Subgroups — C₂×#27134364 #37589903

Order 24608.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₇₆₉	C₂	1	1	yes	maximal, characteristic
2	#27134364	C₂	1	4	yes	maximal, direct product factor
3	C₂×#20259670	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×C₇₆₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₇₆₉	C₄	1	1	yes	characteristic
6	C₂×Dic₇₆₉	C₄	1	1	yes	characteristic
7	C₄×D₇₆₉	C₄	1	2	yes	—
8	C₄×D₇₆₉	C₂²	1	2	yes	—
9	#20259670	C₂²	1	2	yes	complemented
10	C₂×C₄×C₇₆₉	C₂²	1	1	yes	characteristic
11	C₈×C₇₆₉	C₂²	1	2	yes	complemented
12	C₂²×C₇₆₉	C₂×C₄	1	1	yes	characteristic
13	C₂×D₇₆₉	—	2	2	no	—
14	C₂×D₇₆₉	C₂×C₄	1	2	yes	—
15	C₄×C₇₆₉	C₂×C₄	1	1	yes	characteristic
16	C₄×C₇₆₉	C₂³	1	1	yes	characteristic
17	Dic₇₆₉	C₂×C₄	1	2	yes	—
18	C₂×C₇₆₉	M₁₆	1	2	yes	complemented
19	C₂×C₇₆₉	C₂²×C₄	1	1	yes	characteristic
20	D₇₆₉	—	2	2	no	—
21	C₇₆₉	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₂×M₁₆	—	769	1	no	maximal, Sylow
23	C₂²×C₄	—	769	1	no	—
24	M₁₆	—	769	4	no	—
25	C₂×C₈	—	769	1	no	—
26	C₂×C₈	D₇₆₉	1	1	yes	characteristic, complemented
27	C₂³	—	769	1	no	—
28	C₂×C₄	—	769	1	no	—
29	C₂×C₄	—	769	2	no	—
30	C₂×C₄	—	769	2	no	—
31	C₂×C₄	C₂×D₇₆₉	1	1	yes	characteristic
32	C₈	—	769	2	no	—
33	C₈	C₂×D₇₆₉	1	2	yes	complemented
34	C₂²	—	769	2	no	—
35	C₂²	—	1538	2	no	—
36	C₂²	C₄×D₇₆₉	1	1	yes	characteristic
37	C₄	—	769	2	no	—
38	C₄	C₄×D₇₆₉	1	1	yes	characteristic
39	C₄	C₂²×D₇₆₉	1	1	yes	characteristic
40	C₂	—	1538	2	no	—
41	C₂	#27134364	1	2	yes	direct product factor
42	C₂	C₂×C₄×D₇₆₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₇₆₉
commutator	C₂×C₇₆₉	C₂²×C₄
Frattini	C₄	C₂²×D₇₆₉
Fitting	C₂×C₈×C₇₆₉	C₂
socle	C₂²×C₇₆₉	C₂×C₄
prime radical	C₂²×D₇₆₉	C₄
cosocle	C₄×C₇₆₉	C₂³
hypercenter	C₂×C₈	D₇₆₉
hypocenter	C₇₆₉	C₂×M₁₆
LCS	G ▷ C₂×C₇₆₉ ▷ C₇₆₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #27134364	C₂	direct (N × H)
3. C₂×#20259670	C₂	semidirect
4. C₂×C₈×C₇₆₉	C₂	semidirect
9. #20259670	C₂²	semidirect
11. C₈×C₇₆₉	C₂²	semidirect
18. C₂×C₇₆₉	M₁₆	semidirect
21. C₇₆₉	C₂×M₁₆	semidirect
26. C₂×C₈	D₇₆₉	semidirect
33. C₈	C₂×D₇₆₉	semidirect
41. C₂	#27134364	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×D₇₆₉	2
#27134364	2
C₂×#20259670	2
C₂×C₈×C₇₆₉	2
C₂×M₁₆	769

Subgroups — C2×#27134364 #37589903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27134364 #37589903