Subgroups — C₄₃×#29654 #24949671

Order 11008.

948 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#3094	C₂	1	2	yes	maximal
3	C₄₃×#2500	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2061	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2060	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2027	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2027	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1826	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1822	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#544	—	2	2	no	—
11	C₄₃×#544	—	2	2	no	—
12	C₄₃×#544	C₂²	1	2	yes	—
13	C₄₃×#544	C₂²	1	2	yes	—
14	C₄₃×#543	—	2	2	no	—
15	C₄₃×#533	—	2	4	no	—
16	C₄₃×#533	—	2	2	no	—
17	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#117×C₄₃	C₂²	1	2	yes	—
19	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#482	—	2	4	no	—
21	C₄₃×#481	—	2	2	no	—
22	C₄₃×#480	—	2	2	no	—
23	C₄₃×#428	C₂²	1	4	yes	—
24	C₄₃×#418	C₂²	1	4	yes	—
25	C₄₃×#407	C₂²	1	2	yes	—
26	C₄₃×#394	—	2	2	no	—
27	C₄₃×#390	C₂²	1	1	yes	characteristic
28	C₄₃×#390	C₂²	1	1	yes	characteristic
29	C₄₃×#388	—	2	2	no	—
30	C₄₃×#384	C₂²	1	1	yes	characteristic
31	C₄₃×#382	C₂²	1	1	yes	characteristic
32	C₄×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
33	C₄₃×#343	C₂²	1	2	yes	—
34	C₄₃×#343	C₂²	1	2	yes	—
35	C₄₃×#339	C₂²	1	4	yes	—
36	C₄₃×#339	C₂²	1	4	yes	—
37	C₂²×D₄×C₄₃	—	2	1	no	—
38	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
40	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
41	C₄⋊Q₈×C₄₃	—	2	2	no	—
42	C₄⋊Q₈×C₄₃	—	2	2	no	—
43	C₄⋊Q₈×C₄₃	—	2	4	no	—
44	C₄⋊Q₈×C₄₃	—	2	4	no	—
45	#125×C₄₃	—	2	4	no	—
46	#125×C₄₃	—	2	4	no	—
47	#125×C₄₃	—	2	4	no	—
48	C₂²⋊Q₈×C₄₃	—	2	8	no	—
49	C₂²⋊Q₈×C₄₃	—	2	8	no	—
50	C₂²⋊Q₈×C₄₃	—	2	4	no	—
51	C₂²⋊Q₈×C₄₃	—	2	4	no	—
52	#121×C₄₃	—	2	2	no	—
53	#121×C₄₃	—	2	2	no	—
54	C₄×Q₈×C₄₃	—	2	4	no	—
55	C₄×Q₈×C₄₃	—	2	4	no	—
56	#117×C₄₃	—	2	2	no	—
57	#117×C₄₃	—	2	2	no	—
58	#117×C₄₃	—	2	2	no	—
59	#117×C₄₃	—	2	2	no	—
60	#117×C₄₃	D₄	1	4	yes	—
61	#117×C₄₃	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
74	C₂×C₄²×C₄₃	—	2	2	no	—
75	C₂×C₄²×C₄₃	D₄	1	2	yes	—
76	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
78	#107×C₄₃	—	2	4	no	—
79	#106×C₄₃	—	2	4	no	—
80	#102×C₄₃	—	2	4	no	—
81	#102×C₄₃	—	2	4	no	—
82	C₂²⋊C₈×C₄₃	—	2	2	no	—
83	C₂²⋊C₈×C₄₃	—	2	2	no	—
84	#95×C₄₃	—	2	1	no	—
85	#95×C₄₃	—	2	2	no	—
86	C₂⁴×C₄₃	—	2	1	no	—
87	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
88	C₂×Q₈×C₄₃	—	2	4	no	—
89	C₂×Q₈×C₄₃	—	2	4	no	—
90	C₂×D₄×C₄₃	—	2	2	no	—
91	C₂×D₄×C₄₃	—	2	2	no	—
92	C₂×D₄×C₄₃	—	2	2	no	—
93	C₂×D₄×C₄₃	—	4	2	no	—
94	C₂×D₄×C₄₃	—	8	2	no	—
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	2	1	no	—
100	C₂²×C₄×C₄₃	—	2	1	no	—
101	C₂²×C₄×C₄₃	—	2	1	no	—
102	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
108	M₁₆×C₄₃	—	2	4	no	—
109	M₁₆×C₄₃	—	2	4	no	—
110	C₂×C₈×C₄₃	—	2	4	no	—
111	C₄⋊C₄×C₄₃	—	2	8	no	—
112	C₄⋊C₄×C₄₃	—	2	8	no	—
113	C₄⋊C₄×C₄₃	—	2	4	no	—
114	C₄⋊C₄×C₄₃	—	2	4	no	—
115	C₄⋊C₄×C₄₃	—	2	2	no	—
116	C₄⋊C₄×C₄₃	—	2	2	no	—
117	C₄⋊C₄×C₄₃	—	2	2	no	—
118	C₄⋊C₄×C₄₃	—	2	2	no	—
119	C₄⋊C₄×C₄₃	—	2	2	no	—
120	C₄⋊C₄×C₄₃	—	8	2	no	—
121	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
122	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
123	C₂²⋊C₄×C₄₃	—	2	4	no	—
124	C₂²⋊C₄×C₄₃	—	2	4	no	—
125	C₂²⋊C₄×C₄₃	—	2	4	no	—
126	C₂²⋊C₄×C₄₃	—	4	2	no	—
127	C₂²⋊C₄×C₄₃	—	4	4	no	—
128	C₂²⋊C₄×C₄₃	—	4	1	no	—
129	C₂²⋊C₄×C₄₃	—	4	1	no	—
130	C₂²⋊C₄×C₄₃	—	8	2	no	—
131	C₄²×C₄₃	—	2	4	no	—
132	C₄²×C₄₃	—	2	2	no	—
133	C₄²×C₄₃	—	2	2	no	—
134	C₄²×C₄₃	—	2	4	no	—
135	C₄²×C₄₃	—	2	2	no	—
136	C₄²×C₄₃	—	2	2	no	—
137	C₂³×C₄₃	—	2	1	no	—
138	C₂³×C₄₃	—	2	1	no	—
139	C₂³×C₄₃	—	4	1	no	—
140	C₂³×C₄₃	—	4	1	no	—
141	C₂³×C₄₃	—	4	2	no	—
142	C₂³×C₄₃	—	4	2	no	—
143	C₂³×C₄₃	—	4	1	no	—
144	C₂³×C₄₃	—	4	1	no	—
145	C₂³×C₄₃	—	4	1	no	—
146	C₂³×C₄₃	#120	1	2	yes	—
147	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₄₃	—	8	4	no	—
149	Q₈×C₄₃	—	8	4	no	—
150	D₄×C₄₃	—	4	4	no	—
151	D₄×C₄₃	—	8	4	no	—
152	C₂×C₄×C₄₃	—	2	1	no	—
153	C₂×C₄×C₄₃	—	2	1	no	—
154	C₂×C₄×C₄₃	—	2	4	no	—
155	C₂×C₄×C₄₃	—	2	4	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	4	no	—
160	C₂×C₄×C₄₃	—	2	4	no	—
161	C₂×C₄×C₄₃	—	4	1	no	—
162	C₂×C₄×C₄₃	—	4	1	no	—
163	C₂×C₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	—	4	2	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	4	1	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	—	4	1	no	—
170	C₂×C₄×C₄₃	—	8	2	no	—
171	C₂×C₄×C₄₃	—	8	2	no	—
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	2₋¹⁺⁴	1	2	yes	—
176	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
177	C₈×C₄₃	—	4	4	no	—
178	#29654	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	2	no	—
182	C₂²×C₄₃	—	2	2	no	—
183	C₂²×C₄₃	—	2	2	no	—
184	C₂²×C₄₃	—	8	1	no	—
185	C₂²×C₄₃	—	8	1	no	—
186	C₂²×C₄₃	—	8	2	no	—
187	C₂²×C₄₃	—	8	2	no	—
188	C₂²×C₄₃	—	8	1	no	—
189	C₂²×C₄₃	—	8	1	no	—
190	C₂²×C₄₃	—	8	1	no	—
191	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
192	C₂²×C₄₃	#536	1	1	yes	characteristic
193	C₂²×C₄₃	#536	1	1	yes	characteristic
194	C₄×C₄₃	—	2	1	no	—
195	C₄×C₄₃	—	2	1	no	—
196	C₄×C₄₃	—	4	2	no	—
197	C₄×C₄₃	—	4	2	no	—
198	C₄×C₄₃	—	4	4	no	—
199	C₄×C₄₃	—	4	2	no	—
200	C₄×C₄₃	—	4	4	no	—
201	C₄×C₄₃	—	8	1	no	—
202	C₄×C₄₃	—	8	1	no	—
203	C₄×C₄₃	#536	1	4	yes	—
204	#3458	C₂×C₄₃	1	1	yes	characteristic, complemented
205	#3094	C₂×C₄₃	1	2	yes	—
206	#2500	C₂×C₄₃	1	1	yes	characteristic
207	#2061	C₂×C₄₃	1	2	yes	complemented
208	#2060	C₂×C₄₃	1	2	yes	complemented
209	#2027	C₂×C₄₃	1	2	yes	complemented
210	#2027	C₂×C₄₃	1	2	yes	complemented
211	#1826	C₂×C₄₃	1	2	yes	complemented
212	#1822	C₂×C₄₃	1	1	yes	characteristic, complemented
213	C₂×C₄₃	—	2	1	no	—
214	C₂×C₄₃	—	2	1	no	—
215	C₂×C₄₃	—	4	2	no	—
216	C₂×C₄₃	—	16	1	no	—
217	C₂×C₄₃	#2614	1	1	yes	characteristic
218	C₂×C₄₃	#3018	1	1	yes	characteristic
219	C₂×C₄₃	#3021	1	1	yes	characteristic
220	#544	—	2	2	no	—
221	#544	—	2	2	no	—
222	#544	C₂²×C₄₃	1	2	yes	—
223	#544	C₂²×C₄₃	1	2	yes	—
224	#543	—	2	2	no	—
225	#533	—	2	4	no	—
226	#533	—	2	2	no	—
227	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
228	C₂×#117	C₂²×C₄₃	1	2	yes	—
229	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
230	#482	—	2	4	no	—
231	#481	—	2	2	no	—
232	#480	—	2	2	no	—
233	#428	C₂²×C₄₃	1	4	yes	—
234	#418	C₂²×C₄₃	1	4	yes	—
235	#407	C₂²×C₄₃	1	2	yes	—
236	#394	—	2	2	no	—
237	#390	C₂²×C₄₃	1	1	yes	characteristic
238	#390	C₂²×C₄₃	1	1	yes	characteristic
239	#388	—	2	2	no	—
240	#384	C₂²×C₄₃	1	1	yes	characteristic
241	#382	C₂²×C₄₃	1	1	yes	characteristic
242	C₄×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
243	#343	C₂²×C₄₃	1	2	yes	—
244	#343	C₂²×C₄₃	1	2	yes	—
245	#339	C₂²×C₄₃	1	4	yes	—
246	#339	C₂²×C₄₃	1	4	yes	—
247	C₄₃	#29654	1	1	yes	characteristic, direct product factor, Sylow
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
251	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	—	2	2	no	—
254	C₄⋊Q₈	—	2	4	no	—
255	C₄⋊Q₈	—	2	4	no	—
256	#125	—	2	4	no	—
257	#125	—	2	4	no	—
258	#125	—	2	4	no	—
259	C₂²⋊Q₈	—	2	8	no	—
260	C₂²⋊Q₈	—	2	8	no	—
261	C₂²⋊Q₈	—	2	4	no	—
262	C₂²⋊Q₈	—	2	4	no	—
263	#121	—	2	2	no	—
264	#121	—	2	2	no	—
265	C₄×Q₈	—	2	4	no	—
266	C₄×Q₈	—	2	4	no	—
267	#117	—	2	2	no	—
268	#117	—	2	2	no	—
269	#117	—	2	2	no	—
270	#117	—	2	2	no	—
271	#117	D₄×C₄₃	1	4	yes	—
272	#117	C₂³×C₄₃	1	4	yes	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
275	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	D₄×C₄₃	1	2	yes	—
287	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
289	#107	—	2	4	no	—
290	#106	—	2	4	no	—
291	#102	—	2	4	no	—
292	#102	—	2	4	no	—
293	C₂²⋊C₈	—	2	2	no	—
294	C₂²⋊C₈	—	2	2	no	—
295	#95	—	2	1	no	—
296	#95	—	2	2	no	—
297	C₂⁴	—	2	1	no	—
298	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	2	4	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	8	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
318	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
319	M₁₆	—	2	4	no	—
320	M₁₆	—	2	4	no	—
321	C₂×C₈	—	2	4	no	—
322	C₄⋊C₄	—	2	8	no	—
323	C₄⋊C₄	—	2	8	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	8	2	no	—
332	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
333	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
334	C₂²⋊C₄	—	2	4	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₂²⋊C₄	—	4	4	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₂²⋊C₄	—	4	1	no	—
340	C₂²⋊C₄	—	4	1	no	—
341	C₂²⋊C₄	—	8	2	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	4	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	1	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	1	no	—
357	C₂³	#120×C₄₃	1	2	yes	—
358	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
359	Q₈	—	8	4	no	—
360	Q₈	—	8	4	no	—
361	D₄	—	4	4	no	—
362	D₄	—	8	4	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	8	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
384	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
385	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
386	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
387	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
388	C₈	—	4	4	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	8	1	no	—
395	C₂²	—	8	1	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	1	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
402	C₂²	C₄₃×#536	1	1	yes	characteristic
403	C₂²	C₄₃×#536	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	4	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	4	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	1	no	—
413	C₄	C₄₃×#536	1	4	yes	—
414	C₂	—	2	1	no	—
415	C₂	—	2	1	no	—
416	C₂	—	4	2	no	—
417	C₂	—	16	1	no	—
418	C₂	C₄₃×#2614	1	1	yes	characteristic
419	C₂	C₄₃×#3018	1	1	yes	characteristic
420	C₂	C₄₃×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#121×C₄₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂³×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₃×#3458	C₂	semidirect
4. C₄₃×#2061	C₂	semidirect
5. C₄₃×#2060	C₂	semidirect
6. C₄₃×#2027	C₂	semidirect
7. C₄₃×#2027	C₂	semidirect
8. C₄₃×#1826	C₂	semidirect
9. C₄₃×#1822	C₂	semidirect
178. #29654	C₄₃	direct (N × H)
204. #3458	C₂×C₄₃	semidirect
207. #2061	C₂×C₄₃	semidirect
208. #2060	C₂×C₄₃	semidirect
209. #2027	C₂×C₄₃	semidirect
210. #2027	C₂×C₄₃	semidirect
211. #1826	C₂×C₄₃	semidirect
212. #1822	C₂×C₄₃	semidirect
247. C₄₃	#29654	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×#3458	2
C₄₃×#3094	2
C₄₃×#2500	2
C₄₃×#2061	2
C₄₃×#2060	2
C₄₃×#2027	2
C₄₃×#1826	2
C₄₃×#1822	2
#29654	43

Subgroups — C43×#29654 #24949671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29654 #24949671