Subgroups — C₄₃×#18990 #24939007

Order 11008.

862 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3531	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#3171	C₂	1	2	yes	maximal, complemented
3	C₄₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1664	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1663	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1662	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1658	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1657	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1656	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1526	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1524	C₂	1	2	yes	maximal, complemented
12	C₄₃×#564	C₂²	1	1	yes	characteristic
13	C₄₃×#563	—	2	2	no	—
14	C₄₃×#563	—	2	2	no	—
15	C₄₃×#563	C₂²	1	2	yes	—
16	C₄₃×#562	—	2	2	no	—
17	C₄₃×#562	C₂²	1	1	yes	characteristic
18	C₄₃×#533	—	2	2	no	—
19	C₄₃×#533	C₂²	1	1	yes	characteristic
20	C₄₃×#532	C₂²	1	1	yes	characteristic
21	C₄₃×#529	—	2	2	no	—
22	C₄₃×#529	—	2	2	no	—
23	C₄₃×#529	C₂²	1	2	yes	—
24	C₄₃×#501	C₂²	1	2	yes	—
25	C₄₃×#496	C₂²	1	2	yes	—
26	C₄₃×#491	C₂²	1	1	yes	characteristic
27	C₄₃×#491	C₂²	1	1	yes	characteristic
28	C₄₃×#490	C₂²	1	1	yes	characteristic
29	C₄₃×#490	C₂²	1	1	yes	characteristic
30	C₄₃×#490	C₂²	1	2	yes	—
31	C₄₃×#489	—	2	2	no	—
32	C₄₃×#489	C₂²	1	2	yes	—
33	C₄₃×#469	—	2	2	no	—
34	C₄₃×#468	—	2	2	no	—
35	C₄×SD₁₆×C₄₃	—	2	2	no	—
36	C₄×D₈×C₄₃	—	2	2	no	—
37	C₄₃×#416	—	2	2	no	—
38	C₄×M₁₆×C₄₃	C₂²	1	2	yes	—
39	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#330	C₂²	1	1	yes	characteristic
41	C₄₃×#330	C₂²	1	2	yes	—
42	C₄₃×#330	C₂²	1	2	yes	—
43	C₄₃×#330	C₂²	1	1	yes	characteristic
44	C₄₃×#330	C₂²	1	2	yes	—
45	C₄₃×#329	C₂²	1	2	yes	—
46	C₄₃×#329	C₂²	1	2	yes	—
47	C₂×#41×C₄₃	—	2	1	no	—
48	C₂×SD₁₆×C₄₃	—	2	2	no	—
49	C₂×D₈×C₄₃	—	2	2	no	—
50	C₂×M₁₆×C₄₃	—	2	2	no	—
51	C₂²×C₈×C₄₃	—	2	1	no	—
52	C₄⋊Q₈×C₄₃	—	2	2	no	—
53	C₄⋊Q₈×C₄₃	—	2	2	no	—
54	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
55	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
56	#127×C₄₃	C₂³	1	1	yes	characteristic
57	#126×C₄₃	—	2	2	no	—
58	#126×C₄₃	—	2	2	no	—
59	#126×C₄₃	—	2	2	no	—
60	#126×C₄₃	—	2	2	no	—
61	#126×C₄₃	—	2	2	no	—
62	#125×C₄₃	—	2	2	no	—
63	#125×C₄₃	—	2	2	no	—
64	#125×C₄₃	—	2	2	no	—
65	#125×C₄₃	—	2	2	no	—
66	#125×C₄₃	C₂³	1	2	yes	—
67	#125×C₄₃	C₂³	1	1	yes	characteristic
68	#125×C₄₃	C₂³	1	1	yes	characteristic
69	#124×C₄₃	—	2	2	no	—
70	#124×C₄₃	—	2	2	no	—
71	#124×C₄₃	—	2	1	no	—
72	#124×C₄₃	C₂³	1	2	yes	—
73	#123×C₄₃	—	2	2	no	—
74	#123×C₄₃	—	2	2	no	—
75	#123×C₄₃	—	2	2	no	—
76	#123×C₄₃	—	2	2	no	—
77	#123×C₄₃	—	2	2	no	—
78	C₂²⋊Q₈×C₄₃	—	2	2	no	—
79	C₂²⋊Q₈×C₄₃	—	2	2	no	—
80	C₂²⋊Q₈×C₄₃	—	2	2	no	—
81	C₂²⋊Q₈×C₄₃	—	2	2	no	—
82	C₂²⋊Q₈×C₄₃	—	2	2	no	—
83	C₂²⋊Q₈×C₄₃	—	2	2	no	—
84	C₂²⋊Q₈×C₄₃	—	2	2	no	—
85	C₂²⋊Q₈×C₄₃	D₄	1	2	yes	—
86	#121×C₄₃	—	2	2	no	—
87	#121×C₄₃	—	2	2	no	—
88	#121×C₄₃	—	2	2	no	—
89	#121×C₄₃	D₄	1	2	yes	—
90	C₄×Q₈×C₄₃	—	2	2	no	—
91	C₄×Q₈×C₄₃	—	2	2	no	—
92	C₄×Q₈×C₄₃	D₄	1	2	yes	—
93	C₄×D₄×C₄₃	—	2	2	no	—
94	C₄×D₄×C₄₃	—	2	2	no	—
95	C₄×D₄×C₄₃	—	2	2	no	—
96	C₄×D₄×C₄₃	D₄	1	2	yes	—
97	#117×C₄₃	—	2	2	no	—
98	#117×C₄₃	—	2	2	no	—
99	#117×C₄₃	D₄	1	2	yes	—
100	C₂×C₄²×C₄₃	—	2	2	no	—
101	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
102	#107×C₄₃	—	2	2	no	—
103	#106×C₄₃	—	2	2	no	—
104	#103×C₄₃	—	2	2	no	—
105	#103×C₄₃	—	2	2	no	—
106	#103×C₄₃	—	2	2	no	—
107	#102×C₄₃	—	2	2	no	—
108	#102×C₄₃	—	2	2	no	—
109	#102×C₄₃	—	2	2	no	—
110	#102×C₄₃	—	2	2	no	—
111	#102×C₄₃	—	2	2	no	—
112	#97×C₄₃	—	2	1	no	—
113	#97×C₄₃	C₂³	1	2	yes	—
114	#97×C₄₃	C₂³	1	1	yes	characteristic
115	#97×C₄₃	C₂³	1	1	yes	characteristic
116	#97×C₄₃	C₂³	1	2	yes	—
117	C₄×C₈×C₄₃	—	2	2	no	—
118	#41×C₄₃	—	4	4	no	—
119	C₂×Q₈×C₄₃	—	2	2	no	—
120	C₂×Q₈×C₄₃	—	2	2	no	—
121	C₂×Q₈×C₄₃	—	2	1	no	—
122	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₄₃	—	2	2	no	—
124	C₂×D₄×C₄₃	—	2	2	no	—
125	C₂×D₄×C₄₃	—	2	1	no	—
126	C₂×D₄×C₄₃	—	2	2	no	—
127	C₂×D₄×C₄₃	—	4	1	no	—
128	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₄₃	—	2	2	no	—
130	C₂²×C₄×C₄₃	—	2	2	no	—
131	C₂²×C₄×C₄₃	—	2	2	no	—
132	C₂²×C₄×C₄₃	—	4	1	no	—
133	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
135	SD₁₆×C₄₃	—	4	4	no	—
136	D₈×C₄₃	—	4	4	no	—
137	M₁₆×C₄₃	—	4	4	no	—
138	C₂×C₈×C₄₃	—	2	2	no	—
139	C₂×C₈×C₄₃	—	2	2	no	—
140	C₂×C₈×C₄₃	—	2	1	no	—
141	C₂×C₈×C₄₃	—	2	1	no	—
142	C₂×C₈×C₄₃	—	4	2	no	—
143	C₄⋊C₄×C₄₃	—	2	2	no	—
144	C₄⋊C₄×C₄₃	—	2	2	no	—
145	C₄⋊C₄×C₄₃	—	2	2	no	—
146	C₄⋊C₄×C₄₃	—	2	2	no	—
147	C₄⋊C₄×C₄₃	—	2	2	no	—
148	C₄⋊C₄×C₄₃	—	2	2	no	—
149	C₄⋊C₄×C₄₃	—	2	2	no	—
150	C₄⋊C₄×C₄₃	—	2	2	no	—
151	C₄⋊C₄×C₄₃	—	2	2	no	—
152	C₄⋊C₄×C₄₃	—	2	2	no	—
153	C₄⋊C₄×C₄₃	—	2	2	no	—
154	C₄⋊C₄×C₄₃	—	2	2	no	—
155	C₄⋊C₄×C₄₃	—	2	2	no	—
156	C₄⋊C₄×C₄₃	—	2	2	no	—
157	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
158	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
160	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
161	C₂²⋊C₄×C₄₃	—	2	2	no	—
162	C₂²⋊C₄×C₄₃	—	2	2	no	—
163	C₂²⋊C₄×C₄₃	—	2	2	no	—
164	C₂²⋊C₄×C₄₃	—	2	2	no	—
165	C₂²⋊C₄×C₄₃	—	2	2	no	—
166	C₂²⋊C₄×C₄₃	—	2	2	no	—
167	C₂²⋊C₄×C₄₃	—	2	2	no	—
168	C₂²⋊C₄×C₄₃	—	2	2	no	—
169	C₂²⋊C₄×C₄₃	—	2	2	no	—
170	C₂²⋊C₄×C₄₃	—	2	2	no	—
171	C₂²⋊C₄×C₄₃	—	4	2	no	—
172	C₄²×C₄₃	—	2	2	no	—
173	C₄²×C₄₃	—	2	2	no	—
174	C₄²×C₄₃	—	2	2	no	—
175	C₄²×C₄₃	—	2	2	no	—
176	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₄₃	C₂×D₄	1	2	yes	—
178	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
179	C₂³×C₄₃	—	2	2	no	—
180	C₂³×C₄₃	—	4	1	no	—
181	C₂³×C₄₃	#120	1	1	yes	characteristic
182	Q₈×C₄₃	—	4	2	no	—
183	Q₈×C₄₃	—	4	2	no	—
184	Q₈×C₄₃	—	8	2	no	—
185	Q₈×C₄₃	—	8	2	no	—
186	D₄×C₄₃	—	4	2	no	—
187	D₄×C₄₃	—	4	2	no	—
188	D₄×C₄₃	—	4	2	no	—
189	D₄×C₄₃	—	4	2	no	—
190	D₄×C₄₃	—	8	2	no	—
191	D₄×C₄₃	—	8	2	no	—
192	D₄×C₄₃	—	8	2	no	—
193	C₂×C₄×C₄₃	—	2	2	no	—
194	C₂×C₄×C₄₃	—	2	2	no	—
195	C₂×C₄×C₄₃	—	2	2	no	—
196	C₂×C₄×C₄₃	—	2	2	no	—
197	C₂×C₄×C₄₃	—	2	2	no	—
198	C₂×C₄×C₄₃	—	2	2	no	—
199	C₂×C₄×C₄₃	—	4	2	no	—
200	C₂×C₄×C₄₃	—	4	4	no	—
201	C₂×C₄×C₄₃	—	4	1	no	—
202	C₂×C₄×C₄₃	—	8	2	no	—
203	C₂×C₄×C₄₃	—	8	2	no	—
204	C₂×C₄×C₄₃	—	8	2	no	—
205	C₂×C₄×C₄₃	#120	1	2	yes	—
206	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
207	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
209	C₈×C₄₃	—	2	4	no	—
210	C₈×C₄₃	—	4	1	no	—
211	C₈×C₄₃	—	4	1	no	—
212	C₈×C₄₃	—	4	2	no	—
213	#18990	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂²×C₄₃	—	2	1	no	—
215	C₂²×C₄₃	—	2	2	no	—
216	C₂²×C₄₃	—	4	2	no	—
217	C₂²×C₄₃	—	4	2	no	—
218	C₂²×C₄₃	—	4	2	no	—
219	C₂²×C₄₃	—	8	1	no	—
220	C₂²×C₄₃	—	8	2	no	—
221	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
222	C₄×C₄₃	—	2	1	no	—
223	C₄×C₄₃	—	2	2	no	—
224	C₄×C₄₃	—	2	2	no	—
225	C₄×C₄₃	—	4	2	no	—
226	C₄×C₄₃	—	4	2	no	—
227	C₄×C₄₃	—	4	2	no	—
228	C₄×C₄₃	—	4	2	no	—
229	C₄×C₄₃	—	4	2	no	—
230	C₄×C₄₃	—	8	1	no	—
231	C₄×C₄₃	#454	1	2	yes	—
232	#3531	C₂×C₄₃	1	1	yes	characteristic, complemented
233	#3171	C₂×C₄₃	1	2	yes	complemented
234	#3135	C₂×C₄₃	1	1	yes	characteristic, complemented
235	#1664	C₂×C₄₃	1	2	yes	complemented
236	#1663	C₂×C₄₃	1	1	yes	characteristic, complemented
237	#1662	C₂×C₄₃	1	1	yes	characteristic, complemented
238	#1658	C₂×C₄₃	1	1	yes	characteristic, complemented
239	#1657	C₂×C₄₃	1	2	yes	complemented
240	#1656	C₂×C₄₃	1	1	yes	characteristic, complemented
241	#1526	C₂×C₄₃	1	1	yes	characteristic, complemented
242	#1524	C₂×C₄₃	1	2	yes	complemented
243	C₂×C₄₃	—	4	1	no	—
244	C₂×C₄₃	—	8	2	no	—
245	C₂×C₄₃	—	16	1	no	—
246	C₂×C₄₃	C₂×#454	1	1	yes	characteristic
247	C₂×C₄₃	#3018	1	2	yes	—
248	#564	C₂²×C₄₃	1	1	yes	characteristic
249	#563	—	2	2	no	—
250	#563	—	2	2	no	—
251	#563	C₂²×C₄₃	1	2	yes	—
252	#562	—	2	2	no	—
253	#562	C₂²×C₄₃	1	1	yes	characteristic
254	#533	—	2	2	no	—
255	#533	C₂²×C₄₃	1	1	yes	characteristic
256	#532	C₂²×C₄₃	1	1	yes	characteristic
257	#529	—	2	2	no	—
258	#529	—	2	2	no	—
259	#529	C₂²×C₄₃	1	2	yes	—
260	#501	C₂²×C₄₃	1	2	yes	—
261	#496	C₂²×C₄₃	1	2	yes	—
262	#491	C₂²×C₄₃	1	1	yes	characteristic
263	#491	C₂²×C₄₃	1	1	yes	characteristic
264	#490	C₂²×C₄₃	1	1	yes	characteristic
265	#490	C₂²×C₄₃	1	1	yes	characteristic
266	#490	C₂²×C₄₃	1	2	yes	—
267	#489	—	2	2	no	—
268	#489	C₂²×C₄₃	1	2	yes	—
269	#469	—	2	2	no	—
270	#468	—	2	2	no	—
271	C₄×SD₁₆	—	2	2	no	—
272	C₄×D₈	—	2	2	no	—
273	#416	—	2	2	no	—
274	C₄×M₁₆	C₂²×C₄₃	1	2	yes	—
275	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
276	#330	C₂²×C₄₃	1	1	yes	characteristic
277	#330	C₂²×C₄₃	1	2	yes	—
278	#330	C₂²×C₄₃	1	2	yes	—
279	#330	C₂²×C₄₃	1	1	yes	characteristic
280	#330	C₂²×C₄₃	1	2	yes	—
281	#329	C₂²×C₄₃	1	2	yes	—
282	#329	C₂²×C₄₃	1	2	yes	—
283	C₄₃	#18990	1	1	yes	characteristic, direct product factor, Sylow
284	C₂×#41	—	2	1	no	—
285	C₂×SD₁₆	—	2	2	no	—
286	C₂×D₈	—	2	2	no	—
287	C₂×M₁₆	—	2	2	no	—
288	C₂²×C₈	—	2	1	no	—
289	C₄⋊Q₈	—	2	2	no	—
290	C₄⋊Q₈	—	2	2	no	—
291	C₄⋊Q₈	D₄×C₄₃	1	2	yes	—
292	C₄⋊Q₈	C₂³×C₄₃	1	1	yes	characteristic
293	#127	C₂³×C₄₃	1	1	yes	characteristic
294	#126	—	2	2	no	—
295	#126	—	2	2	no	—
296	#126	—	2	2	no	—
297	#126	—	2	2	no	—
298	#126	—	2	2	no	—
299	#125	—	2	2	no	—
300	#125	—	2	2	no	—
301	#125	—	2	2	no	—
302	#125	—	2	2	no	—
303	#125	C₂³×C₄₃	1	2	yes	—
304	#125	C₂³×C₄₃	1	1	yes	characteristic
305	#125	C₂³×C₄₃	1	1	yes	characteristic
306	#124	—	2	2	no	—
307	#124	—	2	2	no	—
308	#124	—	2	1	no	—
309	#124	C₂³×C₄₃	1	2	yes	—
310	#123	—	2	2	no	—
311	#123	—	2	2	no	—
312	#123	—	2	2	no	—
313	#123	—	2	2	no	—
314	#123	—	2	2	no	—
315	C₂²⋊Q₈	—	2	2	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	C₂²⋊Q₈	—	2	2	no	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	D₄×C₄₃	1	2	yes	—
323	#121	—	2	2	no	—
324	#121	—	2	2	no	—
325	#121	—	2	2	no	—
326	#121	D₄×C₄₃	1	2	yes	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	D₄×C₄₃	1	2	yes	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	D₄×C₄₃	1	2	yes	—
334	#117	—	2	2	no	—
335	#117	—	2	2	no	—
336	#117	D₄×C₄₃	1	2	yes	—
337	C₂×C₄²	—	2	2	no	—
338	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
339	#107	—	2	2	no	—
340	#106	—	2	2	no	—
341	#103	—	2	2	no	—
342	#103	—	2	2	no	—
343	#103	—	2	2	no	—
344	#102	—	2	2	no	—
345	#102	—	2	2	no	—
346	#102	—	2	2	no	—
347	#102	—	2	2	no	—
348	#102	—	2	2	no	—
349	#97	—	2	1	no	—
350	#97	C₂³×C₄₃	1	1	yes	characteristic
351	#97	C₂³×C₄₃	1	1	yes	characteristic
352	#97	C₂³×C₄₃	1	2	yes	—
353	#97	C₂³×C₄₃	1	2	yes	—
354	C₄×C₈	—	2	2	no	—
355	#41	—	4	4	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	4	1	no	—
365	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	4	1	no	—
370	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
372	SD₁₆	—	4	4	no	—
373	D₈	—	4	4	no	—
374	M₁₆	—	4	4	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	4	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
395	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
396	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
397	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	4	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	C₂×D₄×C₄₃	1	2	yes	—
414	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
415	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
416	C₂³	—	2	2	no	—
417	C₂³	—	4	1	no	—
418	C₂³	#120×C₄₃	1	1	yes	characteristic
419	Q₈	—	4	2	no	—
420	Q₈	—	4	2	no	—
421	Q₈	—	8	2	no	—
422	Q₈	—	8	2	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	2	no	—
427	D₄	—	8	2	no	—
428	D₄	—	8	2	no	—
429	D₄	—	8	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	8	2	no	—
440	C₂×C₄	—	8	2	no	—
441	C₂×C₄	—	8	2	no	—
442	C₂×C₄	#120×C₄₃	1	2	yes	—
443	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
444	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
445	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
446	C₈	—	2	4	no	—
447	C₈	—	4	1	no	—
448	C₈	—	4	1	no	—
449	C₈	—	4	2	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	2	no	—
457	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
458	C₄	—	2	1	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	8	1	no	—
467	C₄	C₄₃×#454	1	2	yes	—
468	C₂	—	4	1	no	—
469	C₂	—	8	2	no	—
470	C₂	—	16	1	no	—
471	C₂	C₂×C₄₃×#454	1	1	yes	characteristic
472	C₂	C₄₃×#3018	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₃	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₃
socle	C₂²×C₄₃	C₂×#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₃×#3531	C₂	semidirect
2. C₄₃×#3171	C₂	semidirect
3. C₄₃×#3135	C₂	semidirect
4. C₄₃×#1664	C₂	semidirect
5. C₄₃×#1663	C₂	semidirect
6. C₄₃×#1662	C₂	semidirect
7. C₄₃×#1658	C₂	semidirect
8. C₄₃×#1657	C₂	semidirect
9. C₄₃×#1656	C₂	semidirect
10. C₄₃×#1526	C₂	semidirect
11. C₄₃×#1524	C₂	semidirect
213. #18990	C₄₃	direct (N × H)
232. #3531	C₂×C₄₃	semidirect
233. #3171	C₂×C₄₃	semidirect
234. #3135	C₂×C₄₃	semidirect
235. #1664	C₂×C₄₃	semidirect
236. #1663	C₂×C₄₃	semidirect
237. #1662	C₂×C₄₃	semidirect
238. #1658	C₂×C₄₃	semidirect
239. #1657	C₂×C₄₃	semidirect
240. #1656	C₂×C₄₃	semidirect
241. #1526	C₂×C₄₃	semidirect
242. #1524	C₂×C₄₃	semidirect
283. C₄₃	#18990	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×#3531	2
C₄₃×#3171	2
C₄₃×#3135	2
C₄₃×#1664	2
C₄₃×#1663	2
C₄₃×#1662	2
C₄₃×#1658	2
C₄₃×#1657	2
C₄₃×#1656	2
C₄₃×#1526	2
C₄₃×#1524	2
#18990	43

Subgroups — C43×#18990 #24939007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#18990 #24939007