Subgroups — C₄₃×#29598 #24949615

Order 11008.

1786 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2033	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2000	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1824	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1779	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₄₃	—	2	1	no	—
11	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	complemented
14	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
16	C₂×#121×C₄₃	—	2	4	no	—
17	C₂×#121×C₄₃	—	2	2	no	—
18	C₂×#121×C₄₃	—	2	4	no	—
19	C₂×#121×C₄₃	C₂²	1	4	yes	—
20	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
22	C₄₃×#484	—	2	4	no	—
23	C₄₃×#450	—	2	4	no	—
24	C₂×#107×C₄₃	C₂²	1	2	yes	complemented
25	C₂×#103×C₄₃	C₂²	1	2	yes	complemented
26	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
27	C₂×#102×C₄₃	C₂²	1	4	yes	complemented
28	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₄₃	C₂²	1	4	yes	complemented
31	C₄₃×#385	—	2	2	no	—
32	C₄₃×#385	—	2	1	no	—
33	C₄₃×#380	C₂²	1	1	yes	characteristic
34	C₄₃×#380	C₂²	1	2	yes	complemented
35	C₄₃×#379	—	2	1	no	—
36	C₄₃×#340	C₂²	1	4	yes	complemented
37	C₂⁵×C₄₃	—	2	1	no	—
38	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₄₃	—	2	8	no	—
41	C₂²×D₄×C₄₃	—	2	4	no	—
42	C₂²×D₄×C₄₃	—	2	2	no	—
43	C₂²×D₄×C₄₃	—	2	1	no	—
44	C₂²×D₄×C₄₃	—	4	4	no	—
45	C₂²×D₄×C₄₃	—	4	8	no	—
46	C₂²×D₄×C₄₃	D₄	1	4	yes	—
47	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₄₃	—	2	1	no	—
49	C₂³×C₄×C₄₃	—	2	2	no	—
50	C₂³×C₄×C₄₃	—	2	2	no	—
51	C₂³×C₄×C₄₃	—	4	4	no	—
52	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₃	D₄	1	2	yes	—
54	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
56	C₂×SD₁₆×C₄₃	—	2	4	no	—
57	C₂×SD₁₆×C₄₃	—	4	4	no	—
58	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
59	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
60	C₂²⋊Q₈×C₄₃	—	2	2	no	—
61	C₂²⋊Q₈×C₄₃	—	2	2	no	—
62	C₂²⋊Q₈×C₄₃	—	4	4	no	—
63	#121×C₄₃	—	2	16	no	—
64	#121×C₄₃	—	2	8	no	—
65	#121×C₄₃	—	2	8	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
71	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
80	#107×C₄₃	—	2	4	no	—
81	#103×C₄₃	—	2	4	no	—
82	#102×C₄₃	—	2	4	no	—
83	#102×C₄₃	—	4	4	no	—
84	C₂²⋊C₈×C₄₃	—	2	2	no	—
85	C₂²⋊C₈×C₄₃	—	2	2	no	—
86	C₂²⋊C₈×C₄₃	—	4	4	no	—
87	#95×C₄₃	—	2	1	no	—
88	#95×C₄₃	—	2	2	no	—
89	C₂⁴×C₄₃	—	2	2	no	—
90	C₂⁴×C₄₃	—	2	4	no	—
91	C₂⁴×C₄₃	—	2	4	no	—
92	C₂⁴×C₄₃	—	2	2	no	—
93	C₂⁴×C₄₃	—	2	2	no	—
94	C₂⁴×C₄₃	—	2	2	no	—
95	C₂⁴×C₄₃	—	4	2	no	—
96	C₂⁴×C₄₃	—	4	4	no	—
97	C₂⁴×C₄₃	—	4	4	no	—
98	C₂⁴×C₄₃	—	4	2	no	—
99	C₂⁴×C₄₃	—	4	2	no	—
100	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
101	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
102	C₂×Q₈×C₄₃	—	2	1	no	—
103	C₂×Q₈×C₄₃	—	2	1	no	—
104	C₂×Q₈×C₄₃	—	2	4	no	—
105	C₂×D₄×C₄₃	—	2	16	no	—
106	C₂×D₄×C₄₃	—	2	4	no	—
107	C₂×D₄×C₄₃	—	2	2	no	—
108	C₂×D₄×C₄₃	—	2	4	no	—
109	C₂×D₄×C₄₃	—	2	4	no	—
110	C₂×D₄×C₄₃	—	4	32	no	—
111	C₂×D₄×C₄₃	—	4	8	no	—
112	C₂×D₄×C₄₃	—	4	8	no	—
113	C₂×D₄×C₄₃	—	4	8	no	—
114	C₂×D₄×C₄₃	—	4	4	no	—
115	C₂×D₄×C₄₃	—	4	8	no	—
116	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₄₃	—	2	4	no	—
118	C₂²×C₄×C₄₃	—	2	4	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	2	4	no	—
122	C₂²×C₄×C₄₃	—	2	4	no	—
123	C₂²×C₄×C₄₃	—	2	2	no	—
124	C₂²×C₄×C₄₃	—	2	4	no	—
125	C₂²×C₄×C₄₃	—	2	2	no	—
126	C₂²×C₄×C₄₃	—	2	1	no	—
127	C₂²×C₄×C₄₃	—	2	2	no	—
128	C₂²×C₄×C₄₃	—	2	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	—	4	4	no	—
133	C₂²×C₄×C₄₃	—	4	8	no	—
134	C₂²×C₄×C₄₃	—	4	8	no	—
135	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
140	SD₁₆×C₄₃	—	4	8	no	—
141	C₂×C₈×C₄₃	—	2	2	no	—
142	C₂×C₈×C₄₃	—	2	2	no	—
143	C₂×C₈×C₄₃	—	2	4	no	—
144	C₂×C₈×C₄₃	—	2	4	no	—
145	C₄⋊C₄×C₄₃	—	2	4	no	—
146	C₄⋊C₄×C₄₃	—	2	2	no	—
147	C₄⋊C₄×C₄₃	—	2	1	no	—
148	C₄⋊C₄×C₄₃	—	2	1	no	—
149	C₄⋊C₄×C₄₃	—	2	4	no	—
150	C₄⋊C₄×C₄₃	—	4	4	no	—
151	C₄⋊C₄×C₄₃	—	4	2	no	—
152	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
153	C₂²⋊C₄×C₄₃	—	2	16	no	—
154	C₂²⋊C₄×C₄₃	—	4	4	no	—
155	C₂²⋊C₄×C₄₃	—	4	2	no	—
156	C₂²⋊C₄×C₄₃	—	4	2	no	—
157	C₂²⋊C₄×C₄₃	—	4	4	no	—
158	C₂³×C₄₃	—	2	2	no	—
159	C₂³×C₄₃	—	2	2	no	—
160	C₂³×C₄₃	—	2	8	no	—
161	C₂³×C₄₃	—	2	2	no	—
162	C₂³×C₄₃	—	2	2	no	—
163	C₂³×C₄₃	—	2	2	no	—
164	C₂³×C₄₃	—	2	2	no	—
165	C₂³×C₄₃	—	2	2	no	—
166	C₂³×C₄₃	—	2	2	no	—
167	C₂³×C₄₃	—	2	4	no	—
168	C₂³×C₄₃	—	4	8	no	—
169	C₂³×C₄₃	—	4	8	no	—
170	C₂³×C₄₃	—	4	4	no	—
171	C₂³×C₄₃	—	4	8	no	—
172	C₂³×C₄₃	—	4	8	no	—
173	C₂³×C₄₃	—	4	4	no	—
174	C₂³×C₄₃	—	4	4	no	—
175	C₂³×C₄₃	—	4	2	no	—
176	C₂³×C₄₃	—	4	4	no	—
177	C₂³×C₄₃	—	4	2	no	—
178	C₂³×C₄₃	—	4	8	no	—
179	C₂³×C₄₃	—	8	8	no	—
180	C₂³×C₄₃	—	8	8	no	—
181	C₂³×C₄₃	#120	1	2	yes	—
182	C₂³×C₄₃	#135	1	2	yes	—
183	C₂³×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
184	C₂³×C₄₃	#137	1	2	yes	—
185	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₄₃	—	4	2	no	—
187	Q₈×C₄₃	—	4	2	no	—
188	D₄×C₄₃	—	2	4	no	—
189	D₄×C₄₃	—	2	4	no	—
190	D₄×C₄₃	—	4	8	no	—
191	D₄×C₄₃	—	4	32	no	—
192	D₄×C₄₃	—	4	4	no	—
193	C₂×C₄×C₄₃	—	2	2	no	—
194	C₂×C₄×C₄₃	—	2	4	no	—
195	C₂×C₄×C₄₃	—	2	4	no	—
196	C₂×C₄×C₄₃	—	2	2	no	—
197	C₂×C₄×C₄₃	—	2	4	no	—
198	C₂×C₄×C₄₃	—	2	2	no	—
199	C₂×C₄×C₄₃	—	2	2	no	—
200	C₂×C₄×C₄₃	—	4	8	no	—
201	C₂×C₄×C₄₃	—	4	4	no	—
202	C₂×C₄×C₄₃	—	4	8	no	—
203	C₂×C₄×C₄₃	—	4	4	no	—
204	C₂×C₄×C₄₃	—	4	4	no	—
205	C₂×C₄×C₄₃	—	4	4	no	—
206	C₂×C₄×C₄₃	—	4	1	no	—
207	C₂×C₄×C₄₃	—	4	1	no	—
208	C₂×C₄×C₄₃	—	4	2	no	—
209	C₂×C₄×C₄₃	—	4	2	no	—
210	C₂×C₄×C₄₃	—	4	2	no	—
211	C₂×C₄×C₄₃	—	4	2	no	—
212	C₂×C₄×C₄₃	—	4	2	no	—
213	C₂×C₄×C₄₃	#120	1	2	yes	—
214	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
217	C₈×C₄₃	—	4	2	no	—
218	C₈×C₄₃	—	4	2	no	—
219	#29598	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂²×C₄₃	—	2	2	no	—
221	C₂²×C₄₃	—	2	4	no	—
222	C₂²×C₄₃	—	2	4	no	—
223	C₂²×C₄₃	—	2	2	no	—
224	C₂²×C₄₃	—	2	4	no	—
225	C₂²×C₄₃	—	2	4	no	—
226	C₂²×C₄₃	—	2	4	no	—
227	C₂²×C₄₃	—	4	16	no	—
228	C₂²×C₄₃	—	4	2	no	—
229	C₂²×C₄₃	—	4	2	no	—
230	C₂²×C₄₃	—	4	2	no	—
231	C₂²×C₄₃	—	4	2	no	—
232	C₂²×C₄₃	—	4	4	no	—
233	C₂²×C₄₃	—	4	4	no	—
234	C₂²×C₄₃	—	4	4	no	—
235	C₂²×C₄₃	—	8	16	no	—
236	C₂²×C₄₃	—	8	4	no	—
237	C₂²×C₄₃	—	8	4	no	—
238	C₂²×C₄₃	#452	1	4	yes	—
239	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
240	C₂²×C₄₃	#534	1	2	yes	—
241	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
242	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
243	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
244	C₄×C₄₃	—	2	2	no	—
245	C₄×C₄₃	—	4	2	no	—
246	C₄×C₄₃	—	4	4	no	—
247	C₄×C₄₃	—	8	1	no	—
248	C₄×C₄₃	—	8	2	no	—
249	C₄×C₄₃	—	8	1	no	—
250	C₄×C₄₃	#534	1	2	yes	—
251	C₄×C₄₃	#535	1	2	yes	—
252	C₂²×#121	C₂×C₄₃	1	1	yes	characteristic
253	C₂×#484	C₂×C₄₃	1	1	yes	characteristic, complemented
254	C₂×#450	C₂×C₄₃	1	1	yes	characteristic, complemented
255	#2848	C₂×C₄₃	1	1	yes	characteristic, complemented
256	#2033	C₂×C₄₃	1	4	yes	complemented
257	#2000	C₂×C₄₃	1	4	yes	complemented
258	#1824	C₂×C₄₃	1	1	yes	characteristic, complemented
259	#1786	C₂×C₄₃	1	1	yes	characteristic, complemented
260	#1779	C₂×C₄₃	1	1	yes	characteristic, complemented
261	C₂×C₄₃	—	2	4	no	—
262	C₂×C₄₃	—	4	4	no	—
263	C₂×C₄₃	—	8	4	no	—
264	C₂×C₄₃	#2613	1	1	yes	characteristic
265	C₂×C₄₃	C₂×#452	1	1	yes	characteristic
266	C₂×C₄₃	#3003	1	1	yes	characteristic
267	C₂×C₄₃	#3188	1	2	yes	—
268	C₂×C₄₃	#3193	1	2	yes	—
269	C₂³×D₄	—	2	1	no	—
270	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
271	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
272	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	complemented
273	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
274	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	complemented
275	C₂×#121	—	2	4	no	—
276	C₂×#121	—	2	2	no	—
277	C₂×#121	—	2	4	no	—
278	C₂×#121	C₂²×C₄₃	1	4	yes	—
279	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
280	C₂²×C₂²⋊C₄	—	2	1	no	—
281	#484	—	2	4	no	—
282	#450	—	2	4	no	—
283	C₂×#107	C₂²×C₄₃	1	2	yes	complemented
284	C₂×#103	C₂²×C₄₃	1	2	yes	complemented
285	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
286	C₂×#102	C₂²×C₄₃	1	4	yes	complemented
287	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
288	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
289	C₂×C₂²⋊C₈	C₂²×C₄₃	1	4	yes	complemented
290	#385	—	2	2	no	—
291	#385	—	2	1	no	—
292	#380	C₂²×C₄₃	1	1	yes	characteristic
293	#380	C₂²×C₄₃	1	2	yes	complemented
294	#379	—	2	1	no	—
295	#340	C₂²×C₄₃	1	4	yes	complemented
296	C₄₃	#29598	1	1	yes	characteristic, direct product factor, Sylow
297	C₂⁵	—	2	1	no	—
298	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
299	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
300	C₂²×D₄	—	2	8	no	—
301	C₂²×D₄	—	2	4	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	—	4	4	no	—
305	C₂²×D₄	—	4	8	no	—
306	C₂²×D₄	D₄×C₄₃	1	4	yes	—
307	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
308	C₂³×C₄	—	2	1	no	—
309	C₂³×C₄	—	2	2	no	—
310	C₂³×C₄	—	2	2	no	—
311	C₂³×C₄	—	4	4	no	—
312	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
313	C₂³×C₄	D₄×C₄₃	1	2	yes	—
314	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
315	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
316	C₂×SD₁₆	—	2	4	no	—
317	C₂×SD₁₆	—	4	4	no	—
318	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
319	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	—	4	4	no	—
323	#121	—	2	16	no	—
324	#121	—	2	8	no	—
325	#121	—	2	8	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	—
331	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
334	C₂×C₂²⋊C₄	—	2	8	no	—
335	C₂×C₂²⋊C₄	—	2	4	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	#107	—	2	4	no	—
341	#103	—	2	4	no	—
342	#102	—	2	4	no	—
343	#102	—	4	4	no	—
344	C₂²⋊C₈	—	2	2	no	—
345	C₂²⋊C₈	—	2	2	no	—
346	C₂²⋊C₈	—	4	4	no	—
347	#95	—	2	1	no	—
348	#95	—	2	2	no	—
349	C₂⁴	—	2	2	no	—
350	C₂⁴	—	2	4	no	—
351	C₂⁴	—	2	4	no	—
352	C₂⁴	—	2	2	no	—
353	C₂⁴	—	2	2	no	—
354	C₂⁴	—	2	2	no	—
355	C₂⁴	—	4	2	no	—
356	C₂⁴	—	4	4	no	—
357	C₂⁴	—	4	4	no	—
358	C₂⁴	—	4	2	no	—
359	C₂⁴	—	4	2	no	—
360	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
361	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	4	no	—
365	C₂×D₄	—	2	16	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	4	8	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	8	no	—
373	C₂×D₄	—	4	32	no	—
374	C₂×D₄	—	4	8	no	—
375	C₂×D₄	—	4	8	no	—
376	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	4	8	no	—
393	C₂²×C₄	—	4	8	no	—
394	C₂²×C₄	—	4	4	no	—
395	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
396	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
400	SD₁₆	—	4	8	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	4	no	—
404	C₂×C₈	—	2	4	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	4	4	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
413	C₂²⋊C₄	—	2	16	no	—
414	C₂²⋊C₄	—	4	4	no	—
415	C₂²⋊C₄	—	4	2	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	8	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	4	8	no	—
429	C₂³	—	4	8	no	—
430	C₂³	—	4	4	no	—
431	C₂³	—	4	8	no	—
432	C₂³	—	4	8	no	—
433	C₂³	—	4	4	no	—
434	C₂³	—	4	4	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	4	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	8	no	—
439	C₂³	—	8	8	no	—
440	C₂³	—	8	8	no	—
441	C₂³	#120×C₄₃	1	2	yes	—
442	C₂³	#135×C₄₃	1	2	yes	—
443	C₂³	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
444	C₂³	#137×C₄₃	1	2	yes	—
445	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
446	Q₈	—	4	2	no	—
447	Q₈	—	4	2	no	—
448	D₄	—	2	4	no	—
449	D₄	—	2	4	no	—
450	D₄	—	4	8	no	—
451	D₄	—	4	32	no	—
452	D₄	—	4	4	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	4	8	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	#120×C₄₃	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
476	C₂×C₄	H(5,𝔽₂)×C₄₃	1	4	yes	—
477	C₈	—	4	2	no	—
478	C₈	—	4	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	4	16	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	8	16	no	—
495	C₂²	—	8	4	no	—
496	C₂²	—	8	4	no	—
497	C₂²	C₄₃×#452	1	4	yes	—
498	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
499	C₂²	C₄₃×#534	1	2	yes	—
500	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
501	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
502	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
503	C₄	—	2	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	4	no	—
506	C₄	—	8	1	no	—
507	C₄	—	8	2	no	—
508	C₄	—	8	1	no	—
509	C₄	C₄₃×#534	1	2	yes	—
510	C₄	C₄₃×#535	1	2	yes	—
511	C₂	—	2	4	no	—
512	C₂	—	4	4	no	—
513	C₂	—	8	4	no	—
514	C₂	C₄₃×#2613	1	1	yes	characteristic
515	C₂	C₂×C₄₃×#452	1	1	yes	characteristic
516	C₂	C₄₃×#3003	1	1	yes	characteristic
517	C₂	C₄₃×#3188	1	2	yes	—
518	C₂	C₄₃×#3193	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×#121×C₄₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂⁴×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#484	C₂	semidirect
3. C₂×C₄₃×#450	C₂	semidirect
4. C₄₃×#2848	C₂	semidirect
5. C₄₃×#2033	C₂	semidirect
6. C₄₃×#2000	C₂	semidirect
7. C₄₃×#1824	C₂	semidirect
8. C₄₃×#1786	C₂	semidirect
9. C₄₃×#1779	C₂	semidirect
13. C₂²×SD₁₆×C₄₃	C₂²	semidirect
15. C₂×C₂²⋊Q₈×C₄₃	C₂²	semidirect
24. C₂×#107×C₄₃	C₂²	semidirect
25. C₂×#103×C₄₃	C₂²	semidirect
26. C₂×#102×C₄₃	C₂²	semidirect
27. C₂×#102×C₄₃	C₂²	semidirect
30. C₂×C₂²⋊C₈×C₄₃	C₂²	semidirect
34. C₄₃×#380	C₂²	semidirect
36. C₄₃×#340	C₂²	semidirect
219. #29598	C₄₃	direct (N × H)
253. C₂×#484	C₂×C₄₃	semidirect
254. C₂×#450	C₂×C₄₃	semidirect
255. #2848	C₂×C₄₃	semidirect
256. #2033	C₂×C₄₃	semidirect
257. #2000	C₂×C₄₃	semidirect
258. #1824	C₂×C₄₃	semidirect
259. #1786	C₂×C₄₃	semidirect
260. #1779	C₂×C₄₃	semidirect
272. C₂²×SD₁₆	C₂²×C₄₃	semidirect
274. C₂×C₂²⋊Q₈	C₂²×C₄₃	semidirect
283. C₂×#107	C₂²×C₄₃	semidirect
284. C₂×#103	C₂²×C₄₃	semidirect
285. C₂×#102	C₂²×C₄₃	semidirect
286. C₂×#102	C₂²×C₄₃	semidirect
289. C₂×C₂²⋊C₈	C₂²×C₄₃	semidirect
293. #380	C₂²×C₄₃	semidirect
295. #340	C₂²×C₄₃	semidirect
296. C₄₃	#29598	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#121×C₄₃	2
C₂×C₄₃×#484	2
C₂×C₄₃×#450	2
C₄₃×#2848	2
C₄₃×#2033	2
C₄₃×#2000	2
C₄₃×#1824	2
C₄₃×#1786	2
C₄₃×#1779	2
#29598	43

Subgroups — C43×#29598 #24949615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29598 #24949615