Subgroups — C₄₃×#29815 #24949832

Order 11008.

920 conjugacy classes of subgroups.

The subgroup lattice has 564 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×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2850	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2056	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2055	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2001	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2000	C₂	1	2	yes	maximal
9	C₄₃×#1960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1959	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1836	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
18	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#497	—	2	4	no	—
21	C₄₃×#432	—	2	4	no	—
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
23	C₂×#103×C₄₃	C₂²	1	2	yes	—
24	C₂×#103×C₄₃	C₂²	1	2	yes	—
25	C₂×#103×C₄₃	C₂²	1	2	yes	—
26	C₂×#102×C₄₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
28	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#391	C₂²	1	1	yes	characteristic
31	C₄₃×#391	C₂²	1	2	yes	—
32	C₄₃×#390	C₂²	1	1	yes	characteristic
33	C₄₃×#389	—	2	1	no	—
34	C₄₃×#389	—	2	1	no	—
35	C₄₃×#388	—	2	1	no	—
36	C₄₃×#388	—	2	1	no	—
37	C₄₃×#386	—	2	1	no	—
38	C₄₃×#386	—	2	1	no	—
39	C₄₃×#384	C₂²	1	1	yes	characteristic
40	C₄₃×#382	C₂²	1	1	yes	characteristic
41	C₄₃×#380	—	2	1	no	—
42	C₄₃×#380	—	2	1	no	—
43	C₄₃×#340	C₂²	1	2	yes	—
44	C₄₃×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
47	C₂²×D₄×C₄₃	—	2	1	no	—
48	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
52	C₂×Q₁₆×C₄₃	—	2	4	no	—
53	C₂×Q₁₆×C₄₃	—	4	2	no	—
54	C₂×Q₁₆×C₄₃	—	4	2	no	—
55	C₂×SD₁₆×C₄₃	—	2	4	no	—
56	C₂×SD₁₆×C₄₃	—	4	2	no	—
57	C₂×SD₁₆×C₄₃	—	4	2	no	—
58	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
59	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
60	C₄⋊Q₈×C₄₃	—	2	2	no	—
61	C₄⋊Q₈×C₄₃	—	2	2	no	—
62	#124×C₄₃	—	2	2	no	—
63	#124×C₄₃	—	2	2	no	—
64	C₂²⋊Q₈×C₄₃	—	4	2	no	—
65	C₂²⋊Q₈×C₄₃	—	4	2	no	—
66	C₂²⋊Q₈×C₄₃	—	4	2	no	—
67	#121×C₄₃	—	4	2	no	—
68	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
84	C₂×C₄²×C₄₃	—	2	2	no	—
85	C₂×C₄²×C₄₃	—	2	2	no	—
86	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₄₃	—	2	4	no	—
91	#103×C₄₃	—	4	2	no	—
92	#103×C₄₃	—	4	2	no	—
93	#103×C₄₃	—	4	2	no	—
94	#102×C₄₃	—	4	2	no	—
95	C₂²⋊C₈×C₄₃	—	2	4	no	—
96	#97×C₄₃	—	2	2	no	—
97	#97×C₄₃	D₄	1	4	yes	complemented
98	#95×C₄₃	—	2	2	no	—
99	#95×C₄₃	—	2	2	no	—
100	#95×C₄₃	—	2	1	no	—
101	#95×C₄₃	—	2	1	no	—
102	#95×C₄₃	—	2	1	no	—
103	#95×C₄₃	—	2	1	no	—
104	C₂⁴×C₄₃	—	2	1	no	—
105	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂×Q₈×C₄₃	—	2	1	no	—
107	C₂×Q₈×C₄₃	—	2	2	no	—
108	C₂×Q₈×C₄₃	—	2	1	no	—
109	C₂×Q₈×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	—	2	2	no	—
111	C₂×Q₈×C₄₃	—	2	2	no	—
112	C₂×Q₈×C₄₃	—	2	2	no	—
113	C₂×Q₈×C₄₃	—	2	2	no	—
114	C₂×Q₈×C₄₃	—	2	2	no	—
115	C₂×Q₈×C₄₃	—	2	2	no	—
116	C₂×D₄×C₄₃	—	2	1	no	—
117	C₂×D₄×C₄₃	—	2	1	no	—
118	C₂×D₄×C₄₃	—	2	2	no	—
119	C₂×D₄×C₄₃	—	2	2	no	—
120	C₂×D₄×C₄₃	—	4	2	no	—
121	C₂×D₄×C₄₃	—	4	2	no	—
122	C₂×D₄×C₄₃	—	4	2	no	—
123	C₂²×C₄×C₄₃	—	2	2	no	—
124	C₂²×C₄×C₄₃	—	2	2	no	—
125	C₂²×C₄×C₄₃	—	2	2	no	—
126	C₂²×C₄×C₄₃	—	2	1	no	—
127	C₂²×C₄×C₄₃	—	2	1	no	—
128	C₂²×C₄×C₄₃	—	2	2	no	—
129	C₂²×C₄×C₄₃	—	2	2	no	—
130	C₂²×C₄×C₄₃	—	2	2	no	—
131	C₂²×C₄×C₄₃	—	2	1	no	—
132	C₂²×C₄×C₄₃	—	2	1	no	—
133	C₂²×C₄×C₄₃	—	2	1	no	—
134	C₂²×C₄×C₄₃	—	2	2	no	—
135	C₂²×C₄×C₄₃	—	2	2	no	—
136	C₂²×C₄×C₄₃	—	4	1	no	—
137	C₂²×C₄×C₄₃	—	4	1	no	—
138	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
144	Q₁₆×C₄₃	—	4	8	no	—
145	SD₁₆×C₄₃	—	4	8	no	—
146	C₂×C₈×C₄₃	—	2	2	no	—
147	C₂×C₈×C₄₃	—	2	2	no	—
148	C₂×C₈×C₄₃	—	2	2	no	—
149	C₂×C₈×C₄₃	—	2	2	no	—
150	C₂×C₈×C₄₃	—	2	2	no	—
151	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
152	C₄⋊C₄×C₄₃	—	2	2	no	—
153	C₄⋊C₄×C₄₃	—	2	2	no	—
154	C₄⋊C₄×C₄₃	—	2	2	no	—
155	C₄⋊C₄×C₄₃	—	2	2	no	—
156	C₄⋊C₄×C₄₃	—	4	2	no	—
157	C₄⋊C₄×C₄₃	—	4	2	no	—
158	C₄⋊C₄×C₄₃	—	4	2	no	—
159	C₄⋊C₄×C₄₃	—	4	4	no	—
160	C₄⋊C₄×C₄₃	—	4	2	no	—
161	C₄⋊C₄×C₄₃	—	4	2	no	—
162	C₂²⋊C₄×C₄₃	—	4	4	no	—
163	C₂²⋊C₄×C₄₃	—	4	2	no	—
164	C₂²⋊C₄×C₄₃	—	4	2	no	—
165	C₂²⋊C₄×C₄₃	—	4	2	no	—
166	C₂²⋊C₄×C₄₃	—	4	2	no	—
167	C₂²⋊C₄×C₄₃	—	4	2	no	—
168	C₂²⋊C₄×C₄₃	—	4	2	no	—
169	C₄²×C₄₃	—	2	2	no	—
170	C₄²×C₄₃	—	2	2	no	—
171	C₄²×C₄₃	—	2	1	no	—
172	C₄²×C₄₃	—	2	1	no	—
173	C₄²×C₄₃	C₂×D₄	1	2	yes	—
174	C₄²×C₄₃	#41	1	2	yes	—
175	C₂³×C₄₃	—	2	1	no	—
176	C₂³×C₄₃	—	2	1	no	—
177	C₂³×C₄₃	—	2	1	no	—
178	C₂³×C₄₃	—	2	1	no	—
179	C₂³×C₄₃	—	2	1	no	—
180	C₂³×C₄₃	—	2	1	no	—
181	C₂³×C₄₃	—	4	1	no	—
182	C₂³×C₄₃	—	4	1	no	—
183	C₂³×C₄₃	—	4	1	no	—
184	C₂³×C₄₃	—	4	1	no	—
185	C₂³×C₄₃	—	4	1	no	—
186	C₂³×C₄₃	—	4	1	no	—
187	C₂³×C₄₃	—	4	1	no	—
188	C₂³×C₄₃	#137	1	2	yes	—
189	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₄₃	—	4	2	no	—
191	Q₈×C₄₃	—	4	2	no	—
192	Q₈×C₄₃	—	4	2	no	—
193	Q₈×C₄₃	—	4	2	no	—
194	Q₈×C₄₃	—	4	2	no	—
195	Q₈×C₄₃	—	4	2	no	—
196	D₄×C₄₃	—	4	2	no	—
197	D₄×C₄₃	—	4	2	no	—
198	D₄×C₄₃	—	8	4	no	—
199	C₂×C₄×C₄₃	—	2	1	no	—
200	C₂×C₄×C₄₃	—	2	1	no	—
201	C₂×C₄×C₄₃	—	2	1	no	—
202	C₂×C₄×C₄₃	—	2	1	no	—
203	C₂×C₄×C₄₃	—	2	1	no	—
204	C₂×C₄×C₄₃	—	2	1	no	—
205	C₂×C₄×C₄₃	—	2	1	no	—
206	C₂×C₄×C₄₃	—	2	1	no	—
207	C₂×C₄×C₄₃	—	2	1	no	—
208	C₂×C₄×C₄₃	—	2	1	no	—
209	C₂×C₄×C₄₃	—	2	1	no	—
210	C₂×C₄×C₄₃	—	2	1	no	—
211	C₂×C₄×C₄₃	—	4	4	no	—
212	C₂×C₄×C₄₃	—	4	4	no	—
213	C₂×C₄×C₄₃	—	4	2	no	—
214	C₂×C₄×C₄₃	—	4	2	no	—
215	C₂×C₄×C₄₃	—	4	1	no	—
216	C₂×C₄×C₄₃	—	4	2	no	—
217	C₂×C₄×C₄₃	—	4	1	no	—
218	C₂×C₄×C₄₃	—	4	2	no	—
219	C₂×C₄×C₄₃	—	4	1	no	—
220	C₂×C₄×C₄₃	—	4	1	no	—
221	C₂×C₄×C₄₃	—	4	2	no	—
222	C₂×C₄×C₄₃	—	4	2	no	—
223	C₂×C₄×C₄₃	—	4	1	no	—
224	C₂×C₄×C₄₃	—	4	1	no	—
225	C₂×C₄×C₄₃	—	4	1	no	—
226	C₂×C₄×C₄₃	—	4	1	no	—
227	C₂×C₄×C₄₃	—	4	2	no	—
228	C₂×C₄×C₄₃	—	4	2	no	—
229	C₂×C₄×C₄₃	—	4	1	no	—
230	C₂×C₄×C₄₃	#121	1	2	yes	—
231	C₂×C₄×C₄₃	#121	1	2	yes	—
232	C₂×C₄×C₄₃	#137	1	2	yes	—
233	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
236	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
237	C₈×C₄₃	—	2	4	no	—
238	C₈×C₄₃	—	4	2	no	—
239	#29815	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂²×C₄₃	—	2	2	no	—
241	C₂²×C₄₃	—	2	2	no	—
242	C₂²×C₄₃	—	2	2	no	—
243	C₂²×C₄₃	—	4	1	no	—
244	C₂²×C₄₃	—	4	1	no	—
245	C₂²×C₄₃	—	4	1	no	—
246	C₂²×C₄₃	—	4	1	no	—
247	C₂²×C₄₃	—	8	1	no	—
248	C₂²×C₄₃	—	8	1	no	—
249	C₂²×C₄₃	—	8	1	no	—
250	C₂²×C₄₃	—	8	1	no	—
251	C₂²×C₄₃	—	8	1	no	—
252	C₂²×C₄₃	—	8	1	no	—
253	C₂²×C₄₃	—	8	1	no	—
254	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
255	C₂²×C₄₃	#535	1	1	yes	characteristic
256	C₂²×C₄₃	#535	1	1	yes	characteristic
257	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
258	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
259	C₂²×C₄₃	#575	1	1	yes	characteristic
260	C₂²×C₄₃	#575	1	1	yes	characteristic
261	C₄×C₄₃	—	2	2	no	—
262	C₄×C₄₃	—	2	2	no	—
263	C₄×C₄₃	—	2	2	no	—
264	C₄×C₄₃	—	4	1	no	—
265	C₄×C₄₃	—	4	1	no	—
266	C₄×C₄₃	—	8	1	no	—
267	C₄×C₄₃	—	8	2	no	—
268	C₄×C₄₃	—	8	1	no	—
269	C₄×C₄₃	—	8	1	no	—
270	C₄×C₄₃	—	8	2	no	—
271	C₄×C₄₃	#535	1	2	yes	—
272	C₄×C₄₃	#540	1	2	yes	—
273	C₂×#497	C₂×C₄₃	1	1	yes	characteristic, complemented
274	C₂×#432	C₂×C₄₃	1	1	yes	characteristic, complemented
275	#2857	C₂×C₄₃	1	1	yes	characteristic, complemented
276	#2850	C₂×C₄₃	1	1	yes	characteristic
277	#2056	C₂×C₄₃	1	2	yes	complemented
278	#2055	C₂×C₄₃	1	2	yes	complemented
279	#2001	C₂×C₄₃	1	2	yes	complemented
280	#2000	C₂×C₄₃	1	2	yes	—
281	#1960	C₂×C₄₃	1	1	yes	characteristic, complemented
282	#1959	C₂×C₄₃	1	1	yes	characteristic, complemented
283	#1836	C₂×C₄₃	1	1	yes	characteristic, complemented
284	C₂×C₄₃	—	4	2	no	—
285	C₂×C₄₃	—	16	1	no	—
286	C₂×C₄₃	#2619	1	1	yes	characteristic
287	C₂×C₄₃	#3056	1	1	yes	characteristic
288	C₂×C₄₃	#3056	1	1	yes	characteristic
289	C₂×C₄₃	#3215	1	1	yes	characteristic
290	C₂×C₄₃	#3216	1	1	yes	characteristic
291	C₂×C₄₃	#3218	1	1	yes	characteristic
292	C₂×C₄₃	#3219	1	1	yes	characteristic
293	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	—
294	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
295	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
296	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
297	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
298	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
299	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
300	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
301	#497	—	2	4	no	—
302	#432	—	2	4	no	—
303	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
304	C₂×#103	C₂²×C₄₃	1	2	yes	—
305	C₂×#103	C₂²×C₄₃	1	2	yes	—
306	C₂×#103	C₂²×C₄₃	1	2	yes	—
307	C₂×#102	C₂²×C₄₃	1	2	yes	—
308	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
309	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
310	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
311	#391	C₂²×C₄₃	1	2	yes	—
312	#391	C₂²×C₄₃	1	1	yes	characteristic
313	#390	C₂²×C₄₃	1	1	yes	characteristic
314	#389	—	2	1	no	—
315	#389	—	2	1	no	—
316	#388	—	2	1	no	—
317	#388	—	2	1	no	—
318	#386	—	2	1	no	—
319	#386	—	2	1	no	—
320	#384	C₂²×C₄₃	1	1	yes	characteristic
321	#382	C₂²×C₄₃	1	1	yes	characteristic
322	#380	—	2	1	no	—
323	#380	—	2	1	no	—
324	#340	C₂²×C₄₃	1	2	yes	—
325	#340	C₂²×C₄₃	1	2	yes	—
326	C₄₃	#29815	1	1	yes	characteristic, direct product factor, Sylow
327	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
328	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
331	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
332	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
333	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
334	C₂×Q₁₆	—	2	4	no	—
335	C₂×Q₁₆	—	4	2	no	—
336	C₂×Q₁₆	—	4	2	no	—
337	C₂×SD₁₆	—	2	4	no	—
338	C₂×SD₁₆	—	4	2	no	—
339	C₂×SD₁₆	—	4	2	no	—
340	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
341	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
342	C₄⋊Q₈	—	2	2	no	—
343	C₄⋊Q₈	—	2	2	no	—
344	#124	—	2	2	no	—
345	#124	—	2	2	no	—
346	C₂²⋊Q₈	—	4	2	no	—
347	C₂²⋊Q₈	—	4	2	no	—
348	C₂²⋊Q₈	—	4	2	no	—
349	#121	—	4	2	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₄²	—	2	2	no	—
367	C₂×C₄²	—	2	2	no	—
368	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
369	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
370	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
371	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
372	C₄⋊C₈	—	2	4	no	—
373	#103	—	4	2	no	—
374	#103	—	4	2	no	—
375	#103	—	4	2	no	—
376	#102	—	4	2	no	—
377	C₂²⋊C₈	—	2	4	no	—
378	#97	—	2	2	no	—
379	#97	D₄×C₄₃	1	4	yes	complemented
380	#95	—	2	2	no	—
381	#95	—	2	2	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	#95	—	2	1	no	—
386	C₂⁴	—	2	1	no	—
387	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	4	1	no	—
419	C₂²×C₄	—	4	1	no	—
420	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
425	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
426	Q₁₆	—	4	8	no	—
427	SD₁₆	—	4	8	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	4	2	no	—
439	C₄⋊C₄	—	4	4	no	—
440	C₄⋊C₄	—	4	2	no	—
441	C₄⋊C₄	—	4	2	no	—
442	C₄⋊C₄	—	4	2	no	—
443	C₄⋊C₄	—	4	2	no	—
444	C₂²⋊C₄	—	4	2	no	—
445	C₂²⋊C₄	—	4	2	no	—
446	C₂²⋊C₄	—	4	4	no	—
447	C₂²⋊C₄	—	4	2	no	—
448	C₂²⋊C₄	—	4	2	no	—
449	C₂²⋊C₄	—	4	2	no	—
450	C₂²⋊C₄	—	4	2	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	1	no	—
455	C₄²	C₂×D₄×C₄₃	1	2	yes	—
456	C₄²	#41×C₄₃	1	2	yes	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	1	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	1	no	—
470	C₂³	#137×C₄₃	1	2	yes	—
471	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
472	Q₈	—	4	2	no	—
473	Q₈	—	4	2	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	4	2	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	4	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	2	no	—
480	D₄	—	8	4	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	4	4	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	#121×C₄₃	1	2	yes	—
513	C₂×C₄	#121×C₄₃	1	2	yes	—
514	C₂×C₄	#137×C₄₃	1	2	yes	—
515	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
516	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
517	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
518	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
519	C₈	—	2	4	no	—
520	C₈	—	4	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	8	1	no	—
529	C₂²	—	8	1	no	—
530	C₂²	—	8	1	no	—
531	C₂²	—	8	1	no	—
532	C₂²	—	8	1	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	8	1	no	—
535	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
536	C₂²	C₄₃×#535	1	1	yes	characteristic
537	C₂²	C₄₃×#535	1	1	yes	characteristic
538	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
539	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
540	C₂²	C₄₃×#575	1	1	yes	characteristic
541	C₂²	C₄₃×#575	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	2	no	—
549	C₄	—	8	1	no	—
550	C₄	—	8	1	no	—
551	C₄	—	8	2	no	—
552	C₄	C₄₃×#535	1	2	yes	—
553	C₄	C₄₃×#540	1	2	yes	—
554	C₂	—	4	2	no	—
555	C₂	—	16	1	no	—
556	C₂	C₄₃×#2619	1	1	yes	characteristic
557	C₂	C₄₃×#3056	1	1	yes	characteristic
558	C₂	C₄₃×#3056	1	1	yes	characteristic
559	C₂	C₄₃×#3215	1	1	yes	characteristic
560	C₂	C₄₃×#3216	1	1	yes	characteristic
561	C₂	C₄₃×#3218	1	1	yes	characteristic
562	C₂	C₄₃×#3219	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#121×C₄₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×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×#432	C₂	semidirect
3. C₄₃×#2857	C₂	semidirect
5. C₄₃×#2056	C₂	semidirect
6. C₄₃×#2055	C₂	semidirect
7. C₄₃×#2001	C₂	semidirect
9. C₄₃×#1960	C₂	semidirect
10. C₄₃×#1959	C₂	semidirect
11. C₄₃×#1836	C₂	semidirect
97. #97×C₄₃	D₄	semidirect
239. #29815	C₄₃	direct (N × H)
273. C₂×#497	C₂×C₄₃	semidirect
274. C₂×#432	C₂×C₄₃	semidirect
275. #2857	C₂×C₄₃	semidirect
277. #2056	C₂×C₄₃	semidirect
278. #2055	C₂×C₄₃	semidirect
279. #2001	C₂×C₄₃	semidirect
281. #1960	C₂×C₄₃	semidirect
282. #1959	C₂×C₄₃	semidirect
283. #1836	C₂×C₄₃	semidirect
326. C₄₃	#29815	direct (N × H)
379. #97	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×#432	2
C₄₃×#2857	2
C₄₃×#2850	2
C₄₃×#2056	2
C₄₃×#2055	2
C₄₃×#2001	2
C₄₃×#2000	2
C₄₃×#1960	2
C₄₃×#1959	2
C₄₃×#1836	2
#29815	43

Subgroups — C43×#29815 #24949832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29815 #24949832