Subgroups — C₄₃×#17900 #24937917

Order 11008.

774 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3100	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1581	C₂	1	4	yes	maximal, complemented
5	C₈×D₈×C₄₃	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1571	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1450	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#131×C₄₃	—	2	1	no	—
11	C₂³×C₈×C₄₃	—	2	1	no	—
12	C₄₃×#532	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₄₃×#480	C₄	1	2	yes	—
15	C₄₃×#474	C₄	1	2	yes	—
16	C₄₃×#459	C₄	1	2	yes	—
17	C₄₃×#447	C₄	1	2	yes	—
18	C₄×D₈×C₄₃	C₂²	1	4	yes	—
19	C₄₃×#436	—	2	1	no	—
20	C₄₃×#436	C₂²	1	2	yes	complemented
21	C₈×D₄×C₄₃	—	2	1	no	—
22	C₈×D₄×C₄₃	—	2	1	no	—
23	C₈×D₄×C₄₃	—	2	1	no	—
24	C₈×D₄×C₄₃	C₂²	1	2	yes	—
25	C₈×D₄×C₄₃	C₂²	1	2	yes	—
26	C₈×D₄×C₄₃	C₂²	1	2	yes	complemented
27	C₄₃×#431	C₂²	1	1	yes	characteristic
28	C₄₃×#431	C₂²	1	1	yes	characteristic
29	C₄₃×#423	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
31	C₄₃×#408	—	2	1	no	—
32	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
33	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
34	C₄₃×#335	C₂²	1	4	yes	complemented
35	C₄₃×D₄⋊C₈	C₂²	1	4	yes	—
36	C₄₃×D₄⋊C₈	C₂²	1	4	yes	complemented
37	C₄₃×#322	C₂²	1	2	yes	complemented
38	C₈²×C₄₃	C₂²	1	2	yes	complemented
39	C₂×#41×C₄₃	—	2	1	no	—
40	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₃	—	2	1	no	—
42	C₂×D₈×C₄₃	C₂×C₄	1	4	yes	—
43	#131×C₄₃	—	4	4	no	—
44	C₂×M₁₆×C₄₃	—	2	1	no	—
45	C₂×M₁₆×C₄₃	—	2	2	no	—
46	C₂²×C₈×C₄₃	—	2	1	no	—
47	C₂²×C₈×C₄₃	—	2	2	no	—
48	C₂²×C₈×C₄₃	—	2	2	no	—
49	C₂²×C₈×C₄₃	—	2	2	no	—
50	C₂²×C₈×C₄₃	—	4	4	no	—
51	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
53	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
54	#127×C₄₃	C₂×C₄	1	1	yes	characteristic
55	#124×C₄₃	—	2	1	no	—
56	#121×C₄₃	—	2	1	no	—
57	#121×C₄₃	C₂×C₄	1	2	yes	—
58	C₄×D₄×C₄₃	—	2	1	no	—
59	C₄×D₄×C₄₃	—	2	1	no	—
60	C₄×D₄×C₄₃	—	2	1	no	—
61	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
62	C₄×D₄×C₄₃	C₂³	1	2	yes	—
63	C₄×D₄×C₄₃	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
66	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
67	#107×C₄₃	C₂×C₄	1	4	yes	—
68	C₄⋊C₈×C₄₃	—	2	1	no	—
69	C₄⋊C₈×C₄₃	—	2	1	no	—
70	C₄⋊C₈×C₄₃	—	2	1	no	—
71	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
72	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
73	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
74	#102×C₄₃	C₂×C₄	1	4	yes	—
75	#102×C₄₃	C₂×C₄	1	4	yes	—
76	C₂²⋊C₈×C₄₃	—	2	1	no	—
77	C₂²⋊C₈×C₄₃	—	2	2	no	—
78	C₂²⋊C₈×C₄₃	—	2	2	no	—
79	C₂²⋊C₈×C₄₃	—	2	2	no	—
80	C₂²⋊C₈×C₄₃	—	2	2	no	—
81	C₂²⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
82	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
83	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
84	C₄×C₈×C₄₃	C₂³	1	2	yes	—
85	C₄×C₈×C₄₃	C₂³	1	2	yes	—
86	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
88	C₂⁴×C₄₃	—	2	1	no	—
89	#41×C₄₃	—	4	2	no	—
90	#41×C₄₃	—	4	2	no	—
91	C₂×Q₈×C₄₃	—	2	1	no	—
92	C₂×D₄×C₄₃	—	2	4	no	—
93	C₂×D₄×C₄₃	—	2	1	no	—
94	C₂×D₄×C₄₃	—	2	1	no	—
95	C₂×D₄×C₄₃	—	2	1	no	—
96	C₂×D₄×C₄₃	—	2	2	no	—
97	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
98	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
102	C₂²×C₄×C₄₃	—	2	1	no	—
103	C₂²×C₄×C₄₃	—	4	2	no	—
104	C₂²×C₄×C₄₃	—	4	2	no	—
105	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
108	D₈×C₄₃	—	2	8	no	—
109	M₁₆×C₄₃	—	4	2	no	—
110	M₁₆×C₄₃	—	4	4	no	—
111	C₂×C₈×C₄₃	—	2	2	no	—
112	C₂×C₈×C₄₃	—	2	2	no	—
113	C₂×C₈×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	—	2	2	no	—
115	C₂×C₈×C₄₃	—	4	2	no	—
116	C₂×C₈×C₄₃	—	4	4	no	—
117	C₂×C₈×C₄₃	—	4	4	no	—
118	C₂×C₈×C₄₃	—	4	4	no	—
119	C₂×C₈×C₄₃	D₈	1	4	yes	complemented
120	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
121	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₄₃	—	2	1	no	—
126	C₄⋊C₄×C₄₃	—	2	1	no	—
127	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
128	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
129	C₂²⋊C₄×C₄₃	—	2	2	no	—
130	C₂²⋊C₄×C₄₃	—	2	2	no	—
131	C₂²⋊C₄×C₄₃	—	2	2	no	—
132	C₂²⋊C₄×C₄₃	—	2	2	no	—
133	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₃	#41	1	1	yes	characteristic
136	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
137	C₂³×C₄₃	—	2	4	no	—
138	C₂³×C₄₃	—	2	2	no	—
139	C₂³×C₄₃	—	2	2	no	—
140	C₂³×C₄₃	—	4	2	no	—
141	C₂³×C₄₃	—	4	2	no	—
142	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
143	Q₈×C₄₃	—	4	2	no	—
144	D₄×C₄₃	—	2	4	no	—
145	D₄×C₄₃	—	2	2	no	—
146	D₄×C₄₃	—	2	4	no	—
147	D₄×C₄₃	—	4	2	no	—
148	D₄×C₄₃	—	4	4	no	—
149	D₄×C₄₃	—	4	2	no	—
150	D₄×C₄₃	#131	1	4	yes	complemented
151	C₂×C₄×C₄₃	—	2	2	no	—
152	C₂×C₄×C₄₃	—	2	2	no	—
153	C₂×C₄×C₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	—	4	1	no	—
155	C₂×C₄×C₄₃	—	4	2	no	—
156	C₂×C₄×C₄₃	—	4	2	no	—
157	C₂×C₄×C₄₃	—	4	2	no	—
158	C₂×C₄×C₄₃	—	4	2	no	—
159	C₂×C₄×C₄₃	—	4	2	no	—
160	C₂×C₄×C₄₃	—	4	4	no	—
161	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
165	C₂×C₄×C₄₃	#135	1	2	yes	—
166	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
169	C₈×C₄₃	—	2	4	no	—
170	C₈×C₄₃	—	2	1	no	—
171	C₈×C₄₃	—	2	1	no	—
172	C₈×C₄₃	—	4	2	no	—
173	C₈×C₄₃	—	4	2	no	—
174	C₈×C₄₃	—	4	2	no	—
175	C₈×C₄₃	C₂×D₈	1	2	yes	—
176	C₈×C₄₃	C₂×D₈	1	2	yes	—
177	#17900	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂²×C₄₃	—	2	1	no	—
179	C₂²×C₄₃	—	2	1	no	—
180	C₂²×C₄₃	—	2	4	no	—
181	C₂²×C₄₃	—	4	8	no	—
182	C₂²×C₄₃	—	4	2	no	—
183	C₂²×C₄₃	—	4	2	no	—
184	C₂²×C₄₃	—	4	2	no	—
185	C₂²×C₄₃	—	4	2	no	—
186	C₂²×C₄₃	—	4	2	no	—
187	C₂²×C₄₃	C₄×D₈	1	2	yes	—
188	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
189	C₄×C₄₃	—	2	1	no	—
190	C₄×C₄₃	—	2	1	no	—
191	C₄×C₄₃	—	2	1	no	—
192	C₄×C₄₃	—	4	2	no	—
193	C₄×C₄₃	—	4	2	no	—
194	C₄×C₄₃	C₄×D₈	1	2	yes	—
195	C₄×C₄₃	C₂×#131	1	2	yes	—
196	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
197	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
198	#3100	C₂×C₄₃	1	1	yes	characteristic
199	#2931	C₂×C₄₃	1	1	yes	characteristic, complemented
200	C₂×C₈×D₄	C₂×C₄₃	1	1	yes	characteristic, complemented
201	#1581	C₂×C₄₃	1	4	yes	complemented
202	C₈×D₈	C₂×C₄₃	1	4	yes	complemented
203	#1571	C₂×C₄₃	1	1	yes	characteristic, complemented
204	#1486	C₂×C₄₃	1	1	yes	characteristic, complemented
205	#1480	C₂×C₄₃	1	1	yes	characteristic, complemented
206	#1450	C₂×C₄₃	1	1	yes	characteristic, complemented
207	C₂×C₄₃	—	2	2	no	—
208	C₂×C₄₃	—	4	4	no	—
209	C₂×C₄₃	—	8	2	no	—
210	C₂×C₄₃	#2929	1	1	yes	characteristic
211	C₂×C₄₃	C₂×C₄×D₈	1	1	yes	characteristic
212	C₂×C₄₃	#2955	1	1	yes	characteristic
213	C₂×#131	—	2	1	no	—
214	C₂³×C₈	—	2	1	no	—
215	#532	C₂²×C₄₃	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
217	#480	C₄×C₄₃	1	2	yes	—
218	#474	C₄×C₄₃	1	2	yes	—
219	#459	C₄×C₄₃	1	2	yes	—
220	#447	C₄×C₄₃	1	2	yes	—
221	C₄×D₈	C₂²×C₄₃	1	4	yes	—
222	#436	—	2	1	no	—
223	#436	C₂²×C₄₃	1	2	yes	complemented
224	C₈×D₄	—	2	1	no	—
225	C₈×D₄	—	2	1	no	—
226	C₈×D₄	—	2	1	no	—
227	C₈×D₄	C₂²×C₄₃	1	2	yes	—
228	C₈×D₄	C₂²×C₄₃	1	2	yes	—
229	C₈×D₄	C₂²×C₄₃	1	2	yes	complemented
230	#431	C₂²×C₄₃	1	1	yes	characteristic
231	#431	C₂²×C₄₃	1	1	yes	characteristic
232	#423	C₂²×C₄₃	1	1	yes	characteristic
233	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
234	#408	—	2	1	no	—
235	C₂×C₂²⋊C₈	—	2	1	no	—
236	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
237	#335	C₂²×C₄₃	1	4	yes	complemented
238	D₄⋊C₈	C₂²×C₄₃	1	4	yes	—
239	D₄⋊C₈	C₂²×C₄₃	1	4	yes	complemented
240	#322	C₂²×C₄₃	1	2	yes	complemented
241	C₈²	C₂²×C₄₃	1	2	yes	complemented
242	C₄₃	#17900	1	1	yes	characteristic, direct product factor, Sylow
243	C₂×#41	—	2	1	no	—
244	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
245	C₂³×C₄	—	2	1	no	—
246	C₂×D₈	C₂×C₄×C₄₃	1	4	yes	—
247	#131	—	4	4	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	—	4	4	no	—
255	C₂²×C₈	D₄×C₄₃	1	1	yes	characteristic
256	C₂²×C₈	D₄×C₄₃	1	1	yes	characteristic
257	C₄⋊Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
258	#127	C₂×C₄×C₄₃	1	1	yes	characteristic
259	#124	—	2	1	no	—
260	#121	—	2	1	no	—
261	#121	C₂×C₄×C₄₃	1	2	yes	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
266	C₄×D₄	C₂³×C₄₃	1	2	yes	—
267	C₄×D₄	C₂³×C₄₃	1	2	yes	—
268	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
271	#107	C₂×C₄×C₄₃	1	4	yes	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	C₂×C₄×C₄₃	1	2	yes	—
276	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
277	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
278	#102	C₂×C₄×C₄₃	1	4	yes	—
279	#102	C₂×C₄×C₄₃	1	4	yes	—
280	C₂²⋊C₈	—	2	1	no	—
281	C₂²⋊C₈	—	2	2	no	—
282	C₂²⋊C₈	—	2	2	no	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₂²⋊C₈	—	2	2	no	—
285	C₂²⋊C₈	C₂×C₄×C₄₃	1	2	yes	—
286	C₄×C₈	D₄×C₄₃	1	1	yes	characteristic
287	C₄×C₈	D₄×C₄₃	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₄₃	1	2	yes	—
289	C₄×C₈	C₂³×C₄₃	1	2	yes	—
290	C₄×C₈	C₂³×C₄₃	1	1	yes	characteristic
291	C₄×C₈	C₂³×C₄₃	1	1	yes	characteristic
292	C₂⁴	—	2	1	no	—
293	#41	—	4	2	no	—
294	#41	—	4	2	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
302	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
311	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
312	D₈	—	2	8	no	—
313	M₁₆	—	4	2	no	—
314	M₁₆	—	4	4	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	4	2	no	—
320	C₂×C₈	—	4	4	no	—
321	C₂×C₈	—	4	4	no	—
322	C₂×C₈	—	4	4	no	—
323	C₂×C₈	D₈×C₄₃	1	4	yes	complemented
324	C₂×C₈	C₂²×C₄×C₄₃	1	4	yes	—
325	C₂×C₈	C₂×D₄×C₄₃	1	1	yes	characteristic
326	C₂×C₈	C₂×D₄×C₄₃	1	1	yes	characteristic
327	C₂×C₈	C₂×D₄×C₄₃	1	1	yes	characteristic
328	C₂×C₈	C₂×D₄×C₄₃	1	1	yes	characteristic
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
332	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
338	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
339	C₄²	#41×C₄₃	1	1	yes	characteristic
340	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
341	C₂³	—	2	4	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	C₄×D₄×C₄₃	1	1	yes	characteristic
347	Q₈	—	4	2	no	—
348	D₄	—	2	4	no	—
349	D₄	—	2	2	no	—
350	D₄	—	2	4	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	4	no	—
353	D₄	—	4	2	no	—
354	D₄	#131×C₄₃	1	4	yes	complemented
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
366	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
367	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
368	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
369	C₂×C₄	#135×C₄₃	1	2	yes	—
370	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
373	C₈	—	2	4	no	—
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	4	2	no	—
377	C₈	—	4	2	no	—
378	C₈	—	4	2	no	—
379	C₈	C₂×D₈×C₄₃	1	2	yes	—
380	C₈	C₂×D₈×C₄₃	1	2	yes	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	4	8	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	C₄×D₈×C₄₃	1	2	yes	—
391	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	C₄×D₈×C₄₃	1	2	yes	—
398	C₄	C₂×#131×C₄₃	1	2	yes	—
399	C₄	C₂²×D₈×C₄₃	1	1	yes	characteristic
400	C₄	C₂×#135×C₄₃	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	4	4	no	—
403	C₂	—	8	2	no	—
404	C₂	C₄₃×#2929	1	1	yes	characteristic
405	C₂	C₂×C₄×D₈×C₄₃	1	1	yes	characteristic
406	C₂	C₄₃×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₄₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₄²	C₂⁴×C₄₃
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₄₃×#3100	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₄₃ ◁ C₂×C₄×C₈×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#2931	C₂	semidirect
3. C₂×C₈×D₄×C₄₃	C₂	semidirect
4. C₄₃×#1581	C₂	semidirect
5. C₈×D₈×C₄₃	C₂	semidirect
6. C₄₃×#1571	C₂	semidirect
7. C₄₃×#1486	C₂	semidirect
8. C₄₃×#1480	C₂	semidirect
9. C₄₃×#1450	C₂	semidirect
20. C₄₃×#436	C₂²	semidirect
26. C₈×D₄×C₄₃	C₂²	semidirect
34. C₄₃×#335	C₂²	semidirect
36. C₄₃×D₄⋊C₈	C₂²	semidirect
37. C₄₃×#322	C₂²	semidirect
38. C₈²×C₄₃	C₂²	semidirect
119. C₂×C₈×C₄₃	D₈	semidirect
150. D₄×C₄₃	#131	semidirect
177. #17900	C₄₃	direct (N × H)
199. #2931	C₂×C₄₃	semidirect
200. C₂×C₈×D₄	C₂×C₄₃	semidirect
201. #1581	C₂×C₄₃	semidirect
202. C₈×D₈	C₂×C₄₃	semidirect
203. #1571	C₂×C₄₃	semidirect
204. #1486	C₂×C₄₃	semidirect
205. #1480	C₂×C₄₃	semidirect
206. #1450	C₂×C₄₃	semidirect
223. #436	C₂²×C₄₃	semidirect
229. C₈×D₄	C₂²×C₄₃	semidirect
237. #335	C₂²×C₄₃	semidirect
239. D₄⋊C₈	C₂²×C₄₃	semidirect
240. #322	C₂²×C₄₃	semidirect
241. C₈²	C₂²×C₄₃	semidirect
242. C₄₃	#17900	direct (N × H)
323. C₂×C₈	D₈×C₄₃	semidirect
354. D₄	#131×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄₃×#3100	2
C₄₃×#2931	2
C₂×C₈×D₄×C₄₃	2
C₄₃×#1581	2
C₈×D₈×C₄₃	2
C₄₃×#1571	2
C₄₃×#1486	2
C₄₃×#1480	2
C₄₃×#1450	2
#17900	43

Subgroups — C43×#17900 #24937917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#17900 #24937917