Subgroups — #46825901

Order 34432.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771526	C₂	1	1	yes	maximal, characteristic
2	#31771467	C₂	1	1	yes	maximal, characteristic
3	#31771006	C₂	1	1	yes	maximal, characteristic
4	C₂×#16864405	—	2	1	no	—
5	C₄⋊#14524137	—	2	1	no	—
6	#22575444	—	2	1	no	—
7	#22575387	C₄	1	1	yes	characteristic
8	#22575384	—	2	1	no	—
9	C₈×Dic₂₆₉	C₂²	1	1	yes	characteristic
10	#107×C₂₆₉	C₄	1	1	yes	characteristic
11	C₂×#14524137	—	4	1	no	—
12	#16864405	—	4	1	no	—
13	C₂×#14524130	D₄	1	1	yes	characteristic
14	C₄⋊Dic₂₆₉	—	2	1	no	—
15	C₄⋊Dic₂₆₉	—	4	1	no	—
16	#16864381	—	4	1	no	—
17	C₄×Dic₂₆₉	D₄	1	1	yes	characteristic
18	C₂×C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
19	C₄⋊C₄×C₂₆₉	—	2	1	no	—
20	#14524137	—	8	1	no	—
21	C₂×Dic₂₆₉	—	4	1	no	—
22	C₂×Dic₂₆₉	D₈	1	1	yes	characteristic
23	C₂×Dic₂₆₉	SD₁₆	1	1	yes	characteristic
24	#14524130	SD₁₆	1	1	yes	characteristic
25	#14524130	Q₁₆	1	1	yes	characteristic
26	C₂×C₄×C₂₆₉	—	4	1	no	—
27	C₂×C₄×C₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₈×C₂₆₉	—	2	1	no	—
29	C₂²×C₂₆₉	#102	1	1	yes	characteristic
30	C₄×C₂₆₉	—	8	1	no	—
31	C₄×C₂₆₉	#101	1	1	yes	characteristic
32	C₄×C₂₆₉	#103	1	1	yes	characteristic
33	Dic₂₆₉	—	2	1	no	—
34	Dic₂₆₉	—	2	1	no	—
35	Dic₂₆₉	—	8	1	no	—
36	C₂×C₂₆₉	#332	1	1	yes	characteristic
37	C₂×C₂₆₉	#359	1	1	yes	characteristic
38	C₂×C₂₆₉	#360	1	1	yes	characteristic
39	C₂₆₉	#1363	1	1	yes	characteristic, complemented, Sylow
40	#1363	—	269	1	no	maximal, Sylow
41	#499	—	269	1	no	—
42	C₄⋊C₁₆	—	269	1	no	—
43	#334	—	269	1	no	—
44	#125	—	538	1	no	—
45	C₂×C₁₆	—	538	1	no	—
46	#107	—	269	1	no	—
47	#107	#11761640	1	1	yes	characteristic
48	#106	—	538	1	no	—
49	C₄⋊C₈	—	538	1	no	—
50	C₄×C₈	—	269	1	no	—
51	C₂×C₈	—	269	1	no	—
52	C₂×C₈	—	1076	1	no	—
53	C₂×C₈	C₂×#11761640	1	1	yes	characteristic
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	538	1	no	—
56	C₄⋊C₄	—	1076	1	no	—
57	C₄⋊C₄	—	1076	1	no	—
58	C₄²	—	269	1	no	—
59	C₁₆	—	1076	1	no	—
60	C₂×C₄	—	4	1	no	—
61	C₂×C₄	—	269	1	no	—
62	C₂×C₄	—	269	1	no	—
63	C₂×C₄	—	1076	1	no	—
64	C₂×C₄	C₂²⋊#11761640	1	1	yes	characteristic
65	C₈	—	2	1	no	—
66	C₈	—	269	1	no	—
67	C₈	—	269	1	no	—
68	C₈	—	2152	1	no	—
69	C₂²	#22575515	1	1	yes	characteristic
70	C₄	—	8	1	no	—
71	C₄	—	538	1	no	—
72	C₄	—	538	1	no	—
73	C₄	—	2152	1	no	—
74	C₄	#22575514	1	1	yes	characteristic
75	C₄	#22575516	1	1	yes	characteristic
76	C₂	#31771464	1	1	yes	characteristic
77	C₂	#31771519	1	1	yes	characteristic
78	C₂	#31771522	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22575515
commutator	C₂×C₈×C₂₆₉	C₂×C₄
Frattini	C₂×C₈	C₂×#11761640
Fitting	#107×C₂₆₉	C₄
socle, prime radical	C₂²×C₂₆₉	#102
cosocle	C₈×Dic₂₆₉	C₂²
hypercenter	#107	#11761640
hypocenter	C₂₆₉	#1363
LCS	G ▷ C₂×C₈×C₂₆₉ ▷ C₂×C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
39. C₂₆₉	#1363	semidirect

Maximal subgroups

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

subgroup	index
#31771526	2
#31771467	2
#31771006	2
#1363	269