Subgroups — C₂×#6107⋊C₃ #11928310

Order 1248.

120 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
2	C₂×(C₁₃⋊C₃)⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	#6107⋊C₃	C₂	1	4	yes	maximal, direct product factor
4	C₂×#1055⋊C₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#6107	C₃	1	1	yes	maximal, characteristic, complemented, Hall
6	Q₈×C₁₃⋊C₃	—	2	1	no	—
7	Q₈×C₁₃⋊C₃	C₂²	1	2	yes	—
8	C₂×C₄×C₁₃⋊C₃	—	2	1	no	—
9	C₂×C₄×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₃⋊C₃	—	2	1	no	—
11	(C₁₃⋊C₃)⋊Q₈	—	2	1	no	—
12	(C₁₃⋊C₃)⋊Q₈	C₂²	1	2	yes	—
13	#1055⋊C₃	C₂²	1	2	yes	—
14	C₂×Q₈×C₁₃	C₂×C₃	1	1	yes	characteristic
15	C₂×Dic₂₆	C₂×C₃	1	1	yes	characteristic
16	#6107	C₂×C₃	1	4	yes	complemented
17	C₂×#1055	C₂×C₃	1	1	yes	characteristic
18	C₂²×C₁₃⋊C₃	D₄	1	1	yes	characteristic
19	C₄×C₁₃⋊C₃	—	2	2	no	—
20	C₄×C₁₃⋊C₃	D₄	1	1	yes	characteristic
21	C₄×C₁₃⋊C₃	C₂³	1	1	yes	characteristic
22	Dic₁₃⋊C₃	—	2	2	no	—
23	Q₈×C₁₃	—	2	1	no	—
24	Q₈×C₁₃	C₂²×C₃	1	2	yes	—
25	C₂×C₄×C₁₃	—	2	1	no	—
26	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
27	C₂×Dic₁₃	—	2	1	no	—
28	Dic₂₆	—	2	1	no	—
29	Dic₂₆	C₂²×C₃	1	2	yes	—
30	#1055	C₂²×C₃	1	2	yes	—
31	C₂×C₃×Q₁₆	—	13	1	no	maximal, Hall
32	C₂×C₁₃⋊C₃	Q₁₆	1	2	yes	complemented
33	C₂×C₁₃⋊C₃	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₁₃	C₃×D₄	1	1	yes	characteristic
35	C₄×C₁₃	—	2	2	no	—
36	C₄×C₁₃	C₃×D₄	1	1	yes	characteristic
37	C₄×C₁₃	C₂³×C₃	1	1	yes	characteristic
38	Dic₁₃	—	2	2	no	—
39	C₂×C₃×Q₈	—	13	1	no	—
40	C₂×C₃×Q₈	—	13	1	no	—
41	C₃×Q₁₆	—	13	4	no	—
42	C₂×C₃×C₈	—	13	1	no	—
43	C₁₃⋊C₃	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
44	C₂×Q₁₆	—	13	1	no	Sylow
45	C₂×C₁₃	C₃×Q₁₆	1	2	yes	complemented
46	C₂×C₁₃	C₂×C₃×D₄	1	1	yes	characteristic
47	C₃×Q₈	—	13	2	no	—
48	C₃×Q₈	—	13	2	no	—
49	C₃×Q₈	—	26	1	no	—
50	C₃×Q₈	—	26	1	no	—
51	C₂×C₃×C₄	—	13	1	no	—
52	C₂×C₃×C₄	—	26	1	no	—
53	C₂×C₃×C₄	—	26	1	no	—
54	C₃×C₈	—	13	2	no	—
55	C₂×Q₈	—	13	1	no	—
56	C₂×Q₈	D₁₃⋊C₃	1	1	yes	characteristic
57	Q₁₆	—	13	4	no	—
58	C₂×C₈	—	13	1	no	—
59	C₁₃	C₂×C₃×Q₁₆	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₃	—	13	1	no	—
61	C₃×C₄	—	13	1	no	—
62	C₃×C₄	—	13	1	no	—
63	C₃×C₄	—	26	2	no	—
64	C₃×C₄	—	26	2	no	—
65	Q₈	—	2	1	no	—
66	Q₈	—	13	2	no	—
67	Q₈	—	26	1	no	—
68	Q₈	C₂×D₁₃⋊C₃	1	2	yes	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	26	1	no	—
71	C₂×C₄	C₂×D₁₃⋊C₃	1	1	yes	characteristic
72	C₈	—	13	2	no	—
73	C₂×C₃	—	13	1	no	—
74	C₂×C₃	—	13	2	no	—
75	C₂²	(C₂²⋊D₁₃)⋊C₃	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	26	2	no	—
78	C₄	(C₂²⋊D₁₃)⋊C₃	1	1	yes	characteristic
79	C₄	C₂²×D₁₃⋊C₃	1	1	yes	characteristic
80	C₃	—	13	1	no	Sylow
81	C₂	#6107⋊C₃	1	2	yes	direct product factor
82	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	C₂²×C₁₃⋊C₃	D₄
hypercenter	C₂×Q₈	D₁₃⋊C₃
hypocenter	C₁₃	C₂×C₃×Q₁₆
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
3. #6107⋊C₃	C₂	direct (N × H)
5. C₂×#6107	C₃	semidirect
16. #6107	C₂×C₃	semidirect
32. C₂×C₁₃⋊C₃	Q₁₆	semidirect
43. C₁₃⋊C₃	C₂×Q₁₆	semidirect
45. C₂×C₁₃	C₃×Q₁₆	semidirect
59. C₁₃	C₂×C₃×Q₁₆	semidirect
81. C₂	#6107⋊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×(C₁₃⋊C₃)⋊Q₈	2
#6107⋊C₃	2
C₂×#1055⋊C₃	2
C₂×#6107	3
C₂×C₃×Q₁₆	13

Subgroups — C2×#6107⋊C3 #11928310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6107⋊C₃ #11928310