Subgroups — #25002388

Order 11008.

1062 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Dic₄₃⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582654	C₂	1	1	yes	maximal, characteristic
5	C₂×#14582653	C₂	1	1	yes	maximal, characteristic
6	C₂×#14582653	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄₃×#336	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
9	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₂²×Dic₄₃⋊C₄	C₄	1	2	yes	—
11	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
13	C₂×Dic₄₃⋊C₈	—	2	2	no	—
14	C₂×Dic₄₃⋊C₈	—	2	2	no	—
15	C₂×Dic₄₃⋊C₈	C₄	1	4	yes	complemented
16	C₂×C₈×Dic₄₃	—	2	2	no	—
17	C₂×C₈×Dic₄₃	—	2	2	no	—
18	C₂×C₈×Dic₄₃	C₄	1	4	yes	complemented
19	C₄×Dic₄₃⋊C₄	—	2	2	no	—
20	C₄×Dic₄₃⋊C₄	—	2	2	no	—
21	C₂×C₄₃⋊#95	C₄	1	2	yes	—
22	#14582654	—	2	2	no	—
23	#14582653	—	2	2	no	—
24	#14582653	—	2	2	no	—
25	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
28	C₄₃×#336	—	2	2	no	—
29	C₂³×Dic₄₃	C₂×C₄	1	2	yes	—
30	C₂³×Dic₄₃	C₂×C₄	1	1	yes	characteristic
31	C₂³×Dic₄₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄₃⋊C₈	—	2	1	no	—
33	C₂²×C₄₃⋊C₈	—	2	1	no	—
34	C₂²×C₄₃⋊C₈	—	2	1	no	—
35	C₂²×C₄₃⋊C₈	—	2	1	no	—
36	C₂²×C₄₃⋊C₈	—	2	1	no	—
37	C₂²×C₄₃⋊C₈	—	2	1	no	—
38	C₂²×C₄₃⋊C₈	—	2	1	no	—
39	C₂²×C₄₃⋊C₈	—	2	1	no	—
40	C₂²×C₄₃⋊C₈	—	2	1	no	—
41	C₂²×C₄₃⋊C₈	—	2	1	no	—
42	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
43	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
44	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
45	C₂²×C₄₃⋊C₈	Q₈	1	2	yes	—
46	C₂×Dic₄₃⋊C₄	—	2	4	no	—
47	C₂×Dic₄₃⋊C₄	—	2	4	no	—
48	C₂×Dic₄₃⋊C₄	C₈	1	8	yes	complemented
49	C₂×C₄×Dic₄₃	—	2	1	no	—
50	C₂×C₄×Dic₄₃	—	2	1	no	—
51	C₂×C₄×Dic₄₃	—	2	1	no	—
52	C₂×C₄×Dic₄₃	—	2	1	no	—
53	C₂×C₄×Dic₄₃	—	2	1	no	—
54	C₂×C₄×Dic₄₃	—	2	1	no	—
55	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
56	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
57	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
58	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
59	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
60	C₂×C₄×Dic₄₃	Q₈	1	2	yes	—
61	Dic₄₃⋊C₈	—	2	8	no	—
62	C₈×Dic₄₃	—	2	8	no	—
63	C₄₃⋊#95	—	2	4	no	—
64	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
65	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₄₃	—	2	1	no	—
67	C₂²×C₈×C₄₃	—	2	1	no	—
68	C₂²×C₈×C₄₃	—	2	1	no	—
69	C₂²×C₈×C₄₃	—	2	1	no	—
70	C₂²×C₈×C₄₃	—	2	1	no	—
71	C₂²×C₈×C₄₃	—	2	1	no	—
72	C₂²×C₈×C₄₃	—	2	1	no	—
73	C₂²×C₈×C₄₃	—	2	1	no	—
74	C₂²×C₈×C₄₃	—	2	1	no	—
75	C₂²×C₈×C₄₃	—	2	1	no	—
76	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
77	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
78	C₂²×C₈×C₄₃	D₄	1	2	yes	—
79	C₂²×C₈×C₄₃	Q₈	1	2	yes	—
80	C₂×C₄²×C₄₃	—	2	1	no	—
81	C₂×C₄²×C₄₃	—	2	1	no	—
82	C₂×C₄²×C₄₃	—	2	1	no	—
83	C₂×C₄²×C₄₃	—	2	1	no	—
84	C₂×C₄²×C₄₃	—	2	1	no	—
85	C₂×C₄²×C₄₃	—	2	1	no	—
86	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
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	C₂×C₈	1	4	yes	—
94	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
108	C₂²×Dic₄₃	—	2	2	no	—
109	C₂²×Dic₄₃	—	2	2	no	—
110	C₂²×Dic₄₃	—	2	2	no	—
111	C₂²×Dic₄₃	—	2	2	no	—
112	C₂²×Dic₄₃	—	2	2	no	—
113	C₂²×Dic₄₃	—	2	2	no	—
114	C₂²×Dic₄₃	—	2	2	no	—
115	C₂²×Dic₄₃	—	2	2	no	—
116	C₂²×Dic₄₃	C₄²	1	2	yes	—
117	C₂²×Dic₄₃	C₄²	1	2	yes	—
118	C₂²×Dic₄₃	C₂²⋊C₄	1	2	yes	—
119	C₂²×Dic₄₃	C₂²⋊C₄	1	2	yes	—
120	C₂²×Dic₄₃	C₄⋊C₄	1	2	yes	—
121	C₂²×Dic₄₃	C₄⋊C₄	1	2	yes	—
122	C₂²×Dic₄₃	C₂×C₈	1	4	yes	—
123	C₂²×Dic₄₃	C₂×C₈	1	4	yes	—
124	C₂²×Dic₄₃	M₁₆	1	4	yes	—
125	C₂×C₈×C₄₃	—	2	2	no	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	—	2	2	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₂×C₈×C₄₃	—	2	2	no	—
130	C₂×C₈×C₄₃	—	2	2	no	—
131	C₂×C₈×C₄₃	—	2	2	no	—
132	C₂×C₈×C₄₃	—	2	2	no	—
133	C₂×C₈×C₄₃	—	2	2	no	—
134	C₂×C₈×C₄₃	—	4	1	no	—
135	C₂×C₈×C₄₃	—	4	1	no	—
136	C₂×C₈×C₄₃	—	4	1	no	—
137	C₂×C₈×C₄₃	—	4	1	no	—
138	C₂×C₈×C₄₃	C₄⋊C₄	1	4	yes	complemented
139	C₄²×C₄₃	—	4	1	no	—
140	C₄²×C₄₃	—	4	1	no	—
141	C₄²×C₄₃	—	4	1	no	—
142	C₄²×C₄₃	—	4	1	no	—
143	Dic₄₃⋊C₄	—	2	16	no	—
144	C₄×Dic₄₃	—	4	1	no	—
145	C₄×Dic₄₃	—	4	1	no	—
146	C₄×Dic₄₃	—	4	1	no	—
147	C₄×Dic₄₃	—	4	1	no	—
148	C₄×Dic₄₃	C₂²⋊C₄	1	4	yes	—
149	C₄×Dic₄₃	C₂²⋊C₄	1	4	yes	—
150	C₄×Dic₄₃	C₄⋊C₄	1	4	yes	—
151	C₄×Dic₄₃	C₄⋊C₄	1	4	yes	—
152	C₂×C₄₃⋊C₈	—	2	2	no	—
153	C₂×C₄₃⋊C₈	—	2	2	no	—
154	C₂×C₄₃⋊C₈	—	2	2	no	—
155	C₂×C₄₃⋊C₈	—	2	2	no	—
156	C₂×C₄₃⋊C₈	—	2	2	no	—
157	C₂×C₄₃⋊C₈	—	2	2	no	—
158	C₂×C₄₃⋊C₈	—	2	2	no	—
159	C₂×C₄₃⋊C₈	—	2	2	no	—
160	C₂×C₄₃⋊C₈	—	2	2	no	—
161	C₂×C₄₃⋊C₈	—	4	1	no	—
162	C₂×C₄₃⋊C₈	—	4	1	no	—
163	C₂×C₄₃⋊C₈	—	4	1	no	—
164	C₂×C₄₃⋊C₈	—	4	1	no	—
165	C₂×C₄₃⋊C₈	C₄⋊C₄	1	4	yes	complemented
166	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
167	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
170	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
171	C₂³×C₄₃	C₄×Q₈	1	1	yes	characteristic
172	C₂³×C₄₃	C₄×Q₈	1	1	yes	characteristic
173	C₂³×C₄₃	C₂²×C₈	1	2	yes	—
174	C₂³×C₄₃	C₂×M₁₆	1	2	yes	—
175	C₂³×C₄₃	#131	1	2	yes	—
176	C₂³×C₄₃	#131	1	2	yes	—
177	C₂×C₄×C₄₃	—	2	4	no	—
178	C₂×C₄×C₄₃	—	2	4	no	—
179	C₂×C₄×C₄₃	—	2	4	no	—
180	C₂×C₄×C₄₃	—	4	2	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
191	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
197	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
198	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
199	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
203	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
204	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
205	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
206	C₂×C₄×C₄₃	#125	1	1	yes	characteristic
207	C₂×C₄×C₄₃	#125	1	1	yes	characteristic
208	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
209	C₂×C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
212	C₂×Dic₄₃	—	2	2	no	—
213	C₂×Dic₄₃	—	2	2	no	—
214	C₂×Dic₄₃	—	2	4	no	—
215	C₂×Dic₄₃	—	2	4	no	—
216	C₂×Dic₄₃	—	2	4	no	—
217	C₂×Dic₄₃	—	2	4	no	—
218	C₂×Dic₄₃	—	2	4	no	—
219	C₂×Dic₄₃	—	4	2	no	—
220	C₂×Dic₄₃	—	4	2	no	—
221	C₂×Dic₄₃	—	4	2	no	—
222	C₂×Dic₄₃	—	4	2	no	—
223	C₂×Dic₄₃	#95	1	4	yes	—
224	C₂×Dic₄₃	#95	1	4	yes	—
225	C₂×Dic₄₃	C₄×C₈	1	4	yes	—
226	C₂×Dic₄₃	#97	1	4	yes	—
227	C₂×Dic₄₃	C₂²⋊C₈	1	8	yes	—
228	C₂×Dic₄₃	C₄⋊C₈	1	8	yes	—
229	C₈×C₄₃	—	2	4	no	—
230	C₈×C₄₃	—	4	2	no	—
231	C₄₃⋊C₈	—	2	4	no	—
232	C₄₃⋊C₈	—	4	2	no	—
233	#10834	—	43	1	no	maximal, Sylow
234	C₂²×C₄₃	C₂×#95	1	1	yes	characteristic
235	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
236	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
237	C₂²×C₄₃	#389	1	1	yes	characteristic
238	C₂²×C₄₃	#389	1	1	yes	characteristic
239	C₂²×C₄₃	#390	1	1	yes	characteristic
240	C₂²×C₄₃	#391	1	1	yes	characteristic
241	C₂²×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
242	C₂²×C₄₃	C₂×#97	1	1	yes	characteristic
243	C₂²×C₄₃	#405	1	1	yes	characteristic
244	C₂²×C₄₃	#405	1	1	yes	characteristic
245	C₂²×C₄₃	C₂×C₂²⋊C₈	1	2	yes	—
246	C₂²×C₄₃	#408	1	2	yes	—
247	C₂²×C₄₃	C₂×C₄⋊C₈	1	2	yes	—
248	C₂²×C₄₃	#424	1	2	yes	—
249	C₂²×C₄₃	C₈×D₄	1	2	yes	—
250	C₂²×C₄₃	C₈×D₄	1	2	yes	—
251	C₂²×C₄₃	#436	1	2	yes	—
252	C₂²×C₄₃	#436	1	2	yes	—
253	C₂²×C₄₃	C₈×Q₈	1	2	yes	—
254	C₂²×C₄₃	C₈×Q₈	1	2	yes	—
255	C₂²×C₄₃	#446	1	2	yes	—
256	C₂²×C₄₃	#446	1	2	yes	—
257	C₄×C₄₃	—	4	4	no	—
258	C₄×C₄₃	#380	1	1	yes	characteristic
259	C₄×C₄₃	#380	1	1	yes	characteristic
260	C₄×C₄₃	#382	1	1	yes	characteristic
261	C₄×C₄₃	#384	1	1	yes	characteristic
262	C₄×C₄₃	#389	1	1	yes	characteristic
263	C₄×C₄₃	#389	1	1	yes	characteristic
264	C₄×C₄₃	#390	1	1	yes	characteristic
265	C₄×C₄₃	#391	1	1	yes	characteristic
266	Dic₄₃	—	2	4	no	—
267	Dic₄₃	—	4	4	no	—
268	Dic₄₃	#336	1	8	yes	complemented
269	C₂²×C₄⋊C₈	—	43	1	no	—
270	C₂²×C₄×C₈	—	43	1	no	—
271	C₂×C₄×C₄⋊C₄	—	43	1	no	—
272	C₂×#336	—	43	1	no	—
273	C₂×#336	—	43	1	no	—
274	C₂×#336	—	43	1	no	—
275	C₂×#336	D₄₃	1	1	yes	characteristic
276	C₂×C₄₃	C₄⋊#95	1	1	yes	characteristic
277	C₂×C₄₃	C₂×#336	1	1	yes	characteristic
278	C₂×C₄₃	#1729	1	1	yes	characteristic
279	C₂×C₄₃	C₈×C₄⋊C₄	1	1	yes	characteristic
280	C₂×C₄₃	C₈×C₄⋊C₄	1	1	yes	characteristic
281	C₂×C₄₃	#1770	1	1	yes	characteristic
282	C₂×C₄₃	#1770	1	1	yes	characteristic
283	C₂×C₄₃	#1939	1	2	yes	—
284	C₂×C₄₃	#1939	1	2	yes	—
285	C₂×C₄₃	#1954	1	2	yes	—
286	C₂×C₄₃	#1984	1	2	yes	—
287	C₂³×C₈	—	43	1	no	—
288	C₂³×C₈	—	43	1	no	—
289	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
290	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
291	C₂²×C₄⋊C₄	—	43	2	no	—
292	C₂²×C₄²	—	43	1	no	—
293	C₂²×C₄²	—	43	1	no	—
294	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
295	C₂×C₄⋊C₈	—	43	4	no	—
296	C₂×C₄⋊C₈	—	86	2	no	—
297	C₂×C₄⋊C₈	—	86	2	no	—
298	C₂×C₄×C₈	—	43	4	no	—
299	C₂×C₄×C₈	—	86	2	no	—
300	C₂×C₄×C₈	—	86	2	no	—
301	C₄×C₄⋊C₄	—	86	2	no	—
302	C₄×C₄⋊C₄	—	86	2	no	—
303	C₂×#95	—	43	2	no	—
304	#336	—	2	2	no	—
305	#336	—	86	2	no	—
306	#336	—	86	2	no	—
307	#336	—	86	2	no	—
308	C₄₃	#10834	1	1	yes	characteristic, complemented, Sylow
309	C₂³×C₄	—	43	1	no	—
310	C₂³×C₄	—	43	1	no	—
311	C₂³×C₄	—	43	2	no	—
312	C₂³×C₄	C₄×D₄₃	1	2	yes	—
313	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
314	C₂²×C₈	—	2	1	no	—
315	C₂²×C₈	—	2	1	no	—
316	C₂²×C₈	—	2	1	no	—
317	C₂²×C₈	—	2	1	no	—
318	C₂²×C₈	—	2	1	no	—
319	C₂²×C₈	—	2	1	no	—
320	C₂²×C₈	—	2	1	no	—
321	C₂²×C₈	—	2	1	no	—
322	C₂²×C₈	—	2	1	no	—
323	C₂²×C₈	—	2	1	no	—
324	C₂²×C₈	—	43	2	no	—
325	C₂²×C₈	—	43	2	no	—
326	C₂²×C₈	—	43	2	no	—
327	C₂²×C₈	—	43	2	no	—
328	C₂²×C₈	—	86	1	no	—
329	C₂²×C₈	—	86	1	no	—
330	C₂²×C₈	—	86	1	no	—
331	C₂²×C₈	—	86	1	no	—
332	C₂²×C₈	—	86	1	no	—
333	C₂²×C₈	—	86	1	no	—
334	C₂²×C₈	—	86	1	no	—
335	C₂²×C₈	—	86	1	no	—
336	C₂²×C₈	—	86	1	no	—
337	C₂²×C₈	—	86	1	no	—
338	C₂²×C₈	Dic₈₆	1	2	yes	—
339	C₂²×C₈	C₄×D₄₃	1	2	yes	—
340	C₂²×C₈	C₄×D₄₃	1	2	yes	—
341	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
342	C₂×C₄⋊C₄	—	43	8	no	—
343	C₂×C₄⋊C₄	—	86	4	no	—
344	C₂×C₄⋊C₄	—	86	4	no	—
345	C₂×C₄²	—	2	1	no	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	—	43	2	no	—
352	C₂×C₄²	—	43	2	no	—
353	C₂×C₄²	—	43	2	no	—
354	C₂×C₄²	—	43	2	no	—
355	C₂×C₄²	—	43	2	no	—
356	C₂×C₄²	—	43	2	no	—
357	C₂×C₄²	—	86	1	no	—
358	C₂×C₄²	—	86	1	no	—
359	C₂×C₄²	—	86	1	no	—
360	C₂×C₄²	—	86	1	no	—
361	C₂×C₄²	—	86	1	no	—
362	C₂×C₄²	—	86	1	no	—
363	C₄⋊C₈	—	86	8	no	—
364	C₄×C₈	—	86	8	no	—
365	#95	—	86	4	no	—
366	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	43	2	no	—
374	C₂²×C₄	—	43	2	no	—
375	C₂²×C₄	—	43	2	no	—
376	C₂²×C₄	—	43	4	no	—
377	C₂²×C₄	—	43	4	no	—
378	C₂²×C₄	—	43	2	no	—
379	C₂²×C₄	—	43	2	no	—
380	C₂²×C₄	—	43	2	no	—
381	C₂²×C₄	—	43	4	no	—
382	C₂²×C₄	—	86	2	no	—
383	C₂²×C₄	—	86	2	no	—
384	C₂²×C₄	—	86	2	no	—
385	C₂²×C₄	—	86	2	no	—
386	C₂²×C₄	—	86	2	no	—
387	C₂²×C₄	—	86	2	no	—
388	C₂²×C₄	—	86	2	no	—
389	C₂²×C₄	—	86	2	no	—
390	C₂²×C₄	C₈×D₄₃	1	4	yes	—
391	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
392	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
394	C₂²×C₄	#10621898	1	1	yes	characteristic
395	C₂²×C₄	#10621898	1	1	yes	characteristic
396	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
397	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
398	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
399	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
400	C₂²×C₄	#10621900	1	1	yes	characteristic
401	C₂²×C₄	#10621900	1	1	yes	characteristic
402	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
403	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
404	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	4	1	no	—
415	C₂×C₈	—	4	1	no	—
416	C₂×C₈	—	4	1	no	—
417	C₂×C₈	—	4	1	no	—
418	C₂×C₈	—	43	4	no	—
419	C₂×C₈	—	86	2	no	—
420	C₂×C₈	—	86	2	no	—
421	C₂×C₈	—	86	2	no	—
422	C₂×C₈	—	86	2	no	—
423	C₂×C₈	—	86	2	no	—
424	C₂×C₈	—	86	2	no	—
425	C₂×C₈	—	86	2	no	—
426	C₂×C₈	—	86	2	no	—
427	C₂×C₈	—	86	2	no	—
428	C₂×C₈	—	172	1	no	—
429	C₂×C₈	—	172	1	no	—
430	C₂×C₈	—	172	1	no	—
431	C₂×C₈	—	172	1	no	—
432	C₂×C₈	Dic₄₃⋊C₄	1	4	yes	complemented
433	C₄⋊C₄	—	86	16	no	—
434	C₄²	—	4	1	no	—
435	C₄²	—	4	1	no	—
436	C₄²	—	4	1	no	—
437	C₄²	—	4	1	no	—
438	C₄²	—	43	4	no	—
439	C₄²	—	43	4	no	—
440	C₄²	—	43	4	no	—
441	C₄²	—	43	4	no	—
442	C₄²	—	172	1	no	—
443	C₄²	—	172	1	no	—
444	C₄²	—	172	1	no	—
445	C₄²	—	172	1	no	—
446	C₂³	C₄²×D₄₃	1	1	yes	characteristic
447	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
448	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
449	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
450	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
451	C₂³	#13063290	1	1	yes	characteristic
452	C₂³	C₄×Dic₈₆	1	1	yes	characteristic
453	C₂³	C₂×C₈×D₄₃	1	2	yes	—
454	C₂³	M₁₆×D₄₃	1	2	yes	—
455	C₂³	#13063331	1	2	yes	—
456	C₂³	#13063333	1	2	yes	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	43	4	no	—
465	C₂×C₄	—	43	4	no	—
466	C₂×C₄	—	43	8	no	—
467	C₂×C₄	—	43	8	no	—
468	C₂×C₄	—	43	4	no	—
469	C₂×C₄	—	43	4	no	—
470	C₂×C₄	—	86	2	no	—
471	C₂×C₄	—	86	2	no	—
472	C₂×C₄	—	86	4	no	—
473	C₂×C₄	—	86	4	no	—
474	C₂×C₄	—	86	4	no	—
475	C₂×C₄	—	86	4	no	—
476	C₂×C₄	—	86	4	no	—
477	C₂×C₄	—	172	2	no	—
478	C₂×C₄	—	172	2	no	—
479	C₂×C₄	—	172	2	no	—
480	C₂×C₄	—	172	2	no	—
481	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
482	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
483	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
484	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
485	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
486	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
487	C₂×C₄	#13063281	1	1	yes	characteristic
488	C₂×C₄	#13063282	1	1	yes	characteristic
489	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
490	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
491	C₂×C₄	#13063290	1	1	yes	characteristic
492	C₂×C₄	C₄×Dic₈₆	1	1	yes	characteristic
493	C₂×C₄	#13063297	1	1	yes	characteristic
494	C₂×C₄	#13063297	1	1	yes	characteristic
495	C₂×C₄	#13063298	1	1	yes	characteristic
496	C₂×C₄	#13063298	1	1	yes	characteristic
497	C₂×C₄	#13063302	1	1	yes	characteristic
498	C₂×C₄	#13063302	1	1	yes	characteristic
499	C₂×C₄	#13063303	1	1	yes	characteristic
500	C₂×C₄	#13063303	1	1	yes	characteristic
501	C₂×C₄	#13063311	1	1	yes	characteristic
502	C₂×C₄	#13063311	1	1	yes	characteristic
503	C₂×C₄	#13063315	1	1	yes	characteristic
504	C₂×C₄	#13063315	1	1	yes	characteristic
505	C₂×C₄	#13063321	1	1	yes	characteristic
506	C₂×C₄	#13063323	1	1	yes	characteristic
507	C₂×C₄	#13063324	1	1	yes	characteristic
508	C₂×C₄	#13063324	1	1	yes	characteristic
509	C₈	—	2	4	no	—
510	C₈	—	4	2	no	—
511	C₈	—	86	4	no	—
512	C₈	—	172	2	no	—
513	C₂²	#95×D₄₃	1	1	yes	characteristic
514	C₂²	#14582750	1	1	yes	characteristic
515	C₂²	C₄×Dic₄₃⋊C₄	1	1	yes	characteristic
516	C₂²	#14582794	1	1	yes	characteristic
517	C₂²	#14582796	1	1	yes	characteristic
518	C₂²	#14582799	1	1	yes	characteristic
519	C₂²	#14582803	1	1	yes	characteristic
520	C₂²	C₄×C₈×D₄₃	1	1	yes	characteristic
521	C₂²	#97×D₄₃	1	1	yes	characteristic
522	C₂²	#14582853	1	1	yes	characteristic
523	C₂²	#14582856	1	1	yes	characteristic
524	C₂²	C₂²⋊C₈×D₄₃	1	2	yes	—
525	C₂²	#14582864	1	2	yes	—
526	C₂²	C₄⋊C₈×D₄₃	1	2	yes	—
527	C₂²	#14582924	1	2	yes	—
528	C₂²	(C₂²⋊D₄₃)⋊C₈	1	2	yes	—
529	C₂²	C₈×C₂²⋊D₄₃	1	2	yes	—
530	C₂²	#14582974	1	2	yes	—
531	C₂²	#14582975	1	2	yes	—
532	C₂²	#14583023	1	2	yes	—
533	C₂²	C₈×Dic₈₆	1	2	yes	—
534	C₂²	#14583027	1	2	yes	—
535	C₂²	#14583028	1	2	yes	—
536	C₄	—	4	4	no	—
537	C₄	—	43	8	no	—
538	C₄	—	86	4	no	—
539	C₄	—	172	4	no	—
540	C₄	#14582757	1	1	yes	characteristic
541	C₄	#14582758	1	1	yes	characteristic
542	C₄	#14582763	1	1	yes	characteristic
543	C₄	#14582768	1	1	yes	characteristic
544	C₄	#14582794	1	1	yes	characteristic
545	C₄	#14582796	1	1	yes	characteristic
546	C₄	#14582799	1	1	yes	characteristic
547	C₄	#14582803	1	1	yes	characteristic
548	C₂	Dic₄₃⋊#95	1	1	yes	characteristic
549	C₂	#336×D₄₃	1	1	yes	characteristic
550	C₂	#19134290	1	1	yes	characteristic
551	C₂	#19134456	1	1	yes	characteristic
552	C₂	C₈×Dic₄₃⋊C₄	1	1	yes	characteristic
553	C₂	#19134461	1	1	yes	characteristic
554	C₂	#19134463	1	1	yes	characteristic
555	C₂	#19135310	1	2	yes	—
556	C₂	#19135312	1	2	yes	—
557	C₂	#19135387	1	2	yes	—
558	C₂	#19135529	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂×C₄×C₈
Fitting	C₂×C₄₃×#336	C₂
socle, prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#336	D₄₃
hypocenter	C₄₃	#10834
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
15. C₂×Dic₄₃⋊C₈	C₄	semidirect
18. C₂×C₈×Dic₄₃	C₄	semidirect
48. C₂×Dic₄₃⋊C₄	C₈	semidirect
138. C₂×C₈×C₄₃	C₄⋊C₄	semidirect
165. C₂×C₄₃⋊C₈	C₄⋊C₄	semidirect
268. Dic₄₃	#336	semidirect
308. C₄₃	#10834	semidirect
432. C₂×C₈	Dic₄₃⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₄₃⋊C₈	2
C₂²×C₈×Dic₄₃	2
C₂×C₄×Dic₄₃⋊C₄	2
C₂×#14582654	2
C₂×#14582653	2
C₂×C₄₃×#336	2
#10834	43