Subgroups — #27193285

Order 13184.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20268207	C₂	1	1	yes	maximal, characteristic
2	#20267625	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₂×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#15693027	C₄	1	1	yes	characteristic
5	#15692961	C₄	1	1	yes	characteristic
6	#15692960	—	2	1	no	—
7	C₁₆×D₁₀₃	—	2	1	no	—
8	C₁₀₃⋊C₃₂	—	2	1	no	—
9	C₂×C₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
10	C₃₂×C₁₀₃	—	2	1	no	—
11	#13110105	C₈	1	1	yes	characteristic
12	#13110089	C₈	1	1	yes	characteristic
13	#13110088	—	2	1	no	—
14	C₈×D₁₀₃	—	2	1	no	—
15	C₁₀₃⋊C₁₆	—	2	1	no	—
16	C₂×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
17	C₁₆×C₁₀₃	D₄	1	1	yes	characteristic
18	C₁₆×C₁₀₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₀₃	C₂×C₈	1	1	yes	characteristic
20	C₂²⋊D₁₀₃	—	2	1	no	—
21	D₄₁₂	C₁₆	1	1	yes	characteristic
22	C₄×D₁₀₃	—	2	1	no	—
23	Dic₂₀₆	C₁₆	1	1	yes	characteristic
24	C₈×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₁₀₃	M₁₆	1	1	yes	characteristic
26	C₁₀₃⋊C₈	—	2	1	no	—
27	C₂²×C₁₀₃	M₃₂	1	1	yes	characteristic
28	C₂×D₁₀₃	—	2	1	no	—
29	C₄×C₁₀₃	C₂²⋊C₈	1	1	yes	characteristic
30	C₄×C₁₀₃	C₂×C₁₆	1	1	yes	characteristic
31	Dic₁₀₃	—	2	1	no	—
32	C₂×C₁₀₃	—	2	1	no	—
33	C₂×C₁₀₃	C₂²⋊C₁₆	1	1	yes	characteristic
34	D₁₀₃	—	4	1	no	—
35	#1401	—	103	1	no	maximal, Sylow
36	C₁₀₃	#1401	1	1	yes	characteristic, complemented, Sylow
37	#504	—	103	1	no	—
38	M₆₄	—	103	1	no	—
39	C₂×C₃₂	D₁₀₃	1	1	yes	characteristic, complemented
40	#131	—	103	1	no	—
41	M₃₂	—	103	1	no	—
42	M₃₂	—	206	1	no	—
43	C₂×C₁₆	—	206	1	no	—
44	C₂×C₁₆	C₂×D₁₀₃	1	1	yes	characteristic
45	C₃₂	—	2	1	no	—
46	C₃₂	—	206	1	no	—
47	#41	—	103	1	no	—
48	M₁₆	—	103	1	no	—
49	M₁₆	—	206	1	no	—
50	C₂×C₈	—	206	1	no	—
51	C₂×C₈	C₄×D₁₀₃	1	1	yes	characteristic
52	C₁₆	—	206	1	no	—
53	C₁₆	D₄₁₂	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₁₀₃	1	1	yes	characteristic
55	Q₈	—	103	1	no	—
56	D₄	—	103	1	no	—
57	D₄	—	206	1	no	—
58	C₂×C₄	—	206	1	no	—
59	C₂×C₄	C₈×D₁₀₃	1	1	yes	characteristic
60	C₈	—	206	1	no	—
61	C₈	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
62	C₈	#13110088	1	1	yes	characteristic
63	C₂²	—	206	1	no	—
64	C₂²	#15692960	1	1	yes	characteristic
65	C₄	—	206	1	no	—
66	C₄	(C₂×D₁₀₃)⋊C₈	1	1	yes	characteristic
67	C₄	C₁₆×D₁₀₃	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	412	1	no	—
70	C₂	(C₂×D₁₀₃)⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₄₁₂
commutator	C₄×C₁₀₃	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₁₀₃
Fitting	C₂×C₃₂×C₁₀₃	C₂
socle	C₂×C₁₀₃	C₂²⋊C₁₆
prime radical	#13110105	C₈
cosocle	C₂×C₁₆×C₁₀₃	C₂²
hypercenter	C₂×C₃₂	D₁₀₃
hypocenter	C₁₀₃	#1401
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #20267625	C₂	semidirect
3. C₂×C₃₂×C₁₀₃	C₂	semidirect
36. C₁₀₃	#1401	semidirect
39. C₂×C₃₂	D₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
#20268207	2
#20267625	2
C₂×C₃₂×C₁₀₃	2
#1401	103