Subgroups — C₄₃×#29956 #24949973

Order 11008.

1080 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	C₄₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#390	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2092	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2067	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2065	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2025	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1786	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1786	C₂	1	1	yes	maximal, characteristic
12	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
16	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
17	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#107×C₄₃	C₂²	1	2	yes	complemented
19	C₂×#106×C₄₃	C₂²	1	2	yes	complemented
20	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	complemented
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	1	yes	characteristic
26	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₄₃×#390	—	2	1	no	—
28	C₄₃×#390	—	2	1	no	—
29	C₄₃×#390	C₂²	1	2	yes	—
30	C₄₃×#390	C₂²	1	2	yes	—
31	C₄₃×#389	C₂²	1	1	yes	characteristic, complemented
32	C₄₃×#389	C₂²	1	1	yes	characteristic, complemented
33	C₄₃×#387	—	2	1	no	—
34	C₄₃×#387	—	2	1	no	—
35	C₄₃×#385	—	2	1	no	—
36	C₄₃×#385	—	2	1	no	—
37	C₄₃×#382	C₂²	1	1	yes	characteristic, complemented
38	C₄₃×#380	C₂²	1	1	yes	characteristic
39	C₄₃×#380	C₂²	1	1	yes	characteristic
40	C₄₃×#340	C₂²	1	2	yes	complemented
41	C₄₃×#340	C₂²	1	2	yes	complemented
42	C₄₃×#336	C₂²	1	2	yes	complemented
43	C₂⁵×C₄₃	—	2	1	no	—
44	C₂²×D₄×C₄₃	—	2	1	no	—
45	C₂²×D₄×C₄₃	—	2	2	no	—
46	C₂²×D₄×C₄₃	—	4	2	no	—
47	C₂²×D₄×C₄₃	—	4	2	no	—
48	C₂²×D₄×C₄₃	Q₈	1	4	yes	—
49	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₄₃	—	2	1	no	—
51	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
56	#125×C₄₃	—	4	2	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
76	C₂×C₄²×C₄₃	—	4	2	no	—
77	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
81	#107×C₄₃	—	4	2	no	—
82	#106×C₄₃	—	4	2	no	—
83	C₄⋊C₈×C₄₃	—	4	2	no	—
84	#102×C₄₃	—	4	2	no	—
85	#102×C₄₃	—	4	2	no	—
86	#102×C₄₃	—	4	2	no	—
87	#102×C₄₃	—	4	2	no	—
88	C₂²⋊C₈×C₄₃	—	2	2	no	—
89	C₂²⋊C₈×C₄₃	—	2	2	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	#95×C₄₃	—	2	1	no	—
96	C₂⁴×C₄₃	—	2	4	no	—
97	C₂⁴×C₄₃	—	2	2	no	—
98	C₂⁴×C₄₃	—	4	2	no	—
99	C₂⁴×C₄₃	—	4	2	no	—
100	C₂⁴×C₄₃	—	4	2	no	—
101	C₂⁴×C₄₃	—	4	2	no	—
102	C₂⁴×C₄₃	—	4	2	no	—
103	C₂⁴×C₄₃	—	4	2	no	—
104	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₄₃	—	2	4	no	—
106	C₂×D₄×C₄₃	—	2	2	no	—
107	C₂×D₄×C₄₃	—	2	2	no	—
108	C₂×D₄×C₄₃	—	2	2	no	—
109	C₂×D₄×C₄₃	—	2	2	no	—
110	C₂×D₄×C₄₃	—	2	2	no	—
111	C₂×D₄×C₄₃	—	4	8	no	—
112	C₂×D₄×C₄₃	—	4	8	no	—
113	C₂×D₄×C₄₃	—	4	2	no	—
114	C₂×D₄×C₄₃	—	4	2	no	—
115	C₂×D₄×C₄₃	C₂×Q₈	1	4	yes	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	2	1	no	—
122	C₂²×C₄×C₄₃	—	2	1	no	—
123	C₂²×C₄×C₄₃	—	2	1	no	—
124	C₂²×C₄×C₄₃	—	2	1	no	—
125	C₂²×C₄×C₄₃	—	2	2	no	—
126	C₂²×C₄×C₄₃	—	4	1	no	—
127	C₂²×C₄×C₄₃	—	4	1	no	—
128	C₂²×C₄×C₄₃	—	4	1	no	—
129	C₂²×C₄×C₄₃	—	4	2	no	—
130	C₂²×C₄×C₄₃	—	4	2	no	—
131	C₂²×C₄×C₄₃	—	4	2	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×Q₈	1	2	yes	—
138	C₂²×C₄×C₄₃	#41	1	2	yes	—
139	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
140	C₂×C₈×C₄₃	—	2	2	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	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	—	4	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	4	no	—
158	C₂²⋊C₄×C₄₃	—	4	4	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	C₄²×C₄₃	—	2	2	no	—
164	C₄²×C₄₃	—	2	2	no	—
165	C₄²×C₄₃	—	4	1	no	—
166	C₄²×C₄₃	—	4	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	4	no	—
172	C₂³×C₄₃	—	4	8	no	—
173	C₂³×C₄₃	—	4	8	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	—	4	2	no	—
180	C₂³×C₄₃	—	4	8	no	—
181	C₂³×C₄₃	—	8	4	no	—
182	C₂³×C₄₃	—	8	4	no	—
183	C₂³×C₄₃	—	8	4	no	—
184	C₂³×C₄₃	—	8	4	no	—
185	C₂³×C₄₃	C₂²⋊Q₈	1	2	yes	—
186	C₂³×C₄₃	#135	1	2	yes	—
187	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
188	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
189	D₄×C₄₃	—	2	4	no	—
190	D₄×C₄₃	—	2	4	no	—
191	D₄×C₄₃	—	4	8	no	—
192	D₄×C₄₃	—	4	2	no	—
193	D₄×C₄₃	—	4	2	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	4	no	—
199	C₂×C₄×C₄₃	—	2	4	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	—	4	4	no	—
210	C₂×C₄×C₄₃	—	4	4	no	—
211	C₂×C₄×C₄₃	—	4	1	no	—
212	C₂×C₄×C₄₃	—	4	1	no	—
213	C₂×C₄×C₄₃	—	4	2	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	1	no	—
218	C₂×C₄×C₄₃	—	4	2	no	—
219	C₂×C₄×C₄₃	—	4	2	no	—
220	C₂×C₄×C₄₃	—	4	1	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	—	4	1	no	—
226	C₂×C₄×C₄₃	—	8	4	no	—
227	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
228	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
229	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
230	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
232	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
233	C₈×C₄₃	—	4	2	no	—
234	C₈×C₄₃	—	4	2	no	—
235	#29956	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂²×C₄₃	—	2	2	no	—
237	C₂²×C₄₃	—	2	2	no	—
238	C₂²×C₄₃	—	2	2	no	—
239	C₂²×C₄₃	—	2	2	no	—
240	C₂²×C₄₃	—	2	2	no	—
241	C₂²×C₄₃	—	2	2	no	—
242	C₂²×C₄₃	—	4	4	no	—
243	C₂²×C₄₃	—	4	4	no	—
244	C₂²×C₄₃	—	4	4	no	—
245	C₂²×C₄₃	—	8	16	no	—
246	C₂²×C₄₃	—	8	2	no	—
247	C₂²×C₄₃	—	8	2	no	—
248	C₂²×C₄₃	—	8	2	no	—
249	C₂²×C₄₃	—	8	2	no	—
250	C₂²×C₄₃	#478	1	4	yes	—
251	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
252	C₂²×C₄₃	#534	1	1	yes	characteristic
253	C₂²×C₄₃	#535	1	1	yes	characteristic
254	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
255	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	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	—	4	1	no	—
261	C₄×C₄₃	—	4	1	no	—
262	C₄×C₄₃	—	4	1	no	—
263	C₄×C₄₃	—	8	1	no	—
264	C₄×C₄₃	—	8	1	no	—
265	C₄×C₄₃	—	8	1	no	—
266	C₄×C₄₃	—	8	1	no	—
267	C₄×C₄₃	—	8	2	no	—
268	C₄×C₄₃	#538	1	2	yes	—
269	C₄×C₄₃	#543	1	2	yes	—
270	#2851	C₂×C₄₃	1	1	yes	characteristic, complemented
271	C₂×#390	C₂×C₄₃	1	1	yes	characteristic
272	#2092	C₂×C₄₃	1	2	yes	complemented
273	#2067	C₂×C₄₃	1	2	yes	complemented
274	#2065	C₂×C₄₃	1	2	yes	complemented
275	#2025	C₂×C₄₃	1	2	yes	complemented
276	#1853	C₂×C₄₃	1	1	yes	characteristic, complemented
277	#1852	C₂×C₄₃	1	1	yes	characteristic, complemented
278	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
279	#1786	C₂×C₄₃	1	1	yes	characteristic
280	#1786	C₂×C₄₃	1	1	yes	characteristic
281	C₂×C₄₃	—	2	4	no	—
282	C₂×C₄₃	—	8	4	no	—
283	C₂×C₄₃	#2626	1	1	yes	characteristic
284	C₂×C₄₃	C₂×#478	1	1	yes	characteristic
285	C₂×C₄₃	#3077	1	1	yes	characteristic
286	C₂×C₄₃	#3188	1	1	yes	characteristic
287	C₂×C₄₃	#3194	1	1	yes	characteristic
288	C₂×C₄₃	#3211	1	1	yes	characteristic
289	C₂×C₄₃	#3217	1	1	yes	characteristic
290	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
291	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic, complemented
292	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
293	C₂²×C₂²⋊C₄	—	2	1	no	—
294	C₂²×C₂²⋊C₄	—	2	1	no	—
295	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
296	C₂×#107	C₂²×C₄₃	1	2	yes	complemented
297	C₂×#106	C₂²×C₄₃	1	2	yes	complemented
298	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	complemented
299	C₂×#102	C₂²×C₄₃	1	2	yes	—
300	C₂×#102	C₂²×C₄₃	1	2	yes	—
301	C₂×#102	C₂²×C₄₃	1	2	yes	—
302	C₂×#102	C₂²×C₄₃	1	2	yes	—
303	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
304	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
305	#390	—	2	1	no	—
306	#390	—	2	1	no	—
307	#390	C₂²×C₄₃	1	2	yes	—
308	#390	C₂²×C₄₃	1	2	yes	—
309	#389	C₂²×C₄₃	1	1	yes	characteristic, complemented
310	#389	C₂²×C₄₃	1	1	yes	characteristic, complemented
311	#387	—	2	1	no	—
312	#387	—	2	1	no	—
313	#385	—	2	1	no	—
314	#385	—	2	1	no	—
315	#382	C₂²×C₄₃	1	1	yes	characteristic, complemented
316	#380	C₂²×C₄₃	1	1	yes	characteristic
317	#380	C₂²×C₄₃	1	1	yes	characteristic
318	#340	C₂²×C₄₃	1	2	yes	complemented
319	#340	C₂²×C₄₃	1	2	yes	complemented
320	#336	C₂²×C₄₃	1	2	yes	complemented
321	C₄₃	#29956	1	1	yes	characteristic, direct product factor, Sylow
322	C₂⁵	—	2	1	no	—
323	C₂²×D₄	—	2	1	no	—
324	C₂²×D₄	—	2	2	no	—
325	C₂²×D₄	—	4	2	no	—
326	C₂²×D₄	—	4	2	no	—
327	C₂²×D₄	Q₈×C₄₃	1	4	yes	—
328	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
329	C₂³×C₄	—	2	1	no	—
330	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
331	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
332	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
333	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
334	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
335	#125	—	4	2	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	4	2	no	—
342	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	4	4	no	—
354	C₂×C₂²⋊C₄	—	4	4	no	—
355	C₂×C₄²	—	4	2	no	—
356	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
357	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
360	#107	—	4	2	no	—
361	#106	—	4	2	no	—
362	C₄⋊C₈	—	4	2	no	—
363	#102	—	4	2	no	—
364	#102	—	4	2	no	—
365	#102	—	4	2	no	—
366	#102	—	4	2	no	—
367	C₂²⋊C₈	—	2	2	no	—
368	C₂²⋊C₈	—	2	2	no	—
369	#95	—	2	1	no	—
370	#95	—	2	1	no	—
371	#95	—	2	1	no	—
372	#95	—	2	1	no	—
373	#95	—	2	1	no	—
374	#95	—	2	1	no	—
375	C₂⁴	—	2	4	no	—
376	C₂⁴	—	2	2	no	—
377	C₂⁴	—	4	2	no	—
378	C₂⁴	—	4	2	no	—
379	C₂⁴	—	4	2	no	—
380	C₂⁴	—	4	2	no	—
381	C₂⁴	—	4	2	no	—
382	C₂⁴	—	4	2	no	—
383	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	4	8	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	—	4	2	no	—
393	C₂×D₄	—	4	8	no	—
394	C₂×D₄	C₂×Q₈×C₄₃	1	4	yes	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	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	—	4	1	no	—
407	C₂²×C₄	—	4	1	no	—
408	C₂²×C₄	—	4	2	no	—
409	C₂²×C₄	—	4	2	no	—
410	C₂²×C₄	—	4	2	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×Q₈×C₄₃	1	2	yes	—
417	C₂²×C₄	#41×C₄₃	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
419	C₂×C₈	—	2	2	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	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	4	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	4	no	—
439	C₂²⋊C₄	—	4	2	no	—
440	C₂²⋊C₄	—	4	2	no	—
441	C₂²⋊C₄	—	4	4	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	4	1	no	—
445	C₄²	—	4	1	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	4	no	—
451	C₂³	—	4	8	no	—
452	C₂³	—	4	8	no	—
453	C₂³	—	4	2	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	8	no	—
460	C₂³	—	8	4	no	—
461	C₂³	—	8	4	no	—
462	C₂³	—	8	4	no	—
463	C₂³	—	8	4	no	—
464	C₂³	C₂²⋊Q₈×C₄₃	1	2	yes	—
465	C₂³	#135×C₄₃	1	2	yes	—
466	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
467	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
468	D₄	—	2	4	no	—
469	D₄	—	2	4	no	—
470	D₄	—	4	8	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	2	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	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	—	4	4	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	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	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	1	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	—	4	1	no	—
505	C₂×C₄	—	8	4	no	—
506	C₂×C₄	C₂²⋊Q₈×C₄₃	1	2	yes	—
507	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
508	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
509	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
510	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
511	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
512	C₈	—	4	2	no	—
513	C₈	—	4	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	8	16	no	—
524	C₂²	—	8	2	no	—
525	C₂²	—	8	2	no	—
526	C₂²	—	8	2	no	—
527	C₂²	—	8	2	no	—
528	C₂²	C₄₃×#478	1	4	yes	—
529	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
530	C₂²	C₄₃×#534	1	1	yes	characteristic
531	C₂²	C₄₃×#535	1	1	yes	characteristic
532	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
533	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
534	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
535	C₂²	C₄₃×#575	1	1	yes	characteristic
536	C₄	—	2	2	no	—
537	C₄	—	2	2	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	1	no	—
541	C₄	—	8	1	no	—
542	C₄	—	8	1	no	—
543	C₄	—	8	1	no	—
544	C₄	—	8	2	no	—
545	C₄	—	8	1	no	—
546	C₄	C₄₃×#538	1	2	yes	—
547	C₄	C₄₃×#543	1	2	yes	—
548	C₂	—	2	4	no	—
549	C₂	—	8	4	no	—
550	C₂	C₄₃×#2626	1	1	yes	characteristic
551	C₂	C₂×C₄₃×#478	1	1	yes	characteristic
552	C₂	C₄₃×#3077	1	1	yes	characteristic
553	C₂	C₄₃×#3188	1	1	yes	characteristic
554	C₂	C₄₃×#3194	1	1	yes	characteristic
555	C₂	C₄₃×#3211	1	1	yes	characteristic
556	C₂	C₄₃×#3217	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂³×D₄×C₄₃	C₂²
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. C₄₃×#2851	C₂	semidirect
3. C₄₃×#2092	C₂	semidirect
4. C₄₃×#2067	C₂	semidirect
5. C₄₃×#2065	C₂	semidirect
6. C₄₃×#2025	C₂	semidirect
7. C₄₃×#1853	C₂	semidirect
8. C₄₃×#1852	C₂	semidirect
9. C₄₃×#1797	C₂	semidirect
13. C₂×#125×C₄₃	C₂²	semidirect
18. C₂×#107×C₄₃	C₂²	semidirect
19. C₂×#106×C₄₃	C₂²	semidirect
20. C₂×C₄⋊C₈×C₄₃	C₂²	semidirect
31. C₄₃×#389	C₂²	semidirect
32. C₄₃×#389	C₂²	semidirect
37. C₄₃×#382	C₂²	semidirect
40. C₄₃×#340	C₂²	semidirect
41. C₄₃×#340	C₂²	semidirect
42. C₄₃×#336	C₂²	semidirect
235. #29956	C₄₃	direct (N × H)
270. #2851	C₂×C₄₃	semidirect
272. #2092	C₂×C₄₃	semidirect
273. #2067	C₂×C₄₃	semidirect
274. #2065	C₂×C₄₃	semidirect
275. #2025	C₂×C₄₃	semidirect
276. #1853	C₂×C₄₃	semidirect
277. #1852	C₂×C₄₃	semidirect
278. #1797	C₂×C₄₃	semidirect
291. C₂×#125	C₂²×C₄₃	semidirect
296. C₂×#107	C₂²×C₄₃	semidirect
297. C₂×#106	C₂²×C₄₃	semidirect
298. C₂×C₄⋊C₈	C₂²×C₄₃	semidirect
309. #389	C₂²×C₄₃	semidirect
310. #389	C₂²×C₄₃	semidirect
315. #382	C₂²×C₄₃	semidirect
318. #340	C₂²×C₄₃	semidirect
319. #340	C₂²×C₄₃	semidirect
320. #336	C₂²×C₄₃	semidirect
321. C₄₃	#29956	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×#2851	2
C₂×C₄₃×#390	2
C₄₃×#2092	2
C₄₃×#2067	2
C₄₃×#2065	2
C₄₃×#2025	2
C₄₃×#1853	2
C₄₃×#1852	2
C₄₃×#1797	2
C₄₃×#1786	2
#29956	43

Subgroups — C43×#29956 #24949973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29956 #24949973