Subgroups — #24983470

Order 11008.

234 conjugacy classes of subgroups.

The subgroup lattice has 166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582675	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582650	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#334	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄₃⋊C₁₆	C₄	1	2	yes	—
5	C₂×C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
6	#14582675	—	2	1	no	—
7	#14582675	—	2	1	no	—
8	#14582650	—	2	1	no	—
9	#14582650	C₄	1	2	yes	—
10	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
11	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₄₃×#334	—	2	1	no	—
13	C₄₃×#334	C₄	1	2	yes	—
14	C₂²×C₄₃⋊C₈	—	4	1	no	—
15	C₂×C₄₃⋊C₁₆	—	2	2	no	—
16	C₂×C₄₃⋊C₁₆	—	2	2	no	—
17	C₂×C₄₃⋊C₁₆	C₈	1	4	yes	complemented
18	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
19	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
20	C₂²×C₈×C₄₃	—	4	1	no	—
21	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₄₃	Q₈	1	1	yes	characteristic
23	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
24	C₄⋊C₈×C₄₃	—	2	2	no	—
25	C₄⋊C₈×C₄₃	—	4	1	no	—
26	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
27	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
29	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
30	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
31	C₂²×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
32	C₂²×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
33	C₂×C₈×C₄₃	—	2	2	no	—
34	C₂×C₈×C₄₃	—	4	2	no	—
35	C₂×C₈×C₄₃	—	8	2	no	—
36	C₂×C₈×C₄₃	C₄²	1	1	yes	characteristic
37	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₄₃	C₂×C₈	1	2	yes	—
41	C₂×C₈×C₄₃	M₁₆	1	2	yes	—
42	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
43	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
44	C₄²×C₄₃	D₈	1	1	yes	characteristic
45	C₄²×C₄₃	Q₁₆	1	1	yes	characteristic
46	C₂×C₄₃⋊C₈	—	4	2	no	—
47	C₂×C₄₃⋊C₈	—	8	2	no	—
48	C₄₃⋊C₁₆	—	2	4	no	—
49	C₂³×C₄₃	#106	1	1	yes	characteristic
50	C₂×C₄×C₄₃	—	2	2	no	—
51	C₂×C₄×C₄₃	—	2	2	no	—
52	C₂×C₄×C₄₃	#95	1	1	yes	characteristic
53	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
54	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
55	C₂×C₄×C₄₃	#103	1	1	yes	characteristic
56	C₂×C₄×C₄₃	#103	1	1	yes	characteristic
57	C₂×C₄×C₄₃	C₄⋊C₈	1	2	yes	—
58	C₂×C₄×C₄₃	#107	1	1	yes	characteristic
59	C₂×C₄×C₄₃	#108	1	2	yes	—
60	C₈×C₄₃	—	2	1	no	—
61	C₈×C₄₃	—	2	1	no	—
62	C₈×C₄₃	—	8	2	no	—
63	C₈×C₄₃	C₄×C₈	1	1	yes	characteristic
64	C₈×C₄₃	#97	1	1	yes	characteristic
65	C₈×C₄₃	C₂²⋊C₈	1	2	yes	—
66	C₄₃⋊C₈	—	8	2	no	—
67	#7156	—	43	1	no	maximal, Sylow
68	C₂²×C₄₃	#334	1	2	yes	—
69	C₂²×C₄₃	#340	1	1	yes	characteristic
70	C₂²×C₄₃	#365	1	2	yes	—
71	C₂²×C₄₃	#365	1	2	yes	—
72	C₄×C₄₃	—	2	1	no	—
73	C₄×C₄₃	—	2	1	no	—
74	C₄×C₄₃	—	2	1	no	—
75	C₄×C₄₃	—	2	1	no	—
76	C₄×C₄₃	#335	1	2	yes	—
77	C₄×C₄₃	#336	1	1	yes	characteristic
78	C₄×C₄₃	#341	1	1	yes	characteristic
79	C₂×#346	—	43	1	no	—
80	C₂×#334	—	43	1	no	—
81	C₂×#334	D₄₃	1	1	yes	characteristic
82	C₂×C₄₃	#1277	1	1	yes	characteristic
83	C₂×C₄₃	#1368	1	4	yes	—
84	C₂×C₄₃	#1383	1	1	yes	characteristic
85	C₂×C₄₃	#1383	1	1	yes	characteristic
86	C₂²×C₁₆	—	43	2	no	—
87	C₂×C₄⋊C₈	—	2	1	no	—
88	C₂×C₄⋊C₈	—	86	1	no	—
89	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
90	#346	—	86	1	no	—
91	#346	—	86	1	no	—
92	#334	—	2	1	no	—
93	#334	—	43	2	no	—
94	#334	—	86	1	no	—
95	#334	Dic₄₃	1	2	yes	—
96	C₄₃	#7156	1	1	yes	characteristic, complemented, Sylow
97	C₂²×C₈	—	4	1	no	—
98	C₂²×C₈	—	172	1	no	—
99	C₂²×C₈	Dic₈₆	1	1	yes	characteristic
100	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
101	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
102	C₂×C₁₆	—	43	4	no	—
103	C₂×C₁₆	—	86	2	no	—
104	C₂×C₁₆	—	86	2	no	—
105	C₄⋊C₈	—	2	2	no	—
106	C₄⋊C₈	—	4	1	no	—
107	C₄⋊C₈	—	86	2	no	—
108	C₄⋊C₈	—	172	1	no	—
109	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
110	C₄×C₈	D₁₇₂	1	1	yes	characteristic
111	C₄×C₈	C₂×Dic₄₃	1	1	yes	characteristic
112	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
113	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
114	C₂²×C₄	#10621883	1	1	yes	characteristic
115	C₂²×C₄	#10621884	1	1	yes	characteristic
116	C₂×C₈	—	2	2	no	—
117	C₂×C₈	—	4	2	no	—
118	C₂×C₈	—	8	2	no	—
119	C₂×C₈	—	344	2	no	—
120	C₂×C₈	—	172	2	no	—
121	C₂×C₈	C₈×D₄₃	1	2	yes	—
122	C₂×C₈	#10621872	1	2	yes	—
123	C₂×C₈	C₄×Dic₄₃	1	1	yes	characteristic
124	C₂×C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
125	C₂×C₈	C₄⋊Dic₄₃	1	1	yes	characteristic
126	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
127	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
128	C₄²	#10621882	1	1	yes	characteristic
129	C₄²	#10621885	1	1	yes	characteristic
130	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
131	C₁₆	—	86	4	no	—
132	C₂³	#13063256	1	1	yes	characteristic
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	C₄₃⋊#95	1	1	yes	characteristic
136	C₂×C₄	#13063245	1	1	yes	characteristic
137	C₂×C₄	#13063246	1	1	yes	characteristic
138	C₂×C₄	#13063248	1	1	yes	characteristic
139	C₂×C₄	#13063249	1	1	yes	characteristic
140	C₂×C₄	Dic₄₃⋊C₈	1	2	yes	—
141	C₂×C₄	#13063258	1	1	yes	characteristic
142	C₂×C₄	#13063260	1	2	yes	—
143	C₈	—	2	1	no	—
144	C₈	—	2	1	no	—
145	C₈	—	8	2	no	—
146	C₈	—	344	2	no	—
147	C₈	C₈×Dic₄₃	1	1	yes	characteristic
148	C₈	#13063235	1	1	yes	characteristic
149	C₈	(C₂×D₄₃)⋊C₈	1	2	yes	—
150	C₂²	#14582649	1	2	yes	—
151	C₂²	#14582661	1	1	yes	characteristic
152	C₂²	#14582721	1	2	yes	—
153	C₂²	#14582723	1	2	yes	—
154	C₄	—	2	1	no	—
155	C₄	—	2	1	no	—
156	C₄	—	2	1	no	—
157	C₄	—	2	1	no	—
158	C₄	#14582651	1	2	yes	—
159	C₄	#14582653	1	1	yes	characteristic
160	C₄	#14582663	1	1	yes	characteristic
161	C₂	#19132429	1	1	yes	characteristic
162	C₂	#19132660	1	4	yes	—
163	C₂	#19132693	1	1	yes	characteristic
164	C₂	#19132695	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063256
commutator	C₈×C₄₃	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₄₃
Fitting	C₂×C₄₃×#334	C₂
socle, prime radical	C₂³×C₄₃	#106
cosocle	C₂×C₄×C₈×C₄₃	C₂²
hypercenter	C₂×#334	D₄₃
hypocenter	C₄₃	#7156
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
17. C₂×C₄₃⋊C₁₆	C₈	semidirect
96. C₄₃	#7156	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582675	2
C₂×#14582650	2
C₂×C₄₃×#334	2
#7156	43