—
186	C₂³×C₃	—	3	5	no	—
187	C₂³×C₃	—	6	20	no	—
188	C₂³×C₃	C₂³×D₃	1	5	yes	—
189	C₂³×C₃	C₂⁴×C₃	1	5	yes	—
190	C₂²×D₃	—	2	20	no	—
191	C₂²×D₃	C₂⁴×C₃	1	5	yes	—
192	C₂²×D₃	C₂⁴×C₃	1	20	yes	—
193	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
194	C₃×Q₈	—	2	40	no	—
195	C₃×Q₈	—	3	120	no	—
196	C₃×Q₈	C₂³×D₃	1	40	yes	—
197	C₃×Q₈	C₂⁴×C₃	1	40	yes	—
198	C₃×D₄	—	2	40	no	—
199	C₃×D₄	—	3	80	no	—
200	C₃×D₄	—	3	40	no	—
201	C₃×D₄	C₂³×D₃	1	40	yes	—
202	C₃×D₄	C₂⁴×C₃	1	40	yes	—
203	C₂×C₃×C₄	—	2	10	no	—
204	C₂×C₃×C₄	—	2	60	no	—
205	C₂×C₃×C₄	—	3	60	no	—
206	C₂×C₃×C₄	—	3	10	no	—
207	C₂×C₃×C₄	—	3	40	no	—
208	C₂×C₃×C₄	—	3	120	no	—
209	C₂×C₃×C₄	C₂³×D₃	1	60	yes	—
210	C₂×C₃×C₄	C₂³×D₃	1	10	yes	—
211	C₂×C₃×C₄	C₂⁴×C₃	1	10	yes	—
212	C₂×C₃×C₄	C₂⁴×C₃	1	60	yes	—
213	#67	C₂⁴×C₃	1	80	yes	—
214	C₂×Dic₃	C₂⁴×C₃	1	10	yes	—
215	C₂×Dic₃	C₂⁴×C₃	1	60	yes	—
216	D₁₂	C₂⁴×C₃	1	40	yes	—
217	C₄×D₃	C₂⁴×C₃	1	40	yes	—
218	C₄×D₃	C₂⁴×C₃	1	120	yes	—
219	Dic₆	C₂⁴×C₃	1	120	yes	—
220	C₂×C₃²	—	2	10	no	—
221	C₂×C₃²	C₂×2₋¹⁺⁴	1	2	yes	complemented
222	C₂×C₃²	C₂⁶	1	1	yes	characteristic
223	C₃×D₃	—	2	10	no	—
224	C₃×D₃	C₂×2₋¹⁺⁴	1	4	yes	direct product factor
225	C₂⁴	—	3	5	no	—
226	#41	—	3	80	no	—
227	#41	—	3	240	no	—
228	#41	—	3	240	no	—
229	#41	C₂²×C₃×D₃	1	80	yes	complemented
230	C₂×Q₈	—	3	80	no	—
231	C₂×Q₈	—	3	160	no	—
232	C₂×Q₈	—	3	30	no	—
233	C₂×Q₈	—	3	120	no	—
234	C₂×Q₈	C₂²×C₃×D₃	1	10	yes	—
235	C₂×Q₈	C₂²×C₃×D₃	1	40	yes	complemented
236	C₂×D₄	—	3	20	no	—
237	C₂×D₄	—	3	80	no	—
238	C₂×D₄	—	3	10	no	—
239	C₂×D₄	C₂²×C₃×D₃	1	10	yes	—
240	C₂²×C₄	—	3	15	no	—
241	C₂²×C₄	—	3	10	no	—
242	C₂²×C₄	—	3	30	no	—
243	C₂²×C₄	—	3	120	no	—
244	C₂²×C₄	C₂²×C₃×D₃	1	15	yes	—
245	C₂²×C₃	—	2	10	no	—
246	C₂²×C₃	—	2	10	no	—
247	C₂²×C₃	—	2	1	no	—
248	C₂²×C₃	—	2	10	no	—
249	C₂²×C₃	—	3	4	no	—
250	C₂²×C₃	—	3	2	no	—
251	C₂²×C₃	—	3	10	no	—
252	C₂²×C₃	—	4	10	no	—
253	C₂²×C₃	—	6	40	no	—
254	C₂²×C₃	—	6	10	no	—
255	C₂²×C₃	C₂⁴×D₃	1	10	yes	—
256	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
257	C₂²×C₃	C₂⁵×C₃	1	10	yes	—
258	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
259	C₂×D₃	—	2	10	no	—
260	C₂×D₃	—	2	40	no	—
261	C₂×D₃	C₃×2₋¹⁺⁴	1	4	yes	direct product factor
262	C₂×D₃	C₂⁵×C₃	1	10	yes	—
263	C₂×D₃	C₂⁵×C₃	1	2	yes	—
264	C₃×C₄	—	2	20	no	—
265	C₃×C₄	—	3	20	no	—
266	C₃×C₄	C₂⁴×D₃	1	20	yes	—
267	C₃×C₄	C₂⁵×C₃	1	20	yes	—
268	Dic₃	C₂⁵×C₃	1	20	yes	—
269	C₃²	C₂²×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
270	C₂³	—	3	1	no	—
271	C₂³	—	3	20	no	—
272	C₂³	—	3	5	no	—
273	C₂³	—	6	20	no	—
274	C₂³	C₂³×C₃×D₃	1	5	yes	—
275	Q₈	—	3	120	no	—
276	Q₈	C₂³×C₃×D₃	1	40	yes	—
277	D₄	—	3	80	no	—
278	D₄	—	3	40	no	—
279	D₄	C₂³×C₃×D₃	1	40	yes	—
280	C₂×C₄	—	3	10	no	—
281	C₂×C₄	—	3	60	no	—
282	C₂×C₄	—	3	40	no	—
283	C₂×C₄	—	3	120	no	—
284	C₂×C₄	C₂³×C₃×D₃	1	10	yes	—
285	C₂×C₄	C₂³×C₃×D₃	1	60	yes	—
286	C₂×C₃	—	2	10	no	—
287	C₂×C₃	—	2	10	no	—
288	C₂×C₃	—	2	2	no	—
289	C₂×C₃	—	2	1	no	—
290	C₂×C₃	—	3	4	no	—
291	C₂×C₃	—	4	10	no	—
292	C₂×C₃	—	6	10	no	—
293	C₂×C₃	D₃×2₋¹⁺⁴	1	2	yes	direct product factor
294	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	2	yes	complemented
295	C₂×C₃	C₂⁵×D₃	1	1	yes	characteristic
296	C₂×C₃	C₂⁶×C₃	1	1	yes	characteristic
297	D₃	—	2	10	no	—
298	D₃	C₂×C₃×2₋¹⁺⁴	1	4	yes	direct product factor
299	C₂²	—	2	10	no	—
300	C₂²	—	3	4	no	—
301	C₂²	—	3	2	no	—
302	C₂²	—	3	10	no	—
303	C₂²	—	6	40	no	—
304	C₂²	—	6	10	no	—
305	C₂²	C₂⁴×C₃×D₃	1	10	yes	—
306	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
307	C₄	—	3	20	no	—
308	C₄	C₂⁴×C₃×D₃	1	20	yes	—
309	C₃	—	2	1	no	—
310	C₃	C₂×D₃×2₋¹⁺⁴	1	1	yes	characteristic, direct product factor
311	C₃	C₂²×C₃×2₋¹⁺⁴	1	1	yes	characteristic, complemented
312	C₂	—	2	10	no	—
313	C₂	—	3	4	no	—
314	C₂	—	6	10	no	—
315	C₂	C₃×D₃×2₋¹⁺⁴	1	2	yes	direct product factor
316	C₂	C₂⁵×C₃×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂×C₃	C₂⁶×C₃
Frattini	C₂	C₂⁵×C₃×D₃
Fitting	C₂×C₃²×2₋¹⁺⁴	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₂×C₃×2₋¹⁺⁴	D₃
hypocenter	C₃	C₂²×C₃×2₋¹⁺⁴
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×2₋¹⁺⁴	C₂	semidirect
2. C₃×D₃×2₋¹⁺⁴	C₂	direct (N × H)
3. C₂×C₃×#1010	C₂	semidirect
4. C₂×C₃×D₃×#41	C₂	semidirect
5. C₂×C₃×#1007	C₂	semidirect
6. C₂²×C₃×D₃×Q₈	C₂	semidirect
8. C₂×D₃×2₋¹⁺⁴	C₃	direct (N × H)
9. C₃²×2₋¹⁺⁴	C₂²	semidirect
10. C₂×C₃²×#41	C₂²	semidirect
11. C₂²×C₃²×Q₈	C₂²	semidirect
12. C₃×#1010	C₂²	semidirect
13. C₃×D₃×#41	C₂²	semidirect
14. C₃×#1007	C₂²	semidirect
15. C₂×C₃×#239	C₂²	semidirect
17. C₂×C₃×D₃×Q₈	C₂²	semidirect
18. C₂×C₃×D₃×Q₈	C₂²	semidirect
19. C₂×C₃×#237	C₂²	semidirect
21. C₂×C₃×#235	C₂²	semidirect
23. C₂²×C₃×Dic₆	C₂²	semidirect
28. C₂×C₃×2₋¹⁺⁴	D₃	direct (N × H)
29. C₂×C₃×2₋¹⁺⁴	C₂×C₃	semidirect
32. D₃×2₋¹⁺⁴	C₂×C₃	direct (N × H)
33. C₂×#1010	C₂×C₃	semidirect
34. C₂×D₃×#41	C₂×C₃	semidirect
35. C₂×#1007	C₂×C₃	semidirect
36. C₂²×D₃×Q₈	C₂×C₃	semidirect
38. C₃²×#41	C₂³	semidirect
40. C₂×C₃²×Q₈	C₂³	semidirect
45. C₃×#239	C₂³	semidirect
47. C₃×D₃×Q₈	C₂³	semidirect
48. C₃×#237	C₂³	semidirect
50. C₃×#235	C₂³	semidirect
56. C₂×C₃×Dic₆	C₂³	semidirect
61. C₃×2₋¹⁺⁴	C₂×D₃	direct (N × H)
62. C₃×2₋¹⁺⁴	C₂²×C₃	semidirect
68. C₂×C₃×#41	C₂×D₃	semidirect
69. C₂×C₃×#41	C₂²×C₃	semidirect
75. C₂²×C₃×Q₈	C₂×D₃	semidirect
76. C₂²×C₃×Q₈	C₂²×C₃	semidirect
79. #1010	C₂²×C₃	semidirect
80. D₃×#41	C₂²×C₃	semidirect
81. #1007	C₂²×C₃	semidirect
82. C₂×#239	C₂²×C₃	semidirect
84. C₂×D₃×Q₈	C₂²×C₃	semidirect
85. C₂×D₃×Q₈	C₂²×C₃	semidirect
86. C₂×#237	C₂²×C₃	semidirect
88. C₂×#235	C₂²×C₃	semidirect
90. C₂²×Dic₆	C₂²×C₃	semidirect
110. C₂×2₋¹⁺⁴	C₃×D₃	direct (N × H)
119. C₃×#41	C₂²×D₃	semidirect
120. C₃×#41	C₂³×C₃	semidirect
128. C₂×C₃×Q₈	C₂²×D₃	semidirect
130. C₂×C₃×Q₈	C₂³×C₃	semidirect
146. #239	C₂³×C₃	semidirect
148. D₃×Q₈	C₂³×C₃	semidirect
149. #237	C₂³×C₃	semidirect
151. #235	C₂³×C₃	semidirect
157. C₂×Dic₆	C₂³×C₃	semidirect
163. C₂×C₃×D₃	2₋¹⁺⁴	direct (N × H)
170. 2₋¹⁺⁴	C₂×C₃×D₃	direct (N × H)
175. C₂×#41	C₂×C₃×D₃	semidirect
180. C₂²×Q₈	C₂×C₃×D₃	semidirect
221. C₂×C₃²	C₂×2₋¹⁺⁴	semidirect
224. C₃×D₃	C₂×2₋¹⁺⁴	direct (N × H)
229. #41	C₂²×C₃×D₃	semidirect
235. C₂×Q₈	C₂²×C₃×D₃	semidirect
261. C₂×D₃	C₃×2₋¹⁺⁴	direct (N × H)
269. C₃²	C₂²×2₋¹⁺⁴	semidirect
293. C₂×C₃	D₃×2₋¹⁺⁴	direct (N × H)
294. C₂×C₃	C₂×C₃×2₋¹⁺⁴	semidirect
298. D₃	C₂×C₃×2₋¹⁺⁴	direct (N × H)
310. C₃	C₂×D₃×2₋¹⁺⁴	direct (N × H)
311. C₃	C₂²×C₃×2₋¹⁺⁴	semidirect
315. C₂	C₃×D₃×2₋¹⁺⁴	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃²×2₋¹⁺⁴	2
C₃×D₃×2₋¹⁺⁴	2
C₂×C₃×#1010	2
C₂×C₃×D₃×#41	2
C₂×C₃×#1007	2
C₂²×C₃×D₃×Q₈	2
C₂²×C₃×2₋¹⁺⁴	3
C₂×D₃×2₋¹⁺⁴	3

Subgroups — C2×C3×D3×2−1+4 #11919230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₃×2₋¹⁺⁴ #11919230