Subgroups — C₂×#20267631 #27197448

Order 13184.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₈₂₄	C₂	1	1	yes	maximal, characteristic
2	#20267631	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₀₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₃₂×C₁₀₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₄₁₂	—	2	1	no	—
6	Dic₈₂₄	—	2	1	no	—
7	Dic₈₂₄	C₂²	1	2	yes	—
8	C₁₀₃⋊C₃₂	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₁₀₃	—	2	1	no	—
10	Q₃₂×C₁₀₃	—	2	1	no	—
11	Q₃₂×C₁₀₃	C₂²	1	2	yes	—
12	C₂×C₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
13	C₂×Dic₂₀₆	—	4	1	no	—
14	Dic₄₁₂	—	2	2	no	—
15	Dic₄₁₂	—	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	Q₈×C₁₀₃	—	4	2	no	—
23	Q₈×C₁₀₃	—	8	1	no	—
24	C₂×C₄×C₁₀₃	—	8	1	no	—
25	C₂×C₄×C₁₀₃	D₈	1	1	yes	characteristic
26	C₂×Dic₁₀₃	—	8	1	no	—
27	Dic₂₀₆	—	4	2	no	—
28	Dic₂₀₆	—	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	C₄×C₁₀₃	—	8	2	no	—
33	C₄×C₁₀₃	D₁₆	1	1	yes	characteristic
34	C₄×C₁₀₃	C₂×D₈	1	1	yes	characteristic
35	Dic₁₀₃	—	8	2	no	—
36	C₂×C₁₀₃	Q₆₄	1	2	yes	complemented
37	C₂×C₁₀₃	C₂×D₁₆	1	1	yes	characteristic
38	C₂×Q₆₄	—	103	1	no	maximal, Sylow
39	C₁₀₃	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₃₂	—	103	1	no	—
41	C₂×Q₃₂	D₁₀₃	1	1	yes	characteristic
42	Q₆₄	—	103	4	no	—
43	C₂×C₃₂	—	103	1	no	—
44	C₂×Q₁₆	—	2	1	no	—
45	C₂×Q₁₆	—	206	1	no	—
46	Q₃₂	—	2	1	no	—
47	Q₃₂	—	103	2	no	—
48	Q₃₂	—	206	1	no	—
49	Q₃₂	C₂×D₁₀₃	1	2	yes	—
50	C₂×C₁₆	C₂×D₁₀₃	1	1	yes	characteristic
51	C₃₂	—	103	2	no	—
52	C₂×Q₈	—	4	1	no	—
53	C₂×Q₈	—	412	1	no	—
54	Q₁₆	—	2	2	no	—
55	Q₁₆	—	4	1	no	—
56	Q₁₆	—	412	1	no	—
57	Q₁₆	—	206	2	no	—
58	C₂×C₈	C₂²⋊D₁₀₃	1	1	yes	characteristic
59	C₁₆	C₂²⋊D₁₀₃	1	1	yes	characteristic
60	C₁₆	C₂²×D₁₀₃	1	1	yes	characteristic
61	Q₈	—	4	2	no	—
62	Q₈	—	8	1	no	—
63	Q₈	—	824	1	no	—
64	Q₈	—	412	2	no	—
65	C₂×C₄	—	8	1	no	—
66	C₂×C₄	—	824	1	no	—
67	C₂×C₄	#13110090	1	1	yes	characteristic
68	C₈	#13110090	1	1	yes	characteristic
69	C₈	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
70	C₂²	#15692962	1	1	yes	characteristic
71	C₄	—	8	2	no	—
72	C₄	—	824	2	no	—
73	C₄	#15692962	1	1	yes	characteristic
74	C₄	C₂×#13110090	1	1	yes	characteristic
75	C₂	#20267631	1	2	yes	direct product factor
76	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, prime radical	C₂²×C₁₀₃	D₁₆
hypercenter	C₂×Q₃₂	D₁₀₃
hypocenter	C₁₀₃	C₂×Q₆₄
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. #20267631	C₂	direct (N × H)
36. C₂×C₁₀₃	Q₆₄	semidirect
39. C₁₀₃	C₂×Q₆₄	semidirect
75. C₂	#20267631	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×Dic₈₂₄	2
#20267631	2
C₂×C₁₀₃⋊C₃₂	2
C₂×Q₃₂×C₁₀₃	2
C₂×Q₆₄	103

Subgroups — C2×#20267631 #27197448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20267631 #27197448