Subgroups — #20263984

Order 6368.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15691885	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₇₉₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#15691876	C₂	1	1	yes	maximal, characteristic, complemented
5	#15691874	C₂	1	1	yes	maximal, characteristic, complemented
6	#15691869	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆×C₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₃₉₈	—	2	1	no	—
9	Dic₃₉₈	C₂²	1	1	yes	characteristic
10	Dic₃₉₈	C₂²	1	1	yes	characteristic
11	C₂²⋊D₁₉₉	—	2	1	no	—
12	C₂×Dic₁₉₉	—	2	1	no	—
13	C₄×D₁₉₉	—	2	1	no	—
14	C₄×D₁₉₉	C₂²	1	1	yes	characteristic
15	C₁₉₉⋊C₈	C₂²	1	1	yes	characteristic
16	Q₈×C₁₉₉	C₂²	1	1	yes	characteristic
17	D₄×C₁₉₉	C₂²	1	1	yes	characteristic
18	C₈×C₁₉₉	C₂²	1	1	yes	characteristic
19	C₂²×C₁₉₉	—	2	1	no	—
20	C₂×D₁₉₉	D₄	1	1	yes	characteristic
21	C₄×C₁₉₉	—	2	1	no	—
22	C₄×C₁₉₉	C₂³	1	1	yes	characteristic
23	Dic₁₉₉	—	2	1	no	—
24	Dic₁₉₉	—	2	1	no	—
25	Dic₁₉₉	D₄	1	1	yes	characteristic
26	C₂×C₁₉₉	—	4	1	no	—
27	C₂×C₁₉₉	C₂×D₄	1	1	yes	characteristic
28	D₁₉₉	—	2	1	no	—
29	C₁₉₉	#137	1	1	yes	characteristic, complemented, Sylow
30	#137	—	199	1	no	maximal, Sylow
31	#41	—	199	1	no	—
32	C₂×Q₈	—	199	1	no	—
33	Q₁₆	—	199	1	no	—
34	Q₁₆	—	199	1	no	—
35	SD₁₆	—	199	1	no	—
36	SD₁₆	D₁₉₉	1	1	yes	characteristic, complemented
37	M₁₆	—	199	1	no	—
38	Q₈	—	398	1	no	—
39	Q₈	—	199	1	no	—
40	Q₈	—	199	1	no	—
41	Q₈	C₂×D₁₉₉	1	1	yes	characteristic
42	D₄	—	398	1	no	—
43	D₄	C₂×D₁₉₉	1	1	yes	characteristic
44	C₂×C₄	—	398	1	no	—
45	C₂×C₄	—	398	1	no	—
46	C₂×C₄	—	199	1	no	—
47	C₈	—	199	1	no	—
48	C₈	C₂×D₁₉₉	1	1	yes	characteristic
49	C₂²	—	2	1	no	—
50	C₂²	—	199	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	398	1	no	—
53	C₄	—	398	1	no	—
54	C₄	—	199	1	no	—
55	C₄	C₂²×D₁₉₉	1	1	yes	characteristic
56	C₂	—	4	1	no	—
57	C₂	—	398	1	no	—
58	C₂	D₄×D₁₉₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₁₉₉
commutator	C₄×C₁₉₉	C₂³
Frattini	C₄	C₂²×D₁₉₉
Fitting	SD₁₆×C₁₉₉	C₂
socle	C₂×C₁₉₉	C₂×D₄
hypercenter	SD₁₆	D₁₉₉
hypocenter	C₁₉₉	#137
LCS	G ▷ C₄×C₁₉₉ ▷ C₂×C₁₉₉ ▷ C₁₉₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×D₁₉₉	C₂	semidirect
3. Dic₇₉₆	C₂	semidirect
4. #15691876	C₂	semidirect
5. #15691874	C₂	semidirect
6. #15691869	C₂	semidirect
7. SD₁₆×C₁₉₉	C₂	semidirect
29. C₁₉₉	#137	semidirect
36. SD₁₆	D₁₉₉	semidirect