Subgroups — C₄₃×#29785 #24949802

Order 11008.

838 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#469	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2624	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2088	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2067	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2065	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2054	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1893	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1809	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×#121×C₄₃	C₂²	1	2	yes	—
14	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
15	C₄₃×#469	—	2	4	no	—
16	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#424	—	2	4	no	—
20	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×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	C₄₃×#399	—	2	2	no	—
26	C₄₃×#397	—	2	2	no	—
27	C₄₃×#394	—	2	2	no	—
28	C₄₃×#394	—	2	2	no	—
29	C₄₃×#390	C₂²	1	2	yes	—
30	C₄₃×#390	C₂²	1	2	yes	—
31	C₄₃×#389	C₂²	1	2	yes	—
32	C₄₃×#389	C₂²	1	2	yes	—
33	C₄₃×#380	C₂²	1	2	yes	—
34	C₄₃×#340	C₂²	1	2	yes	—
35	C₄₃×#340	C₂²	1	2	yes	—
36	C₄₃×#340	C₂²	1	2	yes	—
37	C₂²×D₄×C₄₃	—	2	2	no	—
38	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
40	C₂×D₈×C₄₃	—	2	2	no	—
41	C₂×D₈×C₄₃	—	4	1	no	—
42	C₂×D₈×C₄₃	—	4	1	no	—
43	C₂×M₁₆×C₄₃	—	4	1	no	—
44	C₂×M₁₆×C₄₃	—	4	1	no	—
45	C₂×M₁₆×C₄₃	D₄	1	4	yes	—
46	C₂²×C₈×C₄₃	—	2	2	no	—
47	C₂²×C₈×C₄₃	—	4	1	no	—
48	C₂²×C₈×C₄₃	—	4	1	no	—
49	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
52	#121×C₄₃	—	2	4	no	—
53	#121×C₄₃	—	2	4	no	—
54	#117×C₄₃	—	2	2	no	—
55	#117×C₄₃	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₄₃	—	2	2	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	C₂³	1	2	yes	—
71	#107×C₄₃	—	4	1	no	—
72	#106×C₄₃	—	2	2	no	—
73	#106×C₄₃	—	4	1	no	—
74	C₄⋊C₈×C₄₃	—	2	4	no	—
75	C₄⋊C₈×C₄₃	—	2	4	no	—
76	#102×C₄₃	—	2	4	no	—
77	#102×C₄₃	—	4	2	no	—
78	#102×C₄₃	—	4	2	no	—
79	#95×C₄₃	—	2	2	no	—
80	#95×C₄₃	—	2	2	no	—
81	#95×C₄₃	—	2	2	no	—
82	C₂⁴×C₄₃	—	2	2	no	—
83	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
84	C₂×D₄×C₄₃	—	2	2	no	—
85	C₂×D₄×C₄₃	—	2	2	no	—
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	—	4	4	no	—
91	C₂×D₄×C₄₃	—	8	2	no	—
92	C₂×D₄×C₄₃	—	8	2	no	—
93	C₂²×C₄×C₄₃	—	2	1	no	—
94	C₂²×C₄×C₄₃	—	2	1	no	—
95	C₂²×C₄×C₄₃	—	2	1	no	—
96	C₂²×C₄×C₄₃	—	2	1	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	#41	1	2	yes	—
105	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
106	D₈×C₄₃	—	4	4	no	—
107	M₁₆×C₄₃	—	4	4	no	—
108	C₂×C₈×C₄₃	—	2	1	no	—
109	C₂×C₈×C₄₃	—	2	1	no	—
110	C₂×C₈×C₄₃	—	2	1	no	—
111	C₂×C₈×C₄₃	—	2	1	no	—
112	C₂×C₈×C₄₃	—	2	2	no	—
113	C₂×C₈×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	—	2	2	no	—
115	C₂×C₈×C₄₃	—	4	4	no	—
116	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
118	C₄⋊C₄×C₄₃	—	2	4	no	—
119	C₄⋊C₄×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	—	8	2	no	—
126	C₄⋊C₄×C₄₃	—	8	2	no	—
127	C₂²⋊C₄×C₄₃	—	2	2	no	—
128	C₂²⋊C₄×C₄₃	—	2	2	no	—
129	C₂²⋊C₄×C₄₃	—	4	4	no	—
130	C₂²⋊C₄×C₄₃	—	8	2	no	—
131	C₂²⋊C₄×C₄₃	—	8	2	no	—
132	C₂²⋊C₄×C₄₃	—	8	2	no	—
133	C₂²⋊C₄×C₄₃	—	8	2	no	—
134	C₂²⋊C₄×C₄₃	—	8	2	no	—
135	C₄²×C₄₃	—	2	2	no	—
136	C₄²×C₄₃	—	2	2	no	—
137	C₂³×C₄₃	—	2	1	no	—
138	C₂³×C₄₃	—	2	1	no	—
139	C₂³×C₄₃	—	2	2	no	—
140	C₂³×C₄₃	—	2	2	no	—
141	C₂³×C₄₃	—	4	2	no	—
142	C₂³×C₄₃	—	4	2	no	—
143	C₂³×C₄₃	—	4	2	no	—
144	C₂³×C₄₃	—	4	2	no	—
145	C₂³×C₄₃	—	4	2	no	—
146	C₂³×C₄₃	—	4	2	no	—
147	C₂³×C₄₃	—	4	2	no	—
148	C₂³×C₄₃	#121	1	2	yes	—
149	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
150	D₄×C₄₃	—	4	2	no	—
151	D₄×C₄₃	—	4	2	no	—
152	D₄×C₄₃	—	4	2	no	—
153	D₄×C₄₃	—	4	2	no	—
154	D₄×C₄₃	—	8	8	no	—
155	C₂×C₄×C₄₃	—	2	1	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	—	4	2	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	4	2	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	#121	1	2	yes	—
177	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
180	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
181	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
182	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
183	C₈×C₄₃	—	2	2	no	—
184	C₈×C₄₃	—	2	2	no	—
185	C₈×C₄₃	—	4	2	no	—
186	#29785	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂²×C₄₃	—	2	2	no	—
188	C₂²×C₄₃	—	2	4	no	—
189	C₂²×C₄₃	—	4	2	no	—
190	C₂²×C₄₃	—	4	1	no	—
191	C₂²×C₄₃	—	4	1	no	—
192	C₂²×C₄₃	—	8	2	no	—
193	C₂²×C₄₃	—	8	2	no	—
194	C₂²×C₄₃	—	8	2	no	—
195	C₂²×C₄₃	—	8	2	no	—
196	C₂²×C₄₃	—	8	2	no	—
197	C₂²×C₄₃	—	8	2	no	—
198	C₂²×C₄₃	—	8	2	no	—
199	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
200	C₂²×C₄₃	#537	1	1	yes	characteristic
201	C₂²×C₄₃	#537	1	1	yes	characteristic
202	C₂²×C₄₃	#576	1	2	yes	—
203	C₂²×C₄₃	#577	1	2	yes	—
204	C₄×C₄₃	—	2	2	no	—
205	C₄×C₄₃	—	4	2	no	—
206	C₄×C₄₃	—	4	2	no	—
207	C₄×C₄₃	—	8	2	no	—
208	C₄×C₄₃	—	8	2	no	—
209	C₄×C₄₃	—	8	2	no	—
210	C₄×C₄₃	#534	1	1	yes	characteristic
211	C₄×C₄₃	#536	1	1	yes	characteristic
212	C₄×C₄₃	#539	1	1	yes	characteristic
213	C₄×C₄₃	#539	1	1	yes	characteristic
214	C₂×#469	C₂×C₄₃	1	1	yes	characteristic
215	C₂×#424	C₂×C₄₃	1	1	yes	characteristic, complemented
216	#2624	C₂×C₄₃	1	2	yes	complemented
217	#2088	C₂×C₄₃	1	2	yes	complemented
218	#2067	C₂×C₄₃	1	2	yes	complemented
219	#2065	C₂×C₄₃	1	2	yes	complemented
220	#2054	C₂×C₄₃	1	2	yes	complemented
221	#1893	C₂×C₄₃	1	2	yes	complemented
222	#1809	C₂×C₄₃	1	1	yes	characteristic, complemented
223	C₂×C₄₃	—	4	2	no	—
224	C₂×C₄₃	—	16	2	no	—
225	C₂×C₄₃	#2618	1	1	yes	characteristic
226	C₂×C₄₃	#3062	1	2	yes	—
227	C₂×C₄₃	#3257	1	2	yes	—
228	C₂×C₄₃	#3259	1	1	yes	characteristic
229	C₂×C₄₃	#3263	1	1	yes	characteristic
230	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic
231	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
232	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
233	C₂×#121	C₂²×C₄₃	1	2	yes	—
234	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
235	#469	—	2	4	no	—
236	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
237	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
238	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
239	#424	—	2	4	no	—
240	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
241	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
242	C₂×#102	C₂²×C₄₃	1	2	yes	—
243	C₂×#102	C₂²×C₄₃	1	2	yes	—
244	C₂×#102	C₂²×C₄₃	1	2	yes	—
245	#399	—	2	2	no	—
246	#397	—	2	2	no	—
247	#394	—	2	2	no	—
248	#394	—	2	2	no	—
249	#390	C₂²×C₄₃	1	2	yes	—
250	#390	C₂²×C₄₃	1	2	yes	—
251	#389	C₂²×C₄₃	1	2	yes	—
252	#389	C₂²×C₄₃	1	2	yes	—
253	#380	C₂²×C₄₃	1	2	yes	—
254	#340	C₂²×C₄₃	1	2	yes	—
255	#340	C₂²×C₄₃	1	2	yes	—
256	#340	C₂²×C₄₃	1	2	yes	—
257	C₄₃	#29785	1	1	yes	characteristic, direct product factor, Sylow
258	C₂²×D₄	—	2	2	no	—
259	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
260	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
261	C₂×D₈	—	2	2	no	—
262	C₂×D₈	—	4	1	no	—
263	C₂×D₈	—	4	1	no	—
264	C₂×M₁₆	—	4	1	no	—
265	C₂×M₁₆	—	4	1	no	—
266	C₂×M₁₆	D₄×C₄₃	1	4	yes	—
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	4	1	no	—
269	C₂²×C₈	—	4	1	no	—
270	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
271	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
273	#121	—	2	4	no	—
274	#121	—	2	4	no	—
275	#117	—	2	2	no	—
276	#117	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
292	#107	—	4	1	no	—
293	#106	—	2	2	no	—
294	#106	—	4	1	no	—
295	C₄⋊C₈	—	2	4	no	—
296	C₄⋊C₈	—	2	4	no	—
297	#102	—	2	4	no	—
298	#102	—	4	2	no	—
299	#102	—	4	2	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	C₂⁴	—	2	2	no	—
304	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	4	4	no	—
312	C₂×D₄	—	8	2	no	—
313	C₂×D₄	—	8	2	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
323	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
325	C₂²×C₄	#41×C₄₃	1	2	yes	—
326	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
327	D₈	—	4	4	no	—
328	M₁₆	—	4	4	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	4	4	no	—
337	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
338	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	8	2	no	—
347	C₄⋊C₄	—	8	2	no	—
348	C₂²⋊C₄	—	2	2	no	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₂²⋊C₄	—	4	4	no	—
351	C₂²⋊C₄	—	8	2	no	—
352	C₂²⋊C₄	—	8	2	no	—
353	C₂²⋊C₄	—	8	2	no	—
354	C₂²⋊C₄	—	8	2	no	—
355	C₂²⋊C₄	—	8	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	#121×C₄₃	1	2	yes	—
370	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	8	8	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	#121×C₄₃	1	2	yes	—
398	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
399	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
400	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
401	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
402	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
403	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
404	C₈	—	2	2	no	—
405	C₈	—	2	2	no	—
406	C₈	—	4	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	4	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	8	2	no	—
419	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
420	C₂²	C₄₃×#537	1	1	yes	characteristic
421	C₂²	C₄₃×#537	1	1	yes	characteristic
422	C₂²	C₄₃×#576	1	2	yes	—
423	C₂²	C₄₃×#577	1	2	yes	—
424	C₄	—	2	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	2	no	—
429	C₄	—	8	2	no	—
430	C₄	C₄₃×#534	1	1	yes	characteristic
431	C₄	C₄₃×#536	1	1	yes	characteristic
432	C₄	C₄₃×#539	1	1	yes	characteristic
433	C₄	C₄₃×#539	1	1	yes	characteristic
434	C₂	—	4	2	no	—
435	C₂	—	16	2	no	—
436	C₂	C₄₃×#2618	1	1	yes	characteristic
437	C₂	C₄₃×#3062	1	2	yes	—
438	C₂	C₄₃×#3257	1	2	yes	—
439	C₂	C₄₃×#3259	1	1	yes	characteristic
440	C₂	C₄₃×#3263	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#469	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. C₂×C₄₃×#424	C₂	semidirect
3. C₄₃×#2624	C₂	semidirect
4. C₄₃×#2088	C₂	semidirect
5. C₄₃×#2067	C₂	semidirect
6. C₄₃×#2065	C₂	semidirect
7. C₄₃×#2054	C₂	semidirect
8. C₄₃×#1893	C₂	semidirect
9. C₄₃×#1809	C₂	semidirect
186. #29785	C₄₃	direct (N × H)
215. C₂×#424	C₂×C₄₃	semidirect
216. #2624	C₂×C₄₃	semidirect
217. #2088	C₂×C₄₃	semidirect
218. #2067	C₂×C₄₃	semidirect
219. #2065	C₂×C₄₃	semidirect
220. #2054	C₂×C₄₃	semidirect
221. #1893	C₂×C₄₃	semidirect
222. #1809	C₂×C₄₃	semidirect
257. C₄₃	#29785	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×#469	2
C₂×C₄₃×#424	2
C₄₃×#2624	2
C₄₃×#2088	2
C₄₃×#2067	2
C₄₃×#2065	2
C₄₃×#2054	2
C₄₃×#1893	2
C₄₃×#1809	2
#29785	43

Subgroups — C43×#29785 #24949802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29785 #24949802