Subgroups — C₂×#11718249 #13131256

Order 1664.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6090	C₂	1	1	yes	maximal, characteristic
2	#11718249	C₂	1	4	yes	maximal, direct product factor
3	C₂×#88036	C₂	1	2	yes	maximal, complemented
4	C₂²×C₈×C₁₃	C₄	1	1	yes	characteristic
5	C₂×#6090	C₄	1	2	yes	—
6	C₂×#6090	C₄	1	1	yes	characteristic
7	C₂×#6090	C₂²	1	1	yes	characteristic
8	C₂×#6090	C₂²	1	2	yes	—
9	#88036	C₂²	1	4	yes	complemented
10	C₂²×C₄×C₁₃	C₈	1	1	yes	characteristic
11	C₂×C₈×C₁₃	C₈	1	1	yes	characteristic
12	C₂×C₈×C₁₃	C₈	1	2	yes	—
13	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	#6090	C₂×C₄	1	1	yes	characteristic
16	#6090	C₂×C₄	1	2	yes	—
17	#6090	C₂³	1	1	yes	characteristic
18	C₂×M₆₄	—	13	1	no	maximal, Sylow
19	C₂³×C₁₃	C₁₆	1	1	yes	characteristic
20	C₂×C₄×C₁₃	C₁₆	1	2	yes	—
21	C₂×C₄×C₁₃	C₁₆	1	1	yes	characteristic
22	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
23	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
24	C₈×C₁₃	C₂×C₈	1	2	yes	—
25	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
26	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₁₆	—	13	1	no	—
28	M₆₄	—	13	4	no	—
29	C₂×C₃₂	—	13	2	no	—
30	C₂²×C₁₃	—	2	2	no	—
31	C₂²×C₁₃	C₂×C₁₆	1	2	yes	—
32	C₂²×C₁₃	C₂×C₁₆	1	1	yes	characteristic
33	C₄×C₁₃	C₂×C₁₆	1	2	yes	—
34	C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
35	C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
36	C₂²×C₈	#261	1	1	yes	characteristic
37	C₂×C₁₆	—	13	2	no	—
38	C₂×C₁₆	—	13	2	no	—
39	C₂×C₁₆	—	13	1	no	—
40	C₂×C₁₆	—	13	1	no	—
41	C₃₂	—	13	4	no	—
42	C₂×C₁₃	—	2	2	no	—
43	C₂×C₁₃	M₆₄	1	2	yes	complemented
44	C₂×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
45	C₂²×C₄	#1057	1	1	yes	characteristic
46	C₂×C₈	#1057	1	1	yes	characteristic
47	C₂×C₈	#1057	1	2	yes	—
48	C₂×C₈	C₂×#261	1	2	yes	—
49	C₂×C₈	C₂×#261	1	1	yes	characteristic
50	C₁₆	—	13	1	no	—
51	C₁₆	—	13	2	no	—
52	C₁₆	—	13	1	no	—
53	C₁₃	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
54	C₂³	#6092	1	1	yes	characteristic
55	C₂×C₄	#6092	1	2	yes	—
56	C₂×C₄	#6092	1	1	yes	characteristic
57	C₂×C₄	C₂×#1057	1	2	yes	—
58	C₂×C₄	C₂×#1057	1	1	yes	characteristic
59	C₈	C₂×#1057	1	2	yes	—
60	C₈	C₂×#1057	1	1	yes	characteristic
61	C₈	C₂²×#261	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	C₂×#6092	1	2	yes	—
64	C₂²	C₂×#6092	1	1	yes	characteristic
65	C₄	C₂×#6092	1	2	yes	—
66	C₄	C₂×#6092	1	1	yes	characteristic
67	C₄	C₂²×#1057	1	1	yes	characteristic
68	C₂	—	2	2	no	—
69	C₂	#11718249	1	2	yes	direct product factor
70	C₂	C₂²×#6092	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×#261
commutator	C₂×C₁₃	C₂²×C₁₆
Frattini	C₈	C₂²×#261
Fitting	C₂²×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂×C₁₆
prime radical	C₂³×C₁₃	C₁₆
cosocle	#6090	C₂³
hypercenter	C₂²×C₈	#261
hypocenter	C₁₃	C₂×M₆₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #11718249	C₂	direct (N × H)
3. C₂×#88036	C₂	semidirect
9. #88036	C₂²	semidirect
43. C₂×C₁₃	M₆₄	semidirect
53. C₁₃	C₂×M₆₄	semidirect
69. C₂	#11718249	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×#6090	2
#11718249	2
C₂×#88036	2
C₂×M₆₄	13

Subgroups — C2×#11718249 #13131256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11718249 #13131256