Subgroups — #46813202

Order 34432.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₁₅₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#31770445	C₂	1	2	yes	maximal, complemented
3	#31770443	C₂	1	2	yes	maximal, complemented
4	#31770439	C₂	1	1	yes	maximal, characteristic, complemented
5	#508×C₂₆₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₀₇₆	—	2	1	no	—
7	Dic₂₁₅₂	—	2	1	no	—
8	Dic₂₁₅₂	C₂²	1	2	yes	—
9	#22575359	C₂²	1	2	yes	—
10	#135×C₂₆₉	—	2	1	no	—
11	Q₃₂×C₂₆₉	C₂²	1	1	yes	characteristic
12	SD₃₂×C₂₆₉	—	2	1	no	—
13	D₁₆×C₂₆₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₂₆₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₅₃₈	—	4	1	no	—
16	Dic₁₀₇₆	—	2	2	no	—
17	Dic₁₀₇₆	—	4	1	no	—
18	#41×C₂₆₉	—	4	1	no	—
19	Q₁₆×C₂₆₉	—	2	1	no	—
20	SD₁₆×C₂₆₉	—	4	1	no	—
21	D₈×C₂₆₉	—	2	1	no	—
22	C₂×C₈×C₂₆₉	D₄	1	1	yes	characteristic
23	C₁₆×C₂₆₉	D₄	1	1	yes	characteristic
24	C₁₆×C₂₆₉	C₂³	1	1	yes	characteristic
25	Dic₅₃₈	—	4	2	no	—
26	Dic₅₃₈	—	8	1	no	—
27	C₂×Dic₂₆₉	—	8	1	no	—
28	Q₈×C₂₆₉	—	4	1	no	—
29	D₄×C₂₆₉	—	4	1	no	—
30	D₄×C₂₆₉	—	8	1	no	—
31	C₂×C₄×C₂₆₉	—	8	1	no	—
32	C₂×C₄×C₂₆₉	D₈	1	1	yes	characteristic
33	C₈×C₂₆₉	D₈	1	1	yes	characteristic
34	C₈×C₂₆₉	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₂₆₉	—	8	1	no	—
36	C₂²×C₂₆₉	D₁₆	1	1	yes	characteristic
37	C₄×C₂₆₉	—	8	1	no	—
38	C₄×C₂₆₉	D₁₆	1	1	yes	characteristic
39	C₄×C₂₆₉	C₂×D₈	1	1	yes	characteristic
40	Dic₂₆₉	—	8	2	no	—
41	C₂×C₂₆₉	—	2	1	no	—
42	C₂×C₂₆₉	—	16	1	no	—
43	C₂×C₂₆₉	C₂×D₁₆	1	1	yes	characteristic
44	C₂₆₉	#2264	1	1	yes	characteristic, complemented, Sylow
45	#2264	—	269	1	no	maximal, Sylow
46	#508	D₂₆₉	1	1	yes	characteristic
47	C₂×Q₃₂	—	269	1	no	—
48	Q₆₄	—	269	2	no	—
49	SD₆₄	—	269	2	no	—
50	M₆₄	—	269	1	no	—
51	#135	—	2	1	no	—
52	C₂×Q₁₆	—	538	1	no	—
53	Q₃₂	—	269	2	no	—
54	Q₃₂	—	538	1	no	—
55	Q₃₂	C₂×D₂₆₉	1	1	yes	characteristic
56	SD₃₂	—	2	1	no	—
57	D₁₆	C₂×D₂₆₉	1	1	yes	characteristic
58	C₂×C₁₆	C₂×D₂₆₉	1	1	yes	characteristic
59	C₃₂	—	269	2	no	—
60	#41	—	4	1	no	—
61	C₂×Q₈	—	1076	1	no	—
62	Q₁₆	—	2	1	no	—
63	Q₁₆	—	538	2	no	—
64	Q₁₆	—	1076	1	no	—
65	SD₁₆	—	4	1	no	—
66	D₈	—	2	1	no	—
67	C₂×C₈	C₂²⋊D₂₆₉	1	1	yes	characteristic
68	C₁₆	C₂²⋊D₂₆₉	1	1	yes	characteristic
69	C₁₆	C₂²×D₂₆₉	1	1	yes	characteristic
70	Q₈	—	4	1	no	—
71	Q₈	—	1076	2	no	—
72	Q₈	—	2152	1	no	—
73	D₄	—	4	1	no	—
74	D₄	—	8	1	no	—
75	C₂×C₄	—	8	1	no	—
76	C₂×C₄	—	2152	1	no	—
77	C₂×C₄	#16864387	1	1	yes	characteristic
78	C₈	#16864387	1	1	yes	characteristic
79	C₈	C₂×C₂²⋊D₂₆₉	1	1	yes	characteristic
80	C₂²	—	8	1	no	—
81	C₂²	#22575394	1	1	yes	characteristic
82	C₄	—	8	1	no	—
83	C₄	—	2152	2	no	—
84	C₄	#22575394	1	1	yes	characteristic
85	C₄	C₂×#16864387	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	16	1	no	—
88	C₂	C₂×#22575394	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#22575394
commutator, cosocle	C₁₆×C₂₆₉	C₂³
Frattini	C₁₆	C₂²×D₂₆₉
Fitting, prime radical	#508×C₂₆₉	C₂
socle	C₂×C₂₆₉	C₂×D₁₆
hypercenter	#508	D₂₆₉
hypocenter	C₂₆₉	#2264
LCS	G ▷ C₁₆×C₂₆₉ ▷ C₈×C₂₆₉ ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #508

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₂₁₅₂	C₂	semidirect
2. #31770445	C₂	semidirect
3. #31770443	C₂	semidirect
4. #31770439	C₂	semidirect
44. C₂₆₉	#2264	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₂₁₅₂	2
#31770445	2
#31770443	2
#31770439	2
#508×C₂₆₉	2
#2264	269