Subgroups — #493×Dic₄₃ #25105028

Order 11008.

1422 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈×Dic₄₃	C₂	1	4	yes	maximal, complemented
2	#127×Dic₄₃	C₂	1	2	yes	maximal, complemented
3	#19135462	C₂	1	4	yes	maximal, complemented
4	#19135402	C₂	1	2	yes	maximal, complemented
5	#19134755	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#493	C₂	1	1	yes	maximal, characteristic
8	C₂×D₄×Dic₄₃	—	2	4	no	—
9	C₂×D₄×Dic₄₃	C₂²	1	4	yes	—
10	D₈×Dic₄₃	—	2	16	no	—
11	C₂×#13063259	C₂²	1	4	yes	—
12	C₂×#13063246	C₂²	1	8	yes	—
13	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
15	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
16	#14582802	—	2	4	no	—
17	#14582802	C₂²	1	4	yes	—
18	#14582769	C₂²	1	2	yes	—
19	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₄₃	C₂²	1	4	yes	—
21	C₂×#127×C₄₃	C₂²	1	2	yes	—
22	C₄₃×#493	C₄	1	8	yes	complemented
23	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂³×Dic₄₃	—	2	4	no	—
25	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
26	D₄×Dic₄₃	—	2	16	no	—
27	D₄×Dic₄₃	—	4	16	no	—
28	C₂×C₄⋊Dic₄₃	—	2	4	no	—
29	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
30	C₂×C₂²⋊Dic₄₃	—	2	4	no	—
31	C₂×C₂²⋊Dic₄₃	—	2	8	no	—
32	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
33	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
34	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
35	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
36	#13063259	—	2	8	no	—
37	#13063246	—	2	16	no	—
38	C₄×C₄₃⋊C₈	—	2	2	no	—
39	C₈×Dic₄₃	—	2	4	no	—
40	C₈×Dic₄₃	D₄	1	8	yes	complemented
41	C₂²×D₄×C₄₃	—	2	4	no	—
42	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
43	C₂×D₈×C₄₃	—	2	8	no	—
44	C₂×D₈×C₄₃	—	2	8	no	—
45	C₂×D₈×C₄₃	C₂×C₄	1	16	yes	complemented
46	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
47	#127×C₄₃	—	2	4	no	—
48	#127×C₄₃	C₂×C₄	1	8	yes	complemented
49	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
50	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	complemented
51	C₂⁴×C₄₃	—	2	4	no	—
52	C₂×D₄×C₄₃	—	2	16	no	—
53	C₂×D₄×C₄₃	—	2	4	no	—
54	C₂×D₄×C₄₃	—	2	8	no	—
55	C₂×D₄×C₄₃	—	2	8	no	—
56	C₂×D₄×C₄₃	—	4	8	no	—
57	C₂×D₄×C₄₃	—	4	8	no	—
58	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
59	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
60	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
61	C₂²×Dic₄₃	—	2	4	no	—
62	C₂²×Dic₄₃	—	4	8	no	—
63	C₂²×Dic₄₃	—	4	16	no	—
64	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
65	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
66	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
67	D₈×C₄₃	—	2	32	no	—
68	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
69	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
70	C₂×C₈×C₄₃	#41	1	4	yes	—
71	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
72	C₄²×C₄₃	#41	1	2	yes	—
73	C₂²⋊Dic₄₃	—	4	8	no	—
74	C₂²⋊Dic₄₃	—	4	16	no	—
75	C₄⋊Dic₄₃	—	2	8	no	—
76	C₄⋊Dic₄₃	—	4	8	no	—
77	C₄×Dic₄₃	—	2	4	no	—
78	C₄×Dic₄₃	—	2	2	no	—
79	C₄×Dic₄₃	D₈	1	8	yes	complemented
80	C₄×Dic₄₃	C₂×D₄	1	4	yes	—
81	C₂×C₄₃⋊C₈	—	2	2	no	—
82	C₂×C₄₃⋊C₈	—	2	2	no	—
83	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
84	C₂³×C₄₃	—	2	8	no	—
85	C₂³×C₄₃	—	4	4	no	—
86	C₂³×C₄₃	—	4	4	no	—
87	C₂³×C₄₃	—	4	8	no	—
88	C₂³×C₄₃	—	4	8	no	—
89	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
90	D₄×C₄₃	—	2	16	no	—
91	D₄×C₄₃	—	4	8	no	—
92	D₄×C₄₃	—	4	32	no	—
93	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
94	C₂×C₄×C₄₃	C₂×D₈	1	4	yes	—
95	C₂×C₄×C₄₃	#135	1	4	yes	—
96	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
97	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
98	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
99	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
100	C₂×Dic₄₃	—	2	2	no	—
101	C₂×Dic₄₃	—	2	2	no	—
102	C₂×Dic₄₃	—	2	2	no	—
103	C₂×Dic₄₃	—	4	4	no	—
104	C₂×Dic₄₃	—	4	8	no	—
105	C₂×Dic₄₃	—	8	16	no	—
106	C₂×Dic₄₃	#127	1	2	yes	—
107	C₂×Dic₄₃	#127	1	2	yes	—
108	C₂×Dic₄₃	C₂×D₈	1	4	yes	—
109	C₂×Dic₄₃	C₂×D₈	1	4	yes	—
110	C₈×C₄₃	C₄×D₄	1	8	yes	complemented
111	C₄₃⋊C₈	—	2	4	no	—
112	C₄×#493	—	43	1	no	maximal, Sylow
113	C₂²×C₄₃	—	4	8	no	—
114	C₂²×C₄₃	—	4	16	no	—
115	C₂²×C₄₃	—	8	4	no	—
116	C₂²×C₄₃	—	8	4	no	—
117	C₂²×C₄₃	—	8	8	no	—
118	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
119	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
120	C₂²×C₄₃	#532	1	1	yes	characteristic
121	C₂²×C₄₃	C₂²×D₈	1	2	yes	—
122	C₂²×C₄₃	C₂×#135	1	2	yes	—
123	C₄×C₄₃	C₄×D₈	1	8	yes	complemented
124	C₄×C₄₃	C₂×C₄×D₄	1	2	yes	—
125	C₄×C₄₃	#532	1	2	yes	—
126	Dic₄₃	—	2	2	no	—
127	Dic₄₃	—	2	4	no	—
128	Dic₄₃	—	8	4	no	—
129	Dic₄₃	#493	1	4	yes	direct product factor
130	C₂×#493	D₄₃	1	1	yes	characteristic
131	C₂×C₄×D₈	—	43	4	no	—
132	C₄×#127	—	43	2	no	—
133	#1970	—	43	4	no	—
134	#1957	—	43	2	no	—
135	#1845	—	43	1	no	—
136	C₄²×C₈	—	43	1	no	—
137	C₂×C₄₃	—	8	8	no	—
138	C₂×C₄₃	C₄×#127	1	1	yes	characteristic
139	C₂×C₄₃	C₂×C₄×D₈	1	2	yes	—
140	C₂×C₄₃	C₂×#493	1	1	yes	characteristic
141	C₂×C₄₃	#3147	1	1	yes	characteristic
142	C₂×C₄₃	#3169	1	2	yes	—
143	C₂²×D₈	C₂×D₄₃	1	4	yes	—
144	C₂×#127	C₂×D₄₃	1	2	yes	—
145	C₂×C₄×D₄	—	43	4	no	—
146	C₂×C₄×D₄	—	86	4	no	—
147	#493	Dic₄₃	1	8	yes	direct product factor
148	C₄×D₈	—	86	16	no	—
149	C₂×#107	—	43	4	no	—
150	C₂×#102	—	43	8	no	—
151	C₂×C₄×C₈	—	43	2	no	—
152	C₂×C₄×C₈	—	43	2	no	—
153	C₂×C₄×C₈	—	43	1	no	—
154	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
155	#390	—	43	4	no	—
156	#390	—	86	4	no	—
157	#384	—	43	2	no	—
158	C₄³	—	43	1	no	—
159	C₄₃	C₄×#493	1	1	yes	characteristic, complemented, Sylow
160	C₂²×D₄	—	2	4	no	—
161	C₂²×D₄	C₂²×D₄₃	1	4	yes	—
162	C₂³×C₄	—	86	4	no	—
163	C₂×D₈	—	2	8	no	—
164	C₂×D₈	—	2	8	no	—
165	C₂×D₈	C₂×Dic₄₃	1	16	yes	complemented
166	C₂²×C₈	—	43	2	no	—
167	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
168	#127	—	2	4	no	—
169	#127	C₂×Dic₄₃	1	8	yes	complemented
170	C₄×D₄	—	86	16	no	—
171	C₄×D₄	—	172	16	no	—
172	C₂×C₄⋊C₄	—	43	4	no	—
173	C₂×C₄⋊C₄	—	86	4	no	—
174	C₂×C₂²⋊C₄	—	86	4	no	—
175	C₂×C₂²⋊C₄	—	86	8	no	—
176	C₂×C₄²	—	43	2	no	—
177	C₂×C₄²	—	43	1	no	—
178	C₂×C₄²	—	43	2	no	—
179	C₂×C₄²	—	43	1	no	—
180	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
181	#107	—	86	8	no	—
182	#102	—	86	16	no	—
183	C₄×C₈	—	43	8	no	—
184	C₄×C₈	—	86	4	no	—
185	C₄×C₈	—	86	2	no	—
186	C₄×C₈	C₂×Dic₄₃	1	4	yes	complemented
187	C₂⁴	—	2	4	no	—
188	C₂×D₄	—	2	16	no	—
189	C₂×D₄	—	2	8	no	—
190	C₂×D₄	—	2	8	no	—
191	C₂×D₄	—	2	4	no	—
192	C₂×D₄	—	4	8	no	—
193	C₂×D₄	—	4	8	no	—
194	C₂×D₄	C₂²×Dic₄₃	1	8	yes	—
195	C₂²×C₄	—	43	1	no	—
196	C₂²×C₄	—	43	2	no	—
197	C₂²×C₄	—	43	1	no	—
198	C₂²×C₄	—	86	4	no	—
199	C₂²×C₄	—	172	8	no	—
200	C₂²×C₄	—	172	16	no	—
201	C₂²×C₄	D₄×D₄₃	1	2	yes	—
202	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
203	D₈	—	2	32	no	—
204	C₂×C₈	—	43	4	no	—
205	C₂×C₈	—	86	2	no	—
206	C₂×C₈	—	86	2	no	—
207	C₂×C₈	D₄×D₄₃	1	4	yes	—
208	C₂×C₈	#10621900	1	4	yes	—
209	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
210	C₄⋊C₄	—	86	8	no	—
211	C₄⋊C₄	—	172	8	no	—
212	C₂²⋊C₄	—	172	8	no	—
213	C₂²⋊C₄	—	172	16	no	—
214	C₄²	—	43	8	no	—
215	C₄²	—	43	4	no	—
216	C₄²	—	86	4	no	—
217	C₄²	—	86	2	no	—
218	C₄²	#10621900	1	2	yes	—
219	C₄²	C₂²×Dic₄₃	1	2	yes	—
220	C₂³	—	2	8	no	—
221	C₂³	—	4	8	no	—
222	C₂³	—	4	8	no	—
223	C₂³	—	4	4	no	—
224	C₂³	—	4	4	no	—
225	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
226	D₄	—	2	16	no	—
227	D₄	—	4	8	no	—
228	D₄	—	4	32	no	—
229	C₂×C₄	—	43	4	no	—
230	C₂×C₄	—	43	2	no	—
231	C₂×C₄	—	43	4	no	—
232	C₂×C₄	—	43	2	no	—
233	C₂×C₄	—	86	2	no	—
234	C₂×C₄	—	86	2	no	—
235	C₂×C₄	—	86	2	no	—
236	C₂×C₄	—	344	16	no	—
237	C₂×C₄	—	172	8	no	—
238	C₂×C₄	—	172	4	no	—
239	C₂×C₄	D₄×Dic₄₃	1	4	yes	—
240	C₂×C₄	D₈×D₄₃	1	4	yes	—
241	C₂×C₄	#13063344	1	4	yes	—
242	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
243	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
244	C₂×C₄	C₂×#10621900	1	2	yes	—
245	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
246	C₈	—	86	4	no	—
247	C₈	D₄×Dic₄₃	1	8	yes	complemented
248	C₂²	—	4	8	no	—
249	C₂²	—	4	16	no	—
250	C₂²	—	8	4	no	—
251	C₂²	—	8	4	no	—
252	C₂²	—	8	8	no	—
253	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
254	C₂²	#127×D₄₃	1	1	yes	characteristic
255	C₂²	#14583447	1	1	yes	characteristic
256	C₂²	C₂×D₈×D₄₃	1	2	yes	—
257	C₂²	C₂×#13063344	1	2	yes	—
258	C₄	—	43	4	no	—
259	C₄	—	86	2	no	—
260	C₄	—	86	4	no	—
261	C₄	—	344	4	no	—
262	C₄	D₈×Dic₄₃	1	8	yes	complemented
263	C₄	C₂×D₄×Dic₄₃	1	2	yes	—
264	C₄	#14583447	1	2	yes	—
265	C₂	—	8	8	no	—
266	C₂	#127×Dic₄₃	1	1	yes	characteristic
267	C₂	C₂×D₈×Dic₄₃	1	2	yes	—
268	C₂	#493×D₄₃	1	1	yes	characteristic
269	C₂	#19145022	1	1	yes	characteristic
270	C₂	#19145172	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting, prime radical	C₂×C₄₃×#493	C₂
socle	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#493	D₄₃
hypocenter	C₄₃	C₄×#493
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#493

Complements

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

N	H ≅ G/N	type
1. C₂×D₈×Dic₄₃	C₂	semidirect
2. #127×Dic₄₃	C₂	semidirect
3. #19135462	C₂	semidirect
4. #19135402	C₂	semidirect
5. #19134755	C₂	semidirect
6. C₄×C₈×Dic₄₃	C₂	semidirect
22. C₄₃×#493	C₄	semidirect
40. C₈×Dic₄₃	D₄	semidirect
45. C₂×D₈×C₄₃	C₂×C₄	semidirect
48. #127×C₄₃	C₂×C₄	semidirect
50. C₄×C₈×C₄₃	C₂×C₄	semidirect
79. C₄×Dic₄₃	D₈	semidirect
110. C₈×C₄₃	C₄×D₄	semidirect
123. C₄×C₄₃	C₄×D₈	semidirect
129. Dic₄₃	#493	direct (N × H)
147. #493	Dic₄₃	direct (N × H)
159. C₄₃	C₄×#493	semidirect
165. C₂×D₈	C₂×Dic₄₃	semidirect
169. #127	C₂×Dic₄₃	semidirect
186. C₄×C₈	C₂×Dic₄₃	semidirect
247. C₈	D₄×Dic₄₃	semidirect
262. C₄	D₈×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₈×Dic₄₃	2
#127×Dic₄₃	2
#19135462	2
#19135402	2
#19134755	2
C₄×C₈×Dic₄₃	2
C₂×C₄₃×#493	2
C₄×#493	43

Subgroups — #493×Dic43 #25105028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #493×Dic₄₃ #25105028