Subgroups — C₄₃×#25726 #24945743

Order 11008.

1560 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#497	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#451	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₃×#448	C₂	1	2	yes	maximal
5	C₄₃×#2850	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#2016	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2013	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1960	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₄₃	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₄₃	C₂²	1	4	yes	—
12	C₂²×SD₁₆×C₄₃	C₂²	1	4	yes	—
13	C₂×C₄⋊Q₈×C₄₃	—	2	8	no	—
14	C₂×C₄⋊Q₈×C₄₃	—	2	2	no	—
15	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
16	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
17	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₄₃	—	2	2	no	—
21	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#497	—	2	8	no	—
23	C₄₃×#451	—	2	8	no	—
24	C₄₃×#448	—	2	8	no	—
25	C₂×#103×C₄₃	C₂²	1	4	yes	—
26	C₂×#103×C₄₃	C₂²	1	4	yes	—
27	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
28	C₂×#97×C₄₃	C₂²	1	2	yes	—
29	C₄₃×#391	C₂²	1	1	yes	characteristic
30	C₄₃×#390	C₂²	1	1	yes	characteristic
31	C₄₃×#388	—	2	2	no	—
32	C₄₃×#386	—	2	2	no	—
33	C₄₃×#382	C₂²	1	1	yes	characteristic
34	C₄₃×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₄₃	—	2	8	no	—
36	C₂²×Q₈×C₄₃	—	2	2	no	—
37	C₂²×Q₈×C₄₃	—	2	4	no	—
38	C₂²×Q₈×C₄₃	—	2	4	no	—
39	C₂²×Q₈×C₄₃	—	4	4	no	—
40	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
41	C₂²×Q₈×C₄₃	C₂³	1	4	yes	—
42	C₂²×D₄×C₄₃	—	2	1	no	—
43	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₃	—	2	2	no	—
45	C₂³×C₄×C₄₃	D₄	1	2	yes	—
46	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₄₃	—	2	8	no	—
48	C₂×Q₁₆×C₄₃	—	2	8	no	—
49	C₂×Q₁₆×C₄₃	—	4	4	no	—
50	C₂×SD₁₆×C₄₃	—	2	8	no	—
51	C₂×SD₁₆×C₄₃	—	2	8	no	—
52	C₂×SD₁₆×C₄₃	—	4	4	no	—
53	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
54	C₄⋊Q₈×C₄₃	—	2	16	no	—
55	C₄⋊Q₈×C₄₃	—	2	8	no	—
56	C₄⋊Q₈×C₄₃	—	2	4	no	—
57	C₄⋊Q₈×C₄₃	D₄	1	8	yes	complemented
58	#124×C₄₃	—	2	4	no	—
59	C₂²⋊Q₈×C₄₃	—	2	4	no	—
60	#121×C₄₃	—	2	4	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	16	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
71	C₂×C₄²×C₄₃	—	2	4	no	—
72	C₂×C₄²×C₄₃	D₄	1	2	yes	—
73	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
75	#103×C₄₃	—	2	8	no	—
76	#103×C₄₃	—	2	8	no	—
77	C₂²⋊C₈×C₄₃	D₄	1	8	yes	—
78	#97×C₄₃	—	2	4	no	—
79	#95×C₄₃	—	2	2	no	—
80	#95×C₄₃	—	2	2	no	—
81	C₂⁴×C₄₃	—	2	1	no	—
82	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
83	C₂×Q₈×C₄₃	—	2	8	no	—
84	C₂×Q₈×C₄₃	—	2	4	no	—
85	C₂×Q₈×C₄₃	—	2	4	no	—
86	C₂×Q₈×C₄₃	—	2	4	no	—
87	C₂×Q₈×C₄₃	—	2	2	no	—
88	C₂×Q₈×C₄₃	—	2	2	no	—
89	C₂×Q₈×C₄₃	—	2	4	no	—
90	C₂×Q₈×C₄₃	—	2	4	no	—
91	C₂×Q₈×C₄₃	—	2	2	no	—
92	C₂×Q₈×C₄₃	—	4	16	no	—
93	C₂×Q₈×C₄₃	—	4	16	no	—
94	C₂×Q₈×C₄₃	—	4	4	no	—
95	C₂×Q₈×C₄₃	—	4	4	no	—
96	C₂×Q₈×C₄₃	C₂×D₄	1	8	yes	—
97	C₂×D₄×C₄₃	—	2	2	no	—
98	C₂×D₄×C₄₃	—	2	2	no	—
99	C₂×D₄×C₄₃	—	2	2	no	—
100	C₂×D₄×C₄₃	—	4	2	no	—
101	C₂×D₄×C₄₃	—	4	4	no	—
102	C₂²×C₄×C₄₃	—	2	4	no	—
103	C₂²×C₄×C₄₃	—	2	4	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	2	8	no	—
107	C₂²×C₄×C₄₃	—	2	4	no	—
108	C₂²×C₄×C₄₃	—	2	4	no	—
109	C₂²×C₄×C₄₃	—	2	1	no	—
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	—	2	1	no	—
112	C₂²×C₄×C₄₃	—	4	4	no	—
113	C₂²×C₄×C₄₃	—	4	4	no	—
114	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
119	Q₁₆×C₄₃	—	4	16	no	—
120	SD₁₆×C₄₃	—	4	16	no	—
121	C₂×C₈×C₄₃	—	2	4	no	—
122	C₂×C₈×C₄₃	—	2	4	no	—
123	C₂×C₈×C₄₃	C₂×D₄	1	8	yes	—
124	C₄⋊C₄×C₄₃	—	2	16	no	—
125	C₄⋊C₄×C₄₃	—	2	16	no	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	2	2	no	—
128	C₄⋊C₄×C₄₃	—	4	2	no	—
129	C₂²⋊C₄×C₄₃	—	4	4	no	—
130	C₂²⋊C₄×C₄₃	—	4	2	no	—
131	C₂²⋊C₄×C₄₃	—	4	4	no	—
132	C₂²⋊C₄×C₄₃	—	4	2	no	—
133	C₄²×C₄₃	—	2	4	no	—
134	C₄²×C₄₃	—	2	2	no	—
135	C₄²×C₄₃	C₂×D₄	1	4	yes	—
136	C₂³×C₄₃	—	2	1	no	—
137	C₂³×C₄₃	—	2	1	no	—
138	C₂³×C₄₃	—	2	2	no	—
139	C₂³×C₄₃	—	4	1	no	—
140	C₂³×C₄₃	—	4	1	no	—
141	C₂³×C₄₃	—	4	1	no	—
142	C₂³×C₄₃	—	4	2	no	—
143	C₂³×C₄₃	—	4	2	no	—
144	C₂³×C₄₃	#127	1	2	yes	—
145	C₂³×C₄₃	#137	1	4	yes	—
146	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₄₃	—	2	8	no	—
148	Q₈×C₄₃	—	2	8	no	—
149	Q₈×C₄₃	—	4	16	no	—
150	Q₈×C₄₃	—	4	4	no	—
151	Q₈×C₄₃	—	4	4	no	—
152	Q₈×C₄₃	—	4	4	no	—
153	D₄×C₄₃	—	4	4	no	—
154	D₄×C₄₃	—	8	4	no	—
155	C₂×C₄×C₄₃	—	2	16	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	1	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	8	no	—
163	C₂×C₄×C₄₃	—	2	8	no	—
164	C₂×C₄×C₄₃	—	4	16	no	—
165	C₂×C₄×C₄₃	—	4	4	no	—
166	C₂×C₄×C₄₃	—	4	4	no	—
167	C₂×C₄×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	—	4	1	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	#120	1	4	yes	—
175	C₂×C₄×C₄₃	#127	1	2	yes	—
176	C₂×C₄×C₄₃	#137	1	4	yes	—
177	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
178	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
179	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
180	C₈×C₄₃	—	2	8	no	—
181	#25726	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂²×C₄₃	—	2	2	no	—
183	C₂²×C₄₃	—	2	2	no	—
184	C₂²×C₄₃	—	2	4	no	—
185	C₂²×C₄₃	—	2	4	no	—
186	C₂²×C₄₃	—	8	1	no	—
187	C₂²×C₄₃	—	8	1	no	—
188	C₂²×C₄₃	—	8	1	no	—
189	C₂²×C₄₃	—	8	2	no	—
190	C₂²×C₄₃	—	8	2	no	—
191	C₂²×C₄₃	#497	1	4	yes	complemented
192	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
193	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
194	C₂²×C₄₃	#535	1	1	yes	characteristic
195	C₂²×C₄₃	C₂×#137	1	2	yes	—
196	C₂²×C₄₃	C₂×#137	1	2	yes	—
197	C₄×C₄₃	—	2	2	no	—
198	C₄×C₄₃	—	2	4	no	—
199	C₄×C₄₃	—	2	4	no	—
200	C₄×C₄₃	—	4	8	no	—
201	C₄×C₄₃	—	8	1	no	—
202	C₄×C₄₃	—	8	1	no	—
203	C₄×C₄₃	—	8	1	no	—
204	C₄×C₄₃	D₄²	1	4	yes	—
205	C₂²×C₄⋊Q₈	C₂×C₄₃	1	1	yes	characteristic, complemented
206	C₂×#497	C₂×C₄₃	1	2	yes	complemented
207	C₂×#451	C₂×C₄₃	1	2	yes	complemented
208	C₂×#448	C₂×C₄₃	1	2	yes	—
209	#2850	C₂×C₄₃	1	1	yes	characteristic
210	#2016	C₂×C₄₃	1	2	yes	complemented
211	#2013	C₂×C₄₃	1	2	yes	complemented
212	#1960	C₂×C₄₃	1	2	yes	complemented
213	#1749	C₂×C₄₃	1	1	yes	characteristic, complemented
214	C₂×C₄₃	—	2	4	no	—
215	C₂×C₄₃	—	16	1	no	—
216	C₂×C₄₃	#2433	1	1	yes	characteristic
217	C₂×C₄₃	#3004	1	2	yes	—
218	C₂×C₄₃	C₂×#497	1	1	yes	characteristic
219	C₂×C₄₃	#3152	1	1	yes	characteristic
220	C₂×C₄₃	#3218	1	2	yes	—
221	C₂³×Q₈	C₂²×C₄₃	1	2	yes	—
222	C₂²×Q₁₆	C₂²×C₄₃	1	4	yes	—
223	C₂²×SD₁₆	C₂²×C₄₃	1	4	yes	—
224	C₂×C₄⋊Q₈	—	2	8	no	—
225	C₂×C₄⋊Q₈	—	2	2	no	—
226	C₂×C₄⋊Q₈	C₂²×C₄₃	1	2	yes	—
227	C₂×C₄⋊Q₈	C₂²×C₄₃	1	2	yes	—
228	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
229	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
230	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
231	C₂²×C₄⋊C₄	—	2	2	no	—
232	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
233	#497	—	2	8	no	—
234	#451	—	2	8	no	—
235	#448	—	2	8	no	—
236	C₂×#103	C₂²×C₄₃	1	4	yes	—
237	C₂×#103	C₂²×C₄₃	1	4	yes	—
238	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
239	C₂×#97	C₂²×C₄₃	1	2	yes	—
240	#391	C₂²×C₄₃	1	1	yes	characteristic
241	#390	C₂²×C₄₃	1	1	yes	characteristic
242	#388	—	2	2	no	—
243	#386	—	2	2	no	—
244	#382	C₂²×C₄₃	1	1	yes	characteristic
245	#336	C₂²×C₄₃	1	2	yes	—
246	C₄₃	#25726	1	1	yes	characteristic, direct product factor, Sylow
247	C₂²×Q₈	—	2	8	no	—
248	C₂²×Q₈	—	2	2	no	—
249	C₂²×Q₈	—	2	4	no	—
250	C₂²×Q₈	—	2	4	no	—
251	C₂²×Q₈	—	4	4	no	—
252	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
253	C₂²×Q₈	C₂³×C₄₃	1	4	yes	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
256	C₂³×C₄	—	2	2	no	—
257	C₂³×C₄	D₄×C₄₃	1	2	yes	—
258	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
259	C₂×Q₁₆	—	2	8	no	—
260	C₂×Q₁₆	—	2	8	no	—
261	C₂×Q₁₆	—	4	4	no	—
262	C₂×SD₁₆	—	2	8	no	—
263	C₂×SD₁₆	—	2	8	no	—
264	C₂×SD₁₆	—	4	4	no	—
265	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
266	C₄⋊Q₈	—	2	16	no	—
267	C₄⋊Q₈	—	2	8	no	—
268	C₄⋊Q₈	—	2	4	no	—
269	C₄⋊Q₈	D₄×C₄₃	1	8	yes	complemented
270	#124	—	2	4	no	—
271	C₂²⋊Q₈	—	2	4	no	—
272	#121	—	2	4	no	—
273	C₂×C₄⋊C₄	—	2	16	no	—
274	C₂×C₄⋊C₄	—	2	4	no	—
275	C₂×C₄⋊C₄	—	2	4	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₄²	—	2	4	no	—
284	C₂×C₄²	D₄×C₄₃	1	2	yes	—
285	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
287	#103	—	2	8	no	—
288	#103	—	2	8	no	—
289	C₂²⋊C₈	D₄×C₄₃	1	8	yes	—
290	#97	—	2	4	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	C₂⁴	—	2	1	no	—
294	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
295	C₂×Q₈	—	2	8	no	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	2	4	no	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	4	16	no	—
305	C₂×Q₈	—	4	16	no	—
306	C₂×Q₈	—	4	4	no	—
307	C₂×Q₈	—	4	4	no	—
308	C₂×Q₈	C₂×D₄×C₄₃	1	8	yes	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	4	4	no	—
325	C₂²×C₄	—	4	4	no	—
326	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
329	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
330	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
331	Q₁₆	—	4	16	no	—
332	SD₁₆	—	4	16	no	—
333	C₂×C₈	—	2	4	no	—
334	C₂×C₈	—	2	4	no	—
335	C₂×C₈	C₂×D₄×C₄₃	1	8	yes	—
336	C₄⋊C₄	—	2	16	no	—
337	C₄⋊C₄	—	2	16	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₂²⋊C₄	—	4	4	no	—
345	C₄²	—	2	4	no	—
346	C₄²	—	2	2	no	—
347	C₄²	C₂×D₄×C₄₃	1	4	yes	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	1	no	—
353	C₂³	—	4	1	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	#127×C₄₃	1	2	yes	—
357	C₂³	#137×C₄₃	1	4	yes	—
358	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
359	Q₈	—	2	8	no	—
360	Q₈	—	2	8	no	—
361	Q₈	—	4	16	no	—
362	Q₈	—	4	4	no	—
363	Q₈	—	4	4	no	—
364	Q₈	—	4	4	no	—
365	D₄	—	4	4	no	—
366	D₄	—	8	4	no	—
367	C₂×C₄	—	2	16	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	4	16	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	#120×C₄₃	1	4	yes	—
387	C₂×C₄	#127×C₄₃	1	2	yes	—
388	C₂×C₄	#137×C₄₃	1	4	yes	—
389	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
390	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
391	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
392	C₈	—	2	8	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	8	1	no	—
398	C₂²	—	8	1	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	C₄₃×#497	1	4	yes	complemented
403	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
404	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
405	C₂²	C₄₃×#535	1	1	yes	characteristic
406	C₂²	C₂×#137×C₄₃	1	2	yes	—
407	C₂²	C₂×#137×C₄₃	1	2	yes	—
408	C₄	—	2	2	no	—
409	C₄	—	2	4	no	—
410	C₄	—	2	4	no	—
411	C₄	—	4	8	no	—
412	C₄	—	8	1	no	—
413	C₄	—	8	1	no	—
414	C₄	—	8	1	no	—
415	C₄	D₄²×C₄₃	1	4	yes	—
416	C₂	—	2	4	no	—
417	C₂	—	16	1	no	—
418	C₂	C₄₃×#2433	1	1	yes	characteristic
419	C₂	C₄₃×#3004	1	2	yes	—
420	C₂	C₂×C₄₃×#497	1	1	yes	characteristic
421	C₂	C₄₃×#3152	1	1	yes	characteristic
422	C₂	C₄₃×#3218	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#121×C₄₃	C₂²
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
1. C₂²×C₄⋊Q₈×C₄₃	C₂	semidirect
2. C₂×C₄₃×#497	C₂	semidirect
3. C₂×C₄₃×#451	C₂	semidirect
6. C₄₃×#2016	C₂	semidirect
7. C₄₃×#2013	C₂	semidirect
8. C₄₃×#1960	C₂	semidirect
9. C₄₃×#1749	C₂	semidirect
57. C₄⋊Q₈×C₄₃	D₄	semidirect
181. #25726	C₄₃	direct (N × H)
191. C₂²×C₄₃	#497	semidirect
205. C₂²×C₄⋊Q₈	C₂×C₄₃	semidirect
206. C₂×#497	C₂×C₄₃	semidirect
207. C₂×#451	C₂×C₄₃	semidirect
210. #2016	C₂×C₄₃	semidirect
211. #2013	C₂×C₄₃	semidirect
212. #1960	C₂×C₄₃	semidirect
213. #1749	C₂×C₄₃	semidirect
246. C₄₃	#25726	direct (N × H)
269. C₄⋊Q₈	D₄×C₄₃	semidirect
402. C₂²	C₄₃×#497	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₄₃	2
C₂×C₄₃×#497	2
C₂×C₄₃×#451	2
C₂×C₄₃×#448	2
C₄₃×#2850	2
C₄₃×#2016	2
C₄₃×#2013	2
C₄₃×#1960	2
C₄₃×#1749	2
#25726	43

Subgroups — C43×#25726 #24945743

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25726 #24945743