Subgroups — C₄₃×#25788 #24945805

Order 11008.

1892 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#496	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2435	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2433	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2012	C₂	1	2	yes	maximal, complemented
9	C₄₃×#2011	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1972	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
15	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	complemented
16	C₂²×D₈×C₄₃	—	2	8	no	—
17	C₂²×D₈×C₄₃	—	2	4	no	—
18	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
19	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
20	C₂²×D₈×C₄₃	C₂²	1	2	yes	complemented
21	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#127×C₄₃	C₂²	1	2	yes	complemented
23	C₂×#124×C₄₃	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#120×C₄₃	—	2	2	no	—
27	C₄₃×#496	—	2	8	no	—
28	C₄₃×#465	—	2	4	no	—
29	C₄₃×#450	—	2	4	no	—
30	C₄₃×#447	—	2	4	no	—
31	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
34	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
35	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×#97×C₄₃	C₂²	1	2	yes	complemented
38	C₄₃×#394	—	2	2	no	—
39	C₄₃×#392	—	2	2	no	—
40	C₄₃×#390	C₂²	1	2	yes	complemented
41	C₄₃×#390	C₂²	1	2	yes	complemented
42	C₄₃×#379	—	2	2	no	—
43	C₄×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#336	C₂²	1	2	yes	complemented
45	C₂⁵×C₄₃	—	2	1	no	—
46	C₂⁵×C₄₃	—	2	1	no	—
47	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₄₃	—	2	4	no	—
49	C₂²×D₄×C₄₃	—	2	4	no	—
50	C₂²×D₄×C₄₃	—	2	1	no	—
51	C₂²×D₄×C₄₃	—	2	2	no	—
52	C₂²×D₄×C₄₃	—	2	2	no	—
53	C₂²×D₄×C₄₃	—	2	2	no	—
54	C₂²×D₄×C₄₃	—	2	2	no	—
55	C₂²×D₄×C₄₃	—	2	1	no	—
56	C₂²×D₄×C₄₃	—	2	1	no	—
57	C₂²×D₄×C₄₃	—	2	4	no	—
58	C₂²×D₄×C₄₃	—	4	2	no	—
59	C₂²×D₄×C₄₃	—	4	2	no	—
60	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
62	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂×SD₁₆×C₄₃	—	2	4	no	—
65	C₂×SD₁₆×C₄₃	—	2	4	no	—
66	C₂×SD₁₆×C₄₃	—	2	2	no	—
67	C₂×SD₁₆×C₄₃	—	2	4	no	—
68	C₂×SD₁₆×C₄₃	—	4	2	no	—
69	C₂×D₈×C₄₃	—	2	32	no	—
70	C₂×D₈×C₄₃	—	2	4	no	—
71	C₂×D₈×C₄₃	—	2	4	no	—
72	C₂×D₈×C₄₃	—	2	4	no	—
73	C₂×D₈×C₄₃	—	2	4	no	—
74	C₂×D₈×C₄₃	—	2	4	no	—
75	C₂×D₈×C₄₃	—	2	4	no	—
76	C₂×D₈×C₄₃	—	2	4	no	—
77	C₂×D₈×C₄₃	—	4	2	no	—
78	C₂×D₈×C₄₃	D₄	1	8	yes	complemented
79	C₂²×C₈×C₄₃	—	2	4	no	—
80	C₂²×C₈×C₄₃	D₄	1	4	yes	complemented
81	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
83	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
84	#127×C₄₃	—	2	4	no	—
85	#127×C₄₃	—	4	2	no	—
86	#124×C₄₃	—	2	4	no	—
87	#124×C₄₃	—	4	2	no	—
88	C₂²⋊Q₈×C₄₃	—	2	2	no	—
89	C₂²⋊Q₈×C₄₃	—	2	2	no	—
90	#121×C₄₃	—	2	2	no	—
91	#121×C₄₃	—	2	2	no	—
92	#120×C₄₃	—	4	8	no	—
93	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
98	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
100	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
101	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
102	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
103	#106×C₄₃	—	2	2	no	—
104	#103×C₄₃	—	2	2	no	—
105	#102×C₄₃	—	2	4	no	—
106	#102×C₄₃	—	2	4	no	—
107	#102×C₄₃	—	2	2	no	—
108	C₂²⋊C₈×C₄₃	D₄	1	4	yes	complemented
109	#97×C₄₃	—	2	4	no	—
110	#95×C₄₃	D₄	1	2	yes	—
111	C₂⁴×C₄₃	—	2	2	no	—
112	C₂⁴×C₄₃	—	2	2	no	—
113	C₂⁴×C₄₃	—	2	1	no	—
114	C₂⁴×C₄₃	—	4	4	no	—
115	C₂⁴×C₄₃	—	4	4	no	—
116	C₂⁴×C₄₃	—	4	2	no	—
117	C₂⁴×C₄₃	—	4	2	no	—
118	C₂⁴×C₄₃	—	4	4	no	—
119	C₂⁴×C₄₃	—	4	4	no	—
120	C₂⁴×C₄₃	—	8	2	no	—
121	C₂⁴×C₄₃	—	8	2	no	—
122	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂×Q₈×C₄₃	—	2	1	no	—
124	C₂×Q₈×C₄₃	—	2	1	no	—
125	C₂×Q₈×C₄₃	—	2	2	no	—
126	C₂×Q₈×C₄₃	—	2	2	no	—
127	C₂×D₄×C₄₃	—	2	2	no	—
128	C₂×D₄×C₄₃	—	2	2	no	—
129	C₂×D₄×C₄₃	—	2	8	no	—
130	C₂×D₄×C₄₃	—	2	8	no	—
131	C₂×D₄×C₄₃	—	2	2	no	—
132	C₂×D₄×C₄₃	—	2	2	no	—
133	C₂×D₄×C₄₃	—	2	2	no	—
134	C₂×D₄×C₄₃	—	2	2	no	—
135	C₂×D₄×C₄₃	—	2	2	no	—
136	C₂×D₄×C₄₃	—	2	2	no	—
137	C₂×D₄×C₄₃	—	2	1	no	—
138	C₂×D₄×C₄₃	—	2	1	no	—
139	C₂×D₄×C₄₃	—	2	2	no	—
140	C₂×D₄×C₄₃	—	2	2	no	—
141	C₂×D₄×C₄₃	—	2	2	no	—
142	C₂×D₄×C₄₃	—	2	2	no	—
143	C₂×D₄×C₄₃	—	4	4	no	—
144	C₂×D₄×C₄₃	—	4	4	no	—
145	C₂×D₄×C₄₃	—	4	8	no	—
146	C₂×D₄×C₄₃	—	4	8	no	—
147	C₂×D₄×C₄₃	—	4	8	no	—
148	C₂×D₄×C₄₃	—	4	4	no	—
149	C₂×D₄×C₄₃	—	4	4	no	—
150	C₂×D₄×C₄₃	—	4	8	no	—
151	C₂×D₄×C₄₃	—	4	2	no	—
152	C₂×D₄×C₄₃	—	4	2	no	—
153	C₂×D₄×C₄₃	—	4	2	no	—
154	C₂×D₄×C₄₃	—	4	4	no	—
155	C₂×D₄×C₄₃	—	8	4	no	—
156	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
157	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₄₃	—	2	2	no	—
159	C₂²×C₄×C₄₃	—	2	2	no	—
160	C₂²×C₄×C₄₃	—	2	1	no	—
161	C₂²×C₄×C₄₃	—	2	1	no	—
162	C₂²×C₄×C₄₃	—	2	1	no	—
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	4	yes	—
166	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
168	SD₁₆×C₄₃	—	4	8	no	—
169	SD₁₆×C₄₃	—	4	4	no	—
170	D₈×C₄₃	—	2	16	no	—
171	D₈×C₄₃	—	2	16	no	—
172	D₈×C₄₃	—	4	8	no	—
173	C₂×C₈×C₄₃	—	2	2	no	—
174	C₂×C₈×C₄₃	—	2	2	no	—
175	C₂×C₈×C₄₃	—	2	2	no	—
176	C₂×C₈×C₄₃	—	2	8	no	—
177	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
178	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
179	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
180	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
181	C₄⋊C₄×C₄₃	—	2	1	no	—
182	C₄⋊C₄×C₄₃	—	2	1	no	—
183	C₄⋊C₄×C₄₃	—	2	1	no	—
184	C₄⋊C₄×C₄₃	—	2	1	no	—
185	C₄⋊C₄×C₄₃	—	4	2	no	—
186	C₂²⋊C₄×C₄₃	—	2	4	no	—
187	C₂²⋊C₄×C₄₃	—	4	8	no	—
188	C₂²⋊C₄×C₄₃	—	4	8	no	—
189	C₂²⋊C₄×C₄₃	—	4	2	no	—
190	C₂²⋊C₄×C₄₃	—	4	2	no	—
191	C₂²⋊C₄×C₄₃	—	8	4	no	—
192	C₄²×C₄₃	—	2	2	no	—
193	C₄²×C₄₃	—	2	2	no	—
194	C₂³×C₄₃	—	2	2	no	—
195	C₂³×C₄₃	—	2	2	no	—
196	C₂³×C₄₃	—	2	4	no	—
197	C₂³×C₄₃	—	2	4	no	—
198	C₂³×C₄₃	—	4	8	no	—
199	C₂³×C₄₃	—	4	8	no	—
200	C₂³×C₄₃	—	4	2	no	—
201	C₂³×C₄₃	—	4	2	no	—
202	C₂³×C₄₃	—	4	2	no	—
203	C₂³×C₄₃	—	4	2	no	—
204	C₂³×C₄₃	—	4	4	no	—
205	C₂³×C₄₃	—	4	4	no	—
206	C₂³×C₄₃	—	4	4	no	—
207	C₂³×C₄₃	—	4	4	no	—
208	C₂³×C₄₃	—	4	1	no	—
209	C₂³×C₄₃	—	4	2	no	—
210	C₂³×C₄₃	—	4	2	no	—
211	C₂³×C₄₃	—	4	2	no	—
212	C₂³×C₄₃	—	8	16	no	—
213	C₂³×C₄₃	—	8	16	no	—
214	C₂³×C₄₃	—	8	4	no	—
215	C₂³×C₄₃	—	8	4	no	—
216	C₂³×C₄₃	—	8	4	no	—
217	C₂³×C₄₃	—	8	4	no	—
218	C₂³×C₄₃	#127	1	2	yes	—
219	C₂³×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
220	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
221	Q₈×C₄₃	—	4	1	no	—
222	Q₈×C₄₃	—	4	1	no	—
223	Q₈×C₄₃	—	4	2	no	—
224	D₄×C₄₃	—	2	4	no	—
225	D₄×C₄₃	—	2	4	no	—
226	D₄×C₄₃	—	2	4	no	—
227	D₄×C₄₃	—	2	4	no	—
228	D₄×C₄₃	—	4	8	no	—
229	D₄×C₄₃	—	4	8	no	—
230	D₄×C₄₃	—	4	1	no	—
231	D₄×C₄₃	—	4	2	no	—
232	D₄×C₄₃	—	4	2	no	—
233	D₄×C₄₃	—	4	1	no	—
234	D₄×C₄₃	—	4	2	no	—
235	D₄×C₄₃	—	4	2	no	—
236	D₄×C₄₃	—	4	2	no	—
237	D₄×C₄₃	—	8	16	no	—
238	D₄×C₄₃	—	8	4	no	—
239	C₂×C₄×C₄₃	—	2	2	no	—
240	C₂×C₄×C₄₃	—	2	2	no	—
241	C₂×C₄×C₄₃	—	2	2	no	—
242	C₂×C₄×C₄₃	—	2	4	no	—
243	C₂×C₄×C₄₃	—	2	4	no	—
244	C₂×C₄×C₄₃	—	2	4	no	—
245	C₂×C₄×C₄₃	—	2	4	no	—
246	C₂×C₄×C₄₃	—	4	1	no	—
247	C₂×C₄×C₄₃	—	4	1	no	—
248	C₂×C₄×C₄₃	—	4	1	no	—
249	C₂×C₄×C₄₃	—	4	2	no	—
250	C₂×C₄×C₄₃	—	4	2	no	—
251	C₂×C₄×C₄₃	—	4	2	no	—
252	C₂×C₄×C₄₃	#127	1	2	yes	—
253	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
257	C₈×C₄₃	—	2	2	no	—
258	C₈×C₄₃	—	2	4	no	—
259	C₈×C₄₃	#120	1	4	yes	complemented
260	#25788	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂²×C₄₃	—	2	2	no	—
262	C₂²×C₄₃	—	2	2	no	—
263	C₂²×C₄₃	—	2	8	no	—
264	C₂²×C₄₃	—	4	4	no	—
265	C₂²×C₄₃	—	4	4	no	—
266	C₂²×C₄₃	—	4	8	no	—
267	C₂²×C₄₃	—	4	8	no	—
268	C₂²×C₄₃	—	8	16	no	—
269	C₂²×C₄₃	—	8	16	no	—
270	C₂²×C₄₃	—	8	2	no	—
271	C₂²×C₄₃	—	8	2	no	—
272	C₂²×C₄₃	—	8	2	no	—
273	C₂²×C₄₃	—	8	2	no	—
274	C₂²×C₄₃	—	8	4	no	—
275	C₂²×C₄₃	—	8	4	no	—
276	C₂²×C₄₃	—	8	1	no	—
277	C₂²×C₄₃	—	8	1	no	—
278	C₂²×C₄₃	—	8	1	no	—
279	C₂²×C₄₃	—	8	4	no	—
280	C₂²×C₄₃	#496	1	4	yes	complemented
281	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
282	C₂²×C₄₃	D₄²	1	2	yes	—
283	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
284	C₂²×C₄₃	#576	1	2	yes	—
285	C₄×C₄₃	—	2	2	no	—
286	C₄×C₄₃	—	4	4	no	—
287	C₄×C₄₃	—	8	1	no	—
288	C₄×C₄₃	—	8	1	no	—
289	C₄×C₄₃	—	8	1	no	—
290	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
291	C₄×C₄₃	#535	1	1	yes	characteristic
292	C₄×C₄₃	D₄²	1	2	yes	—
293	C₂³×D₈	C₂×C₄₃	1	1	yes	characteristic, complemented
294	C₂×#496	C₂×C₄₃	1	2	yes	complemented
295	C₂×#465	C₂×C₄₃	1	1	yes	characteristic, complemented
296	C₂×#450	C₂×C₄₃	1	1	yes	characteristic, complemented
297	C₂×#447	C₂×C₄₃	1	1	yes	characteristic, complemented
298	#2435	C₂×C₄₃	1	1	yes	characteristic, complemented
299	#2433	C₂×C₄₃	1	1	yes	characteristic, complemented
300	#2012	C₂×C₄₃	1	2	yes	complemented
301	#2011	C₂×C₄₃	1	2	yes	complemented
302	#1972	C₂×C₄₃	1	2	yes	complemented
303	#1752	C₂×C₄₃	1	1	yes	characteristic, complemented
304	C₂×C₄₃	—	2	4	no	—
305	C₂×C₄₃	—	8	4	no	—
306	C₂×C₄₃	—	8	4	no	—
307	C₂×C₄₃	—	16	1	no	—
308	C₂×C₄₃	#2433	1	1	yes	characteristic
309	C₂×C₄₃	C₂×#496	1	1	yes	characteristic
310	C₂×C₄₃	#3155	1	1	yes	characteristic
311	C₂×C₄₃	#3264	1	4	yes	—
312	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
313	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
314	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic, complemented
315	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	complemented
316	C₂²×D₈	—	2	8	no	—
317	C₂²×D₈	—	2	4	no	—
318	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
319	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
320	C₂²×D₈	C₂²×C₄₃	1	2	yes	complemented
321	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
322	C₂×#127	C₂²×C₄₃	1	2	yes	complemented
323	C₂×#124	C₂²×C₄₃	1	2	yes	complemented
324	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
325	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
326	C₂×#120	—	2	2	no	—
327	#496	—	2	8	no	—
328	#465	—	2	4	no	—
329	#450	—	2	4	no	—
330	#447	—	2	4	no	—
331	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic, complemented
332	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic, complemented
333	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
334	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
335	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic, complemented
336	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
337	C₂×#97	C₂²×C₄₃	1	2	yes	complemented
338	#394	—	2	2	no	—
339	#392	—	2	2	no	—
340	#390	C₂²×C₄₃	1	2	yes	complemented
341	#390	C₂²×C₄₃	1	2	yes	complemented
342	#379	—	2	2	no	—
343	C₄×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
344	#336	C₂²×C₄₃	1	2	yes	complemented
345	C₄₃	#25788	1	1	yes	characteristic, direct product factor, Sylow
346	C₂⁵	—	2	1	no	—
347	C₂⁵	—	2	1	no	—
348	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
349	C₂²×D₄	—	2	4	no	—
350	C₂²×D₄	—	2	4	no	—
351	C₂²×D₄	—	2	1	no	—
352	C₂²×D₄	—	2	2	no	—
353	C₂²×D₄	—	2	2	no	—
354	C₂²×D₄	—	2	2	no	—
355	C₂²×D₄	—	2	2	no	—
356	C₂²×D₄	—	2	1	no	—
357	C₂²×D₄	—	2	1	no	—
358	C₂²×D₄	—	2	4	no	—
359	C₂²×D₄	—	4	2	no	—
360	C₂²×D₄	—	4	2	no	—
361	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
362	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
363	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
364	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
365	C₂×SD₁₆	—	2	4	no	—
366	C₂×SD₁₆	—	2	4	no	—
367	C₂×SD₁₆	—	2	2	no	—
368	C₂×SD₁₆	—	2	4	no	—
369	C₂×SD₁₆	—	4	2	no	—
370	C₂×D₈	—	2	32	no	—
371	C₂×D₈	—	2	4	no	—
372	C₂×D₈	—	2	4	no	—
373	C₂×D₈	—	2	4	no	—
374	C₂×D₈	—	2	4	no	—
375	C₂×D₈	—	2	4	no	—
376	C₂×D₈	—	2	4	no	—
377	C₂×D₈	—	2	4	no	—
378	C₂×D₈	—	4	2	no	—
379	C₂×D₈	D₄×C₄₃	1	8	yes	complemented
380	C₂²×C₈	—	2	4	no	—
381	C₂²×C₈	D₄×C₄₃	1	4	yes	complemented
382	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
383	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
384	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
385	#127	—	2	4	no	—
386	#127	—	4	2	no	—
387	#124	—	2	4	no	—
388	#124	—	4	2	no	—
389	C₂²⋊Q₈	—	2	2	no	—
390	C₂²⋊Q₈	—	2	2	no	—
391	#121	—	2	2	no	—
392	#121	—	2	2	no	—
393	#120	—	4	8	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	2	4	no	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₂²⋊C₄	—	2	4	no	—
401	C₂×C₂²⋊C₄	—	2	4	no	—
402	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
403	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
404	#106	—	2	2	no	—
405	#103	—	2	2	no	—
406	#102	—	2	4	no	—
407	#102	—	2	4	no	—
408	#102	—	2	2	no	—
409	C₂²⋊C₈	D₄×C₄₃	1	4	yes	complemented
410	#97	—	2	4	no	—
411	#95	D₄×C₄₃	1	2	yes	—
412	C₂⁴	—	2	2	no	—
413	C₂⁴	—	2	2	no	—
414	C₂⁴	—	2	1	no	—
415	C₂⁴	—	4	4	no	—
416	C₂⁴	—	4	4	no	—
417	C₂⁴	—	4	2	no	—
418	C₂⁴	—	4	2	no	—
419	C₂⁴	—	4	4	no	—
420	C₂⁴	—	4	4	no	—
421	C₂⁴	—	8	2	no	—
422	C₂⁴	—	8	2	no	—
423	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×D₄	—	2	8	no	—
429	C₂×D₄	—	2	8	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	4	8	no	—
445	C₂×D₄	—	4	8	no	—
446	C₂×D₄	—	4	4	no	—
447	C₂×D₄	—	4	4	no	—
448	C₂×D₄	—	4	4	no	—
449	C₂×D₄	—	4	4	no	—
450	C₂×D₄	—	4	8	no	—
451	C₂×D₄	—	4	8	no	—
452	C₂×D₄	—	4	2	no	—
453	C₂×D₄	—	4	4	no	—
454	C₂×D₄	—	4	2	no	—
455	C₂×D₄	—	4	2	no	—
456	C₂×D₄	—	8	4	no	—
457	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
458	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
465	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
467	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
468	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
469	SD₁₆	—	4	8	no	—
470	SD₁₆	—	4	4	no	—
471	D₈	—	2	16	no	—
472	D₈	—	2	16	no	—
473	D₈	—	4	8	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	8	no	—
478	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
479	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
480	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
481	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	4	2	no	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	4	8	no	—
489	C₂²⋊C₄	—	4	8	no	—
490	C₂²⋊C₄	—	4	2	no	—
491	C₂²⋊C₄	—	4	2	no	—
492	C₂²⋊C₄	—	8	4	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	4	8	no	—
500	C₂³	—	4	8	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	4	no	—
506	C₂³	—	4	4	no	—
507	C₂³	—	4	4	no	—
508	C₂³	—	4	4	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	2	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	8	16	no	—
514	C₂³	—	8	16	no	—
515	C₂³	—	8	4	no	—
516	C₂³	—	8	4	no	—
517	C₂³	—	8	4	no	—
518	C₂³	—	8	4	no	—
519	C₂³	#127×C₄₃	1	2	yes	—
520	C₂³	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
521	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
522	Q₈	—	4	1	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	4	2	no	—
525	D₄	—	2	4	no	—
526	D₄	—	2	4	no	—
527	D₄	—	2	4	no	—
528	D₄	—	2	4	no	—
529	D₄	—	4	8	no	—
530	D₄	—	4	8	no	—
531	D₄	—	4	1	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	1	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	8	16	no	—
539	D₄	—	8	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	#127×C₄₃	1	2	yes	—
554	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
555	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
556	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
557	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
558	C₈	—	2	2	no	—
559	C₈	—	2	4	no	—
560	C₈	#120×C₄₃	1	4	yes	complemented
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	8	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	8	no	—
567	C₂²	—	4	8	no	—
568	C₂²	—	8	16	no	—
569	C₂²	—	8	16	no	—
570	C₂²	—	8	2	no	—
571	C₂²	—	8	2	no	—
572	C₂²	—	8	2	no	—
573	C₂²	—	8	2	no	—
574	C₂²	—	8	4	no	—
575	C₂²	—	8	4	no	—
576	C₂²	—	8	1	no	—
577	C₂²	—	8	1	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	8	4	no	—
580	C₂²	C₄₃×#496	1	4	yes	complemented
581	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
582	C₂²	D₄²×C₄₃	1	2	yes	—
583	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
584	C₂²	C₄₃×#576	1	2	yes	—
585	C₄	—	2	2	no	—
586	C₄	—	4	4	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	—	8	1	no	—
590	C₄	C₂×#120×C₄₃	1	1	yes	characteristic
591	C₄	C₄₃×#535	1	1	yes	characteristic
592	C₄	D₄²×C₄₃	1	2	yes	—
593	C₂	—	2	4	no	—
594	C₂	—	8	4	no	—
595	C₂	—	8	4	no	—
596	C₂	—	16	1	no	—
597	C₂	C₄₃×#2433	1	1	yes	characteristic
598	C₂	C₂×C₄₃×#496	1	1	yes	characteristic
599	C₂	C₄₃×#3155	1	1	yes	characteristic
600	C₂	C₄₃×#3264	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₄×C₂²⋊C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×D₈×C₄₃	C₂	semidirect
2. C₂×C₄₃×#496	C₂	semidirect
3. C₂×C₄₃×#465	C₂	semidirect
4. C₂×C₄₃×#450	C₂	semidirect
5. C₂×C₄₃×#447	C₂	semidirect
6. C₄₃×#2435	C₂	semidirect
7. C₄₃×#2433	C₂	semidirect
8. C₄₃×#2012	C₂	semidirect
9. C₄₃×#2011	C₂	semidirect
10. C₄₃×#1972	C₂	semidirect
11. C₄₃×#1752	C₂	semidirect
14. C₂²×SD₁₆×C₄₃	C₂²	semidirect
15. C₂²×SD₁₆×C₄₃	C₂²	semidirect
20. C₂²×D₈×C₄₃	C₂²	semidirect
22. C₂×#127×C₄₃	C₂²	semidirect
23. C₂×#124×C₄₃	C₂²	semidirect
31. C₂×#106×C₄₃	C₂²	semidirect
32. C₂×#103×C₄₃	C₂²	semidirect
33. C₂×#102×C₄₃	C₂²	semidirect
34. C₂×#102×C₄₃	C₂²	semidirect
35. C₂×#102×C₄₃	C₂²	semidirect
37. C₂×#97×C₄₃	C₂²	semidirect
40. C₄₃×#390	C₂²	semidirect
41. C₄₃×#390	C₂²	semidirect
44. C₄₃×#336	C₂²	semidirect
78. C₂×D₈×C₄₃	D₄	semidirect
80. C₂²×C₈×C₄₃	D₄	semidirect
108. C₂²⋊C₈×C₄₃	D₄	semidirect
259. C₈×C₄₃	#120	semidirect
260. #25788	C₄₃	direct (N × H)
280. C₂²×C₄₃	#496	semidirect
293. C₂³×D₈	C₂×C₄₃	semidirect
294. C₂×#496	C₂×C₄₃	semidirect
295. C₂×#465	C₂×C₄₃	semidirect
296. C₂×#450	C₂×C₄₃	semidirect
297. C₂×#447	C₂×C₄₃	semidirect
298. #2435	C₂×C₄₃	semidirect
299. #2433	C₂×C₄₃	semidirect
300. #2012	C₂×C₄₃	semidirect
301. #2011	C₂×C₄₃	semidirect
302. #1972	C₂×C₄₃	semidirect
303. #1752	C₂×C₄₃	semidirect
314. C₂²×SD₁₆	C₂²×C₄₃	semidirect
315. C₂²×SD₁₆	C₂²×C₄₃	semidirect
320. C₂²×D₈	C₂²×C₄₃	semidirect
322. C₂×#127	C₂²×C₄₃	semidirect
323. C₂×#124	C₂²×C₄₃	semidirect
331. C₂×#106	C₂²×C₄₃	semidirect
332. C₂×#103	C₂²×C₄₃	semidirect
333. C₂×#102	C₂²×C₄₃	semidirect
334. C₂×#102	C₂²×C₄₃	semidirect
335. C₂×#102	C₂²×C₄₃	semidirect
337. C₂×#97	C₂²×C₄₃	semidirect
340. #390	C₂²×C₄₃	semidirect
341. #390	C₂²×C₄₃	semidirect
344. #336	C₂²×C₄₃	semidirect
345. C₄₃	#25788	direct (N × H)
379. C₂×D₈	D₄×C₄₃	semidirect
381. C₂²×C₈	D₄×C₄₃	semidirect
409. C₂²⋊C₈	D₄×C₄₃	semidirect
560. C₈	#120×C₄₃	semidirect
580. C₂²	C₄₃×#496	semidirect

Maximal subgroups

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

subgroup	index
C₂³×D₈×C₄₃	2
C₂×C₄₃×#496	2
C₂×C₄₃×#465	2
C₂×C₄₃×#450	2
C₂×C₄₃×#447	2
C₄₃×#2435	2
C₄₃×#2433	2
C₄₃×#2012	2
C₄₃×#2011	2
C₄₃×#1972	2
C₄₃×#1752	2
#25788	43

Subgroups — C43×#25788 #24945805

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25788 #24945805