Subgroups — C₂×#13732 #513058

Order 512.

314 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#2253	C₂	1	2	yes	maximal
2	#13732	C₂	1	8	yes	maximal, direct product factor
3	C₂×#1424	C₂	1	2	yes	maximal
4	C₂×#1423	C₂	1	2	yes	maximal
5	C₂×C₄×C₃₂	C₂	1	1	yes	maximal, characteristic
6	C₂×#499	—	2	2	no	—
7	C₂²×C₃₂	C₂²	1	1	yes	characteristic
8	C₂²×C₃₂	C₂²	1	1	yes	characteristic
9	#2253	—	2	4	no	—
10	#2253	C₂²	1	8	yes	—
11	C₂×#367	—	2	2	no	—
12	C₂×#366	C₂²	1	4	yes	—
13	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
14	#1424	C₂²	1	8	yes	—
15	#1423	C₂²	1	8	yes	—
16	C₄×C₃₂	C₂²	1	4	yes	—
17	C₂×#125	—	4	2	no	—
18	C₂²×C₁₆	D₄	1	1	yes	characteristic
19	C₂²×C₁₆	C₂³	1	1	yes	characteristic
20	#499	—	2	8	no	—
21	#499	—	4	4	no	—
22	C₂×#107	—	2	4	no	—
23	C₂×#106	—	4	2	no	—
24	C₂×C₄×C₈	D₄	1	1	yes	characteristic
25	C₂×C₃₂	Q₈	1	4	yes	—
26	C₂×C₃₂	Q₈	1	4	yes	—
27	C₂×C₃₂	C₂³	1	2	yes	—
28	C₂×C₃₂	C₂³	1	2	yes	—
29	#367	—	2	8	no	—
30	#366	—	2	4	no	—
31	#366	C₂³	1	8	yes	—
32	C₄×C₁₆	D₄	1	2	yes	—
33	C₄×C₁₆	C₂³	1	2	yes	—
34	C₂²×C₈	D₈	1	1	yes	characteristic
35	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
36	#125	—	4	8	no	—
37	#125	—	8	4	no	—
38	C₂×C₄⋊C₄	—	4	4	no	—
39	C₂×C₄⋊C₄	—	8	4	no	—
40	C₂×C₄²	D₈	1	1	yes	characteristic
41	C₂×C₁₆	Q₁₆	1	4	yes	—
42	C₂×C₁₆	C₂×D₄	1	1	yes	characteristic
43	C₂×C₁₆	C₂×D₄	1	2	yes	—
44	C₂×C₁₆	C₂×Q₈	1	2	yes	—
45	C₂×C₁₆	C₂×Q₈	1	2	yes	—
46	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
47	#107	—	2	8	no	—
48	#107	—	4	4	no	—
49	#106	—	4	8	no	—
50	C₄×C₈	D₈	1	2	yes	—
51	C₄×C₈	C₂×D₄	1	2	yes	—
52	C₃₂	C₂×Q₈	1	4	yes	—
53	C₃₂	C₂×Q₈	1	4	yes	—
54	C₂²×C₄	—	8	4	no	—
55	C₂²×C₄	D₁₆	1	2	yes	—
56	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
57	C₂×C₈	Q₃₂	1	4	yes	—
58	C₂×C₈	C₄⋊Q₈	1	2	yes	—
59	C₂×C₈	C₂×D₈	1	1	yes	characteristic
60	C₂×C₈	C₂×D₈	1	2	yes	—
61	C₂×C₈	C₂×Q₁₆	1	2	yes	—
62	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
63	C₄⋊C₄	—	4	8	no	—
64	C₄⋊C₄	—	8	4	no	—
65	C₄⋊C₄	—	8	16	no	—
66	C₄²	D₁₆	1	2	yes	—
67	C₄²	C₂×D₈	1	2	yes	—
68	C₁₆	C₄⋊Q₈	1	2	yes	—
69	C₁₆	C₂×Q₁₆	1	4	yes	—
70	C₁₆	C₂²×Q₈	1	1	yes	characteristic
71	C₁₆	C₂²×Q₈	1	1	yes	characteristic
72	C₂³	C₂×D₁₆	1	1	yes	characteristic
73	C₂×C₄	—	2	4	no	—
74	C₂×C₄	—	8	8	no	—
75	C₂×C₄	—	16	8	no	—
76	C₂×C₄	#500	1	2	yes	—
77	C₂×C₄	C₂×D₁₆	1	4	yes	—
78	C₂×C₄	C₂×D₁₆	1	1	yes	characteristic
79	C₂×C₄	C₂×Q₃₂	1	2	yes	—
80	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
81	C₈	#500	1	2	yes	—
82	C₈	C₂×Q₃₂	1	4	yes	—
83	C₈	C₂×C₄⋊Q₈	1	1	yes	characteristic
84	C₈	C₂²×Q₁₆	1	1	yes	characteristic
85	C₂²	#2252	1	2	yes	—
86	C₂²	#2262	1	4	yes	—
87	C₂²	C₂²×D₁₆	1	1	yes	characteristic
88	C₄	—	2	4	no	—
89	C₄	—	16	8	no	—
90	C₄	#2252	1	2	yes	—
91	C₄	C₂×#500	1	1	yes	characteristic
92	C₄	C₂²×Q₃₂	1	1	yes	characteristic
93	C₂	#13732	1	4	yes	direct product factor
94	C₂	C₂×#2252	1	1	yes	characteristic
95	C₂	C₂×#2262	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂⁴
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆ ◁ G
LECS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #13732	C₂	direct (N × H)
93. C₂	#13732	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#2253	2
#13732	2
C₂×#1424	2
C₂×#1423	2
C₂×C₄×C₃₂	2

Subgroups — C2×#13732 #513058

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13732 #513058