Subgroups — C₄₃×#25438 #24945455

Order 11008.

892 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#473	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#3057	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#3044	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#3043	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2047	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2046	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#2005	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#2004	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1977	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₃×#1946	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₃×#1888	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₃×#1886	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#1765	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#137×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#137×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#536	C₂²	1	1	yes	characteristic
24	C₄₃×#535	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
27	C₄₃×#519	C₂²	1	1	yes	characteristic
28	C₄₃×#519	C₂²	1	1	yes	characteristic
29	C₄₃×#497	—	2	4	no	—
30	C₄₃×#473	—	2	4	no	—
31	C₄₃×#468	—	2	2	no	—
32	C₄₃×#465	—	2	2	no	—
33	C₄₃×#464	—	2	2	no	—
34	C₄₃×#464	—	2	2	no	—
35	C₄₃×#462	—	2	2	no	—
36	C₄₃×#460	—	2	2	no	—
37	C₄₃×#441	—	2	2	no	—
38	C₄×Q₁₆×C₄₃	—	2	2	no	—
39	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#427	C₂²	1	1	yes	characteristic
41	C₄₃×#424	C₂²	1	1	yes	characteristic
42	C₄₃×#424	C₂²	1	1	yes	characteristic
43	C₂×#104×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#419	C₂²	1	1	yes	characteristic
45	C₄₃×#419	C₂²	1	1	yes	characteristic
46	C₄₃×#419	C₂²	1	1	yes	characteristic
47	C₄₃×#419	C₂²	1	1	yes	characteristic
48	C₄₃×#418	C₂²	1	1	yes	characteristic
49	C₄₃×#418	C₂²	1	1	yes	characteristic
50	C₄₃×#416	C₂²	1	1	yes	characteristic
51	C₂×#101×C₄₃	C₂²	1	1	yes	characteristic
52	C₂×#101×C₄₃	C₂²	1	1	yes	characteristic
53	C₂×#101×C₄₃	C₂²	1	1	yes	characteristic
54	C₂×#100×C₄₃	C₂²	1	1	yes	characteristic
55	C₄₃×#405	C₂²	1	1	yes	characteristic
56	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
57	C₄₃×#341	C₂²	1	1	yes	characteristic
58	C₄₃×#339	C₂²	1	1	yes	characteristic
59	C₄₃×#339	C₂²	1	1	yes	characteristic
60	C₄₃×#339	C₂²	1	1	yes	characteristic
61	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
66	#137×C₄₃	—	2	2	no	—
67	#137×C₄₃	—	2	2	no	—
68	#137×C₄₃	—	4	1	no	—
69	#137×C₄₃	—	4	1	no	—
70	C₂×Q₁₆×C₄₃	—	2	2	no	—
71	C₂×Q₁₆×C₄₃	—	2	1	no	—
72	C₂×Q₁₆×C₄₃	—	2	1	no	—
73	C₂×Q₁₆×C₄₃	—	2	1	no	—
74	C₂×Q₁₆×C₄₃	—	2	1	no	—
75	C₂×Q₁₆×C₄₃	—	2	2	no	—
76	C₂×Q₁₆×C₄₃	—	2	2	no	—
77	C₂×Q₁₆×C₄₃	—	4	1	no	—
78	C₂×Q₁₆×C₄₃	D₄	1	4	yes	complemented
79	C₂×SD₁₆×C₄₃	—	2	2	no	—
80	C₂×SD₁₆×C₄₃	—	2	1	no	—
81	C₂×SD₁₆×C₄₃	—	2	1	no	—
82	C₂×SD₁₆×C₄₃	—	2	2	no	—
83	C₂×SD₁₆×C₄₃	—	2	2	no	—
84	C₂×SD₁₆×C₄₃	—	2	1	no	—
85	C₂×SD₁₆×C₄₃	—	2	1	no	—
86	C₂×SD₁₆×C₄₃	—	2	2	no	—
87	C₂×SD₁₆×C₄₃	—	4	1	no	—
88	#131×C₄₃	—	2	2	no	—
89	#131×C₄₃	—	2	2	no	—
90	C₂×M₁₆×C₄₃	—	2	1	no	—
91	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
93	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₄₃	—	2	1	no	—
96	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₄₃	—	2	2	no	—
99	C₄⋊Q₈×C₄₃	—	2	1	no	—
100	C₄⋊Q₈×C₄₃	—	2	2	no	—
101	#127×C₄₃	—	2	1	no	—
102	#124×C₄₃	—	2	2	no	—
103	#124×C₄₃	—	2	1	no	—
104	#124×C₄₃	—	2	1	no	—
105	#124×C₄₃	—	2	2	no	—
106	#123×C₄₃	—	4	1	no	—
107	C₂²⋊Q₈×C₄₃	—	2	2	no	—
108	#121×C₄₃	—	2	2	no	—
109	#120×C₄₃	—	4	1	no	—
110	C₄×Q₈×C₄₃	—	2	2	no	—
111	C₄×Q₈×C₄₃	—	2	2	no	—
112	C₄×Q₈×C₄₃	—	2	2	no	—
113	C₄×Q₈×C₄₃	—	2	2	no	—
114	#117×C₄₃	—	4	1	no	—
115	#117×C₄₃	—	4	1	no	—
116	#117×C₄₃	C₂³	1	1	yes	characteristic
117	#117×C₄₃	C₂³	1	1	yes	characteristic
118	#117×C₄₃	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₄₃	—	4	1	no	—
120	C₂×C₂²⋊C₄×C₄₃	—	4	1	no	—
121	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
122	#108×C₄₃	—	2	2	no	—
123	#107×C₄₃	D₄	1	2	yes	—
124	#106×C₄₃	D₄	1	2	yes	—
125	C₄⋊C₈×C₄₃	—	2	2	no	—
126	C₄⋊C₈×C₄₃	—	2	2	no	—
127	#104×C₄₃	—	2	2	no	—
128	#103×C₄₃	—	2	2	no	—
129	#103×C₄₃	—	2	2	no	—
130	#103×C₄₃	—	2	2	no	—
131	#103×C₄₃	—	2	2	no	—
132	#103×C₄₃	D₄	1	2	yes	—
133	#102×C₄₃	—	2	2	no	—
134	#102×C₄₃	—	2	2	no	—
135	#102×C₄₃	D₄	1	2	yes	—
136	#101×C₄₃	—	2	2	no	—
137	#101×C₄₃	—	2	2	no	—
138	#101×C₄₃	—	4	1	no	—
139	#100×C₄₃	—	4	1	no	—
140	#97×C₄₃	—	2	2	no	—
141	#97×C₄₃	—	2	1	no	—
142	C₄×C₈×C₄₃	—	2	1	no	—
143	C₂⁴×C₄₃	—	2	1	no	—
144	#41×C₄₃	—	2	1	no	—
145	#41×C₄₃	—	2	1	no	—
146	#41×C₄₃	—	2	1	no	—
147	#41×C₄₃	—	2	1	no	—
148	C₂×Q₈×C₄₃	—	2	1	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	—	2	1	no	—
155	C₂×Q₈×C₄₃	—	2	1	no	—
156	C₂×Q₈×C₄₃	—	2	1	no	—
157	C₂×Q₈×C₄₃	—	2	1	no	—
158	C₂×Q₈×C₄₃	—	2	1	no	—
159	C₂×Q₈×C₄₃	—	2	1	no	—
160	C₂×Q₈×C₄₃	—	2	1	no	—
161	C₂×Q₈×C₄₃	—	2	1	no	—
162	C₂×Q₈×C₄₃	—	2	1	no	—
163	C₂×Q₈×C₄₃	—	2	1	no	—
164	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
165	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
166	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
167	C₂×D₄×C₄₃	—	2	1	no	—
168	C₂×D₄×C₄₃	—	2	1	no	—
169	C₂×D₄×C₄₃	—	2	1	no	—
170	C₂×D₄×C₄₃	—	2	1	no	—
171	C₂×D₄×C₄₃	—	2	1	no	—
172	C₂×D₄×C₄₃	—	2	1	no	—
173	C₂×D₄×C₄₃	—	2	1	no	—
174	C₂×D₄×C₄₃	—	4	2	no	—
175	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₄₃	—	2	1	no	—
177	C₂²×C₄×C₄₃	—	2	1	no	—
178	C₂²×C₄×C₄₃	—	2	1	no	—
179	C₂²×C₄×C₄₃	—	2	1	no	—
180	C₂²×C₄×C₄₃	—	2	1	no	—
181	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
182	Q₁₆×C₄₃	—	2	4	no	—
183	Q₁₆×C₄₃	—	2	4	no	—
184	Q₁₆×C₄₃	—	4	4	no	—
185	Q₁₆×C₄₃	—	4	2	no	—
186	Q₁₆×C₄₃	—	4	2	no	—
187	SD₁₆×C₄₃	—	4	4	no	—
188	SD₁₆×C₄₃	—	4	2	no	—
189	SD₁₆×C₄₃	—	4	2	no	—
190	SD₁₆×C₄₃	—	4	2	no	—
191	SD₁₆×C₄₃	—	4	2	no	—
192	M₁₆×C₄₃	—	2	1	no	—
193	M₁₆×C₄₃	—	2	1	no	—
194	M₁₆×C₄₃	—	2	1	no	—
195	M₁₆×C₄₃	—	2	1	no	—
196	M₁₆×C₄₃	—	2	1	no	—
197	M₁₆×C₄₃	—	2	1	no	—
198	M₁₆×C₄₃	—	2	1	no	—
199	M₁₆×C₄₃	—	2	1	no	—
200	M₁₆×C₄₃	—	4	2	no	—
201	C₂×C₈×C₄₃	—	2	1	no	—
202	C₂×C₈×C₄₃	—	2	1	no	—
203	C₂×C₈×C₄₃	—	2	1	no	—
204	C₂×C₈×C₄₃	—	2	1	no	—
205	C₂×C₈×C₄₃	—	2	1	no	—
206	C₂×C₈×C₄₃	—	2	1	no	—
207	C₂×C₈×C₄₃	—	4	2	no	—
208	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
209	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
210	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
211	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
212	C₂×C₈×C₄₃	#41	1	2	yes	—
213	C₄⋊C₄×C₄₃	—	4	4	no	—
214	C₄⋊C₄×C₄₃	—	4	2	no	—
215	C₄⋊C₄×C₄₃	—	4	2	no	—
216	C₄⋊C₄×C₄₃	—	4	2	no	—
217	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
218	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
219	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
220	C₂²⋊C₄×C₄₃	—	2	1	no	—
221	C₂²⋊C₄×C₄₃	—	2	1	no	—
222	C₂²⋊C₄×C₄₃	—	2	1	no	—
223	C₂²⋊C₄×C₄₃	—	4	2	no	—
224	C₂²⋊C₄×C₄₃	—	4	4	no	—
225	C₂²⋊C₄×C₄₃	—	4	2	no	—
226	C₄²×C₄₃	—	2	1	no	—
227	C₄²×C₄₃	—	2	1	no	—
228	C₄²×C₄₃	—	2	1	no	—
229	C₄²×C₄₃	—	2	1	no	—
230	C₄²×C₄₃	—	4	2	no	—
231	C₄²×C₄₃	—	4	2	no	—
232	C₄²×C₄₃	#41	1	2	yes	—
233	C₂³×C₄₃	—	2	1	no	—
234	C₂³×C₄₃	—	4	1	no	—
235	C₂³×C₄₃	—	4	1	no	—
236	C₂³×C₄₃	—	4	1	no	—
237	C₂³×C₄₃	—	8	2	no	—
238	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
239	Q₈×C₄₃	—	2	2	no	—
240	Q₈×C₄₃	—	2	2	no	—
241	Q₈×C₄₃	—	2	1	no	—
242	Q₈×C₄₃	—	2	2	no	—
243	Q₈×C₄₃	—	2	2	no	—
244	Q₈×C₄₃	—	2	1	no	—
245	Q₈×C₄₃	—	4	1	no	—
246	Q₈×C₄₃	—	4	1	no	—
247	Q₈×C₄₃	—	4	1	no	—
248	Q₈×C₄₃	—	4	1	no	—
249	Q₈×C₄₃	—	4	1	no	—
250	Q₈×C₄₃	—	4	1	no	—
251	Q₈×C₄₃	—	4	1	no	—
252	Q₈×C₄₃	—	4	1	no	—
253	D₄×C₄₃	—	2	1	no	—
254	D₄×C₄₃	—	2	1	no	—
255	D₄×C₄₃	—	4	1	no	—
256	D₄×C₄₃	—	4	1	no	—
257	D₄×C₄₃	—	4	1	no	—
258	D₄×C₄₃	—	4	1	no	—
259	D₄×C₄₃	—	4	1	no	—
260	D₄×C₄₃	—	4	1	no	—
261	D₄×C₄₃	—	16	2	no	—
262	C₂×C₄×C₄₃	—	2	2	no	—
263	C₂×C₄×C₄₃	—	2	2	no	—
264	C₂×C₄×C₄₃	—	2	2	no	—
265	C₂×C₄×C₄₃	—	2	1	no	—
266	C₂×C₄×C₄₃	—	2	2	no	—
267	C₂×C₄×C₄₃	—	2	2	no	—
268	C₂×C₄×C₄₃	—	2	2	no	—
269	C₂×C₄×C₄₃	—	4	2	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	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
285	C₈×C₄₃	—	2	2	no	—
286	C₈×C₄₃	—	4	1	no	—
287	C₈×C₄₃	—	4	1	no	—
288	C₈×C₄₃	—	4	1	no	—
289	C₈×C₄₃	—	4	1	no	—
290	C₈×C₄₃	#121	1	2	yes	—
291	C₈×C₄₃	#121	1	2	yes	—
292	#25438	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
293	C₂²×C₄₃	—	2	2	no	—
294	C₂²×C₄₃	—	4	1	no	—
295	C₂²×C₄₃	—	4	2	no	—
296	C₂²×C₄₃	—	8	2	no	—
297	C₂²×C₄₃	—	8	1	no	—
298	C₂²×C₄₃	—	8	2	no	—
299	C₂²×C₄₃	—	16	1	no	—
300	C₂²×C₄₃	#540	1	1	yes	characteristic
301	C₂²×C₄₃	D₄²	1	1	yes	characteristic
302	C₂²×C₄₃	#546	1	1	yes	characteristic
303	C₄×C₄₃	—	4	2	no	—
304	C₄×C₄₃	—	4	1	no	—
305	C₄×C₄₃	—	4	2	no	—
306	C₄×C₄₃	—	4	2	no	—
307	C₄×C₄₃	—	4	2	no	—
308	C₄×C₄₃	—	4	2	no	—
309	C₄×C₄₃	—	4	2	no	—
310	C₄×C₄₃	—	8	1	no	—
311	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
312	C₄×C₄₃	#532	1	1	yes	characteristic
313	C₄×C₄₃	D₄²	1	1	yes	characteristic
314	C₄×C₄₃	#550	1	1	yes	characteristic
315	C₂×#497	C₂×C₄₃	1	1	yes	characteristic, complemented
316	C₂×#473	C₂×C₄₃	1	1	yes	characteristic, complemented
317	#3057	C₂×C₄₃	1	1	yes	characteristic
318	#3044	C₂×C₄₃	1	1	yes	characteristic, complemented
319	#3043	C₂×C₄₃	1	1	yes	characteristic
320	#2950	C₂×C₄₃	1	1	yes	characteristic, complemented
321	#2047	C₂×C₄₃	1	1	yes	characteristic, complemented
322	#2046	C₂×C₄₃	1	1	yes	characteristic, complemented
323	#2005	C₂×C₄₃	1	1	yes	characteristic, complemented
324	#2004	C₂×C₄₃	1	1	yes	characteristic
325	#1977	C₂×C₄₃	1	1	yes	characteristic, complemented
326	#1946	C₂×C₄₃	1	1	yes	characteristic, complemented
327	#1888	C₂×C₄₃	1	1	yes	characteristic, complemented
328	#1886	C₂×C₄₃	1	1	yes	characteristic, complemented
329	#1765	C₂×C₄₃	1	1	yes	characteristic, complemented
330	C₂×C₄₃	—	2	1	no	—
331	C₂×C₄₃	—	2	1	no	—
332	C₂×C₄₃	—	8	1	no	—
333	C₂×C₄₃	—	16	1	no	—
334	C₂×C₄₃	#2428	1	1	yes	characteristic
335	C₂×C₄₃	#3289	1	2	yes	—
336	C₂×#137	C₂²×C₄₃	1	1	yes	characteristic
337	C₂×#137	C₂²×C₄₃	1	1	yes	characteristic
338	C₂²×Q₁₆	C₂²×C₄₃	1	1	yes	characteristic
339	C₂²×Q₁₆	C₂²×C₄₃	1	1	yes	characteristic
340	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic
341	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic
342	C₂×#131	C₂²×C₄₃	1	1	yes	characteristic
343	#536	C₂²×C₄₃	1	1	yes	characteristic
344	#535	C₂²×C₄₃	1	1	yes	characteristic
345	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
346	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
347	#519	C₂²×C₄₃	1	1	yes	characteristic
348	#519	C₂²×C₄₃	1	1	yes	characteristic
349	#497	—	2	4	no	—
350	#473	—	2	4	no	—
351	#468	—	2	2	no	—
352	#465	—	2	2	no	—
353	#464	—	2	2	no	—
354	#464	—	2	2	no	—
355	#462	—	2	2	no	—
356	#460	—	2	2	no	—
357	#441	—	2	2	no	—
358	C₄×Q₁₆	—	2	2	no	—
359	C₂×#108	C₂²×C₄₃	1	1	yes	characteristic
360	#427	C₂²×C₄₃	1	1	yes	characteristic
361	#424	C₂²×C₄₃	1	1	yes	characteristic
362	#424	C₂²×C₄₃	1	1	yes	characteristic
363	C₂×#104	C₂²×C₄₃	1	1	yes	characteristic
364	#419	C₂²×C₄₃	1	1	yes	characteristic
365	#419	C₂²×C₄₃	1	1	yes	characteristic
366	#419	C₂²×C₄₃	1	1	yes	characteristic
367	#419	C₂²×C₄₃	1	1	yes	characteristic
368	#418	C₂²×C₄₃	1	1	yes	characteristic
369	#418	C₂²×C₄₃	1	1	yes	characteristic
370	#416	C₂²×C₄₃	1	1	yes	characteristic
371	C₂×#101	C₂²×C₄₃	1	1	yes	characteristic
372	C₂×#101	C₂²×C₄₃	1	1	yes	characteristic
373	C₂×#101	C₂²×C₄₃	1	1	yes	characteristic
374	C₂×#100	C₂²×C₄₃	1	1	yes	characteristic
375	#405	C₂²×C₄₃	1	1	yes	characteristic
376	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
377	#341	C₂²×C₄₃	1	1	yes	characteristic
378	#339	C₂²×C₄₃	1	1	yes	characteristic
379	#339	C₂²×C₄₃	1	1	yes	characteristic
380	#339	C₂²×C₄₃	1	1	yes	characteristic
381	C₄₃	#25438	1	1	yes	characteristic, direct product factor, Sylow
382	C₂×#41	C₂³×C₄₃	1	1	yes	characteristic
383	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
384	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
385	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
386	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
387	#137	—	2	2	no	—
388	#137	—	2	2	no	—
389	#137	—	4	1	no	—
390	#137	—	4	1	no	—
391	C₂×Q₁₆	—	2	2	no	—
392	C₂×Q₁₆	—	2	1	no	—
393	C₂×Q₁₆	—	2	1	no	—
394	C₂×Q₁₆	—	2	1	no	—
395	C₂×Q₁₆	—	2	1	no	—
396	C₂×Q₁₆	—	2	2	no	—
397	C₂×Q₁₆	—	2	2	no	—
398	C₂×Q₁₆	—	4	1	no	—
399	C₂×Q₁₆	D₄×C₄₃	1	4	yes	complemented
400	C₂×SD₁₆	—	2	2	no	—
401	C₂×SD₁₆	—	2	1	no	—
402	C₂×SD₁₆	—	2	1	no	—
403	C₂×SD₁₆	—	2	2	no	—
404	C₂×SD₁₆	—	2	1	no	—
405	C₂×SD₁₆	—	2	1	no	—
406	C₂×SD₁₆	—	2	2	no	—
407	C₂×SD₁₆	—	2	2	no	—
408	C₂×SD₁₆	—	4	1	no	—
409	#131	—	2	2	no	—
410	#131	—	2	2	no	—
411	C₂×M₁₆	—	2	1	no	—
412	C₂×M₁₆	C₂³×C₄₃	1	1	yes	characteristic
413	C₂×M₁₆	C₂³×C₄₃	1	1	yes	characteristic
414	C₂×M₁₆	C₂³×C₄₃	1	1	yes	characteristic
415	C₂×M₁₆	C₂³×C₄₃	1	1	yes	characteristic
416	C₂²×C₈	—	2	1	no	—
417	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
418	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
419	C₄⋊Q₈	—	2	2	no	—
420	C₄⋊Q₈	—	2	1	no	—
421	C₄⋊Q₈	—	2	2	no	—
422	#127	—	2	1	no	—
423	#124	—	2	2	no	—
424	#124	—	2	1	no	—
425	#124	—	2	1	no	—
426	#124	—	2	2	no	—
427	#123	—	4	1	no	—
428	C₂²⋊Q₈	—	2	2	no	—
429	#121	—	2	2	no	—
430	#120	—	4	1	no	—
431	C₄×Q₈	—	2	2	no	—
432	C₄×Q₈	—	2	2	no	—
433	C₄×Q₈	—	2	2	no	—
434	C₄×Q₈	—	2	2	no	—
435	#117	—	4	1	no	—
436	#117	—	4	1	no	—
437	#117	C₂³×C₄₃	1	1	yes	characteristic
438	#117	C₂³×C₄₃	1	1	yes	characteristic
439	#117	C₂³×C₄₃	1	1	yes	characteristic
440	C₂×C₄⋊C₄	—	4	1	no	—
441	C₂×C₂²⋊C₄	—	4	1	no	—
442	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
443	#108	—	2	2	no	—
444	#107	D₄×C₄₃	1	2	yes	—
445	#106	D₄×C₄₃	1	2	yes	—
446	C₄⋊C₈	—	2	2	no	—
447	C₄⋊C₈	—	2	2	no	—
448	#104	—	2	2	no	—
449	#103	—	2	2	no	—
450	#103	—	2	2	no	—
451	#103	—	2	2	no	—
452	#103	—	2	2	no	—
453	#103	D₄×C₄₃	1	2	yes	—
454	#102	—	2	2	no	—
455	#102	—	2	2	no	—
456	#102	D₄×C₄₃	1	2	yes	—
457	#101	—	2	2	no	—
458	#101	—	2	2	no	—
459	#101	—	4	1	no	—
460	#100	—	4	1	no	—
461	#97	—	2	2	no	—
462	#97	—	2	1	no	—
463	C₄×C₈	—	2	1	no	—
464	C₂⁴	—	2	1	no	—
465	#41	—	2	1	no	—
466	#41	—	2	1	no	—
467	#41	—	2	1	no	—
468	#41	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
486	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
487	C₂×Q₈	C₂×D₄×C₄₃	1	1	yes	characteristic
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	4	2	no	—
496	C₂×D₄	C₂×D₄×C₄₃	1	1	yes	characteristic
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
503	Q₁₆	—	2	4	no	—
504	Q₁₆	—	2	4	no	—
505	Q₁₆	—	4	4	no	—
506	Q₁₆	—	4	2	no	—
507	Q₁₆	—	4	2	no	—
508	SD₁₆	—	4	4	no	—
509	SD₁₆	—	4	2	no	—
510	SD₁₆	—	4	2	no	—
511	SD₁₆	—	4	2	no	—
512	SD₁₆	—	4	2	no	—
513	M₁₆	—	2	1	no	—
514	M₁₆	—	2	1	no	—
515	M₁₆	—	2	1	no	—
516	M₁₆	—	2	1	no	—
517	M₁₆	—	2	1	no	—
518	M₁₆	—	2	1	no	—
519	M₁₆	—	2	1	no	—
520	M₁₆	—	2	1	no	—
521	M₁₆	—	4	2	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	—	2	1	no	—
528	C₂×C₈	—	4	2	no	—
529	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
530	C₂×C₈	C₂×D₄×C₄₃	1	1	yes	characteristic
531	C₂×C₈	C₂×D₄×C₄₃	1	1	yes	characteristic
532	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
533	C₂×C₈	#41×C₄₃	1	2	yes	—
534	C₄⋊C₄	—	4	4	no	—
535	C₄⋊C₄	—	4	2	no	—
536	C₄⋊C₄	—	4	2	no	—
537	C₄⋊C₄	—	4	2	no	—
538	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
539	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
540	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
541	C₂²⋊C₄	—	2	1	no	—
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	2	1	no	—
544	C₂²⋊C₄	—	4	4	no	—
545	C₂²⋊C₄	—	4	2	no	—
546	C₂²⋊C₄	—	4	2	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	4	2	no	—
552	C₄²	—	4	2	no	—
553	C₄²	#41×C₄₃	1	2	yes	—
554	C₂³	—	2	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	8	2	no	—
559	C₂³	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
560	Q₈	—	2	2	no	—
561	Q₈	—	2	2	no	—
562	Q₈	—	2	1	no	—
563	Q₈	—	2	2	no	—
564	Q₈	—	2	2	no	—
565	Q₈	—	2	1	no	—
566	Q₈	—	4	1	no	—
567	Q₈	—	4	1	no	—
568	Q₈	—	4	1	no	—
569	Q₈	—	4	1	no	—
570	Q₈	—	4	1	no	—
571	Q₈	—	4	1	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	1	no	—
574	D₄	—	2	1	no	—
575	D₄	—	2	1	no	—
576	D₄	—	4	1	no	—
577	D₄	—	4	1	no	—
578	D₄	—	4	1	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	1	no	—
581	D₄	—	4	1	no	—
582	D₄	—	16	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
601	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
602	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
603	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
604	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
605	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
606	C₈	—	2	2	no	—
607	C₈	—	4	1	no	—
608	C₈	—	4	1	no	—
609	C₈	—	4	1	no	—
610	C₈	—	4	1	no	—
611	C₈	#121×C₄₃	1	2	yes	—
612	C₈	#121×C₄₃	1	2	yes	—
613	C₂²	—	2	2	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	8	2	no	—
617	C₂²	—	8	1	no	—
618	C₂²	—	8	2	no	—
619	C₂²	—	16	1	no	—
620	C₂²	C₄₃×#540	1	1	yes	characteristic
621	C₂²	D₄²×C₄₃	1	1	yes	characteristic
622	C₂²	C₄₃×#546	1	1	yes	characteristic
623	C₄	—	4	2	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	2	no	—
630	C₄	—	8	1	no	—
631	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
632	C₄	C₄₃×#532	1	1	yes	characteristic
633	C₄	D₄²×C₄₃	1	1	yes	characteristic
634	C₄	C₄₃×#550	1	1	yes	characteristic
635	C₂	—	2	1	no	—
636	C₂	—	2	1	no	—
637	C₂	—	8	1	no	—
638	C₂	—	16	1	no	—
639	C₂	C₄₃×#2428	1	1	yes	characteristic
640	C₂	C₄₃×#3289	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#535	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂²×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#497	C₂	semidirect
2. C₂×C₄₃×#473	C₂	semidirect
4. C₄₃×#3044	C₂	semidirect
6. C₄₃×#2950	C₂	semidirect
7. C₄₃×#2047	C₂	semidirect
8. C₄₃×#2046	C₂	semidirect
9. C₄₃×#2005	C₂	semidirect
11. C₄₃×#1977	C₂	semidirect
12. C₄₃×#1946	C₂	semidirect
13. C₄₃×#1888	C₂	semidirect
14. C₄₃×#1886	C₂	semidirect
15. C₄₃×#1765	C₂	semidirect
78. C₂×Q₁₆×C₄₃	D₄	semidirect
292. #25438	C₄₃	direct (N × H)
315. C₂×#497	C₂×C₄₃	semidirect
316. C₂×#473	C₂×C₄₃	semidirect
318. #3044	C₂×C₄₃	semidirect
320. #2950	C₂×C₄₃	semidirect
321. #2047	C₂×C₄₃	semidirect
322. #2046	C₂×C₄₃	semidirect
323. #2005	C₂×C₄₃	semidirect
325. #1977	C₂×C₄₃	semidirect
326. #1946	C₂×C₄₃	semidirect
327. #1888	C₂×C₄₃	semidirect
328. #1886	C₂×C₄₃	semidirect
329. #1765	C₂×C₄₃	semidirect
381. C₄₃	#25438	direct (N × H)
399. C₂×Q₁₆	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×#497	2
C₂×C₄₃×#473	2
C₄₃×#3057	2
C₄₃×#3044	2
C₄₃×#3043	2
C₄₃×#2950	2
C₄₃×#2047	2
C₄₃×#2046	2
C₄₃×#2005	2
C₄₃×#2004	2
C₄₃×#1977	2
C₄₃×#1946	2
C₄₃×#1888	2
C₄₃×#1886	2
C₄₃×#1765	2
#25438	43

Subgroups — C43×#25438 #24945455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25438 #24945455