Subgroups — C₄₃×#25738 #24945755

Order 11008.

1542 conjugacy classes of subgroups.

The subgroup lattice has 416 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
2	C₄₃×#3152	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#455	C₂	1	4	yes	maximal, complemented
4	C₄₃×#2547	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2007	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×#137×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×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
17	C₂×#124×C₄₃	C₂²	1	2	yes	—
18	C₂×#121×C₄₃	—	2	2	no	—
19	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#497	—	2	4	no	—
21	C₄₃×#494	—	2	2	no	—
22	C₄₃×#492	—	2	2	no	—
23	C₄₃×#455	—	2	16	no	—
24	C₂×#104×C₄₃	C₂²	1	8	yes	complemented
25	C₂×#100×C₄₃	C₂²	1	2	yes	—
26	C₄×M₁₆×C₄₃	C₂²	1	2	yes	complemented
27	C₄₃×#397	—	2	2	no	—
28	C₄₃×#391	C₂²	1	2	yes	complemented
29	C₄₃×#380	—	2	2	no	—
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×Q₈×C₄₃	C₂³	1	2	yes	—
37	C₂²×D₄×C₄₃	—	2	4	no	—
38	C₂²×D₄×C₄₃	—	2	2	no	—
39	C₂²×D₄×C₄₃	—	2	4	no	—
40	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₄₃	D₄	1	2	yes	—
42	#137×C₄₃	—	2	16	no	—
43	#137×C₄₃	—	4	8	no	—
44	C₂×Q₁₆×C₄₃	—	2	8	no	—
45	C₂×SD₁₆×C₄₃	—	2	8	no	—
46	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
47	C₄⋊Q₈×C₄₃	—	2	2	no	—
48	C₄⋊Q₈×C₄₃	—	2	2	no	—
49	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
50	#127×C₄₃	D₄	1	2	yes	—
51	#124×C₄₃	—	2	8	no	—
52	#124×C₄₃	D₄	1	4	yes	—
53	#123×C₄₃	—	2	8	no	—
54	C₂²⋊Q₈×C₄₃	—	2	4	no	—
55	#121×C₄₃	—	2	4	no	—
56	#121×C₄₃	—	2	4	no	—
57	#121×C₄₃	—	2	4	no	—
58	#121×C₄₃	—	2	2	no	—
59	#121×C₄₃	—	2	4	no	—
60	#121×C₄₃	—	2	2	no	—
61	#120×C₄₃	—	2	8	no	—
62	C₄×D₄×C₄₃	—	2	2	no	—
63	C₄×D₄×C₄₃	—	2	2	no	—
64	C₄×D₄×C₄₃	—	2	2	no	—
65	C₄×D₄×C₄₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
74	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
75	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
76	#104×C₄₃	—	2	16	no	—
77	#100×C₄₃	D₄	1	8	yes	complemented
78	#97×C₄₃	—	2	2	no	—
79	C₄×C₈×C₄₃	—	2	2	no	—
80	#95×C₄₃	—	2	1	no	—
81	#95×C₄₃	—	2	4	no	—
82	C₂⁴×C₄₃	—	2	4	no	—
83	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
84	#41×C₄₃	—	2	8	no	—
85	#41×C₄₃	—	2	8	no	—
86	#41×C₄₃	—	4	16	no	—
87	C₂×Q₈×C₄₃	—	2	4	no	—
88	C₂×Q₈×C₄₃	—	2	4	no	—
89	C₂×Q₈×C₄₃	—	2	4	no	—
90	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
91	C₂×D₄×C₄₃	—	2	8	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	2	no	—
96	C₂×D₄×C₄₃	—	2	2	no	—
97	C₂×D₄×C₄₃	—	2	4	no	—
98	C₂×D₄×C₄₃	—	4	8	no	—
99	C₂×D₄×C₄₃	—	4	16	no	—
100	C₂×D₄×C₄₃	—	4	8	no	—
101	C₂×D₄×C₄₃	—	8	4	no	—
102	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
103	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₄₃	—	2	4	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	2	4	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	4	4	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	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
115	Q₁₆×C₄₃	—	4	16	no	—
116	SD₁₆×C₄₃	—	4	16	no	—
117	M₁₆×C₄₃	—	2	4	no	—
118	M₁₆×C₄₃	C₂×D₄	1	8	yes	complemented
119	C₂×C₈×C₄₃	—	2	4	no	—
120	C₄⋊C₄×C₄₃	—	2	4	no	—
121	C₄⋊C₄×C₄₃	—	2	2	no	—
122	C₄⋊C₄×C₄₃	—	2	2	no	—
123	C₄⋊C₄×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	—	4	2	no	—
125	C₄⋊C₄×C₄₃	—	4	2	no	—
126	C₄⋊C₄×C₄₃	—	4	1	no	—
127	C₄⋊C₄×C₄₃	—	4	1	no	—
128	C₂²⋊C₄×C₄₃	—	2	8	no	—
129	C₂²⋊C₄×C₄₃	—	2	4	no	—
130	C₂²⋊C₄×C₄₃	—	2	4	no	—
131	C₂²⋊C₄×C₄₃	—	2	4	no	—
132	C₂²⋊C₄×C₄₃	—	4	8	no	—
133	C₄²×C₄₃	—	2	4	no	—
134	C₄²×C₄₃	C₂×D₄	1	2	yes	—
135	C₄²×C₄₃	C₂×D₄	1	2	yes	—
136	C₂³×C₄₃	—	2	2	no	—
137	C₂³×C₄₃	—	2	2	no	—
138	C₂³×C₄₃	—	2	4	no	—
139	C₂³×C₄₃	—	4	2	no	—
140	C₂³×C₄₃	—	4	2	no	—
141	C₂³×C₄₃	—	4	8	no	—
142	C₂³×C₄₃	—	8	4	no	—
143	C₂³×C₄₃	—	8	4	no	—
144	C₂³×C₄₃	#127	1	4	yes	—
145	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₄₃	—	2	8	no	—
147	Q₈×C₄₃	—	4	8	no	—
148	D₄×C₄₃	—	2	8	no	—
149	D₄×C₄₃	—	2	8	no	—
150	D₄×C₄₃	—	4	16	no	—
151	D₄×C₄₃	—	4	4	no	—
152	D₄×C₄₃	—	4	4	no	—
153	D₄×C₄₃	—	4	4	no	—
154	D₄×C₄₃	—	8	2	no	—
155	D₄×C₄₃	—	8	4	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	2	4	no	—
159	C₂×C₄×C₄₃	—	4	1	no	—
160	C₂×C₄×C₄₃	—	4	8	no	—
161	C₂×C₄×C₄₃	—	4	8	no	—
162	C₂×C₄×C₄₃	—	4	4	no	—
163	C₂×C₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	—	4	2	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	—	8	2	no	—
171	C₂×C₄×C₄₃	#120	1	2	yes	—
172	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
173	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
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	#25738	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	—	2	4	no	—
182	C₂²×C₄₃	—	4	4	no	—
183	C₂²×C₄₃	—	4	2	no	—
184	C₂²×C₄₃	—	4	2	no	—
185	C₂²×C₄₃	—	4	4	no	—
186	C₂²×C₄₃	—	4	4	no	—
187	C₂²×C₄₃	—	4	4	no	—
188	C₂²×C₄₃	—	8	2	no	—
189	C₂²×C₄₃	—	16	8	no	—
190	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
191	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
192	C₂²×C₄₃	#535	1	1	yes	characteristic
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	—	8	2	no	—
199	C₄×C₄₃	#455	1	2	yes	complemented
200	C₄×C₄₃	D₄²	1	4	yes	—
201	#3496	C₂×C₄₃	1	1	yes	characteristic
202	#3152	C₂×C₄₃	1	2	yes	complemented
203	C₂×#455	C₂×C₄₃	1	4	yes	complemented
204	#2547	C₂×C₄₃	1	1	yes	characteristic, complemented
205	#2007	C₂×C₄₃	1	4	yes	complemented
206	#1980	C₂×C₄₃	1	2	yes	complemented
207	C₄×#100	C₂×C₄₃	1	1	yes	characteristic, complemented
208	C₂×C₄₃	—	2	1	no	—
209	C₂×C₄₃	—	2	1	no	—
210	C₂×C₄₃	—	4	4	no	—
211	C₂×C₄₃	—	8	4	no	—
212	C₂×C₄₃	#2433	1	1	yes	characteristic
213	C₂×C₄₃	C₂×#455	1	1	yes	characteristic
214	C₂×C₄₃	#3022	1	1	yes	characteristic
215	C₂×H(5,𝔽₂)	C₂²×C₄₃	1	2	yes	—
216	C₂×#137	C₂²×C₄₃	1	8	yes	complemented
217	#547	—	2	2	no	—
218	#546	—	2	4	no	—
219	D₄²	—	2	2	no	—
220	#537	C₂²×C₄₃	1	2	yes	—
221	#534	—	2	2	no	—
222	#532	C₂²×C₄₃	1	2	yes	—
223	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
224	C₂×#124	C₂²×C₄₃	1	2	yes	—
225	C₂×#121	—	2	2	no	—
226	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
227	#497	—	2	4	no	—
228	#494	—	2	2	no	—
229	#492	—	2	2	no	—
230	#455	—	2	16	no	—
231	C₂×#104	C₂²×C₄₃	1	8	yes	complemented
232	C₂×#100	C₂²×C₄₃	1	2	yes	—
233	C₄×M₁₆	C₂²×C₄₃	1	2	yes	complemented
234	#397	—	2	2	no	—
235	#391	C₂²×C₄₃	1	2	yes	complemented
236	#380	—	2	2	no	—
237	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic, complemented
238	#343	C₂²×C₄₃	1	2	yes	complemented
239	C₄₃	#25738	1	1	yes	characteristic, direct product factor, Sylow
240	H(5,𝔽₂)	—	2	8	no	—
241	H(5,𝔽₂)	—	4	4	no	—
242	C₂×#41	—	2	4	no	—
243	C₂×#41	C₂³×C₄₃	1	4	yes	—
244	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
245	C₂²×D₄	—	2	4	no	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	—	2	4	no	—
248	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
249	C₂³×C₄	D₄×C₄₃	1	2	yes	—
250	#137	—	2	16	no	—
251	#137	—	4	8	no	—
252	C₂×Q₁₆	—	2	8	no	—
253	C₂×SD₁₆	—	2	8	no	—
254	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	—	2	2	no	—
257	C₄⋊Q₈	D₄×C₄₃	1	2	yes	—
258	#127	D₄×C₄₃	1	2	yes	—
259	#124	—	2	8	no	—
260	#124	D₄×C₄₃	1	4	yes	—
261	#123	—	2	8	no	—
262	C₂²⋊Q₈	—	2	4	no	—
263	#121	—	2	4	no	—
264	#121	—	2	4	no	—
265	#121	—	2	4	no	—
266	#121	—	2	2	no	—
267	#121	—	2	4	no	—
268	#121	—	2	2	no	—
269	#120	—	2	8	no	—
270	C₄×D₄	—	2	2	no	—
271	C₄×D₄	—	2	2	no	—
272	C₄×D₄	—	2	2	no	—
273	C₄×D₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
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×C₂²⋊C₄	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	#100	D₄×C₄₃	1	8	yes	complemented
286	#97	—	2	2	no	—
287	C₄×C₈	—	2	2	no	—
288	#95	—	2	1	no	—
289	#95	—	2	4	no	—
290	C₂⁴	—	2	4	no	—
291	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
292	#41	—	2	8	no	—
293	#41	—	2	8	no	—
294	#41	—	4	16	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	2	4	no	—
298	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
299	C₂×D₄	—	2	8	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	4	16	no	—
307	C₂×D₄	—	4	8	no	—
308	C₂×D₄	—	4	8	no	—
309	C₂×D₄	—	8	4	no	—
310	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
311	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	4	4	no	—
319	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
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	Q₁₆	—	4	16	no	—
324	SD₁₆	—	4	16	no	—
325	M₁₆	—	2	4	no	—
326	M₁₆	C₂×D₄×C₄₃	1	8	yes	complemented
327	C₂×C₈	—	2	4	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₂²⋊C₄	—	2	8	no	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	4	8	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	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	8	no	—
350	C₂³	—	8	4	no	—
351	C₂³	—	8	4	no	—
352	C₂³	#127×C₄₃	1	4	yes	—
353	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
354	Q₈	—	2	8	no	—
355	Q₈	—	4	8	no	—
356	D₄	—	2	8	no	—
357	D₄	—	2	8	no	—
358	D₄	—	4	16	no	—
359	D₄	—	4	4	no	—
360	D₄	—	4	4	no	—
361	D₄	—	4	4	no	—
362	D₄	—	8	2	no	—
363	D₄	—	8	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	—	4	8	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	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	—	4	2	no	—
378	C₂×C₄	—	8	2	no	—
379	C₂×C₄	#120×C₄₃	1	2	yes	—
380	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
381	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
382	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
383	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
384	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
385	C₈	—	2	8	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	16	8	no	—
397	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
398	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
399	C₂²	C₄₃×#535	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	4	no	—
403	C₄	—	4	2	no	—
404	C₄	—	8	2	no	—
405	C₄	—	8	2	no	—
406	C₄	C₄₃×#455	1	2	yes	complemented
407	C₄	D₄²×C₄₃	1	4	yes	—
408	C₂	—	2	1	no	—
409	C₂	—	2	1	no	—
410	C₂	—	4	4	no	—
411	C₂	—	8	4	no	—
412	C₂	C₄₃×#2433	1	1	yes	characteristic
413	C₂	C₂×C₄₃×#455	1	1	yes	characteristic
414	C₂	C₄₃×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#3496	C₂
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
2. C₄₃×#3152	C₂	semidirect
3. C₂×C₄₃×#455	C₂	semidirect
4. C₄₃×#2547	C₂	semidirect
5. C₄₃×#2007	C₂	semidirect
6. C₄₃×#1980	C₂	semidirect
7. C₄×#100×C₄₃	C₂	semidirect
9. C₂×#137×C₄₃	C₂²	semidirect
16. C₂×C₄⋊Q₈×C₄₃	C₂²	semidirect
24. C₂×#104×C₄₃	C₂²	semidirect
26. C₄×M₁₆×C₄₃	C₂²	semidirect
28. C₄₃×#391	C₂²	semidirect
30. C₄×C₄⋊C₄×C₄₃	C₂²	semidirect
31. C₄₃×#343	C₂²	semidirect
77. #100×C₄₃	D₄	semidirect
118. M₁₆×C₄₃	C₂×D₄	semidirect
178. #25738	C₄₃	direct (N × H)
199. C₄×C₄₃	#455	semidirect
202. #3152	C₂×C₄₃	semidirect
203. C₂×#455	C₂×C₄₃	semidirect
204. #2547	C₂×C₄₃	semidirect
205. #2007	C₂×C₄₃	semidirect
206. #1980	C₂×C₄₃	semidirect
207. C₄×#100	C₂×C₄₃	semidirect
216. C₂×#137	C₂²×C₄₃	semidirect
223. C₂×C₄⋊Q₈	C₂²×C₄₃	semidirect
231. C₂×#104	C₂²×C₄₃	semidirect
233. C₄×M₁₆	C₂²×C₄₃	semidirect
235. #391	C₂²×C₄₃	semidirect
237. C₄×C₄⋊C₄	C₂²×C₄₃	semidirect
238. #343	C₂²×C₄₃	semidirect
239. C₄₃	#25738	direct (N × H)
285. #100	D₄×C₄₃	semidirect
326. M₁₆	C₂×D₄×C₄₃	semidirect
406. C₄	C₄₃×#455	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×#3152	2
C₂×C₄₃×#455	2
C₄₃×#2547	2
C₄₃×#2007	2
C₄₃×#1980	2
C₄×#100×C₄₃	2
#25738	43

Subgroups — C43×#25738 #24945755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25738 #24945755