Subgroups — C₂×C₃×#4510 #11796762

Order 1152.

497 conjugacy classes of subgroups.

The subgroup lattice has 373 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
2	C₂²×C₃²×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4510	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₃×#359	—	3	1	no	maximal
6	C₂×#4510	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₃×#235	—	2	1	no	—
8	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₃×#208	—	2	1	no	—
10	C₂×C₃×Dic₁₂	C₄	1	1	yes	characteristic
11	C₃×#904	—	2	1	no	—
12	C₃×#904	—	2	1	no	—
13	C₃×#904	C₄	1	2	yes	—
14	C₃×#904	C₂²	1	2	yes	—
15	C₂×C₃×D₂₄	C₄	1	1	yes	characteristic
16	C₂×C₃×#204	—	2	1	no	—
17	C₂×C₃²×C₁₆	—	2	1	no	—
18	C₂×C₃²×C₁₆	—	2	1	no	—
19	C₂×C₃²×C₁₆	C₂²	1	2	yes	complemented
20	C₃×#819	—	2	1	no	—
21	C₃×#819	C₂²	1	2	yes	complemented
22	C₂×C₃×#135	—	3	1	no	—
23	C₂×#904	C₂×C₃	1	1	yes	characteristic
24	C₂²×C₃×C₁₆	—	2	1	no	—
25	C₂²×C₃×C₁₆	D₃	1	1	yes	characteristic, complemented
26	C₂²×C₃×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×C₃×#108	—	3	1	no	—
28	C₂×#819	C₂×C₃	1	1	yes	characteristic, complemented
29	C₃×#359	—	3	4	no	—
30	#4510	C₂×C₃	1	4	yes	direct product factor
31	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
32	C₂×C₃×#67	—	4	1	no	—
33	C₃×#235	—	2	2	no	—
34	C₃×#235	—	2	2	no	—
35	C₃×#235	—	4	1	no	—
36	C₃×#235	—	4	1	no	—
37	C₂×C₃×D₁₂	—	2	1	no	—
38	C₂×C₃×C₄×D₃	—	4	1	no	—
39	C₂×C₃×Dic₆	—	2	1	no	—
40	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
43	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
44	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
45	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
46	C₃×#208	—	2	2	no	—
47	C₃×#208	—	4	1	no	—
48	C₂×C₃×C₃⋊C₈	—	4	1	no	—
49	C₃×Dic₁₂	—	2	1	no	—
50	C₃×Dic₁₂	C₂×C₄	1	2	yes	—
51	C₃×D₂₄	—	2	1	no	—
52	C₃×D₂₄	C₂×C₄	1	2	yes	—
53	C₃×#204	—	2	2	no	—
54	C₃×#204	—	2	2	no	—
55	C₃²×C₁₆	—	2	2	no	—
56	C₂×#359	—	3	1	no	Sylow
57	C₂×C₃×#41	—	6	1	no	—
58	C₂×#235	—	2	1	no	—
59	C₃×#135	—	3	2	no	—
60	C₃×#135	—	3	2	no	—
61	C₃×#135	—	6	1	no	—
62	C₃×#135	—	6	1	no	—
63	C₂×C₃×Q₁₆	—	3	1	no	—
64	C₂×C₃×SD₁₆	—	6	1	no	—
65	C₂×C₃×D₈	—	3	1	no	—
66	C₂×C₃×M₁₆	—	6	1	no	—
67	C₂²×C₃×C₈	—	2	1	no	—
68	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
69	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
70	C₂×#208	—	2	1	no	—
71	C₂×Dic₁₂	C₃×C₄	1	1	yes	characteristic
72	#904	—	2	1	no	—
73	#904	—	2	1	no	—
74	#904	C₃×C₄	1	2	yes	—
75	#904	C₂²×C₃	1	2	yes	—
76	C₂×D₂₄	C₃×C₄	1	1	yes	characteristic
77	C₂×#204	—	2	1	no	—
78	C₂×C₃×C₁₆	—	2	2	no	—
79	C₂×C₃×C₁₆	—	2	2	no	—
80	C₂×C₃×C₁₆	—	2	1	no	—
81	C₂×C₃×C₁₆	—	2	1	no	—
82	C₂×C₃×C₁₆	—	2	1	no	—
83	C₂×C₃×C₁₆	—	2	1	no	—
84	C₂×C₃×C₁₆	—	2	2	no	—
85	C₂×C₃×C₁₆	C₂×D₃	1	2	yes	complemented
86	C₂×C₃×C₁₆	C₂²×C₃	1	2	yes	complemented
87	C₃×#108	—	3	2	no	—
88	C₃×#108	—	6	1	no	—
89	#819	—	2	1	no	—
90	#819	C₂²×C₃	1	2	yes	complemented
91	C₂³×C₃²	SD₁₆	1	1	yes	characteristic
92	C₂²×C₃×D₃	—	4	1	no	—
93	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
96	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
97	C₂×C₃²×C₄	SD₁₆	1	1	yes	characteristic
98	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
99	C₃×#67	—	4	2	no	—
100	C₃×#67	—	4	2	no	—
101	C₂×C₃×Dic₃	—	4	1	no	—
102	C₃×D₁₂	—	2	2	no	—
103	C₃×D₁₂	—	4	1	no	—
104	C₃×C₄×D₃	—	4	2	no	—
105	C₃×C₄×D₃	—	4	2	no	—
106	C₃×Dic₆	—	2	2	no	—
107	C₃×Dic₆	—	4	1	no	—
108	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
109	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
110	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
111	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
112	C₃×C₃⋊C₈	—	4	2	no	—
113	C₂×#135	—	3	1	no	—
114	C₂²×C₁₆	C₃×D₃	1	1	yes	characteristic, complemented
115	C₂×#108	—	3	1	no	—
116	#359	—	3	4	no	—
117	C₃×#41	—	6	2	no	—
118	C₃×#41	—	6	2	no	—
119	C₃×#41	—	12	1	no	—
120	C₃×#41	—	12	1	no	—
121	C₂×C₃×Q₈	—	6	1	no	—
122	C₂×C₃×D₄	—	6	1	no	—
123	C₂×C₃×D₄	—	12	1	no	—
124	C₂²×C₃×C₄	—	2	1	no	—
125	C₂²×C₃×C₄	—	12	1	no	—
126	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
127	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
128	C₂×#67	—	4	1	no	—
129	#235	—	2	2	no	—
130	#235	—	2	2	no	—
131	#235	—	4	1	no	—
132	#235	—	4	1	no	—
133	C₂×D₁₂	—	2	1	no	—
134	C₂×C₄×D₃	—	4	1	no	—
135	C₂×Dic₆	—	2	1	no	—
136	C₃×Q₁₆	—	3	2	no	—
137	C₃×Q₁₆	—	6	1	no	—
138	C₃×SD₁₆	—	6	2	no	—
139	C₃×SD₁₆	—	6	2	no	—
140	C₃×D₈	—	3	2	no	—
141	C₃×D₈	—	6	1	no	—
142	C₃×M₁₆	—	6	2	no	—
143	C₃×M₁₆	—	12	1	no	—
144	C₂×C₃×C₈	—	2	1	no	—
145	C₂×C₃×C₈	—	2	1	no	—
146	C₂×C₃×C₈	—	2	1	no	—
147	C₂×C₃×C₈	—	2	1	no	—
148	C₂×C₃×C₈	—	2	1	no	—
149	C₂×C₃×C₈	—	2	1	no	—
150	C₂×C₃×C₈	—	12	1	no	—
151	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
152	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
153	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
154	C₂×C₃×C₈	#67	1	1	yes	characteristic
155	C₂×C₃×C₈	#67	1	1	yes	characteristic
156	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
157	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
158	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
159	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
160	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
161	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
162	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
163	#208	—	2	2	no	—
164	#208	—	4	1	no	—
165	C₂×C₃⋊C₈	—	4	1	no	—
166	Dic₁₂	—	2	1	no	—
167	Dic₁₂	C₂×C₃×C₄	1	2	yes	—
168	D₂₄	—	2	1	no	—
169	D₂₄	C₂×C₃×C₄	1	2	yes	—
170	#204	—	2	2	no	—
171	#204	—	2	2	no	—
172	C₃×C₁₆	—	2	4	no	—
173	C₃×C₁₆	—	2	2	no	—
174	C₃×C₁₆	—	2	2	no	—
175	C₂²×C₃²	—	2	2	no	—
176	C₂²×C₃²	#102	1	1	yes	characteristic
177	C₂²×C₃²	#102	1	1	yes	characteristic
178	C₂²×C₃²	C₂×SD₁₆	1	1	yes	characteristic
179	C₂×C₃×D₃	—	4	2	no	—
180	C₂×C₃×D₃	—	8	2	no	—
181	C₃²×C₄	#102	1	1	yes	characteristic
182	C₃²×C₄	#102	1	1	yes	characteristic
183	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
185	C₃×Dic₃	—	4	2	no	—
186	C₂×#41	—	6	1	no	—
187	#135	—	3	2	no	—
188	#135	—	3	2	no	—
189	#135	—	6	1	no	—
190	#135	—	6	1	no	—
191	C₂×Q₁₆	—	3	1	no	—
192	C₂×SD₁₆	—	6	1	no	—
193	C₂×D₈	—	3	1	no	—
194	C₂×M₁₆	—	6	1	no	—
195	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
196	C₂×C₁₆	—	2	1	no	—
197	C₂×C₁₆	—	2	1	no	—
198	C₂×C₁₆	C₂×C₃×D₃	1	2	yes	complemented
199	#108	—	3	2	no	—
200	#108	—	6	1	no	—
201	C₂³×C₃	—	2	1	no	—
202	C₂³×C₃	—	12	1	no	—
203	C₂³×C₃	#204	1	1	yes	characteristic
204	C₂³×C₃	C₃×SD₁₆	1	1	yes	characteristic
205	C₂²×D₃	—	4	1	no	—
206	C₃×Q₈	—	6	2	no	—
207	C₃×Q₈	—	12	1	no	—
208	C₃×D₄	—	6	2	no	—
209	C₃×D₄	—	12	2	no	—
210	C₃×D₄	—	12	2	no	—
211	C₃×D₄	—	12	1	no	—
212	C₂×C₃×C₄	—	2	1	no	—
213	C₂×C₃×C₄	—	2	1	no	—
214	C₂×C₃×C₄	—	2	1	no	—
215	C₂×C₃×C₄	—	2	1	no	—
216	C₂×C₃×C₄	—	2	1	no	—
217	C₂×C₃×C₄	—	2	1	no	—
218	C₂×C₃×C₄	—	12	1	no	—
219	C₂×C₃×C₄	—	12	2	no	—
220	C₂×C₃×C₄	—	12	2	no	—
221	C₂×C₃×C₄	#204	1	1	yes	characteristic
222	C₂×C₃×C₄	D₂₄	1	1	yes	characteristic
223	C₂×C₃×C₄	D₂₄	1	1	yes	characteristic
224	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
225	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
226	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₃×C₄	C₃×D₈	1	1	yes	characteristic
229	C₂×C₃×C₄	C₃×D₈	1	1	yes	characteristic
230	C₂×C₃×C₄	C₃×SD₁₆	1	1	yes	characteristic
231	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
233	#67	—	4	2	no	—
234	#67	—	4	2	no	—
235	C₂×Dic₃	—	4	1	no	—
236	D₁₂	—	2	2	no	—
237	D₁₂	—	4	1	no	—
238	C₄×D₃	—	4	2	no	—
239	C₄×D₃	—	4	2	no	—
240	Dic₆	—	2	2	no	—
241	Dic₆	—	4	1	no	—
242	C₃×C₈	—	2	1	no	—
243	C₃×C₈	—	2	1	no	—
244	C₃×C₈	—	2	1	no	—
245	C₃×C₈	—	2	1	no	—
246	C₃×C₈	—	12	2	no	—
247	C₃×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
248	C₃×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
249	C₃×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
250	C₃×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
251	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
252	C₃×C₈	C₂×#67	1	1	yes	characteristic
253	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
254	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
255	C₃⋊C₈	—	4	2	no	—
256	C₂×C₃²	—	2	1	no	—
257	C₂×C₃²	—	2	1	no	—
258	C₂×C₃²	#359	1	2	yes	complemented
259	C₂×C₃²	C₂×#102	1	1	yes	characteristic
260	C₃×D₃	—	8	2	no	—
261	#41	—	6	2	no	—
262	#41	—	6	2	no	—
263	#41	—	12	1	no	—
264	#41	—	12	1	no	—
265	C₂×Q₈	—	6	1	no	—
266	C₂×D₄	—	6	1	no	—
267	C₂×D₄	—	12	1	no	—
268	C₂²×C₄	—	12	1	no	—
269	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
270	Q₁₆	—	3	2	no	—
271	Q₁₆	—	6	1	no	—
272	SD₁₆	—	6	2	no	—
273	SD₁₆	—	6	2	no	—
274	D₈	—	3	2	no	—
275	D₈	—	6	1	no	—
276	M₁₆	—	6	2	no	—
277	M₁₆	—	12	1	no	—
278	C₂×C₈	—	12	1	no	—
279	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
280	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
281	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
282	C₂×C₈	C₃×#67	1	1	yes	characteristic
283	C₂×C₈	C₃×#67	1	1	yes	characteristic
284	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
285	C₁₆	—	2	2	no	—
286	C₂²×C₃	—	2	4	no	—
287	C₂²×C₃	—	2	2	no	—
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	—	12	2	no	—
293	C₂²×C₃	—	24	2	no	—
294	C₂²×C₃	#821	1	1	yes	characteristic
295	C₂²×C₃	#821	1	1	yes	characteristic
296	C₂²×C₃	C₃×#102	1	1	yes	characteristic
297	C₂²×C₃	C₃×#102	1	1	yes	characteristic
298	C₂²×C₃	C₂×#204	1	1	yes	characteristic
299	C₂²×C₃	C₂×C₃×SD₁₆	1	1	yes	characteristic
300	C₂×D₃	—	4	2	no	—
301	C₂×D₃	—	8	2	no	—
302	C₃×C₄	—	2	1	no	—
303	C₃×C₄	—	2	1	no	—
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	2	1	no	—
306	C₃×C₄	—	12	2	no	—
307	C₃×C₄	#821	1	1	yes	characteristic
308	C₃×C₄	#821	1	1	yes	characteristic
309	C₃×C₄	C₃×#102	1	1	yes	characteristic
310	C₃×C₄	C₃×#102	1	1	yes	characteristic
311	C₃×C₄	C₂×D₂₄	1	1	yes	characteristic
312	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
313	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
314	C₃×C₄	C₂×C₃×D₈	1	1	yes	characteristic
315	Dic₃	—	4	2	no	—
316	C₃²	C₂×#359	1	1	yes	characteristic, complemented, Sylow
317	C₂³	—	12	1	no	—
318	C₂³	C₃×#204	1	1	yes	characteristic
319	Q₈	—	6	2	no	—
320	Q₈	—	12	1	no	—
321	D₄	—	6	2	no	—
322	D₄	—	12	2	no	—
323	D₄	—	12	2	no	—
324	D₄	—	12	1	no	—
325	C₂×C₄	—	12	1	no	—
326	C₂×C₄	—	12	2	no	—
327	C₂×C₄	—	12	2	no	—
328	C₂×C₄	C₃×#204	1	1	yes	characteristic
329	C₂×C₄	C₃×D₂₄	1	1	yes	characteristic
330	C₂×C₄	C₃×D₂₄	1	1	yes	characteristic
331	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
334	C₈	—	12	2	no	—
335	C₈	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
336	C₈	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
337	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
338	C₈	C₂×C₃×#67	1	1	yes	characteristic
339	C₂×C₃	—	2	2	no	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	—	2	1	no	—
342	C₂×C₃	—	2	1	no	—
343	C₂×C₃	—	2	1	no	—
344	C₂×C₃	—	2	1	no	—
345	C₂×C₃	—	2	2	no	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	—	24	2	no	—
348	C₂×C₃	#4510	1	2	yes	direct product factor
349	C₂×C₃	C₃×#359	1	2	yes	complemented
350	C₂×C₃	C₂×#821	1	1	yes	characteristic
351	C₂×C₃	C₂×C₃×#102	1	1	yes	characteristic
352	D₃	—	8	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	12	2	no	—
355	C₂²	—	24	2	no	—
356	C₂²	C₃×#821	1	1	yes	characteristic
357	C₂²	C₃×#821	1	1	yes	characteristic
358	C₂²	C₂×C₃×#204	1	1	yes	characteristic
359	C₄	—	12	2	no	—
360	C₄	C₃×#821	1	1	yes	characteristic
361	C₄	C₃×#821	1	1	yes	characteristic
362	C₄	C₂×C₃×D₂₄	1	1	yes	characteristic
363	C₄	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
364	C₃	—	2	1	no	—
365	C₃	C₂×#4510	1	1	yes	characteristic, direct product factor
366	C₃	C₂×C₃×#359	1	1	yes	characteristic, complemented
367	C₂	—	2	1	no	—
368	C₂	—	2	1	no	—
369	C₂	—	24	2	no	—
370	C₂	C₃×#4510	1	2	yes	direct product factor
371	C₂	C₂×C₃×#821	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₂₄
commutator	C₃×C₈	C₂²×C₃×C₄
Frattini	C₂×C₈	C₂²×C₃×D₃
Fitting	C₂²×C₃²×C₁₆	C₂
socle	C₂²×C₃²	#102
prime radical	C₂×C₃×#904	C₂
cosocle	C₂×C₃×C₈	C₂³×C₃
hypercenter	C₂²×C₃×C₁₆	D₃
hypocenter	C₃	C₂×C₃×#359
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₈ ◁ C₂²×C₃×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃²×C₁₆	C₂	semidirect
3. C₂×C₃×#819	C₂	semidirect
4. C₃×#4510	C₂	direct (N × H)
6. C₂×#4510	C₃	direct (N × H)
19. C₂×C₃²×C₁₆	C₂²	semidirect
21. C₃×#819	C₂²	semidirect
25. C₂²×C₃×C₁₆	D₃	semidirect
26. C₂²×C₃×C₁₆	C₂×C₃	semidirect
28. C₂×#819	C₂×C₃	semidirect
30. #4510	C₂×C₃	direct (N × H)
85. C₂×C₃×C₁₆	C₂×D₃	semidirect
86. C₂×C₃×C₁₆	C₂²×C₃	semidirect
90. #819	C₂²×C₃	semidirect
114. C₂²×C₁₆	C₃×D₃	semidirect
198. C₂×C₁₆	C₂×C₃×D₃	semidirect
258. C₂×C₃²	#359	semidirect
316. C₃²	C₂×#359	semidirect
348. C₂×C₃	#4510	direct (N × H)
349. C₂×C₃	C₃×#359	semidirect
365. C₃	C₂×#4510	direct (N × H)
366. C₃	C₂×C₃×#359	semidirect
370. C₂	C₃×#4510	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×C₃²×C₁₆	2
C₂×C₃×#819	2
C₃×#4510	2
C₂×C₃×#359	3
C₂×#4510	3

Subgroups — C2×C3×#4510 #11796762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4510 #11796762