Subgroups — C₂×#20267628 #27197444

Order 13184.

112 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	#20267628	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₀₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₃₂×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈₂₄	—	2	1	no	—
6	D₁₆₄₈	—	2	1	no	—
7	D₁₆₄₈	C₂²	1	2	yes	—
8	C₁₀₃⋊C₃₂	C₂²	1	2	yes	complemented
9	C₂×Q₁₆×C₁₀₃	—	2	1	no	—
10	Q₃₂×C₁₀₃	—	2	1	no	—
11	Q₃₂×C₁₀₃	C₂²	1	2	yes	complemented
12	C₂×C₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
13	C₂×D₄₁₂	—	4	1	no	—
14	D₈₂₄	—	2	2	no	—
15	D₈₂₄	—	4	1	no	—
16	C₂×Q₈×C₁₀₃	—	4	1	no	—
17	Q₁₆×C₁₀₃	—	2	2	no	—
18	Q₁₆×C₁₀₃	—	4	1	no	—
19	C₂×C₈×C₁₀₃	D₄	1	1	yes	characteristic
20	C₁₆×C₁₀₃	D₄	1	1	yes	characteristic
21	C₁₆×C₁₀₃	C₂³	1	1	yes	characteristic
22	C₂²×D₁₀₃	—	8	1	no	—
23	Q₈×C₁₀₃	—	4	2	no	—
24	Q₈×C₁₀₃	—	8	1	no	—
25	C₂×C₄×C₁₀₃	—	8	1	no	—
26	C₂×C₄×C₁₀₃	D₈	1	1	yes	characteristic
27	D₄₁₂	—	4	2	no	—
28	D₄₁₂	—	8	1	no	—
29	C₈×C₁₀₃	D₈	1	1	yes	characteristic
30	C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₁₀₃	D₁₆	1	1	yes	characteristic
32	C₂×D₁₀₃	—	8	2	no	—
33	C₂×D₁₀₃	—	16	2	no	—
34	C₄×C₁₀₃	—	8	2	no	—
35	C₄×C₁₀₃	D₁₆	1	1	yes	characteristic
36	C₄×C₁₀₃	C₂×D₈	1	1	yes	characteristic
37	C₂×C₁₀₃	SD₆₄	1	2	yes	complemented
38	C₂×C₁₀₃	C₂×D₁₆	1	1	yes	characteristic
39	D₁₀₃	—	16	2	no	—
40	C₂×SD₆₄	—	103	1	no	maximal, Sylow
41	C₁₀₃	C₂×SD₆₄	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₃₂	D₁₀₃	1	1	yes	characteristic, complemented
43	C₂×D₁₆	—	103	1	no	—
44	SD₆₄	—	103	4	no	—
45	C₂×C₃₂	—	103	1	no	—
46	C₂×Q₁₆	—	2	1	no	—
47	C₂×D₈	—	206	1	no	—
48	Q₃₂	—	2	1	no	—
49	Q₃₂	C₂×D₁₀₃	1	2	yes	complemented
50	D₁₆	—	103	2	no	—
51	D₁₆	—	206	1	no	—
52	C₂×C₁₆	C₂×D₁₀₃	1	1	yes	characteristic
53	C₃₂	—	103	2	no	—
54	C₂×Q₈	—	4	1	no	—
55	C₂×D₄	—	412	1	no	—
56	Q₁₆	—	2	2	no	—
57	Q₁₆	—	4	1	no	—
58	D₈	—	412	1	no	—
59	D₈	—	206	2	no	—
60	C₂×C₈	C₂²⋊D₁₀₃	1	1	yes	characteristic
61	C₁₆	C₂²⋊D₁₀₃	1	1	yes	characteristic
62	C₁₆	C₂²×D₁₀₃	1	1	yes	characteristic
63	C₂³	—	824	1	no	—
64	Q₈	—	4	2	no	—
65	Q₈	—	8	1	no	—
66	D₄	—	824	1	no	—
67	D₄	—	412	2	no	—
68	C₂×C₄	—	8	1	no	—
69	C₂×C₄	#13110090	1	1	yes	characteristic
70	C₈	#13110090	1	1	yes	characteristic
71	C₈	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
72	C₂²	—	824	2	no	—
73	C₂²	—	1648	2	no	—
74	C₂²	#15692962	1	1	yes	characteristic
75	C₄	—	8	2	no	—
76	C₄	#15692962	1	1	yes	characteristic
77	C₄	C₂×#13110090	1	1	yes	characteristic
78	C₂	—	1648	2	no	—
79	C₂	#20267628	1	2	yes	direct product factor
80	C₂	C₂×#15692962	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15692962
commutator, cosocle	C₁₆×C₁₀₃	C₂³
Frattini	C₁₆	C₂²×D₁₀₃
Fitting	C₂×Q₃₂×C₁₀₃	C₂
socle	C₂²×C₁₀₃	D₁₆
prime radical	C₂×D₁₆₄₈	C₂
hypercenter	C₂×Q₃₂	D₁₀₃
hypocenter	C₁₀₃	C₂×SD₆₄
LCS	G ▷ C₁₆×C₁₀₃ ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
2. #20267628	C₂	direct (N × H)
3. C₂×C₁₀₃⋊C₃₂	C₂	semidirect
4. C₂×Q₃₂×C₁₀₃	C₂	semidirect
8. C₁₀₃⋊C₃₂	C₂²	semidirect
11. Q₃₂×C₁₀₃	C₂²	semidirect
37. C₂×C₁₀₃	SD₆₄	semidirect
41. C₁₀₃	C₂×SD₆₄	semidirect
42. C₂×Q₃₂	D₁₀₃	semidirect
49. Q₃₂	C₂×D₁₀₃	semidirect
79. C₂	#20267628	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₁₆₄₈	2
#20267628	2
C₂×C₁₀₃⋊C₃₂	2
C₂×Q₃₂×C₁₀₃	2
C₂×SD₆₄	103

Subgroups — C2×#20267628 #27197444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20267628 #27197444