Subgroups — C₄₃×#29735 #24949752

Order 11008.

1200 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2847	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2077	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2036	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2033	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2000	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1892	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1808	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
14	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
18	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#121×C₄₃	C₂²	1	2	yes	—
20	C₂×#120×C₄₃	—	2	1	no	—
21	C₄₃×#465	—	2	4	no	—
22	C₂×#107×C₄₃	C₂²	1	2	yes	complemented
23	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×#103×C₄₃	C₂²	1	2	yes	complemented
26	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
28	C₂×C₂²⋊C₈×C₄₃	—	2	4	no	—
29	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
31	C₄₃×#386	—	2	1	no	—
32	C₄₃×#386	—	2	2	no	—
33	C₄₃×#385	—	2	1	no	—
34	C₄₃×#385	—	2	2	no	—
35	C₄₃×#380	C₂²	1	1	yes	characteristic
36	C₄₃×#380	C₂²	1	1	yes	characteristic
37	C₄₃×#380	C₂²	1	2	yes	—
38	C₄₃×#380	C₂²	1	2	yes	—
39	C₄₃×#379	—	2	1	no	—
40	C₄₃×#340	C₂²	1	2	yes	complemented
41	C₄₃×#340	C₂²	1	2	yes	complemented
42	C₄₃×#340	C₂²	1	2	yes	complemented
43	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
44	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₃	—	2	2	no	—
46	C₂²×D₄×C₄₃	—	2	1	no	—
47	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₄₃	—	2	2	no	—
49	C₂³×C₄×C₄₃	—	2	2	no	—
50	C₂³×C₄×C₄₃	—	4	2	no	—
51	C₂³×C₄×C₄₃	—	4	2	no	—
52	C₂³×C₄×C₄₃	D₄	1	2	yes	—
53	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
56	C₂×SD₁₆×C₄₃	—	2	2	no	—
57	C₂×SD₁₆×C₄₃	—	4	2	no	—
58	C₂²×C₈×C₄₃	—	2	2	no	—
59	C₂²×C₈×C₄₃	—	4	2	no	—
60	C₂²×C₈×C₄₃	—	4	2	no	—
61	C₂²×C₈×C₄₃	D₄	1	4	yes	complemented
62	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
63	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
65	C₂²⋊Q₈×C₄₃	—	2	2	no	—
66	C₂²⋊Q₈×C₄₃	—	2	2	no	—
67	C₂²⋊Q₈×C₄₃	—	4	2	no	—
68	C₂²⋊Q₈×C₄₃	—	4	2	no	—
69	#121×C₄₃	—	2	2	no	—
70	#121×C₄₃	—	2	2	no	—
71	#121×C₄₃	—	4	2	no	—
72	#121×C₄₃	—	4	2	no	—
73	#120×C₄₃	—	4	4	no	—
74	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
75	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
88	#107×C₄₃	—	4	2	no	—
89	#106×C₄₃	—	2	2	no	—
90	#103×C₄₃	—	2	2	no	—
91	#103×C₄₃	—	4	2	no	—
92	#102×C₄₃	—	2	2	no	—
93	#102×C₄₃	—	4	2	no	—
94	C₂²⋊C₈×C₄₃	—	2	4	no	—
95	C₂²⋊C₈×C₄₃	—	2	4	no	—
96	#95×C₄₃	—	2	2	no	—
97	#95×C₄₃	—	2	1	no	—
98	#95×C₄₃	—	2	2	no	—
99	#95×C₄₃	—	2	1	no	—
100	C₂⁴×C₄₃	—	2	2	no	—
101	C₂⁴×C₄₃	—	2	4	no	—
102	C₂⁴×C₄₃	—	2	2	no	—
103	C₂⁴×C₄₃	—	2	2	no	—
104	C₂⁴×C₄₃	—	2	1	no	—
105	C₂⁴×C₄₃	—	4	2	no	—
106	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
107	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂×Q₈×C₄₃	—	2	1	no	—
109	C₂×Q₈×C₄₃	—	2	1	no	—
110	C₂×Q₈×C₄₃	—	2	2	no	—
111	C₂×Q₈×C₄₃	—	2	2	no	—
112	C₂×D₄×C₄₃	—	2	1	no	—
113	C₂×D₄×C₄₃	—	2	1	no	—
114	C₂×D₄×C₄₃	—	2	2	no	—
115	C₂×D₄×C₄₃	—	2	2	no	—
116	C₂×D₄×C₄₃	—	4	4	no	—
117	C₂×D₄×C₄₃	—	4	4	no	—
118	C₂×D₄×C₄₃	—	4	2	no	—
119	C₂×D₄×C₄₃	—	4	4	no	—
120	C₂×D₄×C₄₃	—	4	2	no	—
121	C₂×D₄×C₄₃	—	4	2	no	—
122	C₂²×C₄×C₄₃	—	2	2	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	2	no	—
127	C₂²×C₄×C₄₃	—	2	2	no	—
128	C₂²×C₄×C₄₃	—	2	2	no	—
129	C₂²×C₄×C₄₃	—	2	2	no	—
130	C₂²×C₄×C₄₃	—	2	2	no	—
131	C₂²×C₄×C₄₃	—	2	2	no	—
132	C₂²×C₄×C₄₃	—	2	1	no	—
133	C₂²×C₄×C₄₃	—	2	2	no	—
134	C₂²×C₄×C₄₃	—	2	1	no	—
135	C₂²×C₄×C₄₃	—	2	2	no	—
136	C₂²×C₄×C₄₃	—	2	1	no	—
137	C₂²×C₄×C₄₃	—	4	2	no	—
138	C₂²×C₄×C₄₃	—	4	2	no	—
139	C₂²×C₄×C₄₃	—	4	2	no	—
140	C₂²×C₄×C₄₃	—	4	4	no	—
141	C₂²×C₄×C₄₃	—	4	4	no	—
142	C₂²×C₄×C₄₃	—	4	8	no	—
143	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₃	#41	1	2	yes	—
147	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
148	SD₁₆×C₄₃	—	4	4	no	—
149	C₂×C₈×C₄₃	—	2	2	no	—
150	C₂×C₈×C₄₃	—	2	2	no	—
151	C₂×C₈×C₄₃	—	2	2	no	—
152	C₂×C₈×C₄₃	—	2	2	no	—
153	C₂×C₈×C₄₃	—	2	2	no	—
154	C₂×C₈×C₄₃	—	4	4	no	—
155	C₂×C₈×C₄₃	—	4	4	no	—
156	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
157	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
158	C₄⋊C₄×C₄₃	—	2	1	no	—
159	C₄⋊C₄×C₄₃	—	2	1	no	—
160	C₄⋊C₄×C₄₃	—	2	1	no	—
161	C₄⋊C₄×C₄₃	—	2	1	no	—
162	C₄⋊C₄×C₄₃	—	2	2	no	—
163	C₄⋊C₄×C₄₃	—	2	2	no	—
164	C₄⋊C₄×C₄₃	—	2	2	no	—
165	C₄⋊C₄×C₄₃	—	2	2	no	—
166	C₄⋊C₄×C₄₃	—	4	4	no	—
167	C₄⋊C₄×C₄₃	—	4	2	no	—
168	C₂²⋊C₄×C₄₃	—	4	4	no	—
169	C₂²⋊C₄×C₄₃	—	4	4	no	—
170	C₂²⋊C₄×C₄₃	—	4	4	no	—
171	C₂²⋊C₄×C₄₃	—	4	2	no	—
172	C₂²⋊C₄×C₄₃	—	4	2	no	—
173	C₂²⋊C₄×C₄₃	—	4	4	no	—
174	C₂²⋊C₄×C₄₃	—	4	2	no	—
175	C₂²⋊C₄×C₄₃	—	4	2	no	—
176	C₂³×C₄₃	—	2	2	no	—
177	C₂³×C₄₃	—	2	2	no	—
178	C₂³×C₄₃	—	2	8	no	—
179	C₂³×C₄₃	—	2	2	no	—
180	C₂³×C₄₃	—	2	2	no	—
181	C₂³×C₄₃	—	2	2	no	—
182	C₂³×C₄₃	—	2	2	no	—
183	C₂³×C₄₃	—	2	2	no	—
184	C₂³×C₄₃	—	2	2	no	—
185	C₂³×C₄₃	—	4	8	no	—
186	C₂³×C₄₃	—	4	8	no	—
187	C₂³×C₄₃	—	4	4	no	—
188	C₂³×C₄₃	—	4	4	no	—
189	C₂³×C₄₃	—	4	1	no	—
190	C₂³×C₄₃	—	4	2	no	—
191	C₂³×C₄₃	—	4	2	no	—
192	C₂³×C₄₃	—	4	1	no	—
193	C₂³×C₄₃	—	4	1	no	—
194	C₂³×C₄₃	#121	1	2	yes	—
195	C₂³×C₄₃	#135	1	4	yes	—
196	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
197	C₂³×C₄₃	#137	1	2	yes	—
198	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
199	Q₈×C₄₃	—	4	1	no	—
200	Q₈×C₄₃	—	4	1	no	—
201	Q₈×C₄₃	—	4	2	no	—
202	D₄×C₄₃	—	4	1	no	—
203	D₄×C₄₃	—	4	1	no	—
204	D₄×C₄₃	—	4	2	no	—
205	D₄×C₄₃	—	8	8	no	—
206	D₄×C₄₃	—	8	4	no	—
207	C₂×C₄×C₄₃	—	2	2	no	—
208	C₂×C₄×C₄₃	—	2	2	no	—
209	C₂×C₄×C₄₃	—	2	2	no	—
210	C₂×C₄×C₄₃	—	2	4	no	—
211	C₂×C₄×C₄₃	—	2	2	no	—
212	C₂×C₄×C₄₃	—	2	2	no	—
213	C₂×C₄×C₄₃	—	2	2	no	—
214	C₂×C₄×C₄₃	—	4	8	no	—
215	C₂×C₄×C₄₃	—	4	4	no	—
216	C₂×C₄×C₄₃	—	4	2	no	—
217	C₂×C₄×C₄₃	—	4	2	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	2	no	—
224	C₂×C₄×C₄₃	—	4	2	no	—
225	C₂×C₄×C₄₃	—	4	2	no	—
226	C₂×C₄×C₄₃	—	4	2	no	—
227	C₂×C₄×C₄₃	—	4	2	no	—
228	C₂×C₄×C₄₃	—	4	2	no	—
229	C₂×C₄×C₄₃	—	4	2	no	—
230	C₂×C₄×C₄₃	—	4	1	no	—
231	C₂×C₄×C₄₃	—	4	2	no	—
232	C₂×C₄×C₄₃	—	4	1	no	—
233	C₂×C₄×C₄₃	#121	1	2	yes	—
234	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
237	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
238	C₈×C₄₃	—	2	2	no	—
239	C₈×C₄₃	—	2	2	no	—
240	C₈×C₄₃	—	4	2	no	—
241	#29735	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂²×C₄₃	—	2	2	no	—
243	C₂²×C₄₃	—	2	4	no	—
244	C₂²×C₄₃	—	2	4	no	—
245	C₂²×C₄₃	—	2	2	no	—
246	C₂²×C₄₃	—	2	4	no	—
247	C₂²×C₄₃	—	2	4	no	—
248	C₂²×C₄₃	—	2	4	no	—
249	C₂²×C₄₃	—	4	16	no	—
250	C₂²×C₄₃	—	4	2	no	—
251	C₂²×C₄₃	—	4	2	no	—
252	C₂²×C₄₃	—	4	2	no	—
253	C₂²×C₄₃	—	4	2	no	—
254	C₂²×C₄₃	—	8	1	no	—
255	C₂²×C₄₃	—	8	2	no	—
256	C₂²×C₄₃	—	8	2	no	—
257	C₂²×C₄₃	—	8	1	no	—
258	C₂²×C₄₃	—	8	1	no	—
259	C₂²×C₄₃	#468	1	4	yes	—
260	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
261	C₂²×C₄₃	#534	1	2	yes	—
262	C₂²×C₄₃	C₂×#135	1	2	yes	—
263	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
264	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
265	C₄×C₄₃	—	2	2	no	—
266	C₄×C₄₃	—	4	2	no	—
267	C₄×C₄₃	—	8	1	no	—
268	C₄×C₄₃	—	8	2	no	—
269	C₄×C₄₃	—	8	2	no	—
270	C₄×C₄₃	—	8	1	no	—
271	C₄×C₄₃	—	8	1	no	—
272	C₄×C₄₃	#534	1	1	yes	characteristic
273	C₄×C₄₃	#535	1	1	yes	characteristic
274	C₄×C₄₃	#538	1	2	yes	—
275	C₂×#465	C₂×C₄₃	1	1	yes	characteristic, complemented
276	C₂²×C₂²⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
277	#2848	C₂×C₄₃	1	1	yes	characteristic, complemented
278	#2847	C₂×C₄₃	1	1	yes	characteristic
279	#2077	C₂×C₄₃	1	2	yes	complemented
280	#2036	C₂×C₄₃	1	2	yes	complemented
281	#2033	C₂×C₄₃	1	2	yes	complemented
282	#2000	C₂×C₄₃	1	2	yes	complemented
283	#1893	C₂×C₄₃	1	1	yes	characteristic, complemented
284	#1892	C₂×C₄₃	1	1	yes	characteristic, complemented
285	#1808	C₂×C₄₃	1	1	yes	characteristic, complemented
286	C₂×C₄₃	—	2	4	no	—
287	C₂×C₄₃	—	4	4	no	—
288	C₂×C₄₃	—	16	1	no	—
289	C₂×C₄₃	#2617	1	1	yes	characteristic
290	C₂×C₄₃	#3050	1	1	yes	characteristic
291	C₂×C₄₃	C₂×#468	1	1	yes	characteristic
292	C₂×C₄₃	#3188	1	2	yes	—
293	C₂×C₄₃	#3190	1	2	yes	—
294	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
295	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic, complemented
296	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
297	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
298	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
299	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
300	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
301	C₂×#121	C₂²×C₄₃	1	2	yes	—
302	C₂×#120	—	2	1	no	—
303	#465	—	2	4	no	—
304	C₂×#107	C₂²×C₄₃	1	2	yes	complemented
305	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic, complemented
306	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic, complemented
307	C₂×#103	C₂²×C₄₃	1	2	yes	complemented
308	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic, complemented
309	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
310	C₂×C₂²⋊C₈	—	2	4	no	—
311	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
312	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
313	#386	—	2	1	no	—
314	#386	—	2	2	no	—
315	#385	—	2	1	no	—
316	#385	—	2	2	no	—
317	#380	C₂²×C₄₃	1	1	yes	characteristic
318	#380	C₂²×C₄₃	1	1	yes	characteristic
319	#380	C₂²×C₄₃	1	2	yes	—
320	#380	C₂²×C₄₃	1	2	yes	—
321	#379	—	2	1	no	—
322	#340	C₂²×C₄₃	1	2	yes	complemented
323	#340	C₂²×C₄₃	1	2	yes	complemented
324	#340	C₂²×C₄₃	1	2	yes	complemented
325	C₄₃	#29735	1	1	yes	characteristic, direct product factor, Sylow
326	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
327	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
331	C₂³×C₄	—	2	2	no	—
332	C₂³×C₄	—	2	2	no	—
333	C₂³×C₄	—	4	2	no	—
334	C₂³×C₄	—	4	2	no	—
335	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
336	C₂³×C₄	D₄×C₄₃	1	2	yes	—
337	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
338	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
339	C₂×SD₁₆	—	2	2	no	—
340	C₂×SD₁₆	—	4	2	no	—
341	C₂²×C₈	—	2	2	no	—
342	C₂²×C₈	—	4	2	no	—
343	C₂²×C₈	—	4	2	no	—
344	C₂²×C₈	D₄×C₄₃	1	4	yes	complemented
345	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
346	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
348	C₂²⋊Q₈	—	2	2	no	—
349	C₂²⋊Q₈	—	2	2	no	—
350	C₂²⋊Q₈	—	4	2	no	—
351	C₂²⋊Q₈	—	4	2	no	—
352	#121	—	2	2	no	—
353	#121	—	2	2	no	—
354	#121	—	4	2	no	—
355	#121	—	4	2	no	—
356	#120	—	4	4	no	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	#107	—	4	2	no	—
372	#106	—	2	2	no	—
373	#103	—	2	2	no	—
374	#103	—	4	2	no	—
375	#102	—	2	2	no	—
376	#102	—	4	2	no	—
377	C₂²⋊C₈	—	2	4	no	—
378	C₂²⋊C₈	—	2	4	no	—
379	#95	—	2	2	no	—
380	#95	—	2	1	no	—
381	#95	—	2	2	no	—
382	#95	—	2	1	no	—
383	C₂⁴	—	2	2	no	—
384	C₂⁴	—	2	4	no	—
385	C₂⁴	—	2	2	no	—
386	C₂⁴	—	2	2	no	—
387	C₂⁴	—	2	1	no	—
388	C₂⁴	—	4	2	no	—
389	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
390	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	4	4	no	—
400	C₂×D₄	—	4	4	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	4	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	4	4	no	—
424	C₂²×C₄	—	4	4	no	—
425	C₂²×C₄	—	4	8	no	—
426	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
427	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
429	C₂²×C₄	#41×C₄₃	1	2	yes	—
430	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
431	SD₁₆	—	4	4	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	4	4	no	—
438	C₂×C₈	—	4	4	no	—
439	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
440	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	4	4	no	—
450	C₄⋊C₄	—	4	2	no	—
451	C₂²⋊C₄	—	4	4	no	—
452	C₂²⋊C₄	—	4	4	no	—
453	C₂²⋊C₄	—	4	4	no	—
454	C₂²⋊C₄	—	4	2	no	—
455	C₂²⋊C₄	—	4	4	no	—
456	C₂²⋊C₄	—	4	2	no	—
457	C₂²⋊C₄	—	4	2	no	—
458	C₂²⋊C₄	—	4	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	8	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	4	8	no	—
469	C₂³	—	4	8	no	—
470	C₂³	—	4	4	no	—
471	C₂³	—	4	4	no	—
472	C₂³	—	4	1	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	4	1	no	—
476	C₂³	—	4	1	no	—
477	C₂³	#121×C₄₃	1	2	yes	—
478	C₂³	#135×C₄₃	1	4	yes	—
479	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
480	C₂³	#137×C₄₃	1	2	yes	—
481	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
482	Q₈	—	4	1	no	—
483	Q₈	—	4	1	no	—
484	Q₈	—	4	2	no	—
485	D₄	—	4	1	no	—
486	D₄	—	4	1	no	—
487	D₄	—	4	2	no	—
488	D₄	—	8	8	no	—
489	D₄	—	8	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	4	8	no	—
498	C₂×C₄	—	4	4	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	#121×C₄₃	1	2	yes	—
517	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
518	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
519	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
520	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
521	C₈	—	2	2	no	—
522	C₈	—	2	2	no	—
523	C₈	—	4	2	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	4	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	2	4	no	—
530	C₂²	—	2	4	no	—
531	C₂²	—	4	16	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	8	2	no	—
538	C₂²	—	8	2	no	—
539	C₂²	—	8	1	no	—
540	C₂²	—	8	1	no	—
541	C₂²	C₄₃×#468	1	4	yes	—
542	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
543	C₂²	C₄₃×#534	1	2	yes	—
544	C₂²	C₂×#135×C₄₃	1	2	yes	—
545	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
546	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
547	C₄	—	2	2	no	—
548	C₄	—	4	2	no	—
549	C₄	—	8	1	no	—
550	C₄	—	8	2	no	—
551	C₄	—	8	2	no	—
552	C₄	—	8	1	no	—
553	C₄	—	8	1	no	—
554	C₄	C₄₃×#534	1	1	yes	characteristic
555	C₄	C₄₃×#535	1	1	yes	characteristic
556	C₄	C₄₃×#538	1	2	yes	—
557	C₂	—	2	4	no	—
558	C₂	—	4	4	no	—
559	C₂	—	16	1	no	—
560	C₂	C₄₃×#2617	1	1	yes	characteristic
561	C₂	C₄₃×#3050	1	1	yes	characteristic
562	C₂	C₂×C₄₃×#468	1	1	yes	characteristic
563	C₂	C₄₃×#3188	1	2	yes	—
564	C₂	C₄₃×#3190	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#2847	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
1. C₂×C₄₃×#465	C₂	semidirect
2. C₂²×C₂²⋊C₈×C₄₃	C₂	semidirect
3. C₄₃×#2848	C₂	semidirect
5. C₄₃×#2077	C₂	semidirect
6. C₄₃×#2036	C₂	semidirect
7. C₄₃×#2033	C₂	semidirect
8. C₄₃×#2000	C₂	semidirect
9. C₄₃×#1893	C₂	semidirect
10. C₄₃×#1892	C₂	semidirect
11. C₄₃×#1808	C₂	semidirect
13. C₂²×SD₁₆×C₄₃	C₂²	semidirect
22. C₂×#107×C₄₃	C₂²	semidirect
23. C₂×#106×C₄₃	C₂²	semidirect
24. C₂×#103×C₄₃	C₂²	semidirect
25. C₂×#103×C₄₃	C₂²	semidirect
26. C₂×#102×C₄₃	C₂²	semidirect
27. C₂×#102×C₄₃	C₂²	semidirect
40. C₄₃×#340	C₂²	semidirect
41. C₄₃×#340	C₂²	semidirect
42. C₄₃×#340	C₂²	semidirect
61. C₂²×C₈×C₄₃	D₄	semidirect
241. #29735	C₄₃	direct (N × H)
275. C₂×#465	C₂×C₄₃	semidirect
276. C₂²×C₂²⋊C₈	C₂×C₄₃	semidirect
277. #2848	C₂×C₄₃	semidirect
279. #2077	C₂×C₄₃	semidirect
280. #2036	C₂×C₄₃	semidirect
281. #2033	C₂×C₄₃	semidirect
282. #2000	C₂×C₄₃	semidirect
283. #1893	C₂×C₄₃	semidirect
284. #1892	C₂×C₄₃	semidirect
285. #1808	C₂×C₄₃	semidirect
295. C₂²×SD₁₆	C₂²×C₄₃	semidirect
304. C₂×#107	C₂²×C₄₃	semidirect
305. C₂×#106	C₂²×C₄₃	semidirect
306. C₂×#103	C₂²×C₄₃	semidirect
307. C₂×#103	C₂²×C₄₃	semidirect
308. C₂×#102	C₂²×C₄₃	semidirect
309. C₂×#102	C₂²×C₄₃	semidirect
322. #340	C₂²×C₄₃	semidirect
323. #340	C₂²×C₄₃	semidirect
324. #340	C₂²×C₄₃	semidirect
325. C₄₃	#29735	direct (N × H)
344. C₂²×C₈	D₄×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×#465	2
C₂²×C₂²⋊C₈×C₄₃	2
C₄₃×#2848	2
C₄₃×#2847	2
C₄₃×#2077	2
C₄₃×#2036	2
C₄₃×#2033	2
C₄₃×#2000	2
C₄₃×#1893	2
C₄₃×#1892	2
C₄₃×#1808	2
#29735	43

Subgroups — C43×#29735 #24949752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29735 #24949752