Subgroups — C₄₃×#28469 #24948486

Order 11008.

1086 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#497	C₂	1	2	yes	maximal, complemented
2	C₂×C₄₃×#495	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#464	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×Q₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2545	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2016	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2012	C₂	1	2	yes	maximal
8	C₄₃×#1973	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1770	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
15	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
17	C₂×#124×C₄₃	C₂²	1	2	yes	—
18	C₂×#124×C₄₃	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
20	C₄₃×#497	—	2	8	no	—
21	C₄₃×#495	—	2	4	no	—
22	C₄₃×#464	—	2	8	no	—
23	C₄×Q₁₆×C₄₃	—	2	4	no	—
24	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#103×C₄₃	C₂²	1	2	yes	—
27	C₂×#103×C₄₃	C₂²	1	2	yes	—
28	C₂×#102×C₄₃	C₂²	1	2	yes	—
29	C₂×#97×C₄₃	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
31	C₄₃×#396	—	2	4	no	—
32	C₄₃×#391	C₂²	1	2	yes	—
33	C₄₃×#390	C₂²	1	2	yes	—
34	C₄₃×#388	—	2	4	no	—
35	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
36	C₄₃×#336	C₂²	1	2	yes	—
37	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
38	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
39	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
40	C₂×Q₁₆×C₄₃	—	2	4	no	—
41	C₂×Q₁₆×C₄₃	—	2	2	no	—
42	C₂×Q₁₆×C₄₃	—	2	4	no	—
43	C₂×Q₁₆×C₄₃	—	2	2	no	—
44	C₂×Q₁₆×C₄₃	—	2	2	no	—
45	C₂×Q₁₆×C₄₃	—	4	1	no	—
46	C₂×Q₁₆×C₄₃	—	4	1	no	—
47	C₂×Q₁₆×C₄₃	—	4	2	no	—
48	C₂×Q₁₆×C₄₃	D₄	1	4	yes	—
49	C₂×SD₁₆×C₄₃	—	2	4	no	—
50	C₂×SD₁₆×C₄₃	—	2	4	no	—
51	C₂×SD₁₆×C₄₃	—	2	4	no	—
52	C₂×SD₁₆×C₄₃	—	2	4	no	—
53	C₂×SD₁₆×C₄₃	—	2	4	no	—
54	C₂×SD₁₆×C₄₃	—	4	2	no	—
55	C₂×D₈×C₄₃	—	2	2	no	—
56	C₂×D₈×C₄₃	—	4	1	no	—
57	C₂×D₈×C₄₃	—	4	1	no	—
58	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
60	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
61	C₄⋊Q₈×C₄₃	—	2	4	no	—
62	C₄⋊Q₈×C₄₃	—	4	2	no	—
63	#124×C₄₃	—	2	4	no	—
64	#124×C₄₃	—	2	4	no	—
65	#124×C₄₃	—	2	4	no	—
66	#124×C₄₃	—	4	2	no	—
67	C₄×Q₈×C₄₃	—	2	4	no	—
68	C₄×Q₈×C₄₃	—	2	4	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
71	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
77	C₂×C₄²×C₄₃	—	2	2	no	—
78	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
79	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
80	#107×C₄₃	—	2	2	no	—
81	C₄⋊C₈×C₄₃	D₄	1	4	yes	—
82	#103×C₄₃	—	2	4	no	—
83	#103×C₄₃	—	2	4	no	—
84	#102×C₄₃	—	2	4	no	—
85	#97×C₄₃	—	2	4	no	—
86	C₄×C₈×C₄₃	D₄	1	4	yes	—
87	#95×C₄₃	—	2	4	no	—
88	#95×C₄₃	D₄	1	2	yes	—
89	C₂⁴×C₄₃	—	2	2	no	—
90	C₂×Q₈×C₄₃	—	2	2	no	—
91	C₂×Q₈×C₄₃	—	2	2	no	—
92	C₂×Q₈×C₄₃	—	2	2	no	—
93	C₂×Q₈×C₄₃	—	2	2	no	—
94	C₂×Q₈×C₄₃	—	2	2	no	—
95	C₂×Q₈×C₄₃	—	2	2	no	—
96	C₂×Q₈×C₄₃	—	2	2	no	—
97	C₂×Q₈×C₄₃	—	2	2	no	—
98	C₂×Q₈×C₄₃	—	2	2	no	—
99	C₂×Q₈×C₄₃	—	2	2	no	—
100	C₂×Q₈×C₄₃	—	2	2	no	—
101	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
102	C₂×D₄×C₄₃	—	2	2	no	—
103	C₂×D₄×C₄₃	—	2	2	no	—
104	C₂×D₄×C₄₃	—	2	2	no	—
105	C₂×D₄×C₄₃	—	2	2	no	—
106	C₂×D₄×C₄₃	—	2	2	no	—
107	C₂×D₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
115	Q₁₆×C₄₃	—	2	8	no	—
116	Q₁₆×C₄₃	—	4	8	no	—
117	Q₁₆×C₄₃	—	4	4	no	—
118	SD₁₆×C₄₃	—	4	8	no	—
119	SD₁₆×C₄₃	—	4	8	no	—
120	D₈×C₄₃	—	4	4	no	—
121	C₂×C₈×C₄₃	—	2	2	no	—
122	C₂×C₈×C₄₃	—	2	1	no	—
123	C₂×C₈×C₄₃	—	2	1	no	—
124	C₂×C₈×C₄₃	—	2	2	no	—
125	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
127	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₄₃	#41	1	2	yes	—
130	C₄⋊C₄×C₄₃	—	2	2	no	—
131	C₄⋊C₄×C₄₃	—	2	2	no	—
132	C₄⋊C₄×C₄₃	—	4	2	no	—
133	C₄⋊C₄×C₄₃	—	4	8	no	—
134	C₄⋊C₄×C₄₃	—	4	4	no	—
135	C₂²⋊C₄×C₄₃	—	4	8	no	—
136	C₂²⋊C₄×C₄₃	—	4	8	no	—
137	C₂²⋊C₄×C₄₃	—	4	4	no	—
138	C₂²⋊C₄×C₄₃	—	4	4	no	—
139	C₄²×C₄₃	—	2	2	no	—
140	C₄²×C₄₃	—	2	2	no	—
141	C₄²×C₄₃	—	4	4	no	—
142	C₄²×C₄₃	C₂×D₄	1	2	yes	—
143	C₄²×C₄₃	C₂×D₄	1	2	yes	—
144	C₂³×C₄₃	—	4	2	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	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₄₃	—	2	4	no	—
151	Q₈×C₄₃	—	2	4	no	—
152	Q₈×C₄₃	—	4	2	no	—
153	Q₈×C₄₃	—	4	2	no	—
154	Q₈×C₄₃	—	4	2	no	—
155	Q₈×C₄₃	—	4	2	no	—
156	Q₈×C₄₃	—	4	2	no	—
157	Q₈×C₄₃	—	4	2	no	—
158	D₄×C₄₃	—	4	2	no	—
159	D₄×C₄₃	—	4	2	no	—
160	D₄×C₄₃	—	4	2	no	—
161	D₄×C₄₃	—	4	2	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	4	no	—
165	C₂×C₄×C₄₃	—	2	4	no	—
166	C₂×C₄×C₄₃	—	2	4	no	—
167	C₂×C₄×C₄₃	—	2	4	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	—	4	2	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	4	4	no	—
175	C₂×C₄×C₄₃	#127	1	2	yes	—
176	C₂×C₄×C₄₃	#127	1	2	yes	—
177	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
183	C₈×C₄₃	—	2	2	no	—
184	C₈×C₄₃	—	2	4	no	—
185	C₈×C₄₃	#121	1	4	yes	—
186	#28469	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂²×C₄₃	—	8	4	no	—
188	C₂²×C₄₃	—	8	2	no	—
189	C₂²×C₄₃	—	8	2	no	—
190	C₂²×C₄₃	—	8	4	no	—
191	C₂²×C₄₃	—	8	2	no	—
192	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
193	C₂²×C₄₃	D₄²	1	1	yes	characteristic
194	C₂²×C₄₃	#550	1	1	yes	characteristic
195	C₂²×C₄₃	#575	1	2	yes	—
196	C₂²×C₄₃	#578	1	2	yes	—
197	C₄×C₄₃	—	2	2	no	—
198	C₄×C₄₃	—	2	2	no	—
199	C₄×C₄₃	—	4	4	no	—
200	C₄×C₄₃	—	4	4	no	—
201	C₄×C₄₃	—	8	2	no	—
202	C₄×C₄₃	—	8	2	no	—
203	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
204	C₄×C₄₃	#535	1	1	yes	characteristic
205	C₄×C₄₃	D₄²	1	1	yes	characteristic
206	C₄×C₄₃	#550	1	1	yes	characteristic
207	C₂×#497	C₂×C₄₃	1	2	yes	complemented
208	C₂×#495	C₂×C₄₃	1	1	yes	characteristic
209	C₂×#464	C₂×C₄₃	1	2	yes	complemented
210	C₂×C₄×Q₁₆	C₂×C₄₃	1	1	yes	characteristic, complemented
211	#2545	C₂×C₄₃	1	2	yes	complemented
212	#2016	C₂×C₄₃	1	2	yes	complemented
213	#2012	C₂×C₄₃	1	2	yes	—
214	#1973	C₂×C₄₃	1	2	yes	complemented
215	#1770	C₂×C₄₃	1	1	yes	characteristic, complemented
216	C₂×C₄₃	—	16	2	no	—
217	C₂×C₄₃	#2541	1	1	yes	characteristic
218	C₂×C₄₃	#3150	1	1	yes	characteristic
219	C₂×C₄₃	#3156	1	1	yes	characteristic
220	C₂×C₄₃	#3277	1	2	yes	—
221	C₂×C₄₃	#3402	1	2	yes	—
222	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	—
223	C₂²×Q₁₆	C₂²×C₄₃	1	1	yes	characteristic
224	C₂²×Q₁₆	C₂²×C₄₃	1	1	yes	characteristic
225	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
226	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
227	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic
228	C₂×C₄⋊Q₈	C₂²×C₄₃	1	2	yes	—
229	C₂×#124	C₂²×C₄₃	1	2	yes	—
230	C₂×#124	C₂²×C₄₃	1	2	yes	—
231	C₂×C₄×Q₈	C₂²×C₄₃	1	2	yes	—
232	#497	—	2	8	no	—
233	#495	—	2	4	no	—
234	#464	—	2	8	no	—
235	C₄×Q₁₆	—	2	4	no	—
236	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
238	C₂×#103	C₂²×C₄₃	1	2	yes	—
239	C₂×#103	C₂²×C₄₃	1	2	yes	—
240	C₂×#102	C₂²×C₄₃	1	2	yes	—
241	C₂×#97	C₂²×C₄₃	1	2	yes	—
242	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
243	#396	—	2	4	no	—
244	#391	C₂²×C₄₃	1	2	yes	—
245	#390	C₂²×C₄₃	1	2	yes	—
246	#388	—	2	4	no	—
247	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
248	#336	C₂²×C₄₃	1	2	yes	—
249	C₄₃	#28469	1	1	yes	characteristic, direct product factor, Sylow
250	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
251	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
252	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
253	C₂×Q₁₆	—	2	4	no	—
254	C₂×Q₁₆	—	2	2	no	—
255	C₂×Q₁₆	—	2	4	no	—
256	C₂×Q₁₆	—	2	2	no	—
257	C₂×Q₁₆	—	2	2	no	—
258	C₂×Q₁₆	—	4	1	no	—
259	C₂×Q₁₆	—	4	1	no	—
260	C₂×Q₁₆	—	4	2	no	—
261	C₂×Q₁₆	D₄×C₄₃	1	4	yes	—
262	C₂×SD₁₆	—	2	4	no	—
263	C₂×SD₁₆	—	2	4	no	—
264	C₂×SD₁₆	—	2	4	no	—
265	C₂×SD₁₆	—	2	4	no	—
266	C₂×SD₁₆	—	2	4	no	—
267	C₂×SD₁₆	—	4	2	no	—
268	C₂×D₈	—	2	2	no	—
269	C₂×D₈	—	4	1	no	—
270	C₂×D₈	—	4	1	no	—
271	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
273	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
274	C₄⋊Q₈	—	2	4	no	—
275	C₄⋊Q₈	—	4	2	no	—
276	#124	—	2	4	no	—
277	#124	—	2	4	no	—
278	#124	—	2	4	no	—
279	#124	—	4	2	no	—
280	C₄×Q₈	—	2	4	no	—
281	C₄×Q₈	—	2	4	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	4	no	—
284	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	4	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₂²⋊C₄	—	2	4	no	—
290	C₂×C₄²	—	2	2	no	—
291	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
292	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
293	#107	—	2	2	no	—
294	C₄⋊C₈	D₄×C₄₃	1	4	yes	—
295	#103	—	2	4	no	—
296	#103	—	2	4	no	—
297	#102	—	2	4	no	—
298	#97	—	2	4	no	—
299	C₄×C₈	D₄×C₄₃	1	4	yes	—
300	#95	—	2	4	no	—
301	#95	D₄×C₄₃	1	2	yes	—
302	C₂⁴	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
325	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
327	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
328	Q₁₆	—	2	8	no	—
329	Q₁₆	—	4	8	no	—
330	Q₁₆	—	4	4	no	—
331	SD₁₆	—	4	8	no	—
332	SD₁₆	—	4	8	no	—
333	D₈	—	4	4	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
339	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
340	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
341	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
342	C₂×C₈	#41×C₄₃	1	2	yes	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	4	8	no	—
347	C₄⋊C₄	—	4	4	no	—
348	C₂²⋊C₄	—	4	8	no	—
349	C₂²⋊C₄	—	4	8	no	—
350	C₂²⋊C₄	—	4	4	no	—
351	C₂²⋊C₄	—	4	4	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	4	4	no	—
355	C₄²	C₂×D₄×C₄₃	1	2	yes	—
356	C₄²	C₂×D₄×C₄₃	1	2	yes	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	4	no	—
361	C₂³	—	4	4	no	—
362	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
363	Q₈	—	2	4	no	—
364	Q₈	—	2	4	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	#127×C₄₃	1	2	yes	—
389	C₂×C₄	#127×C₄₃	1	2	yes	—
390	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
393	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
394	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
395	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
396	C₈	—	2	2	no	—
397	C₈	—	2	4	no	—
398	C₈	#121×C₄₃	1	4	yes	—
399	C₂²	—	8	4	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	4	no	—
403	C₂²	—	8	2	no	—
404	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
405	C₂²	D₄²×C₄₃	1	1	yes	characteristic
406	C₂²	C₄₃×#550	1	1	yes	characteristic
407	C₂²	C₄₃×#575	1	2	yes	—
408	C₂²	C₄₃×#578	1	2	yes	—
409	C₄	—	2	2	no	—
410	C₄	—	2	2	no	—
411	C₄	—	4	4	no	—
412	C₄	—	4	4	no	—
413	C₄	—	8	2	no	—
414	C₄	—	8	2	no	—
415	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
416	C₄	C₄₃×#535	1	1	yes	characteristic
417	C₄	D₄²×C₄₃	1	1	yes	characteristic
418	C₄	C₄₃×#550	1	1	yes	characteristic
419	C₂	—	16	2	no	—
420	C₂	C₄₃×#2541	1	1	yes	characteristic
421	C₂	C₄₃×#3150	1	1	yes	characteristic
422	C₂	C₄₃×#3156	1	1	yes	characteristic
423	C₂	C₄₃×#3277	1	2	yes	—
424	C₂	C₄₃×#3402	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×D₈×C₄₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₄×C₄⋊C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#497	C₂	semidirect
3. C₂×C₄₃×#464	C₂	semidirect
4. C₂×C₄×Q₁₆×C₄₃	C₂	semidirect
5. C₄₃×#2545	C₂	semidirect
6. C₄₃×#2016	C₂	semidirect
8. C₄₃×#1973	C₂	semidirect
9. C₄₃×#1770	C₂	semidirect
186. #28469	C₄₃	direct (N × H)
207. C₂×#497	C₂×C₄₃	semidirect
209. C₂×#464	C₂×C₄₃	semidirect
210. C₂×C₄×Q₁₆	C₂×C₄₃	semidirect
211. #2545	C₂×C₄₃	semidirect
212. #2016	C₂×C₄₃	semidirect
214. #1973	C₂×C₄₃	semidirect
215. #1770	C₂×C₄₃	semidirect
249. C₄₃	#28469	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#497	2
C₂×C₄₃×#495	2
C₂×C₄₃×#464	2
C₂×C₄×Q₁₆×C₄₃	2
C₄₃×#2545	2
C₄₃×#2016	2
C₄₃×#2012	2
C₄₃×#1973	2
C₄₃×#1770	2
#28469	43

Subgroups — C43×#28469 #24948486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28469 #24948486