Subgroups — #25062347

Order 11008.

712 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143228	C₂	1	2	yes	maximal
2	#19132898	C₂	1	4	yes	maximal, complemented
3	#19132895	C₂	1	8	yes	maximal, complemented
4	C₄₃×#2920	C₂	1	1	yes	maximal, characteristic
5	#14582956	C₄	1	8	yes	—
6	#14582952	C₂²	1	8	yes	—
7	#14582923	C₄	1	4	yes	—
8	#14582863	C₄	1	4	yes	—
9	C₄×#10621877	C₂²	1	4	yes	—
10	#14582621	C₂²	1	8	yes	complemented
11	#14582620	C₂²	1	4	yes	complemented
12	C₈×C₄₃⋊C₈	C₂²	1	4	yes	complemented
13	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
14	C₄₃×#432	C₄	1	4	yes	—
15	C₄₃×#431	C₂²	1	4	yes	—
16	C₄₃×#423	C₄	1	2	yes	—
17	C₄₃×#407	C₄	1	2	yes	—
18	C₄×M₁₆×C₄₃	C₂²	1	2	yes	—
19	C₂×#10621877	C₂×C₄	1	8	yes	—
20	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	16	yes	—
21	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	16	yes	—
22	#13063236	C₂×C₄	1	8	yes	—
23	C₄×C₄₃⋊C₈	C₂³	1	8	yes	—
24	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
26	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	—
27	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
29	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
32	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
33	C₄⋊C₈×C₄₃	C₂×C₄	1	8	yes	—
34	C₂²⋊C₈×C₄₃	C₂×C₄	1	8	yes	—
35	#97×C₄₃	C₂×C₄	1	4	yes	—
36	C₄×C₈×C₄₃	C₂³	1	4	yes	—
37	C₂⁴×C₄₃	C₄²	1	1	yes	characteristic
38	C₂²×C₄×C₄₃	—	4	4	no	—
39	C₂²×C₄×C₄₃	—	4	2	no	—
40	C₂²×C₄×C₄₃	C₄²	1	1	yes	characteristic
41	C₂²×C₄×C₄₃	C₄²	1	2	yes	—
42	C₂²×C₄×C₄₃	C₄²	1	2	yes	—
43	C₂²×C₄×C₄₃	C₄²	1	4	yes	—
44	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
45	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
46	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
47	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
48	M₁₆×C₄₃	—	4	4	no	—
49	C₂×C₈×C₄₃	C₂²×C₄	1	8	yes	—
50	C₄²×C₄₃	C₄²	1	4	yes	—
51	C₄²×C₄₃	C₄²	1	2	yes	—
52	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
53	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
54	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
55	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
56	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
57	#10621877	—	4	8	no	—
58	C₂×C₄₃⋊C₈	C₂²×C₄	1	16	yes	—
59	C₂³×C₄₃	—	4	2	no	—
60	C₂³×C₄₃	—	4	1	no	—
61	C₂³×C₄₃	C₂×C₄²	1	2	yes	—
62	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
63	C₂×C₄×C₄₃	—	2	4	no	—
64	C₂×C₄×C₄₃	—	2	2	no	—
65	C₂×C₄×C₄₃	—	2	8	no	—
66	C₂×C₄×C₄₃	—	2	4	no	—
67	C₂×C₄×C₄₃	—	4	4	no	—
68	C₂×C₄×C₄₃	—	4	2	no	—
69	C₂×C₄×C₄₃	—	4	2	no	—
70	C₂×C₄×C₄₃	—	4	1	no	—
71	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
72	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
73	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
74	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
75	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
76	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
77	C₈×C₄₃	—	2	8	no	—
78	C₄₃⋊C₈	—	2	16	no	—
79	#17339	—	43	1	no	maximal, Sylow
80	C₂²×C₄₃	—	2	2	no	—
81	C₂²×C₄₃	—	2	4	no	—
82	C₂²×C₄₃	—	2	1	no	—
83	C₂²×C₄₃	—	2	2	no	—
84	C₂²×C₄₃	—	4	4	no	—
85	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
86	C₄×C₄₃	—	2	2	no	—
87	C₄×C₄₃	—	2	4	no	—
88	C₄×C₄₃	—	2	1	no	—
89	C₄×C₄₃	—	2	2	no	—
90	C₄×C₄₃	#568	1	4	yes	—
91	C₄×C₄₃	#568	1	2	yes	—
92	#2920	—	43	2	no	—
93	#2920	D₄₃	1	1	yes	characteristic
94	#1455	—	43	4	no	—
95	#1454	—	43	8	no	—
96	C₂×C₄₃	—	4	1	no	—
97	C₂×C₄₃	—	4	2	no	—
98	C₂×C₄₃	#2873	1	2	yes	—
99	C₂×C₄₃	#2873	1	1	yes	characteristic
100	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
101	#432	—	43	8	no	—
102	#432	Dic₄₃	1	4	yes	—
103	#431	—	43	8	no	—
104	#431	C₂×D₄₃	1	4	yes	—
105	#423	—	43	4	no	—
106	#423	Dic₄₃	1	2	yes	—
107	#407	—	43	4	no	—
108	#407	Dic₄₃	1	2	yes	—
109	C₄×M₁₆	—	43	4	no	—
110	C₄×M₁₆	C₂×D₄₃	1	2	yes	—
111	#322	—	43	4	no	—
112	#322	—	43	8	no	—
113	C₈²	—	43	4	no	—
114	C₄₃	#17339	1	1	yes	characteristic, complemented, Sylow
115	C₂³×C₄	C₄×D₄₃	1	2	yes	—
116	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
117	C₂×M₁₆	—	43	8	no	—
118	C₂×M₁₆	C₂×Dic₄₃	1	4	yes	—
119	C₂×C₄²	C₄×D₄₃	1	2	yes	—
120	C₂×C₄²	C₄×D₄₃	1	4	yes	—
121	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
122	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
123	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
124	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
125	C₄⋊C₈	—	43	16	no	—
126	C₄⋊C₈	C₂×Dic₄₃	1	8	yes	—
127	C₂²⋊C₈	—	43	16	no	—
128	C₂²⋊C₈	C₂×Dic₄₃	1	8	yes	—
129	#97	—	43	8	no	—
130	#97	C₂×Dic₄₃	1	4	yes	—
131	C₄×C₈	—	43	8	no	—
132	C₄×C₈	C₂²×D₄₃	1	4	yes	—
133	C₂⁴	C₄×Dic₄₃	1	1	yes	characteristic
134	C₂²×C₄	—	4	4	no	—
135	C₂²×C₄	—	4	2	no	—
136	C₂²×C₄	C₄×Dic₄₃	1	1	yes	characteristic
137	C₂²×C₄	C₄×Dic₄₃	1	2	yes	—
138	C₂²×C₄	C₄×Dic₄₃	1	2	yes	—
139	C₂²×C₄	C₄×Dic₄₃	1	4	yes	—
140	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
141	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
142	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
143	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
144	M₁₆	—	4	4	no	—
145	M₁₆	—	172	8	no	—
146	C₂×C₈	—	43	16	no	—
147	C₂×C₈	C₂²×Dic₄₃	1	8	yes	—
148	C₄²	C₄×Dic₄₃	1	4	yes	—
149	C₄²	C₄×Dic₄₃	1	2	yes	—
150	C₄²	C₂×C₄×D₄₃	1	2	yes	—
151	C₄²	C₂×C₄×D₄₃	1	4	yes	—
152	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
153	C₄²	C₂²×Dic₄₃	1	2	yes	—
154	C₄²	C₂³×D₄₃	1	1	yes	characteristic
155	C₂³	—	4	2	no	—
156	C₂³	—	4	1	no	—
157	C₂³	C₂×C₄×Dic₄₃	1	2	yes	—
158	C₂³	C₂×C₄×Dic₄₃	1	1	yes	characteristic
159	C₂×C₄	—	2	4	no	—
160	C₂×C₄	—	2	8	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	—	4	4	no	—
164	C₂×C₄	—	4	2	no	—
165	C₂×C₄	—	4	2	no	—
166	C₂×C₄	—	4	1	no	—
167	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
168	C₂×C₄	C₂×C₄×Dic₄₃	1	2	yes	—
169	C₂×C₄	C₂×C₄×Dic₄₃	1	2	yes	—
170	C₂×C₄	C₂×C₄×Dic₄₃	1	4	yes	—
171	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
172	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
173	C₈	—	2	8	no	—
174	C₈	—	86	16	no	—
175	C₂²	—	2	2	no	—
176	C₂²	—	2	4	no	—
177	C₂²	—	2	1	no	—
178	C₂²	—	2	2	no	—
179	C₂²	—	4	4	no	—
180	C₂²	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
181	C₄	—	2	2	no	—
182	C₄	—	2	4	no	—
183	C₄	—	2	1	no	—
184	C₄	—	2	2	no	—
185	C₄	#14583665	1	4	yes	—
186	C₄	#14583666	1	2	yes	—
187	C₂	—	4	1	no	—
188	C₂	—	4	2	no	—
189	C₂	#19143013	1	2	yes	—
190	C₂	#19143014	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂²×C₄²
Fitting	C₄₃×#2920	C₂
prime radical	C₂⁴×C₄₃	C₄²
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#2920	D₄₃
hypocenter	C₄₃	#17339
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
2. #19132898	C₂	semidirect
3. #19132895	C₂	semidirect
10. #14582621	C₂²	semidirect
11. #14582620	C₂²	semidirect
12. C₈×C₄₃⋊C₈	C₂²	semidirect
114. C₄₃	#17339	semidirect

Maximal subgroups

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

subgroup	index
#19143228	2
#19132898	2
#19132895	2
C₄₃×#2920	2
#17339	43