Subgroups — C₂×#6106⋊C₃ #11928308

Order 1248.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄⋊(D₁₃⋊C₃)	C₂	1	1	yes	maximal, characteristic
3	#6106⋊C₃	C₂	1	4	yes	maximal, direct product factor
4	C₂×#1055⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#6106	C₃	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂²×D₁₃⋊C₃	—	2	1	no	—
7	Q₈×C₁₃⋊C₃	—	2	1	no	—
8	Q₈×C₁₃⋊C₃	C₂²	1	2	yes	complemented
9	C₂×C₄×C₁₃⋊C₃	—	2	1	no	—
10	C₂×C₄×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
11	C₄⋊(D₁₃⋊C₃)	—	2	1	no	—
12	C₄⋊(D₁₃⋊C₃)	C₂²	1	2	yes	—
13	#1055⋊C₃	C₂²	1	2	yes	complemented
14	C₂×Q₈×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂×D₅₂	C₂×C₃	1	1	yes	characteristic
16	#6106	C₂×C₃	1	4	yes	complemented
17	C₂×#1055	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂²×C₁₃⋊C₃	D₄	1	1	yes	characteristic
19	C₂×D₁₃⋊C₃	—	2	2	no	—
20	C₂×D₁₃⋊C₃	—	4	2	no	—
21	C₄×C₁₃⋊C₃	—	2	2	no	—
22	C₄×C₁₃⋊C₃	D₄	1	1	yes	characteristic
23	C₄×C₁₃⋊C₃	C₂³	1	1	yes	characteristic
24	C₂²×D₁₃	—	2	1	no	—
25	Q₈×C₁₃	—	2	1	no	—
26	Q₈×C₁₃	C₂²×C₃	1	2	yes	complemented
27	C₂×C₄×C₁₃	—	2	1	no	—
28	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
29	D₅₂	—	2	1	no	—
30	D₅₂	C₂²×C₃	1	2	yes	—
31	#1055	C₂²×C₃	1	2	yes	complemented
32	C₂×C₃×SD₁₆	—	13	1	no	maximal, Hall
33	C₂×C₁₃⋊C₃	SD₁₆	1	2	yes	complemented
34	C₂×C₁₃⋊C₃	C₂×D₄	1	1	yes	characteristic
35	D₁₃⋊C₃	—	4	2	no	—
36	C₂²×C₁₃	C₃×D₄	1	1	yes	characteristic
37	C₂×D₁₃	—	2	2	no	—
38	C₂×D₁₃	—	4	2	no	—
39	C₄×C₁₃	—	2	2	no	—
40	C₄×C₁₃	C₃×D₄	1	1	yes	characteristic
41	C₄×C₁₃	C₂³×C₃	1	1	yes	characteristic
42	C₂×C₃×Q₈	—	13	1	no	—
43	C₂×C₃×D₄	—	13	1	no	—
44	C₃×SD₁₆	—	13	4	no	—
45	C₂×C₃×C₈	—	13	1	no	—
46	C₁₃⋊C₃	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
47	C₂×SD₁₆	—	13	1	no	Sylow
48	C₂×C₁₃	C₃×SD₁₆	1	2	yes	complemented
49	C₂×C₁₃	C₂×C₃×D₄	1	1	yes	characteristic
50	D₁₃	—	4	2	no	—
51	C₂³×C₃	—	26	1	no	—
52	C₃×Q₈	—	13	2	no	—
53	C₃×Q₈	—	26	1	no	—
54	C₃×D₄	—	13	2	no	—
55	C₃×D₄	—	26	1	no	—
56	C₂×C₃×C₄	—	13	1	no	—
57	C₂×C₃×C₄	—	26	1	no	—
58	C₃×C₈	—	13	2	no	—
59	C₂×Q₈	D₁₃⋊C₃	1	1	yes	characteristic, complemented
60	C₂×D₄	—	13	1	no	—
61	SD₁₆	—	13	4	no	—
62	C₂×C₈	—	13	1	no	—
63	C₁₃	C₂×C₃×SD₁₆	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₃	—	13	1	no	—
65	C₂²×C₃	—	26	2	no	—
66	C₂²×C₃	—	52	2	no	—
67	C₃×C₄	—	13	1	no	—
68	C₃×C₄	—	13	1	no	—
69	C₃×C₄	—	26	2	no	—
70	C₂³	—	26	1	no	—
71	Q₈	—	2	1	no	—
72	Q₈	C₂×D₁₃⋊C₃	1	2	yes	complemented
73	D₄	—	13	2	no	—
74	D₄	—	26	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	C₂×D₁₃⋊C₃	1	1	yes	characteristic
77	C₈	—	13	2	no	—
78	C₂×C₃	—	13	1	no	—
79	C₂×C₃	—	13	2	no	—
80	C₂×C₃	—	52	2	no	—
81	C₂²	—	26	2	no	—
82	C₂²	—	52	2	no	—
83	C₂²	(C₂²⋊D₁₃)⋊C₃	1	1	yes	characteristic
84	C₄	—	2	2	no	—
85	C₄	(C₂²⋊D₁₃)⋊C₃	1	1	yes	characteristic
86	C₄	C₂²×D₁₃⋊C₃	1	1	yes	characteristic
87	C₃	—	13	1	no	Sylow
88	C₂	—	52	2	no	—
89	C₂	#6106⋊C₃	1	2	yes	direct product factor
90	C₂	C₂×(C₂²⋊D₁₃)⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂²⋊D₁₃)⋊C₃
commutator, cosocle	C₄×C₁₃	C₂³×C₃
Frattini	C₄	C₂²×D₁₃⋊C₃
Fitting	C₂×Q₈×C₁₃	C₂×C₃
socle	C₂²×C₁₃	C₃×D₄
prime radical	C₂×C₄⋊(D₁₃⋊C₃)	C₂
hypercenter	C₂×Q₈	D₁₃⋊C₃
hypocenter	C₁₃	C₂×C₃×SD₁₆
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×C₁₃⋊C₃	C₂	semidirect
3. #6106⋊C₃	C₂	direct (N × H)
4. C₂×#1055⋊C₃	C₂	semidirect
5. C₂×#6106	C₃	semidirect
8. Q₈×C₁₃⋊C₃	C₂²	semidirect
13. #1055⋊C₃	C₂²	semidirect
14. C₂×Q₈×C₁₃	C₂×C₃	semidirect
16. #6106	C₂×C₃	semidirect
17. C₂×#1055	C₂×C₃	semidirect
26. Q₈×C₁₃	C₂²×C₃	semidirect
31. #1055	C₂²×C₃	semidirect
33. C₂×C₁₃⋊C₃	SD₁₆	semidirect
46. C₁₃⋊C₃	C₂×SD₁₆	semidirect
48. C₂×C₁₃	C₃×SD₁₆	semidirect
59. C₂×Q₈	D₁₃⋊C₃	semidirect
63. C₁₃	C₂×C₃×SD₁₆	semidirect
72. Q₈	C₂×D₁₃⋊C₃	semidirect
89. C₂	#6106⋊C₃	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×Q₈×C₁₃⋊C₃	2
C₂×C₄⋊(D₁₃⋊C₃)	2
#6106⋊C₃	2
C₂×#1055⋊C₃	2
C₂×#6106	3
C₂×C₃×SD₁₆	13

Subgroups — C2×#6106⋊C3 #11928308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6106⋊C₃ #11928308