Subgroups — C₄₃×#25742 #24945759

Order 11008.

1476 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#3153	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#456	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₃×#454	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2545	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2007	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2006	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1980	C₂	1	2	yes	maximal, complemented
9	C₄×#101×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×2₋¹⁺⁴×C₄₃	C₂²	1	2	yes	—
11	C₂×#137×C₄₃	C₂²	1	4	yes	—
12	C₂×AGL(1,ℤ/8)×C₄₃	C₂²	1	4	yes	—
13	C₄₃×#550	—	2	2	no	—
14	D₄×Q₈×C₄₃	—	2	2	no	—
15	C₄₃×#548	—	2	4	no	—
16	C₄₃×#537	—	2	2	no	—
17	C₄₃×#537	C₂²	1	2	yes	—
18	C₄₃×#532	—	2	2	no	—
19	C₄₃×#532	C₂²	1	2	yes	—
20	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#497	—	2	2	no	—
25	C₄₃×#496	—	2	2	no	—
26	C₄₃×#495	—	2	4	no	—
27	C₄₃×#456	—	2	8	no	—
28	C₄₃×#454	—	2	8	no	—
29	C₂×#104×C₄₃	C₂²	1	4	yes	—
30	C₂×#104×C₄₃	C₂²	1	4	yes	—
31	C₂×#101×C₄₃	C₂²	1	2	yes	—
32	C₄×M₁₆×C₄₃	C₂²	1	2	yes	—
33	C₄₃×#396	—	2	2	no	—
34	C₄₃×#391	C₂²	1	1	yes	characteristic
35	C₄₃×#390	C₂²	1	1	yes	characteristic
36	C₄₃×#388	—	2	2	no	—
37	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
38	C₄₃×#343	C₂²	1	2	yes	—
39	2₋¹⁺⁴×C₄₃	—	2	4	no	—
40	2₋¹⁺⁴×C₄₃	—	2	4	no	—
41	2₋¹⁺⁴×C₄₃	—	4	4	no	—
42	C₂×#41×C₄₃	—	2	4	no	—
43	C₂×#41×C₄₃	—	2	4	no	—
44	C₂×#41×C₄₃	C₂³	1	4	yes	—
45	C₂²×Q₈×C₄₃	—	2	4	no	—
46	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
49	#137×C₄₃	—	2	8	no	—
50	#137×C₄₃	—	4	4	no	—
51	AGL(1,ℤ/8)×C₄₃	—	2	8	no	—
52	AGL(1,ℤ/8)×C₄₃	—	4	4	no	—
53	C₂×Q₁₆×C₄₃	—	2	4	no	—
54	C₂×SD₁₆×C₄₃	—	2	4	no	—
55	C₂×SD₁₆×C₄₃	—	2	4	no	—
56	C₂×D₈×C₄₃	—	2	4	no	—
57	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
58	C₄⋊Q₈×C₄₃	—	2	2	no	—
59	C₄⋊Q₈×C₄₃	—	2	4	no	—
60	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
61	#127×C₄₃	—	2	2	no	—
62	#127×C₄₃	D₄	1	2	yes	—
63	#124×C₄₃	—	2	4	no	—
64	#124×C₄₃	—	2	4	no	—
65	#124×C₄₃	—	2	2	no	—
66	#124×C₄₃	—	2	2	no	—
67	#124×C₄₃	D₄	1	4	yes	—
68	C₂²⋊Q₈×C₄₃	—	2	8	no	—
69	C₂²⋊Q₈×C₄₃	—	2	4	no	—
70	#121×C₄₃	—	2	8	no	—
71	#121×C₄₃	—	2	4	no	—
72	#121×C₄₃	—	2	2	no	—
73	#121×C₄₃	—	2	4	no	—
74	#121×C₄₃	—	2	2	no	—
75	C₄×Q₈×C₄₃	—	2	2	no	—
76	C₄×Q₈×C₄₃	—	2	2	no	—
77	C₄×D₄×C₄₃	—	2	4	no	—
78	C₄×D₄×C₄₃	—	2	4	no	—
79	C₄×D₄×C₄₃	—	2	2	no	—
80	C₄×D₄×C₄₃	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
89	C₂×C₄²×C₄₃	D₄	1	2	yes	—
90	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
93	#104×C₄₃	—	2	8	no	—
94	#104×C₄₃	—	2	8	no	—
95	#101×C₄₃	D₄	1	8	yes	complemented
96	#97×C₄₃	—	2	2	no	—
97	C₄×C₈×C₄₃	—	2	2	no	—
98	#95×C₄₃	—	2	1	no	—
99	#95×C₄₃	—	2	2	no	—
100	C₂⁴×C₄₃	—	2	1	no	—
101	#41×C₄₃	—	2	4	no	—
102	#41×C₄₃	—	2	4	no	—
103	#41×C₄₃	—	2	4	no	—
104	#41×C₄₃	—	2	4	no	—
105	#41×C₄₃	—	4	8	no	—
106	#41×C₄₃	—	4	8	no	—
107	#41×C₄₃	—	4	8	no	—
108	#41×C₄₃	—	4	8	no	—
109	C₂×Q₈×C₄₃	—	2	4	no	—
110	C₂×Q₈×C₄₃	—	2	2	no	—
111	C₂×Q₈×C₄₃	—	2	2	no	—
112	C₂×Q₈×C₄₃	—	2	2	no	—
113	C₂×Q₈×C₄₃	—	2	2	no	—
114	C₂×Q₈×C₄₃	—	2	2	no	—
115	C₂×Q₈×C₄₃	—	4	8	no	—
116	C₂×Q₈×C₄₃	—	4	8	no	—
117	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
118	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
119	C₂×D₄×C₄₃	—	2	4	no	—
120	C₂×D₄×C₄₃	—	2	4	no	—
121	C₂×D₄×C₄₃	—	2	2	no	—
122	C₂×D₄×C₄₃	—	2	2	no	—
123	C₂×D₄×C₄₃	—	2	4	no	—
124	C₂×D₄×C₄₃	—	2	2	no	—
125	C₂×D₄×C₄₃	—	2	2	no	—
126	C₂×D₄×C₄₃	—	2	2	no	—
127	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₄₃	—	2	8	no	—
129	C₂²×C₄×C₄₃	—	2	4	no	—
130	C₂²×C₄×C₄₃	—	2	1	no	—
131	C₂²×C₄×C₄₃	—	2	1	no	—
132	C₂²×C₄×C₄₃	—	2	1	no	—
133	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
138	Q₁₆×C₄₃	—	4	8	no	—
139	SD₁₆×C₄₃	—	4	8	no	—
140	SD₁₆×C₄₃	—	4	8	no	—
141	D₈×C₄₃	—	4	8	no	—
142	M₁₆×C₄₃	—	2	4	no	—
143	M₁₆×C₄₃	C₂×D₄	1	8	yes	—
144	C₂×C₈×C₄₃	—	2	4	no	—
145	C₄⋊C₄×C₄₃	—	2	4	no	—
146	C₄⋊C₄×C₄₃	—	2	4	no	—
147	C₄⋊C₄×C₄₃	—	2	2	no	—
148	C₄⋊C₄×C₄₃	—	2	2	no	—
149	C₄⋊C₄×C₄₃	—	2	2	no	—
150	C₄⋊C₄×C₄₃	—	4	2	no	—
151	C₄⋊C₄×C₄₃	—	4	4	no	—
152	C₂²⋊C₄×C₄₃	—	2	8	no	—
153	C₂²⋊C₄×C₄₃	—	2	4	no	—
154	C₂²⋊C₄×C₄₃	—	2	4	no	—
155	C₂²⋊C₄×C₄₃	—	4	4	no	—
156	C₂²⋊C₄×C₄₃	—	4	1	no	—
157	C₂²⋊C₄×C₄₃	—	4	1	no	—
158	C₂²⋊C₄×C₄₃	—	4	2	no	—
159	C₂²⋊C₄×C₄₃	—	4	4	no	—
160	C₄²×C₄₃	—	2	2	no	—
161	C₄²×C₄₃	—	2	2	no	—
162	C₄²×C₄₃	—	2	2	no	—
163	C₄²×C₄₃	—	2	2	no	—
164	C₄²×C₄₃	C₂×D₄	1	2	yes	—
165	C₄²×C₄₃	C₂×D₄	1	2	yes	—
166	C₂³×C₄₃	—	2	4	no	—
167	C₂³×C₄₃	—	4	2	no	—
168	C₂³×C₄₃	—	4	2	no	—
169	C₂³×C₄₃	—	4	1	no	—
170	C₂³×C₄₃	—	4	1	no	—
171	C₂³×C₄₃	—	4	1	no	—
172	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₄₃	—	2	8	no	—
174	Q₈×C₄₃	—	2	4	no	—
175	Q₈×C₄₃	—	2	4	no	—
176	Q₈×C₄₃	—	4	8	no	—
177	Q₈×C₄₃	—	4	4	no	—
178	D₄×C₄₃	—	2	4	no	—
179	D₄×C₄₃	—	2	4	no	—
180	D₄×C₄₃	—	4	4	no	—
181	D₄×C₄₃	—	4	8	no	—
182	D₄×C₄₃	—	4	4	no	—
183	D₄×C₄₃	—	4	4	no	—
184	D₄×C₄₃	—	4	4	no	—
185	D₄×C₄₃	—	8	2	no	—
186	D₄×C₄₃	—	8	4	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	2	no	—
189	C₂×C₄×C₄₃	—	2	2	no	—
190	C₂×C₄×C₄₃	—	2	2	no	—
191	C₂×C₄×C₄₃	—	2	4	no	—
192	C₂×C₄×C₄₃	—	4	1	no	—
193	C₂×C₄×C₄₃	—	4	1	no	—
194	C₂×C₄×C₄₃	—	4	16	no	—
195	C₂×C₄×C₄₃	—	4	1	no	—
196	C₂×C₄×C₄₃	—	4	1	no	—
197	C₂×C₄×C₄₃	—	4	4	no	—
198	C₂×C₄×C₄₃	—	4	4	no	—
199	C₂×C₄×C₄₃	—	4	2	no	—
200	C₂×C₄×C₄₃	—	4	1	no	—
201	C₂×C₄×C₄₃	—	4	1	no	—
202	C₂×C₄×C₄₃	—	4	1	no	—
203	C₂×C₄×C₄₃	—	4	1	no	—
204	C₂×C₄×C₄₃	—	4	1	no	—
205	C₂×C₄×C₄₃	—	4	1	no	—
206	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
207	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
208	C₂×C₄×C₄₃	#120	1	2	yes	—
209	C₂×C₄×C₄₃	#127	1	4	yes	—
210	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
212	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
213	C₈×C₄₃	—	2	8	no	—
214	#25742	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂²×C₄₃	—	2	1	no	—
216	C₂²×C₄₃	—	2	1	no	—
217	C₂²×C₄₃	—	4	4	no	—
218	C₂²×C₄₃	—	4	4	no	—
219	C₂²×C₄₃	—	4	4	no	—
220	C₂²×C₄₃	—	8	2	no	—
221	C₂²×C₄₃	—	8	2	no	—
222	C₂²×C₄₃	—	8	1	no	—
223	C₂²×C₄₃	—	8	1	no	—
224	C₂²×C₄₃	—	8	1	no	—
225	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
226	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
227	C₂²×C₄₃	#535	1	1	yes	characteristic
228	C₄×C₄₃	—	2	4	no	—
229	C₄×C₄₃	—	2	2	no	—
230	C₄×C₄₃	—	2	1	no	—
231	C₄×C₄₃	—	2	1	no	—
232	C₄×C₄₃	—	4	2	no	—
233	C₄×C₄₃	—	4	4	no	—
234	C₄×C₄₃	—	4	2	no	—
235	C₄×C₄₃	—	8	1	no	—
236	C₄×C₄₃	—	8	1	no	—
237	C₄×C₄₃	D₄²	1	4	yes	—
238	#3497	C₂×C₄₃	1	1	yes	characteristic, complemented
239	#3153	C₂×C₄₃	1	2	yes	complemented
240	C₂×#456	C₂×C₄₃	1	2	yes	complemented
241	C₂×#454	C₂×C₄₃	1	2	yes	complemented
242	#2545	C₂×C₄₃	1	1	yes	characteristic, complemented
243	#2007	C₂×C₄₃	1	2	yes	complemented
244	#2006	C₂×C₄₃	1	2	yes	complemented
245	#1980	C₂×C₄₃	1	2	yes	complemented
246	C₄×#101	C₂×C₄₃	1	1	yes	characteristic, complemented
247	C₂×C₄₃	—	2	1	no	—
248	C₂×C₄₃	—	2	1	no	—
249	C₂×C₄₃	—	8	4	no	—
250	C₂×C₄₃	—	16	1	no	—
251	C₂×C₄₃	#2433	1	1	yes	characteristic
252	C₂×C₄₃	#3018	1	1	yes	characteristic
253	C₂×C₄₃	#3020	1	1	yes	characteristic
254	C₂×2₋¹⁺⁴	C₂²×C₄₃	1	2	yes	—
255	C₂×#137	C₂²×C₄₃	1	4	yes	—
256	C₂×AGL(1,ℤ/8)	C₂²×C₄₃	1	4	yes	—
257	#550	—	2	2	no	—
258	D₄×Q₈	—	2	2	no	—
259	#548	—	2	4	no	—
260	#537	—	2	2	no	—
261	#537	C₂²×C₄₃	1	2	yes	—
262	#532	—	2	2	no	—
263	#532	C₂²×C₄₃	1	2	yes	—
264	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
265	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
266	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
267	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
268	#497	—	2	2	no	—
269	#496	—	2	2	no	—
270	#495	—	2	4	no	—
271	#456	—	2	8	no	—
272	#454	—	2	8	no	—
273	C₂×#104	C₂²×C₄₃	1	4	yes	—
274	C₂×#104	C₂²×C₄₃	1	4	yes	—
275	C₂×#101	C₂²×C₄₃	1	2	yes	—
276	C₄×M₁₆	C₂²×C₄₃	1	2	yes	—
277	#396	—	2	2	no	—
278	#391	C₂²×C₄₃	1	1	yes	characteristic
279	#390	C₂²×C₄₃	1	1	yes	characteristic
280	#388	—	2	2	no	—
281	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
282	#343	C₂²×C₄₃	1	2	yes	—
283	C₄₃	#25742	1	1	yes	characteristic, direct product factor, Sylow
284	2₋¹⁺⁴	—	2	4	no	—
285	2₋¹⁺⁴	—	2	4	no	—
286	2₋¹⁺⁴	—	4	4	no	—
287	C₂×#41	—	2	4	no	—
288	C₂×#41	—	2	4	no	—
289	C₂×#41	C₂³×C₄₃	1	4	yes	—
290	C₂²×Q₈	—	2	4	no	—
291	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
292	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
293	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
294	#137	—	2	8	no	—
295	#137	—	4	4	no	—
296	AGL(1,ℤ/8)	—	2	8	no	—
297	AGL(1,ℤ/8)	—	4	4	no	—
298	C₂×Q₁₆	—	2	4	no	—
299	C₂×SD₁₆	—	2	4	no	—
300	C₂×SD₁₆	—	2	4	no	—
301	C₂×D₈	—	2	4	no	—
302	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
303	C₄⋊Q₈	—	2	2	no	—
304	C₄⋊Q₈	—	2	4	no	—
305	C₄⋊Q₈	D₄×C₄₃	1	2	yes	—
306	#127	—	2	2	no	—
307	#127	D₄×C₄₃	1	2	yes	—
308	#124	—	2	4	no	—
309	#124	—	2	4	no	—
310	#124	—	2	2	no	—
311	#124	—	2	2	no	—
312	#124	D₄×C₄₃	1	4	yes	—
313	C₂²⋊Q₈	—	2	8	no	—
314	C₂²⋊Q₈	—	2	4	no	—
315	#121	—	2	8	no	—
316	#121	—	2	4	no	—
317	#121	—	2	2	no	—
318	#121	—	2	4	no	—
319	#121	—	2	2	no	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×D₄	—	2	4	no	—
323	C₄×D₄	—	2	4	no	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₄²	D₄×C₄₃	1	2	yes	—
335	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
338	#104	—	2	8	no	—
339	#104	—	2	8	no	—
340	#101	D₄×C₄₃	1	8	yes	complemented
341	#97	—	2	2	no	—
342	C₄×C₈	—	2	2	no	—
343	#95	—	2	1	no	—
344	#95	—	2	2	no	—
345	C₂⁴	—	2	1	no	—
346	#41	—	2	4	no	—
347	#41	—	2	4	no	—
348	#41	—	2	4	no	—
349	#41	—	2	4	no	—
350	#41	—	4	8	no	—
351	#41	—	4	8	no	—
352	#41	—	4	8	no	—
353	#41	—	4	8	no	—
354	C₂×Q₈	—	2	4	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	4	8	no	—
361	C₂×Q₈	—	4	8	no	—
362	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
363	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
373	C₂²×C₄	—	2	8	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
379	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
382	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
383	Q₁₆	—	4	8	no	—
384	SD₁₆	—	4	8	no	—
385	SD₁₆	—	4	8	no	—
386	D₈	—	4	8	no	—
387	M₁₆	—	2	4	no	—
388	M₁₆	C₂×D₄×C₄₃	1	8	yes	—
389	C₂×C₈	—	2	4	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	—	4	4	no	—
397	C₂²⋊C₄	—	2	8	no	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	2	4	no	—
400	C₂²⋊C₄	—	4	4	no	—
401	C₂²⋊C₄	—	4	1	no	—
402	C₂²⋊C₄	—	4	1	no	—
403	C₂²⋊C₄	—	4	2	no	—
404	C₂²⋊C₄	—	4	4	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	2	2	no	—
409	C₄²	C₂×D₄×C₄₃	1	2	yes	—
410	C₄²	C₂×D₄×C₄₃	1	2	yes	—
411	C₂³	—	2	4	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
418	Q₈	—	2	8	no	—
419	Q₈	—	2	4	no	—
420	Q₈	—	2	4	no	—
421	Q₈	—	4	8	no	—
422	Q₈	—	4	4	no	—
423	D₄	—	2	4	no	—
424	D₄	—	2	4	no	—
425	D₄	—	4	8	no	—
426	D₄	—	4	4	no	—
427	D₄	—	4	4	no	—
428	D₄	—	4	4	no	—
429	D₄	—	4	4	no	—
430	D₄	—	8	2	no	—
431	D₄	—	8	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	16	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
452	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
453	C₂×C₄	#120×C₄₃	1	2	yes	—
454	C₂×C₄	#127×C₄₃	1	4	yes	—
455	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
456	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
457	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
458	C₈	—	2	8	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	4	4	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	1	no	—
467	C₂²	—	8	1	no	—
468	C₂²	—	8	1	no	—
469	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
470	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
471	C₂²	C₄₃×#535	1	1	yes	characteristic
472	C₄	—	2	4	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	4	no	—
478	C₄	—	4	2	no	—
479	C₄	—	8	1	no	—
480	C₄	—	8	1	no	—
481	C₄	D₄²×C₄₃	1	4	yes	—
482	C₂	—	2	1	no	—
483	C₂	—	2	1	no	—
484	C₂	—	8	4	no	—
485	C₂	—	16	1	no	—
486	C₂	C₄₃×#2433	1	1	yes	characteristic
487	C₂	C₄₃×#3018	1	1	yes	characteristic
488	C₂	C₄₃×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₃×#3497	C₂	semidirect
2. C₄₃×#3153	C₂	semidirect
3. C₂×C₄₃×#456	C₂	semidirect
4. C₂×C₄₃×#454	C₂	semidirect
5. C₄₃×#2545	C₂	semidirect
6. C₄₃×#2007	C₂	semidirect
7. C₄₃×#2006	C₂	semidirect
8. C₄₃×#1980	C₂	semidirect
9. C₄×#101×C₄₃	C₂	semidirect
95. #101×C₄₃	D₄	semidirect
214. #25742	C₄₃	direct (N × H)
238. #3497	C₂×C₄₃	semidirect
239. #3153	C₂×C₄₃	semidirect
240. C₂×#456	C₂×C₄₃	semidirect
241. C₂×#454	C₂×C₄₃	semidirect
242. #2545	C₂×C₄₃	semidirect
243. #2007	C₂×C₄₃	semidirect
244. #2006	C₂×C₄₃	semidirect
245. #1980	C₂×C₄₃	semidirect
246. C₄×#101	C₂×C₄₃	semidirect
283. C₄₃	#25742	direct (N × H)
340. #101	D₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄₃×#3497	2
C₄₃×#3153	2
C₂×C₄₃×#456	2
C₂×C₄₃×#454	2
C₄₃×#2545	2
C₄₃×#2007	2
C₄₃×#2006	2
C₄₃×#1980	2
C₄×#101×C₄₃	2
#25742	43

Subgroups — C43×#25742 #24945759

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25742 #24945759