Subgroups — #13063304

Order 1376.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊Dic₄₃	C₂	1	2	yes	maximal
4	C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₄₃⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₂³×C₄₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₄₃	—	2	2	no	—
8	C₂×C₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₄₃	C₂²	1	2	yes	—
11	C₂×Dic₄₃	C₂²	1	2	yes	—
12	Dic₈₆	—	2	2	no	—
13	C₂²×C₄₃	—	2	1	no	—
14	C₂²×C₄₃	—	2	1	no	—
15	C₂²×C₄₃	Q₈	1	2	yes	complemented
16	C₂²×C₄₃	C₂³	1	1	yes	characteristic
17	C₄×C₄₃	—	2	1	no	—
18	C₄×C₄₃	D₄	1	2	yes	—
19	Dic₄₃	—	2	2	no	—
20	Dic₄₃	—	2	2	no	—
21	C₂×C₄₃	—	2	2	no	—
22	C₂×C₄₃	C₂×D₄	1	1	yes	characteristic
23	C₂×C₄₃	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄₃	#41	1	1	yes	characteristic
25	C₄₃	C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
26	C₂²⋊Q₈	—	43	1	no	maximal, Sylow
27	C₂×Q₈	—	43	1	no	—
28	C₂²×C₄	D₄₃	1	1	yes	characteristic
29	C₄⋊C₄	—	43	2	no	—
30	C₄⋊C₄	—	43	1	no	—
31	C₂²⋊C₄	—	43	2	no	—
32	C₂³	C₂×D₄₃	1	1	yes	characteristic
33	Q₈	—	86	2	no	—
34	C₂×C₄	—	2	2	no	—
35	C₂×C₄	—	43	2	no	—
36	C₂×C₄	—	43	2	no	—
37	C₂×C₄	C₂×D₄₃	1	1	yes	characteristic
38	C₂×C₄	C₂×D₄₃	1	1	yes	characteristic
39	C₂²	—	2	1	no	—
40	C₂²	—	2	1	no	—
41	C₂²	Dic₈₆	1	2	yes	complemented
42	C₂²	C₂²×D₄₃	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	86	2	no	—
45	C₄	—	86	2	no	—
46	C₄	C₂²⋊D₄₃	1	2	yes	—
47	C₂	—	2	2	no	—
48	C₂	C₂×Dic₈₆	1	1	yes	characteristic
49	C₂	#10621898	1	1	yes	characteristic
50	C₂	C₂×C₂²⋊D₄₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₄₃
commutator, socle, cosocle	C₂²×C₄₃	C₂³
Fitting	C₂²×C₄×C₄₃	C₂
prime radical	C₂³×C₄₃	C₂²
hypercenter	C₂²×C₄	D₄₃
hypocenter	C₄₃	C₂²⋊Q₈
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₈₆	C₂	semidirect
4. C₄⋊Dic₄₃	C₂	semidirect
5. Dic₄₃⋊C₄	C₂	semidirect
15. C₂²×C₄₃	Q₈	semidirect
25. C₄₃	C₂²⋊Q₈	semidirect
41. C₂²	Dic₈₆	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₄₃	2
C₂×Dic₈₆	2
C₂²⋊Dic₄₃	2
C₄⋊Dic₄₃	2
Dic₄₃⋊C₄	2
C₂²⋊Q₈	43