Subgroups — C₄₃×#28398 #24948415

Order 11008.

970 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#461	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×#2547	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2097	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2012	C₂	1	2	yes	maximal
9	C₄₃×#1968	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1958	C₂	1	2	yes	maximal, complemented
11	C₈×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
13	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#124×C₄₃	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#487	—	2	4	no	—
20	C₄₃×#476	—	2	4	no	—
21	C₄₃×#461	—	2	4	no	—
22	C₄×D₈×C₄₃	—	2	4	no	—
23	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#106×C₄₃	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#103×C₄₃	C₂²	1	2	yes	—
27	C₂×#103×C₄₃	C₂²	1	2	yes	—
28	C₂×#103×C₄₃	C₂²	1	2	yes	—
29	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×#102×C₄₃	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
34	C₄₃×#397	—	2	2	no	—
35	C₄₃×#393	—	2	2	no	—
36	C₄₃×#391	C₂²	1	2	yes	—
37	C₄₃×#390	C₂²	1	2	yes	—
38	C₄₃×#382	C₂²	1	2	yes	—
39	C₄₃×#380	—	2	2	no	—
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	C₂³	1	2	yes	—
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×SD₁₆×C₄₃	—	2	4	no	—
50	C₂×SD₁₆×C₄₃	—	2	4	no	—
51	C₂×SD₁₆×C₄₃	—	4	2	no	—
52	C₂×D₈×C₄₃	—	2	2	no	—
53	C₂×D₈×C₄₃	—	2	2	no	—
54	C₂×D₈×C₄₃	—	2	2	no	—
55	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₄₃	—	2	2	no	—
59	C₄⋊Q₈×C₄₃	—	2	2	no	—
60	C₄⋊Q₈×C₄₃	—	2	2	no	—
61	C₄⋊Q₈×C₄₃	—	2	2	no	—
62	#124×C₄₃	—	2	4	no	—
63	#124×C₄₃	—	4	2	no	—
64	C₄×D₄×C₄₃	—	2	2	no	—
65	C₄×D₄×C₄₃	—	2	2	no	—
66	C₄×D₄×C₄₃	—	2	2	no	—
67	C₄×D₄×C₄₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
79	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
80	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
81	#107×C₄₃	—	2	2	no	—
82	#106×C₄₃	—	2	4	no	—
83	C₄⋊C₈×C₄₃	D₄	1	4	yes	—
84	#103×C₄₃	—	2	4	no	—
85	#103×C₄₃	—	2	4	no	—
86	#103×C₄₃	—	2	4	no	—
87	#102×C₄₃	—	2	2	no	—
88	#102×C₄₃	—	2	2	no	—
89	#102×C₄₃	—	2	4	no	—
90	C₄×C₈×C₄₃	—	4	2	no	—
91	C₄×C₈×C₄₃	D₄	1	4	yes	—
92	#95×C₄₃	—	2	4	no	—
93	#95×C₄₃	—	2	4	no	—
94	#95×C₄₃	D₄	1	2	yes	—
95	C₂⁴×C₄₃	—	2	1	no	—
96	C₂⁴×C₄₃	—	2	1	no	—
97	C₂×Q₈×C₄₃	—	2	2	no	—
98	C₂×Q₈×C₄₃	—	2	2	no	—
99	C₂×Q₈×C₄₃	—	2	2	no	—
100	C₂×Q₈×C₄₃	—	2	2	no	—
101	C₂×Q₈×C₄₃	—	2	2	no	—
102	C₂×Q₈×C₄₃	—	2	2	no	—
103	C₂×Q₈×C₄₃	—	4	2	no	—
104	C₂×Q₈×C₄₃	—	8	2	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	—	2	1	no	—
109	C₂×D₄×C₄₃	—	2	1	no	—
110	C₂×D₄×C₄₃	—	2	1	no	—
111	C₂×D₄×C₄₃	—	2	1	no	—
112	C₂×D₄×C₄₃	—	2	1	no	—
113	C₂×D₄×C₄₃	—	2	1	no	—
114	C₂×D₄×C₄₃	—	2	1	no	—
115	C₂×D₄×C₄₃	#41	1	2	yes	—
116	C₂×D₄×C₄₃	#41	1	2	yes	—
117	C₂²×C₄×C₄₃	—	2	1	no	—
118	C₂²×C₄×C₄₃	—	2	1	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	4	2	no	—
122	C₂²×C₄×C₄₃	—	4	2	no	—
123	C₂²×C₄×C₄₃	—	4	4	no	—
124	C₂²×C₄×C₄₃	—	4	4	no	—
125	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
129	SD₁₆×C₄₃	—	4	8	no	—
130	D₈×C₄₃	—	2	8	no	—
131	C₂×C₈×C₄₃	—	2	1	no	—
132	C₂×C₈×C₄₃	—	2	1	no	—
133	C₂×C₈×C₄₃	—	2	2	no	—
134	C₂×C₈×C₄₃	—	2	1	no	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	—	2	1	no	—
137	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
140	C₄⋊C₄×C₄₃	—	2	4	no	—
141	C₄⋊C₄×C₄₃	—	2	2	no	—
142	C₄⋊C₄×C₄₃	—	2	1	no	—
143	C₄⋊C₄×C₄₃	—	2	1	no	—
144	C₄⋊C₄×C₄₃	—	2	1	no	—
145	C₄⋊C₄×C₄₃	—	2	2	no	—
146	C₄⋊C₄×C₄₃	—	2	1	no	—
147	C₄⋊C₄×C₄₃	—	4	2	no	—
148	C₄⋊C₄×C₄₃	—	4	2	no	—
149	C₄⋊C₄×C₄₃	—	4	2	no	—
150	C₂²⋊C₄×C₄₃	—	4	8	no	—
151	C₂²⋊C₄×C₄₃	—	4	2	no	—
152	C₂²⋊C₄×C₄₃	—	4	2	no	—
153	C₂²⋊C₄×C₄₃	—	8	4	no	—
154	C₄²×C₄₃	—	2	2	no	—
155	C₄²×C₄₃	—	2	2	no	—
156	C₄²×C₄₃	C₂×D₄	1	2	yes	—
157	C₄²×C₄₃	C₂×D₄	1	2	yes	—
158	C₂³×C₄₃	—	2	2	no	—
159	C₂³×C₄₃	—	2	2	no	—
160	C₂³×C₄₃	—	4	1	no	—
161	C₂³×C₄₃	—	4	1	no	—
162	C₂³×C₄₃	—	4	1	no	—
163	C₂³×C₄₃	—	4	1	no	—
164	C₂³×C₄₃	—	4	2	no	—
165	C₂³×C₄₃	—	4	2	no	—
166	C₂³×C₄₃	—	4	2	no	—
167	C₂³×C₄₃	—	4	2	no	—
168	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₄₃	—	4	2	no	—
170	Q₈×C₄₃	—	4	2	no	—
171	Q₈×C₄₃	—	4	2	no	—
172	Q₈×C₄₃	—	4	2	no	—
173	Q₈×C₄₃	—	8	4	no	—
174	D₄×C₄₃	—	2	2	no	—
175	D₄×C₄₃	—	2	2	no	—
176	D₄×C₄₃	—	2	2	no	—
177	D₄×C₄₃	—	2	2	no	—
178	D₄×C₄₃	—	4	1	no	—
179	D₄×C₄₃	—	4	1	no	—
180	D₄×C₄₃	—	4	1	no	—
181	D₄×C₄₃	—	4	1	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	4	no	—
184	C₂×C₄×C₄₃	—	2	4	no	—
185	C₂×C₄×C₄₃	—	2	4	no	—
186	C₂×C₄×C₄₃	—	4	1	no	—
187	C₂×C₄×C₄₃	—	4	1	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	4	2	no	—
190	C₂×C₄×C₄₃	—	4	2	no	—
191	C₂×C₄×C₄₃	—	4	2	no	—
192	C₂×C₄×C₄₃	—	4	2	no	—
193	C₂×C₄×C₄₃	—	4	2	no	—
194	C₂×C₄×C₄₃	—	4	4	no	—
195	C₂×C₄×C₄₃	—	8	4	no	—
196	C₂×C₄×C₄₃	—	8	4	no	—
197	C₂×C₄×C₄₃	#127	1	2	yes	—
198	C₂×C₄×C₄₃	#127	1	2	yes	—
199	C₂×C₄×C₄₃	#135	1	4	yes	—
200	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
206	C₈×C₄₃	—	2	2	no	—
207	C₈×C₄₃	—	2	2	no	—
208	C₈×C₄₃	—	2	4	no	—
209	#28398	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂²×C₄₃	—	4	4	no	—
211	C₂²×C₄₃	—	4	4	no	—
212	C₂²×C₄₃	—	4	2	no	—
213	C₂²×C₄₃	—	4	2	no	—
214	C₂²×C₄₃	—	8	2	no	—
215	C₂²×C₄₃	—	8	1	no	—
216	C₂²×C₄₃	—	8	1	no	—
217	C₂²×C₄₃	—	8	1	no	—
218	C₂²×C₄₃	—	8	1	no	—
219	C₂²×C₄₃	—	8	2	no	—
220	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
221	C₂²×C₄₃	#546	1	1	yes	characteristic
222	C₂²×C₄₃	#548	1	1	yes	characteristic
223	C₂²×C₄₃	C₂×#135	1	2	yes	—
224	C₂²×C₄₃	#577	1	2	yes	—
225	C₄×C₄₃	—	2	2	no	—
226	C₄×C₄₃	—	4	4	no	—
227	C₄×C₄₃	—	8	1	no	—
228	C₄×C₄₃	—	8	1	no	—
229	C₄×C₄₃	—	8	2	no	—
230	C₄×C₄₃	—	8	2	no	—
231	C₄×C₄₃	#495	1	4	yes	—
232	C₄×C₄₃	#525	1	1	yes	characteristic
233	C₄×C₄₃	#537	1	1	yes	characteristic
234	C₄×C₄₃	#546	1	1	yes	characteristic
235	C₄×C₄₃	#548	1	1	yes	characteristic
236	C₂×#487	C₂×C₄₃	1	1	yes	characteristic, complemented
237	C₂×#476	C₂×C₄₃	1	1	yes	characteristic, complemented
238	C₂×#461	C₂×C₄₃	1	1	yes	characteristic, complemented
239	C₂×C₄×D₈	C₂×C₄₃	1	1	yes	characteristic
240	#2563	C₂×C₄₃	1	1	yes	characteristic, complemented
241	#2547	C₂×C₄₃	1	1	yes	characteristic, complemented
242	#2097	C₂×C₄₃	1	2	yes	complemented
243	#2012	C₂×C₄₃	1	2	yes	—
244	#1968	C₂×C₄₃	1	2	yes	complemented
245	#1958	C₂×C₄₃	1	2	yes	complemented
246	C₈×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic, complemented
247	C₂×C₄₃	—	8	2	no	—
248	C₂×C₄₃	—	8	2	no	—
249	C₂×C₄₃	#2540	1	1	yes	characteristic
250	C₂×C₄₃	C₂×#495	1	1	yes	characteristic
251	C₂×C₄₃	#3154	1	1	yes	characteristic
252	C₂×C₄₃	#3303	1	2	yes	—
253	C₂×C₄₃	#3360	1	2	yes	—
254	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
255	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic
256	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
257	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
258	C₂×#124	C₂²×C₄₃	1	2	yes	—
259	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
260	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
261	#487	—	2	4	no	—
262	#476	—	2	4	no	—
263	#461	—	2	4	no	—
264	C₄×D₈	—	2	4	no	—
265	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
266	C₂×#106	C₂²×C₄₃	1	2	yes	—
267	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
268	C₂×#103	C₂²×C₄₃	1	2	yes	—
269	C₂×#103	C₂²×C₄₃	1	2	yes	—
270	C₂×#103	C₂²×C₄₃	1	2	yes	—
271	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
272	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
273	C₂×#102	C₂²×C₄₃	1	2	yes	—
274	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	—
275	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
276	#397	—	2	2	no	—
277	#393	—	2	2	no	—
278	#391	C₂²×C₄₃	1	2	yes	—
279	#390	C₂²×C₄₃	1	2	yes	—
280	#382	C₂²×C₄₃	1	2	yes	—
281	#380	—	2	2	no	—
282	#380	—	2	2	no	—
283	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
284	#336	C₂²×C₄₃	1	2	yes	—
285	C₄₃	#28398	1	1	yes	characteristic, direct product factor, Sylow
286	C₂²×Q₈	—	2	1	no	—
287	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
288	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
289	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
290	C₂³×C₄	—	2	1	no	—
291	C₂³×C₄	—	2	1	no	—
292	C₂×SD₁₆	—	2	4	no	—
293	C₂×SD₁₆	—	2	4	no	—
294	C₂×SD₁₆	—	4	2	no	—
295	C₂×D₈	—	2	2	no	—
296	C₂×D₈	—	2	2	no	—
297	C₂×D₈	—	2	2	no	—
298	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
300	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	—	2	2	no	—
303	C₄⋊Q₈	—	2	2	no	—
304	C₄⋊Q₈	—	2	2	no	—
305	#124	—	2	4	no	—
306	#124	—	4	2	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	—	2	2	no	—
309	C₄×D₄	—	2	2	no	—
310	C₄×D₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	4	no	—
321	C₂×C₂²⋊C₄	—	2	4	no	—
322	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
323	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
324	#107	—	2	2	no	—
325	#106	—	2	4	no	—
326	C₄⋊C₈	D₄×C₄₃	1	4	yes	—
327	#103	—	2	4	no	—
328	#103	—	2	4	no	—
329	#103	—	2	4	no	—
330	#102	—	2	2	no	—
331	#102	—	2	2	no	—
332	#102	—	2	4	no	—
333	C₄×C₈	—	4	2	no	—
334	C₄×C₈	D₄×C₄₃	1	4	yes	—
335	#95	—	2	4	no	—
336	#95	—	2	4	no	—
337	#95	D₄×C₄₃	1	2	yes	—
338	C₂⁴	—	2	1	no	—
339	C₂⁴	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	4	2	no	—
347	C₂×Q₈	—	8	2	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	#41×C₄₃	1	2	yes	—
359	C₂×D₄	#41×C₄₃	1	2	yes	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	—	4	4	no	—
368	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
369	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
372	SD₁₆	—	4	8	no	—
373	D₈	—	2	8	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
381	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
382	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₂²⋊C₄	—	4	8	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	8	4	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	C₂×D₄×C₄₃	1	2	yes	—
400	C₄²	C₂×D₄×C₄₃	1	2	yes	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
412	Q₈	—	4	2	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	8	4	no	—
417	D₄	—	2	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	2	2	no	—
420	D₄	—	2	2	no	—
421	D₄	—	4	1	no	—
422	D₄	—	4	1	no	—
423	D₄	—	4	1	no	—
424	D₄	—	4	1	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	8	4	no	—
439	C₂×C₄	—	8	4	no	—
440	C₂×C₄	#127×C₄₃	1	2	yes	—
441	C₂×C₄	#127×C₄₃	1	2	yes	—
442	C₂×C₄	#135×C₄₃	1	4	yes	—
443	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
444	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
445	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
446	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
447	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
448	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
449	C₈	—	2	2	no	—
450	C₈	—	2	2	no	—
451	C₈	—	2	4	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	4	4	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	8	2	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	1	no	—
461	C₂²	—	8	2	no	—
462	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
463	C₂²	C₄₃×#546	1	1	yes	characteristic
464	C₂²	C₄₃×#548	1	1	yes	characteristic
465	C₂²	C₂×#135×C₄₃	1	2	yes	—
466	C₂²	C₄₃×#577	1	2	yes	—
467	C₄	—	2	2	no	—
468	C₄	—	4	4	no	—
469	C₄	—	8	1	no	—
470	C₄	—	8	1	no	—
471	C₄	—	8	2	no	—
472	C₄	—	8	2	no	—
473	C₄	C₄₃×#495	1	4	yes	—
474	C₄	C₄₃×#525	1	1	yes	characteristic
475	C₄	C₄₃×#537	1	1	yes	characteristic
476	C₄	C₄₃×#546	1	1	yes	characteristic
477	C₄	C₄₃×#548	1	1	yes	characteristic
478	C₂	—	8	2	no	—
479	C₂	—	8	2	no	—
480	C₂	C₄₃×#2540	1	1	yes	characteristic
481	C₂	C₂×C₄₃×#495	1	1	yes	characteristic
482	C₂	C₄₃×#3154	1	1	yes	characteristic
483	C₂	C₄₃×#3303	1	2	yes	—
484	C₂	C₄₃×#3360	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×#487	C₂	semidirect
2. C₂×C₄₃×#476	C₂	semidirect
3. C₂×C₄₃×#461	C₂	semidirect
5. C₄₃×#2563	C₂	semidirect
6. C₄₃×#2547	C₂	semidirect
7. C₄₃×#2097	C₂	semidirect
9. C₄₃×#1968	C₂	semidirect
10. C₄₃×#1958	C₂	semidirect
11. C₈×C₄⋊C₄×C₄₃	C₂	semidirect
209. #28398	C₄₃	direct (N × H)
236. C₂×#487	C₂×C₄₃	semidirect
237. C₂×#476	C₂×C₄₃	semidirect
238. C₂×#461	C₂×C₄₃	semidirect
240. #2563	C₂×C₄₃	semidirect
241. #2547	C₂×C₄₃	semidirect
242. #2097	C₂×C₄₃	semidirect
244. #1968	C₂×C₄₃	semidirect
245. #1958	C₂×C₄₃	semidirect
246. C₈×C₄⋊C₄	C₂×C₄₃	semidirect
285. C₄₃	#28398	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#487	2
C₂×C₄₃×#476	2
C₂×C₄₃×#461	2
C₂×C₄×D₈×C₄₃	2
C₄₃×#2563	2
C₄₃×#2547	2
C₄₃×#2097	2
C₄₃×#2012	2
C₄₃×#1968	2
C₄₃×#1958	2
C₈×C₄⋊C₄×C₄₃	2
#28398	43

Subgroups — C43×#28398 #24948415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28398 #24948415