Subgroups — #576×Dic₄₃ #25960819

Order 11008.

2826 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	H(5,𝔽₂)×Dic₄₃	C₂	1	2	yes	maximal, complemented
2	#19143471	C₂	1	3	yes	maximal, complemented
3	#19143447	C₂	1	3	yes	maximal, complemented
4	#19143428	C₂	1	6	yes	maximal, complemented
5	AGL(1,ℤ/8)×Dic₄₃	C₂	1	6	yes	maximal, complemented
6	#135×Dic₄₃	C₂	1	3	yes	maximal, complemented
7	C₂×D₈×Dic₄₃	C₂	1	3	yes	maximal, complemented
8	#19143195	C₂	1	1	yes	maximal, characteristic, complemented
9	#19143121	C₂	1	2	yes	maximal, complemented
10	#131×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₃×#576	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063332	C₂²	1	1	yes	characteristic
13	#14583382	—	2	2	no	—
14	#14583382	C₂²	1	2	yes	—
15	#14583382	C₂²	1	6	yes	complemented
16	#14583374	—	2	6	no	—
17	#14583374	C₂²	1	6	yes	complemented
18	#41×Dic₄₃	—	2	2	no	—
19	#41×Dic₄₃	C₂²	1	1	yes	characteristic
20	#41×Dic₄₃	C₂²	1	6	yes	complemented
21	C₂×D₄×Dic₄₃	—	2	6	no	—
22	C₂×D₄×Dic₄₃	C₂²	1	6	yes	complemented
23	#14583011	C₂²	1	12	yes	complemented
24	#14583000	C₂²	1	12	yes	complemented
25	Q₁₆×Dic₄₃	C₂²	1	3	yes	complemented
26	Q₁₆×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
27	SD₁₆×Dic₄₃	C₂²	1	6	yes	complemented
28	SD₁₆×Dic₄₃	C₂²	1	6	yes	complemented
29	D₈×Dic₄₃	C₂²	1	6	yes	complemented
30	D₈×Dic₄₃	C₂²	1	3	yes	complemented
31	D₈×Dic₄₃	C₂²	1	6	yes	complemented
32	D₈×Dic₄₃	C₂²	1	3	yes	complemented
33	D₈×Dic₄₃	C₂²	1	6	yes	complemented
34	#14582941	C₂²	1	6	yes	complemented
35	#14582937	C₂²	1	3	yes	complemented
36	C₂×#13063259	C₂²	1	3	yes	complemented
37	#14582904	C₂²	1	6	yes	complemented
38	#14582900	C₂²	1	6	yes	complemented
39	#14582895	C₂²	1	6	yes	complemented
40	C₂×#13063246	C₂²	1	6	yes	complemented
41	#14582857	C₂²	1	3	yes	complemented
42	#14582854	C₂²	1	3	yes	complemented
43	M₁₆×Dic₄₃	C₂²	1	3	yes	complemented
44	C₂×C₈×Dic₄₃	C₂²	1	3	yes	complemented
45	C₂×H(5,𝔽₂)×C₄₃	C₂²	1	2	yes	—
46	C₄₃×#576	C₄	1	16	yes	complemented
47	C₂×AGL(1,ℤ/8)×C₄₃	C₂²	1	6	yes	—
48	C₂×#135×C₄₃	C₂²	1	3	yes	—
49	C₂²×D₈×C₄₃	C₂²	1	3	yes	—
50	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
51	C₂³×Dic₄₃	—	2	6	no	—
52	#13063332	—	2	4	no	—
53	C₂×#10621877	C₂³	1	3	yes	—
54	C₂²×C₄₃⋊C₈	C₂³	1	3	yes	—
55	Q₈×Dic₄₃	—	2	2	no	—
56	Q₈×Dic₄₃	D₄	1	1	yes	characteristic
57	Q₈×Dic₄₃	D₄	1	1	yes	characteristic
58	Q₈×Dic₄₃	C₂³	1	2	yes	—
59	Q₈×Dic₄₃	C₂³	1	6	yes	—
60	D₄×Dic₄₃	—	2	6	no	—
61	D₄×Dic₄₃	—	2	6	no	—
62	D₄×Dic₄₃	—	2	6	no	—
63	D₄×Dic₄₃	—	2	12	no	—
64	D₄×Dic₄₃	—	2	6	no	—
65	D₄×Dic₄₃	—	2	6	no	—
66	D₄×Dic₄₃	—	2	6	no	—
67	D₄×Dic₄₃	—	2	6	no	—
68	D₄×Dic₄₃	D₄	1	3	yes	—
69	D₄×Dic₄₃	D₄	1	3	yes	—
70	D₄×Dic₄₃	C₂³	1	6	yes	—
71	D₄×Dic₄₃	C₂³	1	12	yes	—
72	D₄×Dic₄₃	C₂³	1	6	yes	—
73	#13063284	—	2	6	no	—
74	#13063284	—	2	6	no	—
75	#13063284	C₂³	1	6	yes	—
76	#13063284	C₂³	1	3	yes	—
77	C₂×C₄⋊Dic₄₃	—	2	6	no	—
78	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
79	C₂×C₂²⋊Dic₄₃	—	2	6	no	—
80	C₂×C₂²⋊Dic₄₃	—	2	12	no	—
81	C₂×C₄×Dic₄₃	—	2	6	no	—
82	C₂×C₄×Dic₄₃	C₂³	1	3	yes	—
83	#13063259	C₂³	1	3	yes	—
84	#13063259	C₂³	1	6	yes	—
85	#13063259	C₂³	1	1	yes	characteristic
86	#13063257	C₂³	1	6	yes	—
87	#13063249	C₂³	1	2	yes	—
88	#13063249	C₂³	1	6	yes	—
89	#13063246	C₂³	1	6	yes	—
90	#13063246	C₂³	1	12	yes	—
91	#13063246	C₂³	1	6	yes	—
92	#13063235	C₂³	1	6	yes	—
93	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
94	C₈×Dic₄₃	C₂³	1	3	yes	—
95	C₈×Dic₄₃	C₂³	1	3	yes	—
96	C₈×Dic₄₃	C₂³	1	3	yes	—
97	H(5,𝔽₂)×C₄₃	—	2	8	no	—
98	H(5,𝔽₂)×C₄₃	C₂×C₄	1	16	yes	complemented
99	C₂×#41×C₄₃	—	2	2	no	—
100	C₂×#41×C₄₃	C₂³	1	6	yes	—
101	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₄₃	—	2	6	no	—
103	C₂²×D₄×C₄₃	C₂³	1	6	yes	—
104	AGL(1,ℤ/8)×C₄₃	C₂×C₄	1	48	yes	complemented
105	#135×C₄₃	C₂×C₄	1	24	yes	complemented
106	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
107	C₂×SD₁₆×C₄₃	C₂³	1	6	yes	—
108	C₂×D₈×C₄₃	C₂×C₄	1	24	yes	complemented
109	C₂×D₈×C₄₃	C₂³	1	3	yes	—
110	C₂×D₈×C₄₃	C₂³	1	6	yes	—
111	#131×C₄₃	C₂×C₄	1	8	yes	complemented
112	C₂×M₁₆×C₄₃	C₂³	1	3	yes	—
113	C₂²×C₈×C₄₃	C₂³	1	3	yes	—
114	C₂⁴×C₄₃	—	2	6	no	—
115	#41×C₄₃	—	2	16	no	—
116	#41×C₄₃	—	2	12	no	—
117	#41×C₄₃	C₂²×C₄	1	4	yes	—
118	#41×C₄₃	C₂²×C₄	1	24	yes	complemented
119	#41×C₄₃	#41	1	4	yes	—
120	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
122	C₂×D₄×C₄₃	—	2	48	no	—
123	C₂×D₄×C₄₃	—	2	6	no	—
124	C₂×D₄×C₄₃	—	2	12	no	—
125	C₂×D₄×C₄₃	—	2	6	no	—
126	C₂×D₄×C₄₃	C₂²×C₄	1	24	yes	complemented
127	C₂×D₄×C₄₃	C₂×D₄	1	3	yes	—
128	C₂×D₄×C₄₃	C₂⁴	1	6	yes	—
129	C₂²×C₄×C₄₃	—	2	6	no	—
130	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
131	C₂²×Dic₄₃	—	2	6	no	—
132	C₂²×Dic₄₃	—	2	6	no	—
133	C₂²×Dic₄₃	—	2	12	no	—
134	C₂²×Dic₄₃	—	2	6	no	—
135	C₂²×Dic₄₃	—	8	12	no	—
136	C₂²×Dic₄₃	C₂×D₄	1	3	yes	—
137	C₂²×Dic₄₃	C₂×D₄	1	3	yes	—
138	Q₁₆×C₄₃	C₂²×C₄	1	4	yes	complemented
139	SD₁₆×C₄₃	C₂²×C₄	1	24	yes	complemented
140	D₈×C₄₃	C₂²×C₄	1	12	yes	complemented
141	D₈×C₄₃	C₂²×C₄	1	24	yes	complemented
142	M₁₆×C₄₃	C₂²×C₄	1	12	yes	complemented
143	C₂×C₈×C₄₃	C₂²×C₄	1	12	yes	complemented
144	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
145	C₂×C₈×C₄₃	C₂⁴	1	3	yes	—
146	C₂²⋊Dic₄₃	—	2	6	no	—
147	C₂²⋊Dic₄₃	—	2	12	no	—
148	C₂²⋊Dic₄₃	—	2	6	no	—
149	C₂²⋊Dic₄₃	—	2	6	no	—
150	C₂²⋊Dic₄₃	C₂×D₄	1	6	yes	—
151	C₄⋊Dic₄₃	—	2	6	no	—
152	C₄⋊Dic₄₃	—	2	6	no	—
153	C₄⋊Dic₄₃	—	2	2	no	—
154	C₄⋊Dic₄₃	C₂×D₄	1	3	yes	—
155	C₄⋊Dic₄₃	C₂×D₄	1	3	yes	—
156	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
157	C₄⋊Dic₄₃	C₂⁴	1	6	yes	—
158	C₄×Dic₄₃	—	2	6	no	—
159	C₄×Dic₄₃	—	2	2	no	—
160	C₄×Dic₄₃	—	2	6	no	—
161	C₄×Dic₄₃	C₂×D₄	1	3	yes	—
162	C₄×Dic₄₃	C₂×D₄	1	3	yes	—
163	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
164	C₄×Dic₄₃	C₂⁴	1	3	yes	—
165	#10621877	—	2	6	no	—
166	C₂×C₄₃⋊C₈	—	2	6	no	—
167	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
168	C₂×C₄₃⋊C₈	C₂⁴	1	3	yes	—
169	C₂³×C₄₃	—	2	6	no	—
170	C₂³×C₄₃	—	2	24	no	—
171	C₂³×C₄₃	—	8	6	no	—
172	C₂³×C₄₃	—	8	6	no	—
173	C₂³×C₄₃	C₂²×D₄	1	3	yes	—
174	Q₈×C₄₃	—	2	2	no	—
175	Q₈×C₄₃	C₄×D₄	1	4	yes	—
176	Q₈×C₄₃	C₂³×C₄	1	4	yes	—
177	D₄×C₄₃	—	2	24	no	—
178	D₄×C₄₃	—	2	24	no	—
179	D₄×C₄₃	—	2	6	no	—
180	D₄×C₄₃	C₄×D₄	1	12	yes	—
181	D₄×C₄₃	C₂³×C₄	1	12	yes	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	24	no	—
184	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
185	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
186	C₂×C₄×C₄₃	C₂×#41	1	6	yes	—
187	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
188	C₂×Dic₄₃	—	2	6	no	—
189	C₂×Dic₄₃	—	2	2	no	—
190	C₂×Dic₄₃	—	2	6	no	—
191	C₂×Dic₄₃	—	4	3	no	—
192	C₂×Dic₄₃	—	4	12	no	—
193	C₂×Dic₄₃	—	8	6	no	—
194	C₂×Dic₄₃	—	8	12	no	—
195	C₂×Dic₄₃	—	8	6	no	—
196	C₂×Dic₄₃	C₂²×D₄	1	3	yes	—
197	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×Dic₄₃	C₂²×D₄	1	3	yes	—
199	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
200	C₈×C₄₃	C₂³×C₄	1	2	yes	—
201	C₈×C₄₃	C₂³×C₄	1	6	yes	—
202	C₄₃⋊C₈	—	2	1	no	—
203	C₄₃⋊C₈	—	2	3	no	—
204	C₄×#576	—	43	1	no	maximal, Sylow
205	C₂²×C₄₃	—	2	3	no	—
206	C₂²×C₄₃	—	2	3	no	—
207	C₂²×C₄₃	—	2	12	no	—
208	C₂²×C₄₃	—	4	6	no	—
209	C₂²×C₄₃	—	4	6	no	—
210	C₂²×C₄₃	—	8	24	no	—
211	C₂²×C₄₃	C₂×C₄×D₄	1	6	yes	—
212	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
213	C₄×C₄₃	—	2	4	no	—
214	C₄×C₄₃	C₂×C₄×D₄	1	6	yes	—
215	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
216	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
217	Dic₄₃	—	2	1	no	—
218	Dic₄₃	—	2	3	no	—
219	Dic₄₃	—	2	3	no	—
220	Dic₄₃	—	4	2	no	—
221	Dic₄₃	—	4	6	no	—
222	Dic₄₃	#576	1	2	yes	direct product factor
223	C₂×#576	D₄₃	1	1	yes	characteristic
224	C₄×H(5,𝔽₂)	—	43	2	no	—
225	#2951	—	43	3	no	—
226	#2948	—	43	3	no	—
227	#2946	—	43	6	no	—
228	C₄×AGL(1,ℤ/8)	—	43	6	no	—
229	C₄×#135	—	43	3	no	—
230	C₂×C₄×D₈	—	43	3	no	—
231	#2913	—	43	1	no	—
232	#2897	—	43	2	no	—
233	C₄×#131	—	43	1	no	—
234	C₂×C₄₃	—	2	6	no	—
235	C₂×C₄₃	—	4	12	no	—
236	C₂×C₄₃	C₂²×C₄×D₄	1	1	yes	characteristic
237	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
238	C₂×C₄₃	#3584	1	1	yes	characteristic
239	C₂×H(5,𝔽₂)	C₂×D₄₃	1	2	yes	—
240	#576	Dic₄₃	1	16	yes	direct product factor
241	C₂×AGL(1,ℤ/8)	C₂×D₄₃	1	6	yes	—
242	C₂×#135	C₂×D₄₃	1	3	yes	—
243	C₂²×D₈	C₂×D₄₃	1	3	yes	—
244	C₂×#131	—	43	1	no	—
245	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
246	#520	—	43	2	no	—
247	#520	—	43	6	no	—
248	#520	—	86	2	no	—
249	#518	—	43	6	no	—
250	#518	—	86	6	no	—
251	C₄×#41	—	43	1	no	—
252	C₄×#41	—	43	6	no	—
253	C₄×#41	—	86	2	no	—
254	C₂×C₄×D₄	—	43	6	no	—
255	C₂×C₄×D₄	—	86	6	no	—
256	#442	—	43	12	no	—
257	#440	—	43	12	no	—
258	C₄×Q₁₆	—	43	1	no	—
259	C₄×Q₁₆	—	43	3	no	—
260	C₄×SD₁₆	—	43	6	no	—
261	C₄×SD₁₆	—	43	6	no	—
262	C₄×D₈	—	43	3	no	—
263	C₄×D₈	—	43	6	no	—
264	C₄×D₈	—	43	6	no	—
265	C₄×D₈	—	43	6	no	—
266	C₄×D₈	—	43	3	no	—
267	#428	—	43	6	no	—
268	#427	—	43	3	no	—
269	C₂×#107	—	43	3	no	—
270	#418	—	43	6	no	—
271	#417	—	43	6	no	—
272	#416	—	43	6	no	—
273	C₂×#102	—	43	6	no	—
274	#405	—	43	3	no	—
275	#405	—	43	3	no	—
276	C₄×M₁₆	—	43	3	no	—
277	C₂×C₄×C₈	—	43	3	no	—
278	C₄₃	C₄×#576	1	1	yes	characteristic, complemented, Sylow
279	H(5,𝔽₂)	—	2	8	no	—
280	H(5,𝔽₂)	C₂×Dic₄₃	1	16	yes	complemented
281	C₂×#41	—	2	2	no	—
282	C₂×#41	C₂²×D₄₃	1	6	yes	—
283	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
284	C₂²×D₄	—	2	6	no	—
285	C₂²×D₄	C₂²×D₄₃	1	6	yes	—
286	C₂³×C₄	—	86	6	no	—
287	AGL(1,ℤ/8)	C₂×Dic₄₃	1	48	yes	complemented
288	#135	C₂×Dic₄₃	1	24	yes	complemented
289	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
290	C₂×SD₁₆	C₂²×D₄₃	1	6	yes	—
291	C₂×D₈	C₂×Dic₄₃	1	24	yes	complemented
292	C₂×D₈	C₂²×D₄₃	1	3	yes	—
293	C₂×D₈	C₂²×D₄₃	1	6	yes	—
294	#131	—	86	4	no	—
295	#131	C₂×Dic₄₃	1	8	yes	complemented
296	C₂×M₁₆	—	43	3	no	—
297	C₂×M₁₆	C₂²×D₄₃	1	3	yes	—
298	C₂²×C₈	—	43	3	no	—
299	C₂²×C₈	C₂²×D₄₃	1	3	yes	—
300	C₄×Q₈	—	43	1	no	—
301	C₄×Q₈	—	43	1	no	—
302	C₄×Q₈	—	43	2	no	—
303	C₄×Q₈	—	43	6	no	—
304	C₄×Q₈	—	86	2	no	—
305	C₄×D₄	—	43	3	no	—
306	C₄×D₄	—	43	3	no	—
307	C₄×D₄	—	43	6	no	—
308	C₄×D₄	—	43	12	no	—
309	C₄×D₄	—	43	6	no	—
310	C₄×D₄	—	86	6	no	—
311	C₄×D₄	—	86	6	no	—
312	C₄×D₄	—	86	12	no	—
313	C₄×D₄	—	86	6	no	—
314	C₄×D₄	—	86	6	no	—
315	C₄×D₄	—	86	6	no	—
316	C₄×D₄	—	86	6	no	—
317	C₄×D₄	—	86	6	no	—
318	#117	—	43	3	no	—
319	#117	—	43	6	no	—
320	#117	—	86	6	no	—
321	#117	—	86	6	no	—
322	C₂×C₄⋊C₄	—	43	6	no	—
323	C₂×C₄⋊C₄	—	86	6	no	—
324	C₂×C₂²⋊C₄	—	86	12	no	—
325	C₂×C₂²⋊C₄	—	86	6	no	—
326	C₂×C₄²	—	43	3	no	—
327	C₂×C₄²	—	86	6	no	—
328	#107	—	43	3	no	—
329	#107	—	43	6	no	—
330	#107	—	43	1	no	—
331	#106	—	43	6	no	—
332	#103	—	43	2	no	—
333	#103	—	43	6	no	—
334	#102	—	43	6	no	—
335	#102	—	43	12	no	—
336	#102	—	43	6	no	—
337	#97	—	43	6	no	—
338	C₄×C₈	—	43	1	no	—
339	C₄×C₈	—	43	3	no	—
340	C₄×C₈	—	43	3	no	—
341	C₄×C₈	—	43	3	no	—
342	C₂⁴	—	2	6	no	—
343	#41	—	2	16	no	—
344	#41	—	2	12	no	—
345	#41	#10621900	1	4	yes	—
346	#41	C₂²×Dic₄₃	1	4	yes	—
347	#41	C₂²×Dic₄₃	1	24	yes	complemented
348	C₂×Q₈	D₄×D₄₃	1	1	yes	characteristic
349	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
350	C₂×D₄	—	2	6	no	—
351	C₂×D₄	—	2	48	no	—
352	C₂×D₄	—	2	6	no	—
353	C₂×D₄	—	2	12	no	—
354	C₂×D₄	D₄×D₄₃	1	3	yes	—
355	C₂×D₄	C₂²×Dic₄₃	1	24	yes	complemented
356	C₂×D₄	C₂³×D₄₃	1	6	yes	—
357	C₂²×C₄	—	2	6	no	—
358	C₂²×C₄	—	43	3	no	—
359	C₂²×C₄	—	43	3	no	—
360	C₂²×C₄	—	86	6	no	—
361	C₂²×C₄	—	86	12	no	—
362	C₂²×C₄	—	86	6	no	—
363	C₂²×C₄	—	86	6	no	—
364	C₂²×C₄	—	344	12	no	—
365	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
366	Q₁₆	C₂²×Dic₄₃	1	4	yes	complemented
367	SD₁₆	C₂²×Dic₄₃	1	24	yes	complemented
368	D₈	C₂²×Dic₄₃	1	12	yes	complemented
369	D₈	C₂²×Dic₄₃	1	24	yes	complemented
370	M₁₆	—	86	6	no	—
371	M₁₆	C₂²×Dic₄₃	1	12	yes	complemented
372	C₂×C₈	—	43	1	no	—
373	C₂×C₈	—	43	3	no	—
374	C₂×C₈	—	86	6	no	—
375	C₂×C₈	C₂²×Dic₄₃	1	12	yes	complemented
376	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
377	C₂×C₈	C₂³×D₄₃	1	3	yes	—
378	C₄⋊C₄	—	43	3	no	—
379	C₄⋊C₄	—	43	3	no	—
380	C₄⋊C₄	—	43	2	no	—
381	C₄⋊C₄	—	43	6	no	—
382	C₄⋊C₄	—	86	6	no	—
383	C₄⋊C₄	—	86	2	no	—
384	C₄⋊C₄	—	86	6	no	—
385	C₂²⋊C₄	—	43	6	no	—
386	C₂²⋊C₄	—	86	6	no	—
387	C₂²⋊C₄	—	86	12	no	—
388	C₂²⋊C₄	—	86	6	no	—
389	C₂²⋊C₄	—	86	6	no	—
390	C₄²	—	43	3	no	—
391	C₄²	—	43	3	no	—
392	C₄²	—	43	1	no	—
393	C₄²	—	43	3	no	—
394	C₄²	—	86	2	no	—
395	C₄²	—	86	6	no	—
396	C₄²	—	86	6	no	—
397	C₂³	—	2	6	no	—
398	C₂³	—	2	24	no	—
399	C₂³	—	8	6	no	—
400	C₂³	—	8	6	no	—
401	C₂³	C₂×D₄×D₄₃	1	3	yes	—
402	Q₈	—	2	2	no	—
403	Q₈	D₄×Dic₄₃	1	4	yes	—
404	Q₈	C₂³×Dic₄₃	1	4	yes	—
405	D₄	—	2	24	no	—
406	D₄	—	2	24	no	—
407	D₄	—	2	6	no	—
408	D₄	D₄×Dic₄₃	1	12	yes	—
409	D₄	C₂³×Dic₄₃	1	12	yes	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	24	no	—
412	C₂×C₄	—	43	1	no	—
413	C₂×C₄	—	43	1	no	—
414	C₂×C₄	—	43	3	no	—
415	C₂×C₄	—	43	3	no	—
416	C₂×C₄	—	86	6	no	—
417	C₂×C₄	—	86	2	no	—
418	C₂×C₄	—	86	6	no	—
419	C₂×C₄	—	344	12	no	—
420	C₂×C₄	—	344	6	no	—
421	C₂×C₄	—	344	6	no	—
422	C₂×C₄	—	172	12	no	—
423	C₂×C₄	—	172	3	no	—
424	C₂×C₄	C₂³×Dic₄₃	1	6	yes	—
425	C₂×C₄	C₂×D₄×D₄₃	1	3	yes	—
426	C₂×C₄	C₂×#10621900	1	6	yes	—
427	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
428	C₈	—	86	1	no	—
429	C₈	—	86	3	no	—
430	C₈	C₂³×Dic₄₃	1	2	yes	—
431	C₈	C₂³×Dic₄₃	1	6	yes	—
432	C₂²	—	2	3	no	—
433	C₂²	—	2	3	no	—
434	C₂²	—	2	12	no	—
435	C₂²	—	4	6	no	—
436	C₂²	—	4	6	no	—
437	C₂²	—	8	24	no	—
438	C₂²	C₂×D₄×Dic₄₃	1	6	yes	—
439	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
440	C₄	—	2	4	no	—
441	C₄	—	43	2	no	—
442	C₄	—	86	3	no	—
443	C₄	—	86	3	no	—
444	C₄	—	86	1	no	—
445	C₄	—	172	6	no	—
446	C₄	—	172	2	no	—
447	C₄	C₂×D₄×Dic₄₃	1	6	yes	—
448	C₄	C₂⁴×Dic₄₃	1	1	yes	characteristic
449	C₄	C₂²×#10621900	1	1	yes	characteristic
450	C₂	—	2	6	no	—
451	C₂	—	4	12	no	—
452	C₂	C₂²×D₄×Dic₄₃	1	1	yes	characteristic
453	C₂	#576×D₄₃	1	1	yes	characteristic
454	C₂	#19149363	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator	C₄×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting, prime radical	C₂×C₄₃×#576	C₂
socle	C₂²×C₄₃	C₂³×D₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×#576	D₄₃
hypocenter	C₄₃	C₄×#576
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×#41 ◁ C₂×#576

Complements

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

N	H ≅ G/N	type
1. H(5,𝔽₂)×Dic₄₃	C₂	semidirect
2. #19143471	C₂	semidirect
3. #19143447	C₂	semidirect
4. #19143428	C₂	semidirect
5. AGL(1,ℤ/8)×Dic₄₃	C₂	semidirect
6. #135×Dic₄₃	C₂	semidirect
7. C₂×D₈×Dic₄₃	C₂	semidirect
8. #19143195	C₂	semidirect
9. #19143121	C₂	semidirect
10. #131×Dic₄₃	C₂	semidirect
15. #14583382	C₂²	semidirect
17. #14583374	C₂²	semidirect
20. #41×Dic₄₃	C₂²	semidirect
22. C₂×D₄×Dic₄₃	C₂²	semidirect
23. #14583011	C₂²	semidirect
24. #14583000	C₂²	semidirect
25. Q₁₆×Dic₄₃	C₂²	semidirect
26. Q₁₆×Dic₄₃	C₂²	semidirect
27. SD₁₆×Dic₄₃	C₂²	semidirect
28. SD₁₆×Dic₄₃	C₂²	semidirect
29. D₈×Dic₄₃	C₂²	semidirect
30. D₈×Dic₄₃	C₂²	semidirect
31. D₈×Dic₄₃	C₂²	semidirect
32. D₈×Dic₄₃	C₂²	semidirect
33. D₈×Dic₄₃	C₂²	semidirect
34. #14582941	C₂²	semidirect
35. #14582937	C₂²	semidirect
36. C₂×#13063259	C₂²	semidirect
37. #14582904	C₂²	semidirect
38. #14582900	C₂²	semidirect
39. #14582895	C₂²	semidirect
40. C₂×#13063246	C₂²	semidirect
41. #14582857	C₂²	semidirect
42. #14582854	C₂²	semidirect
43. M₁₆×Dic₄₃	C₂²	semidirect
44. C₂×C₈×Dic₄₃	C₂²	semidirect
46. C₄₃×#576	C₄	semidirect
98. H(5,𝔽₂)×C₄₃	C₂×C₄	semidirect
104. AGL(1,ℤ/8)×C₄₃	C₂×C₄	semidirect
105. #135×C₄₃	C₂×C₄	semidirect
108. C₂×D₈×C₄₃	C₂×C₄	semidirect
111. #131×C₄₃	C₂×C₄	semidirect
118. #41×C₄₃	C₂²×C₄	semidirect
126. C₂×D₄×C₄₃	C₂²×C₄	semidirect
138. Q₁₆×C₄₃	C₂²×C₄	semidirect
139. SD₁₆×C₄₃	C₂²×C₄	semidirect
140. D₈×C₄₃	C₂²×C₄	semidirect
141. D₈×C₄₃	C₂²×C₄	semidirect
142. M₁₆×C₄₃	C₂²×C₄	semidirect
143. C₂×C₈×C₄₃	C₂²×C₄	semidirect
222. Dic₄₃	#576	direct (N × H)
240. #576	Dic₄₃	direct (N × H)
278. C₄₃	C₄×#576	semidirect
280. H(5,𝔽₂)	C₂×Dic₄₃	semidirect
287. AGL(1,ℤ/8)	C₂×Dic₄₃	semidirect
288. #135	C₂×Dic₄₃	semidirect
291. C₂×D₈	C₂×Dic₄₃	semidirect
295. #131	C₂×Dic₄₃	semidirect
347. #41	C₂²×Dic₄₃	semidirect
355. C₂×D₄	C₂²×Dic₄₃	semidirect
366. Q₁₆	C₂²×Dic₄₃	semidirect
367. SD₁₆	C₂²×Dic₄₃	semidirect
368. D₈	C₂²×Dic₄₃	semidirect
369. D₈	C₂²×Dic₄₃	semidirect
371. M₁₆	C₂²×Dic₄₃	semidirect
375. C₂×C₈	C₂²×Dic₄₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
H(5,𝔽₂)×Dic₄₃	2
#19143471	2
#19143447	2
#19143428	2
AGL(1,ℤ/8)×Dic₄₃	2
#135×Dic₄₃	2
C₂×D₈×Dic₄₃	2
#19143195	2
#19143121	2
#131×Dic₄₃	2
C₂×C₄₃×#576	2
C₄×#576	43

Subgroups — #576×Dic43 #25960819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #576×Dic₄₃ #25960819