Subgroups — #44500827

Order 30656.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29506404	C₂	1	2	yes	maximal, complemented
2	Dic₃₈₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#29506327	C₂	1	2	yes	maximal, complemented
4	D₇₆₆₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₆×C₄₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#21440162	—	2	2	no	—
7	Dic₁₉₁₆	C₂²	1	2	yes	—
8	#21440151	—	2	2	no	—
9	D₃₈₃₂	C₂²	1	2	yes	—
10	C₂×C₈×C₄₇₉	C₂²	1	1	yes	characteristic
11	C₁₆×C₄₇₉	C₂²	1	1	yes	characteristic
12	C₁₆×C₄₇₉	C₂²	1	1	yes	characteristic
13	Dic₉₅₈	—	2	2	no	—
14	D₁₉₁₆	—	2	2	no	—
15	C₂²⋊D₄₇₉	—	4	2	no	—
16	C₄×D₄₇₉	—	4	2	no	—
17	C₂×C₄×C₄₇₉	D₄	1	1	yes	characteristic
18	C₈×C₄₇₉	D₄	1	1	yes	characteristic
19	C₈×C₄₇₉	C₂³	1	1	yes	characteristic
20	C₂²×C₄₇₉	D₈	1	1	yes	characteristic
21	C₂×D₄₇₉	—	4	2	no	—
22	C₄×C₄₇₉	D₈	1	1	yes	characteristic
23	C₄×C₄₇₉	C₂×D₄	1	1	yes	characteristic
24	Dic₄₇₉	—	4	2	no	—
25	C₂×C₄₇₉	—	2	1	no	—
26	C₂×C₄₇₉	C₂×D₈	1	1	yes	characteristic
27	D₄₇₉	—	8	2	no	—
28	C₄₇₉	#508	1	1	yes	characteristic, complemented, Sylow
29	#508	—	479	1	no	maximal, Sylow
30	#135	—	479	2	no	—
31	Q₃₂	—	479	1	no	—
32	SD₃₂	—	479	2	no	—
33	D₁₆	—	479	1	no	—
34	C₂×C₁₆	D₄₇₉	1	1	yes	characteristic, complemented
35	#41	—	958	2	no	—
36	Q₁₆	—	479	2	no	—
37	SD₁₆	—	958	2	no	—
38	D₈	—	479	2	no	—
39	C₂×C₈	C₂×D₄₇₉	1	1	yes	characteristic
40	C₁₆	C₂×D₄₇₉	1	1	yes	characteristic
41	C₁₆	C₂×D₄₇₉	1	1	yes	characteristic
42	Q₈	—	958	2	no	—
43	D₄	—	1916	2	no	—
44	D₄	—	958	2	no	—
45	C₂×C₄	—	1916	2	no	—
46	C₂×C₄	D₁₉₁₆	1	1	yes	characteristic
47	C₈	D₁₉₁₆	1	1	yes	characteristic
48	C₈	C₂²×D₄₇₉	1	1	yes	characteristic
49	C₂²	—	1916	2	no	—
50	C₂²	D₃₈₃₂	1	1	yes	characteristic
51	C₄	—	1916	2	no	—
52	C₄	D₃₈₃₂	1	1	yes	characteristic
53	C₄	C₂×D₁₉₁₆	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	3832	2	no	—
56	C₂	C₂×D₃₈₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₃₈₃₂
commutator, cosocle	C₈×C₄₇₉	C₂³
Frattini	C₈	C₂²×D₄₇₉
Fitting	C₂×C₁₆×C₄₇₉	C₂
socle	C₂×C₄₇₉	C₂×D₈
hypercenter	C₂×C₁₆	D₄₇₉
hypocenter	C₄₇₉	#508
LCS	G ▷ C₈×C₄₇₉ ▷ C₄×C₄₇₉ ▷ C₂×C₄₇₉ ▷ C₄₇₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. #29506404	C₂	semidirect
2. Dic₃₈₃₂	C₂	semidirect
3. #29506327	C₂	semidirect
4. D₇₆₆₄	C₂	semidirect
5. C₂×C₁₆×C₄₇₉	C₂	semidirect
28. C₄₇₉	#508	semidirect
34. C₂×C₁₆	D₄₇₉	semidirect

Maximal subgroups

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

subgroup	index
#29506404	2
Dic₃₈₃₂	2
#29506327	2
D₇₆₆₄	2
C₂×C₁₆×C₄₇₉	2
#508	479