Subgroups — C₄₃×#28490 #24948507

Order 11008.

1230 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#468	C₂	1	4	yes	maximal, complemented
3	C₂×C₄₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2541	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#2000	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#107×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
11	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
12	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#127×C₄₃	—	2	1	no	—
15	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	4	yes	—
17	C₂×#121×C₄₃	C₂²	1	4	yes	—
18	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#492	—	2	4	no	—
20	C₄₃×#468	—	2	16	no	—
21	C₄₃×#436	—	2	4	no	—
22	C₂×#107×C₄₃	C₂²	1	2	yes	—
23	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#103×C₄₃	C₂²	1	4	yes	—
25	C₂×#102×C₄₃	C₂²	1	4	yes	—
26	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₄₃×#399	—	2	2	no	—
29	C₄₃×#392	—	2	2	no	—
30	C₄₃×#390	—	2	1	no	—
31	C₄₃×#390	—	2	1	no	—
32	C₄₃×#384	—	2	1	no	—
33	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
35	C₄₃×#340	C₂²	1	2	yes	—
36	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
37	C₂²×D₄×C₄₃	—	2	4	no	—
38	C₂²×D₄×C₄₃	—	2	1	no	—
39	C₂²×D₄×C₄₃	—	2	1	no	—
40	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
43	C₂×SD₁₆×C₄₃	—	2	8	no	—
44	C₂×SD₁₆×C₄₃	—	2	4	no	—
45	C₂×SD₁₆×C₄₃	—	2	4	no	—
46	C₂×SD₁₆×C₄₃	—	4	4	no	—
47	C₂×M₁₆×C₄₃	—	2	4	no	—
48	C₂×M₁₆×C₄₃	—	2	8	no	—
49	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
52	C₄⋊Q₈×C₄₃	—	2	2	no	—
53	C₄⋊Q₈×C₄₃	—	2	2	no	—
54	#127×C₄₃	—	2	2	no	—
55	#127×C₄₃	—	2	2	no	—
56	#127×C₄₃	—	4	4	no	—
57	C₂²⋊Q₈×C₄₃	—	2	8	no	—
58	C₂²⋊Q₈×C₄₃	—	4	4	no	—
59	#121×C₄₃	—	2	8	no	—
60	#121×C₄₃	—	4	4	no	—
61	C₄×D₄×C₄₃	—	2	2	no	—
62	C₄×D₄×C₄₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
72	C₂×C₄²×C₄₃	—	2	1	no	—
73	C₂×C₄²×C₄₃	—	2	1	no	—
74	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
75	#107×C₄₃	D₄	1	8	yes	complemented
76	C₄⋊C₈×C₄₃	—	2	2	no	—
77	#103×C₄₃	—	2	8	no	—
78	#102×C₄₃	—	2	8	no	—
79	C₂²⋊C₈×C₄₃	—	2	4	no	—
80	C₄×C₈×C₄₃	D₄	1	4	yes	complemented
81	#95×C₄₃	—	2	1	no	—
82	#95×C₄₃	—	2	1	no	—
83	C₂⁴×C₄₃	—	2	2	no	—
84	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
85	C₂×Q₈×C₄₃	—	2	4	no	—
86	C₂×Q₈×C₄₃	—	2	2	no	—
87	C₂×Q₈×C₄₃	—	2	2	no	—
88	C₂×Q₈×C₄₃	—	2	4	no	—
89	C₂×D₄×C₄₃	—	2	2	no	—
90	C₂×D₄×C₄₃	—	2	2	no	—
91	C₂×D₄×C₄₃	—	2	2	no	—
92	C₂×D₄×C₄₃	—	2	4	no	—
93	C₂×D₄×C₄₃	—	2	2	no	—
94	C₂×D₄×C₄₃	—	2	2	no	—
95	C₂×D₄×C₄₃	—	2	4	no	—
96	C₂×D₄×C₄₃	—	4	8	no	—
97	C₂×D₄×C₄₃	—	4	8	no	—
98	C₂×D₄×C₄₃	—	4	2	no	—
99	C₂×D₄×C₄₃	—	4	2	no	—
100	C₂×D₄×C₄₃	—	4	2	no	—
101	C₂×D₄×C₄₃	—	4	2	no	—
102	C₂×D₄×C₄₃	—	8	4	no	—
103	C₂×D₄×C₄₃	—	8	2	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	2	4	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	—	2	4	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	2	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	SD₁₆×C₄₃	—	4	8	no	—
116	SD₁₆×C₄₃	—	4	8	no	—
117	M₁₆×C₄₃	—	4	8	no	—
118	C₂×C₈×C₄₃	—	2	2	no	—
119	C₂×C₈×C₄₃	—	2	2	no	—
120	C₂×C₈×C₄₃	—	2	4	no	—
121	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
124	C₄⋊C₄×C₄₃	—	2	2	no	—
125	C₄⋊C₄×C₄₃	—	2	2	no	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	4	8	no	—
128	C₄⋊C₄×C₄₃	—	4	2	no	—
129	C₄⋊C₄×C₄₃	—	4	2	no	—
130	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
131	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
132	C₂²⋊C₄×C₄₃	—	2	4	no	—
133	C₂²⋊C₄×C₄₃	—	4	8	no	—
134	C₂²⋊C₄×C₄₃	—	4	8	no	—
135	C₄²×C₄₃	—	4	2	no	—
136	C₄²×C₄₃	—	4	2	no	—
137	C₄²×C₄₃	C₂×D₄	1	2	yes	—
138	C₄²×C₄₃	#41	1	2	yes	—
139	C₂³×C₄₃	—	2	2	no	—
140	C₂³×C₄₃	—	2	4	no	—
141	C₂³×C₄₃	—	2	2	no	—
142	C₂³×C₄₃	—	2	2	no	—
143	C₂³×C₄₃	—	2	4	no	—
144	C₂³×C₄₃	—	4	2	no	—
145	C₂³×C₄₃	—	4	4	no	—
146	C₂³×C₄₃	—	4	2	no	—
147	C₂³×C₄₃	—	4	2	no	—
148	C₂³×C₄₃	—	4	4	no	—
149	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₄₃	—	4	2	no	—
151	Q₈×C₄₃	—	4	2	no	—
152	Q₈×C₄₃	—	4	4	no	—
153	D₄×C₄₃	—	4	2	no	—
154	D₄×C₄₃	—	4	2	no	—
155	D₄×C₄₃	—	4	4	no	—
156	D₄×C₄₃	—	4	4	no	—
157	D₄×C₄₃	—	8	4	no	—
158	D₄×C₄₃	—	8	16	no	—
159	D₄×C₄₃	—	8	4	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	4	no	—
163	C₂×C₄×C₄₃	—	2	4	no	—
164	C₂×C₄×C₄₃	—	2	4	no	—
165	C₂×C₄×C₄₃	—	4	2	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	4	2	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	4	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	4	4	no	—
174	C₂×C₄×C₄₃	#121	1	2	yes	—
175	C₂×C₄×C₄₃	#121	1	2	yes	—
176	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₄₃	#137	1	2	yes	—
178	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
180	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
182	C₈×C₄₃	—	2	2	no	—
183	C₈×C₄₃	—	4	2	no	—
184	C₈×C₄₃	#127	1	4	yes	complemented
185	#28490	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂²×C₄₃	—	4	4	no	—
187	C₂²×C₄₃	—	4	4	no	—
188	C₂²×C₄₃	—	4	2	no	—
189	C₂²×C₄₃	—	4	2	no	—
190	C₂²×C₄₃	—	4	2	no	—
191	C₂²×C₄₃	—	8	4	no	—
192	C₂²×C₄₃	—	8	4	no	—
193	C₂²×C₄₃	—	8	2	no	—
194	C₂²×C₄₃	—	8	2	no	—
195	C₂²×C₄₃	—	8	2	no	—
196	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
197	C₂²×C₄₃	D₄²	1	2	yes	—
198	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
200	C₂²×C₄₃	#577	1	2	yes	—
201	C₄×C₄₃	—	2	2	no	—
202	C₄×C₄₃	—	4	4	no	—
203	C₄×C₄₃	—	4	4	no	—
204	C₄×C₄₃	—	4	2	no	—
205	C₄×C₄₃	—	8	2	no	—
206	C₄×C₄₃	#468	1	4	yes	complemented
207	C₄×C₄₃	C₂×#127	1	1	yes	characteristic
208	C₄×C₄₃	#535	1	1	yes	characteristic
209	C₄×C₄₃	#550	1	2	yes	—
210	C₂×#492	C₂×C₄₃	1	1	yes	characteristic, complemented
211	C₂×#468	C₂×C₄₃	1	4	yes	complemented
212	C₂×#436	C₂×C₄₃	1	1	yes	characteristic, complemented
213	#2542	C₂×C₄₃	1	1	yes	characteristic, complemented
214	#2541	C₂×C₄₃	1	1	yes	characteristic
215	#2000	C₂×C₄₃	1	4	yes	complemented
216	#1982	C₂×C₄₃	1	1	yes	characteristic, complemented
217	#1981	C₂×C₄₃	1	1	yes	characteristic, complemented
218	C₄×#107	C₂×C₄₃	1	1	yes	characteristic, complemented
219	C₂×C₄₃	—	8	2	no	—
220	C₂×C₄₃	—	16	2	no	—
221	C₂×C₄₃	#2541	1	1	yes	characteristic
222	C₂×C₄₃	C₂×#468	1	1	yes	characteristic
223	C₂×C₄₃	#3057	1	1	yes	characteristic
224	C₂×C₄₃	#3272	1	2	yes	—
225	C₂×C₄₃	#3278	1	2	yes	—
226	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
227	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
228	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
229	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
230	C₂×#127	—	2	1	no	—
231	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
232	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	4	yes	—
233	C₂×#121	C₂²×C₄₃	1	4	yes	—
234	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
235	#492	—	2	4	no	—
236	#468	—	2	16	no	—
237	#436	—	2	4	no	—
238	C₂×#107	C₂²×C₄₃	1	2	yes	—
239	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
240	C₂×#103	C₂²×C₄₃	1	4	yes	—
241	C₂×#102	C₂²×C₄₃	1	4	yes	—
242	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
243	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
244	#399	—	2	2	no	—
245	#392	—	2	2	no	—
246	#390	—	2	1	no	—
247	#390	—	2	1	no	—
248	#384	—	2	1	no	—
249	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
250	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
251	#340	C₂²×C₄₃	1	2	yes	—
252	C₄₃	#28490	1	1	yes	characteristic, direct product factor, Sylow
253	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
254	C₂²×D₄	—	2	4	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
258	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
259	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
260	C₂×SD₁₆	—	2	8	no	—
261	C₂×SD₁₆	—	2	4	no	—
262	C₂×SD₁₆	—	2	4	no	—
263	C₂×SD₁₆	—	4	4	no	—
264	C₂×M₁₆	—	2	4	no	—
265	C₂×M₁₆	—	2	8	no	—
266	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
267	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
269	C₄⋊Q₈	—	2	2	no	—
270	C₄⋊Q₈	—	2	2	no	—
271	#127	—	2	2	no	—
272	#127	—	2	2	no	—
273	#127	—	4	4	no	—
274	C₂²⋊Q₈	—	2	8	no	—
275	C₂²⋊Q₈	—	4	4	no	—
276	#121	—	2	8	no	—
277	#121	—	4	4	no	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	4	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
286	C₂×C₂²⋊C₄	—	2	4	no	—
287	C₂×C₂²⋊C₄	—	2	4	no	—
288	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
292	#107	D₄×C₄₃	1	8	yes	complemented
293	C₄⋊C₈	—	2	2	no	—
294	#103	—	2	8	no	—
295	#102	—	2	8	no	—
296	C₂²⋊C₈	—	2	4	no	—
297	C₄×C₈	D₄×C₄₃	1	4	yes	complemented
298	#95	—	2	1	no	—
299	#95	—	2	1	no	—
300	C₂⁴	—	2	2	no	—
301	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	4	8	no	—
314	C₂×D₄	—	4	8	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	8	2	no	—
320	C₂×D₄	—	8	4	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
331	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
332	SD₁₆	—	4	8	no	—
333	SD₁₆	—	4	8	no	—
334	M₁₆	—	4	8	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	4	no	—
338	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
339	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
340	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	4	8	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
348	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	—	4	8	no	—
351	C₂²⋊C₄	—	4	8	no	—
352	C₄²	—	4	2	no	—
353	C₄²	—	4	2	no	—
354	C₄²	C₂×D₄×C₄₃	1	2	yes	—
355	C₄²	#41×C₄₃	1	2	yes	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	4	no	—
366	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	4	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	4	no	—
373	D₄	—	4	4	no	—
374	D₄	—	8	4	no	—
375	D₄	—	8	16	no	—
376	D₄	—	8	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	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	2	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	#121×C₄₃	1	2	yes	—
392	C₂×C₄	#121×C₄₃	1	2	yes	—
393	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
394	C₂×C₄	#137×C₄₃	1	2	yes	—
395	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
396	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
397	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
398	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
399	C₈	—	2	2	no	—
400	C₈	—	4	2	no	—
401	C₈	#127×C₄₃	1	4	yes	complemented
402	C₂²	—	4	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	8	4	no	—
408	C₂²	—	8	4	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
413	C₂²	D₄²×C₄₃	1	2	yes	—
414	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
415	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
416	C₂²	C₄₃×#577	1	2	yes	—
417	C₄	—	2	2	no	—
418	C₄	—	4	4	no	—
419	C₄	—	4	4	no	—
420	C₄	—	4	2	no	—
421	C₄	—	8	2	no	—
422	C₄	C₄₃×#468	1	4	yes	complemented
423	C₄	C₂×#127×C₄₃	1	1	yes	characteristic
424	C₄	C₄₃×#535	1	1	yes	characteristic
425	C₄	C₄₃×#550	1	2	yes	—
426	C₂	—	8	2	no	—
427	C₂	—	16	2	no	—
428	C₂	C₄₃×#2541	1	1	yes	characteristic
429	C₂	C₂×C₄₃×#468	1	1	yes	characteristic
430	C₂	C₄₃×#3057	1	1	yes	characteristic
431	C₂	C₄₃×#3272	1	2	yes	—
432	C₂	C₄₃×#3278	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#2541	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×C₄×D₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#492	C₂	semidirect
2. C₂×C₄₃×#468	C₂	semidirect
3. C₂×C₄₃×#436	C₂	semidirect
4. C₄₃×#2542	C₂	semidirect
6. C₄₃×#2000	C₂	semidirect
7. C₄₃×#1982	C₂	semidirect
8. C₄₃×#1981	C₂	semidirect
9. C₄×#107×C₄₃	C₂	semidirect
75. #107×C₄₃	D₄	semidirect
80. C₄×C₈×C₄₃	D₄	semidirect
184. C₈×C₄₃	#127	semidirect
185. #28490	C₄₃	direct (N × H)
206. C₄×C₄₃	#468	semidirect
210. C₂×#492	C₂×C₄₃	semidirect
211. C₂×#468	C₂×C₄₃	semidirect
212. C₂×#436	C₂×C₄₃	semidirect
213. #2542	C₂×C₄₃	semidirect
215. #2000	C₂×C₄₃	semidirect
216. #1982	C₂×C₄₃	semidirect
217. #1981	C₂×C₄₃	semidirect
218. C₄×#107	C₂×C₄₃	semidirect
252. C₄₃	#28490	direct (N × H)
292. #107	D₄×C₄₃	semidirect
297. C₄×C₈	D₄×C₄₃	semidirect
401. C₈	#127×C₄₃	semidirect
422. C₄	C₄₃×#468	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#492	2
C₂×C₄₃×#468	2
C₂×C₄₃×#436	2
C₄₃×#2542	2
C₄₃×#2541	2
C₄₃×#2000	2
C₄₃×#1982	2
C₄₃×#1981	2
C₄×#107×C₄₃	2
#28490	43

Subgroups — C43×#28490 #24948507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28490 #24948507