Subgroups — #24987785

Order 11008.

438 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19134450	C₂	1	2	yes	maximal
2	C₄×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582649	C₂	1	2	yes	maximal
4	#19132430	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#1277	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
7	C₂×#13063235	—	2	2	no	—
8	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₈×Dic₄₃	C₄	1	2	yes	—
10	C₂×C₈×Dic₄₃	C₄	1	2	yes	—
11	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
12	#14582653	—	2	2	no	—
13	#14582649	C₄	1	8	yes	complemented
14	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄₃⋊C₈	—	2	2	no	—
17	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
20	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
21	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
22	C₂×C₄×Dic₄₃	Q₈	1	2	yes	—
23	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
24	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
25	#13063235	—	4	4	no	—
26	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
27	C₈×Dic₄₃	—	2	4	no	—
28	C₈×Dic₄₃	—	2	4	no	—
29	C₂²×C₈×C₄₃	—	2	2	no	—
30	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
32	C₄⋊C₈×C₄₃	—	2	2	no	—
33	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
34	C₄×C₈×C₄₃	—	2	2	no	—
35	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
36	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
37	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
38	C₂²×Dic₄₃	C₄⋊C₄	1	2	yes	—
39	C₂²×Dic₄₃	C₄⋊C₄	1	2	yes	—
40	C₂×C₈×C₄₃	—	2	2	no	—
41	C₂×C₈×C₄₃	—	2	2	no	—
42	C₂×C₈×C₄₃	—	2	4	no	—
43	C₂×C₈×C₄₃	—	4	2	no	—
44	C₂×C₈×C₄₃	—	4	2	no	—
45	C₂×C₈×C₄₃	M₁₆	1	4	yes	—
46	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
47	C₄²×C₄₃	#41	1	2	yes	—
48	C₄×Dic₄₃	—	2	2	no	—
49	C₄×Dic₄₃	—	2	2	no	—
50	C₄×Dic₄₃	—	2	1	no	—
51	C₄×Dic₄₃	—	2	1	no	—
52	C₄×Dic₄₃	—	2	4	no	—
53	C₄×Dic₄₃	SD₁₆	1	4	yes	—
54	C₂×C₄₃⋊C₈	—	2	2	no	—
55	C₂×C₄₃⋊C₈	—	2	4	no	—
56	C₂×C₄₃⋊C₈	—	4	2	no	—
57	C₂×C₄₃⋊C₈	—	4	2	no	—
58	C₂×C₄₃⋊C₈	C₄²	1	2	yes	—
59	C₂×C₄₃⋊C₈	C₄²	1	2	yes	—
60	C₂×C₄₃⋊C₈	M₁₆	1	4	yes	—
61	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₄×C₄₃	—	2	2	no	—
63	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
64	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
65	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
66	C₂×C₄×C₄₃	C₄×Q₈	1	2	yes	—
67	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
68	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
69	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
70	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
71	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
72	C₂×Dic₄₃	—	2	2	no	—
73	C₂×Dic₄₃	—	2	2	no	—
74	C₂×Dic₄₃	—	2	2	no	—
75	C₂×Dic₄₃	—	2	2	no	—
76	C₂×Dic₄₃	#106	1	4	yes	—
77	C₂×Dic₄₃	#108	1	4	yes	—
78	C₈×C₄₃	—	2	4	no	—
79	C₈×C₄₃	—	4	4	no	—
80	C₄₃⋊C₈	—	2	2	no	—
81	C₄₃⋊C₈	—	4	4	no	—
82	C₄₃⋊C₈	#97	1	4	yes	complemented
83	#8273	—	43	1	no	maximal, Sylow
84	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄₃	#423	1	2	yes	—
86	C₂²×C₄₃	C₂×#106	1	1	yes	characteristic
87	C₂²×C₄₃	#427	1	1	yes	characteristic
88	C₂²×C₄₃	C₂×#108	1	2	yes	—
89	C₄×C₄₃	—	2	2	no	—
90	C₄×C₄₃	C₂×#97	1	1	yes	characteristic
91	C₄×C₄₃	C₄×M₁₆	1	1	yes	characteristic
92	C₄×C₄₃	#432	1	2	yes	—
93	C₄×C₄₃	C₄×SD₁₆	1	2	yes	—
94	C₄×C₄₃	C₄×SD₁₆	1	2	yes	—
95	Dic₄₃	—	2	4	no	—
96	Dic₄₃	—	2	4	no	—
97	#1767	—	43	2	no	—
98	C₄²×C₈	—	43	1	no	—
99	C₂×#334	—	43	2	no	—
100	#1277	—	43	1	no	—
101	#1277	D₄₃	1	1	yes	characteristic
102	C₂×C₄₃	#1566	1	2	yes	—
103	C₂×C₄₃	#1568	1	2	yes	—
104	C₂×C₄₃	#1767	1	1	yes	characteristic
105	C₂×C₄₃	C₄×#106	1	1	yes	characteristic
106	C₂×C₄₃	C₄×#108	1	1	yes	characteristic
107	C₂×C₄⋊C₈	—	43	2	no	—
108	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
109	C₂×#97	—	86	2	no	—
110	C₂×C₄×C₈	—	43	1	no	—
111	C₂×C₄×C₈	—	43	2	no	—
112	C₂×C₄×C₈	—	43	2	no	—
113	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
114	C₄³	—	43	1	no	—
115	#336	—	86	2	no	—
116	#334	—	43	8	no	—
117	C₄₃	#8273	1	1	yes	characteristic, complemented, Sylow
118	C₂²×C₈	—	2	2	no	—
119	C₂²×C₈	—	43	1	no	—
120	C₂²×C₈	—	43	1	no	—
121	C₂²×C₈	—	86	2	no	—
122	C₂²×C₈	C₄×D₄₃	1	2	yes	—
123	C₂×C₄²	—	43	1	no	—
124	C₂×C₄²	—	43	2	no	—
125	C₂×C₄²	—	43	1	no	—
126	C₂×C₄²	—	43	2	no	—
127	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
128	C₄⋊C₈	—	2	2	no	—
129	C₄⋊C₈	—	43	4	no	—
130	C₄⋊C₈	—	86	2	no	—
131	C₄⋊C₈	C₄×D₄₃	1	4	yes	—
132	#97	—	172	4	no	—
133	C₄×C₈	—	2	2	no	—
134	C₄×C₈	—	43	4	no	—
135	C₄×C₈	—	86	4	no	—
136	C₄×C₈	—	86	4	no	—
137	C₂²×C₄	—	43	2	no	—
138	C₂²×C₄	—	43	2	no	—
139	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
140	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
141	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
142	C₂×C₈	—	2	2	no	—
143	C₂×C₈	—	2	2	no	—
144	C₂×C₈	—	2	4	no	—
145	C₂×C₈	—	4	2	no	—
146	C₂×C₈	—	4	2	no	—
147	C₂×C₈	—	43	2	no	—
148	C₂×C₈	—	43	4	no	—
149	C₂×C₈	—	43	2	no	—
150	C₂×C₈	—	86	2	no	—
151	C₂×C₈	—	86	4	no	—
152	C₂×C₈	—	172	2	no	—
153	C₂×C₈	—	172	2	no	—
154	C₂×C₈	#10621872	1	4	yes	—
155	C₄²	—	43	4	no	—
156	C₄²	—	86	4	no	—
157	C₄²	—	86	2	no	—
158	C₄²	—	86	2	no	—
159	C₄²	—	86	1	no	—
160	C₄²	—	86	1	no	—
161	C₄²	C₂×C₄×D₄₃	1	2	yes	—
162	C₄²	#10621900	1	2	yes	—
163	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	43	4	no	—
166	C₂×C₄	—	43	4	no	—
167	C₂×C₄	—	86	2	no	—
168	C₂×C₄	—	86	2	no	—
169	C₂×C₄	—	86	2	no	—
170	C₂×C₄	—	86	2	no	—
171	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
172	C₂×C₄	#13063281	1	1	yes	characteristic
173	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
174	C₂×C₄	#13063290	1	2	yes	—
175	C₂×C₄	M₁₆×D₄₃	1	2	yes	—
176	C₂×C₄	C₂×#10621872	1	2	yes	—
177	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
178	C₂×C₄	#13063344	1	1	yes	characteristic
179	C₂×C₄	#13063348	1	1	yes	characteristic
180	C₈	—	2	4	no	—
181	C₈	—	4	4	no	—
182	C₈	—	43	4	no	—
183	C₈	—	86	2	no	—
184	C₈	—	172	4	no	—
185	C₂²	#14582750	1	1	yes	characteristic
186	C₂²	#14582921	1	2	yes	—
187	C₂²	#106×D₄₃	1	1	yes	characteristic
188	C₂²	#14582936	1	1	yes	characteristic
189	C₂²	#108×D₄₃	1	2	yes	—
190	C₄	—	2	2	no	—
191	C₄	—	86	4	no	—
192	C₄	—	86	4	no	—
193	C₄	#97×D₄₃	1	1	yes	characteristic
194	C₄	C₄×#10621872	1	1	yes	characteristic
195	C₄	#14582953	1	2	yes	—
196	C₄	#14582984	1	2	yes	—
197	C₄	#14582990	1	2	yes	—
198	C₂	#19133349	1	2	yes	—
199	C₂	#19133357	1	2	yes	—
200	C₂	#19134447	1	1	yes	characteristic
201	C₂	#19134483	1	1	yes	characteristic
202	C₂	#19134496	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1277	C₂
socle, prime radical	C₂³×C₄₃	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1277	D₄₃
hypocenter	C₄₃	#8273
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

Complements

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

N	H ≅ G/N	type
13. #14582649	C₄	semidirect
82. C₄₃⋊C₈	#97	semidirect
117. C₄₃	#8273	semidirect

Maximal subgroups

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

subgroup	index
#19134450	2
C₄×C₈×Dic₄₃	2
C₂×#14582649	2
#19132430	2
C₄₃×#1277	2
#8273	43