Subgroups — D₄₃×#2230 #25251323

Order 11008.

558 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#498×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#443×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#19136767	C₂	1	1	yes	maximal, characteristic, complemented
4	#19136766	C₂	1	1	yes	maximal, characteristic, complemented
5	#19136765	C₂	1	2	yes	maximal, complemented
6	#19136764	C₂	1	2	yes	maximal, complemented
7	#19136763	C₂	1	1	yes	maximal, characteristic, complemented
8	#365×D₄₃	C₂	1	2	yes	maximal, complemented
9	#364×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#360×D₄₃	C₂	1	2	yes	maximal
11	C₄₃×#2230	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₄₃	C₂²	1	1	yes	characteristic
13	#131×D₄₃	—	2	1	no	—
14	C₄⋊Q₈×D₄₃	—	2	1	no	—
15	M₃₂×D₄₃	C₂²	1	2	yes	—
16	#14583297	C₂²	1	1	yes	characteristic, complemented
17	#14583296	—	2	1	no	—
18	#14583296	C₂²	1	2	yes	complemented
19	#14583295	—	2	1	no	—
20	#14583017	C₂²	1	1	yes	characteristic
21	#14583016	C₂²	1	1	yes	characteristic
22	#14583015	C₂²	1	1	yes	characteristic
23	#14583014	—	2	1	no	—
24	#14583013	—	2	1	no	—
25	#108×D₄₃	C₂²	1	1	yes	characteristic
26	#106×D₄₃	—	2	1	no	—
27	#106×D₄₃	C₂²	1	2	yes	—
28	#104×D₄₃	—	2	1	no	—
29	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
30	#14582723	C₂²	1	2	yes	complemented
31	#14582722	C₂²	1	2	yes	complemented
32	#14582721	C₂²	1	2	yes	complemented
33	#14582720	C₂²	1	1	yes	characteristic, complemented
34	#14582719	C₂²	1	2	yes	complemented
35	#14582710	C₂²	1	2	yes	—
36	#14582709	C₂²	1	2	yes	—
37	#14582708	C₂²	1	2	yes	—
38	C₄₃×#498	C₂²	1	1	yes	characteristic, complemented
39	C₄₃×#443	C₂²	1	1	yes	characteristic
40	C₄₃×#365	C₂²	1	2	yes	complemented
41	C₄₃×#364	C₂²	1	1	yes	characteristic, complemented
42	C₄₃×#360	C₂²	1	2	yes	—
43	#41×D₄₃	—	2	1	no	—
44	C₂×Q₈×D₄₃	—	4	1	no	—
45	#13063348	Q₈	1	1	yes	characteristic, complemented
46	#13063347	C₂³	1	1	yes	characteristic
47	#13063346	—	2	1	no	—
48	#13063345	—	2	1	no	—
49	#13063344	Q₈	1	1	yes	characteristic, complemented
50	Q₁₆×D₄₃	Q₈	1	1	yes	characteristic, complemented
51	SD₁₆×D₄₃	—	2	1	no	—
52	D₈×D₄₃	Q₈	1	1	yes	characteristic, complemented
53	#13063333	—	2	1	no	—
54	#13063333	—	4	1	no	—
55	#13063332	—	2	1	no	—
56	#13063331	—	2	1	no	—
57	#13063331	—	4	1	no	—
58	M₁₆×D₄₃	—	2	1	no	—
59	M₁₆×D₄₃	—	4	1	no	—
60	C₂×C₈×D₄₃	—	4	1	no	—
61	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
62	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
63	#13063325	—	2	1	no	—
64	#13063324	—	2	2	no	—
65	#13063324	—	4	1	no	—
66	#13063323	—	4	1	no	—
67	C₄⋊C₄×D₄₃	—	2	2	no	—
68	C₄⋊C₄×D₄₃	—	4	1	no	—
69	C₄²×D₄₃	D₄	1	1	yes	characteristic
70	#13063265	C₂³	1	2	yes	—
71	#13063264	—	2	2	no	—
72	C₁₆×D₄₃	—	2	2	no	—
73	#13063261	C₂³	1	1	yes	characteristic
74	#13063260	—	2	1	no	—
75	#13063257	—	2	1	no	—
76	#13063257	C₂³	1	2	yes	—
77	#13063256	—	2	2	no	—
78	#13063256	—	2	2	no	—
79	#13063253	—	2	1	no	—
80	#13063252	—	2	1	no	—
81	#13063251	—	2	1	no	—
82	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
83	C₈×Dic₄₃	D₄	1	1	yes	characteristic
84	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
85	#135×C₄₃	C₂³	1	1	yes	characteristic
86	#131×C₄₃	—	2	1	no	—
87	C₄⋊Q₈×C₄₃	—	2	1	no	—
88	M₃₂×C₄₃	C₂³	1	2	yes	—
89	#108×C₄₃	C₂³	1	1	yes	characteristic
90	#106×C₄₃	—	2	1	no	—
91	#106×C₄₃	C₂³	1	2	yes	—
92	#104×C₄₃	—	2	1	no	—
93	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
94	#41×C₄₃	—	2	1	no	—
95	C₂×Q₈×C₄₃	—	4	1	no	—
96	#10621902	—	2	1	no	—
97	Q₈×D₄₃	—	2	1	no	—
98	Q₈×D₄₃	—	8	4	no	—
99	#10621900	—	2	1	no	—
100	#10621900	—	4	1	no	—
101	D₄×D₄₃	—	2	1	no	—
102	D₄×D₄₃	—	4	1	no	—
103	#10621898	—	2	1	no	—
104	#10621898	—	4	1	no	—
105	C₂×C₄×D₄₃	—	2	1	no	—
106	C₂×C₄×D₄₃	—	4	1	no	—
107	C₂×C₄×D₄₃	—	4	2	no	—
108	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂×Dic₈₆	—	4	2	no	—
110	C₂×Dic₈₆	—	4	1	no	—
111	Q₁₆×C₄₃	C₂×Q₈	1	1	yes	characteristic, complemented
112	SD₁₆×C₄₃	—	2	1	no	—
113	D₈×C₄₃	C₂×Q₈	1	1	yes	characteristic, complemented
114	M₁₆×C₄₃	—	2	1	no	—
115	M₁₆×C₄₃	—	4	1	no	—
116	C₂×C₈×C₄₃	—	4	1	no	—
117	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
119	C₄⋊C₄×C₄₃	—	2	2	no	—
120	C₄⋊C₄×C₄₃	—	4	1	no	—
121	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
122	#10621885	—	2	1	no	—
123	#10621884	—	2	1	no	—
124	#10621883	—	2	1	no	—
125	#10621882	—	2	1	no	—
126	C₄⋊Dic₄₃	—	2	2	no	—
127	C₄⋊Dic₄₃	—	4	1	no	—
128	Dic₄₃⋊C₄	—	4	2	no	—
129	Dic₄₃⋊C₄	—	4	2	no	—
130	C₄×Dic₄₃	—	2	1	no	—
131	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
132	#10621877	—	2	1	no	—
133	#10621877	—	4	1	no	—
134	C₂×C₄₃⋊C₈	—	4	1	no	—
135	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
137	Dic₁₇₂	C₂×Q₈	1	1	yes	characteristic, complemented
138	D₃₄₄	C₂×Q₈	1	1	yes	characteristic, complemented
139	#10621873	—	2	1	no	—
140	#10621872	—	4	1	no	—
141	#10621872	—	4	1	no	—
142	#10621872	—	4	1	no	—
143	C₈×D₄₃	—	4	1	no	—
144	C₈×D₄₃	—	4	1	no	—
145	C₈×D₄₃	—	4	1	no	—
146	C₈×D₄₃	SD₁₆	1	1	yes	characteristic
147	C₈×D₄₃	SD₁₆	1	1	yes	characteristic
148	C₈×D₄₃	SD₁₆	1	1	yes	characteristic
149	C₈×D₄₃	SD₁₆	1	1	yes	characteristic
150	C₈×D₄₃	C₂×Q₈	1	1	yes	characteristic
151	C₈×D₄₃	C₂×Q₈	1	1	yes	characteristic
152	C₈×D₄₃	#41	1	1	yes	characteristic
153	C₈×D₄₃	#41	1	1	yes	characteristic
154	C₁₆×C₄₃	—	2	2	no	—
155	C₄₃⋊C₁₆	—	2	2	no	—
156	C₂²×D₄₃	—	4	1	no	—
157	C₂²×D₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
158	Q₈×C₄₃	—	2	1	no	—
159	Q₈×C₄₃	—	8	2	no	—
160	D₄×C₄₃	—	2	1	no	—
161	D₄×C₄₃	—	4	1	no	—
162	C₂×C₄×C₄₃	—	2	1	no	—
163	C₂×C₄×C₄₃	—	4	1	no	—
164	C₂×C₄×C₄₃	—	4	2	no	—
165	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
166	C₂²⋊D₄₃	—	4	1	no	—
167	C₂²⋊D₄₃	—	4	1	no	—
168	C₂²⋊D₄₃	—	4	1	no	—
169	C₂×Dic₄₃	—	2	1	no	—
170	C₂×Dic₄₃	—	4	1	no	—
171	C₂×Dic₄₃	—	4	2	no	—
172	C₂×Dic₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
173	D₁₇₂	—	2	1	no	—
174	D₁₇₂	—	4	1	no	—
175	C₄×D₄₃	—	2	4	no	—
176	C₄×D₄₃	—	4	1	no	—
177	C₄×D₄₃	—	4	1	no	—
178	C₄×D₄₃	—	4	1	no	—
179	C₄×D₄₃	—	8	4	no	—
180	C₄×D₄₃	C₂²⋊Q₈	1	1	yes	characteristic
181	C₄×D₄₃	C₂²⋊Q₈	1	1	yes	characteristic
182	C₄×D₄₃	C₂×SD₁₆	1	1	yes	characteristic
183	C₄×D₄₃	C₂×SD₁₆	1	1	yes	characteristic
184	Dic₈₆	—	2	1	no	—
185	Dic₈₆	—	4	1	no	—
186	Dic₈₆	—	8	4	no	—
187	Dic₈₆	—	8	2	no	—
188	C₈×C₄₃	—	4	1	no	—
189	C₈×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
190	C₈×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
191	C₈×C₄₃	C₂²×Q₈	1	1	yes	characteristic
192	C₈×C₄₃	C₂×#41	1	1	yes	characteristic
193	C₄₃⋊C₈	—	4	1	no	—
194	C₄₃⋊C₈	C₂²⋊Q₈	1	1	yes	characteristic
195	C₄₃⋊C₈	C₂²⋊Q₈	1	1	yes	characteristic
196	C₄₃⋊C₈	C₂×SD₁₆	1	1	yes	characteristic
197	C₄₃⋊C₈	C₂×SD₁₆	1	1	yes	characteristic
198	C₂×#2230	—	43	1	no	maximal, Sylow
199	C₂²×C₄₃	—	4	1	no	—
200	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
201	C₂×D₄₃	—	2	2	no	—
202	C₂×D₄₃	—	4	1	no	—
203	C₂×D₄₃	—	8	2	no	—
204	C₂×D₄₃	#476	1	1	yes	characteristic
205	C₂×D₄₃	#476	1	1	yes	characteristic
206	C₄×C₄₃	—	2	2	no	—
207	C₄×C₄₃	—	4	1	no	—
208	C₄×C₄₃	—	8	2	no	—
209	C₄×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
210	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
211	Dic₄₃	—	2	2	no	—
212	Dic₄₃	—	4	1	no	—
213	Dic₄₃	—	8	2	no	—
214	Dic₄₃	#476	1	1	yes	characteristic
215	Dic₄₃	#476	1	1	yes	characteristic
216	C₂×#498	—	43	1	no	—
217	C₂×#443	—	43	1	no	—
218	#2230	—	43	1	no	—
219	#2230	—	43	1	no	—
220	#2230	—	43	2	no	—
221	#2230	—	43	1	no	—
222	#2230	—	43	2	no	—
223	#2230	D₄₃	1	1	yes	characteristic, direct product factor
224	C₂×#365	—	43	2	no	—
225	C₂×#364	—	43	1	no	—
226	C₂×#360	—	43	2	no	—
227	C₂×C₄₃	—	2	1	no	—
228	C₂×C₄₃	—	8	1	no	—
229	C₂×C₄₃	C₂×#476	1	1	yes	characteristic
230	D₄₃	—	2	1	no	—
231	D₄₃	—	8	1	no	—
232	D₄₃	#2230	1	2	yes	direct product factor
233	C₂×#135	—	43	1	no	—
234	C₂×#131	—	86	1	no	—
235	C₂×C₄⋊Q₈	—	86	1	no	—
236	C₂×M₃₂	—	43	2	no	—
237	#498	—	43	2	no	—
238	#498	—	43	1	no	—
239	#498	—	86	1	no	—
240	#498	—	86	1	no	—
241	#498	C₂×D₄₃	1	1	yes	characteristic, complemented
242	#443	—	43	1	no	—
243	#443	—	43	1	no	—
244	#443	—	43	1	no	—
245	#443	—	86	1	no	—
246	#443	—	86	1	no	—
247	#443	C₂×D₄₃	1	1	yes	characteristic
248	C₂×#108	—	43	1	no	—
249	C₂×#106	—	43	2	no	—
250	C₂×#106	—	86	1	no	—
251	C₂×#104	—	86	1	no	—
252	C₂×C₄×C₈	—	43	1	no	—
253	#365	—	43	2	no	—
254	#365	—	43	2	no	—
255	#365	—	43	2	no	—
256	#365	C₂×D₄₃	1	2	yes	complemented
257	#364	—	43	2	no	—
258	#364	—	43	1	no	—
259	#364	C₂×D₄₃	1	1	yes	characteristic, complemented
260	#360	—	43	2	no	—
261	#360	—	43	2	no	—
262	#360	—	43	2	no	—
263	#360	C₂×D₄₃	1	2	yes	—
264	C₄₃	C₂×#2230	1	1	yes	characteristic, complemented, Sylow
265	C₂×#41	—	86	1	no	—
266	C₂²×Q₈	—	172	1	no	—
267	#135	—	43	1	no	—
268	#135	—	43	1	no	—
269	#135	—	43	1	no	—
270	#135	—	86	1	no	—
271	#135	—	86	1	no	—
272	#135	C₂²×D₄₃	1	1	yes	characteristic
273	C₂×Q₁₆	—	43	1	no	—
274	C₂×SD₁₆	—	86	1	no	—
275	C₂×D₈	—	43	1	no	—
276	#131	—	2	1	no	—
277	#131	—	86	1	no	—
278	#131	—	86	1	no	—
279	#131	—	86	1	no	—
280	#131	—	172	1	no	—
281	#131	—	172	1	no	—
282	C₂×M₁₆	—	86	1	no	—
283	C₂×M₁₆	—	172	1	no	—
284	C₂²×C₈	—	43	1	no	—
285	C₂²×C₈	—	43	1	no	—
286	C₂²×C₈	—	172	1	no	—
287	C₄⋊Q₈	—	2	1	no	—
288	C₄⋊Q₈	—	86	2	no	—
289	C₄⋊Q₈	—	86	1	no	—
290	C₄⋊Q₈	—	172	1	no	—
291	C₄⋊Q₈	—	172	1	no	—
292	C₂×C₄⋊C₄	—	86	2	no	—
293	C₂×C₄⋊C₄	—	172	1	no	—
294	C₂×C₄²	—	43	1	no	—
295	M₃₂	—	43	2	no	—
296	M₃₂	—	86	2	no	—
297	M₃₂	C₂²×D₄₃	1	2	yes	—
298	C₂×C₁₆	—	86	2	no	—
299	#108	—	43	1	no	—
300	#108	—	86	1	no	—
301	#108	C₂²×D₄₃	1	1	yes	characteristic
302	#106	—	2	1	no	—
303	#106	—	43	2	no	—
304	#106	—	86	2	no	—
305	#106	—	86	2	no	—
306	#106	—	86	1	no	—
307	#106	C₂²×D₄₃	1	2	yes	—
308	#104	—	2	1	no	—
309	#104	—	86	1	no	—
310	#104	—	86	1	no	—
311	#104	—	86	1	no	—
312	C₄×C₈	—	43	1	no	—
313	C₄×C₈	—	43	1	no	—
314	C₄×C₈	—	43	1	no	—
315	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
316	#41	—	2	1	no	—
317	#41	—	86	1	no	—
318	#41	—	86	1	no	—
319	#41	—	86	1	no	—
320	#41	—	172	1	no	—
321	#41	—	172	1	no	—
322	C₂×Q₈	—	4	1	no	—
323	C₂×Q₈	—	86	1	no	—
324	C₂×Q₈	—	344	4	no	—
325	C₂×Q₈	—	172	1	no	—
326	C₂×Q₈	—	172	2	no	—
327	C₂×D₄	—	86	1	no	—
328	C₂×D₄	—	172	1	no	—
329	C₂²×C₄	—	43	1	no	—
330	C₂²×C₄	—	86	1	no	—
331	C₂²×C₄	—	172	1	no	—
332	C₂²×C₄	—	172	2	no	—
333	Q₁₆	—	43	1	no	—
334	Q₁₆	—	86	1	no	—
335	Q₁₆	Q₈×D₄₃	1	1	yes	characteristic, complemented
336	SD₁₆	—	2	1	no	—
337	SD₁₆	—	86	1	no	—
338	SD₁₆	—	86	1	no	—
339	SD₁₆	—	86	1	no	—
340	D₈	—	43	1	no	—
341	D₈	—	86	1	no	—
342	D₈	Q₈×D₄₃	1	1	yes	characteristic, complemented
343	M₁₆	—	2	1	no	—
344	M₁₆	—	4	1	no	—
345	M₁₆	—	86	1	no	—
346	M₁₆	—	172	1	no	—
347	M₁₆	—	172	1	no	—
348	M₁₆	—	172	1	no	—
349	M₁₆	—	172	1	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	43	1	no	—
352	C₂×C₈	—	43	1	no	—
353	C₂×C₈	—	43	1	no	—
354	C₂×C₈	—	43	1	no	—
355	C₂×C₈	—	43	1	no	—
356	C₂×C₈	—	43	1	no	—
357	C₂×C₈	—	43	1	no	—
358	C₂×C₈	—	43	1	no	—
359	C₂×C₈	—	43	1	no	—
360	C₂×C₈	—	43	1	no	—
361	C₂×C₈	—	172	1	no	—
362	C₂×C₈	—	172	1	no	—
363	C₂×C₈	—	172	1	no	—
364	C₂×C₈	—	172	1	no	—
365	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
366	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	86	2	no	—
370	C₄⋊C₄	—	172	1	no	—
371	C₄⋊C₄	—	172	2	no	—
372	C₄⋊C₄	—	172	2	no	—
373	C₄²	—	43	1	no	—
374	C₄²	—	86	1	no	—
375	C₄²	D₄×D₄₃	1	1	yes	characteristic
376	C₁₆	—	2	2	no	—
377	C₁₆	—	86	2	no	—
378	C₂³	—	43	1	no	—
379	C₂³	—	172	1	no	—
380	Q₈	—	2	1	no	—
381	Q₈	—	8	2	no	—
382	Q₈	—	86	1	no	—
383	Q₈	—	344	2	no	—
384	Q₈	—	344	4	no	—
385	Q₈	—	172	1	no	—
386	D₄	—	2	1	no	—
387	D₄	—	4	1	no	—
388	D₄	—	86	1	no	—
389	D₄	—	172	1	no	—
390	D₄	—	172	1	no	—
391	D₄	—	172	1	no	—
392	D₄	—	172	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	43	1	no	—
397	C₂×C₄	—	43	1	no	—
398	C₂×C₄	—	43	1	no	—
399	C₂×C₄	—	43	1	no	—
400	C₂×C₄	—	43	1	no	—
401	C₂×C₄	—	86	4	no	—
402	C₂×C₄	—	86	1	no	—
403	C₂×C₄	—	344	4	no	—
404	C₂×C₄	—	172	1	no	—
405	C₂×C₄	—	172	1	no	—
406	C₂×C₄	—	172	1	no	—
407	C₂×C₄	—	172	2	no	—
408	C₂×C₄	—	172	1	no	—
409	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
410	C₈	—	4	1	no	—
411	C₈	—	43	1	no	—
412	C₈	—	43	1	no	—
413	C₈	—	43	1	no	—
414	C₈	—	43	1	no	—
415	C₈	—	172	1	no	—
416	C₈	SD₁₆×D₄₃	1	1	yes	characteristic
417	C₈	SD₁₆×D₄₃	1	1	yes	characteristic
418	C₈	C₂×Q₈×D₄₃	1	1	yes	characteristic
419	C₈	#41×D₄₃	1	1	yes	characteristic
420	C₂²	—	4	1	no	—
421	C₂²	—	43	1	no	—
422	C₂²	—	43	1	no	—
423	C₂²	—	86	2	no	—
424	C₂²	—	344	2	no	—
425	C₂²	—	172	1	no	—
426	C₂²	AGL(1,ℤ/8)×D₄₃	1	1	yes	characteristic
427	C₄	—	2	2	no	—
428	C₄	—	4	1	no	—
429	C₄	—	8	2	no	—
430	C₄	—	43	1	no	—
431	C₄	—	43	1	no	—
432	C₄	—	86	2	no	—
433	C₄	—	344	2	no	—
434	C₄	—	172	1	no	—
435	C₄	C₂²⋊Q₈×D₄₃	1	1	yes	characteristic
436	C₄	C₂×SD₁₆×D₄₃	1	1	yes	characteristic
437	C₂	—	2	1	no	—
438	C₂	—	8	1	no	—
439	C₂	—	43	2	no	—
440	C₂	—	86	1	no	—
441	C₂	—	344	1	no	—
442	C₂	#476×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#476×D₄₃
commutator, cosocle	C₂×C₈×C₄₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₄₃×#2230	C₂
socle	C₂×C₄₃	C₂×#476
prime radical	#135×D₄₃	C₂²
hypercenter	#2230	D₄₃
hypocenter	C₄₃	C₂×#2230
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2230

Complements

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

N	H ≅ G/N	type
1. #498×D₄₃	C₂	semidirect
3. #19136767	C₂	semidirect
4. #19136766	C₂	semidirect
5. #19136765	C₂	semidirect
6. #19136764	C₂	semidirect
7. #19136763	C₂	semidirect
8. #365×D₄₃	C₂	semidirect
9. #364×D₄₃	C₂	semidirect
11. C₄₃×#2230	C₂	semidirect
16. #14583297	C₂²	semidirect
18. #14583296	C₂²	semidirect
30. #14582723	C₂²	semidirect
31. #14582722	C₂²	semidirect
32. #14582721	C₂²	semidirect
33. #14582720	C₂²	semidirect
34. #14582719	C₂²	semidirect
38. C₄₃×#498	C₂²	semidirect
40. C₄₃×#365	C₂²	semidirect
41. C₄₃×#364	C₂²	semidirect
45. #13063348	Q₈	semidirect
49. #13063344	Q₈	semidirect
50. Q₁₆×D₄₃	Q₈	semidirect
52. D₈×D₄₃	Q₈	semidirect
111. Q₁₆×C₄₃	C₂×Q₈	semidirect
113. D₈×C₄₃	C₂×Q₈	semidirect
137. Dic₁₇₂	C₂×Q₈	semidirect
138. D₃₄₄	C₂×Q₈	semidirect
223. #2230	D₄₃	direct (N × H)
232. D₄₃	#2230	direct (N × H)
241. #498	C₂×D₄₃	semidirect
256. #365	C₂×D₄₃	semidirect
259. #364	C₂×D₄₃	semidirect
264. C₄₃	C₂×#2230	semidirect
335. Q₁₆	Q₈×D₄₃	semidirect
342. D₈	Q₈×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#498×D₄₃	2
#443×D₄₃	2
#19136767	2
#19136766	2
#19136765	2
#19136764	2
#19136763	2
#365×D₄₃	2
#364×D₄₃	2
#360×D₄₃	2
C₄₃×#2230	2
C₂×#2230	43

Subgroups — D43×#2230 #25251323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#2230 #25251323