Subgroups — C₄₃×#18515 #24938532

Order 11008.

976 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3483	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#3107	C₂	1	2	yes	maximal, complemented
4	C₄₃×#1646	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1645	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1642	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1641	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1543	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1476	C₂	1	2	yes	maximal, complemented
10	Q₈²×C₄₃	C₂²	1	1	yes	characteristic
11	C₄₃×#555	—	2	2	no	—
12	C₄₃×#555	—	2	2	no	—
13	C₄₃×#555	C₂²	1	1	yes	characteristic
14	C₄₃×#550	—	2	2	no	—
15	C₄₃×#550	C₂²	1	2	yes	—
16	C₄₃×#533	C₂²	1	1	yes	characteristic
17	C₄₃×#532	—	2	2	no	—
18	C₄₃×#532	—	2	2	no	—
19	C₄₃×#532	C₂²	1	1	yes	characteristic
20	C₄×#41×C₄₃	—	2	2	no	—
21	C₄×#41×C₄₃	C₂²	1	2	yes	—
22	C₄₃×#488	—	2	2	no	—
23	C₄₃×#487	C₂²	1	2	yes	—
24	C₄₃×#486	C₂²	1	2	yes	—
25	C₄₃×#485	—	2	2	no	—
26	C₄₃×#475	C₂²	1	2	yes	—
27	C₄₃×#474	C₂²	1	2	yes	—
28	C₄₃×#462	C₂²	1	2	yes	—
29	C₄₃×#461	C₂²	1	2	yes	—
30	C₄₃×#452	—	2	2	no	—
31	C₄×Q₁₆×C₄₃	—	2	2	no	—
32	C₄×SD₁₆×C₄₃	—	2	2	no	—
33	C₄₃×#431	C₂²	1	2	yes	—
34	C₄₃×#416	—	2	2	no	—
35	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₄₃×#333	C₂²	1	2	yes	—
37	C₄₃×#331	C₂²	1	1	yes	characteristic
38	C₄₃×#331	C₂²	1	1	yes	characteristic
39	C₄₃×Q₈⋊C₈	C₂²	1	2	yes	—
40	C₄₃×Q₈⋊C₈	C₂²	1	2	yes	—
41	C₄₃×D₄⋊C₈	C₂²	1	2	yes	—
42	C₄₃×D₄⋊C₈	C₂²	1	2	yes	—
43	C₂×#41×C₄₃	—	2	2	no	—
44	C₂×#41×C₄₃	—	2	2	no	—
45	C₂×#41×C₄₃	D₄	1	2	yes	—
46	C₂×#41×C₄₃	D₄	1	2	yes	—
47	C₂×Q₁₆×C₄₃	—	2	2	no	—
48	C₂×SD₁₆×C₄₃	—	2	2	no	—
49	C₂²×C₈×C₄₃	—	2	1	no	—
50	C₄⋊Q₈×C₄₃	—	2	2	no	—
51	C₄⋊Q₈×C₄₃	—	2	2	no	—
52	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
54	#127×C₄₃	—	2	2	no	—
55	#127×C₄₃	—	2	2	no	—
56	#127×C₄₃	C₂³	1	1	yes	characteristic
57	#125×C₄₃	—	2	1	no	—
58	#124×C₄₃	—	2	2	no	—
59	#124×C₄₃	—	2	4	no	—
60	#124×C₄₃	—	2	2	no	—
61	#124×C₄₃	D₄	1	2	yes	—
62	C₂²⋊Q₈×C₄₃	—	2	2	no	—
63	#121×C₄₃	—	2	4	no	—
64	#121×C₄₃	—	2	4	no	—
65	#121×C₄₃	—	2	2	no	—
66	#121×C₄₃	—	2	4	no	—
67	#121×C₄₃	—	2	2	no	—
68	#121×C₄₃	—	2	2	no	—
69	C₄×Q₈×C₄₃	—	2	2	no	—
70	C₄×Q₈×C₄₃	—	2	2	no	—
71	C₄×Q₈×C₄₃	D₄	1	2	yes	—
72	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
73	C₄×D₄×C₄₃	—	2	4	no	—
74	C₄×D₄×C₄₃	—	2	4	no	—
75	C₄×D₄×C₄₃	—	2	2	no	—
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	C₂³	1	2	yes	—
81	#117×C₄₃	—	2	4	no	—
82	#117×C₄₃	—	2	2	no	—
83	#117×C₄₃	—	2	2	no	—
84	#117×C₄₃	—	2	1	no	—
85	#117×C₄₃	D₄	1	2	yes	—
86	C₂×C₄²×C₄₃	—	2	2	no	—
87	C₂×C₄²×C₄₃	—	2	2	no	—
88	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
89	#107×C₄₃	—	2	2	no	—
90	#106×C₄₃	—	2	2	no	—
91	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
92	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
93	#103×C₄₃	—	2	4	no	—
94	#103×C₄₃	—	2	2	no	—
95	#103×C₄₃	—	2	2	no	—
96	#103×C₄₃	—	2	2	no	—
97	#102×C₄₃	—	2	4	no	—
98	#102×C₄₃	—	2	2	no	—
99	C₂²⋊C₈×C₄₃	—	2	2	no	—
100	C₄×C₈×C₄₃	—	2	1	no	—
101	C₄×C₈×C₄₃	—	2	2	no	—
102	C₄×C₈×C₄₃	C₂³	1	2	yes	—
103	#41×C₄₃	—	2	4	no	—
104	#41×C₄₃	—	4	2	no	—
105	#41×C₄₃	—	4	4	no	—
106	#41×C₄₃	—	4	4	no	—
107	#41×C₄₃	—	4	4	no	—
108	#41×C₄₃	—	8	4	no	—
109	C₂×Q₈×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	—	2	2	no	—
111	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
112	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
113	C₂×D₄×C₄₃	—	2	4	no	—
114	C₂×D₄×C₄₃	—	2	2	no	—
115	C₂×D₄×C₄₃	—	2	4	no	—
116	C₂×D₄×C₄₃	—	2	2	no	—
117	C₂×D₄×C₄₃	—	2	2	no	—
118	C₂×D₄×C₄₃	—	2	2	no	—
119	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
120	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₃	—	2	4	no	—
122	C₂²×C₄×C₄₃	—	2	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	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
128	Q₁₆×C₄₃	—	4	4	no	—
129	SD₁₆×C₄₃	—	4	4	no	—
130	C₂×C₈×C₄₃	—	2	2	no	—
131	C₂×C₈×C₄₃	—	2	2	no	—
132	C₂×C₈×C₄₃	—	2	2	no	—
133	C₂×C₈×C₄₃	—	4	2	no	—
134	C₄⋊C₄×C₄₃	—	2	4	no	—
135	C₄⋊C₄×C₄₃	—	2	2	no	—
136	C₄⋊C₄×C₄₃	—	2	2	no	—
137	C₄⋊C₄×C₄₃	—	2	2	no	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	—	4	2	no	—
141	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
142	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
143	C₂²⋊C₄×C₄₃	—	2	4	no	—
144	C₂²⋊C₄×C₄₃	—	2	4	no	—
145	C₂²⋊C₄×C₄₃	—	2	4	no	—
146	C₂²⋊C₄×C₄₃	—	2	2	no	—
147	C₂²⋊C₄×C₄₃	—	2	2	no	—
148	C₂²⋊C₄×C₄₃	—	2	2	no	—
149	C₂²⋊C₄×C₄₃	—	4	1	no	—
150	C₄²×C₄₃	—	2	2	no	—
151	C₄²×C₄₃	—	2	2	no	—
152	C₄²×C₄₃	—	2	2	no	—
153	C₄²×C₄₃	—	2	2	no	—
154	C₄²×C₄₃	—	2	2	no	—
155	C₄²×C₄₃	—	4	1	no	—
156	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₄₃	C₂×D₄	1	2	yes	—
158	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
159	C₂³×C₄₃	—	2	2	no	—
160	C₂³×C₄₃	—	2	2	no	—
161	C₂³×C₄₃	#120	1	1	yes	characteristic
162	Q₈×C₄₃	—	2	2	no	—
163	Q₈×C₄₃	—	4	2	no	—
164	Q₈×C₄₃	—	4	2	no	—
165	Q₈×C₄₃	—	4	2	no	—
166	Q₈×C₄₃	—	8	2	no	—
167	Q₈×C₄₃	#135	1	4	yes	—
168	D₄×C₄₃	—	2	2	no	—
169	D₄×C₄₃	—	2	2	no	—
170	D₄×C₄₃	—	4	4	no	—
171	D₄×C₄₃	—	4	2	no	—
172	D₄×C₄₃	—	4	8	no	—
173	D₄×C₄₃	—	4	2	no	—
174	D₄×C₄₃	—	4	2	no	—
175	D₄×C₄₃	—	8	2	no	—
176	D₄×C₄₃	—	8	2	no	—
177	D₄×C₄₃	—	8	4	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	2	2	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	2	2	no	—
185	C₂×C₄×C₄₃	—	4	4	no	—
186	C₂×C₄×C₄₃	—	4	8	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	4	4	no	—
190	C₂×C₄×C₄₃	—	4	4	no	—
191	C₂×C₄×C₄₃	—	4	2	no	—
192	C₂×C₄×C₄₃	#120	1	2	yes	—
193	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
196	C₈×C₄₃	—	4	2	no	—
197	C₈×C₄₃	—	4	2	no	—
198	C₈×C₄₃	—	4	2	no	—
199	#18515	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂²×C₄₃	—	2	2	no	—
201	C₂²×C₄₃	—	2	1	no	—
202	C₂²×C₄₃	—	4	2	no	—
203	C₂²×C₄₃	—	4	4	no	—
204	C₂²×C₄₃	—	4	2	no	—
205	C₂²×C₄₃	—	4	2	no	—
206	C₂²×C₄₃	—	4	2	no	—
207	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
208	C₄×C₄₃	—	2	2	no	—
209	C₄×C₄₃	—	2	4	no	—
210	C₄×C₄₃	—	2	1	no	—
211	C₄×C₄₃	—	4	2	no	—
212	C₄×C₄₃	—	4	2	no	—
213	C₄×C₄₃	—	4	2	no	—
214	C₄×C₄₃	—	8	2	no	—
215	C₄×C₄₃	#455	1	2	yes	—
216	C₄×C₄₃	C₂×#135	1	2	yes	—
217	C₄×C₄₃	#575	1	2	yes	—
218	#3483	C₂×C₄₃	1	1	yes	characteristic
219	#3131	C₂×C₄₃	1	1	yes	characteristic, complemented
220	#3107	C₂×C₄₃	1	2	yes	complemented
221	#1646	C₂×C₄₃	1	2	yes	complemented
222	#1645	C₂×C₄₃	1	2	yes	complemented
223	#1642	C₂×C₄₃	1	2	yes	complemented
224	#1641	C₂×C₄₃	1	2	yes	complemented
225	#1543	C₂×C₄₃	1	1	yes	characteristic, complemented
226	#1476	C₂×C₄₃	1	2	yes	complemented
227	C₂×C₄₃	—	4	1	no	—
228	C₂×C₄₃	—	8	2	no	—
229	C₂×C₄₃	—	8	2	no	—
230	C₂×C₄₃	#3002	1	2	yes	—
231	C₂×C₄₃	C₂×#455	1	1	yes	characteristic
232	Q₈²	C₂²×C₄₃	1	1	yes	characteristic
233	#555	—	2	2	no	—
234	#555	—	2	2	no	—
235	#555	C₂²×C₄₃	1	1	yes	characteristic
236	#550	—	2	2	no	—
237	#550	C₂²×C₄₃	1	2	yes	—
238	#533	C₂²×C₄₃	1	1	yes	characteristic
239	#532	—	2	2	no	—
240	#532	—	2	2	no	—
241	#532	C₂²×C₄₃	1	1	yes	characteristic
242	C₄×#41	—	2	2	no	—
243	C₄×#41	C₂²×C₄₃	1	2	yes	—
244	#488	—	2	2	no	—
245	#487	C₂²×C₄₃	1	2	yes	—
246	#486	C₂²×C₄₃	1	2	yes	—
247	#485	—	2	2	no	—
248	#475	C₂²×C₄₃	1	2	yes	—
249	#474	C₂²×C₄₃	1	2	yes	—
250	#462	C₂²×C₄₃	1	2	yes	—
251	#461	C₂²×C₄₃	1	2	yes	—
252	#452	—	2	2	no	—
253	C₄×Q₁₆	—	2	2	no	—
254	C₄×SD₁₆	—	2	2	no	—
255	#431	C₂²×C₄₃	1	2	yes	—
256	#416	—	2	2	no	—
257	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
258	#333	C₂²×C₄₃	1	2	yes	—
259	#331	C₂²×C₄₃	1	1	yes	characteristic
260	#331	C₂²×C₄₃	1	1	yes	characteristic
261	Q₈⋊C₈	C₂²×C₄₃	1	2	yes	—
262	Q₈⋊C₈	C₂²×C₄₃	1	2	yes	—
263	D₄⋊C₈	C₂²×C₄₃	1	2	yes	—
264	D₄⋊C₈	C₂²×C₄₃	1	2	yes	—
265	C₄₃	#18515	1	1	yes	characteristic, direct product factor, Sylow
266	C₂×#41	—	2	2	no	—
267	C₂×#41	—	2	2	no	—
268	C₂×#41	D₄×C₄₃	1	2	yes	—
269	C₂×#41	D₄×C₄₃	1	2	yes	—
270	C₂×Q₁₆	—	2	2	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₄⋊Q₈	—	2	2	no	—
274	C₄⋊Q₈	—	2	2	no	—
275	C₄⋊Q₈	C₂³×C₄₃	1	2	yes	—
276	C₄⋊Q₈	C₂³×C₄₃	1	1	yes	characteristic
277	#127	—	2	2	no	—
278	#127	—	2	2	no	—
279	#127	C₂³×C₄₃	1	1	yes	characteristic
280	#125	—	2	1	no	—
281	#124	—	2	2	no	—
282	#124	—	2	4	no	—
283	#124	—	2	2	no	—
284	#124	D₄×C₄₃	1	2	yes	—
285	C₂²⋊Q₈	—	2	2	no	—
286	#121	—	2	4	no	—
287	#121	—	2	4	no	—
288	#121	—	2	2	no	—
289	#121	—	2	4	no	—
290	#121	—	2	2	no	—
291	#121	—	2	2	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	D₄×C₄₃	1	2	yes	—
295	C₄×Q₈	C₂³×C₄₃	1	2	yes	—
296	C₄×D₄	—	2	4	no	—
297	C₄×D₄	—	2	4	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	D₄×C₄₃	1	2	yes	—
303	C₄×D₄	C₂³×C₄₃	1	2	yes	—
304	#117	—	2	4	no	—
305	#117	—	2	2	no	—
306	#117	—	2	2	no	—
307	#117	—	2	1	no	—
308	#117	D₄×C₄₃	1	2	yes	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
312	#107	—	2	2	no	—
313	#106	—	2	2	no	—
314	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
315	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
316	#103	—	2	4	no	—
317	#103	—	2	2	no	—
318	#103	—	2	2	no	—
319	#103	—	2	2	no	—
320	#102	—	2	4	no	—
321	#102	—	2	2	no	—
322	C₂²⋊C₈	—	2	2	no	—
323	C₄×C₈	—	2	1	no	—
324	C₄×C₈	—	2	2	no	—
325	C₄×C₈	C₂³×C₄₃	1	2	yes	—
326	#41	—	2	4	no	—
327	#41	—	4	2	no	—
328	#41	—	4	4	no	—
329	#41	—	4	4	no	—
330	#41	—	4	4	no	—
331	#41	—	8	4	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
335	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
343	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
351	Q₁₆	—	4	4	no	—
352	SD₁₆	—	4	4	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	4	2	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
365	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	4	1	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	4	1	no	—
379	C₄²	C₂×D₄×C₄₃	1	2	yes	—
380	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
381	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	#120×C₄₃	1	1	yes	characteristic
385	Q₈	—	2	2	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	4	2	no	—
389	Q₈	—	8	2	no	—
390	Q₈	#135×C₄₃	1	4	yes	—
391	D₄	—	2	2	no	—
392	D₄	—	2	2	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	8	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	8	2	no	—
399	D₄	—	8	2	no	—
400	D₄	—	8	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	8	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	#120×C₄₃	1	2	yes	—
416	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
418	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
419	C₈	—	4	2	no	—
420	C₈	—	4	2	no	—
421	C₈	—	4	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
430	C₄	—	2	2	no	—
431	C₄	—	2	4	no	—
432	C₄	—	2	1	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	8	2	no	—
437	C₄	C₄₃×#455	1	2	yes	—
438	C₄	C₂×#135×C₄₃	1	2	yes	—
439	C₄	C₄₃×#575	1	2	yes	—
440	C₂	—	4	1	no	—
441	C₂	—	8	2	no	—
442	C₂	—	8	2	no	—
443	C₂	C₄₃×#3002	1	2	yes	—
444	C₂	C₂×C₄₃×#455	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₃	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₃
socle	C₂²×C₄₃	C₂×#120
prime radical	C₄₃×#3483	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#3131	C₂	semidirect
3. C₄₃×#3107	C₂	semidirect
4. C₄₃×#1646	C₂	semidirect
5. C₄₃×#1645	C₂	semidirect
6. C₄₃×#1642	C₂	semidirect
7. C₄₃×#1641	C₂	semidirect
8. C₄₃×#1543	C₂	semidirect
9. C₄₃×#1476	C₂	semidirect
199. #18515	C₄₃	direct (N × H)
219. #3131	C₂×C₄₃	semidirect
220. #3107	C₂×C₄₃	semidirect
221. #1646	C₂×C₄₃	semidirect
222. #1645	C₂×C₄₃	semidirect
223. #1642	C₂×C₄₃	semidirect
224. #1641	C₂×C₄₃	semidirect
225. #1543	C₂×C₄₃	semidirect
226. #1476	C₂×C₄₃	semidirect
265. C₄₃	#18515	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×#3483	2
C₄₃×#3131	2
C₄₃×#3107	2
C₄₃×#1646	2
C₄₃×#1645	2
C₄₃×#1642	2
C₄₃×#1641	2
C₄₃×#1543	2
C₄₃×#1476	2
#18515	43

Subgroups — C43×#18515 #24938532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#18515 #24938532