Subgroups — #46808987

Order 34432.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31770643	C₂	1	2	yes	maximal
2	C₂×M₃₂×C₂₆₉	C₂	1	1	yes	maximal, characteristic
3	#22575412	—	2	2	no	—
4	#22575387	—	2	2	no	—
5	#22575385	C₄	1	4	yes	complemented
6	C₂²×C₈×C₂₆₉	C₂²	1	1	yes	characteristic
7	M₃₂×C₂₆₉	—	2	2	no	—
8	C₂×C₁₆×C₂₆₉	C₄	1	2	yes	complemented
9	C₄⋊Dic₂₆₉	—	2	4	no	—
10	C₂²⋊Dic₂₆₉	—	4	2	no	—
11	C₄×Dic₂₆₉	—	4	2	no	—
12	C₂²×C₄×C₂₆₉	D₄	1	1	yes	characteristic
13	C₂×C₈×C₂₆₉	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₂₆₉	D₄	1	2	yes	—
16	C₂×C₈×C₂₆₉	Q₈	1	1	yes	characteristic
17	C₁₆×C₂₆₉	—	2	2	no	—
18	C₂×Dic₂₆₉	—	4	4	no	—
19	C₂³×C₂₆₉	D₈	1	1	yes	characteristic
20	C₂×C₄×C₂₆₉	C₂²⋊C₄	1	2	yes	—
21	C₂×C₄×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₂₆₉	SD₁₆	1	2	yes	—
23	C₂×C₄×C₂₆₉	Q₁₆	1	1	yes	characteristic
24	C₈×C₂₆₉	C₄²	1	1	yes	characteristic
25	C₈×C₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₂₆₉	C₄⋊C₄	1	2	yes	—
27	C₂²×C₂₆₉	—	4	1	no	—
28	C₂²×C₂₆₉	#102	1	2	yes	—
29	C₂²×C₂₆₉	#107	1	1	yes	characteristic
30	C₄×C₂₆₉	#95	1	1	yes	characteristic
31	C₄×C₂₆₉	#103	1	2	yes	—
32	C₄×C₂₆₉	#106	1	1	yes	characteristic
33	Dic₂₆₉	—	8	4	no	—
34	C₂×C₂₆₉	—	2	2	no	—
35	C₂×C₂₆₉	—	2	1	no	—
36	C₂×C₂₆₉	#340	1	1	yes	characteristic
37	C₂₆₉	#1384	1	1	yes	characteristic, complemented, Sylow
38	#1384	—	269	1	no	maximal, Sylow
39	C₂×M₃₂	D₂₆₉	1	1	yes	characteristic
40	#427	—	269	2	no	—
41	C₂²×C₈	C₂×D₂₆₉	1	1	yes	characteristic
42	#117	—	538	2	no	—
43	M₃₂	—	2	2	no	—
44	C₂×C₁₆	Dic₂₆₉	1	2	yes	complemented
45	#107	—	538	2	no	—
46	#106	—	269	4	no	—
47	C₂²×C₄	D₁₀₇₆	1	1	yes	characteristic
48	C₂×C₈	C₄×D₂₆₉	1	2	yes	—
49	C₂×C₈	C₂×Dic₂₆₉	1	1	yes	characteristic
50	C₂×C₈	C₂²⋊D₂₆₉	1	2	yes	—
51	C₂×C₈	Dic₅₃₈	1	1	yes	characteristic
52	C₄⋊C₄	—	538	4	no	—
53	C₂²⋊C₄	—	1076	2	no	—
54	C₄²	—	1076	2	no	—
55	C₁₆	—	2	2	no	—
56	C₂³	D₂₁₅₂	1	1	yes	characteristic
57	C₂×C₄	—	1076	4	no	—
58	C₂×C₄	#16864379	1	2	yes	—
59	C₂×C₄	C₄⋊Dic₂₆₉	1	1	yes	characteristic
60	C₂×C₄	#16864391	1	2	yes	—
61	C₂×C₄	Dic₁₀₇₆	1	1	yes	characteristic
62	C₈	C₄×Dic₂₆₉	1	1	yes	characteristic
63	C₈	C₂²⋊Dic₂₆₉	1	1	yes	characteristic
64	C₈	#16864381	1	2	yes	—
65	C₂²	—	4	1	no	—
66	C₂²	#22575375	1	2	yes	—
67	C₂²	#22575387	1	1	yes	characteristic
68	C₄	—	2152	4	no	—
69	C₄	#22575360	1	1	yes	characteristic
70	C₄	#22575378	1	2	yes	—
71	C₄	#22575385	1	1	yes	characteristic
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	C₂	#31770368	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#22575385
commutator	C₈×C₂₆₉	C₄²
Frattini	C₂²×C₈	C₂×D₂₆₉
Fitting	C₂×M₃₂×C₂₆₉	C₂
socle	C₂×C₂₆₉	#340
prime radical	C₂³×C₂₆₉	D₈
cosocle	C₂²×C₈×C₂₆₉	C₂²
hypercenter	C₂×M₃₂	D₂₆₉
hypocenter	C₂₆₉	#1384
LCS	G ▷ C₈×C₂₆₉ ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
5. #22575385	C₄	semidirect
8. C₂×C₁₆×C₂₆₉	C₄	semidirect
37. C₂₆₉	#1384	semidirect
44. C₂×C₁₆	Dic₂₆₉	semidirect

Maximal subgroups

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

subgroup	index
#31770643	2
C₂×M₃₂×C₂₆₉	2
#1384	269