Subgroups — #46825804

Order 34432.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771494	C₂	1	1	yes	maximal, characteristic
2	#31771446	C₂	1	1	yes	maximal, characteristic
3	#31770380	C₂	1	1	yes	maximal, characteristic
4	C₂×#16864405	C₄	1	2	yes	—
5	C₄×#14524137	C₄	1	1	yes	characteristic
6	C₄×#14524137	C₄	1	1	yes	characteristic
7	C₂×#16864377	C₄	1	1	yes	characteristic
8	C₈×Dic₂₆₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₂₆₉	C₄	1	1	yes	characteristic
10	C₂×#14524137	—	2	1	no	—
11	C₂×#14524137	—	2	1	no	—
12	#16864405	C₈	1	4	yes	complemented
13	C₂×#14524130	C₂×C₄	1	1	yes	characteristic
14	C₄×Dic₂₆₉	C₂×C₄	1	1	yes	characteristic
15	#16864377	—	2	1	no	—
16	C₂×C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
17	C₁₆×C₂₆₉	—	2	1	no	—
18	#14524137	—	4	1	no	—
19	#14524137	—	4	1	no	—
20	C₂×Dic₂₆₉	M₁₆	1	1	yes	characteristic
21	C₂×Dic₂₆₉	M₁₆	1	1	yes	characteristic
22	#14524130	C₂×C₈	1	2	yes	—
23	C₂×C₄×C₂₆₉	C₄²	1	1	yes	characteristic
24	C₈×C₂₆₉	M₁₆	1	1	yes	characteristic
25	C₈×C₂₆₉	M₁₆	1	1	yes	characteristic
26	C₂²×C₂₆₉	#97	1	1	yes	characteristic
27	C₄×C₂₆₉	C₄×C₈	1	1	yes	characteristic
28	C₄×C₂₆₉	#97	1	1	yes	characteristic
29	Dic₂₆₉	—	2	1	no	—
30	Dic₂₆₉	—	2	1	no	—
31	C₂×C₂₆₉	#322	1	1	yes	characteristic
32	C₂×C₂₆₉	#347	1	1	yes	characteristic
33	C₂×C₂₆₉	#347	1	1	yes	characteristic
34	C₂₆₉	#1313	1	1	yes	characteristic, complemented, Sylow
35	#1313	—	269	1	no	maximal, Sylow
36	#346	—	269	1	no	—
37	#346	—	269	1	no	—
38	#322	—	269	1	no	—
39	C₂×C₁₆	—	269	2	no	—
40	C₂×C₁₆	—	269	1	no	—
41	C₂×C₁₆	#11761640	1	1	yes	characteristic
42	C₄×C₈	—	269	1	no	—
43	C₄×C₈	—	269	1	no	—
44	C₄×C₈	—	269	1	no	—
45	C₂×C₈	—	269	1	no	—
46	C₂×C₈	—	538	1	no	—
47	C₂×C₈	—	538	1	no	—
48	C₂×C₈	C₂×#11761640	1	1	yes	characteristic
49	C₄²	—	269	1	no	—
50	C₁₆	—	2	1	no	—
51	C₁₆	—	269	4	no	—
52	C₁₆	—	538	1	no	—
53	C₂×C₄	—	269	1	no	—
54	C₂×C₄	—	269	1	no	—
55	C₂×C₄	C₄×#11761640	1	1	yes	characteristic
56	C₈	—	269	2	no	—
57	C₈	—	1076	1	no	—
58	C₈	—	1076	1	no	—
59	C₈	#16864411	1	1	yes	characteristic
60	C₈	#16864412	1	1	yes	characteristic
61	C₂²	#22575507	1	1	yes	characteristic
62	C₄	—	538	1	no	—
63	C₄	—	538	1	no	—
64	C₄	C₈×#11761640	1	1	yes	characteristic
65	C₄	#22575508	1	1	yes	characteristic
66	C₂	#14524137⋊C₈	1	1	yes	characteristic
67	C₂	#31771495	1	1	yes	characteristic
68	C₂	#31771496	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#11761640
commutator	C₄×C₂₆₉	C₄×C₈
Frattini	C₂×C₈	C₂×#11761640
Fitting	C₂×C₁₆×C₂₆₉	C₄
socle, prime radical	C₂²×C₂₆₉	#97
cosocle	C₈×Dic₂₆₉	C₂²
hypercenter	C₂×C₁₆	#11761640
hypocenter	C₂₆₉	#1313
LCS	G ▷ C₄×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
12. #16864405	C₈	semidirect
34. C₂₆₉	#1313	semidirect

Maximal subgroups

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

subgroup	index
#31771494	2
#31771446	2
#31770380	2
#1313	269