Subgroups — C₄×#131×D₄₃ #25959997

Order 11008.

3366 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#131×D₄₃	C₂	1	2	yes	maximal
2	C₄×#41×D₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄×#13063333	C₂	1	3	yes	maximal, complemented
4	C₄×#13063332	C₂	1	1	yes	maximal, characteristic, complemented
5	#19143017	C₂	1	6	yes	maximal, complemented
6	#131×Dic₄₃	C₂	1	2	yes	maximal, complemented
7	C₄×#13063331	C₂	1	3	yes	maximal, complemented
8	#405×D₄₃	C₂	1	6	yes	maximal, complemented
9	C₄×M₁₆×D₄₃	C₂	1	3	yes	maximal, complemented
10	C₂×C₄×C₈×D₄₃	C₂	1	3	yes	maximal, complemented
11	C₄×#131×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#41×D₄₃	C₂²	1	1	yes	characteristic
13	C₂×#13063333	C₂²	1	6	yes	—
14	C₂×#13063332	C₂²	1	2	yes	—
15	C₂×#13063331	C₂²	1	6	yes	—
16	#131×D₄₃	C₄	1	32	yes	direct product factor
17	C₂×M₁₆×D₄₃	C₂²	1	6	yes	—
18	C₂²×C₈×D₄₃	C₂²	1	6	yes	—
19	#41×Dic₄₃	C₂²	1	1	yes	characteristic
20	C₄×#10621902	C₄	1	2	yes	—
21	C₄×#10621898	C₂²	1	3	yes	—
22	#14583367	C₂²	1	3	yes	—
23	C₄×#10621900	C₄	1	6	yes	—
24	C₄×Q₈×D₄₃	C₄	1	2	yes	—
25	C₄×D₄×D₄₃	C₄	1	6	yes	—
26	#117×D₄₃	C₂²	1	3	yes	—
27	C₂×C₄²×D₄₃	C₂²	1	3	yes	—
28	#14582857	C₂²	1	6	yes	complemented
29	#14582856	C₂²	1	12	yes	complemented
30	#14582855	C₂²	1	6	yes	complemented
31	#14582854	C₂²	1	6	yes	complemented
32	#14582853	C₂²	1	12	yes	complemented
33	C₄×#10621877	C₂²	1	3	yes	complemented
34	#14582851	C₂²	1	6	yes	complemented
35	M₁₆×Dic₄₃	C₂²	1	6	yes	complemented
36	C₄×#10621872	C₂²	1	6	yes	complemented
37	#97×D₄₃	C₂²	1	6	yes	—
38	C₂×C₄×C₄₃⋊C₈	C₂²	1	3	yes	complemented
39	C₂×C₈×Dic₄₃	C₂²	1	6	yes	complemented
40	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
41	C₄×C₈×D₄₃	C₂²	1	3	yes	—
42	C₄×C₈×D₄₃	C₂²	1	6	yes	—
43	C₄×C₈×D₄₃	C₂²	1	3	yes	complemented
44	C₄×C₈×D₄₃	C₂²	1	6	yes	complemented
45	C₄×C₈×D₄₃	C₂²	1	3	yes	complemented
46	C₂×#131×C₄₃	C₂²	1	2	yes	—
47	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
48	C₄₃×#405	C₂²	1	6	yes	complemented
49	C₄×M₁₆×C₄₃	C₂²	1	3	yes	complemented
50	C₂×C₄×C₈×C₄₃	C₂²	1	3	yes	complemented
51	C₂×#10621902	C₂×C₄	1	1	yes	characteristic
52	C₂×#10621898	C₂³	1	3	yes	—
53	C₂×#10621900	C₂×C₄	1	3	yes	—
54	#41×D₄₃	C₂×C₄	1	16	yes	—
55	C₂×Q₈×D₄₃	C₂×C₄	1	1	yes	characteristic
56	C₂×D₄×D₄₃	C₂×C₄	1	3	yes	—
57	C₂²×C₄×D₄₃	C₂×C₄	1	6	yes	—
58	C₂²×C₄×D₄₃	C₂³	1	3	yes	—
59	#13063333	C₂×C₄	1	48	yes	complemented
60	#13063332	C₂×C₄	1	16	yes	complemented
61	#13063331	C₂×C₄	1	48	yes	complemented
62	C₂×#10621877	C₂³	1	6	yes	—
63	C₂×#10621872	C₂³	1	12	yes	—
64	M₁₆×D₄₃	C₂×C₄	1	48	yes	complemented
65	C₂²×C₄₃⋊C₈	C₂³	1	6	yes	—
66	C₂×C₈×D₄₃	C₂×C₄	1	48	yes	complemented
67	C₂×C₈×D₄₃	C₂³	1	2	yes	—
68	C₂×C₈×D₄₃	C₂³	1	6	yes	—
69	C₂×C₈×D₄₃	C₂³	1	6	yes	—
70	C₂×C₈×D₄₃	C₂³	1	6	yes	—
71	Q₈×Dic₄₃	C₂×C₄	1	2	yes	—
72	C₄×Dic₈₆	C₂×C₄	1	6	yes	—
73	#13063290	C₂×C₄	1	6	yes	—
74	C₄×D₁₇₂	C₂×C₄	1	6	yes	—
75	D₄×Dic₄₃	C₂×C₄	1	6	yes	—
76	#13063287	C₂×C₄	1	6	yes	—
77	C₄×C₂²⋊D₄₃	C₂×C₄	1	12	yes	—
78	(C₂²⋊D₄₃)⋊C₄	C₂×C₄	1	12	yes	—
79	#13063284	C₂³	1	3	yes	—
80	#13063283	C₂×C₄	1	6	yes	—
81	#13063282	C₂³	1	6	yes	—
82	#13063281	C₂×C₄	1	6	yes	—
83	C₄⋊C₄×D₄₃	C₂×C₄	1	6	yes	—
84	C₂²⋊C₄×D₄₃	C₂×C₄	1	6	yes	—
85	C₂×C₄×Dic₄₃	C₂×C₄	1	6	yes	—
86	C₂×C₄×Dic₄₃	C₂³	1	3	yes	—
87	C₄²×D₄₃	C₂×C₄	1	6	yes	—
88	C₄²×D₄₃	C₂×C₄	1	6	yes	—
89	C₄²×D₄₃	C₂³	1	1	yes	characteristic
90	C₄²×D₄₃	C₂³	1	3	yes	—
91	C₄²×D₄₃	C₂³	1	3	yes	—
92	C₄²×D₄₃	C₂³	1	3	yes	—
93	#13063236	C₂³	1	6	yes	—
94	#13063235	C₂³	1	12	yes	—
95	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
96	C₄×C₄₃⋊C₈	C₂³	1	3	yes	—
97	C₄×C₄₃⋊C₈	C₂³	1	6	yes	—
98	C₈×Dic₄₃	C₂³	1	2	yes	—
99	C₈×Dic₄₃	C₂³	1	6	yes	—
100	C₈×Dic₄₃	C₂³	1	6	yes	—
101	C₈×Dic₄₃	C₂³	1	6	yes	—
102	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
103	#131×C₄₃	C₂×C₄	1	16	yes	complemented
104	C₂×M₁₆×C₄₃	C₂³	1	6	yes	—
105	C₂²×C₈×C₄₃	C₂³	1	6	yes	—
106	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
107	C₄×D₄×C₄₃	C₂×C₄	1	6	yes	—
108	#117×C₄₃	C₂³	1	3	yes	—
109	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
110	#97×C₄₃	C₂³	1	6	yes	—
111	C₄×C₈×C₄₃	C₂³	1	3	yes	—
112	C₄×C₈×C₄₃	C₂³	1	6	yes	—
113	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
114	C₂³×D₄₃	C₂²×C₄	1	3	yes	—
115	#41×C₄₃	C₂²×C₄	1	8	yes	—
116	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×D₄×C₄₃	C₂²×C₄	1	3	yes	—
118	C₂²×C₄×C₄₃	C₂²×C₄	1	6	yes	—
119	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
120	C₂×C₂²⋊D₄₃	C₂²×C₄	1	6	yes	—
121	C₂²×Dic₄₃	C₂²×C₄	1	6	yes	—
122	C₂²×Dic₄₃	C₂²×C₄	1	3	yes	—
123	#10621902	C₄²	1	8	yes	—
124	Q₈×D₄₃	C₄²	1	8	yes	—
125	#10621900	C₄²	1	24	yes	—
126	D₄×D₄₃	C₄²	1	24	yes	—
127	#10621898	C₂²×C₄	1	24	yes	—
128	C₂×D₁₇₂	C₂²×C₄	1	3	yes	—
129	C₂×C₄×D₄₃	—	2	24	no	—
130	C₂×C₄×D₄₃	C₂²×C₄	1	24	yes	—
131	C₂×C₄×D₄₃	C₂²×C₄	1	6	yes	—
132	C₂×C₄×D₄₃	C₂²×C₄	1	6	yes	—
133	C₂×C₄×D₄₃	C₂²×C₄	1	6	yes	—
134	C₂×C₄×D₄₃	C₂²×C₄	1	3	yes	—
135	C₂×C₄×D₄₃	C₂²×C₄	1	3	yes	—
136	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
137	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
138	C₂×C₄×D₄₃	C₂⁴	1	3	yes	—
139	C₂×Dic₈₆	C₂²×C₄	1	3	yes	—
140	M₁₆×C₄₃	C₂²×C₄	1	24	yes	complemented
141	C₂×C₈×C₄₃	C₂²×C₄	1	24	yes	complemented
142	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
143	C₂×C₈×C₄₃	C₂⁴	1	6	yes	—
144	C₄⋊C₄×C₄₃	C₂²×C₄	1	6	yes	—
145	C₂²⋊C₄×C₄₃	C₂²×C₄	1	6	yes	—
146	C₄²×C₄₃	C₂²×C₄	1	6	yes	—
147	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
148	C₄²×C₄₃	C₂⁴	1	3	yes	—
149	C₂²⋊Dic₄₃	C₂²×C₄	1	6	yes	—
150	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	12	yes	—
151	C₄⋊Dic₄₃	C₂²×C₄	1	6	yes	—
152	Dic₄₃⋊C₄	C₂²×C₄	1	12	yes	—
153	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
154	C₄×Dic₄₃	C₂²×C₄	1	6	yes	—
155	C₄×Dic₄₃	C₂²×C₄	1	6	yes	—
156	C₄×Dic₄₃	C₂²×C₄	1	6	yes	—
157	C₄×Dic₄₃	C₂²×C₄	1	6	yes	—
158	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
159	C₄×Dic₄₃	C₂⁴	1	3	yes	—
160	#10621877	C₂²×C₄	1	24	yes	complemented
161	C₂×C₄₃⋊C₈	C₂²×C₄	1	24	yes	complemented
162	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
163	C₂×C₄₃⋊C₈	C₂⁴	1	6	yes	—
164	#10621872	C₂²×C₄	1	48	yes	complemented
165	C₈×D₄₃	C₂²×C₄	1	8	yes	—
166	C₈×D₄₃	C₂²×C₄	1	24	yes	—
167	C₈×D₄₃	C₂²×C₄	1	24	yes	complemented
168	C₈×D₄₃	C₂²×C₄	1	24	yes	complemented
169	C₂³×C₄₃	C₂³×C₄	1	3	yes	—
170	C₂²×D₄₃	—	2	12	no	—
171	C₂²×D₄₃	C₂×C₄²	1	12	yes	—
172	C₂²×D₄₃	C₂³×C₄	1	3	yes	—
173	C₂²×D₄₃	C₂³×C₄	1	1	yes	characteristic
174	Q₈×C₄₃	C₂×C₄²	1	4	yes	—
175	D₄×C₄₃	C₂×C₄²	1	12	yes	—
176	C₂×C₄×C₄₃	—	2	12	no	—
177	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
178	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
179	C₂×C₄×C₄₃	C₂³×C₄	1	12	yes	—
180	C₂×C₄×C₄₃	C₂³×C₄	1	3	yes	—
181	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
182	C₂²⋊D₄₃	C₂×C₄²	1	24	yes	—
183	C₂×Dic₄₃	—	2	12	no	—
184	C₂×Dic₄₃	C₂×C₄²	1	12	yes	—
185	C₂×Dic₄₃	C₂³×C₄	1	6	yes	—
186	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
187	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
188	C₂×Dic₄₃	C₂³×C₄	1	3	yes	—
189	D₁₇₂	C₂×C₄²	1	12	yes	—
190	C₄×D₄₃	—	2	12	no	—
191	C₄×D₄₃	—	2	12	no	—
192	C₄×D₄₃	—	2	12	no	—
193	C₄×D₄₃	C₂×C₄²	1	12	yes	—
194	C₄×D₄₃	C₂×C₄²	1	12	yes	—
195	C₄×D₄₃	#131	1	8	yes	direct product factor
196	C₄×D₄₃	C₂³×C₄	1	4	yes	—
197	C₄×D₄₃	C₂³×C₄	1	12	yes	—
198	Dic₈₆	C₂×C₄²	1	12	yes	—
199	C₈×C₄₃	C₂³×C₄	1	4	yes	—
200	C₈×C₄₃	C₂³×C₄	1	12	yes	—
201	C₄₃⋊C₈	C₂³×C₄	1	4	yes	—
202	C₄₃⋊C₈	C₂³×C₄	1	12	yes	—
203	C₂×C₄×#131	—	43	1	no	maximal, Sylow
204	C₂²×C₄₃	—	2	6	no	—
205	C₂²×C₄₃	C₂²×C₄²	1	6	yes	—
206	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
207	C₂×D₄₃	—	2	6	no	—
208	C₂×D₄₃	—	2	24	no	—
209	C₂×D₄₃	C₂²×C₄²	1	6	yes	—
210	C₂×D₄₃	C₂²×C₄²	1	2	yes	—
211	C₂×D₄₃	C₂×#131	1	4	yes	—
212	C₄×C₄₃	—	2	6	no	—
213	C₄×C₄₃	C₂²×C₄²	1	6	yes	—
214	C₄×C₄₃	C₂×#131	1	4	yes	complemented
215	C₄×C₄₃	C₂⁴×C₄	1	2	yes	—
216	Dic₄₃	—	2	6	no	—
217	Dic₄₃	C₂²×C₄²	1	6	yes	—
218	Dic₄₃	C₂²×C₄²	1	2	yes	—
219	Dic₄₃	C₂×#131	1	4	yes	complemented
220	C₂²×#131	—	43	2	no	—
221	C₂×C₄×#41	—	43	1	no	—
222	C₄×#131	—	43	6	no	—
223	C₄×#131	—	43	3	no	—
224	C₄×#131	—	43	3	no	—
225	C₄×#131	—	43	2	no	—
226	C₄×#131	—	43	1	no	—
227	C₄×#131	D₄₃	1	1	yes	characteristic, direct product factor
228	C₂×#405	—	43	6	no	—
229	C₂×C₄×M₁₆	—	43	3	no	—
230	C₂²×C₄×C₈	—	43	3	no	—
231	C₂×C₄₃	—	2	6	no	—
232	C₂×C₄₃	C₂³×C₄²	1	1	yes	characteristic
233	C₂×C₄₃	C₂²×#131	1	2	yes	—
234	D₄₃	—	2	6	no	—
235	D₄₃	C₄×#131	1	4	yes	direct product factor
236	C₂²×#41	—	43	1	no	—
237	C₂×#131	—	43	2	no	—
238	C₂×#131	—	43	32	no	—
239	C₂×#131	—	43	6	no	—
240	C₂×#131	—	43	6	no	—
241	C₂×#131	C₂×D₄₃	1	2	yes	—
242	C₂²×M₁₆	—	43	6	no	—
243	C₂³×C₈	—	43	6	no	—
244	C₄×#41	—	43	1	no	—
245	C₄×#41	—	43	2	no	—
246	C₄×#41	—	43	6	no	—
247	C₄×#41	—	43	3	no	—
248	C₄×#41	—	43	3	no	—
249	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
250	C₂×C₄×Q₈	—	43	2	no	—
251	C₂×C₄×D₄	—	43	6	no	—
252	C₂×#117	—	43	3	no	—
253	C₂²×C₄²	—	43	3	no	—
254	#405	—	43	6	no	—
255	#405	—	43	6	no	—
256	#405	—	43	6	no	—
257	#405	—	43	12	no	—
258	#405	—	43	12	no	—
259	#405	C₂×D₄₃	1	6	yes	complemented
260	C₄×M₁₆	—	43	6	no	—
261	C₄×M₁₆	—	43	3	no	—
262	C₄×M₁₆	—	43	6	no	—
263	C₄×M₁₆	—	43	6	no	—
264	C₄×M₁₆	C₂×D₄₃	1	3	yes	complemented
265	C₂×#97	—	43	6	no	—
266	C₂×C₄×C₈	—	43	6	no	—
267	C₂×C₄×C₈	—	43	3	no	—
268	C₂×C₄×C₈	—	43	3	no	—
269	C₂×C₄×C₈	—	43	6	no	—
270	C₂×C₄×C₈	—	43	6	no	—
271	C₂×C₄×C₈	—	43	3	no	—
272	C₂×C₄×C₈	—	43	1	no	—
273	C₂×C₄×C₈	—	43	3	no	—
274	C₂×C₄×C₈	C₂×D₄₃	1	3	yes	complemented
275	C₄₃	C₂×C₄×#131	1	1	yes	characteristic, complemented, Sylow
276	C₂×#41	—	43	16	no	—
277	C₂×#41	—	43	1	no	—
278	C₂×#41	—	43	3	no	—
279	C₂×#41	—	43	3	no	—
280	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
281	C₂²×Q₈	—	43	1	no	—
282	C₂²×D₄	—	43	3	no	—
283	C₂³×C₄	—	43	3	no	—
284	C₂³×C₄	—	43	6	no	—
285	#131	—	43	16	no	—
286	#131	—	43	48	no	—
287	#131	—	43	48	no	—
288	#131	C₄×D₄₃	1	16	yes	direct product factor
289	C₂×M₁₆	—	43	6	no	—
290	C₂×M₁₆	—	43	48	no	—
291	C₂×M₁₆	—	43	12	no	—
292	C₂×M₁₆	C₂²×D₄₃	1	6	yes	—
293	C₂²×C₈	—	43	6	no	—
294	C₂²×C₈	—	43	48	no	—
295	C₂²×C₈	—	43	2	no	—
296	C₂²×C₈	—	43	6	no	—
297	C₂²×C₈	—	43	6	no	—
298	C₂²×C₈	—	43	6	no	—
299	C₂²×C₈	C₂²×D₄₃	1	6	yes	—
300	C₄×Q₈	—	43	2	no	—
301	C₄×Q₈	—	43	6	no	—
302	C₄×Q₈	—	43	6	no	—
303	C₄×Q₈	C₄×D₄₃	1	2	yes	—
304	C₄×D₄	—	43	6	no	—
305	C₄×D₄	—	43	12	no	—
306	C₄×D₄	—	43	6	no	—
307	C₄×D₄	—	43	12	no	—
308	C₄×D₄	—	43	6	no	—
309	C₄×D₄	C₄×D₄₃	1	6	yes	—
310	#117	—	43	3	no	—
311	#117	—	43	6	no	—
312	#117	—	43	6	no	—
313	#117	—	43	6	no	—
314	#117	C₂²×D₄₃	1	3	yes	—
315	C₂×C₄⋊C₄	—	43	6	no	—
316	C₂×C₂²⋊C₄	—	43	6	no	—
317	C₂×C₄²	—	43	6	no	—
318	C₂×C₄²	—	43	3	no	—
319	C₂×C₄²	—	43	6	no	—
320	C₂×C₄²	—	43	6	no	—
321	C₂×C₄²	—	43	3	no	—
322	C₂×C₄²	—	43	3	no	—
323	C₂×C₄²	—	43	3	no	—
324	C₂×C₄²	—	43	1	no	—
325	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
326	#97	—	43	12	no	—
327	#97	—	43	6	no	—
328	#97	C₂²×D₄₃	1	6	yes	—
329	C₄×C₈	—	43	2	no	—
330	C₄×C₈	—	43	6	no	—
331	C₄×C₈	—	43	6	no	—
332	C₄×C₈	—	43	6	no	—
333	C₄×C₈	—	43	1	no	—
334	C₄×C₈	—	43	3	no	—
335	C₄×C₈	—	43	6	no	—
336	C₄×C₈	C₂²×D₄₃	1	3	yes	—
337	C₄×C₈	C₂²×D₄₃	1	6	yes	—
338	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
339	C₂⁴	—	43	3	no	—
340	#41	—	43	8	no	—
341	#41	—	43	24	no	—
342	#41	—	43	24	no	—
343	#41	C₂×C₄×D₄₃	1	8	yes	—
344	C₂×Q₈	—	43	8	no	—
345	C₂×Q₈	—	43	3	no	—
346	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
347	C₂×D₄	—	43	6	no	—
348	C₂×D₄	—	43	24	no	—
349	C₂×D₄	—	43	3	no	—
350	C₂×D₄	C₂×C₄×D₄₃	1	3	yes	—
351	C₂²×C₄	—	43	3	no	—
352	C₂²×C₄	—	43	2	no	—
353	C₂²×C₄	—	43	3	no	—
354	C₂²×C₄	—	43	3	no	—
355	C₂²×C₄	—	43	24	no	—
356	C₂²×C₄	—	43	1	no	—
357	C₂²×C₄	—	43	3	no	—
358	C₂²×C₄	—	43	6	no	—
359	C₂²×C₄	—	43	6	no	—
360	C₂²×C₄	—	43	6	no	—
361	C₂²×C₄	—	43	6	no	—
362	C₂²×C₄	—	86	24	no	—
363	C₂²×C₄	C₂×C₄×D₄₃	1	6	yes	—
364	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
365	M₁₆	—	43	24	no	—
366	M₁₆	—	43	48	no	—
367	M₁₆	C₂×C₄×D₄₃	1	24	yes	complemented
368	C₂×C₈	—	43	24	no	—
369	C₂×C₈	—	43	2	no	—
370	C₂×C₈	—	43	6	no	—
371	C₂×C₈	—	43	8	no	—
372	C₂×C₈	—	43	24	no	—
373	C₂×C₈	—	43	24	no	—
374	C₂×C₈	—	43	24	no	—
375	C₂×C₈	C₂×C₄×D₄₃	1	24	yes	complemented
376	C₂×C₈	C₂³×D₄₃	1	2	yes	—
377	C₂×C₈	C₂³×D₄₃	1	6	yes	—
378	C₄⋊C₄	—	43	12	no	—
379	C₄⋊C₄	—	43	6	no	—
380	C₄⋊C₄	C₂×C₄×D₄₃	1	6	yes	—
381	C₂²⋊C₄	—	43	6	no	—
382	C₂²⋊C₄	—	43	12	no	—
383	C₂²⋊C₄	C₂×C₄×D₄₃	1	6	yes	—
384	C₄²	—	43	2	no	—
385	C₄²	—	43	6	no	—
386	C₄²	—	43	6	no	—
387	C₄²	—	43	6	no	—
388	C₄²	—	43	6	no	—
389	C₄²	—	43	1	no	—
390	C₄²	—	43	3	no	—
391	C₄²	C₂×C₄×D₄₃	1	6	yes	—
392	C₄²	C₂³×D₄₃	1	1	yes	characteristic
393	C₄²	C₂³×D₄₃	1	3	yes	—
394	C₂³	—	43	1	no	—
395	C₂³	—	43	12	no	—
396	C₂³	—	43	3	no	—
397	C₂³	—	86	12	no	—
398	C₂³	C₂²×C₄×D₄₃	1	3	yes	—
399	Q₈	—	43	12	no	—
400	Q₈	C₄²×D₄₃	1	4	yes	—
401	D₄	—	43	24	no	—
402	D₄	—	43	12	no	—
403	D₄	C₄²×D₄₃	1	12	yes	—
404	C₂×C₄	—	2	12	no	—
405	C₂×C₄	—	43	12	no	—
406	C₂×C₄	—	43	1	no	—
407	C₂×C₄	—	43	2	no	—
408	C₂×C₄	—	43	3	no	—
409	C₂×C₄	—	43	12	no	—
410	C₂×C₄	—	43	12	no	—
411	C₂×C₄	—	43	8	no	—
412	C₂×C₄	—	43	4	no	—
413	C₂×C₄	—	43	12	no	—
414	C₂×C₄	—	43	6	no	—
415	C₂×C₄	—	86	12	no	—
416	C₂×C₄	—	86	12	no	—
417	C₂×C₄	—	86	12	no	—
418	C₂×C₄	—	86	12	no	—
419	C₂×C₄	C₂²×C₄×D₄₃	1	6	yes	—
420	C₂×C₄	C₂²×C₄×D₄₃	1	3	yes	—
421	C₂×C₄	C₂²×C₄×D₄₃	1	12	yes	—
422	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
423	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
424	C₈	—	43	4	no	—
425	C₈	—	43	12	no	—
426	C₈	C₂²×C₄×D₄₃	1	4	yes	—
427	C₈	C₂²×C₄×D₄₃	1	12	yes	—
428	C₂²	—	2	6	no	—
429	C₂²	—	43	2	no	—
430	C₂²	—	43	4	no	—
431	C₂²	—	43	6	no	—
432	C₂²	—	86	24	no	—
433	C₂²	—	86	6	no	—
434	C₂²	C₂×C₄²×D₄₃	1	6	yes	—
435	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
436	C₄	—	2	6	no	—
437	C₄	—	43	2	no	—
438	C₄	—	43	6	no	—
439	C₄	—	43	4	no	—
440	C₄	—	86	6	no	—
441	C₄	C₂×C₄²×D₄₃	1	6	yes	—
442	C₄	#131×D₄₃	1	4	yes	direct product factor
443	C₄	C₂³×C₄×D₄₃	1	2	yes	—
444	C₂	—	2	6	no	—
445	C₂	—	43	4	no	—
446	C₂	—	86	6	no	—
447	C₂	C₂²×C₄²×D₄₃	1	1	yes	characteristic
448	C₂	C₂×#131×D₄₃	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂²×D₄₃
commutator	C₂×C₄₃	C₂³×C₄²
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄×#131×C₄₃	C₂
socle	C₂²×C₄₃	C₂⁴×C₄
prime radical	C₂×#41×D₄₃	C₂²
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₄×#131	D₄₃
hypocenter	C₄₃	C₂×C₄×#131
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄×C₈ ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
3. C₄×#13063333	C₂	semidirect
4. C₄×#13063332	C₂	semidirect
5. #19143017	C₂	semidirect
6. #131×Dic₄₃	C₂	semidirect
7. C₄×#13063331	C₂	semidirect
8. #405×D₄₃	C₂	semidirect
9. C₄×M₁₆×D₄₃	C₂	semidirect
10. C₂×C₄×C₈×D₄₃	C₂	semidirect
11. C₄×#131×C₄₃	C₂	semidirect
16. #131×D₄₃	C₄	direct (N × H)
28. #14582857	C₂²	semidirect
29. #14582856	C₂²	semidirect
30. #14582855	C₂²	semidirect
31. #14582854	C₂²	semidirect
32. #14582853	C₂²	semidirect
33. C₄×#10621877	C₂²	semidirect
34. #14582851	C₂²	semidirect
35. M₁₆×Dic₄₃	C₂²	semidirect
36. C₄×#10621872	C₂²	semidirect
38. C₂×C₄×C₄₃⋊C₈	C₂²	semidirect
39. C₂×C₈×Dic₄₃	C₂²	semidirect
43. C₄×C₈×D₄₃	C₂²	semidirect
44. C₄×C₈×D₄₃	C₂²	semidirect
45. C₄×C₈×D₄₃	C₂²	semidirect
48. C₄₃×#405	C₂²	semidirect
49. C₄×M₁₆×C₄₃	C₂²	semidirect
50. C₂×C₄×C₈×C₄₃	C₂²	semidirect
59. #13063333	C₂×C₄	semidirect
60. #13063332	C₂×C₄	semidirect
61. #13063331	C₂×C₄	semidirect
64. M₁₆×D₄₃	C₂×C₄	semidirect
66. C₂×C₈×D₄₃	C₂×C₄	semidirect
103. #131×C₄₃	C₂×C₄	semidirect
140. M₁₆×C₄₃	C₂²×C₄	semidirect
141. C₂×C₈×C₄₃	C₂²×C₄	semidirect
160. #10621877	C₂²×C₄	semidirect
161. C₂×C₄₃⋊C₈	C₂²×C₄	semidirect
164. #10621872	C₂²×C₄	semidirect
167. C₈×D₄₃	C₂²×C₄	semidirect
168. C₈×D₄₃	C₂²×C₄	semidirect
195. C₄×D₄₃	#131	direct (N × H)
214. C₄×C₄₃	C₂×#131	semidirect
219. Dic₄₃	C₂×#131	semidirect
227. C₄×#131	D₄₃	direct (N × H)
235. D₄₃	C₄×#131	direct (N × H)
259. #405	C₂×D₄₃	semidirect
264. C₄×M₁₆	C₂×D₄₃	semidirect
274. C₂×C₄×C₈	C₂×D₄₃	semidirect
275. C₄₃	C₂×C₄×#131	semidirect
288. #131	C₄×D₄₃	direct (N × H)
367. M₁₆	C₂×C₄×D₄₃	semidirect
375. C₂×C₈	C₂×C₄×D₄₃	semidirect
442. C₄	#131×D₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#131×D₄₃	2
C₄×#41×D₄₃	2
C₄×#13063333	2
C₄×#13063332	2
#19143017	2
#131×Dic₄₃	2
C₄×#13063331	2
#405×D₄₃	2
C₄×M₁₆×D₄₃	2
C₂×C₄×C₈×D₄₃	2
C₄×#131×C₄₃	2
C₂×C₄×#131	43

Subgroups — C4×#131×D43 #25959997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#131×D₄₃ #25959997