Subgroups — C₄₃×#24419 #24944436

Order 11008.

1360 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3486	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#3056	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#456	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#101×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2434	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2038	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2005	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1886	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1871	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1857	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1793	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₄₃	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#137×C₄₃	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
16	D₄×Q₈×C₄₃	—	2	2	no	—
17	D₄×Q₈×C₄₃	—	2	2	no	—
18	C₄₃×#548	—	2	2	no	—
19	C₄₃×#548	—	2	2	no	—
20	C₄₃×#536	—	2	2	no	—
21	C₄₃×#536	C₂²	1	2	yes	—
22	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#525	—	2	2	no	—
25	C₄₃×#525	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₄₃×#519	C₂²	1	1	yes	characteristic
28	C₄₃×#470	—	2	2	no	—
29	C₄₃×#468	—	2	2	no	—
30	C₄₃×#467	—	2	2	no	—
31	C₄₃×#465	—	2	2	no	—
32	C₄₃×#456	—	2	4	no	—
33	C₄₃×#428	C₂²	1	2	yes	—
34	C₂×#104×C₄₃	C₂²	1	2	yes	—
35	C₂×#104×C₄₃	C₂²	1	2	yes	—
36	C₄₃×#419	C₂²	1	2	yes	—
37	C₄₃×#417	C₂²	1	2	yes	—
38	C₂×#101×C₄₃	—	2	4	no	—
39	C₂×#101×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×#101×C₄₃	C₂²	1	2	yes	—
41	C₂×#101×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#395	—	2	2	no	—
43	C₄₃×#391	C₂²	1	1	yes	characteristic
44	C₄₃×#391	C₂²	1	1	yes	characteristic
45	C₄₃×#385	—	2	2	no	—
46	C₄×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#339	C₂²	1	2	yes	—
48	C₄₃×#339	C₂²	1	2	yes	—
49	2₋¹⁺⁴×C₄₃	—	2	2	no	—
50	2₋¹⁺⁴×C₄₃	—	2	2	no	—
51	2₋¹⁺⁴×C₄₃	—	4	2	no	—
52	C₂×#41×C₄₃	—	2	2	no	—
53	C₂×#41×C₄₃	—	2	2	no	—
54	C₂×#41×C₄₃	C₂³	1	2	yes	—
55	C₂²×Q₈×C₄₃	—	2	2	no	—
56	C₂²×Q₈×C₄₃	—	2	2	no	—
57	C₂²×Q₈×C₄₃	—	2	2	no	—
58	C₂²×Q₈×C₄₃	—	2	2	no	—
59	C₂²×Q₈×C₄₃	—	2	2	no	—
60	C₂²×Q₈×C₄₃	—	4	2	no	—
61	C₂²×Q₈×C₄₃	D₄	1	2	yes	—
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	C₂³×C₄×C₄₃	D₄	1	2	yes	—
66	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
67	#137×C₄₃	—	2	4	no	—
68	#137×C₄₃	—	4	2	no	—
69	C₂×Q₁₆×C₄₃	—	2	2	no	—
70	C₂×SD₁₆×C₄₃	—	2	2	no	—
71	C₂×M₁₆×C₄₃	—	2	2	no	—
72	C₂×M₁₆×C₄₃	—	2	4	no	—
73	C₂×M₁₆×C₄₃	—	4	2	no	—
74	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
75	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
76	C₂²×C₈×C₄₃	—	2	2	no	—
77	C₄⋊Q₈×C₄₃	—	2	4	no	—
78	C₄⋊Q₈×C₄₃	—	2	2	no	—
79	C₄⋊Q₈×C₄₃	—	2	2	no	—
80	C₄⋊Q₈×C₄₃	—	2	2	no	—
81	C₄⋊Q₈×C₄₃	—	4	2	no	—
82	#124×C₄₃	—	2	4	no	—
83	#124×C₄₃	—	2	2	no	—
84	#123×C₄₃	—	2	4	no	—
85	#123×C₄₃	—	2	2	no	—
86	C₂²⋊Q₈×C₄₃	—	2	2	no	—
87	C₂²⋊Q₈×C₄₃	—	2	2	no	—
88	C₂²⋊Q₈×C₄₃	—	2	4	no	—
89	C₂²⋊Q₈×C₄₃	—	2	4	no	—
90	C₂²⋊Q₈×C₄₃	—	2	2	no	—
91	C₂²⋊Q₈×C₄₃	—	2	2	no	—
92	C₂²⋊Q₈×C₄₃	—	2	2	no	—
93	C₂²⋊Q₈×C₄₃	—	2	2	no	—
94	C₂²⋊Q₈×C₄₃	D₄	1	2	yes	—
95	C₂²⋊Q₈×C₄₃	D₄	1	2	yes	—
96	#121×C₄₃	—	2	2	no	—
97	#121×C₄₃	—	2	2	no	—
98	#121×C₄₃	D₄	1	2	yes	—
99	#121×C₄₃	D₄	1	2	yes	—
100	#120×C₄₃	—	2	2	no	—
101	C₄×Q₈×C₄₃	—	2	2	no	—
102	C₄×Q₈×C₄₃	—	2	2	no	—
103	C₄×D₄×C₄₃	—	2	4	no	—
104	C₄×D₄×C₄₃	—	2	4	no	—
105	C₄×D₄×C₄₃	—	2	2	no	—
106	C₄×D₄×C₄₃	—	2	2	no	—
107	#117×C₄₃	—	2	2	no	—
108	#117×C₄₃	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
110	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
111	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
112	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
113	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
115	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
117	#107×C₄₃	—	2	2	no	—
118	#106×C₄₃	—	2	2	no	—
119	#104×C₄₃	—	2	4	no	—
120	#104×C₄₃	—	4	2	no	—
121	#103×C₄₃	—	2	2	no	—
122	#103×C₄₃	—	2	2	no	—
123	#103×C₄₃	—	2	2	no	—
124	#102×C₄₃	—	2	2	no	—
125	#101×C₄₃	—	2	2	no	—
126	#101×C₄₃	—	2	4	no	—
127	#101×C₄₃	D₄	1	4	yes	complemented
128	#95×C₄₃	—	2	1	no	—
129	#95×C₄₃	—	2	2	no	—
130	#95×C₄₃	—	2	2	no	—
131	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
132	#41×C₄₃	—	2	2	no	—
133	#41×C₄₃	—	2	2	no	—
134	#41×C₄₃	—	2	2	no	—
135	#41×C₄₃	—	2	2	no	—
136	#41×C₄₃	—	4	4	no	—
137	#41×C₄₃	—	4	4	no	—
138	#41×C₄₃	—	4	4	no	—
139	#41×C₄₃	—	4	4	no	—
140	C₂×Q₈×C₄₃	—	2	2	no	—
141	C₂×Q₈×C₄₃	—	2	4	no	—
142	C₂×Q₈×C₄₃	—	2	4	no	—
143	C₂×Q₈×C₄₃	—	2	2	no	—
144	C₂×Q₈×C₄₃	—	2	1	no	—
145	C₂×Q₈×C₄₃	—	2	2	no	—
146	C₂×Q₈×C₄₃	—	2	1	no	—
147	C₂×Q₈×C₄₃	—	2	2	no	—
148	C₂×Q₈×C₄₃	—	2	2	no	—
149	C₂×Q₈×C₄₃	—	2	2	no	—
150	C₂×Q₈×C₄₃	—	2	1	no	—
151	C₂×Q₈×C₄₃	—	2	1	no	—
152	C₂×Q₈×C₄₃	—	2	2	no	—
153	C₂×Q₈×C₄₃	—	4	2	no	—
154	C₂×Q₈×C₄₃	—	4	4	no	—
155	C₂×Q₈×C₄₃	—	4	4	no	—
156	C₂×Q₈×C₄₃	—	4	4	no	—
157	C₂×Q₈×C₄₃	—	4	4	no	—
158	C₂×Q₈×C₄₃	—	4	4	no	—
159	C₂×Q₈×C₄₃	—	4	4	no	—
160	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
161	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
162	C₂×Q₈×C₄₃	#41	1	2	yes	—
163	C₂×D₄×C₄₃	—	2	2	no	—
164	C₂×D₄×C₄₃	—	2	2	no	—
165	C₂×D₄×C₄₃	—	2	2	no	—
166	C₂×D₄×C₄₃	—	2	2	no	—
167	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₄₃	—	2	1	no	—
169	C₂²×C₄×C₄₃	—	2	1	no	—
170	C₂²×C₄×C₄₃	—	2	2	no	—
171	C₂²×C₄×C₄₃	—	2	4	no	—
172	C₂²×C₄×C₄₃	—	2	4	no	—
173	C₂²×C₄×C₄₃	—	2	2	no	—
174	C₂²×C₄×C₄₃	—	2	2	no	—
175	C₂²×C₄×C₄₃	—	2	2	no	—
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	—	4	2	no	—
181	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
186	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
187	Q₁₆×C₄₃	—	4	4	no	—
188	SD₁₆×C₄₃	—	4	4	no	—
189	M₁₆×C₄₃	—	2	2	no	—
190	M₁₆×C₄₃	—	2	2	no	—
191	M₁₆×C₄₃	—	2	2	no	—
192	M₁₆×C₄₃	—	4	4	no	—
193	M₁₆×C₄₃	C₂×D₄	1	4	yes	—
194	C₂×C₈×C₄₃	—	2	2	no	—
195	C₂×C₈×C₄₃	—	2	2	no	—
196	C₂×C₈×C₄₃	—	4	4	no	—
197	C₄⋊C₄×C₄₃	—	2	2	no	—
198	C₄⋊C₄×C₄₃	—	2	2	no	—
199	C₄⋊C₄×C₄₃	—	2	4	no	—
200	C₄⋊C₄×C₄₃	—	2	4	no	—
201	C₄⋊C₄×C₄₃	—	2	2	no	—
202	C₄⋊C₄×C₄₃	—	2	2	no	—
203	C₄⋊C₄×C₄₃	—	2	2	no	—
204	C₄⋊C₄×C₄₃	—	4	4	no	—
205	C₄⋊C₄×C₄₃	—	4	2	no	—
206	C₄⋊C₄×C₄₃	—	4	4	no	—
207	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
208	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
209	C₂²⋊C₄×C₄₃	—	2	4	no	—
210	C₂²⋊C₄×C₄₃	—	2	4	no	—
211	C₂²⋊C₄×C₄₃	—	2	4	no	—
212	C₂²⋊C₄×C₄₃	—	2	2	no	—
213	C₂²⋊C₄×C₄₃	—	2	2	no	—
214	C₂²⋊C₄×C₄₃	—	2	2	no	—
215	C₂²⋊C₄×C₄₃	—	2	2	no	—
216	C₂²⋊C₄×C₄₃	—	2	2	no	—
217	C₂²⋊C₄×C₄₃	—	4	1	no	—
218	C₂²⋊C₄×C₄₃	—	4	1	no	—
219	C₄²×C₄₃	—	2	4	no	—
220	C₄²×C₄₃	—	2	2	no	—
221	C₄²×C₄₃	—	2	1	no	—
222	C₄²×C₄₃	—	2	1	no	—
223	C₄²×C₄₃	—	2	2	no	—
224	C₂³×C₄₃	—	2	1	no	—
225	C₂³×C₄₃	—	2	1	no	—
226	C₂³×C₄₃	—	2	2	no	—
227	C₂³×C₄₃	—	2	2	no	—
228	C₂³×C₄₃	—	4	1	no	—
229	C₂³×C₄₃	#120	1	1	yes	characteristic
230	C₂³×C₄₃	#120	1	1	yes	characteristic
231	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
232	Q₈×C₄₃	—	2	4	no	—
233	Q₈×C₄₃	—	2	4	no	—
234	Q₈×C₄₃	—	2	2	no	—
235	Q₈×C₄₃	—	2	2	no	—
236	Q₈×C₄₃	—	4	8	no	—
237	Q₈×C₄₃	—	4	4	no	—
238	Q₈×C₄₃	—	4	2	no	—
239	Q₈×C₄₃	—	4	2	no	—
240	Q₈×C₄₃	—	4	2	no	—
241	Q₈×C₄₃	—	4	2	no	—
242	D₄×C₄₃	—	2	2	no	—
243	D₄×C₄₃	—	2	2	no	—
244	D₄×C₄₃	—	4	4	no	—
245	D₄×C₄₃	—	4	4	no	—
246	D₄×C₄₃	—	4	2	no	—
247	D₄×C₄₃	—	4	2	no	—
248	D₄×C₄₃	—	4	4	no	—
249	C₂×C₄×C₄₃	—	2	2	no	—
250	C₂×C₄×C₄₃	—	2	1	no	—
251	C₂×C₄×C₄₃	—	2	1	no	—
252	C₂×C₄×C₄₃	—	2	2	no	—
253	C₂×C₄×C₄₃	—	2	2	no	—
254	C₂×C₄×C₄₃	—	2	2	no	—
255	C₂×C₄×C₄₃	—	2	2	no	—
256	C₂×C₄×C₄₃	—	2	2	no	—
257	C₂×C₄×C₄₃	—	2	2	no	—
258	C₂×C₄×C₄₃	—	2	2	no	—
259	C₂×C₄×C₄₃	—	2	2	no	—
260	C₂×C₄×C₄₃	—	2	2	no	—
261	C₂×C₄×C₄₃	—	2	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	—	4	4	no	—
266	C₂×C₄×C₄₃	—	4	4	no	—
267	C₂×C₄×C₄₃	—	4	8	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	2	no	—
273	C₂×C₄×C₄₃	—	4	2	no	—
274	C₂×C₄×C₄₃	—	4	2	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	#120	1	2	yes	—
280	C₂×C₄×C₄₃	#121	1	4	yes	—
281	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
283	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
285	C₈×C₄₃	—	2	4	no	—
286	C₈×C₄₃	—	4	2	no	—
287	#24419	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₂²×C₄₃	—	2	1	no	—
289	C₂²×C₄₃	—	2	1	no	—
290	C₂²×C₄₃	—	2	1	no	—
291	C₂²×C₄₃	—	2	1	no	—
292	C₂²×C₄₃	—	2	1	no	—
293	C₂²×C₄₃	—	2	1	no	—
294	C₂²×C₄₃	—	2	1	no	—
295	C₂²×C₄₃	—	4	2	no	—
296	C₂²×C₄₃	—	4	2	no	—
297	C₂²×C₄₃	—	4	2	no	—
298	C₂²×C₄₃	—	4	2	no	—
299	C₂²×C₄₃	—	4	2	no	—
300	C₂²×C₄₃	#456	1	2	yes	complemented
301	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
302	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
303	C₂²×C₄₃	#534	1	1	yes	characteristic
304	C₄×C₄₃	—	2	2	no	—
305	C₄×C₄₃	—	2	4	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	—	4	2	no	—
311	C₄×C₄₃	—	4	2	no	—
312	C₄×C₄₃	—	8	1	no	—
313	C₄×C₄₃	—	8	1	no	—
314	C₄×C₄₃	D₄²	1	2	yes	—
315	C₄×C₄₃	#546	1	2	yes	—
316	#3486	C₂×C₄₃	1	1	yes	characteristic
317	#3056	C₂×C₄₃	1	2	yes	complemented
318	C₂×#456	C₂×C₄₃	1	1	yes	characteristic, complemented
319	C₂²×#101	C₂×C₄₃	1	1	yes	characteristic, complemented
320	#2434	C₂×C₄₃	1	1	yes	characteristic, complemented
321	#2038	C₂×C₄₃	1	2	yes	complemented
322	#2005	C₂×C₄₃	1	2	yes	complemented
323	#1886	C₂×C₄₃	1	1	yes	characteristic, complemented
324	#1871	C₂×C₄₃	1	2	yes	complemented
325	#1857	C₂×C₄₃	1	1	yes	characteristic, complemented
326	#1793	C₂×C₄₃	1	1	yes	characteristic, complemented
327	C₂×C₄₃	—	2	1	no	—
328	C₂×C₄₃	—	2	1	no	—
329	C₂×C₄₃	—	2	2	no	—
330	C₂×C₄₃	—	4	1	no	—
331	C₂×C₄₃	—	8	2	no	—
332	C₂×C₄₃	#2410	1	1	yes	characteristic
333	C₂×C₄₃	C₂×#456	1	1	yes	characteristic
334	C₂×C₄₃	#3020	1	1	yes	characteristic
335	C₂×2₋¹⁺⁴	C₂²×C₄₃	1	1	yes	characteristic
336	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
337	C₂×#137	C₂²×C₄₃	1	2	yes	—
338	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
339	D₄×Q₈	—	2	2	no	—
340	D₄×Q₈	—	2	2	no	—
341	#548	—	2	2	no	—
342	#548	—	2	2	no	—
343	#536	—	2	2	no	—
344	#536	C₂²×C₄₃	1	2	yes	—
345	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
346	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
347	#525	—	2	2	no	—
348	#525	C₂²×C₄₃	1	2	yes	—
349	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
350	#519	C₂²×C₄₃	1	1	yes	characteristic
351	#470	—	2	2	no	—
352	#468	—	2	2	no	—
353	#467	—	2	2	no	—
354	#465	—	2	2	no	—
355	#456	—	2	4	no	—
356	#428	C₂²×C₄₃	1	2	yes	—
357	C₂×#104	C₂²×C₄₃	1	2	yes	—
358	C₂×#104	C₂²×C₄₃	1	2	yes	—
359	#419	C₂²×C₄₃	1	2	yes	—
360	#417	C₂²×C₄₃	1	2	yes	—
361	C₂×#101	—	2	4	no	—
362	C₂×#101	C₂²×C₄₃	1	1	yes	characteristic
363	C₂×#101	C₂²×C₄₃	1	2	yes	—
364	C₂×#101	C₂²×C₄₃	1	1	yes	characteristic
365	#395	—	2	2	no	—
366	#391	C₂²×C₄₃	1	1	yes	characteristic
367	#391	C₂²×C₄₃	1	1	yes	characteristic
368	#385	—	2	2	no	—
369	C₄×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
370	#339	C₂²×C₄₃	1	2	yes	—
371	#339	C₂²×C₄₃	1	2	yes	—
372	C₄₃	#24419	1	1	yes	characteristic, direct product factor, Sylow
373	2₋¹⁺⁴	—	2	2	no	—
374	2₋¹⁺⁴	—	2	2	no	—
375	2₋¹⁺⁴	—	4	2	no	—
376	C₂×#41	—	2	2	no	—
377	C₂×#41	—	2	2	no	—
378	C₂×#41	C₂³×C₄₃	1	2	yes	—
379	C₂²×Q₈	—	2	2	no	—
380	C₂²×Q₈	—	2	2	no	—
381	C₂²×Q₈	—	2	2	no	—
382	C₂²×Q₈	—	2	2	no	—
383	C₂²×Q₈	—	2	2	no	—
384	C₂²×Q₈	—	4	2	no	—
385	C₂²×Q₈	D₄×C₄₃	1	2	yes	—
386	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
387	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
388	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
389	C₂³×C₄	D₄×C₄₃	1	2	yes	—
390	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
391	#137	—	2	4	no	—
392	#137	—	4	2	no	—
393	C₂×Q₁₆	—	2	2	no	—
394	C₂×SD₁₆	—	2	2	no	—
395	C₂×M₁₆	—	2	2	no	—
396	C₂×M₁₆	—	2	4	no	—
397	C₂×M₁₆	—	4	2	no	—
398	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
399	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
400	C₂²×C₈	—	2	2	no	—
401	C₄⋊Q₈	—	2	4	no	—
402	C₄⋊Q₈	—	2	2	no	—
403	C₄⋊Q₈	—	2	2	no	—
404	C₄⋊Q₈	—	2	2	no	—
405	C₄⋊Q₈	—	4	2	no	—
406	#124	—	2	4	no	—
407	#124	—	2	2	no	—
408	#123	—	2	4	no	—
409	#123	—	2	2	no	—
410	C₂²⋊Q₈	—	2	2	no	—
411	C₂²⋊Q₈	—	2	2	no	—
412	C₂²⋊Q₈	—	2	4	no	—
413	C₂²⋊Q₈	—	2	4	no	—
414	C₂²⋊Q₈	—	2	2	no	—
415	C₂²⋊Q₈	—	2	2	no	—
416	C₂²⋊Q₈	—	2	2	no	—
417	C₂²⋊Q₈	—	2	2	no	—
418	C₂²⋊Q₈	D₄×C₄₃	1	2	yes	—
419	C₂²⋊Q₈	D₄×C₄₃	1	2	yes	—
420	#121	—	2	2	no	—
421	#121	—	2	2	no	—
422	#121	D₄×C₄₃	1	2	yes	—
423	#121	D₄×C₄₃	1	2	yes	—
424	#120	—	2	2	no	—
425	C₄×Q₈	—	2	2	no	—
426	C₄×Q₈	—	2	2	no	—
427	C₄×D₄	—	2	4	no	—
428	C₄×D₄	—	2	4	no	—
429	C₄×D₄	—	2	2	no	—
430	C₄×D₄	—	2	2	no	—
431	#117	—	2	2	no	—
432	#117	C₂³×C₄₃	1	2	yes	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	2	no	—
435	C₂×C₄⋊C₄	—	2	2	no	—
436	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
441	#107	—	2	2	no	—
442	#106	—	2	2	no	—
443	#104	—	2	4	no	—
444	#104	—	4	2	no	—
445	#103	—	2	2	no	—
446	#103	—	2	2	no	—
447	#103	—	2	2	no	—
448	#102	—	2	2	no	—
449	#101	—	2	2	no	—
450	#101	—	2	4	no	—
451	#101	D₄×C₄₃	1	4	yes	complemented
452	#95	—	2	1	no	—
453	#95	—	2	2	no	—
454	#95	—	2	2	no	—
455	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
456	#41	—	2	2	no	—
457	#41	—	2	2	no	—
458	#41	—	2	2	no	—
459	#41	—	2	2	no	—
460	#41	—	4	4	no	—
461	#41	—	4	4	no	—
462	#41	—	4	4	no	—
463	#41	—	4	4	no	—
464	C₂×Q₈	—	2	2	no	—
465	C₂×Q₈	—	2	4	no	—
466	C₂×Q₈	—	2	4	no	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	2	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	2	no	—
472	C₂×Q₈	—	2	2	no	—
473	C₂×Q₈	—	2	2	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	2	no	—
477	C₂×Q₈	—	4	2	no	—
478	C₂×Q₈	—	4	4	no	—
479	C₂×Q₈	—	4	4	no	—
480	C₂×Q₈	—	4	4	no	—
481	C₂×Q₈	—	4	4	no	—
482	C₂×Q₈	—	4	4	no	—
483	C₂×Q₈	—	4	4	no	—
484	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
485	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
486	C₂×Q₈	#41×C₄₃	1	2	yes	—
487	C₂×D₄	—	2	2	no	—
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	4	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	4	2	no	—
505	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
506	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
508	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
509	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
510	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
511	Q₁₆	—	4	4	no	—
512	SD₁₆	—	4	4	no	—
513	M₁₆	—	2	2	no	—
514	M₁₆	—	2	2	no	—
515	M₁₆	—	2	2	no	—
516	M₁₆	—	4	4	no	—
517	M₁₆	C₂×D₄×C₄₃	1	4	yes	—
518	C₂×C₈	—	2	2	no	—
519	C₂×C₈	—	2	2	no	—
520	C₂×C₈	—	4	4	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	4	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	4	4	no	—
529	C₄⋊C₄	—	4	2	no	—
530	C₄⋊C₄	—	4	4	no	—
531	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
532	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	4	1	no	—
542	C₂²⋊C₄	—	4	1	no	—
543	C₄²	—	2	4	no	—
544	C₄²	—	2	2	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	2	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	4	1	no	—
553	C₂³	#120×C₄₃	1	1	yes	characteristic
554	C₂³	#120×C₄₃	1	1	yes	characteristic
555	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
556	Q₈	—	2	4	no	—
557	Q₈	—	2	4	no	—
558	Q₈	—	2	2	no	—
559	Q₈	—	2	2	no	—
560	Q₈	—	4	8	no	—
561	Q₈	—	4	4	no	—
562	Q₈	—	4	2	no	—
563	Q₈	—	4	2	no	—
564	Q₈	—	4	2	no	—
565	Q₈	—	4	2	no	—
566	D₄	—	2	2	no	—
567	D₄	—	2	2	no	—
568	D₄	—	4	4	no	—
569	D₄	—	4	4	no	—
570	D₄	—	4	2	no	—
571	D₄	—	4	2	no	—
572	D₄	—	4	4	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	4	4	no	—
590	C₂×C₄	—	4	4	no	—
591	C₂×C₄	—	4	8	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	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	#120×C₄₃	1	2	yes	—
604	C₂×C₄	#121×C₄₃	1	4	yes	—
605	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
606	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
607	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
608	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
609	C₈	—	2	4	no	—
610	C₈	—	4	2	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	C₄₃×#456	1	2	yes	complemented
624	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
625	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
626	C₂²	C₄₃×#534	1	1	yes	characteristic
627	C₄	—	2	2	no	—
628	C₄	—	2	4	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	2	no	—
631	C₄	—	4	2	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	2	no	—
634	C₄	—	4	2	no	—
635	C₄	—	8	1	no	—
636	C₄	—	8	1	no	—
637	C₄	D₄²×C₄₃	1	2	yes	—
638	C₄	C₄₃×#546	1	2	yes	—
639	C₂	—	2	1	no	—
640	C₂	—	2	1	no	—
641	C₂	—	2	2	no	—
642	C₂	—	4	1	no	—
643	C₂	—	8	2	no	—
644	C₂	C₄₃×#2410	1	1	yes	characteristic
645	C₂	C₂×C₄₃×#456	1	1	yes	characteristic
646	C₂	C₄₃×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#3486	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂³×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#3056	C₂	semidirect
3. C₂×C₄₃×#456	C₂	semidirect
4. C₂²×#101×C₄₃	C₂	semidirect
5. C₄₃×#2434	C₂	semidirect
6. C₄₃×#2038	C₂	semidirect
7. C₄₃×#2005	C₂	semidirect
8. C₄₃×#1886	C₂	semidirect
9. C₄₃×#1871	C₂	semidirect
10. C₄₃×#1857	C₂	semidirect
11. C₄₃×#1793	C₂	semidirect
127. #101×C₄₃	D₄	semidirect
287. #24419	C₄₃	direct (N × H)
300. C₂²×C₄₃	#456	semidirect
317. #3056	C₂×C₄₃	semidirect
318. C₂×#456	C₂×C₄₃	semidirect
319. C₂²×#101	C₂×C₄₃	semidirect
320. #2434	C₂×C₄₃	semidirect
321. #2038	C₂×C₄₃	semidirect
322. #2005	C₂×C₄₃	semidirect
323. #1886	C₂×C₄₃	semidirect
324. #1871	C₂×C₄₃	semidirect
325. #1857	C₂×C₄₃	semidirect
326. #1793	C₂×C₄₃	semidirect
372. C₄₃	#24419	direct (N × H)
451. #101	D₄×C₄₃	semidirect
623. C₂²	C₄₃×#456	semidirect

Maximal subgroups

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

subgroup	index
C₄₃×#3486	2
C₄₃×#3056	2
C₂×C₄₃×#456	2
C₂²×#101×C₄₃	2
C₄₃×#2434	2
C₄₃×#2038	2
C₄₃×#2005	2
C₄₃×#1886	2
C₄₃×#1871	2
C₄₃×#1857	2
C₄₃×#1793	2
#24419	43

Subgroups — C43×#24419 #24944436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#24419 #24944436