Subgroups — #27193217

Order 13184.

70 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	#20267544	C₂	1	1	yes	maximal, characteristic
3	#335×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₀₃⋊C₁₆	C₄	1	1	yes	characteristic
5	C₂×C₁₀₃⋊C₁₆	C₄	1	1	yes	characteristic
6	C₄⋊(C₁₀₃⋊C₈)	—	2	1	no	—
7	C₄⋊C₈×C₁₀₃	—	2	1	no	—
8	C₄×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
9	C₂×C₁₀₃⋊C₈	—	4	1	no	—
10	C₁₀₃⋊C₁₆	—	2	1	no	—
11	C₁₀₃⋊C₁₆	C₈	1	2	yes	complemented
12	C₂×C₈×C₁₀₃	—	4	1	no	—
13	C₂×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₁₀₃	Q₈	1	1	yes	characteristic
15	C₄²×C₁₀₃	D₄	1	1	yes	characteristic
16	C₂×C₄×C₁₀₃	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₃	D₈	1	1	yes	characteristic
18	C₂×C₄×C₁₀₃	Q₁₆	1	1	yes	characteristic
19	C₈×C₁₀₃	—	2	1	no	—
20	C₈×C₁₀₃	—	8	1	no	—
21	C₈×C₁₀₃	C₂×C₈	1	1	yes	characteristic
22	C₈×C₁₀₃	M₁₆	1	1	yes	characteristic
23	C₁₀₃⋊C₈	—	8	1	no	—
24	C₂²×C₁₀₃	#107	1	1	yes	characteristic
25	C₄×C₁₀₃	—	2	1	no	—
26	C₄×C₁₀₃	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₁₀₃	#108	1	1	yes	characteristic
28	C₄×C₁₀₃	SD₃₂	1	1	yes	characteristic
29	C₄×C₁₀₃	SD₃₂	1	1	yes	characteristic
30	C₂×C₁₀₃	#335	1	1	yes	characteristic
31	C₂×C₁₀₃	#367	1	1	yes	characteristic
32	C₂×C₁₀₃	#368	1	1	yes	characteristic
33	#1372	—	103	1	no	maximal, Sylow
34	C₁₀₃	#1372	1	1	yes	characteristic, complemented, Sylow
35	C₄×C₁₆	—	103	1	no	—
36	#335	—	103	1	no	—
37	#335	D₁₀₃	1	1	yes	characteristic
38	C₂×C₁₆	—	103	1	no	—
39	C₂×C₁₆	—	103	1	no	—
40	C₄⋊C₈	—	2	1	no	—
41	C₄⋊C₈	—	206	1	no	—
42	C₄×C₈	C₂×D₁₀₃	1	1	yes	characteristic
43	C₂×C₈	—	4	1	no	—
44	C₂×C₈	—	412	1	no	—
45	C₂×C₈	Dic₂₀₆	1	1	yes	characteristic
46	C₂×C₈	C₄×D₁₀₃	1	1	yes	characteristic
47	C₄²	C₂²⋊D₁₀₃	1	1	yes	characteristic
48	C₁₆	—	103	2	no	—
49	C₁₆	—	206	1	no	—
50	C₂×C₄	Dic₁₀₃⋊C₄	1	1	yes	characteristic
51	C₂×C₄	#13110090	1	1	yes	characteristic
52	C₂×C₄	#13110095	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	—	8	1	no	—
55	C₈	—	824	1	no	—
56	C₈	C₈×D₁₀₃	1	1	yes	characteristic
57	C₈	#13110088	1	1	yes	characteristic
58	C₂²	#15692954	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	Dic₁₀₃⋊C₈	1	1	yes	characteristic
61	C₄	#15692956	1	1	yes	characteristic
62	C₄	#15692964	1	1	yes	characteristic
63	C₄	#15692965	1	1	yes	characteristic
64	C₂	#20267543	1	1	yes	characteristic
65	C₂	#20267618	1	1	yes	characteristic
66	C₂	#20267620	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13110090
commutator	C₈×C₁₀₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₀₃
Fitting	#335×C₁₀₃	C₂
socle, prime radical	C₂²×C₁₀₃	#107
cosocle	C₄×C₈×C₁₀₃	C₂²
hypercenter	#335	D₁₀₃
hypocenter	C₁₀₃	#1372
LCS	G ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
11. C₁₀₃⋊C₁₆	C₈	semidirect
34. C₁₀₃	#1372	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
#20267544	2
#335×C₁₀₃	2
#1372	103