Subgroups — #20268139

Order 6592.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15693018	C₂	1	1	yes	maximal, characteristic
2	#15692941	C₂	1	4	yes	maximal, complemented
3	C₄×C₁₀₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊Q₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄₁₂	—	2	1	no	—
6	C₂×D₄₁₂	—	2	1	no	—
7	C₂×D₄₁₂	C₂²	1	2	yes	—
8	C₂×C₁₀₃⋊C₈	C₂²	1	2	yes	—
9	C₂×Q₈×C₁₀₃	—	2	1	no	—
10	C₄⋊C₄×C₁₀₃	—	2	1	no	—
11	C₄⋊C₄×C₁₀₃	C₂²	1	2	yes	—
12	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
13	C₂²×D₁₀₃	—	2	2	no	—
14	Q₈×C₁₀₃	—	4	2	no	—
15	C₂×C₄×C₁₀₃	—	2	2	no	—
16	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
18	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
19	D₄₁₂	—	2	4	no	—
20	D₄₁₂	—	4	2	no	—
21	D₄₁₂	—	4	2	no	—
22	C₁₀₃⋊C₈	—	2	2	no	—
23	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
24	C₂×D₁₀₃	—	4	2	no	—
25	C₂×D₁₀₃	—	4	2	no	—
26	C₂×D₁₀₃	—	4	2	no	—
27	C₄×C₁₀₃	—	4	2	no	—
28	C₄×C₁₀₃	D₈	1	2	yes	—
29	C₄×C₁₀₃	SD₁₆	1	2	yes	—
30	C₄×C₁₀₃	#41	1	2	yes	—
31	C₂×C₁₀₃	#124	1	1	yes	characteristic
32	C₂×C₁₀₃	C₂×D₈	1	1	yes	characteristic
33	C₂×C₁₀₃	C₂×SD₁₆	1	1	yes	characteristic
34	D₁₀₃	—	8	2	no	—
35	C₁₀₃	#486	1	1	yes	characteristic, complemented, Sylow
36	#486	—	103	1	no	maximal, Sylow
37	C₄⋊Q₈	D₁₀₃	1	1	yes	characteristic, complemented
38	#127	—	103	1	no	—
39	#102	—	103	4	no	—
40	C₄×C₈	—	103	1	no	—
41	C₂×Q₈	—	2	1	no	—
42	C₂×D₄	—	103	2	no	—
43	C₂×D₄	—	206	1	no	—
44	C₂×D₄	—	206	1	no	—
45	C₂×C₈	—	103	2	no	—
46	C₄⋊C₄	—	2	1	no	—
47	C₄⋊C₄	C₂×D₁₀₃	1	2	yes	—
48	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
49	C₂³	—	206	2	no	—
50	Q₈	—	4	2	no	—
51	D₄	—	412	2	no	—
52	D₄	—	412	2	no	—
53	D₄	—	206	4	no	—
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
57	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
58	C₈	—	206	2	no	—
59	C₂²	—	412	2	no	—
60	C₂²	—	412	2	no	—
61	C₂²	—	412	2	no	—
62	C₂²	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
63	C₄	—	4	2	no	—
64	C₄	#13110090	1	2	yes	—
65	C₄	#13110092	1	2	yes	—
66	C₄	#13110106	1	2	yes	—
67	C₂	—	824	2	no	—
68	C₂	#15693010	1	1	yes	characteristic
69	C₂	C₂×#13110090	1	1	yes	characteristic
70	C₂	C₂×#13110092	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₀₃
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	C₄⋊Q₈×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	C₄⋊Q₈	D₁₀₃
hypocenter	C₁₀₃	#486
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
2. #15692941	C₂	semidirect
3. C₄×C₁₀₃⋊C₈	C₂	semidirect
4. C₄⋊Q₈×C₁₀₃	C₂	semidirect
35. C₁₀₃	#486	semidirect
37. C₄⋊Q₈	D₁₀₃	semidirect