Subgroups — C₄₃×#28578 #24948595

Order 11008.

1116 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#469	C₂	1	2	yes	maximal, complemented
2	C₄₃×#2856	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#121×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2071	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2041	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2011	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1926	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1895	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1879	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1728	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#121×C₄₃	—	2	1	no	—
16	C₂×#121×C₄₃	—	2	1	no	—
17	C₂×#121×C₄₃	C₂²	1	2	yes	—
18	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₃	—	2	1	no	—
20	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#469	—	2	8	no	—
23	C₂×#106×C₄₃	C₂²	1	2	yes	—
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×#102×C₄₃	C₂²	1	2	yes	—
28	C₄₃×#390	—	2	1	no	—
29	C₄₃×#390	—	2	1	no	—
30	C₄₃×#390	C₂²	1	1	yes	characteristic
31	C₄₃×#390	C₂²	1	2	yes	—
32	C₄₃×#389	C₂²	1	1	yes	characteristic
33	C₄₃×#388	—	2	1	no	—
34	C₄₃×#386	—	2	1	no	—
35	C₄₃×#384	C₂²	1	1	yes	characteristic
36	C₄₃×#380	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
39	C₄₃×#340	C₂²	1	2	yes	—
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₄₃×#336	C₂²	1	1	yes	characteristic
42	C₄₃×#336	C₂²	1	1	yes	characteristic
43	C₄₃×#336	C₂²	1	2	yes	—
44	C₂²×D₄×C₄₃	—	2	1	no	—
45	C₂²×D₄×C₄₃	—	2	2	no	—
46	C₂²×D₄×C₄₃	—	2	1	no	—
47	C₂²×D₄×C₄₃	—	2	1	no	—
48	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
49	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	—	2	1	no	—
51	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
54	C₂×D₈×C₄₃	—	2	4	no	—
55	C₂×D₈×C₄₃	—	2	4	no	—
56	C₂×D₈×C₄₃	—	4	2	no	—
57	C₂×M₁₆×C₄₃	—	2	4	no	—
58	C₂×M₁₆×C₄₃	—	2	4	no	—
59	C₂×M₁₆×C₄₃	—	4	2	no	—
60	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
61	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
62	#127×C₄₃	—	4	2	no	—
63	#121×C₄₃	—	2	2	no	—
64	#121×C₄₃	—	2	4	no	—
65	#121×C₄₃	—	2	4	no	—
66	#121×C₄₃	—	4	4	no	—
67	#121×C₄₃	—	4	4	no	—
68	#121×C₄₃	D₄	1	4	yes	complemented
69	C₄×D₄×C₄₃	—	4	2	no	—
70	C₄×D₄×C₄₃	—	4	4	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₄²×C₄₃	—	2	1	no	—
87	C₂×C₄²×C₄₃	—	4	2	no	—
88	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
92	#106×C₄₃	—	2	4	no	—
93	#102×C₄₃	—	2	4	no	—
94	#102×C₄₃	—	2	4	no	—
95	#102×C₄₃	—	2	4	no	—
96	#102×C₄₃	—	4	2	no	—
97	#95×C₄₃	—	2	1	no	—
98	#95×C₄₃	—	2	1	no	—
99	#95×C₄₃	—	2	1	no	—
100	C₂⁴×C₄₃	—	2	1	no	—
101	C₂⁴×C₄₃	—	2	2	no	—
102	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂×D₄×C₄₃	—	2	1	no	—
104	C₂×D₄×C₄₃	—	2	4	no	—
105	C₂×D₄×C₄₃	—	2	2	no	—
106	C₂×D₄×C₄₃	—	2	2	no	—
107	C₂×D₄×C₄₃	—	2	2	no	—
108	C₂×D₄×C₄₃	—	2	2	no	—
109	C₂×D₄×C₄₃	—	2	2	no	—
110	C₂×D₄×C₄₃	—	2	2	no	—
111	C₂×D₄×C₄₃	—	2	2	no	—
112	C₂×D₄×C₄₃	—	2	2	no	—
113	C₂×D₄×C₄₃	—	4	2	no	—
114	C₂×D₄×C₄₃	—	4	2	no	—
115	C₂×D₄×C₄₃	—	4	4	no	—
116	C₂×D₄×C₄₃	—	4	4	no	—
117	C₂×D₄×C₄₃	—	4	2	no	—
118	C₂×D₄×C₄₃	—	4	2	no	—
119	C₂×D₄×C₄₃	—	4	2	no	—
120	C₂×D₄×C₄₃	—	4	2	no	—
121	C₂×D₄×C₄₃	—	4	2	no	—
122	C₂×D₄×C₄₃	—	4	2	no	—
123	C₂×D₄×C₄₃	—	4	4	no	—
124	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₄₃	—	2	2	no	—
126	C₂²×C₄×C₄₃	—	2	2	no	—
127	C₂²×C₄×C₄₃	—	2	2	no	—
128	C₂²×C₄×C₄₃	—	2	2	no	—
129	C₂²×C₄×C₄₃	—	2	2	no	—
130	C₂²×C₄×C₄₃	—	2	1	no	—
131	C₂²×C₄×C₄₃	—	2	1	no	—
132	C₂²×C₄×C₄₃	—	2	1	no	—
133	C₂²×C₄×C₄₃	—	2	2	no	—
134	C₂²×C₄×C₄₃	—	4	1	no	—
135	C₂²×C₄×C₄₃	—	4	1	no	—
136	C₂²×C₄×C₄₃	—	4	1	no	—
137	C₂²×C₄×C₄₃	—	4	2	no	—
138	C₂²×C₄×C₄₃	—	4	2	no	—
139	C₂²×C₄×C₄₃	—	4	2	no	—
140	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₃	#41	1	2	yes	—
147	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
148	D₈×C₄₃	—	4	8	no	—
149	M₁₆×C₄₃	—	4	8	no	—
150	C₂×C₈×C₄₃	—	2	2	no	—
151	C₂×C₈×C₄₃	—	2	2	no	—
152	C₂×C₈×C₄₃	—	2	2	no	—
153	C₂×C₈×C₄₃	—	2	2	no	—
154	C₂×C₈×C₄₃	—	2	2	no	—
155	C₂×C₈×C₄₃	#41	1	4	yes	—
156	C₄⋊C₄×C₄₃	—	2	1	no	—
157	C₄⋊C₄×C₄₃	—	2	2	no	—
158	C₄⋊C₄×C₄₃	—	2	2	no	—
159	C₄⋊C₄×C₄₃	—	2	2	no	—
160	C₄⋊C₄×C₄₃	—	2	2	no	—
161	C₄⋊C₄×C₄₃	—	4	2	no	—
162	C₄⋊C₄×C₄₃	—	4	2	no	—
163	C₄⋊C₄×C₄₃	—	4	2	no	—
164	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
165	C₂²⋊C₄×C₄₃	—	2	4	no	—
166	C₂²⋊C₄×C₄₃	—	4	2	no	—
167	C₂²⋊C₄×C₄₃	—	4	2	no	—
168	C₂²⋊C₄×C₄₃	—	4	4	no	—
169	C₂²⋊C₄×C₄₃	—	4	4	no	—
170	C₂²⋊C₄×C₄₃	—	4	2	no	—
171	C₂²⋊C₄×C₄₃	—	4	2	no	—
172	C₂²⋊C₄×C₄₃	—	4	4	no	—
173	C₄²×C₄₃	—	2	2	no	—
174	C₄²×C₄₃	—	2	2	no	—
175	C₄²×C₄₃	—	4	1	no	—
176	C₄²×C₄₃	—	4	1	no	—
177	C₄²×C₄₃	—	4	2	no	—
178	C₂³×C₄₃	—	2	1	no	—
179	C₂³×C₄₃	—	2	1	no	—
180	C₂³×C₄₃	—	2	1	no	—
181	C₂³×C₄₃	—	2	1	no	—
182	C₂³×C₄₃	—	2	1	no	—
183	C₂³×C₄₃	—	2	1	no	—
184	C₂³×C₄₃	—	2	2	no	—
185	C₂³×C₄₃	—	4	1	no	—
186	C₂³×C₄₃	—	4	1	no	—
187	C₂³×C₄₃	—	4	1	no	—
188	C₂³×C₄₃	—	4	1	no	—
189	C₂³×C₄₃	—	4	1	no	—
190	C₂³×C₄₃	—	4	1	no	—
191	C₂³×C₄₃	—	4	2	no	—
192	C₂³×C₄₃	—	4	2	no	—
193	C₂³×C₄₃	—	4	2	no	—
194	C₂³×C₄₃	—	4	2	no	—
195	C₂³×C₄₃	—	4	2	no	—
196	C₂³×C₄₃	—	4	2	no	—
197	C₂³×C₄₃	—	4	2	no	—
198	C₂³×C₄₃	#121	1	2	yes	—
199	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
200	D₄×C₄₃	—	2	4	no	—
201	D₄×C₄₃	—	4	8	no	—
202	D₄×C₄₃	—	4	2	no	—
203	D₄×C₄₃	—	4	2	no	—
204	D₄×C₄₃	—	4	2	no	—
205	D₄×C₄₃	—	4	2	no	—
206	D₄×C₄₃	—	4	2	no	—
207	D₄×C₄₃	—	8	4	no	—
208	D₄×C₄₃	—	8	4	no	—
209	D₄×C₄₃	—	8	8	no	—
210	C₂×C₄×C₄₃	—	2	1	no	—
211	C₂×C₄×C₄₃	—	2	1	no	—
212	C₂×C₄×C₄₃	—	2	1	no	—
213	C₂×C₄×C₄₃	—	2	1	no	—
214	C₂×C₄×C₄₃	—	2	1	no	—
215	C₂×C₄×C₄₃	—	2	1	no	—
216	C₂×C₄×C₄₃	—	2	1	no	—
217	C₂×C₄×C₄₃	—	2	1	no	—
218	C₂×C₄×C₄₃	—	2	4	no	—
219	C₂×C₄×C₄₃	—	2	4	no	—
220	C₂×C₄×C₄₃	—	2	2	no	—
221	C₂×C₄×C₄₃	—	2	1	no	—
222	C₂×C₄×C₄₃	—	2	1	no	—
223	C₂×C₄×C₄₃	—	2	1	no	—
224	C₂×C₄×C₄₃	—	4	4	no	—
225	C₂×C₄×C₄₃	—	4	4	no	—
226	C₂×C₄×C₄₃	—	4	1	no	—
227	C₂×C₄×C₄₃	—	4	1	no	—
228	C₂×C₄×C₄₃	—	4	2	no	—
229	C₂×C₄×C₄₃	—	4	1	no	—
230	C₂×C₄×C₄₃	—	4	1	no	—
231	C₂×C₄×C₄₃	—	4	1	no	—
232	C₂×C₄×C₄₃	—	4	1	no	—
233	C₂×C₄×C₄₃	—	4	2	no	—
234	C₂×C₄×C₄₃	—	4	2	no	—
235	C₂×C₄×C₄₃	—	4	1	no	—
236	C₂×C₄×C₄₃	—	4	1	no	—
237	C₂×C₄×C₄₃	—	8	4	no	—
238	C₂×C₄×C₄₃	#121	1	2	yes	—
239	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
240	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
241	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
242	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
244	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
246	C₈×C₄₃	—	2	4	no	—
247	C₈×C₄₃	—	4	2	no	—
248	#28578	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
249	C₂²×C₄₃	—	2	2	no	—
250	C₂²×C₄₃	—	2	2	no	—
251	C₂²×C₄₃	—	2	2	no	—
252	C₂²×C₄₃	—	4	1	no	—
253	C₂²×C₄₃	—	4	1	no	—
254	C₂²×C₄₃	—	4	1	no	—
255	C₂²×C₄₃	—	4	1	no	—
256	C₂²×C₄₃	—	4	2	no	—
257	C₂²×C₄₃	—	4	2	no	—
258	C₂²×C₄₃	—	4	2	no	—
259	C₂²×C₄₃	—	8	1	no	—
260	C₂²×C₄₃	—	8	1	no	—
261	C₂²×C₄₃	—	8	1	no	—
262	C₂²×C₄₃	—	8	1	no	—
263	C₂²×C₄₃	—	8	2	no	—
264	C₂²×C₄₃	—	8	2	no	—
265	C₂²×C₄₃	—	8	2	no	—
266	C₂²×C₄₃	—	8	2	no	—
267	C₂²×C₄₃	—	8	2	no	—
268	C₂²×C₄₃	—	8	2	no	—
269	C₂²×C₄₃	—	8	2	no	—
270	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
271	C₂²×C₄₃	#532	1	1	yes	characteristic
272	C₂²×C₄₃	#534	1	1	yes	characteristic
273	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
274	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
275	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
276	C₂²×C₄₃	#575	1	1	yes	characteristic
277	C₄×C₄₃	—	2	2	no	—
278	C₄×C₄₃	—	2	2	no	—
279	C₄×C₄₃	—	2	2	no	—
280	C₄×C₄₃	—	2	2	no	—
281	C₄×C₄₃	—	4	1	no	—
282	C₄×C₄₃	—	4	2	no	—
283	C₄×C₄₃	—	8	1	no	—
284	C₄×C₄₃	—	8	1	no	—
285	C₄×C₄₃	—	8	2	no	—
286	C₄×C₄₃	#546	1	2	yes	—
287	C₄×C₄₃	#553	1	2	yes	—
288	C₂×#469	C₂×C₄₃	1	2	yes	complemented
289	#2856	C₂×C₄₃	1	1	yes	characteristic, complemented
290	C₄×#121	C₂×C₄₃	1	1	yes	characteristic, complemented
291	#2084	C₂×C₄₃	1	1	yes	characteristic, complemented
292	#2071	C₂×C₄₃	1	1	yes	characteristic, complemented
293	#2041	C₂×C₄₃	1	1	yes	characteristic, complemented
294	#2011	C₂×C₄₃	1	1	yes	characteristic, complemented
295	#1926	C₂×C₄₃	1	2	yes	complemented
296	#1895	C₂×C₄₃	1	2	yes	complemented
297	#1879	C₂×C₄₃	1	2	yes	complemented
298	#1728	C₂×C₄₃	1	1	yes	characteristic, complemented
299	C₂×C₄₃	—	4	2	no	—
300	C₂×C₄₃	—	8	2	no	—
301	C₂×C₄₃	—	16	2	no	—
302	C₂×C₄₃	#2543	1	1	yes	characteristic
303	C₂×C₄₃	#3036	1	1	yes	characteristic
304	C₂×C₄₃	#3038	1	1	yes	characteristic
305	C₂×C₄₃	#3171	1	1	yes	characteristic
306	C₂×C₄₃	#3184	1	1	yes	characteristic
307	C₂×C₄₃	#3192	1	1	yes	characteristic
308	C₂×C₄₃	#3194	1	1	yes	characteristic
309	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
310	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
311	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
312	C₂×#121	—	2	1	no	—
313	C₂×#121	—	2	1	no	—
314	C₂×#121	C₂²×C₄₃	1	2	yes	—
315	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
316	C₂×C₄×D₄	—	2	1	no	—
317	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
318	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
319	#469	—	2	8	no	—
320	C₂×#106	C₂²×C₄₃	1	2	yes	—
321	C₂×#102	C₂²×C₄₃	1	2	yes	—
322	C₂×#102	C₂²×C₄₃	1	2	yes	—
323	C₂×#102	C₂²×C₄₃	1	2	yes	—
324	C₂×#102	C₂²×C₄₃	1	2	yes	—
325	#390	—	2	1	no	—
326	#390	—	2	1	no	—
327	#390	C₂²×C₄₃	1	1	yes	characteristic
328	#390	C₂²×C₄₃	1	2	yes	—
329	#389	C₂²×C₄₃	1	1	yes	characteristic
330	#388	—	2	1	no	—
331	#386	—	2	1	no	—
332	#384	C₂²×C₄₃	1	1	yes	characteristic
333	#380	C₂²×C₄₃	1	1	yes	characteristic
334	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
335	C₄×C₂²⋊C₄	—	2	1	no	—
336	#340	C₂²×C₄₃	1	2	yes	—
337	#340	C₂²×C₄₃	1	2	yes	—
338	#336	C₂²×C₄₃	1	1	yes	characteristic
339	#336	C₂²×C₄₃	1	1	yes	characteristic
340	#336	C₂²×C₄₃	1	2	yes	—
341	C₄₃	#28578	1	1	yes	characteristic, direct product factor, Sylow
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	—	2	2	no	—
344	C₂²×D₄	—	2	1	no	—
345	C₂²×D₄	—	2	1	no	—
346	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
347	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
348	C₂³×C₄	—	2	1	no	—
349	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
350	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
351	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
352	C₂×D₈	—	2	4	no	—
353	C₂×D₈	—	2	4	no	—
354	C₂×D₈	—	4	2	no	—
355	C₂×M₁₆	—	2	4	no	—
356	C₂×M₁₆	—	2	4	no	—
357	C₂×M₁₆	—	4	2	no	—
358	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
359	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
360	#127	—	4	2	no	—
361	#121	—	2	2	no	—
362	#121	—	2	4	no	—
363	#121	—	2	4	no	—
364	#121	—	4	4	no	—
365	#121	—	4	4	no	—
366	#121	D₄×C₄₃	1	4	yes	complemented
367	C₄×D₄	—	4	2	no	—
368	C₄×D₄	—	4	4	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
374	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	—	4	2	no	—
386	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
387	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
388	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
390	#106	—	2	4	no	—
391	#102	—	2	4	no	—
392	#102	—	2	4	no	—
393	#102	—	2	4	no	—
394	#102	—	4	2	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	#95	—	2	1	no	—
398	C₂⁴	—	2	1	no	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	4	2	no	—
412	C₂×D₄	—	4	2	no	—
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	—	4	2	no	—
416	C₂×D₄	—	4	2	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	—	4	4	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	—	4	2	no	—
422	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	4	1	no	—
433	C₂²×C₄	—	4	1	no	—
434	C₂²×C₄	—	4	1	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
441	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
444	C₂²×C₄	#41×C₄₃	1	2	yes	—
445	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
446	D₈	—	4	8	no	—
447	M₁₆	—	4	8	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	#41×C₄₃	1	4	yes	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	4	2	no	—
460	C₄⋊C₄	—	4	2	no	—
461	C₄⋊C₄	—	4	2	no	—
462	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₂²⋊C₄	—	4	4	no	—
466	C₂²⋊C₄	—	4	2	no	—
467	C₂²⋊C₄	—	4	4	no	—
468	C₂²⋊C₄	—	4	2	no	—
469	C₂²⋊C₄	—	4	4	no	—
470	C₂²⋊C₄	—	4	2	no	—
471	C₄²	—	2	2	no	—
472	C₄²	—	2	2	no	—
473	C₄²	—	4	1	no	—
474	C₄²	—	4	1	no	—
475	C₄²	—	4	2	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	1	no	—
479	C₂³	—	2	1	no	—
480	C₂³	—	2	1	no	—
481	C₂³	—	2	1	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	1	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	2	no	—
496	C₂³	#121×C₄₃	1	2	yes	—
497	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
498	D₄	—	2	4	no	—
499	D₄	—	4	8	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	2	no	—
503	D₄	—	4	2	no	—
504	D₄	—	4	2	no	—
505	D₄	—	8	4	no	—
506	D₄	—	8	4	no	—
507	D₄	—	8	8	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	4	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	8	4	no	—
536	C₂×C₄	#121×C₄₃	1	2	yes	—
537	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
538	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
539	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
540	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
541	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
542	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
543	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
544	C₈	—	2	4	no	—
545	C₈	—	4	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	8	1	no	—
557	C₂²	—	8	1	no	—
558	C₂²	—	8	1	no	—
559	C₂²	—	8	1	no	—
560	C₂²	—	8	2	no	—
561	C₂²	—	8	2	no	—
562	C₂²	—	8	2	no	—
563	C₂²	—	8	2	no	—
564	C₂²	—	8	2	no	—
565	C₂²	—	8	2	no	—
566	C₂²	—	8	2	no	—
567	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
568	C₂²	C₄₃×#532	1	1	yes	characteristic
569	C₂²	C₄₃×#534	1	1	yes	characteristic
570	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
571	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
572	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
573	C₂²	C₄₃×#575	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	2	no	—
580	C₄	—	8	1	no	—
581	C₄	—	8	1	no	—
582	C₄	—	8	2	no	—
583	C₄	C₄₃×#546	1	2	yes	—
584	C₄	C₄₃×#553	1	2	yes	—
585	C₂	—	4	2	no	—
586	C₂	—	8	2	no	—
587	C₂	—	16	2	no	—
588	C₂	C₄₃×#2543	1	1	yes	characteristic
589	C₂	C₄₃×#3036	1	1	yes	characteristic
590	C₂	C₄₃×#3038	1	1	yes	characteristic
591	C₂	C₄₃×#3171	1	1	yes	characteristic
592	C₂	C₄₃×#3184	1	1	yes	characteristic
593	C₂	C₄₃×#3192	1	1	yes	characteristic
594	C₂	C₄₃×#3194	1	1	yes	characteristic

	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 ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#469	C₂	semidirect
2. C₄₃×#2856	C₂	semidirect
3. C₄×#121×C₄₃	C₂	semidirect
4. C₄₃×#2084	C₂	semidirect
5. C₄₃×#2071	C₂	semidirect
6. C₄₃×#2041	C₂	semidirect
7. C₄₃×#2011	C₂	semidirect
8. C₄₃×#1926	C₂	semidirect
9. C₄₃×#1895	C₂	semidirect
10. C₄₃×#1879	C₂	semidirect
11. C₄₃×#1728	C₂	semidirect
68. #121×C₄₃	D₄	semidirect
248. #28578	C₄₃	direct (N × H)
288. C₂×#469	C₂×C₄₃	semidirect
289. #2856	C₂×C₄₃	semidirect
290. C₄×#121	C₂×C₄₃	semidirect
291. #2084	C₂×C₄₃	semidirect
292. #2071	C₂×C₄₃	semidirect
293. #2041	C₂×C₄₃	semidirect
294. #2011	C₂×C₄₃	semidirect
295. #1926	C₂×C₄₃	semidirect
296. #1895	C₂×C₄₃	semidirect
297. #1879	C₂×C₄₃	semidirect
298. #1728	C₂×C₄₃	semidirect
341. C₄₃	#28578	direct (N × H)
366. #121	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×#469	2
C₄₃×#2856	2
C₄×#121×C₄₃	2
C₄₃×#2084	2
C₄₃×#2071	2
C₄₃×#2041	2
C₄₃×#2011	2
C₄₃×#1926	2
C₄₃×#1895	2
C₄₃×#1879	2
C₄₃×#1728	2
#28578	43

Subgroups — C43×#28578 #24948595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28578 #24948595