Subgroups — C₂×C₃×#4711 #11860153

Order 1152.

1289 conjugacy classes of subgroups.

The subgroup lattice has 341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₂₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×D₁₂	C₂	1	2	yes	maximal, complemented
3	C₂×C₃²×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#821	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#817	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4711	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#442	—	3	1	no	maximal
8	C₂×#4711	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
10	C₂²×C₃×C₄×D₃	—	2	2	no	—
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₂×C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
15	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
16	C₂×C₃×D₂₄	C₄	1	8	yes	complemented
17	C₂×C₃×D₂₄	C₂²	1	4	yes	—
18	C₃×C₄×D₁₂	—	2	4	no	—
19	C₃×C₄×D₁₂	C₂²	1	8	yes	complemented
20	C₃²×#97	C₂²	1	4	yes	complemented
21	C₃×#821	C₂²	1	8	yes	complemented
22	C₃×#817	C₂²	1	4	yes	complemented
23	C₂²×C₃×D₈	—	3	1	no	—
24	C₂×C₃×C₄×D₄	—	3	2	no	—
25	C₂²×D₂₄	C₂×C₃	1	1	yes	characteristic
26	C₂×C₄×D₁₂	C₂×C₃	1	2	yes	complemented
27	C₃×#442	—	3	8	no	—
28	C₂×C₃×#106	—	3	1	no	—
29	C₂×C₃×#102	—	3	2	no	—
30	C₂×C₃×#97	—	2	1	no	—
31	C₂×C₃×#97	D₃	1	1	yes	characteristic, complemented
32	C₂×C₃×#97	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×#821	C₂×C₃	1	2	yes	complemented
34	C₂×#817	C₂×C₃	1	1	yes	characteristic, complemented
35	#4711	C₂×C₃	1	8	yes	direct product factor
36	C₂³×C₃×D₃	—	2	2	no	—
37	C₂²×C₃²×C₄	D₄	1	2	yes	—
38	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
39	C₂²×C₃×Dic₃	—	2	2	no	—
40	C₂×C₃×D₁₂	—	2	2	no	—
41	C₂×C₃×D₁₂	—	2	4	no	—
42	C₂×C₃×D₁₂	C₂×C₄	1	8	yes	complemented
43	C₂×C₃×D₁₂	C₂³	1	4	yes	—
44	C₂×C₃×C₄×D₃	—	2	8	no	—
45	C₂×C₃×C₄×D₃	—	4	8	no	—
46	C₂×C₃²×C₈	—	2	2	no	—
47	C₂×C₃²×C₈	C₂×C₄	1	4	yes	complemented
48	C₂×C₃²×C₈	C₂³	1	2	yes	—
49	C₂×C₃²×C₈	C₂³	1	2	yes	—
50	C₃²×C₄²	D₄	1	2	yes	—
51	C₃²×C₄²	C₂³	1	2	yes	—
52	C₃×(C₂×D₃)⋊C₄	—	2	8	no	—
53	C₃×C₄⋊Dic₃	—	2	2	no	—
54	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
55	C₃×D₂₄	C₂×C₄	1	16	yes	complemented
56	C₂×#442	—	3	1	no	Sylow
57	C₂²×C₃×D₄	—	3	2	no	—
58	C₂³×C₃×C₄	—	6	2	no	—
59	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
60	C₂²×C₄×D₃	—	2	2	no	—
61	C₂×C₃×D₈	—	3	8	no	—
62	C₂×C₃×D₈	—	3	4	no	—
63	C₂²×C₃×C₈	—	2	1	no	—
64	C₂²×C₃×C₈	—	2	1	no	—
65	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
66	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
67	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
69	C₃×C₄×D₄	—	3	8	no	—
70	C₃×C₄×D₄	—	6	4	no	—
71	C₂×C₃×C₄⋊C₄	—	3	2	no	—
72	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
73	C₂×C₃×C₄²	—	2	1	no	—
74	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
75	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
76	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
77	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
78	C₂×D₂₄	C₃×C₄	1	8	yes	complemented
79	C₂×D₂₄	C₂²×C₃	1	4	yes	—
80	C₄×D₁₂	—	2	4	no	—
81	C₄×D₁₂	C₂²×C₃	1	8	yes	complemented
82	C₃×#106	—	3	4	no	—
83	C₃×#102	—	3	8	no	—
84	C₃×#97	—	2	4	no	—
85	C₃×#97	C₂×D₃	1	4	yes	complemented
86	C₃×#97	C₂²×C₃	1	4	yes	complemented
87	#821	C₂²×C₃	1	8	yes	complemented
88	#817	C₂²×C₃	1	4	yes	complemented
89	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₃×D₃	—	2	8	no	—
91	C₂²×C₃×D₃	—	2	4	no	—
92	C₂²×C₃×D₃	—	4	4	no	—
93	C₂²×C₃×D₃	—	4	4	no	—
94	C₂×C₃²×C₄	—	2	4	no	—
95	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
96	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
97	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃²×C₄	#41	1	2	yes	—
99	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
100	C₂×C₃×Dic₃	—	2	4	no	—
101	C₂×C₃×Dic₃	—	4	4	no	—
102	C₃×D₁₂	—	2	8	no	—
103	C₃×D₁₂	—	2	4	no	—
104	C₃×D₁₂	C₂²×C₄	1	8	yes	complemented
105	C₃×C₄×D₃	—	4	16	no	—
106	C₃²×C₈	—	2	2	no	—
107	C₃²×C₈	C₂²×C₄	1	4	yes	complemented
108	C₂²×D₈	—	3	1	no	—
109	C₂×C₄×D₄	—	3	2	no	—
110	#442	—	3	8	no	—
111	C₂×#106	—	3	1	no	—
112	C₂×#102	—	3	2	no	—
113	C₂×#97	C₃×D₃	1	1	yes	characteristic, complemented
114	C₂⁴×C₃	—	6	2	no	—
115	C₂³×D₃	—	2	2	no	—
116	C₂×C₃×D₄	—	3	8	no	—
117	C₂×C₃×D₄	—	3	4	no	—
118	C₂×C₃×D₄	—	6	2	no	—
119	C₂×C₃×D₄	—	6	4	no	—
120	C₂²×C₃×C₄	—	2	2	no	—
121	C₂²×C₃×C₄	—	2	1	no	—
122	C₂²×C₃×C₄	—	6	2	no	—
123	C₂²×C₃×C₄	—	6	8	no	—
124	C₂²×C₃×C₄	—	12	8	no	—
125	C₂²×C₃×C₄	D₁₂	1	2	yes	—
126	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
127	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
128	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
129	C₂²×Dic₃	—	2	2	no	—
130	C₂×D₁₂	—	2	2	no	—
131	C₂×D₁₂	—	2	4	no	—
132	C₂×D₁₂	C₂×C₃×C₄	1	8	yes	complemented
133	C₂×D₁₂	C₂³×C₃	1	4	yes	—
134	C₂×C₄×D₃	—	2	8	no	—
135	C₂×C₄×D₃	—	4	8	no	—
136	C₃×D₈	—	3	16	no	—
137	C₂×C₃×C₈	—	2	4	no	—
138	C₂×C₃×C₈	—	2	2	no	—
139	C₂×C₃×C₈	—	2	2	no	—
140	C₂×C₃×C₈	—	2	4	no	—
141	C₂×C₃×C₈	—	2	2	no	—
142	C₂×C₃×C₈	—	2	2	no	—
143	C₂×C₃×C₈	C₄×D₃	1	4	yes	complemented
144	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
145	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
146	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
147	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
148	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
149	C₃×C₄⋊C₄	—	3	4	no	—
150	C₃×C₄⋊C₄	—	6	2	no	—
151	C₃×C₂²⋊C₄	—	6	8	no	—
152	C₃×C₄²	—	2	2	no	—
153	C₃×C₄²	—	2	2	no	—
154	C₃×C₄²	D₁₂	1	2	yes	—
155	C₃×C₄²	C₃×D₄	1	2	yes	—
156	C₃×C₄²	C₂²×D₃	1	2	yes	—
157	C₃×C₄²	C₂³×C₃	1	2	yes	—
158	(C₂×D₃)⋊C₄	—	2	8	no	—
159	C₄⋊Dic₃	—	2	2	no	—
160	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
161	D₂₄	C₂×C₃×C₄	1	16	yes	complemented
162	C₂²×C₃²	C₄×D₄	1	2	yes	—
163	C₂²×C₃²	AGL(1,ℤ/8)	1	4	yes	—
164	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₃×D₃	—	2	8	no	—
166	C₂×C₃×D₃	—	4	4	no	—
167	C₂×C₃×D₃	—	4	4	no	—
168	C₂×C₃×D₃	—	4	16	no	—
169	C₃²×C₄	—	2	4	no	—
170	C₃²×C₄	C₄×D₄	1	2	yes	—
171	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
172	C₃²×C₄	C₂×#41	1	1	yes	characteristic
173	C₃×Dic₃	—	4	4	no	—
174	C₂²×D₄	—	3	2	no	—
175	C₂³×C₄	—	6	2	no	—
176	C₂×D₈	—	3	8	no	—
177	C₂×D₈	—	3	4	no	—
178	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
179	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
180	C₄×D₄	—	3	8	no	—
181	C₄×D₄	—	6	4	no	—
182	C₂×C₄⋊C₄	—	3	2	no	—
183	C₂×C₂²⋊C₄	—	6	2	no	—
184	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
185	#106	—	3	4	no	—
186	#102	—	3	8	no	—
187	#97	C₂×C₃×D₃	1	4	yes	complemented
188	C₂³×C₃	—	2	1	no	—
189	C₂³×C₃	—	6	8	no	—
190	C₂³×C₃	—	6	4	no	—
191	C₂³×C₃	—	12	4	no	—
192	C₂³×C₃	—	12	4	no	—
193	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
194	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
195	C₂²×D₃	—	2	8	no	—
196	C₂²×D₃	—	2	4	no	—
197	C₂²×D₃	—	4	4	no	—
198	C₂²×D₃	—	4	4	no	—
199	C₃×D₄	—	3	8	no	—
200	C₃×D₄	—	6	8	no	—
201	C₃×D₄	—	6	4	no	—
202	C₂×C₃×C₄	—	2	4	no	—
203	C₂×C₃×C₄	—	2	4	no	—
204	C₂×C₃×C₄	—	2	1	no	—
205	C₂×C₃×C₄	—	2	2	no	—
206	C₂×C₃×C₄	—	2	1	no	—
207	C₂×C₃×C₄	—	2	4	no	—
208	C₂×C₃×C₄	—	2	2	no	—
209	C₂×C₃×C₄	—	4	4	no	—
210	C₂×C₃×C₄	—	6	4	no	—
211	C₂×C₃×C₄	—	12	16	no	—
212	C₂×C₃×C₄	—	12	4	no	—
213	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
214	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
215	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
216	C₂×C₃×C₄	#235	1	2	yes	—
217	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
218	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
219	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
220	C₂×C₃×C₄	C₃×#41	1	2	yes	—
221	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
222	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
223	C₂×Dic₃	—	2	4	no	—
224	C₂×Dic₃	—	4	4	no	—
225	D₁₂	—	2	8	no	—
226	D₁₂	—	2	4	no	—
227	D₁₂	C₂²×C₃×C₄	1	8	yes	complemented
228	C₄×D₃	—	4	16	no	—
229	C₃×C₈	—	2	4	no	—
230	C₃×C₈	—	2	2	no	—
231	C₃×C₈	—	2	2	no	—
232	C₃×C₈	—	2	4	no	—
233	C₃×C₈	C₂×C₄×D₃	1	4	yes	complemented
234	C₃×C₈	C₂²×C₃×C₄	1	4	yes	complemented
235	C₂×C₃²	#442	1	4	yes	complemented
236	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
237	C₂×C₃²	C₂×AGL(1,ℤ/8)	1	2	yes	—
238	C₃×D₃	—	4	8	no	—
239	C₂⁴	—	6	2	no	—
240	C₂×D₄	—	3	4	no	—
241	C₂×D₄	—	3	8	no	—
242	C₂×D₄	—	6	2	no	—
243	C₂×D₄	—	6	4	no	—
244	C₂²×C₄	—	6	2	no	—
245	C₂²×C₄	—	6	8	no	—
246	C₂²×C₄	—	12	8	no	—
247	C₂²×C₄	C₃×D₁₂	1	2	yes	—
248	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
249	D₈	—	3	16	no	—
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	C₃×C₄×D₃	1	4	yes	complemented
252	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
253	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
254	C₄⋊C₄	—	3	4	no	—
255	C₄⋊C₄	—	6	2	no	—
256	C₂²⋊C₄	—	6	8	no	—
257	C₄²	C₃×D₁₂	1	2	yes	—
258	C₄²	C₂²×C₃×D₃	1	2	yes	—
259	C₂²×C₃	—	2	4	no	—
260	C₂²×C₃	—	2	1	no	—
261	C₂²×C₃	—	2	2	no	—
262	C₂²×C₃	—	6	8	no	—
263	C₂²×C₃	—	12	16	no	—
264	C₂²×C₃	—	12	4	no	—
265	C₂²×C₃	—	12	4	no	—
266	C₂²×C₃	C₄×D₁₂	1	2	yes	—
267	C₂²×C₃	#908	1	4	yes	—
268	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
269	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	4	yes	—
270	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
271	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
272	C₂×D₃	—	2	8	no	—
273	C₂×D₃	—	4	4	no	—
274	C₂×D₃	—	4	4	no	—
275	C₂×D₃	—	4	16	no	—
276	C₃×C₄	—	2	4	no	—
277	C₃×C₄	—	2	4	no	—
278	C₃×C₄	—	2	1	no	—
279	C₃×C₄	—	2	1	no	—
280	C₃×C₄	—	2	2	no	—
281	C₃×C₄	—	4	4	no	—
282	C₃×C₄	—	12	4	no	—
283	C₃×C₄	C₄×D₁₂	1	2	yes	—
284	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
285	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
286	C₃×C₄	C₂×#235	1	1	yes	characteristic
287	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
288	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
289	Dic₃	—	4	4	no	—
290	C₃²	C₂×#442	1	1	yes	characteristic, complemented, Sylow
291	C₂³	—	6	4	no	—
292	C₂³	—	6	8	no	—
293	C₂³	—	12	4	no	—
294	C₂³	—	12	4	no	—
295	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
296	D₄	—	3	8	no	—
297	D₄	—	6	4	no	—
298	D₄	—	6	8	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	6	4	no	—
301	C₂×C₄	—	12	16	no	—
302	C₂×C₄	—	12	4	no	—
303	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
304	C₂×C₄	C₂×C₃×D₁₂	1	4	yes	—
305	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
306	C₂×C₄	C₃×#235	1	2	yes	—
307	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
308	C₈	—	2	2	no	—
309	C₈	C₂×C₃×C₄×D₃	1	4	yes	complemented
310	C₂×C₃	—	2	2	no	—
311	C₂×C₃	—	2	4	no	—
312	C₂×C₃	—	2	1	no	—
313	C₂×C₃	—	12	8	no	—
314	C₂×C₃	#4711	1	4	yes	direct product factor
315	C₂×C₃	C₃×#442	1	4	yes	complemented
316	C₂×C₃	C₂×C₄×D₁₂	1	1	yes	characteristic
317	C₂×C₃	C₂×#908	1	2	yes	—
318	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
319	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
320	D₃	—	4	8	no	—
321	C₂²	—	6	8	no	—
322	C₂²	—	12	4	no	—
323	C₂²	—	12	4	no	—
324	C₂²	—	12	16	no	—
325	C₂²	C₃×C₄×D₁₂	1	2	yes	—
326	C₂²	C₃×#908	1	4	yes	—
327	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
328	C₄	—	2	4	no	—
329	C₄	—	12	4	no	—
330	C₄	C₃×C₄×D₁₂	1	2	yes	—
331	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
332	C₄	C₂×C₃×#235	1	1	yes	characteristic
333	C₃	—	2	1	no	—
334	C₃	C₂×#4711	1	1	yes	characteristic, direct product factor
335	C₃	C₂×C₃×#442	1	1	yes	characteristic, complemented
336	C₂	—	12	8	no	—
337	C₂	C₃×#4711	1	4	yes	direct product factor
338	C₂	C₂×C₃×C₄×D₁₂	1	1	yes	characteristic
339	C₂	C₂×C₃×#908	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂×D₁₂
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#97	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂²×C₃×D₂₄	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×#97	D₃
hypocenter	C₃	C₂×C₃×#442
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×#97

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×D₁₂	C₂	semidirect
3. C₂×C₃²×#97	C₂	semidirect
4. C₂×C₃×#821	C₂	semidirect
5. C₂×C₃×#817	C₂	semidirect
6. C₃×#4711	C₂	direct (N × H)
8. C₂×#4711	C₃	direct (N × H)
16. C₂×C₃×D₂₄	C₄	semidirect
19. C₃×C₄×D₁₂	C₂²	semidirect
20. C₃²×#97	C₂²	semidirect
21. C₃×#821	C₂²	semidirect
22. C₃×#817	C₂²	semidirect
26. C₂×C₄×D₁₂	C₂×C₃	semidirect
31. C₂×C₃×#97	D₃	semidirect
32. C₂×C₃×#97	C₂×C₃	semidirect
33. C₂×#821	C₂×C₃	semidirect
34. C₂×#817	C₂×C₃	semidirect
35. #4711	C₂×C₃	direct (N × H)
42. C₂×C₃×D₁₂	C₂×C₄	semidirect
47. C₂×C₃²×C₈	C₂×C₄	semidirect
55. C₃×D₂₄	C₂×C₄	semidirect
78. C₂×D₂₄	C₃×C₄	semidirect
81. C₄×D₁₂	C₂²×C₃	semidirect
85. C₃×#97	C₂×D₃	semidirect
86. C₃×#97	C₂²×C₃	semidirect
87. #821	C₂²×C₃	semidirect
88. #817	C₂²×C₃	semidirect
104. C₃×D₁₂	C₂²×C₄	semidirect
107. C₃²×C₈	C₂²×C₄	semidirect
113. C₂×#97	C₃×D₃	semidirect
132. C₂×D₁₂	C₂×C₃×C₄	semidirect
143. C₂×C₃×C₈	C₄×D₃	semidirect
144. C₂×C₃×C₈	C₂×C₃×C₄	semidirect
161. D₂₄	C₂×C₃×C₄	semidirect
187. #97	C₂×C₃×D₃	semidirect
227. D₁₂	C₂²×C₃×C₄	semidirect
233. C₃×C₈	C₂×C₄×D₃	semidirect
234. C₃×C₈	C₂²×C₃×C₄	semidirect
235. C₂×C₃²	#442	semidirect
251. C₂×C₈	C₃×C₄×D₃	semidirect
290. C₃²	C₂×#442	semidirect
309. C₈	C₂×C₃×C₄×D₃	semidirect
314. C₂×C₃	#4711	direct (N × H)
315. C₂×C₃	C₃×#442	semidirect
334. C₃	C₂×#4711	direct (N × H)
335. C₃	C₂×C₃×#442	semidirect
337. C₂	C₃×#4711	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×C₃×D₂₄	2
C₂×C₃×C₄×D₁₂	2
C₂×C₃²×#97	2
C₂×C₃×#821	2
C₂×C₃×#817	2
C₃×#4711	2
C₂×C₃×#442	3
C₂×#4711	3

Subgroups — C2×C3×#4711 #11860153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4711 #11860153