Subgroups — C₄₃×#20716 #24940733

Order 11008.

1418 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#433	C₂	1	2	yes	maximal, complemented
3	C₄₃×#1818	C₂	1	2	yes	maximal, complemented
4	C₄₃×#1798	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1797	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1779	C₂	1	2	yes	maximal
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	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×#117×C₄₃	—	2	8	no	—
12	C₂×#117×C₄₃	C₄	1	2	yes	—
13	C₂×#117×C₄₃	C₄	1	2	yes	—
14	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₄₃	C₄	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₄₃	C₄	1	2	yes	—
20	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#433	—	2	8	no	—
23	C₂×C₄⋊C₈×C₄₃	C₂²	1	4	yes	complemented
24	C₂×C₂²⋊C₈×C₄₃	C₂²	1	4	yes	—
25	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₃	C₂²	1	4	yes	—
28	C₂×#97×C₄₃	C₂²	1	2	yes	complemented
29	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	complemented
30	C₄₃×#336	C₂²	1	2	yes	complemented
31	C₄₃×#336	C₂²	1	2	yes	complemented
32	C₄₃×#336	C₂²	1	4	yes	complemented
33	C₂⁵×C₄₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₄₃	—	2	4	no	—
35	C₂³×C₄×C₄₃	—	2	4	no	—
36	C₂³×C₄×C₄₃	—	2	4	no	—
37	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
46	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
47	#117×C₄₃	—	2	4	no	—
48	#117×C₄₃	—	2	8	no	—
49	#117×C₄₃	—	2	8	no	—
50	#117×C₄₃	—	2	4	no	—
51	#117×C₄₃	—	2	4	no	—
52	#117×C₄₃	D₄	1	8	yes	—
53	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
54	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
58	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
59	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₄₃	—	2	4	no	—
64	C₂×C₄²×C₄₃	—	2	4	no	—
65	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₄₃	—	2	8	no	—
72	C₂²⋊C₈×C₄₃	—	2	8	no	—
73	C₂²⋊C₈×C₄₃	—	2	4	no	—
74	C₂²⋊C₈×C₄₃	—	2	4	no	—
75	C₂²⋊C₈×C₄₃	—	2	8	no	—
76	#97×C₄₃	—	2	4	no	—
77	C₄×C₈×C₄₃	—	2	4	no	—
78	C₂⁴×C₄₃	—	2	2	no	—
79	C₂⁴×C₄₃	—	2	2	no	—
80	C₂⁴×C₄₃	—	2	2	no	—
81	C₂⁴×C₄₃	—	2	4	no	—
82	C₂⁴×C₄₃	—	4	2	no	—
83	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
84	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
85	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	—	2	32	no	—
87	C₂²×C₄×C₄₃	—	2	2	no	—
88	C₂²×C₄×C₄₃	—	2	2	no	—
89	C₂²×C₄×C₄₃	—	2	2	no	—
90	C₂²×C₄×C₄₃	—	2	2	no	—
91	C₂²×C₄×C₄₃	—	2	2	no	—
92	C₂²×C₄×C₄₃	—	2	2	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	2	no	—
99	C₂²×C₄×C₄₃	—	2	4	no	—
100	C₂²×C₄×C₄₃	—	2	4	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	4	no	—
105	C₂²×C₄×C₄₃	—	2	4	no	—
106	C₂²×C₄×C₄₃	—	4	2	no	—
107	C₂²×C₄×C₄₃	—	4	2	no	—
108	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₄₃	#41	1	4	yes	—
117	C₂²×C₄×C₄₃	#41	1	4	yes	—
118	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
119	C₂×C₈×C₄₃	—	2	4	no	—
120	C₂×C₈×C₄₃	—	2	4	no	—
121	C₂×C₈×C₄₃	—	2	4	no	—
122	C₂×C₈×C₄₃	—	2	4	no	—
123	C₂×C₈×C₄₃	—	2	4	no	—
124	C₂×C₈×C₄₃	—	2	4	no	—
125	C₄⋊C₄×C₄₃	—	2	4	no	—
126	C₄⋊C₄×C₄₃	—	2	4	no	—
127	C₄⋊C₄×C₄₃	—	2	4	no	—
128	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	8	yes	—
129	C₂²⋊C₄×C₄₃	—	2	4	no	—
130	C₂²⋊C₄×C₄₃	—	2	4	no	—
131	C₂²⋊C₄×C₄₃	—	2	4	no	—
132	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	8	yes	—
133	C₄²×C₄₃	—	2	4	no	—
134	C₄²×C₄₃	—	2	4	no	—
135	C₄²×C₄₃	—	2	2	no	—
136	C₄²×C₄₃	—	2	2	no	—
137	C₄²×C₄₃	C₂×D₄	1	4	yes	—
138	C₄²×C₄₃	C₂×D₄	1	4	yes	—
139	C₂³×C₄₃	—	2	1	no	—
140	C₂³×C₄₃	—	2	1	no	—
141	C₂³×C₄₃	—	2	2	no	—
142	C₂³×C₄₃	—	2	8	no	—
143	C₂³×C₄₃	—	2	1	no	—
144	C₂³×C₄₃	—	2	1	no	—
145	C₂³×C₄₃	—	2	1	no	—
146	C₂³×C₄₃	—	2	1	no	—
147	C₂³×C₄₃	—	2	2	no	—
148	C₂³×C₄₃	—	2	2	no	—
149	C₂³×C₄₃	—	2	2	no	—
150	C₂³×C₄₃	—	2	2	no	—
151	C₂³×C₄₃	—	4	8	no	—
152	C₂³×C₄₃	—	4	8	no	—
153	C₂³×C₄₃	—	4	4	no	—
154	C₂³×C₄₃	—	4	4	no	—
155	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂³×C₄₃	#117	1	2	yes	—
157	C₂³×C₄₃	#117	1	2	yes	—
158	C₂³×C₄₃	#131	1	4	yes	—
159	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	—	2	8	no	—
161	C₂×C₄×C₄₃	—	2	8	no	—
162	C₂×C₄×C₄₃	—	2	8	no	—
163	C₂×C₄×C₄₃	—	2	1	no	—
164	C₂×C₄×C₄₃	—	2	1	no	—
165	C₂×C₄×C₄₃	—	2	1	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	2	1	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	8	no	—
174	C₂×C₄×C₄₃	—	2	8	no	—
175	C₂×C₄×C₄₃	—	2	8	no	—
176	C₂×C₄×C₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	2	2	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	4	8	no	—
183	C₂×C₄×C₄₃	—	4	8	no	—
184	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
185	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
186	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂×C₄×C₄₃	#117	1	2	yes	—
188	C₂×C₄×C₄₃	#117	1	2	yes	—
189	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
190	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
191	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
192	C₈×C₄₃	—	4	4	no	—
193	C₈×C₄₃	—	4	4	no	—
194	#20716	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂²×C₄₃	—	2	4	no	—
196	C₂²×C₄₃	—	2	2	no	—
197	C₂²×C₄₃	—	2	4	no	—
198	C₂²×C₄₃	—	2	2	no	—
199	C₂²×C₄₃	—	2	4	no	—
200	C₂²×C₄₃	—	2	4	no	—
201	C₂²×C₄₃	—	2	2	no	—
202	C₂²×C₄₃	—	2	2	no	—
203	C₂²×C₄₃	—	4	16	no	—
204	C₂²×C₄₃	—	4	2	no	—
205	C₂²×C₄₃	—	4	1	no	—
206	C₂²×C₄₃	—	4	1	no	—
207	C₂²×C₄₃	—	4	1	no	—
208	C₂²×C₄₃	—	4	1	no	—
209	C₂²×C₄₃	—	4	2	no	—
210	C₂²×C₄₃	#433	1	4	yes	complemented
211	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
212	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
213	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
214	C₂²×C₄₃	C₂×#131	1	2	yes	—
215	C₂²×C₄₃	#568	1	2	yes	—
216	C₄×C₄₃	—	2	4	no	—
217	C₄×C₄₃	—	2	4	no	—
218	C₄×C₄₃	—	2	2	no	—
219	C₄×C₄₃	—	2	2	no	—
220	C₄×C₄₃	—	2	2	no	—
221	C₄×C₄₃	—	4	2	no	—
222	C₄×C₄₃	—	4	2	no	—
223	C₄×C₄₃	#525	1	4	yes	—
224	C₂²×#117	C₂×C₄₃	1	1	yes	characteristic
225	C₂×#433	C₂×C₄₃	1	2	yes	complemented
226	#1818	C₂×C₄₃	1	2	yes	complemented
227	#1798	C₂×C₄₃	1	2	yes	complemented
228	#1797	C₂×C₄₃	1	2	yes	complemented
229	#1779	C₂×C₄₃	1	2	yes	—
230	#1750	C₂×C₄₃	1	2	yes	complemented
231	#1749	C₂×C₄₃	1	1	yes	characteristic, complemented
232	C₄×C₂²⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
233	C₂×C₄₃	—	2	4	no	—
234	C₂×C₄₃	—	4	2	no	—
235	C₂×C₄₃	—	4	2	no	—
236	C₂×C₄₃	#2280	1	1	yes	characteristic
237	C₂×C₄₃	#2880	1	2	yes	—
238	C₂×C₄₃	C₂×#433	1	1	yes	characteristic
239	C₂×C₄₃	#2921	1	1	yes	characteristic
240	C₂×C₄₃	#2924	1	2	yes	—
241	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
242	C₂×#117	—	2	8	no	—
243	C₂×#117	C₄×C₄₃	1	2	yes	—
244	C₂×#117	C₄×C₄₃	1	2	yes	—
245	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
246	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
247	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
248	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
249	C₂²×C₄⋊C₄	C₄×C₄₃	1	2	yes	—
250	C₂²×C₂²⋊C₄	C₄×C₄₃	1	2	yes	—
251	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
252	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
253	#433	—	2	8	no	—
254	C₂×C₄⋊C₈	C₂²×C₄₃	1	4	yes	complemented
255	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
256	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
257	C₂×C₂²⋊C₈	C₂²×C₄₃	1	4	yes	—
258	C₂×C₂²⋊C₈	C₂²×C₄₃	1	4	yes	—
259	C₂×#97	C₂²×C₄₃	1	2	yes	complemented
260	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	complemented
261	#336	C₂²×C₄₃	1	4	yes	complemented
262	#336	C₂²×C₄₃	1	2	yes	complemented
263	#336	C₂²×C₄₃	1	2	yes	complemented
264	C₄₃	#20716	1	1	yes	characteristic, direct product factor, Sylow
265	C₂⁵	C₂×C₄×C₄₃	1	1	yes	characteristic
266	C₂³×C₄	—	2	4	no	—
267	C₂³×C₄	—	2	4	no	—
268	C₂³×C₄	—	2	4	no	—
269	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
270	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
271	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
272	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
273	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
274	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
275	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
278	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
279	#117	—	2	4	no	—
280	#117	—	2	8	no	—
281	#117	—	2	8	no	—
282	#117	—	2	4	no	—
283	#117	—	2	4	no	—
284	#117	D₄×C₄₃	1	8	yes	—
285	C₂×C₄⋊C₄	—	2	8	no	—
286	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
287	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
288	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	8	no	—
291	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
292	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
293	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
294	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
295	C₂×C₄²	—	2	4	no	—
296	C₂×C₄²	—	2	4	no	—
297	C₂×C₄²	C₂×C₄×C₄₃	1	2	yes	—
298	C₂×C₄²	C₂×C₄×C₄₃	1	2	yes	—
299	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
303	C₄⋊C₈	—	2	8	no	—
304	C₂²⋊C₈	—	2	8	no	—
305	C₂²⋊C₈	—	2	4	no	—
306	C₂²⋊C₈	—	2	4	no	—
307	C₂²⋊C₈	—	2	8	no	—
308	#97	—	2	4	no	—
309	C₄×C₈	—	2	4	no	—
310	C₂⁴	—	2	2	no	—
311	C₂⁴	—	2	2	no	—
312	C₂⁴	—	2	2	no	—
313	C₂⁴	—	2	4	no	—
314	C₂⁴	—	4	2	no	—
315	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
316	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
317	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
318	C₂²×C₄	—	2	32	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
341	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
342	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
343	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
344	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
348	C₂²×C₄	#41×C₄₃	1	4	yes	—
349	C₂²×C₄	#41×C₄₃	1	4	yes	—
350	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	2	4	no	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	2	4	no	—
356	C₂×C₈	—	2	4	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	8	yes	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	C₂²⋊C₄×C₄₃	1	8	yes	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	4	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	C₂×D₄×C₄₃	1	4	yes	—
370	C₄²	C₂×D₄×C₄₃	1	4	yes	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	8	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	4	8	no	—
384	C₂³	—	4	8	no	—
385	C₂³	—	4	4	no	—
386	C₂³	—	4	4	no	—
387	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
388	C₂³	#117×C₄₃	1	2	yes	—
389	C₂³	#117×C₄₃	1	2	yes	—
390	C₂³	#131×C₄₃	1	4	yes	—
391	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	2	8	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	8	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
417	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
418	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
419	C₂×C₄	#117×C₄₃	1	2	yes	—
420	C₂×C₄	#117×C₄₃	1	2	yes	—
421	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
422	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
423	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
424	C₈	—	4	4	no	—
425	C₈	—	4	4	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	16	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	2	no	—
441	C₂²	C₄₃×#433	1	4	yes	complemented
442	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
443	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
444	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
445	C₂²	C₂×#131×C₄₃	1	2	yes	—
446	C₂²	C₄₃×#568	1	2	yes	—
447	C₄	—	2	4	no	—
448	C₄	—	2	4	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	C₄₃×#525	1	4	yes	—
455	C₂	—	2	4	no	—
456	C₂	—	4	2	no	—
457	C₂	—	4	2	no	—
458	C₂	C₄₃×#2280	1	1	yes	characteristic
459	C₂	C₄₃×#2880	1	2	yes	—
460	C₂	C₂×C₄₃×#433	1	1	yes	characteristic
461	C₂	C₄₃×#2921	1	1	yes	characteristic
462	C₂	C₄₃×#2924	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂³×C₄₃	C₂³×C₄
prime radical	C₂⁵×C₄₃	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#433	C₂	semidirect
3. C₄₃×#1818	C₂	semidirect
4. C₄₃×#1798	C₂	semidirect
5. C₄₃×#1797	C₂	semidirect
7. C₄₃×#1750	C₂	semidirect
8. C₄₃×#1749	C₂	semidirect
9. C₄×C₂²⋊C₈×C₄₃	C₂	semidirect
23. C₂×C₄⋊C₈×C₄₃	C₂²	semidirect
28. C₂×#97×C₄₃	C₂²	semidirect
29. C₂×C₄×C₈×C₄₃	C₂²	semidirect
30. C₄₃×#336	C₂²	semidirect
31. C₄₃×#336	C₂²	semidirect
32. C₄₃×#336	C₂²	semidirect
194. #20716	C₄₃	direct (N × H)
210. C₂²×C₄₃	#433	semidirect
225. C₂×#433	C₂×C₄₃	semidirect
226. #1818	C₂×C₄₃	semidirect
227. #1798	C₂×C₄₃	semidirect
228. #1797	C₂×C₄₃	semidirect
230. #1750	C₂×C₄₃	semidirect
231. #1749	C₂×C₄₃	semidirect
232. C₄×C₂²⋊C₈	C₂×C₄₃	semidirect
254. C₂×C₄⋊C₈	C₂²×C₄₃	semidirect
259. C₂×#97	C₂²×C₄₃	semidirect
260. C₂×C₄×C₈	C₂²×C₄₃	semidirect
261. #336	C₂²×C₄₃	semidirect
262. #336	C₂²×C₄₃	semidirect
263. #336	C₂²×C₄₃	semidirect
264. C₄₃	#20716	direct (N × H)
441. C₂²	C₄₃×#433	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#117×C₄₃	2
C₂×C₄₃×#433	2
C₄₃×#1818	2
C₄₃×#1798	2
C₄₃×#1797	2
C₄₃×#1779	2
C₄₃×#1750	2
C₄₃×#1749	2
C₄×C₂²⋊C₈×C₄₃	2
#20716	43

Subgroups — C43×#20716 #24940733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20716 #24940733