Subgroups — C₄₃×#20942 #24940959

Order 11008.

1778 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#575	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#104×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2896	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1883	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1882	C₂	1	4	yes	maximal, complemented
8	C₄₃×#1742	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₃×#339	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
12	C₄₃×#575	—	2	4	no	—
13	C₄₃×#575	C₄	1	8	yes	complemented
14	C₂×#137×C₄₃	—	2	1	no	—
15	C₂×#137×C₄₃	C₂²	1	2	yes	—
16	C₂×AGL(1,ℤ/8)×C₄₃	—	2	1	no	—
17	C₂×AGL(1,ℤ/8)×C₄₃	C₂²	1	2	yes	—
18	C₂×#135×C₄₃	—	2	2	no	—
19	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
21	C₄₃×#520	—	2	2	no	—
22	C₄₃×#520	C₂²	1	4	yes	—
23	C₄₃×#519	—	2	1	no	—
24	C₄₃×#518	—	2	1	no	—
25	C₄₃×#518	—	2	2	no	—
26	C₄×#41×C₄₃	—	2	2	no	—
27	C₄×#41×C₄₃	—	2	2	no	—
28	C₂×#117×C₄₃	—	2	2	no	—
29	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×#104×C₄₃	—	2	4	no	—
33	C₂×#104×C₄₃	C₂²	1	4	yes	—
34	C₄₃×#419	C₂²	1	2	yes	complemented
35	C₄₃×#418	C₂²	1	2	yes	complemented
36	C₄₃×#417	—	2	2	no	—
37	C₄₃×#416	—	2	2	no	—
38	C₄₃×#391	C₂²	1	2	yes	complemented
39	C₄₃×#390	C₂²	1	2	yes	complemented
40	C₄₃×#386	—	2	2	no	—
41	C₄×C₂²⋊C₄×C₄₃	—	2	2	no	—
42	C₄₃×#343	C₂²	1	4	yes	complemented
43	C₄₃×#339	C₂²	1	4	yes	complemented
44	C₂×#41×C₄₃	—	2	1	no	—
45	C₂×#41×C₄₃	—	2	1	no	—
46	C₂×#41×C₄₃	—	2	2	no	—
47	C₂×#41×C₄₃	—	2	2	no	—
48	C₂×#41×C₄₃	—	2	2	no	—
49	C₂×#41×C₄₃	—	2	1	no	—
50	C₂×#41×C₄₃	—	2	1	no	—
51	C₂×#41×C₄₃	—	2	2	no	—
52	C₂×#41×C₄₃	—	2	1	no	—
53	C₂×#41×C₄₃	—	2	1	no	—
54	C₂×#41×C₄₃	—	2	2	no	—
55	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
56	C₂×#41×C₄₃	C₂×C₄	1	4	yes	complemented
57	C₂×#41×C₄₃	D₄	1	4	yes	—
58	C₂×#41×C₄₃	D₄	1	2	yes	—
59	C₂×#41×C₄₃	C₂³	1	2	yes	—
60	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
61	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₄₃	—	2	1	no	—
63	C₂²×D₄×C₄₃	—	2	1	no	—
64	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
65	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₄₃	—	2	1	no	—
67	C₂³×C₄×C₄₃	—	2	1	no	—
68	C₂³×C₄×C₄₃	—	2	1	no	—
69	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
70	#137×C₄₃	—	2	4	no	—
71	#137×C₄₃	—	2	8	no	—
72	#137×C₄₃	C₂×C₄	1	8	yes	complemented
73	AGL(1,ℤ/8)×C₄₃	—	2	4	no	—
74	AGL(1,ℤ/8)×C₄₃	—	2	8	no	—
75	AGL(1,ℤ/8)×C₄₃	C₂×C₄	1	8	yes	complemented
76	#135×C₄₃	—	2	16	no	—
77	C₂×Q₁₆×C₄₃	—	2	2	no	—
78	C₂×SD₁₆×C₄₃	—	2	2	no	—
79	C₂×SD₁₆×C₄₃	—	2	2	no	—
80	C₂×D₈×C₄₃	—	2	2	no	—
81	C₂×M₁₆×C₄₃	—	2	1	no	—
82	C₂×M₁₆×C₄₃	—	2	2	no	—
83	C₂×M₁₆×C₄₃	—	2	1	no	—
84	C₂×M₁₆×C₄₃	—	2	2	no	—
85	C₂×M₁₆×C₄₃	—	2	2	no	—
86	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	complemented
87	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
88	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
89	C₂²×C₈×C₄₃	—	2	1	no	—
90	C₂²×C₈×C₄₃	—	2	1	no	—
91	C₄×Q₈×C₄₃	—	2	4	no	—
92	C₄×Q₈×C₄₃	—	2	4	no	—
93	C₄×D₄×C₄₃	—	2	8	no	—
94	C₄×D₄×C₄₃	—	2	4	no	—
95	C₄×D₄×C₄₃	—	2	4	no	—
96	C₄×D₄×C₄₃	—	2	8	no	—
97	#117×C₄₃	—	2	4	no	—
98	#117×C₄₃	—	2	4	no	—
99	#117×C₄₃	—	2	1	no	—
100	#117×C₄₃	—	2	1	no	—
101	#117×C₄₃	—	2	1	no	—
102	#117×C₄₃	—	2	1	no	—
103	#117×C₄₃	—	2	1	no	—
104	#117×C₄₃	—	2	1	no	—
105	#117×C₄₃	—	2	4	no	—
106	#117×C₄₃	D₄	1	2	yes	—
107	#117×C₄₃	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
109	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
110	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
111	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
112	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
114	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
115	C₂×C₄²×C₄₃	—	2	4	no	—
116	C₂×C₄²×C₄₃	—	2	1	no	—
117	C₂×C₄²×C₄₃	—	2	2	no	—
118	C₂×C₄²×C₄₃	—	2	2	no	—
119	C₂×C₄²×C₄₃	—	2	1	no	—
120	C₂×C₄²×C₄₃	D₄	1	2	yes	—
121	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
122	#104×C₄₃	—	2	8	no	—
123	#103×C₄₃	—	2	4	no	—
124	#102×C₄₃	—	2	4	no	—
125	#95×C₄₃	—	2	4	no	—
126	C₂⁴×C₄₃	—	2	1	no	—
127	C₂⁴×C₄₃	—	2	1	no	—
128	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
129	#41×C₄₃	—	2	4	no	—
130	#41×C₄₃	—	2	4	no	—
131	#41×C₄₃	—	2	4	no	—
132	#41×C₄₃	—	2	4	no	—
133	#41×C₄₃	—	2	4	no	—
134	#41×C₄₃	—	2	2	no	—
135	#41×C₄₃	—	2	2	no	—
136	#41×C₄₃	—	2	4	no	—
137	#41×C₄₃	—	2	4	no	—
138	#41×C₄₃	—	2	4	no	—
139	#41×C₄₃	—	2	4	no	—
140	#41×C₄₃	—	4	2	no	—
141	#41×C₄₃	—	4	2	no	—
142	#41×C₄₃	—	4	2	no	—
143	#41×C₄₃	—	4	2	no	—
144	#41×C₄₃	C₂²⋊C₄	1	8	yes	complemented
145	#41×C₄₃	C₂²×C₄	1	4	yes	—
146	#41×C₄₃	C₂×D₄	1	4	yes	—
147	C₂×Q₈×C₄₃	—	2	1	no	—
148	C₂×Q₈×C₄₃	—	2	2	no	—
149	C₂×Q₈×C₄₃	—	2	1	no	—
150	C₂×Q₈×C₄₃	—	2	1	no	—
151	C₂×Q₈×C₄₃	—	2	1	no	—
152	C₂×Q₈×C₄₃	—	2	1	no	—
153	C₂×Q₈×C₄₃	—	2	1	no	—
154	C₂×Q₈×C₄₃	C₂²⋊C₄	1	4	yes	complemented
155	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
156	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
157	C₂×D₄×C₄₃	—	2	1	no	—
158	C₂×D₄×C₄₃	—	2	2	no	—
159	C₂×D₄×C₄₃	—	2	1	no	—
160	C₂×D₄×C₄₃	—	2	4	no	—
161	C₂×D₄×C₄₃	—	2	4	no	—
162	C₂×D₄×C₄₃	—	2	2	no	—
163	C₂×D₄×C₄₃	—	2	4	no	—
164	C₂×D₄×C₄₃	—	2	2	no	—
165	C₂×D₄×C₄₃	—	2	1	no	—
166	C₂×D₄×C₄₃	—	2	1	no	—
167	C₂×D₄×C₄₃	—	2	1	no	—
168	C₂×D₄×C₄₃	—	2	1	no	—
169	C₂×D₄×C₄₃	—	4	1	no	—
170	C₂×D₄×C₄₃	—	4	1	no	—
171	C₂×D₄×C₄₃	—	4	2	no	—
172	C₂×D₄×C₄₃	C₂²⋊C₄	1	4	yes	complemented
173	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
174	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₄₃	—	2	4	no	—
176	C₂²×C₄×C₄₃	—	2	2	no	—
177	C₂²×C₄×C₄₃	—	2	4	no	—
178	C₂²×C₄×C₄₃	—	2	2	no	—
179	C₂²×C₄×C₄₃	—	2	8	no	—
180	C₂²×C₄×C₄₃	—	2	4	no	—
181	C₂²×C₄×C₄₃	—	2	1	no	—
182	C₂²×C₄×C₄₃	—	2	2	no	—
183	C₂²×C₄×C₄₃	—	2	1	no	—
184	C₂²×C₄×C₄₃	—	2	2	no	—
185	C₂²×C₄×C₄₃	—	4	4	no	—
186	C₂²×C₄×C₄₃	—	4	1	no	—
187	C₂²×C₄×C₄₃	—	4	1	no	—
188	C₂²×C₄×C₄₃	—	4	2	no	—
189	C₂²×C₄×C₄₃	—	4	2	no	—
190	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
191	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
197	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₄₃	#41	1	2	yes	—
199	C₂²×C₄×C₄₃	#41	1	2	yes	—
200	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
201	Q₁₆×C₄₃	—	2	8	no	—
202	SD₁₆×C₄₃	—	2	8	no	—
203	SD₁₆×C₄₃	—	2	8	no	—
204	D₈×C₄₃	—	2	8	no	—
205	M₁₆×C₄₃	—	2	4	no	—
206	M₁₆×C₄₃	—	2	2	no	—
207	M₁₆×C₄₃	—	2	2	no	—
208	M₁₆×C₄₃	—	2	2	no	—
209	M₁₆×C₄₃	—	4	2	no	—
210	M₁₆×C₄₃	C₂²×C₄	1	4	yes	—
211	C₂×C₈×C₄₃	—	2	4	no	—
212	C₂×C₈×C₄₃	—	2	2	no	—
213	C₂×C₈×C₄₃	—	2	2	no	—
214	C₂×C₈×C₄₃	—	4	2	no	—
215	C₄⋊C₄×C₄₃	—	2	8	no	—
216	C₄⋊C₄×C₄₃	—	2	2	no	—
217	C₄⋊C₄×C₄₃	—	2	2	no	—
218	C₄⋊C₄×C₄₃	—	2	2	no	—
219	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
220	C₂²⋊C₄×C₄₃	—	2	8	no	—
221	C₂²⋊C₄×C₄₃	—	2	2	no	—
222	C₂²⋊C₄×C₄₃	—	2	2	no	—
223	C₂²⋊C₄×C₄₃	—	2	2	no	—
224	C₂²⋊C₄×C₄₃	—	2	2	no	—
225	C₂²⋊C₄×C₄₃	—	4	8	no	—
226	C₄²×C₄₃	—	2	8	no	—
227	C₄²×C₄₃	—	2	2	no	—
228	C₄²×C₄₃	—	2	2	no	—
229	C₄²×C₄₃	—	2	2	no	—
230	C₄²×C₄₃	—	2	2	no	—
231	C₄²×C₄₃	—	2	2	no	—
232	C₄²×C₄₃	—	2	2	no	—
233	C₄²×C₄₃	—	4	2	no	—
234	C₂³×C₄₃	—	2	2	no	—
235	C₂³×C₄₃	—	2	4	no	—
236	C₂³×C₄₃	—	2	2	no	—
237	C₂³×C₄₃	—	4	2	no	—
238	C₂³×C₄₃	—	4	4	no	—
239	C₂³×C₄₃	—	4	1	no	—
240	C₂³×C₄₃	—	4	1	no	—
241	C₂³×C₄₃	—	8	2	no	—
242	C₂³×C₄₃	C₄×D₄	1	2	yes	—
243	C₂³×C₄₃	#120	1	1	yes	characteristic
244	C₂³×C₄₃	#120	1	1	yes	characteristic
245	C₂³×C₄₃	#121	1	2	yes	—
246	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
247	Q₈×C₄₃	—	2	2	no	—
248	Q₈×C₄₃	—	2	4	no	—
249	Q₈×C₄₃	—	2	2	no	—
250	Q₈×C₄₃	—	2	2	no	—
251	Q₈×C₄₃	—	4	1	no	—
252	Q₈×C₄₃	—	4	1	no	—
253	Q₈×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
254	D₄×C₄₃	—	2	4	no	—
255	D₄×C₄₃	—	2	4	no	—
256	D₄×C₄₃	—	2	8	no	—
257	D₄×C₄₃	—	2	2	no	—
258	D₄×C₄₃	—	2	2	no	—
259	D₄×C₄₃	—	2	2	no	—
260	D₄×C₄₃	—	2	4	no	—
261	D₄×C₄₃	—	4	4	no	—
262	D₄×C₄₃	—	4	4	no	—
263	D₄×C₄₃	—	4	1	no	—
264	D₄×C₄₃	—	4	1	no	—
265	D₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
266	C₂×C₄×C₄₃	—	2	2	no	—
267	C₂×C₄×C₄₃	—	2	4	no	—
268	C₂×C₄×C₄₃	—	2	4	no	—
269	C₂×C₄×C₄₃	—	2	4	no	—
270	C₂×C₄×C₄₃	—	2	8	no	—
271	C₂×C₄×C₄₃	—	2	4	no	—
272	C₂×C₄×C₄₃	—	2	2	no	—
273	C₂×C₄×C₄₃	—	2	4	no	—
274	C₂×C₄×C₄₃	—	2	4	no	—
275	C₂×C₄×C₄₃	—	4	2	no	—
276	C₂×C₄×C₄₃	—	4	8	no	—
277	C₂×C₄×C₄₃	—	4	1	no	—
278	C₂×C₄×C₄₃	—	4	2	no	—
279	C₂×C₄×C₄₃	—	4	1	no	—
280	C₂×C₄×C₄₃	—	4	4	no	—
281	C₂×C₄×C₄₃	—	4	4	no	—
282	C₂×C₄×C₄₃	—	4	4	no	—
283	C₂×C₄×C₄₃	—	8	2	no	—
284	C₂×C₄×C₄₃	—	8	8	no	—
285	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
286	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
287	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
288	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
289	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
290	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
291	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
292	C₂×C₄×C₄₃	#121	1	2	yes	—
293	C₂×C₄×C₄₃	#121	1	2	yes	—
294	C₂×C₄×C₄₃	#121	1	2	yes	—
295	C₂×C₄×C₄₃	#123	1	2	yes	—
296	C₂×C₄×C₄₃	#123	1	2	yes	—
297	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
298	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
302	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
303	C₈×C₄₃	—	2	4	no	—
304	C₈×C₄₃	—	4	2	no	—
305	#20942	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
306	C₂²×C₄₃	—	2	2	no	—
307	C₂²×C₄₃	—	2	2	no	—
308	C₂²×C₄₃	—	2	2	no	—
309	C₂²×C₄₃	—	2	4	no	—
310	C₂²×C₄₃	—	4	2	no	—
311	C₂²×C₄₃	—	4	2	no	—
312	C₂²×C₄₃	—	4	4	no	—
313	C₂²×C₄₃	—	4	4	no	—
314	C₂²×C₄₃	—	4	2	no	—
315	C₂²×C₄₃	—	8	4	no	—
316	C₂²×C₄₃	—	8	2	no	—
317	C₂²×C₄₃	—	8	2	no	—
318	C₂²×C₄₃	#386	1	2	yes	—
319	C₂²×C₄₃	#386	1	2	yes	—
320	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
321	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
322	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
323	C₄×C₄₃	—	2	4	no	—
324	C₄×C₄₃	—	4	4	no	—
325	C₄×C₄₃	—	4	4	no	—
326	C₄×C₄₃	—	4	4	no	—
327	C₄×C₄₃	—	4	2	no	—
328	C₄×C₄₃	#386	1	2	yes	—
329	C₄×C₄₃	#386	1	2	yes	—
330	C₄×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
331	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
332	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
333	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
334	C₂×#575	C₂×C₄₃	1	1	yes	characteristic
335	#3428	C₂×C₄₃	1	1	yes	characteristic, complemented
336	C₂²×#104	C₂×C₄₃	1	1	yes	characteristic, complemented
337	#2896	C₂×C₄₃	1	1	yes	characteristic, complemented
338	#2297	C₂×C₄₃	1	1	yes	characteristic, complemented
339	#1883	C₂×C₄₃	1	4	yes	complemented
340	#1882	C₂×C₄₃	1	4	yes	complemented
341	#1742	C₂×C₄₃	1	1	yes	characteristic, complemented
342	C₂×#339	C₂×C₄₃	1	1	yes	characteristic, complemented
343	C₂×C₄₃	—	2	1	no	—
344	C₂×C₄₃	—	2	1	no	—
345	C₂×C₄₃	—	2	2	no	—
346	C₂×C₄₃	—	2	2	no	—
347	C₂×C₄₃	—	4	4	no	—
348	C₂×C₄₃	—	8	2	no	—
349	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
350	C₂×C₄₃	#3018	1	2	yes	—
351	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
352	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
353	#575	—	2	4	no	—
354	#575	C₄×C₄₃	1	8	yes	complemented
355	C₂×#137	—	2	1	no	—
356	C₂×#137	C₂²×C₄₃	1	2	yes	—
357	C₂×AGL(1,ℤ/8)	—	2	1	no	—
358	C₂×AGL(1,ℤ/8)	C₂²×C₄₃	1	2	yes	—
359	C₂×#135	—	2	2	no	—
360	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
361	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
362	#520	—	2	2	no	—
363	#520	C₂²×C₄₃	1	4	yes	—
364	#519	—	2	1	no	—
365	#518	—	2	1	no	—
366	#518	—	2	2	no	—
367	C₄×#41	—	2	2	no	—
368	C₄×#41	—	2	2	no	—
369	C₂×#117	—	2	2	no	—
370	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
371	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
372	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
373	C₂×#104	—	2	4	no	—
374	C₂×#104	C₂²×C₄₃	1	4	yes	—
375	#419	C₂²×C₄₃	1	2	yes	complemented
376	#418	C₂²×C₄₃	1	2	yes	complemented
377	#417	—	2	2	no	—
378	#416	—	2	2	no	—
379	#391	C₂²×C₄₃	1	2	yes	complemented
380	#390	C₂²×C₄₃	1	2	yes	complemented
381	#386	—	2	2	no	—
382	C₄×C₂²⋊C₄	—	2	2	no	—
383	#343	C₂²×C₄₃	1	4	yes	complemented
384	#339	C₂²×C₄₃	1	4	yes	complemented
385	C₄₃	#20942	1	1	yes	characteristic, direct product factor, Sylow
386	C₂×#41	—	2	1	no	—
387	C₂×#41	—	2	1	no	—
388	C₂×#41	—	2	2	no	—
389	C₂×#41	—	2	2	no	—
390	C₂×#41	—	2	2	no	—
391	C₂×#41	—	2	1	no	—
392	C₂×#41	—	2	1	no	—
393	C₂×#41	—	2	2	no	—
394	C₂×#41	—	2	1	no	—
395	C₂×#41	—	2	1	no	—
396	C₂×#41	—	2	2	no	—
397	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
398	C₂×#41	C₂×C₄×C₄₃	1	4	yes	complemented
399	C₂×#41	D₄×C₄₃	1	4	yes	—
400	C₂×#41	D₄×C₄₃	1	2	yes	—
401	C₂×#41	C₂³×C₄₃	1	2	yes	—
402	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
403	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
404	C₂²×D₄	—	2	1	no	—
405	C₂²×D₄	—	2	1	no	—
406	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
407	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
408	C₂³×C₄	—	2	1	no	—
409	C₂³×C₄	—	2	1	no	—
410	C₂³×C₄	—	2	1	no	—
411	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
412	#137	—	2	4	no	—
413	#137	—	2	8	no	—
414	#137	C₂×C₄×C₄₃	1	8	yes	complemented
415	AGL(1,ℤ/8)	—	2	4	no	—
416	AGL(1,ℤ/8)	—	2	8	no	—
417	AGL(1,ℤ/8)	C₂×C₄×C₄₃	1	8	yes	complemented
418	#135	—	2	16	no	—
419	C₂×Q₁₆	—	2	2	no	—
420	C₂×SD₁₆	—	2	2	no	—
421	C₂×SD₁₆	—	2	2	no	—
422	C₂×D₈	—	2	2	no	—
423	C₂×M₁₆	—	2	1	no	—
424	C₂×M₁₆	—	2	2	no	—
425	C₂×M₁₆	—	2	1	no	—
426	C₂×M₁₆	—	2	2	no	—
427	C₂×M₁₆	—	2	2	no	—
428	C₂×M₁₆	C₂×C₄×C₄₃	1	4	yes	complemented
429	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
430	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
431	C₂²×C₈	—	2	1	no	—
432	C₂²×C₈	—	2	1	no	—
433	C₄×Q₈	—	2	4	no	—
434	C₄×Q₈	—	2	4	no	—
435	C₄×D₄	—	2	8	no	—
436	C₄×D₄	—	2	4	no	—
437	C₄×D₄	—	2	4	no	—
438	C₄×D₄	—	2	8	no	—
439	#117	—	2	4	no	—
440	#117	—	2	4	no	—
441	#117	—	2	1	no	—
442	#117	—	2	1	no	—
443	#117	—	2	1	no	—
444	#117	—	2	1	no	—
445	#117	—	2	1	no	—
446	#117	—	2	1	no	—
447	#117	—	2	4	no	—
448	#117	D₄×C₄₃	1	2	yes	—
449	#117	C₂³×C₄₃	1	2	yes	—
450	C₂×C₄⋊C₄	—	2	4	no	—
451	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
453	C₂×C₂²⋊C₄	—	2	4	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	4	no	—
456	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
457	C₂×C₄²	—	2	4	no	—
458	C₂×C₄²	—	2	1	no	—
459	C₂×C₄²	—	2	2	no	—
460	C₂×C₄²	—	2	2	no	—
461	C₂×C₄²	—	2	1	no	—
462	C₂×C₄²	D₄×C₄₃	1	2	yes	—
463	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
464	#104	—	2	8	no	—
465	#103	—	2	4	no	—
466	#102	—	2	4	no	—
467	#95	—	2	4	no	—
468	C₂⁴	—	2	1	no	—
469	C₂⁴	—	2	1	no	—
470	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
471	#41	—	2	4	no	—
472	#41	—	2	4	no	—
473	#41	—	2	4	no	—
474	#41	—	2	4	no	—
475	#41	—	2	4	no	—
476	#41	—	2	2	no	—
477	#41	—	2	2	no	—
478	#41	—	2	4	no	—
479	#41	—	2	4	no	—
480	#41	—	2	4	no	—
481	#41	—	2	4	no	—
482	#41	—	4	2	no	—
483	#41	—	4	2	no	—
484	#41	—	4	2	no	—
485	#41	—	4	2	no	—
486	#41	C₂²⋊C₄×C₄₃	1	8	yes	complemented
487	#41	C₂²×C₄×C₄₃	1	4	yes	—
488	#41	C₂×D₄×C₄₃	1	4	yes	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	2	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	C₂²⋊C₄×C₄₃	1	4	yes	complemented
497	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
498	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
499	C₂×D₄	—	2	4	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	4	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	4	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	2	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	4	1	no	—
512	C₂×D₄	—	4	1	no	—
513	C₂×D₄	—	4	2	no	—
514	C₂×D₄	C₂²⋊C₄×C₄₃	1	4	yes	complemented
515	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
516	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	8	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	4	no	—
527	C₂²×C₄	—	4	4	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	1	no	—
530	C₂²×C₄	—	4	1	no	—
531	C₂²×C₄	—	4	2	no	—
532	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
533	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
534	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
535	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
536	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
537	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
538	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
539	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
540	C₂²×C₄	#41×C₄₃	1	2	yes	—
541	C₂²×C₄	#41×C₄₃	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
543	Q₁₆	—	2	8	no	—
544	SD₁₆	—	2	8	no	—
545	SD₁₆	—	2	8	no	—
546	D₈	—	2	8	no	—
547	M₁₆	—	2	4	no	—
548	M₁₆	—	2	2	no	—
549	M₁₆	—	2	2	no	—
550	M₁₆	—	2	2	no	—
551	M₁₆	—	4	2	no	—
552	M₁₆	C₂²×C₄×C₄₃	1	4	yes	—
553	C₂×C₈	—	2	4	no	—
554	C₂×C₈	—	2	2	no	—
555	C₂×C₈	—	2	2	no	—
556	C₂×C₈	—	4	2	no	—
557	C₄⋊C₄	—	2	8	no	—
558	C₄⋊C₄	—	2	2	no	—
559	C₄⋊C₄	—	2	2	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
562	C₂²⋊C₄	—	2	8	no	—
563	C₂²⋊C₄	—	2	2	no	—
564	C₂²⋊C₄	—	2	2	no	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	4	8	no	—
568	C₄²	—	2	8	no	—
569	C₄²	—	2	2	no	—
570	C₄²	—	2	2	no	—
571	C₄²	—	2	2	no	—
572	C₄²	—	2	2	no	—
573	C₄²	—	2	2	no	—
574	C₄²	—	2	2	no	—
575	C₄²	—	4	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	4	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	4	2	no	—
580	C₂³	—	4	4	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	8	2	no	—
584	C₂³	C₄×D₄×C₄₃	1	2	yes	—
585	C₂³	#120×C₄₃	1	1	yes	characteristic
586	C₂³	#120×C₄₃	1	1	yes	characteristic
587	C₂³	#121×C₄₃	1	2	yes	—
588	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
589	Q₈	—	2	2	no	—
590	Q₈	—	2	4	no	—
591	Q₈	—	2	2	no	—
592	Q₈	—	2	2	no	—
593	Q₈	—	4	1	no	—
594	Q₈	—	4	1	no	—
595	Q₈	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
596	D₄	—	2	4	no	—
597	D₄	—	2	4	no	—
598	D₄	—	2	8	no	—
599	D₄	—	2	2	no	—
600	D₄	—	2	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	2	4	no	—
603	D₄	—	4	4	no	—
604	D₄	—	4	4	no	—
605	D₄	—	4	1	no	—
606	D₄	—	4	1	no	—
607	D₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	8	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	4	8	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	4	no	—
623	C₂×C₄	—	4	4	no	—
624	C₂×C₄	—	4	4	no	—
625	C₂×C₄	—	8	2	no	—
626	C₂×C₄	—	8	8	no	—
627	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
628	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
629	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
630	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
631	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
632	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
633	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
634	C₂×C₄	#121×C₄₃	1	2	yes	—
635	C₂×C₄	#121×C₄₃	1	2	yes	—
636	C₂×C₄	#121×C₄₃	1	2	yes	—
637	C₂×C₄	#123×C₄₃	1	2	yes	—
638	C₂×C₄	#123×C₄₃	1	2	yes	—
639	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
640	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
641	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
642	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
643	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
644	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
645	C₈	—	2	4	no	—
646	C₈	—	4	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	4	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	4	no	—
654	C₂²	—	4	4	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	8	4	no	—
657	C₂²	—	8	2	no	—
658	C₂²	—	8	2	no	—
659	C₂²	C₄₃×#386	1	2	yes	—
660	C₂²	C₄₃×#386	1	2	yes	—
661	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
662	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
663	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
664	C₄	—	2	4	no	—
665	C₄	—	4	4	no	—
666	C₄	—	4	4	no	—
667	C₄	—	4	4	no	—
668	C₄	—	4	2	no	—
669	C₄	C₄₃×#386	1	2	yes	—
670	C₄	C₄₃×#386	1	2	yes	—
671	C₄	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
672	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
673	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
674	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
675	C₂	—	2	1	no	—
676	C₂	—	2	1	no	—
677	C₂	—	2	2	no	—
678	C₂	—	2	2	no	—
679	C₂	—	4	4	no	—
680	C₂	—	8	2	no	—
681	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
682	C₂	C₄₃×#3018	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₃	#120
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂²×C₄₃	C₂×#120
prime radical	C₂×C₄₃×#575	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ C₂³×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#3428	C₂	semidirect
3. C₂²×#104×C₄₃	C₂	semidirect
4. C₄₃×#2896	C₂	semidirect
5. C₄₃×#2297	C₂	semidirect
6. C₄₃×#1883	C₂	semidirect
7. C₄₃×#1882	C₂	semidirect
8. C₄₃×#1742	C₂	semidirect
9. C₂×C₄₃×#339	C₂	semidirect
13. C₄₃×#575	C₄	semidirect
34. C₄₃×#419	C₂²	semidirect
35. C₄₃×#418	C₂²	semidirect
38. C₄₃×#391	C₂²	semidirect
39. C₄₃×#390	C₂²	semidirect
42. C₄₃×#343	C₂²	semidirect
43. C₄₃×#339	C₂²	semidirect
56. C₂×#41×C₄₃	C₂×C₄	semidirect
72. #137×C₄₃	C₂×C₄	semidirect
75. AGL(1,ℤ/8)×C₄₃	C₂×C₄	semidirect
86. C₂×M₁₆×C₄₃	C₂×C₄	semidirect
144. #41×C₄₃	C₂²⋊C₄	semidirect
154. C₂×Q₈×C₄₃	C₂²⋊C₄	semidirect
172. C₂×D₄×C₄₃	C₂²⋊C₄	semidirect
305. #20942	C₄₃	direct (N × H)
335. #3428	C₂×C₄₃	semidirect
336. C₂²×#104	C₂×C₄₃	semidirect
337. #2896	C₂×C₄₃	semidirect
338. #2297	C₂×C₄₃	semidirect
339. #1883	C₂×C₄₃	semidirect
340. #1882	C₂×C₄₃	semidirect
341. #1742	C₂×C₄₃	semidirect
342. C₂×#339	C₂×C₄₃	semidirect
354. #575	C₄×C₄₃	semidirect
375. #419	C₂²×C₄₃	semidirect
376. #418	C₂²×C₄₃	semidirect
379. #391	C₂²×C₄₃	semidirect
380. #390	C₂²×C₄₃	semidirect
383. #343	C₂²×C₄₃	semidirect
384. #339	C₂²×C₄₃	semidirect
385. C₄₃	#20942	direct (N × H)
398. C₂×#41	C₂×C₄×C₄₃	semidirect
414. #137	C₂×C₄×C₄₃	semidirect
417. AGL(1,ℤ/8)	C₂×C₄×C₄₃	semidirect
428. C₂×M₁₆	C₂×C₄×C₄₃	semidirect
486. #41	C₂²⋊C₄×C₄₃	semidirect
496. C₂×Q₈	C₂²⋊C₄×C₄₃	semidirect
514. C₂×D₄	C₂²⋊C₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#575	2
C₄₃×#3428	2
C₂²×#104×C₄₃	2
C₄₃×#2896	2
C₄₃×#2297	2
C₄₃×#1883	2
C₄₃×#1882	2
C₄₃×#1742	2
C₂×C₄₃×#339	2
#20942	43

Subgroups — C43×#20942 #24940959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20942 #24940959