Subgroups — C₂×C₄₃×#1621 #24938521

Order 11008.

1438 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1621	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₃×#331	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₃	—	2	1	no	—
10	C₂²×SD₁₆×C₄₃	—	2	1	no	—
11	C₂²×D₈×C₄₃	—	2	2	no	—
12	C₂²×D₈×C₄₃	—	2	1	no	—
13	C₄₃×#550	—	2	2	no	—
14	C₄₃×#550	—	2	2	no	—
15	C₄₃×#550	—	2	2	no	—
16	C₄₃×#550	C₂²	1	4	yes	complemented
17	C₂×#127×C₄₃	—	2	1	no	—
18	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#121×C₄₃	—	2	2	no	—
21	C₂×#121×C₄₃	—	2	1	no	—
22	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₄₃	—	2	1	no	—
24	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
25	C₄₃×#493	—	2	2	no	—
26	C₄₃×#493	C₂²	1	4	yes	complemented
27	C₄₃×#460	—	2	2	no	—
28	C₄₃×#460	C₂²	1	4	yes	complemented
29	C₄₃×#459	—	2	2	no	—
30	C₄₃×#459	C₂²	1	4	yes	complemented
31	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
33	C₂×#102×C₄₃	—	2	1	no	—
34	C₂×#102×C₄₃	—	2	1	no	—
35	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₄₃×#331	C₂²	1	4	yes	complemented
37	C₄₃×Q₈⋊C₈	C₂²	1	4	yes	complemented
38	C₄₃×D₄⋊C₈	C₂²	1	4	yes	complemented
39	C₂×#41×C₄₃	—	2	4	no	—
40	C₂×#41×C₄₃	—	2	4	no	—
41	C₂×#41×C₄₃	—	4	4	no	—
42	C₂×#41×C₄₃	—	4	4	no	—
43	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₄₃	—	2	2	no	—
45	C₂²×D₄×C₄₃	—	2	2	no	—
46	C₂²×D₄×C₄₃	—	2	1	no	—
47	C₂²×D₄×C₄₃	—	2	1	no	—
48	C₂²×D₄×C₄₃	—	2	1	no	—
49	C₂²×D₄×C₄₃	—	2	1	no	—
50	C₂²×D₄×C₄₃	—	2	1	no	—
51	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
52	C₂²×D₄×C₄₃	D₄	1	2	yes	—
53	C₂³×C₄×C₄₃	—	2	2	no	—
54	C₂³×C₄×C₄₃	—	2	1	no	—
55	C₂×SD₁₆×C₄₃	—	2	4	no	—
56	C₂×SD₁₆×C₄₃	—	4	4	no	—
57	C₂×D₈×C₄₃	—	2	4	no	—
58	C₂×D₈×C₄₃	—	2	8	no	—
59	C₂×D₈×C₄₃	—	4	8	no	—
60	C₂×D₈×C₄₃	—	4	4	no	—
61	C₂²×C₈×C₄₃	—	2	1	no	—
62	C₂²×C₈×C₄₃	—	2	1	no	—
63	C₂²×C₈×C₄₃	—	2	1	no	—
64	#127×C₄₃	—	2	4	no	—
65	#127×C₄₃	—	2	4	no	—
66	#127×C₄₃	—	2	1	no	—
67	#127×C₄₃	—	2	1	no	—
68	#127×C₄₃	—	2	1	no	—
69	#127×C₄₃	—	2	1	no	—
70	#127×C₄₃	—	2	1	no	—
71	#127×C₄₃	D₄	1	2	yes	—
72	#127×C₄₃	C₂³	1	2	yes	—
73	#127×C₄₃	C₂³	1	2	yes	—
74	#121×C₄₃	—	2	4	no	—
75	#121×C₄₃	—	2	8	no	—
76	#121×C₄₃	—	2	8	no	—
77	#121×C₄₃	—	2	4	no	—
78	C₄×Q₈×C₄₃	—	2	1	no	—
79	C₄×Q₈×C₄₃	—	2	1	no	—
80	C₄×Q₈×C₄₃	D₄	1	2	yes	—
81	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
82	C₄×D₄×C₄₃	—	2	4	no	—
83	C₄×D₄×C₄₃	—	2	4	no	—
84	C₄×D₄×C₄₃	—	2	1	no	—
85	C₄×D₄×C₄₃	—	2	1	no	—
86	C₄×D₄×C₄₃	D₄	1	2	yes	—
87	C₄×D₄×C₄₃	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
89	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
93	C₂×C₄²×C₄₃	—	2	1	no	—
94	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₃	—	2	1	no	—
96	C₄⋊C₈×C₄₃	—	2	1	no	—
97	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
98	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
99	#102×C₄₃	—	2	4	no	—
100	#102×C₄₃	—	2	4	no	—
101	C₄×C₈×C₄₃	—	2	1	no	—
102	C₄×C₈×C₄₃	C₂³	1	2	yes	—
103	C₂⁴×C₄₃	—	2	1	no	—
104	C₂⁴×C₄₃	—	2	2	no	—
105	C₂⁴×C₄₃	—	4	1	no	—
106	#41×C₄₃	—	4	8	no	—
107	#41×C₄₃	—	4	16	no	—
108	#41×C₄₃	—	4	8	no	—
109	C₂×Q₈×C₄₃	—	2	1	no	—
110	C₂×Q₈×C₄₃	—	2	2	no	—
111	C₂×Q₈×C₄₃	D₈	1	4	yes	complemented
112	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
113	C₂×D₄×C₄₃	—	2	8	no	—
114	C₂×D₄×C₄₃	—	2	8	no	—
115	C₂×D₄×C₄₃	—	2	1	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	—	2	2	no	—
120	C₂×D₄×C₄₃	—	2	2	no	—
121	C₂×D₄×C₄₃	—	2	2	no	—
122	C₂×D₄×C₄₃	—	2	2	no	—
123	C₂×D₄×C₄₃	—	2	2	no	—
124	C₂×D₄×C₄₃	—	2	2	no	—
125	C₂×D₄×C₄₃	—	2	2	no	—
126	C₂×D₄×C₄₃	—	4	8	no	—
127	C₂×D₄×C₄₃	—	4	1	no	—
128	C₂×D₄×C₄₃	—	4	1	no	—
129	C₂×D₄×C₄₃	—	4	1	no	—
130	C₂×D₄×C₄₃	—	4	2	no	—
131	C₂×D₄×C₄₃	—	4	2	no	—
132	C₂×D₄×C₄₃	—	4	2	no	—
133	C₂×D₄×C₄₃	—	4	2	no	—
134	C₂×D₄×C₄₃	—	4	4	no	—
135	C₂×D₄×C₄₃	—	4	4	no	—
136	C₂×D₄×C₄₃	—	4	2	no	—
137	C₂×D₄×C₄₃	—	4	2	no	—
138	C₂×D₄×C₄₃	—	4	2	no	—
139	C₂×D₄×C₄₃	—	4	2	no	—
140	C₂×D₄×C₄₃	—	8	4	no	—
141	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
142	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₄₃	—	2	8	no	—
144	C₂²×C₄×C₄₃	—	2	2	no	—
145	C₂²×C₄×C₄₃	—	2	2	no	—
146	C₂²×C₄×C₄₃	—	2	1	no	—
147	C₂²×C₄×C₄₃	—	2	1	no	—
148	C₂²×C₄×C₄₃	—	2	1	no	—
149	C₂²×C₄×C₄₃	—	4	8	no	—
150	C₂²×C₄×C₄₃	—	4	2	no	—
151	C₂²×C₄×C₄₃	—	4	2	no	—
152	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
155	SD₁₆×C₄₃	—	4	8	no	—
156	D₈×C₄₃	—	4	16	no	—
157	D₈×C₄₃	—	4	8	no	—
158	C₂×C₈×C₄₃	—	2	4	no	—
159	C₂×C₈×C₄₃	—	2	2	no	—
160	C₂×C₈×C₄₃	—	2	2	no	—
161	C₂×C₈×C₄₃	—	2	2	no	—
162	C₂×C₈×C₄₃	—	4	2	no	—
163	C₂×C₈×C₄₃	—	4	2	no	—
164	C₄⋊C₄×C₄₃	—	2	2	no	—
165	C₄⋊C₄×C₄₃	—	2	1	no	—
166	C₄⋊C₄×C₄₃	—	2	1	no	—
167	C₄⋊C₄×C₄₃	—	2	2	no	—
168	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
170	C₂²⋊C₄×C₄₃	—	2	8	no	—
171	C₂²⋊C₄×C₄₃	—	2	2	no	—
172	C₂²⋊C₄×C₄₃	—	2	2	no	—
173	C₄²×C₄₃	—	2	2	no	—
174	C₄²×C₄₃	—	2	2	no	—
175	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
179	C₂³×C₄₃	—	2	2	no	—
180	C₂³×C₄₃	—	2	4	no	—
181	C₂³×C₄₃	—	4	4	no	—
182	C₂³×C₄₃	—	4	2	no	—
183	C₂³×C₄₃	—	4	2	no	—
184	C₂³×C₄₃	—	4	4	no	—
185	C₂³×C₄₃	—	4	4	no	—
186	C₂³×C₄₃	—	4	2	no	—
187	C₂³×C₄₃	—	4	2	no	—
188	C₂³×C₄₃	—	8	2	no	—
189	C₂³×C₄₃	—	8	2	no	—
190	C₂³×C₄₃	—	8	2	no	—
191	C₂³×C₄₃	#120	1	1	yes	characteristic
192	Q₈×C₄₃	—	2	2	no	—
193	Q₈×C₄₃	—	2	4	no	—
194	Q₈×C₄₃	C₂×D₈	1	4	yes	complemented
195	D₄×C₄₃	—	2	2	no	—
196	D₄×C₄₃	—	2	2	no	—
197	D₄×C₄₃	—	4	4	no	—
198	D₄×C₄₃	—	4	16	no	—
199	D₄×C₄₃	—	4	4	no	—
200	D₄×C₄₃	—	4	2	no	—
201	D₄×C₄₃	—	4	2	no	—
202	D₄×C₄₃	—	4	2	no	—
203	D₄×C₄₃	—	4	2	no	—
204	D₄×C₄₃	—	4	2	no	—
205	D₄×C₄₃	—	4	2	no	—
206	D₄×C₄₃	—	4	2	no	—
207	D₄×C₄₃	—	4	2	no	—
208	D₄×C₄₃	—	4	4	no	—
209	D₄×C₄₃	—	4	2	no	—
210	D₄×C₄₃	—	4	4	no	—
211	D₄×C₄₃	—	8	2	no	—
212	D₄×C₄₃	—	8	2	no	—
213	D₄×C₄₃	—	8	8	no	—
214	D₄×C₄₃	—	8	2	no	—
215	D₄×C₄₃	—	8	2	no	—
216	C₂×C₄×C₄₃	—	2	2	no	—
217	C₂×C₄×C₄₃	—	2	4	no	—
218	C₂×C₄×C₄₃	—	2	2	no	—
219	C₂×C₄×C₄₃	—	2	2	no	—
220	C₂×C₄×C₄₃	—	2	2	no	—
221	C₂×C₄×C₄₃	—	4	16	no	—
222	C₂×C₄×C₄₃	—	4	2	no	—
223	C₂×C₄×C₄₃	—	4	2	no	—
224	C₂×C₄×C₄₃	—	4	2	no	—
225	C₂×C₄×C₄₃	—	4	2	no	—
226	C₂×C₄×C₄₃	—	4	4	no	—
227	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
228	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
229	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
230	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
231	C₂×C₄×C₄₃	#135	1	2	yes	—
232	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
233	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
234	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
237	C₈×C₄₃	—	2	4	no	—
238	C₈×C₄₃	—	4	2	no	—
239	C₈×C₄₃	—	4	2	no	—
240	C₂×#1621	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂²×C₄₃	—	4	4	no	—
242	C₂²×C₄₃	—	4	2	no	—
243	C₂²×C₄₃	—	4	2	no	—
244	C₂²×C₄₃	—	4	4	no	—
245	C₂²×C₄₃	—	4	4	no	—
246	C₂²×C₄₃	—	4	2	no	—
247	C₂²×C₄₃	—	8	4	no	—
248	C₂²×C₄₃	—	8	8	no	—
249	C₂²×C₄₃	—	8	2	no	—
250	C₂²×C₄₃	—	8	2	no	—
251	C₂²×C₄₃	—	8	2	no	—
252	C₂²×C₄₃	—	16	4	no	—
253	C₂²×C₄₃	#447	1	2	yes	—
254	C₂²×C₄₃	#449	1	2	yes	—
255	C₂²×C₄₃	#453	1	2	yes	—
256	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
257	C₄×C₄₃	—	2	4	no	—
258	C₄×C₄₃	—	2	1	no	—
259	C₄×C₄₃	—	2	1	no	—
260	C₄×C₄₃	—	4	2	no	—
261	C₄×C₄₃	—	4	2	no	—
262	C₄×C₄₃	#447	1	2	yes	—
263	C₄×C₄₃	#449	1	2	yes	—
264	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
265	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
266	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
267	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
268	C₂×#550	C₂×C₄₃	1	1	yes	characteristic, complemented
269	C₂×#493	C₂×C₄₃	1	1	yes	characteristic, complemented
270	C₂×#460	C₂×C₄₃	1	1	yes	characteristic, complemented
271	C₂×#459	C₂×C₄₃	1	1	yes	characteristic, complemented
272	#1621	C₂×C₄₃	1	8	yes	direct product factor
273	C₂×#331	C₂×C₄₃	1	1	yes	characteristic, complemented
274	C₂×Q₈⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
275	C₂×D₄⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
276	C₂×C₄₃	—	8	2	no	—
277	C₂×C₄₃	—	8	4	no	—
278	C₂×C₄₃	—	16	2	no	—
279	C₂×C₄₃	#1621	1	4	yes	direct product factor
280	C₂×C₄₃	C₂×#447	1	1	yes	characteristic
281	C₂×C₄₃	C₂×#449	1	1	yes	characteristic
282	C₂×C₄₃	C₂×#453	1	1	yes	characteristic
283	C₂²×#41	—	2	1	no	—
284	C₂²×SD₁₆	—	2	1	no	—
285	C₂²×D₈	—	2	2	no	—
286	C₂²×D₈	—	2	1	no	—
287	#550	—	2	2	no	—
288	#550	—	2	2	no	—
289	#550	—	2	2	no	—
290	#550	C₂²×C₄₃	1	4	yes	complemented
291	C₂×#127	—	2	1	no	—
292	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
293	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
294	C₂×#121	—	2	2	no	—
295	C₂×#121	—	2	1	no	—
296	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
297	C₂×C₄×D₄	—	2	1	no	—
298	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
299	#493	—	2	2	no	—
300	#493	C₂²×C₄₃	1	4	yes	complemented
301	#460	—	2	2	no	—
302	#460	C₂²×C₄₃	1	4	yes	complemented
303	#459	—	2	2	no	—
304	#459	C₂²×C₄₃	1	4	yes	complemented
305	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
306	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
307	C₂×#102	—	2	1	no	—
308	C₂×#102	—	2	1	no	—
309	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
310	#331	C₂²×C₄₃	1	4	yes	complemented
311	Q₈⋊C₈	C₂²×C₄₃	1	4	yes	complemented
312	D₄⋊C₈	C₂²×C₄₃	1	4	yes	complemented
313	C₄₃	C₂×#1621	1	1	yes	characteristic, direct product factor, Sylow
314	C₂×#41	—	2	4	no	—
315	C₂×#41	—	2	4	no	—
316	C₂×#41	—	4	4	no	—
317	C₂×#41	—	4	4	no	—
318	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
319	C₂²×D₄	—	2	2	no	—
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	—	2	1	no	—
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	—	2	1	no	—
324	C₂²×D₄	—	2	1	no	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
327	C₂²×D₄	D₄×C₄₃	1	2	yes	—
328	C₂³×C₄	—	2	2	no	—
329	C₂³×C₄	—	2	1	no	—
330	C₂×SD₁₆	—	2	4	no	—
331	C₂×SD₁₆	—	4	4	no	—
332	C₂×D₈	—	2	4	no	—
333	C₂×D₈	—	2	8	no	—
334	C₂×D₈	—	4	8	no	—
335	C₂×D₈	—	4	4	no	—
336	C₂²×C₈	—	2	1	no	—
337	C₂²×C₈	—	2	1	no	—
338	C₂²×C₈	—	2	1	no	—
339	#127	—	2	4	no	—
340	#127	—	2	4	no	—
341	#127	—	2	1	no	—
342	#127	—	2	1	no	—
343	#127	—	2	1	no	—
344	#127	—	2	1	no	—
345	#127	—	2	1	no	—
346	#127	D₄×C₄₃	1	2	yes	—
347	#127	C₂³×C₄₃	1	2	yes	—
348	#127	C₂³×C₄₃	1	2	yes	—
349	#121	—	2	4	no	—
350	#121	—	2	8	no	—
351	#121	—	2	8	no	—
352	#121	—	2	4	no	—
353	C₄×Q₈	—	2	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	D₄×C₄₃	1	2	yes	—
356	C₄×Q₈	C₂³×C₄₃	1	2	yes	—
357	C₄×D₄	—	2	4	no	—
358	C₄×D₄	—	2	4	no	—
359	C₄×D₄	—	2	1	no	—
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	D₄×C₄₃	1	2	yes	—
362	C₄×D₄	C₂³×C₄₃	1	2	yes	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
370	C₄⋊C₈	—	2	1	no	—
371	C₄⋊C₈	—	2	1	no	—
372	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
373	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
374	#102	—	2	4	no	—
375	#102	—	2	4	no	—
376	C₄×C₈	—	2	1	no	—
377	C₄×C₈	C₂³×C₄₃	1	2	yes	—
378	C₂⁴	—	2	1	no	—
379	C₂⁴	—	2	2	no	—
380	C₂⁴	—	4	1	no	—
381	#41	—	4	8	no	—
382	#41	—	4	16	no	—
383	#41	—	4	8	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	D₈×C₄₃	1	4	yes	complemented
387	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
388	C₂×D₄	—	2	8	no	—
389	C₂×D₄	—	2	8	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	4	8	no	—
402	C₂×D₄	—	4	4	no	—
403	C₂×D₄	—	4	4	no	—
404	C₂×D₄	—	4	1	no	—
405	C₂×D₄	—	4	1	no	—
406	C₂×D₄	—	4	1	no	—
407	C₂×D₄	—	4	2	no	—
408	C₂×D₄	—	4	2	no	—
409	C₂×D₄	—	4	2	no	—
410	C₂×D₄	—	4	2	no	—
411	C₂×D₄	—	4	2	no	—
412	C₂×D₄	—	4	2	no	—
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	—	8	4	no	—
416	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
417	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	8	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	4	8	no	—
425	C₂²×C₄	—	4	2	no	—
426	C₂²×C₄	—	4	2	no	—
427	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
430	SD₁₆	—	4	8	no	—
431	D₈	—	4	16	no	—
432	D₈	—	4	8	no	—
433	C₂×C₈	—	2	4	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	4	2	no	—
438	C₂×C₈	—	4	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
444	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
451	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
452	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
453	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
454	C₂³	—	2	2	no	—
455	C₂³	—	2	4	no	—
456	C₂³	—	4	4	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	4	no	—
460	C₂³	—	4	4	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	8	2	no	—
464	C₂³	—	8	2	no	—
465	C₂³	—	8	2	no	—
466	C₂³	#120×C₄₃	1	1	yes	characteristic
467	Q₈	—	2	2	no	—
468	Q₈	—	2	4	no	—
469	Q₈	C₂×D₈×C₄₃	1	4	yes	complemented
470	D₄	—	2	2	no	—
471	D₄	—	2	2	no	—
472	D₄	—	4	4	no	—
473	D₄	—	4	16	no	—
474	D₄	—	4	4	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	2	no	—
485	D₄	—	4	4	no	—
486	D₄	—	8	2	no	—
487	D₄	—	8	2	no	—
488	D₄	—	8	8	no	—
489	D₄	—	8	2	no	—
490	D₄	—	8	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	4	16	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	4	no	—
502	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
503	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
504	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
505	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
506	C₂×C₄	#135×C₄₃	1	2	yes	—
507	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
508	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
509	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
512	C₈	—	2	4	no	—
513	C₈	—	4	2	no	—
514	C₈	—	4	2	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	4	no	—
519	C₂²	—	4	4	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	8	4	no	—
522	C₂²	—	8	8	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	2	no	—
525	C₂²	—	8	2	no	—
526	C₂²	—	16	4	no	—
527	C₂²	C₄₃×#447	1	2	yes	—
528	C₂²	C₄₃×#449	1	2	yes	—
529	C₂²	C₄₃×#453	1	2	yes	—
530	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
531	C₄	—	2	4	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	C₄₃×#447	1	2	yes	—
537	C₄	C₄₃×#449	1	2	yes	—
538	C₄	C₂²×D₈×C₄₃	1	1	yes	characteristic
539	C₄	C₂×#135×C₄₃	1	1	yes	characteristic
540	C₄	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
541	C₄	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
542	C₂	—	8	2	no	—
543	C₂	—	8	4	no	—
544	C₂	—	16	2	no	—
545	C₂	C₄₃×#1621	1	4	yes	direct product factor
546	C₂	C₂×C₄₃×#447	1	1	yes	characteristic
547	C₂	C₂×C₄₃×#449	1	1	yes	characteristic
548	C₂	C₂×C₄₃×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#550	C₂	semidirect
2. C₂×C₄₃×#493	C₂	semidirect
3. C₂×C₄₃×#460	C₂	semidirect
4. C₂×C₄₃×#459	C₂	semidirect
5. C₄₃×#1621	C₂	direct (N × H)
6. C₂×C₄₃×#331	C₂	semidirect
7. C₂×C₄₃×Q₈⋊C₈	C₂	semidirect
8. C₂×C₄₃×D₄⋊C₈	C₂	semidirect
16. C₄₃×#550	C₂²	semidirect
26. C₄₃×#493	C₂²	semidirect
28. C₄₃×#460	C₂²	semidirect
30. C₄₃×#459	C₂²	semidirect
36. C₄₃×#331	C₂²	semidirect
37. C₄₃×Q₈⋊C₈	C₂²	semidirect
38. C₄₃×D₄⋊C₈	C₂²	semidirect
111. C₂×Q₈×C₄₃	D₈	semidirect
194. Q₈×C₄₃	C₂×D₈	semidirect
240. C₂×#1621	C₄₃	direct (N × H)
268. C₂×#550	C₂×C₄₃	semidirect
269. C₂×#493	C₂×C₄₃	semidirect
270. C₂×#460	C₂×C₄₃	semidirect
271. C₂×#459	C₂×C₄₃	semidirect
272. #1621	C₂×C₄₃	direct (N × H)
273. C₂×#331	C₂×C₄₃	semidirect
274. C₂×Q₈⋊C₈	C₂×C₄₃	semidirect
275. C₂×D₄⋊C₈	C₂×C₄₃	semidirect
279. C₂×C₄₃	#1621	direct (N × H)
290. #550	C₂²×C₄₃	semidirect
300. #493	C₂²×C₄₃	semidirect
302. #460	C₂²×C₄₃	semidirect
304. #459	C₂²×C₄₃	semidirect
310. #331	C₂²×C₄₃	semidirect
311. Q₈⋊C₈	C₂²×C₄₃	semidirect
312. D₄⋊C₈	C₂²×C₄₃	semidirect
313. C₄₃	C₂×#1621	direct (N × H)
386. C₂×Q₈	D₈×C₄₃	semidirect
469. Q₈	C₂×D₈×C₄₃	semidirect
545. C₂	C₄₃×#1621	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×#550	2
C₂×C₄₃×#493	2
C₂×C₄₃×#460	2
C₂×C₄₃×#459	2
C₄₃×#1621	2
C₂×C₄₃×#331	2
C₂×C₄₃×Q₈⋊C₈	2
C₂×C₄₃×D₄⋊C₈	2
C₂×#1621	43

Subgroups — C2×C43×#1621 #24938521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1621 #24938521