Subgroups — C₂×C₃×#4908 #11899549

Order 1152.

845 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#904	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4908	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#800	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×D₄₈	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#509	—	3	1	no	maximal
8	C₂×#4908	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₃×#235	—	2	1	no	—
10	C₂²×C₃×D₁₂	—	2	1	no	—
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
13	C₃×#904	—	2	2	no	—
14	C₃×#904	C₂²	1	4	yes	complemented
15	C₂×C₃×D₂₄	—	2	2	no	—
16	C₂×C₃×D₂₄	—	2	1	no	—
17	C₂×C₃×D₂₄	C₂²	1	2	yes	—
18	C₂×C₃×D₂₄	C₂²	1	4	yes	complemented
19	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×#204	—	2	1	no	—
21	C₃²×M₃₂	C₂²	1	4	yes	complemented
22	C₂×C₃²×C₁₆	C₂²	1	2	yes	complemented
23	C₃×#800	C₂²	1	8	yes	complemented
24	C₃×D₄₈	C₂²	1	8	yes	complemented
25	C₂×C₃×#135	—	3	1	no	—
26	C₂²×C₃×D₈	—	3	1	no	—
27	C₂×#904	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂²×D₂₄	C₂×C₃	1	1	yes	characteristic, complemented
29	C₃×#509	—	3	8	no	—
30	C₂×C₃×SD₃₂	—	3	2	no	—
31	C₂×C₃×D₁₆	—	3	2	no	—
32	C₂×C₃×M₃₂	—	2	1	no	—
33	C₂×C₃×M₃₂	D₃	1	1	yes	characteristic, complemented
34	C₂×C₃×M₃₂	C₂×C₃	1	1	yes	characteristic, complemented
35	#4908	C₂×C₃	1	8	yes	direct product factor
36	C₂×#800	C₂×C₃	1	2	yes	complemented
37	C₂×D₄₈	C₂×C₃	1	2	yes	complemented
38	C₂³×C₃×D₃	—	4	1	no	—
39	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
40	C₂×C₃×#67	—	4	1	no	—
41	C₃×#235	—	2	4	no	—
42	C₃×#235	—	4	2	no	—
43	C₂×C₃×D₁₂	—	2	1	no	—
44	C₂×C₃×D₁₂	—	2	2	no	—
45	C₂×C₃×D₁₂	—	2	4	no	—
46	C₂×C₃×D₁₂	—	4	1	no	—
47	C₂×C₃×D₁₂	—	4	2	no	—
48	C₂×C₃×C₄×D₃	—	4	1	no	—
49	C₂×C₃×Dic₆	—	2	1	no	—
50	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
51	C₂×C₃²×C₈	D₄	1	2	yes	—
52	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
53	C₂×C₃²×C₈	C₂³	1	2	yes	—
54	C₃×Dic₁₂	—	2	1	no	—
55	C₃×Dic₁₂	C₂³	1	2	yes	complemented
56	C₃×D₂₄	—	2	2	no	—
57	C₃×D₂₄	—	2	4	no	—
58	C₃×D₂₄	—	2	1	no	—
59	C₃×D₂₄	C₂³	1	4	yes	—
60	C₃×D₂₄	C₂³	1	2	yes	complemented
61	C₃×#204	—	2	4	no	—
62	C₃²×C₁₆	C₂³	1	4	yes	complemented
63	C₂×#509	—	3	1	no	Sylow
64	C₂×C₃×#41	—	6	1	no	—
65	C₂²×C₃×D₄	—	6	1	no	—
66	C₂×#235	—	2	1	no	—
67	C₂²×D₁₂	—	2	1	no	—
68	C₃×#135	—	3	4	no	—
69	C₃×#135	—	6	2	no	—
70	C₂×C₃×Q₁₆	—	3	1	no	—
71	C₂×C₃×SD₁₆	—	6	1	no	—
72	C₂×C₃×D₈	—	3	1	no	—
73	C₂×C₃×D₈	—	3	2	no	—
74	C₂×C₃×D₈	—	3	4	no	—
75	C₂×C₃×D₈	—	6	1	no	—
76	C₂×C₃×D₈	—	6	2	no	—
77	C₂²×C₃×C₈	—	2	1	no	—
78	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
79	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
80	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
81	#904	—	2	2	no	—
82	#904	C₂²×C₃	1	4	yes	complemented
83	C₂×D₂₄	—	2	2	no	—
84	C₂×D₂₄	—	2	1	no	—
85	C₂×D₂₄	C₂²×C₃	1	2	yes	—
86	C₂×D₂₄	C₂²×C₃	1	4	yes	complemented
87	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic, complemented
88	C₂×#204	—	2	1	no	—
89	C₃×SD₃₂	—	3	8	no	—
90	C₃×D₁₆	—	3	8	no	—
91	C₃×M₃₂	—	2	4	no	—
92	C₃×M₃₂	C₂×D₃	1	4	yes	complemented
93	C₃×M₃₂	C₂²×C₃	1	4	yes	complemented
94	C₂×C₃×C₁₆	—	2	2	no	—
95	C₂×C₃×C₁₆	C₂×D₃	1	2	yes	complemented
96	C₂×C₃×C₁₆	C₂²×C₃	1	2	yes	complemented
97	#800	C₂²×C₃	1	8	yes	complemented
98	D₄₈	C₂²×C₃	1	8	yes	complemented
99	C₂³×C₃²	D₈	1	1	yes	characteristic
100	C₂²×C₃×D₃	—	4	4	no	—
101	C₂²×C₃×D₃	—	4	2	no	—
102	C₂²×C₃×D₃	—	4	1	no	—
103	C₂²×C₃×D₃	—	8	4	no	—
104	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
105	C₂×C₃²×C₄	D₈	1	2	yes	—
106	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
108	C₃×#67	—	4	4	no	—
109	C₂×C₃×Dic₃	—	4	1	no	—
110	C₃×D₁₂	—	2	2	no	—
111	C₃×D₁₂	—	2	4	no	—
112	C₃×D₁₂	—	4	2	no	—
113	C₃×D₁₂	—	4	4	no	—
114	C₃×D₁₂	—	4	1	no	—
115	C₃×C₄×D₃	—	4	4	no	—
116	C₃×Dic₆	—	2	2	no	—
117	C₃×Dic₆	—	4	1	no	—
118	C₃²×C₈	C₂×D₄	1	2	yes	—
119	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
120	C₃²×C₈	C₂⁴	1	1	yes	characteristic
121	C₂×#135	—	3	1	no	—
122	C₂²×D₈	—	3	1	no	—
123	#509	—	3	8	no	—
124	C₂×SD₃₂	—	3	2	no	—
125	C₂×D₁₆	—	3	2	no	—
126	C₂×M₃₂	C₃×D₃	1	1	yes	characteristic, complemented
127	C₂⁴×C₃	—	12	1	no	—
128	C₂³×D₃	—	4	1	no	—
129	C₃×#41	—	6	4	no	—
130	C₃×#41	—	12	2	no	—
131	C₂×C₃×Q₈	—	6	1	no	—
132	C₂×C₃×D₄	—	6	4	no	—
133	C₂×C₃×D₄	—	6	2	no	—
134	C₂×C₃×D₄	—	6	1	no	—
135	C₂×C₃×D₄	—	12	1	no	—
136	C₂×C₃×D₄	—	12	2	no	—
137	C₂×C₃×D₄	—	12	1	no	—
138	C₂²×C₃×C₄	—	2	1	no	—
139	C₂²×C₃×C₄	—	12	1	no	—
140	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
141	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
142	C₂×#67	—	4	1	no	—
143	#235	—	2	4	no	—
144	#235	—	4	2	no	—
145	C₂×D₁₂	—	2	1	no	—
146	C₂×D₁₂	—	2	2	no	—
147	C₂×D₁₂	—	2	4	no	—
148	C₂×D₁₂	—	4	1	no	—
149	C₂×D₁₂	—	4	2	no	—
150	C₂×C₄×D₃	—	4	1	no	—
151	C₂×Dic₆	—	2	1	no	—
152	C₃×Q₁₆	—	3	2	no	—
153	C₃×Q₁₆	—	6	1	no	—
154	C₃×SD₁₆	—	6	4	no	—
155	C₃×D₈	—	3	2	no	—
156	C₃×D₈	—	3	4	no	—
157	C₃×D₈	—	6	2	no	—
158	C₃×D₈	—	6	4	no	—
159	C₃×D₈	—	6	1	no	—
160	C₂×C₃×C₈	—	2	1	no	—
161	C₂×C₃×C₈	—	2	2	no	—
162	C₂×C₃×C₈	—	2	1	no	—
163	C₂×C₃×C₈	—	2	2	no	—
164	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
165	C₂×C₃×C₈	D₁₂	1	2	yes	—
166	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
167	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
168	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
169	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
170	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
171	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
172	Dic₁₂	—	2	1	no	—
173	Dic₁₂	C₂³×C₃	1	2	yes	complemented
174	D₂₄	—	2	2	no	—
175	D₂₄	—	2	4	no	—
176	D₂₄	—	2	1	no	—
177	D₂₄	C₂³×C₃	1	4	yes	—
178	D₂₄	C₂³×C₃	1	2	yes	complemented
179	#204	—	2	4	no	—
180	C₃×C₁₆	—	2	4	no	—
181	C₃×C₁₆	C₂²×D₃	1	4	yes	complemented
182	C₃×C₁₆	C₂³×C₃	1	4	yes	complemented
183	C₂²×C₃²	—	2	2	no	—
184	C₂²×C₃²	C₂×D₈	1	2	yes	—
185	C₂²×C₃²	C₂×D₈	1	1	yes	characteristic
186	C₂×C₃×D₃	—	4	2	no	—
187	C₂×C₃×D₃	—	4	4	no	—
188	C₂×C₃×D₃	—	8	8	no	—
189	C₂×C₃×D₃	—	8	2	no	—
190	C₂×C₃×D₃	—	8	4	no	—
191	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
192	C₃²×C₄	C₂×D₈	1	2	yes	—
193	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
194	C₃×Dic₃	—	4	2	no	—
195	C₂×#41	—	6	1	no	—
196	C₂²×D₄	—	6	1	no	—
197	#135	—	3	4	no	—
198	#135	—	6	2	no	—
199	C₂×Q₁₆	—	3	1	no	—
200	C₂×SD₁₆	—	6	1	no	—
201	C₂×D₈	—	3	2	no	—
202	C₂×D₈	—	3	4	no	—
203	C₂×D₈	—	3	1	no	—
204	C₂×D₈	—	6	1	no	—
205	C₂×D₈	—	6	2	no	—
206	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
207	SD₃₂	—	3	8	no	—
208	D₁₆	—	3	8	no	—
209	M₃₂	C₂×C₃×D₃	1	4	yes	complemented
210	C₂×C₁₆	C₂×C₃×D₃	1	2	yes	complemented
211	C₂³×C₃	—	2	1	no	—
212	C₂³×C₃	—	12	4	no	—
213	C₂³×C₃	—	12	1	no	—
214	C₂³×C₃	—	12	2	no	—
215	C₂³×C₃	—	24	4	no	—
216	C₂³×C₃	D₂₄	1	1	yes	characteristic
217	C₂³×C₃	C₃×D₈	1	1	yes	characteristic
218	C₂²×D₃	—	4	1	no	—
219	C₂²×D₃	—	4	4	no	—
220	C₂²×D₃	—	4	2	no	—
221	C₂²×D₃	—	8	4	no	—
222	C₃×Q₈	—	6	2	no	—
223	C₃×Q₈	—	12	1	no	—
224	C₃×D₄	—	6	4	no	—
225	C₃×D₄	—	6	2	no	—
226	C₃×D₄	—	12	4	no	—
227	C₃×D₄	—	12	4	no	—
228	C₃×D₄	—	12	2	no	—
229	C₃×D₄	—	12	1	no	—
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	1	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	12	1	no	—
235	C₂×C₃×C₄	—	12	4	no	—
236	C₂×C₃×C₄	D₂₄	1	2	yes	—
237	C₂×C₃×C₄	D₂₄	1	1	yes	characteristic
238	C₂×C₃×C₄	C₃×D₈	1	1	yes	characteristic
239	C₂×C₃×C₄	C₃×D₈	1	2	yes	—
240	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
241	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
244	#67	—	4	4	no	—
245	C₂×Dic₃	—	4	1	no	—
246	D₁₂	—	2	2	no	—
247	D₁₂	—	2	4	no	—
248	D₁₂	—	4	2	no	—
249	D₁₂	—	4	4	no	—
250	D₁₂	—	4	1	no	—
251	C₄×D₃	—	4	4	no	—
252	Dic₆	—	2	2	no	—
253	Dic₆	—	4	1	no	—
254	C₃×C₈	—	2	1	no	—
255	C₃×C₈	—	2	1	no	—
256	C₃×C₈	—	2	2	no	—
257	C₃×C₈	C₂×D₁₂	1	1	yes	characteristic
258	C₃×C₈	C₂×D₁₂	1	2	yes	—
259	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
260	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
261	C₃×C₈	C₂³×D₃	1	1	yes	characteristic
262	C₃×C₈	C₂⁴×C₃	1	1	yes	characteristic
263	C₂×C₃²	—	2	2	no	—
264	C₂×C₃²	#509	1	2	yes	complemented
265	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
266	C₃×D₃	—	8	2	no	—
267	C₃×D₃	—	8	4	no	—
268	C₂⁴	—	12	1	no	—
269	#41	—	6	4	no	—
270	#41	—	12	2	no	—
271	C₂×Q₈	—	6	1	no	—
272	C₂×D₄	—	6	2	no	—
273	C₂×D₄	—	6	4	no	—
274	C₂×D₄	—	6	1	no	—
275	C₂×D₄	—	12	1	no	—
276	C₂×D₄	—	12	1	no	—
277	C₂×D₄	—	12	2	no	—
278	C₂²×C₄	—	12	1	no	—
279	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
280	Q₁₆	—	3	2	no	—
281	Q₁₆	—	6	1	no	—
282	SD₁₆	—	6	4	no	—
283	D₈	—	3	2	no	—
284	D₈	—	3	4	no	—
285	D₈	—	6	2	no	—
286	D₈	—	6	4	no	—
287	D₈	—	6	1	no	—
288	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
289	C₂×C₈	C₃×D₁₂	1	2	yes	—
290	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
291	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
292	C₁₆	C₂²×C₃×D₃	1	4	yes	complemented
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	2	2	no	—
295	C₂²×C₃	—	2	1	no	—
296	C₂²×C₃	—	2	2	no	—
297	C₂²×C₃	—	4	2	no	—
298	C₂²×C₃	—	12	2	no	—
299	C₂²×C₃	—	12	4	no	—
300	C₂²×C₃	—	24	8	no	—
301	C₂²×C₃	—	24	4	no	—
302	C₂²×C₃	—	24	2	no	—
303	C₂²×C₃	C₂×D₂₄	1	2	yes	—
304	C₂²×C₃	C₂×D₂₄	1	1	yes	characteristic
305	C₂²×C₃	C₂×C₃×D₈	1	2	yes	—
306	C₂²×C₃	C₂×C₃×D₈	1	1	yes	characteristic
307	C₂×D₃	—	4	2	no	—
308	C₂×D₃	—	4	4	no	—
309	C₂×D₃	—	8	8	no	—
310	C₂×D₃	—	8	4	no	—
311	C₂×D₃	—	8	2	no	—
312	C₃×C₄	—	2	2	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	12	2	no	—
316	C₃×C₄	C₂×D₂₄	1	2	yes	—
317	C₃×C₄	C₂×D₂₄	1	1	yes	characteristic
318	C₃×C₄	C₂×C₃×D₈	1	1	yes	characteristic
319	C₃×C₄	C₂×C₃×D₈	1	2	yes	—
320	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
321	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
322	Dic₃	—	4	2	no	—
323	C₃²	C₂×#509	1	1	yes	characteristic, complemented, Sylow
324	C₂³	—	12	1	no	—
325	C₂³	—	12	4	no	—
326	C₂³	—	12	2	no	—
327	C₂³	—	24	4	no	—
328	C₂³	C₃×D₂₄	1	1	yes	characteristic
329	Q₈	—	6	2	no	—
330	Q₈	—	12	1	no	—
331	D₄	—	6	4	no	—
332	D₄	—	6	2	no	—
333	D₄	—	12	4	no	—
334	D₄	—	12	4	no	—
335	D₄	—	12	2	no	—
336	D₄	—	12	1	no	—
337	C₂×C₄	—	12	1	no	—
338	C₂×C₄	—	12	4	no	—
339	C₂×C₄	C₃×D₂₄	1	1	yes	characteristic
340	C₂×C₄	C₃×D₂₄	1	2	yes	—
341	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
342	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
343	C₈	C₂×C₃×D₁₂	1	1	yes	characteristic
344	C₈	C₂×C₃×D₁₂	1	2	yes	—
345	C₈	C₂³×C₃×D₃	1	1	yes	characteristic
346	C₂×C₃	—	2	2	no	—
347	C₂×C₃	—	2	2	no	—
348	C₂×C₃	—	2	2	no	—
349	C₂×C₃	—	2	1	no	—
350	C₂×C₃	—	4	2	no	—
351	C₂×C₃	—	24	4	no	—
352	C₂×C₃	—	24	2	no	—
353	C₂×C₃	#4908	1	2	yes	direct product factor
354	C₂×C₃	C₃×#509	1	2	yes	complemented
355	C₂×C₃	C₂²×D₂₄	1	1	yes	characteristic
356	C₂×C₃	C₂²×C₃×D₈	1	1	yes	characteristic
357	D₃	—	8	4	no	—
358	D₃	—	8	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	12	2	no	—
361	C₂²	—	12	4	no	—
362	C₂²	—	24	8	no	—
363	C₂²	—	24	4	no	—
364	C₂²	—	24	2	no	—
365	C₂²	C₂×C₃×D₂₄	1	2	yes	—
366	C₂²	C₂×C₃×D₂₄	1	1	yes	characteristic
367	C₄	—	12	2	no	—
368	C₄	C₂×C₃×D₂₄	1	2	yes	—
369	C₄	C₂×C₃×D₂₄	1	1	yes	characteristic
370	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
371	C₃	—	2	1	no	—
372	C₃	C₂×#4908	1	1	yes	characteristic, direct product factor
373	C₃	C₂×C₃×#509	1	1	yes	characteristic, complemented
374	C₂	—	2	2	no	—
375	C₂	—	24	4	no	—
376	C₂	—	24	2	no	—
377	C₂	C₃×#4908	1	2	yes	direct product factor
378	C₂	C₂²×C₃×D₂₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₂₄
commutator, cosocle	C₃×C₈	C₂⁴×C₃
Frattini	C₈	C₂³×C₃×D₃
Fitting	C₂×C₃²×M₃₂	C₂
socle	C₂²×C₃²	C₂×D₈
hypercenter	C₂×C₃×M₃₂	D₃
hypocenter	C₃	C₂×C₃×#509
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₈ ◁ C₂×C₃×M₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#904	C₂	semidirect
2. C₂²×C₃×D₂₄	C₂	semidirect
3. C₂×C₃²×M₃₂	C₂	semidirect
4. C₃×#4908	C₂	direct (N × H)
5. C₂×C₃×#800	C₂	semidirect
6. C₂×C₃×D₄₈	C₂	semidirect
8. C₂×#4908	C₃	direct (N × H)
12. C₂×C₃×Dic₁₂	C₂²	semidirect
14. C₃×#904	C₂²	semidirect
18. C₂×C₃×D₂₄	C₂²	semidirect
19. C₂×C₃×D₂₄	C₂²	semidirect
21. C₃²×M₃₂	C₂²	semidirect
22. C₂×C₃²×C₁₆	C₂²	semidirect
23. C₃×#800	C₂²	semidirect
24. C₃×D₄₈	C₂²	semidirect
27. C₂×#904	C₂×C₃	semidirect
28. C₂²×D₂₄	C₂×C₃	semidirect
33. C₂×C₃×M₃₂	D₃	semidirect
34. C₂×C₃×M₃₂	C₂×C₃	semidirect
35. #4908	C₂×C₃	direct (N × H)
36. C₂×#800	C₂×C₃	semidirect
37. C₂×D₄₈	C₂×C₃	semidirect
55. C₃×Dic₁₂	C₂³	semidirect
60. C₃×D₂₄	C₂³	semidirect
62. C₃²×C₁₆	C₂³	semidirect
80. C₂×Dic₁₂	C₂²×C₃	semidirect
82. #904	C₂²×C₃	semidirect
86. C₂×D₂₄	C₂²×C₃	semidirect
87. C₂×D₂₄	C₂²×C₃	semidirect
92. C₃×M₃₂	C₂×D₃	semidirect
93. C₃×M₃₂	C₂²×C₃	semidirect
95. C₂×C₃×C₁₆	C₂×D₃	semidirect
96. C₂×C₃×C₁₆	C₂²×C₃	semidirect
97. #800	C₂²×C₃	semidirect
98. D₄₈	C₂²×C₃	semidirect
126. C₂×M₃₂	C₃×D₃	semidirect
173. Dic₁₂	C₂³×C₃	semidirect
178. D₂₄	C₂³×C₃	semidirect
181. C₃×C₁₆	C₂²×D₃	semidirect
182. C₃×C₁₆	C₂³×C₃	semidirect
209. M₃₂	C₂×C₃×D₃	semidirect
210. C₂×C₁₆	C₂×C₃×D₃	semidirect
264. C₂×C₃²	#509	semidirect
292. C₁₆	C₂²×C₃×D₃	semidirect
323. C₃²	C₂×#509	semidirect
353. C₂×C₃	#4908	direct (N × H)
354. C₂×C₃	C₃×#509	semidirect
372. C₃	C₂×#4908	direct (N × H)
373. C₃	C₂×C₃×#509	semidirect
377. C₂	C₃×#4908	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×C₃×#904	2
C₂²×C₃×D₂₄	2
C₂×C₃²×M₃₂	2
C₃×#4908	2
C₂×C₃×#800	2
C₂×C₃×D₄₈	2
C₂×C₃×#509	3
C₂×#4908	3

Subgroups — C2×C3×#4908 #11899549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4908 #11899549