Subgroups — C₄₃×#29662 #24949679

Order 11008.

1304 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2856	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2025	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2012	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2000	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1999	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
13	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
14	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
15	C₄₃×#529	—	2	4	no	—
16	C₄₃×#529	—	2	4	no	—
17	C₂×#126×C₄₃	—	2	1	no	—
18	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#123×C₄₃	—	2	1	no	—
21	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#121×C₄₃	—	2	1	no	—
23	C₂×#121×C₄₃	—	2	1	no	—
24	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#121×C₄₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₄₃	—	2	1	no	—
28	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×#117×C₄₃	—	2	1	no	—
30	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
31	C₄₃×#460	—	2	4	no	—
32	C₄₃×#459	—	2	4	no	—
33	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×#103×C₄₃	C₂²	1	2	yes	—
36	C₂×#102×C₄₃	C₂²	1	2	yes	—
37	C₂×#102×C₄₃	C₂²	1	2	yes	—
38	C₂×#102×C₄₃	C₂²	1	2	yes	—
39	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
40	C₄₃×#390	—	2	1	no	—
41	C₄₃×#390	—	2	1	no	—
42	C₄₃×#390	C₂²	1	2	yes	—
43	C₄₃×#384	C₂²	1	1	yes	characteristic
44	C₄₃×#340	C₂²	1	2	yes	—
45	C₄₃×#340	C₂²	1	2	yes	—
46	C₄₃×#336	C₂²	1	2	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	1	no	—
51	C₂²×D₄×C₄₃	—	2	1	no	—
52	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
53	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₄₃	—	2	1	no	—
55	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
58	C₂×SD₁₆×C₄₃	—	2	4	no	—
59	C₂×SD₁₆×C₄₃	—	4	2	no	—
60	C₂×SD₁₆×C₄₃	—	4	2	no	—
61	C₂×D₈×C₄₃	—	2	4	no	—
62	C₂×D₈×C₄₃	—	4	2	no	—
63	C₂×D₈×C₄₃	—	4	2	no	—
64	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
65	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
66	#127×C₄₃	—	2	2	no	—
67	#127×C₄₃	—	2	2	no	—
68	#126×C₄₃	—	2	8	no	—
69	#125×C₄₃	—	2	2	no	—
70	#125×C₄₃	—	2	2	no	—
71	#124×C₄₃	—	2	2	no	—
72	#124×C₄₃	—	2	2	no	—
73	#123×C₄₃	—	2	8	no	—
74	C₂²⋊Q₈×C₄₃	—	2	2	no	—
75	C₂²⋊Q₈×C₄₃	—	2	2	no	—
76	#121×C₄₃	—	2	2	no	—
77	#121×C₄₃	—	2	2	no	—
78	#121×C₄₃	—	4	2	no	—
79	#121×C₄₃	—	4	2	no	—
80	#121×C₄₃	—	4	4	no	—
81	#121×C₄₃	—	4	4	no	—
82	C₄×Q₈×C₄₃	—	2	2	no	—
83	C₄×Q₈×C₄₃	D₄	1	4	yes	complemented
84	C₄×D₄×C₄₃	—	2	8	no	—
85	C₄×D₄×C₄₃	—	2	2	no	—
86	C₄×D₄×C₄₃	D₄	1	4	yes	complemented
87	#117×C₄₃	—	2	8	no	—
88	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
89	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
91	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
92	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
93	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
103	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
104	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
105	C₂×C₄²×C₄₃	—	2	1	no	—
106	C₂×C₄²×C₄₃	—	2	2	no	—
107	C₂×C₄²×C₄₃	—	2	2	no	—
108	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
112	C₄⋊C₈×C₄₃	—	2	2	no	—
113	C₄⋊C₈×C₄₃	—	2	2	no	—
114	#103×C₄₃	—	4	2	no	—
115	#102×C₄₃	—	2	4	no	—
116	#102×C₄₃	—	2	4	no	—
117	#102×C₄₃	—	4	2	no	—
118	C₂²⋊C₈×C₄₃	—	4	2	no	—
119	C₂⁴×C₄₃	—	2	1	no	—
120	C₂⁴×C₄₃	—	2	2	no	—
121	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂×Q₈×C₄₃	—	2	1	no	—
123	C₂×Q₈×C₄₃	—	2	1	no	—
124	C₂×Q₈×C₄₃	—	2	1	no	—
125	C₂×Q₈×C₄₃	—	2	1	no	—
126	C₂×Q₈×C₄₃	—	2	1	no	—
127	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
128	C₂×D₄×C₄₃	—	2	4	no	—
129	C₂×D₄×C₄₃	—	2	1	no	—
130	C₂×D₄×C₄₃	—	2	2	no	—
131	C₂×D₄×C₄₃	—	2	2	no	—
132	C₂×D₄×C₄₃	—	2	1	no	—
133	C₂×D₄×C₄₃	—	2	1	no	—
134	C₂×D₄×C₄₃	—	2	1	no	—
135	C₂×D₄×C₄₃	—	2	2	no	—
136	C₂×D₄×C₄₃	—	2	2	no	—
137	C₂×D₄×C₄₃	—	2	2	no	—
138	C₂×D₄×C₄₃	—	2	1	no	—
139	C₂×D₄×C₄₃	—	2	2	no	—
140	C₂×D₄×C₄₃	—	4	2	no	—
141	C₂×D₄×C₄₃	—	4	4	no	—
142	C₂×D₄×C₄₃	—	4	4	no	—
143	C₂×D₄×C₄₃	—	4	2	no	—
144	C₂×D₄×C₄₃	—	4	2	no	—
145	C₂×D₄×C₄₃	—	4	2	no	—
146	C₂×D₄×C₄₃	—	4	2	no	—
147	C₂×D₄×C₄₃	—	4	2	no	—
148	C₂×D₄×C₄₃	—	4	2	no	—
149	C₂×D₄×C₄₃	—	4	2	no	—
150	C₂×D₄×C₄₃	—	4	4	no	—
151	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₄₃	—	2	2	no	—
153	C₂²×C₄×C₄₃	—	2	2	no	—
154	C₂²×C₄×C₄₃	—	2	4	no	—
155	C₂²×C₄×C₄₃	—	2	2	no	—
156	C₂²×C₄×C₄₃	—	2	2	no	—
157	C₂²×C₄×C₄₃	—	2	1	no	—
158	C₂²×C₄×C₄₃	—	2	1	no	—
159	C₂²×C₄×C₄₃	—	2	1	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	—	2	2	no	—
164	C₂²×C₄×C₄₃	—	2	1	no	—
165	C₂²×C₄×C₄₃	—	2	1	no	—
166	C₂²×C₄×C₄₃	—	2	1	no	—
167	C₂²×C₄×C₄₃	—	2	2	no	—
168	C₂²×C₄×C₄₃	—	4	1	no	—
169	C₂²×C₄×C₄₃	—	4	2	no	—
170	C₂²×C₄×C₄₃	—	4	2	no	—
171	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
177	SD₁₆×C₄₃	—	4	8	no	—
178	D₈×C₄₃	—	4	8	no	—
179	C₂×C₈×C₄₃	—	2	2	no	—
180	C₂×C₈×C₄₃	—	2	2	no	—
181	C₂×C₈×C₄₃	—	2	2	no	—
182	C₂×C₈×C₄₃	—	2	2	no	—
183	C₂×C₈×C₄₃	—	2	2	no	—
184	C₂×C₈×C₄₃	—	2	2	no	—
185	C₄⋊C₄×C₄₃	—	2	4	no	—
186	C₄⋊C₄×C₄₃	—	2	4	no	—
187	C₄⋊C₄×C₄₃	—	2	4	no	—
188	C₄⋊C₄×C₄₃	—	2	4	no	—
189	C₄⋊C₄×C₄₃	—	2	1	no	—
190	C₄⋊C₄×C₄₃	—	2	1	no	—
191	C₄⋊C₄×C₄₃	—	2	2	no	—
192	C₄⋊C₄×C₄₃	—	2	2	no	—
193	C₄⋊C₄×C₄₃	—	4	2	no	—
194	C₄⋊C₄×C₄₃	—	4	2	no	—
195	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
196	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
197	C₂²⋊C₄×C₄₃	—	2	4	no	—
198	C₂²⋊C₄×C₄₃	—	2	4	no	—
199	C₂²⋊C₄×C₄₃	—	2	4	no	—
200	C₂²⋊C₄×C₄₃	—	2	4	no	—
201	C₂²⋊C₄×C₄₃	—	2	4	no	—
202	C₂²⋊C₄×C₄₃	—	4	4	no	—
203	C₂²⋊C₄×C₄₃	—	4	4	no	—
204	C₂²⋊C₄×C₄₃	—	4	4	no	—
205	C₄²×C₄₃	—	2	2	no	—
206	C₄²×C₄₃	—	2	2	no	—
207	C₄²×C₄₃	—	2	4	no	—
208	C₄²×C₄₃	—	2	1	no	—
209	C₄²×C₄₃	—	2	1	no	—
210	C₄²×C₄₃	C₂×D₄	1	2	yes	—
211	C₄²×C₄₃	C₂×D₄	1	2	yes	—
212	C₂³×C₄₃	—	2	1	no	—
213	C₂³×C₄₃	—	2	1	no	—
214	C₂³×C₄₃	—	2	1	no	—
215	C₂³×C₄₃	—	2	1	no	—
216	C₂³×C₄₃	—	2	1	no	—
217	C₂³×C₄₃	—	2	1	no	—
218	C₂³×C₄₃	—	2	2	no	—
219	C₂³×C₄₃	—	4	1	no	—
220	C₂³×C₄₃	—	4	1	no	—
221	C₂³×C₄₃	—	4	1	no	—
222	C₂³×C₄₃	—	4	1	no	—
223	C₂³×C₄₃	—	4	1	no	—
224	C₂³×C₄₃	—	4	1	no	—
225	C₂³×C₄₃	—	4	2	no	—
226	C₂³×C₄₃	—	4	2	no	—
227	C₂³×C₄₃	—	4	2	no	—
228	C₂³×C₄₃	—	4	2	no	—
229	C₂³×C₄₃	—	4	2	no	—
230	C₂³×C₄₃	—	4	2	no	—
231	C₂³×C₄₃	—	4	2	no	—
232	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
233	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₄₃	—	2	2	no	—
235	Q₈×C₄₃	—	2	2	no	—
236	Q₈×C₄₃	—	4	1	no	—
237	Q₈×C₄₃	—	4	1	no	—
238	D₄×C₄₃	—	2	2	no	—
239	D₄×C₄₃	—	2	2	no	—
240	D₄×C₄₃	—	4	8	no	—
241	D₄×C₄₃	—	4	1	no	—
242	D₄×C₄₃	—	4	2	no	—
243	D₄×C₄₃	—	4	2	no	—
244	D₄×C₄₃	—	4	1	no	—
245	D₄×C₄₃	—	4	2	no	—
246	D₄×C₄₃	—	4	2	no	—
247	D₄×C₄₃	—	8	4	no	—
248	D₄×C₄₃	—	8	8	no	—
249	D₄×C₄₃	—	8	4	no	—
250	C₂×C₄×C₄₃	—	2	1	no	—
251	C₂×C₄×C₄₃	—	2	1	no	—
252	C₂×C₄×C₄₃	—	2	1	no	—
253	C₂×C₄×C₄₃	—	2	1	no	—
254	C₂×C₄×C₄₃	—	2	1	no	—
255	C₂×C₄×C₄₃	—	2	2	no	—
256	C₂×C₄×C₄₃	—	2	2	no	—
257	C₂×C₄×C₄₃	—	2	2	no	—
258	C₂×C₄×C₄₃	—	2	1	no	—
259	C₂×C₄×C₄₃	—	2	1	no	—
260	C₂×C₄×C₄₃	—	2	1	no	—
261	C₂×C₄×C₄₃	—	2	1	no	—
262	C₂×C₄×C₄₃	—	2	1	no	—
263	C₂×C₄×C₄₃	—	2	1	no	—
264	C₂×C₄×C₄₃	—	4	4	no	—
265	C₂×C₄×C₄₃	—	4	1	no	—
266	C₂×C₄×C₄₃	—	4	1	no	—
267	C₂×C₄×C₄₃	—	4	1	no	—
268	C₂×C₄×C₄₃	—	4	1	no	—
269	C₂×C₄×C₄₃	—	4	1	no	—
270	C₂×C₄×C₄₃	—	4	1	no	—
271	C₂×C₄×C₄₃	—	4	1	no	—
272	C₂×C₄×C₄₃	—	4	1	no	—
273	C₂×C₄×C₄₃	—	4	1	no	—
274	C₂×C₄×C₄₃	—	4	1	no	—
275	C₂×C₄×C₄₃	—	4	4	no	—
276	C₂×C₄×C₄₃	—	4	8	no	—
277	C₂×C₄×C₄₃	—	4	2	no	—
278	C₂×C₄×C₄₃	—	4	2	no	—
279	C₂×C₄×C₄₃	—	4	2	no	—
280	C₂×C₄×C₄₃	#120	1	2	yes	—
281	C₂×C₄×C₄₃	#120	1	2	yes	—
282	C₂×C₄×C₄₃	#135	1	2	yes	—
283	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
284	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
287	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
288	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
289	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
290	C₈×C₄₃	—	4	2	no	—
291	C₈×C₄₃	—	4	2	no	—
292	#29662	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
293	C₂²×C₄₃	—	2	2	no	—
294	C₂²×C₄₃	—	2	2	no	—
295	C₂²×C₄₃	—	2	2	no	—
296	C₂²×C₄₃	—	4	1	no	—
297	C₂²×C₄₃	—	4	1	no	—
298	C₂²×C₄₃	—	4	1	no	—
299	C₂²×C₄₃	—	4	1	no	—
300	C₂²×C₄₃	—	4	2	no	—
301	C₂²×C₄₃	—	4	2	no	—
302	C₂²×C₄₃	—	4	2	no	—
303	C₂²×C₄₃	—	8	1	no	—
304	C₂²×C₄₃	—	8	1	no	—
305	C₂²×C₄₃	—	8	1	no	—
306	C₂²×C₄₃	—	8	1	no	—
307	C₂²×C₄₃	—	8	2	no	—
308	C₂²×C₄₃	—	8	2	no	—
309	C₂²×C₄₃	—	8	2	no	—
310	C₂²×C₄₃	—	8	2	no	—
311	C₂²×C₄₃	—	8	2	no	—
312	C₂²×C₄₃	—	8	2	no	—
313	C₂²×C₄₃	—	8	2	no	—
314	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
315	C₂²×C₄₃	#535	1	1	yes	characteristic
316	C₂²×C₄₃	#537	1	1	yes	characteristic
317	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
318	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
319	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
320	C₂²×C₄₃	#575	1	1	yes	characteristic
321	C₄×C₄₃	—	2	2	no	—
322	C₄×C₄₃	—	4	1	no	—
323	C₄×C₄₃	—	4	2	no	—
324	C₄×C₄₃	—	4	1	no	—
325	C₄×C₄₃	—	4	2	no	—
326	C₄×C₄₃	—	4	1	no	—
327	C₄×C₄₃	—	4	2	no	—
328	C₄×C₄₃	—	8	2	no	—
329	C₄×C₄₃	#449	1	4	yes	—
330	C₄×C₄₃	#535	1	1	yes	characteristic
331	C₄×C₄₃	#535	1	1	yes	characteristic
332	C₄×C₄₃	#537	1	1	yes	characteristic
333	C₄×C₄₃	#537	1	1	yes	characteristic
334	C₂×#529	C₂×C₄₃	1	1	yes	characteristic, complemented
335	C₂×#460	C₂×C₄₃	1	1	yes	characteristic, complemented
336	C₂×#459	C₂×C₄₃	1	1	yes	characteristic, complemented
337	#2856	C₂×C₄₃	1	1	yes	characteristic, complemented
338	#2025	C₂×C₄₃	1	2	yes	complemented
339	#2012	C₂×C₄₃	1	2	yes	complemented
340	#2000	C₂×C₄₃	1	2	yes	complemented
341	#1999	C₂×C₄₃	1	2	yes	complemented
342	#1803	C₂×C₄₃	1	1	yes	characteristic, complemented
343	#1802	C₂×C₄₃	1	1	yes	characteristic, complemented
344	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
345	C₂×C₄₃	—	4	2	no	—
346	C₂×C₄₃	—	8	2	no	—
347	C₂×C₄₃	—	16	2	no	—
348	C₂×C₄₃	#2615	1	1	yes	characteristic
349	C₂×C₄₃	C₂×#449	1	1	yes	characteristic
350	C₂×C₄₃	#3006	1	1	yes	characteristic
351	C₂×C₄₃	#3212	1	1	yes	characteristic
352	C₂×C₄₃	#3217	1	1	yes	characteristic
353	C₂×C₄₃	#3247	1	1	yes	characteristic
354	C₂×C₄₃	#3251	1	1	yes	characteristic
355	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
356	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
357	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
358	#529	—	2	4	no	—
359	#529	—	2	4	no	—
360	C₂×#126	—	2	1	no	—
361	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
362	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
363	C₂×#123	—	2	1	no	—
364	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
365	C₂×#121	—	2	1	no	—
366	C₂×#121	—	2	1	no	—
367	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
368	C₂×#121	C₂²×C₄₃	1	2	yes	—
369	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
370	C₂×C₄×D₄	—	2	1	no	—
371	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
372	C₂×#117	—	2	1	no	—
373	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
374	#460	—	2	4	no	—
375	#459	—	2	4	no	—
376	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
377	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
378	C₂×#103	C₂²×C₄₃	1	2	yes	—
379	C₂×#102	C₂²×C₄₃	1	2	yes	—
380	C₂×#102	C₂²×C₄₃	1	2	yes	—
381	C₂×#102	C₂²×C₄₃	1	2	yes	—
382	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
383	#390	—	2	1	no	—
384	#390	—	2	1	no	—
385	#390	C₂²×C₄₃	1	2	yes	—
386	#384	C₂²×C₄₃	1	1	yes	characteristic
387	#340	C₂²×C₄₃	1	2	yes	—
388	#340	C₂²×C₄₃	1	2	yes	—
389	#336	C₂²×C₄₃	1	2	yes	—
390	C₄₃	#29662	1	1	yes	characteristic, direct product factor, Sylow
391	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
392	C₂²×D₄	—	2	1	no	—
393	C₂²×D₄	—	2	2	no	—
394	C₂²×D₄	—	2	1	no	—
395	C₂²×D₄	—	2	1	no	—
396	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
397	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
398	C₂³×C₄	—	2	1	no	—
399	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
400	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
401	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
402	C₂×SD₁₆	—	2	4	no	—
403	C₂×SD₁₆	—	4	2	no	—
404	C₂×SD₁₆	—	4	2	no	—
405	C₂×D₈	—	2	4	no	—
406	C₂×D₈	—	4	2	no	—
407	C₂×D₈	—	4	2	no	—
408	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
409	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
410	#127	—	2	2	no	—
411	#127	—	2	2	no	—
412	#126	—	2	8	no	—
413	#125	—	2	2	no	—
414	#125	—	2	2	no	—
415	#124	—	2	2	no	—
416	#124	—	2	2	no	—
417	#123	—	2	8	no	—
418	C₂²⋊Q₈	—	2	2	no	—
419	C₂²⋊Q₈	—	2	2	no	—
420	#121	—	2	2	no	—
421	#121	—	2	2	no	—
422	#121	—	4	2	no	—
423	#121	—	4	2	no	—
424	#121	—	4	4	no	—
425	#121	—	4	4	no	—
426	C₄×Q₈	—	2	2	no	—
427	C₄×Q₈	D₄×C₄₃	1	4	yes	complemented
428	C₄×D₄	—	2	8	no	—
429	C₄×D₄	—	2	2	no	—
430	C₄×D₄	D₄×C₄₃	1	4	yes	complemented
431	#117	—	2	8	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	2	no	—
447	C₂×C₂²⋊C₄	—	2	2	no	—
448	C₂×C₂²⋊C₄	—	2	2	no	—
449	C₂×C₄²	—	2	1	no	—
450	C₂×C₄²	—	2	2	no	—
451	C₂×C₄²	—	2	2	no	—
452	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
453	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
454	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
455	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
456	C₄⋊C₈	—	2	2	no	—
457	C₄⋊C₈	—	2	2	no	—
458	#103	—	4	2	no	—
459	#102	—	2	4	no	—
460	#102	—	2	4	no	—
461	#102	—	4	2	no	—
462	C₂²⋊C₈	—	4	2	no	—
463	C₂⁴	—	2	1	no	—
464	C₂⁴	—	2	2	no	—
465	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
472	C₂×D₄	—	2	4	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	4	2	no	—
485	C₂×D₄	—	4	2	no	—
486	C₂×D₄	—	4	2	no	—
487	C₂×D₄	—	4	2	no	—
488	C₂×D₄	—	4	4	no	—
489	C₂×D₄	—	4	4	no	—
490	C₂×D₄	—	4	4	no	—
491	C₂×D₄	—	4	2	no	—
492	C₂×D₄	—	4	2	no	—
493	C₂×D₄	—	4	2	no	—
494	C₂×D₄	—	4	2	no	—
495	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	4	1	no	—
513	C₂²×C₄	—	4	2	no	—
514	C₂²×C₄	—	4	2	no	—
515	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
516	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
517	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
518	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
519	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
520	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
521	SD₁₆	—	4	8	no	—
522	D₈	—	4	8	no	—
523	C₂×C₈	—	2	2	no	—
524	C₂×C₈	—	2	2	no	—
525	C₂×C₈	—	2	2	no	—
526	C₂×C₈	—	2	2	no	—
527	C₂×C₈	—	2	2	no	—
528	C₂×C₈	—	2	2	no	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	4	no	—
531	C₄⋊C₄	—	2	4	no	—
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	4	2	no	—
538	C₄⋊C₄	—	4	2	no	—
539	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
540	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
541	C₂²⋊C₄	—	2	4	no	—
542	C₂²⋊C₄	—	2	4	no	—
543	C₂²⋊C₄	—	2	4	no	—
544	C₂²⋊C₄	—	2	4	no	—
545	C₂²⋊C₄	—	2	4	no	—
546	C₂²⋊C₄	—	4	4	no	—
547	C₂²⋊C₄	—	4	4	no	—
548	C₂²⋊C₄	—	4	4	no	—
549	C₄²	—	2	2	no	—
550	C₄²	—	2	2	no	—
551	C₄²	—	2	4	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	2	1	no	—
554	C₄²	C₂×D₄×C₄₃	1	2	yes	—
555	C₄²	C₂×D₄×C₄₃	1	2	yes	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	2	no	—
563	C₂³	—	4	1	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	2	no	—
570	C₂³	—	4	2	no	—
571	C₂³	—	4	2	no	—
572	C₂³	—	4	2	no	—
573	C₂³	—	4	2	no	—
574	C₂³	—	4	2	no	—
575	C₂³	—	4	2	no	—
576	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
577	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
578	Q₈	—	2	2	no	—
579	Q₈	—	2	2	no	—
580	Q₈	—	4	1	no	—
581	Q₈	—	4	1	no	—
582	D₄	—	2	2	no	—
583	D₄	—	2	2	no	—
584	D₄	—	4	8	no	—
585	D₄	—	4	1	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	2	no	—
588	D₄	—	4	1	no	—
589	D₄	—	4	2	no	—
590	D₄	—	4	2	no	—
591	D₄	—	8	4	no	—
592	D₄	—	8	8	no	—
593	D₄	—	8	4	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	4	4	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	4	no	—
620	C₂×C₄	—	4	8	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	#120×C₄₃	1	2	yes	—
625	C₂×C₄	#120×C₄₃	1	2	yes	—
626	C₂×C₄	#135×C₄₃	1	2	yes	—
627	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
628	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
629	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
630	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
631	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
632	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
633	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
634	C₈	—	4	2	no	—
635	C₈	—	4	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	1	no	—
643	C₂²	—	4	2	no	—
644	C₂²	—	4	2	no	—
645	C₂²	—	4	2	no	—
646	C₂²	—	8	1	no	—
647	C₂²	—	8	1	no	—
648	C₂²	—	8	1	no	—
649	C₂²	—	8	1	no	—
650	C₂²	—	8	2	no	—
651	C₂²	—	8	2	no	—
652	C₂²	—	8	2	no	—
653	C₂²	—	8	2	no	—
654	C₂²	—	8	2	no	—
655	C₂²	—	8	2	no	—
656	C₂²	—	8	2	no	—
657	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
658	C₂²	C₄₃×#535	1	1	yes	characteristic
659	C₂²	C₄₃×#537	1	1	yes	characteristic
660	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
661	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
662	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
663	C₂²	C₄₃×#575	1	1	yes	characteristic
664	C₄	—	2	2	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	2	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	2	no	—
671	C₄	—	8	2	no	—
672	C₄	C₄₃×#449	1	4	yes	—
673	C₄	C₄₃×#535	1	1	yes	characteristic
674	C₄	C₄₃×#535	1	1	yes	characteristic
675	C₄	C₄₃×#537	1	1	yes	characteristic
676	C₄	C₄₃×#537	1	1	yes	characteristic
677	C₂	—	4	2	no	—
678	C₂	—	8	2	no	—
679	C₂	—	16	2	no	—
680	C₂	C₄₃×#2615	1	1	yes	characteristic
681	C₂	C₂×C₄₃×#449	1	1	yes	characteristic
682	C₂	C₄₃×#3006	1	1	yes	characteristic
683	C₂	C₄₃×#3212	1	1	yes	characteristic
684	C₂	C₄₃×#3217	1	1	yes	characteristic
685	C₂	C₄₃×#3247	1	1	yes	characteristic
686	C₂	C₄₃×#3251	1	1	yes	characteristic

	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 ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#529	C₂	semidirect
2. C₂×C₄₃×#460	C₂	semidirect
3. C₂×C₄₃×#459	C₂	semidirect
4. C₄₃×#2856	C₂	semidirect
5. C₄₃×#2025	C₂	semidirect
6. C₄₃×#2012	C₂	semidirect
7. C₄₃×#2000	C₂	semidirect
8. C₄₃×#1999	C₂	semidirect
9. C₄₃×#1803	C₂	semidirect
10. C₄₃×#1802	C₂	semidirect
11. C₄₃×#1797	C₂	semidirect
83. C₄×Q₈×C₄₃	D₄	semidirect
86. C₄×D₄×C₄₃	D₄	semidirect
292. #29662	C₄₃	direct (N × H)
334. C₂×#529	C₂×C₄₃	semidirect
335. C₂×#460	C₂×C₄₃	semidirect
336. C₂×#459	C₂×C₄₃	semidirect
337. #2856	C₂×C₄₃	semidirect
338. #2025	C₂×C₄₃	semidirect
339. #2012	C₂×C₄₃	semidirect
340. #2000	C₂×C₄₃	semidirect
341. #1999	C₂×C₄₃	semidirect
342. #1803	C₂×C₄₃	semidirect
343. #1802	C₂×C₄₃	semidirect
344. #1797	C₂×C₄₃	semidirect
390. C₄₃	#29662	direct (N × H)
427. C₄×Q₈	D₄×C₄₃	semidirect
430. C₄×D₄	D₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#529	2
C₂×C₄₃×#460	2
C₂×C₄₃×#459	2
C₄₃×#2856	2
C₄₃×#2025	2
C₄₃×#2012	2
C₄₃×#2000	2
C₄₃×#1999	2
C₄₃×#1803	2
C₄₃×#1802	2
C₄₃×#1797	2
#29662	43

Subgroups — C43×#29662 #24949679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29662 #24949679