Subgroups — C₄₃×#28618 #24948635

Order 11008.

1024 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#496	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2861	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#127×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2055	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2054	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1992	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1959	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1879	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1877	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
13	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
14	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₄₃	—	2	1	no	—
18	C₂×C₄×D₄×C₄₃	—	2	1	no	—
19	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
20	C₄₃×#496	—	2	4	no	—
21	C₄₃×#490	—	2	4	no	—
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
23	C₂×#103×C₄₃	C₂²	1	2	yes	—
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×#97×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
29	C₄₃×#391	C₂²	1	1	yes	characteristic
30	C₄₃×#391	C₂²	1	1	yes	characteristic
31	C₄₃×#390	—	2	1	no	—
32	C₄₃×#390	—	2	1	no	—
33	C₄₃×#390	C₂²	1	1	yes	characteristic
34	C₄₃×#390	C₂²	1	1	yes	characteristic
35	C₄₃×#390	C₂²	1	2	yes	—
36	C₄₃×#388	—	2	1	no	—
37	C₄₃×#388	—	2	1	no	—
38	C₄₃×#388	—	2	1	no	—
39	C₄₃×#388	—	2	1	no	—
40	C₄₃×#384	C₂²	1	1	yes	characteristic
41	C₄³×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#340	C₂²	1	2	yes	—
43	C₄₃×#340	C₂²	1	2	yes	—
44	C₄₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₄₃	—	2	1	no	—
47	C₂²×D₄×C₄₃	—	2	1	no	—
48	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₄₃	—	2	2	no	—
51	C₂×SD₁₆×C₄₃	—	2	4	no	—
52	C₂×SD₁₆×C₄₃	—	2	4	no	—
53	C₂×SD₁₆×C₄₃	—	4	2	no	—
54	C₂×D₈×C₄₃	—	2	4	no	—
55	C₂×D₈×C₄₃	—	2	4	no	—
56	C₂×D₈×C₄₃	—	4	2	no	—
57	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
59	#127×C₄₃	—	2	2	no	—
60	#127×C₄₃	D₄	1	4	yes	—
61	#125×C₄₃	—	2	2	no	—
62	#125×C₄₃	—	2	2	no	—
63	#124×C₄₃	—	2	2	no	—
64	#124×C₄₃	—	2	2	no	—
65	C₄×D₄×C₄₃	—	4	2	no	—
66	C₄×D₄×C₄₃	—	4	2	no	—
67	C₄×D₄×C₄₃	—	4	4	no	—
68	C₄×D₄×C₄₃	—	4	4	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
85	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₄₃	—	2	4	no	—
93	#103×C₄₃	—	4	2	no	—
94	#102×C₄₃	—	2	4	no	—
95	#102×C₄₃	—	2	4	no	—
96	#102×C₄₃	—	4	2	no	—
97	#97×C₄₃	—	2	2	no	—
98	#97×C₄₃	—	2	2	no	—
99	#95×C₄₃	—	2	1	no	—
100	#95×C₄₃	—	2	1	no	—
101	#95×C₄₃	—	2	1	no	—
102	#95×C₄₃	—	2	1	no	—
103	C₂⁴×C₄₃	—	2	2	no	—
104	C₂⁴×C₄₃	—	2	1	no	—
105	C₂×Q₈×C₄₃	—	2	1	no	—
106	C₂×Q₈×C₄₃	—	2	1	no	—
107	C₂×Q₈×C₄₃	—	2	2	no	—
108	C₂×Q₈×C₄₃	—	2	2	no	—
109	C₂×D₄×C₄₃	—	2	4	no	—
110	C₂×D₄×C₄₃	—	2	4	no	—
111	C₂×D₄×C₄₃	—	2	2	no	—
112	C₂×D₄×C₄₃	—	2	1	no	—
113	C₂×D₄×C₄₃	—	2	2	no	—
114	C₂×D₄×C₄₃	—	2	2	no	—
115	C₂×D₄×C₄₃	—	2	1	no	—
116	C₂×D₄×C₄₃	—	2	2	no	—
117	C₂×D₄×C₄₃	—	2	2	no	—
118	C₂×D₄×C₄₃	—	2	2	no	—
119	C₂×D₄×C₄₃	—	2	2	no	—
120	C₂×D₄×C₄₃	—	4	2	no	—
121	C₂×D₄×C₄₃	—	4	2	no	—
122	C₂×D₄×C₄₃	—	4	2	no	—
123	C₂×D₄×C₄₃	—	4	2	no	—
124	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₄₃	—	2	1	no	—
126	C₂²×C₄×C₄₃	—	2	1	no	—
127	C₂²×C₄×C₄₃	—	2	1	no	—
128	C₂²×C₄×C₄₃	—	2	2	no	—
129	C₂²×C₄×C₄₃	—	4	4	no	—
130	C₂²×C₄×C₄₃	—	4	4	no	—
131	C₂²×C₄×C₄₃	—	4	4	no	—
132	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
139	SD₁₆×C₄₃	—	4	8	no	—
140	D₈×C₄₃	—	4	8	no	—
141	C₂×C₈×C₄₃	—	2	2	no	—
142	C₂×C₈×C₄₃	—	2	2	no	—
143	C₂×C₈×C₄₃	—	2	2	no	—
144	C₂×C₈×C₄₃	—	2	2	no	—
145	C₂×C₈×C₄₃	—	2	2	no	—
146	C₂×C₈×C₄₃	#41	1	4	yes	—
147	C₄⋊C₄×C₄₃	—	2	1	no	—
148	C₄⋊C₄×C₄₃	—	2	1	no	—
149	C₄⋊C₄×C₄₃	—	2	1	no	—
150	C₄⋊C₄×C₄₃	—	2	1	no	—
151	C₄⋊C₄×C₄₃	—	2	2	no	—
152	C₄⋊C₄×C₄₃	—	2	2	no	—
153	C₄⋊C₄×C₄₃	—	4	2	no	—
154	C₄⋊C₄×C₄₃	—	4	2	no	—
155	C₄⋊C₄×C₄₃	—	4	2	no	—
156	C₄⋊C₄×C₄₃	—	4	2	no	—
157	C₂²⋊C₄×C₄₃	—	4	2	no	—
158	C₂²⋊C₄×C₄₃	—	4	2	no	—
159	C₂²⋊C₄×C₄₃	—	4	4	no	—
160	C₂²⋊C₄×C₄₃	—	4	4	no	—
161	C₂²⋊C₄×C₄₃	—	4	2	no	—
162	C₂²⋊C₄×C₄₃	—	4	2	no	—
163	C₂²⋊C₄×C₄₃	—	4	2	no	—
164	C₂²⋊C₄×C₄₃	—	4	2	no	—
165	C₂²⋊C₄×C₄₃	—	4	4	no	—
166	C₄²×C₄₃	—	2	2	no	—
167	C₄²×C₄₃	—	2	2	no	—
168	C₄²×C₄₃	—	2	2	no	—
169	C₄²×C₄₃	—	2	2	no	—
170	C₄²×C₄₃	—	4	1	no	—
171	C₄²×C₄₃	—	4	1	no	—
172	C₄²×C₄₃	C₂×D₄	1	2	yes	—
173	C₄²×C₄₃	#41	1	2	yes	—
174	C₂³×C₄₃	—	2	4	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	—	4	2	no	—
180	C₂³×C₄₃	—	4	2	no	—
181	C₂³×C₄₃	—	4	1	no	—
182	C₂³×C₄₃	—	4	1	no	—
183	C₂³×C₄₃	—	4	1	no	—
184	C₂³×C₄₃	—	4	1	no	—
185	C₂³×C₄₃	—	4	1	no	—
186	C₂³×C₄₃	—	4	1	no	—
187	C₂³×C₄₃	—	4	1	no	—
188	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
189	Q₈×C₄₃	—	4	2	no	—
190	Q₈×C₄₃	—	4	2	no	—
191	D₄×C₄₃	—	2	4	no	—
192	D₄×C₄₃	—	2	4	no	—
193	D₄×C₄₃	—	4	8	no	—
194	D₄×C₄₃	—	4	8	no	—
195	D₄×C₄₃	—	4	2	no	—
196	D₄×C₄₃	—	4	2	no	—
197	D₄×C₄₃	—	4	2	no	—
198	D₄×C₄₃	—	4	2	no	—
199	C₂×C₄×C₄₃	—	2	1	no	—
200	C₂×C₄×C₄₃	—	2	1	no	—
201	C₂×C₄×C₄₃	—	2	1	no	—
202	C₂×C₄×C₄₃	—	2	1	no	—
203	C₂×C₄×C₄₃	—	2	1	no	—
204	C₂×C₄×C₄₃	—	2	1	no	—
205	C₂×C₄×C₄₃	—	2	1	no	—
206	C₂×C₄×C₄₃	—	2	1	no	—
207	C₂×C₄×C₄₃	—	2	1	no	—
208	C₂×C₄×C₄₃	—	2	1	no	—
209	C₂×C₄×C₄₃	—	2	1	no	—
210	C₂×C₄×C₄₃	—	2	1	no	—
211	C₂×C₄×C₄₃	—	2	1	no	—
212	C₂×C₄×C₄₃	—	2	1	no	—
213	C₂×C₄×C₄₃	—	4	1	no	—
214	C₂×C₄×C₄₃	—	4	1	no	—
215	C₂×C₄×C₄₃	—	4	1	no	—
216	C₂×C₄×C₄₃	—	4	1	no	—
217	C₂×C₄×C₄₃	—	4	2	no	—
218	C₂×C₄×C₄₃	—	4	1	no	—
219	C₂×C₄×C₄₃	—	4	2	no	—
220	C₂×C₄×C₄₃	—	4	2	no	—
221	C₂×C₄×C₄₃	—	4	1	no	—
222	C₂×C₄×C₄₃	—	4	1	no	—
223	C₂×C₄×C₄₃	—	4	1	no	—
224	C₂×C₄×C₄₃	—	4	1	no	—
225	C₂×C₄×C₄₃	—	8	8	no	—
226	C₂×C₄×C₄₃	#121	1	2	yes	—
227	C₂×C₄×C₄₃	#121	1	2	yes	—
228	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
229	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
230	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
232	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
234	C₈×C₄₃	—	2	4	no	—
235	C₈×C₄₃	—	4	2	no	—
236	#28618	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂²×C₄₃	—	4	4	no	—
238	C₂²×C₄₃	—	4	4	no	—
239	C₂²×C₄₃	—	4	4	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	1	no	—
245	C₂²×C₄₃	—	8	1	no	—
246	C₂²×C₄₃	—	8	1	no	—
247	C₂²×C₄₃	—	8	1	no	—
248	C₂²×C₄₃	—	8	1	no	—
249	C₂²×C₄₃	—	8	1	no	—
250	C₂²×C₄₃	—	8	1	no	—
251	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
252	C₂²×C₄₃	#532	1	1	yes	characteristic
253	C₂²×C₄₃	#535	1	1	yes	characteristic
254	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
255	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₂²×C₄₃	#575	1	1	yes	characteristic
257	C₂²×C₄₃	#575	1	1	yes	characteristic
258	C₄×C₄₃	—	2	2	no	—
259	C₄×C₄₃	—	2	2	no	—
260	C₄×C₄₃	—	2	2	no	—
261	C₄×C₄₃	—	2	2	no	—
262	C₄×C₄₃	—	4	1	no	—
263	C₄×C₄₃	—	4	1	no	—
264	C₄×C₄₃	—	8	2	no	—
265	C₄×C₄₃	—	8	1	no	—
266	C₄×C₄₃	—	8	1	no	—
267	C₄×C₄₃	—	8	1	no	—
268	C₄×C₄₃	#546	1	2	yes	—
269	C₄×C₄₃	#559	1	2	yes	—
270	C₂×#496	C₂×C₄₃	1	1	yes	characteristic
271	C₂×#490	C₂×C₄₃	1	1	yes	characteristic, complemented
272	#2861	C₂×C₄₃	1	1	yes	characteristic, complemented
273	C₄×#127	C₂×C₄₃	1	1	yes	characteristic, complemented
274	#2055	C₂×C₄₃	1	2	yes	complemented
275	#2054	C₂×C₄₃	1	2	yes	complemented
276	#1992	C₂×C₄₃	1	1	yes	characteristic, complemented
277	#1959	C₂×C₄₃	1	1	yes	characteristic, complemented
278	#1879	C₂×C₄₃	1	2	yes	complemented
279	#1877	C₂×C₄₃	1	2	yes	complemented
280	#1767	C₂×C₄₃	1	1	yes	characteristic, complemented
281	C₂×C₄₃	—	8	4	no	—
282	C₂×C₄₃	—	16	1	no	—
283	C₂×C₄₃	#2544	1	1	yes	characteristic
284	C₂×C₄₃	#3036	1	1	yes	characteristic
285	C₂×C₄₃	#3036	1	1	yes	characteristic
286	C₂×C₄₃	#3171	1	1	yes	characteristic
287	C₂×C₄₃	#3180	1	1	yes	characteristic
288	C₂×C₄₃	#3217	1	1	yes	characteristic
289	C₂×C₄₃	#3219	1	1	yes	characteristic
290	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
291	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
292	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
293	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
294	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
295	C₂×C₄×D₄	—	2	1	no	—
296	C₂×C₄×D₄	—	2	1	no	—
297	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
298	#496	—	2	4	no	—
299	#490	—	2	4	no	—
300	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
301	C₂×#103	C₂²×C₄₃	1	2	yes	—
302	C₂×#102	C₂²×C₄₃	1	2	yes	—
303	C₂×#102	C₂²×C₄₃	1	2	yes	—
304	C₂×#102	C₂²×C₄₃	1	2	yes	—
305	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
306	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
307	#391	C₂²×C₄₃	1	1	yes	characteristic
308	#391	C₂²×C₄₃	1	1	yes	characteristic
309	#390	—	2	1	no	—
310	#390	—	2	1	no	—
311	#390	C₂²×C₄₃	1	2	yes	—
312	#390	C₂²×C₄₃	1	1	yes	characteristic
313	#390	C₂²×C₄₃	1	1	yes	characteristic
314	#388	—	2	1	no	—
315	#388	—	2	1	no	—
316	#388	—	2	1	no	—
317	#388	—	2	1	no	—
318	#384	C₂²×C₄₃	1	1	yes	characteristic
319	C₄³	C₂²×C₄₃	1	1	yes	characteristic
320	#340	C₂²×C₄₃	1	2	yes	—
321	#340	C₂²×C₄₃	1	2	yes	—
322	#336	C₂²×C₄₃	1	2	yes	—
323	C₄₃	#28618	1	1	yes	characteristic, direct product factor, Sylow
324	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
328	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
329	C₂³×C₄	—	2	2	no	—
330	C₂×SD₁₆	—	2	4	no	—
331	C₂×SD₁₆	—	2	4	no	—
332	C₂×SD₁₆	—	4	2	no	—
333	C₂×D₈	—	2	4	no	—
334	C₂×D₈	—	2	4	no	—
335	C₂×D₈	—	4	2	no	—
336	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
337	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
338	#127	—	2	2	no	—
339	#127	D₄×C₄₃	1	4	yes	—
340	#125	—	2	2	no	—
341	#125	—	2	2	no	—
342	#124	—	2	2	no	—
343	#124	—	2	2	no	—
344	C₄×D₄	—	4	2	no	—
345	C₄×D₄	—	4	2	no	—
346	C₄×D₄	—	4	4	no	—
347	C₄×D₄	—	4	4	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
365	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
366	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
367	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
370	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
371	C₄⋊C₈	—	2	4	no	—
372	#103	—	4	2	no	—
373	#102	—	2	4	no	—
374	#102	—	2	4	no	—
375	#102	—	4	2	no	—
376	#97	—	2	2	no	—
377	#97	—	2	2	no	—
378	#95	—	2	1	no	—
379	#95	—	2	1	no	—
380	#95	—	2	1	no	—
381	#95	—	2	1	no	—
382	C₂⁴	—	2	2	no	—
383	C₂⁴	—	2	1	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	4	2	no	—
400	C₂×D₄	—	4	2	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	4	4	no	—
409	C₂²×C₄	—	4	4	no	—
410	C₂²×C₄	—	4	4	no	—
411	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
418	SD₁₆	—	4	8	no	—
419	D₈	—	4	8	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	#41×C₄₃	1	4	yes	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	4	2	no	—
433	C₄⋊C₄	—	4	2	no	—
434	C₄⋊C₄	—	4	2	no	—
435	C₄⋊C₄	—	4	2	no	—
436	C₂²⋊C₄	—	4	4	no	—
437	C₂²⋊C₄	—	4	4	no	—
438	C₂²⋊C₄	—	4	2	no	—
439	C₂²⋊C₄	—	4	2	no	—
440	C₂²⋊C₄	—	4	2	no	—
441	C₂²⋊C₄	—	4	2	no	—
442	C₂²⋊C₄	—	4	4	no	—
443	C₂²⋊C₄	—	4	2	no	—
444	C₂²⋊C₄	—	4	2	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	4	1	no	—
450	C₄²	—	4	1	no	—
451	C₄²	C₂×D₄×C₄₃	1	2	yes	—
452	C₄²	#41×C₄₃	1	2	yes	—
453	C₂³	—	2	4	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	1	no	—
461	C₂³	—	4	1	no	—
462	C₂³	—	4	1	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	1	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	1	no	—
467	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
468	Q₈	—	4	2	no	—
469	Q₈	—	4	2	no	—
470	D₄	—	2	4	no	—
471	D₄	—	2	4	no	—
472	D₄	—	4	8	no	—
473	D₄	—	4	8	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	8	8	no	—
505	C₂×C₄	#121×C₄₃	1	2	yes	—
506	C₂×C₄	#121×C₄₃	1	2	yes	—
507	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
508	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
509	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
510	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
511	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
512	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
513	C₈	—	2	4	no	—
514	C₈	—	4	2	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	4	4	no	—
518	C₂²	—	8	2	no	—
519	C₂²	—	8	2	no	—
520	C₂²	—	8	2	no	—
521	C₂²	—	8	2	no	—
522	C₂²	—	8	1	no	—
523	C₂²	—	8	1	no	—
524	C₂²	—	8	1	no	—
525	C₂²	—	8	1	no	—
526	C₂²	—	8	1	no	—
527	C₂²	—	8	1	no	—
528	C₂²	—	8	1	no	—
529	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
530	C₂²	C₄₃×#532	1	1	yes	characteristic
531	C₂²	C₄₃×#535	1	1	yes	characteristic
532	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
533	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
534	C₂²	C₄₃×#575	1	1	yes	characteristic
535	C₂²	C₄₃×#575	1	1	yes	characteristic
536	C₄	—	2	2	no	—
537	C₄	—	2	2	no	—
538	C₄	—	2	2	no	—
539	C₄	—	2	2	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	1	no	—
542	C₄	—	8	2	no	—
543	C₄	—	8	1	no	—
544	C₄	—	8	1	no	—
545	C₄	—	8	1	no	—
546	C₄	C₄₃×#546	1	2	yes	—
547	C₄	C₄₃×#559	1	2	yes	—
548	C₂	—	8	4	no	—
549	C₂	—	16	1	no	—
550	C₂	C₄₃×#2544	1	1	yes	characteristic
551	C₂	C₄₃×#3036	1	1	yes	characteristic
552	C₂	C₄₃×#3036	1	1	yes	characteristic
553	C₂	C₄₃×#3171	1	1	yes	characteristic
554	C₂	C₄₃×#3180	1	1	yes	characteristic
555	C₂	C₄₃×#3217	1	1	yes	characteristic
556	C₂	C₄₃×#3219	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#496	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₄³×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#490	C₂	semidirect
3. C₄₃×#2861	C₂	semidirect
4. C₄×#127×C₄₃	C₂	semidirect
5. C₄₃×#2055	C₂	semidirect
6. C₄₃×#2054	C₂	semidirect
7. C₄₃×#1992	C₂	semidirect
8. C₄₃×#1959	C₂	semidirect
9. C₄₃×#1879	C₂	semidirect
10. C₄₃×#1877	C₂	semidirect
11. C₄₃×#1767	C₂	semidirect
236. #28618	C₄₃	direct (N × H)
271. C₂×#490	C₂×C₄₃	semidirect
272. #2861	C₂×C₄₃	semidirect
273. C₄×#127	C₂×C₄₃	semidirect
274. #2055	C₂×C₄₃	semidirect
275. #2054	C₂×C₄₃	semidirect
276. #1992	C₂×C₄₃	semidirect
277. #1959	C₂×C₄₃	semidirect
278. #1879	C₂×C₄₃	semidirect
279. #1877	C₂×C₄₃	semidirect
280. #1767	C₂×C₄₃	semidirect
323. C₄₃	#28618	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#496	2
C₂×C₄₃×#490	2
C₄₃×#2861	2
C₄×#127×C₄₃	2
C₄₃×#2055	2
C₄₃×#2054	2
C₄₃×#1992	2
C₄₃×#1959	2
C₄₃×#1879	2
C₄₃×#1877	2
C₄₃×#1767	2
#28618	43

Subgroups — C43×#28618 #24948635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28618 #24948635