Subgroups — C₄₃×#28541 #24948558

Order 11008.

962 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2563	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2094	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2092	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1972	C₂	1	2	yes	maximal
10	C₄₃×#1847	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1770	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₄₃	—	2	2	no	—
16	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃×#498	—	2	4	no	—
19	C₄₃×#476	—	2	4	no	—
20	C₄₃×#474	—	2	4	no	—
21	C₄×D₈×C₄₃	—	2	4	no	—
22	C₂×#107×C₄₃	C₂²	1	2	yes	—
23	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#106×C₄₃	C₂²	1	2	yes	—
25	C₂×#106×C₄₃	C₂²	1	2	yes	—
26	C₂×#106×C₄₃	C₂²	1	2	yes	—
27	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×#102×C₄₃	C₂²	1	2	yes	—
30	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×#102×C₄₃	C₂²	1	2	yes	—
32	C₂×#97×C₄₃	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
34	C₄₃×#399	—	2	2	no	—
35	C₄₃×#393	—	2	2	no	—
36	C₄₃×#390	C₂²	1	2	yes	—
37	C₄₃×#390	C₂²	1	2	yes	—
38	C₄₃×#384	C₂²	1	2	yes	—
39	C₄₃×#382	C₂²	1	2	yes	—
40	C₄₃×#380	—	2	2	no	—
41	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₃	—	2	1	no	—
44	C₂²×Q₈×C₄₃	—	2	1	no	—
45	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	—	2	1	no	—
48	C₂³×C₄×C₄₃	—	2	1	no	—
49	C₂×D₈×C₄₃	—	2	2	no	—
50	C₂×D₈×C₄₃	—	2	2	no	—
51	C₂×D₈×C₄₃	Q₈	1	4	yes	complemented
52	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
54	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
55	C₄⋊Q₈×C₄₃	—	2	2	no	—
56	C₄⋊Q₈×C₄₃	—	2	2	no	—
57	C₄⋊Q₈×C₄₃	—	2	2	no	—
58	C₄⋊Q₈×C₄₃	—	2	2	no	—
59	C₂²⋊Q₈×C₄₃	—	4	8	no	—
60	C₄×D₄×C₄₃	—	2	2	no	—
61	C₄×D₄×C₄₃	—	2	2	no	—
62	C₄×D₄×C₄₃	—	2	2	no	—
63	C₄×D₄×C₄₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
76	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
77	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
78	#107×C₄₃	—	2	2	no	—
79	#107×C₄₃	—	2	4	no	—
80	#106×C₄₃	—	2	4	no	—
81	#106×C₄₃	—	2	4	no	—
82	#106×C₄₃	—	2	4	no	—
83	C₄⋊C₈×C₄₃	D₄	1	4	yes	—
84	#102×C₄₃	—	2	2	no	—
85	#102×C₄₃	—	2	2	no	—
86	#102×C₄₃	—	2	4	no	—
87	#102×C₄₃	—	2	4	no	—
88	#97×C₄₃	—	2	4	no	—
89	C₄×C₈×C₄₃	D₄	1	4	yes	—
90	#95×C₄₃	—	2	4	no	—
91	#95×C₄₃	D₄	1	2	yes	—
92	C₂⁴×C₄₃	—	2	1	no	—
93	C₂⁴×C₄₃	—	2	1	no	—
94	C₂×Q₈×C₄₃	—	4	2	no	—
95	C₂×Q₈×C₄₃	—	4	2	no	—
96	C₂×Q₈×C₄₃	—	4	4	no	—
97	C₂×Q₈×C₄₃	—	8	2	no	—
98	C₂×D₄×C₄₃	—	2	1	no	—
99	C₂×D₄×C₄₃	—	2	1	no	—
100	C₂×D₄×C₄₃	—	2	1	no	—
101	C₂×D₄×C₄₃	—	2	1	no	—
102	C₂×D₄×C₄₃	—	2	1	no	—
103	C₂×D₄×C₄₃	—	2	1	no	—
104	C₂×D₄×C₄₃	—	2	1	no	—
105	C₂×D₄×C₄₃	—	2	1	no	—
106	C₂×D₄×C₄₃	—	2	1	no	—
107	C₂×D₄×C₄₃	—	2	1	no	—
108	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
109	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	—	2	1	no	—
114	C₂²×C₄×C₄₃	—	4	2	no	—
115	C₂²×C₄×C₄₃	—	4	2	no	—
116	C₂²×C₄×C₄₃	—	4	4	no	—
117	C₂²×C₄×C₄₃	—	4	4	no	—
118	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
122	D₈×C₄₃	—	2	8	no	—
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₂×C₈×C₄₃	—	2	1	no	—
125	C₂×C₈×C₄₃	—	2	1	no	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
129	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
131	C₂×C₈×C₄₃	#41	1	2	yes	—
132	C₄⋊C₄×C₄₃	—	2	4	no	—
133	C₄⋊C₄×C₄₃	—	2	2	no	—
134	C₄⋊C₄×C₄₃	—	2	1	no	—
135	C₄⋊C₄×C₄₃	—	2	1	no	—
136	C₄⋊C₄×C₄₃	—	2	2	no	—
137	C₄⋊C₄×C₄₃	—	2	1	no	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	—	2	1	no	—
141	C₄⋊C₄×C₄₃	—	4	8	no	—
142	C₄⋊C₄×C₄₃	—	4	2	no	—
143	C₄⋊C₄×C₄₃	—	4	2	no	—
144	C₂²⋊C₄×C₄₃	—	4	8	no	—
145	C₂²⋊C₄×C₄₃	—	4	2	no	—
146	C₂²⋊C₄×C₄₃	—	4	2	no	—
147	C₂²⋊C₄×C₄₃	—	8	4	no	—
148	C₄²×C₄₃	—	2	2	no	—
149	C₄²×C₄₃	—	2	2	no	—
150	C₄²×C₄₃	C₂×D₄	1	2	yes	—
151	C₄²×C₄₃	C₂×D₄	1	2	yes	—
152	C₂³×C₄₃	—	2	2	no	—
153	C₂³×C₄₃	—	2	2	no	—
154	C₂³×C₄₃	—	4	1	no	—
155	C₂³×C₄₃	—	4	1	no	—
156	C₂³×C₄₃	—	4	1	no	—
157	C₂³×C₄₃	—	4	1	no	—
158	C₂³×C₄₃	—	4	2	no	—
159	C₂³×C₄₃	—	4	2	no	—
160	C₂³×C₄₃	—	4	2	no	—
161	C₂³×C₄₃	—	4	2	no	—
162	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₄₃	—	8	4	no	—
164	Q₈×C₄₃	—	8	4	no	—
165	D₄×C₄₃	—	2	2	no	—
166	D₄×C₄₃	—	2	2	no	—
167	D₄×C₄₃	—	2	2	no	—
168	D₄×C₄₃	—	2	2	no	—
169	D₄×C₄₃	—	4	1	no	—
170	D₄×C₄₃	—	4	1	no	—
171	D₄×C₄₃	—	4	1	no	—
172	D₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	4	no	—
175	C₂×C₄×C₄₃	—	2	4	no	—
176	C₂×C₄×C₄₃	—	2	4	no	—
177	C₂×C₄×C₄₃	—	4	1	no	—
178	C₂×C₄×C₄₃	—	4	1	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	—	4	2	no	—
181	C₂×C₄×C₄₃	—	4	4	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	4	4	no	—
185	C₂×C₄×C₄₃	—	8	4	no	—
186	C₂×C₄×C₄₃	—	8	4	no	—
187	C₂×C₄×C₄₃	#127	1	2	yes	—
188	C₂×C₄×C₄₃	#127	1	2	yes	—
189	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
190	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
195	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
196	C₈×C₄₃	—	2	2	no	—
197	C₈×C₄₃	—	2	4	no	—
198	C₈×C₄₃	C₂²⋊Q₈	1	4	yes	complemented
199	#28541	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂²×C₄₃	—	4	4	no	—
201	C₂²×C₄₃	—	4	4	no	—
202	C₂²×C₄₃	—	4	2	no	—
203	C₂²×C₄₃	—	4	2	no	—
204	C₂²×C₄₃	—	8	2	no	—
205	C₂²×C₄₃	—	8	2	no	—
206	C₂²×C₄₃	—	8	1	no	—
207	C₂²×C₄₃	—	8	1	no	—
208	C₂²×C₄₃	—	8	1	no	—
209	C₂²×C₄₃	—	8	1	no	—
210	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
211	C₂²×C₄₃	#547	1	1	yes	characteristic
212	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
213	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
214	C₂²×C₄₃	#577	1	2	yes	—
215	C₄×C₄₃	—	2	2	no	—
216	C₄×C₄₃	—	4	4	no	—
217	C₄×C₄₃	—	8	1	no	—
218	C₄×C₄₃	—	8	1	no	—
219	C₄×C₄₃	—	8	2	no	—
220	C₄×C₄₃	—	8	2	no	—
221	C₄×C₄₃	#496	1	4	yes	—
222	C₄×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
223	C₄×C₄₃	#536	1	1	yes	characteristic
224	C₄×C₄₃	#547	1	1	yes	characteristic
225	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
226	C₂×#498	C₂×C₄₃	1	1	yes	characteristic, complemented
227	C₂×#476	C₂×C₄₃	1	1	yes	characteristic, complemented
228	C₂×#474	C₂×C₄₃	1	1	yes	characteristic, complemented
229	C₂×C₄×D₈	C₂×C₄₃	1	1	yes	characteristic
230	#2563	C₂×C₄₃	1	1	yes	characteristic, complemented
231	#2542	C₂×C₄₃	1	1	yes	characteristic, complemented
232	#2094	C₂×C₄₃	1	2	yes	complemented
233	#2092	C₂×C₄₃	1	2	yes	complemented
234	#1972	C₂×C₄₃	1	2	yes	—
235	#1847	C₂×C₄₃	1	2	yes	complemented
236	#1770	C₂×C₄₃	1	1	yes	characteristic, complemented
237	C₂×C₄₃	—	8	2	no	—
238	C₂×C₄₃	—	8	2	no	—
239	C₂×C₄₃	#2542	1	1	yes	characteristic
240	C₂×C₄₃	C₂×#496	1	1	yes	characteristic
241	C₂×C₄₃	#3154	1	1	yes	characteristic
242	C₂×C₄₃	#3354	1	2	yes	—
243	C₂×C₄₃	#3384	1	2	yes	—
244	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic
245	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
246	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
247	C₂×C₂²⋊Q₈	—	2	2	no	—
248	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
250	#498	—	2	4	no	—
251	#476	—	2	4	no	—
252	#474	—	2	4	no	—
253	C₄×D₈	—	2	4	no	—
254	C₂×#107	C₂²×C₄₃	1	2	yes	—
255	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
256	C₂×#106	C₂²×C₄₃	1	2	yes	—
257	C₂×#106	C₂²×C₄₃	1	2	yes	—
258	C₂×#106	C₂²×C₄₃	1	2	yes	—
259	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
260	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
261	C₂×#102	C₂²×C₄₃	1	2	yes	—
262	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
263	C₂×#102	C₂²×C₄₃	1	2	yes	—
264	C₂×#97	C₂²×C₄₃	1	2	yes	—
265	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
266	#399	—	2	2	no	—
267	#393	—	2	2	no	—
268	#390	C₂²×C₄₃	1	2	yes	—
269	#390	C₂²×C₄₃	1	2	yes	—
270	#384	C₂²×C₄₃	1	2	yes	—
271	#382	C₂²×C₄₃	1	2	yes	—
272	#380	—	2	2	no	—
273	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
274	#336	C₂²×C₄₃	1	2	yes	—
275	C₄₃	#28541	1	1	yes	characteristic, direct product factor, Sylow
276	C₂²×Q₈	—	2	1	no	—
277	C₂²×Q₈	—	2	1	no	—
278	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
279	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
280	C₂³×C₄	—	2	1	no	—
281	C₂³×C₄	—	2	1	no	—
282	C₂×D₈	—	2	2	no	—
283	C₂×D₈	—	2	2	no	—
284	C₂×D₈	Q₈×C₄₃	1	4	yes	complemented
285	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
287	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
288	C₄⋊Q₈	—	2	2	no	—
289	C₄⋊Q₈	—	2	2	no	—
290	C₄⋊Q₈	—	2	2	no	—
291	C₄⋊Q₈	—	2	2	no	—
292	C₂²⋊Q₈	—	4	8	no	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	2	4	no	—
308	C₂×C₂²⋊C₄	—	2	4	no	—
309	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
310	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
311	#107	—	2	2	no	—
312	#107	—	2	4	no	—
313	#106	—	2	4	no	—
314	#106	—	2	4	no	—
315	#106	—	2	4	no	—
316	C₄⋊C₈	D₄×C₄₃	1	4	yes	—
317	#102	—	2	2	no	—
318	#102	—	2	2	no	—
319	#102	—	2	4	no	—
320	#102	—	2	4	no	—
321	#97	—	2	4	no	—
322	C₄×C₈	D₄×C₄₃	1	4	yes	—
323	#95	—	2	4	no	—
324	#95	D₄×C₄₃	1	2	yes	—
325	C₂⁴	—	2	1	no	—
326	C₂⁴	—	2	1	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	4	4	no	—
330	C₂×Q₈	—	8	2	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	C₂×Q₈×C₄₃	1	2	yes	—
342	C₂×D₄	C₂×Q₈×C₄₃	1	2	yes	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	—	4	4	no	—
351	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
352	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
354	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
355	D₈	—	2	8	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
361	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
362	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
363	C₂×C₈	C₂×Q₈×C₄₃	1	2	yes	—
364	C₂×C₈	#41×C₄₃	1	2	yes	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	4	8	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₂²⋊C₄	—	4	8	no	—
378	C₂²⋊C₄	—	4	2	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	—	8	4	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	C₂×D₄×C₄₃	1	2	yes	—
384	C₄²	C₂×D₄×C₄₃	1	2	yes	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
396	Q₈	—	8	4	no	—
397	Q₈	—	8	4	no	—
398	D₄	—	2	2	no	—
399	D₄	—	2	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	4	1	no	—
403	D₄	—	4	1	no	—
404	D₄	—	4	1	no	—
405	D₄	—	4	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	8	4	no	—
419	C₂×C₄	—	8	4	no	—
420	C₂×C₄	#127×C₄₃	1	2	yes	—
421	C₂×C₄	#127×C₄₃	1	2	yes	—
422	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
423	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
425	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
426	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
427	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
428	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
429	C₈	—	2	2	no	—
430	C₈	—	2	4	no	—
431	C₈	C₂²⋊Q₈×C₄₃	1	4	yes	complemented
432	C₂²	—	4	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	8	1	no	—
441	C₂²	—	8	1	no	—
442	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
443	C₂²	C₄₃×#547	1	1	yes	characteristic
444	C₂²	D₄×Q₈×C₄₃	1	1	yes	characteristic
445	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
446	C₂²	C₄₃×#577	1	2	yes	—
447	C₄	—	2	2	no	—
448	C₄	—	4	4	no	—
449	C₄	—	8	1	no	—
450	C₄	—	8	1	no	—
451	C₄	—	8	2	no	—
452	C₄	—	8	2	no	—
453	C₄	C₄₃×#496	1	4	yes	—
454	C₄	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
455	C₄	C₄₃×#536	1	1	yes	characteristic
456	C₄	C₄₃×#547	1	1	yes	characteristic
457	C₄	D₄×Q₈×C₄₃	1	1	yes	characteristic
458	C₂	—	8	2	no	—
459	C₂	—	8	2	no	—
460	C₂	C₄₃×#2542	1	1	yes	characteristic
461	C₂	C₂×C₄₃×#496	1	1	yes	characteristic
462	C₂	C₄₃×#3154	1	1	yes	characteristic
463	C₂	C₄₃×#3354	1	2	yes	—
464	C₂	C₄₃×#3384	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×D₈×C₄₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₄×C₄⋊C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#498	C₂	semidirect
2. C₂×C₄₃×#476	C₂	semidirect
3. C₂×C₄₃×#474	C₂	semidirect
5. C₄₃×#2563	C₂	semidirect
6. C₄₃×#2542	C₂	semidirect
7. C₄₃×#2094	C₂	semidirect
8. C₄₃×#2092	C₂	semidirect
10. C₄₃×#1847	C₂	semidirect
11. C₄₃×#1770	C₂	semidirect
51. C₂×D₈×C₄₃	Q₈	semidirect
198. C₈×C₄₃	C₂²⋊Q₈	semidirect
199. #28541	C₄₃	direct (N × H)
226. C₂×#498	C₂×C₄₃	semidirect
227. C₂×#476	C₂×C₄₃	semidirect
228. C₂×#474	C₂×C₄₃	semidirect
230. #2563	C₂×C₄₃	semidirect
231. #2542	C₂×C₄₃	semidirect
232. #2094	C₂×C₄₃	semidirect
233. #2092	C₂×C₄₃	semidirect
235. #1847	C₂×C₄₃	semidirect
236. #1770	C₂×C₄₃	semidirect
275. C₄₃	#28541	direct (N × H)
284. C₂×D₈	Q₈×C₄₃	semidirect
431. C₈	C₂²⋊Q₈×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×#498	2
C₂×C₄₃×#476	2
C₂×C₄₃×#474	2
C₂×C₄×D₈×C₄₃	2
C₄₃×#2563	2
C₄₃×#2542	2
C₄₃×#2094	2
C₄₃×#2092	2
C₄₃×#1972	2
C₄₃×#1847	2
C₄₃×#1770	2
#28541	43

Subgroups — C43×#28541 #24948558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28541 #24948558