Subgroups — SD₁₆×D₉₄₇ #44476262

Order 30304.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₉₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₉₄₇	C₂	1	1	yes	maximal, characteristic
3	#29502974	C₂	1	1	yes	maximal, characteristic, complemented
4	#29502973	C₂	1	1	yes	maximal, characteristic, complemented
5	#29502972	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×D₉₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆×C₉₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₉₄₇	—	2	1	no	—
9	Dic₁₈₉₄	—	2	1	no	—
10	Dic₁₈₉₄	C₂²	1	1	yes	characteristic, complemented
11	D₃₇₈₈	C₂²	1	1	yes	characteristic
12	C₂²⋊D₉₄₇	—	2	1	no	—
13	C₄×D₉₄₇	—	2	1	no	—
14	C₄×D₉₄₇	C₂²	1	1	yes	characteristic
15	C₉₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
16	Q₈×C₉₄₇	C₂²	1	1	yes	characteristic, complemented
17	D₄×C₉₄₇	C₂²	1	1	yes	characteristic
18	C₈×C₉₄₇	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₉₄₇	—	2	1	no	—
20	C₂×D₉₄₇	—	2	1	no	—
21	C₂×D₉₄₇	—	4	2	no	—
22	C₂×D₉₄₇	D₄	1	1	yes	characteristic
23	C₄×C₉₄₇	—	2	1	no	—
24	C₄×C₉₄₇	C₂³	1	1	yes	characteristic
25	Dic₉₄₇	—	2	1	no	—
26	Dic₉₄₇	D₄	1	1	yes	characteristic
27	C₂×C₉₄₇	—	4	1	no	—
28	C₂×C₉₄₇	C₂×D₄	1	1	yes	characteristic
29	D₉₄₇	—	4	1	no	—
30	D₉₄₇	SD₁₆	1	2	yes	direct product factor
31	C₉₄₇	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
32	C₂×SD₁₆	—	947	1	no	maximal, Sylow
33	C₂×Q₈	—	947	1	no	—
34	C₂×D₄	—	947	1	no	—
35	SD₁₆	—	947	1	no	—
36	SD₁₆	—	947	1	no	—
37	SD₁₆	—	947	1	no	—
38	SD₁₆	D₉₄₇	1	1	yes	characteristic, direct product factor
39	C₂×C₈	—	947	1	no	—
40	C₂³	—	1894	1	no	—
41	Q₈	—	1894	1	no	—
42	Q₈	—	947	1	no	—
43	Q₈	C₂×D₉₄₇	1	1	yes	characteristic, complemented
44	D₄	—	1894	1	no	—
45	D₄	—	947	1	no	—
46	D₄	C₂×D₉₄₇	1	1	yes	characteristic
47	C₂×C₄	—	1894	1	no	—
48	C₂×C₄	—	947	1	no	—
49	C₈	—	947	1	no	—
50	C₈	C₂×D₉₄₇	1	1	yes	characteristic, complemented
51	C₂²	—	2	1	no	—
52	C₂²	—	1894	1	no	—
53	C₂²	—	947	1	no	—
54	C₂²	—	3788	2	no	—
55	C₄	—	2	1	no	—
56	C₄	—	1894	1	no	—
57	C₄	—	947	1	no	—
58	C₄	C₂²×D₉₄₇	1	1	yes	characteristic
59	C₂	—	4	1	no	—
60	C₂	—	947	2	no	—
61	C₂	—	3788	1	no	—
62	C₂	D₄×D₉₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₉₄₇
commutator, cosocle	C₄×C₉₄₇	C₂³
Frattini	C₄	C₂²×D₉₄₇
Fitting	SD₁₆×C₉₄₇	C₂
socle	C₂×C₉₄₇	C₂×D₄
prime radical	D₄×D₉₄₇	C₂
hypercenter	SD₁₆	D₉₄₇
hypocenter	C₉₄₇	C₂×SD₁₆
LCS	G ▷ C₄×C₉₄₇ ▷ C₂×C₉₄₇ ▷ C₉₄₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
1. Q₈×D₉₄₇	C₂	semidirect
3. #29502974	C₂	semidirect
4. #29502973	C₂	semidirect
5. #29502972	C₂	semidirect
6. C₈×D₉₄₇	C₂	semidirect
7. SD₁₆×C₉₄₇	C₂	semidirect
10. Dic₁₈₉₄	C₂²	semidirect
15. C₉₄₇⋊C₈	C₂²	semidirect
16. Q₈×C₉₄₇	C₂²	semidirect
18. C₈×C₉₄₇	C₂²	semidirect
30. D₉₄₇	SD₁₆	direct (N × H)
31. C₉₄₇	C₂×SD₁₆	semidirect
38. SD₁₆	D₉₄₇	direct (N × H)
43. Q₈	C₂×D₉₄₇	semidirect
50. C₈	C₂×D₉₄₇	semidirect

Maximal subgroups

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

subgroup	index
Q₈×D₉₄₇	2
D₄×D₉₄₇	2
#29502974	2
#29502973	2
#29502972	2
C₈×D₉₄₇	2
SD₁₆×C₉₄₇	2
C₂×SD₁₆	947

Subgroups — SD16×D947 #44476262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆×D₉₄₇ #44476262