Subgroups — C₄₃×#25741 #24945758

Order 11008.

1526 conjugacy classes of subgroups.

The subgroup lattice has 414 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×#3151	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#454	C₂	1	4	yes	maximal, complemented
4	C₄₃×#2548	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2006	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1980	C₂	1	2	yes	maximal, complemented
7	C₄×#101×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×2₋¹⁺⁴×C₄₃	C₂²	1	2	yes	—
9	C₂×AGL(1,ℤ/8)×C₄₃	C₂²	1	8	yes	—
10	C₄₃×#550	—	2	2	no	—
11	D₄×Q₈×C₄₃	—	2	2	no	—
12	C₄₃×#548	—	2	4	no	—
13	C₄₃×#537	—	2	2	no	—
14	C₄₃×#537	C₂²	1	2	yes	—
15	C₄₃×#532	—	2	2	no	—
16	C₄₃×#532	C₂²	1	2	yes	—
17	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#124×C₄₃	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#496	—	2	4	no	—
21	C₄₃×#493	—	2	2	no	—
22	C₄₃×#492	—	2	2	no	—
23	C₄₃×#454	—	2	16	no	—
24	C₂×#104×C₄₃	C₂²	1	8	yes	—
25	C₂×#101×C₄₃	C₂²	1	2	yes	—
26	C₄×M₁₆×C₄₃	C₂²	1	2	yes	—
27	C₄₃×#394	—	2	2	no	—
28	C₄₃×#390	—	2	2	no	—
29	C₄₃×#390	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
31	C₄₃×#343	C₂²	1	2	yes	—
32	2₋¹⁺⁴×C₄₃	—	2	8	no	—
33	2₋¹⁺⁴×C₄₃	—	4	4	no	—
34	C₂×#41×C₄₃	—	2	4	no	—
35	C₂×#41×C₄₃	—	2	4	no	—
36	C₂×#41×C₄₃	C₂³	1	4	yes	—
37	C₂²×Q₈×C₄₃	—	2	4	no	—
38	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₄₃	—	2	1	no	—
40	C₂²×D₄×C₄₃	—	2	1	no	—
41	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
42	AGL(1,ℤ/8)×C₄₃	—	2	16	no	—
43	AGL(1,ℤ/8)×C₄₃	—	4	8	no	—
44	C₂×SD₁₆×C₄₃	—	2	8	no	—
45	C₂×D₈×C₄₃	—	2	8	no	—
46	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
47	C₄⋊Q₈×C₄₃	—	2	2	no	—
48	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
49	#127×C₄₃	—	2	2	no	—
50	#127×C₄₃	—	2	2	no	—
51	#127×C₄₃	—	2	2	no	—
52	#127×C₄₃	D₄	1	2	yes	—
53	#124×C₄₃	—	2	4	no	—
54	#124×C₄₃	—	2	8	no	—
55	#124×C₄₃	D₄	1	4	yes	—
56	C₂²⋊Q₈×C₄₃	—	2	8	no	—
57	C₂²⋊Q₈×C₄₃	—	2	4	no	—
58	#121×C₄₃	—	2	8	no	—
59	#121×C₄₃	—	2	4	no	—
60	#121×C₄₃	—	2	2	no	—
61	#121×C₄₃	—	2	4	no	—
62	#121×C₄₃	—	2	2	no	—
63	C₄×Q₈×C₄₃	—	2	2	no	—
64	C₄×Q₈×C₄₃	—	2	2	no	—
65	C₄×D₄×C₄₃	—	2	4	no	—
66	C₄×D₄×C₄₃	—	2	4	no	—
67	C₄×D₄×C₄₃	—	2	2	no	—
68	C₄×D₄×C₄₃	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
74	C₂×C₄²×C₄₃	D₄	1	2	yes	—
75	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
76	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
77	#104×C₄₃	—	2	16	no	—
78	#101×C₄₃	D₄	1	8	yes	complemented
79	#97×C₄₃	—	2	2	no	—
80	C₄×C₈×C₄₃	—	2	2	no	—
81	#95×C₄₃	—	2	1	no	—
82	C₂⁴×C₄₃	—	2	2	no	—
83	#41×C₄₃	—	2	8	no	—
84	#41×C₄₃	—	2	8	no	—
85	#41×C₄₃	—	4	8	no	—
86	#41×C₄₃	—	4	16	no	—
87	#41×C₄₃	—	4	8	no	—
88	C₂×Q₈×C₄₃	—	2	4	no	—
89	C₂×Q₈×C₄₃	—	2	2	no	—
90	C₂×Q₈×C₄₃	—	2	2	no	—
91	C₂×Q₈×C₄₃	—	4	16	no	—
92	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
93	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
94	C₂×D₄×C₄₃	—	2	4	no	—
95	C₂×D₄×C₄₃	—	2	4	no	—
96	C₂×D₄×C₄₃	—	2	2	no	—
97	C₂×D₄×C₄₃	—	2	2	no	—
98	C₂×D₄×C₄₃	—	2	4	no	—
99	C₂×D₄×C₄₃	—	2	4	no	—
100	C₂×D₄×C₄₃	—	2	4	no	—
101	C₂×D₄×C₄₃	—	2	4	no	—
102	C₂×D₄×C₄₃	—	4	4	no	—
103	C₂×D₄×C₄₃	—	4	1	no	—
104	C₂×D₄×C₄₃	—	4	2	no	—
105	C₂×D₄×C₄₃	—	4	1	no	—
106	C₂×D₄×C₄₃	—	8	2	no	—
107	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₄₃	—	2	8	no	—
109	C₂²×C₄×C₄₃	—	2	4	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
116	SD₁₆×C₄₃	—	4	16	no	—
117	D₈×C₄₃	—	4	16	no	—
118	M₁₆×C₄₃	—	2	4	no	—
119	M₁₆×C₄₃	C₂×D₄	1	8	yes	—
120	C₂×C₈×C₄₃	—	2	4	no	—
121	C₄⋊C₄×C₄₃	—	2	4	no	—
122	C₄⋊C₄×C₄₃	—	2	4	no	—
123	C₄⋊C₄×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	—	2	2	no	—
125	C₄⋊C₄×C₄₃	—	2	2	no	—
126	C₄⋊C₄×C₄₃	—	4	2	no	—
127	C₂²⋊C₄×C₄₃	—	2	8	no	—
128	C₂²⋊C₄×C₄₃	—	2	4	no	—
129	C₂²⋊C₄×C₄₃	—	2	4	no	—
130	C₂²⋊C₄×C₄₃	—	4	8	no	—
131	C₂²⋊C₄×C₄₃	—	8	4	no	—
132	C₄²×C₄₃	—	2	2	no	—
133	C₄²×C₄₃	—	2	2	no	—
134	C₄²×C₄₃	—	2	4	no	—
135	C₄²×C₄₃	C₂×D₄	1	2	yes	—
136	C₄²×C₄₃	C₂×D₄	1	2	yes	—
137	C₂³×C₄₃	—	2	4	no	—
138	C₂³×C₄₃	—	4	4	no	—
139	C₂³×C₄₃	—	4	4	no	—
140	C₂³×C₄₃	—	4	2	no	—
141	C₂³×C₄₃	—	4	2	no	—
142	C₂³×C₄₃	—	4	2	no	—
143	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₄₃	—	2	8	no	—
145	Q₈×C₄₃	—	2	8	no	—
146	Q₈×C₄₃	—	4	8	no	—
147	D₄×C₄₃	—	2	8	no	—
148	D₄×C₄₃	—	4	8	no	—
149	D₄×C₄₃	—	4	4	no	—
150	D₄×C₄₃	—	4	4	no	—
151	D₄×C₄₃	—	4	8	no	—
152	D₄×C₄₃	—	4	4	no	—
153	D₄×C₄₃	—	8	2	no	—
154	D₄×C₄₃	—	8	2	no	—
155	D₄×C₄₃	—	8	4	no	—
156	D₄×C₄₃	—	8	4	no	—
157	D₄×C₄₃	—	8	2	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	2	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	—	4	1	no	—
164	C₂×C₄×C₄₃	—	4	16	no	—
165	C₂×C₄×C₄₃	—	4	8	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	#120	1	1	yes	characteristic
171	C₂×C₄×C₄₃	#120	1	2	yes	—
172	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
173	C₂×C₄×C₄₃	#127	1	4	yes	—
174	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
175	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
176	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
177	C₈×C₄₃	—	2	8	no	—
178	#25741	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₄₃	—	2	1	no	—
180	C₂²×C₄₃	—	2	1	no	—
181	C₂²×C₄₃	—	4	4	no	—
182	C₂²×C₄₃	—	4	4	no	—
183	C₂²×C₄₃	—	4	4	no	—
184	C₂²×C₄₃	—	8	4	no	—
185	C₂²×C₄₃	—	8	4	no	—
186	C₂²×C₄₃	—	8	2	no	—
187	C₂²×C₄₃	—	8	2	no	—
188	C₂²×C₄₃	—	8	2	no	—
189	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
190	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
191	C₂²×C₄₃	#535	1	1	yes	characteristic
192	C₄×C₄₃	—	2	4	no	—
193	C₄×C₄₃	—	2	1	no	—
194	C₄×C₄₃	—	2	2	no	—
195	C₄×C₄₃	—	4	4	no	—
196	C₄×C₄₃	—	4	2	no	—
197	C₄×C₄₃	—	8	2	no	—
198	C₄×C₄₃	#454	1	2	yes	complemented
199	C₄×C₄₃	D₄²	1	4	yes	—
200	#3497	C₂×C₄₃	1	1	yes	characteristic, complemented
201	#3151	C₂×C₄₃	1	2	yes	complemented
202	C₂×#454	C₂×C₄₃	1	4	yes	complemented
203	#2548	C₂×C₄₃	1	1	yes	characteristic, complemented
204	#2006	C₂×C₄₃	1	4	yes	complemented
205	#1980	C₂×C₄₃	1	2	yes	complemented
206	C₄×#101	C₂×C₄₃	1	1	yes	characteristic, complemented
207	C₂×C₄₃	—	2	1	no	—
208	C₂×C₄₃	—	2	1	no	—
209	C₂×C₄₃	—	8	4	no	—
210	C₂×C₄₃	—	16	2	no	—
211	C₂×C₄₃	#2433	1	1	yes	characteristic
212	C₂×C₄₃	C₂×#454	1	1	yes	characteristic
213	C₂×C₄₃	#3021	1	1	yes	characteristic
214	C₂×2₋¹⁺⁴	C₂²×C₄₃	1	2	yes	—
215	C₂×AGL(1,ℤ/8)	C₂²×C₄₃	1	8	yes	—
216	#550	—	2	2	no	—
217	D₄×Q₈	—	2	2	no	—
218	#548	—	2	4	no	—
219	#537	—	2	2	no	—
220	#537	C₂²×C₄₃	1	2	yes	—
221	#532	—	2	2	no	—
222	#532	C₂²×C₄₃	1	2	yes	—
223	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
224	C₂×#124	C₂²×C₄₃	1	2	yes	—
225	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
226	#496	—	2	4	no	—
227	#493	—	2	2	no	—
228	#492	—	2	2	no	—
229	#454	—	2	16	no	—
230	C₂×#104	C₂²×C₄₃	1	8	yes	—
231	C₂×#101	C₂²×C₄₃	1	2	yes	—
232	C₄×M₁₆	C₂²×C₄₃	1	2	yes	—
233	#394	—	2	2	no	—
234	#390	—	2	2	no	—
235	#390	C₂²×C₄₃	1	2	yes	—
236	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
237	#343	C₂²×C₄₃	1	2	yes	—
238	C₄₃	#25741	1	1	yes	characteristic, direct product factor, Sylow
239	2₋¹⁺⁴	—	2	8	no	—
240	2₋¹⁺⁴	—	4	4	no	—
241	C₂×#41	—	2	4	no	—
242	C₂×#41	—	2	4	no	—
243	C₂×#41	C₂³×C₄₃	1	4	yes	—
244	C₂²×Q₈	—	2	4	no	—
245	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
249	AGL(1,ℤ/8)	—	2	16	no	—
250	AGL(1,ℤ/8)	—	4	8	no	—
251	C₂×SD₁₆	—	2	8	no	—
252	C₂×D₈	—	2	8	no	—
253	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
254	C₄⋊Q₈	—	2	2	no	—
255	C₄⋊Q₈	D₄×C₄₃	1	2	yes	—
256	#127	—	2	2	no	—
257	#127	—	2	2	no	—
258	#127	—	2	2	no	—
259	#127	D₄×C₄₃	1	2	yes	—
260	#124	—	2	4	no	—
261	#124	—	2	8	no	—
262	#124	D₄×C₄₃	1	4	yes	—
263	C₂²⋊Q₈	—	2	8	no	—
264	C₂²⋊Q₈	—	2	4	no	—
265	#121	—	2	8	no	—
266	#121	—	2	4	no	—
267	#121	—	2	2	no	—
268	#121	—	2	4	no	—
269	#121	—	2	2	no	—
270	C₄×Q₈	—	2	2	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	2	4	no	—
280	C₂×C₂²⋊C₄	—	2	4	no	—
281	C₂×C₄²	D₄×C₄₃	1	2	yes	—
282	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
283	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
284	#104	—	2	16	no	—
285	#101	D₄×C₄₃	1	8	yes	complemented
286	#97	—	2	2	no	—
287	C₄×C₈	—	2	2	no	—
288	#95	—	2	1	no	—
289	C₂⁴	—	2	2	no	—
290	#41	—	2	8	no	—
291	#41	—	2	8	no	—
292	#41	—	4	8	no	—
293	#41	—	4	16	no	—
294	#41	—	4	8	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	4	16	no	—
299	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
300	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	4	4	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	8	2	no	—
314	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
315	C₂²×C₄	—	2	8	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
321	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
322	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
323	SD₁₆	—	4	16	no	—
324	D₈	—	4	16	no	—
325	M₁₆	—	2	4	no	—
326	M₁₆	C₂×D₄×C₄₃	1	8	yes	—
327	C₂×C₈	—	2	4	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	2	8	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₂²⋊C₄	—	4	8	no	—
338	C₂²⋊C₄	—	8	4	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	4	no	—
342	C₄²	C₂×D₄×C₄₃	1	2	yes	—
343	C₄²	C₂×D₄×C₄₃	1	2	yes	—
344	C₂³	—	2	4	no	—
345	C₂³	—	4	4	no	—
346	C₂³	—	4	4	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
351	Q₈	—	2	8	no	—
352	Q₈	—	2	8	no	—
353	Q₈	—	4	8	no	—
354	D₄	—	2	8	no	—
355	D₄	—	4	8	no	—
356	D₄	—	4	4	no	—
357	D₄	—	4	4	no	—
358	D₄	—	4	8	no	—
359	D₄	—	4	4	no	—
360	D₄	—	8	2	no	—
361	D₄	—	8	2	no	—
362	D₄	—	8	4	no	—
363	D₄	—	8	4	no	—
364	D₄	—	8	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	16	no	—
372	C₂×C₄	—	4	8	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
378	C₂×C₄	#120×C₄₃	1	2	yes	—
379	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
380	C₂×C₄	#127×C₄₃	1	4	yes	—
381	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
382	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
383	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
384	C₈	—	2	8	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	8	4	no	—
391	C₂²	—	8	4	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
396	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
397	C₂²	C₄₃×#535	1	1	yes	characteristic
398	C₄	—	2	4	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	—	4	4	no	—
402	C₄	—	4	2	no	—
403	C₄	—	8	2	no	—
404	C₄	C₄₃×#454	1	2	yes	complemented
405	C₄	D₄²×C₄₃	1	4	yes	—
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	8	4	no	—
409	C₂	—	16	2	no	—
410	C₂	C₄₃×#2433	1	1	yes	characteristic
411	C₂	C₂×C₄₃×#454	1	1	yes	characteristic
412	C₂	C₄₃×#3021	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×#3151	C₂	semidirect
3. C₂×C₄₃×#454	C₂	semidirect
4. C₄₃×#2548	C₂	semidirect
5. C₄₃×#2006	C₂	semidirect
6. C₄₃×#1980	C₂	semidirect
7. C₄×#101×C₄₃	C₂	semidirect
78. #101×C₄₃	D₄	semidirect
178. #25741	C₄₃	direct (N × H)
198. C₄×C₄₃	#454	semidirect
200. #3497	C₂×C₄₃	semidirect
201. #3151	C₂×C₄₃	semidirect
202. C₂×#454	C₂×C₄₃	semidirect
203. #2548	C₂×C₄₃	semidirect
204. #2006	C₂×C₄₃	semidirect
205. #1980	C₂×C₄₃	semidirect
206. C₄×#101	C₂×C₄₃	semidirect
238. C₄₃	#25741	direct (N × H)
285. #101	D₄×C₄₃	semidirect
404. C₄	C₄₃×#454	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×#3151	2
C₂×C₄₃×#454	2
C₄₃×#2548	2
C₄₃×#2006	2
C₄₃×#1980	2
C₄×#101×C₄₃	2
#25741	43

Subgroups — C43×#25741 #24945758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25741 #24945758