Subgroups — C₄₃×#25776 #24945793

Order 11008.

1656 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×SD₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#495	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#447	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#2436	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2435	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×#1968	C₂	1	2	yes	maximal, complemented
11	C₈×C₂²⋊C₄×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	—	2	8	no	—
16	C₂²×SD₁₆×C₄₃	—	2	4	no	—
17	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
18	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
21	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#124×C₄₃	C₂²	1	2	yes	—
23	C₂×#124×C₄₃	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
26	C₄₃×#495	—	2	8	no	—
27	C₄₃×#465	—	2	4	no	—
28	C₄₃×#451	—	2	4	no	—
29	C₄₃×#447	—	2	4	no	—
30	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×#103×C₄₃	C₂²	1	2	yes	complemented
32	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×#102×C₄₃	C₂²	1	2	yes	—
34	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	complemented
37	C₄₃×#394	—	2	2	no	—
38	C₄₃×#393	—	2	2	no	—
39	C₄₃×#391	C₂²	1	2	yes	complemented
40	C₄₃×#390	C₂²	1	2	yes	—
41	C₄₃×#386	—	2	2	no	—
42	C₄₃×#379	—	2	2	no	—
43	C₄×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#336	C₂²	1	2	yes	complemented
45	C₂⁵×C₄₃	—	2	1	no	—
46	C₂²×Q₈×C₄₃	—	2	1	no	—
47	C₂²×Q₈×C₄₃	—	2	4	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	2	no	—
56	C₂²×D₄×C₄₃	—	2	2	no	—
57	C₂²×D₄×C₄₃	—	2	1	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	C₂³	1	1	yes	characteristic
63	C₂×Q₁₆×C₄₃	—	2	4	no	—
64	C₂×Q₁₆×C₄₃	—	2	4	no	—
65	C₂×Q₁₆×C₄₃	—	4	2	no	—
66	C₂×SD₁₆×C₄₃	—	2	32	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	—	2	4	no	—
72	C₂×SD₁₆×C₄₃	—	2	2	no	—
73	C₂×SD₁₆×C₄₃	—	2	4	no	—
74	C₂×SD₁₆×C₄₃	D₄	1	8	yes	complemented
75	C₂×D₈×C₄₃	—	2	4	no	—
76	C₂×D₈×C₄₃	—	2	4	no	—
77	C₂×D₈×C₄₃	—	4	2	no	—
78	C₂²×C₈×C₄₃	—	2	4	no	—
79	C₂²×C₈×C₄₃	D₄	1	4	yes	—
80	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
82	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
83	#124×C₄₃	—	2	4	no	—
84	#124×C₄₃	—	2	4	no	—
85	#124×C₄₃	—	4	2	no	—
86	#124×C₄₃	—	4	2	no	—
87	C₂²⋊Q₈×C₄₃	—	2	2	no	—
88	C₂²⋊Q₈×C₄₃	—	2	2	no	—
89	#121×C₄₃	—	2	2	no	—
90	#121×C₄₃	—	2	2	no	—
91	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
92	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
97	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
98	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
99	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
100	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
101	#106×C₄₃	—	2	2	no	—
102	#103×C₄₃	—	2	4	no	—
103	#103×C₄₃	—	2	2	no	—
104	#102×C₄₃	—	2	4	no	—
105	#102×C₄₃	—	2	2	no	—
106	C₂²⋊C₈×C₄₃	D₄	1	4	yes	—
107	C₄×C₈×C₄₃	—	2	4	no	—
108	#95×C₄₃	—	2	4	no	—
109	#95×C₄₃	D₄	1	2	yes	—
110	C₂⁴×C₄₃	—	2	2	no	—
111	C₂⁴×C₄₃	—	2	1	no	—
112	C₂⁴×C₄₃	—	4	4	no	—
113	C₂⁴×C₄₃	—	4	2	no	—
114	C₂⁴×C₄₃	—	4	4	no	—
115	C₂⁴×C₄₃	—	8	2	no	—
116	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂×Q₈×C₄₃	—	2	2	no	—
118	C₂×Q₈×C₄₃	—	2	8	no	—
119	C₂×Q₈×C₄₃	—	2	2	no	—
120	C₂×Q₈×C₄₃	—	2	2	no	—
121	C₂×Q₈×C₄₃	—	2	2	no	—
122	C₂×Q₈×C₄₃	—	2	1	no	—
123	C₂×Q₈×C₄₃	—	2	1	no	—
124	C₂×Q₈×C₄₃	—	2	2	no	—
125	C₂×Q₈×C₄₃	—	2	2	no	—
126	C₂×Q₈×C₄₃	—	2	2	no	—
127	C₂×Q₈×C₄₃	—	4	4	no	—
128	C₂×Q₈×C₄₃	—	4	8	no	—
129	C₂×Q₈×C₄₃	—	4	4	no	—
130	C₂×Q₈×C₄₃	—	4	2	no	—
131	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
132	C₂×D₄×C₄₃	—	2	2	no	—
133	C₂×D₄×C₄₃	—	2	8	no	—
134	C₂×D₄×C₄₃	—	2	2	no	—
135	C₂×D₄×C₄₃	—	2	2	no	—
136	C₂×D₄×C₄₃	—	2	2	no	—
137	C₂×D₄×C₄₃	—	2	1	no	—
138	C₂×D₄×C₄₃	—	2	1	no	—
139	C₂×D₄×C₄₃	—	2	2	no	—
140	C₂×D₄×C₄₃	—	2	2	no	—
141	C₂×D₄×C₄₃	—	2	2	no	—
142	C₂×D₄×C₄₃	—	4	4	no	—
143	C₂×D₄×C₄₃	—	4	8	no	—
144	C₂×D₄×C₄₃	—	4	4	no	—
145	C₂×D₄×C₄₃	—	4	2	no	—
146	C₂×D₄×C₄₃	—	4	2	no	—
147	C₂×D₄×C₄₃	—	4	4	no	—
148	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₄₃	—	2	2	no	—
150	C₂²×C₄×C₄₃	—	2	2	no	—
151	C₂²×C₄×C₄₃	—	2	2	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	—	4	4	no	—
156	C₂²×C₄×C₄₃	—	4	2	no	—
157	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
162	Q₁₆×C₄₃	—	4	8	no	—
163	SD₁₆×C₄₃	—	2	16	no	—
164	SD₁₆×C₄₃	—	2	16	no	—
165	SD₁₆×C₄₃	—	4	4	no	—
166	D₈×C₄₃	—	4	8	no	—
167	C₂×C₈×C₄₃	—	2	2	no	—
168	C₂×C₈×C₄₃	—	2	2	no	—
169	C₂×C₈×C₄₃	—	2	2	no	—
170	C₂×C₈×C₄₃	—	2	8	no	—
171	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
172	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
173	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
174	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
175	C₄⋊C₄×C₄₃	—	2	1	no	—
176	C₄⋊C₄×C₄₃	—	2	1	no	—
177	C₄⋊C₄×C₄₃	—	2	1	no	—
178	C₄⋊C₄×C₄₃	—	2	1	no	—
179	C₄⋊C₄×C₄₃	—	4	2	no	—
180	C₂²⋊C₄×C₄₃	—	2	4	no	—
181	C₂²⋊C₄×C₄₃	—	4	8	no	—
182	C₂²⋊C₄×C₄₃	—	4	8	no	—
183	C₂²⋊C₄×C₄₃	—	4	2	no	—
184	C₂²⋊C₄×C₄₃	—	4	2	no	—
185	C₂²⋊C₄×C₄₃	—	8	4	no	—
186	C₄²×C₄₃	—	2	2	no	—
187	C₄²×C₄₃	—	2	2	no	—
188	C₂³×C₄₃	—	2	2	no	—
189	C₂³×C₄₃	—	2	2	no	—
190	C₂³×C₄₃	—	2	4	no	—
191	C₂³×C₄₃	—	4	8	no	—
192	C₂³×C₄₃	—	4	2	no	—
193	C₂³×C₄₃	—	4	2	no	—
194	C₂³×C₄₃	—	4	4	no	—
195	C₂³×C₄₃	—	4	4	no	—
196	C₂³×C₄₃	—	4	1	no	—
197	C₂³×C₄₃	—	4	2	no	—
198	C₂³×C₄₃	—	4	2	no	—
199	C₂³×C₄₃	—	4	2	no	—
200	C₂³×C₄₃	—	8	16	no	—
201	C₂³×C₄₃	—	8	4	no	—
202	C₂³×C₄₃	—	8	4	no	—
203	C₂³×C₄₃	#127	1	2	yes	—
204	C₂³×C₄₃	#135	1	4	yes	—
205	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
206	Q₈×C₄₃	—	2	4	no	—
207	Q₈×C₄₃	—	2	4	no	—
208	Q₈×C₄₃	—	4	8	no	—
209	Q₈×C₄₃	—	4	2	no	—
210	Q₈×C₄₃	—	4	2	no	—
211	Q₈×C₄₃	—	4	1	no	—
212	Q₈×C₄₃	—	4	1	no	—
213	Q₈×C₄₃	—	4	2	no	—
214	D₄×C₄₃	—	2	4	no	—
215	D₄×C₄₃	—	2	4	no	—
216	D₄×C₄₃	—	4	8	no	—
217	D₄×C₄₃	—	4	1	no	—
218	D₄×C₄₃	—	4	2	no	—
219	D₄×C₄₃	—	4	1	no	—
220	D₄×C₄₃	—	4	2	no	—
221	D₄×C₄₃	—	4	2	no	—
222	D₄×C₄₃	—	8	4	no	—
223	C₂×C₄×C₄₃	—	2	2	no	—
224	C₂×C₄×C₄₃	—	2	2	no	—
225	C₂×C₄×C₄₃	—	2	2	no	—
226	C₂×C₄×C₄₃	—	2	4	no	—
227	C₂×C₄×C₄₃	—	2	4	no	—
228	C₂×C₄×C₄₃	—	2	4	no	—
229	C₂×C₄×C₄₃	—	2	4	no	—
230	C₂×C₄×C₄₃	—	2	4	no	—
231	C₂×C₄×C₄₃	—	4	8	no	—
232	C₂×C₄×C₄₃	—	4	2	no	—
233	C₂×C₄×C₄₃	—	4	2	no	—
234	C₂×C₄×C₄₃	—	4	1	no	—
235	C₂×C₄×C₄₃	—	4	1	no	—
236	C₂×C₄×C₄₃	—	4	1	no	—
237	C₂×C₄×C₄₃	—	4	2	no	—
238	C₂×C₄×C₄₃	—	4	2	no	—
239	C₂×C₄×C₄₃	—	4	2	no	—
240	C₂×C₄×C₄₃	#127	1	2	yes	—
241	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
245	C₈×C₄₃	—	2	2	no	—
246	C₈×C₄₃	—	2	4	no	—
247	C₈×C₄₃	#120	1	4	yes	—
248	#25776	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	8	no	—
252	C₂²×C₄₃	—	4	4	no	—
253	C₂²×C₄₃	—	4	8	no	—
254	C₂²×C₄₃	—	8	16	no	—
255	C₂²×C₄₃	—	8	2	no	—
256	C₂²×C₄₃	—	8	2	no	—
257	C₂²×C₄₃	—	8	4	no	—
258	C₂²×C₄₃	—	8	1	no	—
259	C₂²×C₄₃	—	8	1	no	—
260	C₂²×C₄₃	—	8	1	no	—
261	C₂²×C₄₃	—	8	4	no	—
262	C₂²×C₄₃	#495	1	4	yes	complemented
263	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
264	C₂²×C₄₃	D₄²	1	2	yes	—
265	C₂²×C₄₃	C₂×#135	1	2	yes	—
266	C₂²×C₄₃	#577	1	2	yes	—
267	C₄×C₄₃	—	2	2	no	—
268	C₄×C₄₃	—	4	4	no	—
269	C₄×C₄₃	—	4	4	no	—
270	C₄×C₄₃	—	8	1	no	—
271	C₄×C₄₃	—	8	1	no	—
272	C₄×C₄₃	—	8	1	no	—
273	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
274	C₄×C₄₃	#535	1	1	yes	characteristic
275	C₄×C₄₃	D₄²	1	2	yes	—
276	C₂³×SD₁₆	C₂×C₄₃	1	1	yes	characteristic, complemented
277	C₂×#495	C₂×C₄₃	1	2	yes	complemented
278	C₂×#465	C₂×C₄₃	1	1	yes	characteristic, complemented
279	C₂×#451	C₂×C₄₃	1	1	yes	characteristic, complemented
280	C₂×#447	C₂×C₄₃	1	1	yes	characteristic
281	#2436	C₂×C₄₃	1	1	yes	characteristic, complemented
282	#2435	C₂×C₄₃	1	1	yes	characteristic, complemented
283	#2015	C₂×C₄₃	1	2	yes	complemented
284	#2012	C₂×C₄₃	1	2	yes	complemented
285	#1968	C₂×C₄₃	1	2	yes	complemented
286	C₈×C₂²⋊C₄	C₂×C₄₃	1	1	yes	characteristic, complemented
287	C₂×C₄₃	—	2	4	no	—
288	C₂×C₄₃	—	8	4	no	—
289	C₂×C₄₃	—	16	1	no	—
290	C₂×C₄₃	#2433	1	1	yes	characteristic
291	C₂×C₄₃	C₂×#495	1	1	yes	characteristic
292	C₂×C₄₃	#3154	1	1	yes	characteristic
293	C₂×C₄₃	#3282	1	4	yes	—
294	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
295	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
296	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	complemented
297	C₂²×SD₁₆	—	2	8	no	—
298	C₂²×SD₁₆	—	2	4	no	—
299	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
300	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
301	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic, complemented
302	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
303	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
304	C₂×#124	C₂²×C₄₃	1	2	yes	—
305	C₂×#124	C₂²×C₄₃	1	2	yes	complemented
306	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
307	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
308	#495	—	2	8	no	—
309	#465	—	2	4	no	—
310	#451	—	2	4	no	—
311	#447	—	2	4	no	—
312	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic, complemented
313	C₂×#103	C₂²×C₄₃	1	2	yes	complemented
314	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic, complemented
315	C₂×#102	C₂²×C₄₃	1	2	yes	—
316	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic, complemented
317	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
318	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	complemented
319	#394	—	2	2	no	—
320	#393	—	2	2	no	—
321	#391	C₂²×C₄₃	1	2	yes	complemented
322	#390	C₂²×C₄₃	1	2	yes	—
323	#386	—	2	2	no	—
324	#379	—	2	2	no	—
325	C₄×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
326	#336	C₂²×C₄₃	1	2	yes	complemented
327	C₄₃	#25776	1	1	yes	characteristic, direct product factor, Sylow
328	C₂⁵	—	2	1	no	—
329	C₂²×Q₈	—	2	1	no	—
330	C₂²×Q₈	—	2	4	no	—
331	C₂²×Q₈	—	2	2	no	—
332	C₂²×Q₈	—	2	2	no	—
333	C₂²×Q₈	—	4	2	no	—
334	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
335	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
336	C₂²×D₄	—	2	4	no	—
337	C₂²×D₄	—	2	1	no	—
338	C₂²×D₄	—	2	2	no	—
339	C₂²×D₄	—	2	2	no	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	—	4	2	no	—
342	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
343	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
344	C₂³×C₄	—	2	1	no	—
345	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
346	C₂×Q₁₆	—	2	4	no	—
347	C₂×Q₁₆	—	2	4	no	—
348	C₂×Q₁₆	—	4	2	no	—
349	C₂×SD₁₆	—	2	32	no	—
350	C₂×SD₁₆	—	2	4	no	—
351	C₂×SD₁₆	—	2	4	no	—
352	C₂×SD₁₆	—	2	4	no	—
353	C₂×SD₁₆	—	2	4	no	—
354	C₂×SD₁₆	—	2	4	no	—
355	C₂×SD₁₆	—	2	2	no	—
356	C₂×SD₁₆	—	2	4	no	—
357	C₂×SD₁₆	D₄×C₄₃	1	8	yes	complemented
358	C₂×D₈	—	2	4	no	—
359	C₂×D₈	—	2	4	no	—
360	C₂×D₈	—	4	2	no	—
361	C₂²×C₈	—	2	4	no	—
362	C₂²×C₈	D₄×C₄₃	1	4	yes	—
363	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
365	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
366	#124	—	2	4	no	—
367	#124	—	2	4	no	—
368	#124	—	4	2	no	—
369	#124	—	4	2	no	—
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	—	2	2	no	—
372	#121	—	2	2	no	—
373	#121	—	2	2	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	4	no	—
380	C₂×C₂²⋊C₄	—	2	4	no	—
381	C₂×C₂²⋊C₄	—	2	4	no	—
382	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
383	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
384	#106	—	2	2	no	—
385	#103	—	2	4	no	—
386	#103	—	2	2	no	—
387	#102	—	2	4	no	—
388	#102	—	2	2	no	—
389	C₂²⋊C₈	D₄×C₄₃	1	4	yes	—
390	C₄×C₈	—	2	4	no	—
391	#95	—	2	4	no	—
392	#95	D₄×C₄₃	1	2	yes	—
393	C₂⁴	—	2	2	no	—
394	C₂⁴	—	2	1	no	—
395	C₂⁴	—	4	4	no	—
396	C₂⁴	—	4	2	no	—
397	C₂⁴	—	4	4	no	—
398	C₂⁴	—	8	2	no	—
399	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	8	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	4	4	no	—
411	C₂×Q₈	—	4	8	no	—
412	C₂×Q₈	—	4	4	no	—
413	C₂×Q₈	—	4	2	no	—
414	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
415	C₂×D₄	—	2	8	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	4	8	no	—
426	C₂×D₄	—	4	4	no	—
427	C₂×D₄	—	4	4	no	—
428	C₂×D₄	—	4	2	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	4	4	no	—
439	C₂²×C₄	—	4	2	no	—
440	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
441	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
444	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
445	Q₁₆	—	4	8	no	—
446	SD₁₆	—	2	16	no	—
447	SD₁₆	—	2	16	no	—
448	SD₁₆	—	4	4	no	—
449	D₈	—	4	8	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	8	no	—
454	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
455	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
456	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
457	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	4	2	no	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	4	8	no	—
465	C₂²⋊C₄	—	4	8	no	—
466	C₂²⋊C₄	—	4	2	no	—
467	C₂²⋊C₄	—	4	2	no	—
468	C₂²⋊C₄	—	8	4	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	2	2	no	—
471	C₂³	—	2	2	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	2	4	no	—
474	C₂³	—	4	8	no	—
475	C₂³	—	4	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	4	no	—
478	C₂³	—	4	4	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	8	16	no	—
484	C₂³	—	8	4	no	—
485	C₂³	—	8	4	no	—
486	C₂³	#127×C₄₃	1	2	yes	—
487	C₂³	#135×C₄₃	1	4	yes	—
488	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
489	Q₈	—	2	4	no	—
490	Q₈	—	2	4	no	—
491	Q₈	—	4	8	no	—
492	Q₈	—	4	2	no	—
493	Q₈	—	4	2	no	—
494	Q₈	—	4	1	no	—
495	Q₈	—	4	1	no	—
496	Q₈	—	4	2	no	—
497	D₄	—	2	4	no	—
498	D₄	—	2	4	no	—
499	D₄	—	4	8	no	—
500	D₄	—	4	1	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	1	no	—
503	D₄	—	4	2	no	—
504	D₄	—	4	2	no	—
505	D₄	—	8	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	4	8	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	#127×C₄₃	1	2	yes	—
524	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
525	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
526	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
527	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
528	C₈	—	2	2	no	—
529	C₈	—	2	4	no	—
530	C₈	#120×C₄₃	1	4	yes	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	8	no	—
534	C₂²	—	4	4	no	—
535	C₂²	—	4	8	no	—
536	C₂²	—	8	16	no	—
537	C₂²	—	8	2	no	—
538	C₂²	—	8	2	no	—
539	C₂²	—	8	4	no	—
540	C₂²	—	8	1	no	—
541	C₂²	—	8	1	no	—
542	C₂²	—	8	1	no	—
543	C₂²	—	8	4	no	—
544	C₂²	C₄₃×#495	1	4	yes	complemented
545	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
546	C₂²	D₄²×C₄₃	1	2	yes	—
547	C₂²	C₂×#135×C₄₃	1	2	yes	—
548	C₂²	C₄₃×#577	1	2	yes	—
549	C₄	—	2	2	no	—
550	C₄	—	4	4	no	—
551	C₄	—	4	4	no	—
552	C₄	—	8	1	no	—
553	C₄	—	8	1	no	—
554	C₄	—	8	1	no	—
555	C₄	C₂×#120×C₄₃	1	1	yes	characteristic
556	C₄	C₄₃×#535	1	1	yes	characteristic
557	C₄	D₄²×C₄₃	1	2	yes	—
558	C₂	—	2	4	no	—
559	C₂	—	8	4	no	—
560	C₂	—	16	1	no	—
561	C₂	C₄₃×#2433	1	1	yes	characteristic
562	C₂	C₂×C₄₃×#495	1	1	yes	characteristic
563	C₂	C₄₃×#3154	1	1	yes	characteristic
564	C₂	C₄₃×#3282	1	4	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 ◁ C₄×C₂²⋊C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×SD₁₆×C₄₃	C₂	semidirect
2. C₂×C₄₃×#495	C₂	semidirect
3. C₂×C₄₃×#465	C₂	semidirect
4. C₂×C₄₃×#451	C₂	semidirect
6. C₄₃×#2436	C₂	semidirect
7. C₄₃×#2435	C₂	semidirect
8. C₄₃×#2015	C₂	semidirect
9. C₄₃×#2012	C₂	semidirect
10. C₄₃×#1968	C₂	semidirect
11. C₈×C₂²⋊C₄×C₄₃	C₂	semidirect
14. C₂²×Q₁₆×C₄₃	C₂²	semidirect
19. C₂²×SD₁₆×C₄₃	C₂²	semidirect
23. C₂×#124×C₄₃	C₂²	semidirect
30. C₂×#106×C₄₃	C₂²	semidirect
31. C₂×#103×C₄₃	C₂²	semidirect
32. C₂×#103×C₄₃	C₂²	semidirect
34. C₂×#102×C₄₃	C₂²	semidirect
36. C₂×C₄×C₈×C₄₃	C₂²	semidirect
39. C₄₃×#391	C₂²	semidirect
44. C₄₃×#336	C₂²	semidirect
74. C₂×SD₁₆×C₄₃	D₄	semidirect
248. #25776	C₄₃	direct (N × H)
262. C₂²×C₄₃	#495	semidirect
276. C₂³×SD₁₆	C₂×C₄₃	semidirect
277. C₂×#495	C₂×C₄₃	semidirect
278. C₂×#465	C₂×C₄₃	semidirect
279. C₂×#451	C₂×C₄₃	semidirect
281. #2436	C₂×C₄₃	semidirect
282. #2435	C₂×C₄₃	semidirect
283. #2015	C₂×C₄₃	semidirect
284. #2012	C₂×C₄₃	semidirect
285. #1968	C₂×C₄₃	semidirect
286. C₈×C₂²⋊C₄	C₂×C₄₃	semidirect
296. C₂²×Q₁₆	C₂²×C₄₃	semidirect
301. C₂²×SD₁₆	C₂²×C₄₃	semidirect
305. C₂×#124	C₂²×C₄₃	semidirect
312. C₂×#106	C₂²×C₄₃	semidirect
313. C₂×#103	C₂²×C₄₃	semidirect
314. C₂×#103	C₂²×C₄₃	semidirect
316. C₂×#102	C₂²×C₄₃	semidirect
318. C₂×C₄×C₈	C₂²×C₄₃	semidirect
321. #391	C₂²×C₄₃	semidirect
326. #336	C₂²×C₄₃	semidirect
327. C₄₃	#25776	direct (N × H)
357. C₂×SD₁₆	D₄×C₄₃	semidirect
544. 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
C₂³×SD₁₆×C₄₃	2
C₂×C₄₃×#495	2
C₂×C₄₃×#465	2
C₂×C₄₃×#451	2
C₂×C₄₃×#447	2
C₄₃×#2436	2
C₄₃×#2435	2
C₄₃×#2015	2
C₄₃×#2012	2
C₄₃×#1968	2
C₈×C₂²⋊C₄×C₄₃	2
#25776	43

Subgroups — C43×#25776 #24945793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25776 #24945793