Subgroups — C₄₃×#32945 #24952962

Order 11008.

1346 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#472	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#3006	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1907	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1900	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1815	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1811	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×AGL(1,ℤ/8)×C₄₃	C₂²	1	4	yes	—
11	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
12	C₄₃×#568	—	2	8	no	—
13	C₂×#131×C₄₃	—	2	2	no	—
14	C₂×#131×C₄₃	C₂²	1	2	yes	—
15	C₂×#131×C₄₃	C₂²	1	2	yes	—
16	C₂²×M₁₆×C₄₃	—	2	2	no	—
17	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#121×C₄₃	C₂²	1	2	yes	—
20	C₄₃×#472	—	2	8	no	—
21	C₄₃×#469	—	2	2	no	—
22	C₄₃×#469	—	2	2	no	—
23	C₄₃×#449	—	2	4	no	—
24	C₄₃×#448	—	2	2	no	—
25	C₄₃×#447	—	2	2	no	—
26	C₂×#108×C₄₃	C₂²	1	2	yes	complemented
27	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic, complemented
28	C₄₃×#417	C₂²	1	4	yes	—
29	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
30	C₂×#100×C₄₃	C₂²	1	4	yes	complemented
31	C₄₃×#407	C₂²	1	2	yes	—
32	C₄₃×#343	C₂²	1	4	yes	complemented
33	C₄₃×#341	C₂²	1	2	yes	complemented
34	C₂×#41×C₄₃	—	2	4	no	—
35	C₂×#41×C₄₃	—	2	4	no	—
36	C₂×#41×C₄₃	—	2	1	no	—
37	C₂×#41×C₄₃	—	2	1	no	—
38	C₂×#41×C₄₃	D₄	1	2	yes	—
39	C₂×#41×C₄₃	C₂³	1	2	yes	—
40	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₄₃	—	2	1	no	—
42	C₂²×D₄×C₄₃	—	2	2	no	—
43	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₃	—	2	1	no	—
46	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
47	AGL(1,ℤ/8)×C₄₃	—	2	8	no	—
48	AGL(1,ℤ/8)×C₄₃	—	2	8	no	—
49	C₂×SD₁₆×C₄₃	—	2	4	no	—
50	C₂×D₈×C₄₃	—	2	4	no	—
51	C₂×D₈×C₄₃	—	2	2	no	—
52	C₂×D₈×C₄₃	—	2	4	no	—
53	#131×C₄₃	—	2	16	no	—
54	#131×C₄₃	—	2	4	no	—
55	#131×C₄₃	—	2	4	no	—
56	#131×C₄₃	—	2	4	no	—
57	#131×C₄₃	D₄	1	8	yes	complemented
58	C₂×M₁₆×C₄₃	—	2	16	no	—
59	C₂×M₁₆×C₄₃	—	2	1	no	—
60	C₂×M₁₆×C₄₃	—	2	4	no	—
61	C₂×M₁₆×C₄₃	—	2	2	no	—
62	C₂×M₁₆×C₄₃	—	2	2	no	—
63	C₂×M₁₆×C₄₃	—	2	4	no	—
64	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
65	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
66	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
67	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
68	C₂²×C₈×C₄₃	—	2	1	no	—
69	C₂²×C₈×C₄₃	—	2	2	no	—
70	C₂²×C₈×C₄₃	—	2	2	no	—
71	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
73	#121×C₄₃	—	2	2	no	—
74	#121×C₄₃	—	2	2	no	—
75	#121×C₄₃	—	2	2	no	—
76	#121×C₄₃	—	2	2	no	—
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
79	#108×C₄₃	—	2	4	no	—
80	#106×C₄₃	—	2	2	no	—
81	#103×C₄₃	—	2	4	no	—
82	#102×C₄₃	—	2	4	no	—
83	#102×C₄₃	—	2	4	no	—
84	#100×C₄₃	—	2	8	no	—
85	C₂²⋊C₈×C₄₃	—	2	2	no	—
86	C₂²⋊C₈×C₄₃	—	2	2	no	—
87	C₂⁴×C₄₃	—	2	1	no	—
88	C₂⁴×C₄₃	—	2	2	no	—
89	C₂⁴×C₄₃	#41	1	1	yes	characteristic
90	#41×C₄₃	—	2	4	no	—
91	#41×C₄₃	—	2	8	no	—
92	#41×C₄₃	—	2	4	no	—
93	#41×C₄₃	—	2	4	no	—
94	#41×C₄₃	—	2	4	no	—
95	#41×C₄₃	—	2	2	no	—
96	#41×C₄₃	—	2	2	no	—
97	#41×C₄₃	C₂×D₄	1	4	yes	—
98	#41×C₄₃	#41	1	4	yes	—
99	C₂×Q₈×C₄₃	—	2	4	no	—
100	C₂×Q₈×C₄₃	—	2	1	no	—
101	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
102	C₂×D₄×C₄₃	—	2	8	no	—
103	C₂×D₄×C₄₃	—	2	4	no	—
104	C₂×D₄×C₄₃	—	2	1	no	—
105	C₂×D₄×C₄₃	—	2	2	no	—
106	C₂×D₄×C₄₃	—	2	2	no	—
107	C₂×D₄×C₄₃	—	2	4	no	—
108	C₂×D₄×C₄₃	—	2	2	no	—
109	C₂×D₄×C₄₃	—	2	2	no	—
110	C₂×D₄×C₄₃	—	2	4	no	—
111	C₂×D₄×C₄₃	—	4	2	no	—
112	C₂×D₄×C₄₃	—	4	2	no	—
113	C₂×D₄×C₄₃	—	8	4	no	—
114	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₄₃	—	2	4	no	—
116	C₂²×C₄×C₄₃	—	2	4	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	2	1	no	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
129	SD₁₆×C₄₃	—	4	8	no	—
130	D₈×C₄₃	—	4	8	no	—
131	D₈×C₄₃	—	4	4	no	—
132	M₁₆×C₄₃	—	2	4	no	—
133	M₁₆×C₄₃	—	2	8	no	—
134	M₁₆×C₄₃	—	2	2	no	—
135	M₁₆×C₄₃	—	2	4	no	—
136	M₁₆×C₄₃	—	2	8	no	—
137	M₁₆×C₄₃	—	2	4	no	—
138	M₁₆×C₄₃	—	2	4	no	—
139	M₁₆×C₄₃	—	2	4	no	—
140	M₁₆×C₄₃	C₂×D₄	1	4	yes	—
141	C₂×C₈×C₄₃	—	2	4	no	—
142	C₂×C₈×C₄₃	—	2	8	no	—
143	C₂×C₈×C₄₃	—	2	2	no	—
144	C₂×C₈×C₄₃	—	2	2	no	—
145	C₂×C₈×C₄₃	—	2	8	no	—
146	C₂×C₈×C₄₃	—	2	4	no	—
147	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
150	C₄⋊C₄×C₄₃	—	2	2	no	—
151	C₄⋊C₄×C₄₃	—	2	2	no	—
152	C₂²⋊C₄×C₄₃	—	4	2	no	—
153	C₂²⋊C₄×C₄₃	—	4	2	no	—
154	C₂³×C₄₃	—	2	4	no	—
155	C₂³×C₄₃	—	2	2	no	—
156	C₂³×C₄₃	—	2	2	no	—
157	C₂³×C₄₃	—	4	2	no	—
158	C₂³×C₄₃	—	4	2	no	—
159	C₂³×C₄₃	—	4	4	no	—
160	C₂³×C₄₃	—	8	2	no	—
161	C₂³×C₄₃	—	8	2	no	—
162	C₂³×C₄₃	—	8	2	no	—
163	C₂³×C₄₃	#121	1	1	yes	characteristic
164	C₂³×C₄₃	#121	1	1	yes	characteristic
165	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
166	Q₈×C₄₃	—	2	4	no	—
167	Q₈×C₄₃	—	2	2	no	—
168	Q₈×C₄₃	#121	1	4	yes	—
169	D₄×C₄₃	—	2	8	no	—
170	D₄×C₄₃	—	2	4	no	—
171	D₄×C₄₃	—	2	4	no	—
172	D₄×C₄₃	—	2	4	no	—
173	D₄×C₄₃	—	2	2	no	—
174	D₄×C₄₃	—	4	2	no	—
175	D₄×C₄₃	—	4	4	no	—
176	D₄×C₄₃	—	4	2	no	—
177	D₄×C₄₃	—	8	4	no	—
178	D₄×C₄₃	—	8	4	no	—
179	D₄×C₄₃	#121	1	4	yes	—
180	C₂×C₄×C₄₃	—	2	4	no	—
181	C₂×C₄×C₄₃	—	2	8	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	2	4	no	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	2	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	2	4	no	—
191	C₂×C₄×C₄₃	—	2	1	no	—
192	C₂×C₄×C₄₃	—	4	2	no	—
193	C₂×C₄×C₄₃	—	8	2	no	—
194	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
195	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
200	C₈×C₄₃	—	2	4	no	—
201	C₈×C₄₃	—	2	2	no	—
202	C₈×C₄₃	—	4	4	no	—
203	C₈×C₄₃	#120	1	4	yes	—
204	#32945	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂²×C₄₃	—	2	2	no	—
206	C₂²×C₄₃	—	2	1	no	—
207	C₂²×C₄₃	—	2	4	no	—
208	C₂²×C₄₃	—	2	1	no	—
209	C₂²×C₄₃	—	2	2	no	—
210	C₂²×C₄₃	—	2	2	no	—
211	C₂²×C₄₃	—	4	4	no	—
212	C₂²×C₄₃	—	8	2	no	—
213	C₂²×C₄₃	—	8	4	no	—
214	C₂²×C₄₃	—	8	2	no	—
215	C₂²×C₄₃	—	8	2	no	—
216	C₂²×C₄₃	—	8	2	no	—
217	C₂²×C₄₃	—	16	4	no	—
218	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
219	C₂²×C₄₃	#525	1	2	yes	—
220	C₄×C₄₃	—	2	1	no	—
221	C₄×C₄₃	—	2	4	no	—
222	C₄×C₄₃	—	2	1	no	—
223	C₄×C₄₃	—	8	2	no	—
224	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
225	C₄×C₄₃	C₂×#121	1	2	yes	—
226	C₄×C₄₃	#525	1	1	yes	characteristic
227	C₂×#568	C₂×C₄₃	1	1	yes	characteristic, complemented
228	C₂×#472	C₂×C₄₃	1	2	yes	complemented
229	C₂×#469	C₂×C₄₃	1	1	yes	characteristic, complemented
230	#3006	C₂×C₄₃	1	2	yes	complemented
231	#1907	C₂×C₄₃	1	4	yes	complemented
232	#1900	C₂×C₄₃	1	2	yes	complemented
233	#1815	C₂×C₄₃	1	2	yes	complemented
234	#1811	C₂×C₄₃	1	1	yes	characteristic, complemented
235	C₂×C₄₃	—	2	2	no	—
236	C₂×C₄₃	—	4	1	no	—
237	C₂×C₄₃	—	4	1	no	—
238	C₂×C₄₃	—	4	4	no	—
239	C₂×C₄₃	—	16	2	no	—
240	C₂×C₄₃	#2847	1	1	yes	characteristic
241	C₂×C₄₃	#3068	1	2	yes	—
242	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
243	C₂×AGL(1,ℤ/8)	C₂²×C₄₃	1	4	yes	—
244	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
245	#568	—	2	8	no	—
246	C₂×#131	—	2	2	no	—
247	C₂×#131	C₂²×C₄₃	1	2	yes	—
248	C₂×#131	C₂²×C₄₃	1	2	yes	—
249	C₂²×M₁₆	—	2	2	no	—
250	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
251	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
252	C₂×#121	C₂²×C₄₃	1	2	yes	—
253	#472	—	2	8	no	—
254	#469	—	2	2	no	—
255	#469	—	2	2	no	—
256	#449	—	2	4	no	—
257	#448	—	2	2	no	—
258	#447	—	2	2	no	—
259	C₂×#108	C₂²×C₄₃	1	2	yes	complemented
260	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic, complemented
261	#417	C₂²×C₄₃	1	4	yes	—
262	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
263	C₂×#100	C₂²×C₄₃	1	4	yes	complemented
264	#407	C₂²×C₄₃	1	2	yes	—
265	#343	C₂²×C₄₃	1	4	yes	complemented
266	#341	C₂²×C₄₃	1	2	yes	complemented
267	C₄₃	#32945	1	1	yes	characteristic, direct product factor, Sylow
268	C₂×#41	—	2	4	no	—
269	C₂×#41	—	2	4	no	—
270	C₂×#41	—	2	1	no	—
271	C₂×#41	—	2	1	no	—
272	C₂×#41	D₄×C₄₃	1	2	yes	—
273	C₂×#41	C₂³×C₄₃	1	2	yes	—
274	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
275	C₂²×D₄	—	2	1	no	—
276	C₂²×D₄	—	2	2	no	—
277	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
278	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
279	C₂³×C₄	—	2	1	no	—
280	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
281	AGL(1,ℤ/8)	—	2	8	no	—
282	AGL(1,ℤ/8)	—	2	8	no	—
283	C₂×SD₁₆	—	2	4	no	—
284	C₂×D₈	—	2	4	no	—
285	C₂×D₈	—	2	2	no	—
286	C₂×D₈	—	2	4	no	—
287	#131	—	2	16	no	—
288	#131	—	2	4	no	—
289	#131	—	2	4	no	—
290	#131	—	2	4	no	—
291	#131	D₄×C₄₃	1	8	yes	complemented
292	C₂×M₁₆	—	2	16	no	—
293	C₂×M₁₆	—	2	1	no	—
294	C₂×M₁₆	—	2	4	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	—	2	4	no	—
298	C₂×M₁₆	D₄×C₄₃	1	2	yes	—
299	C₂×M₁₆	D₄×C₄₃	1	2	yes	—
300	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
301	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	—	2	2	no	—
304	C₂²×C₈	—	2	2	no	—
305	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
307	#121	—	2	2	no	—
308	#121	—	2	2	no	—
309	#121	—	2	2	no	—
310	#121	—	2	2	no	—
311	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	#108	—	2	4	no	—
314	#106	—	2	2	no	—
315	#103	—	2	4	no	—
316	#102	—	2	4	no	—
317	#102	—	2	4	no	—
318	#100	—	2	8	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	C₂²⋊C₈	—	2	2	no	—
321	C₂⁴	—	2	1	no	—
322	C₂⁴	—	2	2	no	—
323	C₂⁴	#41×C₄₃	1	1	yes	characteristic
324	#41	—	2	4	no	—
325	#41	—	2	8	no	—
326	#41	—	2	4	no	—
327	#41	—	2	4	no	—
328	#41	—	2	4	no	—
329	#41	—	2	2	no	—
330	#41	—	2	2	no	—
331	#41	C₂×D₄×C₄₃	1	4	yes	—
332	#41	#41×C₄₃	1	4	yes	—
333	C₂×Q₈	—	2	4	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
336	C₂×D₄	—	2	8	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	8	4	no	—
348	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
361	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
363	SD₁₆	—	4	8	no	—
364	D₈	—	4	8	no	—
365	D₈	—	4	4	no	—
366	M₁₆	—	2	4	no	—
367	M₁₆	—	2	8	no	—
368	M₁₆	—	2	2	no	—
369	M₁₆	—	2	4	no	—
370	M₁₆	—	2	8	no	—
371	M₁₆	—	2	4	no	—
372	M₁₆	—	2	4	no	—
373	M₁₆	—	2	4	no	—
374	M₁₆	C₂×D₄×C₄₃	1	4	yes	—
375	C₂×C₈	—	2	4	no	—
376	C₂×C₈	—	2	8	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	8	no	—
380	C₂×C₈	—	2	4	no	—
381	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
382	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
383	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₂²⋊C₄	—	4	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	4	no	—
394	C₂³	—	8	2	no	—
395	C₂³	—	8	2	no	—
396	C₂³	—	8	2	no	—
397	C₂³	#121×C₄₃	1	1	yes	characteristic
398	C₂³	#121×C₄₃	1	1	yes	characteristic
399	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
400	Q₈	—	2	4	no	—
401	Q₈	—	2	2	no	—
402	Q₈	#121×C₄₃	1	4	yes	—
403	D₄	—	2	8	no	—
404	D₄	—	2	4	no	—
405	D₄	—	2	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	2	no	—
411	D₄	—	8	4	no	—
412	D₄	—	8	4	no	—
413	D₄	#121×C₄₃	1	4	yes	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	8	2	no	—
428	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
429	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
430	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
434	C₈	—	2	4	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	4	no	—
437	C₈	#120×C₄₃	1	4	yes	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	4	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	16	4	no	—
451	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
452	C₂²	C₄₃×#525	1	2	yes	—
453	C₄	—	2	1	no	—
454	C₄	—	2	4	no	—
455	C₄	—	2	1	no	—
456	C₄	—	8	2	no	—
457	C₄	C₂×#120×C₄₃	1	1	yes	characteristic
458	C₄	C₂×#121×C₄₃	1	2	yes	—
459	C₄	C₄₃×#525	1	1	yes	characteristic
460	C₂	—	2	2	no	—
461	C₂	—	4	1	no	—
462	C₂	—	4	1	no	—
463	C₂	—	4	4	no	—
464	C₂	—	16	2	no	—
465	C₂	C₄₃×#2847	1	1	yes	characteristic
466	C₂	C₄₃×#3068	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂³×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#568	C₂	semidirect
2. C₂×C₄₃×#472	C₂	semidirect
3. C₂×C₄₃×#469	C₂	semidirect
4. C₄₃×#3006	C₂	semidirect
5. C₄₃×#1907	C₂	semidirect
6. C₄₃×#1900	C₂	semidirect
7. C₄₃×#1815	C₂	semidirect
8. C₄₃×#1811	C₂	semidirect
11. C₂²×D₈×C₄₃	C₂²	semidirect
26. C₂×#108×C₄₃	C₂²	semidirect
27. C₂×#106×C₄₃	C₂²	semidirect
29. C₂×#102×C₄₃	C₂²	semidirect
30. C₂×#100×C₄₃	C₂²	semidirect
32. C₄₃×#343	C₂²	semidirect
33. C₄₃×#341	C₂²	semidirect
57. #131×C₄₃	D₄	semidirect
204. #32945	C₄₃	direct (N × H)
227. C₂×#568	C₂×C₄₃	semidirect
228. C₂×#472	C₂×C₄₃	semidirect
229. C₂×#469	C₂×C₄₃	semidirect
230. #3006	C₂×C₄₃	semidirect
231. #1907	C₂×C₄₃	semidirect
232. #1900	C₂×C₄₃	semidirect
233. #1815	C₂×C₄₃	semidirect
234. #1811	C₂×C₄₃	semidirect
244. C₂²×D₈	C₂²×C₄₃	semidirect
259. C₂×#108	C₂²×C₄₃	semidirect
260. C₂×#106	C₂²×C₄₃	semidirect
262. C₂×#102	C₂²×C₄₃	semidirect
263. C₂×#100	C₂²×C₄₃	semidirect
265. #343	C₂²×C₄₃	semidirect
266. #341	C₂²×C₄₃	semidirect
267. C₄₃	#32945	direct (N × H)
291. #131	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×#568	2
C₂×C₄₃×#472	2
C₂×C₄₃×#469	2
C₄₃×#3006	2
C₄₃×#1907	2
C₄₃×#1900	2
C₄₃×#1815	2
C₄₃×#1811	2
#32945	43

Subgroups — C43×#32945 #24952962

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#32945 #24952962