Subgroups — D₆₁₇⋊M₁₆ #34089787

Order 19744.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23754610	C₂	1	2	yes	maximal, complemented
2	#23754609	C₂	1	2	yes	maximal, complemented
3	#23754608	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₆₁₇	C₂	1	1	yes	maximal, characteristic
5	#19096928	C₂²	1	4	yes	complemented
6	C₂²×D₆₁₇	C₄	1	1	yes	characteristic
7	C₂×Dic₆₁₇	C₂²	1	1	yes	characteristic
8	C₄×D₆₁₇	C₄	1	1	yes	characteristic
9	C₄×D₆₁₇	C₄	1	1	yes	characteristic
10	C₄×D₆₁₇	C₂²	1	1	yes	characteristic
11	C₄×D₆₁₇	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₆₁₇	C₄	1	1	yes	characteristic
13	C₂²×C₆₁₇	C₂×C₄	1	1	yes	characteristic
14	C₂×D₆₁₇	—	2	2	no	—
15	C₂×D₆₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂×D₆₁₇	C₂×C₄	1	1	yes	characteristic
17	C₄×C₆₁₇	C₂×C₄	1	1	yes	characteristic
18	C₄×C₆₁₇	C₂×C₄	1	1	yes	characteristic
19	Dic₆₁₇	C₂×C₄	1	1	yes	characteristic
20	Dic₆₁₇	C₂³	1	1	yes	characteristic
21	C₂×C₆₁₇	—	2	1	no	—
22	C₂×C₆₁₇	C₂²×C₄	1	1	yes	characteristic
23	D₆₁₇	—	2	1	no	—
24	D₆₁₇	M₁₆	1	2	yes	complemented
25	C₆₁₇	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	—	617	1	no	maximal, Sylow
27	C₂²×C₄	—	617	1	no	—
28	M₁₆	—	617	2	no	—
29	M₁₆	—	617	2	no	—
30	C₂×C₈	—	617	2	no	—
31	C₂³	—	617	1	no	—
32	C₂×C₄	—	617	1	no	—
33	C₂×C₄	—	617	1	no	—
34	C₂×C₄	—	617	1	no	—
35	C₂×C₄	—	617	1	no	—
36	C₂×C₄	—	617	1	no	—
37	C₂×C₄	#14578674	1	1	yes	characteristic
38	C₈	—	617	4	no	—
39	C₂²	—	617	1	no	—
40	C₂²	—	617	1	no	—
41	C₂²	—	1234	2	no	—
42	C₂²	C₂×#14578674	1	1	yes	characteristic
43	C₄	—	617	1	no	—
44	C₄	—	617	1	no	—
45	C₄	C₂×#14578674	1	1	yes	characteristic
46	C₄	C₂×#14578674	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	—	617	2	no	—
49	C₂	—	1234	1	no	—
50	C₂	C₂²×#14578674	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#14578674
commutator, socle	C₂×C₆₁₇	C₂²×C₄
Frattini	C₂	C₂²×#14578674
Fitting	C₂×C₄×C₆₁₇	C₄
prime radical	C₂²×D₆₁₇	C₄
cosocle	Dic₆₁₇	C₂³
hypercenter	C₂×C₄	#14578674
hypocenter	C₆₁₇	C₂×M₁₆
LCS	G ▷ C₂×C₆₁₇ ▷ C₆₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #23754610	C₂	semidirect
2. #23754609	C₂	semidirect
3. #23754608	C₂	semidirect
5. #19096928	C₂²	semidirect
24. D₆₁₇	M₁₆	semidirect
25. C₆₁₇	C₂×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
#23754610	2
#23754609	2
#23754608	2
C₂×C₄×D₆₁₇	2
C₂×M₁₆	617

Subgroups — D617⋊M16 #34089787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₁₇⋊M₁₆ #34089787