Subgroups — SD₃₂×D₁₉₉ #27164440

Order 12736.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈×D₁₉₉	C₂	1	1	yes	maximal, characteristic
3	#20263900	C₂	1	1	yes	maximal, characteristic, complemented
4	#20263899	C₂	1	1	yes	maximal, characteristic, complemented
5	#20263898	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×D₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₃₂×C₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×D₁₉₉	—	2	1	no	—
9	D₄×D₁₉₉	—	2	1	no	—
10	Dic₇₉₆	C₂²	1	1	yes	characteristic, complemented
11	#15691876	—	2	1	no	—
12	D₁₅₉₂	C₂²	1	1	yes	characteristic
13	#15691871	—	2	1	no	—
14	C₈×D₁₉₉	C₂²	1	1	yes	characteristic
15	C₁₉₉⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
16	Q₁₆×C₁₉₉	C₂²	1	1	yes	characteristic, complemented
17	D₈×C₁₉₉	C₂²	1	1	yes	characteristic
18	C₁₆×C₁₉₉	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₁₉₉	—	4	1	no	—
20	Dic₃₉₈	—	2	1	no	—
21	Dic₃₉₈	—	4	1	no	—
22	D₇₉₆	—	2	1	no	—
23	C₂²⋊D₁₉₉	—	4	1	no	—
24	C₄×D₁₉₉	—	4	1	no	—
25	C₄×D₁₉₉	D₄	1	1	yes	characteristic
26	C₁₉₉⋊C₈	D₄	1	1	yes	characteristic
27	Q₈×C₁₉₉	—	2	1	no	—
28	D₄×C₁₉₉	—	2	1	no	—
29	C₈×C₁₉₉	C₂³	1	1	yes	characteristic
30	C₂²×C₁₉₉	—	4	1	no	—
31	C₂×D₁₉₉	—	4	1	no	—
32	C₂×D₁₉₉	—	8	2	no	—
33	C₂×D₁₉₉	D₈	1	1	yes	characteristic
34	C₄×C₁₉₉	—	4	1	no	—
35	C₄×C₁₉₉	C₂×D₄	1	1	yes	characteristic
36	Dic₁₉₉	—	4	1	no	—
37	Dic₁₉₉	D₈	1	1	yes	characteristic
38	C₂×C₁₉₉	—	8	1	no	—
39	C₂×C₁₉₉	C₂×D₈	1	1	yes	characteristic
40	D₁₉₉	—	8	1	no	—
41	D₁₉₉	SD₃₂	1	2	yes	direct product factor
42	C₁₉₉	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
43	C₂×SD₃₂	—	199	1	no	maximal, Sylow
44	C₂×Q₁₆	—	199	1	no	—
45	C₂×D₈	—	199	1	no	—
46	SD₃₂	—	199	1	no	—
47	SD₃₂	—	199	1	no	—
48	SD₃₂	—	199	1	no	—
49	SD₃₂	D₁₉₉	1	1	yes	characteristic, direct product factor
50	C₂×C₁₆	—	199	1	no	—
51	C₂×Q₈	—	398	1	no	—
52	C₂×D₄	—	398	1	no	—
53	Q₁₆	—	398	1	no	—
54	Q₁₆	—	199	1	no	—
55	Q₁₆	C₂×D₁₉₉	1	1	yes	characteristic, complemented
56	D₈	—	398	1	no	—
57	D₈	—	199	1	no	—
58	D₈	C₂×D₁₉₉	1	1	yes	characteristic
59	C₂×C₈	—	199	1	no	—
60	C₁₆	—	199	1	no	—
61	C₁₆	C₂×D₁₉₉	1	1	yes	characteristic, complemented
62	C₂³	—	796	1	no	—
63	Q₈	—	2	1	no	—
64	Q₈	—	796	1	no	—
65	Q₈	—	398	1	no	—
66	D₄	—	2	1	no	—
67	D₄	—	796	1	no	—
68	D₄	—	398	1	no	—
69	C₂×C₄	—	796	1	no	—
70	C₂×C₄	—	199	1	no	—
71	C₈	—	199	1	no	—
72	C₈	C₂²×D₁₉₉	1	1	yes	characteristic
73	C₂²	—	4	1	no	—
74	C₂²	—	796	1	no	—
75	C₂²	—	1592	2	no	—
76	C₂²	—	199	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	796	1	no	—
79	C₄	—	199	1	no	—
80	C₄	D₄×D₁₉₉	1	1	yes	characteristic
81	C₂	—	8	1	no	—
82	C₂	—	1592	1	no	—
83	C₂	—	199	2	no	—
84	C₂	D₈×D₁₉₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₁₉₉
commutator, cosocle	C₈×C₁₉₉	C₂³
Frattini	C₈	C₂²×D₁₉₉
Fitting	SD₃₂×C₁₉₉	C₂
socle	C₂×C₁₉₉	C₂×D₈
prime radical	D₈×D₁₉₉	C₂
hypercenter	SD₃₂	D₁₉₉
hypocenter	C₁₉₉	C₂×SD₃₂
LCS	G ▷ C₈×C₁₉₉ ▷ C₄×C₁₉₉ ▷ C₂×C₁₉₉ ▷ C₁₉₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ SD₃₂

Complements

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

N	H ≅ G/N	type
1. Q₁₆×D₁₉₉	C₂	semidirect
3. #20263900	C₂	semidirect
4. #20263899	C₂	semidirect
5. #20263898	C₂	semidirect
6. C₁₆×D₁₉₉	C₂	semidirect
7. SD₃₂×C₁₉₉	C₂	semidirect
10. Dic₇₉₆	C₂²	semidirect
15. C₁₉₉⋊C₁₆	C₂²	semidirect
16. Q₁₆×C₁₉₉	C₂²	semidirect
18. C₁₆×C₁₉₉	C₂²	semidirect
41. D₁₉₉	SD₃₂	direct (N × H)
42. C₁₉₉	C₂×SD₃₂	semidirect
49. SD₃₂	D₁₉₉	direct (N × H)
55. Q₁₆	C₂×D₁₉₉	semidirect
61. C₁₆	C₂×D₁₉₉	semidirect

Maximal subgroups

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

subgroup	index
Q₁₆×D₁₉₉	2
D₈×D₁₉₉	2
#20263900	2
#20263899	2
#20263898	2
C₁₆×D₁₉₉	2
SD₃₂×C₁₉₉	2
C₂×SD₃₂	199

Subgroups — SD32×D199 #27164440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₃₂×D₁₉₉ #27164440