Subgroups — C₄₃×#25735 #24945752

Order 11008.

1466 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#536	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#452	C₂	1	2	yes	maximal
5	C₂×C₄₃×#451	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2621	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2016	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2015	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1958	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1750	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
15	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
16	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
17	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
18	C₄₃×#536	—	2	4	no	—
19	C₄₃×#536	—	2	4	no	—
20	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#123×C₄₃	—	2	2	no	—
26	C₂×C₂²⋊Q₈×C₄₃	—	2	2	no	—
27	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
28	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
29	C₄₃×#497	—	2	4	no	—
30	C₄₃×#494	—	2	4	no	—
31	C₄₃×#452	—	2	8	no	—
32	C₄₃×#451	—	2	8	no	—
33	C₂×#103×C₄₃	C₂²	1	2	yes	—
34	C₂×#103×C₄₃	C₂²	1	2	yes	—
35	C₂×#103×C₄₃	C₂²	1	2	yes	—
36	C₂×#102×C₄₃	C₂²	1	2	yes	—
37	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
38	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#398	—	2	2	no	—
41	C₄₃×#397	—	2	2	no	—
42	C₄₃×#391	C₂²	1	2	yes	—
43	C₄₃×#382	C₂²	1	1	yes	characteristic
44	C₄₃×#336	C₂²	1	2	yes	—
45	C₂×#41×C₄₃	—	2	2	no	—
46	C₂×#41×C₄₃	—	2	2	no	—
47	C₂×#41×C₄₃	—	2	4	no	—
48	C₂×#41×C₄₃	—	4	2	no	—
49	C₂²×Q₈×C₄₃	—	2	2	no	—
50	C₂²×Q₈×C₄₃	—	2	2	no	—
51	C₂²×Q₈×C₄₃	—	2	1	no	—
52	C₂²×Q₈×C₄₃	—	2	4	no	—
53	C₂²×Q₈×C₄₃	—	4	2	no	—
54	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
55	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
56	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₄₃	—	2	1	no	—
59	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₄₃	—	2	1	no	—
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	—	2	4	no	—
66	C₂×Q₁₆×C₄₃	—	2	4	no	—
67	C₂×Q₁₆×C₄₃	—	2	4	no	—
68	C₂×Q₁₆×C₄₃	—	2	4	no	—
69	C₂×Q₁₆×C₄₃	—	4	2	no	—
70	C₂×Q₁₆×C₄₃	—	4	2	no	—
71	C₂×Q₁₆×C₄₃	—	4	2	no	—
72	C₂×SD₁₆×C₄₃	—	2	4	no	—
73	C₂×SD₁₆×C₄₃	—	2	4	no	—
74	C₂×SD₁₆×C₄₃	—	4	2	no	—
75	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
76	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
77	C₄⋊Q₈×C₄₃	—	2	2	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	—	2	2	no	—
82	C₄⋊Q₈×C₄₃	D₄	1	4	yes	—
83	#124×C₄₃	—	2	2	no	—
84	#124×C₄₃	—	2	2	no	—
85	#124×C₄₃	—	2	2	no	—
86	#124×C₄₃	D₄	1	4	yes	—
87	#123×C₄₃	—	2	16	no	—
88	C₂²⋊Q₈×C₄₃	—	2	16	no	—
89	C₂²⋊Q₈×C₄₃	—	2	4	no	—
90	C₂²⋊Q₈×C₄₃	—	2	4	no	—
91	#117×C₄₃	—	2	2	no	—
92	#117×C₄₃	—	2	2	no	—
93	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
94	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
95	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
96	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
97	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
98	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
99	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
105	#103×C₄₃	—	2	4	no	—
106	#103×C₄₃	—	2	4	no	—
107	#103×C₄₃	—	2	4	no	—
108	#102×C₄₃	—	2	4	no	—
109	C₂²⋊C₈×C₄₃	D₄	1	8	yes	—
110	#97×C₄₃	—	2	2	no	—
111	C₄×C₈×C₄₃	—	2	2	no	—
112	#95×C₄₃	—	2	2	no	—
113	#95×C₄₃	—	2	4	no	—
114	C₂⁴×C₄₃	—	2	1	no	—
115	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
116	#41×C₄₃	—	4	8	no	—
117	#41×C₄₃	—	4	8	no	—
118	C₂×Q₈×C₄₃	—	2	4	no	—
119	C₂×Q₈×C₄₃	—	2	1	no	—
120	C₂×Q₈×C₄₃	—	2	1	no	—
121	C₂×Q₈×C₄₃	—	2	1	no	—
122	C₂×Q₈×C₄₃	—	2	2	no	—
123	C₂×Q₈×C₄₃	—	2	2	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	—	2	2	no	—
128	C₂×Q₈×C₄₃	—	2	2	no	—
129	C₂×Q₈×C₄₃	—	2	2	no	—
130	C₂×Q₈×C₄₃	—	2	2	no	—
131	C₂×Q₈×C₄₃	—	2	2	no	—
132	C₂×Q₈×C₄₃	—	2	2	no	—
133	C₂×Q₈×C₄₃	—	2	2	no	—
134	C₂×Q₈×C₄₃	—	4	8	no	—
135	C₂×Q₈×C₄₃	—	4	8	no	—
136	C₂×Q₈×C₄₃	—	4	2	no	—
137	C₂×Q₈×C₄₃	—	4	2	no	—
138	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
139	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
140	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
141	C₂×D₄×C₄₃	—	2	4	no	—
142	C₂×D₄×C₄₃	—	2	1	no	—
143	C₂×D₄×C₄₃	—	2	2	no	—
144	C₂×D₄×C₄₃	—	2	2	no	—
145	C₂×D₄×C₄₃	—	4	2	no	—
146	C₂×D₄×C₄₃	—	4	2	no	—
147	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₄₃	—	2	1	no	—
149	C₂²×C₄×C₄₃	—	2	1	no	—
150	C₂²×C₄×C₄₃	—	2	2	no	—
151	C₂²×C₄×C₄₃	—	2	4	no	—
152	C₂²×C₄×C₄₃	—	2	4	no	—
153	C₂²×C₄×C₄₃	—	2	1	no	—
154	C₂²×C₄×C₄₃	—	2	1	no	—
155	C₂²×C₄×C₄₃	—	2	1	no	—
156	C₂²×C₄×C₄₃	—	2	2	no	—
157	C₂²×C₄×C₄₃	—	2	2	no	—
158	C₂²×C₄×C₄₃	—	4	2	no	—
159	C₂²×C₄×C₄₃	—	4	2	no	—
160	C₂²×C₄×C₄₃	—	4	2	no	—
161	C₂²×C₄×C₄₃	—	4	2	no	—
162	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
167	Q₁₆×C₄₃	—	4	8	no	—
168	Q₁₆×C₄₃	—	4	8	no	—
169	Q₁₆×C₄₃	—	4	8	no	—
170	SD₁₆×C₄₃	—	4	8	no	—
171	C₂×C₈×C₄₃	—	2	2	no	—
172	C₂×C₈×C₄₃	—	2	2	no	—
173	C₂×C₈×C₄₃	—	2	2	no	—
174	C₂×C₈×C₄₃	—	2	2	no	—
175	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
176	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
177	C₄⋊C₄×C₄₃	—	2	8	no	—
178	C₄⋊C₄×C₄₃	—	2	8	no	—
179	C₄⋊C₄×C₄₃	—	2	4	no	—
180	C₄⋊C₄×C₄₃	—	2	2	no	—
181	C₄⋊C₄×C₄₃	—	2	2	no	—
182	C₄⋊C₄×C₄₃	—	4	4	no	—
183	C₄⋊C₄×C₄₃	—	4	4	no	—
184	C₂²⋊C₄×C₄₃	—	2	8	no	—
185	C₂²⋊C₄×C₄₃	—	2	8	no	—
186	C₂²⋊C₄×C₄₃	—	2	4	no	—
187	C₂²⋊C₄×C₄₃	—	4	4	no	—
188	C₄²×C₄₃	—	2	1	no	—
189	C₄²×C₄₃	—	2	1	no	—
190	C₄²×C₄₃	C₂×D₄	1	2	yes	—
191	C₄²×C₄₃	C₂×D₄	1	2	yes	—
192	C₂³×C₄₃	—	2	1	no	—
193	C₂³×C₄₃	—	2	1	no	—
194	C₂³×C₄₃	—	2	4	no	—
195	C₂³×C₄₃	—	2	2	no	—
196	C₂³×C₄₃	—	4	1	no	—
197	C₂³×C₄₃	—	4	1	no	—
198	C₂³×C₄₃	—	4	4	no	—
199	C₂³×C₄₃	#127	1	2	yes	—
200	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₄₃	—	2	4	no	—
202	Q₈×C₄₃	—	2	4	no	—
203	Q₈×C₄₃	—	2	4	no	—
204	Q₈×C₄₃	—	4	8	no	—
205	Q₈×C₄₃	—	4	2	no	—
206	Q₈×C₄₃	—	4	2	no	—
207	Q₈×C₄₃	—	4	2	no	—
208	Q₈×C₄₃	—	4	2	no	—
209	Q₈×C₄₃	—	4	2	no	—
210	Q₈×C₄₃	—	4	2	no	—
211	Q₈×C₄₃	—	4	2	no	—
212	D₄×C₄₃	—	2	4	no	—
213	D₄×C₄₃	—	4	8	no	—
214	D₄×C₄₃	—	4	2	no	—
215	C₂×C₄×C₄₃	—	2	1	no	—
216	C₂×C₄×C₄₃	—	2	1	no	—
217	C₂×C₄×C₄₃	—	2	4	no	—
218	C₂×C₄×C₄₃	—	2	4	no	—
219	C₂×C₄×C₄₃	—	2	4	no	—
220	C₂×C₄×C₄₃	—	2	2	no	—
221	C₂×C₄×C₄₃	—	2	2	no	—
222	C₂×C₄×C₄₃	—	2	2	no	—
223	C₂×C₄×C₄₃	—	2	2	no	—
224	C₂×C₄×C₄₃	—	2	4	no	—
225	C₂×C₄×C₄₃	—	4	8	no	—
226	C₂×C₄×C₄₃	—	4	8	no	—
227	C₂×C₄×C₄₃	—	4	1	no	—
228	C₂×C₄×C₄₃	—	4	1	no	—
229	C₂×C₄×C₄₃	—	4	1	no	—
230	C₂×C₄×C₄₃	—	4	1	no	—
231	C₂×C₄×C₄₃	—	4	1	no	—
232	C₂×C₄×C₄₃	—	4	1	no	—
233	C₂×C₄×C₄₃	—	4	2	no	—
234	C₂×C₄×C₄₃	—	4	2	no	—
235	C₂×C₄×C₄₃	—	4	2	no	—
236	C₂×C₄×C₄₃	—	4	2	no	—
237	C₂×C₄×C₄₃	—	4	4	no	—
238	C₂×C₄×C₄₃	#120	1	4	yes	—
239	C₂×C₄×C₄₃	#127	1	2	yes	—
240	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
244	C₈×C₄₃	—	2	4	no	—
245	C₈×C₄₃	—	2	4	no	—
246	#25735	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂²×C₄₃	—	2	4	no	—
248	C₂²×C₄₃	—	2	2	no	—
249	C₂²×C₄₃	—	4	2	no	—
250	C₂²×C₄₃	—	4	2	no	—
251	C₂²×C₄₃	—	4	2	no	—
252	C₂²×C₄₃	—	4	4	no	—
253	C₂²×C₄₃	—	8	2	no	—
254	C₂²×C₄₃	—	8	2	no	—
255	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
256	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
257	C₂²×C₄₃	#535	1	1	yes	characteristic
258	C₂²×C₄₃	#578	1	4	yes	—
259	C₄×C₄₃	—	2	2	no	—
260	C₄×C₄₃	—	2	4	no	—
261	C₄×C₄₃	—	4	2	no	—
262	C₄×C₄₃	—	4	2	no	—
263	C₄×C₄₃	—	4	2	no	—
264	C₄×C₄₃	—	4	2	no	—
265	C₄×C₄₃	—	8	2	no	—
266	C₄×C₄₃	—	8	2	no	—
267	C₄×C₄₃	D₄²	1	2	yes	—
268	C₄×C₄₃	D₄²	1	2	yes	—
269	C₂×#536	C₂×C₄₃	1	1	yes	characteristic
270	C₂×#497	C₂×C₄₃	1	1	yes	characteristic, complemented
271	C₂×#494	C₂×C₄₃	1	1	yes	characteristic, complemented
272	C₂×#452	C₂×C₄₃	1	2	yes	—
273	C₂×#451	C₂×C₄₃	1	2	yes	complemented
274	#2621	C₂×C₄₃	1	1	yes	characteristic, complemented
275	#2016	C₂×C₄₃	1	2	yes	complemented
276	#2015	C₂×C₄₃	1	2	yes	complemented
277	#1960	C₂×C₄₃	1	1	yes	characteristic, complemented
278	#1958	C₂×C₄₃	1	1	yes	characteristic, complemented
279	#1750	C₂×C₄₃	1	1	yes	characteristic, complemented
280	C₂×C₄₃	—	4	2	no	—
281	C₂×C₄₃	—	8	2	no	—
282	C₂×C₄₃	#2433	1	1	yes	characteristic
283	C₂×C₄₃	#3011	1	2	yes	—
284	C₂×C₄₃	#3156	1	2	yes	—
285	C₂×C₄₃	#3223	1	2	yes	—
286	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
287	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
288	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	—
289	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	—
290	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	—
291	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
292	#536	—	2	4	no	—
293	#536	—	2	4	no	—
294	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
295	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
296	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
297	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
298	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
299	C₂×#123	—	2	2	no	—
300	C₂×C₂²⋊Q₈	—	2	2	no	—
301	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
302	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
303	#497	—	2	4	no	—
304	#494	—	2	4	no	—
305	#452	—	2	8	no	—
306	#451	—	2	8	no	—
307	C₂×#103	C₂²×C₄₃	1	2	yes	—
308	C₂×#103	C₂²×C₄₃	1	2	yes	—
309	C₂×#103	C₂²×C₄₃	1	2	yes	—
310	C₂×#102	C₂²×C₄₃	1	2	yes	—
311	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
312	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
313	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
314	#398	—	2	2	no	—
315	#397	—	2	2	no	—
316	#391	C₂²×C₄₃	1	2	yes	—
317	#382	C₂²×C₄₃	1	1	yes	characteristic
318	#336	C₂²×C₄₃	1	2	yes	—
319	C₄₃	#25735	1	1	yes	characteristic, direct product factor, Sylow
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	4	no	—
323	C₂×#41	—	4	2	no	—
324	C₂²×Q₈	—	2	2	no	—
325	C₂²×Q₈	—	2	2	no	—
326	C₂²×Q₈	—	2	1	no	—
327	C₂²×Q₈	—	2	4	no	—
328	C₂²×Q₈	—	4	2	no	—
329	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
330	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
331	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
332	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
335	C₂³×C₄	—	2	1	no	—
336	C₂³×C₄	—	2	1	no	—
337	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
338	C₂×Q₁₆	—	2	4	no	—
339	C₂×Q₁₆	—	2	4	no	—
340	C₂×Q₁₆	—	2	4	no	—
341	C₂×Q₁₆	—	2	4	no	—
342	C₂×Q₁₆	—	2	4	no	—
343	C₂×Q₁₆	—	2	4	no	—
344	C₂×Q₁₆	—	4	2	no	—
345	C₂×Q₁₆	—	4	2	no	—
346	C₂×Q₁₆	—	4	2	no	—
347	C₂×SD₁₆	—	2	4	no	—
348	C₂×SD₁₆	—	2	4	no	—
349	C₂×SD₁₆	—	4	2	no	—
350	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
351	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
352	C₄⋊Q₈	—	2	2	no	—
353	C₄⋊Q₈	—	2	2	no	—
354	C₄⋊Q₈	—	2	2	no	—
355	C₄⋊Q₈	—	2	2	no	—
356	C₄⋊Q₈	—	2	2	no	—
357	C₄⋊Q₈	D₄×C₄₃	1	4	yes	—
358	#124	—	2	2	no	—
359	#124	—	2	2	no	—
360	#124	—	2	2	no	—
361	#124	D₄×C₄₃	1	4	yes	—
362	#123	—	2	16	no	—
363	C₂²⋊Q₈	—	2	16	no	—
364	C₂²⋊Q₈	—	2	4	no	—
365	C₂²⋊Q₈	—	2	4	no	—
366	#117	—	2	2	no	—
367	#117	—	2	2	no	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	—	2	2	no	—
372	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
378	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
380	#103	—	2	4	no	—
381	#103	—	2	4	no	—
382	#103	—	2	4	no	—
383	#102	—	2	4	no	—
384	C₂²⋊C₈	D₄×C₄₃	1	8	yes	—
385	#97	—	2	2	no	—
386	C₄×C₈	—	2	2	no	—
387	#95	—	2	2	no	—
388	#95	—	2	4	no	—
389	C₂⁴	—	2	1	no	—
390	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
391	#41	—	4	8	no	—
392	#41	—	4	8	no	—
393	C₂×Q₈	—	2	4	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	4	8	no	—
410	C₂×Q₈	—	4	8	no	—
411	C₂×Q₈	—	4	2	no	—
412	C₂×Q₈	—	4	2	no	—
413	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
414	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
415	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	—	4	2	no	—
422	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	—	4	2	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
438	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
439	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
441	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
442	Q₁₆	—	4	8	no	—
443	Q₁₆	—	4	8	no	—
444	Q₁₆	—	4	8	no	—
445	SD₁₆	—	4	8	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
451	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
452	C₄⋊C₄	—	2	8	no	—
453	C₄⋊C₄	—	2	8	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	4	4	no	—
458	C₄⋊C₄	—	4	4	no	—
459	C₂²⋊C₄	—	2	8	no	—
460	C₂²⋊C₄	—	2	8	no	—
461	C₂²⋊C₄	—	2	4	no	—
462	C₂²⋊C₄	—	4	4	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	C₂×D₄×C₄₃	1	2	yes	—
466	C₄²	C₂×D₄×C₄₃	1	2	yes	—
467	C₂³	—	2	1	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	4	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	1	no	—
473	C₂³	—	4	4	no	—
474	C₂³	#127×C₄₃	1	2	yes	—
475	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
476	Q₈	—	2	4	no	—
477	Q₈	—	2	4	no	—
478	Q₈	—	2	4	no	—
479	Q₈	—	4	8	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	4	2	no	—
484	Q₈	—	4	2	no	—
485	Q₈	—	4	2	no	—
486	Q₈	—	4	2	no	—
487	D₄	—	2	4	no	—
488	D₄	—	4	8	no	—
489	D₄	—	4	2	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	4	8	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	#120×C₄₃	1	4	yes	—
514	C₂×C₄	#127×C₄₃	1	2	yes	—
515	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
518	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
519	C₈	—	2	4	no	—
520	C₈	—	2	4	no	—
521	C₂²	—	2	4	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	8	2	no	—
529	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
530	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
531	C₂²	C₄₃×#535	1	1	yes	characteristic
532	C₂²	C₄₃×#578	1	4	yes	—
533	C₄	—	2	2	no	—
534	C₄	—	2	4	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	2	no	—
539	C₄	—	8	2	no	—
540	C₄	—	8	2	no	—
541	C₄	D₄²×C₄₃	1	2	yes	—
542	C₄	D₄²×C₄₃	1	2	yes	—
543	C₂	—	4	2	no	—
544	C₂	—	8	2	no	—
545	C₂	C₄₃×#2433	1	1	yes	characteristic
546	C₂	C₄₃×#3011	1	2	yes	—
547	C₂	C₄₃×#3156	1	2	yes	—
548	C₂	C₄₃×#3223	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×#41×C₄₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×#117×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#497	C₂	semidirect
3. C₂×C₄₃×#494	C₂	semidirect
5. C₂×C₄₃×#451	C₂	semidirect
6. C₄₃×#2621	C₂	semidirect
7. C₄₃×#2016	C₂	semidirect
8. C₄₃×#2015	C₂	semidirect
9. C₄₃×#1960	C₂	semidirect
10. C₄₃×#1958	C₂	semidirect
11. C₄₃×#1750	C₂	semidirect
246. #25735	C₄₃	direct (N × H)
270. C₂×#497	C₂×C₄₃	semidirect
271. C₂×#494	C₂×C₄₃	semidirect
273. C₂×#451	C₂×C₄₃	semidirect
274. #2621	C₂×C₄₃	semidirect
275. #2016	C₂×C₄₃	semidirect
276. #2015	C₂×C₄₃	semidirect
277. #1960	C₂×C₄₃	semidirect
278. #1958	C₂×C₄₃	semidirect
279. #1750	C₂×C₄₃	semidirect
319. C₄₃	#25735	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×#536	2
C₂×C₄₃×#497	2
C₂×C₄₃×#494	2
C₂×C₄₃×#452	2
C₂×C₄₃×#451	2
C₄₃×#2621	2
C₄₃×#2016	2
C₄₃×#2015	2
C₄₃×#1960	2
C₄₃×#1958	2
C₄₃×#1750	2
#25735	43

Subgroups — C43×#25735 #24945752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25735 #24945752