Subgroups — SD₁₆×D₇₇₃ #37613002

Order 24736.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₇₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₇₇₃	C₂	1	1	yes	maximal, characteristic
3	#27136468	C₂	1	1	yes	maximal, characteristic, complemented
4	#27136467	C₂	1	1	yes	maximal, characteristic, complemented
5	#27136466	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×D₇₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆×C₇₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₇₇₃	—	2	1	no	—
9	Dic₁₅₄₆	—	2	1	no	—
10	Dic₁₅₄₆	C₂²	1	1	yes	characteristic, complemented
11	D₃₀₉₂	C₂²	1	1	yes	characteristic
12	C₂²⋊D₇₇₃	—	2	1	no	—
13	C₄×D₇₇₃	—	2	1	no	—
14	C₄×D₇₇₃	C₂²	1	1	yes	characteristic
15	#20260070	C₂²	1	1	yes	characteristic, complemented
16	Q₈×C₇₇₃	C₂²	1	1	yes	characteristic, complemented
17	D₄×C₇₇₃	C₂²	1	1	yes	characteristic
18	C₈×C₇₇₃	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₇₇₃	—	2	1	no	—
20	C₂×D₇₇₃	—	2	1	no	—
21	C₂×D₇₇₃	—	4	2	no	—
22	C₂×D₇₇₃	D₄	1	1	yes	characteristic
23	C₄×C₇₇₃	—	2	1	no	—
24	C₄×C₇₇₃	C₂³	1	1	yes	characteristic
25	Dic₇₇₃	—	2	1	no	—
26	Dic₇₇₃	D₄	1	1	yes	characteristic
27	C₂×C₇₇₃	—	4	1	no	—
28	C₂×C₇₇₃	C₂×D₄	1	1	yes	characteristic
29	D₇₇₃	—	4	1	no	—
30	D₇₇₃	SD₁₆	1	2	yes	direct product factor
31	C₇₇₃	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
32	C₂×SD₁₆	—	773	1	no	maximal, Sylow
33	C₂×Q₈	—	773	1	no	—
34	C₂×D₄	—	773	1	no	—
35	SD₁₆	—	773	1	no	—
36	SD₁₆	—	773	1	no	—
37	SD₁₆	—	773	1	no	—
38	SD₁₆	D₇₇₃	1	1	yes	characteristic, direct product factor
39	C₂×C₈	—	773	1	no	—
40	C₂³	—	1546	1	no	—
41	Q₈	—	773	1	no	—
42	Q₈	—	1546	1	no	—
43	Q₈	C₂×D₇₇₃	1	1	yes	characteristic, complemented
44	D₄	—	773	1	no	—
45	D₄	—	1546	1	no	—
46	D₄	C₂×D₇₇₃	1	1	yes	characteristic
47	C₂×C₄	—	773	1	no	—
48	C₂×C₄	—	1546	1	no	—
49	C₈	—	773	1	no	—
50	C₈	C₂×D₇₇₃	1	1	yes	characteristic, complemented
51	C₂²	—	2	1	no	—
52	C₂²	—	773	1	no	—
53	C₂²	—	1546	1	no	—
54	C₂²	—	3092	2	no	—
55	C₄	—	2	1	no	—
56	C₄	—	773	1	no	—
57	C₄	—	1546	1	no	—
58	C₄	C₂²×D₇₇₃	1	1	yes	characteristic
59	C₂	—	4	1	no	—
60	C₂	—	773	2	no	—
61	C₂	—	3092	1	no	—
62	C₂	D₄×D₇₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₇₇₃
commutator, cosocle	C₄×C₇₇₃	C₂³
Frattini	C₄	C₂²×D₇₇₃
Fitting	SD₁₆×C₇₇₃	C₂
socle	C₂×C₇₇₃	C₂×D₄
prime radical	D₄×D₇₇₃	C₂
hypercenter	SD₁₆	D₇₇₃
hypocenter	C₇₇₃	C₂×SD₁₆
LCS	G ▷ C₄×C₇₇₃ ▷ C₂×C₇₇₃ ▷ C₇₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
1. Q₈×D₇₇₃	C₂	semidirect
3. #27136468	C₂	semidirect
4. #27136467	C₂	semidirect
5. #27136466	C₂	semidirect
6. C₈×D₇₇₃	C₂	semidirect
7. SD₁₆×C₇₇₃	C₂	semidirect
10. Dic₁₅₄₆	C₂²	semidirect
15. #20260070	C₂²	semidirect
16. Q₈×C₇₇₃	C₂²	semidirect
18. C₈×C₇₇₃	C₂²	semidirect
30. D₇₇₃	SD₁₆	direct (N × H)
31. C₇₇₃	C₂×SD₁₆	semidirect
38. SD₁₆	D₇₇₃	direct (N × H)
43. Q₈	C₂×D₇₇₃	semidirect
50. C₈	C₂×D₇₇₃	semidirect

Maximal subgroups

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

subgroup	index
Q₈×D₇₇₃	2
D₄×D₇₇₃	2
#27136468	2
#27136467	2
#27136466	2
C₈×D₇₇₃	2
SD₁₆×C₇₇₃	2
C₂×SD₁₆	773

Subgroups — SD16×D773 #37613002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆×D₇₇₃ #37613002