Subgroups — #27193333

Order 13184.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₆₄₈	C₂	1	1	yes	maximal, characteristic
2	#20267625	C₂	1	1	yes	maximal, characteristic, complemented
3	#368×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈₂₄	—	2	1	no	—
5	D₁₆₄₈	—	2	1	no	—
6	D₁₆₄₈	C₄	1	2	yes	—
7	C₁₀₃⋊C₃₂	—	2	1	no	—
8	C₂×C₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
9	#108×C₁₀₃	—	2	1	no	—
10	C₂×D₄₁₂	—	4	1	no	—
11	D₈₂₄	—	2	2	no	—
12	D₈₂₄	—	4	1	no	—
13	M₁₆×C₁₀₃	—	4	1	no	—
14	C₂×C₈×C₁₀₃	D₄	1	1	yes	characteristic
15	C₁₆×C₁₀₃	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₁₀₃	D₄	1	1	yes	characteristic
17	C₂²×D₁₀₃	—	8	1	no	—
18	C₂×C₄×C₁₀₃	D₈	1	1	yes	characteristic
19	D₄₁₂	—	4	2	no	—
20	D₄₁₂	—	8	1	no	—
21	C₈×C₁₀₃	—	8	1	no	—
22	C₈×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₁₀₃	SD₁₆	1	1	yes	characteristic
24	C₂²×C₁₀₃	SD₃₂	1	1	yes	characteristic
25	C₂×D₁₀₃	—	8	2	no	—
26	C₂×D₁₀₃	—	16	2	no	—
27	C₄×C₁₀₃	#102	1	1	yes	characteristic
28	C₄×C₁₀₃	D₁₆	1	1	yes	characteristic
29	C₂×C₁₀₃	—	2	1	no	—
30	C₂×C₁₀₃	#357	1	1	yes	characteristic
31	D₁₀₃	—	16	2	no	—
32	#1419	—	103	1	no	maximal, Sylow
33	C₁₀₃	#1419	1	1	yes	characteristic, complemented, Sylow
34	C₂×D₁₆	—	103	1	no	—
35	M₆₄	—	103	1	no	—
36	#368	D₁₀₃	1	1	yes	characteristic, complemented
37	C₂×D₈	—	206	1	no	—
38	D₁₆	—	103	2	no	—
39	D₁₆	—	206	1	no	—
40	C₂×C₁₆	C₂×D₁₀₃	1	1	yes	characteristic
41	#108	—	2	1	no	—
42	C₃₂	—	206	1	no	—
43	C₂×D₄	—	412	1	no	—
44	D₈	—	412	1	no	—
45	D₈	—	206	2	no	—
46	M₁₆	—	4	1	no	—
47	C₂×C₈	C₂²⋊D₁₀₃	1	1	yes	characteristic
48	C₁₆	C₄×D₁₀₃	1	1	yes	characteristic
49	C₁₆	D₄₁₂	1	1	yes	characteristic
50	C₂³	—	824	1	no	—
51	D₄	—	824	1	no	—
52	D₄	—	412	2	no	—
53	C₂×C₄	#13110090	1	1	yes	characteristic
54	C₈	—	8	1	no	—
55	C₈	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
56	C₈	#13110092	1	1	yes	characteristic
57	C₂²	—	824	2	no	—
58	C₂²	—	1648	2	no	—
59	C₂²	#15692964	1	1	yes	characteristic
60	C₄	#15692941	1	1	yes	characteristic
61	C₄	#15692962	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	1648	2	no	—
64	C₂	#20267591	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20267591
commutator	C₁₆×C₁₀₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₀₃
Fitting	#368×C₁₀₃	C₂
socle	C₂×C₁₀₃	#357
prime radical	C₂×D₁₆₄₈	C₂
cosocle	C₂×C₁₆×C₁₀₃	C₂²
hypercenter	#368	D₁₀₃
hypocenter	C₁₀₃	#1419
LCS	G ▷ C₁₆×C₁₀₃ ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
2. #20267625	C₂	semidirect
3. #368×C₁₀₃	C₂	semidirect
33. C₁₀₃	#1419	semidirect
36. #368	D₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₆₄₈	2
#20267625	2
#368×C₁₀₃	2
#1419	103