Subgroups — C₂×#15692954 #20267824

Order 6592.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₀₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₁₀₃	C₂	1	1	yes	maximal, characteristic
3	#15692954	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊C₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₀₃	—	2	1	no	—
6	C₂×C₁₀₃⋊C₈	C₄	1	4	yes	complemented
7	C₂×C₁₀₃⋊C₈	C₂²	1	2	yes	—
8	C₄⋊Dic₁₀₃	—	2	1	no	—
9	C₄⋊Dic₁₀₃	C₂²	1	2	yes	—
10	C₂²×C₄×C₁₀₃	—	2	1	no	—
11	C₂²×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₀₃	—	2	1	no	—
13	C₄⋊C₄×C₁₀₃	C₂²	1	2	yes	—
14	C₂³×C₁₀₃	D₄	1	1	yes	characteristic
15	C₂×C₄×C₁₀₃	—	2	2	no	—
16	C₂×C₄×C₁₀₃	—	4	2	no	—
17	C₂×C₄×C₁₀₃	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₀₃	Q₈	1	2	yes	—
20	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
21	C₂×Dic₁₀₃	—	2	2	no	—
22	C₂×Dic₁₀₃	—	4	2	no	—
23	C₁₀₃⋊C₈	C₂×C₄	1	4	yes	complemented
24	C₂²×C₁₀₃	C₄⋊C₄	1	2	yes	—
25	C₂²×C₁₀₃	D₈	1	2	yes	—
26	C₂²×C₁₀₃	Q₁₆	1	2	yes	—
27	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
28	C₄×C₁₀₃	—	4	2	no	—
29	C₄×C₁₀₃	C₄⋊C₄	1	2	yes	—
30	C₄×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
32	Dic₁₀₃	—	4	2	no	—
33	C₂×C₁₀₃	#107	1	4	yes	complemented
34	C₂×C₁₀₃	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₁₀₃	C₂×D₈	1	1	yes	characteristic
36	C₂×C₁₀₃	C₂×Q₁₆	1	1	yes	characteristic
37	C₁₀₃	C₂×#107	1	1	yes	characteristic, complemented, Sylow
38	C₂×#107	—	103	1	no	maximal, Sylow
39	C₂²×C₈	—	103	1	no	—
40	C₂×C₄⋊C₄	—	103	1	no	—
41	C₂×C₄⋊C₄	D₁₀₃	1	1	yes	characteristic
42	#107	—	103	4	no	—
43	C₂²×C₄	—	2	1	no	—
44	C₂²×C₄	—	206	1	no	—
45	C₂²×C₄	C₂×D₁₀₃	1	1	yes	characteristic
46	C₂×C₈	—	103	4	no	—
47	C₂×C₈	—	103	2	no	—
48	C₄⋊C₄	—	2	1	no	—
49	C₄⋊C₄	—	103	2	no	—
50	C₄⋊C₄	—	206	1	no	—
51	C₄⋊C₄	C₂×D₁₀₃	1	2	yes	—
52	C₂³	C₂²⋊D₁₀₃	1	1	yes	characteristic
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	4	2	no	—
55	C₂×C₄	—	412	2	no	—
56	C₂×C₄	—	206	2	no	—
57	C₂×C₄	Dic₂₀₆	1	2	yes	—
58	C₂×C₄	C₄×D₁₀₃	1	2	yes	—
59	C₂×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
60	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
61	C₈	—	103	4	no	—
62	C₂²	Dic₁₀₃⋊C₄	1	2	yes	—
63	C₂²	#13110090	1	2	yes	—
64	C₂²	#13110095	1	2	yes	—
65	C₂²	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	—	412	2	no	—
68	C₄	Dic₁₀₃⋊C₄	1	2	yes	—
69	C₄	C₂×C₄×D₁₀₃	1	1	yes	characteristic
70	C₄	C₂×Dic₂₀₆	1	1	yes	characteristic
71	C₂	#15692954	1	4	yes	direct product factor
72	C₂	C₂×Dic₁₀₃⋊C₄	1	1	yes	characteristic
73	C₂	C₂×#13110090	1	1	yes	characteristic
74	C₂	C₂×#13110095	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₁₀₃
commutator	C₄×C₁₀₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	C₂×C₄⋊C₄×C₁₀₃	C₂
socle	C₂³×C₁₀₃	D₄
hypercenter	C₂×C₄⋊C₄	D₁₀₃
hypocenter	C₁₀₃	C₂×#107
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #15692954	C₂	direct (N × H)
6. C₂×C₁₀₃⋊C₈	C₄	semidirect
23. C₁₀₃⋊C₈	C₂×C₄	semidirect
33. C₂×C₁₀₃	#107	semidirect
37. C₁₀₃	C₂×#107	semidirect
71. C₂	#15692954	direct (N × H)

Subgroups — C2×#15692954 #20267824

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15692954 #20267824