Subgroups — C₂×#11718223 #13131189

Order 1664.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88104	C₂	1	2	yes	maximal
2	C₂×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
3	#11718223	C₂	1	4	yes	maximal, direct product factor
4	C₂×#6118	—	2	2	no	—
5	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
6	#88104	—	2	2	no	—
7	#88104	C₂²	1	4	yes	—
8	C₂×C₁₃×C₁₆	C₄	1	1	yes	characteristic
9	C₂×#6090	C₄	1	1	yes	characteristic
10	C₁₆×D₁₃	C₄	1	2	yes	—
11	C₁₆×D₁₃	C₂²	1	2	yes	—
12	C₂×C₄×D₁₃	D₄	1	1	yes	characteristic
13	C₂×#1057	—	4	2	no	—
14	#6118	—	2	4	no	—
15	#6118	—	4	2	no	—
16	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×#1055	Q₈	1	1	yes	characteristic
18	C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
19	C₈×D₁₃	D₄	1	1	yes	characteristic
20	C₈×D₁₃	Q₈	1	1	yes	characteristic
21	C₈×D₁₃	C₂³	1	1	yes	characteristic
22	C₁₃×C₁₆	C₂×C₄	1	2	yes	—
23	#6090	C₂×C₄	1	2	yes	—
24	C₂×#368	—	13	1	no	maximal, Sylow
25	C₂²×D₁₃	Q₁₆	1	1	yes	characteristic
26	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
27	C₂×Dic₁₃	D₈	1	1	yes	characteristic
28	C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
29	C₄×D₁₃	D₈	1	1	yes	characteristic
30	C₄×D₁₃	Q₁₆	1	1	yes	characteristic
31	C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
32	#1057	—	4	4	no	—
33	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
34	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
35	#1055	C₄⋊C₄	1	1	yes	characteristic
36	#1055	C₂×Q₈	1	1	yes	characteristic
37	C₂²×C₁₆	—	13	1	no	—
38	C₂×#108	—	13	2	no	—
39	#368	—	13	4	no	—
40	C₂²×C₁₃	#107	1	1	yes	characteristic
41	C₂×D₁₃	—	2	2	no	—
42	C₂×D₁₃	#107	1	1	yes	characteristic
43	C₂×D₁₃	C₂×Q₁₆	1	1	yes	characteristic
44	C₄×C₁₃	#107	1	1	yes	characteristic
45	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
46	Dic₁₃	#107	1	1	yes	characteristic
47	Dic₁₃	C₂×D₈	1	1	yes	characteristic
48	C₂×M₁₆	—	26	2	no	—
49	C₂²×C₈	—	13	1	no	—
50	C₂×C₁₆	—	13	1	no	—
51	C₂×C₁₆	—	13	2	no	—
52	C₂×C₁₆	—	13	2	no	—
53	C₂×C₁₆	#261	1	1	yes	characteristic
54	#108	—	13	4	no	—
55	#108	—	26	2	no	—
56	C₂×C₁₃	#368	1	2	yes	complemented
57	C₂×C₁₃	C₂×#107	1	1	yes	characteristic
58	D₁₃	—	2	1	no	—
59	D₁₃	—	2	1	no	—
60	C₂²×C₄	—	13	1	no	—
61	M₁₆	—	26	4	no	—
62	M₁₆	—	52	2	no	—
63	C₂×C₈	—	13	1	no	—
64	C₂×C₈	—	13	1	no	—
65	C₂×C₈	—	13	1	no	—
66	C₂×C₈	—	13	1	no	—
67	C₂×C₈	—	13	1	no	—
68	C₂×C₈	—	52	2	no	—
69	C₂×C₈	C₂×#261	1	1	yes	characteristic
70	C₁₆	—	13	2	no	—
71	C₁₆	C₂×#261	1	2	yes	—
72	C₁₃	C₂×#368	1	1	yes	characteristic, complemented, Sylow
73	C₂³	—	13	1	no	—
74	C₂×C₄	—	13	1	no	—
75	C₂×C₄	—	13	1	no	—
76	C₂×C₄	—	13	1	no	—
77	C₂×C₄	—	13	1	no	—
78	C₂×C₄	—	13	1	no	—
79	C₂×C₄	C₄⋊#261	1	1	yes	characteristic
80	C₈	—	13	1	no	—
81	C₈	—	13	1	no	—
82	C₈	—	52	4	no	—
83	C₈	C₄⋊#261	1	1	yes	characteristic
84	C₈	C₂²×#261	1	1	yes	characteristic
85	C₂²	—	13	1	no	—
86	C₂²	—	13	1	no	—
87	C₂²	—	26	2	no	—
88	C₂²	#88102	1	1	yes	characteristic
89	C₄	—	13	1	no	—
90	C₄	—	13	1	no	—
91	C₄	#88102	1	1	yes	characteristic
92	C₄	C₂×C₄⋊#261	1	1	yes	characteristic
93	C₂	—	26	1	no	—
94	C₂	—	26	1	no	—
95	C₂	#11718223	1	2	yes	direct product factor
96	C₂	C₂×#88102	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#88102
commutator	C₈×C₁₃	C₂²×C₄
Frattini	C₈	C₂²×#261
Fitting	C₂×C₁₃×C₁₆	C₄
socle	C₂²×C₁₃	#107
prime radical	C₂²×D₁₃	Q₁₆
cosocle	C₈×D₁₃	C₂³
hypercenter	C₂×C₁₆	#261
hypocenter	C₁₃	C₂×#368
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
3. #11718223	C₂	direct (N × H)
56. C₂×C₁₃	#368	semidirect
72. C₁₃	C₂×#368	semidirect
95. C₂	#11718223	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×#88104	2
C₂×C₁₆×D₁₃	2
#11718223	2
C₂×#368	13

Subgroups — C2×#11718223 #13131189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11718223 #13131189