Subgroups — #25065926

Order 11008.

592 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143725	C₂	1	1	yes	maximal, characteristic
2	#19143721	C₂	1	1	yes	maximal, characteristic
3	#19143561	C₂	1	1	yes	maximal, characteristic
4	#19133386	C₂	1	1	yes	maximal, characteristic, complemented
5	#19133386	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133374	C₂	1	2	yes	maximal, complemented
7	#19133368	C₂	1	2	yes	maximal, complemented
8	#19133361	C₂	1	2	yes	maximal, complemented
9	#19133346	C₂	1	2	yes	maximal, complemented
10	#19133343	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1567	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#10621898	C₂²	1	1	yes	characteristic
13	#14583029	C₄	1	1	yes	characteristic
14	#14583029	C₄	1	1	yes	characteristic
15	#14583026	—	2	1	no	—
16	#14583023	—	2	1	no	—
17	#14582978	C₄	1	1	yes	characteristic
18	#14582978	C₄	1	1	yes	characteristic
19	#14582976	—	2	1	no	—
20	#14582975	—	2	2	no	—
21	#14582970	C₄	1	2	yes	—
22	#14582970	C₄	1	2	yes	—
23	#14582968	—	2	2	no	—
24	#14582964	—	2	1	no	—
25	#14582955	C₂²	1	2	yes	—
26	#14582952	C₂²	1	1	yes	characteristic
27	#14582952	C₂²	1	1	yes	characteristic
28	#14582952	C₂²	1	1	yes	characteristic
29	#14582951	C₂²	1	2	yes	—
30	#14582950	C₂²	1	2	yes	—
31	#14582921	C₂²	1	2	yes	—
32	C₄⋊C₈×D₄₃	C₂²	1	2	yes	—
33	C₄×#10621872	C₂²	1	2	yes	—
34	#14582652	C₂²	1	1	yes	characteristic
35	#14582652	C₂²	1	1	yes	characteristic
36	#14582651	C₂²	1	2	yes	—
37	#14582651	C₂²	1	2	yes	—
38	#14582650	C₂²	1	1	yes	characteristic
39	#14582650	C₂²	1	1	yes	characteristic
40	#14582649	C₂²	1	2	yes	—
41	#14582649	C₂²	1	2	yes	—
42	C₄₃×#423	C₂²	1	1	yes	characteristic
43	C₄₃×#423	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#335	C₂²	1	2	yes	—
46	C₄₃×#335	C₂²	1	2	yes	—
47	C₂×#10621898	Q₈	1	1	yes	characteristic
48	C₂×#10621872	—	2	2	no	—
49	C₂×#10621872	C₂×C₄	1	2	yes	—
50	C₂×#10621872	C₂×C₄	1	2	yes	—
51	C₂×C₈×D₄₃	—	2	2	no	—
52	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
53	C₄×Dic₈₆	D₄	1	1	yes	characteristic
54	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
55	C₄×D₁₇₂	D₄	1	1	yes	characteristic
56	C₄×C₂²⋊D₄₃	C₂×C₄	1	2	yes	—
57	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
58	#13063284	Q₈	1	1	yes	characteristic
59	#13063282	Q₈	1	2	yes	—
60	C₄²×D₄₃	C₂³	1	2	yes	—
61	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
62	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
63	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
64	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
65	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
66	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
67	Dic₄₃⋊C₈	—	2	2	no	—
68	Dic₄₃⋊C₈	—	2	2	no	—
69	Dic₄₃⋊C₈	C₂×C₄	1	2	yes	—
70	Dic₄₃⋊C₈	C₂×C₄	1	2	yes	—
71	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
72	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
73	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
74	(C₂×D₄₃)⋊C₈	—	2	2	no	—
75	(C₂×D₄₃)⋊C₈	—	2	2	no	—
76	(C₂×D₄₃)⋊C₈	C₂×C₄	1	2	yes	—
77	(C₂×D₄₃)⋊C₈	C₂×C₄	1	2	yes	—
78	#13063235	—	2	2	no	—
79	#13063235	C₂×C₄	1	2	yes	—
80	#13063235	C₂×C₄	1	2	yes	—
81	C₄×C₄₃⋊C₈	—	2	1	no	—
82	C₄×C₄₃⋊C₈	—	2	1	no	—
83	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
84	C₈×Dic₄₃	—	2	2	no	—
85	C₂×M₁₆×C₄₃	—	2	1	no	—
86	C₂×M₁₆×C₄₃	—	2	1	no	—
87	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
88	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₄₃	—	2	1	no	—
91	C₄⋊C₈×C₄₃	—	2	1	no	—
92	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
93	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
94	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
96	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
101	C₂×C₂²⋊D₄₃	C₄⋊C₄	1	2	yes	—
102	#10621898	—	4	2	no	—
103	C₂×D₁₇₂	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
105	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
106	C₂×C₄×D₄₃	C₂×Q₈	1	2	yes	—
107	C₂×Dic₈₆	C₄⋊C₄	1	1	yes	characteristic
108	M₁₆×C₄₃	—	8	1	no	—
109	M₁₆×C₄₃	—	8	1	no	—
110	C₂×C₈×C₄₃	—	2	2	no	—
111	C₂×C₈×C₄₃	—	2	2	no	—
112	C₂×C₈×C₄₃	—	2	2	no	—
113	C₂×C₈×C₄₃	—	4	1	no	—
114	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
121	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
122	C₂²⋊Dic₄₃	C₄⋊C₄	1	2	yes	—
123	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	2	yes	—
124	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	2	yes	—
125	C₄⋊Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
126	C₄⋊Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
127	Dic₄₃⋊C₄	C₄⋊C₄	1	2	yes	—
128	Dic₄₃⋊C₄	C₄⋊C₄	1	2	yes	—
129	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
130	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
131	C₄×Dic₄₃	C₂×Q₈	1	2	yes	—
132	C₂×C₄₃⋊C₈	—	2	1	no	—
133	C₂×C₄₃⋊C₈	—	2	1	no	—
134	C₂×C₄₃⋊C₈	—	2	1	no	—
135	C₂×C₄₃⋊C₈	—	2	1	no	—
136	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
137	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
138	#10621872	—	2	4	no	—
139	#10621872	—	4	2	no	—
140	#10621872	—	8	2	no	—
141	C₈×D₄₃	—	8	2	no	—
142	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂²×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×C₄×C₄₃	—	2	1	no	—
145	C₂×C₄×C₄₃	—	2	1	no	—
146	C₂×C₄×C₄₃	—	2	1	no	—
147	C₂×C₄×C₄₃	—	2	1	no	—
148	C₂×C₄×C₄₃	—	2	2	no	—
149	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
155	C₂²⋊D₄₃	—	4	2	no	—
156	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
159	D₁₇₂	—	2	2	no	—
160	C₄×D₄₃	—	2	2	no	—
161	C₄×D₄₃	—	2	2	no	—
162	C₄×D₄₃	—	2	2	no	—
163	C₄×D₄₃	—	2	2	no	—
164	C₄×D₄₃	—	4	2	no	—
165	Dic₈₆	—	2	2	no	—
166	C₈×C₄₃	—	2	1	no	—
167	C₈×C₄₃	—	2	1	no	—
168	C₈×C₄₃	—	2	1	no	—
169	C₈×C₄₃	—	4	2	no	—
170	C₈×C₄₃	—	4	2	no	—
171	C₈×C₄₃	#131	1	2	yes	—
172	C₄₃⋊C₈	—	2	2	no	—
173	C₄₃⋊C₈	—	2	2	no	—
174	C₄₃⋊C₈	—	4	1	no	—
175	C₄₃⋊C₈	—	4	1	no	—
176	C₄₃⋊C₈	—	4	1	no	—
177	C₄₃⋊C₈	—	4	1	no	—
178	#17839	—	43	1	no	maximal, Sylow
179	C₂²×C₄₃	—	2	1	no	—
180	C₂²×C₄₃	—	2	1	no	—
181	C₂²×C₄₃	—	2	1	no	—
182	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₂×D₄₃	—	2	2	no	—
184	C₂×D₄₃	—	2	2	no	—
185	C₂×D₄₃	—	2	2	no	—
186	C₄×C₄₃	—	2	1	no	—
187	C₄×C₄₃	—	2	1	no	—
188	C₄×C₄₃	—	2	1	no	—
189	C₄×C₄₃	#430	1	2	yes	—
190	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
191	C₄×C₄₃	#568	1	1	yes	characteristic
192	C₄×C₄₃	#576	1	1	yes	characteristic
193	C₄×C₄₃	#578	1	1	yes	characteristic
194	Dic₄₃	—	2	2	no	—
195	Dic₄₃	—	2	2	no	—
196	Dic₄₃	—	2	2	no	—
197	#2991	—	43	1	no	—
198	#2990	—	43	1	no	—
199	#2965	—	43	1	no	—
200	#1574	—	43	1	no	—
201	#1574	—	43	1	no	—
202	#1572	—	43	2	no	—
203	#1571	—	43	2	no	—
204	#1569	—	43	2	no	—
205	#1567	D₄₃	1	1	yes	characteristic, complemented
206	#1565	—	43	2	no	—
207	#1564	—	43	1	no	—
208	C₂×C₄₃	—	4	1	no	—
209	C₂×C₄₃	#2906	1	1	yes	characteristic
210	C₂×C₄₃	#2913	1	1	yes	characteristic
211	C₂×C₄₃	C₂×#430	1	1	yes	characteristic
212	D₄₃	—	4	2	no	—
213	C₄×#41	—	43	1	no	—
214	#446	—	43	1	no	—
215	#446	—	43	1	no	—
216	#446	—	86	1	no	—
217	C₈×Q₈	—	86	1	no	—
218	#436	—	43	1	no	—
219	#436	—	43	1	no	—
220	#436	—	86	1	no	—
221	#436	—	86	2	no	—
222	#435	—	43	2	no	—
223	#435	—	43	2	no	—
224	#435	—	86	2	no	—
225	C₈×D₄	—	86	1	no	—
226	#432	—	43	2	no	—
227	#431	—	43	1	no	—
228	#431	—	43	2	no	—
229	#431	—	43	1	no	—
230	#431	—	43	1	no	—
231	#431	—	43	2	no	—
232	#423	—	43	2	no	—
233	#423	C₂×D₄₃	1	1	yes	characteristic
234	#423	C₂×D₄₃	1	1	yes	characteristic
235	C₂×C₄⋊C₈	—	43	2	no	—
236	C₄×M₁₆	—	43	2	no	—
237	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
238	#335	—	43	2	no	—
239	#335	—	43	2	no	—
240	#335	—	43	1	no	—
241	#335	—	43	1	no	—
242	#335	C₂×D₄₃	1	2	yes	—
243	#335	C₂×D₄₃	1	2	yes	—
244	#334	—	43	2	no	—
245	#334	—	43	2	no	—
246	#334	—	43	1	no	—
247	#334	—	43	1	no	—
248	C₄₃	#17839	1	1	yes	characteristic, complemented, Sylow
249	C₂×#41	—	43	1	no	—
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	43	2	no	—
253	C₂×M₁₆	—	43	2	no	—
254	C₂×M₁₆	—	86	2	no	—
255	C₂²×C₈	—	86	2	no	—
256	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
257	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
258	C₄×Q₈	—	43	1	no	—
259	C₄×Q₈	—	43	1	no	—
260	C₄×D₄	—	43	2	no	—
261	C₄×D₄	—	43	2	no	—
262	C₄×D₄	—	43	1	no	—
263	C₄×D₄	—	43	1	no	—
264	#117	—	43	1	no	—
265	#117	—	43	2	no	—
266	C₂×C₄²	—	43	2	no	—
267	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	43	2	no	—
271	C₄⋊C₈	—	43	2	no	—
272	C₄⋊C₈	—	43	1	no	—
273	C₄⋊C₈	—	43	1	no	—
274	C₄⋊C₈	—	43	1	no	—
275	C₄⋊C₈	—	43	1	no	—
276	C₄⋊C₈	—	43	1	no	—
277	C₄⋊C₈	—	43	1	no	—
278	C₄⋊C₈	—	86	2	no	—
279	C₄⋊C₈	—	86	2	no	—
280	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
281	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
282	C₂²⋊C₈	—	43	2	no	—
283	C₂²⋊C₈	—	43	2	no	—
284	C₂²⋊C₈	—	43	2	no	—
285	C₂²⋊C₈	—	86	2	no	—
286	C₂²⋊C₈	—	86	2	no	—
287	C₂²⋊C₈	—	86	1	no	—
288	C₂²⋊C₈	—	86	1	no	—
289	#97	—	43	2	no	—
290	#97	—	43	2	no	—
291	#97	—	86	2	no	—
292	C₄×C₈	—	43	2	no	—
293	C₄×C₈	—	86	2	no	—
294	C₄×C₈	—	86	1	no	—
295	C₄×C₈	—	86	1	no	—
296	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
297	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
299	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
300	#41	—	172	2	no	—
301	C₂×Q₈	—	43	1	no	—
302	C₂×D₄	—	43	2	no	—
303	C₂×D₄	—	43	1	no	—
304	C₂²×C₄	—	43	2	no	—
305	C₂²×C₄	—	43	2	no	—
306	C₂²×C₄	—	43	2	no	—
307	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
308	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
309	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
310	M₁₆	—	8	1	no	—
311	M₁₆	—	8	1	no	—
312	M₁₆	—	86	4	no	—
313	M₁₆	—	344	2	no	—
314	M₁₆	—	172	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	43	2	no	—
320	C₂×C₈	—	43	2	no	—
321	C₂×C₈	—	86	1	no	—
322	C₂×C₈	—	86	1	no	—
323	C₂×C₈	—	86	1	no	—
324	C₂×C₈	—	86	1	no	—
325	C₂×C₈	—	344	2	no	—
326	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
327	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
328	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
329	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
330	C₄⋊C₄	—	43	2	no	—
331	C₄⋊C₄	—	43	2	no	—
332	C₄⋊C₄	—	43	1	no	—
333	C₄⋊C₄	—	43	1	no	—
334	C₂²⋊C₄	—	43	2	no	—
335	C₂²⋊C₄	—	43	2	no	—
336	C₂²⋊C₄	—	43	2	no	—
337	C₄²	—	43	2	no	—
338	C₄²	—	43	2	no	—
339	C₄²	—	43	2	no	—
340	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
341	C₄²	D₄×D₄₃	1	1	yes	characteristic
342	C₄²	Q₈×D₄₃	1	1	yes	characteristic
343	C₄²	C₂³×D₄₃	1	1	yes	characteristic
344	C₂³	—	43	2	no	—
345	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
346	Q₈	—	86	2	no	—
347	D₄	—	86	2	no	—
348	D₄	—	172	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	43	2	no	—
355	C₂×C₄	—	43	2	no	—
356	C₂×C₄	—	43	2	no	—
357	C₂×C₄	—	86	2	no	—
358	C₂×C₄	—	86	2	no	—
359	C₂×C₄	—	86	2	no	—
360	C₂×C₄	—	86	2	no	—
361	C₂×C₄	—	172	2	no	—
362	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
363	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
364	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
365	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
366	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
367	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
368	C₈	—	2	1	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	4	2	no	—
372	C₈	—	4	2	no	—
373	C₈	—	86	2	no	—
374	C₈	—	86	2	no	—
375	C₈	—	172	1	no	—
376	C₈	—	172	1	no	—
377	C₈	—	172	1	no	—
378	C₈	—	172	1	no	—
379	C₈	#13063333	1	2	yes	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	86	2	no	—
384	C₂²	—	86	2	no	—
385	C₂²	—	86	2	no	—
386	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	86	2	no	—
391	C₄	—	86	2	no	—
392	C₄	—	86	2	no	—
393	C₄	#14582946	1	2	yes	—
394	C₄	C₂×#13063333	1	1	yes	characteristic
395	C₄	#14583665	1	1	yes	characteristic
396	C₄	#14583700	1	1	yes	characteristic
397	C₄	#14583712	1	1	yes	characteristic
398	C₂	—	4	1	no	—
399	C₂	—	172	2	no	—
400	C₂	#19143164	1	1	yes	characteristic
401	C₂	#19143191	1	1	yes	characteristic
402	C₂	C₂×#14582946	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1567	C₂
socle	C₂²×C₄₃	C₂²×C₄⋊C₄
prime radical	C₂×#10621898	Q₈
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1567	D₄₃
hypocenter	C₄₃	#17839
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

Complements

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

N	H ≅ G/N	type
4. #19133386	C₂	semidirect
5. #19133386	C₂	semidirect
6. #19133374	C₂	semidirect
7. #19133368	C₂	semidirect
8. #19133361	C₂	semidirect
9. #19133346	C₂	semidirect
10. #19133343	C₂	semidirect
11. C₄₃×#1567	C₂	semidirect
205. #1567	D₄₃	semidirect
248. C₄₃	#17839	semidirect

Maximal subgroups

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

subgroup	index
#19143725	2
#19143721	2
#19143561	2
#19133386	2
#19133374	2
#19133368	2
#19133361	2
#19133346	2
#19133343	2
C₄₃×#1567	2
#17839	43