Subgroups — C₂×#11719162 #13131800

Order 1664.

368 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88202	C₂	1	1	yes	maximal, characteristic
2	#11719162	C₂	1	8	yes	maximal, direct product factor
3	C₂×#88106	C₂	1	3	yes	maximal, complemented
4	C₂²×#6092	C₂	1	3	yes	maximal, complemented
5	C₂×C₁₃×#41	C₄	1	1	yes	characteristic
6	#88202	C₄	1	4	yes	—
7	#88202	C₂²	1	4	yes	—
8	C₂×#6099	C₄	1	3	yes	—
9	C₂²×#1055	C₂²	1	3	yes	—
10	#88106	C₂²	1	12	yes	complemented
11	C₂×#6092	C₂²	1	1	yes	characteristic
12	C₂×#6092	C₂²	1	3	yes	—
13	C₂×#6092	C₂²	1	12	yes	complemented
14	C₁₃×#41	C₈	1	4	yes	—
15	C₁₃×#41	C₂×C₄	1	4	yes	—
16	C₂×Q₈×C₁₃	C₈	1	1	yes	characteristic
17	C₂×D₄×C₁₃	C₈	1	3	yes	—
18	C₂²×C₄×C₁₃	C₂×C₄	1	3	yes	—
19	#6099	C₂×C₄	1	12	yes	—
20	C₂×#1055	C₂×C₄	1	3	yes	—
21	C₂×#1055	C₂×C₄	1	6	yes	—
22	C₂×#1055	C₂³	1	1	yes	characteristic
23	C₂×#1055	C₂³	1	6	yes	—
24	#6092	C₂³	1	2	yes	—
25	#6092	C₂³	1	6	yes	—
26	C₂×#504	—	13	1	no	maximal, Sylow
27	C₂³×C₁₃	C₂×C₈	1	3	yes	—
28	Q₈×C₁₃	C₂×C₈	1	4	yes	—
29	D₄×C₁₃	C₂×C₈	1	12	yes	—
30	C₂×C₄×C₁₃	C₂×C₈	1	3	yes	—
31	C₂×C₄×C₁₃	C₂×C₈	1	6	yes	—
32	C₂×C₄×C₁₃	C₂²×C₄	1	6	yes	—
33	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
34	#1055	C₂²×C₄	1	1	yes	characteristic
35	#1055	C₂²×C₄	1	6	yes	—
36	#1055	C₂⁴	1	1	yes	characteristic
37	C₂×#131	—	13	1	no	—
38	#504	—	13	8	no	—
39	C₂×M₃₂	—	13	3	no	—
40	C₂²×C₁₆	—	13	3	no	—
41	C₂²×C₁₃	—	2	6	no	—
42	C₂²×C₁₃	C₂²×C₈	1	6	yes	—
43	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
44	C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
45	C₄×C₁₃	C₂²×C₈	1	6	yes	—
46	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
47	C₂×#41	#261	1	1	yes	characteristic
48	#131	—	13	4	no	—
49	#131	—	13	4	no	—
50	C₂×M₁₆	—	13	3	no	—
51	C₂²×C₈	—	13	3	no	—
52	M₃₂	—	13	12	no	—
53	C₂×C₁₆	—	13	1	no	—
54	C₂×C₁₆	—	13	3	no	—
55	C₂×C₁₆	—	13	12	no	—
56	C₂×C₁₃	—	2	6	no	—
57	C₂×C₁₃	#504	1	2	yes	complemented
58	C₂×C₁₃	C₂³×C₈	1	1	yes	characteristic
59	#41	#1057	1	4	yes	—
60	#41	C₂×#261	1	4	yes	—
61	C₂×Q₈	#1057	1	1	yes	characteristic
62	C₂×D₄	#1057	1	3	yes	—
63	C₂²×C₄	C₂×#261	1	3	yes	—
64	M₁₆	—	13	12	no	—
65	C₂×C₈	—	13	6	no	—
66	C₂×C₈	—	13	6	no	—
67	C₂×C₈	—	13	1	no	—
68	C₂×C₈	—	13	3	no	—
69	C₁₆	—	13	2	no	—
70	C₁₆	—	13	6	no	—
71	C₁₃	C₂×#504	1	1	yes	characteristic, complemented, Sylow
72	C₂³	C₂×#1057	1	3	yes	—
73	Q₈	C₂×#1057	1	4	yes	—
74	D₄	C₂×#1057	1	12	yes	—
75	C₂×C₄	C₂×#1057	1	3	yes	—
76	C₂×C₄	C₂×#1057	1	6	yes	—
77	C₂×C₄	C₂²×#261	1	6	yes	—
78	C₂×C₄	C₂²×#261	1	1	yes	characteristic
79	C₈	—	13	1	no	—
80	C₈	—	13	1	no	—
81	C₈	—	13	6	no	—
82	C₂²	—	2	6	no	—
83	C₂²	C₂²×#1057	1	6	yes	—
84	C₂²	C₂²×#1057	1	1	yes	characteristic
85	C₄	C₂²×#1057	1	1	yes	characteristic
86	C₄	C₂²×#1057	1	6	yes	—
87	C₄	C₂³×#261	1	1	yes	characteristic
88	C₂	—	2	6	no	—
89	C₂	#11719162	1	2	yes	direct product factor
90	C₂	C₂³×#1057	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#261
commutator	C₂×C₁₃	C₂³×C₈
Frattini	C₄	C₂³×#261
Fitting, prime radical	C₂×C₁₃×#41	C₄
socle	C₂²×C₁₃	C₂²×C₈
cosocle	#1055	C₂⁴
hypercenter	C₂×#41	#261
hypocenter	C₁₃	C₂×#504
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
2. #11719162	C₂	direct (N × H)
3. C₂×#88106	C₂	semidirect
4. C₂²×#6092	C₂	semidirect
10. #88106	C₂²	semidirect
13. C₂×#6092	C₂²	semidirect
57. C₂×C₁₃	#504	semidirect
71. C₁₃	C₂×#504	semidirect
89. C₂	#11719162	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×#88202	2
#11719162	2
C₂×#88106	2
C₂²×#6092	2
C₂×#504	13

Subgroups — C2×#11719162 #13131800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11719162 #13131800