Subgroups — #27193213

Order 13184.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₁₀₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
2	C₈×C₁₀₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₀₃⋊C₁₆	—	2	1	no	—
5	C₄×C₁₀₃⋊C₈	C₄	1	1	yes	characteristic
6	C₄×C₁₀₃⋊C₈	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₀₃	—	2	1	no	—
8	C₄×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
9	C₂×C₁₀₃⋊C₈	—	2	1	no	—
10	C₂×C₁₀₃⋊C₈	C₈	1	1	yes	characteristic
11	C₂×C₁₀₃⋊C₈	C₈	1	1	yes	characteristic
12	C₁₀₃⋊C₁₆	—	4	1	no	—
13	C₂×C₈×C₁₀₃	D₄	1	1	yes	characteristic
14	C₂×C₈×C₁₀₃	Q₈	1	1	yes	characteristic
15	C₄²×C₁₀₃	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₁₀₃	—	4	1	no	—
17	C₂×C₄×C₁₀₃	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₁₀₃	C₂×C₈	1	1	yes	characteristic
19	C₂×C₄×C₁₀₃	M₁₆	1	1	yes	characteristic
20	C₈×C₁₀₃	—	2	1	no	—
21	C₈×C₁₀₃	D₈	1	1	yes	characteristic
22	C₈×C₁₀₃	Q₁₆	1	1	yes	characteristic
23	C₁₀₃⋊C₈	—	2	2	no	—
24	C₁₀₃⋊C₈	—	2	1	no	—
25	C₁₀₃⋊C₈	C₁₆	1	2	yes	complemented
26	C₂²×C₁₀₃	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₁₀₃	—	2	1	no	—
28	C₄×C₁₀₃	#107	1	1	yes	characteristic
29	C₄×C₁₀₃	#108	1	1	yes	characteristic
30	C₄×C₁₀₃	C₂×C₁₆	1	1	yes	characteristic
31	C₄×C₁₀₃	M₃₂	1	1	yes	characteristic
32	C₂×C₁₀₃	#335	1	1	yes	characteristic
33	C₂×C₁₀₃	C₄⋊C₁₆	1	1	yes	characteristic
34	C₂×C₁₀₃	#364	1	1	yes	characteristic
35	#1370	—	103	1	no	maximal, Sylow
36	C₁₀₃	#1370	1	1	yes	characteristic, complemented, Sylow
37	C₄⋊C₁₆	—	103	1	no	—
38	C₄⋊C₁₆	D₁₀₃	1	1	yes	characteristic
39	C₈²	—	103	1	no	—
40	C₂×C₁₆	—	2	1	no	—
41	C₂×C₁₆	—	206	1	no	—
42	C₄×C₈	—	103	1	no	—
43	C₄×C₈	—	103	1	no	—
44	C₄×C₈	C₂×D₁₀₃	1	1	yes	characteristic
45	C₂×C₈	—	103	1	no	—
46	C₂×C₈	—	103	1	no	—
47	C₂×C₈	—	206	1	no	—
48	C₂×C₈	Dic₂₀₆	1	1	yes	characteristic
49	C₂×C₈	C₂²⋊D₁₀₃	1	1	yes	characteristic
50	C₄²	C₄×D₁₀₃	1	1	yes	characteristic
51	C₁₆	—	4	1	no	—
52	C₁₆	—	412	1	no	—
53	C₂×C₄	Dic₁₀₃⋊C₄	1	1	yes	characteristic
54	C₂×C₄	C₈×D₁₀₃	1	1	yes	characteristic
55	C₂×C₄	#13110088	1	1	yes	characteristic
56	C₈	—	2	1	no	—
57	C₈	—	103	2	no	—
58	C₈	—	206	2	no	—
59	C₈	—	206	1	no	—
60	C₈	#13110090	1	1	yes	characteristic
61	C₈	#13110095	1	1	yes	characteristic
62	C₂²	Dic₁₀₃⋊C₈	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	#15692954	1	1	yes	characteristic
65	C₄	#15692956	1	1	yes	characteristic
66	C₄	C₁₆×D₁₀₃	1	1	yes	characteristic
67	C₄	#15692960	1	1	yes	characteristic
68	C₂	#20267543	1	1	yes	characteristic
69	C₂	Dic₁₀₃⋊C₁₆	1	1	yes	characteristic
70	C₂	#20267611	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₁₀₃
commutator	C₄×C₁₀₃	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₁₀₃
Fitting	C₄⋊C₁₆×C₁₀₃	C₂
socle, prime radical	C₂²×C₁₀₃	C₄⋊C₈
cosocle	C₄×C₈×C₁₀₃	C₂²
hypercenter	C₄⋊C₁₆	D₁₀₃
hypocenter	C₁₀₃	#1370
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
25. C₁₀₃⋊C₈	C₁₆	semidirect
36. C₁₀₃	#1370	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊(C₁₀₃⋊C₁₆)	2
C₈×C₁₀₃⋊C₈	2
C₄⋊C₁₆×C₁₀₃	2
#1370	103