Subgroups — C₄₃×#28561 #24948578

Order 11008.

1060 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2416	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2076	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2054	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1936	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1895	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1874	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₃×#340	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#121×C₄₃	—	2	2	no	—
16	C₂×#121×C₄₃	C₂²	1	2	yes	—
17	C₂×#121×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
20	C₄₃×#466	—	2	4	no	—
21	C₄₃×#435	—	2	4	no	—
22	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#102×C₄₃	C₂²	1	2	yes	—
25	C₂×#102×C₄₃	C₂²	1	2	yes	—
26	C₂×#102×C₄₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#396	—	2	2	no	—
31	C₄₃×#394	—	2	2	no	—
32	C₄₃×#390	C₂²	1	2	yes	—
33	C₄₃×#389	C₂²	1	2	yes	—
34	C₄₃×#386	—	2	2	no	—
35	C₄₃×#380	C₂²	1	2	yes	—
36	C₄₃×#340	C₂²	1	2	yes	—
37	C₄₃×#340	C₂²	1	1	yes	characteristic
38	C₄₃×#340	C₂²	1	2	yes	—
39	C₄₃×#340	C₂²	1	1	yes	characteristic
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₂²×D₄×C₄₃	—	2	2	no	—
42	C₂²×D₄×C₄₃	—	2	2	no	—
43	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₃	—	2	2	no	—
46	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
48	C₂×D₈×C₄₃	—	2	2	no	—
49	C₂×D₈×C₄₃	—	4	2	no	—
50	C₂×M₁₆×C₄₃	—	2	2	no	—
51	C₂×M₁₆×C₄₃	—	4	2	no	—
52	C₂²×C₈×C₄₃	—	4	2	no	—
53	C₂²×C₈×C₄₃	D₄	1	4	yes	complemented
54	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
58	#121×C₄₃	—	2	4	no	—
59	#121×C₄₃	—	2	4	no	—
60	#121×C₄₃	—	2	4	no	—
61	#121×C₄₃	—	4	2	no	—
62	#121×C₄₃	—	4	8	no	—
63	C₄×D₄×C₄₃	—	2	2	no	—
64	C₄×D₄×C₄₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
69	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
81	#107×C₄₃	—	2	2	no	—
82	C₄⋊C₈×C₄₃	—	2	2	no	—
83	#102×C₄₃	—	2	4	no	—
84	#102×C₄₃	—	2	4	no	—
85	#102×C₄₃	—	4	2	no	—
86	C₂²⋊C₈×C₄₃	—	2	2	no	—
87	C₂²⋊C₈×C₄₃	—	2	2	no	—
88	#97×C₄₃	—	2	2	no	—
89	#95×C₄₃	—	2	2	no	—
90	#95×C₄₃	—	2	2	no	—
91	C₂⁴×C₄₃	—	2	2	no	—
92	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
94	C₂×D₄×C₄₃	—	2	2	no	—
95	C₂×D₄×C₄₃	—	2	4	no	—
96	C₂×D₄×C₄₃	—	2	2	no	—
97	C₂×D₄×C₄₃	—	2	2	no	—
98	C₂×D₄×C₄₃	—	2	2	no	—
99	C₂×D₄×C₄₃	—	2	2	no	—
100	C₂×D₄×C₄₃	—	2	2	no	—
101	C₂×D₄×C₄₃	—	2	2	no	—
102	C₂×D₄×C₄₃	—	4	4	no	—
103	C₂×D₄×C₄₃	—	4	4	no	—
104	C₂×D₄×C₄₃	—	4	4	no	—
105	C₂×D₄×C₄₃	—	4	4	no	—
106	C₂×D₄×C₄₃	—	4	4	no	—
107	C₂×D₄×C₄₃	—	8	2	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	—	2	1	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	—	2	2	no	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	4	4	no	—
118	C₂²×C₄×C₄₃	—	4	4	no	—
119	C₂²×C₄×C₄₃	—	8	2	no	—
120	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	#41	1	2	yes	—
126	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
127	D₈×C₄₃	—	4	4	no	—
128	M₁₆×C₄₃	—	4	4	no	—
129	C₂×C₈×C₄₃	—	2	2	no	—
130	C₂×C₈×C₄₃	—	2	2	no	—
131	C₂×C₈×C₄₃	—	2	1	no	—
132	C₂×C₈×C₄₃	—	2	1	no	—
133	C₂×C₈×C₄₃	—	2	2	no	—
134	C₂×C₈×C₄₃	—	2	2	no	—
135	C₂×C₈×C₄₃	—	4	4	no	—
136	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	—	2	2	no	—
141	C₄⋊C₄×C₄₃	—	2	2	no	—
142	C₄⋊C₄×C₄₃	—	2	2	no	—
143	C₄⋊C₄×C₄₃	—	2	2	no	—
144	C₄⋊C₄×C₄₃	—	4	4	no	—
145	C₄⋊C₄×C₄₃	—	4	4	no	—
146	C₄⋊C₄×C₄₃	#41	1	4	yes	—
147	C₂²⋊C₄×C₄₃	—	2	2	no	—
148	C₂²⋊C₄×C₄₃	—	2	2	no	—
149	C₂²⋊C₄×C₄₃	—	4	4	no	—
150	C₂²⋊C₄×C₄₃	—	4	4	no	—
151	C₂²⋊C₄×C₄₃	—	4	4	no	—
152	C₂²⋊C₄×C₄₃	—	4	4	no	—
153	C₂²⋊C₄×C₄₃	—	8	2	no	—
154	C₄²×C₄₃	—	2	1	no	—
155	C₄²×C₄₃	—	2	1	no	—
156	C₂³×C₄₃	—	2	2	no	—
157	C₂³×C₄₃	—	2	1	no	—
158	C₂³×C₄₃	—	2	1	no	—
159	C₂³×C₄₃	—	2	1	no	—
160	C₂³×C₄₃	—	2	2	no	—
161	C₂³×C₄₃	—	2	2	no	—
162	C₂³×C₄₃	—	2	1	no	—
163	C₂³×C₄₃	—	2	1	no	—
164	C₂³×C₄₃	—	4	2	no	—
165	C₂³×C₄₃	—	4	2	no	—
166	C₂³×C₄₃	—	4	2	no	—
167	C₂³×C₄₃	—	4	2	no	—
168	C₂³×C₄₃	—	4	2	no	—
169	C₂³×C₄₃	—	4	2	no	—
170	C₂³×C₄₃	—	4	2	no	—
171	C₂³×C₄₃	#121	1	2	yes	—
172	C₂³×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
173	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
174	D₄×C₄₃	—	4	4	no	—
175	D₄×C₄₃	—	4	2	no	—
176	D₄×C₄₃	—	4	2	no	—
177	D₄×C₄₃	—	4	2	no	—
178	D₄×C₄₃	—	4	2	no	—
179	D₄×C₄₃	—	8	8	no	—
180	D₄×C₄₃	—	8	8	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	2	4	no	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	2	1	no	—
188	C₂×C₄×C₄₃	—	2	2	no	—
189	C₂×C₄×C₄₃	—	2	4	no	—
190	C₂×C₄×C₄₃	—	2	2	no	—
191	C₂×C₄×C₄₃	—	2	1	no	—
192	C₂×C₄×C₄₃	—	2	1	no	—
193	C₂×C₄×C₄₃	—	4	2	no	—
194	C₂×C₄×C₄₃	—	4	2	no	—
195	C₂×C₄×C₄₃	—	4	1	no	—
196	C₂×C₄×C₄₃	—	4	1	no	—
197	C₂×C₄×C₄₃	—	4	2	no	—
198	C₂×C₄×C₄₃	—	4	2	no	—
199	C₂×C₄×C₄₃	—	4	2	no	—
200	C₂×C₄×C₄₃	—	4	2	no	—
201	C₂×C₄×C₄₃	—	4	2	no	—
202	C₂×C₄×C₄₃	—	4	2	no	—
203	C₂×C₄×C₄₃	—	4	2	no	—
204	C₂×C₄×C₄₃	—	8	8	no	—
205	C₂×C₄×C₄₃	#121	1	2	yes	—
206	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
208	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
210	C₈×C₄₃	—	2	2	no	—
211	C₈×C₄₃	—	2	2	no	—
212	C₈×C₄₃	—	4	1	no	—
213	C₈×C₄₃	—	4	1	no	—
214	#28561	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂²×C₄₃	—	2	4	no	—
216	C₂²×C₄₃	—	2	2	no	—
217	C₂²×C₄₃	—	2	2	no	—
218	C₂²×C₄₃	—	2	4	no	—
219	C₂²×C₄₃	—	4	1	no	—
220	C₂²×C₄₃	—	4	2	no	—
221	C₂²×C₄₃	—	4	1	no	—
222	C₂²×C₄₃	—	4	1	no	—
223	C₂²×C₄₃	—	4	2	no	—
224	C₂²×C₄₃	—	8	2	no	—
225	C₂²×C₄₃	—	8	2	no	—
226	C₂²×C₄₃	—	8	2	no	—
227	C₂²×C₄₃	—	8	2	no	—
228	C₂²×C₄₃	—	8	2	no	—
229	C₂²×C₄₃	—	8	2	no	—
230	C₂²×C₄₃	—	8	2	no	—
231	C₂²×C₄₃	#469	1	4	yes	—
232	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
233	C₂²×C₄₃	#546	1	2	yes	—
234	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
235	C₂²×C₄₃	#576	1	1	yes	characteristic
236	C₂²×C₄₃	#578	1	1	yes	characteristic
237	C₄×C₄₃	—	2	2	no	—
238	C₄×C₄₃	—	4	1	no	—
239	C₄×C₄₃	—	4	1	no	—
240	C₄×C₄₃	—	4	1	no	—
241	C₄×C₄₃	—	4	4	no	—
242	C₄×C₄₃	—	8	2	no	—
243	C₄×C₄₃	—	8	2	no	—
244	C₄×C₄₃	#532	1	1	yes	characteristic
245	C₄×C₄₃	#534	1	1	yes	characteristic
246	C₄×C₄₃	#553	1	2	yes	—
247	C₂×#466	C₂×C₄₃	1	1	yes	characteristic, complemented
248	C₂×#435	C₂×C₄₃	1	1	yes	characteristic, complemented
249	#2416	C₂×C₄₃	1	2	yes	complemented
250	#2087	C₂×C₄₃	1	1	yes	characteristic, complemented
251	#2076	C₂×C₄₃	1	1	yes	characteristic, complemented
252	#2054	C₂×C₄₃	1	1	yes	characteristic, complemented
253	#1999	C₂×C₄₃	1	1	yes	characteristic, complemented
254	#1936	C₂×C₄₃	1	2	yes	complemented
255	#1895	C₂×C₄₃	1	2	yes	complemented
256	#1874	C₂×C₄₃	1	2	yes	complemented
257	C₂×#340	C₂×C₄₃	1	1	yes	characteristic, complemented
258	C₂×C₄₃	—	2	4	no	—
259	C₂×C₄₃	—	8	1	no	—
260	C₂×C₄₃	—	16	2	no	—
261	C₂×C₄₃	#2543	1	1	yes	characteristic
262	C₂×C₄₃	C₂×#469	1	1	yes	characteristic
263	C₂×C₄₃	#3061	1	1	yes	characteristic
264	C₂×C₄₃	#3308	1	2	yes	—
265	C₂×C₄₃	#3318	1	2	yes	—
266	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic
267	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
268	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
269	C₂×#121	—	2	2	no	—
270	C₂×#121	C₂²×C₄₃	1	2	yes	—
271	C₂×#121	C₂²×C₄₃	1	2	yes	—
272	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
274	#466	—	2	4	no	—
275	#435	—	2	4	no	—
276	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
277	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
278	C₂×#102	C₂²×C₄₃	1	2	yes	—
279	C₂×#102	C₂²×C₄₃	1	2	yes	—
280	C₂×#102	C₂²×C₄₃	1	2	yes	—
281	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
282	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
283	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
284	#396	—	2	2	no	—
285	#394	—	2	2	no	—
286	#390	C₂²×C₄₃	1	2	yes	—
287	#389	C₂²×C₄₃	1	2	yes	—
288	#386	—	2	2	no	—
289	#380	C₂²×C₄₃	1	2	yes	—
290	#340	C₂²×C₄₃	1	1	yes	characteristic
291	#340	C₂²×C₄₃	1	2	yes	—
292	#340	C₂²×C₄₃	1	2	yes	—
293	#340	C₂²×C₄₃	1	1	yes	characteristic
294	#340	C₂²×C₄₃	1	2	yes	—
295	C₄₃	#28561	1	1	yes	characteristic, direct product factor, Sylow
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	—	2	2	no	—
298	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
299	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
300	C₂³×C₄	—	2	2	no	—
301	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
302	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
303	C₂×D₈	—	2	2	no	—
304	C₂×D₈	—	4	2	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	—	4	2	no	—
307	C₂²×C₈	—	4	2	no	—
308	C₂²×C₈	D₄×C₄₃	1	4	yes	complemented
309	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
313	#121	—	2	4	no	—
314	#121	—	2	4	no	—
315	#121	—	2	4	no	—
316	#121	—	4	2	no	—
317	#121	—	4	8	no	—
318	C₄×D₄	—	2	2	no	—
319	C₄×D₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	4	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	4	2	no	—
324	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
336	#107	—	2	2	no	—
337	C₄⋊C₈	—	2	2	no	—
338	#102	—	2	4	no	—
339	#102	—	2	4	no	—
340	#102	—	4	2	no	—
341	C₂²⋊C₈	—	2	2	no	—
342	C₂²⋊C₈	—	2	2	no	—
343	#97	—	2	2	no	—
344	#95	—	2	2	no	—
345	#95	—	2	2	no	—
346	C₂⁴	—	2	2	no	—
347	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
348	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	4	4	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	—	4	4	no	—
361	C₂×D₄	—	4	4	no	—
362	C₂×D₄	—	8	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	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	—	4	4	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	—	8	2	no	—
375	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
380	C₂²×C₄	#41×C₄₃	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
382	D₈	—	4	4	no	—
383	M₁₆	—	4	4	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	4	4	no	—
391	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
392	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	4	4	no	—
400	C₄⋊C₄	—	4	4	no	—
401	C₄⋊C₄	#41×C₄₃	1	4	yes	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	4	4	no	—
405	C₂²⋊C₄	—	4	4	no	—
406	C₂²⋊C₄	—	4	4	no	—
407	C₂²⋊C₄	—	4	4	no	—
408	C₂²⋊C₄	—	8	2	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	1	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	#121×C₄₃	1	2	yes	—
427	C₂³	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
428	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
429	D₄	—	4	4	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	2	no	—
434	D₄	—	8	8	no	—
435	D₄	—	8	8	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	8	8	no	—
460	C₂×C₄	#121×C₄₃	1	2	yes	—
461	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
462	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
463	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
464	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
465	C₈	—	2	2	no	—
466	C₈	—	2	2	no	—
467	C₈	—	4	1	no	—
468	C₈	—	4	1	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	8	2	no	—
481	C₂²	—	8	2	no	—
482	C₂²	—	8	2	no	—
483	C₂²	—	8	2	no	—
484	C₂²	—	8	2	no	—
485	C₂²	C₄₃×#469	1	4	yes	—
486	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
487	C₂²	C₄₃×#546	1	2	yes	—
488	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
489	C₂²	C₄₃×#576	1	1	yes	characteristic
490	C₂²	C₄₃×#578	1	1	yes	characteristic
491	C₄	—	2	2	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	4	no	—
496	C₄	—	8	2	no	—
497	C₄	—	8	2	no	—
498	C₄	C₄₃×#532	1	1	yes	characteristic
499	C₄	C₄₃×#534	1	1	yes	characteristic
500	C₄	C₄₃×#553	1	2	yes	—
501	C₂	—	2	4	no	—
502	C₂	—	8	1	no	—
503	C₂	—	16	2	no	—
504	C₂	C₄₃×#2543	1	1	yes	characteristic
505	C₂	C₂×C₄₃×#469	1	1	yes	characteristic
506	C₂	C₄₃×#3061	1	1	yes	characteristic
507	C₂	C₄₃×#3308	1	2	yes	—
508	C₂	C₄₃×#3318	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#466	C₂	semidirect
2. C₂×C₄₃×#435	C₂	semidirect
3. C₄₃×#2416	C₂	semidirect
4. C₄₃×#2087	C₂	semidirect
5. C₄₃×#2076	C₂	semidirect
6. C₄₃×#2054	C₂	semidirect
7. C₄₃×#1999	C₂	semidirect
8. C₄₃×#1936	C₂	semidirect
9. C₄₃×#1895	C₂	semidirect
10. C₄₃×#1874	C₂	semidirect
11. C₂×C₄₃×#340	C₂	semidirect
53. C₂²×C₈×C₄₃	D₄	semidirect
214. #28561	C₄₃	direct (N × H)
247. C₂×#466	C₂×C₄₃	semidirect
248. C₂×#435	C₂×C₄₃	semidirect
249. #2416	C₂×C₄₃	semidirect
250. #2087	C₂×C₄₃	semidirect
251. #2076	C₂×C₄₃	semidirect
252. #2054	C₂×C₄₃	semidirect
253. #1999	C₂×C₄₃	semidirect
254. #1936	C₂×C₄₃	semidirect
255. #1895	C₂×C₄₃	semidirect
256. #1874	C₂×C₄₃	semidirect
257. C₂×#340	C₂×C₄₃	semidirect
295. C₄₃	#28561	direct (N × H)
308. C₂²×C₈	D₄×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×#466	2
C₂×C₄₃×#435	2
C₄₃×#2416	2
C₄₃×#2087	2
C₄₃×#2076	2
C₄₃×#2054	2
C₄₃×#1999	2
C₄₃×#1936	2
C₄₃×#1895	2
C₄₃×#1874	2
C₂×C₄₃×#340	2
#28561	43

Subgroups — C43×#28561 #24948578

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28561 #24948578