Subgroups — #25960016

Order 11008.

3178 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583665	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13063331	C₂	1	1	yes	maximal, characteristic
3	#19147796	C₂	1	1	yes	maximal, characteristic
4	#19143022	C₂	1	4	yes	maximal, complemented
5	#19143020	C₂	1	4	yes	maximal, complemented
6	#19143017	C₂	1	4	yes	maximal, complemented
7	C₄×#13063331	C₂	1	4	yes	maximal, complemented
8	#19143014	C₂	1	1	yes	maximal, characteristic, complemented
9	#19143013	C₂	1	1	yes	maximal, characteristic, complemented
10	#19143011	C₂	1	4	yes	maximal, complemented
11	C₂×#14582854	C₂	1	1	yes	maximal, characteristic, complemented
12	#405×D₄₃	C₂	1	4	yes	maximal, complemented
13	C₂×C₄₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#10621898	C₂²	1	1	yes	characteristic
15	#14583665	C₄	1	16	yes	complemented
16	C₂×#13063333	C₂²	1	4	yes	—
17	C₂×#13063331	C₄	1	16	yes	complemented
18	C₂×#13063331	C₂²	1	2	yes	—
19	C₂×#13063331	C₂²	1	4	yes	—
20	C₂×#13063331	C₂²	1	2	yes	—
21	C₂×#13063331	C₂²	1	2	yes	—
22	C₂×#13063331	C₂²	1	2	yes	—
23	C₂²×#10621877	C₂²	1	1	yes	characteristic
24	C₂²×#10621877	C₂²	1	1	yes	characteristic
25	C₂²×#10621872	C₂²	1	2	yes	—
26	C₂×M₁₆×D₄₃	C₂²	1	4	yes	—
27	C₂²×C₈×D₄₃	C₂²	1	2	yes	—
28	#14583380	C₄	1	4	yes	—
29	#14583379	C₄	1	4	yes	—
30	#14583376	C₄	1	2	yes	—
31	#14583373	C₄	1	2	yes	—
32	#14583372	C₄	1	4	yes	—
33	C₄×#10621898	C₂²	1	4	yes	—
34	#14583367	C₂²	1	4	yes	—
35	C₂×#13063284	C₂²	1	1	yes	characteristic
36	#117×D₄₃	C₂²	1	4	yes	—
37	#14582857	C₂²	1	4	yes	—
38	#14582856	C₂²	1	8	yes	complemented
39	#14582856	C₂²	1	8	yes	complemented
40	#14582855	C₂²	1	4	yes	—
41	#14582855	C₂²	1	4	yes	complemented
42	#14582854	C₂²	1	2	yes	—
43	#14582854	C₂²	1	2	yes	—
44	#14582854	C₂²	1	2	yes	complemented
45	#14582854	C₂²	1	2	yes	complemented
46	#14582854	C₂²	1	4	yes	complemented
47	#14582853	C₂²	1	8	yes	complemented
48	#14582853	C₂²	1	8	yes	complemented
49	C₄×#10621877	C₂²	1	4	yes	complemented
50	#14582851	C₂²	1	8	yes	complemented
51	M₁₆×Dic₄₃	C₂²	1	4	yes	complemented
52	C₄×#10621872	C₂²	1	8	yes	complemented
53	C₂×#13063235	C₂²	1	2	yes	complemented
54	#97×D₄₃	C₂²	1	8	yes	complemented
55	C₂×C₈×Dic₄₃	C₂²	1	2	yes	complemented
56	C₄×C₈×D₄₃	C₂²	1	8	yes	complemented
57	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
58	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
59	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
60	C₄₃×#405	C₂²	1	2	yes	—
61	C₄₃×#405	C₂²	1	2	yes	—
62	C₄₃×#405	C₂²	1	2	yes	complemented
63	C₄₃×#405	C₂²	1	2	yes	complemented
64	C₂×#97×C₄₃	C₂²	1	2	yes	complemented
65	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	complemented
66	C₂×#10621898	C₂×C₄	1	8	yes	—
67	C₂×#10621898	C₂×C₄	1	8	yes	—
68	C₂×#10621898	C₂×C₄	1	2	yes	—
69	C₂×#10621898	C₂×C₄	1	2	yes	—
70	C₂×#10621898	C₂³	1	2	yes	—
71	C₂×#10621898	C₂³	1	2	yes	—
72	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
73	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₂²⋊D₄₃	C₂×C₄	1	2	yes	—
75	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
76	#13063333	C₂×C₄	1	32	yes	complemented
77	#13063331	C₂×C₄	1	16	yes	complemented
78	#13063331	C₂×C₄	1	16	yes	complemented
79	#13063331	C₂×C₄	1	16	yes	complemented
80	#13063331	C₂×C₄	1	16	yes	complemented
81	#13063331	C₂×C₄	1	32	yes	complemented
82	C₂×#10621877	C₂×C₄	1	8	yes	complemented
83	C₂×#10621877	C₂×C₄	1	8	yes	complemented
84	C₂×#10621877	C₂³	1	2	yes	—
85	C₂×#10621877	C₂³	1	2	yes	—
86	C₂×#10621877	C₂³	1	2	yes	—
87	C₂×#10621877	C₂³	1	2	yes	—
88	C₂×#10621872	C₂×C₄	1	16	yes	complemented
89	C₂×#10621872	C₂³	1	4	yes	—
90	C₂×#10621872	C₂³	1	8	yes	—
91	C₂×#10621872	C₂³	1	4	yes	—
92	M₁₆×D₄₃	C₂×C₄	1	32	yes	complemented
93	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
94	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
95	C₂×C₈×D₄₃	C₂×C₄	1	16	yes	complemented
96	C₂×C₈×D₄₃	C₂³	1	4	yes	—
97	C₂×C₈×D₄₃	C₂³	1	8	yes	—
98	C₂×C₈×D₄₃	C₂³	1	4	yes	—
99	C₄×Dic₈₆	C₂×C₄	1	8	yes	—
100	#13063290	C₂×C₄	1	8	yes	—
101	C₄×D₁₇₂	C₂×C₄	1	8	yes	—
102	#13063287	C₂×C₄	1	8	yes	—
103	C₄×C₂²⋊D₄₃	C₂×C₄	1	16	yes	—
104	(C₂²⋊D₄₃)⋊C₄	C₂×C₄	1	16	yes	—
105	#13063284	C₂×C₄	1	2	yes	—
106	#13063284	C₂×C₄	1	2	yes	—
107	#13063284	C₂³	1	2	yes	—
108	#13063284	C₂³	1	2	yes	—
109	#13063283	C₂×C₄	1	8	yes	—
110	#13063282	C₂³	1	8	yes	—
111	#13063281	C₂×C₄	1	8	yes	—
112	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
113	C₄⋊C₄×D₄₃	C₂×C₄	1	8	yes	—
114	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
115	C₂²⋊C₄×D₄₃	C₂×C₄	1	8	yes	—
116	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
117	C₄²×D₄₃	C₂³	1	8	yes	—
118	#13063236	C₂³	1	8	yes	—
119	#13063235	C₂³	1	4	yes	—
120	#13063235	C₂³	1	8	yes	—
121	#13063235	C₂³	1	4	yes	—
122	C₄×C₄₃⋊C₈	C₂³	1	8	yes	—
123	C₈×Dic₄₃	C₂³	1	4	yes	—
124	C₈×Dic₄₃	C₂³	1	8	yes	—
125	C₈×Dic₄₃	C₂³	1	4	yes	—
126	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
127	C₂×M₁₆×C₄₃	C₂×C₄	1	8	yes	complemented
128	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
129	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
130	C₂²×C₈×C₄₃	C₂×C₄	1	8	yes	complemented
131	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
136	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
137	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
138	#117×C₄₃	C₂×C₄	1	2	yes	—
139	#117×C₄₃	C₂×C₄	1	2	yes	—
140	#117×C₄₃	C₂³	1	2	yes	—
141	#117×C₄₃	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
143	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
144	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
145	#97×C₄₃	C₂³	1	4	yes	—
146	#97×C₄₃	C₂³	1	4	yes	—
147	C₄×C₈×C₄₃	C₂³	1	4	yes	—
148	C₄×C₈×C₄₃	C₂³	1	4	yes	—
149	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
150	C₂³×D₄₃	C₂²×C₄	1	2	yes	—
151	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
152	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
153	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
154	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
158	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
160	C₂×C₂²⋊D₄₃	C₄²	1	16	yes	—
161	C₂×C₂²⋊D₄₃	C₂²×C₄	1	4	yes	—
162	C₂×C₂²⋊D₄₃	C₂²×C₄	1	4	yes	—
163	C₂²×Dic₄₃	C₂²×C₄	1	4	yes	—
164	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
165	#10621898	C₄²	1	16	yes	—
166	#10621898	C₄²	1	16	yes	—
167	#10621898	C₂²×C₄	1	8	yes	—
168	#10621898	C₂²×C₄	1	8	yes	—
169	#10621898	C₂²×C₄	1	8	yes	—
170	#10621898	C₂²×C₄	1	8	yes	—
171	C₂×D₁₇₂	C₄²	1	8	yes	—
172	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
173	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
174	C₂×C₄×D₄₃	C₂²×C₄	1	8	yes	—
175	C₂×C₄×D₄₃	C₂²×C₄	1	8	yes	—
176	C₂×C₄×D₄₃	C₂²×C₄	1	16	yes	—
177	C₂×C₄×D₄₃	C₂²×C₄	1	4	yes	—
178	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
179	C₂×Dic₈₆	C₄²	1	8	yes	—
180	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
181	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
182	M₁₆×C₄₃	C₂²×C₄	1	8	yes	—
183	M₁₆×C₄₃	C₂²×C₄	1	8	yes	—
184	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
185	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
186	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
187	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
188	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
189	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
190	C₂×C₈×C₄₃	C₂²×C₄	1	8	yes	—
191	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
192	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
193	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
194	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
195	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
196	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
197	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
198	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
199	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
200	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
201	C₄²×C₄₃	C₂⁴	1	4	yes	—
202	C₂²⋊Dic₄₃	C₂²×C₄	1	4	yes	—
203	C₂²⋊Dic₄₃	C₂²×C₄	1	4	yes	—
204	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	16	yes	—
205	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
206	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
207	Dic₄₃⋊C₄	C₂²×C₄	1	16	yes	—
208	C₄×Dic₄₃	C₂²×C₄	1	16	yes	—
209	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
210	C₄×Dic₄₃	C₂⁴	1	4	yes	—
211	#10621877	C₂²×C₄	1	8	yes	—
212	#10621877	C₂²×C₄	1	8	yes	—
213	#10621877	C₂²×C₄	1	8	yes	—
214	#10621877	C₂²×C₄	1	8	yes	—
215	C₂×C₄₃⋊C₈	C₂²×C₄	1	8	yes	—
216	C₂×C₄₃⋊C₈	C₂²×C₄	1	8	yes	—
217	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
218	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
219	#10621872	C₂²×C₄	1	32	yes	—
220	#10621872	C₂²×C₄	1	16	yes	—
221	#10621872	C₂²×C₄	1	16	yes	—
222	C₈×D₄₃	C₂²×C₄	1	16	yes	—
223	C₈×D₄₃	C₂²×C₄	1	16	yes	—
224	C₈×D₄₃	C₂²×C₄	1	32	yes	—
225	C₂³×C₄₃	—	4	2	no	—
226	C₂³×C₄₃	C₂×C₄²	1	4	yes	—
227	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
228	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
229	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
230	C₂²×D₄₃	—	4	4	no	—
231	C₂²×D₄₃	C₂×C₄²	1	8	yes	—
232	C₂²×D₄₃	C₂³×C₄	1	4	yes	—
233	C₂×C₄×C₄₃	—	4	4	no	—
234	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
235	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
236	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
237	C₂×C₄×C₄₃	C₂³×C₄	1	8	yes	—
238	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
239	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
240	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
241	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
242	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
243	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
244	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
248	C₂²⋊D₄₃	C₂×C₄²	1	16	yes	—
249	C₂²⋊D₄₃	C₂×C₄²	1	16	yes	—
250	C₂×Dic₄₃	—	4	4	no	—
251	C₂×Dic₄₃	C₂×C₄²	1	8	yes	—
252	C₂×Dic₄₃	C₂³×C₄	1	8	yes	—
253	C₂×Dic₄₃	C₂³×C₄	1	4	yes	—
254	D₁₇₂	C₂×C₄²	1	8	yes	—
255	D₁₇₂	C₂×C₄²	1	8	yes	—
256	C₄×D₄₃	—	4	16	no	—
257	C₄×D₄₃	C₂×C₄²	1	16	yes	—
258	C₄×D₄₃	C₂³×C₄	1	8	yes	—
259	C₄×D₄₃	C₂³×C₄	1	8	yes	—
260	Dic₈₆	C₂×C₄²	1	8	yes	—
261	Dic₈₆	C₂×C₄²	1	8	yes	—
262	C₈×C₄₃	C₂³×C₄	1	2	yes	—
263	C₈×C₄₃	C₂³×C₄	1	2	yes	—
264	C₈×C₄₃	C₂³×C₄	1	8	yes	—
265	C₈×C₄₃	C₂³×C₄	1	2	yes	—
266	C₈×C₄₃	C₂³×C₄	1	2	yes	—
267	C₄₃⋊C₈	C₂³×C₄	1	8	yes	—
268	C₄₃⋊C₈	C₂³×C₄	1	8	yes	—
269	#60058	—	43	1	no	maximal, Sylow
270	C₂²×C₄₃	—	2	2	no	—
271	C₂²×C₄₃	—	2	2	no	—
272	C₂²×C₄₃	—	2	2	no	—
273	C₂²×C₄₃	—	4	4	no	—
274	C₂²×C₄₃	C₂²×C₄²	1	2	yes	—
275	C₂²×C₄₃	C₂²×C₄²	1	2	yes	—
276	C₂²×C₄₃	C₂²×C₄²	1	2	yes	—
277	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
278	C₂×D₄₃	—	2	8	no	—
279	C₂×D₄₃	—	4	8	no	—
280	C₂×D₄₃	C₂²×C₄²	1	8	yes	—
281	C₄×C₄₃	—	2	8	no	—
282	C₄×C₄₃	C₂²×C₄²	1	2	yes	—
283	C₄×C₄₃	C₂²×C₄²	1	2	yes	—
284	C₄×C₄₃	C₂²×C₄²	1	2	yes	—
285	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
286	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
287	Dic₄₃	—	2	8	no	—
288	Dic₄₃	C₂²×C₄²	1	8	yes	—
289	C₂×#568	—	43	1	no	—
290	C₂²×#131	—	43	1	no	—
291	#3428	—	43	1	no	—
292	#2875	—	43	4	no	—
293	#2875	—	43	4	no	—
294	C₄×#131	—	43	4	no	—
295	C₄×#131	—	43	4	no	—
296	#2873	—	43	4	no	—
297	#2873	—	43	1	no	—
298	#2873	—	43	1	no	—
299	C₂×#405	—	43	4	no	—
300	C₂×#405	—	43	1	no	—
301	C₂×#405	D₄₃	1	1	yes	characteristic, complemented
302	C₂×C₄₃	—	2	2	no	—
303	C₂×C₄₃	—	2	2	no	—
304	C₂×C₄₃	—	2	2	no	—
305	C₂×C₄₃	C₂³×C₄²	1	1	yes	characteristic
306	C₂×C₄₃	#3573	1	2	yes	—
307	D₄₃	—	2	8	no	—
308	C₂²×#41	—	43	1	no	—
309	#568	—	43	16	no	—
310	C₂×#131	—	43	4	no	—
311	C₂×#131	—	43	2	no	—
312	C₂×#131	—	43	2	no	—
313	C₂×#131	—	43	4	no	—
314	C₂×#131	—	43	2	no	—
315	C₂×#131	—	43	2	no	—
316	C₂×#131	—	43	16	no	—
317	C₂²×M₁₆	—	43	1	no	—
318	C₂²×M₁₆	—	43	1	no	—
319	C₂²×M₁₆	—	43	4	no	—
320	C₂²×M₁₆	—	43	2	no	—
321	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
322	C₂³×C₈	—	43	2	no	—
323	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
324	#520	—	43	4	no	—
325	#520	—	43	4	no	—
326	#519	—	43	2	no	—
327	#518	—	43	2	no	—
328	#518	—	43	4	no	—
329	C₄×#41	—	43	4	no	—
330	C₄×#41	—	43	4	no	—
331	C₂×#117	—	43	1	no	—
332	C₂×#117	—	43	4	no	—
333	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
334	#405	—	43	4	no	—
335	#405	—	43	2	no	—
336	#405	—	43	2	no	—
337	#405	—	43	2	no	—
338	#405	—	43	2	no	—
339	#405	—	43	4	no	—
340	#405	—	43	4	no	—
341	#405	—	43	4	no	—
342	#405	—	43	8	no	—
343	#405	—	43	8	no	—
344	#405	—	43	8	no	—
345	#405	—	43	8	no	—
346	#405	C₂×D₄₃	1	2	yes	—
347	#405	C₂×D₄₃	1	2	yes	—
348	#405	C₂×D₄₃	1	2	yes	complemented
349	#405	C₂×D₄₃	1	2	yes	complemented
350	C₄×M₁₆	—	43	4	no	—
351	C₄×M₁₆	—	43	4	no	—
352	C₄×M₁₆	—	43	8	no	—
353	C₄×M₁₆	—	43	8	no	—
354	C₂×#97	—	43	2	no	—
355	C₂×#97	—	43	8	no	—
356	C₂×#97	C₂×D₄₃	1	2	yes	complemented
357	C₂×C₄×C₈	—	43	2	no	—
358	C₂×C₄×C₈	—	43	8	no	—
359	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	complemented
360	C₄₃	#60058	1	1	yes	characteristic, complemented, Sylow
361	C₂×#41	—	43	2	no	—
362	C₂×#41	—	43	2	no	—
363	C₂×#41	—	43	8	no	—
364	C₂×#41	—	43	8	no	—
365	C₂×#41	—	43	2	no	—
366	C₂×#41	—	43	2	no	—
367	C₂²×Q₈	—	43	1	no	—
368	C₂²×D₄	—	43	2	no	—
369	C₂²×D₄	—	43	1	no	—
370	C₂³×C₄	—	43	2	no	—
371	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
372	#131	—	43	32	no	—
373	#131	—	43	16	no	—
374	#131	—	43	16	no	—
375	#131	—	43	16	no	—
376	#131	—	43	16	no	—
377	#131	—	43	32	no	—
378	C₂×M₁₆	—	43	8	no	—
379	C₂×M₁₆	—	43	8	no	—
380	C₂×M₁₆	—	43	2	no	—
381	C₂×M₁₆	—	43	2	no	—
382	C₂×M₁₆	—	43	2	no	—
383	C₂×M₁₆	—	43	2	no	—
384	C₂×M₁₆	—	43	32	no	—
385	C₂×M₁₆	—	43	16	no	—
386	C₂×M₁₆	—	43	4	no	—
387	C₂×M₁₆	—	43	8	no	—
388	C₂×M₁₆	—	43	4	no	—
389	C₂×M₁₆	C₄×D₄₃	1	8	yes	complemented
390	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
391	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
392	C₂²×C₈	—	43	2	no	—
393	C₂²×C₈	—	43	2	no	—
394	C₂²×C₈	—	43	16	no	—
395	C₂²×C₈	—	43	4	no	—
396	C₂²×C₈	—	43	8	no	—
397	C₂²×C₈	—	43	4	no	—
398	C₂²×C₈	C₄×D₄₃	1	8	yes	complemented
399	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
400	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
401	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
402	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
403	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
404	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
405	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
406	C₄×Q₈	—	43	8	no	—
407	C₄×Q₈	—	43	8	no	—
408	C₄×D₄	—	43	16	no	—
409	C₄×D₄	—	43	8	no	—
410	C₄×D₄	—	43	16	no	—
411	C₄×D₄	—	43	8	no	—
412	#117	—	43	2	no	—
413	#117	—	43	2	no	—
414	#117	—	43	2	no	—
415	#117	—	43	2	no	—
416	#117	—	43	8	no	—
417	#117	—	43	8	no	—
418	#117	—	43	8	no	—
419	#117	C₄×D₄₃	1	2	yes	—
420	#117	C₄×D₄₃	1	2	yes	—
421	#117	C₂²×D₄₃	1	2	yes	—
422	#117	C₂²×D₄₃	1	2	yes	—
423	C₂×C₄⋊C₄	—	43	2	no	—
424	C₂×C₄⋊C₄	—	43	8	no	—
425	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
426	C₂×C₂²⋊C₄	—	43	2	no	—
427	C₂×C₂²⋊C₄	—	43	8	no	—
428	C₂×C₂²⋊C₄	C₄×D₄₃	1	2	yes	—
429	C₂×C₄²	—	43	2	no	—
430	C₂×C₄²	—	43	8	no	—
431	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
432	#97	—	43	4	no	—
433	#97	—	43	8	no	—
434	#97	—	43	4	no	—
435	#97	—	43	8	no	—
436	#97	C₂²×D₄₃	1	4	yes	—
437	#97	C₂²×D₄₃	1	4	yes	—
438	C₄×C₈	—	43	4	no	—
439	C₄×C₈	—	43	8	no	—
440	C₄×C₈	—	43	4	no	—
441	C₄×C₈	—	43	8	no	—
442	C₄×C₈	C₂²×D₄₃	1	4	yes	—
443	C₄×C₈	C₂²×D₄₃	1	4	yes	—
444	C₂⁴	—	43	2	no	—
445	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
446	#41	—	43	16	no	—
447	#41	—	43	16	no	—
448	#41	—	43	8	no	—
449	#41	—	43	8	no	—
450	#41	—	43	8	no	—
451	#41	—	43	8	no	—
452	C₂×Q₈	—	43	8	no	—
453	C₂×Q₈	—	43	2	no	—
454	C₂×Q₈	—	43	2	no	—
455	C₂×D₄	—	43	16	no	—
456	C₂×D₄	—	43	4	no	—
457	C₂×D₄	—	43	4	no	—
458	C₂×D₄	—	43	8	no	—
459	C₂×D₄	—	43	2	no	—
460	C₂×D₄	—	43	2	no	—
461	C₂²×C₄	—	43	2	no	—
462	C₂²×C₄	—	43	4	no	—
463	C₂²×C₄	—	43	8	no	—
464	C₂²×C₄	—	43	8	no	—
465	C₂²×C₄	—	43	4	no	—
466	C₂²×C₄	—	43	4	no	—
467	C₂²×C₄	—	43	16	no	—
468	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
469	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
473	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
474	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
475	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
476	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
477	M₁₆	—	43	8	no	—
478	M₁₆	—	43	8	no	—
479	M₁₆	—	43	8	no	—
480	M₁₆	—	43	8	no	—
481	M₁₆	—	43	32	no	—
482	M₁₆	—	43	16	no	—
483	M₁₆	—	43	16	no	—
484	M₁₆	C₂×C₄×D₄₃	1	8	yes	—
485	M₁₆	C₂×C₄×D₄₃	1	8	yes	—
486	C₂×C₈	—	43	8	no	—
487	C₂×C₈	—	43	8	no	—
488	C₂×C₈	—	43	4	no	—
489	C₂×C₈	—	43	4	no	—
490	C₂×C₈	—	43	16	no	—
491	C₂×C₈	—	43	16	no	—
492	C₂×C₈	—	43	32	no	—
493	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
494	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
495	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
496	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
497	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
498	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
499	C₂×C₈	C₂×C₄×D₄₃	1	8	yes	—
500	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
501	C₂×C₈	C₂³×D₄₃	1	4	yes	—
502	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
503	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
504	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
505	C₄⋊C₄	—	43	4	no	—
506	C₄⋊C₄	—	43	16	no	—
507	C₄⋊C₄	—	43	4	no	—
508	C₄⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
509	C₄⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
510	C₂²⋊C₄	—	43	4	no	—
511	C₂²⋊C₄	—	43	4	no	—
512	C₂²⋊C₄	—	43	16	no	—
513	C₂²⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
514	C₂²⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
515	C₄²	—	43	16	no	—
516	C₄²	—	43	4	no	—
517	C₄²	—	43	4	no	—
518	C₄²	C₂×C₄×D₄₃	1	4	yes	—
519	C₄²	C₂³×D₄₃	1	4	yes	—
520	C₂³	—	4	2	no	—
521	C₂³	—	43	4	no	—
522	C₂³	—	43	8	no	—
523	C₂³	—	172	4	no	—
524	C₂³	C₄²×D₄₃	1	4	yes	—
525	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
526	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
527	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
528	Q₈	—	43	8	no	—
529	Q₈	—	43	8	no	—
530	D₄	—	43	16	no	—
531	D₄	—	43	16	no	—
532	D₄	—	43	8	no	—
533	D₄	—	43	8	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	43	8	no	—
536	C₂×C₄	—	43	4	no	—
537	C₂×C₄	—	43	16	no	—
538	C₂×C₄	—	43	8	no	—
539	C₂×C₄	—	43	8	no	—
540	C₂×C₄	—	43	8	no	—
541	C₂×C₄	—	172	16	no	—
542	C₂×C₄	—	172	4	no	—
543	C₂×C₄	C₄²×D₄₃	1	4	yes	—
544	C₂×C₄	C₄²×D₄₃	1	4	yes	—
545	C₂×C₄	C₄²×D₄₃	1	4	yes	—
546	C₂×C₄	C₂²×C₄×D₄₃	1	8	yes	—
547	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
548	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
549	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
550	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
551	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
552	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
553	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
554	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
555	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
556	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
557	C₈	—	43	8	no	—
558	C₈	—	43	8	no	—
559	C₈	C₂²×C₄×D₄₃	1	2	yes	—
560	C₈	C₂²×C₄×D₄₃	1	2	yes	—
561	C₈	C₂²×C₄×D₄₃	1	8	yes	—
562	C₈	C₂²×C₄×D₄₃	1	2	yes	—
563	C₈	C₂²×C₄×D₄₃	1	2	yes	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	4	4	no	—
568	C₂²	—	43	8	no	—
569	C₂²	—	86	8	no	—
570	C₂²	—	172	8	no	—
571	C₂²	C₂×C₄²×D₄₃	1	2	yes	—
572	C₂²	C₂×C₄²×D₄₃	1	2	yes	—
573	C₂²	C₂×C₄²×D₄₃	1	2	yes	—
574	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
575	C₄	—	2	8	no	—
576	C₄	—	43	8	no	—
577	C₄	—	86	8	no	—
578	C₄	C₂×C₄²×D₄₃	1	2	yes	—
579	C₄	C₂×C₄²×D₄₃	1	2	yes	—
580	C₄	C₂×C₄²×D₄₃	1	2	yes	—
581	C₄	C₂³×C₄×D₄₃	1	1	yes	characteristic
582	C₄	C₂³×C₄×D₄₃	1	1	yes	characteristic
583	C₂	—	2	2	no	—
584	C₂	—	2	2	no	—
585	C₂	—	2	2	no	—
586	C₂	—	86	8	no	—
587	C₂	C₂²×C₄²×D₄₃	1	1	yes	characteristic
588	C₂	#19149306	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂³×D₄₃
commutator	C₂×C₄₃	C₂³×C₄²
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#405	C₂
socle	C₂²×C₄₃	C₂⁴×C₄
prime radical	C₂²×#10621898	C₂²
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×#405	D₄₃
hypocenter	C₄₃	#60058
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
4. #19143022	C₂	semidirect
5. #19143020	C₂	semidirect
6. #19143017	C₂	semidirect
7. C₄×#13063331	C₂	semidirect
8. #19143014	C₂	semidirect
9. #19143013	C₂	semidirect
10. #19143011	C₂	semidirect
11. C₂×#14582854	C₂	semidirect
12. #405×D₄₃	C₂	semidirect
13. C₂×C₄₃×#405	C₂	semidirect
15. #14583665	C₄	semidirect
17. C₂×#13063331	C₄	semidirect
38. #14582856	C₂²	semidirect
39. #14582856	C₂²	semidirect
41. #14582855	C₂²	semidirect
44. #14582854	C₂²	semidirect
45. #14582854	C₂²	semidirect
46. #14582854	C₂²	semidirect
47. #14582853	C₂²	semidirect
48. #14582853	C₂²	semidirect
49. C₄×#10621877	C₂²	semidirect
50. #14582851	C₂²	semidirect
51. M₁₆×Dic₄₃	C₂²	semidirect
52. C₄×#10621872	C₂²	semidirect
53. C₂×#13063235	C₂²	semidirect
54. #97×D₄₃	C₂²	semidirect
55. C₂×C₈×Dic₄₃	C₂²	semidirect
56. C₄×C₈×D₄₃	C₂²	semidirect
62. C₄₃×#405	C₂²	semidirect
63. C₄₃×#405	C₂²	semidirect
64. C₂×#97×C₄₃	C₂²	semidirect
65. C₂×C₄×C₈×C₄₃	C₂²	semidirect
76. #13063333	C₂×C₄	semidirect
77. #13063331	C₂×C₄	semidirect
78. #13063331	C₂×C₄	semidirect
79. #13063331	C₂×C₄	semidirect
80. #13063331	C₂×C₄	semidirect
81. #13063331	C₂×C₄	semidirect
82. C₂×#10621877	C₂×C₄	semidirect
83. C₂×#10621877	C₂×C₄	semidirect
88. C₂×#10621872	C₂×C₄	semidirect
92. M₁₆×D₄₃	C₂×C₄	semidirect
95. C₂×C₈×D₄₃	C₂×C₄	semidirect
127. C₂×M₁₆×C₄₃	C₂×C₄	semidirect
130. C₂²×C₈×C₄₃	C₂×C₄	semidirect
301. C₂×#405	D₄₃	semidirect
348. #405	C₂×D₄₃	semidirect
349. #405	C₂×D₄₃	semidirect
356. C₂×#97	C₂×D₄₃	semidirect
359. C₂×C₄×C₈	C₂×D₄₃	semidirect
360. C₄₃	#60058	semidirect
389. C₂×M₁₆	C₄×D₄₃	semidirect
398. C₂²×C₈	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×#14583665	2
C₂²×#13063331	2
#19147796	2
#19143022	2
#19143020	2
#19143017	2
C₄×#13063331	2
#19143014	2
#19143013	2
#19143011	2
C₂×#14582854	2
#405×D₄₃	2
C₂×C₄₃×#405	2
#60058	43