Subgroups — #25250262

Order 11008.

444 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143529	C₂	1	1	yes	maximal, characteristic
2	#19136502	C₂	1	4	yes	maximal, complemented
3	#19136501	C₂	1	4	yes	maximal, complemented
4	#19136399	C₂	1	4	yes	maximal
5	#19136398	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#2163	C₂	1	1	yes	maximal, characteristic
7	#14583456	C₄	1	1	yes	characteristic
8	#14583029	C₄	1	2	yes	—
9	#14583029	C₄	1	2	yes	—
10	C₈×Dic₈₆	C₂²	1	2	yes	—
11	C₈×Dic₈₆	C₂²	1	2	yes	—
12	#14582925	C₄	1	2	yes	—
13	#14582923	C₄	1	1	yes	characteristic
14	#14582854	C₂²	1	2	yes	—
15	C₄⋊(C₄₃⋊C₁₆)	C₂²	1	2	yes	—
16	Dic₄₃⋊C₁₆	C₂²	1	8	yes	—
17	C₂²⋊(C₄₃⋊C₁₆)	C₂²	1	2	yes	—
18	#14582675	C₂²	1	2	yes	—
19	#14582674	C₂²	1	4	yes	—
20	C₁₆×Dic₄₃	C₂²	1	4	yes	—
21	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×C₄⋊C₁₆	C₂²	1	2	yes	—
23	C₄₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
24	C₄₃×#346	C₂²	1	2	yes	—
25	C₂×#10621877	C₂×C₄	1	2	yes	—
26	#13063325	C₈	1	1	yes	characteristic
27	#13063325	C₈	1	1	yes	characteristic
28	#13063317	C₈	1	2	yes	—
29	#13063304	C₈	1	2	yes	—
30	#13063304	C₈	1	2	yes	—
31	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
32	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
33	#13063284	C₂×C₄	1	2	yes	—
34	C₂×C₄₃⋊C₁₆	C₂³	1	4	yes	—
35	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
36	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
37	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
38	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
39	#13063235	C₂×C₄	1	4	yes	—
40	C₈×Dic₄₃	C₂³	1	4	yes	—
41	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
43	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₁₆×C₄₃	C₂³	1	4	yes	—
45	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
48	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
49	C₂²×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
50	C₂²×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
51	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
52	C₂×Dic₈₆	C₂×C₈	1	2	yes	—
53	C₂×Dic₈₆	C₂×C₈	1	2	yes	—
54	C₂×C₈×C₄₃	—	2	2	no	—
55	C₂×C₈×C₄₃	—	4	1	no	—
56	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
60	C₄²×C₄₃	C₂×C₈	1	1	yes	characteristic
61	C₄²×C₄₃	C₂×C₈	1	1	yes	characteristic
62	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
63	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
64	C₂²⋊Dic₄₃	C₂×C₈	1	4	yes	—
65	C₄⋊Dic₄₃	C₂×C₈	1	2	yes	—
66	C₄⋊Dic₄₃	C₂×C₈	1	2	yes	—
67	C₄⋊Dic₄₃	C₂×C₈	1	2	yes	—
68	C₄⋊Dic₄₃	C₂×C₈	1	2	yes	—
69	Dic₄₃⋊C₄	C₂×C₈	1	4	yes	—
70	Dic₄₃⋊C₄	C₂×C₈	1	4	yes	—
71	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
72	#10621877	—	4	2	no	—
73	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
74	C₁₆×C₄₃	—	2	4	no	—
75	C₄₃⋊C₁₆	—	2	4	no	—
76	C₂³×C₄₃	C₂²×C₈	1	1	yes	characteristic
77	C₂×C₄×C₄₃	—	2	1	no	—
78	C₂×C₄×C₄₃	—	2	1	no	—
79	C₂×C₄×C₄₃	—	4	1	no	—
80	C₂×C₄×C₄₃	—	4	1	no	—
81	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
82	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
83	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
84	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
85	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
86	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
87	C₂×Dic₄₃	C₂²×C₈	1	4	yes	—
88	C₂×Dic₄₃	C₂²×C₈	1	4	yes	—
89	Dic₈₆	—	4	2	no	—
90	Dic₈₆	—	4	2	no	—
91	C₈×C₄₃	—	2	1	no	—
92	C₈×C₄₃	—	2	1	no	—
93	C₈×C₄₃	—	2	1	no	—
94	C₈×C₄₃	2₋¹⁺⁴	1	2	yes	—
95	C₄₃⋊C₈	—	2	4	no	—
96	#33501	—	43	1	no	maximal, Sylow
97	C₂²×C₄₃	—	2	1	no	—
98	C₂²×C₄₃	—	2	1	no	—
99	C₂²×C₄₃	—	2	1	no	—
100	C₂²×C₄₃	C₂³×C₈	1	1	yes	characteristic
101	C₄×C₄₃	—	2	1	no	—
102	C₄×C₄₃	—	2	1	no	—
103	C₄×C₄₃	—	2	1	no	—
104	C₄×C₄₃	—	2	1	no	—
105	C₄×C₄₃	—	2	1	no	—
106	C₄×C₄₃	#519	1	1	yes	characteristic
107	C₄×C₄₃	#568	1	1	yes	characteristic
108	Dic₄₃	—	2	4	no	—
109	Dic₄₃	—	2	4	no	—
110	#2960	—	43	1	no	—
111	#2183	—	43	4	no	—
112	#2183	—	43	4	no	—
113	#2164	—	43	4	no	—
114	#2163	—	43	1	no	—
115	#2163	D₄₃	1	1	yes	characteristic
116	C₂×C₄₃	—	4	1	no	—
117	C₂×C₄₃	#2982	1	1	yes	characteristic
118	C₂×C₄₃	#3407	1	1	yes	characteristic
119	C₂×C₄₃	#3407	1	1	yes	characteristic
120	#533	—	43	1	no	—
121	#446	—	43	2	no	—
122	#446	—	43	2	no	—
123	C₈×Q₈	—	43	2	no	—
124	C₈×Q₈	—	43	2	no	—
125	#424	—	43	2	no	—
126	#423	—	43	1	no	—
127	#405	—	43	2	no	—
128	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
129	C₄⋊C₁₆	—	43	8	no	—
130	C₄⋊C₁₆	—	43	2	no	—
131	C₄⋊C₁₆	C₂×D₄₃	1	2	yes	—
132	C₂²⋊C₁₆	—	43	2	no	—
133	C₂²⋊C₁₆	C₂×D₄₃	1	2	yes	—
134	#346	—	43	4	no	—
135	#346	—	43	2	no	—
136	#346	C₂×D₄₃	1	2	yes	—
137	C₄×C₁₆	—	43	4	no	—
138	C₄₃	#33501	1	1	yes	characteristic, complemented, Sylow
139	C₂×M₁₆	—	43	2	no	—
140	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
141	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
142	C₄⋊Q₈	—	43	1	no	—
143	C₄⋊Q₈	—	43	1	no	—
144	#125	—	43	2	no	—
145	C₂²⋊Q₈	—	43	2	no	—
146	C₂²⋊Q₈	—	43	2	no	—
147	C₄×Q₈	—	43	2	no	—
148	C₄×Q₈	—	43	2	no	—
149	#117	—	43	2	no	—
150	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
151	C₂×C₁₆	—	43	4	no	—
152	C₂×C₁₆	C₂²×D₄₃	1	4	yes	—
153	C₄⋊C₈	—	43	4	no	—
154	C₄⋊C₈	—	43	4	no	—
155	C₄⋊C₈	—	43	2	no	—
156	C₄⋊C₈	—	43	2	no	—
157	#97	—	43	4	no	—
158	C₄×C₈	—	43	4	no	—
159	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
160	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
161	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
162	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
163	C₂×Q₈	—	43	2	no	—
164	C₂×Q₈	—	43	2	no	—
165	C₂²×C₄	C₈×D₄₃	1	1	yes	characteristic
166	C₂²×C₄	C₈×D₄₃	1	1	yes	characteristic
167	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
168	M₁₆	—	172	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	4	1	no	—
171	C₂×C₈	—	43	4	no	—
172	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
173	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
174	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
175	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
176	C₄⋊C₄	—	43	2	no	—
177	C₄⋊C₄	—	43	2	no	—
178	C₄⋊C₄	—	43	4	no	—
179	C₄⋊C₄	—	43	4	no	—
180	C₄⋊C₄	—	43	2	no	—
181	C₄⋊C₄	—	43	2	no	—
182	C₂²⋊C₄	—	43	4	no	—
183	C₄²	—	43	4	no	—
184	C₄²	C₈×D₄₃	1	1	yes	characteristic
185	C₄²	C₈×D₄₃	1	1	yes	characteristic
186	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
187	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
188	C₁₆	—	2	4	no	—
189	C₁₆	—	86	4	no	—
190	C₂³	C₂×C₈×D₄₃	1	1	yes	characteristic
191	Q₈	—	172	2	no	—
192	Q₈	—	172	2	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	—	4	1	no	—
197	C₂×C₄	—	43	4	no	—
198	C₂×C₄	—	43	4	no	—
199	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
200	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
201	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
202	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
203	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
204	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
205	C₈	—	2	1	no	—
206	C₈	—	2	1	no	—
207	C₈	—	2	1	no	—
208	C₈	—	86	4	no	—
209	C₈	#13063372	1	2	yes	—
210	C₂²	—	2	1	no	—
211	C₂²	—	2	1	no	—
212	C₂²	—	2	1	no	—
213	C₂²	C₂²×C₈×D₄₃	1	1	yes	characteristic
214	C₄	—	2	1	no	—
215	C₄	—	2	1	no	—
216	C₄	—	2	1	no	—
217	C₄	—	2	1	no	—
218	C₄	—	2	1	no	—
219	C₄	—	86	4	no	—
220	C₄	—	86	4	no	—
221	C₄	#14583376	1	1	yes	characteristic
222	C₄	#14583665	1	1	yes	characteristic
223	C₂	—	4	1	no	—
224	C₂	#19143675	1	1	yes	characteristic
225	C₂	#19147697	1	1	yes	characteristic
226	C₂	#19147697	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂³×C₈
Fitting	C₄₃×#2163	C₂
prime radical	C₂³×C₄₃	C₂²×C₈
cosocle	C₂×C₈×C₄₃	C₂⁴
hypercenter	#2163	D₄₃
hypocenter	C₄₃	#33501
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ #2163

Complements

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

N	H ≅ G/N	type
2. #19136502	C₂	semidirect
3. #19136501	C₂	semidirect
138. C₄₃	#33501	semidirect

Maximal subgroups

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

subgroup	index
#19143529	2
#19136502	2
#19136501	2
#19136399	2
#19136398	2
C₄₃×#2163	2
#33501	43