Subgroups — C₁₀₃×#7538 #39912813

Order 26368.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₆₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic
3	C₁₀₃×#1423	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₃₂×C₁₀₃	—	2	1	no	—
5	Q₆₄×C₁₀₃	—	2	1	no	—
6	Q₆₄×C₁₀₃	C₄	1	2	yes	complemented
7	C₂×C₃₂×C₁₀₃	C₂²	1	1	yes	characteristic
8	#366×C₁₀₃	—	2	1	no	—
9	C₆₄×C₁₀₃	—	2	1	no	—
10	C₂×Q₁₆×C₁₀₃	—	4	1	no	—
11	Q₃₂×C₁₀₃	—	2	2	no	—
12	Q₃₂×C₁₀₃	—	4	1	no	—
13	C₂×C₁₆×C₁₀₃	D₄	1	1	yes	characteristic
14	#107×C₁₀₃	—	4	1	no	—
15	C₃₂×C₁₀₃	C₂×C₄	1	1	yes	characteristic
16	C₃₂×C₁₀₃	D₄	1	1	yes	characteristic
17	C₂×Q₈×C₁₀₃	—	8	1	no	—
18	Q₁₆×C₁₀₃	—	4	2	no	—
19	Q₁₆×C₁₀₃	—	8	1	no	—
20	C₂×C₈×C₁₀₃	D₈	1	1	yes	characteristic
21	C₄⋊C₄×C₁₀₃	—	8	1	no	—
22	C₁₆×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₁₀₃	SD₁₆	1	1	yes	characteristic
24	Q₈×C₁₀₃	—	8	2	no	—
25	Q₈×C₁₀₃	—	16	1	no	—
26	C₂×C₄×C₁₀₃	—	16	1	no	—
27	C₂×C₄×C₁₀₃	—	16	1	no	—
28	C₂×C₄×C₁₀₃	D₁₆	1	1	yes	characteristic
29	C₈×C₁₀₃	#102	1	1	yes	characteristic
30	C₈×C₁₀₃	SD₃₂	1	1	yes	characteristic
31	C₂²×C₁₀₃	D₃₂	1	1	yes	characteristic
32	C₄×C₁₀₃	—	16	2	no	—
33	C₄×C₁₀₃	—	32	1	no	—
34	C₄×C₁₀₃	#357	1	1	yes	characteristic
35	C₄×C₁₀₃	SD₆₄	1	1	yes	characteristic
36	#7538	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×C₁₀₃	#1415	1	1	yes	characteristic
38	C₂×C₁₀₃	SD₁₂₈	1	1	yes	characteristic
39	C₂×C₁₀₃	Q₁₂₈	1	1	yes	characteristic
40	C₂×Q₆₄	C₂×C₁₀₃	1	1	yes	characteristic
41	C₂×C₆₄	C₂×C₁₀₃	1	1	yes	characteristic
42	#1423	C₂×C₁₀₃	1	1	yes	characteristic
43	C₁₀₃	#7538	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×Q₃₂	—	2	1	no	—
45	Q₆₄	—	2	1	no	—
46	Q₆₄	C₄×C₁₀₃	1	2	yes	complemented
47	C₂×C₃₂	C₂²×C₁₀₃	1	1	yes	characteristic
48	#366	—	2	1	no	—
49	C₆₄	—	2	1	no	—
50	C₂×Q₁₆	—	4	1	no	—
51	Q₃₂	—	2	2	no	—
52	Q₃₂	—	4	1	no	—
53	C₂×C₁₆	D₄×C₁₀₃	1	1	yes	characteristic
54	#107	—	4	1	no	—
55	C₃₂	C₂×C₄×C₁₀₃	1	1	yes	characteristic
56	C₃₂	D₄×C₁₀₃	1	1	yes	characteristic
57	C₂×Q₈	—	8	1	no	—
58	Q₁₆	—	4	2	no	—
59	Q₁₆	—	8	1	no	—
60	C₂×C₈	D₈×C₁₀₃	1	1	yes	characteristic
61	C₄⋊C₄	—	8	1	no	—
62	C₁₆	C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
63	C₁₆	SD₁₆×C₁₀₃	1	1	yes	characteristic
64	Q₈	—	8	2	no	—
65	Q₈	—	16	1	no	—
66	C₂×C₄	—	16	1	no	—
67	C₂×C₄	—	16	1	no	—
68	C₂×C₄	D₁₆×C₁₀₃	1	1	yes	characteristic
69	C₈	#102×C₁₀₃	1	1	yes	characteristic
70	C₈	SD₃₂×C₁₀₃	1	1	yes	characteristic
71	C₂²	D₃₂×C₁₀₃	1	1	yes	characteristic
72	C₄	—	16	2	no	—
73	C₄	—	32	1	no	—
74	C₄	#357×C₁₀₃	1	1	yes	characteristic
75	C₄	SD₆₄×C₁₀₃	1	1	yes	characteristic
76	C₂	C₁₀₃×#1415	1	1	yes	characteristic
77	C₂	C₁₀₃×SD₁₂₈	1	1	yes	characteristic
78	C₂	C₁₀₃×Q₁₂₈	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₀₃	D₃₂
commutator	C₃₂	C₂×C₄×C₁₀₃
Frattini, cosocle	C₂×C₃₂	C₂²×C₁₀₃
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₂×C₄×C₁₀₃ ◁ C₂×C₈×C₁₀₃ ◁ C₂×C₁₆×C₁₀₃ ◁ C₂×C₃₂×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
6. Q₆₄×C₁₀₃	C₄	semidirect
36. #7538	C₁₀₃	direct (N × H)
43. C₁₀₃	#7538	direct (N × H)
46. Q₆₄	C₄×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₆₄×C₁₀₃	2
C₂×C₆₄×C₁₀₃	2
C₁₀₃×#1423	2
#7538	103

Subgroups — C103×#7538 #39912813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#7538 #39912813