Subgroups — D₄₃×#3415 #26003104

Order 11008.

2126 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#576×D₄₃	C₂	1	2	yes	maximal, complemented
2	#19147736	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147735	C₂	1	6	yes	maximal, complemented
4	#19147734	C₂	1	2	yes	maximal, complemented
5	#19147733	C₂	1	3	yes	maximal, complemented
6	#19147732	C₂	1	3	yes	maximal, complemented
7	#509×D₄₃	C₂	1	6	yes	maximal, complemented
8	#508×D₄₃	C₂	1	3	yes	maximal, complemented
9	C₂×D₁₆×D₄₃	C₂	1	3	yes	maximal, complemented
10	#504×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3415	C₂	1	1	yes	maximal, characteristic, complemented
12	H(5,𝔽₂)×D₄₃	—	2	2	no	—
13	#14583704	C₂²	1	2	yes	complemented
14	#14583703	—	2	6	no	—
15	#14583702	—	2	2	no	—
16	#14583701	C₂²	1	6	yes	complemented
17	#14583700	C₂²	1	6	yes	complemented
18	AGL(1,ℤ/8)×D₄₃	—	2	6	no	—
19	#135×D₄₃	C₂²	1	6	yes	complemented
20	C₂×D₈×D₄₃	C₂²	1	6	yes	complemented
21	#131×D₄₃	C₂²	1	1	yes	characteristic
22	#14583337	C₂²	1	6	yes	complemented
23	#14583336	C₂²	1	12	yes	complemented
24	#14583335	C₂²	1	6	yes	complemented
25	#14583334	C₂²	1	6	yes	complemented
26	#14583333	C₂²	1	12	yes	complemented
27	#14583332	C₂²	1	3	yes	complemented
28	#14583331	C₂²	1	3	yes	complemented
29	#14583330	C₂²	1	6	yes	complemented
30	#14583329	C₂²	1	6	yes	complemented
31	#14583328	C₂²	1	3	yes	complemented
32	Q₃₂×D₄₃	C₂²	1	1	yes	characteristic, complemented
33	SD₃₂×D₄₃	C₂²	1	6	yes	complemented
34	C₂×D₆₈₈	C₂²	1	3	yes	complemented
35	C₂×#13063266	C₂²	1	6	yes	complemented
36	D₁₆×D₄₃	C₂²	1	3	yes	complemented
37	D₁₆×D₄₃	C₂²	1	6	yes	complemented
38	D₁₆×D₄₃	C₂²	1	6	yes	complemented
39	D₁₆×D₄₃	C₂²	1	6	yes	complemented
40	#14583317	C₂²	1	3	yes	complemented
41	#14583316	C₂²	1	1	yes	characteristic, complemented
42	#14583315	C₂²	1	3	yes	complemented
43	M₃₂×D₄₃	C₂²	1	3	yes	complemented
44	C₂×C₁₆×D₄₃	C₂²	1	3	yes	complemented
45	C₄₃×#576	C₂²	1	2	yes	complemented
46	C₄₃×#509	C₂²	1	6	yes	complemented
47	C₄₃×#508	C₂²	1	3	yes	complemented
48	C₂×D₁₆×C₄₃	C₂²	1	3	yes	complemented
49	C₄₃×#504	C₂²	1	1	yes	characteristic, complemented
50	#13063371	—	2	2	no	—
51	#13063371	—	2	6	no	—
52	#13063371	—	4	2	no	—
53	#13063370	—	2	6	no	—
54	#13063370	—	4	6	no	—
55	#41×D₄₃	—	2	6	no	—
56	#41×D₄₃	—	4	2	no	—
57	#41×D₄₃	D₄	1	1	yes	characteristic
58	C₂×D₄×D₄₃	—	2	6	no	—
59	C₂×D₄×D₄₃	—	4	6	no	—
60	#13063353	—	2	6	no	—
61	#13063352	—	2	12	no	—
62	#13063351	—	2	6	no	—
63	#13063350	—	2	6	no	—
64	#13063349	—	2	12	no	—
65	#13063348	C₂³	1	6	yes	complemented
66	#13063347	C₂³	1	6	yes	complemented
67	#13063346	—	2	6	no	—
68	#13063345	—	2	6	no	—
69	#13063344	C₂³	1	6	yes	complemented
70	Q₁₆×D₄₃	C₂³	1	2	yes	—
71	SD₁₆×D₄₃	—	2	6	no	—
72	C₂×D₃₄₄	C₂³	1	6	yes	complemented
73	C₂×#10621882	—	2	6	no	—
74	D₈×D₄₃	—	2	6	no	—
75	D₈×D₄₃	—	2	6	no	—
76	D₈×D₄₃	C₂³	1	6	yes	—
77	D₈×D₄₃	C₂³	1	12	yes	complemented
78	#13063333	D₄	1	3	yes	—
79	#13063332	D₄	1	1	yes	characteristic
80	#13063331	C₂³	1	3	yes	—
81	M₁₆×D₄₃	D₄	1	3	yes	—
82	C₂×C₈×D₄₃	C₂³	1	3	yes	—
83	Dic₃₄₄	C₂³	1	1	yes	characteristic, complemented
84	#13063271	C₂³	1	2	yes	complemented
85	#13063270	C₂³	1	6	yes	complemented
86	#13063269	C₂³	1	6	yes	complemented
87	#13063268	C₂³	1	6	yes	complemented
88	D₆₈₈	C₂³	1	3	yes	complemented
89	D₆₈₈	C₂³	1	6	yes	complemented
90	#13063266	C₂³	1	6	yes	complemented
91	#13063266	C₂³	1	12	yes	complemented
92	#13063265	C₂³	1	3	yes	complemented
93	#13063264	C₂³	1	6	yes	complemented
94	C₂×C₄₃⋊C₁₆	C₂³	1	3	yes	complemented
95	C₁₆×D₄₃	C₂³	1	1	yes	characteristic
96	C₁₆×D₄₃	C₂³	1	3	yes	—
97	C₁₆×D₄₃	C₂³	1	3	yes	complemented
98	C₁₆×D₄₃	C₂³	1	3	yes	complemented
99	H(5,𝔽₂)×C₄₃	—	2	2	no	—
100	AGL(1,ℤ/8)×C₄₃	—	2	6	no	—
101	#135×C₄₃	C₂³	1	6	yes	complemented
102	C₂×D₈×C₄₃	C₂³	1	6	yes	complemented
103	#131×C₄₃	C₂³	1	1	yes	characteristic
104	Q₃₂×C₄₃	C₂³	1	1	yes	characteristic, complemented
105	SD₃₂×C₄₃	C₂³	1	6	yes	complemented
106	D₁₆×C₄₃	C₂³	1	3	yes	complemented
107	D₁₆×C₄₃	C₂³	1	6	yes	complemented
108	M₃₂×C₄₃	C₂³	1	3	yes	complemented
109	C₂×C₁₆×C₄₃	C₂³	1	3	yes	complemented
110	C₂³×D₄₃	—	4	6	no	—
111	#41×C₄₃	—	2	6	no	—
112	#41×C₄₃	—	4	2	no	—
113	#41×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂×D₄×C₄₃	—	2	6	no	—
115	C₂×D₄×C₄₃	—	4	6	no	—
116	C₂×C₂²⋊D₄₃	—	4	12	no	—
117	C₂×C₂²⋊D₄₃	—	4	6	no	—
118	#10621902	—	2	6	no	—
119	#10621902	—	4	2	no	—
120	#10621902	D₈	1	1	yes	characteristic
121	Q₈×D₄₃	—	2	2	no	—
122	Q₈×D₄₃	D₈	1	1	yes	characteristic
123	#10621900	—	2	6	no	—
124	#10621900	—	4	6	no	—
125	#10621900	—	4	6	no	—
126	#10621900	D₈	1	3	yes	—
127	D₄×D₄₃	—	2	6	no	—
128	D₄×D₄₃	—	2	12	no	—
129	D₄×D₄₃	—	4	6	no	—
130	D₄×D₄₃	—	4	12	no	—
131	D₄×D₄₃	—	4	6	no	—
132	D₄×D₄₃	—	4	6	no	—
133	D₄×D₄₃	—	4	6	no	—
134	D₄×D₄₃	—	4	6	no	—
135	D₄×D₄₃	D₈	1	3	yes	—
136	#10621898	—	2	6	no	—
137	#10621898	—	4	6	no	—
138	#10621898	—	4	6	no	—
139	#10621898	C₂×D₄	1	3	yes	—
140	C₂×D₁₇₂	—	2	6	no	—
141	C₂×D₁₇₂	—	4	6	no	—
142	C₂×C₄×D₄₃	—	4	6	no	—
143	C₂×C₄×D₄₃	C₂×D₄	1	3	yes	—
144	Q₁₆×C₄₃	C₂⁴	1	2	yes	—
145	SD₁₆×C₄₃	—	2	6	no	—
146	D₈×C₄₃	—	2	6	no	—
147	D₈×C₄₃	C₂⁴	1	6	yes	—
148	M₁₆×C₄₃	C₂×D₄	1	3	yes	—
149	C₂×C₈×C₄₃	C₂⁴	1	3	yes	—
150	#10621885	—	2	2	no	—
151	#10621884	—	2	6	no	—
152	#10621883	—	2	6	no	—
153	#10621882	—	2	6	no	—
154	#10621882	—	2	12	no	—
155	#10621877	C₂×D₄	1	3	yes	—
156	C₂×C₄₃⋊C₈	C₂×D₄	1	3	yes	—
157	Dic₁₇₂	C₂⁴	1	2	yes	—
158	D₃₄₄	—	2	6	no	—
159	D₃₄₄	C₂⁴	1	6	yes	—
160	#10621873	—	2	6	no	—
161	#10621872	C₂×D₄	1	6	yes	—
162	C₈×D₄₃	C₂×D₄	1	3	yes	—
163	C₈×D₄₃	C₂×D₄	1	3	yes	—
164	C₈×D₄₃	C₂⁴	1	1	yes	characteristic
165	C₈×D₄₃	C₂⁴	1	3	yes	—
166	C₁₆×C₄₃	C₂⁴	1	1	yes	characteristic
167	C₁₆×C₄₃	C₂⁴	1	3	yes	—
168	C₄₃⋊C₁₆	C₂⁴	1	1	yes	characteristic
169	C₄₃⋊C₁₆	C₂⁴	1	3	yes	—
170	C₂³×C₄₃	—	4	6	no	—
171	C₂²×D₄₃	—	4	6	no	—
172	C₂²×D₄₃	—	4	6	no	—
173	C₂²×D₄₃	—	4	12	no	—
174	C₂²×D₄₃	—	16	12	no	—
175	C₂²×D₄₃	C₂×D₈	1	3	yes	—
176	Q₈×C₄₃	—	2	2	no	—
177	Q₈×C₄₃	C₂×D₈	1	1	yes	characteristic
178	D₄×C₄₃	—	2	6	no	—
179	D₄×C₄₃	—	4	6	no	—
180	D₄×C₄₃	—	4	6	no	—
181	D₄×C₄₃	C₂×D₈	1	3	yes	—
182	C₂×C₄×C₄₃	—	4	6	no	—
183	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
184	C₂²⋊D₄₃	—	4	6	no	—
185	C₂²⋊D₄₃	—	4	6	no	—
186	C₂²⋊D₄₃	—	4	6	no	—
187	C₂²⋊D₄₃	—	4	12	no	—
188	C₂²⋊D₄₃	C₂×D₈	1	6	yes	—
189	C₂×Dic₄₃	—	4	6	no	—
190	C₂×Dic₄₃	C₂×D₈	1	3	yes	—
191	D₁₇₂	—	2	6	no	—
192	D₁₇₂	—	4	6	no	—
193	D₁₇₂	—	4	6	no	—
194	D₁₇₂	C₂×D₈	1	3	yes	—
195	C₄×D₄₃	—	4	2	no	—
196	C₄×D₄₃	—	4	6	no	—
197	C₄×D₄₃	—	4	6	no	—
198	C₄×D₄₃	C₂×D₈	1	3	yes	—
199	C₄×D₄₃	C₂×D₈	1	3	yes	—
200	C₄×D₄₃	C₂²×D₄	1	1	yes	characteristic
201	C₄×D₄₃	C₂²×D₄	1	3	yes	—
202	Dic₈₆	—	2	2	no	—
203	Dic₈₆	—	4	2	no	—
204	Dic₈₆	C₂×D₈	1	3	yes	—
205	C₈×C₄₃	C₂²×D₄	1	3	yes	—
206	C₈×C₄₃	C₂⁵	1	1	yes	characteristic
207	C₄₃⋊C₈	C₂²×D₄	1	1	yes	characteristic
208	C₄₃⋊C₈	C₂²×D₄	1	3	yes	—
209	C₂×#3415	—	43	1	no	maximal, Sylow
210	C₂²×C₄₃	—	4	6	no	—
211	C₂²×C₄₃	—	16	6	no	—
212	C₂²×C₄₃	C₂²×D₈	1	3	yes	—
213	C₂×D₄₃	—	2	6	no	—
214	C₂×D₄₃	—	4	6	no	—
215	C₂×D₄₃	—	8	12	no	—
216	C₂×D₄₃	—	16	12	no	—
217	C₂×D₄₃	—	16	6	no	—
218	C₂×D₄₃	C₂²×D₈	1	3	yes	—
219	C₂×D₄₃	C₂²×D₈	1	1	yes	characteristic
220	C₄×C₄₃	—	4	2	no	—
221	C₄×C₄₃	C₂²×D₈	1	3	yes	—
222	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
223	Dic₄₃	—	4	2	no	—
224	Dic₄₃	C₂²×D₈	1	1	yes	characteristic
225	Dic₄₃	C₂²×D₈	1	3	yes	—
226	C₂×#576	—	43	2	no	—
227	#3415	—	43	6	no	—
228	#3415	—	43	3	no	—
229	#3415	—	43	3	no	—
230	#3415	—	43	1	no	—
231	#3415	—	43	2	no	—
232	#3415	D₄₃	1	1	yes	characteristic, direct product factor
233	C₂×#509	—	43	6	no	—
234	C₂×#508	—	43	3	no	—
235	C₂²×D₁₆	—	43	3	no	—
236	C₂×#504	—	43	1	no	—
237	C₂×C₄₃	—	2	3	no	—
238	C₂×C₄₃	—	8	6	no	—
239	C₂×C₄₃	C₂³×D₈	1	1	yes	characteristic
240	D₄₃	—	2	3	no	—
241	D₄₃	—	8	6	no	—
242	D₄₃	#3415	1	2	yes	direct product factor
243	C₂×H(5,𝔽₂)	—	86	2	no	—
244	#576	—	43	6	no	—
245	#576	—	43	6	no	—
246	#576	—	43	2	no	—
247	#576	—	86	6	no	—
248	#576	—	86	2	no	—
249	#576	C₂×D₄₃	1	2	yes	complemented
250	C₂×AGL(1,ℤ/8)	—	86	6	no	—
251	C₂×#135	—	43	6	no	—
252	C₂²×D₈	—	43	6	no	—
253	C₂×#131	—	43	1	no	—
254	#509	—	43	6	no	—
255	#509	—	43	6	no	—
256	#509	—	43	12	no	—
257	#509	—	43	12	no	—
258	#509	—	43	6	no	—
259	#509	C₂×D₄₃	1	6	yes	complemented
260	#508	—	43	6	no	—
261	#508	—	43	3	no	—
262	#508	—	43	6	no	—
263	#508	—	43	3	no	—
264	#508	—	43	3	no	—
265	#508	C₂×D₄₃	1	3	yes	complemented
266	C₂×Q₃₂	—	43	1	no	—
267	C₂×SD₃₂	—	43	6	no	—
268	C₂×D₁₆	—	43	6	no	—
269	C₂×D₁₆	—	43	3	no	—
270	C₂×D₁₆	—	43	6	no	—
271	C₂×D₁₆	—	43	6	no	—
272	C₂×D₁₆	—	43	6	no	—
273	C₂×D₁₆	—	43	3	no	—
274	C₂×D₁₆	C₂×D₄₃	1	3	yes	complemented
275	#504	—	43	1	no	—
276	#504	—	43	3	no	—
277	#504	—	43	3	no	—
278	#504	C₂×D₄₃	1	1	yes	characteristic, complemented
279	C₂×M₃₂	—	43	3	no	—
280	C₂²×C₁₆	—	43	3	no	—
281	C₄₃	C₂×#3415	1	1	yes	characteristic, complemented, Sylow
282	H(5,𝔽₂)	—	2	2	no	—
283	H(5,𝔽₂)	—	86	6	no	—
284	H(5,𝔽₂)	—	86	6	no	—
285	H(5,𝔽₂)	—	86	2	no	—
286	H(5,𝔽₂)	—	172	6	no	—
287	H(5,𝔽₂)	—	172	2	no	—
288	C₂×#41	—	43	1	no	—
289	C₂×#41	—	86	6	no	—
290	C₂×#41	—	172	2	no	—
291	C₂²×D₄	—	86	6	no	—
292	C₂²×D₄	—	172	6	no	—
293	AGL(1,ℤ/8)	—	2	6	no	—
294	AGL(1,ℤ/8)	—	86	12	no	—
295	AGL(1,ℤ/8)	—	86	12	no	—
296	AGL(1,ℤ/8)	—	86	6	no	—
297	AGL(1,ℤ/8)	—	86	6	no	—
298	AGL(1,ℤ/8)	—	86	6	no	—
299	#135	—	43	6	no	—
300	#135	—	43	6	no	—
301	#135	—	43	6	no	—
302	#135	—	86	6	no	—
303	#135	—	86	6	no	—
304	#135	C₂²×D₄₃	1	6	yes	complemented
305	C₂×Q₁₆	—	43	2	no	—
306	C₂×SD₁₆	—	86	6	no	—
307	C₂×D₈	—	43	6	no	—
308	C₂×D₈	—	43	12	no	—
309	C₂×D₈	—	43	6	no	—
310	C₂×D₈	—	86	6	no	—
311	C₂×D₈	—	86	6	no	—
312	C₂×D₈	—	86	6	no	—
313	C₂×D₈	C₂²×D₄₃	1	6	yes	complemented
314	#131	—	43	1	no	—
315	#131	—	43	3	no	—
316	#131	—	43	3	no	—
317	#131	C₂²×D₄₃	1	1	yes	characteristic
318	C₂×M₁₆	—	43	3	no	—
319	C₂²×C₈	—	43	3	no	—
320	Q₃₂	—	43	2	no	—
321	Q₃₂	—	43	1	no	—
322	Q₃₂	C₂²×D₄₃	1	1	yes	characteristic, complemented
323	SD₃₂	—	43	6	no	—
324	SD₃₂	—	43	6	no	—
325	SD₃₂	—	43	6	no	—
326	SD₃₂	C₂²×D₄₃	1	6	yes	complemented
327	D₁₆	—	43	6	no	—
328	D₁₆	—	43	12	no	—
329	D₁₆	—	43	3	no	—
330	D₁₆	—	43	6	no	—
331	D₁₆	C₂²×D₄₃	1	3	yes	complemented
332	D₁₆	C₂²×D₄₃	1	6	yes	complemented
333	M₃₂	—	43	3	no	—
334	M₃₂	—	43	6	no	—
335	M₃₂	C₂²×D₄₃	1	3	yes	complemented
336	C₂×C₁₆	—	43	3	no	—
337	C₂×C₁₆	—	43	1	no	—
338	C₂×C₁₆	—	43	3	no	—
339	C₂×C₁₆	—	43	3	no	—
340	C₂×C₁₆	—	43	3	no	—
341	C₂×C₁₆	C₂²×D₄₃	1	3	yes	complemented
342	C₂⁴	—	172	6	no	—
343	#41	—	2	6	no	—
344	#41	—	4	2	no	—
345	#41	—	43	1	no	—
346	#41	—	43	3	no	—
347	#41	—	43	3	no	—
348	#41	—	86	6	no	—
349	#41	—	86	6	no	—
350	#41	—	86	6	no	—
351	#41	—	172	6	no	—
352	#41	—	172	6	no	—
353	#41	—	172	6	no	—
354	#41	—	172	6	no	—
355	#41	—	172	2	no	—
356	#41	D₄×D₄₃	1	1	yes	characteristic
357	C₂×Q₈	—	43	1	no	—
358	C₂×Q₈	—	86	2	no	—
359	C₂×D₄	—	2	6	no	—
360	C₂×D₄	—	4	6	no	—
361	C₂×D₄	—	43	3	no	—
362	C₂×D₄	—	86	6	no	—
363	C₂×D₄	—	86	12	no	—
364	C₂×D₄	—	86	6	no	—
365	C₂×D₄	—	172	6	no	—
366	C₂×D₄	—	172	6	no	—
367	C₂×D₄	—	172	6	no	—
368	C₂×D₄	—	172	6	no	—
369	C₂×D₄	—	172	12	no	—
370	C₂×D₄	—	172	6	no	—
371	C₂×D₄	—	172	6	no	—
372	C₂×D₄	—	172	12	no	—
373	C₂×D₄	—	172	6	no	—
374	C₂²×C₄	—	43	3	no	—
375	C₂²×C₄	—	172	6	no	—
376	Q₁₆	—	43	2	no	—
377	Q₁₆	—	86	2	no	—
378	Q₁₆	C₂³×D₄₃	1	2	yes	—
379	SD₁₆	—	2	6	no	—
380	SD₁₆	—	86	6	no	—
381	SD₁₆	—	86	6	no	—
382	SD₁₆	—	86	6	no	—
383	D₈	—	2	6	no	—
384	D₈	—	43	6	no	—
385	D₈	—	86	6	no	—
386	D₈	—	86	12	no	—
387	D₈	—	86	6	no	—
388	D₈	C₂³×D₄₃	1	6	yes	—
389	M₁₆	—	43	3	no	—
390	M₁₆	—	43	6	no	—
391	M₁₆	D₄×D₄₃	1	3	yes	—
392	C₂×C₈	—	43	3	no	—
393	C₂×C₈	—	43	3	no	—
394	C₂×C₈	—	43	3	no	—
395	C₂×C₈	—	43	1	no	—
396	C₂×C₈	—	43	3	no	—
397	C₂×C₈	C₂³×D₄₃	1	3	yes	—
398	C₁₆	—	43	1	no	—
399	C₁₆	—	43	3	no	—
400	C₁₆	C₂³×D₄₃	1	1	yes	characteristic
401	C₁₆	C₂³×D₄₃	1	3	yes	—
402	C₂³	—	4	6	no	—
403	C₂³	—	43	3	no	—
404	C₂³	—	172	6	no	—
405	C₂³	—	172	12	no	—
406	C₂³	—	172	6	no	—
407	C₂³	—	688	12	no	—
408	Q₈	—	2	2	no	—
409	Q₈	—	43	3	no	—
410	Q₈	—	86	2	no	—
411	Q₈	—	172	2	no	—
412	Q₈	D₈×D₄₃	1	1	yes	characteristic
413	D₄	—	2	6	no	—
414	D₄	—	4	6	no	—
415	D₄	—	4	6	no	—
416	D₄	—	43	6	no	—
417	D₄	—	43	3	no	—
418	D₄	—	86	6	no	—
419	D₄	—	172	6	no	—
420	D₄	—	172	6	no	—
421	D₄	—	172	12	no	—
422	D₄	—	172	6	no	—
423	D₄	—	172	6	no	—
424	D₄	—	172	6	no	—
425	D₄	D₈×D₄₃	1	3	yes	—
426	C₂×C₄	—	4	6	no	—
427	C₂×C₄	—	43	3	no	—
428	C₂×C₄	—	43	3	no	—
429	C₂×C₄	—	43	3	no	—
430	C₂×C₄	—	43	1	no	—
431	C₂×C₄	—	43	3	no	—
432	C₂×C₄	—	172	6	no	—
433	C₂×C₄	—	172	2	no	—
434	C₂×C₄	—	172	6	no	—
435	C₂×C₄	—	172	6	no	—
436	C₂×C₄	C₂×D₄×D₄₃	1	3	yes	—
437	C₈	—	43	1	no	—
438	C₈	—	43	3	no	—
439	C₈	C₂×D₄×D₄₃	1	3	yes	—
440	C₈	C₂⁴×D₄₃	1	1	yes	characteristic
441	C₂²	—	4	6	no	—
442	C₂²	—	16	6	no	—
443	C₂²	—	43	1	no	—
444	C₂²	—	43	3	no	—
445	C₂²	—	86	6	no	—
446	C₂²	—	344	12	no	—
447	C₂²	—	172	6	no	—
448	C₂²	—	688	6	no	—
449	C₂²	—	688	12	no	—
450	C₂²	C₂×D₈×D₄₃	1	3	yes	—
451	C₄	—	4	2	no	—
452	C₄	—	43	1	no	—
453	C₄	—	43	3	no	—
454	C₄	—	172	2	no	—
455	C₄	C₂×D₈×D₄₃	1	3	yes	—
456	C₄	C₂²×D₄×D₄₃	1	1	yes	characteristic
457	C₂	—	2	3	no	—
458	C₂	—	8	6	no	—
459	C₂	—	43	2	no	—
460	C₂	—	86	3	no	—
461	C₂	—	344	6	no	—
462	C₂	C₂²×D₈×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₈×D₄₃
commutator, cosocle	C₈×C₄₃	C₂⁵
Frattini	C₈	C₂⁴×D₄₃
Fitting	C₄₃×#3415	C₂
socle	C₂×C₄₃	C₂³×D₈
hypercenter	#3415	D₄₃
hypocenter	C₄₃	C₂×#3415
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131 ◁ #3415

Complements

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

N	H ≅ G/N	type
1. #576×D₄₃	C₂	semidirect
2. #19147736	C₂	semidirect
3. #19147735	C₂	semidirect
4. #19147734	C₂	semidirect
5. #19147733	C₂	semidirect
6. #19147732	C₂	semidirect
7. #509×D₄₃	C₂	semidirect
8. #508×D₄₃	C₂	semidirect
9. C₂×D₁₆×D₄₃	C₂	semidirect
10. #504×D₄₃	C₂	semidirect
11. C₄₃×#3415	C₂	semidirect
13. #14583704	C₂²	semidirect
16. #14583701	C₂²	semidirect
17. #14583700	C₂²	semidirect
19. #135×D₄₃	C₂²	semidirect
20. C₂×D₈×D₄₃	C₂²	semidirect
22. #14583337	C₂²	semidirect
23. #14583336	C₂²	semidirect
24. #14583335	C₂²	semidirect
25. #14583334	C₂²	semidirect
26. #14583333	C₂²	semidirect
27. #14583332	C₂²	semidirect
28. #14583331	C₂²	semidirect
29. #14583330	C₂²	semidirect
30. #14583329	C₂²	semidirect
31. #14583328	C₂²	semidirect
32. Q₃₂×D₄₃	C₂²	semidirect
33. SD₃₂×D₄₃	C₂²	semidirect
34. C₂×D₆₈₈	C₂²	semidirect
35. C₂×#13063266	C₂²	semidirect
36. D₁₆×D₄₃	C₂²	semidirect
37. D₁₆×D₄₃	C₂²	semidirect
38. D₁₆×D₄₃	C₂²	semidirect
39. D₁₆×D₄₃	C₂²	semidirect
40. #14583317	C₂²	semidirect
41. #14583316	C₂²	semidirect
42. #14583315	C₂²	semidirect
43. M₃₂×D₄₃	C₂²	semidirect
44. C₂×C₁₆×D₄₃	C₂²	semidirect
45. C₄₃×#576	C₂²	semidirect
46. C₄₃×#509	C₂²	semidirect
47. C₄₃×#508	C₂²	semidirect
48. C₂×D₁₆×C₄₃	C₂²	semidirect
49. C₄₃×#504	C₂²	semidirect
65. #13063348	C₂³	semidirect
66. #13063347	C₂³	semidirect
69. #13063344	C₂³	semidirect
72. C₂×D₃₄₄	C₂³	semidirect
77. D₈×D₄₃	C₂³	semidirect
83. Dic₃₄₄	C₂³	semidirect
84. #13063271	C₂³	semidirect
85. #13063270	C₂³	semidirect
86. #13063269	C₂³	semidirect
87. #13063268	C₂³	semidirect
88. D₆₈₈	C₂³	semidirect
89. D₆₈₈	C₂³	semidirect
90. #13063266	C₂³	semidirect
91. #13063266	C₂³	semidirect
92. #13063265	C₂³	semidirect
93. #13063264	C₂³	semidirect
94. C₂×C₄₃⋊C₁₆	C₂³	semidirect
97. C₁₆×D₄₃	C₂³	semidirect
98. C₁₆×D₄₃	C₂³	semidirect
101. #135×C₄₃	C₂³	semidirect
102. C₂×D₈×C₄₃	C₂³	semidirect
104. Q₃₂×C₄₃	C₂³	semidirect
105. SD₃₂×C₄₃	C₂³	semidirect
106. D₁₆×C₄₃	C₂³	semidirect
107. D₁₆×C₄₃	C₂³	semidirect
108. M₃₂×C₄₃	C₂³	semidirect
109. C₂×C₁₆×C₄₃	C₂³	semidirect
232. #3415	D₄₃	direct (N × H)
242. D₄₃	#3415	direct (N × H)
249. #576	C₂×D₄₃	semidirect
259. #509	C₂×D₄₃	semidirect
265. #508	C₂×D₄₃	semidirect
274. C₂×D₁₆	C₂×D₄₃	semidirect
278. #504	C₂×D₄₃	semidirect
281. C₄₃	C₂×#3415	semidirect
304. #135	C₂²×D₄₃	semidirect
313. C₂×D₈	C₂²×D₄₃	semidirect
322. Q₃₂	C₂²×D₄₃	semidirect
326. SD₃₂	C₂²×D₄₃	semidirect
331. D₁₆	C₂²×D₄₃	semidirect
332. D₁₆	C₂²×D₄₃	semidirect
335. M₃₂	C₂²×D₄₃	semidirect
341. C₂×C₁₆	C₂²×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#576×D₄₃	2
#19147736	2
#19147735	2
#19147734	2
#19147733	2
#19147732	2
#509×D₄₃	2
#508×D₄₃	2
C₂×D₁₆×D₄₃	2
#504×D₄₃	2
C₄₃×#3415	2
C₂×#3415	43

Subgroups — D43×#3415 #26003104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#3415 #26003104