Subgroups — #25960015

Order 11008.

3178 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583664	C₂	1	1	yes	maximal, characteristic
2	C₂×#131×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#19147794	C₂	1	1	yes	maximal, characteristic
4	#19143024	C₂	1	3	yes	maximal, complemented
5	#19143023	C₂	1	1	yes	maximal, characteristic, complemented
6	#19143022	C₂	1	3	yes	maximal, complemented
7	#19143021	C₂	1	1	yes	maximal, characteristic, complemented
8	#19143017	C₂	1	3	yes	maximal, complemented
9	#131×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13063331	C₂	1	3	yes	maximal, complemented
11	#19143012	C₂	1	3	yes	maximal, complemented
12	#19143011	C₂	1	3	yes	maximal, complemented
13	C₂×#14582853	C₂	1	3	yes	maximal, complemented
14	#405×D₄₃	C₂	1	3	yes	maximal, complemented
15	C₄×#131×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×D₄₃	C₂²	1	1	yes	characteristic
17	#14583664	C₄	1	16	yes	complemented
18	C₂×#13063333	C₂²	1	3	yes	—
19	C₂×#13063333	C₂²	1	3	yes	—
20	C₂×#13063332	C₂²	1	1	yes	characteristic
21	C₂×#13063332	C₂²	1	1	yes	characteristic
22	C₂×#13063331	C₂²	1	3	yes	—
23	C₂×#13063331	C₂²	1	3	yes	—
24	#131×D₄₃	C₄	1	16	yes	complemented
25	C₂²×#10621872	C₂²	1	3	yes	—
26	C₂×M₁₆×D₄₃	C₂²	1	3	yes	—
27	C₂×M₁₆×D₄₃	C₂²	1	3	yes	—
28	C₂²×C₈×D₄₃	C₂²	1	3	yes	—
29	#14583381	C₄	1	2	yes	—
30	#14583378	C₄	1	6	yes	—
31	#14583375	C₄	1	2	yes	—
32	#14583371	C₄	1	6	yes	—
33	#41×Dic₄₃	C₂²	1	1	yes	characteristic
34	C₄×#10621898	C₂²	1	3	yes	—
35	#14583367	C₂²	1	3	yes	—
36	C₂×#13063282	C₂²	1	3	yes	—
37	#117×D₄₃	C₂²	1	3	yes	—
38	#14582857	C₂²	1	3	yes	complemented
39	#14582857	C₂²	1	3	yes	complemented
40	#14582856	C₂²	1	6	yes	—
41	#14582856	C₂²	1	6	yes	complemented
42	#14582855	C₂²	1	3	yes	complemented
43	#14582855	C₂²	1	3	yes	complemented
44	#14582854	C₂²	1	3	yes	complemented
45	#14582854	C₂²	1	3	yes	complemented
46	#14582853	C₂²	1	3	yes	—
47	#14582853	C₂²	1	1	yes	characteristic
48	#14582853	C₂²	1	3	yes	—
49	#14582853	C₂²	1	3	yes	—
50	#14582853	C₂²	1	3	yes	complemented
51	#14582853	C₂²	1	3	yes	complemented
52	#14582853	C₂²	1	3	yes	complemented
53	#14582853	C₂²	1	3	yes	complemented
54	#14582853	C₂²	1	6	yes	complemented
55	C₄×#10621877	C₂²	1	3	yes	complemented
56	#14582851	C₂²	1	6	yes	complemented
57	M₁₆×Dic₄₃	C₂²	1	3	yes	complemented
58	M₁₆×Dic₄₃	C₂²	1	3	yes	complemented
59	C₄×#10621872	C₂²	1	6	yes	complemented
60	C₂×#13063236	C₂²	1	3	yes	complemented
61	C₂×#13063235	C₂²	1	3	yes	complemented
62	#97×D₄₃	C₂²	1	6	yes	complemented
63	C₂×C₈×Dic₄₃	C₂²	1	3	yes	complemented
64	C₄×C₈×D₄₃	C₂²	1	6	yes	complemented
65	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
66	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
67	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
68	C₄₃×#405	C₂²	1	3	yes	complemented
69	C₄₃×#405	C₂²	1	3	yes	complemented
70	C₄×M₁₆×C₄₃	C₂²	1	3	yes	complemented
71	C₂×C₄×C₈×C₄₃	C₂²	1	3	yes	complemented
72	C₂×#10621902	C₂×C₄	1	1	yes	characteristic
73	C₂×#10621898	C₂³	1	3	yes	—
74	C₂×#10621900	C₂×C₄	1	3	yes	—
75	#41×D₄₃	C₂×C₄	1	8	yes	—
76	#41×D₄₃	C₂×C₄	1	8	yes	—
77	C₂×Q₈×D₄₃	C₂×C₄	1	1	yes	characteristic
78	C₂×D₄×D₄₃	C₂×C₄	1	3	yes	—
79	C₂²×C₄×D₄₃	C₂³	1	3	yes	—
80	#13063333	C₂×C₄	1	24	yes	complemented
81	#13063333	C₂×C₄	1	24	yes	complemented
82	#13063332	C₂×C₄	1	8	yes	complemented
83	#13063332	C₂×C₄	1	8	yes	complemented
84	#13063331	C₂×C₄	1	24	yes	complemented
85	#13063331	C₂×C₄	1	24	yes	complemented
86	C₂×#10621877	C₂³	1	3	yes	—
87	C₂×#10621877	C₂³	1	3	yes	—
88	C₂×#10621872	C₂×C₄	1	24	yes	complemented
89	C₂×#10621872	C₂³	1	3	yes	—
90	C₂×#10621872	C₂³	1	6	yes	—
91	C₂×#10621872	C₂³	1	3	yes	—
92	C₂×#10621872	C₂³	1	1	yes	characteristic
93	C₂×#10621872	C₂³	1	3	yes	—
94	M₁₆×D₄₃	C₂×C₄	1	24	yes	complemented
95	M₁₆×D₄₃	C₂×C₄	1	24	yes	complemented
96	C₂²×C₄₃⋊C₈	C₂³	1	3	yes	—
97	C₂²×C₄₃⋊C₈	C₂³	1	3	yes	—
98	C₂×C₈×D₄₃	C₂×C₄	1	24	yes	complemented
99	C₂×C₈×D₄₃	C₂³	1	3	yes	—
100	C₂×C₈×D₄₃	C₂³	1	6	yes	—
101	C₂×C₈×D₄₃	C₂³	1	3	yes	—
102	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
103	C₂×C₈×D₄₃	C₂³	1	3	yes	—
104	Q₈×Dic₄₃	C₂×C₄	1	2	yes	—
105	C₄×Dic₈₆	C₂×C₄	1	6	yes	—
106	#13063290	C₂×C₄	1	6	yes	—
107	C₄×D₁₇₂	C₂×C₄	1	6	yes	—
108	D₄×Dic₄₃	C₂×C₄	1	6	yes	—
109	#13063287	C₂×C₄	1	6	yes	—
110	C₄×C₂²⋊D₄₃	C₂×C₄	1	12	yes	—
111	(C₂²⋊D₄₃)⋊C₄	C₂×C₄	1	12	yes	—
112	#13063284	C₂³	1	3	yes	—
113	#13063283	C₂×C₄	1	6	yes	—
114	#13063282	C₂×C₄	1	6	yes	—
115	#13063282	C₂×C₄	1	6	yes	—
116	#13063282	C₂³	1	3	yes	—
117	#13063282	C₂³	1	1	yes	characteristic
118	#13063282	C₂³	1	3	yes	—
119	#13063282	C₂³	1	3	yes	—
120	#13063281	C₂×C₄	1	6	yes	—
121	C₂×Dic₄₃⋊C₄	C₂×C₄	1	6	yes	—
122	C₄⋊C₄×D₄₃	C₂×C₄	1	6	yes	—
123	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	6	yes	—
124	C₂²⋊C₄×D₄₃	C₂×C₄	1	6	yes	—
125	C₂×C₄×Dic₄₃	C₂³	1	3	yes	—
126	C₄²×D₄₃	C₂³	1	6	yes	—
127	#13063236	C₂³	1	3	yes	—
128	#13063236	C₂³	1	1	yes	characteristic
129	#13063236	C₂³	1	3	yes	—
130	#13063236	C₂³	1	3	yes	—
131	#13063235	C₂³	1	3	yes	—
132	#13063235	C₂³	1	6	yes	—
133	#13063235	C₂³	1	1	yes	characteristic
134	#13063235	C₂³	1	3	yes	—
135	#13063235	C₂³	1	3	yes	—
136	C₄×C₄₃⋊C₈	C₂³	1	6	yes	—
137	C₈×Dic₄₃	C₂³	1	3	yes	—
138	C₈×Dic₄₃	C₂³	1	6	yes	—
139	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
140	C₈×Dic₄₃	C₂³	1	3	yes	—
141	C₈×Dic₄₃	C₂³	1	3	yes	—
142	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
143	#131×C₄₃	C₂×C₄	1	8	yes	complemented
144	#131×C₄₃	C₂×C₄	1	8	yes	complemented
145	C₂×M₁₆×C₄₃	C₂³	1	3	yes	—
146	C₂×M₁₆×C₄₃	C₂³	1	3	yes	—
147	C₂²×C₈×C₄₃	C₂³	1	3	yes	—
148	C₂²×C₈×C₄₃	C₂³	1	3	yes	—
149	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
150	C₄×D₄×C₄₃	C₂×C₄	1	6	yes	—
151	#117×C₄₃	C₂³	1	3	yes	—
152	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
153	#97×C₄₃	C₂³	1	6	yes	—
154	C₄×C₈×C₄₃	C₂³	1	3	yes	—
155	C₄×C₈×C₄₃	C₂³	1	3	yes	—
156	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
157	C₄×C₈×C₄₃	C₂³	1	3	yes	—
158	C₂³×D₄₃	C₂²×C₄	1	3	yes	—
159	#41×C₄₃	C₂²×C₄	1	4	yes	—
160	#41×C₄₃	C₂²×C₄	1	4	yes	—
161	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
162	C₂×D₄×C₄₃	C₂²×C₄	1	3	yes	—
163	C₂²×C₄×C₄₃	C₂²×C₄	1	6	yes	—
164	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
165	C₂×C₂²⋊D₄₃	C₂²×C₄	1	6	yes	—
166	C₂²×Dic₄₃	C₂²×C₄	1	6	yes	—
167	C₂²×Dic₄₃	C₂²×C₄	1	3	yes	—
168	#10621902	C₄²	1	8	yes	—
169	Q₈×D₄₃	C₄²	1	8	yes	—
170	#10621900	C₄²	1	24	yes	—
171	D₄×D₄₃	C₄²	1	24	yes	—
172	#10621898	C₂²×C₄	1	12	yes	—
173	#10621898	C₂²×C₄	1	12	yes	—
174	C₂×D₁₇₂	C₂²×C₄	1	3	yes	—
175	C₂×C₄×D₄₃	C₂²×C₄	1	12	yes	—
176	C₂×C₄×D₄₃	C₂²×C₄	1	12	yes	—
177	C₂×C₄×D₄₃	C₂²×C₄	1	12	yes	—
178	C₂×C₄×D₄₃	C₂²×C₄	1	3	yes	—
179	C₂×C₄×D₄₃	C₂²×C₄	1	3	yes	—
180	C₂×C₄×D₄₃	C₂⁴	1	3	yes	—
181	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
182	C₂×Dic₈₆	C₂²×C₄	1	3	yes	—
183	M₁₆×C₄₃	C₂²×C₄	1	12	yes	—
184	M₁₆×C₄₃	C₂²×C₄	1	12	yes	—
185	C₂×C₈×C₄₃	C₂²×C₄	1	12	yes	—
186	C₂×C₈×C₄₃	C₂²×C₄	1	12	yes	—
187	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
188	C₂×C₈×C₄₃	C₂⁴	1	3	yes	—
189	C₂×C₈×C₄₃	C₂⁴	1	3	yes	—
190	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
191	C₄⋊C₄×C₄₃	C₂²×C₄	1	6	yes	—
192	C₂²⋊C₄×C₄₃	C₂²×C₄	1	6	yes	—
193	C₄²×C₄₃	C₂²×C₄	1	6	yes	—
194	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
195	C₄²×C₄₃	C₂⁴	1	3	yes	—
196	C₂²⋊Dic₄₃	C₂²×C₄	1	6	yes	—
197	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	6	yes	—
198	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
199	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	6	yes	—
200	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	6	yes	—
201	C₄⋊Dic₄₃	C₂²×C₄	1	6	yes	—
202	Dic₄₃⋊C₄	C₂²×C₄	1	6	yes	—
203	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
204	Dic₄₃⋊C₄	C₂²×C₄	1	6	yes	—
205	Dic₄₃⋊C₄	C₂²×C₄	1	6	yes	—
206	C₄×Dic₄₃	C₂²×C₄	1	12	yes	—
207	C₄×Dic₄₃	C₂²×C₄	1	6	yes	—
208	C₄×Dic₄₃	C₂⁴	1	3	yes	—
209	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
210	#10621877	C₂²×C₄	1	12	yes	—
211	#10621877	C₂²×C₄	1	12	yes	—
212	C₂×C₄₃⋊C₈	C₂²×C₄	1	12	yes	—
213	C₂×C₄₃⋊C₈	C₂²×C₄	1	12	yes	—
214	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
215	C₂×C₄₃⋊C₈	C₂⁴	1	3	yes	—
216	C₂×C₄₃⋊C₈	C₂⁴	1	3	yes	—
217	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
218	#10621872	C₂²×C₄	1	12	yes	—
219	#10621872	C₂²×C₄	1	24	yes	—
220	#10621872	C₂²×C₄	1	4	yes	—
221	#10621872	C₂²×C₄	1	12	yes	—
222	#10621872	C₂²×C₄	1	12	yes	—
223	C₈×D₄₃	C₂²×C₄	1	4	yes	—
224	C₈×D₄₃	C₂²×C₄	1	12	yes	—
225	C₈×D₄₃	C₂²×C₄	1	12	yes	—
226	C₈×D₄₃	C₂²×C₄	1	12	yes	—
227	C₈×D₄₃	C₂²×C₄	1	24	yes	—
228	C₂³×C₄₃	C₂³×C₄	1	3	yes	—
229	C₂²×D₄₃	—	4	6	no	—
230	C₂²×D₄₃	C₂×C₄²	1	12	yes	—
231	C₂²×D₄₃	C₂³×C₄	1	1	yes	characteristic
232	C₂²×D₄₃	C₂³×C₄	1	3	yes	—
233	Q₈×C₄₃	C₂×C₄²	1	4	yes	—
234	D₄×C₄₃	C₂×C₄²	1	12	yes	—
235	C₂×C₄×C₄₃	—	4	6	no	—
236	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
237	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
238	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
239	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
240	C₂×C₄×C₄₃	C₂³×C₄	1	3	yes	—
241	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
242	C₂²⋊D₄₃	C₂×C₄²	1	24	yes	—
243	C₂×Dic₄₃	—	4	6	no	—
244	C₂×Dic₄₃	C₂×C₄²	1	12	yes	—
245	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
246	C₂×Dic₄₃	C₂³×C₄	1	6	yes	—
247	C₂×Dic₄₃	C₂³×C₄	1	3	yes	—
248	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
249	D₁₇₂	C₂×C₄²	1	12	yes	—
250	C₄×D₄₃	—	4	12	no	—
251	C₄×D₄₃	C₂×C₄²	1	12	yes	—
252	C₄×D₄₃	C₂×C₄²	1	12	yes	—
253	C₄×D₄₃	C₂³×C₄	1	2	yes	—
254	C₄×D₄₃	C₂³×C₄	1	6	yes	—
255	C₄×D₄₃	C₂³×C₄	1	6	yes	—
256	C₄×D₄₃	C₂³×C₄	1	2	yes	—
257	Dic₈₆	C₂×C₄²	1	12	yes	—
258	C₈×C₄₃	C₂³×C₄	1	2	yes	—
259	C₈×C₄₃	C₂³×C₄	1	6	yes	—
260	C₈×C₄₃	C₂³×C₄	1	6	yes	—
261	C₈×C₄₃	C₂³×C₄	1	2	yes	—
262	C₄₃⋊C₈	C₂³×C₄	1	2	yes	—
263	C₄₃⋊C₈	C₂³×C₄	1	6	yes	—
264	C₄₃⋊C₈	C₂³×C₄	1	6	yes	—
265	C₄₃⋊C₈	C₂³×C₄	1	2	yes	—
266	#60058	—	43	1	no	maximal, Sylow
267	C₂²×C₄₃	—	2	6	no	—
268	C₂²×C₄₃	C₂²×C₄²	1	6	yes	—
269	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
270	C₂×D₄₃	—	2	2	no	—
271	C₂×D₄₃	—	2	6	no	—
272	C₂×D₄₃	—	4	12	no	—
273	C₂×D₄₃	C₂²×C₄²	1	2	yes	—
274	C₂×D₄₃	C₂²×C₄²	1	6	yes	—
275	C₄×C₄₃	—	2	6	no	—
276	C₄×C₄₃	—	2	2	no	—
277	C₄×C₄₃	C₂²×C₄²	1	6	yes	—
278	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
279	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
280	Dic₄₃	—	2	6	no	—
281	Dic₄₃	—	2	2	no	—
282	Dic₄₃	C₂²×C₄²	1	6	yes	—
283	Dic₄₃	C₂²×C₄²	1	2	yes	—
284	C₂×#568	—	43	1	no	—
285	C₂²×#131	—	43	1	no	—
286	#3428	—	43	1	no	—
287	#2875	—	43	3	no	—
288	#2875	—	43	3	no	—
289	#2875	—	43	1	no	—
290	#2875	—	43	1	no	—
291	C₄×#131	—	43	3	no	—
292	C₄×#131	—	43	3	no	—
293	C₄×#131	—	43	1	no	—
294	C₄×#131	D₄₃	1	1	yes	characteristic, complemented
295	#2873	—	43	3	no	—
296	#2873	—	43	3	no	—
297	C₂×#405	—	43	3	no	—
298	C₂×#405	—	43	3	no	—
299	C₂×C₄₃	—	2	6	no	—
300	C₂×C₄₃	C₂³×C₄²	1	1	yes	characteristic
301	C₂×C₄₃	#3573	1	2	yes	—
302	D₄₃	—	2	2	no	—
303	D₄₃	—	2	6	no	—
304	C₂²×#41	—	43	1	no	—
305	#568	—	43	16	no	—
306	C₂×#131	—	43	1	no	—
307	C₂×#131	—	43	1	no	—
308	C₂×#131	—	43	16	no	—
309	C₂×#131	—	43	3	no	—
310	C₂×#131	—	43	3	no	—
311	C₂×#131	—	43	3	no	—
312	C₂×#131	—	43	3	no	—
313	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
314	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
315	C₂²×M₁₆	—	43	3	no	—
316	C₂²×M₁₆	—	43	3	no	—
317	C₂²×M₁₆	—	43	3	no	—
318	C₂³×C₈	—	43	3	no	—
319	#520	—	43	2	no	—
320	#520	—	43	6	no	—
321	#519	—	43	2	no	—
322	#518	—	43	6	no	—
323	C₄×#41	—	43	1	no	—
324	C₄×#41	—	43	3	no	—
325	C₄×#41	—	43	3	no	—
326	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
327	C₂×#117	—	43	3	no	—
328	C₂×#117	—	43	3	no	—
329	#405	—	43	3	no	—
330	#405	—	43	3	no	—
331	#405	—	43	3	no	—
332	#405	—	43	3	no	—
333	#405	—	43	3	no	—
334	#405	—	43	3	no	—
335	#405	—	43	6	no	—
336	#405	—	43	6	no	—
337	#405	—	43	3	no	—
338	#405	—	43	1	no	—
339	#405	—	43	3	no	—
340	#405	—	43	3	no	—
341	#405	—	43	3	no	—
342	#405	—	43	3	no	—
343	#405	—	43	3	no	—
344	#405	—	43	3	no	—
345	#405	—	43	6	no	—
346	#405	C₂×D₄₃	1	3	yes	complemented
347	#405	C₂×D₄₃	1	3	yes	complemented
348	C₄×M₁₆	—	43	3	no	—
349	C₄×M₁₆	—	43	3	no	—
350	C₄×M₁₆	—	43	3	no	—
351	C₄×M₁₆	—	43	6	no	—
352	C₄×M₁₆	—	43	6	no	—
353	C₄×M₁₆	C₂×D₄₃	1	3	yes	complemented
354	C₂×#97	—	43	3	no	—
355	C₂×#97	—	43	3	no	—
356	C₂×#97	—	43	6	no	—
357	C₂×C₄×C₈	—	43	3	no	—
358	C₂×C₄×C₈	—	43	6	no	—
359	C₂×C₄×C₈	C₂×D₄₃	1	3	yes	complemented
360	C₄₃	#60058	1	1	yes	characteristic, complemented, Sylow
361	C₂×#41	—	43	8	no	—
362	C₂×#41	—	43	8	no	—
363	C₂×#41	—	43	1	no	—
364	C₂×#41	—	43	3	no	—
365	C₂×#41	—	43	3	no	—
366	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
367	C₂²×Q₈	—	43	1	no	—
368	C₂²×D₄	—	43	3	no	—
369	C₂³×C₄	—	43	3	no	—
370	#131	—	43	8	no	—
371	#131	—	43	8	no	—
372	#131	—	43	24	no	—
373	#131	—	43	24	no	—
374	#131	—	43	24	no	—
375	#131	—	43	24	no	—
376	#131	C₄×D₄₃	1	8	yes	complemented
377	#131	C₄×D₄₃	1	8	yes	complemented
378	C₂×M₁₆	—	43	3	no	—
379	C₂×M₁₆	—	43	3	no	—
380	C₂×M₁₆	—	43	24	no	—
381	C₂×M₁₆	—	43	24	no	—
382	C₂×M₁₆	—	43	24	no	—
383	C₂×M₁₆	—	43	3	no	—
384	C₂×M₁₆	—	43	1	no	—
385	C₂×M₁₆	—	43	6	no	—
386	C₂×M₁₆	—	43	3	no	—
387	C₂×M₁₆	—	43	3	no	—
388	C₂×M₁₆	C₂²×D₄₃	1	3	yes	—
389	C₂×M₁₆	C₂²×D₄₃	1	3	yes	—
390	C₂²×C₈	—	43	3	no	—
391	C₂²×C₈	—	43	3	no	—
392	C₂²×C₈	—	43	24	no	—
393	C₂²×C₈	—	43	3	no	—
394	C₂²×C₈	—	43	3	no	—
395	C₂²×C₈	—	43	6	no	—
396	C₂²×C₈	—	43	1	no	—
397	C₂²×C₈	—	43	3	no	—
398	C₂²×C₈	C₂²×D₄₃	1	3	yes	—
399	C₂²×C₈	C₂²×D₄₃	1	3	yes	—
400	C₄×Q₈	—	43	2	no	—
401	C₄×Q₈	—	43	6	no	—
402	C₄×Q₈	—	43	6	no	—
403	C₄×Q₈	C₄×D₄₃	1	2	yes	—
404	C₄×D₄	—	43	6	no	—
405	C₄×D₄	—	43	12	no	—
406	C₄×D₄	—	43	6	no	—
407	C₄×D₄	—	43	12	no	—
408	C₄×D₄	—	43	6	no	—
409	C₄×D₄	C₄×D₄₃	1	6	yes	—
410	#117	—	43	3	no	—
411	#117	—	43	6	no	—
412	#117	—	43	6	no	—
413	#117	—	43	6	no	—
414	#117	—	43	6	no	—
415	#117	—	43	3	no	—
416	#117	—	43	1	no	—
417	#117	—	43	3	no	—
418	#117	—	43	3	no	—
419	#117	C₂²×D₄₃	1	3	yes	—
420	C₂×C₄⋊C₄	—	43	6	no	—
421	C₂×C₄⋊C₄	—	43	6	no	—
422	C₂×C₂²⋊C₄	—	43	6	no	—
423	C₂×C₂²⋊C₄	—	43	6	no	—
424	C₂×C₄²	—	43	3	no	—
425	C₂×C₄²	—	43	6	no	—
426	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
427	#97	—	43	3	no	—
428	#97	—	43	1	no	—
429	#97	—	43	6	no	—
430	#97	—	43	3	no	—
431	#97	—	43	3	no	—
432	#97	—	43	3	no	—
433	#97	—	43	1	no	—
434	#97	—	43	3	no	—
435	#97	—	43	3	no	—
436	#97	C₂²×D₄₃	1	6	yes	—
437	C₄×C₈	—	43	6	no	—
438	C₄×C₈	—	43	3	no	—
439	C₄×C₈	—	43	3	no	—
440	C₄×C₈	—	43	3	no	—
441	C₄×C₈	—	43	1	no	—
442	C₄×C₈	—	43	6	no	—
443	C₄×C₈	C₂²×D₄₃	1	3	yes	—
444	C₄×C₈	C₂²×D₄₃	1	3	yes	—
445	C₄×C₈	C₂²×D₄₃	1	3	yes	—
446	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
447	C₂⁴	—	43	3	no	—
448	#41	—	43	8	no	—
449	#41	—	43	24	no	—
450	#41	—	43	12	no	—
451	#41	—	43	12	no	—
452	#41	C₂×C₄×D₄₃	1	4	yes	—
453	#41	C₂×C₄×D₄₃	1	4	yes	—
454	C₂×Q₈	—	43	8	no	—
455	C₂×Q₈	—	43	3	no	—
456	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
457	C₂×D₄	—	43	6	no	—
458	C₂×D₄	—	43	24	no	—
459	C₂×D₄	—	43	3	no	—
460	C₂×D₄	C₂×C₄×D₄₃	1	3	yes	—
461	C₂²×C₄	—	43	3	no	—
462	C₂²×C₄	—	43	3	no	—
463	C₂²×C₄	—	43	3	no	—
464	C₂²×C₄	—	43	12	no	—
465	C₂²×C₄	—	43	12	no	—
466	C₂²×C₄	—	43	3	no	—
467	C₂²×C₄	—	43	1	no	—
468	C₂²×C₄	—	43	6	no	—
469	C₂²×C₄	—	43	12	no	—
470	C₂²×C₄	C₂×C₄×D₄₃	1	6	yes	—
471	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
472	M₁₆	—	43	12	no	—
473	M₁₆	—	43	12	no	—
474	M₁₆	—	43	12	no	—
475	M₁₆	—	43	4	no	—
476	M₁₆	—	43	24	no	—
477	M₁₆	—	43	12	no	—
478	M₁₆	—	43	12	no	—
479	M₁₆	C₂×C₄×D₄₃	1	12	yes	—
480	M₁₆	C₂×C₄×D₄₃	1	12	yes	—
481	C₂×C₈	—	43	12	no	—
482	C₂×C₈	—	43	12	no	—
483	C₂×C₈	—	43	1	no	—
484	C₂×C₈	—	43	3	no	—
485	C₂×C₈	—	43	3	no	—
486	C₂×C₈	—	43	1	no	—
487	C₂×C₈	—	43	4	no	—
488	C₂×C₈	—	43	12	no	—
489	C₂×C₈	—	43	12	no	—
490	C₂×C₈	—	43	12	no	—
491	C₂×C₈	—	43	24	no	—
492	C₂×C₈	C₂×C₄×D₄₃	1	12	yes	—
493	C₂×C₈	C₂×C₄×D₄₃	1	12	yes	—
494	C₂×C₈	C₂³×D₄₃	1	3	yes	—
495	C₂×C₈	C₂³×D₄₃	1	3	yes	—
496	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
497	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
498	C₄⋊C₄	—	43	6	no	—
499	C₄⋊C₄	—	43	2	no	—
500	C₄⋊C₄	—	43	6	no	—
501	C₄⋊C₄	—	43	6	no	—
502	C₄⋊C₄	—	43	6	no	—
503	C₄⋊C₄	C₂×C₄×D₄₃	1	6	yes	—
504	C₂²⋊C₄	—	43	6	no	—
505	C₂²⋊C₄	—	43	6	no	—
506	C₂²⋊C₄	—	43	2	no	—
507	C₂²⋊C₄	—	43	6	no	—
508	C₂²⋊C₄	—	43	6	no	—
509	C₂²⋊C₄	C₂×C₄×D₄₃	1	6	yes	—
510	C₄²	—	43	12	no	—
511	C₄²	—	43	6	no	—
512	C₄²	—	43	1	no	—
513	C₄²	—	43	3	no	—
514	C₄²	C₂×C₄×D₄₃	1	6	yes	—
515	C₄²	C₂³×D₄₃	1	3	yes	—
516	C₄²	C₂³×D₄₃	1	1	yes	characteristic
517	C₂³	—	43	1	no	—
518	C₂³	—	43	3	no	—
519	C₂³	—	43	12	no	—
520	C₂³	—	172	6	no	—
521	C₂³	C₂²×C₄×D₄₃	1	3	yes	—
522	Q₈	—	43	12	no	—
523	Q₈	C₄²×D₄₃	1	4	yes	—
524	D₄	—	43	24	no	—
525	D₄	—	43	12	no	—
526	D₄	C₄²×D₄₃	1	12	yes	—
527	C₂×C₄	—	4	6	no	—
528	C₂×C₄	—	43	12	no	—
529	C₂×C₄	—	43	3	no	—
530	C₂×C₄	—	43	1	no	—
531	C₂×C₄	—	43	12	no	—
532	C₂×C₄	—	43	12	no	—
533	C₂×C₄	—	43	2	no	—
534	C₂×C₄	—	43	6	no	—
535	C₂×C₄	—	43	6	no	—
536	C₂×C₄	—	43	2	no	—
537	C₂×C₄	—	43	6	no	—
538	C₂×C₄	—	43	2	no	—
539	C₂×C₄	—	172	12	no	—
540	C₂×C₄	—	172	6	no	—
541	C₂×C₄	C₂²×C₄×D₄₃	1	6	yes	—
542	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
543	C₂×C₄	C₂²×C₄×D₄₃	1	3	yes	—
544	C₂×C₄	C₂²×C₄×D₄₃	1	6	yes	—
545	C₂×C₄	C₂²×C₄×D₄₃	1	6	yes	—
546	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
547	C₈	—	43	2	no	—
548	C₈	—	43	6	no	—
549	C₈	—	43	2	no	—
550	C₈	—	43	6	no	—
551	C₈	C₂²×C₄×D₄₃	1	2	yes	—
552	C₈	C₂²×C₄×D₄₃	1	6	yes	—
553	C₈	C₂²×C₄×D₄₃	1	6	yes	—
554	C₈	C₂²×C₄×D₄₃	1	2	yes	—
555	C₂²	—	2	6	no	—
556	C₂²	—	43	2	no	—
557	C₂²	—	43	6	no	—
558	C₂²	—	86	6	no	—
559	C₂²	—	86	2	no	—
560	C₂²	—	172	12	no	—
561	C₂²	C₂×C₄²×D₄₃	1	6	yes	—
562	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
563	C₄	—	2	2	no	—
564	C₄	—	2	6	no	—
565	C₄	—	43	2	no	—
566	C₄	—	43	6	no	—
567	C₄	—	86	6	no	—
568	C₄	—	86	2	no	—
569	C₄	C₂×C₄²×D₄₃	1	6	yes	—
570	C₄	C₂³×C₄×D₄₃	1	1	yes	characteristic
571	C₄	C₂³×C₄×D₄₃	1	1	yes	characteristic
572	C₂	—	2	6	no	—
573	C₂	—	86	2	no	—
574	C₂	—	86	6	no	—
575	C₂	C₂²×C₄²×D₄₃	1	1	yes	characteristic
576	C₂	#19149306	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂³×D₄₃
commutator	C₂×C₄₃	C₂³×C₄²
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄×#131×C₄₃	C₂
socle	C₂²×C₄₃	C₂⁴×C₄
prime radical	C₂×#41×D₄₃	C₂²
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₄×#131	D₄₃
hypocenter	C₄₃	#60058
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
4. #19143024	C₂	semidirect
5. #19143023	C₂	semidirect
6. #19143022	C₂	semidirect
7. #19143021	C₂	semidirect
8. #19143017	C₂	semidirect
9. #131×Dic₄₃	C₂	semidirect
10. C₄×#13063331	C₂	semidirect
11. #19143012	C₂	semidirect
12. #19143011	C₂	semidirect
13. C₂×#14582853	C₂	semidirect
14. #405×D₄₃	C₂	semidirect
15. C₄×#131×C₄₃	C₂	semidirect
17. #14583664	C₄	semidirect
24. #131×D₄₃	C₄	semidirect
38. #14582857	C₂²	semidirect
39. #14582857	C₂²	semidirect
41. #14582856	C₂²	semidirect
42. #14582855	C₂²	semidirect
43. #14582855	C₂²	semidirect
44. #14582854	C₂²	semidirect
45. #14582854	C₂²	semidirect
50. #14582853	C₂²	semidirect
51. #14582853	C₂²	semidirect
52. #14582853	C₂²	semidirect
53. #14582853	C₂²	semidirect
54. #14582853	C₂²	semidirect
55. C₄×#10621877	C₂²	semidirect
56. #14582851	C₂²	semidirect
57. M₁₆×Dic₄₃	C₂²	semidirect
58. M₁₆×Dic₄₃	C₂²	semidirect
59. C₄×#10621872	C₂²	semidirect
60. C₂×#13063236	C₂²	semidirect
61. C₂×#13063235	C₂²	semidirect
62. #97×D₄₃	C₂²	semidirect
63. C₂×C₈×Dic₄₃	C₂²	semidirect
64. C₄×C₈×D₄₃	C₂²	semidirect
68. C₄₃×#405	C₂²	semidirect
69. C₄₃×#405	C₂²	semidirect
70. C₄×M₁₆×C₄₃	C₂²	semidirect
71. C₂×C₄×C₈×C₄₃	C₂²	semidirect
80. #13063333	C₂×C₄	semidirect
81. #13063333	C₂×C₄	semidirect
82. #13063332	C₂×C₄	semidirect
83. #13063332	C₂×C₄	semidirect
84. #13063331	C₂×C₄	semidirect
85. #13063331	C₂×C₄	semidirect
88. C₂×#10621872	C₂×C₄	semidirect
94. M₁₆×D₄₃	C₂×C₄	semidirect
95. M₁₆×D₄₃	C₂×C₄	semidirect
98. C₂×C₈×D₄₃	C₂×C₄	semidirect
143. #131×C₄₃	C₂×C₄	semidirect
144. #131×C₄₃	C₂×C₄	semidirect
294. C₄×#131	D₄₃	semidirect
346. #405	C₂×D₄₃	semidirect
347. #405	C₂×D₄₃	semidirect
353. C₄×M₁₆	C₂×D₄₃	semidirect
359. C₂×C₄×C₈	C₂×D₄₃	semidirect
360. C₄₃	#60058	semidirect
376. #131	C₄×D₄₃	semidirect
377. #131	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583664	2
C₂×#131×D₄₃	2
#19147794	2
#19143024	2
#19143023	2
#19143022	2
#19143021	2
#19143017	2
#131×Dic₄₃	2
C₄×#13063331	2
#19143012	2
#19143011	2
C₂×#14582853	2
#405×D₄₃	2
C₄×#131×C₄₃	2
#60058	43