Subgroups — C₄₃×#25730 #24945747

Order 11008.

1662 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#497	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#451	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₃×#450	C₂	1	2	yes	maximal
5	C₄₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2015	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1959	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²×Q₁₆×C₄₃	C₂²	1	4	yes	complemented
12	C₂²×SD₁₆×C₄₃	C₂²	1	4	yes	—
13	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
14	C₂×#124×C₄₃	—	2	8	no	—
15	C₂×#124×C₄₃	—	2	2	no	—
16	C₂×#124×C₄₃	C₂²	1	2	yes	—
17	C₂×#124×C₄₃	C₂²	1	2	yes	—
18	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₄₃	—	2	2	no	—
20	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₄₃×#497	—	2	8	no	—
22	C₄₃×#451	—	2	8	no	—
23	C₄₃×#450	—	2	8	no	—
24	C₂×#103×C₄₃	C₂²	1	4	yes	complemented
25	C₂×#102×C₄₃	C₂²	1	4	yes	—
26	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
27	C₂×#97×C₄₃	C₂²	1	2	yes	complemented
28	C₄₃×#391	C₂²	1	2	yes	complemented
29	C₄₃×#389	—	2	2	no	—
30	C₄₃×#384	C₂²	1	1	yes	characteristic, complemented
31	C₄₃×#380	—	2	2	no	—
32	C₄₃×#336	C₂²	1	2	yes	complemented
33	C₂⁵×C₄₃	—	2	1	no	—
34	C₂²×Q₈×C₄₃	—	2	4	no	—
35	C₂²×Q₈×C₄₃	—	2	1	no	—
36	C₂²×Q₈×C₄₃	—	2	4	no	—
37	C₂²×Q₈×C₄₃	—	4	2	no	—
38	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
39	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
40	C₂²×D₄×C₄₃	—	2	4	no	—
41	C₂²×D₄×C₄₃	—	2	1	no	—
42	C₂²×D₄×C₄₃	—	2	4	no	—
43	C₂²×D₄×C₄₃	—	4	2	no	—
44	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₃	—	2	1	no	—
46	C₂³×C₄×C₄₃	D₄	1	2	yes	—
47	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
48	C₂×Q₁₆×C₄₃	—	2	8	no	—
49	C₂×Q₁₆×C₄₃	—	2	8	no	—
50	C₂×Q₁₆×C₄₃	—	4	4	no	—
51	C₂×SD₁₆×C₄₃	—	2	8	no	—
52	C₂×SD₁₆×C₄₃	—	2	8	no	—
53	C₂×SD₁₆×C₄₃	—	4	4	no	—
54	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
55	C₄⋊Q₈×C₄₃	—	2	4	no	—
56	#124×C₄₃	—	2	16	no	—
57	#124×C₄₃	—	2	4	no	—
58	#124×C₄₃	—	2	4	no	—
59	#124×C₄₃	—	2	4	no	—
60	#124×C₄₃	D₄	1	8	yes	—
61	C₂²⋊Q₈×C₄₃	—	2	4	no	—
62	C₂²⋊Q₈×C₄₃	—	2	4	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	16	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
71	C₂×C₄²×C₄₃	—	2	4	no	—
72	C₂×C₄²×C₄₃	D₄	1	2	yes	—
73	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
75	#103×C₄₃	—	2	8	no	—
76	#102×C₄₃	—	2	8	no	—
77	C₂²⋊C₈×C₄₃	D₄	1	8	yes	—
78	#97×C₄₃	—	2	4	no	—
79	#95×C₄₃	—	2	4	no	—
80	C₂⁴×C₄₃	—	2	4	no	—
81	C₂⁴×C₄₃	—	2	2	no	—
82	C₂⁴×C₄₃	—	4	2	no	—
83	C₂⁴×C₄₃	—	4	4	no	—
84	C₂⁴×C₄₃	—	4	2	no	—
85	C₂⁴×C₄₃	—	4	4	no	—
86	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
87	C₂×Q₈×C₄₃	—	2	4	no	—
88	C₂×Q₈×C₄₃	—	2	2	no	—
89	C₂×Q₈×C₄₃	—	2	4	no	—
90	C₂×Q₈×C₄₃	—	2	2	no	—
91	C₂×Q₈×C₄₃	—	2	2	no	—
92	C₂×Q₈×C₄₃	—	2	4	no	—
93	C₂×Q₈×C₄₃	—	2	4	no	—
94	C₂×Q₈×C₄₃	—	2	4	no	—
95	C₂×Q₈×C₄₃	—	4	16	no	—
96	C₂×Q₈×C₄₃	—	4	2	no	—
97	C₂×Q₈×C₄₃	—	4	2	no	—
98	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
99	C₂×D₄×C₄₃	—	2	4	no	—
100	C₂×D₄×C₄₃	—	2	2	no	—
101	C₂×D₄×C₄₃	—	2	4	no	—
102	C₂×D₄×C₄₃	—	2	4	no	—
103	C₂×D₄×C₄₃	—	4	16	no	—
104	C₂×D₄×C₄₃	—	4	2	no	—
105	C₂×D₄×C₄₃	—	4	2	no	—
106	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	4	no	—
110	C₂²×C₄×C₄₃	—	2	4	no	—
111	C₂²×C₄×C₄₃	—	2	4	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	—	2	2	no	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	4	2	no	—
116	C₂²×C₄×C₄₃	—	4	2	no	—
117	C₂²×C₄×C₄₃	—	4	2	no	—
118	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
123	Q₁₆×C₄₃	—	4	16	no	—
124	SD₁₆×C₄₃	—	4	16	no	—
125	C₂×C₈×C₄₃	—	2	4	no	—
126	C₂×C₈×C₄₃	—	2	4	no	—
127	C₂×C₈×C₄₃	C₂×D₄	1	8	yes	—
128	C₄⋊C₄×C₄₃	—	2	2	no	—
129	C₄⋊C₄×C₄₃	—	2	2	no	—
130	C₄⋊C₄×C₄₃	—	4	4	no	—
131	C₄⋊C₄×C₄₃	—	4	4	no	—
132	C₄⋊C₄×C₄₃	—	4	4	no	—
133	C₂²⋊C₄×C₄₃	—	2	16	no	—
134	C₂²⋊C₄×C₄₃	—	2	16	no	—
135	C₂²⋊C₄×C₄₃	—	4	4	no	—
136	C₄²×C₄₃	—	2	4	no	—
137	C₄²×C₄₃	—	2	2	no	—
138	C₄²×C₄₃	C₂×D₄	1	4	yes	—
139	C₂³×C₄₃	—	2	1	no	—
140	C₂³×C₄₃	—	2	1	no	—
141	C₂³×C₄₃	—	2	2	no	—
142	C₂³×C₄₃	—	2	4	no	—
143	C₂³×C₄₃	—	4	8	no	—
144	C₂³×C₄₃	—	4	16	no	—
145	C₂³×C₄₃	—	4	2	no	—
146	C₂³×C₄₃	—	4	2	no	—
147	C₂³×C₄₃	—	4	4	no	—
148	C₂³×C₄₃	—	4	4	no	—
149	C₂³×C₄₃	—	8	4	no	—
150	C₂³×C₄₃	—	8	8	no	—
151	C₂³×C₄₃	—	8	4	no	—
152	C₂³×C₄₃	#127	1	2	yes	—
153	C₂³×C₄₃	#137	1	4	yes	—
154	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₄₃	—	2	8	no	—
156	Q₈×C₄₃	—	4	8	no	—
157	Q₈×C₄₃	—	4	4	no	—
158	Q₈×C₄₃	—	4	4	no	—
159	Q₈×C₄₃	—	4	4	no	—
160	D₄×C₄₃	—	2	8	no	—
161	D₄×C₄₃	—	4	8	no	—
162	D₄×C₄₃	—	4	4	no	—
163	C₂×C₄×C₄₃	—	2	1	no	—
164	C₂×C₄×C₄₃	—	2	1	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	2	8	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	4	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	4	8	no	—
173	C₂×C₄×C₄₃	—	4	8	no	—
174	C₂×C₄×C₄₃	—	4	2	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	4	2	no	—
178	C₂×C₄×C₄₃	—	4	2	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	—	4	4	no	—
181	C₂×C₄×C₄₃	#120	1	4	yes	—
182	C₂×C₄×C₄₃	#127	1	2	yes	—
183	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
184	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
186	C₈×C₄₃	—	2	8	no	—
187	#25730	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂²×C₄₃	—	2	2	no	—
189	C₂²×C₄₃	—	2	2	no	—
190	C₂²×C₄₃	—	2	4	no	—
191	C₂²×C₄₃	—	2	4	no	—
192	C₂²×C₄₃	—	4	4	no	—
193	C₂²×C₄₃	—	4	8	no	—
194	C₂²×C₄₃	—	8	16	no	—
195	C₂²×C₄₃	—	8	2	no	—
196	C₂²×C₄₃	—	8	2	no	—
197	C₂²×C₄₃	—	8	4	no	—
198	C₂²×C₄₃	#497	1	4	yes	complemented
199	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
200	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
201	C₂²×C₄₃	#535	1	1	yes	characteristic
202	C₂²×C₄₃	C₂×#137	1	2	yes	—
203	C₂²×C₄₃	#575	1	2	yes	—
204	C₄×C₄₃	—	2	2	no	—
205	C₄×C₄₃	—	2	4	no	—
206	C₄×C₄₃	—	4	4	no	—
207	C₄×C₄₃	—	4	2	no	—
208	C₄×C₄₃	—	8	2	no	—
209	C₄×C₄₃	—	8	2	no	—
210	C₄×C₄₃	D₄²	1	4	yes	—
211	C₂²×#124	C₂×C₄₃	1	1	yes	characteristic
212	C₂×#497	C₂×C₄₃	1	2	yes	complemented
213	C₂×#451	C₂×C₄₃	1	2	yes	complemented
214	C₂×#450	C₂×C₄₃	1	2	yes	—
215	#2857	C₂×C₄₃	1	1	yes	characteristic, complemented
216	#2015	C₂×C₄₃	1	4	yes	complemented
217	#1959	C₂×C₄₃	1	2	yes	complemented
218	#1749	C₂×C₄₃	1	1	yes	characteristic, complemented
219	C₂×C₄₃	—	2	4	no	—
220	C₂×C₄₃	—	8	4	no	—
221	C₂×C₄₃	#2433	1	1	yes	characteristic
222	C₂×C₄₃	#3007	1	2	yes	—
223	C₂×C₄₃	C₂×#497	1	1	yes	characteristic
224	C₂×C₄₃	#3153	1	1	yes	characteristic
225	C₂×C₄₃	#3215	1	2	yes	—
226	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
227	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
228	C₂²×Q₁₆	C₂²×C₄₃	1	4	yes	complemented
229	C₂²×SD₁₆	C₂²×C₄₃	1	4	yes	—
230	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
231	C₂×#124	—	2	8	no	—
232	C₂×#124	—	2	2	no	—
233	C₂×#124	C₂²×C₄₃	1	2	yes	—
234	C₂×#124	C₂²×C₄₃	1	2	yes	—
235	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
236	C₂²×C₂²⋊C₄	—	2	2	no	—
237	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
238	#497	—	2	8	no	—
239	#451	—	2	8	no	—
240	#450	—	2	8	no	—
241	C₂×#103	C₂²×C₄₃	1	4	yes	complemented
242	C₂×#102	C₂²×C₄₃	1	4	yes	—
243	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
244	C₂×#97	C₂²×C₄₃	1	2	yes	complemented
245	#391	C₂²×C₄₃	1	2	yes	complemented
246	#389	—	2	2	no	—
247	#384	C₂²×C₄₃	1	1	yes	characteristic, complemented
248	#380	—	2	2	no	—
249	#336	C₂²×C₄₃	1	2	yes	complemented
250	C₄₃	#25730	1	1	yes	characteristic, direct product factor, Sylow
251	C₂⁵	—	2	1	no	—
252	C₂²×Q₈	—	2	4	no	—
253	C₂²×Q₈	—	2	1	no	—
254	C₂²×Q₈	—	2	4	no	—
255	C₂²×Q₈	—	4	2	no	—
256	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
257	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
258	C₂²×D₄	—	2	4	no	—
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	—	2	4	no	—
261	C₂²×D₄	—	4	2	no	—
262	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	D₄×C₄₃	1	2	yes	—
265	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
266	C₂×Q₁₆	—	2	8	no	—
267	C₂×Q₁₆	—	2	8	no	—
268	C₂×Q₁₆	—	4	4	no	—
269	C₂×SD₁₆	—	2	8	no	—
270	C₂×SD₁₆	—	2	8	no	—
271	C₂×SD₁₆	—	4	4	no	—
272	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
273	C₄⋊Q₈	—	2	4	no	—
274	#124	—	2	16	no	—
275	#124	—	2	4	no	—
276	#124	—	2	4	no	—
277	#124	—	2	4	no	—
278	#124	D₄×C₄₃	1	8	yes	—
279	C₂²⋊Q₈	—	2	4	no	—
280	C₂²⋊Q₈	—	2	4	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
285	C₂×C₂²⋊C₄	—	2	16	no	—
286	C₂×C₂²⋊C₄	—	2	4	no	—
287	C₂×C₂²⋊C₄	—	2	4	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₄²	—	2	4	no	—
290	C₂×C₄²	D₄×C₄₃	1	2	yes	—
291	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
293	#103	—	2	8	no	—
294	#102	—	2	8	no	—
295	C₂²⋊C₈	D₄×C₄₃	1	8	yes	—
296	#97	—	2	4	no	—
297	#95	—	2	4	no	—
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	2	2	no	—
300	C₂⁴	—	4	2	no	—
301	C₂⁴	—	4	4	no	—
302	C₂⁴	—	4	2	no	—
303	C₂⁴	—	4	4	no	—
304	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	2	4	no	—
313	C₂×Q₈	—	4	16	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×Q₈	—	4	2	no	—
316	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	4	16	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
340	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
341	Q₁₆	—	4	16	no	—
342	SD₁₆	—	4	16	no	—
343	C₂×C₈	—	2	4	no	—
344	C₂×C₈	—	2	4	no	—
345	C₂×C₈	C₂×D₄×C₄₃	1	8	yes	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	4	4	no	—
349	C₄⋊C₄	—	4	4	no	—
350	C₄⋊C₄	—	4	4	no	—
351	C₂²⋊C₄	—	2	16	no	—
352	C₂²⋊C₄	—	2	16	no	—
353	C₂²⋊C₄	—	4	4	no	—
354	C₄²	—	2	4	no	—
355	C₄²	—	2	2	no	—
356	C₄²	C₂×D₄×C₄₃	1	4	yes	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	4	8	no	—
362	C₂³	—	4	16	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	4	no	—
366	C₂³	—	4	4	no	—
367	C₂³	—	8	4	no	—
368	C₂³	—	8	8	no	—
369	C₂³	—	8	4	no	—
370	C₂³	#127×C₄₃	1	2	yes	—
371	C₂³	#137×C₄₃	1	4	yes	—
372	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
373	Q₈	—	2	8	no	—
374	Q₈	—	4	8	no	—
375	Q₈	—	4	4	no	—
376	Q₈	—	4	4	no	—
377	Q₈	—	4	4	no	—
378	D₄	—	2	8	no	—
379	D₄	—	4	8	no	—
380	D₄	—	4	4	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	8	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	#120×C₄₃	1	4	yes	—
400	C₂×C₄	#127×C₄₃	1	2	yes	—
401	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
402	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
403	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
404	C₈	—	2	8	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	2	4	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	8	no	—
411	C₂²	—	8	16	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	4	no	—
415	C₂²	C₄₃×#497	1	4	yes	complemented
416	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
417	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
418	C₂²	C₄₃×#535	1	1	yes	characteristic
419	C₂²	C₂×#137×C₄₃	1	2	yes	—
420	C₂²	C₄₃×#575	1	2	yes	—
421	C₄	—	2	2	no	—
422	C₄	—	2	4	no	—
423	C₄	—	4	4	no	—
424	C₄	—	4	2	no	—
425	C₄	—	8	2	no	—
426	C₄	—	8	2	no	—
427	C₄	D₄²×C₄₃	1	4	yes	—
428	C₂	—	2	4	no	—
429	C₂	—	8	4	no	—
430	C₂	C₄₃×#2433	1	1	yes	characteristic
431	C₂	C₄₃×#3007	1	2	yes	—
432	C₂	C₂×C₄₃×#497	1	1	yes	characteristic
433	C₂	C₄₃×#3153	1	1	yes	characteristic
434	C₂	C₄₃×#3215	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂³×D₄×C₄₃	C₂²
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×#497	C₂	semidirect
3. C₂×C₄₃×#451	C₂	semidirect
5. C₄₃×#2857	C₂	semidirect
6. C₄₃×#2015	C₂	semidirect
7. C₄₃×#1959	C₂	semidirect
8. C₄₃×#1749	C₂	semidirect
11. C₂²×Q₁₆×C₄₃	C₂²	semidirect
13. C₂×C₄⋊Q₈×C₄₃	C₂²	semidirect
24. C₂×#103×C₄₃	C₂²	semidirect
27. C₂×#97×C₄₃	C₂²	semidirect
28. C₄₃×#391	C₂²	semidirect
30. C₄₃×#384	C₂²	semidirect
32. C₄₃×#336	C₂²	semidirect
187. #25730	C₄₃	direct (N × H)
198. C₂²×C₄₃	#497	semidirect
212. C₂×#497	C₂×C₄₃	semidirect
213. C₂×#451	C₂×C₄₃	semidirect
215. #2857	C₂×C₄₃	semidirect
216. #2015	C₂×C₄₃	semidirect
217. #1959	C₂×C₄₃	semidirect
218. #1749	C₂×C₄₃	semidirect
228. C₂²×Q₁₆	C₂²×C₄₃	semidirect
230. C₂×C₄⋊Q₈	C₂²×C₄₃	semidirect
241. C₂×#103	C₂²×C₄₃	semidirect
244. C₂×#97	C₂²×C₄₃	semidirect
245. #391	C₂²×C₄₃	semidirect
247. #384	C₂²×C₄₃	semidirect
249. #336	C₂²×C₄₃	semidirect
250. C₄₃	#25730	direct (N × H)
415. C₂²	C₄₃×#497	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#124×C₄₃	2
C₂×C₄₃×#497	2
C₂×C₄₃×#451	2
C₂×C₄₃×#450	2
C₄₃×#2857	2
C₄₃×#2015	2
C₄₃×#1959	2
C₄₃×#1749	2
#25730	43

Subgroups — C43×#25730 #24945747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25730 #24945747