Subgroups — C₄₃×#25728 #24945745

Order 11008.

1586 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#497	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#452	C₂	1	4	yes	maximal, complemented
4	C₄₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2016	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2014	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1959	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₃	C₂²	1	2	yes	—
10	C₂²×Q₁₆×C₄₃	C₂²	1	4	yes	—
11	C₂²×SD₁₆×C₄₃	C₂²	1	4	yes	—
12	C₄₃×#532	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#124×C₄₃	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
18	C₂×#121×C₄₃	—	2	2	no	—
19	C₂×C₄×D₄×C₄₃	—	2	2	no	—
20	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₄₃×#497	—	2	8	no	—
22	C₄₃×#452	—	2	16	no	—
23	C₂×#103×C₄₃	C₂²	1	4	yes	—
24	C₂×#102×C₄₃	C₂²	1	4	yes	—
25	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
26	C₂×#97×C₄₃	C₂²	1	2	yes	—
27	C₄₃×#391	C₂²	1	2	yes	—
28	C₄₃×#389	—	2	2	no	—
29	C₄₃×#384	C₂²	1	1	yes	characteristic
30	C₄₃×#380	—	2	2	no	—
31	C₄₃×#336	C₂²	1	2	yes	—
32	C₂×#41×C₄₃	—	2	4	no	—
33	C₂×#41×C₄₃	—	2	4	no	—
34	C₂×#41×C₄₃	—	2	8	no	—
35	C₂×#41×C₄₃	—	4	4	no	—
36	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
37	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
38	C₂²×D₄×C₄₃	—	2	2	no	—
39	C₂²×D₄×C₄₃	—	2	2	no	—
40	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₃	—	2	2	no	—
42	C₂³×C₄×C₄₃	D₄	1	2	yes	—
43	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂×Q₁₆×C₄₃	—	2	8	no	—
45	C₂×Q₁₆×C₄₃	—	2	8	no	—
46	C₂×Q₁₆×C₄₃	—	4	4	no	—
47	C₂×SD₁₆×C₄₃	—	2	8	no	—
48	C₂×SD₁₆×C₄₃	—	2	8	no	—
49	C₂×SD₁₆×C₄₃	—	4	4	no	—
50	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
51	C₄⋊Q₈×C₄₃	—	2	4	no	—
52	C₄⋊Q₈×C₄₃	—	2	4	no	—
53	#127×C₄₃	—	2	4	no	—
54	#124×C₄₃	—	2	4	no	—
55	#124×C₄₃	D₄	1	8	yes	—
56	C₂²⋊Q₈×C₄₃	—	2	8	no	—
57	#121×C₄₃	—	2	16	no	—
58	C₄×D₄×C₄₃	—	2	16	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₄²×C₄₃	—	2	4	no	—
67	C₂×C₄²×C₄₃	D₄	1	2	yes	—
68	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
70	#103×C₄₃	—	2	8	no	—
71	#102×C₄₃	—	2	8	no	—
72	C₂²⋊C₈×C₄₃	D₄	1	8	yes	complemented
73	#97×C₄₃	—	2	4	no	—
74	#95×C₄₃	—	2	4	no	—
75	C₂⁴×C₄₃	—	2	2	no	—
76	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
77	#41×C₄₃	—	4	16	no	—
78	#41×C₄₃	—	4	16	no	—
79	C₂×Q₈×C₄₃	—	2	2	no	—
80	C₂×Q₈×C₄₃	—	2	4	no	—
81	C₂×Q₈×C₄₃	—	2	4	no	—
82	C₂×Q₈×C₄₃	—	2	4	no	—
83	C₂×Q₈×C₄₃	—	2	4	no	—
84	C₂×Q₈×C₄₃	—	2	2	no	—
85	C₂×Q₈×C₄₃	—	2	2	no	—
86	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
87	C₂×D₄×C₄₃	—	2	8	no	—
88	C₂×D₄×C₄₃	—	2	8	no	—
89	C₂×D₄×C₄₃	—	2	2	no	—
90	C₂×D₄×C₄₃	—	2	4	no	—
91	C₂×D₄×C₄₃	—	2	4	no	—
92	C₂×D₄×C₄₃	—	4	4	no	—
93	C₂×D₄×C₄₃	—	4	4	no	—
94	C₂×D₄×C₄₃	—	4	4	no	—
95	C₂×D₄×C₄₃	—	4	4	no	—
96	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	2	8	no	—
100	C₂²×C₄×C₄₃	—	2	4	no	—
101	C₂²×C₄×C₄₃	—	2	4	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	4	2	no	—
106	C₂²×C₄×C₄₃	—	4	4	no	—
107	C₂²×C₄×C₄₃	—	4	4	no	—
108	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
113	Q₁₆×C₄₃	—	4	16	no	—
114	SD₁₆×C₄₃	—	4	16	no	—
115	C₂×C₈×C₄₃	—	2	4	no	—
116	C₂×C₈×C₄₃	—	2	4	no	—
117	C₂×C₈×C₄₃	C₂×D₄	1	8	yes	—
118	C₄⋊C₄×C₄₃	—	2	8	no	—
119	C₄⋊C₄×C₄₃	—	2	4	no	—
120	C₄⋊C₄×C₄₃	—	4	4	no	—
121	C₄⋊C₄×C₄₃	—	4	4	no	—
122	C₄⋊C₄×C₄₃	—	4	4	no	—
123	C₂²⋊C₄×C₄₃	—	2	16	no	—
124	C₂²⋊C₄×C₄₃	—	4	4	no	—
125	C₄²×C₄₃	—	2	4	no	—
126	C₄²×C₄₃	—	2	2	no	—
127	C₄²×C₄₃	C₂×D₄	1	4	yes	—
128	C₂³×C₄₃	—	2	1	no	—
129	C₂³×C₄₃	—	2	1	no	—
130	C₂³×C₄₃	—	2	2	no	—
131	C₂³×C₄₃	—	2	2	no	—
132	C₂³×C₄₃	—	2	4	no	—
133	C₂³×C₄₃	—	4	2	no	—
134	C₂³×C₄₃	—	4	2	no	—
135	C₂³×C₄₃	—	4	4	no	—
136	C₂³×C₄₃	—	4	4	no	—
137	C₂³×C₄₃	#127	1	2	yes	—
138	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₄₃	—	2	8	no	—
140	Q₈×C₄₃	—	4	4	no	—
141	Q₈×C₄₃	—	4	4	no	—
142	Q₈×C₄₃	—	4	4	no	—
143	D₄×C₄₃	—	2	8	no	—
144	D₄×C₄₃	—	4	16	no	—
145	D₄×C₄₃	—	4	16	no	—
146	D₄×C₄₃	—	4	4	no	—
147	C₂×C₄×C₄₃	—	2	2	no	—
148	C₂×C₄×C₄₃	—	2	1	no	—
149	C₂×C₄×C₄₃	—	2	1	no	—
150	C₂×C₄×C₄₃	—	2	2	no	—
151	C₂×C₄×C₄₃	—	2	2	no	—
152	C₂×C₄×C₄₃	—	2	2	no	—
153	C₂×C₄×C₄₃	—	2	8	no	—
154	C₂×C₄×C₄₃	—	2	4	no	—
155	C₂×C₄×C₄₃	—	4	8	no	—
156	C₂×C₄×C₄₃	—	4	16	no	—
157	C₂×C₄×C₄₃	—	4	2	no	—
158	C₂×C₄×C₄₃	—	4	2	no	—
159	C₂×C₄×C₄₃	—	4	2	no	—
160	C₂×C₄×C₄₃	—	4	2	no	—
161	C₂×C₄×C₄₃	—	4	2	no	—
162	C₂×C₄×C₄₃	—	4	2	no	—
163	C₂×C₄×C₄₃	—	4	4	no	—
164	C₂×C₄×C₄₃	#120	1	4	yes	—
165	C₂×C₄×C₄₃	#127	1	2	yes	—
166	C₂×C₄×C₄₃	#137	1	4	yes	—
167	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
168	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
170	C₈×C₄₃	—	2	8	no	—
171	#25728	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂²×C₄₃	—	2	2	no	—
173	C₂²×C₄₃	—	2	2	no	—
174	C₂²×C₄₃	—	2	2	no	—
175	C₂²×C₄₃	—	4	2	no	—
176	C₂²×C₄₃	—	4	2	no	—
177	C₂²×C₄₃	—	4	4	no	—
178	C₂²×C₄₃	—	4	8	no	—
179	C₂²×C₄₃	—	8	2	no	—
180	C₂²×C₄₃	—	8	2	no	—
181	C₂²×C₄₃	—	8	4	no	—
182	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
183	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
184	C₂²×C₄₃	#535	1	1	yes	characteristic
185	C₂²×C₄₃	C₂×#137	1	2	yes	—
186	C₂²×C₄₃	#575	1	2	yes	—
187	C₄×C₄₃	—	2	2	no	—
188	C₄×C₄₃	—	2	4	no	—
189	C₄×C₄₃	—	2	4	no	—
190	C₄×C₄₃	—	4	4	no	—
191	C₄×C₄₃	—	8	2	no	—
192	C₄×C₄₃	—	8	2	no	—
193	C₄×C₄₃	D₄²	1	4	yes	—
194	C₂×#532	C₂×C₄₃	1	1	yes	characteristic
195	C₂×#497	C₂×C₄₃	1	2	yes	complemented
196	C₂×#452	C₂×C₄₃	1	4	yes	complemented
197	#2857	C₂×C₄₃	1	1	yes	characteristic, complemented
198	#2016	C₂×C₄₃	1	2	yes	complemented
199	#2014	C₂×C₄₃	1	2	yes	complemented
200	#1959	C₂×C₄₃	1	2	yes	complemented
201	#1749	C₂×C₄₃	1	1	yes	characteristic, complemented
202	C₂×C₄₃	—	4	2	no	—
203	C₂×C₄₃	—	8	4	no	—
204	C₂×C₄₃	#2433	1	1	yes	characteristic
205	C₂×C₄₃	#3007	1	2	yes	—
206	C₂×C₄₃	#3150	1	1	yes	characteristic
207	C₂×C₄₃	#3152	1	1	yes	characteristic
208	C₂×C₄₃	#3216	1	2	yes	—
209	C₂²×#41	C₂²×C₄₃	1	2	yes	—
210	C₂²×Q₁₆	C₂²×C₄₃	1	4	yes	—
211	C₂²×SD₁₆	C₂²×C₄₃	1	4	yes	—
212	#532	—	2	8	no	—
213	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
214	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
215	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
216	C₂×#124	C₂²×C₄₃	1	2	yes	—
217	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
218	C₂×#121	—	2	2	no	—
219	C₂×C₄×D₄	—	2	2	no	—
220	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
221	#497	—	2	8	no	—
222	#452	—	2	16	no	—
223	C₂×#103	C₂²×C₄₃	1	4	yes	—
224	C₂×#102	C₂²×C₄₃	1	4	yes	—
225	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
226	C₂×#97	C₂²×C₄₃	1	2	yes	—
227	#391	C₂²×C₄₃	1	2	yes	—
228	#389	—	2	2	no	—
229	#384	C₂²×C₄₃	1	1	yes	characteristic
230	#380	—	2	2	no	—
231	#336	C₂²×C₄₃	1	2	yes	—
232	C₄₃	#25728	1	1	yes	characteristic, direct product factor, Sylow
233	C₂×#41	—	2	4	no	—
234	C₂×#41	—	2	4	no	—
235	C₂×#41	—	2	8	no	—
236	C₂×#41	—	4	4	no	—
237	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
238	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
242	C₂³×C₄	—	2	2	no	—
243	C₂³×C₄	D₄×C₄₃	1	2	yes	—
244	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
245	C₂×Q₁₆	—	2	8	no	—
246	C₂×Q₁₆	—	2	8	no	—
247	C₂×Q₁₆	—	4	4	no	—
248	C₂×SD₁₆	—	2	8	no	—
249	C₂×SD₁₆	—	2	8	no	—
250	C₂×SD₁₆	—	4	4	no	—
251	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
252	C₄⋊Q₈	—	2	4	no	—
253	C₄⋊Q₈	—	2	4	no	—
254	#127	—	2	4	no	—
255	#124	—	2	4	no	—
256	#124	D₄×C₄₃	1	8	yes	—
257	C₂²⋊Q₈	—	2	8	no	—
258	#121	—	2	16	no	—
259	C₄×D₄	—	2	16	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	4	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	—	2	4	no	—
268	C₂×C₄²	D₄×C₄₃	1	2	yes	—
269	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
271	#103	—	2	8	no	—
272	#102	—	2	8	no	—
273	C₂²⋊C₈	D₄×C₄₃	1	8	yes	complemented
274	#97	—	2	4	no	—
275	#95	—	2	4	no	—
276	C₂⁴	—	2	2	no	—
277	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
278	#41	—	4	16	no	—
279	#41	—	4	16	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	4	no	—
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	2	4	no	—
284	C₂×Q₈	—	2	4	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
288	C₂×D₄	—	2	8	no	—
289	C₂×D₄	—	2	8	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	—	4	4	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	8	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	—	4	4	no	—
309	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
312	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
314	Q₁₆	—	4	16	no	—
315	SD₁₆	—	4	16	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	C₂×D₄×C₄₃	1	8	yes	—
319	C₄⋊C₄	—	2	8	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	4	4	no	—
322	C₄⋊C₄	—	4	4	no	—
323	C₄⋊C₄	—	4	4	no	—
324	C₂²⋊C₄	—	2	16	no	—
325	C₂²⋊C₄	—	4	4	no	—
326	C₄²	—	2	4	no	—
327	C₄²	—	2	2	no	—
328	C₄²	C₂×D₄×C₄₃	1	4	yes	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	4	no	—
338	C₂³	#127×C₄₃	1	2	yes	—
339	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
340	Q₈	—	2	8	no	—
341	Q₈	—	4	4	no	—
342	Q₈	—	4	4	no	—
343	Q₈	—	4	4	no	—
344	D₄	—	2	8	no	—
345	D₄	—	4	16	no	—
346	D₄	—	4	16	no	—
347	D₄	—	4	4	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	4	8	no	—
357	C₂×C₄	—	4	16	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	#120×C₄₃	1	4	yes	—
366	C₂×C₄	#127×C₄₃	1	2	yes	—
367	C₂×C₄	#137×C₄₃	1	4	yes	—
368	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
369	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
370	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
371	C₈	—	2	8	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	4	8	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	4	no	—
382	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
383	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
384	C₂²	C₄₃×#535	1	1	yes	characteristic
385	C₂²	C₂×#137×C₄₃	1	2	yes	—
386	C₂²	C₄₃×#575	1	2	yes	—
387	C₄	—	2	2	no	—
388	C₄	—	2	4	no	—
389	C₄	—	2	4	no	—
390	C₄	—	4	4	no	—
391	C₄	—	8	2	no	—
392	C₄	—	8	2	no	—
393	C₄	D₄²×C₄₃	1	4	yes	—
394	C₂	—	4	2	no	—
395	C₂	—	8	4	no	—
396	C₂	C₄₃×#2433	1	1	yes	characteristic
397	C₂	C₄₃×#3007	1	2	yes	—
398	C₂	C₄₃×#3150	1	1	yes	characteristic
399	C₂	C₄₃×#3152	1	1	yes	characteristic
400	C₂	C₄₃×#3216	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#532	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#497	C₂	semidirect
3. C₂×C₄₃×#452	C₂	semidirect
4. C₄₃×#2857	C₂	semidirect
5. C₄₃×#2016	C₂	semidirect
6. C₄₃×#2014	C₂	semidirect
7. C₄₃×#1959	C₂	semidirect
8. C₄₃×#1749	C₂	semidirect
72. C₂²⋊C₈×C₄₃	D₄	semidirect
171. #25728	C₄₃	direct (N × H)
195. C₂×#497	C₂×C₄₃	semidirect
196. C₂×#452	C₂×C₄₃	semidirect
197. #2857	C₂×C₄₃	semidirect
198. #2016	C₂×C₄₃	semidirect
199. #2014	C₂×C₄₃	semidirect
200. #1959	C₂×C₄₃	semidirect
201. #1749	C₂×C₄₃	semidirect
232. C₄₃	#25728	direct (N × H)
273. C₂²⋊C₈	D₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#532	2
C₂×C₄₃×#497	2
C₂×C₄₃×#452	2
C₄₃×#2857	2
C₄₃×#2016	2
C₄₃×#2014	2
C₄₃×#1959	2
C₄₃×#1749	2
#25728	43

Subgroups — C43×#25728 #24945745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25728 #24945745