Subgroups — C₄₃×#28551 #24948568

Order 11008.

1086 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2416	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2086	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2075	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2054	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1934	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1893	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1874	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₃×#340	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#121×C₄₃	—	2	2	no	—
16	C₂×#121×C₄₃	C₂²	1	2	yes	—
17	C₂×#121×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
20	C₄₃×#466	—	2	4	no	—
21	C₈×D₄×C₄₃	—	2	4	no	—
22	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#102×C₄₃	C₂²	1	2	yes	—
25	C₂×#102×C₄₃	C₂²	1	2	yes	—
26	C₂×#102×C₄₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#396	—	2	2	no	—
31	C₄₃×#394	—	2	2	no	—
32	C₄₃×#390	C₂²	1	2	yes	—
33	C₄₃×#389	C₂²	1	2	yes	—
34	C₄₃×#386	—	2	2	no	—
35	C₄₃×#380	C₂²	1	2	yes	—
36	C₄₃×#340	C₂²	1	2	yes	—
37	C₄₃×#340	C₂²	1	1	yes	characteristic
38	C₄₃×#340	C₂²	1	2	yes	—
39	C₄₃×#340	C₂²	1	1	yes	characteristic
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₂²×D₄×C₄₃	—	2	2	no	—
42	C₂²×D₄×C₄₃	—	2	2	no	—
43	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₃	—	2	2	no	—
46	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
48	C₂×D₈×C₄₃	—	2	2	no	—
49	C₂×D₈×C₄₃	—	4	2	no	—
50	C₂²×C₈×C₄₃	—	2	2	no	—
51	C₂²×C₈×C₄₃	—	4	2	no	—
52	C₂²×C₈×C₄₃	—	4	2	no	—
53	C₂²×C₈×C₄₃	D₄	1	4	yes	complemented
54	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
58	#121×C₄₃	—	2	4	no	—
59	#121×C₄₃	—	2	4	no	—
60	#121×C₄₃	—	2	4	no	—
61	#121×C₄₃	—	4	2	no	—
62	#121×C₄₃	—	4	8	no	—
63	C₄×D₄×C₄₃	—	2	2	no	—
64	C₄×D₄×C₄₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
69	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
81	#107×C₄₃	—	2	2	no	—
82	C₄⋊C₈×C₄₃	—	2	2	no	—
83	#102×C₄₃	—	2	4	no	—
84	#102×C₄₃	—	2	4	no	—
85	#102×C₄₃	—	4	2	no	—
86	C₂²⋊C₈×C₄₃	—	2	2	no	—
87	C₂²⋊C₈×C₄₃	—	2	2	no	—
88	C₄×C₈×C₄₃	—	2	2	no	—
89	#95×C₄₃	—	2	2	no	—
90	#95×C₄₃	—	2	2	no	—
91	C₂⁴×C₄₃	—	2	2	no	—
92	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
94	C₂×D₄×C₄₃	—	2	2	no	—
95	C₂×D₄×C₄₃	—	2	2	no	—
96	C₂×D₄×C₄₃	—	2	2	no	—
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	—	4	4	no	—
103	C₂×D₄×C₄₃	—	4	4	no	—
104	C₂×D₄×C₄₃	—	4	4	no	—
105	C₂×D₄×C₄₃	—	4	4	no	—
106	C₂×D₄×C₄₃	—	4	4	no	—
107	C₂×D₄×C₄₃	—	8	2	no	—
108	C₂×D₄×C₄₃	D₈	1	4	yes	complemented
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	2	1	no	—
112	C₂²×C₄×C₄₃	—	2	1	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	2	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	4	4	no	—
119	C₂²×C₄×C₄₃	—	4	4	no	—
120	C₂²×C₄×C₄₃	—	8	2	no	—
121	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	#41	1	2	yes	—
127	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
128	D₈×C₄₃	—	4	4	no	—
129	C₂×C₈×C₄₃	—	2	2	no	—
130	C₂×C₈×C₄₃	—	2	2	no	—
131	C₂×C₈×C₄₃	—	2	1	no	—
132	C₂×C₈×C₄₃	—	2	1	no	—
133	C₂×C₈×C₄₃	—	2	2	no	—
134	C₂×C₈×C₄₃	—	2	2	no	—
135	C₂×C₈×C₄₃	—	4	4	no	—
136	C₂×C₈×C₄₃	—	4	4	no	—
137	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	—	2	2	no	—
141	C₄⋊C₄×C₄₃	—	2	2	no	—
142	C₄⋊C₄×C₄₃	—	2	2	no	—
143	C₄⋊C₄×C₄₃	—	2	2	no	—
144	C₄⋊C₄×C₄₃	—	2	2	no	—
145	C₄⋊C₄×C₄₃	—	4	4	no	—
146	C₄⋊C₄×C₄₃	—	4	4	no	—
147	C₄⋊C₄×C₄₃	#41	1	4	yes	—
148	C₂²⋊C₄×C₄₃	—	2	2	no	—
149	C₂²⋊C₄×C₄₃	—	2	2	no	—
150	C₂²⋊C₄×C₄₃	—	4	4	no	—
151	C₂²⋊C₄×C₄₃	—	4	4	no	—
152	C₂²⋊C₄×C₄₃	—	4	4	no	—
153	C₂²⋊C₄×C₄₃	—	4	4	no	—
154	C₂²⋊C₄×C₄₃	—	8	2	no	—
155	C₄²×C₄₃	—	2	1	no	—
156	C₄²×C₄₃	—	2	1	no	—
157	C₂³×C₄₃	—	2	2	no	—
158	C₂³×C₄₃	—	2	2	no	—
159	C₂³×C₄₃	—	2	1	no	—
160	C₂³×C₄₃	—	2	2	no	—
161	C₂³×C₄₃	—	2	1	no	—
162	C₂³×C₄₃	—	2	2	no	—
163	C₂³×C₄₃	—	4	2	no	—
164	C₂³×C₄₃	—	4	2	no	—
165	C₂³×C₄₃	—	4	2	no	—
166	C₂³×C₄₃	—	4	2	no	—
167	C₂³×C₄₃	—	4	2	no	—
168	C₂³×C₄₃	—	4	2	no	—
169	C₂³×C₄₃	—	4	2	no	—
170	C₂³×C₄₃	#121	1	2	yes	—
171	C₂³×C₄₃	C₂×D₈	1	2	yes	—
172	C₂³×C₄₃	C₂×D₈	1	2	yes	—
173	C₂³×C₄₃	#135	1	2	yes	—
174	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
175	D₄×C₄₃	—	2	8	no	—
176	D₄×C₄₃	—	4	2	no	—
177	D₄×C₄₃	—	4	2	no	—
178	D₄×C₄₃	—	4	2	no	—
179	D₄×C₄₃	—	4	2	no	—
180	D₄×C₄₃	—	8	8	no	—
181	D₄×C₄₃	—	8	8	no	—
182	C₂×C₄×C₄₃	—	2	1	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	2	1	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	2	no	—
187	C₂×C₄×C₄₃	—	2	4	no	—
188	C₂×C₄×C₄₃	—	2	1	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	2	2	no	—
191	C₂×C₄×C₄₃	—	2	4	no	—
192	C₂×C₄×C₄₃	—	2	2	no	—
193	C₂×C₄×C₄₃	—	4	2	no	—
194	C₂×C₄×C₄₃	—	4	2	no	—
195	C₂×C₄×C₄₃	—	4	1	no	—
196	C₂×C₄×C₄₃	—	4	1	no	—
197	C₂×C₄×C₄₃	—	4	2	no	—
198	C₂×C₄×C₄₃	—	4	2	no	—
199	C₂×C₄×C₄₃	—	4	2	no	—
200	C₂×C₄×C₄₃	—	4	2	no	—
201	C₂×C₄×C₄₃	—	4	2	no	—
202	C₂×C₄×C₄₃	—	4	2	no	—
203	C₂×C₄×C₄₃	—	4	2	no	—
204	C₂×C₄×C₄₃	—	8	8	no	—
205	C₂×C₄×C₄₃	#121	1	2	yes	—
206	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
207	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
209	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
211	C₈×C₄₃	—	2	2	no	—
212	C₈×C₄₃	—	2	2	no	—
213	C₈×C₄₃	—	4	1	no	—
214	C₈×C₄₃	—	4	1	no	—
215	#28551	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂²×C₄₃	—	2	4	no	—
217	C₂²×C₄₃	—	2	4	no	—
218	C₂²×C₄₃	—	2	2	no	—
219	C₂²×C₄₃	—	2	2	no	—
220	C₂²×C₄₃	—	2	4	no	—
221	C₂²×C₄₃	—	2	2	no	—
222	C₂²×C₄₃	—	4	2	no	—
223	C₂²×C₄₃	—	4	1	no	—
224	C₂²×C₄₃	—	4	1	no	—
225	C₂²×C₄₃	—	8	2	no	—
226	C₂²×C₄₃	—	8	2	no	—
227	C₂²×C₄₃	—	8	2	no	—
228	C₂²×C₄₃	—	8	2	no	—
229	C₂²×C₄₃	—	8	2	no	—
230	C₂²×C₄₃	—	8	2	no	—
231	C₂²×C₄₃	—	8	2	no	—
232	C₂²×C₄₃	#466	1	4	yes	—
233	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
234	C₂²×C₄₃	#546	1	2	yes	—
235	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
236	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
237	C₂²×C₄₃	#577	1	2	yes	—
238	C₄×C₄₃	—	2	2	no	—
239	C₄×C₄₃	—	2	2	no	—
240	C₄×C₄₃	—	4	4	no	—
241	C₄×C₄₃	—	4	1	no	—
242	C₄×C₄₃	—	4	1	no	—
243	C₄×C₄₃	—	8	2	no	—
244	C₄×C₄₃	—	8	2	no	—
245	C₄×C₄₃	#532	1	1	yes	characteristic
246	C₄×C₄₃	#534	1	1	yes	characteristic
247	C₄×C₄₃	#553	1	2	yes	—
248	C₂×#466	C₂×C₄₃	1	1	yes	characteristic, complemented
249	C₂×C₈×D₄	C₂×C₄₃	1	1	yes	characteristic, complemented
250	#2416	C₂×C₄₃	1	2	yes	complemented
251	#2086	C₂×C₄₃	1	1	yes	characteristic, complemented
252	#2075	C₂×C₄₃	1	1	yes	characteristic, complemented
253	#2054	C₂×C₄₃	1	1	yes	characteristic, complemented
254	#1999	C₂×C₄₃	1	1	yes	characteristic, complemented
255	#1934	C₂×C₄₃	1	2	yes	complemented
256	#1893	C₂×C₄₃	1	2	yes	complemented
257	#1874	C₂×C₄₃	1	2	yes	complemented
258	C₂×#340	C₂×C₄₃	1	1	yes	characteristic, complemented
259	C₂×C₄₃	—	2	4	no	—
260	C₂×C₄₃	—	4	2	no	—
261	C₂×C₄₃	—	16	2	no	—
262	C₂×C₄₃	#2543	1	1	yes	characteristic
263	C₂×C₄₃	C₂×#466	1	1	yes	characteristic
264	C₂×C₄₃	#3060	1	1	yes	characteristic
265	C₂×C₄₃	#3294	1	2	yes	—
266	C₂×C₄₃	#3301	1	2	yes	—
267	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic
268	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
269	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
270	C₂×#121	—	2	2	no	—
271	C₂×#121	C₂²×C₄₃	1	2	yes	—
272	C₂×#121	C₂²×C₄₃	1	2	yes	—
273	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
275	#466	—	2	4	no	—
276	C₈×D₄	—	2	4	no	—
277	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
278	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
279	C₂×#102	C₂²×C₄₃	1	2	yes	—
280	C₂×#102	C₂²×C₄₃	1	2	yes	—
281	C₂×#102	C₂²×C₄₃	1	2	yes	—
282	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
284	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
285	#396	—	2	2	no	—
286	#394	—	2	2	no	—
287	#390	C₂²×C₄₃	1	2	yes	—
288	#389	C₂²×C₄₃	1	2	yes	—
289	#386	—	2	2	no	—
290	#380	C₂²×C₄₃	1	2	yes	—
291	#340	C₂²×C₄₃	1	1	yes	characteristic
292	#340	C₂²×C₄₃	1	2	yes	—
293	#340	C₂²×C₄₃	1	2	yes	—
294	#340	C₂²×C₄₃	1	1	yes	characteristic
295	#340	C₂²×C₄₃	1	2	yes	—
296	C₄₃	#28551	1	1	yes	characteristic, direct product factor, Sylow
297	C₂²×D₄	—	2	2	no	—
298	C₂²×D₄	—	2	2	no	—
299	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
300	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
301	C₂³×C₄	—	2	2	no	—
302	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
303	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
304	C₂×D₈	—	2	2	no	—
305	C₂×D₈	—	4	2	no	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	4	2	no	—
308	C₂²×C₈	—	4	2	no	—
309	C₂²×C₈	D₄×C₄₃	1	4	yes	complemented
310	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
314	#121	—	2	4	no	—
315	#121	—	2	4	no	—
316	#121	—	2	4	no	—
317	#121	—	4	2	no	—
318	#121	—	4	8	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	4	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	4	2	no	—
325	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
337	#107	—	2	2	no	—
338	C₄⋊C₈	—	2	2	no	—
339	#102	—	2	4	no	—
340	#102	—	2	4	no	—
341	#102	—	4	2	no	—
342	C₂²⋊C₈	—	2	2	no	—
343	C₂²⋊C₈	—	2	2	no	—
344	C₄×C₈	—	2	2	no	—
345	#95	—	2	2	no	—
346	#95	—	2	2	no	—
347	C₂⁴	—	2	2	no	—
348	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
349	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	—	4	4	no	—
361	C₂×D₄	—	4	4	no	—
362	C₂×D₄	—	4	4	no	—
363	C₂×D₄	—	8	2	no	—
364	C₂×D₄	D₈×C₄₃	1	4	yes	complemented
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	4	4	no	—
375	C₂²×C₄	—	4	4	no	—
376	C₂²×C₄	—	8	2	no	—
377	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
382	C₂²×C₄	#41×C₄₃	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
384	D₈	—	4	4	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	4	4	no	—
392	C₂×C₈	—	4	4	no	—
393	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
394	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	4	4	no	—
402	C₄⋊C₄	—	4	4	no	—
403	C₄⋊C₄	#41×C₄₃	1	4	yes	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	4	4	no	—
407	C₂²⋊C₄	—	4	4	no	—
408	C₂²⋊C₄	—	4	4	no	—
409	C₂²⋊C₄	—	4	4	no	—
410	C₂²⋊C₄	—	8	2	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	#121×C₄₃	1	2	yes	—
427	C₂³	C₂×D₈×C₄₃	1	2	yes	—
428	C₂³	C₂×D₈×C₄₃	1	2	yes	—
429	C₂³	#135×C₄₃	1	2	yes	—
430	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
431	D₄	—	2	8	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	8	8	no	—
437	D₄	—	8	8	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	8	8	no	—
461	C₂×C₄	#121×C₄₃	1	2	yes	—
462	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
463	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
464	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
465	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
466	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	4	1	no	—
470	C₈	—	4	1	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	8	2	no	—
481	C₂²	—	8	2	no	—
482	C₂²	—	8	2	no	—
483	C₂²	—	8	2	no	—
484	C₂²	—	8	2	no	—
485	C₂²	—	8	2	no	—
486	C₂²	—	8	2	no	—
487	C₂²	C₄₃×#466	1	4	yes	—
488	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
489	C₂²	C₄₃×#546	1	2	yes	—
490	C₂²	C₂²×D₈×C₄₃	1	1	yes	characteristic
491	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
492	C₂²	C₄₃×#577	1	2	yes	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	8	2	no	—
499	C₄	—	8	2	no	—
500	C₄	C₄₃×#532	1	1	yes	characteristic
501	C₄	C₄₃×#534	1	1	yes	characteristic
502	C₄	C₄₃×#553	1	2	yes	—
503	C₂	—	2	4	no	—
504	C₂	—	4	2	no	—
505	C₂	—	16	2	no	—
506	C₂	C₄₃×#2543	1	1	yes	characteristic
507	C₂	C₂×C₄₃×#466	1	1	yes	characteristic
508	C₂	C₄₃×#3060	1	1	yes	characteristic
509	C₂	C₄₃×#3294	1	2	yes	—
510	C₂	C₄₃×#3301	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#466	C₂	semidirect
2. C₂×C₈×D₄×C₄₃	C₂	semidirect
3. C₄₃×#2416	C₂	semidirect
4. C₄₃×#2086	C₂	semidirect
5. C₄₃×#2075	C₂	semidirect
6. C₄₃×#2054	C₂	semidirect
7. C₄₃×#1999	C₂	semidirect
8. C₄₃×#1934	C₂	semidirect
9. C₄₃×#1893	C₂	semidirect
10. C₄₃×#1874	C₂	semidirect
11. C₂×C₄₃×#340	C₂	semidirect
53. C₂²×C₈×C₄₃	D₄	semidirect
108. C₂×D₄×C₄₃	D₈	semidirect
215. #28551	C₄₃	direct (N × H)
248. C₂×#466	C₂×C₄₃	semidirect
249. C₂×C₈×D₄	C₂×C₄₃	semidirect
250. #2416	C₂×C₄₃	semidirect
251. #2086	C₂×C₄₃	semidirect
252. #2075	C₂×C₄₃	semidirect
253. #2054	C₂×C₄₃	semidirect
254. #1999	C₂×C₄₃	semidirect
255. #1934	C₂×C₄₃	semidirect
256. #1893	C₂×C₄₃	semidirect
257. #1874	C₂×C₄₃	semidirect
258. C₂×#340	C₂×C₄₃	semidirect
296. C₄₃	#28551	direct (N × H)
309. C₂²×C₈	D₄×C₄₃	semidirect
364. C₂×D₄	D₈×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×#466	2
C₂×C₈×D₄×C₄₃	2
C₄₃×#2416	2
C₄₃×#2086	2
C₄₃×#2075	2
C₄₃×#2054	2
C₄₃×#1999	2
C₄₃×#1934	2
C₄₃×#1893	2
C₄₃×#1874	2
C₂×C₄₃×#340	2
#28551	43

Subgroups — C43×#28551 #24948568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28551 #24948568