Subgroups — C₂×#23754579 #34089656

Order 19744.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₆₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₆₁₇	C₂	1	1	yes	maximal, characteristic
3	#23754579	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₆₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₆₁₇	—	2	2	no	—
6	C₂×Dic₆₁₇	C₄	1	4	yes	complemented
7	C₂×Dic₆₁₇	C₂²	1	2	yes	—
8	C₂×Dic₆₁₇	C₂²	1	2	yes	—
9	C₂³×C₆₁₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₆₁₇	—	2	2	no	—
11	C₂×C₄×C₆₁₇	C₂²	1	2	yes	—
12	C₂²×C₆₁₇	C₂×C₄	1	2	yes	—
13	C₂²×C₆₁₇	D₄	1	2	yes	—
14	C₂²×C₆₁₇	Q₈	1	2	yes	—
15	C₂²×C₆₁₇	C₂³	1	1	yes	characteristic
16	C₄×C₆₁₇	—	2	2	no	—
17	Dic₆₁₇	—	2	2	no	—
18	Dic₆₁₇	C₂×C₄	1	4	yes	complemented
19	C₂×C₆₁₇	C₄⋊C₄	1	4	yes	complemented
20	C₂×C₆₁₇	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₆₁₇	C₂×D₄	1	1	yes	characteristic
22	C₂×C₆₁₇	C₂×Q₈	1	1	yes	characteristic
23	C₆₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₄⋊C₄	—	617	1	no	maximal, Sylow
25	C₂²×C₄	—	617	1	no	—
26	C₂²×C₄	—	617	1	no	—
27	C₂²×C₄	D₆₁₇	1	1	yes	characteristic
28	C₄⋊C₄	—	617	4	no	—
29	C₂³	C₂×D₆₁₇	1	1	yes	characteristic
30	C₂×C₄	—	2	2	no	—
31	C₂×C₄	—	617	4	no	—
32	C₂×C₄	—	617	2	no	—
33	C₂×C₄	—	617	2	no	—
34	C₂×C₄	—	1234	2	no	—
35	C₂×C₄	C₂×D₆₁₇	1	2	yes	—
36	C₂²	C₄×D₆₁₇	1	2	yes	—
37	C₂²	C₂²⋊D₆₁₇	1	2	yes	—
38	C₂²	Dic₁₂₃₄	1	2	yes	—
39	C₂²	C₂²×D₆₁₇	1	1	yes	characteristic
40	C₄	—	2	2	no	—
41	C₄	—	617	4	no	—
42	C₄	—	1234	2	no	—
43	C₂	#23754579	1	4	yes	direct product factor
44	C₂	C₂×C₄×D₆₁₇	1	1	yes	characteristic
45	C₂	C₂×C₂²⋊D₆₁₇	1	1	yes	characteristic
46	C₂	C₂×Dic₁₂₃₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₆₁₇
commutator	C₂×C₆₁₇	C₂²×C₄
Frattini	C₂²	C₂²×D₆₁₇
Fitting	C₂²×C₄×C₆₁₇	C₂
socle, prime radical	C₂³×C₆₁₇	C₂²
cosocle	C₂²×C₆₁₇	C₂³
hypercenter	C₂²×C₄	D₆₁₇
hypocenter	C₆₁₇	C₂×C₄⋊C₄
LCS	G ▷ C₂×C₆₁₇ ▷ C₆₁₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
3. #23754579	C₂	direct (N × H)
6. C₂×Dic₆₁₇	C₄	semidirect
18. Dic₆₁₇	C₂×C₄	semidirect
19. C₂×C₆₁₇	C₄⋊C₄	semidirect
23. C₆₁₇	C₂×C₄⋊C₄	semidirect
43. C₂	#23754579	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₆₁₇	2
#23754579	2
C₂²×C₄×C₆₁₇	2
C₂×C₄⋊C₄	617

Subgroups — C2×#23754579 #34089656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23754579 #34089656