Subgroups — #46809062

Order 34432.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₃₀₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#22575359	C₂	1	1	yes	maximal, characteristic, complemented
3	#366×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₁₅₂	—	2	1	no	—
5	D₄₃₀₄	—	2	1	no	—
6	D₄₃₀₄	C₄	1	2	yes	complemented
7	#22575359	—	2	1	no	—
8	C₂×C₁₆×C₂₆₉	C₂²	1	1	yes	characteristic
9	#107×C₂₆₉	—	2	1	no	—
10	C₂×D₁₀₇₆	—	4	1	no	—
11	D₂₁₅₂	—	2	2	no	—
12	D₂₁₅₂	—	4	1	no	—
13	C₂×C₈×C₂₆₉	D₄	1	1	yes	characteristic
14	C₄⋊C₄×C₂₆₉	—	4	1	no	—
15	C₁₆×C₂₆₉	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₂₆₉	D₄	1	1	yes	characteristic
17	C₂²×D₂₆₉	—	8	1	no	—
18	D₁₀₇₆	—	4	2	no	—
19	D₁₀₇₆	—	8	1	no	—
20	C₂×C₄×C₂₆₉	—	8	1	no	—
21	C₂×C₄×C₂₆₉	D₈	1	1	yes	characteristic
22	C₈×C₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₂₆₉	SD₁₆	1	1	yes	characteristic
24	C₂²×C₂₆₉	D₁₆	1	1	yes	characteristic
25	C₂×D₂₆₉	—	8	2	no	—
26	C₂×D₂₆₉	—	16	1	no	—
27	C₂×D₂₆₉	—	16	1	no	—
28	C₄×C₂₆₉	—	16	1	no	—
29	C₄×C₂₆₉	#102	1	1	yes	characteristic
30	C₄×C₂₆₉	SD₃₂	1	1	yes	characteristic
31	C₂×C₂₆₉	#357	1	1	yes	characteristic
32	C₂×C₂₆₉	D₃₂	1	1	yes	characteristic
33	C₂×C₂₆₉	SD₆₄	1	1	yes	characteristic
34	D₂₆₉	—	16	2	no	—
35	C₂₆₉	#1415	1	1	yes	characteristic, complemented, Sylow
36	#1415	—	269	1	no	maximal, Sylow
37	C₂×D₁₆	—	269	1	no	—
38	C₂×C₃₂	—	269	1	no	—
39	#366	D₂₆₉	1	1	yes	characteristic, complemented
40	C₂×D₈	—	538	1	no	—
41	D₁₆	—	269	2	no	—
42	D₁₆	—	538	1	no	—
43	C₂×C₁₆	C₂×D₂₆₉	1	1	yes	characteristic
44	#107	—	2	1	no	—
45	C₃₂	—	538	1	no	—
46	C₂×D₄	—	1076	1	no	—
47	D₈	—	538	2	no	—
48	D₈	—	1076	1	no	—
49	C₂×C₈	C₂²⋊D₂₆₉	1	1	yes	characteristic
50	C₄⋊C₄	—	4	1	no	—
51	C₁₆	C₄×D₂₆₉	1	1	yes	characteristic
52	C₁₆	D₁₀₇₆	1	1	yes	characteristic
53	C₂³	—	2152	1	no	—
54	D₄	—	1076	2	no	—
55	D₄	—	2152	1	no	—
56	C₂×C₄	—	8	1	no	—
57	C₂×C₄	#16864387	1	1	yes	characteristic
58	C₈	#16864379	1	1	yes	characteristic
59	C₈	#16864389	1	1	yes	characteristic
60	C₂²	—	2152	2	no	—
61	C₂²	—	4304	1	no	—
62	C₂²	—	4304	1	no	—
63	C₂²	#22575394	1	1	yes	characteristic
64	C₄	—	16	1	no	—
65	C₄	#22575373	1	1	yes	characteristic
66	C₄	#22575396	1	1	yes	characteristic
67	C₂	—	4304	2	no	—
68	C₂	#31770405	1	1	yes	characteristic
69	C₂	#31770440	1	1	yes	characteristic
70	C₂	#31770442	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22575394
commutator	C₁₆×C₂₆₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₆₉
Fitting	#366×C₂₆₉	C₂
socle	C₂²×C₂₆₉	D₁₆
prime radical	C₂×D₄₃₀₄	C₂
cosocle	C₂×C₁₆×C₂₆₉	C₂²
hypercenter	#366	D₂₆₉
hypocenter	C₂₆₉	#1415
LCS	G ▷ C₁₆×C₂₆₉ ▷ C₈×C₂₆₉ ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
2. C₂×#22575359	C₂	semidirect
3. #366×C₂₆₉	C₂	semidirect
6. D₄₃₀₄	C₄	semidirect
35. C₂₆₉	#1415	semidirect
39. #366	D₂₆₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄₃₀₄	2
C₂×#22575359	2
#366×C₂₆₉	2
#1415	269