Subgroups — C₂×C₃×#63647 #13163145

Order 1728.

1516 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63647	C₂	1	4	yes	maximal, direct product factor
5	C₂×#63647	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃×(C₂×D₃)⋊C₈	—	3	4	no	maximal
7	C₂³×C₃×C₃⋊D₃	C₄	1	1	yes	characteristic
8	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₃⋊Dic₃	C₄	1	1	yes	characteristic
10	C₂×C₃×C₄×C₃⋊D₃	—	2	2	no	—
11	C₂×C₃×C₄×C₃⋊D₃	—	2	2	no	—
12	C₂×C₃×C₄×C₃⋊D₃	C₄	1	2	yes	—
13	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	—
14	C₂×C₃³×C₈	—	2	2	no	—
15	C₂×C₃³×C₈	C₂²	1	2	yes	complemented
16	C₂×C₃×C₃⋊(C₃⋊C₈)	—	2	2	no	—
17	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
18	C₂²×C₄×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic
19	C₂²×C₃×C₄×D₃	—	3	4	no	—
20	C₂²×C₃²×C₈	—	2	4	no	—
21	C₂²×C₃²×C₈	D₃	1	4	yes	complemented
22	C₂²×C₃²×C₈	C₂×C₃	1	1	yes	characteristic, complemented
23	C₂²×C₃⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂²×C₃×C₃⋊C₈	—	3	4	no	—
25	#63647	C₂×C₃	1	4	yes	direct product factor
26	C₃×(C₂×D₃)⋊C₈	—	3	16	no	—
27	C₂³×C₃³	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
29	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
30	C₂²×C₃×C₃⋊D₃	C₈	1	4	yes	complemented
31	C₂²×C₃×C₃⋊D₃	C₂×C₄	1	2	yes	—
32	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
33	C₂×C₃³×C₄	D₄	1	2	yes	—
34	C₂×C₃³×C₄	D₄	1	2	yes	—
35	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
36	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
37	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	2	yes	—
38	C₃×C₄×C₃⋊D₃	—	2	4	no	—
39	C₃×C₄×C₃⋊D₃	—	2	2	no	—
40	C₃×C₄×C₃⋊D₃	—	2	2	no	—
41	C₃³×C₈	—	2	2	no	—
42	C₃×C₃⋊(C₃⋊C₈)	—	2	2	no	—
43	C₂×C₃×C₂²⋊C₈	—	9	1	no	—
44	C₂×(C₂×D₃)⋊C₈	—	3	4	no	—
45	C₂³×C₃⋊D₃	C₃×C₄	1	1	yes	characteristic
46	C₂³×C₃×D₃	—	3	4	no	—
47	C₂²×C₃²×C₄	—	2	4	no	—
48	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
49	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
50	C₂²×C₃⋊Dic₃	C₃×C₄	1	1	yes	characteristic
51	C₂×C₄×C₃⋊D₃	—	2	2	no	—
52	C₂×C₄×C₃⋊D₃	—	2	2	no	—
53	C₂×C₄×C₃⋊D₃	C₃×C₄	1	2	yes	—
54	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
55	C₂²×C₃×Dic₃	—	3	4	no	—
56	C₂×C₃×C₄×D₃	—	3	8	no	—
57	C₂×C₃×C₄×D₃	—	3	8	no	—
58	C₂×C₃×C₄×D₃	—	6	8	no	—
59	C₂×C₃×C₄×D₃	—	6	8	no	—
60	C₂×C₃²×C₈	—	2	16	no	—
61	C₂×C₃²×C₈	—	2	8	no	—
62	C₂×C₃²×C₈	—	2	8	no	—
63	C₂×C₃²×C₈	—	2	2	no	—
64	C₂×C₃²×C₈	C₂×D₃	1	8	yes	complemented
65	C₂×C₃²×C₈	C₂²×C₃	1	2	yes	complemented
66	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
67	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	complemented
68	C₂×C₃×C₃⋊C₈	—	3	8	no	—
69	C₂×C₃×C₃⋊C₈	—	6	8	no	—
70	C₂²×C₃³	C₂²⋊C₄	1	2	yes	—
71	C₂²×C₃³	C₂×C₈	1	2	yes	—
72	C₂²×C₃³	M₁₆	1	2	yes	—
73	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₃×C₃⋊D₃	—	2	8	no	—
75	C₂×C₃×C₃⋊D₃	—	2	2	no	—
76	C₂×C₃×C₃⋊D₃	—	2	2	no	—
77	C₂×C₃×C₃⋊D₃	C₂×C₈	1	4	yes	complemented
78	C₃³×C₄	C₂²⋊C₄	1	2	yes	—
79	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
80	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
81	C₃×C₃⋊Dic₃	—	2	2	no	—
82	C₂³×C₃×C₄	—	9	1	no	—
83	C₂²×C₄×D₃	—	3	4	no	—
84	C₂²×C₃×C₈	—	2	4	no	—
85	C₂²×C₃×C₈	—	9	1	no	—
86	C₂²×C₃×C₈	C₃×D₃	1	4	yes	complemented
87	C₂²×C₃×C₈	C₃⋊D₃	1	1	yes	characteristic, complemented
88	C₂²×C₃⋊C₈	—	3	4	no	—
89	C₃×C₂²⋊C₈	—	9	4	no	—
90	(C₂×D₃)⋊C₈	—	3	16	no	—
91	C₂³×C₃²	—	2	4	no	—
92	C₂³×C₃²	C₄×D₃	1	4	yes	—
93	C₂³×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
94	C₂²×C₃⋊D₃	—	2	2	no	—
95	C₂²×C₃⋊D₃	—	2	2	no	—
96	C₂²×C₃⋊D₃	C₃×C₈	1	4	yes	complemented
97	C₂²×C₃⋊D₃	C₂×C₃×C₄	1	2	yes	—
98	C₂²×C₃×D₃	—	3	16	no	—
99	C₂²×C₃×D₃	—	3	8	no	—
100	C₂²×C₃×D₃	—	6	8	no	—
101	C₂²×C₃×D₃	—	6	8	no	—
102	C₂×C₃²×C₄	—	2	4	no	—
103	C₂×C₃²×C₄	—	2	8	no	—
104	C₂×C₃²×C₄	—	2	8	no	—
105	C₂×C₃²×C₄	—	2	4	no	—
106	C₂×C₃²×C₄	C₄×D₃	1	4	yes	—
107	C₂×C₃²×C₄	D₁₂	1	8	yes	—
108	C₂×C₃²×C₄	#67	1	8	yes	—
109	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
110	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
111	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
112	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
113	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
114	C₂×C₃⋊Dic₃	—	2	2	no	—
115	C₂×C₃⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
116	C₄×C₃⋊D₃	—	2	4	no	—
117	C₄×C₃⋊D₃	—	2	2	no	—
118	C₄×C₃⋊D₃	—	2	2	no	—
119	C₂×C₃×Dic₃	—	3	8	no	—
120	C₂×C₃×Dic₃	—	6	8	no	—
121	C₃×C₄×D₃	—	6	16	no	—
122	C₃×C₄×D₃	—	6	8	no	—
123	C₃×C₄×D₃	—	6	8	no	—
124	C₃²×C₈	—	2	16	no	—
125	C₃²×C₈	—	2	8	no	—
126	C₃²×C₈	—	2	2	no	—
127	C₃⋊(C₃⋊C₈)	—	2	2	no	—
128	C₃×C₃⋊C₈	—	6	8	no	—
129	C₂×C₂²⋊C₈	—	9	1	no	Sylow
130	C₂×C₃³	C₂²⋊C₈	1	4	yes	complemented
131	C₂×C₃³	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₃³	C₂²×C₈	1	1	yes	characteristic
133	C₂×C₃³	C₂×M₁₆	1	1	yes	characteristic
134	C₃×C₃⋊D₃	—	2	4	no	—
135	C₂⁴×C₃	—	9	1	no	—
136	C₂³×D₃	—	3	4	no	—
137	C₂²×C₃×C₄	—	2	4	no	—
138	C₂²×C₃×C₄	—	9	1	no	—
139	C₂²×C₃×C₄	—	9	2	no	—
140	C₂²×C₃×C₄	—	9	2	no	—
141	C₂²×C₃×C₄	—	18	2	no	—
142	C₂²×C₃×C₄	—	18	2	no	—
143	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
144	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
145	C₂²×Dic₃	—	3	4	no	—
146	C₂×C₄×D₃	—	3	8	no	—
147	C₂×C₄×D₃	—	3	8	no	—
148	C₂×C₄×D₃	—	6	8	no	—
149	C₂×C₄×D₃	—	6	8	no	—
150	C₂×C₃×C₈	—	2	16	no	—
151	C₂×C₃×C₈	—	2	8	no	—
152	C₂×C₃×C₈	—	2	2	no	—
153	C₂×C₃×C₈	—	2	8	no	—
154	C₂×C₃×C₈	—	9	2	no	—
155	C₂×C₃×C₈	—	18	2	no	—
156	C₂×C₃×C₈	C₂×C₃×D₃	1	8	yes	complemented
157	C₂×C₃×C₈	C₂×C₃⋊D₃	1	2	yes	complemented
158	C₂×C₃⋊C₈	—	3	8	no	—
159	C₂×C₃⋊C₈	—	6	8	no	—
160	C₂²×C₃²	—	2	8	no	—
161	C₂²×C₃²	—	2	8	no	—
162	C₂²×C₃²	—	2	8	no	—
163	C₂²×C₃²	—	2	4	no	—
164	C₂²×C₃²	D₃×C₈	1	8	yes	—
165	C₂²×C₃²	ΓL(1,𝔽₂₅)	1	8	yes	—
166	C₂²×C₃²	(C₂×D₃)⋊C₄	1	8	yes	—
167	C₂²×C₃²	C₃×C₂²⋊C₄	1	2	yes	—
168	C₂²×C₃²	C₂×C₃×C₈	1	2	yes	—
169	C₂²×C₃²	C₃×M₁₆	1	2	yes	—
170	C₂²×C₃²	C₂×C₄×D₃	1	4	yes	—
171	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
172	C₂×C₃⋊D₃	—	2	8	no	—
173	C₂×C₃⋊D₃	—	2	2	no	—
174	C₂×C₃⋊D₃	—	2	2	no	—
175	C₂×C₃⋊D₃	C₂×C₃×C₈	1	4	yes	complemented
176	C₂×C₃×D₃	—	3	16	no	—
177	C₂×C₃×D₃	—	6	32	no	—
178	C₂×C₃×D₃	—	6	8	no	—
179	C₂×C₃×D₃	—	6	8	no	—
180	C₃²×C₄	—	2	8	no	—
181	C₃²×C₄	—	2	4	no	—
182	C₃²×C₄	—	2	4	no	—
183	C₃²×C₄	(C₂×D₃)⋊C₄	1	8	yes	—
184	C₃²×C₄	C₃×C₂²⋊C₄	1	2	yes	—
185	C₃²×C₄	C₂×D₁₂	1	4	yes	—
186	C₃²×C₄	C₂×#67	1	4	yes	—
187	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
188	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
189	C₃⋊Dic₃	—	2	2	no	—
190	C₃×Dic₃	—	6	8	no	—
191	C₂³×C₄	—	9	1	no	—
192	C₂²×C₈	—	9	1	no	—
193	C₂²×C₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
194	C₂²⋊C₈	—	9	4	no	—
195	C₃³	C₂×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
196	C₂³×C₃	—	2	4	no	—
197	C₂³×C₃	—	9	4	no	—
198	C₂³×C₃	—	9	2	no	—
199	C₂³×C₃	—	18	2	no	—
200	C₂³×C₃	—	18	2	no	—
201	C₂³×C₃	C₃×C₄×D₃	1	4	yes	—
202	C₂³×C₃	C₄×C₃⋊D₃	1	1	yes	characteristic
203	C₂²×D₃	—	3	16	no	—
204	C₂²×D₃	—	3	8	no	—
205	C₂²×D₃	—	6	8	no	—
206	C₂²×D₃	—	6	8	no	—
207	C₂×C₃×C₄	—	2	4	no	—
208	C₂×C₃×C₄	—	2	8	no	—
209	C₂×C₃×C₄	—	2	8	no	—
210	C₂×C₃×C₄	—	2	4	no	—
211	C₂×C₃×C₄	—	9	2	no	—
212	C₂×C₃×C₄	—	18	2	no	—
213	C₂×C₃×C₄	—	18	4	no	—
214	C₂×C₃×C₄	—	18	2	no	—
215	C₂×C₃×C₄	—	18	2	no	—
216	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
217	C₂×C₃×C₄	C₃×D₁₂	1	8	yes	—
218	C₂×C₃×C₄	C₃×#67	1	8	yes	—
219	C₂×C₃×C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
220	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	1	2	yes	—
221	C₂×C₃×C₄	#638	1	2	yes	—
222	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
223	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
224	C₂×Dic₃	—	3	8	no	—
225	C₂×Dic₃	—	6	8	no	—
226	C₄×D₃	—	6	16	no	—
227	C₄×D₃	—	6	8	no	—
228	C₄×D₃	—	6	8	no	—
229	C₃×C₈	—	2	16	no	—
230	C₃×C₈	—	2	8	no	—
231	C₃×C₈	—	2	2	no	—
232	C₃×C₈	—	18	2	no	—
233	C₃⋊C₈	—	6	8	no	—
234	C₂×C₃²	—	2	4	no	—
235	C₂×C₃²	—	2	4	no	—
236	C₂×C₃²	—	2	4	no	—
237	C₂×C₃²	—	2	16	no	—
238	C₂×C₃²	(C₂×D₃)⋊C₈	1	16	yes	complemented
239	C₂×C₃²	C₃×C₂²⋊C₈	1	4	yes	complemented
240	C₂×C₃²	C₂×D₃×C₈	1	4	yes	—
241	C₂×C₃²	C₂×ΓL(1,𝔽₂₅)	1	4	yes	—
242	C₂×C₃²	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
243	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₃²	C₂²×C₃×C₈	1	1	yes	characteristic
245	C₂×C₃²	C₂×C₃×M₁₆	1	1	yes	characteristic
246	C₃⋊D₃	—	2	4	no	—
247	C₃×D₃	—	6	16	no	—
248	C₂⁴	—	9	1	no	—
249	C₂²×C₄	—	9	1	no	—
250	C₂²×C₄	—	9	2	no	—
251	C₂²×C₄	—	9	2	no	—
252	C₂²×C₄	—	18	2	no	—
253	C₂²×C₄	—	18	2	no	—
254	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	9	2	no	—
257	C₂×C₈	—	18	2	no	—
258	C₂×C₈	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
259	C₂²×C₃	—	2	8	no	—
260	C₂²×C₃	—	2	8	no	—
261	C₂²×C₃	—	2	8	no	—
262	C₂²×C₃	—	2	4	no	—
263	C₂²×C₃	—	9	4	no	—
264	C₂²×C₃	—	18	2	no	—
265	C₂²×C₃	—	18	2	no	—
266	C₂²×C₃	—	18	8	no	—
267	C₂²×C₃	C₃×D₃×C₈	1	8	yes	—
268	C₂²×C₃	C₃×ΓL(1,𝔽₂₅)	1	8	yes	—
269	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	8	yes	—
270	C₂²×C₃	C₈×C₃⋊D₃	1	2	yes	—
271	C₂²×C₃	#3743	1	2	yes	—
272	C₂²×C₃	#3752	1	2	yes	—
273	C₂²×C₃	C₂×C₃×C₄×D₃	1	4	yes	—
274	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
275	C₂×D₃	—	3	16	no	—
276	C₂×D₃	—	6	8	no	—
277	C₂×D₃	—	6	8	no	—
278	C₂×D₃	—	6	32	no	—
279	C₃×C₄	—	2	8	no	—
280	C₃×C₄	—	2	4	no	—
281	C₃×C₄	—	2	4	no	—
282	C₃×C₄	—	18	2	no	—
283	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	8	yes	—
284	C₃×C₄	#3752	1	2	yes	—
285	C₃×C₄	C₂×C₃×D₁₂	1	4	yes	—
286	C₃×C₄	C₂×C₃×#67	1	4	yes	—
287	C₃×C₄	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
288	C₃×C₄	C₂×#638	1	1	yes	characteristic
289	Dic₃	—	6	8	no	—
290	C₃²	—	2	4	no	—
291	C₃²	C₂×(C₂×D₃)⋊C₈	1	4	yes	complemented
292	C₃²	C₂×C₃×C₂²⋊C₈	1	1	yes	characteristic, complemented
293	C₂³	—	9	4	no	—
294	C₂³	—	9	2	no	—
295	C₂³	—	18	2	no	—
296	C₂³	—	18	2	no	—
297	C₂³	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
298	C₂×C₄	—	9	2	no	—
299	C₂×C₄	—	18	2	no	—
300	C₂×C₄	—	18	4	no	—
301	C₂×C₄	—	18	2	no	—
302	C₂×C₄	—	18	2	no	—
303	C₂×C₄	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
304	C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
305	C₂×C₄	C₃×#638	1	2	yes	—
306	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
307	C₈	—	2	2	no	—
308	C₈	—	18	2	no	—
309	C₂×C₃	—	2	4	no	—
310	C₂×C₃	—	2	4	no	—
311	C₂×C₃	—	2	4	no	—
312	C₂×C₃	—	2	16	no	—
313	C₂×C₃	—	18	4	no	—
314	C₂×C₃	C₃×(C₂×D₃)⋊C₈	1	16	yes	complemented
315	C₂×C₃	#63647	1	4	yes	direct product factor
316	C₂×C₃	C₂×C₃×D₃×C₈	1	4	yes	—
317	C₂×C₃	C₂×C₃×ΓL(1,𝔽₂₅)	1	4	yes	—
318	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	4	yes	—
319	C₂×C₃	C₂×C₈×C₃⋊D₃	1	1	yes	characteristic
320	C₂×C₃	C₂×#3743	1	1	yes	characteristic
321	C₂×C₃	C₂×#3752	1	1	yes	characteristic
322	D₃	—	6	16	no	—
323	C₂²	—	9	4	no	—
324	C₂²	—	18	2	no	—
325	C₂²	—	18	2	no	—
326	C₂²	—	18	8	no	—
327	C₂²	C₃×C₈×C₃⋊D₃	1	2	yes	—
328	C₂²	C₃×#3743	1	2	yes	—
329	C₂²	C₃×#3752	1	2	yes	—
330	C₂²	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
331	C₄	—	18	2	no	—
332	C₄	C₃×#3752	1	2	yes	—
333	C₄	C₂×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
334	C₄	C₂×C₃×#638	1	1	yes	characteristic
335	C₃	—	2	4	no	—
336	C₃	C₂×C₃×(C₂×D₃)⋊C₈	1	4	yes	complemented
337	C₃	C₂×#63647	1	1	yes	characteristic, direct product factor
338	C₂	—	18	4	no	—
339	C₂	C₃×#63647	1	4	yes	direct product factor
340	C₂	C₂×C₃×C₈×C₃⋊D₃	1	1	yes	characteristic
341	C₂	C₂×C₃×#3743	1	1	yes	characteristic
342	C₂	C₂×C₃×#3752	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂×C₃⋊D₃
commutator	C₂×C₃²	C₂²×C₃×C₈
Frattini	C₂×C₄	C₂²×C₃×C₃⋊D₃
Fitting	C₂²×C₃³×C₈	C₂
socle	C₂³×C₃³	C₂×C₄
prime radical	C₂³×C₃×C₃⋊D₃	C₄
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂²×C₃×C₈	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×C₂²⋊C₈
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃³×C₈	C₂	semidirect
3. C₂²×C₃×C₃⋊(C₃⋊C₈)	C₂	semidirect
4. C₃×#63647	C₂	direct (N × H)
5. C₂×#63647	C₃	direct (N × H)
15. C₂×C₃³×C₈	C₂²	semidirect
17. C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	semidirect
21. C₂²×C₃²×C₈	D₃	semidirect
22. C₂²×C₃²×C₈	C₂×C₃	semidirect
23. C₂²×C₃⋊(C₃⋊C₈)	C₂×C₃	semidirect
25. #63647	C₂×C₃	direct (N × H)
30. C₂²×C₃×C₃⋊D₃	C₈	semidirect
64. C₂×C₃²×C₈	C₂×D₃	semidirect
65. C₂×C₃²×C₈	C₂²×C₃	semidirect
67. C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	semidirect
77. C₂×C₃×C₃⋊D₃	C₂×C₈	semidirect
86. C₂²×C₃×C₈	C₃×D₃	semidirect
87. C₂²×C₃×C₈	C₃⋊D₃	semidirect
96. C₂²×C₃⋊D₃	C₃×C₈	semidirect
130. C₂×C₃³	C₂²⋊C₈	semidirect
156. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
157. C₂×C₃×C₈	C₂×C₃⋊D₃	semidirect
175. C₂×C₃⋊D₃	C₂×C₃×C₈	semidirect
193. C₂²×C₈	C₃×C₃⋊D₃	semidirect
195. C₃³	C₂×C₂²⋊C₈	semidirect
238. C₂×C₃²	(C₂×D₃)⋊C₈	semidirect
239. C₂×C₃²	C₃×C₂²⋊C₈	semidirect
258. C₂×C₈	C₂×C₃×C₃⋊D₃	semidirect
291. C₃²	C₂×(C₂×D₃)⋊C₈	semidirect
292. C₃²	C₂×C₃×C₂²⋊C₈	semidirect
314. C₂×C₃	C₃×(C₂×D₃)⋊C₈	semidirect
315. C₂×C₃	#63647	direct (N × H)
336. C₃	C₂×C₃×(C₂×D₃)⋊C₈	semidirect
337. C₃	C₂×#63647	direct (N × H)
339. C₂	C₃×#63647	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×C₄×C₃⋊D₃	2
C₂²×C₃³×C₈	2
C₂²×C₃×C₃⋊(C₃⋊C₈)	2
C₃×#63647	2
C₂×#63647	3
C₂×C₃×(C₂×D₃)⋊C₈	3

Subgroups — C2×C3×#63647 #13163145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#63647 #13163145