Subgroups — C₄₃×#20928 #24940945

Order 11008.

2046 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1880	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1879	C₂	1	4	yes	maximal, complemented
8	C₄₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1728	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×AGL(1,ℤ/8)×C₄₃	—	2	4	no	—
13	C₂×AGL(1,ℤ/8)×C₄₃	—	2	4	no	—
14	C₂×AGL(1,ℤ/8)×C₄₃	C₄	1	8	yes	complemented
15	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
16	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
17	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	C₄×#41×C₄₃	—	2	4	no	—
20	C₄×#41×C₄₃	—	2	4	no	—
21	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	complemented
22	C₂×C₄×D₄×C₄₃	—	2	2	no	—
23	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
24	C₂×#117×C₄₃	—	2	1	no	—
25	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₄₃	—	2	2	no	—
28	C₂²×C₄²×C₄₃	—	2	1	no	—
29	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#418	—	2	4	no	—
31	C₄₃×#417	—	2	4	no	—
32	C₂×#103×C₄₃	C₂²	1	2	yes	complemented
33	C₂×#102×C₄₃	C₂²	1	4	yes	—
34	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
35	C₄₃×#390	—	2	1	no	—
36	C₄₃×#390	—	2	1	no	—
37	C₄₃×#390	C₂²	1	4	yes	—
38	C₄₃×#340	C₂²	1	4	yes	complemented
39	C₄₃×#336	C₂²	1	4	yes	complemented
40	C₂⁵×C₄₃	—	2	1	no	—
41	C₂×#41×C₄₃	—	2	2	no	—
42	C₂×#41×C₄₃	—	2	2	no	—
43	C₂×#41×C₄₃	—	2	2	no	—
44	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
45	C₂×#41×C₄₃	D₄	1	4	yes	—
46	C₂×#41×C₄₃	D₄	1	4	yes	—
47	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₄₃	—	2	1	no	—
49	C₂²×D₄×C₄₃	—	2	2	no	—
50	C₂²×D₄×C₄₃	—	2	2	no	—
51	C₂²×D₄×C₄₃	—	2	2	no	—
52	C₂²×D₄×C₄₃	—	2	1	no	—
53	C₂²×D₄×C₄₃	—	2	2	no	—
54	C₂²×D₄×C₄₃	—	2	2	no	—
55	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	complemented
56	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
57	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₄₃	—	2	1	no	—
59	C₂³×C₄×C₄₃	—	2	2	no	—
60	C₂³×C₄×C₄₃	—	2	1	no	—
61	C₂³×C₄×C₄₃	D₄	1	2	yes	—
62	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
63	AGL(1,ℤ/8)×C₄₃	—	2	32	no	—
64	C₂×SD₁₆×C₄₃	—	2	4	no	—
65	C₂×SD₁₆×C₄₃	—	2	4	no	—
66	C₂×SD₁₆×C₄₃	C₂×C₄	1	8	yes	complemented
67	C₂×D₈×C₄₃	—	2	4	no	—
68	C₂×D₈×C₄₃	—	2	4	no	—
69	C₂×D₈×C₄₃	C₂×C₄	1	8	yes	complemented
70	C₂×M₁₆×C₄₃	—	2	2	no	—
71	C₂×M₁₆×C₄₃	—	2	2	no	—
72	C₂×M₁₆×C₄₃	—	2	2	no	—
73	C₂×M₁₆×C₄₃	—	2	2	no	—
74	C₂×M₁₆×C₄₃	—	2	2	no	—
75	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	complemented
76	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
77	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
78	C₄×Q₈×C₄₃	—	2	4	no	—
79	C₄×Q₈×C₄₃	—	2	4	no	—
80	C₄×D₄×C₄₃	—	2	16	no	—
81	C₄×D₄×C₄₃	—	2	4	no	—
82	C₄×D₄×C₄₃	—	2	4	no	—
83	#117×C₄₃	—	2	8	no	—
84	#117×C₄₃	—	2	2	no	—
85	#117×C₄₃	D₄	1	4	yes	—
86	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
89	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
95	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
96	C₂×C₂²⋊C₄×C₄₃	—	4	8	no	—
97	C₂×C₄²×C₄₃	—	2	8	no	—
98	C₂×C₄²×C₄₃	—	2	1	no	—
99	C₂×C₄²×C₄₃	—	2	2	no	—
100	C₂×C₄²×C₄₃	—	2	2	no	—
101	C₂×C₄²×C₄₃	—	2	2	no	—
102	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
105	#103×C₄₃	—	2	4	no	—
106	#102×C₄₃	—	2	4	no	—
107	#102×C₄₃	—	2	8	no	—
108	C₂⁴×C₄₃	—	2	1	no	—
109	C₂⁴×C₄₃	—	2	4	no	—
110	C₂⁴×C₄₃	—	2	2	no	—
111	C₂⁴×C₄₃	—	4	4	no	—
112	C₂⁴×C₄₃	—	4	4	no	—
113	C₂⁴×C₄₃	—	4	2	no	—
114	C₂⁴×C₄₃	—	4	2	no	—
115	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
116	#41×C₄₃	—	2	8	no	—
117	#41×C₄₃	—	2	8	no	—
118	#41×C₄₃	—	2	8	no	—
119	#41×C₄₃	C₂²⋊C₄	1	16	yes	complemented
120	C₂×Q₈×C₄₃	—	2	1	no	—
121	C₂×Q₈×C₄₃	—	2	1	no	—
122	C₂×Q₈×C₄₃	—	2	1	no	—
123	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
124	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
125	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
126	C₂×D₄×C₄₃	—	2	4	no	—
127	C₂×D₄×C₄₃	—	2	1	no	—
128	C₂×D₄×C₄₃	—	2	1	no	—
129	C₂×D₄×C₄₃	—	2	1	no	—
130	C₂×D₄×C₄₃	—	2	2	no	—
131	C₂×D₄×C₄₃	—	2	4	no	—
132	C₂×D₄×C₄₃	—	2	4	no	—
133	C₂×D₄×C₄₃	—	2	4	no	—
134	C₂×D₄×C₄₃	—	2	8	no	—
135	C₂×D₄×C₄₃	—	2	8	no	—
136	C₂×D₄×C₄₃	—	2	2	no	—
137	C₂×D₄×C₄₃	—	2	2	no	—
138	C₂×D₄×C₄₃	—	2	2	no	—
139	C₂×D₄×C₄₃	—	2	2	no	—
140	C₂×D₄×C₄₃	—	4	2	no	—
141	C₂×D₄×C₄₃	—	4	2	no	—
142	C₂×D₄×C₄₃	—	4	4	no	—
143	C₂×D₄×C₄₃	—	4	4	no	—
144	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
145	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
146	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
147	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₄₃	—	2	4	no	—
149	C₂²×C₄×C₄₃	—	2	4	no	—
150	C₂²×C₄×C₄₃	—	2	4	no	—
151	C₂²×C₄×C₄₃	—	2	8	no	—
152	C₂²×C₄×C₄₃	—	2	4	no	—
153	C₂²×C₄×C₄₃	—	2	4	no	—
154	C₂²×C₄×C₄₃	—	2	1	no	—
155	C₂²×C₄×C₄₃	—	2	2	no	—
156	C₂²×C₄×C₄₃	—	2	2	no	—
157	C₂²×C₄×C₄₃	—	4	2	no	—
158	C₂²×C₄×C₄₃	—	4	4	no	—
159	C₂²×C₄×C₄₃	—	4	4	no	—
160	C₂²×C₄×C₄₃	—	4	4	no	—
161	C₂²×C₄×C₄₃	—	4	2	no	—
162	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
163	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₄₃	#41	1	2	yes	—
170	C₂²×C₄×C₄₃	#41	1	2	yes	—
171	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
172	SD₁₆×C₄₃	—	2	16	no	—
173	D₈×C₄₃	—	2	16	no	—
174	M₁₆×C₄₃	—	2	8	no	—
175	M₁₆×C₄₃	—	4	4	no	—
176	C₂×C₈×C₄₃	—	2	2	no	—
177	C₂×C₈×C₄₃	—	2	2	no	—
178	C₂×C₈×C₄₃	—	2	2	no	—
179	C₂×C₈×C₄₃	—	2	2	no	—
180	C₂×C₈×C₄₃	—	2	2	no	—
181	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
182	C₄⋊C₄×C₄₃	—	2	8	no	—
183	C₄⋊C₄×C₄₃	—	2	2	no	—
184	C₄⋊C₄×C₄₃	—	2	2	no	—
185	C₄⋊C₄×C₄₃	—	2	2	no	—
186	C₄⋊C₄×C₄₃	—	4	2	no	—
187	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
188	C₂²⋊C₄×C₄₃	—	2	8	no	—
189	C₂²⋊C₄×C₄₃	—	2	4	no	—
190	C₂²⋊C₄×C₄₃	—	4	8	no	—
191	C₂²⋊C₄×C₄₃	—	4	8	no	—
192	C₄²×C₄₃	—	2	8	no	—
193	C₄²×C₄₃	—	2	2	no	—
194	C₄²×C₄₃	—	2	4	no	—
195	C₄²×C₄₃	—	2	2	no	—
196	C₄²×C₄₃	—	2	2	no	—
197	C₄²×C₄₃	—	2	2	no	—
198	C₂³×C₄₃	—	2	2	no	—
199	C₂³×C₄₃	—	2	2	no	—
200	C₂³×C₄₃	—	2	2	no	—
201	C₂³×C₄₃	—	2	2	no	—
202	C₂³×C₄₃	—	2	2	no	—
203	C₂³×C₄₃	—	2	4	no	—
204	C₂³×C₄₃	—	4	16	no	—
205	C₂³×C₄₃	—	4	2	no	—
206	C₂³×C₄₃	—	4	2	no	—
207	C₂³×C₄₃	—	4	2	no	—
208	C₂³×C₄₃	—	4	2	no	—
209	C₂³×C₄₃	—	4	4	no	—
210	C₂³×C₄₃	—	4	4	no	—
211	C₂³×C₄₃	—	4	8	no	—
212	C₂³×C₄₃	—	8	8	no	—
213	C₂³×C₄₃	—	8	4	no	—
214	C₂³×C₄₃	—	8	4	no	—
215	C₂³×C₄₃	C₄×D₄	1	2	yes	—
216	C₂³×C₄₃	#120	1	2	yes	—
217	C₂³×C₄₃	#121	1	2	yes	—
218	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
219	Q₈×C₄₃	—	2	2	no	—
220	Q₈×C₄₃	—	2	2	no	—
221	Q₈×C₄₃	—	2	2	no	—
222	Q₈×C₄₃	C₂×C₂²⋊C₄	1	4	yes	complemented
223	D₄×C₄₃	—	2	16	no	—
224	D₄×C₄₃	—	2	4	no	—
225	D₄×C₄₃	—	2	2	no	—
226	D₄×C₄₃	—	2	4	no	—
227	D₄×C₄₃	—	2	2	no	—
228	D₄×C₄₃	—	2	2	no	—
229	D₄×C₄₃	—	4	2	no	—
230	D₄×C₄₃	—	4	2	no	—
231	D₄×C₄₃	—	4	8	no	—
232	D₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	complemented
233	C₂×C₄×C₄₃	—	2	2	no	—
234	C₂×C₄×C₄₃	—	2	2	no	—
235	C₂×C₄×C₄₃	—	2	2	no	—
236	C₂×C₄×C₄₃	—	2	2	no	—
237	C₂×C₄×C₄₃	—	2	2	no	—
238	C₂×C₄×C₄₃	—	2	16	no	—
239	C₂×C₄×C₄₃	—	2	2	no	—
240	C₂×C₄×C₄₃	—	2	4	no	—
241	C₂×C₄×C₄₃	—	2	2	no	—
242	C₂×C₄×C₄₃	—	2	2	no	—
243	C₂×C₄×C₄₃	—	4	8	no	—
244	C₂×C₄×C₄₃	—	4	16	no	—
245	C₂×C₄×C₄₃	—	4	2	no	—
246	C₂×C₄×C₄₃	—	4	2	no	—
247	C₂×C₄×C₄₃	—	4	2	no	—
248	C₂×C₄×C₄₃	—	4	4	no	—
249	C₂×C₄×C₄₃	—	8	4	no	—
250	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
251	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
252	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
253	C₂×C₄×C₄₃	#120	1	2	yes	—
254	C₂×C₄×C₄₃	#121	1	4	yes	—
255	C₂×C₄×C₄₃	#121	1	2	yes	—
256	C₂×C₄×C₄₃	#123	1	4	yes	—
257	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	complemented
258	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
259	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
264	C₈×C₄₃	—	2	4	no	—
265	C₈×C₄₃	—	4	2	no	—
266	#20928	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂²×C₄₃	—	2	4	no	—
268	C₂²×C₄₃	—	2	4	no	—
269	C₂²×C₄₃	—	2	2	no	—
270	C₂²×C₄₃	—	2	2	no	—
271	C₂²×C₄₃	—	2	4	no	—
272	C₂²×C₄₃	—	4	4	no	—
273	C₂²×C₄₃	—	4	4	no	—
274	C₂²×C₄₃	—	4	2	no	—
275	C₂²×C₄₃	—	4	2	no	—
276	C₂²×C₄₃	—	4	8	no	—
277	C₂²×C₄₃	—	4	4	no	—
278	C₂²×C₄₃	—	8	16	no	—
279	C₂²×C₄₃	—	8	4	no	—
280	C₂²×C₄₃	—	8	2	no	—
281	C₂²×C₄₃	—	8	2	no	—
282	C₂²×C₄₃	#386	1	4	yes	—
283	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
284	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
285	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
286	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
287	C₂²×C₄₃	#575	1	2	yes	—
288	C₄×C₄₃	—	2	4	no	—
289	C₄×C₄₃	—	2	4	no	—
290	C₄×C₄₃	—	4	2	no	—
291	C₄×C₄₃	—	4	4	no	—
292	C₄×C₄₃	—	8	2	no	—
293	C₄×C₄₃	#386	1	4	yes	—
294	C₄×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
295	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
296	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
297	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
298	C₂²×AGL(1,ℤ/8)	C₂×C₄₃	1	1	yes	characteristic
299	C₂×C₄×#41	C₂×C₄₃	1	1	yes	characteristic, complemented
300	C₂×#417	C₂×C₄₃	1	1	yes	characteristic, complemented
301	C₂×#418	C₂×C₄₃	1	1	yes	characteristic, complemented
302	C₂×#390	C₂×C₄₃	1	1	yes	characteristic, complemented
303	#1880	C₂×C₄₃	1	4	yes	complemented
304	#1879	C₂×C₄₃	1	4	yes	complemented
305	#1736	C₂×C₄₃	1	1	yes	characteristic, complemented
306	#1728	C₂×C₄₃	1	1	yes	characteristic, complemented
307	C₂×C₄₃	—	2	4	no	—
308	C₂×C₄₃	—	4	4	no	—
309	C₂×C₄₃	—	8	4	no	—
310	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
311	C₂×C₄₃	C₄×AGL(1,ℤ/8)	1	2	yes	—
312	C₂×C₄₃	#3006	1	2	yes	—
313	C₂×C₄₃	#3038	1	1	yes	characteristic
314	C₂×C₄₃	#3040	1	1	yes	characteristic
315	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
316	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
317	C₂×AGL(1,ℤ/8)	—	2	4	no	—
318	C₂×AGL(1,ℤ/8)	—	2	4	no	—
319	C₂×AGL(1,ℤ/8)	C₄×C₄₃	1	8	yes	complemented
320	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
321	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
322	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
323	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
324	C₄×#41	—	2	4	no	—
325	C₄×#41	—	2	4	no	—
326	C₂×C₄×Q₈	C₂²×C₄₃	1	2	yes	complemented
327	C₂×C₄×D₄	—	2	2	no	—
328	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	complemented
329	C₂×#117	—	2	1	no	—
330	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
331	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
332	C₂²×C₂²⋊C₄	—	2	2	no	—
333	C₂²×C₄²	—	2	1	no	—
334	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
335	#418	—	2	4	no	—
336	#417	—	2	4	no	—
337	C₂×#103	C₂²×C₄₃	1	2	yes	complemented
338	C₂×#102	C₂²×C₄₃	1	4	yes	—
339	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
340	#390	—	2	1	no	—
341	#390	—	2	1	no	—
342	#390	C₂²×C₄₃	1	4	yes	—
343	#340	C₂²×C₄₃	1	4	yes	complemented
344	#336	C₂²×C₄₃	1	4	yes	complemented
345	C₄₃	#20928	1	1	yes	characteristic, direct product factor, Sylow
346	C₂⁵	—	2	1	no	—
347	C₂×#41	—	2	2	no	—
348	C₂×#41	—	2	2	no	—
349	C₂×#41	—	2	2	no	—
350	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
351	C₂×#41	D₄×C₄₃	1	4	yes	—
352	C₂×#41	D₄×C₄₃	1	4	yes	—
353	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
354	C₂²×D₄	—	2	1	no	—
355	C₂²×D₄	—	2	2	no	—
356	C₂²×D₄	—	2	2	no	—
357	C₂²×D₄	—	2	2	no	—
358	C₂²×D₄	—	2	1	no	—
359	C₂²×D₄	—	2	2	no	—
360	C₂²×D₄	—	2	2	no	—
361	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	complemented
362	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
363	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
364	C₂³×C₄	—	2	1	no	—
365	C₂³×C₄	—	2	2	no	—
366	C₂³×C₄	—	2	1	no	—
367	C₂³×C₄	D₄×C₄₃	1	2	yes	—
368	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
369	AGL(1,ℤ/8)	—	2	32	no	—
370	C₂×SD₁₆	—	2	4	no	—
371	C₂×SD₁₆	—	2	4	no	—
372	C₂×SD₁₆	C₂×C₄×C₄₃	1	8	yes	complemented
373	C₂×D₈	—	2	4	no	—
374	C₂×D₈	—	2	4	no	—
375	C₂×D₈	C₂×C₄×C₄₃	1	8	yes	complemented
376	C₂×M₁₆	—	2	2	no	—
377	C₂×M₁₆	—	2	2	no	—
378	C₂×M₁₆	—	2	2	no	—
379	C₂×M₁₆	—	2	2	no	—
380	C₂×M₁₆	—	2	2	no	—
381	C₂×M₁₆	C₂×C₄×C₄₃	1	4	yes	complemented
382	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
383	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
384	C₄×Q₈	—	2	4	no	—
385	C₄×Q₈	—	2	4	no	—
386	C₄×D₄	—	2	16	no	—
387	C₄×D₄	—	2	4	no	—
388	C₄×D₄	—	2	4	no	—
389	#117	—	2	8	no	—
390	#117	—	2	2	no	—
391	#117	D₄×C₄₃	1	4	yes	—
392	C₂×C₄⋊C₄	—	2	2	no	—
393	C₂×C₄⋊C₄	—	2	2	no	—
394	C₂×C₄⋊C₄	—	2	2	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	2	no	—
400	C₂×C₂²⋊C₄	—	2	4	no	—
401	C₂×C₂²⋊C₄	—	2	4	no	—
402	C₂×C₂²⋊C₄	—	4	8	no	—
403	C₂×C₄²	—	2	8	no	—
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	—	2	2	no	—
406	C₂×C₄²	—	2	2	no	—
407	C₂×C₄²	—	2	2	no	—
408	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
409	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
411	#103	—	2	4	no	—
412	#102	—	2	4	no	—
413	#102	—	2	8	no	—
414	C₂⁴	—	2	1	no	—
415	C₂⁴	—	2	4	no	—
416	C₂⁴	—	2	2	no	—
417	C₂⁴	—	4	4	no	—
418	C₂⁴	—	4	4	no	—
419	C₂⁴	—	4	2	no	—
420	C₂⁴	—	4	2	no	—
421	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
422	#41	—	2	8	no	—
423	#41	—	2	8	no	—
424	#41	—	2	8	no	—
425	#41	C₂²⋊C₄×C₄₃	1	16	yes	complemented
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
430	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
431	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	2	4	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	8	no	—
436	C₂×D₄	—	2	8	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	4	2	no	—
447	C₂×D₄	—	4	4	no	—
448	C₂×D₄	—	4	2	no	—
449	C₂×D₄	—	4	4	no	—
450	C₂×D₄	C₂²×C₄×C₄₃	1	4	yes	—
451	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
452	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
453	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	8	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	4	2	no	—
464	C₂²×C₄	—	4	4	no	—
465	C₂²×C₄	—	4	4	no	—
466	C₂²×C₄	—	4	4	no	—
467	C₂²×C₄	—	4	2	no	—
468	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
469	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
470	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
471	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
472	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
473	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
475	C₂²×C₄	#41×C₄₃	1	2	yes	—
476	C₂²×C₄	#41×C₄₃	1	2	yes	—
477	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
478	SD₁₆	—	2	16	no	—
479	D₈	—	2	16	no	—
480	M₁₆	—	2	8	no	—
481	M₁₆	—	4	4	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	2	2	no	—
487	C₂×C₈	C₂²×C₄×C₄₃	1	4	yes	—
488	C₄⋊C₄	—	2	8	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	4	2	no	—
493	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
494	C₂²⋊C₄	—	2	8	no	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	4	8	no	—
497	C₂²⋊C₄	—	4	8	no	—
498	C₄²	—	2	8	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	4	no	—
501	C₄²	—	2	2	no	—
502	C₄²	—	2	2	no	—
503	C₄²	—	2	2	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	2	2	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	4	16	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	4	4	no	—
516	C₂³	—	4	4	no	—
517	C₂³	—	4	8	no	—
518	C₂³	—	8	8	no	—
519	C₂³	—	8	4	no	—
520	C₂³	—	8	4	no	—
521	C₂³	C₄×D₄×C₄₃	1	2	yes	—
522	C₂³	#120×C₄₃	1	2	yes	—
523	C₂³	#121×C₄₃	1	2	yes	—
524	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
525	Q₈	—	2	2	no	—
526	Q₈	—	2	2	no	—
527	Q₈	—	2	2	no	—
528	Q₈	C₂×C₂²⋊C₄×C₄₃	1	4	yes	complemented
529	D₄	—	2	16	no	—
530	D₄	—	2	4	no	—
531	D₄	—	2	2	no	—
532	D₄	—	2	4	no	—
533	D₄	—	2	2	no	—
534	D₄	—	2	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	8	no	—
538	D₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	complemented
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	16	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	4	8	no	—
550	C₂×C₄	—	4	16	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	8	4	no	—
556	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
557	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
558	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
559	C₂×C₄	#120×C₄₃	1	2	yes	—
560	C₂×C₄	#121×C₄₃	1	4	yes	—
561	C₂×C₄	#121×C₄₃	1	2	yes	—
562	C₂×C₄	#123×C₄₃	1	4	yes	—
563	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	4	yes	complemented
564	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
565	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
566	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
568	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
569	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
570	C₈	—	2	4	no	—
571	C₈	—	4	2	no	—
572	C₂²	—	2	4	no	—
573	C₂²	—	2	4	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	4	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	4	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	8	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	8	16	no	—
584	C₂²	—	8	4	no	—
585	C₂²	—	8	2	no	—
586	C₂²	—	8	2	no	—
587	C₂²	C₄₃×#386	1	4	yes	—
588	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
589	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
590	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
591	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
592	C₂²	C₄₃×#575	1	2	yes	—
593	C₄	—	2	4	no	—
594	C₄	—	2	4	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	4	no	—
597	C₄	—	8	2	no	—
598	C₄	C₄₃×#386	1	4	yes	—
599	C₄	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
600	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
601	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
602	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
603	C₂	—	2	4	no	—
604	C₂	—	4	4	no	—
605	C₂	—	8	4	no	—
606	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
607	C₂	C₄×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
608	C₂	C₄₃×#3006	1	2	yes	—
609	C₂	C₄₃×#3038	1	1	yes	characteristic
610	C₂	C₄₃×#3040	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×AGL(1,ℤ/8)×C₄₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₄₃	C₂	semidirect
3. C₂×C₄₃×#417	C₂	semidirect
4. C₂×C₄₃×#418	C₂	semidirect
5. C₂×C₄₃×#390	C₂	semidirect
6. C₄₃×#1880	C₂	semidirect
7. C₄₃×#1879	C₂	semidirect
8. C₄₃×#1736	C₂	semidirect
9. C₄₃×#1728	C₂	semidirect
14. C₂×AGL(1,ℤ/8)×C₄₃	C₄	semidirect
21. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
23. C₂×C₄×D₄×C₄₃	C₂²	semidirect
32. C₂×#103×C₄₃	C₂²	semidirect
34. C₂×#102×C₄₃	C₂²	semidirect
38. C₄₃×#340	C₂²	semidirect
39. C₄₃×#336	C₂²	semidirect
55. C₂²×D₄×C₄₃	C₂×C₄	semidirect
66. C₂×SD₁₆×C₄₃	C₂×C₄	semidirect
69. C₂×D₈×C₄₃	C₂×C₄	semidirect
75. C₂×M₁₆×C₄₃	C₂×C₄	semidirect
119. #41×C₄₃	C₂²⋊C₄	semidirect
222. Q₈×C₄₃	C₂×C₂²⋊C₄	semidirect
232. D₄×C₄₃	C₂×C₂²⋊C₄	semidirect
257. C₂×C₄×C₄₃	AGL(1,ℤ/8)	semidirect
266. #20928	C₄₃	direct (N × H)
299. C₂×C₄×#41	C₂×C₄₃	semidirect
300. C₂×#417	C₂×C₄₃	semidirect
301. C₂×#418	C₂×C₄₃	semidirect
302. C₂×#390	C₂×C₄₃	semidirect
303. #1880	C₂×C₄₃	semidirect
304. #1879	C₂×C₄₃	semidirect
305. #1736	C₂×C₄₃	semidirect
306. #1728	C₂×C₄₃	semidirect
319. C₂×AGL(1,ℤ/8)	C₄×C₄₃	semidirect
326. C₂×C₄×Q₈	C₂²×C₄₃	semidirect
328. C₂×C₄×D₄	C₂²×C₄₃	semidirect
337. C₂×#103	C₂²×C₄₃	semidirect
339. C₂×#102	C₂²×C₄₃	semidirect
343. #340	C₂²×C₄₃	semidirect
344. #336	C₂²×C₄₃	semidirect
345. C₄₃	#20928	direct (N × H)
361. C₂²×D₄	C₂×C₄×C₄₃	semidirect
372. C₂×SD₁₆	C₂×C₄×C₄₃	semidirect
375. C₂×D₈	C₂×C₄×C₄₃	semidirect
381. C₂×M₁₆	C₂×C₄×C₄₃	semidirect
425. #41	C₂²⋊C₄×C₄₃	semidirect
528. Q₈	C₂×C₂²⋊C₄×C₄₃	semidirect
538. D₄	C₂×C₂²⋊C₄×C₄₃	semidirect
563. C₂×C₄	AGL(1,ℤ/8)×C₄₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×AGL(1,ℤ/8)×C₄₃	2
C₂×C₄×#41×C₄₃	2
C₂×C₄₃×#417	2
C₂×C₄₃×#418	2
C₂×C₄₃×#390	2
C₄₃×#1880	2
C₄₃×#1879	2
C₄₃×#1736	2
C₄₃×#1728	2
#20928	43

Subgroups — C43×#20928 #24940945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20928 #24940945