Subgroups — D₇₀₉⋊M₁₆ #36383988

Order 22688.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26015403	C₂	1	2	yes	maximal, complemented
2	#26015402	C₂	1	2	yes	maximal, complemented
3	D₇₀₉⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₇₀₉	C₂	1	1	yes	maximal, characteristic
5	#19150893	C₂²	1	4	yes	complemented
6	C₂²×D₇₀₉	C₄	1	1	yes	characteristic
7	C₂×Dic₇₀₉	C₂²	1	1	yes	characteristic
8	C₄×D₇₀₉	C₄	1	1	yes	characteristic
9	C₄×D₇₀₉	C₄	1	1	yes	characteristic
10	C₄×D₇₀₉	C₂²	1	1	yes	characteristic
11	C₄×D₇₀₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₇₀₉	C₄	1	1	yes	characteristic
13	C₂²×C₇₀₉	C₂×C₄	1	1	yes	characteristic
14	C₂×D₇₀₉	—	2	2	no	—
15	C₂×D₇₀₉	C₂×C₄	1	1	yes	characteristic
16	C₂×D₇₀₉	C₂×C₄	1	1	yes	characteristic
17	C₄×C₇₀₉	C₂×C₄	1	1	yes	characteristic
18	C₄×C₇₀₉	C₂×C₄	1	1	yes	characteristic
19	Dic₇₀₉	C₂×C₄	1	1	yes	characteristic
20	Dic₇₀₉	C₂³	1	1	yes	characteristic
21	C₂×C₇₀₉	—	2	1	no	—
22	C₂×C₇₀₉	C₂²×C₄	1	1	yes	characteristic
23	D₇₀₉	—	2	1	no	—
24	D₇₀₉	M₁₆	1	2	yes	complemented
25	C₇₀₉	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	—	709	1	no	maximal, Sylow
27	C₂²×C₄	—	709	1	no	—
28	M₁₆	—	709	2	no	—
29	M₁₆	—	709	2	no	—
30	C₂×C₈	—	709	2	no	—
31	C₂³	—	709	1	no	—
32	C₂×C₄	—	709	1	no	—
33	C₂×C₄	—	709	1	no	—
34	C₂×C₄	—	709	1	no	—
35	C₂×C₄	—	709	1	no	—
36	C₂×C₄	—	709	1	no	—
37	C₂×C₄	#15667778	1	1	yes	characteristic
38	C₈	—	709	4	no	—
39	C₂²	—	1418	2	no	—
40	C₂²	—	709	1	no	—
41	C₂²	—	709	1	no	—
42	C₂²	C₂×#15667778	1	1	yes	characteristic
43	C₄	—	709	1	no	—
44	C₄	—	709	1	no	—
45	C₄	C₂×#15667778	1	1	yes	characteristic
46	C₄	C₂×#15667778	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	—	1418	1	no	—
49	C₂	—	709	2	no	—
50	C₂	C₂²×#15667778	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#15667778
commutator, socle	C₂×C₇₀₉	C₂²×C₄
Frattini	C₂	C₂²×#15667778
Fitting	C₂×C₄×C₇₀₉	C₄
prime radical	C₂²×D₇₀₉	C₄
cosocle	Dic₇₀₉	C₂³
hypercenter	C₂×C₄	#15667778
hypocenter	C₇₀₉	C₂×M₁₆
LCS	G ▷ C₂×C₇₀₉ ▷ C₇₀₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #26015403	C₂	semidirect
2. #26015402	C₂	semidirect
3. D₇₀₉⋊C₈	C₂	semidirect
5. #19150893	C₂²	semidirect
24. D₇₀₉	M₁₆	semidirect
25. C₇₀₉	C₂×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
#26015403	2
#26015402	2
D₇₀₉⋊C₈	2
C₂×C₄×D₇₀₉	2
C₂×M₁₆	709

Subgroups — D709⋊M16 #36383988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇₀₉⋊M₁₆ #36383988