Subgroups — C₄₃×#20531 #24940548

Order 11008.

1126 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#408	C₂	1	2	yes	maximal
2	C₄₃×#2297	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1753	C₂	1	2	yes	maximal, complemented
4	C₄₃×#1753	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1752	C₂	1	2	yes	maximal, complemented
6	C₈×C₂²⋊C₄×C₄₃	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1750	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₂²⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
12	C₂³×C₈×C₄₃	C₂²	1	2	yes	—
13	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	C₄₃×#408	C₄	1	16	yes	complemented
16	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
18	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
20	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#97×C₄₃	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
26	C₄₃×#391	C₄	1	2	yes	—
27	C₄₃×#390	C₄	1	2	yes	—
28	C₄₃×#386	C₄	1	4	yes	—
29	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
30	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
31	C₄₃×#336	C₂²	1	2	yes	—
32	C₄₃×#336	C₂²	1	2	yes	—
33	C₄₃×#336	C₂²	1	2	yes	—
34	C₄₃×#336	C₂²	1	2	yes	—
35	C₂×#41×C₄₃	—	4	1	no	—
36	C₂×#41×C₄₃	—	4	1	no	—
37	C₂×#41×C₄₃	—	4	2	no	—
38	C₂×#41×C₄₃	C₂×C₄	1	8	yes	—
39	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
41	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
45	C₂×M₁₆×C₄₃	—	4	2	no	—
46	C₂×M₁₆×C₄₃	—	4	2	no	—
47	C₂×M₁₆×C₄₃	C₂×C₄	1	8	yes	complemented
48	C₂²×C₈×C₄₃	—	4	2	no	—
49	C₂²×C₈×C₄₃	—	4	2	no	—
50	C₂²×C₈×C₄₃	C₂×C₄	1	8	yes	complemented
51	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
54	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
55	#117×C₄₃	—	4	2	no	—
56	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
58	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
60	C₂×C₄²×C₄₃	—	4	1	no	—
61	C₂×C₄²×C₄₃	—	4	1	no	—
62	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
66	C₂²⋊C₈×C₄₃	C₂×C₄	1	8	yes	—
67	C₂²⋊C₈×C₄₃	C₂×C₄	1	8	yes	—
68	C₂²⋊C₈×C₄₃	C₂×C₄	1	8	yes	complemented
69	C₂²⋊C₈×C₄₃	C₂×C₄	1	8	yes	complemented
70	#97×C₄₃	—	4	1	no	—
71	#97×C₄₃	—	4	1	no	—
72	#97×C₄₃	—	4	2	no	—
73	C₄×C₈×C₄₃	—	4	1	no	—
74	C₄×C₈×C₄₃	—	4	1	no	—
75	C₄×C₈×C₄₃	—	4	2	no	—
76	#95×C₄₃	C₂×C₄	1	4	yes	—
77	#95×C₄₃	C₂×C₄	1	4	yes	—
78	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
79	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
80	#41×C₄₃	—	4	8	no	—
81	#41×C₄₃	—	4	8	no	—
82	C₂×Q₈×C₄₃	—	4	1	no	—
83	C₂×Q₈×C₄₃	—	4	1	no	—
84	C₂×Q₈×C₄₃	C₄²	1	4	yes	—
85	C₂×D₄×C₄₃	—	4	2	no	—
86	C₂×D₄×C₄₃	—	4	2	no	—
87	C₂×D₄×C₄₃	—	4	1	no	—
88	C₂×D₄×C₄₃	—	4	1	no	—
89	C₂×D₄×C₄₃	C₄²	1	8	yes	—
90	C₂×D₄×C₄₃	C₄²	1	4	yes	—
91	C₂²×C₄×C₄₃	—	2	1	no	—
92	C₂²×C₄×C₄₃	—	2	1	no	—
93	C₂²×C₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	—	2	2	no	—
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	2	4	no	—
99	C₂²×C₄×C₄₃	—	4	2	no	—
100	C₂²×C₄×C₄₃	—	4	2	no	—
101	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
104	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
110	M₁₆×C₄₃	—	4	8	no	—
111	C₂×C₈×C₄₃	—	2	2	no	—
112	C₂×C₈×C₄₃	—	2	2	no	—
113	C₂×C₈×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	—	2	2	no	—
115	C₂×C₈×C₄₃	—	2	2	no	—
116	C₂×C₈×C₄₃	—	2	2	no	—
117	C₂×C₈×C₄₃	—	2	2	no	—
118	C₂×C₈×C₄₃	—	2	2	no	—
119	C₂×C₈×C₄₃	—	4	8	no	—
120	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
121	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
122	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
123	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
124	C₄⋊C₄×C₄₃	—	4	2	no	—
125	C₂²⋊C₄×C₄₃	—	2	8	no	—
126	C₂²⋊C₄×C₄₃	—	4	4	no	—
127	C₂²⋊C₄×C₄₃	—	4	2	no	—
128	C₄²×C₄₃	—	2	1	no	—
129	C₄²×C₄₃	—	2	1	no	—
130	C₄²×C₄₃	—	2	2	no	—
131	C₄²×C₄₃	—	2	1	no	—
132	C₄²×C₄₃	—	2	1	no	—
133	C₄²×C₄₃	—	2	2	no	—
134	C₄²×C₄₃	—	4	2	no	—
135	C₂³×C₄₃	—	2	1	no	—
136	C₂³×C₄₃	—	2	1	no	—
137	C₂³×C₄₃	—	2	2	no	—
138	C₂³×C₄₃	—	2	2	no	—
139	C₂³×C₄₃	—	2	4	no	—
140	C₂³×C₄₃	—	2	2	no	—
141	C₂³×C₄₃	—	2	4	no	—
142	C₂³×C₄₃	—	2	2	no	—
143	C₂³×C₄₃	C₂×C₄²	1	2	yes	—
144	C₂³×C₄₃	C₂×C₄²	1	4	yes	—
145	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
146	Q₈×C₄₃	—	4	4	no	—
147	D₄×C₄₃	—	4	4	no	—
148	D₄×C₄₃	—	4	8	no	—
149	C₂×C₄×C₄₃	—	2	2	no	—
150	C₂×C₄×C₄₃	—	2	1	no	—
151	C₂×C₄×C₄₃	—	2	1	no	—
152	C₂×C₄×C₄₃	—	2	2	no	—
153	C₂×C₄×C₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	—	2	4	no	—
156	C₂×C₄×C₄₃	—	2	4	no	—
157	C₂×C₄×C₄₃	—	2	4	no	—
158	C₂×C₄×C₄₃	—	2	4	no	—
159	C₂×C₄×C₄₃	—	2	4	no	—
160	C₂×C₄×C₄₃	—	2	4	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	4	no	—
163	C₂×C₄×C₄₃	—	2	4	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	4	no	—
167	C₂×C₄×C₄₃	—	4	8	no	—
168	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
169	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
170	C₂×C₄×C₄₃	#131	1	4	yes	—
171	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
172	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
175	C₈×C₄₃	—	2	4	no	—
176	C₈×C₄₃	—	2	4	no	—
177	C₈×C₄₃	—	2	4	no	—
178	C₈×C₄₃	—	2	4	no	—
179	#20531	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂²×C₄₃	—	2	4	no	—
181	C₂²×C₄₃	—	2	2	no	—
182	C₂²×C₄₃	—	2	4	no	—
183	C₂²×C₄₃	—	2	2	no	—
184	C₂²×C₄₃	—	2	2	no	—
185	C₂²×C₄₃	—	2	4	no	—
186	C₂²×C₄₃	—	4	4	no	—
187	C₂²×C₄₃	—	4	2	no	—
188	C₂²×C₄₃	—	4	2	no	—
189	C₂²×C₄₃	—	4	4	no	—
190	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
191	C₂²×C₄₃	#518	1	1	yes	characteristic
192	C₂²×C₄₃	#518	1	1	yes	characteristic
193	C₂²×C₄₃	C₂×#131	1	2	yes	—
194	C₂²×C₄₃	#568	1	2	yes	—
195	C₄×C₄₃	—	2	4	no	—
196	C₄×C₄₃	—	2	2	no	—
197	C₄×C₄₃	—	2	4	no	—
198	C₄×C₄₃	—	4	2	no	—
199	C₄×C₄₃	—	4	4	no	—
200	C₄×C₄₃	#518	1	2	yes	—
201	C₄×C₄₃	#518	1	2	yes	—
202	C₂×#408	C₂×C₄₃	1	2	yes	—
203	#2297	C₂×C₄₃	1	1	yes	characteristic
204	#1753	C₂×C₄₃	1	2	yes	complemented
205	#1753	C₂×C₄₃	1	2	yes	complemented
206	#1752	C₂×C₄₃	1	2	yes	complemented
207	C₈×C₂²⋊C₄	C₂×C₄₃	1	2	yes	complemented
208	#1750	C₂×C₄₃	1	2	yes	complemented
209	#1749	C₂×C₄₃	1	1	yes	characteristic, complemented
210	C₄×C₂²⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
211	C₂×C₄₃	—	4	4	no	—
212	C₂×C₄₃	—	4	2	no	—
213	C₂×C₄₃	#2273	1	1	yes	characteristic
214	C₂×C₄₃	C₄×#131	1	1	yes	characteristic
215	C₂×C₄₃	#2875	1	1	yes	characteristic
216	C₂×C₄₃	#2976	1	2	yes	—
217	C₂×C₄₃	#2981	1	2	yes	—
218	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
219	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
220	C₂³×C₈	C₂²×C₄₃	1	2	yes	—
221	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
222	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
223	#408	C₄×C₄₃	1	16	yes	complemented
224	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
225	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
226	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
227	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
228	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
229	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
230	C₂×#97	C₂²×C₄₃	1	2	yes	—
231	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
232	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
233	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	—
234	#391	C₄×C₄₃	1	2	yes	—
235	#390	C₄×C₄₃	1	2	yes	—
236	#386	C₄×C₄₃	1	4	yes	—
237	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
238	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
239	#336	C₂²×C₄₃	1	2	yes	—
240	#336	C₂²×C₄₃	1	2	yes	—
241	#336	C₂²×C₄₃	1	2	yes	—
242	#336	C₂²×C₄₃	1	2	yes	—
243	C₄₃	#20531	1	1	yes	characteristic, direct product factor, Sylow
244	C₂×#41	—	4	1	no	—
245	C₂×#41	—	4	1	no	—
246	C₂×#41	—	4	2	no	—
247	C₂×#41	C₂×C₄×C₄₃	1	8	yes	—
248	C₂²×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
249	C₂²×D₄	C₂×C₄×C₄₃	1	2	yes	—
250	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
251	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
252	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
253	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
254	C₂×M₁₆	—	4	2	no	—
255	C₂×M₁₆	—	4	2	no	—
256	C₂×M₁₆	C₂×C₄×C₄₃	1	8	yes	complemented
257	C₂²×C₈	—	4	2	no	—
258	C₂²×C₈	—	4	2	no	—
259	C₂²×C₈	C₂×C₄×C₄₃	1	8	yes	complemented
260	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
261	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
262	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
263	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
264	#117	—	4	2	no	—
265	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
266	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
267	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
269	C₂×C₄²	—	4	1	no	—
270	C₂×C₄²	—	4	1	no	—
271	C₂×C₄²	C₂×C₄×C₄₃	1	2	yes	—
272	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
273	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
275	C₂²⋊C₈	C₂×C₄×C₄₃	1	8	yes	—
276	C₂²⋊C₈	C₂×C₄×C₄₃	1	8	yes	—
277	C₂²⋊C₈	C₂×C₄×C₄₃	1	8	yes	complemented
278	C₂²⋊C₈	C₂×C₄×C₄₃	1	8	yes	complemented
279	#97	—	4	1	no	—
280	#97	—	4	1	no	—
281	#97	—	4	2	no	—
282	C₄×C₈	—	4	1	no	—
283	C₄×C₈	—	4	1	no	—
284	C₄×C₈	—	4	2	no	—
285	#95	C₂×C₄×C₄₃	1	4	yes	—
286	#95	C₂×C₄×C₄₃	1	4	yes	—
287	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
288	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
289	#41	—	4	8	no	—
290	#41	—	4	8	no	—
291	C₂×Q₈	—	4	1	no	—
292	C₂×Q₈	—	4	1	no	—
293	C₂×Q₈	C₄²×C₄₃	1	4	yes	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	C₄²×C₄₃	1	8	yes	—
299	C₂×D₄	C₄²×C₄₃	1	4	yes	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
311	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
312	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
313	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
314	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
315	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
316	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
317	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
318	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
319	M₁₆	—	4	8	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	4	8	no	—
329	C₂×C₈	C₂²×C₄×C₄₃	1	4	yes	—
330	C₂×C₈	C₂²×C₄×C₄₃	1	4	yes	—
331	C₂×C₈	C₂²×C₄×C₄₃	1	4	yes	—
332	C₂×C₈	C₂²×C₄×C₄₃	1	4	yes	—
333	C₄⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	2	8	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	4	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	4	2	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	4	no	—
351	C₂³	—	2	2	no	—
352	C₂³	C₂×C₄²×C₄₃	1	2	yes	—
353	C₂³	C₂×C₄²×C₄₃	1	4	yes	—
354	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
355	Q₈	—	4	4	no	—
356	D₄	—	4	4	no	—
357	D₄	—	4	8	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	4	8	no	—
377	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
378	C₂×C₄	C₂×C₄²×C₄₃	1	2	yes	—
379	C₂×C₄	#131×C₄₃	1	4	yes	—
380	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
381	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
382	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
383	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
384	C₈	—	2	4	no	—
385	C₈	—	2	4	no	—
386	C₈	—	2	4	no	—
387	C₈	—	2	4	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	4	no	—
398	C₂²	C₂²×C₄²×C₄₃	1	1	yes	characteristic
399	C₂²	C₄₃×#518	1	1	yes	characteristic
400	C₂²	C₄₃×#518	1	1	yes	characteristic
401	C₂²	C₂×#131×C₄₃	1	2	yes	—
402	C₂²	C₄₃×#568	1	2	yes	—
403	C₄	—	2	4	no	—
404	C₄	—	2	2	no	—
405	C₄	—	2	4	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	4	no	—
408	C₄	C₄₃×#518	1	2	yes	—
409	C₄	C₄₃×#518	1	2	yes	—
410	C₂	—	4	2	no	—
411	C₂	—	4	4	no	—
412	C₂	C₄₃×#2273	1	1	yes	characteristic
413	C₂	C₄×#131×C₄₃	1	1	yes	characteristic
414	C₂	C₄₃×#2875	1	1	yes	characteristic
415	C₂	C₄₃×#2976	1	2	yes	—
416	C₂	C₄₃×#2981	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂⁴
commutator	C₂²	C₂²×C₄²×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂³×C₄₃	C₂³×C₄
prime radical	C₂²×#41×C₄₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₃×#1753	C₂	semidirect
4. C₄₃×#1753	C₂	semidirect
5. C₄₃×#1752	C₂	semidirect
6. C₈×C₂²⋊C₄×C₄₃	C₂	semidirect
7. C₄₃×#1750	C₂	semidirect
8. C₄₃×#1749	C₂	semidirect
9. C₄×C₂²⋊C₈×C₄₃	C₂	semidirect
15. C₄₃×#408	C₄	semidirect
47. C₂×M₁₆×C₄₃	C₂×C₄	semidirect
50. C₂²×C₈×C₄₃	C₂×C₄	semidirect
68. C₂²⋊C₈×C₄₃	C₂×C₄	semidirect
69. C₂²⋊C₈×C₄₃	C₂×C₄	semidirect
179. #20531	C₄₃	direct (N × H)
204. #1753	C₂×C₄₃	semidirect
205. #1753	C₂×C₄₃	semidirect
206. #1752	C₂×C₄₃	semidirect
207. C₈×C₂²⋊C₄	C₂×C₄₃	semidirect
208. #1750	C₂×C₄₃	semidirect
209. #1749	C₂×C₄₃	semidirect
210. C₄×C₂²⋊C₈	C₂×C₄₃	semidirect
223. #408	C₄×C₄₃	semidirect
243. C₄₃	#20531	direct (N × H)
256. C₂×M₁₆	C₂×C₄×C₄₃	semidirect
259. C₂²×C₈	C₂×C₄×C₄₃	semidirect
277. C₂²⋊C₈	C₂×C₄×C₄₃	semidirect
278. C₂²⋊C₈	C₂×C₄×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×#408	2
C₄₃×#2297	2
C₄₃×#1753	2
C₄₃×#1752	2
C₈×C₂²⋊C₄×C₄₃	2
C₄₃×#1750	2
C₄₃×#1749	2
C₄×C₂²⋊C₈×C₄₃	2
#20531	43

Subgroups — C43×#20531 #24940548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20531 #24940548