Subgroups — C₄₃×#29843 #24949860

Order 11008.

990 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2856	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2065	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2034	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1844	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
13	C₂×#121×C₄₃	—	2	1	no	—
14	C₂×#121×C₄₃	—	2	1	no	—
15	C₂×#121×C₄₃	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#486	—	2	4	no	—
18	C₄₃×#431	—	2	4	no	—
19	C₂×#106×C₄₃	C₂²	1	4	yes	—
20	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
21	C₂×#102×C₄₃	C₂²	1	4	yes	—
22	C₂×#102×C₄₃	C₂²	1	4	yes	—
23	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₄₃×#391	—	2	1	no	—
27	C₄₃×#390	—	2	1	no	—
28	C₄₃×#390	—	2	1	no	—
29	C₄₃×#390	C₂²	1	2	yes	—
30	C₄₃×#389	—	2	1	no	—
31	C₄₃×#389	C₂²	1	2	yes	—
32	C₄₃×#384	C₂²	1	1	yes	characteristic
33	C₄₃×#384	C₂²	1	1	yes	characteristic
34	C₄₃×#380	—	2	1	no	—
35	C₄₃×#380	C₂²	1	2	yes	—
36	C₄₃×#340	C₂²	1	4	yes	—
37	C₂²×Q₈×C₄₃	—	2	1	no	—
38	C₂²×D₄×C₄₃	—	2	2	no	—
39	C₂²×D₄×C₄₃	—	2	1	no	—
40	C₂²×D₄×C₄₃	—	2	1	no	—
41	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
47	C₄⋊Q₈×C₄₃	—	2	2	no	—
48	C₄⋊Q₈×C₄₃	—	2	2	no	—
49	#127×C₄₃	—	2	2	no	—
50	#127×C₄₃	—	2	2	no	—
51	C₂²⋊Q₈×C₄₃	—	4	4	no	—
52	#121×C₄₃	—	4	4	no	—
53	#121×C₄₃	—	4	4	no	—
54	#121×C₄₃	—	4	4	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₄²×C₄₃	—	2	2	no	—
69	C₂×C₄²×C₄₃	—	2	2	no	—
70	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
74	#106×C₄₃	—	4	4	no	—
75	C₄⋊C₈×C₄₃	—	2	4	no	—
76	#102×C₄₃	—	2	8	no	—
77	#102×C₄₃	—	4	4	no	—
78	C₂²⋊C₈×C₄₃	—	2	4	no	—
79	C₄×C₈×C₄₃	—	2	2	no	—
80	C₄×C₈×C₄₃	D₄	1	4	yes	complemented
81	#95×C₄₃	—	2	2	no	—
82	#95×C₄₃	—	2	2	no	—
83	C₂⁴×C₄₃	—	2	2	no	—
84	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂×Q₈×C₄₃	—	4	2	no	—
86	C₂×Q₈×C₄₃	—	4	2	no	—
87	C₂×Q₈×C₄₃	—	4	2	no	—
88	C₂×D₄×C₄₃	—	2	2	no	—
89	C₂×D₄×C₄₃	—	2	2	no	—
90	C₂×D₄×C₄₃	—	2	4	no	—
91	C₂×D₄×C₄₃	—	2	4	no	—
92	C₂×D₄×C₄₃	—	4	4	no	—
93	C₂×D₄×C₄₃	—	4	4	no	—
94	C₂×D₄×C₄₃	—	4	2	no	—
95	C₂×D₄×C₄₃	—	4	2	no	—
96	C₂×D₄×C₄₃	—	4	2	no	—
97	C₂×D₄×C₄₃	—	4	2	no	—
98	C₂×D₄×C₄₃	—	4	2	no	—
99	C₂×D₄×C₄₃	—	4	2	no	—
100	C₂×D₄×C₄₃	—	4	4	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	2	1	no	—
107	C₂²×C₄×C₄₃	—	2	1	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	SD₁₆	1	4	yes	—
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₄₃	—	2	2	no	—
121	C₂×C₈×C₄₃	—	2	2	no	—
122	C₂×C₈×C₄₃	—	2	2	no	—
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₂×C₈×C₄₃	—	2	2	no	—
125	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	2	2	no	—
128	C₄⋊C₄×C₄₃	—	2	4	no	—
129	C₄⋊C₄×C₄₃	—	2	4	no	—
130	C₄⋊C₄×C₄₃	—	4	4	no	—
131	C₄⋊C₄×C₄₃	—	4	2	no	—
132	C₄⋊C₄×C₄₃	—	4	2	no	—
133	C₄⋊C₄×C₄₃	—	4	2	no	—
134	C₄⋊C₄×C₄₃	—	4	2	no	—
135	C₄⋊C₄×C₄₃	—	4	2	no	—
136	C₂²⋊C₄×C₄₃	—	4	4	no	—
137	C₂²⋊C₄×C₄₃	—	4	4	no	—
138	C₂²⋊C₄×C₄₃	—	4	4	no	—
139	C₂²⋊C₄×C₄₃	—	4	4	no	—
140	C₄²×C₄₃	—	2	2	no	—
141	C₄²×C₄₃	—	2	2	no	—
142	C₄²×C₄₃	—	2	1	no	—
143	C₄²×C₄₃	—	2	1	no	—
144	C₄²×C₄₃	C₂×D₄	1	2	yes	—
145	C₄²×C₄₃	#41	1	2	yes	—
146	C₂³×C₄₃	—	2	1	no	—
147	C₂³×C₄₃	—	2	1	no	—
148	C₂³×C₄₃	—	2	1	no	—
149	C₂³×C₄₃	—	2	1	no	—
150	C₂³×C₄₃	—	2	1	no	—
151	C₂³×C₄₃	—	2	1	no	—
152	C₂³×C₄₃	—	4	2	no	—
153	C₂³×C₄₃	—	4	2	no	—
154	C₂³×C₄₃	—	4	2	no	—
155	C₂³×C₄₃	—	4	2	no	—
156	C₂³×C₄₃	—	4	2	no	—
157	C₂³×C₄₃	—	4	2	no	—
158	C₂³×C₄₃	—	4	2	no	—
159	C₂³×C₄₃	C₂×SD₁₆	1	2	yes	—
160	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₄₃	—	8	4	no	—
162	D₄×C₄₃	—	4	4	no	—
163	D₄×C₄₃	—	4	4	no	—
164	D₄×C₄₃	—	8	8	no	—
165	D₄×C₄₃	—	8	4	no	—
166	D₄×C₄₃	—	8	4	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	2	1	no	—
169	C₂×C₄×C₄₃	—	2	8	no	—
170	C₂×C₄×C₄₃	—	2	1	no	—
171	C₂×C₄×C₄₃	—	2	1	no	—
172	C₂×C₄×C₄₃	—	2	1	no	—
173	C₂×C₄×C₄₃	—	2	1	no	—
174	C₂×C₄×C₄₃	—	2	1	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	4	2	no	—
178	C₂×C₄×C₄₃	—	4	4	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	—	4	2	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	—	4	2	no	—
186	C₂×C₄×C₄₃	—	4	2	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	#121	1	2	yes	—
189	C₂×C₄×C₄₃	#121	1	2	yes	—
190	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
191	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
192	C₂×C₄×C₄₃	#135	1	2	yes	—
193	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
194	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
195	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
198	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
199	C₈×C₄₃	—	2	4	no	—
200	C₈×C₄₃	—	4	2	no	—
201	#29843	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₄₃	—	2	2	no	—
203	C₂²×C₄₃	—	2	2	no	—
204	C₂²×C₄₃	—	2	2	no	—
205	C₂²×C₄₃	—	4	1	no	—
206	C₂²×C₄₃	—	4	1	no	—
207	C₂²×C₄₃	—	4	1	no	—
208	C₂²×C₄₃	—	4	1	no	—
209	C₂²×C₄₃	—	8	2	no	—
210	C₂²×C₄₃	—	8	2	no	—
211	C₂²×C₄₃	—	8	2	no	—
212	C₂²×C₄₃	—	8	2	no	—
213	C₂²×C₄₃	—	8	2	no	—
214	C₂²×C₄₃	—	8	2	no	—
215	C₂²×C₄₃	—	8	2	no	—
216	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
217	C₂²×C₄₃	#535	1	1	yes	characteristic
218	C₂²×C₄₃	#536	1	1	yes	characteristic
219	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
220	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
221	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
222	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
223	C₄×C₄₃	—	2	2	no	—
224	C₄×C₄₃	—	4	1	no	—
225	C₄×C₄₃	—	4	1	no	—
226	C₄×C₄₃	—	8	2	no	—
227	C₄×C₄₃	—	8	2	no	—
228	C₄×C₄₃	—	8	2	no	—
229	C₄×C₄₃	#465	1	4	yes	—
230	C₄×C₄₃	#469	1	4	yes	—
231	C₄×C₄₃	#537	1	2	yes	—
232	C₄×C₄₃	#542	1	2	yes	—
233	C₂×#486	C₂×C₄₃	1	1	yes	characteristic, complemented
234	C₂×#431	C₂×C₄₃	1	1	yes	characteristic, complemented
235	#2857	C₂×C₄₃	1	1	yes	characteristic, complemented
236	#2856	C₂×C₄₃	1	1	yes	characteristic
237	#2065	C₂×C₄₃	1	4	yes	complemented
238	#2034	C₂×C₄₃	1	4	yes	complemented
239	#1990	C₂×C₄₃	1	1	yes	characteristic, complemented
240	#1957	C₂×C₄₃	1	1	yes	characteristic, complemented
241	#1844	C₂×C₄₃	1	1	yes	characteristic, complemented
242	C₂×C₄₃	—	4	2	no	—
243	C₂×C₄₃	—	16	2	no	—
244	C₂×C₄₃	#2620	1	1	yes	characteristic
245	C₂×C₄₃	C₂×#465	1	1	yes	characteristic
246	C₂×C₄₃	C₂×#469	1	1	yes	characteristic
247	C₂×C₄₃	#3207	1	1	yes	characteristic
248	C₂×C₄₃	#3208	1	1	yes	characteristic
249	C₂×C₄₃	#3227	1	1	yes	characteristic
250	C₂×C₄₃	#3228	1	1	yes	characteristic
251	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
252	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
253	C₂×C₂²⋊Q₈	—	2	1	no	—
254	C₂×#121	—	2	1	no	—
255	C₂×#121	—	2	1	no	—
256	C₂×#121	C₂²×C₄₃	1	2	yes	—
257	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
258	#486	—	2	4	no	—
259	#431	—	2	4	no	—
260	C₂×#106	C₂²×C₄₃	1	4	yes	—
261	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
262	C₂×#102	C₂²×C₄₃	1	4	yes	—
263	C₂×#102	C₂²×C₄₃	1	4	yes	—
264	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
265	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
266	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
267	#391	—	2	1	no	—
268	#390	—	2	1	no	—
269	#390	—	2	1	no	—
270	#390	C₂²×C₄₃	1	2	yes	—
271	#389	—	2	1	no	—
272	#389	C₂²×C₄₃	1	2	yes	—
273	#384	C₂²×C₄₃	1	1	yes	characteristic
274	#384	C₂²×C₄₃	1	1	yes	characteristic
275	#380	—	2	1	no	—
276	#380	C₂²×C₄₃	1	2	yes	—
277	#340	C₂²×C₄₃	1	4	yes	—
278	C₄₃	#29843	1	1	yes	characteristic, direct product factor, Sylow
279	C₂²×Q₈	—	2	1	no	—
280	C₂²×D₄	—	2	2	no	—
281	C₂²×D₄	—	2	1	no	—
282	C₂²×D₄	—	2	1	no	—
283	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
284	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
285	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
288	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
289	C₄⋊Q₈	—	2	2	no	—
290	C₄⋊Q₈	—	2	2	no	—
291	#127	—	2	2	no	—
292	#127	—	2	2	no	—
293	C₂²⋊Q₈	—	4	4	no	—
294	#121	—	4	4	no	—
295	#121	—	4	4	no	—
296	#121	—	4	4	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
313	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
316	#106	—	4	4	no	—
317	C₄⋊C₈	—	2	4	no	—
318	#102	—	2	8	no	—
319	#102	—	4	4	no	—
320	C₂²⋊C₈	—	2	4	no	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	D₄×C₄₃	1	4	yes	complemented
323	#95	—	2	2	no	—
324	#95	—	2	2	no	—
325	C₂⁴	—	2	2	no	—
326	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	4	4	no	—
335	C₂×D₄	—	4	4	no	—
336	C₂×D₄	—	4	4	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	SD₁₆×C₄₃	1	4	yes	—
356	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
361	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	4	4	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₂²⋊C₄	—	4	4	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	C₂×D₄×C₄₃	1	2	yes	—
387	C₄²	#41×C₄₃	1	2	yes	—
388	C₂³	—	2	1	no	—
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	C₂×SD₁₆×C₄₃	1	2	yes	—
402	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
403	Q₈	—	8	4	no	—
404	D₄	—	4	4	no	—
405	D₄	—	4	4	no	—
406	D₄	—	8	8	no	—
407	D₄	—	8	4	no	—
408	D₄	—	8	4	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	#121×C₄₃	1	2	yes	—
431	C₂×C₄	#121×C₄₃	1	2	yes	—
432	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
433	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
434	C₂×C₄	#135×C₄₃	1	2	yes	—
435	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
436	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
437	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
438	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
439	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
440	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
441	C₈	—	2	4	no	—
442	C₈	—	4	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	8	2	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	2	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	8	2	no	—
457	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
458	C₂²	C₄₃×#535	1	1	yes	characteristic
459	C₂²	C₄₃×#536	1	1	yes	characteristic
460	C₂²	C₂²×SD₁₆×C₄₃	1	1	yes	characteristic
461	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
462	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
463	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
464	C₄	—	2	2	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	1	no	—
467	C₄	—	8	2	no	—
468	C₄	—	8	2	no	—
469	C₄	—	8	2	no	—
470	C₄	C₄₃×#465	1	4	yes	—
471	C₄	C₄₃×#469	1	4	yes	—
472	C₄	C₄₃×#537	1	2	yes	—
473	C₄	C₄₃×#542	1	2	yes	—
474	C₂	—	4	2	no	—
475	C₂	—	16	2	no	—
476	C₂	C₄₃×#2620	1	1	yes	characteristic
477	C₂	C₂×C₄₃×#465	1	1	yes	characteristic
478	C₂	C₂×C₄₃×#469	1	1	yes	characteristic
479	C₂	C₄₃×#3207	1	1	yes	characteristic
480	C₂	C₄₃×#3208	1	1	yes	characteristic
481	C₂	C₄₃×#3227	1	1	yes	characteristic
482	C₂	C₄₃×#3228	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#2856	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#486	C₂	semidirect
2. C₂×C₄₃×#431	C₂	semidirect
3. C₄₃×#2857	C₂	semidirect
5. C₄₃×#2065	C₂	semidirect
6. C₄₃×#2034	C₂	semidirect
7. C₄₃×#1990	C₂	semidirect
8. C₄₃×#1957	C₂	semidirect
9. C₄₃×#1844	C₂	semidirect
80. C₄×C₈×C₄₃	D₄	semidirect
201. #29843	C₄₃	direct (N × H)
233. C₂×#486	C₂×C₄₃	semidirect
234. C₂×#431	C₂×C₄₃	semidirect
235. #2857	C₂×C₄₃	semidirect
237. #2065	C₂×C₄₃	semidirect
238. #2034	C₂×C₄₃	semidirect
239. #1990	C₂×C₄₃	semidirect
240. #1957	C₂×C₄₃	semidirect
241. #1844	C₂×C₄₃	semidirect
278. C₄₃	#29843	direct (N × H)
322. C₄×C₈	D₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#486	2
C₂×C₄₃×#431	2
C₄₃×#2857	2
C₄₃×#2856	2
C₄₃×#2065	2
C₄₃×#2034	2
C₄₃×#1990	2
C₄₃×#1957	2
C₄₃×#1844	2
#29843	43

Subgroups — C43×#29843 #24949860

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29843 #24949860