Subgroups — C₃×C₈×#123 #10640167

Order 768.

1034 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×#123	C₂	1	1	yes	maximal, characteristic
4	C₃×#1923	C₂	1	2	yes	maximal, complemented
5	C₃×#1916	C₂	1	2	yes	maximal, complemented
6	C₃×#1869	C₂	1	1	yes	maximal, characteristic
7	C₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1817	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₈×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₃×C₈×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₃×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×#123	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×#123	C₄	1	1	yes	characteristic
17	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
19	C₃×C₈×D₄	—	2	4	no	—
20	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×C₈	—	2	4	no	—
27	C₂×C₃×C₄×C₈	C₂²	1	2	yes	—
28	C₂×C₃×C₄×C₈	C₂²	1	2	yes	—
29	C₂×C₃×C₄×C₈	C₂²	1	2	yes	—
30	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
31	C₃×#388	C₄	1	2	yes	—
32	C₃×#387	C₄	1	2	yes	—
33	C₃×#386	C₄	1	1	yes	characteristic
34	C₃×#385	C₄	1	1	yes	characteristic
35	C₃×#381	C₄	1	1	yes	characteristic
36	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
37	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₃×#336	C₂²	1	2	yes	—
40	C₃×#336	C₂²	1	2	yes	—
41	C₃×#336	C₂²	1	2	yes	—
42	C₃×#336	C₂²	1	2	yes	—
43	C₃×#336	C₂²	1	2	yes	—
44	C₂×C₈×D₄	C₂×C₃	1	1	yes	characteristic
45	C₂²×C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
46	C₄×#123	C₂×C₃	1	1	yes	characteristic
47	#1923	C₂×C₃	1	2	yes	complemented
48	#1916	C₂×C₃	1	2	yes	complemented
49	#1869	C₂×C₃	1	1	yes	characteristic
50	#1850	C₂×C₃	1	1	yes	characteristic, complemented
51	#1817	C₂×C₃	1	1	yes	characteristic, complemented
52	C₈×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
53	C₈×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
54	C₈×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
59	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₈	—	2	2	no	—
61	C₂²×C₃×C₈	—	2	4	no	—
62	C₂²×C₃×C₈	—	2	4	no	—
63	C₂²×C₃×C₈	—	2	2	no	—
64	C₂²×C₃×C₈	—	2	4	no	—
65	C₂²×C₃×C₈	D₄	1	4	yes	—
66	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₃×C₈	C₂³	1	2	yes	—
69	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₈	C₂³	1	2	yes	—
71	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
72	C₃×#123	C₈	1	8	yes	direct product factor
73	C₃×C₄×D₄	—	2	2	no	—
74	C₃×C₄×D₄	—	2	2	no	—
75	C₂×C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
76	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
78	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
80	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
84	C₂×C₃×C₄²	—	2	2	no	—
85	C₂×C₃×C₄²	—	2	2	no	—
86	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
87	C₂×C₃×C₄²	C₂³	1	2	yes	—
88	C₂×C₃×C₄²	C₂³	1	2	yes	—
89	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
90	C₃×C₄⋊C₈	—	2	2	no	—
91	C₃×C₄⋊C₈	—	2	4	no	—
92	C₃×C₂²⋊C₈	—	2	2	no	—
93	C₃×C₂²⋊C₈	—	2	2	no	—
94	C₃×C₂²⋊C₈	—	2	2	no	—
95	C₃×C₂²⋊C₈	—	2	4	no	—
96	C₃×C₄×C₈	—	2	4	no	—
97	C₃×C₄×C₈	—	2	4	no	—
98	C₃×C₄×C₈	—	2	2	no	—
99	C₃×C₄×C₈	—	2	4	no	—
100	C₃×#95	C₂×C₄	1	2	yes	—
101	C₃×#95	C₂×C₄	1	2	yes	—
102	C₃×#95	C₂×C₄	1	2	yes	—
103	C₃×#95	C₂×C₄	1	2	yes	—
104	C₃×#95	C₂×C₄	1	2	yes	—
105	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
106	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
107	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
108	C₂×#123	C₃×C₄	1	1	yes	characteristic
109	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
110	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
111	C₈×D₄	—	2	4	no	—
112	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	—
113	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
117	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₄×C₈	—	2	4	no	—
119	C₂×C₄×C₈	C₂²×C₃	1	2	yes	—
120	C₂×C₄×C₈	C₂²×C₃	1	2	yes	—
121	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₄×C₈	C₂²×C₃	1	2	yes	—
123	#388	C₃×C₄	1	2	yes	—
124	#387	C₃×C₄	1	2	yes	—
125	#386	C₃×C₄	1	1	yes	characteristic
126	#385	C₃×C₄	1	1	yes	characteristic
127	#381	C₃×C₄	1	1	yes	characteristic
128	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
129	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
131	#336	C₂²×C₃	1	2	yes	—
132	#336	C₂²×C₃	1	2	yes	—
133	#336	C₂²×C₃	1	2	yes	—
134	#336	C₂²×C₃	1	2	yes	—
135	#336	C₂²×C₃	1	2	yes	—
136	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
137	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃×D₄	—	2	2	no	—
139	C₂×C₃×D₄	—	2	2	no	—
140	C₂×C₃×D₄	C₂×C₈	1	4	yes	—
141	C₂²×C₃×C₄	—	2	2	no	—
142	C₂²×C₃×C₄	—	2	2	no	—
143	C₂²×C₃×C₄	—	2	2	no	—
144	C₂²×C₃×C₄	—	2	4	no	—
145	C₂²×C₃×C₄	—	2	2	no	—
146	C₂²×C₃×C₄	—	2	2	no	—
147	C₂²×C₃×C₄	—	2	1	no	—
148	C₂²×C₃×C₄	—	2	2	no	—
149	C₂²×C₃×C₄	—	2	1	no	—
150	C₂²×C₃×C₄	—	2	2	no	—
151	C₂²×C₃×C₄	C₂×C₈	1	4	yes	complemented
152	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
153	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
157	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
158	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
160	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
161	C₂²×C₃×C₄	#41	1	2	yes	—
162	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
163	C₂×C₃×C₈	—	2	8	no	—
164	C₂×C₃×C₈	—	2	2	no	—
165	C₂×C₃×C₈	—	2	2	no	—
166	C₂×C₃×C₈	—	2	2	no	—
167	C₂×C₃×C₈	—	2	8	no	—
168	C₂×C₃×C₈	—	2	1	no	—
169	C₂×C₃×C₈	—	2	1	no	—
170	C₂×C₃×C₈	—	2	2	no	—
171	C₂×C₃×C₈	—	2	2	no	—
172	C₂×C₃×C₈	—	2	2	no	—
173	C₂×C₃×C₈	—	2	2	no	—
174	C₂×C₃×C₈	—	2	2	no	—
175	C₂×C₃×C₈	—	4	4	no	—
176	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
177	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
178	C₂×C₃×C₈	#41	1	4	yes	—
179	C₂×C₃×C₈	#41	1	4	yes	—
180	C₃×C₄⋊C₄	—	2	2	no	—
181	C₃×C₄⋊C₄	—	2	4	no	—
182	C₃×C₄⋊C₄	C₂×C₈	1	8	yes	complemented
183	C₃×C₂²⋊C₄	—	2	2	no	—
184	C₃×C₂²⋊C₄	—	2	2	no	—
185	C₃×C₂²⋊C₄	—	2	2	no	—
186	C₃×C₂²⋊C₄	—	2	4	no	—
187	C₃×C₂²⋊C₄	C₂×C₈	1	4	yes	complemented
188	C₃×C₂²⋊C₄	C₂×C₈	1	8	yes	complemented
189	C₃×C₄²	—	2	4	no	—
190	C₃×C₄²	—	2	2	no	—
191	C₃×C₄²	—	2	1	no	—
192	C₃×C₄²	—	2	2	no	—
193	C₃×C₄²	—	2	2	no	—
194	C₃×C₄²	—	2	2	no	—
195	C₃×C₄²	—	2	1	no	—
196	C₂²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
197	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
198	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
199	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
200	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
201	C₂²×C₈	—	2	2	no	—
202	C₂²×C₈	—	2	4	no	—
203	C₂²×C₈	—	2	4	no	—
204	C₂²×C₈	—	2	2	no	—
205	C₂²×C₈	—	2	4	no	—
206	C₂²×C₈	C₃×D₄	1	4	yes	—
207	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
208	C₂²×C₈	C₂³×C₃	1	2	yes	—
209	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
210	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
211	C₂²×C₈	C₂³×C₃	1	2	yes	—
212	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
213	#123	C₃×C₈	1	8	yes	direct product factor
214	C₄×D₄	—	2	2	no	—
215	C₄×D₄	—	2	2	no	—
216	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
218	C₂×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
219	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
220	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
221	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
222	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
223	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
224	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
225	C₂×C₄²	—	2	2	no	—
226	C₂×C₄²	—	2	2	no	—
227	C₂×C₄²	C₂×C₃×C₄	1	2	yes	—
228	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₃	1	2	yes	—
230	C₂×C₄²	C₂³×C₃	1	2	yes	—
231	C₄⋊C₈	—	2	2	no	—
232	C₄⋊C₈	—	2	4	no	—
233	C₂²⋊C₈	—	2	2	no	—
234	C₂²⋊C₈	—	2	2	no	—
235	C₂²⋊C₈	—	2	2	no	—
236	C₂²⋊C₈	—	2	4	no	—
237	C₄×C₈	—	2	4	no	—
238	C₄×C₈	—	2	4	no	—
239	C₄×C₈	—	2	2	no	—
240	C₄×C₈	—	2	4	no	—
241	#95	C₂×C₃×C₄	1	2	yes	—
242	#95	C₂×C₃×C₄	1	2	yes	—
243	#95	C₂×C₃×C₄	1	2	yes	—
244	#95	C₂×C₃×C₄	1	2	yes	—
245	#95	C₂×C₃×C₄	1	2	yes	—
246	C₂³×C₃	—	2	2	no	—
247	C₂³×C₃	—	2	2	no	—
248	C₂³×C₃	—	2	1	no	—
249	C₂³×C₃	—	2	2	no	—
250	C₂³×C₃	—	2	2	no	—
251	C₂³×C₃	—	2	1	no	—
252	C₂³×C₃	C₄×D₄	1	2	yes	—
253	C₂³×C₃	C₂²×C₈	1	2	yes	—
254	C₂³×C₃	C₂²×C₈	1	2	yes	—
255	C₂³×C₃	#131	1	2	yes	—
256	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
257	C₃×D₄	—	2	8	no	—
258	C₂×C₃×C₄	—	2	8	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	8	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	4	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	4	1	no	—
280	C₂×C₃×C₄	—	4	1	no	—
281	C₂×C₃×C₄	—	4	2	no	—
282	C₂×C₃×C₄	C₄×D₄	1	2	yes	—
283	C₂×C₃×C₄	C₂²×C₈	1	4	yes	—
284	C₂×C₃×C₄	C₂²×C₈	1	4	yes	—
285	C₂×C₃×C₄	C₂²×C₈	1	2	yes	—
286	C₂×C₃×C₄	#131	1	4	yes	—
287	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂×#41	1	2	yes	—
289	C₂×C₃×C₄	C₂×#41	1	2	yes	—
290	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
291	C₃×C₈	—	2	2	no	—
292	C₃×C₈	—	2	4	no	—
293	C₃×C₈	—	4	1	no	—
294	C₃×C₈	—	4	1	no	—
295	C₃×C₈	—	4	2	no	—
296	C₃×C₈	#123	1	4	yes	direct product factor
297	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
298	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	C₂×C₃×C₈	1	4	yes	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	C₂×C₃×C₈	1	4	yes	complemented
313	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
314	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
315	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
316	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
318	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
319	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
320	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
321	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
322	C₂²×C₄	C₃×#41	1	2	yes	—
323	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
324	C₂×C₈	—	2	8	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	8	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	4	4	no	—
337	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
338	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
339	C₂×C₈	C₃×#41	1	4	yes	—
340	C₂×C₈	C₃×#41	1	4	yes	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	C₂×C₃×C₈	1	8	yes	complemented
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	2	2	no	—
347	C₂²⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	C₂×C₃×C₈	1	4	yes	complemented
349	C₂²⋊C₄	C₂×C₃×C₈	1	8	yes	complemented
350	C₄²	—	2	4	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	1	no	—
357	C₂²×C₃	—	2	2	no	—
358	C₂²×C₃	—	2	4	no	—
359	C₂²×C₃	—	2	4	no	—
360	C₂²×C₃	—	2	2	no	—
361	C₂²×C₃	—	2	2	no	—
362	C₂²×C₃	—	2	4	no	—
363	C₂²×C₃	—	4	1	no	—
364	C₂²×C₃	—	4	2	no	—
365	C₂²×C₃	—	4	1	no	—
366	C₂²×C₃	C₈×D₄	1	4	yes	—
367	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
368	C₂²×C₃	C₄×#41	1	2	yes	—
369	C₂²×C₃	C₂³×C₈	1	1	yes	characteristic
370	C₂²×C₃	C₂×#131	1	1	yes	characteristic
371	C₂²×C₃	C₂×#131	1	2	yes	—
372	C₃×C₄	—	2	4	no	—
373	C₃×C₄	—	2	2	no	—
374	C₃×C₄	—	2	4	no	—
375	C₃×C₄	—	2	4	no	—
376	C₃×C₄	—	2	2	no	—
377	C₃×C₄	—	4	1	no	—
378	C₃×C₄	—	4	2	no	—
379	C₃×C₄	—	4	1	no	—
380	C₃×C₄	C₂×#123	1	1	yes	characteristic
381	C₃×C₄	#525	1	1	yes	characteristic
382	C₃×C₄	#529	1	2	yes	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	2	no	—
389	C₂³	C₃×C₄×D₄	1	2	yes	—
390	C₂³	C₂²×C₃×C₈	1	2	yes	—
391	C₂³	C₂²×C₃×C₈	1	2	yes	—
392	C₂³	C₃×#131	1	2	yes	—
393	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
394	D₄	—	2	8	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	C₃×C₄×D₄	1	2	yes	—
420	C₂×C₄	C₂²×C₃×C₈	1	4	yes	—
421	C₂×C₄	C₂²×C₃×C₈	1	4	yes	—
422	C₂×C₄	C₂²×C₃×C₈	1	2	yes	—
423	C₂×C₄	C₃×#131	1	4	yes	—
424	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
425	C₂×C₄	C₂×C₃×#41	1	2	yes	—
426	C₂×C₄	C₂×C₃×#41	1	2	yes	—
427	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
428	C₈	—	2	2	no	—
429	C₈	—	2	4	no	—
430	C₈	—	4	1	no	—
431	C₈	—	4	1	no	—
432	C₈	—	4	2	no	—
433	C₈	C₃×#123	1	4	yes	direct product factor
434	C₂×C₃	—	2	4	no	—
435	C₂×C₃	—	4	2	no	—
436	C₂×C₃	C₄×#123	1	1	yes	characteristic
437	C₂×C₃	C₂×C₈×D₄	1	1	yes	characteristic
438	C₂×C₃	#2929	1	1	yes	characteristic
439	C₂×C₃	C₈×#41	1	2	yes	—
440	C₂×C₃	#2966	1	2	yes	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	1	no	—
450	C₂²	C₃×C₈×D₄	1	4	yes	—
451	C₂²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
452	C₂²	C₃×C₄×#41	1	2	yes	—
453	C₂²	C₂³×C₃×C₈	1	1	yes	characteristic
454	C₂²	C₂×C₃×#131	1	1	yes	characteristic
455	C₂²	C₂×C₃×#131	1	2	yes	—
456	C₄	—	2	4	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	4	no	—
459	C₄	—	2	4	no	—
460	C₄	—	2	2	no	—
461	C₄	—	4	1	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	1	no	—
464	C₄	C₂×C₃×#123	1	1	yes	characteristic
465	C₄	C₃×#525	1	1	yes	characteristic
466	C₄	C₃×#529	1	2	yes	—
467	C₃	C₈×#123	1	1	yes	characteristic, direct product factor, Sylow
468	C₂	—	2	4	no	—
469	C₂	—	4	2	no	—
470	C₂	C₃×C₄×#123	1	1	yes	characteristic
471	C₂	C₂×C₃×C₈×D₄	1	1	yes	characteristic
472	C₂	C₃×#2929	1	1	yes	characteristic
473	C₂	C₃×C₈×#41	1	2	yes	—
474	C₂	C₃×#2966	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₈	C₂³
commutator	C₂²	C₂³×C₃×C₈
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
socle	C₂³×C₃	C₂³×C₄
prime radical	C₂²×C₃×D₄	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₄×C₈	C₂	semidirect
4. C₃×#1923	C₂	semidirect
5. C₃×#1916	C₂	semidirect
7. C₃×#1850	C₂	semidirect
8. C₃×#1817	C₂	semidirect
9. C₃×C₈×C₄⋊C₄	C₂	semidirect
10. C₃×C₈×C₂²⋊C₄	C₂	semidirect
11. C₃×C₈×C₂²⋊C₄	C₂	semidirect
12. C₈×#123	C₃	direct (N × H)
45. C₂²×C₄×C₈	C₂×C₃	semidirect
47. #1923	C₂×C₃	semidirect
48. #1916	C₂×C₃	semidirect
50. #1850	C₂×C₃	semidirect
51. #1817	C₂×C₃	semidirect
52. C₈×C₄⋊C₄	C₂×C₃	semidirect
53. C₈×C₂²⋊C₄	C₂×C₃	semidirect
54. C₈×C₂²⋊C₄	C₂×C₃	semidirect
72. C₃×#123	C₈	direct (N × H)
151. C₂²×C₃×C₄	C₂×C₈	semidirect
182. C₃×C₄⋊C₄	C₂×C₈	semidirect
187. C₃×C₂²⋊C₄	C₂×C₈	semidirect
188. C₃×C₂²⋊C₄	C₂×C₈	semidirect
213. #123	C₃×C₈	direct (N × H)
296. C₃×C₈	#123	direct (N × H)
312. C₂²×C₄	C₂×C₃×C₈	semidirect
343. C₄⋊C₄	C₂×C₃×C₈	semidirect
348. C₂²⋊C₄	C₂×C₃×C₈	semidirect
349. C₂²⋊C₄	C₂×C₃×C₈	semidirect
433. C₈	C₃×#123	direct (N × H)
467. C₃	C₈×#123	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×C₈×D₄	2
C₂²×C₃×C₄×C₈	2
C₃×C₄×#123	2
C₃×#1923	2
C₃×#1916	2
C₃×#1869	2
C₃×#1850	2
C₃×#1817	2
C₃×C₈×C₄⋊C₄	2
C₃×C₈×C₂²⋊C₄	2
C₈×#123	3

Subgroups — C3×C8×#123 #10640167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈×#123 #10640167