Subgroups — D₂₆₉⋊M₁₆ #22575538

Order 8608.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864412	C₂	1	2	yes	maximal, complemented
2	#16864411	C₂	1	2	yes	maximal, complemented
3	D₂₆₉⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₂₆₉	C₂	1	1	yes	maximal, characteristic
5	#14524137	C₂²	1	4	yes	complemented
6	C₂²×D₂₆₉	C₄	1	1	yes	characteristic
7	C₂×Dic₂₆₉	C₂²	1	1	yes	characteristic
8	C₄×D₂₆₉	C₄	1	1	yes	characteristic
9	C₄×D₂₆₉	C₄	1	1	yes	characteristic
10	C₄×D₂₆₉	C₂²	1	1	yes	characteristic
11	C₄×D₂₆₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₂₆₉	C₄	1	1	yes	characteristic
13	C₂²×C₂₆₉	C₂×C₄	1	1	yes	characteristic
14	C₂×D₂₆₉	—	2	2	no	—
15	C₂×D₂₆₉	C₂×C₄	1	1	yes	characteristic
16	C₂×D₂₆₉	C₂×C₄	1	1	yes	characteristic
17	C₄×C₂₆₉	C₂×C₄	1	1	yes	characteristic
18	C₄×C₂₆₉	C₂×C₄	1	1	yes	characteristic
19	Dic₂₆₉	C₂×C₄	1	1	yes	characteristic
20	Dic₂₆₉	C₂³	1	1	yes	characteristic
21	C₂×C₂₆₉	—	2	1	no	—
22	C₂×C₂₆₉	C₂²×C₄	1	1	yes	characteristic
23	D₂₆₉	—	2	1	no	—
24	D₂₆₉	M₁₆	1	2	yes	complemented
25	C₂₆₉	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	—	269	1	no	maximal, Sylow
27	C₂²×C₄	—	269	1	no	—
28	M₁₆	—	269	2	no	—
29	M₁₆	—	269	2	no	—
30	C₂×C₈	—	269	2	no	—
31	C₂³	—	269	1	no	—
32	C₂×C₄	—	269	1	no	—
33	C₂×C₄	—	269	1	no	—
34	C₂×C₄	—	269	1	no	—
35	C₂×C₄	—	269	1	no	—
36	C₂×C₄	—	269	1	no	—
37	C₂×C₄	#11761640	1	1	yes	characteristic
38	C₈	—	269	4	no	—
39	C₂²	—	269	1	no	—
40	C₂²	—	269	1	no	—
41	C₂²	—	538	2	no	—
42	C₂²	C₂×#11761640	1	1	yes	characteristic
43	C₄	—	269	1	no	—
44	C₄	—	269	1	no	—
45	C₄	C₂×#11761640	1	1	yes	characteristic
46	C₄	C₂×#11761640	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	—	269	2	no	—
49	C₂	—	538	1	no	—
50	C₂	C₂²×#11761640	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#11761640
commutator, socle	C₂×C₂₆₉	C₂²×C₄
Frattini	C₂	C₂²×#11761640
Fitting	C₂×C₄×C₂₆₉	C₄
hypercenter	C₂×C₄	#11761640
hypocenter	C₂₆₉	C₂×M₁₆
LCS	G ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #16864412	C₂	semidirect
2. #16864411	C₂	semidirect
3. D₂₆₉⋊C₈	C₂	semidirect
5. #14524137	C₂²	semidirect
24. D₂₆₉	M₁₆	semidirect
25. C₂₆₉	C₂×M₁₆	semidirect

Subgroups — D269⋊M16 #22575538

Conjugacy classes of subgroups

Complements

Subgroups — D₂₆₉⋊M₁₆ #22575538