Subgroups — #46826034

Order 34432.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₆₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#31771531	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×D₂₆₉	C₂	1	1	yes	maximal, characteristic
4	#22575522	—	2	1	no	—
5	#22575503	—	2	1	no	—
6	D₈×D₂₆₉	—	2	1	no	—
7	D₄₃₀₄	C₄	1	1	yes	characteristic, complemented
8	#22575394	—	2	1	no	—
9	C₁₆×D₂₆₉	C₂²	1	1	yes	characteristic
10	D₁₆×C₂₆₉	C₄	1	1	yes	characteristic, complemented
11	C₄⋊#11761640	—	4	1	no	—
12	D₄×D₂₆₉	—	4	1	no	—
13	D₂₁₅₂	—	2	1	no	—
14	#16864387	—	4	1	no	—
15	C₈×D₂₆₉	D₄	1	1	yes	characteristic
16	#16864377	D₄	1	1	yes	characteristic
17	D₈×C₂₆₉	—	2	1	no	—
18	C₁₆×C₂₆₉	C₂×C₄	1	1	yes	characteristic
19	C₂×#11761640	—	8	1	no	—
20	C₂²×D₂₆₉	—	8	1	no	—
21	D₁₀₇₆	—	4	1	no	—
22	C₂²⋊D₂₆₉	—	8	1	no	—
23	C₄×D₂₆₉	D₈	1	1	yes	characteristic
24	#14524130	SD₁₆	1	1	yes	characteristic
25	D₄×C₂₆₉	—	4	1	no	—
26	C₈×C₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₂₆₉	—	8	1	no	—
28	C₂×D₂₆₉	—	8	1	no	—
29	C₂×D₂₆₉	—	16	1	no	—
30	C₂×D₂₆₉	—	16	1	no	—
31	C₂×D₂₆₉	D₁₆	1	1	yes	characteristic
32	#11761640	—	16	1	no	—
33	C₄×C₂₆₉	#102	1	1	yes	characteristic
34	Dic₂₆₉	SD₃₂	1	1	yes	characteristic
35	C₂×C₂₆₉	—	16	1	no	—
36	C₂×C₂₆₉	#357	1	1	yes	characteristic
37	D₂₆₉	—	16	1	no	—
38	D₂₆₉	D₃₂	1	1	yes	characteristic
39	D₂₆₉	SD₆₄	1	1	yes	characteristic
40	C₂₆₉	#1415	1	1	yes	characteristic, complemented, Sylow
41	#1415	—	269	1	no	maximal, Sylow
42	C₂×D₁₆	—	269	1	no	—
43	C₂×C₃₂	—	269	1	no	—
44	#366	—	269	1	no	—
45	C₂×D₈	—	538	1	no	—
46	D₁₆	—	269	1	no	—
47	D₁₆	—	538	1	no	—
48	D₁₆	#11761640	1	1	yes	characteristic, complemented
49	C₂×C₁₆	—	269	1	no	—
50	#107	—	538	1	no	—
51	C₃₂	—	538	1	no	—
52	C₂×D₄	—	1076	1	no	—
53	D₈	—	2	1	no	—
54	D₈	—	538	1	no	—
55	D₈	—	1076	1	no	—
56	C₂×C₈	—	269	1	no	—
57	C₄⋊C₄	—	1076	1	no	—
58	C₁₆	—	269	1	no	—
59	C₁₆	C₂×#11761640	1	1	yes	characteristic
60	C₂³	—	2152	1	no	—
61	D₄	—	4	1	no	—
62	D₄	—	1076	1	no	—
63	D₄	—	2152	1	no	—
64	C₂×C₄	—	269	1	no	—
65	C₂×C₄	—	2152	1	no	—
66	C₈	—	269	1	no	—
67	C₈	C₂²⋊#11761640	1	1	yes	characteristic
68	C₂²	—	8	1	no	—
69	C₂²	—	269	1	no	—
70	C₂²	—	2152	1	no	—
71	C₂²	—	4304	1	no	—
72	C₂²	—	4304	1	no	—
73	C₄	—	269	1	no	—
74	C₄	—	4304	1	no	—
75	C₄	#22575515	1	1	yes	characteristic
76	C₂	—	269	1	no	—
77	C₂	—	269	1	no	—
78	C₂	—	16	1	no	—
79	C₂	—	4304	1	no	—
80	C₂	#31771517	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31771517
commutator	C₁₆×C₂₆₉	C₂×C₄
Frattini	C₁₆	C₂×#11761640
Fitting	D₁₆×C₂₆₉	C₄
socle	C₂×C₂₆₉	#357
prime radical	D₁₆×D₂₆₉	C₂
cosocle	C₁₆×D₂₆₉	C₂²
hypercenter	D₁₆	#11761640
hypocenter	C₂₆₉	#1415
LCS	G ▷ C₁₆×C₂₆₉ ▷ C₈×C₂₆₉ ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. D₂₆₉⋊C₃₂	C₂	semidirect
2. #31771531	C₂	semidirect
7. D₄₃₀₄	C₄	semidirect
10. D₁₆×C₂₆₉	C₄	semidirect
40. C₂₆₉	#1415	semidirect
48. D₁₆	#11761640	semidirect

Maximal subgroups

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

subgroup	index
D₂₆₉⋊C₃₂	2
#31771531	2
D₁₆×D₂₆₉	2
#1415	269