Subgroups — C₄₃×#25739 #24945756

Order 11008.

1714 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#3151	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#453	C₂	1	4	yes	maximal, complemented
4	C₄₃×#2541	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×#100×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×H(5,𝔽₂)×C₄₃	C₂²	1	2	yes	—
9	C₂×AGL(1,ℤ/8)×C₄₃	C₂²	1	8	yes	complemented
10	C₄₃×#547	—	2	2	no	—
11	C₄₃×#546	—	2	4	no	—
12	D₄²×C₄₃	—	2	2	no	—
13	C₄₃×#537	C₂²	1	2	yes	—
14	C₄₃×#534	—	2	2	no	—
15	C₄₃×#532	C₂²	1	2	yes	—
16	C₂×#127×C₄₃	C₂²	1	2	yes	—
17	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic, complemented
18	C₂×#121×C₄₃	—	2	2	no	—
19	C₂×#121×C₄₃	—	2	2	no	—
20	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
21	C₄₃×#496	—	2	4	no	—
22	C₄₃×#493	—	2	2	no	—
23	C₄₃×#492	—	2	2	no	—
24	C₄₃×#453	—	2	16	no	—
25	C₂×#104×C₄₃	C₂²	1	8	yes	complemented
26	C₂×#100×C₄₃	C₂²	1	2	yes	—
27	C₄×M₁₆×C₄₃	C₂²	1	2	yes	complemented
28	C₄₃×#392	—	2	2	no	—
29	C₄₃×#390	C₂²	1	2	yes	complemented
30	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
31	C₄₃×#343	C₂²	1	2	yes	complemented
32	H(5,𝔽₂)×C₄₃	—	2	8	no	—
33	H(5,𝔽₂)×C₄₃	—	4	4	no	—
34	C₂×#41×C₄₃	—	2	4	no	—
35	C₂×#41×C₄₃	C₂³	1	4	yes	—
36	C₂²×D₄×C₄₃	—	2	4	no	—
37	C₂²×D₄×C₄₃	—	2	2	no	—
38	C₂²×D₄×C₄₃	—	2	4	no	—
39	C₂²×D₄×C₄₃	—	2	4	no	—
40	C₂²×D₄×C₄₃	—	2	1	no	—
41	C₂²×D₄×C₄₃	—	2	1	no	—
42	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
43	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₃	D₄	1	2	yes	—
45	AGL(1,ℤ/8)×C₄₃	—	2	16	no	—
46	AGL(1,ℤ/8)×C₄₃	—	4	8	no	—
47	C₂×SD₁₆×C₄₃	—	2	8	no	—
48	C₂×D₈×C₄₃	—	2	8	no	—
49	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
50	C₄⋊Q₈×C₄₃	D₄	1	2	yes	complemented
51	#127×C₄₃	—	2	8	no	—
52	#127×C₄₃	—	2	2	no	—
53	#127×C₄₃	—	2	2	no	—
54	#127×C₄₃	D₄	1	2	yes	complemented
55	#124×C₄₃	D₄	1	4	yes	complemented
56	#123×C₄₃	—	2	8	no	—
57	C₂²⋊Q₈×C₄₃	—	2	4	no	—
58	#121×C₄₃	—	2	4	no	—
59	#121×C₄₃	—	2	4	no	—
60	#121×C₄₃	—	2	4	no	—
61	#121×C₄₃	—	2	2	no	—
62	#121×C₄₃	—	2	4	no	—
63	#121×C₄₃	—	2	2	no	—
64	#121×C₄₃	—	4	8	no	—
65	#120×C₄₃	—	2	8	no	—
66	C₄×D₄×C₄₃	—	2	2	no	—
67	C₄×D₄×C₄₃	—	2	2	no	—
68	C₄×D₄×C₄₃	—	2	2	no	—
69	C₄×D₄×C₄₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
76	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
77	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
78	#104×C₄₃	—	2	16	no	—
79	#100×C₄₃	D₄	1	8	yes	complemented
80	#97×C₄₃	—	2	2	no	—
81	C₄×C₈×C₄₃	—	2	2	no	—
82	#95×C₄₃	—	2	1	no	—
83	C₂⁴×C₄₃	—	2	4	no	—
84	C₂⁴×C₄₃	—	2	2	no	—
85	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
86	#41×C₄₃	—	2	8	no	—
87	#41×C₄₃	—	2	8	no	—
88	#41×C₄₃	—	4	16	no	—
89	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
90	C₂×D₄×C₄₃	—	2	8	no	—
91	C₂×D₄×C₄₃	—	2	4	no	—
92	C₂×D₄×C₄₃	—	2	2	no	—
93	C₂×D₄×C₄₃	—	2	2	no	—
94	C₂×D₄×C₄₃	—	2	2	no	—
95	C₂×D₄×C₄₃	—	2	2	no	—
96	C₂×D₄×C₄₃	—	2	4	no	—
97	C₂×D₄×C₄₃	—	2	4	no	—
98	C₂×D₄×C₄₃	—	2	4	no	—
99	C₂×D₄×C₄₃	—	2	4	no	—
100	C₂×D₄×C₄₃	—	4	8	no	—
101	C₂×D₄×C₄₃	—	4	8	no	—
102	C₂×D₄×C₄₃	—	4	4	no	—
103	C₂×D₄×C₄₃	—	4	16	no	—
104	C₂×D₄×C₄₃	—	4	2	no	—
105	C₂×D₄×C₄₃	—	4	1	no	—
106	C₂×D₄×C₄₃	—	4	1	no	—
107	C₂×D₄×C₄₃	—	4	8	no	—
108	C₂×D₄×C₄₃	—	4	8	no	—
109	C₂×D₄×C₄₃	—	8	4	no	—
110	C₂×D₄×C₄₃	—	8	2	no	—
111	C₂×D₄×C₄₃	—	8	4	no	—
112	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
113	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₄₃	—	2	4	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	4	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	4	4	no	—
120	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
124	SD₁₆×C₄₃	—	4	16	no	—
125	D₈×C₄₃	—	4	16	no	—
126	M₁₆×C₄₃	—	2	4	no	—
127	M₁₆×C₄₃	C₂×D₄	1	8	yes	complemented
128	C₂×C₈×C₄₃	—	2	4	no	—
129	C₄⋊C₄×C₄₃	—	2	4	no	—
130	C₄⋊C₄×C₄₃	—	2	4	no	—
131	C₄⋊C₄×C₄₃	—	2	2	no	—
132	C₄⋊C₄×C₄₃	—	2	2	no	—
133	C₄⋊C₄×C₄₃	—	2	2	no	—
134	C₂²⋊C₄×C₄₃	—	2	8	no	—
135	C₂²⋊C₄×C₄₃	—	2	4	no	—
136	C₂²⋊C₄×C₄₃	—	2	4	no	—
137	C₂²⋊C₄×C₄₃	—	2	4	no	—
138	C₂²⋊C₄×C₄₃	—	4	8	no	—
139	C₄²×C₄₃	—	2	4	no	—
140	C₄²×C₄₃	C₂×D₄	1	2	yes	—
141	C₄²×C₄₃	C₂×D₄	1	2	yes	—
142	C₂³×C₄₃	—	2	2	no	—
143	C₂³×C₄₃	—	2	2	no	—
144	C₂³×C₄₃	—	2	4	no	—
145	C₂³×C₄₃	—	4	2	no	—
146	C₂³×C₄₃	—	4	2	no	—
147	C₂³×C₄₃	—	4	8	no	—
148	C₂³×C₄₃	—	4	4	no	—
149	C₂³×C₄₃	—	4	4	no	—
150	C₂³×C₄₃	—	4	2	no	—
151	C₂³×C₄₃	—	4	2	no	—
152	C₂³×C₄₃	—	4	2	no	—
153	C₂³×C₄₃	—	8	4	no	—
154	C₂³×C₄₃	—	8	4	no	—
155	C₂³×C₄₃	#127	1	4	yes	—
156	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₄₃	—	2	8	no	—
158	D₄×C₄₃	—	2	8	no	—
159	D₄×C₄₃	—	2	8	no	—
160	D₄×C₄₃	—	4	16	no	—
161	D₄×C₄₃	—	4	4	no	—
162	D₄×C₄₃	—	4	4	no	—
163	D₄×C₄₃	—	4	8	no	—
164	D₄×C₄₃	—	4	4	no	—
165	D₄×C₄₃	—	8	2	no	—
166	D₄×C₄₃	—	8	2	no	—
167	D₄×C₄₃	—	8	4	no	—
168	D₄×C₄₃	—	8	4	no	—
169	D₄×C₄₃	—	8	16	no	—
170	D₄×C₄₃	—	8	2	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	2	4	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	4	no	—
175	C₂×C₄×C₄₃	—	4	1	no	—
176	C₂×C₄×C₄₃	—	4	8	no	—
177	C₂×C₄×C₄₃	—	4	2	no	—
178	C₂×C₄×C₄₃	—	4	2	no	—
179	C₂×C₄×C₄₃	—	4	8	no	—
180	C₂×C₄×C₄₃	—	4	4	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	8	2	no	—
183	C₂×C₄×C₄₃	#120	1	2	yes	—
184	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
185	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
187	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
188	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
189	C₈×C₄₃	—	2	8	no	—
190	#25739	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	—	2	1	no	—
193	C₂²×C₄₃	—	2	4	no	—
194	C₂²×C₄₃	—	4	4	no	—
195	C₂²×C₄₃	—	4	2	no	—
196	C₂²×C₄₃	—	4	2	no	—
197	C₂²×C₄₃	—	4	4	no	—
198	C₂²×C₄₃	—	4	4	no	—
199	C₂²×C₄₃	—	4	4	no	—
200	C₂²×C₄₃	—	8	2	no	—
201	C₂²×C₄₃	—	8	4	no	—
202	C₂²×C₄₃	—	8	4	no	—
203	C₂²×C₄₃	—	8	2	no	—
204	C₂²×C₄₃	—	8	2	no	—
205	C₂²×C₄₃	—	8	2	no	—
206	C₂²×C₄₃	—	16	8	no	—
207	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
208	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
209	C₂²×C₄₃	#535	1	1	yes	characteristic
210	C₄×C₄₃	—	2	1	no	—
211	C₄×C₄₃	—	2	2	no	—
212	C₄×C₄₃	—	4	4	no	—
213	C₄×C₄₃	—	4	4	no	—
214	C₄×C₄₃	—	4	2	no	—
215	C₄×C₄₃	#453	1	2	yes	complemented
216	C₄×C₄₃	D₄²	1	4	yes	—
217	#3496	C₂×C₄₃	1	1	yes	characteristic, complemented
218	#3151	C₂×C₄₃	1	2	yes	complemented
219	C₂×#453	C₂×C₄₃	1	4	yes	complemented
220	#2541	C₂×C₄₃	1	1	yes	characteristic, complemented
221	#2006	C₂×C₄₃	1	4	yes	complemented
222	#1980	C₂×C₄₃	1	2	yes	complemented
223	C₄×#100	C₂×C₄₃	1	1	yes	characteristic, complemented
224	C₂×C₄₃	—	2	1	no	—
225	C₂×C₄₃	—	2	1	no	—
226	C₂×C₄₃	—	4	4	no	—
227	C₂×C₄₃	—	8	4	no	—
228	C₂×C₄₃	—	16	2	no	—
229	C₂×C₄₃	#2433	1	1	yes	characteristic
230	C₂×C₄₃	C₂×#453	1	1	yes	characteristic
231	C₂×C₄₃	#3021	1	1	yes	characteristic
232	C₂×H(5,𝔽₂)	C₂²×C₄₃	1	2	yes	—
233	C₂×AGL(1,ℤ/8)	C₂²×C₄₃	1	8	yes	complemented
234	#547	—	2	2	no	—
235	#546	—	2	4	no	—
236	D₄²	—	2	2	no	—
237	#537	C₂²×C₄₃	1	2	yes	—
238	#534	—	2	2	no	—
239	#532	C₂²×C₄₃	1	2	yes	—
240	C₂×#127	C₂²×C₄₃	1	2	yes	—
241	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic, complemented
242	C₂×#121	—	2	2	no	—
243	C₂×#121	—	2	2	no	—
244	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
245	#496	—	2	4	no	—
246	#493	—	2	2	no	—
247	#492	—	2	2	no	—
248	#453	—	2	16	no	—
249	C₂×#104	C₂²×C₄₃	1	8	yes	complemented
250	C₂×#100	C₂²×C₄₃	1	2	yes	—
251	C₄×M₁₆	C₂²×C₄₃	1	2	yes	complemented
252	#392	—	2	2	no	—
253	#390	C₂²×C₄₃	1	2	yes	complemented
254	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic, complemented
255	#343	C₂²×C₄₃	1	2	yes	complemented
256	C₄₃	#25739	1	1	yes	characteristic, direct product factor, Sylow
257	H(5,𝔽₂)	—	2	8	no	—
258	H(5,𝔽₂)	—	4	4	no	—
259	C₂×#41	—	2	4	no	—
260	C₂×#41	C₂³×C₄₃	1	4	yes	—
261	C₂²×D₄	—	2	4	no	—
262	C₂²×D₄	—	2	2	no	—
263	C₂²×D₄	—	2	4	no	—
264	C₂²×D₄	—	2	4	no	—
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
268	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
269	C₂³×C₄	D₄×C₄₃	1	2	yes	—
270	AGL(1,ℤ/8)	—	2	16	no	—
271	AGL(1,ℤ/8)	—	4	8	no	—
272	C₂×SD₁₆	—	2	8	no	—
273	C₂×D₈	—	2	8	no	—
274	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
275	C₄⋊Q₈	D₄×C₄₃	1	2	yes	complemented
276	#127	—	2	8	no	—
277	#127	—	2	2	no	—
278	#127	—	2	2	no	—
279	#127	D₄×C₄₃	1	2	yes	complemented
280	#124	D₄×C₄₃	1	4	yes	complemented
281	#123	—	2	8	no	—
282	C₂²⋊Q₈	—	2	4	no	—
283	#121	—	2	4	no	—
284	#121	—	2	4	no	—
285	#121	—	2	4	no	—
286	#121	—	2	2	no	—
287	#121	—	2	4	no	—
288	#121	—	2	2	no	—
289	#121	—	4	8	no	—
290	#120	—	2	8	no	—
291	C₄×D₄	—	2	2	no	—
292	C₄×D₄	—	2	2	no	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	—	2	4	no	—
299	C₂×C₂²⋊C₄	—	2	4	no	—
300	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
301	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
302	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
303	#104	—	2	16	no	—
304	#100	D₄×C₄₃	1	8	yes	complemented
305	#97	—	2	2	no	—
306	C₄×C₈	—	2	2	no	—
307	#95	—	2	1	no	—
308	C₂⁴	—	2	4	no	—
309	C₂⁴	—	2	2	no	—
310	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
311	#41	—	2	8	no	—
312	#41	—	2	8	no	—
313	#41	—	4	16	no	—
314	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
315	C₂×D₄	—	2	8	no	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	—	4	4	no	—
326	C₂×D₄	—	4	8	no	—
327	C₂×D₄	—	4	16	no	—
328	C₂×D₄	—	4	8	no	—
329	C₂×D₄	—	4	8	no	—
330	C₂×D₄	—	4	8	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	8	4	no	—
335	C₂×D₄	—	8	2	no	—
336	C₂×D₄	—	8	4	no	—
337	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
338	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	4	4	no	—
345	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
348	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
349	SD₁₆	—	4	16	no	—
350	D₈	—	4	16	no	—
351	M₁₆	—	2	4	no	—
352	M₁₆	C₂×D₄×C₄₃	1	8	yes	complemented
353	C₂×C₈	—	2	4	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	8	no	—
360	C₂²⋊C₄	—	2	4	no	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	4	8	no	—
364	C₄²	—	2	4	no	—
365	C₄²	C₂×D₄×C₄₃	1	2	yes	—
366	C₄²	C₂×D₄×C₄₃	1	2	yes	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	8	no	—
373	C₂³	—	4	4	no	—
374	C₂³	—	4	4	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	8	4	no	—
379	C₂³	—	8	4	no	—
380	C₂³	#127×C₄₃	1	4	yes	—
381	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
382	Q₈	—	2	8	no	—
383	D₄	—	2	8	no	—
384	D₄	—	2	8	no	—
385	D₄	—	4	16	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	8	no	—
389	D₄	—	4	4	no	—
390	D₄	—	8	2	no	—
391	D₄	—	8	2	no	—
392	D₄	—	8	4	no	—
393	D₄	—	8	4	no	—
394	D₄	—	8	16	no	—
395	D₄	—	8	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	8	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	8	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	8	2	no	—
408	C₂×C₄	#120×C₄₃	1	2	yes	—
409	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
410	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
412	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
413	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
414	C₈	—	2	8	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	4	no	—
426	C₂²	—	8	4	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	16	8	no	—
431	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
432	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
433	C₂²	C₄₃×#535	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	4	no	—
437	C₄	—	4	4	no	—
438	C₄	—	4	2	no	—
439	C₄	C₄₃×#453	1	2	yes	complemented
440	C₄	D₄²×C₄₃	1	4	yes	—
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	4	4	no	—
444	C₂	—	8	4	no	—
445	C₂	—	16	2	no	—
446	C₂	C₄₃×#2433	1	1	yes	characteristic
447	C₂	C₂×C₄₃×#453	1	1	yes	characteristic
448	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×#3496	C₂	semidirect
2. C₄₃×#3151	C₂	semidirect
3. C₂×C₄₃×#453	C₂	semidirect
4. C₄₃×#2541	C₂	semidirect
5. C₄₃×#2006	C₂	semidirect
6. C₄₃×#1980	C₂	semidirect
7. C₄×#100×C₄₃	C₂	semidirect
9. C₂×AGL(1,ℤ/8)×C₄₃	C₂²	semidirect
17. C₂×#127×C₄₃	C₂²	semidirect
25. C₂×#104×C₄₃	C₂²	semidirect
27. C₄×M₁₆×C₄₃	C₂²	semidirect
29. C₄₃×#390	C₂²	semidirect
30. C₄×C₄⋊C₄×C₄₃	C₂²	semidirect
31. C₄₃×#343	C₂²	semidirect
50. C₄⋊Q₈×C₄₃	D₄	semidirect
54. #127×C₄₃	D₄	semidirect
55. #124×C₄₃	D₄	semidirect
79. #100×C₄₃	D₄	semidirect
127. M₁₆×C₄₃	C₂×D₄	semidirect
190. #25739	C₄₃	direct (N × H)
215. C₄×C₄₃	#453	semidirect
217. #3496	C₂×C₄₃	semidirect
218. #3151	C₂×C₄₃	semidirect
219. C₂×#453	C₂×C₄₃	semidirect
220. #2541	C₂×C₄₃	semidirect
221. #2006	C₂×C₄₃	semidirect
222. #1980	C₂×C₄₃	semidirect
223. C₄×#100	C₂×C₄₃	semidirect
233. C₂×AGL(1,ℤ/8)	C₂²×C₄₃	semidirect
241. C₂×#127	C₂²×C₄₃	semidirect
249. C₂×#104	C₂²×C₄₃	semidirect
251. C₄×M₁₆	C₂²×C₄₃	semidirect
253. #390	C₂²×C₄₃	semidirect
254. C₄×C₄⋊C₄	C₂²×C₄₃	semidirect
255. #343	C₂²×C₄₃	semidirect
256. C₄₃	#25739	direct (N × H)
275. C₄⋊Q₈	D₄×C₄₃	semidirect
279. #127	D₄×C₄₃	semidirect
280. #124	D₄×C₄₃	semidirect
304. #100	D₄×C₄₃	semidirect
352. M₁₆	C₂×D₄×C₄₃	semidirect
439. C₄	C₄₃×#453	semidirect

Maximal subgroups

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

subgroup	index
C₄₃×#3496	2
C₄₃×#3151	2
C₂×C₄₃×#453	2
C₄₃×#2541	2
C₄₃×#2006	2
C₄₃×#1980	2
C₄×#100×C₄₃	2
#25739	43

Subgroups — C43×#25739 #24945756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25739 #24945756