Subgroups — C₂×#10597612 #11928680

Order 1248.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₃×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	#10597612	C₂	1	4	yes	maximal, direct product factor
5	C₂×#6101	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×Dic₃₉	C₄	1	4	yes	complemented
8	C₂×Dic₃₉	C₂²	1	2	yes	—
9	C₂×Dic₃×C₁₃	—	2	2	no	—
10	C₂×Dic₃×C₁₃	C₂²	1	2	yes	—
11	C₂×C₃×Dic₁₃	—	2	2	no	—
12	C₂×C₃×Dic₁₃	C₂²	1	2	yes	—
13	C₂²×C₄×C₁₃	—	3	1	no	—
14	C₂²×Dic₁₃	—	3	1	no	—
15	C₂²×Dic₁₃	D₃	1	1	yes	characteristic
16	#6101	—	3	4	no	—
17	C₂²×C₃×C₁₃	C₂×C₄	1	2	yes	—
18	C₂²×C₃×C₁₃	D₄	1	2	yes	—
19	C₂²×C₃×C₁₃	Q₈	1	2	yes	—
20	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
21	Dic₃₉	C₂×C₄	1	4	yes	complemented
22	C₃×Dic₁₃	—	2	2	no	—
23	Dic₃×C₁₃	—	2	2	no	—
24	C₂³×C₁₃	C₂×D₃	1	1	yes	characteristic
25	C₂×C₄×C₁₃	—	3	2	no	—
26	C₂×C₄×C₁₃	—	6	2	no	—
27	C₂×Dic₁₃	—	2	2	no	—
28	C₂×Dic₁₃	—	3	4	no	—
29	C₂×Dic₁₃	—	3	2	no	—
30	C₂×Dic₁₃	C₂×D₃	1	2	yes	—
31	C₂×Dic₃⋊C₄	—	13	1	no	maximal, Hall
32	C₂×C₃×C₁₃	C₄⋊C₄	1	4	yes	complemented
33	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic
36	C₂²×C₁₃	Dic₆	1	2	yes	—
37	C₂²×C₁₃	C₄×D₃	1	2	yes	—
38	C₂²×C₁₃	#67	1	2	yes	—
39	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
40	C₄×C₁₃	—	6	2	no	—
41	Dic₁₃	—	2	2	no	—
42	Dic₁₃	—	3	4	no	—
43	C₂²×C₃×C₄	—	13	1	no	—
44	C₂²×Dic₃	—	13	1	no	—
45	C₂²×Dic₃	D₁₃	1	1	yes	characteristic
46	Dic₃⋊C₄	—	13	4	no	—
47	C₃×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
48	C₂×C₄⋊C₄	—	39	1	no	Sylow
49	C₂×C₁₃	Dic₃⋊C₄	1	4	yes	complemented
50	C₂×C₁₃	C₂×Dic₆	1	1	yes	characteristic
51	C₂×C₁₃	C₂×C₄×D₃	1	1	yes	characteristic
52	C₂×C₁₃	C₂×#67	1	1	yes	characteristic
53	C₂³×C₃	C₂×D₁₃	1	1	yes	characteristic
54	C₂×C₃×C₄	—	13	2	no	—
55	C₂×C₃×C₄	—	26	2	no	—
56	C₂×Dic₃	—	2	2	no	—
57	C₂×Dic₃	—	13	4	no	—
58	C₂×Dic₃	—	13	2	no	—
59	C₂×Dic₃	C₂×D₁₃	1	2	yes	—
60	C₂²×C₄	—	3	1	no	—
61	C₂²×C₄	—	13	1	no	—
62	C₂²×C₄	—	39	1	no	—
63	C₄⋊C₄	—	39	4	no	—
64	C₁₃	C₂×Dic₃⋊C₄	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₃	Dic₂₆	1	2	yes	—
66	C₂²×C₃	C₄×D₁₃	1	2	yes	—
67	C₂²×C₃	C₂²⋊D₁₃	1	2	yes	—
68	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
69	C₃×C₄	—	26	2	no	—
70	Dic₃	—	2	2	no	—
71	Dic₃	—	13	4	no	—
72	C₂³	D₃×D₁₃	1	1	yes	characteristic
73	C₂×C₄	—	3	2	no	—
74	C₂×C₄	—	6	2	no	—
75	C₂×C₄	—	13	2	no	—
76	C₂×C₄	—	26	2	no	—
77	C₂×C₄	—	39	4	no	—
78	C₂×C₄	—	39	2	no	—
79	C₂×C₃	#6101	1	4	yes	complemented
80	C₂×C₃	C₂×Dic₂₆	1	1	yes	characteristic
81	C₂×C₃	C₂×C₄×D₁₃	1	1	yes	characteristic
82	C₂×C₃	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
83	C₂²	#64601	1	2	yes	—
84	C₂²	#64602	1	2	yes	—
85	C₂²	#64605	1	2	yes	—
86	C₂²	C₂×D₃×D₁₃	1	1	yes	characteristic
87	C₄	—	6	2	no	—
88	C₄	—	26	2	no	—
89	C₄	—	39	4	no	—
90	C₃	C₂×#6101	1	1	yes	characteristic, complemented, Sylow
91	C₂	#10597612	1	4	yes	direct product factor
92	C₂	C₂×#64601	1	1	yes	characteristic
93	C₂	C₂×#64602	1	1	yes	characteristic
94	C₂	C₂×#64605	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³	D₃×D₁₃
commutator	C₂×C₃×C₁₃	C₂²×C₄
Frattini	C₂²	C₂×D₃×D₁₃
Fitting, socle, prime radical	C₂³×C₃×C₁₃	C₂²
cosocle	C₂²×C₃×C₁₃	C₂³
hypocenter	C₃×C₁₃	C₂×C₄⋊C₄
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
4. #10597612	C₂	direct (N × H)
7. C₂×Dic₃₉	C₄	semidirect
21. Dic₃₉	C₂×C₄	semidirect
32. C₂×C₃×C₁₃	C₄⋊C₄	semidirect
47. C₃×C₁₃	C₂×C₄⋊C₄	semidirect
49. C₂×C₁₃	Dic₃⋊C₄	semidirect
64. C₁₃	C₂×Dic₃⋊C₄	semidirect
79. C₂×C₃	#6101	semidirect
90. C₃	C₂×#6101	semidirect
91. C₂	#10597612	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₃₉	2
C₂²×Dic₃×C₁₃	2
C₂²×C₃×Dic₁₃	2
#10597612	2
C₂×#6101	3
C₂×Dic₃⋊C₄	13

Subgroups — C2×#10597612 #11928680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10597612 #11928680