Subgroups — C₄₃×#29925 #24949942

Order 11008.

868 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#2856	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2092	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2073	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2034	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2033	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
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	C₂×#107×C₄₃	C₂²	1	2	yes	—
18	C₂×#106×C₄₃	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#102×C₄₃	C₂²	1	2	yes	—
22	C₂×#102×C₄₃	C₂²	1	2	yes	—
23	C₂×#102×C₄₃	C₂²	1	2	yes	—
24	C₂×#102×C₄₃	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
26	C₄₃×#390	—	2	1	no	—
27	C₄₃×#390	—	2	1	no	—
28	C₄₃×#390	C₂²	1	2	yes	—
29	C₄₃×#384	C₂²	1	1	yes	characteristic
30	C₄₃×#383	—	2	1	no	—
31	C₄₃×#382	C₂²	1	1	yes	characteristic
32	C₄₃×#382	C₂²	1	1	yes	characteristic
33	C₄₃×#381	—	2	1	no	—
34	C₄₃×#380	C₂²	1	1	yes	characteristic
35	C₄₃×#380	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
39	C₄₃×#376	—	2	1	no	—
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₄₃×#340	C₂²	1	2	yes	—
42	C₄₃×#336	C₂²	1	2	yes	—
43	C₂²×D₄×C₄₃	—	2	2	no	—
44	C₂²×D₄×C₄₃	—	2	1	no	—
45	C₂²×D₄×C₄₃	—	2	1	no	—
46	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
52	#127×C₄₃	—	2	2	no	—
53	#127×C₄₃	—	2	2	no	—
54	#121×C₄₃	—	4	2	no	—
55	#121×C₄₃	—	4	2	no	—
56	#121×C₄₃	—	4	4	no	—
57	#121×C₄₃	—	4	4	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₄²×C₄₃	—	2	2	no	—
71	C₂×C₄²×C₄₃	—	2	2	no	—
72	C₂×C₄²×C₄₃	—	2	1	no	—
73	C₂×C₄²×C₄₃	—	2	1	no	—
74	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
78	#107×C₄₃	—	4	2	no	—
79	#106×C₄₃	—	4	2	no	—
80	C₄⋊C₈×C₄₃	—	2	2	no	—
81	C₄⋊C₈×C₄₃	—	2	2	no	—
82	#102×C₄₃	—	4	2	no	—
83	#102×C₄₃	—	4	2	no	—
84	#102×C₄₃	—	4	2	no	—
85	#102×C₄₃	—	4	2	no	—
86	C₂²⋊C₈×C₄₃	—	4	2	no	—
87	#95×C₄₃	—	2	1	no	—
88	#95×C₄₃	—	2	1	no	—
89	#95×C₄₃	—	2	1	no	—
90	#95×C₄₃	—	2	1	no	—
91	#95×C₄₃	—	2	1	no	—
92	#95×C₄₃	—	2	1	no	—
93	#95×C₄₃	—	2	1	no	—
94	#95×C₄₃	—	2	1	no	—
95	C₂⁴×C₄₃	—	2	2	no	—
96	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₄₃	—	2	2	no	—
98	C₂×D₄×C₄₃	—	2	2	no	—
99	C₂×D₄×C₄₃	—	2	2	no	—
100	C₂×D₄×C₄₃	—	2	2	no	—
101	C₂×D₄×C₄₃	—	2	2	no	—
102	C₂×D₄×C₄₃	—	2	2	no	—
103	C₂×D₄×C₄₃	—	4	4	no	—
104	C₂×D₄×C₄₃	—	4	4	no	—
105	C₂×D₄×C₄₃	—	4	2	no	—
106	C₂×D₄×C₄₃	—	4	2	no	—
107	C₂×D₄×C₄₃	—	4	2	no	—
108	C₂×D₄×C₄₃	—	4	2	no	—
109	C₂×D₄×C₄₃	—	4	2	no	—
110	C₂×D₄×C₄₃	—	4	2	no	—
111	C₂×D₄×C₄₃	—	4	4	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	—	2	2	no	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	1	no	—
117	C₂²×C₄×C₄₃	—	2	1	no	—
118	C₂²×C₄×C₄₃	—	2	1	no	—
119	C₂²×C₄×C₄₃	—	2	1	no	—
120	C₂²×C₄×C₄₃	—	2	1	no	—
121	C₂²×C₄×C₄₃	—	2	1	no	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	—	2	1	no	—
124	C₂²×C₄×C₄₃	—	2	1	no	—
125	C₂²×C₄×C₄₃	—	2	1	no	—
126	C₂²×C₄×C₄₃	—	2	1	no	—
127	C₂²×C₄×C₄₃	—	2	2	no	—
128	C₂²×C₄×C₄₃	—	4	1	no	—
129	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	—	2	2	no	—
137	C₂×C₈×C₄₃	—	2	2	no	—
138	C₂×C₈×C₄₃	—	2	2	no	—
139	C₂×C₈×C₄₃	—	2	2	no	—
140	C₂×C₈×C₄₃	—	2	2	no	—
141	C₄⋊C₄×C₄₃	—	2	1	no	—
142	C₄⋊C₄×C₄₃	—	2	1	no	—
143	C₄⋊C₄×C₄₃	—	2	1	no	—
144	C₄⋊C₄×C₄₃	—	2	1	no	—
145	C₄⋊C₄×C₄₃	—	2	1	no	—
146	C₄⋊C₄×C₄₃	—	2	2	no	—
147	C₄⋊C₄×C₄₃	—	2	1	no	—
148	C₄⋊C₄×C₄₃	—	2	2	no	—
149	C₄⋊C₄×C₄₃	—	2	1	no	—
150	C₄⋊C₄×C₄₃	—	2	1	no	—
151	C₄⋊C₄×C₄₃	—	4	2	no	—
152	C₄⋊C₄×C₄₃	—	4	2	no	—
153	C₂²⋊C₄×C₄₃	—	4	2	no	—
154	C₂²⋊C₄×C₄₃	—	4	4	no	—
155	C₂²⋊C₄×C₄₃	—	4	4	no	—
156	C₂²⋊C₄×C₄₃	—	4	4	no	—
157	C₂²⋊C₄×C₄₃	—	4	2	no	—
158	C₄²×C₄₃	—	2	2	no	—
159	C₄²×C₄₃	—	2	2	no	—
160	C₄²×C₄₃	—	2	1	no	—
161	C₄²×C₄₃	—	2	1	no	—
162	C₄²×C₄₃	—	4	2	no	—
163	C₄²×C₄₃	—	4	2	no	—
164	C₄²×C₄₃	#41	1	2	yes	—
165	C₄²×C₄₃	#41	1	2	yes	—
166	C₂³×C₄₃	—	2	1	no	—
167	C₂³×C₄₃	—	2	1	no	—
168	C₂³×C₄₃	—	2	1	no	—
169	C₂³×C₄₃	—	2	1	no	—
170	C₂³×C₄₃	—	2	1	no	—
171	C₂³×C₄₃	—	2	1	no	—
172	C₂³×C₄₃	—	4	2	no	—
173	C₂³×C₄₃	—	4	2	no	—
174	C₂³×C₄₃	—	4	2	no	—
175	C₂³×C₄₃	—	4	2	no	—
176	C₂³×C₄₃	—	4	2	no	—
177	C₂³×C₄₃	—	4	2	no	—
178	C₂³×C₄₃	—	4	2	no	—
179	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
180	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
181	D₄×C₄₃	—	4	2	no	—
182	D₄×C₄₃	—	4	2	no	—
183	D₄×C₄₃	—	4	2	no	—
184	D₄×C₄₃	—	4	2	no	—
185	D₄×C₄₃	—	8	4	no	—
186	D₄×C₄₃	—	8	8	no	—
187	D₄×C₄₃	—	8	4	no	—
188	C₂×C₄×C₄₃	—	2	1	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	2	1	no	—
191	C₂×C₄×C₄₃	—	2	1	no	—
192	C₂×C₄×C₄₃	—	2	1	no	—
193	C₂×C₄×C₄₃	—	2	1	no	—
194	C₂×C₄×C₄₃	—	2	1	no	—
195	C₂×C₄×C₄₃	—	2	1	no	—
196	C₂×C₄×C₄₃	—	2	1	no	—
197	C₂×C₄×C₄₃	—	2	1	no	—
198	C₂×C₄×C₄₃	—	2	1	no	—
199	C₂×C₄×C₄₃	—	4	4	no	—
200	C₂×C₄×C₄₃	—	4	1	no	—
201	C₂×C₄×C₄₃	—	4	1	no	—
202	C₂×C₄×C₄₃	—	4	1	no	—
203	C₂×C₄×C₄₃	—	4	1	no	—
204	C₂×C₄×C₄₃	—	4	4	no	—
205	C₂×C₄×C₄₃	—	4	2	no	—
206	C₂×C₄×C₄₃	—	4	1	no	—
207	C₂×C₄×C₄₃	—	4	1	no	—
208	C₂×C₄×C₄₃	—	4	1	no	—
209	C₂×C₄×C₄₃	—	4	1	no	—
210	C₂×C₄×C₄₃	—	4	1	no	—
211	C₂×C₄×C₄₃	—	4	1	no	—
212	C₂×C₄×C₄₃	—	4	1	no	—
213	C₂×C₄×C₄₃	—	4	1	no	—
214	C₂×C₄×C₄₃	—	4	2	no	—
215	C₂×C₄×C₄₃	—	4	2	no	—
216	C₂×C₄×C₄₃	—	4	1	no	—
217	C₂×C₄×C₄₃	—	4	1	no	—
218	C₂×C₄×C₄₃	—	4	1	no	—
219	C₂×C₄×C₄₃	—	4	1	no	—
220	C₂×C₄×C₄₃	#123	1	2	yes	—
221	C₂×C₄×C₄₃	#123	1	2	yes	—
222	C₂×C₄×C₄₃	#135	1	2	yes	—
223	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
224	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
229	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
230	C₈×C₄₃	—	4	2	no	—
231	C₈×C₄₃	—	4	2	no	—
232	#29925	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂²×C₄₃	—	2	2	no	—
234	C₂²×C₄₃	—	2	2	no	—
235	C₂²×C₄₃	—	2	2	no	—
236	C₂²×C₄₃	—	4	1	no	—
237	C₂²×C₄₃	—	4	1	no	—
238	C₂²×C₄₃	—	4	1	no	—
239	C₂²×C₄₃	—	4	1	no	—
240	C₂²×C₄₃	—	8	2	no	—
241	C₂²×C₄₃	—	8	2	no	—
242	C₂²×C₄₃	—	8	2	no	—
243	C₂²×C₄₃	—	8	2	no	—
244	C₂²×C₄₃	—	8	2	no	—
245	C₂²×C₄₃	—	8	2	no	—
246	C₂²×C₄₃	—	8	2	no	—
247	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
248	C₂²×C₄₃	#535	1	1	yes	characteristic
249	C₂²×C₄₃	#537	1	1	yes	characteristic
250	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
251	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
252	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
253	C₂²×C₄₃	#575	1	1	yes	characteristic
254	C₄×C₄₃	—	2	2	no	—
255	C₄×C₄₃	—	4	1	no	—
256	C₄×C₄₃	—	4	1	no	—
257	C₄×C₄₃	—	4	1	no	—
258	C₄×C₄₃	—	8	1	no	—
259	C₄×C₄₃	—	8	1	no	—
260	C₄×C₄₃	—	8	2	no	—
261	C₄×C₄₃	—	8	1	no	—
262	C₄×C₄₃	—	8	1	no	—
263	C₄×C₄₃	#482	1	4	yes	—
264	C₄×C₄₃	#540	1	1	yes	characteristic
265	C₄×C₄₃	#540	1	1	yes	characteristic
266	C₄×C₄₃	#542	1	1	yes	characteristic
267	C₄×C₄₃	#542	1	1	yes	characteristic
268	#2856	C₂×C₄₃	1	1	yes	characteristic
269	#2283	C₂×C₄₃	1	1	yes	characteristic, complemented
270	#2092	C₂×C₄₃	1	2	yes	complemented
271	#2073	C₂×C₄₃	1	2	yes	complemented
272	#2034	C₂×C₄₃	1	2	yes	complemented
273	#2033	C₂×C₄₃	1	2	yes	complemented
274	#1982	C₂×C₄₃	1	1	yes	characteristic, complemented
275	#1982	C₂×C₄₃	1	1	yes	characteristic, complemented
276	#1948	C₂×C₄₃	1	1	yes	characteristic, complemented
277	#1947	C₂×C₄₃	1	1	yes	characteristic, complemented
278	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
279	C₂×C₄₃	—	4	2	no	—
280	C₂×C₄₃	—	16	2	no	—
281	C₂×C₄₃	#2624	1	1	yes	characteristic
282	C₂×C₄₃	C₂×#482	1	1	yes	characteristic
283	C₂×C₄₃	#3094	1	1	yes	characteristic
284	C₂×C₄₃	#3212	1	1	yes	characteristic
285	C₂×C₄₃	#3217	1	1	yes	characteristic
286	C₂×C₄₃	#3247	1	1	yes	characteristic
287	C₂×C₄₃	#3251	1	1	yes	characteristic
288	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
289	C₂×#121	—	2	1	no	—
290	C₂×#121	—	2	1	no	—
291	C₂×#121	C₂²×C₄₃	1	2	yes	—
292	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
293	C₂×#107	C₂²×C₄₃	1	2	yes	—
294	C₂×#106	C₂²×C₄₃	1	2	yes	—
295	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
296	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
297	C₂×#102	C₂²×C₄₃	1	2	yes	—
298	C₂×#102	C₂²×C₄₃	1	2	yes	—
299	C₂×#102	C₂²×C₄₃	1	2	yes	—
300	C₂×#102	C₂²×C₄₃	1	2	yes	—
301	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
302	#390	—	2	1	no	—
303	#390	—	2	1	no	—
304	#390	C₂²×C₄₃	1	2	yes	—
305	#384	C₂²×C₄₃	1	1	yes	characteristic
306	#383	—	2	1	no	—
307	#382	C₂²×C₄₃	1	1	yes	characteristic
308	#382	C₂²×C₄₃	1	1	yes	characteristic
309	#381	—	2	1	no	—
310	#380	C₂²×C₄₃	1	1	yes	characteristic
311	#380	C₂²×C₄₃	1	1	yes	characteristic
312	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
313	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
314	C₄×C₂²⋊C₄	—	2	1	no	—
315	#376	—	2	1	no	—
316	#340	C₂²×C₄₃	1	2	yes	—
317	#340	C₂²×C₄₃	1	2	yes	—
318	#336	C₂²×C₄₃	1	2	yes	—
319	C₄₃	#29925	1	1	yes	characteristic, direct product factor, Sylow
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	—	2	1	no	—
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
324	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
325	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
328	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
329	#127	—	2	2	no	—
330	#127	—	2	2	no	—
331	#121	—	4	2	no	—
332	#121	—	4	2	no	—
333	#121	—	4	4	no	—
334	#121	—	4	4	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	—	2	2	no	—
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
352	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
355	#107	—	4	2	no	—
356	#106	—	4	2	no	—
357	C₄⋊C₈	—	2	2	no	—
358	C₄⋊C₈	—	2	2	no	—
359	#102	—	4	2	no	—
360	#102	—	4	2	no	—
361	#102	—	4	2	no	—
362	#102	—	4	2	no	—
363	C₂²⋊C₈	—	4	2	no	—
364	#95	—	2	1	no	—
365	#95	—	2	1	no	—
366	#95	—	2	1	no	—
367	#95	—	2	1	no	—
368	#95	—	2	1	no	—
369	#95	—	2	1	no	—
370	#95	—	2	1	no	—
371	#95	—	2	1	no	—
372	C₂⁴	—	2	2	no	—
373	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	4	4	no	—
383	C₂×D₄	—	4	4	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂×D₄	—	4	2	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	—	4	2	no	—
388	C₂×D₄	—	4	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	4	1	no	—
406	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
411	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	4	2	no	—
429	C₄⋊C₄	—	4	2	no	—
430	C₂²⋊C₄	—	4	4	no	—
431	C₂²⋊C₄	—	4	4	no	—
432	C₂²⋊C₄	—	4	4	no	—
433	C₂²⋊C₄	—	4	2	no	—
434	C₂²⋊C₄	—	4	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	4	2	no	—
440	C₄²	—	4	2	no	—
441	C₄²	#41×C₄₃	1	2	yes	—
442	C₄²	#41×C₄₃	1	2	yes	—
443	C₂³	—	2	1	no	—
444	C₂³	—	2	1	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
457	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	4	2	no	—
462	D₄	—	8	4	no	—
463	D₄	—	8	8	no	—
464	D₄	—	8	4	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	#123×C₄₃	1	2	yes	—
498	C₂×C₄	#123×C₄₃	1	2	yes	—
499	C₂×C₄	#135×C₄₃	1	2	yes	—
500	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
501	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
502	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
503	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
504	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
505	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
506	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
507	C₈	—	4	2	no	—
508	C₈	—	4	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	4	1	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	1	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	8	2	no	—
517	C₂²	—	8	2	no	—
518	C₂²	—	8	2	no	—
519	C₂²	—	8	2	no	—
520	C₂²	—	8	2	no	—
521	C₂²	—	8	2	no	—
522	C₂²	—	8	2	no	—
523	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
524	C₂²	C₄₃×#535	1	1	yes	characteristic
525	C₂²	C₄₃×#537	1	1	yes	characteristic
526	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
527	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
528	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
529	C₂²	C₄₃×#575	1	1	yes	characteristic
530	C₄	—	2	2	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	8	1	no	—
535	C₄	—	8	2	no	—
536	C₄	—	8	1	no	—
537	C₄	—	8	1	no	—
538	C₄	—	8	1	no	—
539	C₄	C₄₃×#482	1	4	yes	—
540	C₄	C₄₃×#540	1	1	yes	characteristic
541	C₄	C₄₃×#540	1	1	yes	characteristic
542	C₄	C₄₃×#542	1	1	yes	characteristic
543	C₄	C₄₃×#542	1	1	yes	characteristic
544	C₂	—	4	2	no	—
545	C₂	—	16	2	no	—
546	C₂	C₄₃×#2624	1	1	yes	characteristic
547	C₂	C₂×C₄₃×#482	1	1	yes	characteristic
548	C₂	C₄₃×#3094	1	1	yes	characteristic
549	C₂	C₄₃×#3212	1	1	yes	characteristic
550	C₂	C₄₃×#3217	1	1	yes	characteristic
551	C₂	C₄₃×#3247	1	1	yes	characteristic
552	C₂	C₄₃×#3251	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
2. C₄₃×#2283	C₂	semidirect
3. C₄₃×#2092	C₂	semidirect
4. C₄₃×#2073	C₂	semidirect
5. C₄₃×#2034	C₂	semidirect
6. C₄₃×#2033	C₂	semidirect
7. C₄₃×#1982	C₂	semidirect
8. C₄₃×#1982	C₂	semidirect
9. C₄₃×#1948	C₂	semidirect
10. C₄₃×#1947	C₂	semidirect
11. C₄₃×#1797	C₂	semidirect
232. #29925	C₄₃	direct (N × H)
269. #2283	C₂×C₄₃	semidirect
270. #2092	C₂×C₄₃	semidirect
271. #2073	C₂×C₄₃	semidirect
272. #2034	C₂×C₄₃	semidirect
273. #2033	C₂×C₄₃	semidirect
274. #1982	C₂×C₄₃	semidirect
275. #1982	C₂×C₄₃	semidirect
276. #1948	C₂×C₄₃	semidirect
277. #1947	C₂×C₄₃	semidirect
278. #1797	C₂×C₄₃	semidirect
319. C₄₃	#29925	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×#2856	2
C₄₃×#2283	2
C₄₃×#2092	2
C₄₃×#2073	2
C₄₃×#2034	2
C₄₃×#2033	2
C₄₃×#1982	2
C₄₃×#1948	2
C₄₃×#1947	2
C₄₃×#1797	2
#29925	43

Subgroups — C43×#29925 #24949942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29925 #24949942