Subgroups — C₄₃×#20970 #24940987

Order 11008.

1914 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#525	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#416	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1895	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1894	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1735	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₄₃	—	2	4	no	—
11	C₂²×M₁₆×C₄₃	—	2	8	no	—
12	C₂²×M₁₆×C₄₃	C₂²	1	4	yes	—
13	C₂³×C₈×C₄₃	C₂²	1	2	yes	—
14	C₄₃×#525	—	2	4	no	—
15	C₄₃×#525	C₄	1	8	yes	complemented
16	C₂×#123×C₄₃	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
18	C₂×#121×C₄₃	C₂²	1	2	yes	—
19	C₂×#120×C₄₃	—	2	1	no	—
20	C₂×C₄×D₄×C₄₃	—	2	2	no	—
21	C₂×#117×C₄₃	C₂²	1	2	yes	—
22	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#416	—	2	8	no	—
24	C₂×#103×C₄₃	C₂²	1	4	yes	complemented
25	C₂×#102×C₄₃	C₂²	1	4	yes	complemented
26	C₄₃×#381	—	2	1	no	—
27	C₄₃×#380	C₂²	1	4	yes	—
28	C₄₃×#379	—	2	1	no	—
29	C₄×C₂²⋊C₄×C₄₃	—	2	2	no	—
30	C₄₃×#340	C₂²	1	8	yes	complemented
31	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
32	C₂×#41×C₄₃	—	2	2	no	—
33	C₂×#41×C₄₃	—	2	4	no	—
34	C₂×#41×C₄₃	—	2	4	no	—
35	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
36	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₄₃	—	2	2	no	—
38	C₂²×D₄×C₄₃	—	2	1	no	—
39	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₄₃	—	2	4	no	—
41	C₂³×C₄×C₄₃	—	2	4	no	—
42	C₂³×C₄×C₄₃	—	2	1	no	—
43	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
44	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₃	D₄	1	2	yes	—
46	C₂³×C₄×C₄₃	D₄	1	4	yes	—
47	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₄₃	—	2	32	no	—
50	C₂×M₁₆×C₄₃	—	2	8	no	—
51	C₂×M₁₆×C₄₃	—	2	16	no	—
52	C₂²×C₈×C₄₃	—	2	4	no	—
53	C₂²×C₈×C₄₃	—	2	4	no	—
54	C₂²×C₈×C₄₃	D₄	1	8	yes	complemented
55	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
56	#123×C₄₃	—	2	8	no	—
57	C₂²⋊Q₈×C₄₃	—	2	4	no	—
58	C₂²⋊Q₈×C₄₃	C₂×C₄	1	8	yes	—
59	#121×C₄₃	—	2	4	no	—
60	#121×C₄₃	C₂×C₄	1	8	yes	—
61	#120×C₄₃	—	2	8	no	—
62	C₄×D₄×C₄₃	—	2	16	no	—
63	#117×C₄₃	—	2	2	no	—
64	#117×C₄₃	—	2	4	no	—
65	#117×C₄₃	—	2	4	no	—
66	#117×C₄₃	C₂×C₄	1	4	yes	—
67	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
75	C₂×C₄²×C₄₃	—	2	1	no	—
76	C₂×C₄²×C₄₃	—	2	2	no	—
77	#103×C₄₃	—	2	8	no	—
78	#102×C₄₃	—	2	8	no	—
79	#95×C₄₃	—	2	4	no	—
80	C₂⁴×C₄₃	—	2	4	no	—
81	C₂⁴×C₄₃	—	2	1	no	—
82	C₂⁴×C₄₃	—	4	4	no	—
83	C₂⁴×C₄₃	C₂²⋊C₄	1	4	yes	—
84	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
85	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
86	#41×C₄₃	—	2	16	no	—
87	#41×C₄₃	—	4	4	no	—
88	#41×C₄₃	—	4	4	no	—
89	C₂×Q₈×C₄₃	—	2	1	no	—
90	C₂×Q₈×C₄₃	—	2	2	no	—
91	C₂×Q₈×C₄₃	—	2	2	no	—
92	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
93	C₂×D₄×C₄₃	—	2	1	no	—
94	C₂×D₄×C₄₃	—	2	8	no	—
95	C₂×D₄×C₄₃	—	2	4	no	—
96	C₂×D₄×C₄₃	—	2	2	no	—
97	C₂×D₄×C₄₃	—	2	2	no	—
98	C₂×D₄×C₄₃	—	4	8	no	—
99	C₂×D₄×C₄₃	—	4	4	no	—
100	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₃	—	2	16	no	—
102	C₂²×C₄×C₄₃	—	2	8	no	—
103	C₂²×C₄×C₄₃	—	2	8	no	—
104	C₂²×C₄×C₄₃	—	2	8	no	—
105	C₂²×C₄×C₄₃	—	2	4	no	—
106	C₂²×C₄×C₄₃	—	2	4	no	—
107	C₂²×C₄×C₄₃	—	2	4	no	—
108	C₂²×C₄×C₄₃	—	2	4	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	—	2	4	no	—
112	C₂²×C₄×C₄₃	—	4	4	no	—
113	C₂²×C₄×C₄₃	C₂²⋊C₄	1	8	yes	—
114	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
115	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
116	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
120	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	#41	1	4	yes	—
123	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
124	M₁₆×C₄₃	—	2	32	no	—
125	C₂×C₈×C₄₃	—	2	16	no	—
126	C₂×C₈×C₄₃	—	2	4	no	—
127	C₂×C₈×C₄₃	—	2	4	no	—
128	C₂×C₈×C₄₃	C₂×D₄	1	8	yes	—
129	C₄⋊C₄×C₄₃	—	2	8	no	—
130	C₄⋊C₄×C₄₃	—	2	2	no	—
131	C₄⋊C₄×C₄₃	—	2	4	no	—
132	C₄⋊C₄×C₄₃	—	2	4	no	—
133	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
134	C₂²⋊C₄×C₄₃	—	2	8	no	—
135	C₂²⋊C₄×C₄₃	—	2	4	no	—
136	C₂²⋊C₄×C₄₃	—	2	8	no	—
137	C₂²⋊C₄×C₄₃	—	4	8	no	—
138	C₂²⋊C₄×C₄₃	—	4	4	no	—
139	C₄²×C₄₃	—	2	4	no	—
140	C₄²×C₄₃	—	4	4	no	—
141	C₂³×C₄₃	—	2	4	no	—
142	C₂³×C₄₃	—	2	4	no	—
143	C₂³×C₄₃	—	2	4	no	—
144	C₂³×C₄₃	—	2	4	no	—
145	C₂³×C₄₃	—	2	8	no	—
146	C₂³×C₄₃	—	2	2	no	—
147	C₂³×C₄₃	—	4	8	no	—
148	C₂³×C₄₃	—	4	16	no	—
149	C₂³×C₄₃	—	4	2	no	—
150	C₂³×C₄₃	—	4	4	no	—
151	C₂³×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
152	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂³×C₄₃	#121	1	4	yes	—
154	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₄₃	—	2	4	no	—
156	Q₈×C₄₃	—	4	1	no	—
157	Q₈×C₄₃	—	4	1	no	—
158	D₄×C₄₃	—	2	4	no	—
159	D₄×C₄₃	—	4	16	no	—
160	D₄×C₄₃	—	4	8	no	—
161	D₄×C₄₃	—	4	1	no	—
162	D₄×C₄₃	—	4	1	no	—
163	C₂×C₄×C₄₃	—	2	4	no	—
164	C₂×C₄×C₄₃	—	2	8	no	—
165	C₂×C₄×C₄₃	—	2	8	no	—
166	C₂×C₄×C₄₃	—	2	4	no	—
167	C₂×C₄×C₄₃	—	2	4	no	—
168	C₂×C₄×C₄₃	—	2	16	no	—
169	C₂×C₄×C₄₃	—	2	4	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	4	2	no	—
172	C₂×C₄×C₄₃	—	4	4	no	—
173	C₂×C₄×C₄₃	—	4	8	no	—
174	C₂×C₄×C₄₃	—	4	4	no	—
175	C₂×C₄×C₄₃	—	4	8	no	—
176	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
177	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
179	C₂×C₄×C₄₃	#120	1	4	yes	—
180	C₂×C₄×C₄₃	#121	1	4	yes	—
181	C₂×C₄×C₄₃	#123	1	4	yes	—
182	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
184	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
186	C₈×C₄₃	—	2	8	no	—
187	#20970	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂²×C₄₃	—	2	4	no	—
189	C₂²×C₄₃	—	2	8	no	—
190	C₂²×C₄₃	—	2	4	no	—
191	C₂²×C₄₃	—	2	4	no	—
192	C₂²×C₄₃	—	2	4	no	—
193	C₂²×C₄₃	—	4	16	no	—
194	C₂²×C₄₃	—	4	8	no	—
195	C₂²×C₄₃	—	4	4	no	—
196	C₂²×C₄₃	—	4	2	no	—
197	C₂²×C₄₃	—	8	4	no	—
198	C₂²×C₄₃	#386	1	4	yes	—
199	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×C₄₃	C₂×#121	1	2	yes	—
201	C₂²×C₄₃	#575	1	4	yes	—
202	C₄×C₄₃	—	2	4	no	—
203	C₄×C₄₃	—	4	4	no	—
204	C₄×C₄₃	—	4	2	no	—
205	C₄×C₄₃	—	8	4	no	—
206	C₄×C₄₃	#386	1	4	yes	—
207	C₄×C₄₃	C₂×C₄×D₄	1	2	yes	—
208	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
209	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
210	C₂³×M₁₆	C₂×C₄₃	1	1	yes	characteristic, complemented
211	C₂×#525	C₂×C₄₃	1	1	yes	characteristic
212	C₂×#416	C₂×C₄₃	1	2	yes	complemented
213	#2280	C₂×C₄₃	1	1	yes	characteristic, complemented
214	#1895	C₂×C₄₃	1	4	yes	complemented
215	#1894	C₂×C₄₃	1	4	yes	complemented
216	#1735	C₂×C₄₃	1	2	yes	complemented
217	C₂×C₄₃	—	2	4	no	—
218	C₂×C₄₃	—	4	4	no	—
219	C₂×C₄₃	—	8	2	no	—
220	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
221	C₂×C₄₃	#2896	1	2	yes	—
222	C₂×C₄₃	#3054	1	4	yes	—
223	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
224	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
225	C₂²×M₁₆	—	2	4	no	—
226	C₂²×M₁₆	—	2	8	no	—
227	C₂²×M₁₆	C₂²×C₄₃	1	4	yes	—
228	C₂³×C₈	C₂²×C₄₃	1	2	yes	—
229	#525	—	2	4	no	—
230	#525	C₄×C₄₃	1	8	yes	complemented
231	C₂×#123	—	2	1	no	—
232	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
233	C₂×#121	C₂²×C₄₃	1	2	yes	—
234	C₂×#120	—	2	1	no	—
235	C₂×C₄×D₄	—	2	2	no	—
236	C₂×#117	C₂²×C₄₃	1	2	yes	—
237	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
238	#416	—	2	8	no	—
239	C₂×#103	C₂²×C₄₃	1	4	yes	complemented
240	C₂×#102	C₂²×C₄₃	1	4	yes	complemented
241	#381	—	2	1	no	—
242	#380	C₂²×C₄₃	1	4	yes	—
243	#379	—	2	1	no	—
244	C₄×C₂²⋊C₄	—	2	2	no	—
245	#340	C₂²×C₄₃	1	8	yes	complemented
246	C₄₃	#20970	1	1	yes	characteristic, direct product factor, Sylow
247	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
248	C₂×#41	—	2	2	no	—
249	C₂×#41	—	2	4	no	—
250	C₂×#41	—	2	4	no	—
251	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
252	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
253	C₂²×D₄	—	2	2	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
256	C₂³×C₄	—	2	4	no	—
257	C₂³×C₄	—	2	4	no	—
258	C₂³×C₄	—	2	1	no	—
259	C₂³×C₄	C₂×C₄×C₄₃	1	4	yes	—
260	C₂³×C₄	D₄×C₄₃	1	2	yes	—
261	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
262	C₂³×C₄	D₄×C₄₃	1	4	yes	—
263	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
264	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
265	C₂×M₁₆	—	2	32	no	—
266	C₂×M₁₆	—	2	8	no	—
267	C₂×M₁₆	—	2	16	no	—
268	C₂²×C₈	—	2	4	no	—
269	C₂²×C₈	—	2	4	no	—
270	C₂²×C₈	D₄×C₄₃	1	8	yes	complemented
271	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
272	#123	—	2	8	no	—
273	C₂²⋊Q₈	—	2	4	no	—
274	C₂²⋊Q₈	C₂×C₄×C₄₃	1	8	yes	—
275	#121	—	2	4	no	—
276	#121	C₂×C₄×C₄₃	1	8	yes	—
277	#120	—	2	8	no	—
278	C₄×D₄	—	2	16	no	—
279	#117	—	2	2	no	—
280	#117	—	2	4	no	—
281	#117	—	2	4	no	—
282	#117	C₂×C₄×C₄₃	1	4	yes	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
285	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₂²⋊C₄	—	2	4	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	—	2	2	no	—
293	#103	—	2	8	no	—
294	#102	—	2	8	no	—
295	#95	—	2	4	no	—
296	C₂⁴	—	2	4	no	—
297	C₂⁴	—	2	1	no	—
298	C₂⁴	—	4	4	no	—
299	C₂⁴	C₂²⋊C₄×C₄₃	1	4	yes	—
300	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
301	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
302	#41	—	2	16	no	—
303	#41	—	4	4	no	—
304	#41	—	4	4	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
309	C₂×D₄	—	2	8	no	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	4	8	no	—
315	C₂×D₄	—	4	4	no	—
316	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	16	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	8	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	C₂²⋊C₄×C₄₃	1	8	yes	—
330	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
331	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
332	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
335	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
338	C₂²×C₄	#41×C₄₃	1	4	yes	—
339	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
340	M₁₆	—	2	32	no	—
341	C₂×C₈	—	2	16	no	—
342	C₂×C₈	—	2	4	no	—
343	C₂×C₈	—	2	4	no	—
344	C₂×C₈	C₂×D₄×C₄₃	1	8	yes	—
345	C₄⋊C₄	—	2	8	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
350	C₂²⋊C₄	—	2	4	no	—
351	C₂²⋊C₄	—	2	8	no	—
352	C₂²⋊C₄	—	2	8	no	—
353	C₂²⋊C₄	—	4	8	no	—
354	C₂²⋊C₄	—	4	4	no	—
355	C₄²	—	2	4	no	—
356	C₄²	—	4	4	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	8	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	4	8	no	—
364	C₂³	—	4	16	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	4	no	—
367	C₂³	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
368	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
369	C₂³	#121×C₄₃	1	4	yes	—
370	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
371	Q₈	—	2	4	no	—
372	Q₈	—	4	1	no	—
373	Q₈	—	4	1	no	—
374	D₄	—	2	4	no	—
375	D₄	—	4	16	no	—
376	D₄	—	4	8	no	—
377	D₄	—	4	1	no	—
378	D₄	—	4	1	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	8	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	16	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
393	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
394	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
395	C₂×C₄	#120×C₄₃	1	4	yes	—
396	C₂×C₄	#121×C₄₃	1	4	yes	—
397	C₂×C₄	#123×C₄₃	1	4	yes	—
398	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
400	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
401	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
402	C₈	—	2	8	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	8	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	4	16	no	—
409	C₂²	—	4	8	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	8	4	no	—
413	C₂²	C₄₃×#386	1	4	yes	—
414	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
415	C₂²	C₂×#121×C₄₃	1	2	yes	—
416	C₂²	C₄₃×#575	1	4	yes	—
417	C₄	—	2	4	no	—
418	C₄	—	4	4	no	—
419	C₄	—	4	2	no	—
420	C₄	—	8	4	no	—
421	C₄	C₄₃×#386	1	4	yes	—
422	C₄	C₂×C₄×D₄×C₄₃	1	2	yes	—
423	C₄	C₂×#120×C₄₃	1	1	yes	characteristic
424	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
425	C₂	—	2	4	no	—
426	C₂	—	4	4	no	—
427	C₂	—	8	2	no	—
428	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
429	C₂	C₄₃×#2896	1	2	yes	—
430	C₂	C₄₃×#3054	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂×C₄₃×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₃ ◁ C₂⁴×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×M₁₆×C₄₃	C₂	semidirect
3. C₂×C₄₃×#416	C₂	semidirect
4. C₄₃×#2280	C₂	semidirect
5. C₄₃×#1895	C₂	semidirect
6. C₄₃×#1894	C₂	semidirect
7. C₄₃×#1735	C₂	semidirect
15. C₄₃×#525	C₄	semidirect
24. C₂×#103×C₄₃	C₂²	semidirect
25. C₂×#102×C₄₃	C₂²	semidirect
30. C₄₃×#340	C₂²	semidirect
54. C₂²×C₈×C₄₃	D₄	semidirect
187. #20970	C₄₃	direct (N × H)
210. C₂³×M₁₆	C₂×C₄₃	semidirect
212. C₂×#416	C₂×C₄₃	semidirect
213. #2280	C₂×C₄₃	semidirect
214. #1895	C₂×C₄₃	semidirect
215. #1894	C₂×C₄₃	semidirect
216. #1735	C₂×C₄₃	semidirect
230. #525	C₄×C₄₃	semidirect
239. C₂×#103	C₂²×C₄₃	semidirect
240. C₂×#102	C₂²×C₄₃	semidirect
245. #340	C₂²×C₄₃	semidirect
246. C₄₃	#20970	direct (N × H)
270. C₂²×C₈	D₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₄₃	2
C₂×C₄₃×#525	2
C₂×C₄₃×#416	2
C₄₃×#2280	2
C₄₃×#1895	2
C₄₃×#1894	2
C₄₃×#1735	2
#20970	43

Subgroups — C43×#20970 #24940987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20970 #24940987