Subgroups — C₂×C₃²×#914 #13179136

Order 1728.

2060 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#239	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃³×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃²×#215	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃²×#213	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#914	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃²×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃²×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃²×AGL(1,ℤ/8)	—	3	1	no	maximal
10	C₂×C₃×#914	C₃	1	4	yes	maximal, direct product factor
11	C₂³×C₃²×D₃	—	2	1	no	—
12	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₃²×#67	—	2	1	no	—
15	C₃²×#239	—	2	2	no	—
16	C₃²×#239	C₂²	1	4	yes	complemented
17	C₃²×D₃×D₄	—	2	2	no	—
18	C₃²×D₃×D₄	C₂²	1	4	yes	complemented
19	C₂×C₃²×D₁₂	—	2	1	no	—
20	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
21	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃²×C₄×D₃	—	2	1	no	—
23	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
24	C₃³×SD₁₆	C₂²	1	4	yes	complemented
25	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic, complemented
26	C₃²×#215	C₂²	1	4	yes	complemented
27	C₃²×#213	C₂²	1	4	yes	complemented
28	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
29	C₃²×D₂₄	C₂²	1	4	yes	complemented
30	C₃²×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	complemented
31	C₂×C₃²×#41	—	3	1	no	—
32	C₂²×C₃²×D₄	—	3	1	no	—
33	C₂×C₃×#239	C₂×C₃	1	4	yes	complemented
34	C₂×C₃×D₃×D₄	C₂×C₃	1	4	yes	complemented
35	C₃²×AGL(1,ℤ/8)	—	3	8	no	—
36	C₂×C₃²×SD₁₆	—	2	4	no	—
37	C₂×C₃²×SD₁₆	—	3	1	no	—
38	C₂×C₃²×SD₁₆	D₃	1	1	yes	characteristic, complemented
39	C₂×C₃²×SD₁₆	C₂×C₃	1	4	yes	complemented
40	C₂×C₃²×D₈	—	3	1	no	—
41	C₂×C₃²×D₈	—	3	1	no	—
42	C₂×C₃²×M₁₆	—	3	1	no	—
43	C₂×C₃×#215	C₂×C₃	1	4	yes	complemented
44	C₂×C₃×#213	C₂×C₃	1	4	yes	complemented
45	C₃×#914	C₂×C₃	1	32	yes	direct product factor
46	C₂×C₃×D₂₄	C₂×C₃	1	4	yes	complemented
47	C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	1	4	yes	complemented
48	C₂³×C₃³	—	2	1	no	—
49	C₂²×C₃²×D₃	—	2	1	no	—
50	C₂²×C₃²×D₃	—	2	1	no	—
51	C₂²×C₃²×D₃	—	2	4	no	—
52	C₂²×C₃²×D₃	—	4	4	no	—
53	C₂²×C₃²×D₃	D₄	1	1	yes	characteristic
54	C₃³×Q₈	—	2	1	no	—
55	C₃³×Q₈	C₂³	1	2	yes	complemented
56	C₃³×D₄	—	2	1	no	—
57	C₃³×D₄	C₂³	1	2	yes	—
58	C₂×C₃³×C₄	—	2	1	no	—
59	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
60	C₃²×#67	—	2	4	no	—
61	C₂×C₃²×Dic₃	D₄	1	1	yes	characteristic
62	C₃²×D₁₂	—	2	4	no	—
63	C₃²×D₁₂	—	2	1	no	—
64	C₃²×D₁₂	—	2	1	no	—
65	C₃²×D₁₂	C₂³	1	2	yes	—
66	C₃²×D₁₂	C₂³	1	2	yes	complemented
67	C₃²×C₄×D₃	—	2	4	no	—
68	C₃²×C₄×D₃	D₄	1	2	yes	—
69	C₃²×C₄×D₃	C₂³	1	2	yes	—
70	C₃³×C₈	C₂³	1	2	yes	complemented
71	C₃²×C₃⋊C₈	C₂³	1	2	yes	complemented
72	C₂×C₃×AGL(1,ℤ/8)	—	3	4	no	—
73	C₂×#914	C₃²	1	1	yes	characteristic, direct product factor
74	C₂⁴×C₃²	—	6	1	no	—
75	C₂³×C₃×D₃	—	2	4	no	—
76	C₃²×#41	—	3	4	no	—
77	C₃²×#41	—	6	2	no	—
78	C₂×C₃²×Q₈	—	2	4	no	—
79	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
80	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	complemented
81	C₂×C₃²×D₄	—	2	4	no	—
82	C₂×C₃²×D₄	—	3	4	no	—
83	C₂×C₃²×D₄	—	3	1	no	—
84	C₂×C₃²×D₄	—	3	1	no	—
85	C₂×C₃²×D₄	—	6	1	no	—
86	C₂×C₃²×D₄	—	6	2	no	—
87	C₂×C₃²×D₄	—	6	1	no	—
88	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
89	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
90	C₂²×C₃²×C₄	—	3	1	no	—
91	C₂²×C₃²×C₄	—	6	1	no	—
92	C₂×C₃×#67	—	2	4	no	—
93	C₃×#239	—	2	8	no	—
94	C₃×#239	C₂²×C₃	1	16	yes	complemented
95	C₃×D₃×D₄	—	2	8	no	—
96	C₃×D₃×D₄	C₂²×C₃	1	16	yes	complemented
97	C₂×C₃×D₁₂	—	2	4	no	—
98	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
99	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	complemented
100	C₂×C₃×C₄×D₃	—	2	4	no	—
101	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
102	C₃²×SD₁₆	—	2	16	no	—
103	C₃²×SD₁₆	—	3	4	no	—
104	C₃²×SD₁₆	C₂×D₃	1	4	yes	complemented
105	C₃²×SD₁₆	C₂²×C₃	1	16	yes	complemented
106	C₃²×D₈	—	3	4	no	—
107	C₃²×D₈	—	3	4	no	—
108	C₃²×M₁₆	—	3	4	no	—
109	C₂×C₃²×C₈	—	2	4	no	—
110	C₂×C₃²×C₈	—	3	1	no	—
111	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic, complemented
112	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	complemented
113	C₃×#215	C₂²×C₃	1	16	yes	complemented
114	C₃×#213	C₂²×C₃	1	16	yes	complemented
115	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	complemented
116	C₃×D₂₄	C₂²×C₃	1	16	yes	complemented
117	C₃×ΓL(1,𝔽₂₅)	C₂²×C₃	1	16	yes	complemented
118	C₂²×C₃³	—	2	2	no	—
119	C₂²×C₃³	—	4	2	no	—
120	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
121	C₂×C₃²×D₃	—	2	2	no	—
122	C₂×C₃²×D₃	—	2	2	no	—
123	C₂×C₃²×D₃	—	2	2	no	—
124	C₂×C₃²×D₃	—	4	8	no	—
125	C₂×C₃²×D₃	—	4	2	no	—
126	C₂×C₃²×D₃	—	4	2	no	—
127	C₂×C₃²×D₃	C₂×D₄	1	2	yes	—
128	C₃³×C₄	—	2	2	no	—
129	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
130	C₃³×C₄	C₂⁴	1	1	yes	characteristic
131	C₃²×Dic₃	C₂×D₄	1	2	yes	—
132	C₂×C₃×#41	—	3	4	no	—
133	C₂²×C₃×D₄	—	3	4	no	—
134	C₂×#239	C₂×C₃²	1	1	yes	characteristic, complemented
135	C₂×D₃×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
136	C₃×AGL(1,ℤ/8)	—	3	32	no	—
137	C₂×C₃×SD₁₆	—	2	4	no	—
138	C₂×C₃×SD₁₆	—	3	4	no	—
139	C₂×C₃×SD₁₆	C₃×D₃	1	4	yes	complemented
140	C₂×C₃×SD₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
141	C₂×C₃×D₈	—	3	4	no	—
142	C₂×C₃×D₈	—	3	4	no	—
143	C₂×C₃×M₁₆	—	3	4	no	—
144	C₂×#215	C₂×C₃²	1	1	yes	characteristic, complemented
145	C₂×#213	C₂×C₃²	1	1	yes	characteristic, complemented
146	#914	C₂×C₃²	1	8	yes	direct product factor
147	C₂×D₂₄	C₂×C₃²	1	1	yes	characteristic, complemented
148	C₂×ΓL(1,𝔽₂₅)	C₂×C₃²	1	1	yes	characteristic, complemented
149	C₂³×C₃²	—	2	1	no	—
150	C₂³×C₃²	—	2	4	no	—
151	C₂³×C₃²	—	3	1	no	—
152	C₂³×C₃²	—	4	4	no	—
153	C₂³×C₃²	—	6	4	no	—
154	C₂³×C₃²	—	6	1	no	—
155	C₂³×C₃²	—	6	1	no	—
156	C₂³×C₃²	—	12	4	no	—
157	C₂²×C₃×D₃	—	2	4	no	—
158	C₂²×C₃×D₃	—	2	4	no	—
159	C₂²×C₃×D₃	—	2	16	no	—
160	C₂²×C₃×D₃	—	4	16	no	—
161	C₂²×C₃×D₃	C₃×D₄	1	4	yes	—
162	C₃²×Q₈	—	2	1	no	—
163	C₃²×Q₈	—	2	8	no	—
164	C₃²×Q₈	—	2	4	no	—
165	C₃²×Q₈	—	4	4	no	—
166	C₃²×Q₈	C₂²×D₃	1	2	yes	complemented
167	C₃²×Q₈	C₂³×C₃	1	8	yes	complemented
168	C₃²×D₄	—	2	1	no	—
169	C₃²×D₄	—	2	8	no	—
170	C₃²×D₄	—	2	4	no	—
171	C₃²×D₄	—	3	2	no	—
172	C₃²×D₄	—	3	2	no	—
173	C₃²×D₄	—	4	4	no	—
174	C₃²×D₄	—	6	4	no	—
175	C₃²×D₄	—	6	4	no	—
176	C₃²×D₄	—	6	1	no	—
177	C₃²×D₄	—	6	1	no	—
178	C₃²×D₄	C₂²×D₃	1	2	yes	—
179	C₃²×D₄	C₂³×C₃	1	8	yes	—
180	C₂×C₃²×C₄	—	2	1	no	—
181	C₂×C₃²×C₄	—	2	4	no	—
182	C₂×C₃²×C₄	—	2	4	no	—
183	C₂×C₃²×C₄	—	3	1	no	—
184	C₂×C₃²×C₄	—	3	2	no	—
185	C₂×C₃²×C₄	—	3	2	no	—
186	C₂×C₃²×C₄	—	4	4	no	—
187	C₂×C₃²×C₄	—	6	4	no	—
188	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
189	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
190	C₃×#67	—	2	16	no	—
191	C₂×C₃×Dic₃	C₃×D₄	1	4	yes	—
192	C₃×D₁₂	—	2	16	no	—
193	C₃×D₁₂	—	2	4	no	—
194	C₃×D₁₂	—	2	4	no	—
195	C₃×D₁₂	C₂³×C₃	1	8	yes	—
196	C₃×D₁₂	C₂³×C₃	1	8	yes	complemented
197	C₃×C₄×D₃	—	2	16	no	—
198	C₃×C₄×D₃	C₃×D₄	1	8	yes	—
199	C₃×C₄×D₃	C₂³×C₃	1	8	yes	—
200	C₃²×C₈	—	2	8	no	—
201	C₃²×C₈	—	3	2	no	—
202	C₃²×C₈	C₂²×D₃	1	2	yes	complemented
203	C₃²×C₈	C₂³×C₃	1	8	yes	complemented
204	C₃×C₃⋊C₈	C₂³×C₃	1	8	yes	complemented
205	C₂×AGL(1,ℤ/8)	—	3	1	no	Sylow
206	C₂×C₃³	—	4	2	no	—
207	C₂×C₃³	AGL(1,ℤ/8)	1	2	yes	complemented
208	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
209	C₃²×D₃	—	2	2	no	—
210	C₃²×D₃	—	4	2	no	—
211	C₃²×D₃	—	4	2	no	—
212	C₂⁴×C₃	—	6	4	no	—
213	C₂³×D₃	—	2	1	no	—
214	C₃×#41	—	3	16	no	—
215	C₃×#41	—	6	8	no	—
216	C₂×C₃×Q₈	—	2	4	no	—
217	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	complemented
218	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
219	C₂×C₃×D₄	—	2	4	no	—
220	C₂×C₃×D₄	—	3	16	no	—
221	C₂×C₃×D₄	—	3	4	no	—
222	C₂×C₃×D₄	—	3	4	no	—
223	C₂×C₃×D₄	—	6	4	no	—
224	C₂×C₃×D₄	—	6	8	no	—
225	C₂×C₃×D₄	—	6	4	no	—
226	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
227	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
228	C₂²×C₃×C₄	—	3	4	no	—
229	C₂²×C₃×C₄	—	6	4	no	—
230	C₂×#67	—	2	1	no	—
231	#239	—	2	2	no	—
232	#239	C₂²×C₃²	1	4	yes	complemented
233	D₃×D₄	—	2	2	no	—
234	D₃×D₄	C₂²×C₃²	1	4	yes	complemented
235	C₂×D₁₂	—	2	1	no	—
236	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
237	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic, complemented
238	C₂×C₄×D₃	—	2	1	no	—
239	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
240	C₃×SD₁₆	—	2	16	no	—
241	C₃×SD₁₆	—	3	16	no	—
242	C₃×SD₁₆	C₂×C₃×D₃	1	16	yes	complemented
243	C₃×SD₁₆	C₂²×C₃²	1	4	yes	complemented
244	C₃×D₈	—	3	16	no	—
245	C₃×D₈	—	3	16	no	—
246	C₃×M₁₆	—	3	16	no	—
247	C₂×C₃×C₈	—	2	4	no	—
248	C₂×C₃×C₈	—	3	4	no	—
249	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	complemented
250	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic, complemented
251	#215	C₂²×C₃²	1	4	yes	complemented
252	#213	C₂²×C₃²	1	4	yes	complemented
253	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic, complemented
254	D₂₄	C₂²×C₃²	1	4	yes	complemented
255	ΓL(1,𝔽₂₅)	C₂²×C₃²	1	4	yes	complemented
256	C₂²×C₃²	—	2	2	no	—
257	C₂²×C₃²	—	2	4	no	—
258	C₂²×C₃²	—	2	8	no	—
259	C₂²×C₃²	—	3	2	no	—
260	C₂²×C₃²	—	4	8	no	—
261	C₂²×C₃²	—	4	2	no	—
262	C₂²×C₃²	—	4	8	no	—
263	C₂²×C₃²	—	6	2	no	—
264	C₂²×C₃²	—	6	2	no	—
265	C₂²×C₃²	—	6	2	no	—
266	C₂²×C₃²	—	8	8	no	—
267	C₂²×C₃²	—	12	8	no	—
268	C₂²×C₃²	—	12	2	no	—
269	C₂²×C₃²	—	12	2	no	—
270	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
271	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
272	C₂×C₃×D₃	—	2	8	no	—
273	C₂×C₃×D₃	—	2	8	no	—
274	C₂×C₃×D₃	—	2	8	no	—
275	C₂×C₃×D₃	—	4	32	no	—
276	C₂×C₃×D₃	—	4	8	no	—
277	C₂×C₃×D₃	—	4	8	no	—
278	C₂×C₃×D₃	C₂×C₃×D₄	1	8	yes	—
279	C₃²×C₄	—	2	2	no	—
280	C₃²×C₄	—	2	4	no	—
281	C₃²×C₄	—	2	4	no	—
282	C₃²×C₄	—	2	8	no	—
283	C₃²×C₄	—	3	2	no	—
284	C₃²×C₄	—	4	8	no	—
285	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
286	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
287	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
288	C₃²×C₄	C₂⁴×C₃	1	4	yes	—
289	C₃×Dic₃	C₂×C₃×D₄	1	8	yes	—
290	C₂×#41	—	3	1	no	—
291	C₂²×D₄	—	3	1	no	—
292	AGL(1,ℤ/8)	—	3	8	no	—
293	C₂×SD₁₆	—	3	1	no	—
294	C₂×SD₁₆	C₃²×D₃	1	1	yes	characteristic, complemented
295	C₂×D₈	—	3	1	no	—
296	C₂×D₈	—	3	1	no	—
297	C₂×M₁₆	—	3	1	no	—
298	C₃³	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
299	C₂³×C₃	—	2	4	no	—
300	C₂³×C₃	—	2	1	no	—
301	C₂³×C₃	—	3	4	no	—
302	C₂³×C₃	—	4	4	no	—
303	C₂³×C₃	—	6	16	no	—
304	C₂³×C₃	—	6	4	no	—
305	C₂³×C₃	—	6	4	no	—
306	C₂³×C₃	—	12	16	no	—
307	C₂²×D₃	—	2	1	no	—
308	C₂²×D₃	—	2	1	no	—
309	C₂²×D₃	—	2	4	no	—
310	C₂²×D₃	—	4	4	no	—
311	C₂²×D₃	C₃²×D₄	1	1	yes	characteristic
312	C₃×Q₈	—	2	4	no	—
313	C₃×Q₈	—	2	1	no	—
314	C₃×Q₈	—	2	8	no	—
315	C₃×Q₈	—	4	4	no	—
316	C₃×Q₈	C₂²×C₃×D₃	1	8	yes	complemented
317	C₃×Q₈	C₂³×C₃²	1	2	yes	complemented
318	C₃×D₄	—	2	4	no	—
319	C₃×D₄	—	2	1	no	—
320	C₃×D₄	—	2	8	no	—
321	C₃×D₄	—	3	8	no	—
322	C₃×D₄	—	3	8	no	—
323	C₃×D₄	—	4	4	no	—
324	C₃×D₄	—	6	16	no	—
325	C₃×D₄	—	6	16	no	—
326	C₃×D₄	—	6	4	no	—
327	C₃×D₄	—	6	4	no	—
328	C₃×D₄	C₂²×C₃×D₃	1	8	yes	—
329	C₃×D₄	C₂³×C₃²	1	2	yes	—
330	C₂×C₃×C₄	—	2	4	no	—
331	C₂×C₃×C₄	—	2	1	no	—
332	C₂×C₃×C₄	—	2	4	no	—
333	C₂×C₃×C₄	—	3	4	no	—
334	C₂×C₃×C₄	—	3	8	no	—
335	C₂×C₃×C₄	—	3	8	no	—
336	C₂×C₃×C₄	—	4	4	no	—
337	C₂×C₃×C₄	—	6	16	no	—
338	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
339	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
340	#67	—	2	4	no	—
341	C₂×Dic₃	C₃²×D₄	1	1	yes	characteristic
342	D₁₂	—	2	4	no	—
343	D₁₂	—	2	1	no	—
344	D₁₂	—	2	1	no	—
345	D₁₂	C₂³×C₃²	1	2	yes	—
346	D₁₂	C₂³×C₃²	1	2	yes	complemented
347	C₄×D₃	—	2	4	no	—
348	C₄×D₃	C₃²×D₄	1	2	yes	—
349	C₄×D₃	C₂³×C₃²	1	2	yes	—
350	C₃×C₈	—	2	8	no	—
351	C₃×C₈	—	3	8	no	—
352	C₃×C₈	C₂²×C₃×D₃	1	8	yes	complemented
353	C₃×C₈	C₂³×C₃²	1	2	yes	complemented
354	C₃⋊C₈	C₂³×C₃²	1	2	yes	complemented
355	C₂×C₃²	—	2	8	no	—
356	C₂×C₃²	—	2	4	no	—
357	C₂×C₃²	—	4	2	no	—
358	C₂×C₃²	—	4	8	no	—
359	C₂×C₃²	—	6	2	no	—
360	C₂×C₃²	—	8	8	no	—
361	C₂×C₃²	—	12	2	no	—
362	C₂×C₃²	—	12	2	no	—
363	C₂×C₃²	#914	1	2	yes	direct product factor
364	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	8	yes	complemented
365	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
366	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
367	C₃×D₃	—	2	8	no	—
368	C₃×D₃	—	4	8	no	—
369	C₃×D₃	—	4	8	no	—
370	C₂⁴	—	6	1	no	—
371	#41	—	3	4	no	—
372	#41	—	6	2	no	—
373	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
374	C₂×D₄	—	3	4	no	—
375	C₂×D₄	—	3	1	no	—
376	C₂×D₄	—	3	1	no	—
377	C₂×D₄	—	6	1	no	—
378	C₂×D₄	—	6	2	no	—
379	C₂×D₄	—	6	1	no	—
380	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic
381	C₂²×C₄	—	3	1	no	—
382	C₂²×C₄	—	6	1	no	—
383	SD₁₆	—	3	4	no	—
384	SD₁₆	C₂×C₃²×D₃	1	4	yes	complemented
385	D₈	—	3	4	no	—
386	D₈	—	3	4	no	—
387	M₁₆	—	3	4	no	—
388	C₂×C₈	—	3	1	no	—
389	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
390	C₂²×C₃	—	2	8	no	—
391	C₂²×C₃	—	2	2	no	—
392	C₂²×C₃	—	2	4	no	—
393	C₂²×C₃	—	3	8	no	—
394	C₂²×C₃	—	4	8	no	—
395	C₂²×C₃	—	4	8	no	—
396	C₂²×C₃	—	4	2	no	—
397	C₂²×C₃	—	6	8	no	—
398	C₂²×C₃	—	6	8	no	—
399	C₂²×C₃	—	6	8	no	—
400	C₂²×C₃	—	8	8	no	—
401	C₂²×C₃	—	12	32	no	—
402	C₂²×C₃	—	12	8	no	—
403	C₂²×C₃	—	12	8	no	—
404	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
405	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
406	C₂×D₃	—	2	2	no	—
407	C₂×D₃	—	2	2	no	—
408	C₂×D₃	—	2	2	no	—
409	C₂×D₃	—	4	8	no	—
410	C₂×D₃	—	4	2	no	—
411	C₂×D₃	—	4	2	no	—
412	C₂×D₃	C₂×C₃²×D₄	1	2	yes	—
413	C₃×C₄	—	2	8	no	—
414	C₃×C₄	—	2	2	no	—
415	C₃×C₄	—	2	4	no	—
416	C₃×C₄	—	2	4	no	—
417	C₃×C₄	—	3	8	no	—
418	C₃×C₄	—	4	8	no	—
419	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
420	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
421	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
422	C₃×C₄	C₂⁴×C₃²	1	1	yes	characteristic
423	Dic₃	C₂×C₃²×D₄	1	2	yes	—
424	C₃²	—	2	4	no	—
425	C₃²	C₂×#914	1	1	yes	characteristic, direct product factor
426	C₃²	C₂×C₃×AGL(1,ℤ/8)	1	4	yes	complemented
427	C₂³	—	2	1	no	—
428	C₂³	—	3	1	no	—
429	C₂³	—	6	4	no	—
430	C₂³	—	6	1	no	—
431	C₂³	—	6	1	no	—
432	C₂³	—	12	4	no	—
433	Q₈	—	2	1	no	—
434	Q₈	C₂²×C₃²×D₃	1	2	yes	complemented
435	D₄	—	2	1	no	—
436	D₄	—	3	2	no	—
437	D₄	—	3	2	no	—
438	D₄	—	6	4	no	—
439	D₄	—	6	4	no	—
440	D₄	—	6	1	no	—
441	D₄	—	6	1	no	—
442	D₄	C₂²×C₃²×D₃	1	2	yes	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	3	1	no	—
445	C₂×C₄	—	3	2	no	—
446	C₂×C₄	—	3	2	no	—
447	C₂×C₄	—	6	4	no	—
448	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
449	C₈	—	3	2	no	—
450	C₈	C₂²×C₃²×D₃	1	2	yes	complemented
451	C₂×C₃	—	2	8	no	—
452	C₂×C₃	—	2	4	no	—
453	C₂×C₃	—	4	8	no	—
454	C₂×C₃	—	4	2	no	—
455	C₂×C₃	—	6	8	no	—
456	C₂×C₃	—	8	8	no	—
457	C₂×C₃	—	12	8	no	—
458	C₂×C₃	—	12	8	no	—
459	C₂×C₃	C₃×#914	1	8	yes	direct product factor
460	C₂×C₃	C₃²×AGL(1,ℤ/8)	1	2	yes	complemented
461	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
462	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
463	D₃	—	2	2	no	—
464	D₃	—	4	2	no	—
465	D₃	—	4	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	3	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	6	2	no	—
470	C₂²	—	6	2	no	—
471	C₂²	—	6	2	no	—
472	C₂²	—	12	8	no	—
473	C₂²	—	12	2	no	—
474	C₂²	—	12	2	no	—
475	C₂²	C₃²×D₃×D₄	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	3	2	no	—
478	C₄	C₃²×D₃×D₄	1	1	yes	characteristic
479	C₄	C₂³×C₃²×D₃	1	1	yes	characteristic
480	C₃	—	2	4	no	—
481	C₃	C₂×C₃×#914	1	4	yes	direct product factor
482	C₃	C₂×C₃²×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented
483	C₂	—	4	2	no	—
484	C₂	—	6	2	no	—
485	C₂	—	12	2	no	—
486	C₂	—	12	2	no	—
487	C₂	C₃²×#914	1	2	yes	direct product factor
488	C₂	C₂×C₃²×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁴×C₃²
Frattini	C₄	C₂³×C₃²×D₃
Fitting	C₂×C₃³×SD₁₆	C₂
socle	C₂²×C₃³	C₂×D₄
hypercenter	C₂×C₃²×SD₁₆	D₃
hypocenter	C₃	C₂×C₃²×AGL(1,ℤ/8)
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₂×C₃²×C₄ ◁ C₂×C₃²×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#239	C₂	semidirect
2. C₂×C₃²×D₃×D₄	C₂	semidirect
3. C₂×C₃³×SD₁₆	C₂	semidirect
4. C₂×C₃²×#215	C₂	semidirect
5. C₂×C₃²×#213	C₂	semidirect
6. C₃²×#914	C₂	direct (N × H)
7. C₂×C₃²×D₂₄	C₂	semidirect
8. C₂×C₃²×ΓL(1,𝔽₂₅)	C₂	semidirect
10. C₂×C₃×#914	C₃	direct (N × H)
12. C₂×C₃³×Q₈	C₂²	semidirect
16. C₃²×#239	C₂²	semidirect
18. C₃²×D₃×D₄	C₂²	semidirect
21. C₂×C₃²×D₁₂	C₂²	semidirect
24. C₃³×SD₁₆	C₂²	semidirect
25. C₂×C₃³×C₈	C₂²	semidirect
26. C₃²×#215	C₂²	semidirect
27. C₃²×#213	C₂²	semidirect
28. C₂×C₃²×C₃⋊C₈	C₂²	semidirect
29. C₃²×D₂₄	C₂²	semidirect
30. C₃²×ΓL(1,𝔽₂₅)	C₂²	semidirect
33. C₂×C₃×#239	C₂×C₃	semidirect
34. C₂×C₃×D₃×D₄	C₂×C₃	semidirect
38. C₂×C₃²×SD₁₆	D₃	semidirect
39. C₂×C₃²×SD₁₆	C₂×C₃	semidirect
43. C₂×C₃×#215	C₂×C₃	semidirect
44. C₂×C₃×#213	C₂×C₃	semidirect
45. C₃×#914	C₂×C₃	direct (N × H)
46. C₂×C₃×D₂₄	C₂×C₃	semidirect
47. C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	semidirect
55. C₃³×Q₈	C₂³	semidirect
66. C₃²×D₁₂	C₂³	semidirect
70. C₃³×C₈	C₂³	semidirect
71. C₃²×C₃⋊C₈	C₂³	semidirect
73. C₂×#914	C₃²	direct (N × H)
79. C₂×C₃²×Q₈	C₂×D₃	semidirect
80. C₂×C₃²×Q₈	C₂²×C₃	semidirect
94. C₃×#239	C₂²×C₃	semidirect
96. C₃×D₃×D₄	C₂²×C₃	semidirect
99. C₂×C₃×D₁₂	C₂²×C₃	semidirect
104. C₃²×SD₁₆	C₂×D₃	semidirect
105. C₃²×SD₁₆	C₂²×C₃	semidirect
111. C₂×C₃²×C₈	C₂×D₃	semidirect
112. C₂×C₃²×C₈	C₂²×C₃	semidirect
113. C₃×#215	C₂²×C₃	semidirect
114. C₃×#213	C₂²×C₃	semidirect
115. C₂×C₃×C₃⋊C₈	C₂²×C₃	semidirect
116. C₃×D₂₄	C₂²×C₃	semidirect
117. C₃×ΓL(1,𝔽₂₅)	C₂²×C₃	semidirect
134. C₂×#239	C₂×C₃²	semidirect
135. C₂×D₃×D₄	C₂×C₃²	semidirect
139. C₂×C₃×SD₁₆	C₃×D₃	semidirect
140. C₂×C₃×SD₁₆	C₂×C₃²	semidirect
144. C₂×#215	C₂×C₃²	semidirect
145. C₂×#213	C₂×C₃²	semidirect
146. #914	C₂×C₃²	direct (N × H)
147. C₂×D₂₄	C₂×C₃²	semidirect
148. C₂×ΓL(1,𝔽₂₅)	C₂×C₃²	semidirect
166. C₃²×Q₈	C₂²×D₃	semidirect
167. C₃²×Q₈	C₂³×C₃	semidirect
196. C₃×D₁₂	C₂³×C₃	semidirect
202. C₃²×C₈	C₂²×D₃	semidirect
203. C₃²×C₈	C₂³×C₃	semidirect
204. C₃×C₃⋊C₈	C₂³×C₃	semidirect
207. C₂×C₃³	AGL(1,ℤ/8)	semidirect
217. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
218. C₂×C₃×Q₈	C₂²×C₃²	semidirect
232. #239	C₂²×C₃²	semidirect
234. D₃×D₄	C₂²×C₃²	semidirect
237. C₂×D₁₂	C₂²×C₃²	semidirect
242. C₃×SD₁₆	C₂×C₃×D₃	semidirect
243. C₃×SD₁₆	C₂²×C₃²	semidirect
249. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
250. C₂×C₃×C₈	C₂²×C₃²	semidirect
251. #215	C₂²×C₃²	semidirect
252. #213	C₂²×C₃²	semidirect
253. C₂×C₃⋊C₈	C₂²×C₃²	semidirect
254. D₂₄	C₂²×C₃²	semidirect
255. ΓL(1,𝔽₂₅)	C₂²×C₃²	semidirect
294. C₂×SD₁₆	C₃²×D₃	semidirect
298. C₃³	C₂×AGL(1,ℤ/8)	semidirect
316. C₃×Q₈	C₂²×C₃×D₃	semidirect
317. C₃×Q₈	C₂³×C₃²	semidirect
346. D₁₂	C₂³×C₃²	semidirect
352. C₃×C₈	C₂²×C₃×D₃	semidirect
353. C₃×C₈	C₂³×C₃²	semidirect
354. C₃⋊C₈	C₂³×C₃²	semidirect
363. C₂×C₃²	#914	direct (N × H)
364. C₂×C₃²	C₃×AGL(1,ℤ/8)	semidirect
373. C₂×Q₈	C₂×C₃²×D₃	semidirect
384. SD₁₆	C₂×C₃²×D₃	semidirect
389. C₂×C₈	C₂×C₃²×D₃	semidirect
425. C₃²	C₂×#914	direct (N × H)
426. C₃²	C₂×C₃×AGL(1,ℤ/8)	semidirect
434. Q₈	C₂²×C₃²×D₃	semidirect
450. C₈	C₂²×C₃²×D₃	semidirect
459. C₂×C₃	C₃×#914	direct (N × H)
460. C₂×C₃	C₃²×AGL(1,ℤ/8)	semidirect
481. C₃	C₂×C₃×#914	direct (N × H)
482. C₃	C₂×C₃²×AGL(1,ℤ/8)	semidirect
487. C₂	C₃²×#914	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×C₃²×#239	2
C₂×C₃²×D₃×D₄	2
C₂×C₃³×SD₁₆	2
C₂×C₃²×#215	2
C₂×C₃²×#213	2
C₃²×#914	2
C₂×C₃²×D₂₄	2
C₂×C₃²×ΓL(1,𝔽₂₅)	2
C₂×C₃²×AGL(1,ℤ/8)	3
C₂×C₃×#914	3

Subgroups — C2×C32×#914 #13179136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×#914 #13179136