Subgroups — C₄₃×#18211 #24938228

Order 11008.

1254 conjugacy classes of subgroups.

The subgroup lattice has 424 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×#3103	C₂	1	2	yes	maximal, complemented
3	C₄₃×#2580	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1613	C₂	1	4	yes	maximal, complemented
5	C₄₃×#1601	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1517	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1460	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×H(5,𝔽₂)×C₄₃	—	2	1	no	—
9	C₄₃×#547	—	2	2	no	—
10	C₄₃×#546	—	2	4	no	—
11	D₄²×C₄₃	—	2	2	no	—
12	C₄₃×#537	—	2	1	no	—
13	C₄₃×#534	C₂²	1	4	yes	—
14	C₄₃×#532	C₂²	1	2	yes	—
15	C₂×#121×C₄₃	—	2	2	no	—
16	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃×#481	C₂²	1	4	yes	complemented
19	C₄₃×#475	—	2	2	no	—
20	C₄₃×#460	—	2	2	no	—
21	C₄₃×#448	C₂²	1	4	yes	complemented
22	C₄×SD₁₆×C₄₃	—	2	4	no	—
23	C₄₃×#431	C₂²	1	2	yes	complemented
24	C₄₃×#399	C₂²	1	2	yes	complemented
25	C₄₃×#393	C₂²	1	2	yes	complemented
26	C₄₃×#390	—	2	1	no	—
27	C₄₃×#389	—	2	1	no	—
28	C₄₃×#385	—	2	2	no	—
29	C₄₃×#382	C₂²	1	1	yes	characteristic, complemented
30	C₄₃×#327	C₂²	1	8	yes	complemented
31	C₄₃×#323	C₂²	1	4	yes	complemented
32	H(5,𝔽₂)×C₄₃	—	4	4	no	—
33	H(5,𝔽₂)×C₄₃	—	4	4	no	—
34	C₂×#41×C₄₃	—	2	4	no	—
35	C₂×#41×C₄₃	—	2	2	no	—
36	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₄₃	—	2	4	no	—
38	C₂²×D₄×C₄₃	—	2	4	no	—
39	C₂²×D₄×C₄₃	—	2	2	no	—
40	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₃	D₄	1	2	yes	—
42	C₂×SD₁₆×C₄₃	—	2	4	no	—
43	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
44	#127×C₄₃	D₄	1	2	yes	—
45	#124×C₄₃	—	2	2	no	—
46	#123×C₄₃	—	2	8	no	—
47	C₂²⋊Q₈×C₄₃	—	2	4	no	—
48	#121×C₄₃	—	2	4	no	—
49	#121×C₄₃	—	2	4	no	—
50	#121×C₄₃	—	2	4	no	—
51	#121×C₄₃	—	2	2	no	—
52	#121×C₄₃	—	2	4	no	—
53	#121×C₄₃	C₂³	1	4	yes	—
54	#120×C₄₃	—	2	8	no	—
55	C₄×Q₈×C₄₃	—	2	2	no	—
56	C₄×Q₈×C₄₃	—	2	2	no	—
57	C₄×D₄×C₄₃	—	2	2	no	—
58	C₄×D₄×C₄₃	—	2	2	no	—
59	C₄×D₄×C₄₃	—	2	2	no	—
60	C₄×D₄×C₄₃	D₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
71	C₂×C₄²×C₄₃	—	2	1	no	—
72	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
73	#106×C₄₃	—	2	4	no	—
74	C₄⋊C₈×C₄₃	—	2	2	no	—
75	#103×C₄₃	—	2	4	no	—
76	#102×C₄₃	—	2	4	no	—
77	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
78	C₄×C₈×C₄₃	—	2	2	no	—
79	#95×C₄₃	—	2	1	no	—
80	#95×C₄₃	—	2	2	no	—
81	#95×C₄₃	C₂³	1	2	yes	—
82	C₂⁴×C₄₃	—	2	4	no	—
83	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
84	#41×C₄₃	—	4	16	no	—
85	#41×C₄₃	—	4	4	no	—
86	#41×C₄₃	—	4	4	no	—
87	C₂×Q₈×C₄₃	—	2	2	no	—
88	C₂×Q₈×C₄₃	—	2	2	no	—
89	C₂×Q₈×C₄₃	—	4	2	no	—
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	—	4	8	no	—
98	C₂×D₄×C₄₃	—	4	16	no	—
99	C₂×D₄×C₄₃	—	4	8	no	—
100	C₂×D₄×C₄₃	—	8	4	no	—
101	C₂×D₄×C₄₃	SD₁₆	1	4	yes	complemented
102	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₄₃	—	2	4	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	1	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	1	no	—
110	C₂²×C₄×C₄₃	—	8	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	C₂×C₈×C₄₃	—	2	4	no	—
117	C₄⋊C₄×C₄₃	—	2	4	no	—
118	C₄⋊C₄×C₄₃	—	2	2	no	—
119	C₄⋊C₄×C₄₃	—	2	2	no	—
120	C₄⋊C₄×C₄₃	—	2	2	no	—
121	C₄⋊C₄×C₄₃	—	4	1	no	—
122	C₄⋊C₄×C₄₃	—	4	1	no	—
123	C₄⋊C₄×C₄₃	—	4	2	no	—
124	C₄⋊C₄×C₄₃	—	8	2	no	—
125	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
126	C₂²⋊C₄×C₄₃	—	2	8	no	—
127	C₂²⋊C₄×C₄₃	—	2	4	no	—
128	C₂²⋊C₄×C₄₃	—	2	4	no	—
129	C₂²⋊C₄×C₄₃	—	2	4	no	—
130	C₂²⋊C₄×C₄₃	—	4	4	no	—
131	C₂²⋊C₄×C₄₃	—	8	2	no	—
132	C₄²×C₄₃	—	4	2	no	—
133	C₄²×C₄₃	C₂×D₄	1	2	yes	—
134	C₄²×C₄₃	C₂×D₄	1	2	yes	—
135	C₂³×C₄₃	—	2	2	no	—
136	C₂³×C₄₃	—	2	2	no	—
137	C₂³×C₄₃	—	2	4	no	—
138	C₂³×C₄₃	—	4	2	no	—
139	C₂³×C₄₃	—	4	2	no	—
140	C₂³×C₄₃	—	4	8	no	—
141	C₂³×C₄₃	—	8	4	no	—
142	C₂³×C₄₃	—	8	4	no	—
143	C₂³×C₄₃	C₂×SD₁₆	1	4	yes	—
144	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₄₃	—	2	4	no	—
146	Q₈×C₄₃	—	4	2	no	—
147	Q₈×C₄₃	—	4	4	no	—
148	D₄×C₄₃	—	2	8	no	—
149	D₄×C₄₃	—	4	4	no	—
150	D₄×C₄₃	—	4	4	no	—
151	D₄×C₄₃	—	4	16	no	—
152	D₄×C₄₃	—	4	4	no	—
153	D₄×C₄₃	—	4	4	no	—
154	D₄×C₄₃	—	4	4	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	1	no	—
161	C₂×C₄×C₄₃	—	4	4	no	—
162	C₂×C₄×C₄₃	—	4	8	no	—
163	C₂×C₄×C₄₃	—	4	1	no	—
164	C₂×C₄×C₄₃	—	4	1	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	1	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	8	2	no	—
174	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
175	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
176	C₂×C₄×C₄₃	#120	1	2	yes	—
177	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
178	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
179	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
180	C₈×C₄₃	—	4	4	no	—
181	#18211	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂²×C₄₃	—	2	1	no	—
183	C₂²×C₄₃	—	2	1	no	—
184	C₂²×C₄₃	—	2	4	no	—
185	C₂²×C₄₃	—	4	4	no	—
186	C₂²×C₄₃	—	4	2	no	—
187	C₂²×C₄₃	—	4	2	no	—
188	C₂²×C₄₃	—	4	4	no	—
189	C₂²×C₄₃	—	4	4	no	—
190	C₂²×C₄₃	—	4	4	no	—
191	C₂²×C₄₃	—	8	2	no	—
192	C₂²×C₄₃	—	16	8	no	—
193	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
194	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
195	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
196	C₄×C₄₃	—	2	1	no	—
197	C₄×C₄₃	—	2	1	no	—
198	C₄×C₄₃	—	2	2	no	—
199	C₄×C₄₃	—	4	4	no	—
200	C₄×C₄₃	—	4	2	no	—
201	C₄×C₄₃	—	4	2	no	—
202	C₄×C₄₃	—	8	2	no	—
203	C₄×C₄₃	—	8	1	no	—
204	C₄×C₄₃	#450	1	4	yes	—
205	#3496	C₂×C₄₃	1	1	yes	characteristic
206	#3103	C₂×C₄₃	1	2	yes	complemented
207	#2580	C₂×C₄₃	1	1	yes	characteristic, complemented
208	#1613	C₂×C₄₃	1	4	yes	complemented
209	#1601	C₂×C₄₃	1	4	yes	complemented
210	#1517	C₂×C₄₃	1	2	yes	complemented
211	#1460	C₂×C₄₃	1	1	yes	characteristic, complemented
212	C₂×C₄₃	—	2	1	no	—
213	C₂×C₄₃	—	2	1	no	—
214	C₂×C₄₃	—	4	4	no	—
215	C₂×C₄₃	—	8	4	no	—
216	C₂×C₄₃	C₂×#450	1	1	yes	characteristic
217	C₂×C₄₃	#3019	1	1	yes	characteristic
218	C₂×C₄₃	#3025	1	1	yes	characteristic
219	C₂×H(5,𝔽₂)	—	2	1	no	—
220	#547	—	2	2	no	—
221	#546	—	2	4	no	—
222	D₄²	—	2	2	no	—
223	#537	—	2	1	no	—
224	#534	C₂²×C₄₃	1	4	yes	—
225	#532	C₂²×C₄₃	1	2	yes	—
226	C₂×#121	—	2	2	no	—
227	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
228	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
229	#481	C₂²×C₄₃	1	4	yes	complemented
230	#475	—	2	2	no	—
231	#460	—	2	2	no	—
232	#448	C₂²×C₄₃	1	4	yes	complemented
233	C₄×SD₁₆	—	2	4	no	—
234	#431	C₂²×C₄₃	1	2	yes	complemented
235	#399	C₂²×C₄₃	1	2	yes	complemented
236	#393	C₂²×C₄₃	1	2	yes	complemented
237	#390	—	2	1	no	—
238	#389	—	2	1	no	—
239	#385	—	2	2	no	—
240	#382	C₂²×C₄₃	1	1	yes	characteristic, complemented
241	#327	C₂²×C₄₃	1	8	yes	complemented
242	#323	C₂²×C₄₃	1	4	yes	complemented
243	C₄₃	#18211	1	1	yes	characteristic, direct product factor, Sylow
244	H(5,𝔽₂)	—	4	4	no	—
245	H(5,𝔽₂)	—	4	4	no	—
246	C₂×#41	—	2	4	no	—
247	C₂×#41	—	2	2	no	—
248	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
249	C₂²×D₄	—	2	4	no	—
250	C₂²×D₄	—	2	4	no	—
251	C₂²×D₄	—	2	2	no	—
252	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
253	C₂³×C₄	D₄×C₄₃	1	2	yes	—
254	C₂×SD₁₆	—	2	4	no	—
255	C₄⋊Q₈	D₄×C₄₃	1	2	yes	—
256	#127	D₄×C₄₃	1	2	yes	—
257	#124	—	2	2	no	—
258	#123	—	2	8	no	—
259	C₂²⋊Q₈	—	2	4	no	—
260	#121	—	2	4	no	—
261	#121	—	2	4	no	—
262	#121	—	2	4	no	—
263	#121	—	2	2	no	—
264	#121	—	2	4	no	—
265	#121	C₂³×C₄₃	1	4	yes	—
266	#120	—	2	8	no	—
267	C₄×Q₈	—	2	2	no	—
268	C₄×Q₈	—	2	2	no	—
269	C₄×D₄	—	2	2	no	—
270	C₄×D₄	—	2	2	no	—
271	C₄×D₄	—	2	2	no	—
272	C₄×D₄	D₄×C₄₃	1	4	yes	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	2	4	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
285	#106	—	2	4	no	—
286	C₄⋊C₈	—	2	2	no	—
287	#103	—	2	4	no	—
288	#102	—	2	4	no	—
289	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	—
290	C₄×C₈	—	2	2	no	—
291	#95	—	2	1	no	—
292	#95	—	2	2	no	—
293	#95	C₂³×C₄₃	1	2	yes	—
294	C₂⁴	—	2	4	no	—
295	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
296	#41	—	4	16	no	—
297	#41	—	4	4	no	—
298	#41	—	4	4	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	4	2	no	—
302	C₂×D₄	—	2	8	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	4	16	no	—
310	C₂×D₄	—	4	8	no	—
311	C₂×D₄	—	4	8	no	—
312	C₂×D₄	—	8	4	no	—
313	C₂×D₄	SD₁₆×C₄₃	1	4	yes	complemented
314	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	8	2	no	—
323	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
326	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
327	SD₁₆	—	4	8	no	—
328	C₂×C₈	—	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	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	8	2	no	—
337	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
338	C₂²⋊C₄	—	2	8	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	—	8	2	no	—
344	C₄²	—	4	2	no	—
345	C₄²	C₂×D₄×C₄₃	1	2	yes	—
346	C₄²	C₂×D₄×C₄₃	1	2	yes	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	8	no	—
353	C₂³	—	8	4	no	—
354	C₂³	—	8	4	no	—
355	C₂³	C₂×SD₁₆×C₄₃	1	4	yes	—
356	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
357	Q₈	—	2	4	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	4	no	—
360	D₄	—	2	8	no	—
361	D₄	—	4	4	no	—
362	D₄	—	4	4	no	—
363	D₄	—	4	16	no	—
364	D₄	—	4	4	no	—
365	D₄	—	4	4	no	—
366	D₄	—	4	4	no	—
367	D₄	—	8	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	8	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
387	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
388	C₂×C₄	#120×C₄₃	1	2	yes	—
389	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
390	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
391	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
392	C₈	—	4	4	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	16	8	no	—
404	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
405	C₂²	C₂²×SD₁₆×C₄₃	1	1	yes	characteristic
406	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	2	2	no	—
410	C₄	—	4	4	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	8	2	no	—
414	C₄	—	8	1	no	—
415	C₄	C₄₃×#450	1	4	yes	—
416	C₂	—	2	1	no	—
417	C₂	—	2	1	no	—
418	C₂	—	4	4	no	—
419	C₂	—	8	4	no	—
420	C₂	C₂×C₄₃×#450	1	1	yes	characteristic
421	C₂	C₄₃×#3019	1	1	yes	characteristic
422	C₂	C₄₃×#3025	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 ▷ C₂² ▷ 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×#3103	C₂	semidirect
3. C₄₃×#2580	C₂	semidirect
4. C₄₃×#1613	C₂	semidirect
5. C₄₃×#1601	C₂	semidirect
6. C₄₃×#1517	C₂	semidirect
7. C₄₃×#1460	C₂	semidirect
16. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
18. C₄₃×#481	C₂²	semidirect
21. C₄₃×#448	C₂²	semidirect
23. C₄₃×#431	C₂²	semidirect
24. C₄₃×#399	C₂²	semidirect
25. C₄₃×#393	C₂²	semidirect
29. C₄₃×#382	C₂²	semidirect
30. C₄₃×#327	C₂²	semidirect
31. C₄₃×#323	C₂²	semidirect
101. C₂×D₄×C₄₃	SD₁₆	semidirect
181. #18211	C₄₃	direct (N × H)
206. #3103	C₂×C₄₃	semidirect
207. #2580	C₂×C₄₃	semidirect
208. #1613	C₂×C₄₃	semidirect
209. #1601	C₂×C₄₃	semidirect
210. #1517	C₂×C₄₃	semidirect
211. #1460	C₂×C₄₃	semidirect
227. C₂×C₄×Q₈	C₂²×C₄₃	semidirect
229. #481	C₂²×C₄₃	semidirect
232. #448	C₂²×C₄₃	semidirect
234. #431	C₂²×C₄₃	semidirect
235. #399	C₂²×C₄₃	semidirect
236. #393	C₂²×C₄₃	semidirect
240. #382	C₂²×C₄₃	semidirect
241. #327	C₂²×C₄₃	semidirect
242. #323	C₂²×C₄₃	semidirect
243. C₄₃	#18211	direct (N × H)
313. C₂×D₄	SD₁₆×C₄₃	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×#3103	2
C₄₃×#2580	2
C₄₃×#1613	2
C₄₃×#1601	2
C₄₃×#1517	2
C₄₃×#1460	2
#18211	43

Subgroups — C43×#18211 #24938228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#18211 #24938228