Subgroups — #14582959

Order 2752.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063282	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₂×D₄₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
4	(C₂×D₄₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
5	#13063235	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₄²×C₄₃	C₂²	1	1	yes	characteristic
12	(C₂×D₄₃)⋊C₄	C₄	1	1	yes	characteristic
13	(C₂×D₄₃)⋊C₄	C₄	1	1	yes	characteristic
14	Dic₄₃⋊C₄	C₄	1	1	yes	characteristic
15	Dic₄₃⋊C₄	C₄	1	1	yes	characteristic
16	C₄×Dic₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×D₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
23	C₂×Dic₄₃	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₄₃	C₂×C₄	1	1	yes	characteristic
25	C₂×Dic₄₃	C₂×C₄	1	1	yes	characteristic
26	C₄×D₄₃	—	2	1	no	—
27	C₄×D₄₃	—	2	1	no	—
28	C₈×C₄₃	—	2	1	no	—
29	C₈×C₄₃	—	2	1	no	—
30	C₄₃⋊C₈	—	2	1	no	—
31	C₄₃⋊C₈	—	2	1	no	—
32	C₂²×C₄₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×D₄₃	—	2	1	no	—
34	C₂×D₄₃	—	2	1	no	—
35	C₂×D₄₃	—	2	1	no	—
36	C₄×C₄₃	—	2	1	no	—
37	C₄×C₄₃	—	2	1	no	—
38	C₄×C₄₃	#41	1	1	yes	characteristic
39	C₄×C₄₃	#41	1	1	yes	characteristic
40	Dic₄₃	—	2	1	no	—
41	Dic₄₃	—	2	1	no	—
42	Dic₄₃	—	2	1	no	—
43	C₂×C₄₃	#117	1	1	yes	characteristic
44	C₂×C₄₃	#131	1	1	yes	characteristic
45	C₂×C₄₃	#131	1	1	yes	characteristic
46	D₄₃	—	4	1	no	—
47	#433	—	43	1	no	maximal, Sylow
48	C₄₃	#433	1	1	yes	characteristic, complemented, Sylow
49	#117	—	43	1	no	—
50	C₄⋊C₈	—	43	1	no	—
51	C₄⋊C₈	D₄₃	1	1	yes	characteristic, complemented
52	C₂²⋊C₈	—	43	1	no	—
53	C₂²⋊C₈	—	43	1	no	—
54	#97	—	43	1	no	—
55	C₄×C₈	—	43	1	no	—
56	C₂²×C₄	—	43	1	no	—
57	C₂×C₈	—	43	1	no	—
58	C₂×C₈	—	43	1	no	—
59	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
60	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
61	C₄⋊C₄	—	43	1	no	—
62	C₄⋊C₄	—	43	1	no	—
63	C₂²⋊C₄	—	43	1	no	—
64	C₂²⋊C₄	—	43	1	no	—
65	C₄²	—	43	1	no	—
66	C₄²	C₂×D₄₃	1	1	yes	characteristic
67	C₂³	—	43	1	no	—
68	C₂×C₄	—	43	1	no	—
69	C₂×C₄	—	43	1	no	—
70	C₂×C₄	—	43	1	no	—
71	C₂×C₄	—	86	1	no	—
72	C₂×C₄	—	86	1	no	—
73	C₂×C₄	C₄×D₄₃	1	1	yes	characteristic
74	C₂×C₄	C₄×D₄₃	1	1	yes	characteristic
75	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
76	C₈	—	2	1	no	—
77	C₈	—	2	1	no	—
78	C₈	—	86	1	no	—
79	C₈	—	86	1	no	—
80	C₂²	—	86	1	no	—
81	C₂²	—	86	1	no	—
82	C₂²	—	86	1	no	—
83	C₂²	C₂×C₄×D₄₃	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	2	1	no	—
86	C₄	—	86	1	no	—
87	C₄	—	86	1	no	—
88	C₄	—	86	1	no	—
89	C₄	#10621900	1	1	yes	characteristic
90	C₄	#10621902	1	1	yes	characteristic
91	C₂	—	172	1	no	—
92	C₂	#13063283	1	1	yes	characteristic
93	C₂	#13063331	1	1	yes	characteristic
94	C₂	#13063333	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₃
commutator, socle	C₂²×C₄₃	C₂²×C₄
Fitting	C₄⋊C₈×C₄₃	C₂
prime radical	C₂²×D₄₃	C₂×C₄
cosocle	C₂×C₄×C₄₃	C₂³
hypercenter	C₄⋊C₈	D₄₃
hypocenter	C₄₃	#433
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₄⋊(C₄₃⋊C₈)	C₂	semidirect
5. #13063235	C₂	semidirect
6. C₈×Dic₄₃	C₂	semidirect
7. C₄⋊C₈×C₄₃	C₂	semidirect
48. C₄₃	#433	semidirect
51. C₄⋊C₈	D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#13063282	2
C₄⋊(C₄₃⋊C₈)	2
(C₂×D₄₃)⋊C₈	2
#13063235	2
C₈×Dic₄₃	2
C₄⋊C₈×C₄₃	2
#433	43