Subgroups — C₄₃×#24211 #24944228

Order 11008.

2118 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#127×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#460	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#450	C₂	1	2	yes	maximal, complemented
4	C₄×C₂²⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2041	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2014	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1982	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1786	C₂	1	2	yes	maximal, complemented
10	C₂³×D₄×C₄₃	—	2	1	no	—
11	C₂³×D₄×C₄₃	—	2	1	no	—
12	C₂³×D₄×C₄₃	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₄₃	C₂²	1	4	yes	complemented
14	C₂×#127×C₄₃	—	2	8	no	—
15	C₂×#127×C₄₃	—	2	1	no	—
16	C₂×#127×C₄₃	—	2	1	no	—
17	C₂×#127×C₄₃	C₂²	1	2	yes	—
18	C₂×#127×C₄₃	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#460	—	2	8	no	—
23	C₄₃×#450	—	2	8	no	—
24	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	complemented
25	C₂×#102×C₄₃	C₂²	1	4	yes	complemented
26	C₂×#102×C₄₃	C₂²	1	4	yes	complemented
27	C₂×#102×C₄₃	C₂²	1	4	yes	complemented
28	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
29	C₄₃×#391	C₂²	1	1	yes	characteristic, complemented
30	C₄₃×#389	C₂²	1	1	yes	characteristic, complemented
31	C₄₃×#387	—	2	1	no	—
32	C₄₃×#385	—	2	1	no	—
33	C₄₃×#380	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
35	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
36	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
37	C₄₃×#336	C₂²	1	2	yes	complemented
38	C₂⁵×C₄₃	—	2	2	no	—
39	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₄₃	—	2	8	no	—
41	C₂²×D₄×C₄₃	—	2	8	no	—
42	C₂²×D₄×C₄₃	—	2	8	no	—
43	C₂²×D₄×C₄₃	—	2	2	no	—
44	C₂²×D₄×C₄₃	—	2	2	no	—
45	C₂²×D₄×C₄₃	—	2	2	no	—
46	C₂²×D₄×C₄₃	—	2	2	no	—
47	C₂²×D₄×C₄₃	—	2	2	no	—
48	C₂²×D₄×C₄₃	—	2	4	no	—
49	C₂²×D₄×C₄₃	—	2	4	no	—
50	C₂²×D₄×C₄₃	—	4	4	no	—
51	C₂²×D₄×C₄₃	—	4	4	no	—
52	C₂²×D₄×C₄₃	—	4	4	no	—
53	C₂²×D₄×C₄₃	—	4	4	no	—
54	C₂²×D₄×C₄₃	—	4	4	no	—
55	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
56	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
59	C₂×SD₁₆×C₄₃	—	2	8	no	—
60	C₂×SD₁₆×C₄₃	—	2	8	no	—
61	C₂×SD₁₆×C₄₃	—	4	4	no	—
62	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
63	#127×C₄₃	—	2	8	no	—
64	#127×C₄₃	—	2	8	no	—
65	#127×C₄₃	—	2	8	no	—
66	#127×C₄₃	—	2	4	no	—
67	#127×C₄₃	D₄	1	8	yes	—
68	C₂²⋊Q₈×C₄₃	—	2	2	no	—
69	C₂²⋊Q₈×C₄₃	D₄	1	4	yes	complemented
70	C₄×Q₈×C₄₃	—	2	4	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₄²×C₄₃	—	2	4	no	—
80	C₂×C₄²×C₄₃	—	2	1	no	—
81	C₂×C₄²×C₄₃	—	2	1	no	—
82	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₄₃	—	2	4	no	—
87	#102×C₄₃	—	2	8	no	—
88	#102×C₄₃	—	2	8	no	—
89	#102×C₄₃	—	4	4	no	—
90	C₂²⋊C₈×C₄₃	—	2	4	no	—
91	#95×C₄₃	—	2	1	no	—
92	#95×C₄₃	—	2	1	no	—
93	#95×C₄₃	—	2	1	no	—
94	#95×C₄₃	—	2	1	no	—
95	#95×C₄₃	—	2	1	no	—
96	C₂⁴×C₄₃	—	2	8	no	—
97	C₂⁴×C₄₃	—	2	4	no	—
98	C₂⁴×C₄₃	—	4	4	no	—
99	C₂⁴×C₄₃	—	4	4	no	—
100	C₂⁴×C₄₃	—	4	4	no	—
101	C₂⁴×C₄₃	—	4	4	no	—
102	C₂⁴×C₄₃	—	4	4	no	—
103	C₂⁴×C₄₃	—	4	4	no	—
104	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂×Q₈×C₄₃	—	2	1	no	—
106	C₂×Q₈×C₄₃	—	2	2	no	—
107	C₂×Q₈×C₄₃	—	2	2	no	—
108	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	complemented
109	C₂×D₄×C₄₃	—	2	8	no	—
110	C₂×D₄×C₄₃	—	2	8	no	—
111	C₂×D₄×C₄₃	—	2	8	no	—
112	C₂×D₄×C₄₃	—	2	8	no	—
113	C₂×D₄×C₄₃	—	2	8	no	—
114	C₂×D₄×C₄₃	—	2	4	no	—
115	C₂×D₄×C₄₃	—	2	4	no	—
116	C₂×D₄×C₄₃	—	2	4	no	—
117	C₂×D₄×C₄₃	—	2	4	no	—
118	C₂×D₄×C₄₃	—	2	4	no	—
119	C₂×D₄×C₄₃	—	4	16	no	—
120	C₂×D₄×C₄₃	—	4	16	no	—
121	C₂×D₄×C₄₃	—	4	32	no	—
122	C₂×D₄×C₄₃	—	4	32	no	—
123	C₂×D₄×C₄₃	—	4	4	no	—
124	C₂×D₄×C₄₃	—	4	4	no	—
125	C₂×D₄×C₄₃	—	4	4	no	—
126	C₂×D₄×C₄₃	—	4	4	no	—
127	C₂×D₄×C₄₃	—	4	4	no	—
128	C₂×D₄×C₄₃	—	4	4	no	—
129	C₂×D₄×C₄₃	—	4	4	no	—
130	C₂×D₄×C₄₃	—	4	4	no	—
131	C₂×D₄×C₄₃	—	4	4	no	—
132	C₂×D₄×C₄₃	—	4	4	no	—
133	C₂×D₄×C₄₃	C₂×D₄	1	8	yes	—
134	C₂²×C₄×C₄₃	—	2	2	no	—
135	C₂²×C₄×C₄₃	—	2	2	no	—
136	C₂²×C₄×C₄₃	—	2	2	no	—
137	C₂²×C₄×C₄₃	—	2	2	no	—
138	C₂²×C₄×C₄₃	—	2	2	no	—
139	C₂²×C₄×C₄₃	—	2	2	no	—
140	C₂²×C₄×C₄₃	—	2	2	no	—
141	C₂²×C₄×C₄₃	—	2	1	no	—
142	C₂²×C₄×C₄₃	—	2	1	no	—
143	C₂²×C₄×C₄₃	—	2	1	no	—
144	C₂²×C₄×C₄₃	—	2	1	no	—
145	C₂²×C₄×C₄₃	SD₁₆	1	4	yes	complemented
146	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₃	#41	1	2	yes	—
153	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
154	SD₁₆×C₄₃	—	4	16	no	—
155	C₂×C₈×C₄₃	—	2	4	no	—
156	C₂×C₈×C₄₃	—	2	4	no	—
157	C₂×C₈×C₄₃	—	2	4	no	—
158	C₄⋊C₄×C₄₃	—	2	4	no	—
159	C₄⋊C₄×C₄₃	—	2	1	no	—
160	C₄⋊C₄×C₄₃	—	2	2	no	—
161	C₄⋊C₄×C₄₃	—	2	2	no	—
162	C₄⋊C₄×C₄₃	—	4	2	no	—
163	C₄⋊C₄×C₄₃	—	4	2	no	—
164	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	complemented
165	C₂²⋊C₄×C₄₃	—	2	4	no	—
166	C₂²⋊C₄×C₄₃	—	4	2	no	—
167	C₄²×C₄₃	—	2	2	no	—
168	C₄²×C₄₃	—	2	2	no	—
169	C₄²×C₄₃	—	2	2	no	—
170	C₄²×C₄₃	—	4	2	no	—
171	C₄²×C₄₃	—	4	2	no	—
172	C₄²×C₄₃	C₂×D₄	1	4	yes	—
173	C₂³×C₄₃	—	2	1	no	—
174	C₂³×C₄₃	—	2	1	no	—
175	C₂³×C₄₃	—	2	1	no	—
176	C₂³×C₄₃	—	2	1	no	—
177	C₂³×C₄₃	—	2	8	no	—
178	C₂³×C₄₃	—	4	16	no	—
179	C₂³×C₄₃	—	4	16	no	—
180	C₂³×C₄₃	—	4	16	no	—
181	C₂³×C₄₃	—	4	4	no	—
182	C₂³×C₄₃	—	4	4	no	—
183	C₂³×C₄₃	—	4	4	no	—
184	C₂³×C₄₃	—	4	4	no	—
185	C₂³×C₄₃	—	4	4	no	—
186	C₂³×C₄₃	—	4	4	no	—
187	C₂³×C₄₃	—	8	8	no	—
188	C₂³×C₄₃	—	8	8	no	—
189	C₂³×C₄₃	—	8	8	no	—
190	C₂³×C₄₃	—	8	8	no	—
191	C₂³×C₄₃	#121	1	2	yes	—
192	C₂³×C₄₃	C₂×SD₁₆	1	2	yes	—
193	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
194	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₄₃	—	2	4	no	—
196	Q₈×C₄₃	—	4	2	no	—
197	D₄×C₄₃	—	2	8	no	—
198	D₄×C₄₃	—	2	8	no	—
199	D₄×C₄₃	—	4	16	no	—
200	D₄×C₄₃	—	4	16	no	—
201	D₄×C₄₃	—	4	16	no	—
202	D₄×C₄₃	—	4	16	no	—
203	D₄×C₄₃	—	4	4	no	—
204	D₄×C₄₃	—	4	4	no	—
205	D₄×C₄₃	—	4	16	no	—
206	C₂×C₄×C₄₃	—	2	8	no	—
207	C₂×C₄×C₄₃	—	2	1	no	—
208	C₂×C₄×C₄₃	—	2	1	no	—
209	C₂×C₄×C₄₃	—	2	1	no	—
210	C₂×C₄×C₄₃	—	2	1	no	—
211	C₂×C₄×C₄₃	—	2	1	no	—
212	C₂×C₄×C₄₃	—	2	1	no	—
213	C₂×C₄×C₄₃	—	2	1	no	—
214	C₂×C₄×C₄₃	—	2	1	no	—
215	C₂×C₄×C₄₃	—	2	4	no	—
216	C₂×C₄×C₄₃	—	2	4	no	—
217	C₂×C₄×C₄₃	—	2	8	no	—
218	C₂×C₄×C₄₃	—	2	2	no	—
219	C₂×C₄×C₄₃	—	2	2	no	—
220	C₂×C₄×C₄₃	—	4	1	no	—
221	C₂×C₄×C₄₃	—	4	1	no	—
222	C₂×C₄×C₄₃	—	4	1	no	—
223	C₂×C₄×C₄₃	—	4	1	no	—
224	C₂×C₄×C₄₃	—	4	1	no	—
225	C₂×C₄×C₄₃	—	4	1	no	—
226	C₂×C₄×C₄₃	—	4	1	no	—
227	C₂×C₄×C₄₃	—	4	1	no	—
228	C₂×C₄×C₄₃	—	4	1	no	—
229	C₂×C₄×C₄₃	—	4	1	no	—
230	C₂×C₄×C₄₃	#120	1	2	yes	—
231	C₂×C₄×C₄₃	#120	1	2	yes	—
232	C₂×C₄×C₄₃	#121	1	2	yes	—
233	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
234	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
235	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
236	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
237	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
239	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
241	C₈×C₄₃	—	4	4	no	—
242	#24211	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂²×C₄₃	—	2	2	no	—
244	C₂²×C₄₃	—	2	2	no	—
245	C₂²×C₄₃	—	2	2	no	—
246	C₂²×C₄₃	—	2	2	no	—
247	C₂²×C₄₃	—	2	2	no	—
248	C₂²×C₄₃	—	2	2	no	—
249	C₂²×C₄₃	—	4	8	no	—
250	C₂²×C₄₃	—	4	8	no	—
251	C₂²×C₄₃	—	4	8	no	—
252	C₂²×C₄₃	—	8	32	no	—
253	C₂²×C₄₃	—	8	4	no	—
254	C₂²×C₄₃	—	8	4	no	—
255	C₂²×C₄₃	—	8	4	no	—
256	C₂²×C₄₃	—	8	4	no	—
257	C₂²×C₄₃	#460	1	4	yes	complemented
258	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
259	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
260	C₂²×C₄₃	#535	1	1	yes	characteristic
261	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
262	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
263	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
264	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
265	C₄×C₄₃	—	2	2	no	—
266	C₄×C₄₃	—	2	2	no	—
267	C₄×C₄₃	—	2	2	no	—
268	C₄×C₄₃	—	2	2	no	—
269	C₄×C₄₃	—	4	2	no	—
270	C₄×C₄₃	—	4	2	no	—
271	C₄×C₄₃	—	8	1	no	—
272	C₄×C₄₃	—	8	1	no	—
273	C₄×C₄₃	#450	1	4	yes	complemented
274	C₄×C₄₃	D₄²	1	2	yes	—
275	C₄×C₄₃	#546	1	2	yes	—
276	C₂²×#127	C₂×C₄₃	1	1	yes	characteristic
277	C₂×#460	C₂×C₄₃	1	2	yes	complemented
278	C₂×#450	C₂×C₄₃	1	2	yes	complemented
279	C₄×C₂²⋊Q₈	C₂×C₄₃	1	1	yes	characteristic, complemented
280	#2041	C₂×C₄₃	1	2	yes	complemented
281	#2014	C₂×C₄₃	1	2	yes	complemented
282	#1982	C₂×C₄₃	1	2	yes	complemented
283	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
284	#1786	C₂×C₄₃	1	2	yes	complemented
285	C₂×C₄₃	—	2	4	no	—
286	C₂×C₄₃	—	8	8	no	—
287	C₂×C₄₃	#2408	1	1	yes	characteristic
288	C₂×C₄₃	C₂×#450	1	1	yes	characteristic
289	C₂×C₄₃	#3003	1	1	yes	characteristic
290	C₂×C₄₃	C₂×#460	1	1	yes	characteristic
291	C₂×C₄₃	#3038	1	1	yes	characteristic
292	C₂×C₄₃	#3208	1	1	yes	characteristic
293	C₂×C₄₃	#3217	1	1	yes	characteristic
294	C₂³×D₄	—	2	1	no	—
295	C₂³×D₄	—	2	1	no	—
296	C₂³×D₄	C₂²×C₄₃	1	2	yes	—
297	C₂²×SD₁₆	C₂²×C₄₃	1	4	yes	complemented
298	C₂×#127	—	2	8	no	—
299	C₂×#127	—	2	1	no	—
300	C₂×#127	—	2	1	no	—
301	C₂×#127	C₂²×C₄₃	1	2	yes	—
302	C₂×#127	C₂²×C₄₃	1	2	yes	—
303	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
304	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
305	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
306	#460	—	2	8	no	—
307	#450	—	2	8	no	—
308	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	complemented
309	C₂×#102	C₂²×C₄₃	1	4	yes	complemented
310	C₂×#102	C₂²×C₄₃	1	4	yes	complemented
311	C₂×#102	C₂²×C₄₃	1	4	yes	complemented
312	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
313	#391	C₂²×C₄₃	1	1	yes	characteristic, complemented
314	#389	C₂²×C₄₃	1	1	yes	characteristic, complemented
315	#387	—	2	1	no	—
316	#385	—	2	1	no	—
317	#380	C₂²×C₄₃	1	1	yes	characteristic
318	C₄×C₄⋊C₄	—	2	1	no	—
319	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic, complemented
320	C₄×C₂²⋊C₄	—	2	1	no	—
321	#336	C₂²×C₄₃	1	2	yes	complemented
322	C₄₃	#24211	1	1	yes	characteristic, direct product factor, Sylow
323	C₂⁵	—	2	2	no	—
324	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
325	C₂²×D₄	—	2	8	no	—
326	C₂²×D₄	—	2	8	no	—
327	C₂²×D₄	—	2	8	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	—	2	2	no	—
331	C₂²×D₄	—	2	2	no	—
332	C₂²×D₄	—	2	2	no	—
333	C₂²×D₄	—	2	4	no	—
334	C₂²×D₄	—	2	4	no	—
335	C₂²×D₄	—	4	4	no	—
336	C₂²×D₄	—	4	4	no	—
337	C₂²×D₄	—	4	4	no	—
338	C₂²×D₄	—	4	4	no	—
339	C₂²×D₄	—	4	4	no	—
340	C₂²×D₄	C₂³×C₄₃	1	4	yes	—
341	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
342	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
343	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
344	C₂×SD₁₆	—	2	8	no	—
345	C₂×SD₁₆	—	2	8	no	—
346	C₂×SD₁₆	—	4	4	no	—
347	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
348	#127	—	2	8	no	—
349	#127	—	2	8	no	—
350	#127	—	2	8	no	—
351	#127	—	2	4	no	—
352	#127	D₄×C₄₃	1	8	yes	—
353	C₂²⋊Q₈	—	2	2	no	—
354	C₂²⋊Q₈	D₄×C₄₃	1	4	yes	complemented
355	C₄×Q₈	—	2	4	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₄²	—	2	4	no	—
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	—	2	1	no	—
367	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
368	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
370	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
371	C₄⋊C₈	—	2	4	no	—
372	#102	—	2	8	no	—
373	#102	—	2	8	no	—
374	#102	—	4	4	no	—
375	C₂²⋊C₈	—	2	4	no	—
376	#95	—	2	1	no	—
377	#95	—	2	1	no	—
378	#95	—	2	1	no	—
379	#95	—	2	1	no	—
380	#95	—	2	1	no	—
381	C₂⁴	—	2	8	no	—
382	C₂⁴	—	2	4	no	—
383	C₂⁴	—	4	4	no	—
384	C₂⁴	—	4	4	no	—
385	C₂⁴	—	4	4	no	—
386	C₂⁴	—	4	4	no	—
387	C₂⁴	—	4	4	no	—
388	C₂⁴	—	4	4	no	—
389	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	complemented
394	C₂×D₄	—	2	8	no	—
395	C₂×D₄	—	2	8	no	—
396	C₂×D₄	—	2	8	no	—
397	C₂×D₄	—	2	8	no	—
398	C₂×D₄	—	2	8	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	4	16	no	—
405	C₂×D₄	—	4	16	no	—
406	C₂×D₄	—	4	32	no	—
407	C₂×D₄	—	4	4	no	—
408	C₂×D₄	—	4	4	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	—	4	4	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂×D₄	—	4	32	no	—
413	C₂×D₄	—	4	4	no	—
414	C₂×D₄	—	4	4	no	—
415	C₂×D₄	—	4	4	no	—
416	C₂×D₄	—	4	4	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	C₂×D₄×C₄₃	1	8	yes	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	SD₁₆×C₄₃	1	4	yes	complemented
431	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
434	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
437	C₂²×C₄	#41×C₄₃	1	2	yes	—
438	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
439	SD₁₆	—	4	16	no	—
440	C₂×C₈	—	2	4	no	—
441	C₂×C₈	—	2	4	no	—
442	C₂×C₈	—	2	4	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	4	2	no	—
448	C₄⋊C₄	—	4	2	no	—
449	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	complemented
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	4	2	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	4	2	no	—
456	C₄²	—	4	2	no	—
457	C₄²	C₂×D₄×C₄₃	1	4	yes	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	8	no	—
463	C₂³	—	4	16	no	—
464	C₂³	—	4	16	no	—
465	C₂³	—	4	16	no	—
466	C₂³	—	4	4	no	—
467	C₂³	—	4	4	no	—
468	C₂³	—	4	4	no	—
469	C₂³	—	4	4	no	—
470	C₂³	—	4	4	no	—
471	C₂³	—	4	4	no	—
472	C₂³	—	8	8	no	—
473	C₂³	—	8	8	no	—
474	C₂³	—	8	8	no	—
475	C₂³	—	8	8	no	—
476	C₂³	#121×C₄₃	1	2	yes	—
477	C₂³	C₂×SD₁₆×C₄₃	1	2	yes	—
478	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
479	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
480	Q₈	—	2	4	no	—
481	Q₈	—	4	2	no	—
482	D₄	—	2	8	no	—
483	D₄	—	2	8	no	—
484	D₄	—	4	16	no	—
485	D₄	—	4	16	no	—
486	D₄	—	4	16	no	—
487	D₄	—	4	16	no	—
488	D₄	—	4	4	no	—
489	D₄	—	4	4	no	—
490	D₄	—	4	16	no	—
491	C₂×C₄	—	2	8	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	#120×C₄₃	1	2	yes	—
516	C₂×C₄	#120×C₄₃	1	2	yes	—
517	C₂×C₄	#121×C₄₃	1	2	yes	—
518	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
519	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
520	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
521	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
522	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
524	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
525	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
526	C₈	—	4	4	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	8	no	—
534	C₂²	—	4	8	no	—
535	C₂²	—	4	8	no	—
536	C₂²	—	8	32	no	—
537	C₂²	—	8	4	no	—
538	C₂²	—	8	4	no	—
539	C₂²	—	8	4	no	—
540	C₂²	—	8	4	no	—
541	C₂²	C₄₃×#460	1	4	yes	complemented
542	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
543	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
544	C₂²	C₄₃×#535	1	1	yes	characteristic
545	C₂²	C₂²×SD₁₆×C₄₃	1	1	yes	characteristic
546	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
547	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
548	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	2	no	—
552	C₄	—	2	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	2	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	C₄₃×#450	1	4	yes	complemented
558	C₄	D₄²×C₄₃	1	2	yes	—
559	C₄	C₄₃×#546	1	2	yes	—
560	C₂	—	2	4	no	—
561	C₂	—	8	8	no	—
562	C₂	C₄₃×#2408	1	1	yes	characteristic
563	C₂	C₂×C₄₃×#450	1	1	yes	characteristic
564	C₂	C₄₃×#3003	1	1	yes	characteristic
565	C₂	C₂×C₄₃×#460	1	1	yes	characteristic
566	C₂	C₄₃×#3038	1	1	yes	characteristic
567	C₂	C₄₃×#3208	1	1	yes	characteristic
568	C₂	C₄₃×#3217	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×#127×C₄₃	C₂
LCS	G ▷ C₂²×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×C₄₃×#460	C₂	semidirect
3. C₂×C₄₃×#450	C₂	semidirect
4. C₄×C₂²⋊Q₈×C₄₃	C₂	semidirect
5. C₄₃×#2041	C₂	semidirect
6. C₄₃×#2014	C₂	semidirect
7. C₄₃×#1982	C₂	semidirect
8. C₄₃×#1797	C₂	semidirect
9. C₄₃×#1786	C₂	semidirect
13. C₂²×SD₁₆×C₄₃	C₂²	semidirect
20. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
24. C₂×C₄⋊C₈×C₄₃	C₂²	semidirect
25. C₂×#102×C₄₃	C₂²	semidirect
26. C₂×#102×C₄₃	C₂²	semidirect
27. C₂×#102×C₄₃	C₂²	semidirect
29. C₄₃×#391	C₂²	semidirect
30. C₄₃×#389	C₂²	semidirect
35. C₄×C₄⋊C₄×C₄₃	C₂²	semidirect
37. C₄₃×#336	C₂²	semidirect
69. C₂²⋊Q₈×C₄₃	D₄	semidirect
108. C₂×Q₈×C₄₃	C₂×D₄	semidirect
145. C₂²×C₄×C₄₃	SD₁₆	semidirect
164. C₄⋊C₄×C₄₃	C₂×D₄	semidirect
242. #24211	C₄₃	direct (N × H)
257. C₂²×C₄₃	#460	semidirect
273. C₄×C₄₃	#450	semidirect
277. C₂×#460	C₂×C₄₃	semidirect
278. C₂×#450	C₂×C₄₃	semidirect
279. C₄×C₂²⋊Q₈	C₂×C₄₃	semidirect
280. #2041	C₂×C₄₃	semidirect
281. #2014	C₂×C₄₃	semidirect
282. #1982	C₂×C₄₃	semidirect
283. #1797	C₂×C₄₃	semidirect
284. #1786	C₂×C₄₃	semidirect
297. C₂²×SD₁₆	C₂²×C₄₃	semidirect
304. C₂×C₄×Q₈	C₂²×C₄₃	semidirect
308. C₂×C₄⋊C₈	C₂²×C₄₃	semidirect
309. C₂×#102	C₂²×C₄₃	semidirect
310. C₂×#102	C₂²×C₄₃	semidirect
311. C₂×#102	C₂²×C₄₃	semidirect
313. #391	C₂²×C₄₃	semidirect
314. #389	C₂²×C₄₃	semidirect
319. C₄×C₄⋊C₄	C₂²×C₄₃	semidirect
321. #336	C₂²×C₄₃	semidirect
322. C₄₃	#24211	direct (N × H)
354. C₂²⋊Q₈	D₄×C₄₃	semidirect
393. C₂×Q₈	C₂×D₄×C₄₃	semidirect
430. C₂²×C₄	SD₁₆×C₄₃	semidirect
449. C₄⋊C₄	C₂×D₄×C₄₃	semidirect
541. C₂²	C₄₃×#460	semidirect
557. C₄	C₄₃×#450	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#127×C₄₃	2
C₂×C₄₃×#460	2
C₂×C₄₃×#450	2
C₄×C₂²⋊Q₈×C₄₃	2
C₄₃×#2041	2
C₄₃×#2014	2
C₄₃×#1982	2
C₄₃×#1797	2
C₄₃×#1786	2
#24211	43

Subgroups — C43×#24211 #24944228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#24211 #24944228