Subgroups — C₄₃×#29708 #24949725

Order 11008.

930 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3461	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#3080	C₂	1	2	yes	maximal, complemented
3	C₄₃×#2565	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2061	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2060	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2040	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#2039	C₂	1	1	yes	maximal, characteristic
8	C₄₃×#2038	C₂	1	2	yes	maximal, complemented
9	C₄₃×#2038	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1806	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1801	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₃×#544	C₂²	1	1	yes	characteristic
13	C₄₃×#542	—	2	2	no	—
14	C₄₃×#541	—	2	2	no	—
15	C₄₃×#539	—	2	2	no	—
16	C₄₃×#537	C₂²	1	1	yes	characteristic
17	C₄₃×#536	C₂²	1	2	yes	—
18	C₄₃×#533	—	2	2	no	—
19	C₄₃×#529	—	2	2	no	—
20	C₄₃×#529	—	2	2	no	—
21	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
22	C₄×#41×C₄₃	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#479	—	2	2	no	—
25	C₄₃×#479	—	2	2	no	—
26	C₄₃×#478	—	2	2	no	—
27	C₄₃×#478	—	2	2	no	—
28	C₄₃×#428	C₂²	1	2	yes	—
29	C₄₃×#428	C₂²	1	2	yes	—
30	C₄₃×#423	C₂²	1	2	yes	—
31	C₂×#104×C₄₃	C₂²	1	2	yes	—
32	C₂×#104×C₄₃	C₂²	1	2	yes	—
33	C₄₃×#417	C₂²	1	2	yes	—
34	C₄₃×#417	C₂²	1	2	yes	—
35	C₂×#101×C₄₃	C₂²	1	2	yes	—
36	C₄₃×#398	—	2	2	no	—
37	C₄₃×#391	C₂²	1	1	yes	characteristic
38	C₄₃×#391	C₂²	1	1	yes	characteristic
39	C₄₃×#387	—	2	2	no	—
40	C₄₃×#384	C₂²	1	1	yes	characteristic
41	C₄₃×#382	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
43	C₄₃×#343	C₂²	1	1	yes	characteristic
44	C₄₃×#343	C₂²	1	1	yes	characteristic
45	C₄₃×#339	C₂²	1	2	yes	—
46	C₄₃×#339	C₂²	1	2	yes	—
47	C₂×#41×C₄₃	C₂³	1	2	yes	—
48	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
50	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₄₃	—	2	2	no	—
52	C₄⋊Q₈×C₄₃	—	2	2	no	—
53	#126×C₄₃	—	2	4	no	—
54	#126×C₄₃	—	2	4	no	—
55	#125×C₄₃	—	2	2	no	—
56	#125×C₄₃	—	2	4	no	—
57	#125×C₄₃	—	2	2	no	—
58	#125×C₄₃	—	2	2	no	—
59	#125×C₄₃	—	2	2	no	—
60	#124×C₄₃	—	2	2	no	—
61	#124×C₄₃	—	2	2	no	—
62	#123×C₄₃	—	2	4	no	—
63	#123×C₄₃	—	2	4	no	—
64	C₂²⋊Q₈×C₄₃	—	2	4	no	—
65	C₂²⋊Q₈×C₄₃	—	2	2	no	—
66	C₂²⋊Q₈×C₄₃	—	2	2	no	—
67	C₂²⋊Q₈×C₄₃	—	2	2	no	—
68	C₂²⋊Q₈×C₄₃	—	2	2	no	—
69	#121×C₄₃	—	2	2	no	—
70	#121×C₄₃	—	2	2	no	—
71	C₄×Q₈×C₄₃	—	2	2	no	—
72	C₄×Q₈×C₄₃	—	2	2	no	—
73	C₄×Q₈×C₄₃	—	2	2	no	—
74	C₄×Q₈×C₄₃	D₄	1	2	yes	—
75	C₄×Q₈×C₄₃	D₄	1	2	yes	—
76	C₄×D₄×C₄₃	—	2	2	no	—
77	C₄×D₄×C₄₃	—	2	2	no	—
78	C₄×D₄×C₄₃	—	2	2	no	—
79	C₄×D₄×C₄₃	D₄	1	2	yes	—
80	C₄×D₄×C₄₃	D₄	1	2	yes	—
81	#117×C₄₃	—	2	4	no	—
82	#117×C₄₃	—	2	2	no	—
83	#117×C₄₃	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
89	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₄₃	—	2	2	no	—
93	C₂×C₄²×C₄₃	D₄	1	2	yes	—
94	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
97	#107×C₄₃	—	2	2	no	—
98	#107×C₄₃	—	2	2	no	—
99	#106×C₄₃	—	2	2	no	—
100	#106×C₄₃	—	2	2	no	—
101	C₄⋊C₈×C₄₃	—	2	2	no	—
102	C₄⋊C₈×C₄₃	—	2	2	no	—
103	#104×C₄₃	—	4	2	no	—
104	#104×C₄₃	—	4	2	no	—
105	#103×C₄₃	—	2	2	no	—
106	#103×C₄₃	—	2	2	no	—
107	#102×C₄₃	—	2	2	no	—
108	#102×C₄₃	—	2	2	no	—
109	#101×C₄₃	—	4	2	no	—
110	#95×C₄₃	—	2	1	no	—
111	#95×C₄₃	—	2	2	no	—
112	#95×C₄₃	—	2	2	no	—
113	#95×C₄₃	—	2	2	no	—
114	#41×C₄₃	—	2	2	no	—
115	#41×C₄₃	—	2	2	no	—
116	#41×C₄₃	—	2	2	no	—
117	#41×C₄₃	—	2	2	no	—
118	C₂×Q₈×C₄₃	—	2	2	no	—
119	C₂×Q₈×C₄₃	—	2	2	no	—
120	C₂×Q₈×C₄₃	—	2	1	no	—
121	C₂×Q₈×C₄₃	—	2	2	no	—
122	C₂×Q₈×C₄₃	—	2	1	no	—
123	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
124	C₂×D₄×C₄₃	—	2	2	no	—
125	C₂×D₄×C₄₃	—	2	2	no	—
126	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₃	—	2	2	no	—
128	C₂²×C₄×C₄₃	—	2	2	no	—
129	C₂²×C₄×C₄₃	—	2	2	no	—
130	C₂²×C₄×C₄₃	—	2	1	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	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
139	M₁₆×C₄₃	—	2	2	no	—
140	M₁₆×C₄₃	—	2	2	no	—
141	M₁₆×C₄₃	—	2	2	no	—
142	M₁₆×C₄₃	—	2	2	no	—
143	C₂×C₈×C₄₃	—	2	2	no	—
144	C₂×C₈×C₄₃	—	2	2	no	—
145	C₄⋊C₄×C₄₃	—	2	4	no	—
146	C₄⋊C₄×C₄₃	—	2	4	no	—
147	C₄⋊C₄×C₄₃	—	2	2	no	—
148	C₄⋊C₄×C₄₃	—	2	2	no	—
149	C₄⋊C₄×C₄₃	—	2	4	no	—
150	C₄⋊C₄×C₄₃	—	2	4	no	—
151	C₄⋊C₄×C₄₃	—	2	2	no	—
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	4	no	—
158	C₄⋊C₄×C₄₃	—	4	1	no	—
159	C₄⋊C₄×C₄₃	—	4	1	no	—
160	C₄⋊C₄×C₄₃	—	4	2	no	—
161	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
162	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
163	C₂²⋊C₄×C₄₃	—	2	4	no	—
164	C₂²⋊C₄×C₄₃	—	2	4	no	—
165	C₂²⋊C₄×C₄₃	—	2	4	no	—
166	C₂²⋊C₄×C₄₃	—	2	2	no	—
167	C₂²⋊C₄×C₄₃	—	2	2	no	—
168	C₂²⋊C₄×C₄₃	—	2	2	no	—
169	C₄²×C₄₃	—	2	2	no	—
170	C₄²×C₄₃	—	2	2	no	—
171	C₄²×C₄₃	—	2	2	no	—
172	C₄²×C₄₃	—	2	2	no	—
173	C₄²×C₄₃	—	2	2	no	—
174	C₄²×C₄₃	—	2	1	no	—
175	C₄²×C₄₃	—	2	1	no	—
176	C₄²×C₄₃	—	2	1	no	—
177	C₄²×C₄₃	—	2	1	no	—
178	C₄²×C₄₃	C₂×D₄	1	2	yes	—
179	C₄²×C₄₃	C₂×D₄	1	2	yes	—
180	C₂³×C₄₃	—	2	2	no	—
181	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₄₃	—	2	2	no	—
183	Q₈×C₄₃	—	2	2	no	—
184	Q₈×C₄₃	—	4	2	no	—
185	Q₈×C₄₃	—	4	2	no	—
186	Q₈×C₄₃	—	8	2	no	—
187	D₄×C₄₃	—	2	2	no	—
188	D₄×C₄₃	—	2	2	no	—
189	D₄×C₄₃	—	4	2	no	—
190	D₄×C₄₃	—	4	2	no	—
191	D₄×C₄₃	—	8	2	no	—
192	C₂×C₄×C₄₃	—	2	2	no	—
193	C₂×C₄×C₄₃	—	2	2	no	—
194	C₂×C₄×C₄₃	—	2	2	no	—
195	C₂×C₄×C₄₃	—	2	2	no	—
196	C₂×C₄×C₄₃	—	2	2	no	—
197	C₂×C₄×C₄₃	—	2	2	no	—
198	C₂×C₄×C₄₃	—	2	2	no	—
199	C₂×C₄×C₄₃	—	2	2	no	—
200	C₂×C₄×C₄₃	—	4	1	no	—
201	C₂×C₄×C₄₃	—	4	1	no	—
202	C₂×C₄×C₄₃	—	4	4	no	—
203	C₂×C₄×C₄₃	—	4	1	no	—
204	C₂×C₄×C₄₃	—	4	1	no	—
205	C₂×C₄×C₄₃	—	4	2	no	—
206	C₂×C₄×C₄₃	—	4	2	no	—
207	C₂×C₄×C₄₃	—	4	2	no	—
208	C₂×C₄×C₄₃	—	4	1	no	—
209	C₂×C₄×C₄₃	—	4	2	no	—
210	C₂×C₄×C₄₃	—	4	1	no	—
211	C₂×C₄×C₄₃	—	4	2	no	—
212	C₂×C₄×C₄₃	—	4	1	no	—
213	C₂×C₄×C₄₃	—	4	1	no	—
214	C₂×C₄×C₄₃	—	4	1	no	—
215	C₂×C₄×C₄₃	—	8	2	no	—
216	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
217	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
218	C₂×C₄×C₄₃	#120	1	2	yes	—
219	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
221	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
222	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
223	C₈×C₄₃	—	4	2	no	—
224	C₈×C₄₃	—	4	2	no	—
225	#29708	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂²×C₄₃	—	2	1	no	—
227	C₂²×C₄₃	—	2	1	no	—
228	C₂²×C₄₃	—	4	2	no	—
229	C₂²×C₄₃	—	4	2	no	—
230	C₂²×C₄₃	—	4	2	no	—
231	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
232	C₂²×C₄₃	#536	1	1	yes	characteristic
233	C₂²×C₄₃	#537	1	1	yes	characteristic
234	C₄×C₄₃	—	2	2	no	—
235	C₄×C₄₃	—	2	1	no	—
236	C₄×C₄₃	—	2	1	no	—
237	C₄×C₄₃	—	4	2	no	—
238	C₄×C₄₃	—	4	2	no	—
239	C₄×C₄₃	—	4	2	no	—
240	C₄×C₄₃	—	4	2	no	—
241	C₄×C₄₃	—	4	2	no	—
242	C₄×C₄₃	—	4	2	no	—
243	C₄×C₄₃	—	8	1	no	—
244	C₄×C₄₃	—	8	1	no	—
245	C₄×C₄₃	—	8	1	no	—
246	C₄×C₄₃	#536	1	2	yes	—
247	C₄×C₄₃	#537	1	2	yes	—
248	#3461	C₂×C₄₃	1	1	yes	characteristic
249	#3080	C₂×C₄₃	1	2	yes	complemented
250	#2565	C₂×C₄₃	1	1	yes	characteristic, complemented
251	#2061	C₂×C₄₃	1	1	yes	characteristic, complemented
252	#2060	C₂×C₄₃	1	1	yes	characteristic, complemented
253	#2040	C₂×C₄₃	1	1	yes	characteristic
254	#2039	C₂×C₄₃	1	1	yes	characteristic
255	#2038	C₂×C₄₃	1	2	yes	complemented
256	#2038	C₂×C₄₃	1	2	yes	complemented
257	#1806	C₂×C₄₃	1	2	yes	complemented
258	#1801	C₂×C₄₃	1	1	yes	characteristic, complemented
259	C₂×C₄₃	—	2	1	no	—
260	C₂×C₄₃	—	2	1	no	—
261	C₂×C₄₃	—	8	2	no	—
262	C₂×C₄₃	#2616	1	1	yes	characteristic
263	C₂×C₄₃	#3018	1	1	yes	characteristic
264	C₂×C₄₃	#3020	1	1	yes	characteristic
265	#544	C₂²×C₄₃	1	1	yes	characteristic
266	#542	—	2	2	no	—
267	#541	—	2	2	no	—
268	#539	—	2	2	no	—
269	#537	C₂²×C₄₃	1	1	yes	characteristic
270	#536	C₂²×C₄₃	1	2	yes	—
271	#533	—	2	2	no	—
272	#529	—	2	2	no	—
273	#529	—	2	2	no	—
274	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
275	C₄×#41	C₂²×C₄₃	1	2	yes	—
276	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
277	#479	—	2	2	no	—
278	#479	—	2	2	no	—
279	#478	—	2	2	no	—
280	#478	—	2	2	no	—
281	#428	C₂²×C₄₃	1	2	yes	—
282	#428	C₂²×C₄₃	1	2	yes	—
283	#423	C₂²×C₄₃	1	2	yes	—
284	C₂×#104	C₂²×C₄₃	1	2	yes	—
285	C₂×#104	C₂²×C₄₃	1	2	yes	—
286	#417	C₂²×C₄₃	1	2	yes	—
287	#417	C₂²×C₄₃	1	2	yes	—
288	C₂×#101	C₂²×C₄₃	1	2	yes	—
289	#398	—	2	2	no	—
290	#391	C₂²×C₄₃	1	1	yes	characteristic
291	#391	C₂²×C₄₃	1	1	yes	characteristic
292	#387	—	2	2	no	—
293	#384	C₂²×C₄₃	1	1	yes	characteristic
294	#382	C₂²×C₄₃	1	1	yes	characteristic
295	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
296	#343	C₂²×C₄₃	1	1	yes	characteristic
297	#343	C₂²×C₄₃	1	1	yes	characteristic
298	#339	C₂²×C₄₃	1	2	yes	—
299	#339	C₂²×C₄₃	1	2	yes	—
300	C₄₃	#29708	1	1	yes	characteristic, direct product factor, Sylow
301	C₂×#41	C₂³×C₄₃	1	2	yes	—
302	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
303	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
304	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
305	C₄⋊Q₈	—	2	2	no	—
306	C₄⋊Q₈	—	2	2	no	—
307	#126	—	2	4	no	—
308	#126	—	2	4	no	—
309	#125	—	2	2	no	—
310	#125	—	2	4	no	—
311	#125	—	2	2	no	—
312	#125	—	2	2	no	—
313	#125	—	2	2	no	—
314	#124	—	2	2	no	—
315	#124	—	2	2	no	—
316	#123	—	2	4	no	—
317	#123	—	2	4	no	—
318	C₂²⋊Q₈	—	2	4	no	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	—	2	2	no	—
323	#121	—	2	2	no	—
324	#121	—	2	2	no	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	D₄×C₄₃	1	2	yes	—
329	C₄×Q₈	D₄×C₄₃	1	2	yes	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	D₄×C₄₃	1	2	yes	—
334	C₄×D₄	D₄×C₄₃	1	2	yes	—
335	#117	—	2	4	no	—
336	#117	—	2	2	no	—
337	#117	C₂³×C₄₃	1	2	yes	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	D₄×C₄₃	1	2	yes	—
348	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
349	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
350	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
351	#107	—	2	2	no	—
352	#107	—	2	2	no	—
353	#106	—	2	2	no	—
354	#106	—	2	2	no	—
355	C₄⋊C₈	—	2	2	no	—
356	C₄⋊C₈	—	2	2	no	—
357	#104	—	4	2	no	—
358	#104	—	4	2	no	—
359	#103	—	2	2	no	—
360	#103	—	2	2	no	—
361	#102	—	2	2	no	—
362	#102	—	2	2	no	—
363	#101	—	4	2	no	—
364	#95	—	2	1	no	—
365	#95	—	2	2	no	—
366	#95	—	2	2	no	—
367	#95	—	2	2	no	—
368	#41	—	2	2	no	—
369	#41	—	2	2	no	—
370	#41	—	2	2	no	—
371	#41	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
392	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
393	M₁₆	—	2	2	no	—
394	M₁₆	—	2	2	no	—
395	M₁₆	—	2	2	no	—
396	M₁₆	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	4	4	no	—
412	C₄⋊C₄	—	4	1	no	—
413	C₄⋊C₄	—	4	1	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
416	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₄²	C₂×D₄×C₄₃	1	2	yes	—
433	C₄²	C₂×D₄×C₄₃	1	2	yes	—
434	C₂³	—	2	2	no	—
435	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
436	Q₈	—	2	2	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	4	2	no	—
439	Q₈	—	4	2	no	—
440	Q₈	—	8	2	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	2	no	—
443	D₄	—	4	2	no	—
444	D₄	—	4	2	no	—
445	D₄	—	8	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	8	2	no	—
470	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
471	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
472	C₂×C₄	#120×C₄₃	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
474	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
475	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
476	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
477	C₈	—	4	2	no	—
478	C₈	—	4	2	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
485	C₂²	C₄₃×#536	1	1	yes	characteristic
486	C₂²	C₄₃×#537	1	1	yes	characteristic
487	C₄	—	2	2	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	2	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	8	1	no	—
497	C₄	—	8	1	no	—
498	C₄	—	8	1	no	—
499	C₄	C₄₃×#536	1	2	yes	—
500	C₄	C₄₃×#537	1	2	yes	—
501	C₂	—	2	1	no	—
502	C₂	—	2	1	no	—
503	C₂	—	8	2	no	—
504	C₂	C₄₃×#2616	1	1	yes	characteristic
505	C₂	C₄₃×#3018	1	1	yes	characteristic
506	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×#537	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#3080	C₂	semidirect
3. C₄₃×#2565	C₂	semidirect
4. C₄₃×#2061	C₂	semidirect
5. C₄₃×#2060	C₂	semidirect
8. C₄₃×#2038	C₂	semidirect
9. C₄₃×#2038	C₂	semidirect
10. C₄₃×#1806	C₂	semidirect
11. C₄₃×#1801	C₂	semidirect
225. #29708	C₄₃	direct (N × H)
249. #3080	C₂×C₄₃	semidirect
250. #2565	C₂×C₄₃	semidirect
251. #2061	C₂×C₄₃	semidirect
252. #2060	C₂×C₄₃	semidirect
255. #2038	C₂×C₄₃	semidirect
256. #2038	C₂×C₄₃	semidirect
257. #1806	C₂×C₄₃	semidirect
258. #1801	C₂×C₄₃	semidirect
300. C₄₃	#29708	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×#3461	2
C₄₃×#3080	2
C₄₃×#2565	2
C₄₃×#2061	2
C₄₃×#2060	2
C₄₃×#2040	2
C₄₃×#2039	2
C₄₃×#2038	2
C₄₃×#1806	2
C₄₃×#1801	2
#29708	43

Subgroups — C43×#29708 #24949725

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29708 #24949725