Subgroups — C₄₃×#25724 #24945741

Order 11008.

1700 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#495	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₃×#447	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2015	C₂	1	2	yes	maximal, complemented
9	C₄₃×#2012	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1958	C₂	1	2	yes	maximal, complemented
11	C₄×C₂²⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	complemented
15	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
16	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	complemented
17	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
18	C₂×#124×C₄₃	—	2	8	no	—
19	C₂×#124×C₄₃	—	2	2	no	—
20	C₂×#124×C₄₃	C₂²	1	2	yes	—
21	C₂×#124×C₄₃	C₂²	1	2	yes	—
22	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₄₃	—	2	2	no	—
26	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
27	C₄₃×#495	—	2	8	no	—
28	C₄₃×#451	—	2	4	no	—
29	C₄₃×#450	—	2	4	no	—
30	C₄₃×#448	—	2	4	no	—
31	C₄₃×#447	—	2	4	no	—
32	C₂×#103×C₄₃	C₂²	1	2	yes	complemented
33	C₂×#103×C₄₃	C₂²	1	2	yes	complemented
34	C₂×#102×C₄₃	C₂²	1	2	yes	—
35	C₂×#102×C₄₃	C₂²	1	2	yes	—
36	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	complemented
39	C₄₃×#391	C₂²	1	1	yes	characteristic, complemented
40	C₄₃×#390	C₂²	1	1	yes	characteristic, complemented
41	C₄₃×#388	—	2	2	no	—
42	C₄₃×#386	—	2	2	no	—
43	C₄₃×#382	C₂²	1	1	yes	characteristic, complemented
44	C₄₃×#336	C₂²	1	2	yes	complemented
45	C₂⁵×C₄₃	—	2	1	no	—
46	C₂²×Q₈×C₄₃	—	2	4	no	—
47	C₂²×Q₈×C₄₃	—	2	1	no	—
48	C₂²×Q₈×C₄₃	—	2	2	no	—
49	C₂²×Q₈×C₄₃	—	2	2	no	—
50	C₂²×Q₈×C₄₃	—	4	2	no	—
51	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
53	C₂²×D₄×C₄₃	—	2	4	no	—
54	C₂²×D₄×C₄₃	—	2	1	no	—
55	C₂²×D₄×C₄₃	—	2	1	no	—
56	C₂²×D₄×C₄₃	—	2	2	no	—
57	C₂²×D₄×C₄₃	—	2	2	no	—
58	C₂²×D₄×C₄₃	—	4	2	no	—
59	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₄₃	—	2	1	no	—
62	C₂³×C₄×C₄₃	D₄	1	2	yes	—
63	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂×Q₁₆×C₄₃	—	2	4	no	—
65	C₂×Q₁₆×C₄₃	—	2	4	no	—
66	C₂×Q₁₆×C₄₃	—	4	2	no	—
67	C₂×SD₁₆×C₄₃	—	2	4	no	—
68	C₂×SD₁₆×C₄₃	—	2	4	no	—
69	C₂×SD₁₆×C₄₃	—	2	4	no	—
70	C₂×SD₁₆×C₄₃	—	2	4	no	—
71	C₂×SD₁₆×C₄₃	—	4	2	no	—
72	C₂×SD₁₆×C₄₃	—	4	2	no	—
73	C₂×D₈×C₄₃	—	2	4	no	—
74	C₂×D₈×C₄₃	—	2	4	no	—
75	C₂×D₈×C₄₃	—	4	2	no	—
76	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
77	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
78	#124×C₄₃	—	2	16	no	—
79	#124×C₄₃	—	2	4	no	—
80	#124×C₄₃	—	2	4	no	—
81	#124×C₄₃	—	2	4	no	—
82	#124×C₄₃	—	2	4	no	—
83	#124×C₄₃	D₄	1	8	yes	complemented
84	C₂²⋊Q₈×C₄₃	—	2	2	no	—
85	C₂²⋊Q₈×C₄₃	—	2	2	no	—
86	#121×C₄₃	—	2	2	no	—
87	#121×C₄₃	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
89	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₄₃	—	2	16	no	—
92	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
94	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
98	C₂×C₄²×C₄₃	—	2	4	no	—
99	C₂×C₄²×C₄₃	D₄	1	2	yes	—
100	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
102	#103×C₄₃	—	2	4	no	—
103	#103×C₄₃	—	2	4	no	—
104	#102×C₄₃	—	2	4	no	—
105	#102×C₄₃	—	2	4	no	—
106	C₂²⋊C₈×C₄₃	D₄	1	4	yes	—
107	C₂²⋊C₈×C₄₃	D₄	1	4	yes	—
108	C₄×C₈×C₄₃	—	2	4	no	—
109	#95×C₄₃	—	2	2	no	—
110	#95×C₄₃	—	2	2	no	—
111	C₂⁴×C₄₃	—	2	4	no	—
112	C₂⁴×C₄₃	—	2	2	no	—
113	C₂⁴×C₄₃	—	2	1	no	—
114	C₂⁴×C₄₃	—	4	2	no	—
115	C₂⁴×C₄₃	—	4	4	no	—
116	C₂⁴×C₄₃	—	4	2	no	—
117	C₂⁴×C₄₃	—	4	4	no	—
118	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂×Q₈×C₄₃	—	2	4	no	—
120	C₂×Q₈×C₄₃	—	2	2	no	—
121	C₂×Q₈×C₄₃	—	2	2	no	—
122	C₂×Q₈×C₄₃	—	2	2	no	—
123	C₂×Q₈×C₄₃	—	2	1	no	—
124	C₂×Q₈×C₄₃	—	2	1	no	—
125	C₂×Q₈×C₄₃	—	2	2	no	—
126	C₂×Q₈×C₄₃	—	2	2	no	—
127	C₂×Q₈×C₄₃	—	2	2	no	—
128	C₂×Q₈×C₄₃	—	2	2	no	—
129	C₂×Q₈×C₄₃	—	4	8	no	—
130	C₂×Q₈×C₄₃	—	4	8	no	—
131	C₂×Q₈×C₄₃	—	4	2	no	—
132	C₂×Q₈×C₄₃	—	4	2	no	—
133	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
134	C₂×D₄×C₄₃	—	2	4	no	—
135	C₂×D₄×C₄₃	—	2	2	no	—
136	C₂×D₄×C₄₃	—	2	2	no	—
137	C₂×D₄×C₄₃	—	2	2	no	—
138	C₂×D₄×C₄₃	—	2	1	no	—
139	C₂×D₄×C₄₃	—	2	1	no	—
140	C₂×D₄×C₄₃	—	2	2	no	—
141	C₂×D₄×C₄₃	—	2	2	no	—
142	C₂×D₄×C₄₃	—	2	2	no	—
143	C₂×D₄×C₄₃	—	2	2	no	—
144	C₂×D₄×C₄₃	—	4	8	no	—
145	C₂×D₄×C₄₃	—	4	8	no	—
146	C₂×D₄×C₄₃	—	4	2	no	—
147	C₂×D₄×C₄₃	—	4	2	no	—
148	C₂×D₄×C₄₃	—	4	2	no	—
149	C₂×D₄×C₄₃	—	4	4	no	—
150	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₄₃	—	2	2	no	—
152	C₂²×C₄×C₄₃	—	2	2	no	—
153	C₂²×C₄×C₄₃	—	2	4	no	—
154	C₂²×C₄×C₄₃	—	2	4	no	—
155	C₂²×C₄×C₄₃	—	2	4	no	—
156	C₂²×C₄×C₄₃	—	2	2	no	—
157	C₂²×C₄×C₄₃	—	2	1	no	—
158	C₂²×C₄×C₄₃	—	2	1	no	—
159	C₂²×C₄×C₄₃	—	2	1	no	—
160	C₂²×C₄×C₄₃	—	4	2	no	—
161	C₂²×C₄×C₄₃	—	4	2	no	—
162	C₂²×C₄×C₄₃	—	4	2	no	—
163	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
169	Q₁₆×C₄₃	—	4	8	no	—
170	SD₁₆×C₄₃	—	4	8	no	—
171	SD₁₆×C₄₃	—	4	8	no	—
172	D₈×C₄₃	—	4	8	no	—
173	C₂×C₈×C₄₃	—	2	2	no	—
174	C₂×C₈×C₄₃	—	2	2	no	—
175	C₂×C₈×C₄₃	—	2	2	no	—
176	C₂×C₈×C₄₃	—	2	2	no	—
177	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
178	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
179	C₄⋊C₄×C₄₃	—	2	1	no	—
180	C₄⋊C₄×C₄₃	—	2	1	no	—
181	C₄⋊C₄×C₄₃	—	2	1	no	—
182	C₄⋊C₄×C₄₃	—	2	1	no	—
183	C₄⋊C₄×C₄₃	—	4	2	no	—
184	C₂²⋊C₄×C₄₃	—	2	16	no	—
185	C₂²⋊C₄×C₄₃	—	2	16	no	—
186	C₂²⋊C₄×C₄₃	—	4	4	no	—
187	C₂²⋊C₄×C₄₃	—	4	4	no	—
188	C₂²⋊C₄×C₄₃	—	4	2	no	—
189	C₂²⋊C₄×C₄₃	—	4	2	no	—
190	C₄²×C₄₃	—	2	4	no	—
191	C₄²×C₄₃	—	2	2	no	—
192	C₄²×C₄₃	C₂×D₄	1	4	yes	—
193	C₂³×C₄₃	—	2	1	no	—
194	C₂³×C₄₃	—	2	1	no	—
195	C₂³×C₄₃	—	2	2	no	—
196	C₂³×C₄₃	—	2	4	no	—
197	C₂³×C₄₃	—	4	8	no	—
198	C₂³×C₄₃	—	4	16	no	—
199	C₂³×C₄₃	—	4	2	no	—
200	C₂³×C₄₃	—	4	2	no	—
201	C₂³×C₄₃	—	4	4	no	—
202	C₂³×C₄₃	—	4	4	no	—
203	C₂³×C₄₃	—	4	1	no	—
204	C₂³×C₄₃	—	4	1	no	—
205	C₂³×C₄₃	—	4	1	no	—
206	C₂³×C₄₃	—	4	2	no	—
207	C₂³×C₄₃	—	4	2	no	—
208	C₂³×C₄₃	—	8	4	no	—
209	C₂³×C₄₃	—	8	8	no	—
210	C₂³×C₄₃	—	8	4	no	—
211	C₂³×C₄₃	#127	1	2	yes	—
212	C₂³×C₄₃	#135	1	4	yes	—
213	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
214	Q₈×C₄₃	—	2	4	no	—
215	Q₈×C₄₃	—	2	4	no	—
216	Q₈×C₄₃	—	4	8	no	—
217	Q₈×C₄₃	—	4	2	no	—
218	Q₈×C₄₃	—	4	2	no	—
219	Q₈×C₄₃	—	4	2	no	—
220	Q₈×C₄₃	—	4	2	no	—
221	D₄×C₄₃	—	2	4	no	—
222	D₄×C₄₃	—	2	4	no	—
223	D₄×C₄₃	—	4	8	no	—
224	D₄×C₄₃	—	4	2	no	—
225	D₄×C₄₃	—	4	2	no	—
226	D₄×C₄₃	—	4	2	no	—
227	D₄×C₄₃	—	4	2	no	—
228	D₄×C₄₃	—	8	4	no	—
229	C₂×C₄×C₄₃	—	2	1	no	—
230	C₂×C₄×C₄₃	—	2	1	no	—
231	C₂×C₄×C₄₃	—	2	2	no	—
232	C₂×C₄×C₄₃	—	2	2	no	—
233	C₂×C₄×C₄₃	—	2	4	no	—
234	C₂×C₄×C₄₃	—	2	4	no	—
235	C₂×C₄×C₄₃	—	2	2	no	—
236	C₂×C₄×C₄₃	—	2	4	no	—
237	C₂×C₄×C₄₃	—	2	2	no	—
238	C₂×C₄×C₄₃	—	2	2	no	—
239	C₂×C₄×C₄₃	—	4	8	no	—
240	C₂×C₄×C₄₃	—	4	8	no	—
241	C₂×C₄×C₄₃	—	4	2	no	—
242	C₂×C₄×C₄₃	—	4	2	no	—
243	C₂×C₄×C₄₃	—	4	1	no	—
244	C₂×C₄×C₄₃	—	4	1	no	—
245	C₂×C₄×C₄₃	—	4	1	no	—
246	C₂×C₄×C₄₃	—	4	1	no	—
247	C₂×C₄×C₄₃	—	4	1	no	—
248	C₂×C₄×C₄₃	—	4	2	no	—
249	C₂×C₄×C₄₃	—	4	2	no	—
250	C₂×C₄×C₄₃	#120	1	4	yes	—
251	C₂×C₄×C₄₃	#127	1	2	yes	—
252	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
256	C₈×C₄₃	—	2	4	no	—
257	C₈×C₄₃	—	2	4	no	—
258	#25724	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂²×C₄₃	—	2	2	no	—
260	C₂²×C₄₃	—	2	2	no	—
261	C₂²×C₄₃	—	2	4	no	—
262	C₂²×C₄₃	—	2	4	no	—
263	C₂²×C₄₃	—	4	4	no	—
264	C₂²×C₄₃	—	4	8	no	—
265	C₂²×C₄₃	—	8	16	no	—
266	C₂²×C₄₃	—	8	2	no	—
267	C₂²×C₄₃	—	8	2	no	—
268	C₂²×C₄₃	—	8	4	no	—
269	C₂²×C₄₃	—	8	1	no	—
270	C₂²×C₄₃	—	8	1	no	—
271	C₂²×C₄₃	—	8	1	no	—
272	C₂²×C₄₃	—	8	2	no	—
273	C₂²×C₄₃	—	8	2	no	—
274	C₂²×C₄₃	#495	1	4	yes	complemented
275	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
276	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
277	C₂²×C₄₃	#535	1	1	yes	characteristic
278	C₂²×C₄₃	C₂×#135	1	2	yes	—
279	C₂²×C₄₃	#575	1	2	yes	—
280	C₄×C₄₃	—	2	2	no	—
281	C₄×C₄₃	—	2	4	no	—
282	C₄×C₄₃	—	4	4	no	—
283	C₄×C₄₃	—	4	2	no	—
284	C₄×C₄₃	—	8	1	no	—
285	C₄×C₄₃	—	8	1	no	—
286	C₄×C₄₃	—	8	1	no	—
287	C₄×C₄₃	D₄²	1	2	yes	—
288	C₄×C₄₃	D₄²	1	2	yes	—
289	C₂²×#124	C₂×C₄₃	1	1	yes	characteristic, complemented
290	C₂×#495	C₂×C₄₃	1	2	yes	complemented
291	C₂×#451	C₂×C₄₃	1	1	yes	characteristic, complemented
292	C₂×#448	C₂×C₄₃	1	1	yes	characteristic, complemented
293	C₂×#450	C₂×C₄₃	1	1	yes	characteristic, complemented
294	C₂×#447	C₂×C₄₃	1	1	yes	characteristic
295	#2850	C₂×C₄₃	1	1	yes	characteristic, complemented
296	#2015	C₂×C₄₃	1	2	yes	complemented
297	#2012	C₂×C₄₃	1	2	yes	complemented
298	#1958	C₂×C₄₃	1	2	yes	complemented
299	C₄×C₂²⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
300	C₂×C₄₃	—	2	4	no	—
301	C₂×C₄₃	—	8	4	no	—
302	C₂×C₄₃	—	16	1	no	—
303	C₂×C₄₃	#2433	1	1	yes	characteristic
304	C₂×C₄₃	#3002	1	2	yes	—
305	C₂×C₄₃	C₂×#495	1	1	yes	characteristic
306	C₂×C₄₃	#3153	1	1	yes	characteristic
307	C₂×C₄₃	#3211	1	2	yes	—
308	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
309	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
310	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	complemented
311	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
312	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	complemented
313	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
314	C₂×#124	—	2	8	no	—
315	C₂×#124	—	2	2	no	—
316	C₂×#124	C₂²×C₄₃	1	2	yes	—
317	C₂×#124	C₂²×C₄₃	1	2	yes	—
318	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic, complemented
319	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
320	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
321	C₂²×C₂²⋊C₄	—	2	2	no	—
322	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
323	#495	—	2	8	no	—
324	#451	—	2	4	no	—
325	#450	—	2	4	no	—
326	#448	—	2	4	no	—
327	#447	—	2	4	no	—
328	C₂×#103	C₂²×C₄₃	1	2	yes	complemented
329	C₂×#103	C₂²×C₄₃	1	2	yes	complemented
330	C₂×#102	C₂²×C₄₃	1	2	yes	—
331	C₂×#102	C₂²×C₄₃	1	2	yes	—
332	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
333	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
334	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	complemented
335	#391	C₂²×C₄₃	1	1	yes	characteristic, complemented
336	#390	C₂²×C₄₃	1	1	yes	characteristic, complemented
337	#388	—	2	2	no	—
338	#386	—	2	2	no	—
339	#382	C₂²×C₄₃	1	1	yes	characteristic, complemented
340	#336	C₂²×C₄₃	1	2	yes	complemented
341	C₄₃	#25724	1	1	yes	characteristic, direct product factor, Sylow
342	C₂⁵	—	2	1	no	—
343	C₂²×Q₈	—	2	4	no	—
344	C₂²×Q₈	—	2	1	no	—
345	C₂²×Q₈	—	2	2	no	—
346	C₂²×Q₈	—	2	2	no	—
347	C₂²×Q₈	—	4	2	no	—
348	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
349	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
350	C₂²×D₄	—	2	4	no	—
351	C₂²×D₄	—	2	1	no	—
352	C₂²×D₄	—	2	1	no	—
353	C₂²×D₄	—	2	2	no	—
354	C₂²×D₄	—	2	2	no	—
355	C₂²×D₄	—	4	2	no	—
356	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
357	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
358	C₂³×C₄	—	2	1	no	—
359	C₂³×C₄	D₄×C₄₃	1	2	yes	—
360	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
361	C₂×Q₁₆	—	2	4	no	—
362	C₂×Q₁₆	—	2	4	no	—
363	C₂×Q₁₆	—	4	2	no	—
364	C₂×SD₁₆	—	2	4	no	—
365	C₂×SD₁₆	—	2	4	no	—
366	C₂×SD₁₆	—	2	4	no	—
367	C₂×SD₁₆	—	2	4	no	—
368	C₂×SD₁₆	—	4	2	no	—
369	C₂×SD₁₆	—	4	2	no	—
370	C₂×D₈	—	2	4	no	—
371	C₂×D₈	—	2	4	no	—
372	C₂×D₈	—	4	2	no	—
373	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
374	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
375	#124	—	2	16	no	—
376	#124	—	2	4	no	—
377	#124	—	2	4	no	—
378	#124	—	2	4	no	—
379	#124	—	2	4	no	—
380	#124	D₄×C₄₃	1	8	yes	complemented
381	C₂²⋊Q₈	—	2	2	no	—
382	C₂²⋊Q₈	—	2	2	no	—
383	#121	—	2	2	no	—
384	#121	—	2	2	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	—	2	16	no	—
389	C₂×C₂²⋊C₄	—	2	4	no	—
390	C₂×C₂²⋊C₄	—	2	4	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	—	2	2	no	—
394	C₂×C₂²⋊C₄	—	2	2	no	—
395	C₂×C₄²	—	2	4	no	—
396	C₂×C₄²	D₄×C₄₃	1	2	yes	—
397	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
398	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
399	#103	—	2	4	no	—
400	#103	—	2	4	no	—
401	#102	—	2	4	no	—
402	#102	—	2	4	no	—
403	C₂²⋊C₈	D₄×C₄₃	1	4	yes	—
404	C₂²⋊C₈	D₄×C₄₃	1	4	yes	—
405	C₄×C₈	—	2	4	no	—
406	#95	—	2	2	no	—
407	#95	—	2	2	no	—
408	C₂⁴	—	2	4	no	—
409	C₂⁴	—	2	2	no	—
410	C₂⁴	—	2	1	no	—
411	C₂⁴	—	4	2	no	—
412	C₂⁴	—	4	4	no	—
413	C₂⁴	—	4	2	no	—
414	C₂⁴	—	4	4	no	—
415	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
416	C₂×Q₈	—	2	4	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	2	2	no	—
423	C₂×Q₈	—	2	2	no	—
424	C₂×Q₈	—	2	2	no	—
425	C₂×Q₈	—	2	2	no	—
426	C₂×Q₈	—	4	8	no	—
427	C₂×Q₈	—	4	8	no	—
428	C₂×Q₈	—	4	2	no	—
429	C₂×Q₈	—	4	2	no	—
430	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	4	8	no	—
442	C₂×D₄	—	4	8	no	—
443	C₂×D₄	—	4	2	no	—
444	C₂×D₄	—	4	2	no	—
445	C₂×D₄	—	4	4	no	—
446	C₂×D₄	—	4	2	no	—
447	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	4	2	no	—
458	C₂²×C₄	—	4	2	no	—
459	C₂²×C₄	—	4	2	no	—
460	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
461	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
462	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
464	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
465	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
466	Q₁₆	—	4	8	no	—
467	SD₁₆	—	4	8	no	—
468	SD₁₆	—	4	8	no	—
469	D₈	—	4	8	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
475	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	4	2	no	—
481	C₂²⋊C₄	—	2	16	no	—
482	C₂²⋊C₄	—	2	16	no	—
483	C₂²⋊C₄	—	4	4	no	—
484	C₂²⋊C₄	—	4	2	no	—
485	C₂²⋊C₄	—	4	4	no	—
486	C₂²⋊C₄	—	4	2	no	—
487	C₄²	—	2	4	no	—
488	C₄²	—	2	2	no	—
489	C₄²	C₂×D₄×C₄₃	1	4	yes	—
490	C₂³	—	2	1	no	—
491	C₂³	—	2	1	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	4	no	—
494	C₂³	—	4	8	no	—
495	C₂³	—	4	16	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	4	no	—
499	C₂³	—	4	4	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	8	4	no	—
506	C₂³	—	8	8	no	—
507	C₂³	—	8	4	no	—
508	C₂³	#127×C₄₃	1	2	yes	—
509	C₂³	#135×C₄₃	1	4	yes	—
510	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
511	Q₈	—	2	4	no	—
512	Q₈	—	2	4	no	—
513	Q₈	—	4	8	no	—
514	Q₈	—	4	2	no	—
515	Q₈	—	4	2	no	—
516	Q₈	—	4	2	no	—
517	Q₈	—	4	2	no	—
518	D₄	—	2	4	no	—
519	D₄	—	2	4	no	—
520	D₄	—	4	8	no	—
521	D₄	—	4	2	no	—
522	D₄	—	4	2	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	8	4	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	4	8	no	—
537	C₂×C₄	—	4	8	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	#120×C₄₃	1	4	yes	—
548	C₂×C₄	#127×C₄₃	1	2	yes	—
549	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
550	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
552	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
553	C₈	—	2	4	no	—
554	C₈	—	2	4	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	4	no	—
558	C₂²	—	2	4	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	4	8	no	—
561	C₂²	—	8	16	no	—
562	C₂²	—	8	2	no	—
563	C₂²	—	8	2	no	—
564	C₂²	—	8	4	no	—
565	C₂²	—	8	1	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	8	1	no	—
568	C₂²	—	8	2	no	—
569	C₂²	—	8	2	no	—
570	C₂²	C₄₃×#495	1	4	yes	complemented
571	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
572	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
573	C₂²	C₄₃×#535	1	1	yes	characteristic
574	C₂²	C₂×#135×C₄₃	1	2	yes	—
575	C₂²	C₄₃×#575	1	2	yes	—
576	C₄	—	2	2	no	—
577	C₄	—	2	4	no	—
578	C₄	—	4	4	no	—
579	C₄	—	4	2	no	—
580	C₄	—	8	1	no	—
581	C₄	—	8	1	no	—
582	C₄	—	8	1	no	—
583	C₄	D₄²×C₄₃	1	2	yes	—
584	C₄	D₄²×C₄₃	1	2	yes	—
585	C₂	—	2	4	no	—
586	C₂	—	8	4	no	—
587	C₂	—	16	1	no	—
588	C₂	C₄₃×#2433	1	1	yes	characteristic
589	C₂	C₄₃×#3002	1	2	yes	—
590	C₂	C₂×C₄₃×#495	1	1	yes	characteristic
591	C₂	C₄₃×#3153	1	1	yes	characteristic
592	C₂	C₄₃×#3211	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#447	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#124×C₄₃	C₂	semidirect
2. C₂×C₄₃×#495	C₂	semidirect
3. C₂×C₄₃×#451	C₂	semidirect
4. C₂×C₄₃×#448	C₂	semidirect
5. C₂×C₄₃×#450	C₂	semidirect
7. C₄₃×#2850	C₂	semidirect
8. C₄₃×#2015	C₂	semidirect
9. C₄₃×#2012	C₂	semidirect
10. C₄₃×#1958	C₂	semidirect
11. C₄×C₂²⋊C₈×C₄₃	C₂	semidirect
14. C₂²×Q₁₆×C₄₃	C₂²	semidirect
16. C₂²×SD₁₆×C₄₃	C₂²	semidirect
22. C₂×#124×C₄₃	C₂²	semidirect
32. C₂×#103×C₄₃	C₂²	semidirect
33. C₂×#103×C₄₃	C₂²	semidirect
38. C₂×C₄×C₈×C₄₃	C₂²	semidirect
39. C₄₃×#391	C₂²	semidirect
40. C₄₃×#390	C₂²	semidirect
43. C₄₃×#382	C₂²	semidirect
44. C₄₃×#336	C₂²	semidirect
83. #124×C₄₃	D₄	semidirect
258. #25724	C₄₃	direct (N × H)
274. C₂²×C₄₃	#495	semidirect
289. C₂²×#124	C₂×C₄₃	semidirect
290. C₂×#495	C₂×C₄₃	semidirect
291. C₂×#451	C₂×C₄₃	semidirect
292. C₂×#448	C₂×C₄₃	semidirect
293. C₂×#450	C₂×C₄₃	semidirect
295. #2850	C₂×C₄₃	semidirect
296. #2015	C₂×C₄₃	semidirect
297. #2012	C₂×C₄₃	semidirect
298. #1958	C₂×C₄₃	semidirect
299. C₄×C₂²⋊C₈	C₂×C₄₃	semidirect
310. C₂²×Q₁₆	C₂²×C₄₃	semidirect
312. C₂²×SD₁₆	C₂²×C₄₃	semidirect
318. C₂×#124	C₂²×C₄₃	semidirect
328. C₂×#103	C₂²×C₄₃	semidirect
329. C₂×#103	C₂²×C₄₃	semidirect
334. C₂×C₄×C₈	C₂²×C₄₃	semidirect
335. #391	C₂²×C₄₃	semidirect
336. #390	C₂²×C₄₃	semidirect
339. #382	C₂²×C₄₃	semidirect
340. #336	C₂²×C₄₃	semidirect
341. C₄₃	#25724	direct (N × H)
380. #124	D₄×C₄₃	semidirect
570. C₂²	C₄₃×#495	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#124×C₄₃	2
C₂×C₄₃×#495	2
C₂×C₄₃×#451	2
C₂×C₄₃×#448	2
C₂×C₄₃×#450	2
C₂×C₄₃×#447	2
C₄₃×#2850	2
C₄₃×#2015	2
C₄₃×#2012	2
C₄₃×#1958	2
C₄×C₂²⋊C₈×C₄₃	2
#25724	43

Subgroups — C43×#25724 #24945741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25724 #24945741