Subgroups — C₄₃×#26336 #24946353

Order 11008.

966 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×#474	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#107×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2361	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2086	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2067	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1918	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1893	C₂	1	1	yes	maximal, characteristic
12	C₄₃×#1874	C₂	1	1	yes	maximal, characteristic
13	C₄₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
19	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₄₃	—	2	1	no	—
21	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#474	—	2	4	no	—
25	C₂×#107×C₄₃	—	2	4	no	—
26	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#398	—	2	1	no	—
40	C₄₃×#395	—	2	1	no	—
41	C₄₃×#390	C₂²	1	1	yes	characteristic
42	C₄₃×#389	C₂²	1	1	yes	characteristic
43	C₄₃×#389	C₂²	1	1	yes	characteristic
44	C₄₃×#389	C₂²	1	1	yes	characteristic
45	C₄₃×#388	—	2	1	no	—
46	C₄₃×#386	—	2	1	no	—
47	C₄₃×#385	—	2	1	no	—
48	C₄₃×#385	—	2	1	no	—
49	C₄₃×#384	C₂²	1	1	yes	characteristic
50	C₄₃×#380	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
53	C₄₃×#340	C₂²	1	1	yes	characteristic
54	C₄₃×#340	C₂²	1	1	yes	characteristic
55	C₄₃×#340	C₂²	1	1	yes	characteristic
56	C₄₃×#340	C₂²	1	1	yes	characteristic
57	C₄₃×#340	C₂²	1	1	yes	characteristic
58	C₄₃×#340	C₂²	1	1	yes	characteristic
59	C₄₃×#336	C₂²	1	1	yes	characteristic
60	C₄₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₄₃	—	2	1	no	—
62	C₂²×D₄×C₄₃	—	2	1	no	—
63	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₄₃	—	2	1	no	—
65	C₂³×C₄×C₄₃	—	2	1	no	—
66	C₂³×C₄×C₄₃	—	2	1	no	—
67	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₄₃	—	2	2	no	—
69	C₂²×C₈×C₄₃	—	2	2	no	—
70	C₂²×C₈×C₄₃	—	2	2	no	—
71	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
75	C₄⋊Q₈×C₄₃	—	2	2	no	—
76	C₄⋊Q₈×C₄₃	—	4	1	no	—
77	C₂²⋊Q₈×C₄₃	—	4	4	no	—
78	#121×C₄₃	—	2	2	no	—
79	#121×C₄₃	Q₈	1	4	yes	complemented
80	C₄×D₄×C₄₃	—	2	2	no	—
81	C₄×D₄×C₄₃	—	4	1	no	—
82	C₄×D₄×C₄₃	—	4	4	no	—
83	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
84	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
85	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
89	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
91	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
92	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
93	C₂×C₄⋊C₄×C₄₃	—	4	1	no	—
94	C₂×C₄⋊C₄×C₄₃	—	4	1	no	—
95	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₄₃	—	2	1	no	—
110	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
112	#107×C₄₃	—	2	2	no	—
113	#107×C₄₃	—	2	2	no	—
114	#107×C₄₃	—	2	2	no	—
115	#107×C₄₃	—	2	2	no	—
116	#107×C₄₃	—	4	1	no	—
117	#107×C₄₃	D₄	1	4	yes	complemented
118	C₄⋊C₈×C₄₃	—	2	2	no	—
119	C₄⋊C₈×C₄₃	—	2	2	no	—
120	#102×C₄₃	—	2	2	no	—
121	#102×C₄₃	—	2	2	no	—
122	#102×C₄₃	—	2	2	no	—
123	#102×C₄₃	—	4	1	no	—
124	C₂²⋊C₈×C₄₃	—	2	2	no	—
125	#95×C₄₃	—	2	1	no	—
126	#95×C₄₃	—	2	1	no	—
127	#95×C₄₃	—	2	1	no	—
128	#95×C₄₃	—	2	1	no	—
129	#95×C₄₃	—	2	1	no	—
130	#95×C₄₃	D₄	1	1	yes	characteristic
131	#95×C₄₃	D₄	1	1	yes	characteristic
132	C₂⁴×C₄₃	—	2	1	no	—
133	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₂×Q₈×C₄₃	—	4	2	no	—
135	C₂×Q₈×C₄₃	—	4	2	no	—
136	C₂×Q₈×C₄₃	—	8	1	no	—
137	C₂×D₄×C₄₃	—	2	1	no	—
138	C₂×D₄×C₄₃	—	2	4	no	—
139	C₂×D₄×C₄₃	—	2	1	no	—
140	C₂×D₄×C₄₃	—	2	1	no	—
141	C₂×D₄×C₄₃	—	2	1	no	—
142	C₂×D₄×C₄₃	—	2	1	no	—
143	C₂×D₄×C₄₃	—	4	2	no	—
144	C₂×D₄×C₄₃	—	4	2	no	—
145	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
146	C₂²×C₄×C₄₃	—	2	1	no	—
147	C₂²×C₄×C₄₃	—	2	1	no	—
148	C₂²×C₄×C₄₃	—	2	1	no	—
149	C₂²×C₄×C₄₃	—	2	1	no	—
150	C₂²×C₄×C₄₃	—	2	1	no	—
151	C₂²×C₄×C₄₃	—	2	1	no	—
152	C₂²×C₄×C₄₃	—	2	1	no	—
153	C₂²×C₄×C₄₃	—	2	1	no	—
154	C₂²×C₄×C₄₃	—	2	1	no	—
155	C₂²×C₄×C₄₃	—	2	1	no	—
156	C₂²×C₄×C₄₃	—	2	1	no	—
157	C₂²×C₄×C₄₃	—	4	2	no	—
158	C₂²×C₄×C₄₃	—	4	2	no	—
159	C₂²×C₄×C₄₃	—	4	2	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	—	8	1	no	—
164	C₂²×C₄×C₄₃	—	8	1	no	—
165	C₂²×C₄×C₄₃	—	8	1	no	—
166	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
172	C₂²×C₄×C₄₃	#41	1	2	yes	—
173	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
174	C₂×C₈×C₄₃	—	2	8	no	—
175	C₂×C₈×C₄₃	—	2	1	no	—
176	C₂×C₈×C₄₃	—	2	1	no	—
177	C₂×C₈×C₄₃	—	2	1	no	—
178	C₂×C₈×C₄₃	—	2	1	no	—
179	C₂×C₈×C₄₃	—	2	1	no	—
180	C₂×C₈×C₄₃	—	2	1	no	—
181	C₂×C₈×C₄₃	—	2	1	no	—
182	C₂×C₈×C₄₃	—	2	1	no	—
183	C₂×C₈×C₄₃	—	2	1	no	—
184	C₂×C₈×C₄₃	—	2	1	no	—
185	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
186	C₂×C₈×C₄₃	#41	1	2	yes	—
187	C₄⋊C₄×C₄₃	—	2	1	no	—
188	C₄⋊C₄×C₄₃	—	2	1	no	—
189	C₄⋊C₄×C₄₃	—	2	1	no	—
190	C₄⋊C₄×C₄₃	—	2	1	no	—
191	C₄⋊C₄×C₄₃	—	2	1	no	—
192	C₄⋊C₄×C₄₃	—	2	1	no	—
193	C₄⋊C₄×C₄₃	—	2	1	no	—
194	C₄⋊C₄×C₄₃	—	2	1	no	—
195	C₄⋊C₄×C₄₃	—	2	1	no	—
196	C₄⋊C₄×C₄₃	—	2	1	no	—
197	C₄⋊C₄×C₄₃	—	2	1	no	—
198	C₄⋊C₄×C₄₃	—	4	2	no	—
199	C₄⋊C₄×C₄₃	—	4	2	no	—
200	C₄⋊C₄×C₄₃	—	4	2	no	—
201	C₄⋊C₄×C₄₃	—	4	2	no	—
202	C₄⋊C₄×C₄₃	—	4	2	no	—
203	C₄⋊C₄×C₄₃	—	4	2	no	—
204	C₄⋊C₄×C₄₃	—	4	2	no	—
205	C₄⋊C₄×C₄₃	—	8	1	no	—
206	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
207	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
208	C₄⋊C₄×C₄₃	C₂×Q₈	1	2	yes	—
209	C₂²⋊C₄×C₄₃	—	2	4	no	—
210	C₂²⋊C₄×C₄₃	—	2	2	no	—
211	C₂²⋊C₄×C₄₃	—	4	2	no	—
212	C₂²⋊C₄×C₄₃	—	4	2	no	—
213	C₂²⋊C₄×C₄₃	—	4	2	no	—
214	C₂²⋊C₄×C₄₃	—	8	1	no	—
215	C₂²⋊C₄×C₄₃	D₈	1	4	yes	—
216	C₄²×C₄₃	—	2	1	no	—
217	C₄²×C₄₃	—	2	1	no	—
218	C₄²×C₄₃	—	2	1	no	—
219	C₄²×C₄₃	—	2	1	no	—
220	C₄²×C₄₃	—	4	2	no	—
221	C₂³×C₄₃	—	2	1	no	—
222	C₂³×C₄₃	—	2	1	no	—
223	C₂³×C₄₃	—	2	1	no	—
224	C₂³×C₄₃	—	2	1	no	—
225	C₂³×C₄₃	—	2	2	no	—
226	C₂³×C₄₃	—	4	1	no	—
227	C₂³×C₄₃	—	4	1	no	—
228	C₂³×C₄₃	—	4	1	no	—
229	C₂³×C₄₃	—	4	1	no	—
230	C₂³×C₄₃	—	4	1	no	—
231	C₂³×C₄₃	—	4	1	no	—
232	C₂³×C₄₃	C₂²⋊Q₈	1	2	yes	—
233	C₂³×C₄₃	C₂×D₈	1	2	yes	—
234	C₂³×C₄₃	#137	1	2	yes	—
235	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
236	Q₈×C₄₃	—	8	4	no	—
237	D₄×C₄₃	—	2	2	no	—
238	D₄×C₄₃	—	2	2	no	—
239	D₄×C₄₃	—	4	8	no	—
240	D₄×C₄₃	—	4	1	no	—
241	D₄×C₄₃	—	4	1	no	—
242	C₂×C₄×C₄₃	—	2	1	no	—
243	C₂×C₄×C₄₃	—	2	1	no	—
244	C₂×C₄×C₄₃	—	2	1	no	—
245	C₂×C₄×C₄₃	—	2	1	no	—
246	C₂×C₄×C₄₃	—	2	1	no	—
247	C₂×C₄×C₄₃	—	2	1	no	—
248	C₂×C₄×C₄₃	—	2	2	no	—
249	C₂×C₄×C₄₃	—	2	2	no	—
250	C₂×C₄×C₄₃	—	2	2	no	—
251	C₂×C₄×C₄₃	—	2	2	no	—
252	C₂×C₄×C₄₃	—	2	2	no	—
253	C₂×C₄×C₄₃	—	2	1	no	—
254	C₂×C₄×C₄₃	—	2	2	no	—
255	C₂×C₄×C₄₃	—	2	2	no	—
256	C₂×C₄×C₄₃	—	2	1	no	—
257	C₂×C₄×C₄₃	—	2	1	no	—
258	C₂×C₄×C₄₃	—	2	1	no	—
259	C₂×C₄×C₄₃	—	2	1	no	—
260	C₂×C₄×C₄₃	—	2	1	no	—
261	C₂×C₄×C₄₃	—	4	1	no	—
262	C₂×C₄×C₄₃	—	4	1	no	—
263	C₂×C₄×C₄₃	—	4	1	no	—
264	C₂×C₄×C₄₃	—	4	1	no	—
265	C₂×C₄×C₄₃	—	4	1	no	—
266	C₂×C₄×C₄₃	—	4	1	no	—
267	C₂×C₄×C₄₃	—	4	1	no	—
268	C₂×C₄×C₄₃	—	4	1	no	—
269	C₂×C₄×C₄₃	—	4	1	no	—
270	C₂×C₄×C₄₃	—	4	1	no	—
271	C₂×C₄×C₄₃	—	4	1	no	—
272	C₂×C₄×C₄₃	—	4	1	no	—
273	C₂×C₄×C₄₃	—	4	1	no	—
274	C₂×C₄×C₄₃	—	4	1	no	—
275	C₂×C₄×C₄₃	—	4	1	no	—
276	C₂×C₄×C₄₃	—	4	1	no	—
277	C₂×C₄×C₄₃	—	4	1	no	—
278	C₂×C₄×C₄₃	—	4	1	no	—
279	C₂×C₄×C₄₃	—	8	4	no	—
280	C₂×C₄×C₄₃	—	8	4	no	—
281	C₂×C₄×C₄₃	—	8	4	no	—
282	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
283	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
284	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
285	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
287	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
290	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
291	C₈×C₄₃	—	2	2	no	—
292	C₈×C₄₃	—	2	2	no	—
293	C₈×C₄₃	—	4	1	no	—
294	C₈×C₄₃	—	4	1	no	—
295	#26336	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
296	C₂²×C₄₃	—	2	2	no	—
297	C₂²×C₄₃	—	2	2	no	—
298	C₂²×C₄₃	—	2	2	no	—
299	C₂²×C₄₃	—	2	2	no	—
300	C₂²×C₄₃	—	2	2	no	—
301	C₂²×C₄₃	—	2	2	no	—
302	C₂²×C₄₃	—	4	2	no	—
303	C₂²×C₄₃	—	4	2	no	—
304	C₂²×C₄₃	—	4	2	no	—
305	C₂²×C₄₃	—	8	1	no	—
306	C₂²×C₄₃	—	8	1	no	—
307	C₂²×C₄₃	—	8	1	no	—
308	C₂²×C₄₃	—	8	1	no	—
309	C₂²×C₄₃	#474	1	4	yes	complemented
310	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
311	C₂²×C₄₃	D₄²	1	1	yes	characteristic
312	C₂²×C₄₃	#547	1	1	yes	characteristic
313	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
314	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
315	C₂²×C₄₃	#576	1	1	yes	characteristic
316	C₂²×C₄₃	#578	1	1	yes	characteristic
317	C₄×C₄₃	—	2	2	no	—
318	C₄×C₄₃	—	2	2	no	—
319	C₄×C₄₃	—	2	2	no	—
320	C₄×C₄₃	—	4	1	no	—
321	C₄×C₄₃	—	4	1	no	—
322	C₄×C₄₃	—	4	2	no	—
323	C₄×C₄₃	—	4	2	no	—
324	C₄×C₄₃	—	4	2	no	—
325	C₄×C₄₃	—	8	1	no	—
326	C₄×C₄₃	—	8	1	no	—
327	C₄×C₄₃	—	8	1	no	—
328	C₄×C₄₃	—	8	1	no	—
329	C₄×C₄₃	#525	1	1	yes	characteristic
330	C₄×C₄₃	#539	1	1	yes	characteristic
331	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
332	C₄×C₄₃	#554	1	1	yes	characteristic
333	C₂×#474	C₂×C₄₃	1	1	yes	characteristic, complemented
334	C₂²×#107	C₂×C₄₃	1	1	yes	characteristic, complemented
335	#2440	C₂×C₄₃	1	1	yes	characteristic, complemented
336	#2361	C₂×C₄₃	1	1	yes	characteristic
337	#2093	C₂×C₄₃	1	1	yes	characteristic, complemented
338	#2086	C₂×C₄₃	1	1	yes	characteristic, complemented
339	#2067	C₂×C₄₃	1	1	yes	characteristic, complemented
340	#2057	C₂×C₄₃	1	1	yes	characteristic, complemented
341	#1947	C₂×C₄₃	1	1	yes	characteristic, complemented
342	#1918	C₂×C₄₃	1	1	yes	characteristic, complemented
343	#1893	C₂×C₄₃	1	1	yes	characteristic
344	#1874	C₂×C₄₃	1	1	yes	characteristic
345	#1862	C₂×C₄₃	1	1	yes	characteristic, complemented
346	#1852	C₂×C₄₃	1	1	yes	characteristic, complemented
347	#1850	C₂×C₄₃	1	1	yes	characteristic, complemented
348	C₂×C₄₃	—	2	4	no	—
349	C₂×C₄₃	—	8	2	no	—
350	C₂×C₄₃	#2449	1	1	yes	characteristic
351	C₂×C₄₃	C₂×#474	1	1	yes	characteristic
352	C₂×C₄₃	#3083	1	1	yes	characteristic
353	C₂×C₄₃	#3270	1	1	yes	characteristic
354	C₂×C₄₃	D₄×D₈	1	1	yes	characteristic
355	C₂×C₄₃	#3334	1	1	yes	characteristic
356	C₂×C₄₃	#3346	1	1	yes	characteristic
357	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
358	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
359	C₂×C₂²⋊Q₈	—	2	1	no	—
360	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
361	C₂×C₄×D₄	—	2	1	no	—
362	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
363	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
364	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
365	#474	—	2	4	no	—
366	C₂×#107	—	2	4	no	—
367	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
368	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
369	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
370	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
371	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
372	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
373	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
374	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
375	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
376	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
377	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
378	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
379	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
380	#398	—	2	1	no	—
381	#395	—	2	1	no	—
382	#390	C₂²×C₄₃	1	1	yes	characteristic
383	#389	C₂²×C₄₃	1	1	yes	characteristic
384	#389	C₂²×C₄₃	1	1	yes	characteristic
385	#389	C₂²×C₄₃	1	1	yes	characteristic
386	#388	—	2	1	no	—
387	#386	—	2	1	no	—
388	#385	—	2	1	no	—
389	#385	—	2	1	no	—
390	#384	C₂²×C₄₃	1	1	yes	characteristic
391	#380	C₂²×C₄₃	1	1	yes	characteristic
392	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
393	C₄×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
394	#340	C₂²×C₄₃	1	1	yes	characteristic
395	#340	C₂²×C₄₃	1	1	yes	characteristic
396	#340	C₂²×C₄₃	1	1	yes	characteristic
397	#340	C₂²×C₄₃	1	1	yes	characteristic
398	#340	C₂²×C₄₃	1	1	yes	characteristic
399	#340	C₂²×C₄₃	1	1	yes	characteristic
400	#336	C₂²×C₄₃	1	1	yes	characteristic
401	#336	C₂²×C₄₃	1	1	yes	characteristic
402	C₄₃	#26336	1	1	yes	characteristic, direct product factor, Sylow
403	C₂²×Q₈	—	2	1	no	—
404	C₂²×D₄	—	2	1	no	—
405	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
406	C₂³×C₄	—	2	1	no	—
407	C₂³×C₄	—	2	1	no	—
408	C₂³×C₄	—	2	1	no	—
409	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
410	C₂²×C₈	—	2	2	no	—
411	C₂²×C₈	—	2	2	no	—
412	C₂²×C₈	—	2	2	no	—
413	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
414	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
415	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
416	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
417	C₄⋊Q₈	—	2	2	no	—
418	C₄⋊Q₈	—	4	1	no	—
419	C₂²⋊Q₈	—	4	4	no	—
420	#121	—	2	2	no	—
421	#121	Q₈×C₄₃	1	4	yes	complemented
422	C₄×D₄	—	2	2	no	—
423	C₄×D₄	—	4	1	no	—
424	C₄×D₄	—	4	4	no	—
425	C₂×C₄⋊C₄	—	2	2	no	—
426	C₂×C₄⋊C₄	—	2	2	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	4	1	no	—
436	C₂×C₄⋊C₄	—	4	1	no	—
437	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
451	C₂×C₄²	—	2	1	no	—
452	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
453	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
454	#107	—	2	2	no	—
455	#107	—	2	2	no	—
456	#107	—	2	2	no	—
457	#107	—	2	2	no	—
458	#107	—	4	1	no	—
459	#107	D₄×C₄₃	1	4	yes	complemented
460	C₄⋊C₈	—	2	2	no	—
461	C₄⋊C₈	—	2	2	no	—
462	#102	—	2	2	no	—
463	#102	—	2	2	no	—
464	#102	—	2	2	no	—
465	#102	—	4	1	no	—
466	C₂²⋊C₈	—	2	2	no	—
467	#95	—	2	1	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	D₄×C₄₃	1	1	yes	characteristic
473	#95	D₄×C₄₃	1	1	yes	characteristic
474	C₂⁴	—	2	1	no	—
475	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
476	C₂×Q₈	—	4	2	no	—
477	C₂×Q₈	—	4	2	no	—
478	C₂×Q₈	—	8	1	no	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	4	2	no	—
486	C₂×D₄	—	4	2	no	—
487	C₂×D₄	C₂×Q₈×C₄₃	1	2	yes	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	—	4	2	no	—
501	C₂²×C₄	—	4	2	no	—
502	C₂²×C₄	—	4	2	no	—
503	C₂²×C₄	—	4	2	no	—
504	C₂²×C₄	—	4	2	no	—
505	C₂²×C₄	—	8	1	no	—
506	C₂²×C₄	—	8	1	no	—
507	C₂²×C₄	—	8	1	no	—
508	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
512	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
513	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
514	C₂²×C₄	#41×C₄₃	1	2	yes	—
515	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
516	C₂×C₈	—	2	8	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
528	C₂×C₈	#41×C₄₃	1	2	yes	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	4	2	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	—	4	2	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	8	1	no	—
548	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
549	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
550	C₄⋊C₄	C₂×Q₈×C₄₃	1	2	yes	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	4	2	no	—
554	C₂²⋊C₄	—	4	2	no	—
555	C₂²⋊C₄	—	4	2	no	—
556	C₂²⋊C₄	—	8	1	no	—
557	C₂²⋊C₄	D₈×C₄₃	1	4	yes	—
558	C₄²	—	2	1	no	—
559	C₄²	—	2	1	no	—
560	C₄²	—	2	1	no	—
561	C₄²	—	2	1	no	—
562	C₄²	—	4	2	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	2	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	1	no	—
570	C₂³	—	4	1	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	C₂²⋊Q₈×C₄₃	1	2	yes	—
575	C₂³	C₂×D₈×C₄₃	1	2	yes	—
576	C₂³	#137×C₄₃	1	2	yes	—
577	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
578	Q₈	—	8	4	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	4	8	no	—
582	D₄	—	4	1	no	—
583	D₄	—	4	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	8	4	no	—
622	C₂×C₄	—	8	4	no	—
623	C₂×C₄	—	8	4	no	—
624	C₂×C₄	C₂²⋊Q₈×C₄₃	1	2	yes	—
625	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
626	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
627	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
628	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
629	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
630	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
631	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
632	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
633	C₈	—	2	2	no	—
634	C₈	—	2	2	no	—
635	C₈	—	4	1	no	—
636	C₈	—	4	1	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	4	2	no	—
644	C₂²	—	4	2	no	—
645	C₂²	—	4	2	no	—
646	C₂²	—	8	1	no	—
647	C₂²	—	8	1	no	—
648	C₂²	—	8	1	no	—
649	C₂²	—	8	1	no	—
650	C₂²	C₄₃×#474	1	4	yes	complemented
651	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
652	C₂²	D₄²×C₄₃	1	1	yes	characteristic
653	C₂²	C₄₃×#547	1	1	yes	characteristic
654	C₂²	C₂²×D₈×C₄₃	1	1	yes	characteristic
655	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
656	C₂²	C₄₃×#576	1	1	yes	characteristic
657	C₂²	C₄₃×#578	1	1	yes	characteristic
658	C₄	—	2	2	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	2	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	2	no	—
666	C₄	—	8	1	no	—
667	C₄	—	8	1	no	—
668	C₄	—	8	1	no	—
669	C₄	—	8	1	no	—
670	C₄	C₄₃×#525	1	1	yes	characteristic
671	C₄	C₄₃×#539	1	1	yes	characteristic
672	C₄	D₄×Q₈×C₄₃	1	1	yes	characteristic
673	C₄	C₄₃×#554	1	1	yes	characteristic
674	C₂	—	2	4	no	—
675	C₂	—	8	2	no	—
676	C₂	C₄₃×#2449	1	1	yes	characteristic
677	C₂	C₂×C₄₃×#474	1	1	yes	characteristic
678	C₂	C₄₃×#3083	1	1	yes	characteristic
679	C₂	C₄₃×#3270	1	1	yes	characteristic
680	C₂	D₄×D₈×C₄₃	1	1	yes	characteristic
681	C₂	C₄₃×#3334	1	1	yes	characteristic
682	C₂	C₄₃×#3346	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#121×C₄₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₄×C₂²⋊C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#474	C₂	semidirect
2. C₂²×#107×C₄₃	C₂	semidirect
3. C₄₃×#2440	C₂	semidirect
5. C₄₃×#2093	C₂	semidirect
6. C₄₃×#2086	C₂	semidirect
7. C₄₃×#2067	C₂	semidirect
8. C₄₃×#2057	C₂	semidirect
9. C₄₃×#1947	C₂	semidirect
10. C₄₃×#1918	C₂	semidirect
13. C₄₃×#1862	C₂	semidirect
14. C₄₃×#1852	C₂	semidirect
15. C₄₃×#1850	C₂	semidirect
79. #121×C₄₃	Q₈	semidirect
117. #107×C₄₃	D₄	semidirect
295. #26336	C₄₃	direct (N × H)
309. C₂²×C₄₃	#474	semidirect
333. C₂×#474	C₂×C₄₃	semidirect
334. C₂²×#107	C₂×C₄₃	semidirect
335. #2440	C₂×C₄₃	semidirect
337. #2093	C₂×C₄₃	semidirect
338. #2086	C₂×C₄₃	semidirect
339. #2067	C₂×C₄₃	semidirect
340. #2057	C₂×C₄₃	semidirect
341. #1947	C₂×C₄₃	semidirect
342. #1918	C₂×C₄₃	semidirect
345. #1862	C₂×C₄₃	semidirect
346. #1852	C₂×C₄₃	semidirect
347. #1850	C₂×C₄₃	semidirect
402. C₄₃	#26336	direct (N × H)
421. #121	Q₈×C₄₃	semidirect
459. #107	D₄×C₄₃	semidirect
650. C₂²	C₄₃×#474	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#474	2
C₂²×#107×C₄₃	2
C₄₃×#2440	2
C₄₃×#2361	2
C₄₃×#2093	2
C₄₃×#2086	2
C₄₃×#2067	2
C₄₃×#2057	2
C₄₃×#1947	2
C₄₃×#1918	2
C₄₃×#1893	2
C₄₃×#1874	2
C₄₃×#1862	2
C₄₃×#1852	2
C₄₃×#1850	2
#26336	43

Subgroups — C43×#26336 #24946353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#26336 #24946353