Subgroups — C₄₃×#29822 #24949839

Order 11008.

834 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2046	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2045	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2019	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2018	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1967	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1965	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1838	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×AGL(1,ℤ/8)×C₄₃	C₂²	1	2	yes	—
14	C₂×AGL(1,ℤ/8)×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
16	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
17	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
19	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#496	—	2	2	no	—
21	C₄₃×#496	—	2	2	no	—
22	C₄₃×#464	—	2	2	no	—
23	C₄₃×#463	—	2	2	no	—
24	C₄₃×#460	—	2	2	no	—
25	C₄₃×#459	—	2	2	no	—
26	C₄₃×#433	—	2	2	no	—
27	C₄₃×#432	—	2	2	no	—
28	C₄₃×#424	C₂²	1	2	yes	—
29	C₄₃×#423	C₂²	1	1	yes	characteristic
30	C₄₃×#423	C₂²	1	1	yes	characteristic
31	C₄₃×#419	C₂²	1	1	yes	characteristic
32	C₄₃×#418	C₂²	1	2	yes	—
33	C₄₃×#418	C₂²	1	1	yes	characteristic
34	C₂×#101×C₄₃	C₂²	1	2	yes	—
35	C₂×#100×C₄₃	C₂²	1	2	yes	—
36	C₂×#100×C₄₃	C₂²	1	2	yes	—
37	C₂×#100×C₄₃	C₂²	1	2	yes	—
38	C₄₃×#408	C₂²	1	2	yes	—
39	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#341	C₂²	1	2	yes	—
42	C₄₃×#341	C₂²	1	2	yes	—
43	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₃	—	2	2	no	—
46	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
48	#137×C₄₃	—	4	2	no	—
49	AGL(1,ℤ/8)×C₄₃	—	4	2	no	—
50	AGL(1,ℤ/8)×C₄₃	—	4	2	no	—
51	AGL(1,ℤ/8)×C₄₃	—	4	2	no	—
52	C₂×Q₁₆×C₄₃	—	2	1	no	—
53	C₂×SD₁₆×C₄₃	—	2	2	no	—
54	C₂×SD₁₆×C₄₃	—	2	1	no	—
55	C₂×SD₁₆×C₄₃	—	2	1	no	—
56	C₂×SD₁₆×C₄₃	—	2	4	no	—
57	C₂×SD₁₆×C₄₃	—	4	2	no	—
58	C₂×SD₁₆×C₄₃	—	4	2	no	—
59	C₂×D₈×C₄₃	—	2	2	no	—
60	C₂×D₈×C₄₃	—	2	1	no	—
61	C₂×D₈×C₄₃	—	2	4	no	—
62	C₂×D₈×C₄₃	—	4	2	no	—
63	C₂×D₈×C₄₃	—	4	2	no	—
64	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
65	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
66	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
68	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
69	#127×C₄₃	—	2	2	no	—
70	#127×C₄₃	—	2	1	no	—
71	#127×C₄₃	—	2	1	no	—
72	#124×C₄₃	—	2	2	no	—
73	#124×C₄₃	—	2	1	no	—
74	#124×C₄₃	—	2	1	no	—
75	C₄×Q₈×C₄₃	D₄	1	2	yes	—
76	C₄×D₄×C₄₃	—	2	2	no	—
77	C₄×D₄×C₄₃	D₄	1	2	yes	—
78	#117×C₄₃	—	2	1	no	—
79	#117×C₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
81	C₂×C₄²×C₄₃	—	2	1	no	—
82	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₄₃	—	2	4	no	—
84	C₄⋊C₈×C₄₃	—	2	2	no	—
85	C₄⋊C₈×C₄₃	—	2	2	no	—
86	#103×C₄₃	—	2	2	no	—
87	#102×C₄₃	—	2	4	no	—
88	#102×C₄₃	—	2	2	no	—
89	#101×C₄₃	—	4	2	no	—
90	#100×C₄₃	—	4	2	no	—
91	#100×C₄₃	—	4	2	no	—
92	#100×C₄₃	—	4	2	no	—
93	C₂²⋊C₈×C₄₃	—	2	4	no	—
94	#97×C₄₃	—	2	1	no	—
95	#97×C₄₃	D₄	1	2	yes	—
96	#97×C₄₃	D₄	1	2	yes	—
97	C₄×C₈×C₄₃	—	2	1	no	—
98	C₂⁴×C₄₃	—	2	1	no	—
99	C₂⁴×C₄₃	—	2	2	no	—
100	#41×C₄₃	—	2	2	no	—
101	#41×C₄₃	—	2	2	no	—
102	C₂×Q₈×C₄₃	—	2	1	no	—
103	C₂×Q₈×C₄₃	—	2	1	no	—
104	C₂×Q₈×C₄₃	—	2	2	no	—
105	C₂×Q₈×C₄₃	—	2	2	no	—
106	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂×D₄×C₄₃	—	2	1	no	—
108	C₂×D₄×C₄₃	—	2	1	no	—
109	C₂×D₄×C₄₃	—	2	2	no	—
110	C₂×D₄×C₄₃	—	2	1	no	—
111	C₂×D₄×C₄₃	—	2	2	no	—
112	C₂×D₄×C₄₃	—	2	2	no	—
113	C₂×D₄×C₄₃	—	2	2	no	—
114	C₂×D₄×C₄₃	—	2	2	no	—
115	C₂×D₄×C₄₃	—	2	2	no	—
116	C₂×D₄×C₄₃	—	2	2	no	—
117	C₂×D₄×C₄₃	—	2	2	no	—
118	C₂×D₄×C₄₃	—	4	2	no	—
119	C₂×D₄×C₄₃	—	4	2	no	—
120	C₂×D₄×C₄₃	—	8	4	no	—
121	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	—	2	1	no	—
123	C₂²×C₄×C₄₃	—	2	2	no	—
124	C₂²×C₄×C₄₃	—	2	1	no	—
125	C₂²×C₄×C₄₃	#41	1	2	yes	—
126	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
127	Q₁₆×C₄₃	—	4	2	no	—
128	SD₁₆×C₄₃	—	4	8	no	—
129	SD₁₆×C₄₃	—	4	2	no	—
130	SD₁₆×C₄₃	—	4	4	no	—
131	SD₁₆×C₄₃	—	4	2	no	—
132	D₈×C₄₃	—	4	8	no	—
133	D₈×C₄₃	—	4	4	no	—
134	D₈×C₄₃	—	4	2	no	—
135	M₁₆×C₄₃	—	2	2	no	—
136	M₁₆×C₄₃	—	2	2	no	—
137	M₁₆×C₄₃	—	2	2	no	—
138	M₁₆×C₄₃	—	2	2	no	—
139	M₁₆×C₄₃	—	2	2	no	—
140	M₁₆×C₄₃	—	2	2	no	—
141	C₂×C₈×C₄₃	—	2	2	no	—
142	C₂×C₈×C₄₃	—	2	2	no	—
143	C₂×C₈×C₄₃	—	2	2	no	—
144	C₂×C₈×C₄₃	—	2	2	no	—
145	C₂×C₈×C₄₃	—	2	1	no	—
146	C₂×C₈×C₄₃	—	2	1	no	—
147	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
148	C₄⋊C₄×C₄₃	—	2	2	no	—
149	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
150	C₂²⋊C₄×C₄₃	—	2	2	no	—
151	C₂²⋊C₄×C₄₃	—	2	1	no	—
152	C₂²⋊C₄×C₄₃	—	4	2	no	—
153	C₂²⋊C₄×C₄₃	—	4	2	no	—
154	C₄²×C₄₃	—	2	2	no	—
155	C₄²×C₄₃	—	2	1	no	—
156	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₄₃	C₂×D₄	1	2	yes	—
159	C₂³×C₄₃	—	2	1	no	—
160	C₂³×C₄₃	—	4	1	no	—
161	C₂³×C₄₃	—	4	2	no	—
162	C₂³×C₄₃	—	4	2	no	—
163	C₂³×C₄₃	—	4	2	no	—
164	C₂³×C₄₃	—	4	2	no	—
165	C₂³×C₄₃	—	8	4	no	—
166	C₂³×C₄₃	—	8	2	no	—
167	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
168	Q₈×C₄₃	—	2	1	no	—
169	Q₈×C₄₃	—	2	1	no	—
170	Q₈×C₄₃	—	4	2	no	—
171	Q₈×C₄₃	—	4	1	no	—
172	Q₈×C₄₃	—	4	1	no	—
173	D₄×C₄₃	—	2	1	no	—
174	D₄×C₄₃	—	2	1	no	—
175	D₄×C₄₃	—	4	2	no	—
176	D₄×C₄₃	—	4	2	no	—
177	D₄×C₄₃	—	4	2	no	—
178	D₄×C₄₃	—	4	1	no	—
179	D₄×C₄₃	—	4	2	no	—
180	D₄×C₄₃	—	4	2	no	—
181	D₄×C₄₃	—	4	1	no	—
182	D₄×C₄₃	—	4	2	no	—
183	D₄×C₄₃	—	8	4	no	—
184	D₄×C₄₃	—	8	4	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	4	1	no	—
190	C₂×C₄×C₄₃	—	4	2	no	—
191	C₂×C₄×C₄₃	—	8	2	no	—
192	C₂×C₄×C₄₃	#121	1	2	yes	—
193	C₂×C₄×C₄₃	#121	1	2	yes	—
194	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
197	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
198	C₈×C₄₃	—	2	4	no	—
199	C₈×C₄₃	—	4	2	no	—
200	C₈×C₄₃	—	4	2	no	—
201	C₈×C₄₃	—	4	1	no	—
202	C₈×C₄₃	—	4	1	no	—
203	#29822	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂²×C₄₃	—	2	2	no	—
205	C₂²×C₄₃	—	4	1	no	—
206	C₂²×C₄₃	—	4	2	no	—
207	C₂²×C₄₃	—	8	1	no	—
208	C₂²×C₄₃	—	8	2	no	—
209	C₂²×C₄₃	—	8	2	no	—
210	C₂²×C₄₃	—	8	4	no	—
211	C₂²×C₄₃	—	16	2	no	—
212	C₂²×C₄₃	—	16	2	no	—
213	C₂²×C₄₃	—	16	2	no	—
214	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
215	C₂²×C₄₃	#540	1	2	yes	—
216	C₄×C₄₃	—	2	2	no	—
217	C₄×C₄₃	—	2	2	no	—
218	C₄×C₄₃	—	4	1	no	—
219	C₄×C₄₃	—	4	2	no	—
220	C₄×C₄₃	—	8	1	no	—
221	C₄×C₄₃	#535	1	2	yes	—
222	C₄×C₄₃	#535	1	1	yes	characteristic
223	C₄×C₄₃	#535	1	1	yes	characteristic
224	C₂×#496	C₂×C₄₃	1	1	yes	characteristic, complemented
225	#3040	C₂×C₄₃	1	1	yes	characteristic, complemented
226	#3038	C₂×C₄₃	1	1	yes	characteristic, complemented
227	#2923	C₂×C₄₃	1	1	yes	characteristic, complemented
228	#2046	C₂×C₄₃	1	2	yes	complemented
229	#2045	C₂×C₄₃	1	2	yes	complemented
230	#2019	C₂×C₄₃	1	2	yes	complemented
231	#2018	C₂×C₄₃	1	2	yes	complemented
232	#1967	C₂×C₄₃	1	1	yes	characteristic, complemented
233	#1965	C₂×C₄₃	1	1	yes	characteristic, complemented
234	#1838	C₂×C₄₃	1	1	yes	characteristic, complemented
235	C₂×C₄₃	—	2	2	no	—
236	C₂×C₄₃	—	8	1	no	—
237	C₂×C₄₃	—	16	1	no	—
238	C₂×C₄₃	—	16	2	no	—
239	C₂×C₄₃	#2619	1	1	yes	characteristic
240	C₂×C₄₃	#3068	1	2	yes	—
241	C₂×#137	C₂²×C₄₃	1	1	yes	characteristic
242	C₂×AGL(1,ℤ/8)	C₂²×C₄₃	1	2	yes	—
243	C₂×AGL(1,ℤ/8)	C₂²×C₄₃	1	1	yes	characteristic
244	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
245	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
246	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
247	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
248	C₄×#41	C₂²×C₄₃	1	1	yes	characteristic
249	#496	—	2	2	no	—
250	#496	—	2	2	no	—
251	#464	—	2	2	no	—
252	#463	—	2	2	no	—
253	#460	—	2	2	no	—
254	#459	—	2	2	no	—
255	#433	—	2	2	no	—
256	#432	—	2	2	no	—
257	#424	C₂²×C₄₃	1	2	yes	—
258	#423	C₂²×C₄₃	1	1	yes	characteristic
259	#423	C₂²×C₄₃	1	1	yes	characteristic
260	#419	C₂²×C₄₃	1	1	yes	characteristic
261	#418	C₂²×C₄₃	1	2	yes	—
262	#418	C₂²×C₄₃	1	1	yes	characteristic
263	C₂×#101	C₂²×C₄₃	1	2	yes	—
264	C₂×#100	C₂²×C₄₃	1	2	yes	—
265	C₂×#100	C₂²×C₄₃	1	2	yes	—
266	C₂×#100	C₂²×C₄₃	1	2	yes	—
267	#408	C₂²×C₄₃	1	2	yes	—
268	C₄×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
269	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
270	#341	C₂²×C₄₃	1	2	yes	—
271	#341	C₂²×C₄₃	1	2	yes	—
272	C₄₃	#29822	1	1	yes	characteristic, direct product factor, Sylow
273	C₂×#41	C₂³×C₄₃	1	1	yes	characteristic
274	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
275	C₂²×D₄	—	2	2	no	—
276	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
277	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
278	#137	—	4	2	no	—
279	AGL(1,ℤ/8)	—	4	2	no	—
280	AGL(1,ℤ/8)	—	4	2	no	—
281	AGL(1,ℤ/8)	—	4	2	no	—
282	C₂×Q₁₆	—	2	1	no	—
283	C₂×SD₁₆	—	2	2	no	—
284	C₂×SD₁₆	—	2	1	no	—
285	C₂×SD₁₆	—	2	1	no	—
286	C₂×SD₁₆	—	2	4	no	—
287	C₂×SD₁₆	—	4	2	no	—
288	C₂×SD₁₆	—	4	2	no	—
289	C₂×D₈	—	2	2	no	—
290	C₂×D₈	—	2	1	no	—
291	C₂×D₈	—	2	4	no	—
292	C₂×D₈	—	4	2	no	—
293	C₂×D₈	—	4	2	no	—
294	C₂×M₁₆	C₂³×C₄₃	1	1	yes	characteristic
295	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
296	C₂×M₁₆	C₂³×C₄₃	1	1	yes	characteristic
297	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
298	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
299	#127	—	2	2	no	—
300	#127	—	2	1	no	—
301	#127	—	2	1	no	—
302	#124	—	2	2	no	—
303	#124	—	2	1	no	—
304	#124	—	2	1	no	—
305	C₄×Q₈	D₄×C₄₃	1	2	yes	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	D₄×C₄₃	1	2	yes	—
308	#117	—	2	1	no	—
309	#117	C₂³×C₄₃	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
313	C₄⋊C₈	—	2	4	no	—
314	C₄⋊C₈	—	2	2	no	—
315	C₄⋊C₈	—	2	2	no	—
316	#103	—	2	2	no	—
317	#102	—	2	4	no	—
318	#102	—	2	2	no	—
319	#101	—	4	2	no	—
320	#100	—	4	2	no	—
321	#100	—	4	2	no	—
322	#100	—	4	2	no	—
323	C₂²⋊C₈	—	2	4	no	—
324	#97	—	2	1	no	—
325	#97	D₄×C₄₃	1	2	yes	—
326	#97	D₄×C₄₃	1	2	yes	—
327	C₄×C₈	—	2	1	no	—
328	C₂⁴	—	2	1	no	—
329	C₂⁴	—	2	2	no	—
330	#41	—	2	2	no	—
331	#41	—	2	2	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	C₂×D₄×C₄₃	1	1	yes	characteristic
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	—	8	4	no	—
351	C₂×D₄	C₂×D₄×C₄₃	1	1	yes	characteristic
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	#41×C₄₃	1	2	yes	—
356	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
357	Q₁₆	—	4	2	no	—
358	SD₁₆	—	4	8	no	—
359	SD₁₆	—	4	2	no	—
360	SD₁₆	—	4	4	no	—
361	SD₁₆	—	4	2	no	—
362	D₈	—	4	8	no	—
363	D₈	—	4	4	no	—
364	D₈	—	4	2	no	—
365	M₁₆	—	2	2	no	—
366	M₁₆	—	2	2	no	—
367	M₁₆	—	2	2	no	—
368	M₁₆	—	2	2	no	—
369	M₁₆	—	2	2	no	—
370	M₁₆	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
380	C₂²⋊C₄	—	2	1	no	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	1	no	—
386	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
387	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
388	C₄²	C₂×D₄×C₄₃	1	2	yes	—
389	C₂³	—	2	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	8	4	no	—
396	C₂³	—	8	2	no	—
397	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
398	Q₈	—	2	1	no	—
399	Q₈	—	2	1	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	1	no	—
402	Q₈	—	4	1	no	—
403	D₄	—	2	1	no	—
404	D₄	—	2	1	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	1	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	1	no	—
412	D₄	—	4	2	no	—
413	D₄	—	8	4	no	—
414	D₄	—	8	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	8	2	no	—
422	C₂×C₄	#121×C₄₃	1	2	yes	—
423	C₂×C₄	#121×C₄₃	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
425	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
426	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
427	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
428	C₈	—	2	4	no	—
429	C₈	—	4	2	no	—
430	C₈	—	4	1	no	—
431	C₈	—	4	1	no	—
432	C₈	—	4	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	8	4	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	16	2	no	—
441	C₂²	—	16	2	no	—
442	C₂²	—	16	2	no	—
443	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
444	C₂²	C₄₃×#540	1	2	yes	—
445	C₄	—	2	2	no	—
446	C₄	—	2	2	no	—
447	C₄	—	4	1	no	—
448	C₄	—	4	2	no	—
449	C₄	—	8	1	no	—
450	C₄	C₄₃×#535	1	2	yes	—
451	C₄	C₄₃×#535	1	1	yes	characteristic
452	C₄	C₄₃×#535	1	1	yes	characteristic
453	C₂	—	2	2	no	—
454	C₂	—	8	1	no	—
455	C₂	—	16	2	no	—
456	C₂	—	16	1	no	—
457	C₂	C₄₃×#2619	1	1	yes	characteristic
458	C₂	C₄₃×#3068	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#496	C₂	semidirect
2. C₄₃×#3040	C₂	semidirect
3. C₄₃×#3038	C₂	semidirect
4. C₄₃×#2923	C₂	semidirect
5. C₄₃×#2046	C₂	semidirect
6. C₄₃×#2045	C₂	semidirect
7. C₄₃×#2019	C₂	semidirect
8. C₄₃×#2018	C₂	semidirect
9. C₄₃×#1967	C₂	semidirect
10. C₄₃×#1965	C₂	semidirect
11. C₄₃×#1838	C₂	semidirect
203. #29822	C₄₃	direct (N × H)
224. C₂×#496	C₂×C₄₃	semidirect
225. #3040	C₂×C₄₃	semidirect
226. #3038	C₂×C₄₃	semidirect
227. #2923	C₂×C₄₃	semidirect
228. #2046	C₂×C₄₃	semidirect
229. #2045	C₂×C₄₃	semidirect
230. #2019	C₂×C₄₃	semidirect
231. #2018	C₂×C₄₃	semidirect
232. #1967	C₂×C₄₃	semidirect
233. #1965	C₂×C₄₃	semidirect
234. #1838	C₂×C₄₃	semidirect
272. C₄₃	#29822	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×#496	2
C₄₃×#3040	2
C₄₃×#3038	2
C₄₃×#2923	2
C₄₃×#2046	2
C₄₃×#2045	2
C₄₃×#2019	2
C₄₃×#2018	2
C₄₃×#1967	2
C₄₃×#1965	2
C₄₃×#1838	2
#29822	43

Subgroups — C43×#29822 #24949839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29822 #24949839