Subgroups — #440×Dic₄₃ #25095090

Order 11008.

1206 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583000	C₂	1	1	yes	maximal, characteristic
2	C₂×SD₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₄×Dic₄₃	C₂	1	1	yes	maximal, characteristic
5	#19134494	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134492	C₂	1	1	yes	maximal, characteristic, complemented
7	#107×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134427	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134425	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134422	C₂	1	1	yes	maximal, characteristic
11	#19134420	C₂	1	1	yes	maximal, characteristic
12	#103×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#102×Dic₄₃	C₂	1	1	yes	maximal, characteristic
14	#97×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₃×#440	C₂	1	1	yes	maximal, characteristic
16	C₂×Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
17	C₂×Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
18	C₂×D₄×Dic₄₃	C₂²	1	1	yes	characteristic
19	C₂×D₄×Dic₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄×Dic₄₃	—	2	1	no	—
21	#14583000	C₄	1	8	yes	complemented
22	SD₁₆×Dic₄₃	C₄	1	8	yes	complemented
23	C₂×#13063259	C₂²	1	1	yes	characteristic
24	C₂×#13063257	C₂²	1	1	yes	characteristic
25	C₂×#13063249	C₂²	1	1	yes	characteristic
26	C₂×#13063249	C₂²	1	1	yes	characteristic
27	C₂×#13063246	C₂²	1	1	yes	characteristic
28	C₂×#13063246	C₂²	1	1	yes	characteristic
29	C₂×#13063236	C₂²	1	1	yes	characteristic
30	C₂×#13063235	C₂²	1	1	yes	characteristic
31	C₂×#13063235	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
34	C₄⋊C₄×Dic₄₃	—	2	1	no	—
35	C₄⋊C₄×Dic₄₃	—	2	1	no	—
36	C₄⋊C₄×Dic₄₃	C₂²	1	1	yes	characteristic
37	C₄⋊C₄×Dic₄₃	C₂²	1	1	yes	characteristic
38	C₄⋊C₄×Dic₄₃	C₂²	1	1	yes	characteristic
39	C₄⋊C₄×Dic₄₃	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊Dic₄₃	—	2	1	no	—
41	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
43	C₂²⋊C₄×Dic₄₃	—	2	1	no	—
44	C₂²⋊C₄×Dic₄₃	—	2	1	no	—
45	C₄×C₂²⋊Dic₄₃	—	2	1	no	—
46	C₄²×Dic₄₃	—	2	1	no	—
47	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
48	#14582662	C₂²	1	1	yes	characteristic
49	#14582662	C₂²	1	1	yes	characteristic
50	#14582661	C₂²	1	1	yes	characteristic
51	#14582661	C₂²	1	1	yes	characteristic
52	#14582661	C₂²	1	1	yes	characteristic
53	#14582661	C₂²	1	1	yes	characteristic
54	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
57	C₄₃×#440	C₄	1	8	yes	complemented
58	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
59	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
60	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
61	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
62	C₂³×Dic₄₃	—	2	1	no	—
63	C₂³×Dic₄₃	—	2	1	no	—
64	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
66	Q₈×Dic₄₃	—	2	2	no	—
67	Q₈×Dic₄₃	—	2	2	no	—
68	Q₈×Dic₄₃	C₂×C₄	1	4	yes	complemented
69	Q₈×Dic₄₃	C₂×C₄	1	4	yes	complemented
70	D₄×Dic₄₃	—	2	2	no	—
71	D₄×Dic₄₃	—	2	2	no	—
72	D₄×Dic₄₃	C₂×C₄	1	4	yes	—
73	D₄×Dic₄₃	C₂×C₄	1	4	yes	—
74	C₂×C₄⋊Dic₄₃	—	2	1	no	—
75	C₂×C₄⋊Dic₄₃	—	2	1	no	—
76	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
81	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
82	C₂×C₄×Dic₄₃	—	2	1	no	—
83	C₂×C₄×Dic₄₃	—	2	1	no	—
84	C₂×C₄×Dic₄₃	—	2	1	no	—
85	C₂×C₄×Dic₄₃	—	2	1	no	—
86	C₂×C₄×Dic₄₃	—	2	1	no	—
87	C₂×C₄×Dic₄₃	—	2	1	no	—
88	C₂×C₄×Dic₄₃	—	2	1	no	—
89	C₂×C₄×Dic₄₃	—	2	1	no	—
90	C₂×C₄×Dic₄₃	—	4	4	no	—
91	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
92	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
93	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
94	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
95	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
96	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
97	#13063259	C₂×C₄	1	4	yes	complemented
98	#13063257	C₂×C₄	1	4	yes	complemented
99	#13063249	C₂×C₄	1	4	yes	complemented
100	#13063249	C₂×C₄	1	4	yes	complemented
101	#13063246	C₂×C₄	1	4	yes	—
102	#13063246	C₂×C₄	1	4	yes	—
103	#13063236	—	2	2	no	—
104	#13063235	—	2	2	no	—
105	#13063235	C₂×C₄	1	4	yes	complemented
106	C₈×Dic₄₃	—	2	2	no	—
107	C₈×Dic₄₃	C₂×C₄	1	4	yes	complemented
108	C₄₃⋊#95	—	2	1	no	—
109	C₄₃⋊#95	—	2	1	no	—
110	C₄₃⋊#95	—	2	1	no	—
111	C₄₃⋊#95	—	2	1	no	—
112	C₄₃⋊#95	—	2	1	no	—
113	C₄₃⋊#95	—	2	1	no	—
114	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₄₃	—	2	1	no	—
117	C₂×SD₁₆×C₄₃	C₂×C₄	1	4	yes	—
118	C₂×SD₁₆×C₄₃	C₂×C₄	1	4	yes	—
119	C₂×SD₁₆×C₄₃	C₂×C₄	1	4	yes	—
120	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
122	C₄×Q₈×C₄₃	—	2	2	no	—
123	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	complemented
124	C₄×D₄×C₄₃	—	2	2	no	—
125	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
126	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
127	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
130	C₂×C₄²×C₄₃	—	2	1	no	—
131	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
132	#107×C₄₃	C₂×C₄	1	4	yes	complemented
133	#103×C₄₃	C₂×C₄	1	4	yes	complemented
134	#102×C₄₃	C₂×C₄	1	4	yes	—
135	#97×C₄₃	C₂×C₄	1	4	yes	complemented
136	C₂⁴×C₄₃	—	2	1	no	—
137	C₂×Q₈×C₄₃	—	2	1	no	—
138	C₂×Q₈×C₄₃	—	2	1	no	—
139	C₂×Q₈×C₄₃	—	2	1	no	—
140	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
141	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
142	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
143	C₂×D₄×C₄₃	—	2	1	no	—
144	C₂×D₄×C₄₃	—	2	1	no	—
145	C₂×D₄×C₄₃	—	2	1	no	—
146	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
147	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
148	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₄₃	—	2	4	no	—
150	C₂²×C₄×C₄₃	—	2	1	no	—
151	C₂²×C₄×C₄₃	—	2	1	no	—
152	C₂²×C₄×C₄₃	—	2	1	no	—
153	C₂²×C₄×C₄₃	—	4	2	no	—
154	C₂²×C₄×C₄₃	—	4	2	no	—
155	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
158	C₂²×Dic₄₃	—	2	4	no	—
159	C₂²×Dic₄₃	—	2	4	no	—
160	C₂²×Dic₄₃	—	2	1	no	—
161	C₂²×Dic₄₃	—	2	1	no	—
162	C₂²×Dic₄₃	—	2	1	no	—
163	C₂²×Dic₄₃	—	2	1	no	—
164	C₂²×Dic₄₃	—	4	2	no	—
165	C₂²×Dic₄₃	—	4	2	no	—
166	C₂²×Dic₄₃	—	4	2	no	—
167	C₂²×Dic₄₃	—	4	2	no	—
168	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
172	SD₁₆×C₄₃	C₄²	1	16	yes	complemented
173	C₂×C₈×C₄₃	—	2	1	no	—
174	C₂×C₈×C₄₃	—	2	1	no	—
175	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
176	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
177	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
178	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
179	C₄⋊C₄×C₄₃	—	2	4	no	—
180	C₄⋊C₄×C₄₃	—	2	1	no	—
181	C₄⋊C₄×C₄₃	—	2	1	no	—
182	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
183	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
184	C₂²⋊C₄×C₄₃	—	2	4	no	—
185	C₄²×C₄₃	—	2	4	no	—
186	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
187	C₄²×C₄₃	#41	1	2	yes	—
188	C₂²⋊Dic₄₃	—	2	4	no	—
189	C₂²⋊Dic₄₃	—	2	4	no	—
190	C₄⋊Dic₄₃	—	2	1	no	—
191	C₄⋊Dic₄₃	—	2	1	no	—
192	C₄⋊Dic₄₃	—	2	1	no	—
193	C₄⋊Dic₄₃	—	2	1	no	—
194	C₄⋊Dic₄₃	—	2	4	no	—
195	C₄⋊Dic₄₃	—	2	4	no	—
196	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
197	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
198	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
199	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
200	C₄×Dic₄₃	—	2	4	no	—
201	C₄×Dic₄₃	—	2	4	no	—
202	C₄×Dic₄₃	—	2	2	no	—
203	C₄×Dic₄₃	—	2	2	no	—
204	C₄×Dic₄₃	—	4	1	no	—
205	C₄×Dic₄₃	—	4	1	no	—
206	C₄×Dic₄₃	—	4	2	no	—
207	C₄×Dic₄₃	—	4	2	no	—
208	C₄×Dic₄₃	—	4	2	no	—
209	C₄×Dic₄₃	—	4	2	no	—
210	C₄×Dic₄₃	—	4	2	no	—
211	C₄×Dic₄₃	—	4	2	no	—
212	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
213	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
214	C₄×Dic₄₃	#41	1	2	yes	—
215	C₄×Dic₄₃	#41	1	2	yes	—
216	C₂×C₄₃⋊C₈	—	2	1	no	—
217	C₂×C₄₃⋊C₈	—	2	1	no	—
218	C₂×C₄₃⋊C₈	—	2	1	no	—
219	C₂×C₄₃⋊C₈	—	2	1	no	—
220	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
221	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
222	C₂³×C₄₃	—	2	2	no	—
223	C₂³×C₄₃	—	2	2	no	—
224	C₂³×C₄₃	—	2	2	no	—
225	C₂³×C₄₃	—	4	1	no	—
226	C₂³×C₄₃	—	4	1	no	—
227	C₂³×C₄₃	—	4	1	no	—
228	C₂³×C₄₃	—	4	1	no	—
229	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
230	Q₈×C₄₃	—	2	2	no	—
231	Q₈×C₄₃	—	2	2	no	—
232	Q₈×C₄₃	—	2	2	no	—
233	Q₈×C₄₃	C₂×C₄²	1	4	yes	complemented
234	D₄×C₄₃	—	2	2	no	—
235	D₄×C₄₃	—	2	2	no	—
236	D₄×C₄₃	—	2	2	no	—
237	D₄×C₄₃	C₂×C₄²	1	4	yes	—
238	C₂×C₄×C₄₃	—	2	2	no	—
239	C₂×C₄×C₄₃	—	2	2	no	—
240	C₂×C₄×C₄₃	—	2	2	no	—
241	C₂×C₄×C₄₃	—	2	1	no	—
242	C₂×C₄×C₄₃	—	2	1	no	—
243	C₂×C₄×C₄₃	—	2	1	no	—
244	C₂×C₄×C₄₃	—	2	1	no	—
245	C₂×C₄×C₄₃	—	2	2	no	—
246	C₂×C₄×C₄₃	—	2	2	no	—
247	C₂×C₄×C₄₃	—	4	8	no	—
248	C₂×C₄×C₄₃	—	4	1	no	—
249	C₂×C₄×C₄₃	—	4	1	no	—
250	C₂×C₄×C₄₃	—	4	1	no	—
251	C₂×C₄×C₄₃	—	4	1	no	—
252	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
253	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
254	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
256	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
257	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
260	C₂×Dic₄₃	—	2	1	no	—
261	C₂×Dic₄₃	—	2	1	no	—
262	C₂×Dic₄₃	—	2	1	no	—
263	C₂×Dic₄₃	—	2	1	no	—
264	C₂×Dic₄₃	—	2	1	no	—
265	C₂×Dic₄₃	—	2	1	no	—
266	C₂×Dic₄₃	—	2	2	no	—
267	C₂×Dic₄₃	—	2	2	no	—
268	C₂×Dic₄₃	—	2	2	no	—
269	C₂×Dic₄₃	—	2	2	no	—
270	C₂×Dic₄₃	—	4	8	no	—
271	C₂×Dic₄₃	—	4	1	no	—
272	C₂×Dic₄₃	—	4	1	no	—
273	C₂×Dic₄₃	—	4	1	no	—
274	C₂×Dic₄₃	—	4	1	no	—
275	C₂×Dic₄₃	—	4	1	no	—
276	C₂×Dic₄₃	—	4	1	no	—
277	C₂×Dic₄₃	—	4	1	no	—
278	C₂×Dic₄₃	—	4	1	no	—
279	C₂×Dic₄₃	—	4	8	no	—
280	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
281	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
282	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
283	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
284	C₂×Dic₄₃	AGL(1,ℤ/8)	1	2	yes	—
285	C₂×Dic₄₃	#137	1	2	yes	—
286	C₈×C₄₃	—	2	2	no	—
287	C₈×C₄₃	C₂×C₄²	1	4	yes	complemented
288	C₄₃⋊C₈	—	2	2	no	—
289	C₄₃⋊C₈	—	2	2	no	—
290	C₄×#440	—	43	1	no	maximal, Sylow
291	C₂²×C₄₃	—	2	4	no	—
292	C₂²×C₄₃	—	4	2	no	—
293	C₂²×C₄₃	—	4	2	no	—
294	C₂²×C₄₃	—	4	2	no	—
295	C₂²×C₄₃	—	4	2	no	—
296	C₂²×C₄₃	—	4	2	no	—
297	C₂²×C₄₃	—	4	2	no	—
298	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
299	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
300	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
301	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
302	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
303	C₂²×C₄₃	#575	1	1	yes	characteristic
304	C₂²×C₄₃	#575	1	1	yes	characteristic
305	C₄×C₄₃	—	2	2	no	—
306	C₄×C₄₃	—	2	2	no	—
307	C₄×C₄₃	—	2	4	no	—
308	C₄×C₄₃	—	4	2	no	—
309	C₄×C₄₃	—	4	2	no	—
310	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
311	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
312	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
313	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
314	Dic₄₃	—	2	2	no	—
315	Dic₄₃	—	2	2	no	—
316	Dic₄₃	—	2	2	no	—
317	Dic₄₃	—	4	2	no	—
318	Dic₄₃	—	4	2	no	—
319	Dic₄₃	—	4	2	no	—
320	Dic₄₃	—	4	2	no	—
321	Dic₄₃	#440	1	4	yes	direct product factor
322	C₂×#440	—	43	1	no	—
323	C₂×#440	D₄₃	1	1	yes	characteristic
324	C₂×C₄×SD₁₆	—	43	1	no	—
325	C₄²×Q₈	—	43	1	no	—
326	C₄²×D₄	—	43	1	no	—
327	#1776	—	43	1	no	—
328	#1776	—	43	1	no	—
329	C₄×#107	—	43	1	no	—
330	#1763	—	43	1	no	—
331	#1763	—	43	1	no	—
332	#1762	—	43	1	no	—
333	#1762	—	43	1	no	—
334	C₄×#103	—	43	1	no	—
335	C₄×#102	—	43	1	no	—
336	C₄×#97	—	43	1	no	—
337	C₂×C₄₃	—	4	4	no	—
338	C₂×C₄₃	C₄²×D₄	1	1	yes	characteristic
339	C₂×C₄₃	C₂×#440	1	1	yes	characteristic
340	C₂×C₄₃	#2943	1	1	yes	characteristic
341	C₂×C₄₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
342	C₂×C₄₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
343	C₂×C₄₃	C₄×#137	1	1	yes	characteristic
344	C₂×C₄₃	C₄×#137	1	1	yes	characteristic
345	C₂²×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
346	C₂×C₄×Q₈	—	43	1	no	—
347	C₂×C₄×Q₈	—	43	1	no	—
348	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
349	C₂×C₄×D₄	—	43	1	no	—
350	C₂×C₄×D₄	—	43	1	no	—
351	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
352	C₂²×C₄²	—	86	1	no	—
353	#440	—	43	8	no	—
354	#440	Dic₄₃	1	8	yes	direct product factor
355	C₄×SD₁₆	—	43	8	no	—
356	C₂×#107	—	43	1	no	—
357	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
358	C₂×#106	—	43	1	no	—
359	C₂×#103	—	43	1	no	—
360	C₂×#103	—	43	1	no	—
361	C₂×#103	C₂×D₄₃	1	1	yes	characteristic
362	C₂×#102	—	43	1	no	—
363	C₂×#102	—	43	1	no	—
364	C₂×#102	C₂×D₄₃	1	1	yes	characteristic
365	C₂×#97	—	43	1	no	—
366	C₂×#97	—	43	1	no	—
367	C₂×#97	—	43	1	no	—
368	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
369	C₂×C₄×C₈	—	43	1	no	—
370	C₂×C₄×C₈	—	43	1	no	—
371	C₄×C₄⋊C₄	—	43	1	no	—
372	C₄×C₄⋊C₄	—	43	1	no	—
373	C₄×C₄⋊C₄	—	43	1	no	—
374	C₄×C₄⋊C₄	—	43	1	no	—
375	C₄×C₄⋊C₄	—	43	1	no	—
376	C₄×C₄⋊C₄	—	43	1	no	—
377	C₄×C₄⋊C₄	—	86	1	no	—
378	C₄×C₄⋊C₄	—	86	1	no	—
379	C₄×C₄⋊C₄	—	86	1	no	—
380	C₄×C₂²⋊C₄	—	86	1	no	—
381	C₄×C₂²⋊C₄	—	86	1	no	—
382	C₄×C₂²⋊C₄	—	86	1	no	—
383	C₄³	—	43	1	no	—
384	C₄³	—	86	1	no	—
385	#340	—	43	1	no	—
386	#340	—	43	1	no	—
387	#340	—	43	1	no	—
388	#340	—	43	1	no	—
389	#340	—	43	1	no	—
390	#340	—	43	1	no	—
391	C₄₃	C₄×#440	1	1	yes	characteristic, complemented, Sylow
392	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
393	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
394	C₂³×C₄	—	2	1	no	—
395	C₂³×C₄	—	86	1	no	—
396	C₂³×C₄	—	86	1	no	—
397	C₂×SD₁₆	C₄×D₄₃	1	4	yes	—
398	C₂×SD₁₆	C₄×D₄₃	1	4	yes	—
399	C₂×SD₁₆	C₂×Dic₄₃	1	4	yes	—
400	C₂²×C₈	—	43	1	no	—
401	C₂²×C₈	—	43	1	no	—
402	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
403	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
404	C₄×Q₈	—	2	2	no	—
405	C₄×Q₈	—	43	4	no	—
406	C₄×Q₈	—	43	4	no	—
407	C₄×Q₈	—	86	2	no	—
408	C₄×Q₈	—	86	2	no	—
409	C₄×Q₈	C₂×Dic₄₃	1	4	yes	complemented
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	—	43	4	no	—
412	C₄×D₄	—	43	4	no	—
413	C₄×D₄	—	86	2	no	—
414	C₄×D₄	—	86	2	no	—
415	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	43	1	no	—
418	C₂×C₄⋊C₄	—	43	1	no	—
419	C₂×C₄⋊C₄	—	43	1	no	—
420	C₂×C₄⋊C₄	—	43	1	no	—
421	C₂×C₄⋊C₄	—	86	1	no	—
422	C₂×C₄⋊C₄	—	86	1	no	—
423	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	86	1	no	—
427	C₂×C₂²⋊C₄	—	86	1	no	—
428	C₂×C₄²	—	2	1	no	—
429	C₂×C₄²	—	43	1	no	—
430	C₂×C₄²	—	43	1	no	—
431	C₂×C₄²	—	43	1	no	—
432	C₂×C₄²	—	43	1	no	—
433	C₂×C₄²	—	43	1	no	—
434	C₂×C₄²	—	43	1	no	—
435	C₂×C₄²	—	86	1	no	—
436	C₂×C₄²	—	86	1	no	—
437	C₂×C₄²	—	86	1	no	—
438	C₂×C₄²	—	86	1	no	—
439	C₂×C₄²	—	86	1	no	—
440	C₂×C₄²	—	86	1	no	—
441	C₂×C₄²	—	86	1	no	—
442	C₂×C₄²	—	86	1	no	—
443	C₂×C₄²	—	172	4	no	—
444	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
445	#107	—	43	4	no	—
446	#107	C₂×Dic₄₃	1	4	yes	complemented
447	#106	—	43	4	no	—
448	#103	—	43	4	no	—
449	#103	—	43	4	no	—
450	#103	C₂×Dic₄₃	1	4	yes	complemented
451	#102	—	43	4	no	—
452	#102	—	43	4	no	—
453	#102	C₂×Dic₄₃	1	4	yes	—
454	#97	—	43	4	no	—
455	#97	—	86	2	no	—
456	#97	—	86	2	no	—
457	#97	C₂×Dic₄₃	1	4	yes	complemented
458	C₄×C₈	—	43	4	no	—
459	C₄×C₈	—	86	2	no	—
460	#95	—	86	1	no	—
461	#95	—	86	1	no	—
462	#95	—	86	1	no	—
463	#95	—	86	1	no	—
464	#95	—	86	1	no	—
465	#95	—	86	1	no	—
466	C₂⁴	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
471	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
472	C₂×Q₈	C₂²×Dic₄₃	1	2	yes	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
477	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
478	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	—	43	1	no	—
486	C₂²×C₄	—	43	1	no	—
487	C₂²×C₄	—	43	1	no	—
488	C₂²×C₄	—	43	1	no	—
489	C₂²×C₄	—	86	4	no	—
490	C₂²×C₄	—	86	4	no	—
491	C₂²×C₄	—	86	1	no	—
492	C₂²×C₄	—	86	1	no	—
493	C₂²×C₄	—	86	1	no	—
494	C₂²×C₄	—	86	1	no	—
495	C₂²×C₄	—	172	2	no	—
496	C₂²×C₄	—	172	2	no	—
497	C₂²×C₄	—	172	2	no	—
498	C₂²×C₄	—	172	2	no	—
499	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
500	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
501	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
502	SD₁₆	C₄×Dic₄₃	1	16	yes	complemented
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	43	2	no	—
506	C₂×C₈	—	43	2	no	—
507	C₂×C₈	—	86	1	no	—
508	C₂×C₈	—	86	1	no	—
509	C₂×C₈	—	86	1	no	—
510	C₂×C₈	—	86	1	no	—
511	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
512	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
513	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
514	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
515	C₄⋊C₄	—	2	4	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	43	2	no	—
519	C₄⋊C₄	—	43	2	no	—
520	C₄⋊C₄	—	43	2	no	—
521	C₄⋊C₄	—	43	2	no	—
522	C₄⋊C₄	—	86	4	no	—
523	C₄⋊C₄	—	86	4	no	—
524	C₄⋊C₄	—	86	1	no	—
525	C₄⋊C₄	—	86	1	no	—
526	C₄⋊C₄	—	86	1	no	—
527	C₄⋊C₄	—	86	1	no	—
528	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
529	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
530	C₂²⋊C₄	—	2	4	no	—
531	C₂²⋊C₄	—	86	4	no	—
532	C₂²⋊C₄	—	86	4	no	—
533	C₄²	—	2	4	no	—
534	C₄²	—	43	2	no	—
535	C₄²	—	43	2	no	—
536	C₄²	—	43	2	no	—
537	C₄²	—	43	2	no	—
538	C₄²	—	86	2	no	—
539	C₄²	—	86	2	no	—
540	C₄²	—	86	4	no	—
541	C₄²	—	86	4	no	—
542	C₄²	—	172	1	no	—
543	C₄²	—	172	1	no	—
544	C₄²	—	172	2	no	—
545	C₄²	—	172	2	no	—
546	C₄²	—	172	2	no	—
547	C₄²	—	172	2	no	—
548	C₄²	—	172	2	no	—
549	C₄²	—	172	2	no	—
550	C₄²	#10621900	1	2	yes	—
551	C₄²	C₂²×Dic₄₃	1	2	yes	—
552	C₂³	—	2	2	no	—
553	C₂³	—	2	2	no	—
554	C₂³	—	2	2	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
560	Q₈	—	2	2	no	—
561	Q₈	—	2	2	no	—
562	Q₈	—	2	2	no	—
563	Q₈	C₂×C₄×Dic₄₃	1	4	yes	complemented
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	—	2	2	no	—
567	D₄	C₂×C₄×Dic₄₃	1	4	yes	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	4	8	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	43	2	no	—
583	C₂×C₄	—	43	2	no	—
584	C₂×C₄	—	43	2	no	—
585	C₂×C₄	—	43	2	no	—
586	C₂×C₄	—	43	2	no	—
587	C₂×C₄	—	43	2	no	—
588	C₂×C₄	—	86	1	no	—
589	C₂×C₄	—	86	1	no	—
590	C₂×C₄	—	86	1	no	—
591	C₂×C₄	—	86	1	no	—
592	C₂×C₄	—	86	1	no	—
593	C₂×C₄	—	86	1	no	—
594	C₂×C₄	—	86	2	no	—
595	C₂×C₄	—	86	2	no	—
596	C₂×C₄	—	86	2	no	—
597	C₂×C₄	—	86	2	no	—
598	C₂×C₄	—	172	8	no	—
599	C₂×C₄	—	172	8	no	—
600	C₂×C₄	—	172	1	no	—
601	C₂×C₄	—	172	1	no	—
602	C₂×C₄	—	172	1	no	—
603	C₂×C₄	—	172	1	no	—
604	C₂×C₄	—	172	1	no	—
605	C₂×C₄	—	172	1	no	—
606	C₂×C₄	—	172	1	no	—
607	C₂×C₄	—	172	1	no	—
608	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
609	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
610	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
611	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
612	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
613	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
614	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
615	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
616	C₈	—	2	2	no	—
617	C₈	—	86	2	no	—
618	C₈	—	86	2	no	—
619	C₈	C₂×C₄×Dic₄₃	1	4	yes	complemented
620	C₂²	—	2	4	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	4	2	no	—
627	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
628	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
629	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
630	C₂²	AGL(1,ℤ/8)×D₄₃	1	1	yes	characteristic
631	C₂²	#137×D₄₃	1	1	yes	characteristic
632	C₂²	#14583695	1	1	yes	characteristic
633	C₂²	#14583698	1	1	yes	characteristic
634	C₄	—	2	4	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	2	no	—
639	C₄	—	43	4	no	—
640	C₄	—	86	2	no	—
641	C₄	—	86	2	no	—
642	C₄	—	86	2	no	—
643	C₄	—	172	2	no	—
644	C₄	—	172	2	no	—
645	C₄	—	172	2	no	—
646	C₄	—	172	2	no	—
647	C₄	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
648	C₄	C₄×#10621900	1	1	yes	characteristic
649	C₄	C₄×#10621900	1	1	yes	characteristic
650	C₄	#41×Dic₄₃	1	1	yes	characteristic
651	C₂	—	4	4	no	—
652	C₂	C₄×D₄×Dic₄₃	1	1	yes	characteristic
653	C₂	#440×D₄₃	1	1	yes	characteristic
654	C₂	#19143390	1	1	yes	characteristic
655	C₂	#19143400	1	1	yes	characteristic
656	C₂	AGL(1,ℤ/8)×Dic₄₃	1	1	yes	characteristic
657	C₂	#137×Dic₄₃	1	1	yes	characteristic
658	C₂	#19143417	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator	C₄×C₄₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#440	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×D₄×C₄₃	C₂³
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#440	D₄₃
hypocenter	C₄₃	C₄×#440
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#440

Complements

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

N	H ≅ G/N	type
3. C₄×Q₈×Dic₄₃	C₂	semidirect
5. #19134494	C₂	semidirect
6. #19134492	C₂	semidirect
7. #107×Dic₄₃	C₂	semidirect
8. #19134427	C₂	semidirect
9. #19134425	C₂	semidirect
12. #103×Dic₄₃	C₂	semidirect
14. #97×Dic₄₃	C₂	semidirect
21. #14583000	C₄	semidirect
22. SD₁₆×Dic₄₃	C₄	semidirect
57. C₄₃×#440	C₄	semidirect
68. Q₈×Dic₄₃	C₂×C₄	semidirect
69. Q₈×Dic₄₃	C₂×C₄	semidirect
97. #13063259	C₂×C₄	semidirect
98. #13063257	C₂×C₄	semidirect
99. #13063249	C₂×C₄	semidirect
100. #13063249	C₂×C₄	semidirect
105. #13063235	C₂×C₄	semidirect
107. C₈×Dic₄₃	C₂×C₄	semidirect
123. C₄×Q₈×C₄₃	C₂×C₄	semidirect
132. #107×C₄₃	C₂×C₄	semidirect
133. #103×C₄₃	C₂×C₄	semidirect
135. #97×C₄₃	C₂×C₄	semidirect
172. SD₁₆×C₄₃	C₄²	semidirect
233. Q₈×C₄₃	C₂×C₄²	semidirect
287. C₈×C₄₃	C₂×C₄²	semidirect
321. Dic₄₃	#440	direct (N × H)
354. #440	Dic₄₃	direct (N × H)
391. C₄₃	C₄×#440	semidirect
409. C₄×Q₈	C₂×Dic₄₃	semidirect
446. #107	C₂×Dic₄₃	semidirect
450. #103	C₂×Dic₄₃	semidirect
457. #97	C₂×Dic₄₃	semidirect
502. SD₁₆	C₄×Dic₄₃	semidirect
563. Q₈	C₂×C₄×Dic₄₃	semidirect
619. C₈	C₂×C₄×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583000	2
C₂×SD₁₆×Dic₄₃	2
C₄×Q₈×Dic₄₃	2
C₄×D₄×Dic₄₃	2
#19134494	2
#19134492	2
#107×Dic₄₃	2
#19134427	2
#19134425	2
#19134422	2
#19134420	2
#103×Dic₄₃	2
#102×Dic₄₃	2
#97×Dic₄₃	2
C₂×C₄₃×#440	2
C₄×#440	43

Subgroups — #440×Dic43 #25095090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #440×Dic₄₃ #25095090