Subgroups — #46825887

Order 34432.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771497	C₂	1	2	yes	maximal, complemented
2	#31770969	C₂	1	1	yes	maximal, characteristic
3	#22575527	—	2	2	no	—
4	#22575445	C₄	1	1	yes	characteristic
5	#22575374	—	2	2	no	—
6	#22575364	C₂²	1	1	yes	characteristic
7	#127×C₂₆₉	C₄	1	1	yes	characteristic
8	#16864405	—	2	4	no	—
9	C₂×#14524130	D₄	1	2	yes	—
10	C₄⋊Dic₂₆₉	—	2	1	no	—
11	#16864381	—	4	1	no	—
12	C₂×D₄×C₂₆₉	—	2	1	no	—
13	C₂×D₄×C₂₆₉	—	4	1	no	—
14	C₄²×C₂₆₉	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₂₆₉	—	4	1	no	—
16	#14524130	—	2	2	no	—
17	C₂³×C₂₆₉	—	4	1	no	—
18	D₄×C₂₆₉	—	4	2	no	—
19	D₄×C₂₆₉	—	8	2	no	—
20	C₂×C₄×C₂₆₉	—	2	1	no	—
21	C₂×C₄×C₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₂²×C₂₆₉	—	8	2	no	—
23	C₂²×C₂₆₉	—	8	1	no	—
24	C₂²×C₂₆₉	#100	1	1	yes	characteristic
25	C₄×C₂₆₉	—	4	1	no	—
26	C₄×C₂₆₉	#104	1	2	yes	—
27	Dic₂₆₉	—	8	1	no	—
28	C₂×C₂₆₉	—	2	1	no	—
29	C₂×C₂₆₉	—	16	1	no	—
30	C₂×C₂₆₉	#329	1	1	yes	characteristic
31	C₂₆₉	#1355	1	1	yes	characteristic, complemented, Sylow
32	#1355	—	269	1	no	maximal, Sylow
33	#490	—	269	1	no	—
34	#347	—	269	2	no	—
35	#127	#11761640	1	1	yes	characteristic
36	#125	—	269	1	no	—
37	M₃₂	—	538	2	no	—
38	#102	—	538	2	no	—
39	#97	—	269	1	no	—
40	C₂×D₄	—	2	1	no	—
41	C₂×D₄	—	4	1	no	—
42	C₂×C₈	—	269	2	no	—
43	C₄⋊C₄	—	538	1	no	—
44	C₄⋊C₄	—	1076	1	no	—
45	C₄²	C₂×#11761640	1	1	yes	characteristic
46	C₁₆	—	538	4	no	—
47	C₂³	—	4	1	no	—
48	D₄	—	4	2	no	—
49	D₄	—	8	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	1076	1	no	—
52	C₂×C₄	C₂²⋊#11761640	1	1	yes	characteristic
53	C₈	—	538	2	no	—
54	C₂²	—	8	2	no	—
55	C₂²	—	8	1	no	—
56	C₂²	#22575513	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	2152	1	no	—
59	C₄	#22575517	1	2	yes	—
60	C₂	—	2	1	no	—
61	C₂	—	16	1	no	—
62	C₂	#31771460	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31771460
commutator	C₄²×C₂₆₉	C₂×C₄
Frattini	C₄²	C₂×#11761640
Fitting, prime radical	#127×C₂₆₉	C₄
socle	C₂×C₂₆₉	#329
cosocle	#22575364	C₂²
hypercenter	#127	#11761640
hypocenter	C₂₆₉	#1355
LCS	G ▷ C₄²×C₂₆₉ ▷ C₂×C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. #31771497	C₂	semidirect
31. C₂₆₉	#1355	semidirect

Maximal subgroups

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

subgroup	index
#31771497	2
#31770969	2
#1355	269