Subgroups — #14583272

Order 2752.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10621873	C₂	1	4	yes	maximal, complemented
2	#13063325	C₂	1	1	yes	maximal, characteristic, complemented
3	#13063322	C₂	1	1	yes	maximal, characteristic
4	C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₇₂	—	2	2	no	—
6	C₂×D₁₇₂	C₂²	1	2	yes	—
7	C₂×Dic₈₆	C₂²	1	2	yes	—
8	C₂×C₈×C₄₃	C₂²	1	2	yes	—
9	C₄²×C₄₃	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₄₃	—	2	2	no	—
11	#10621873	—	2	8	no	—
12	C₂²×D₄₃	—	2	2	no	—
13	C₂×C₄×C₄₃	D₄	1	2	yes	—
14	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
15	C₂×Dic₄₃	—	2	2	no	—
16	D₁₇₂	—	2	4	no	—
17	D₁₇₂	—	4	4	no	—
18	Dic₈₆	—	2	4	no	—
19	C₈×C₄₃	D₄	1	4	yes	complemented
20	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
21	C₂×D₄₃	—	4	2	no	—
22	C₂×D₄₃	—	4	4	no	—
23	C₄×C₄₃	SD₁₆	1	4	yes	complemented
24	C₄×C₄₃	C₂×D₄	1	2	yes	—
25	Dic₄₃	—	4	2	no	—
26	C₂×C₄₃	#127	1	1	yes	characteristic
27	C₂×C₄₃	C₂×SD₁₆	1	2	yes	—
28	D₄₃	—	8	2	no	—
29	#492	—	43	1	no	maximal, Sylow
30	C₄₃	#492	1	1	yes	characteristic, complemented, Sylow
31	C₂×SD₁₆	—	43	4	no	—
32	C₄⋊Q₈	—	43	1	no	—
33	#127	—	43	1	no	—
34	C₄×C₈	D₄₃	1	1	yes	characteristic, complemented
35	C₂×Q₈	—	43	2	no	—
36	C₂×D₄	—	43	2	no	—
37	C₂×D₄	—	86	2	no	—
38	SD₁₆	—	86	8	no	—
39	C₂×C₈	C₂×D₄₃	1	2	yes	—
40	C₄⋊C₄	—	86	2	no	—
41	C₄²	C₂×D₄₃	1	1	yes	characteristic
42	C₂³	—	86	2	no	—
43	Q₈	—	86	4	no	—
44	D₄	—	86	4	no	—
45	D₄	—	172	4	no	—
46	C₂×C₄	—	86	2	no	—
47	C₂×C₄	D₁₇₂	1	2	yes	—
48	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
49	C₈	D₁₇₂	1	4	yes	complemented
50	C₂²	—	172	2	no	—
51	C₂²	—	172	4	no	—
52	C₂²	C₂×D₁₇₂	1	1	yes	characteristic
53	C₄	—	172	2	no	—
54	C₄	#10621873	1	4	yes	complemented
55	C₄	C₂×D₁₇₂	1	2	yes	—
56	C₂	—	344	2	no	—
57	C₂	#13063322	1	1	yes	characteristic
58	C₂	C₂×#10621873	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₇₂
commutator, cosocle	C₂×C₄×C₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	C₄×C₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₄
prime radical	#13063322	C₂
hypercenter	C₄×C₈	D₄₃
hypocenter	C₄₃	#492
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#10621873	C₂	semidirect
2. #13063325	C₂	semidirect
4. C₄×C₈×C₄₃	C₂	semidirect
19. C₈×C₄₃	D₄	semidirect
23. C₄×C₄₃	SD₁₆	semidirect
30. C₄₃	#492	semidirect
34. C₄×C₈	D₄₃	semidirect
49. C₈	D₁₇₂	semidirect
54. C₄	#10621873	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10621873	2
#13063325	2
#13063322	2
C₄×C₈×C₄₃	2
#492	43