Subgroups — C₄₃×#29795 #24949812

Order 11008.

994 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#459	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2042	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2012	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1831	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
11	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
12	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#124×C₄₃	C₂²	1	4	yes	—
15	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₃	—	2	1	no	—
17	C₄₃×#461	—	2	4	no	—
18	C₄₃×#459	—	2	4	no	—
19	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#103×C₄₃	C₂²	1	2	yes	—
22	C₂×#103×C₄₃	C₂²	1	4	yes	—
23	C₂×#102×C₄₃	C₂²	1	2	yes	—
24	C₂×#102×C₄₃	C₂²	1	4	yes	—
25	C₄₃×#390	—	2	1	no	—
26	C₄₃×#390	—	2	1	no	—
27	C₄₃×#390	—	2	2	no	—
28	C₄₃×#390	C₂²	1	2	yes	—
29	C₄₃×#389	C₂²	1	2	yes	—
30	C₄₃×#388	—	2	2	no	—
31	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
32	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
33	C₄³×C₄₃	C₂²	1	1	yes	characteristic
34	C₄₃×#336	C₂²	1	4	yes	—
35	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
36	C₂²×D₄×C₄₃	—	2	1	no	—
37	C₂²×D₄×C₄₃	—	2	1	no	—
38	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
39	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₄₃	—	2	1	no	—
41	C₂×SD₁₆×C₄₃	—	2	4	no	—
42	C₂×SD₁₆×C₄₃	—	4	4	no	—
43	C₂×D₈×C₄₃	—	2	4	no	—
44	C₂×D₈×C₄₃	—	4	4	no	—
45	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
47	C₄⋊Q₈×C₄₃	—	2	2	no	—
48	C₄⋊Q₈×C₄₃	—	2	2	no	—
49	#127×C₄₃	—	2	2	no	—
50	#127×C₄₃	—	2	2	no	—
51	#124×C₄₃	—	4	4	no	—
52	#124×C₄₃	—	4	4	no	—
53	C₄×D₄×C₄₃	—	2	2	no	—
54	C₄×D₄×C₄₃	D₄	1	4	yes	—
55	#117×C₄₃	—	4	4	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₄²×C₄₃	—	2	1	no	—
67	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₃	D₄	1	2	yes	—
70	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
71	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
72	C₄⋊C₈×C₄₃	—	2	2	no	—
73	C₄⋊C₈×C₄₃	—	2	2	no	—
74	#103×C₄₃	—	2	4	no	—
75	#103×C₄₃	—	4	4	no	—
76	#102×C₄₃	—	2	4	no	—
77	#102×C₄₃	—	4	4	no	—
78	#95×C₄₃	—	2	2	no	—
79	#95×C₄₃	—	2	1	no	—
80	C₂⁴×C₄₃	—	2	1	no	—
81	C₂⁴×C₄₃	—	2	2	no	—
82	C₂×Q₈×C₄₃	—	2	2	no	—
83	C₂×Q₈×C₄₃	—	2	2	no	—
84	C₂×Q₈×C₄₃	—	2	4	no	—
85	C₂×Q₈×C₄₃	—	2	4	no	—
86	C₂×D₄×C₄₃	—	2	1	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	4	no	—
92	C₂×D₄×C₄₃	—	2	4	no	—
93	C₂×D₄×C₄₃	—	4	4	no	—
94	C₂×D₄×C₄₃	—	4	2	no	—
95	C₂×D₄×C₄₃	—	4	2	no	—
96	C₂×D₄×C₄₃	—	4	2	no	—
97	C₂×D₄×C₄₃	—	4	2	no	—
98	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₃	—	2	4	no	—
100	C₂²×C₄×C₄₃	—	2	1	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	4	2	no	—
104	C₂²×C₄×C₄₃	—	4	2	no	—
105	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
110	SD₁₆×C₄₃	—	4	8	no	—
111	D₈×C₄₃	—	4	8	no	—
112	C₂×C₈×C₄₃	—	2	2	no	—
113	C₂×C₈×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	—	2	4	no	—
115	C₂×C₈×C₄₃	—	2	4	no	—
116	C₄⋊C₄×C₄₃	—	2	1	no	—
117	C₄⋊C₄×C₄₃	—	2	2	no	—
118	C₄⋊C₄×C₄₃	—	2	2	no	—
119	C₄⋊C₄×C₄₃	—	4	4	no	—
120	C₄⋊C₄×C₄₃	—	4	2	no	—
121	C₄⋊C₄×C₄₃	—	4	2	no	—
122	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
123	C₂²⋊C₄×C₄₃	—	2	4	no	—
124	C₂²⋊C₄×C₄₃	—	4	4	no	—
125	C₂²⋊C₄×C₄₃	—	4	4	no	—
126	C₂²⋊C₄×C₄₃	—	4	8	no	—
127	C₂²⋊C₄×C₄₃	—	4	8	no	—
128	C₄²×C₄₃	—	2	2	no	—
129	C₄²×C₄₃	—	2	2	no	—
130	C₄²×C₄₃	—	2	2	no	—
131	C₄²×C₄₃	—	2	2	no	—
132	C₄²×C₄₃	—	4	2	no	—
133	C₄²×C₄₃	—	4	2	no	—
134	C₄²×C₄₃	C₂×D₄	1	2	yes	—
135	C₄²×C₄₃	#41	1	2	yes	—
136	C₂³×C₄₃	—	2	2	no	—
137	C₂³×C₄₃	—	4	2	no	—
138	C₂³×C₄₃	—	4	1	no	—
139	C₂³×C₄₃	—	4	1	no	—
140	C₂³×C₄₃	—	4	2	no	—
141	C₂³×C₄₃	—	4	2	no	—
142	C₂³×C₄₃	—	4	4	no	—
143	C₂³×C₄₃	—	4	2	no	—
144	C₂³×C₄₃	—	4	2	no	—
145	C₂³×C₄₃	—	4	4	no	—
146	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₄₃	—	4	2	no	—
148	Q₈×C₄₃	—	4	2	no	—
149	Q₈×C₄₃	—	4	4	no	—
150	D₄×C₄₃	—	2	2	no	—
151	D₄×C₄₃	—	2	2	no	—
152	D₄×C₄₃	—	4	2	no	—
153	D₄×C₄₃	—	4	2	no	—
154	D₄×C₄₃	—	4	2	no	—
155	D₄×C₄₃	—	4	4	no	—
156	D₄×C₄₃	—	8	4	no	—
157	D₄×C₄₃	—	8	4	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	—	4	1	no	—
167	C₂×C₄×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	—	4	8	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	4	4	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	#121	1	2	yes	—
175	C₂×C₄×C₄₃	#121	1	2	yes	—
176	C₂×C₄×C₄₃	#135	1	2	yes	—
177	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
178	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
181	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
182	C₈×C₄₃	—	4	2	no	—
183	C₈×C₄₃	—	4	2	no	—
184	#29795	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂²×C₄₃	—	4	2	no	—
186	C₂²×C₄₃	—	4	2	no	—
187	C₂²×C₄₃	—	4	2	no	—
188	C₂²×C₄₃	—	8	2	no	—
189	C₂²×C₄₃	—	8	2	no	—
190	C₂²×C₄₃	—	8	2	no	—
191	C₂²×C₄₃	—	8	4	no	—
192	C₂²×C₄₃	—	8	4	no	—
193	C₂²×C₄₃	—	8	2	no	—
194	C₂²×C₄₃	—	8	2	no	—
195	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
196	C₂²×C₄₃	#535	1	2	yes	—
197	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
198	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₂²×C₄₃	#575	1	2	yes	—
200	C₄×C₄₃	—	2	2	no	—
201	C₄×C₄₃	—	4	2	no	—
202	C₄×C₄₃	—	4	2	no	—
203	C₄×C₄₃	—	4	2	no	—
204	C₄×C₄₃	—	8	2	no	—
205	C₄×C₄₃	—	8	2	no	—
206	C₄×C₄₃	#463	1	4	yes	—
207	C₄×C₄₃	#535	1	1	yes	characteristic
208	C₄×C₄₃	#535	1	1	yes	characteristic
209	C₄×C₄₃	#540	1	2	yes	—
210	C₂×#461	C₂×C₄₃	1	1	yes	characteristic, complemented
211	C₂×#459	C₂×C₄₃	1	1	yes	characteristic
212	#2858	C₂×C₄₃	1	1	yes	characteristic, complemented
213	#2293	C₂×C₄₃	1	1	yes	characteristic, complemented
214	#2042	C₂×C₄₃	1	4	yes	complemented
215	#2012	C₂×C₄₃	1	4	yes	complemented
216	#1982	C₂×C₄₃	1	1	yes	characteristic, complemented
217	#1981	C₂×C₄₃	1	1	yes	characteristic, complemented
218	#1831	C₂×C₄₃	1	1	yes	characteristic, complemented
219	C₂×C₄₃	—	8	2	no	—
220	C₂×C₄₃	—	16	2	no	—
221	C₂×C₄₃	#2619	1	1	yes	characteristic
222	C₂×C₄₃	C₂×#463	1	1	yes	characteristic
223	C₂×C₄₃	#3040	1	1	yes	characteristic
224	C₂×C₄₃	#3212	1	2	yes	—
225	C₂×C₄₃	#3214	1	2	yes	—
226	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
227	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
228	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
229	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
230	C₂×#124	C₂²×C₄₃	1	4	yes	—
231	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
232	C₂×#117	—	2	1	no	—
233	#461	—	2	4	no	—
234	#459	—	2	4	no	—
235	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
236	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
237	C₂×#103	C₂²×C₄₃	1	2	yes	—
238	C₂×#103	C₂²×C₄₃	1	4	yes	—
239	C₂×#102	C₂²×C₄₃	1	2	yes	—
240	C₂×#102	C₂²×C₄₃	1	4	yes	—
241	#390	—	2	1	no	—
242	#390	—	2	1	no	—
243	#390	—	2	2	no	—
244	#390	C₂²×C₄₃	1	2	yes	—
245	#389	C₂²×C₄₃	1	2	yes	—
246	#388	—	2	2	no	—
247	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
248	C₄×C₂²⋊C₄	—	2	1	no	—
249	C₄³	C₂²×C₄₃	1	1	yes	characteristic
250	#336	C₂²×C₄₃	1	4	yes	—
251	C₄₃	#29795	1	1	yes	characteristic, direct product factor, Sylow
252	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
253	C₂²×D₄	—	2	1	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
256	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
257	C₂³×C₄	—	2	1	no	—
258	C₂×SD₁₆	—	2	4	no	—
259	C₂×SD₁₆	—	4	4	no	—
260	C₂×D₈	—	2	4	no	—
261	C₂×D₈	—	4	4	no	—
262	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
263	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
264	C₄⋊Q₈	—	2	2	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	#127	—	2	2	no	—
267	#127	—	2	2	no	—
268	#124	—	4	4	no	—
269	#124	—	4	4	no	—
270	C₄×D₄	—	2	2	no	—
271	C₄×D₄	D₄×C₄₃	1	4	yes	—
272	#117	—	4	4	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	4	no	—
281	C₂×C₂²⋊C₄	—	2	4	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
285	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
286	C₂×C₄²	D₄×C₄₃	1	2	yes	—
287	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
288	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
289	C₄⋊C₈	—	2	2	no	—
290	C₄⋊C₈	—	2	2	no	—
291	#103	—	2	4	no	—
292	#103	—	4	4	no	—
293	#102	—	2	4	no	—
294	#102	—	4	4	no	—
295	#95	—	2	2	no	—
296	#95	—	2	1	no	—
297	C₂⁴	—	2	1	no	—
298	C₂⁴	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	4	4	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
323	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
326	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
327	SD₁₆	—	4	8	no	—
328	D₈	—	4	8	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	4	no	—
332	C₂×C₈	—	2	4	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	4	4	no	—
342	C₂²⋊C₄	—	4	8	no	—
343	C₂²⋊C₄	—	4	8	no	—
344	C₂²⋊C₄	—	4	4	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	4	2	no	—
350	C₄²	—	4	2	no	—
351	C₄²	C₂×D₄×C₄₃	1	2	yes	—
352	C₄²	#41×C₄₃	1	2	yes	—
353	C₂³	—	2	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	4	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	4	no	—
363	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
364	Q₈	—	4	2	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	4	4	no	—
367	D₄	—	2	2	no	—
368	D₄	—	2	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	4	no	—
373	D₄	—	8	4	no	—
374	D₄	—	8	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	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	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	8	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	#121×C₄₃	1	2	yes	—
392	C₂×C₄	#121×C₄₃	1	2	yes	—
393	C₂×C₄	#135×C₄₃	1	2	yes	—
394	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
395	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
396	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
397	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
398	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
399	C₈	—	4	2	no	—
400	C₈	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	4	no	—
408	C₂²	—	8	4	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
412	C₂²	C₄₃×#535	1	2	yes	—
413	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
414	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
415	C₂²	C₄₃×#575	1	2	yes	—
416	C₄	—	2	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	8	2	no	—
421	C₄	—	8	2	no	—
422	C₄	C₄₃×#463	1	4	yes	—
423	C₄	C₄₃×#535	1	1	yes	characteristic
424	C₄	C₄₃×#535	1	1	yes	characteristic
425	C₄	C₄₃×#540	1	2	yes	—
426	C₂	—	8	2	no	—
427	C₂	—	16	2	no	—
428	C₂	C₄₃×#2619	1	1	yes	characteristic
429	C₂	C₂×C₄₃×#463	1	1	yes	characteristic
430	C₂	C₄₃×#3040	1	1	yes	characteristic
431	C₂	C₄₃×#3212	1	2	yes	—
432	C₂	C₄₃×#3214	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#459	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₄³×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#461	C₂	semidirect
3. C₄₃×#2858	C₂	semidirect
4. C₄₃×#2293	C₂	semidirect
5. C₄₃×#2042	C₂	semidirect
6. C₄₃×#2012	C₂	semidirect
7. C₄₃×#1982	C₂	semidirect
8. C₄₃×#1981	C₂	semidirect
9. C₄₃×#1831	C₂	semidirect
184. #29795	C₄₃	direct (N × H)
210. C₂×#461	C₂×C₄₃	semidirect
212. #2858	C₂×C₄₃	semidirect
213. #2293	C₂×C₄₃	semidirect
214. #2042	C₂×C₄₃	semidirect
215. #2012	C₂×C₄₃	semidirect
216. #1982	C₂×C₄₃	semidirect
217. #1981	C₂×C₄₃	semidirect
218. #1831	C₂×C₄₃	semidirect
251. C₄₃	#29795	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×#461	2
C₂×C₄₃×#459	2
C₄₃×#2858	2
C₄₃×#2293	2
C₄₃×#2042	2
C₄₃×#2012	2
C₄₃×#1982	2
C₄₃×#1981	2
C₄₃×#1831	2
#29795	43

Subgroups — C43×#29795 #24949812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29795 #24949812