Subgroups — C₄₃×#25945 #24945962

Order 11008.

1072 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#491	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#461	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2026	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2024	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1877	C₂	1	2	yes	maximal
10	C₄₃×#1877	C₂	1	2	yes	maximal
11	C₄₃×#1762	C₂	1	1	yes	maximal, characteristic
12	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
13	C₄₃×#554	—	2	4	no	—
14	C₄₃×#554	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
20	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
21	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
22	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
27	C₄₃×#491	—	2	4	no	—
28	C₄₃×#461	—	2	4	no	—
29	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#103×C₄₃	C₂²	1	2	yes	—
31	C₂×#103×C₄₃	C₂²	1	2	yes	—
32	C₂×#103×C₄₃	C₂²	1	2	yes	—
33	C₂×#102×C₄₃	C₂²	1	2	yes	—
34	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
35	C₄₃×#400	—	2	1	no	—
36	C₄₃×#400	—	2	1	no	—
37	C₄₃×#391	—	2	1	no	—
38	C₄₃×#391	C₂²	1	2	yes	—
39	C₄₃×#391	C₂²	1	2	yes	—
40	C₄₃×#382	—	2	1	no	—
41	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#340	C₂²	1	2	yes	—
43	C₄₃×#340	C₂²	1	2	yes	—
44	C₄₃×#340	C₂²	1	2	yes	—
45	C₄₃×#336	C₂²	1	2	yes	—
46	C₄₃×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₄₃	—	2	1	no	—
48	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
49	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
50	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₄₃	—	2	1	no	—
52	C₂³×C₄×C₄₃	—	2	1	no	—
53	C₂³×C₄×C₄₃	—	2	1	no	—
54	C₂×SD₁₆×C₄₃	—	2	4	no	—
55	C₂×SD₁₆×C₄₃	—	2	8	no	—
56	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₄₃	—	2	2	no	—
59	C₄⋊Q₈×C₄₃	—	2	2	no	—
60	C₄⋊Q₈×C₄₃	—	2	2	no	—
61	C₄⋊Q₈×C₄₃	—	2	2	no	—
62	#125×C₄₃	—	2	2	no	—
63	#125×C₄₃	—	2	2	no	—
64	#125×C₄₃	—	2	2	no	—
65	#125×C₄₃	D₄	1	4	yes	—
66	C₂²⋊Q₈×C₄₃	—	2	8	no	—
67	C₂²⋊Q₈×C₄₃	—	2	8	no	—
68	C₂²⋊Q₈×C₄₃	—	2	8	no	—
69	C₄×Q₈×C₄₃	—	2	2	no	—
70	C₄×Q₈×C₄₃	—	2	2	no	—
71	C₄×D₄×C₄₃	—	2	2	no	—
72	C₄×D₄×C₄₃	—	2	2	no	—
73	C₄×D₄×C₄₃	—	2	2	no	—
74	C₄×D₄×C₄₃	—	2	2	no	—
75	C₄×D₄×C₄₃	—	2	2	no	—
76	C₄×D₄×C₄₃	D₄	1	4	yes	—
77	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
78	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
81	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₄₃	C₂³	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×C₂²⋊C₄×C₄₃	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₄²×C₄₃	—	2	1	no	—
96	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₄₃	—	2	2	no	—
100	#103×C₄₃	—	2	4	no	—
101	#103×C₄₃	—	2	4	no	—
102	#103×C₄₃	—	2	4	no	—
103	#102×C₄₃	—	2	4	no	—
104	#97×C₄₃	—	2	2	no	—
105	#95×C₄₃	—	2	1	no	—
106	#95×C₄₃	—	2	2	no	—
107	#95×C₄₃	—	2	2	no	—
108	#95×C₄₃	—	2	2	no	—
109	#95×C₄₃	—	2	2	no	—
110	C₂⁴×C₄₃	—	2	1	no	—
111	C₂×Q₈×C₄₃	—	2	4	no	—
112	C₂×Q₈×C₄₃	—	2	2	no	—
113	C₂×Q₈×C₄₃	—	2	2	no	—
114	C₂×Q₈×C₄₃	—	2	2	no	—
115	C₂×Q₈×C₄₃	—	2	2	no	—
116	C₂×Q₈×C₄₃	—	2	4	no	—
117	C₂×Q₈×C₄₃	—	2	4	no	—
118	C₂×Q₈×C₄₃	—	4	1	no	—
119	C₂×Q₈×C₄₃	—	8	2	no	—
120	C₂×D₄×C₄₃	—	2	1	no	—
121	C₂×D₄×C₄₃	—	2	2	no	—
122	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₄₃	#41	1	4	yes	—
124	C₂²×C₄×C₄₃	—	2	4	no	—
125	C₂²×C₄×C₄₃	—	2	4	no	—
126	C₂²×C₄×C₄₃	—	2	4	no	—
127	C₂²×C₄×C₄₃	—	2	1	no	—
128	C₂²×C₄×C₄₃	—	2	1	no	—
129	C₂²×C₄×C₄₃	—	2	1	no	—
130	C₂²×C₄×C₄₃	—	2	2	no	—
131	C₂²×C₄×C₄₃	—	2	2	no	—
132	C₂²×C₄×C₄₃	—	4	2	no	—
133	C₂²×C₄×C₄₃	—	4	2	no	—
134	C₂²×C₄×C₄₃	—	8	2	no	—
135	C₂²×C₄×C₄₃	—	8	2	no	—
136	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
143	SD₁₆×C₄₃	—	4	8	no	—
144	C₂×C₈×C₄₃	—	2	2	no	—
145	C₂×C₈×C₄₃	—	2	2	no	—
146	C₂×C₈×C₄₃	—	2	2	no	—
147	C₂×C₈×C₄₃	—	2	4	no	—
148	C₂×C₈×C₄₃	—	2	2	no	—
149	C₄⋊C₄×C₄₃	—	2	4	no	—
150	C₄⋊C₄×C₄₃	—	2	4	no	—
151	C₄⋊C₄×C₄₃	—	2	4	no	—
152	C₄⋊C₄×C₄₃	—	2	2	no	—
153	C₄⋊C₄×C₄₃	—	2	4	no	—
154	C₄⋊C₄×C₄₃	—	2	4	no	—
155	C₄⋊C₄×C₄₃	—	2	2	no	—
156	C₄⋊C₄×C₄₃	—	2	2	no	—
157	C₄⋊C₄×C₄₃	—	2	1	no	—
158	C₄⋊C₄×C₄₃	—	2	1	no	—
159	C₄⋊C₄×C₄₃	—	2	1	no	—
160	C₄⋊C₄×C₄₃	—	2	2	no	—
161	C₄⋊C₄×C₄₃	—	2	2	no	—
162	C₄⋊C₄×C₄₃	—	4	2	no	—
163	C₄⋊C₄×C₄₃	—	4	2	no	—
164	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
165	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
166	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
167	C₂²⋊C₄×C₄₃	—	2	4	no	—
168	C₂²⋊C₄×C₄₃	—	2	4	no	—
169	C₂²⋊C₄×C₄₃	—	2	4	no	—
170	C₄²×C₄₃	—	2	1	no	—
171	C₄²×C₄₃	—	2	1	no	—
172	C₄²×C₄₃	—	2	1	no	—
173	C₄²×C₄₃	—	2	1	no	—
174	C₄²×C₄₃	—	4	2	no	—
175	C₄²×C₄₃	C₂×D₄	1	2	yes	—
176	C₄²×C₄₃	C₂×D₄	1	2	yes	—
177	C₂³×C₄₃	—	2	2	no	—
178	C₂³×C₄₃	—	2	4	no	—
179	C₂³×C₄₃	—	4	1	no	—
180	C₂³×C₄₃	—	4	1	no	—
181	C₂³×C₄₃	—	4	2	no	—
182	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₄₃	—	4	4	no	—
184	Q₈×C₄₃	—	4	2	no	—
185	Q₈×C₄₃	—	4	2	no	—
186	Q₈×C₄₃	—	4	4	no	—
187	Q₈×C₄₃	—	8	4	no	—
188	D₄×C₄₃	—	2	2	no	—
189	D₄×C₄₃	—	2	4	no	—
190	D₄×C₄₃	#124	1	4	yes	—
191	C₂×C₄×C₄₃	—	2	1	no	—
192	C₂×C₄×C₄₃	—	2	1	no	—
193	C₂×C₄×C₄₃	—	2	1	no	—
194	C₂×C₄×C₄₃	—	2	1	no	—
195	C₂×C₄×C₄₃	—	2	2	no	—
196	C₂×C₄×C₄₃	—	2	1	no	—
197	C₂×C₄×C₄₃	—	2	1	no	—
198	C₂×C₄×C₄₃	—	2	1	no	—
199	C₂×C₄×C₄₃	—	2	2	no	—
200	C₂×C₄×C₄₃	—	2	2	no	—
201	C₂×C₄×C₄₃	—	2	2	no	—
202	C₂×C₄×C₄₃	—	2	1	no	—
203	C₂×C₄×C₄₃	—	2	1	no	—
204	C₂×C₄×C₄₃	—	2	2	no	—
205	C₂×C₄×C₄₃	—	2	2	no	—
206	C₂×C₄×C₄₃	—	4	8	no	—
207	C₂×C₄×C₄₃	—	4	1	no	—
208	C₂×C₄×C₄₃	—	4	1	no	—
209	C₂×C₄×C₄₃	—	4	2	no	—
210	C₂×C₄×C₄₃	—	4	2	no	—
211	C₂×C₄×C₄₃	—	4	2	no	—
212	C₂×C₄×C₄₃	—	4	2	no	—
213	C₂×C₄×C₄₃	—	4	4	no	—
214	C₂×C₄×C₄₃	—	4	2	no	—
215	C₂×C₄×C₄₃	—	4	2	no	—
216	C₂×C₄×C₄₃	—	8	4	no	—
217	C₂×C₄×C₄₃	—	8	4	no	—
218	C₂×C₄×C₄₃	#120	1	2	yes	—
219	C₂×C₄×C₄₃	#120	1	2	yes	—
220	C₂×C₄×C₄₃	#137	1	2	yes	—
221	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
224	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
225	C₈×C₄₃	—	4	2	no	—
226	C₈×C₄₃	—	4	2	no	—
227	#25945	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂²×C₄₃	—	2	4	no	—
229	C₂²×C₄₃	—	4	4	no	—
230	C₂²×C₄₃	—	4	4	no	—
231	C₂²×C₄₃	—	4	2	no	—
232	C₂²×C₄₃	—	4	2	no	—
233	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
234	C₂²×C₄₃	#548	1	2	yes	—
235	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
236	C₂²×C₄₃	#575	1	1	yes	characteristic
237	C₂²×C₄₃	#577	1	2	yes	—
238	C₄×C₄₃	—	2	2	no	—
239	C₄×C₄₃	—	2	2	no	—
240	C₄×C₄₃	—	2	2	no	—
241	C₄×C₄₃	—	4	1	no	—
242	C₄×C₄₃	—	4	2	no	—
243	C₄×C₄₃	—	4	1	no	—
244	C₄×C₄₃	—	4	1	no	—
245	C₄×C₄₃	—	4	2	no	—
246	C₄×C₄₃	—	4	2	no	—
247	C₄×C₄₃	—	8	2	no	—
248	C₄×C₄₃	—	8	2	no	—
249	C₄×C₄₃	C₂×#124	1	1	yes	characteristic
250	C₄×C₄₃	#536	1	1	yes	characteristic
251	C₄×C₄₃	#548	1	2	yes	—
252	C₂×#554	C₂×C₄₃	1	1	yes	characteristic
253	C₂×#491	C₂×C₄₃	1	1	yes	characteristic, complemented
254	C₂×#461	C₂×C₄₃	1	1	yes	characteristic
255	#2568	C₂×C₄₃	1	1	yes	characteristic, complemented
256	#2026	C₂×C₄₃	1	2	yes	complemented
257	#2024	C₂×C₄₃	1	2	yes	complemented
258	#1989	C₂×C₄₃	1	1	yes	characteristic, complemented
259	#1985	C₂×C₄₃	1	1	yes	characteristic, complemented
260	#1877	C₂×C₄₃	1	2	yes	—
261	#1877	C₂×C₄₃	1	2	yes	—
262	#1762	C₂×C₄₃	1	1	yes	characteristic
263	C₂×C₄₃	—	4	4	no	—
264	C₂×C₄₃	#2436	1	1	yes	characteristic
265	C₂×C₄₃	#3007	1	1	yes	characteristic
266	C₂×C₄₃	#3009	1	1	yes	characteristic
267	C₂×C₄₃	#3372	1	2	yes	—
268	C₂×C₄₃	#3376	1	2	yes	—
269	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
270	#554	—	2	4	no	—
271	#554	—	2	4	no	—
272	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
273	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
274	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
275	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
276	C₂×C₂²⋊Q₈	—	2	1	no	—
277	C₂×C₂²⋊Q₈	—	2	1	no	—
278	C₂×C₂²⋊Q₈	—	2	1	no	—
279	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
280	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
281	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
282	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
283	C₂²×C₄⋊C₄	—	2	1	no	—
284	#491	—	2	4	no	—
285	#461	—	2	4	no	—
286	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
287	C₂×#103	C₂²×C₄₃	1	2	yes	—
288	C₂×#103	C₂²×C₄₃	1	2	yes	—
289	C₂×#103	C₂²×C₄₃	1	2	yes	—
290	C₂×#102	C₂²×C₄₃	1	2	yes	—
291	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
292	#400	—	2	1	no	—
293	#400	—	2	1	no	—
294	#391	—	2	1	no	—
295	#391	C₂²×C₄₃	1	2	yes	—
296	#391	C₂²×C₄₃	1	2	yes	—
297	#382	—	2	1	no	—
298	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
299	#340	C₂²×C₄₃	1	2	yes	—
300	#340	C₂²×C₄₃	1	2	yes	—
301	#340	C₂²×C₄₃	1	2	yes	—
302	#336	C₂²×C₄₃	1	2	yes	—
303	#336	C₂²×C₄₃	1	2	yes	—
304	C₄₃	#25945	1	1	yes	characteristic, direct product factor, Sylow
305	C₂²×Q₈	—	2	1	no	—
306	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
307	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
308	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
309	C₂³×C₄	—	2	1	no	—
310	C₂³×C₄	—	2	1	no	—
311	C₂³×C₄	—	2	1	no	—
312	C₂×SD₁₆	—	2	4	no	—
313	C₂×SD₁₆	—	2	8	no	—
314	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
315	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	—	2	2	no	—
318	C₄⋊Q₈	—	2	2	no	—
319	C₄⋊Q₈	—	2	2	no	—
320	#125	—	2	2	no	—
321	#125	—	2	2	no	—
322	#125	—	2	2	no	—
323	#125	D₄×C₄₃	1	4	yes	—
324	C₂²⋊Q₈	—	2	8	no	—
325	C₂²⋊Q₈	—	2	8	no	—
326	C₂²⋊Q₈	—	2	8	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×D₄	—	2	2	no	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	D₄×C₄₃	1	4	yes	—
335	C₂×C₄⋊C₄	—	2	8	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
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	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
344	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
345	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	2	1	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
357	C₄⋊C₈	—	2	2	no	—
358	#103	—	2	4	no	—
359	#103	—	2	4	no	—
360	#103	—	2	4	no	—
361	#102	—	2	4	no	—
362	#97	—	2	2	no	—
363	#95	—	2	1	no	—
364	#95	—	2	2	no	—
365	#95	—	2	2	no	—
366	#95	—	2	2	no	—
367	#95	—	2	2	no	—
368	C₂⁴	—	2	1	no	—
369	C₂×Q₈	—	2	4	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	4	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	4	1	no	—
377	C₂×Q₈	—	8	2	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
381	C₂×D₄	#41×C₄₃	1	4	yes	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	8	2	no	—
393	C₂²×C₄	—	8	2	no	—
394	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
400	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
401	SD₁₆	—	4	8	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	4	no	—
406	C₂×C₈	—	2	2	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	4	2	no	—
421	C₄⋊C₄	—	4	2	no	—
422	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
423	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
424	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	2	4	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	4	2	no	—
433	C₄²	C₂×D₄×C₄₃	1	2	yes	—
434	C₄²	C₂×D₄×C₄₃	1	2	yes	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	4	2	no	—
440	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
441	Q₈	—	4	4	no	—
442	Q₈	—	4	2	no	—
443	Q₈	—	4	2	no	—
444	Q₈	—	4	4	no	—
445	Q₈	—	8	4	no	—
446	D₄	—	2	2	no	—
447	D₄	—	2	4	no	—
448	D₄	#124×C₄₃	1	4	yes	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	8	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	8	4	no	—
475	C₂×C₄	—	8	4	no	—
476	C₂×C₄	#120×C₄₃	1	2	yes	—
477	C₂×C₄	#120×C₄₃	1	2	yes	—
478	C₂×C₄	#137×C₄₃	1	2	yes	—
479	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
480	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
481	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
482	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
483	C₈	—	4	2	no	—
484	C₈	—	4	2	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
491	C₂²	C₄₃×#548	1	2	yes	—
492	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
493	C₂²	C₄₃×#575	1	1	yes	characteristic
494	C₂²	C₄₃×#577	1	2	yes	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	4	1	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	1	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	2	no	—
504	C₄	—	8	2	no	—
505	C₄	—	8	2	no	—
506	C₄	C₂×#124×C₄₃	1	1	yes	characteristic
507	C₄	C₄₃×#536	1	1	yes	characteristic
508	C₄	C₄₃×#548	1	2	yes	—
509	C₂	—	4	4	no	—
510	C₂	C₄₃×#2436	1	1	yes	characteristic
511	C₂	C₄₃×#3007	1	1	yes	characteristic
512	C₂	C₄₃×#3009	1	1	yes	characteristic
513	C₂	C₄₃×#3372	1	2	yes	—
514	C₂	C₄₃×#3376	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×D₄×C₄₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×C₄×Q₈×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#491	C₂	semidirect
4. C₄₃×#2568	C₂	semidirect
5. C₄₃×#2026	C₂	semidirect
6. C₄₃×#2024	C₂	semidirect
7. C₄₃×#1989	C₂	semidirect
8. C₄₃×#1985	C₂	semidirect
227. #25945	C₄₃	direct (N × H)
253. C₂×#491	C₂×C₄₃	semidirect
255. #2568	C₂×C₄₃	semidirect
256. #2026	C₂×C₄₃	semidirect
257. #2024	C₂×C₄₃	semidirect
258. #1989	C₂×C₄₃	semidirect
259. #1985	C₂×C₄₃	semidirect
304. C₄₃	#25945	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×C₄₃×#554	2
C₂×C₄₃×#491	2
C₂×C₄₃×#461	2
C₄₃×#2568	2
C₄₃×#2026	2
C₄₃×#2024	2
C₄₃×#1989	2
C₄₃×#1985	2
C₄₃×#1877	2
C₄₃×#1762	2
#25945	43

Subgroups — C43×#25945 #24945962

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25945 #24945962