Subgroups — C₄₃×#29343 #24949360

Order 11008.

830 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#2619	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2101	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2041	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1936	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1934	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1875	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1874	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1750	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×#121×C₄₃	C₂²	1	2	yes	—
12	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#102×C₄₃	C₂²	1	2	yes	—
16	C₂×#102×C₄₃	C₂²	1	2	yes	—
17	C₂×#102×C₄₃	C₂²	1	2	yes	—
18	C₂×#102×C₄₃	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
20	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#394	—	2	1	no	—
23	C₄₃×#394	—	2	1	no	—
24	C₄₃×#392	—	2	1	no	—
25	C₄₃×#392	—	2	1	no	—
26	C₄₃×#390	C₂²	1	2	yes	—
27	C₄₃×#389	C₂²	1	2	yes	—
28	C₄₃×#389	C₂²	1	2	yes	—
29	C₄₃×#385	—	2	1	no	—
30	C₄₃×#385	—	2	1	no	—
31	C₄₃×#384	—	2	1	no	—
32	C₄₃×#382	—	2	1	no	—
33	C₄₃×#382	C₂²	1	1	yes	characteristic
34	C₄₃×#340	C₂²	1	2	yes	—
35	C₄₃×#340	C₂²	1	2	yes	—
36	C₄₃×#340	C₂²	1	2	yes	—
37	C₄₃×#340	C₂²	1	2	yes	—
38	C₄₃×#336	C₂²	1	2	yes	—
39	C₂²×D₄×C₄₃	—	2	2	no	—
40	C₂²×D₄×C₄₃	—	2	1	no	—
41	C₂²×D₄×C₄₃	—	2	1	no	—
42	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₃	—	2	1	no	—
44	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
47	#127×C₄₃	—	4	1	no	—
48	#127×C₄₃	—	4	1	no	—
49	#121×C₄₃	—	2	4	no	—
50	#121×C₄₃	—	2	4	no	—
51	#117×C₄₃	—	2	4	no	—
52	#117×C₄₃	—	4	1	no	—
53	#117×C₄₃	—	4	1	no	—
54	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₃	—	4	1	no	—
58	C₂×C₄⋊C₄×C₄₃	—	4	1	no	—
59	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₃	—	2	1	no	—
71	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
73	#102×C₄₃	—	2	4	no	—
74	#102×C₄₃	—	2	4	no	—
75	#102×C₄₃	—	4	2	no	—
76	#102×C₄₃	—	4	2	no	—
77	C₂²⋊C₈×C₄₃	—	2	4	no	—
78	#97×C₄₃	—	4	1	no	—
79	C₄×C₈×C₄₃	—	4	1	no	—
80	#95×C₄₃	—	2	2	no	—
81	#95×C₄₃	—	2	2	no	—
82	#95×C₄₃	—	2	1	no	—
83	#95×C₄₃	—	2	1	no	—
84	C₂⁴×C₄₃	—	2	2	no	—
85	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
86	C₂×D₄×C₄₃	—	2	2	no	—
87	C₂×D₄×C₄₃	—	2	2	no	—
88	C₂×D₄×C₄₃	—	2	2	no	—
89	C₂×D₄×C₄₃	—	2	2	no	—
90	C₂×D₄×C₄₃	—	2	2	no	—
91	C₂×D₄×C₄₃	—	2	2	no	—
92	C₂×D₄×C₄₃	—	4	2	no	—
93	C₂×D₄×C₄₃	—	4	2	no	—
94	C₂×D₄×C₄₃	—	4	4	no	—
95	C₂×D₄×C₄₃	—	8	2	no	—
96	C₂×D₄×C₄₃	—	8	2	no	—
97	C₂×D₄×C₄₃	—	8	2	no	—
98	C₂×D₄×C₄₃	—	8	2	no	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	—	2	1	no	—
101	C₂²×C₄×C₄₃	—	2	1	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	4	2	no	—
106	C₂²×C₄×C₄₃	—	8	2	no	—
107	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	#41	1	4	yes	—
113	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
114	C₂×C₈×C₄₃	—	2	2	no	—
115	C₂×C₈×C₄₃	—	2	2	no	—
116	C₂×C₈×C₄₃	—	2	2	no	—
117	C₂×C₈×C₄₃	—	2	2	no	—
118	C₂×C₈×C₄₃	—	2	2	no	—
119	C₂×C₈×C₄₃	—	2	2	no	—
120	C₄⋊C₄×C₄₃	—	2	2	no	—
121	C₄⋊C₄×C₄₃	—	2	2	no	—
122	C₄⋊C₄×C₄₃	—	2	2	no	—
123	C₄⋊C₄×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	—	2	2	no	—
125	C₄⋊C₄×C₄₃	—	4	1	no	—
126	C₄⋊C₄×C₄₃	—	4	1	no	—
127	C₄⋊C₄×C₄₃	—	4	2	no	—
128	C₄⋊C₄×C₄₃	—	8	2	no	—
129	C₄⋊C₄×C₄₃	—	8	2	no	—
130	C₄⋊C₄×C₄₃	#41	1	4	yes	—
131	C₂²⋊C₄×C₄₃	—	2	4	no	—
132	C₂²⋊C₄×C₄₃	—	4	1	no	—
133	C₂²⋊C₄×C₄₃	—	4	1	no	—
134	C₂²⋊C₄×C₄₃	—	4	4	no	—
135	C₂²⋊C₄×C₄₃	—	8	2	no	—
136	C₂²⋊C₄×C₄₃	—	8	2	no	—
137	C₄²×C₄₃	—	2	4	no	—
138	C₄²×C₄₃	—	2	1	no	—
139	C₄²×C₄₃	—	2	1	no	—
140	C₄²×C₄₃	—	2	1	no	—
141	C₄²×C₄₃	—	2	1	no	—
142	C₂³×C₄₃	—	2	1	no	—
143	C₂³×C₄₃	—	2	1	no	—
144	C₂³×C₄₃	—	2	2	no	—
145	C₂³×C₄₃	—	2	2	no	—
146	C₂³×C₄₃	—	4	2	no	—
147	C₂³×C₄₃	—	4	2	no	—
148	C₂³×C₄₃	—	4	2	no	—
149	C₂³×C₄₃	—	4	2	no	—
150	C₂³×C₄₃	—	4	2	no	—
151	C₂³×C₄₃	—	4	2	no	—
152	C₂³×C₄₃	—	4	2	no	—
153	C₂³×C₄₃	#124	1	2	yes	—
154	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
155	D₄×C₄₃	—	4	2	no	—
156	D₄×C₄₃	—	4	2	no	—
157	D₄×C₄₃	—	4	2	no	—
158	D₄×C₄₃	—	4	2	no	—
159	D₄×C₄₃	—	8	4	no	—
160	D₄×C₄₃	—	8	4	no	—
161	D₄×C₄₃	—	8	8	no	—
162	C₂×C₄×C₄₃	—	2	1	no	—
163	C₂×C₄×C₄₃	—	2	1	no	—
164	C₂×C₄×C₄₃	—	2	4	no	—
165	C₂×C₄×C₄₃	—	2	4	no	—
166	C₂×C₄×C₄₃	—	2	4	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	2	1	no	—
169	C₂×C₄×C₄₃	—	2	1	no	—
170	C₂×C₄×C₄₃	—	2	1	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	4	2	no	—
178	C₂×C₄×C₄₃	—	4	2	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	—	4	2	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	8	4	no	—
184	C₂×C₄×C₄₃	#124	1	2	yes	—
185	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
186	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
187	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
189	C₈×C₄₃	—	4	2	no	—
190	C₈×C₄₃	—	4	2	no	—
191	#29343	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂²×C₄₃	—	2	2	no	—
193	C₂²×C₄₃	—	2	4	no	—
194	C₂²×C₄₃	—	4	2	no	—
195	C₂²×C₄₃	—	4	1	no	—
196	C₂²×C₄₃	—	4	1	no	—
197	C₂²×C₄₃	—	8	2	no	—
198	C₂²×C₄₃	—	8	2	no	—
199	C₂²×C₄₃	—	8	2	no	—
200	C₂²×C₄₃	—	8	2	no	—
201	C₂²×C₄₃	—	8	2	no	—
202	C₂²×C₄₃	—	8	2	no	—
203	C₂²×C₄₃	—	8	2	no	—
204	C₂²×C₄₃	#525	1	1	yes	characteristic
205	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
206	C₂²×C₄₃	#534	1	1	yes	characteristic
207	C₂²×C₄₃	#576	1	2	yes	—
208	C₂²×C₄₃	#577	1	2	yes	—
209	C₄×C₄₃	—	2	2	no	—
210	C₄×C₄₃	—	4	4	no	—
211	C₄×C₄₃	—	4	1	no	—
212	C₄×C₄₃	—	4	1	no	—
213	C₄×C₄₃	—	4	1	no	—
214	C₄×C₄₃	—	4	1	no	—
215	C₄×C₄₃	—	8	2	no	—
216	C₄×C₄₃	—	8	2	no	—
217	C₄×C₄₃	#553	1	2	yes	—
218	C₄×C₄₃	#553	1	2	yes	—
219	#2619	C₂×C₄₃	1	1	yes	characteristic
220	#2317	C₂×C₄₃	1	1	yes	characteristic, complemented
221	#2101	C₂×C₄₃	1	2	yes	complemented
222	#2041	C₂×C₄₃	1	2	yes	complemented
223	#1936	C₂×C₄₃	1	2	yes	complemented
224	#1934	C₂×C₄₃	1	2	yes	complemented
225	#1875	C₂×C₄₃	1	2	yes	complemented
226	#1874	C₂×C₄₃	1	2	yes	complemented
227	#1750	C₂×C₄₃	1	1	yes	characteristic, complemented
228	C₂×C₄₃	—	4	2	no	—
229	C₂×C₄₃	—	16	2	no	—
230	C₂×C₄₃	#2591	1	1	yes	characteristic
231	C₂×C₄₃	#3119	1	2	yes	—
232	C₂×C₄₃	#3136	1	2	yes	—
233	C₂×C₄₃	#3199	1	1	yes	characteristic
234	C₂×C₄₃	#3200	1	1	yes	characteristic
235	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
236	C₂×#121	C₂²×C₄₃	1	2	yes	—
237	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
238	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
240	C₂×#102	C₂²×C₄₃	1	2	yes	—
241	C₂×#102	C₂²×C₄₃	1	2	yes	—
242	C₂×#102	C₂²×C₄₃	1	2	yes	—
243	C₂×#102	C₂²×C₄₃	1	2	yes	—
244	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
245	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
246	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
247	#394	—	2	1	no	—
248	#394	—	2	1	no	—
249	#392	—	2	1	no	—
250	#392	—	2	1	no	—
251	#390	C₂²×C₄₃	1	2	yes	—
252	#389	C₂²×C₄₃	1	2	yes	—
253	#389	C₂²×C₄₃	1	2	yes	—
254	#385	—	2	1	no	—
255	#385	—	2	1	no	—
256	#384	—	2	1	no	—
257	#382	—	2	1	no	—
258	#382	C₂²×C₄₃	1	1	yes	characteristic
259	#340	C₂²×C₄₃	1	2	yes	—
260	#340	C₂²×C₄₃	1	2	yes	—
261	#340	C₂²×C₄₃	1	2	yes	—
262	#340	C₂²×C₄₃	1	2	yes	—
263	#336	C₂²×C₄₃	1	2	yes	—
264	C₄₃	#29343	1	1	yes	characteristic, direct product factor, Sylow
265	C₂²×D₄	—	2	2	no	—
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
269	C₂³×C₄	—	2	1	no	—
270	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
272	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
273	#127	—	4	1	no	—
274	#127	—	4	1	no	—
275	#121	—	2	4	no	—
276	#121	—	2	4	no	—
277	#117	—	2	4	no	—
278	#117	—	4	1	no	—
279	#117	—	4	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	4	1	no	—
284	C₂×C₄⋊C₄	—	4	1	no	—
285	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
286	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
299	#102	—	2	4	no	—
300	#102	—	2	4	no	—
301	#102	—	4	2	no	—
302	#102	—	4	2	no	—
303	C₂²⋊C₈	—	2	4	no	—
304	#97	—	4	1	no	—
305	C₄×C₈	—	4	1	no	—
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	#95	—	2	1	no	—
309	#95	—	2	1	no	—
310	C₂⁴	—	2	2	no	—
311	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	4	4	no	—
321	C₂×D₄	—	8	2	no	—
322	C₂×D₄	—	8	2	no	—
323	C₂×D₄	—	8	2	no	—
324	C₂×D₄	—	8	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	8	2	no	—
333	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
338	C₂²×C₄	#41×C₄₃	1	4	yes	—
339	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	8	2	no	—
355	C₄⋊C₄	—	8	2	no	—
356	C₄⋊C₄	#41×C₄₃	1	4	yes	—
357	C₂²⋊C₄	—	2	4	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	4	4	no	—
361	C₂²⋊C₄	—	8	2	no	—
362	C₂²⋊C₄	—	8	2	no	—
363	C₄²	—	2	4	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	#124×C₄₃	1	2	yes	—
380	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	8	4	no	—
386	D₄	—	8	4	no	—
387	D₄	—	8	8	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	8	4	no	—
410	C₂×C₄	#124×C₄₃	1	2	yes	—
411	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
412	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
413	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
414	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
415	C₈	—	4	2	no	—
416	C₈	—	4	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	C₄₃×#525	1	1	yes	characteristic
430	C₂²	C₂×#124×C₄₃	1	1	yes	characteristic
431	C₂²	C₄₃×#534	1	1	yes	characteristic
432	C₂²	C₄₃×#576	1	2	yes	—
433	C₂²	C₄₃×#577	1	2	yes	—
434	C₄	—	2	2	no	—
435	C₄	—	4	4	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	2	no	—
442	C₄	C₄₃×#553	1	2	yes	—
443	C₄	C₄₃×#553	1	2	yes	—
444	C₂	—	4	2	no	—
445	C₂	—	16	2	no	—
446	C₂	C₄₃×#2591	1	1	yes	characteristic
447	C₂	C₄₃×#3119	1	2	yes	—
448	C₂	C₄₃×#3136	1	2	yes	—
449	C₂	C₄₃×#3199	1	1	yes	characteristic
450	C₂	C₄₃×#3200	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#2619	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×#117×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#2317	C₂	semidirect
3. C₄₃×#2101	C₂	semidirect
4. C₄₃×#2041	C₂	semidirect
5. C₄₃×#1936	C₂	semidirect
6. C₄₃×#1934	C₂	semidirect
7. C₄₃×#1875	C₂	semidirect
8. C₄₃×#1874	C₂	semidirect
9. C₄₃×#1750	C₂	semidirect
191. #29343	C₄₃	direct (N × H)
220. #2317	C₂×C₄₃	semidirect
221. #2101	C₂×C₄₃	semidirect
222. #2041	C₂×C₄₃	semidirect
223. #1936	C₂×C₄₃	semidirect
224. #1934	C₂×C₄₃	semidirect
225. #1875	C₂×C₄₃	semidirect
226. #1874	C₂×C₄₃	semidirect
227. #1750	C₂×C₄₃	semidirect
264. C₄₃	#29343	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×#2619	2
C₄₃×#2317	2
C₄₃×#2101	2
C₄₃×#2041	2
C₄₃×#1936	2
C₄₃×#1934	2
C₄₃×#1875	2
C₄₃×#1874	2
C₄₃×#1750	2
#29343	43

Subgroups — C43×#29343 #24949360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29343 #24949360