Subgroups — C₂×D₃×#818 #11858404

Order 1152.

1265 conjugacy classes of subgroups.

The subgroup lattice has 363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×D₃×C₄⋊Dic₃	C₂	1	2	yes	maximal
3	C₂×#63645	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#818	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#63575	C₂	1	2	yes	maximal, complemented
6	D₃×#818	C₂	1	8	yes	maximal, direct product factor
7	C₂²×#818	—	3	1	no	maximal
8	C₂×D₃×#107	—	3	1	no	maximal
9	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
10	C₂²×D₃×Dic₃	—	2	2	no	—
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
13	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
14	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₃×C₈	C₄	1	8	yes	complemented
16	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
17	C₂×Dic₃⋊Dic₃	—	2	2	no	—
18	D₃×C₄⋊Dic₃	—	2	4	no	—
19	D₃×C₄⋊Dic₃	C₂²	1	8	yes	—
20	#63645	C₂²	1	4	yes	complemented
21	C₃×#818	C₂²	1	4	yes	complemented
22	#63575	C₂²	1	8	yes	complemented
23	C₂³×C₃×C₈	—	3	1	no	—
24	C₂²×C₄⋊Dic₃	—	3	2	no	—
25	C₂²×D₃×C₈	D₃	1	1	yes	characteristic
26	C₂×D₃×C₄⋊C₄	—	3	2	no	—
27	C₂×C₃×#107	—	3	1	no	—
28	C₂×#818	—	3	1	no	—
29	C₂×#818	—	3	1	no	—
30	C₂×#818	—	3	2	no	—
31	C₂×#818	—	3	8	no	—
32	C₂×#818	—	6	1	no	—
33	C₂×#818	D₃	1	1	yes	characteristic, direct product factor
34	C₂×#807	—	3	2	no	—
35	D₃×#107	—	3	8	no	—
36	C₂³×C₃×D₃	D₄	1	1	yes	characteristic
37	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
38	C₂²×C₃⋊Dic₃	—	2	2	no	—
39	C₂²×C₃×Dic₃	—	2	2	no	—
40	C₂²×C₃×Dic₃	D₄	1	1	yes	characteristic
41	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
42	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
43	C₂×C₃×C₄×D₃	Q₈	1	4	yes	—
44	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
45	C₂×D₃×Dic₃	—	2	8	no	—
46	C₂×D₃×Dic₃	—	4	8	no	—
47	C₂×C₃²×C₈	C₂×C₄	1	4	yes	complemented
48	C₂×C₃²×C₈	C₂³	1	2	yes	—
49	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
50	C₄⋊(C₃⋊Dic₃)	C₂³	1	4	yes	—
51	C₃×C₄⋊Dic₃	—	2	2	no	—
52	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
53	C₂×C₃×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
54	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
55	C₃×D₃×C₈	C₂×C₄	1	16	yes	complemented
56	Dic₃⋊Dic₃	—	2	8	no	—
57	C₂²×#107	—	9	1	no	Sylow
58	C₂³×C₃×C₄	—	3	1	no	—
59	C₂³×Dic₃	—	6	2	no	—
60	C₂²×C₄×D₃	—	6	2	no	—
61	C₂²×C₄×D₃	C₂×D₃	1	1	yes	characteristic
62	C₂²×C₃×C₈	—	2	1	no	—
63	C₂²×C₃×C₈	—	3	1	no	—
64	C₂²×C₃×C₈	—	3	8	no	—
65	C₂²×C₃×C₈	—	3	4	no	—
66	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
67	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
68	C₂×C₃×C₄⋊C₄	—	3	2	no	—
69	C₂×C₄⋊Dic₃	—	3	2	no	—
70	C₂×C₄⋊Dic₃	—	3	2	no	—
71	C₂×C₄⋊Dic₃	—	3	8	no	—
72	C₂×C₄⋊Dic₃	—	6	2	no	—
73	C₂×C₄⋊Dic₃	—	6	4	no	—
74	C₂×C₄⋊Dic₃	—	6	2	no	—
75	C₂×C₄⋊Dic₃	C₂×D₃	1	2	yes	—
76	C₂×Dic₃⋊C₄	—	6	2	no	—
77	C₂²×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
78	C₂×D₃×C₈	Dic₃	1	8	yes	complemented
79	C₂×D₃×C₈	C₂×D₃	1	4	yes	—
80	D₃×C₄⋊C₄	—	3	8	no	—
81	D₃×C₄⋊C₄	—	6	4	no	—
82	C₃×#107	—	3	4	no	—
83	#818	—	3	4	no	—
84	#818	—	3	4	no	—
85	#818	—	3	8	no	—
86	#818	—	6	4	no	—
87	#818	C₂×D₃	1	4	yes	direct product factor
88	#807	—	3	8	no	—
89	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₃×D₃	C₄⋊C₄	1	4	yes	—
91	C₂²×C₃×D₃	D₈	1	4	yes	—
92	C₂²×C₃×D₃	Q₁₆	1	4	yes	—
93	C₂²×C₃×D₃	C₂×D₄	1	2	yes	—
94	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
95	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
97	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
98	C₂×C₃⋊Dic₃	—	2	4	no	—
99	C₂×C₃⋊Dic₃	—	4	4	no	—
100	C₂×C₃×Dic₃	—	2	4	no	—
101	C₂×C₃×Dic₃	—	4	4	no	—
102	C₂×C₃×Dic₃	C₄⋊C₄	1	4	yes	—
103	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
104	C₃×C₄×D₃	C₄⋊C₄	1	8	yes	—
105	C₃×C₄×D₃	C₂²×C₄	1	4	yes	—
106	C₃×C₄×D₃	C₂×Q₈	1	4	yes	—
107	D₃×Dic₃	—	4	16	no	—
108	C₃²×C₈	C₂²×C₄	1	4	yes	complemented
109	C₃×C₃⋊C₈	C₂²×C₄	1	4	yes	complemented
110	C₂³×C₈	—	3	1	no	—
111	C₂²×C₄⋊C₄	—	9	2	no	—
112	C₂×#107	—	3	1	no	—
113	C₂×#107	—	9	8	no	—
114	C₂×#107	—	9	2	no	—
115	C₂×#107	—	9	1	no	—
116	C₂⁴×C₃	—	3	1	no	—
117	C₂³×D₃	D₁₂	1	1	yes	characteristic
118	C₂²×C₃×C₄	—	2	1	no	—
119	C₂²×C₃×C₄	—	3	1	no	—
120	C₂²×C₃×C₄	—	3	4	no	—
121	C₂²×C₃×C₄	—	3	2	no	—
122	C₂²×C₃×C₄	—	3	4	no	—
123	C₂²×C₃×C₄	—	3	2	no	—
124	C₂²×C₃×C₄	—	6	2	no	—
125	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
126	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
127	C₂²×Dic₃	—	2	2	no	—
128	C₂²×Dic₃	—	6	8	no	—
129	C₂²×Dic₃	—	6	2	no	—
130	C₂²×Dic₃	—	6	2	no	—
131	C₂²×Dic₃	—	12	2	no	—
132	C₂²×Dic₃	—	12	8	no	—
133	C₂²×Dic₃	D₁₂	1	1	yes	characteristic
134	C₂×C₄×D₃	—	6	8	no	—
135	C₂×C₄×D₃	—	12	8	no	—
136	C₂×C₄×D₃	Dic₆	1	4	yes	—
137	C₂×C₄×D₃	D₁₂	1	2	yes	—
138	C₂×C₄×D₃	C₂×Dic₃	1	4	yes	—
139	C₂×C₄×D₃	C₂²×D₃	1	2	yes	—
140	C₂×C₃×C₈	—	2	4	no	—
141	C₂×C₃×C₈	—	2	2	no	—
142	C₂×C₃×C₈	—	3	4	no	—
143	C₂×C₃×C₈	—	3	2	no	—
144	C₂×C₃×C₈	—	3	16	no	—
145	C₂×C₃×C₈	C₄×D₃	1	4	yes	complemented
146	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	complemented
147	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
148	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
149	C₃×C₄⋊C₄	—	3	4	no	—
150	C₃×C₄⋊C₄	—	6	2	no	—
151	C₄⋊Dic₃	—	2	2	no	—
152	C₄⋊Dic₃	—	3	4	no	—
153	C₄⋊Dic₃	—	3	4	no	—
154	C₄⋊Dic₃	—	6	4	no	—
155	C₄⋊Dic₃	—	6	8	no	—
156	C₄⋊Dic₃	—	6	2	no	—
157	C₄⋊Dic₃	—	6	2	no	—
158	C₄⋊Dic₃	—	12	2	no	—
159	C₄⋊Dic₃	C₂²×D₃	1	4	yes	—
160	Dic₃⋊C₄	—	6	8	no	—
161	C₂×C₃⋊C₈	C₂×Dic₃	1	4	yes	complemented
162	C₂×C₃⋊C₈	C₂²×D₃	1	2	yes	—
163	D₃×C₈	C₂×Dic₃	1	16	yes	complemented
164	C₂²×C₃²	C₂×C₄⋊C₄	1	2	yes	—
165	C₂²×C₃²	C₂×D₈	1	2	yes	—
166	C₂²×C₃²	C₂×Q₁₆	1	2	yes	—
167	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₃×D₃	#107	1	16	yes	complemented
169	C₂×C₃×D₃	C₂×C₄⋊C₄	1	4	yes	—
170	C₂×C₃×D₃	C₂×D₈	1	4	yes	—
171	C₂×C₃×D₃	C₂×Q₁₆	1	4	yes	—
172	C₃²×C₄	C₂×C₄⋊C₄	1	2	yes	—
173	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
174	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
175	C₃⋊Dic₃	—	4	4	no	—
176	C₃×Dic₃	—	4	4	no	—
177	C₃×Dic₃	C₂×C₄⋊C₄	1	4	yes	—
178	C₂³×C₄	—	3	1	no	—
179	C₂³×C₄	—	18	2	no	—
180	C₂²×C₈	—	3	1	no	—
181	C₂²×C₈	—	3	8	no	—
182	C₂²×C₈	—	3	4	no	—
183	C₂²×C₈	D₃²	1	1	yes	characteristic
184	C₂×C₄⋊C₄	—	3	2	no	—
185	C₂×C₄⋊C₄	—	9	8	no	—
186	C₂×C₄⋊C₄	—	9	2	no	—
187	C₂×C₄⋊C₄	—	18	4	no	—
188	C₂×C₄⋊C₄	—	18	2	no	—
189	#107	—	3	4	no	—
190	#107	—	9	8	no	—
191	#107	—	9	4	no	—
192	C₂³×C₃	—	2	1	no	—
193	C₂³×C₃	—	3	4	no	—
194	C₂³×C₃	—	3	4	no	—
195	C₂³×C₃	—	3	4	no	—
196	C₂³×C₃	—	3	2	no	—
197	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
198	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
199	C₂²×D₃	D₂₄	1	4	yes	—
200	C₂²×D₃	Dic₁₂	1	4	yes	—
201	C₂²×D₃	C₄⋊Dic₃	1	4	yes	—
202	C₂²×D₃	C₂×D₁₂	1	2	yes	—
203	C₂×C₃×C₄	—	2	1	no	—
204	C₂×C₃×C₄	—	2	2	no	—
205	C₂×C₃×C₄	—	2	1	no	—
206	C₂×C₃×C₄	—	2	2	no	—
207	C₂×C₃×C₄	—	3	4	no	—
208	C₂×C₃×C₄	—	3	2	no	—
209	C₂×C₃×C₄	—	3	8	no	—
210	C₂×C₃×C₄	—	3	4	no	—
211	C₂×C₃×C₄	—	3	4	no	—
212	C₂×C₃×C₄	—	6	4	no	—
213	C₂×C₃×C₄	—	12	4	no	—
214	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
215	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
216	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
217	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
218	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
219	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
220	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
221	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
222	C₂×Dic₃	—	2	4	no	—
223	C₂×Dic₃	—	4	4	no	—
224	C₂×Dic₃	—	6	4	no	—
225	C₂×Dic₃	—	6	4	no	—
226	C₂×Dic₃	—	12	4	no	—
227	C₂×Dic₃	—	12	16	no	—
228	C₂×Dic₃	—	12	4	no	—
229	C₂×Dic₃	—	12	4	no	—
230	C₂×Dic₃	—	24	4	no	—
231	C₂×Dic₃	C₄⋊Dic₃	1	4	yes	—
232	C₂×Dic₃	C₂×D₁₂	1	2	yes	—
233	C₄×D₃	—	12	16	no	—
234	C₄×D₃	C₄⋊Dic₃	1	8	yes	—
235	C₄×D₃	C₂×Dic₆	1	4	yes	—
236	C₄×D₃	C₂²×Dic₃	1	4	yes	—
237	C₃×C₈	—	2	4	no	—
238	C₃×C₈	—	3	4	no	—
239	C₃×C₈	C₂×C₄×D₃	1	4	yes	complemented
240	C₃×C₈	C₂²×Dic₃	1	4	yes	complemented
241	C₃⋊C₈	C₂²×Dic₃	1	4	yes	complemented
242	C₂×C₃²	C₂×#107	1	4	yes	complemented
243	C₂×C₃²	C₂²×C₄⋊C₄	1	1	yes	characteristic
244	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
245	C₂×C₃²	C₂²×Q₁₆	1	1	yes	characteristic
246	C₃×D₃	C₂×#107	1	8	yes	complemented
247	C₂⁴	—	3	1	no	—
248	C₂²×C₄	—	3	1	no	—
249	C₂²×C₄	—	3	2	no	—
250	C₂²×C₄	—	3	4	no	—
251	C₂²×C₄	—	3	2	no	—
252	C₂²×C₄	—	3	4	no	—
253	C₂²×C₄	—	6	2	no	—
254	C₂²×C₄	—	18	8	no	—
255	C₂²×C₄	—	18	2	no	—
256	C₂²×C₄	—	36	8	no	—
257	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
258	C₂×C₈	—	3	2	no	—
259	C₂×C₈	—	3	4	no	—
260	C₂×C₈	—	3	16	no	—
261	C₂×C₈	D₃×Dic₃	1	4	yes	complemented
262	C₂×C₈	C₂×D₃²	1	2	yes	—
263	C₄⋊C₄	—	3	4	no	—
264	C₄⋊C₄	—	6	2	no	—
265	C₄⋊C₄	—	9	4	no	—
266	C₄⋊C₄	—	18	8	no	—
267	C₄⋊C₄	—	18	2	no	—
268	C₂²×C₃	—	2	1	no	—
269	C₂²×C₃	—	2	2	no	—
270	C₂²×C₃	—	2	2	no	—
271	C₂²×C₃	—	2	2	no	—
272	C₂²×C₃	—	3	16	no	—
273	C₂²×C₃	—	3	4	no	—
274	C₂²×C₃	—	3	4	no	—
275	C₂²×C₃	—	3	4	no	—
276	C₂²×C₃	D₃×C₄⋊C₄	1	2	yes	—
277	C₂²×C₃	C₂×D₂₄	1	2	yes	—
278	C₂²×C₃	C₂×Dic₁₂	1	2	yes	—
279	C₂²×C₃	D₃×D₈	1	2	yes	—
280	C₂²×C₃	D₃×Q₁₆	1	2	yes	—
281	C₂²×C₃	C₂×C₄⋊Dic₃	1	2	yes	—
282	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
283	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
284	C₂×D₃	#818	1	16	yes	direct product factor
285	C₂×D₃	C₂×D₂₄	1	4	yes	—
286	C₂×D₃	C₂×Dic₁₂	1	4	yes	—
287	C₂×D₃	C₂×C₄⋊Dic₃	1	4	yes	—
288	C₃×C₄	—	2	1	no	—
289	C₃×C₄	—	2	1	no	—
290	C₃×C₄	—	2	2	no	—
291	C₃×C₄	—	3	4	no	—
292	C₃×C₄	—	12	4	no	—
293	C₃×C₄	D₃×C₄⋊C₄	1	2	yes	—
294	C₃×C₄	C₂×C₄⋊Dic₃	1	2	yes	—
295	C₃×C₄	C₂²×Dic₆	1	1	yes	characteristic
296	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
297	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
298	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
299	Dic₃	—	4	4	no	—
300	Dic₃	—	12	4	no	—
301	Dic₃	—	12	4	no	—
302	Dic₃	—	24	4	no	—
303	Dic₃	C₂×C₄⋊Dic₃	1	4	yes	—
304	C₃²	C₂²×#107	1	1	yes	characteristic, complemented, Sylow
305	C₂³	—	3	2	no	—
306	C₂³	—	3	4	no	—
307	C₂³	—	3	4	no	—
308	C₂³	—	3	4	no	—
309	C₂³	D₃×D₁₂	1	1	yes	characteristic
310	C₂×C₄	—	3	2	no	—
311	C₂×C₄	—	3	4	no	—
312	C₂×C₄	—	3	4	no	—
313	C₂×C₄	—	3	4	no	—
314	C₂×C₄	—	3	8	no	—
315	C₂×C₄	—	6	4	no	—
316	C₂×C₄	—	12	4	no	—
317	C₂×C₄	—	18	4	no	—
318	C₂×C₄	—	36	16	no	—
319	C₂×C₄	—	36	4	no	—
320	C₂×C₄	D₃×Dic₆	1	2	yes	—
321	C₂×C₄	D₃×D₁₂	1	1	yes	characteristic
322	C₂×C₄	C₂×D₃×Dic₃	1	2	yes	—
323	C₂×C₄	C₂²×D₃²	1	1	yes	characteristic
324	C₈	—	3	4	no	—
325	C₈	C₂×D₃×Dic₃	1	4	yes	complemented
326	C₂×C₃	—	2	1	no	—
327	C₂×C₃	—	2	1	no	—
328	C₂×C₃	—	2	1	no	—
329	C₂×C₃	—	2	4	no	—
330	C₂×C₃	—	3	8	no	—
331	C₂×C₃	D₃×#107	1	4	yes	complemented
332	C₂×C₃	C₂×#818	1	4	yes	complemented
333	C₂×C₃	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
334	C₂×C₃	C₂²×D₂₄	1	1	yes	characteristic
335	C₂×C₃	C₂²×Dic₁₂	1	1	yes	characteristic
336	C₂×C₃	C₂×D₃×D₈	1	1	yes	characteristic
337	C₂×C₃	C₂×D₃×Q₁₆	1	1	yes	characteristic
338	C₂×C₃	C₂²×C₄⋊Dic₃	1	1	yes	characteristic
339	D₃	C₂×#818	1	8	yes	direct product factor
340	C₂²	—	3	4	no	—
341	C₂²	—	3	4	no	—
342	C₂²	—	3	4	no	—
343	C₂²	—	3	16	no	—
344	C₂²	D₃×D₂₄	1	2	yes	—
345	C₂²	D₃×Dic₁₂	1	2	yes	—
346	C₂²	D₃×C₄⋊Dic₃	1	2	yes	—
347	C₂²	C₂×D₃×D₁₂	1	1	yes	characteristic
348	C₄	—	3	4	no	—
349	C₄	—	12	4	no	—
350	C₄	—	36	4	no	—
351	C₄	D₃×C₄⋊Dic₃	1	2	yes	—
352	C₄	C₂×D₃×Dic₆	1	1	yes	characteristic
353	C₄	C₂²×D₃×Dic₃	1	1	yes	characteristic
354	C₃	—	2	1	no	—
355	C₃	C₂×D₃×#107	1	1	yes	characteristic, complemented
356	C₃	C₂²×#818	1	1	yes	characteristic, complemented
357	C₂	—	3	8	no	—
358	C₂	D₃×#818	1	4	yes	direct product factor
359	C₂	C₂×D₃×D₂₄	1	1	yes	characteristic
360	C₂	C₂×D₃×Dic₁₂	1	1	yes	characteristic
361	C₂	C₂×D₃×C₄⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₃×D₁₂
commutator	C₃²×C₄	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃²
Fitting	C₂²×C₃²×C₈	C₂²
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂³×C₃×D₃	D₄
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	C₂²×C₈	D₃²
hypocenter	C₃²	C₂²×#107
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×#63645	C₂	semidirect
4. C₂×C₃×#818	C₂	semidirect
5. C₂×#63575	C₂	semidirect
6. D₃×#818	C₂	direct (N × H)
15. C₂×C₃×D₃×C₈	C₄	semidirect
20. #63645	C₂²	semidirect
21. C₃×#818	C₂²	semidirect
22. #63575	C₂²	semidirect
33. C₂×#818	D₃	direct (N × H)
47. C₂×C₃²×C₈	C₂×C₄	semidirect
53. C₂×C₃×C₃⋊C₈	C₂×C₄	semidirect
55. C₃×D₃×C₈	C₂×C₄	semidirect
78. C₂×D₃×C₈	Dic₃	semidirect
87. #818	C₂×D₃	direct (N × H)
108. C₃²×C₈	C₂²×C₄	semidirect
109. C₃×C₃⋊C₈	C₂²×C₄	semidirect
145. C₂×C₃×C₈	C₄×D₃	semidirect
146. C₂×C₃×C₈	C₂×Dic₃	semidirect
161. C₂×C₃⋊C₈	C₂×Dic₃	semidirect
163. D₃×C₈	C₂×Dic₃	semidirect
168. C₂×C₃×D₃	#107	semidirect
239. C₃×C₈	C₂×C₄×D₃	semidirect
240. C₃×C₈	C₂²×Dic₃	semidirect
241. C₃⋊C₈	C₂²×Dic₃	semidirect
242. C₂×C₃²	C₂×#107	semidirect
246. C₃×D₃	C₂×#107	semidirect
261. C₂×C₈	D₃×Dic₃	semidirect
284. C₂×D₃	#818	direct (N × H)
304. C₃²	C₂²×#107	semidirect
325. C₈	C₂×D₃×Dic₃	semidirect
331. C₂×C₃	D₃×#107	semidirect
332. C₂×C₃	C₂×#818	semidirect
339. D₃	C₂×#818	direct (N × H)
355. C₃	C₂×D₃×#107	semidirect
356. C₃	C₂²×#818	semidirect
358. C₂	D₃×#818	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×D₃×C₈	2
C₂×D₃×C₄⋊Dic₃	2
C₂×#63645	2
C₂×C₃×#818	2
C₂×#63575	2
D₃×#818	2
C₂²×#818	3
C₂×D₃×#107	3

Subgroups — C2×D3×#818 #11858404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×#818 #11858404