Subgroups — C₂×C₃×#5966 #11919252

Order 1152.

12361 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5966	C₂	1	32	yes	maximal, direct product factor
3	C₂×C₃×#1010	C₂	1	6	yes	maximal, complemented
4	C₂×C₃×D₃×#41	C₂	1	6	yes	maximal, complemented
5	C₂×C₃×#1004	C₂	1	9	yes	maximal, complemented
6	C₂²×C₃×#237	C₂	1	9	yes	maximal, complemented
7	C₂×C₃×#585	—	3	1	no	maximal
8	C₂×#5966	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₃²×H(5,𝔽₂)	C₂²	1	16	yes	complemented
10	C₂×C₃²×#41	C₂²	1	6	yes	complemented
11	C₂²×C₃²×D₄	C₂²	1	9	yes	complemented
12	C₂²×C₃×#67	C₂²	1	18	yes	complemented
13	C₂³×C₃×Dic₃	C₂²	1	6	yes	complemented
14	C₃×#1010	C₂²	1	96	yes	complemented
15	C₃×D₃×#41	C₂²	1	96	yes	complemented
16	C₂×C₃×#239	C₂²	1	2	yes	complemented
17	C₂×C₃×D₃×Q₈	C₂²	1	6	yes	complemented
18	C₃×#1004	C₂²	1	144	yes	complemented
19	C₂×C₃×#237	C₂²	1	18	yes	complemented
20	C₂×C₃×#237	C₂²	1	36	yes	complemented
21	C₂×C₃×#237	C₂²	1	144	yes	complemented
22	C₂×C₃×D₃×D₄	C₂²	1	18	yes	complemented
23	C₂×C₃×#235	C₂²	1	18	yes	complemented
24	C₂²×C₃×C₄×D₃	C₂²	1	9	yes	complemented
25	C₂²×C₃×Dic₆	C₂²	1	9	yes	complemented
26	C₃×#585	—	3	32	no	—
27	C₂×C₃×2₋¹⁺⁴	—	3	6	no	—
28	C₂×C₃×H(5,𝔽₂)	—	2	1	no	—
29	C₂×C₃×H(5,𝔽₂)	—	3	9	no	—
30	C₂×C₃×H(5,𝔽₂)	D₃	1	1	yes	characteristic, complemented
31	C₂×C₃×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂²×C₃×#41	—	3	6	no	—
33	C₂²×C₃×#41	—	3	9	no	—
34	#5966	C₂×C₃	1	32	yes	direct product factor
35	C₂×#1010	C₂×C₃	1	6	yes	complemented
36	C₂×D₃×#41	C₂×C₃	1	6	yes	complemented
37	C₂×#1004	C₂×C₃	1	9	yes	complemented
38	C₂²×#237	C₂×C₃	1	9	yes	complemented
39	C₂⁴×C₃²	C₂³	1	6	yes	—
40	C₂³×C₃×D₃	C₂³	1	9	yes	—
41	C₃²×#41	C₂³	1	48	yes	complemented
42	C₂×C₃²×Q₈	C₂³	1	2	yes	—
43	C₂×C₃²×D₄	C₂³	1	18	yes	—
44	C₂×C₃²×D₄	C₂³	1	72	yes	complemented
45	C₂²×C₃²×C₄	C₂³	1	9	yes	—
46	C₂×C₃×#67	C₂³	1	36	yes	—
47	C₂×C₃×#67	C₂³	1	144	yes	complemented
48	C₂²×C₃×Dic₃	C₂³	1	18	yes	—
49	C₂²×C₃×Dic₃	C₂³	1	9	yes	—
50	C₂²×C₃×Dic₃	C₂³	1	48	yes	complemented
51	C₃×#239	C₂³	1	16	yes	complemented
52	C₃×D₃×Q₈	C₂³	1	48	yes	complemented
53	C₃×#237	C₂³	1	144	yes	complemented
54	C₃×#237	C₂³	1	288	yes	complemented
55	C₃×D₃×D₄	C₂³	1	144	yes	complemented
56	C₃×#235	C₂³	1	144	yes	complemented
57	C₂×C₃×D₁₂	C₂³	1	6	yes	—
58	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
59	C₂×C₃×C₄×D₃	C₂³	1	18	yes	—
60	C₂×C₃×C₄×D₃	C₂³	1	72	yes	complemented
61	C₂×C₃×Dic₆	C₂³	1	18	yes	—
62	C₂×C₃×Dic₆	C₂³	1	72	yes	complemented
63	C₂×#585	—	3	1	no	Sylow
64	C₃×2₋¹⁺⁴	—	3	96	no	—
65	C₃×H(5,𝔽₂)	—	2	16	no	—
66	C₃×H(5,𝔽₂)	—	3	144	no	—
67	C₃×H(5,𝔽₂)	C₂×D₃	1	16	yes	complemented
68	C₃×H(5,𝔽₂)	C₂²×C₃	1	16	yes	complemented
69	C₂×C₃×#41	—	2	6	no	—
70	C₂×C₃×#41	—	3	96	no	—
71	C₂×C₃×#41	—	3	2	no	—
72	C₂×C₃×#41	—	3	18	no	—
73	C₂×C₃×#41	—	3	36	no	—
74	C₂×C₃×#41	—	3	144	no	—
75	C₂×C₃×#41	—	3	18	no	—
76	C₂×C₃×#41	C₂×D₃	1	6	yes	complemented
77	C₂×C₃×#41	C₂²×C₃	1	6	yes	complemented
78	C₂²×C₃×Q₈	—	3	6	no	—
79	C₂²×C₃×Q₈	—	3	9	no	—
80	C₂²×C₃×D₄	—	2	9	no	—
81	C₂²×C₃×D₄	—	3	18	no	—
82	C₂²×C₃×D₄	—	3	18	no	—
83	C₂²×C₃×D₄	C₂×D₃	1	9	yes	complemented
84	C₂²×C₃×D₄	C₂²×C₃	1	9	yes	complemented
85	C₂³×C₃×C₄	—	3	6	no	—
86	C₂³×C₃×C₄	—	3	9	no	—
87	C₂²×#67	C₂²×C₃	1	18	yes	complemented
88	C₂³×Dic₃	C₂²×C₃	1	6	yes	complemented
89	#1010	C₂²×C₃	1	96	yes	complemented
90	D₃×#41	C₂²×C₃	1	96	yes	complemented
91	C₂×#239	C₂²×C₃	1	2	yes	complemented
92	C₂×D₃×Q₈	C₂²×C₃	1	6	yes	complemented
93	#1004	C₂²×C₃	1	144	yes	complemented
94	C₂×#237	C₂²×C₃	1	18	yes	complemented
95	C₂×#237	C₂²×C₃	1	36	yes	complemented
96	C₂×#237	C₂²×C₃	1	144	yes	complemented
97	C₂×D₃×D₄	C₂²×C₃	1	18	yes	complemented
98	C₂×#235	C₂²×C₃	1	18	yes	complemented
99	C₂²×C₄×D₃	C₂²×C₃	1	9	yes	complemented
100	C₂²×Dic₆	C₂²×C₃	1	9	yes	complemented
101	C₂³×C₃²	—	4	12	no	—
102	C₂³×C₃²	C₂⁴	1	9	yes	—
103	C₂³×C₃²	C₂⁴	1	24	yes	—
104	C₂²×C₃×D₃	—	4	18	no	—
105	C₂²×C₃×D₃	C₂⁴	1	6	yes	—
106	C₂²×C₃×D₃	C₂⁴	1	36	yes	—
107	C₃²×Q₈	C₂⁴	1	8	yes	—
108	C₃²×D₄	C₂⁴	1	72	yes	—
109	C₂×C₃²×C₄	C₂⁴	1	6	yes	—
110	C₂×C₃²×C₄	C₂⁴	1	36	yes	—
111	C₃×#67	C₂⁴	1	144	yes	—
112	C₂×C₃×Dic₃	C₂⁴	1	9	yes	—
113	C₂×C₃×Dic₃	C₂⁴	1	72	yes	—
114	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
115	C₂×C₃×Dic₃	C₂⁴	1	36	yes	—
116	C₃×D₁₂	C₂⁴	1	24	yes	—
117	C₃×C₄×D₃	C₂⁴	1	24	yes	—
118	C₃×C₄×D₃	C₂⁴	1	72	yes	—
119	C₃×Dic₆	C₂⁴	1	72	yes	—
120	#585	—	3	32	no	—
121	C₂×2₋¹⁺⁴	—	3	6	no	—
122	C₂×H(5,𝔽₂)	—	3	9	no	—
123	C₂×H(5,𝔽₂)	C₃×D₃	1	1	yes	characteristic, complemented
124	C₂²×#41	—	3	6	no	—
125	C₂²×#41	—	3	9	no	—
126	C₂⁴×C₃	—	2	6	no	—
127	C₂⁴×C₃	—	3	9	no	—
128	C₂⁴×C₃	C₂²×D₃	1	6	yes	—
129	C₂⁴×C₃	C₂³×C₃	1	6	yes	—
130	C₂³×D₃	C₂³×C₃	1	9	yes	—
131	C₃×#41	—	2	48	no	—
132	C₃×#41	—	3	16	no	—
133	C₃×#41	—	3	144	no	—
134	C₃×#41	—	3	288	no	—
135	C₃×#41	—	3	144	no	—
136	C₃×#41	C₂²×D₃	1	48	yes	complemented
137	C₃×#41	C₂³×C₃	1	48	yes	complemented
138	C₂×C₃×Q₈	—	2	2	no	—
139	C₂×C₃×Q₈	—	3	48	no	—
140	C₂×C₃×Q₈	—	3	18	no	—
141	C₂×C₃×Q₈	—	3	72	no	—
142	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
143	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
144	C₂×C₃×D₄	—	2	18	no	—
145	C₂×C₃×D₄	—	2	72	no	—
146	C₂×C₃×D₄	—	3	36	no	—
147	C₂×C₃×D₄	—	3	144	no	—
148	C₂×C₃×D₄	—	3	144	no	—
149	C₂×C₃×D₄	—	3	6	no	—
150	C₂×C₃×D₄	C₂²×D₃	1	18	yes	—
151	C₂×C₃×D₄	C₂²×D₃	1	72	yes	complemented
152	C₂×C₃×D₄	C₂³×C₃	1	18	yes	—
153	C₂×C₃×D₄	C₂³×C₃	1	72	yes	complemented
154	C₂²×C₃×C₄	—	2	9	no	—
155	C₂²×C₃×C₄	—	3	9	no	—
156	C₂²×C₃×C₄	—	3	18	no	—
157	C₂²×C₃×C₄	—	3	48	no	—
158	C₂²×C₃×C₄	—	3	6	no	—
159	C₂²×C₃×C₄	—	3	18	no	—
160	C₂²×C₃×C₄	—	3	72	no	—
161	C₂²×C₃×C₄	C₂²×D₃	1	9	yes	—
162	C₂²×C₃×C₄	C₂³×C₃	1	9	yes	—
163	C₂×#67	C₂³×C₃	1	36	yes	—
164	C₂×#67	C₂³×C₃	1	144	yes	complemented
165	C₂²×Dic₃	C₂³×C₃	1	18	yes	—
166	C₂²×Dic₃	C₂³×C₃	1	9	yes	—
167	C₂²×Dic₃	C₂³×C₃	1	48	yes	complemented
168	#239	C₂³×C₃	1	16	yes	complemented
169	D₃×Q₈	C₂³×C₃	1	48	yes	complemented
170	#237	C₂³×C₃	1	144	yes	complemented
171	#237	C₂³×C₃	1	288	yes	complemented
172	D₃×D₄	C₂³×C₃	1	144	yes	complemented
173	#235	C₂³×C₃	1	144	yes	complemented
174	C₂×D₁₂	C₂³×C₃	1	6	yes	—
175	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
176	C₂×C₄×D₃	C₂³×C₃	1	18	yes	—
177	C₂×C₄×D₃	C₂³×C₃	1	72	yes	complemented
178	C₂×Dic₆	C₂³×C₃	1	18	yes	—
179	C₂×Dic₆	C₂³×C₃	1	72	yes	complemented
180	C₂²×C₃²	—	2	18	no	—
181	C₂²×C₃²	—	4	24	no	—
182	C₂²×C₃²	C₂⁵	1	18	yes	—
183	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
184	C₂×C₃×D₃	—	2	12	no	—
185	C₂×C₃×D₃	—	4	36	no	—
186	C₂×C₃×D₃	C₂⁵	1	12	yes	—
187	C₃²×C₄	C₂⁵	1	12	yes	—
188	C₃×Dic₃	C₂⁵	1	18	yes	—
189	C₃×Dic₃	C₂⁵	1	2	yes	—
190	2₋¹⁺⁴	—	3	96	no	—
191	H(5,𝔽₂)	—	3	144	no	—
192	H(5,𝔽₂)	C₂×C₃×D₃	1	16	yes	complemented
193	C₂×#41	—	3	96	no	—
194	C₂×#41	—	3	2	no	—
195	C₂×#41	—	3	18	no	—
196	C₂×#41	—	3	36	no	—
197	C₂×#41	—	3	144	no	—
198	C₂×#41	—	3	18	no	—
199	C₂×#41	C₂×C₃×D₃	1	6	yes	complemented
200	C₂²×Q₈	—	3	6	no	—
201	C₂²×Q₈	—	3	9	no	—
202	C₂²×D₄	—	3	18	no	—
203	C₂²×D₄	—	3	18	no	—
204	C₂²×D₄	C₂×C₃×D₃	1	9	yes	complemented
205	C₂³×C₄	—	3	6	no	—
206	C₂³×C₄	—	3	9	no	—
207	C₂³×C₃	—	2	9	no	—
208	C₂³×C₃	—	2	24	no	—
209	C₂³×C₃	—	3	6	no	—
210	C₂³×C₃	—	3	36	no	—
211	C₂³×C₃	—	4	12	no	—
212	C₂³×C₃	—	4	12	no	—
213	C₂³×C₃	—	8	12	no	—
214	C₂³×C₃	—	12	18	no	—
215	C₂³×C₃	C₂³×D₃	1	9	yes	—
216	C₂³×C₃	C₂³×D₃	1	24	yes	—
217	C₂³×C₃	C₂⁴×C₃	1	9	yes	—
218	C₂³×C₃	C₂⁴×C₃	1	24	yes	—
219	C₂²×D₃	—	4	18	no	—
220	C₂²×D₃	C₂⁴×C₃	1	6	yes	—
221	C₂²×D₃	C₂⁴×C₃	1	36	yes	—
222	C₃×Q₈	—	2	8	no	—
223	C₃×Q₈	—	3	72	no	—
224	C₃×Q₈	C₂³×D₃	1	8	yes	—
225	C₃×Q₈	C₂⁴×C₃	1	8	yes	—
226	C₃×D₄	—	2	72	no	—
227	C₃×D₄	—	3	144	no	—
228	C₃×D₄	—	3	24	no	—
229	C₃×D₄	C₂³×D₃	1	72	yes	—
230	C₃×D₄	C₂⁴×C₃	1	72	yes	—
231	C₂×C₃×C₄	—	2	6	no	—
232	C₂×C₃×C₄	—	2	36	no	—
233	C₂×C₃×C₄	—	3	36	no	—
234	C₂×C₃×C₄	—	3	72	no	—
235	C₂×C₃×C₄	—	3	1	no	—
236	C₂×C₃×C₄	—	3	9	no	—
237	C₂×C₃×C₄	—	3	24	no	—
238	C₂×C₃×C₄	—	3	72	no	—
239	C₂×C₃×C₄	C₂³×D₃	1	36	yes	—
240	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
241	C₂×C₃×C₄	C₂⁴×C₃	1	6	yes	—
242	C₂×C₃×C₄	C₂⁴×C₃	1	36	yes	—
243	#67	C₂⁴×C₃	1	144	yes	—
244	C₂×Dic₃	C₂⁴×C₃	1	9	yes	—
245	C₂×Dic₃	C₂⁴×C₃	1	72	yes	—
246	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
247	C₂×Dic₃	C₂⁴×C₃	1	36	yes	—
248	D₁₂	C₂⁴×C₃	1	24	yes	—
249	C₄×D₃	C₂⁴×C₃	1	24	yes	—
250	C₄×D₃	C₂⁴×C₃	1	72	yes	—
251	Dic₆	C₂⁴×C₃	1	72	yes	—
252	C₂×C₃²	—	2	18	no	—
253	C₂×C₃²	#585	1	2	yes	complemented
254	C₂×C₃²	C₂⁶	1	1	yes	characteristic
255	C₃×D₃	—	2	12	no	—
256	C₂⁴	—	3	9	no	—
257	C₂⁴	C₂²×C₃×D₃	1	6	yes	—
258	#41	—	3	16	no	—
259	#41	—	3	144	no	—
260	#41	—	3	288	no	—
261	#41	—	3	144	no	—
262	#41	C₂²×C₃×D₃	1	48	yes	complemented
263	C₂×Q₈	—	3	48	no	—
264	C₂×Q₈	—	3	18	no	—
265	C₂×Q₈	—	3	72	no	—
266	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
267	C₂×D₄	—	3	36	no	—
268	C₂×D₄	—	3	144	no	—
269	C₂×D₄	—	3	144	no	—
270	C₂×D₄	—	3	6	no	—
271	C₂×D₄	C₂²×C₃×D₃	1	18	yes	—
272	C₂×D₄	C₂²×C₃×D₃	1	72	yes	complemented
273	C₂²×C₄	—	3	9	no	—
274	C₂²×C₄	—	3	18	no	—
275	C₂²×C₄	—	3	48	no	—
276	C₂²×C₄	—	3	6	no	—
277	C₂²×C₄	—	3	18	no	—
278	C₂²×C₄	—	3	72	no	—
279	C₂²×C₄	C₂²×C₃×D₃	1	9	yes	—
280	C₂²×C₃	—	2	18	no	—
281	C₂²×C₃	—	2	18	no	—
282	C₂²×C₃	—	2	1	no	—
283	C₂²×C₃	—	2	18	no	—
284	C₂²×C₃	—	3	12	no	—
285	C₂²×C₃	—	4	18	no	—
286	C₂²×C₃	—	4	24	no	—
287	C₂²×C₃	—	4	24	no	—
288	C₂²×C₃	—	6	12	no	—
289	C₂²×C₃	—	8	24	no	—
290	C₂²×C₃	—	12	36	no	—
291	C₂²×C₃	C₂⁴×D₃	1	18	yes	—
292	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
293	C₂²×C₃	C₂⁵×C₃	1	18	yes	—
294	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
295	C₂×D₃	—	2	12	no	—
296	C₂×D₃	—	4	36	no	—
297	C₂×D₃	C₂⁵×C₃	1	12	yes	—
298	C₃×C₄	—	2	12	no	—
299	C₃×C₄	—	3	2	no	—
300	C₃×C₄	—	3	18	no	—
301	C₃×C₄	C₂⁴×D₃	1	12	yes	—
302	C₃×C₄	C₂⁵×C₃	1	12	yes	—
303	Dic₃	C₂⁵×C₃	1	18	yes	—
304	Dic₃	C₂⁵×C₃	1	2	yes	—
305	C₃²	C₂×#585	1	1	yes	characteristic, complemented, Sylow
306	C₂³	—	3	6	no	—
307	C₂³	—	3	36	no	—
308	C₂³	—	4	12	no	—
309	C₂³	—	12	18	no	—
310	C₂³	C₂³×C₃×D₃	1	9	yes	—
311	C₂³	C₂³×C₃×D₃	1	24	yes	—
312	Q₈	—	3	72	no	—
313	Q₈	C₂³×C₃×D₃	1	8	yes	—
314	D₄	—	3	144	no	—
315	D₄	—	3	24	no	—
316	D₄	C₂³×C₃×D₃	1	72	yes	—
317	C₂×C₄	—	3	1	no	—
318	C₂×C₄	—	3	9	no	—
319	C₂×C₄	—	3	36	no	—
320	C₂×C₄	—	3	72	no	—
321	C₂×C₄	—	3	24	no	—
322	C₂×C₄	—	3	72	no	—
323	C₂×C₄	C₂³×C₃×D₃	1	6	yes	—
324	C₂×C₄	C₂³×C₃×D₃	1	36	yes	—
325	C₂×C₃	—	2	18	no	—
326	C₂×C₃	—	2	18	no	—
327	C₂×C₃	—	2	2	no	—
328	C₂×C₃	—	2	1	no	—
329	C₂×C₃	—	4	18	no	—
330	C₂×C₃	—	6	12	no	—
331	C₂×C₃	#5966	1	2	yes	direct product factor
332	C₂×C₃	C₃×#585	1	2	yes	complemented
333	C₂×C₃	C₂⁵×D₃	1	1	yes	characteristic
334	C₂×C₃	C₂⁶×C₃	1	1	yes	characteristic
335	D₃	—	2	12	no	—
336	C₂²	—	2	18	no	—
337	C₂²	—	3	12	no	—
338	C₂²	—	4	24	no	—
339	C₂²	—	6	12	no	—
340	C₂²	—	12	36	no	—
341	C₂²	C₂⁴×C₃×D₃	1	18	yes	—
342	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
343	C₄	—	3	2	no	—
344	C₄	—	3	18	no	—
345	C₄	C₂⁴×C₃×D₃	1	12	yes	—
346	C₃	—	2	1	no	—
347	C₃	C₂×#5966	1	1	yes	characteristic, direct product factor
348	C₃	C₂×C₃×#585	1	1	yes	characteristic, complemented
349	C₂	—	2	18	no	—
350	C₂	—	6	12	no	—
351	C₂	C₃×#5966	1	2	yes	direct product factor
352	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×H(5,𝔽₂)	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₂×C₃×H(5,𝔽₂)	D₃
hypocenter	C₃	C₂×C₃×#585
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×H(5,𝔽₂)	C₂	semidirect
2. C₃×#5966	C₂	direct (N × H)
3. C₂×C₃×#1010	C₂	semidirect
4. C₂×C₃×D₃×#41	C₂	semidirect
5. C₂×C₃×#1004	C₂	semidirect
6. C₂²×C₃×#237	C₂	semidirect
8. C₂×#5966	C₃	direct (N × H)
9. C₃²×H(5,𝔽₂)	C₂²	semidirect
10. C₂×C₃²×#41	C₂²	semidirect
11. C₂²×C₃²×D₄	C₂²	semidirect
12. C₂²×C₃×#67	C₂²	semidirect
13. C₂³×C₃×Dic₃	C₂²	semidirect
14. C₃×#1010	C₂²	semidirect
15. C₃×D₃×#41	C₂²	semidirect
16. C₂×C₃×#239	C₂²	semidirect
17. C₂×C₃×D₃×Q₈	C₂²	semidirect
18. C₃×#1004	C₂²	semidirect
19. C₂×C₃×#237	C₂²	semidirect
20. C₂×C₃×#237	C₂²	semidirect
21. C₂×C₃×#237	C₂²	semidirect
22. C₂×C₃×D₃×D₄	C₂²	semidirect
23. C₂×C₃×#235	C₂²	semidirect
24. C₂²×C₃×C₄×D₃	C₂²	semidirect
25. C₂²×C₃×Dic₆	C₂²	semidirect
30. C₂×C₃×H(5,𝔽₂)	D₃	semidirect
31. C₂×C₃×H(5,𝔽₂)	C₂×C₃	semidirect
34. #5966	C₂×C₃	direct (N × H)
35. C₂×#1010	C₂×C₃	semidirect
36. C₂×D₃×#41	C₂×C₃	semidirect
37. C₂×#1004	C₂×C₃	semidirect
38. C₂²×#237	C₂×C₃	semidirect
41. C₃²×#41	C₂³	semidirect
44. C₂×C₃²×D₄	C₂³	semidirect
47. C₂×C₃×#67	C₂³	semidirect
50. C₂²×C₃×Dic₃	C₂³	semidirect
51. C₃×#239	C₂³	semidirect
52. C₃×D₃×Q₈	C₂³	semidirect
53. C₃×#237	C₂³	semidirect
54. C₃×#237	C₂³	semidirect
55. C₃×D₃×D₄	C₂³	semidirect
56. C₃×#235	C₂³	semidirect
60. C₂×C₃×C₄×D₃	C₂³	semidirect
62. C₂×C₃×Dic₆	C₂³	semidirect
67. C₃×H(5,𝔽₂)	C₂×D₃	semidirect
68. C₃×H(5,𝔽₂)	C₂²×C₃	semidirect
76. C₂×C₃×#41	C₂×D₃	semidirect
77. C₂×C₃×#41	C₂²×C₃	semidirect
83. C₂²×C₃×D₄	C₂×D₃	semidirect
84. C₂²×C₃×D₄	C₂²×C₃	semidirect
87. C₂²×#67	C₂²×C₃	semidirect
88. C₂³×Dic₃	C₂²×C₃	semidirect
89. #1010	C₂²×C₃	semidirect
90. D₃×#41	C₂²×C₃	semidirect
91. C₂×#239	C₂²×C₃	semidirect
92. C₂×D₃×Q₈	C₂²×C₃	semidirect
93. #1004	C₂²×C₃	semidirect
94. C₂×#237	C₂²×C₃	semidirect
95. C₂×#237	C₂²×C₃	semidirect
96. C₂×#237	C₂²×C₃	semidirect
97. C₂×D₃×D₄	C₂²×C₃	semidirect
98. C₂×#235	C₂²×C₃	semidirect
99. C₂²×C₄×D₃	C₂²×C₃	semidirect
100. C₂²×Dic₆	C₂²×C₃	semidirect
123. C₂×H(5,𝔽₂)	C₃×D₃	semidirect
136. C₃×#41	C₂²×D₃	semidirect
137. C₃×#41	C₂³×C₃	semidirect
151. C₂×C₃×D₄	C₂²×D₃	semidirect
153. C₂×C₃×D₄	C₂³×C₃	semidirect
164. C₂×#67	C₂³×C₃	semidirect
167. C₂²×Dic₃	C₂³×C₃	semidirect
168. #239	C₂³×C₃	semidirect
169. D₃×Q₈	C₂³×C₃	semidirect
170. #237	C₂³×C₃	semidirect
171. #237	C₂³×C₃	semidirect
172. D₃×D₄	C₂³×C₃	semidirect
173. #235	C₂³×C₃	semidirect
177. C₂×C₄×D₃	C₂³×C₃	semidirect
179. C₂×Dic₆	C₂³×C₃	semidirect
192. H(5,𝔽₂)	C₂×C₃×D₃	semidirect
199. C₂×#41	C₂×C₃×D₃	semidirect
204. C₂²×D₄	C₂×C₃×D₃	semidirect
253. C₂×C₃²	#585	semidirect
262. #41	C₂²×C₃×D₃	semidirect
272. C₂×D₄	C₂²×C₃×D₃	semidirect
305. C₃²	C₂×#585	semidirect
331. C₂×C₃	#5966	direct (N × H)
332. C₂×C₃	C₃×#585	semidirect
347. C₃	C₂×#5966	direct (N × H)
348. C₃	C₂×C₃×#585	semidirect
351. C₂	C₃×#5966	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×H(5,𝔽₂)	2
C₃×#5966	2
C₂×C₃×#1010	2
C₂×C₃×D₃×#41	2
C₂×C₃×#1004	2
C₂²×C₃×#237	2
C₂×C₃×#585	3
C₂×#5966	3

Subgroups — C2×C3×#5966 #11919252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5966 #11919252