Subgroups — C₂×#11718098 #13116628

Order 1664.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#88059	C₂	1	2	yes	maximal
3	#11718098	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
5	C₂×#6099	—	2	2	no	—
6	C₂×C₁₃×C₁₆	C₄	1	2	yes	—
7	C₂×C₁₃×C₁₆	C₄	1	2	yes	—
8	C₂×C₁₃×C₁₆	C₂²	1	2	yes	—
9	#88059	—	2	2	no	—
10	#88059	C₂²	1	4	yes	—
11	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
12	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
15	C₂×C₈×C₁₃	Q₈	1	1	yes	characteristic
16	C₂×C₈×C₁₃	Q₈	1	1	yes	characteristic
17	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	#6099	—	2	4	no	—
19	#6099	—	4	2	no	—
20	C₂×#1055	—	4	2	no	—
21	C₁₃×C₁₆	C₂×C₄	1	4	yes	—
22	C₂×#368	—	13	1	no	maximal, Sylow
23	C₂³×C₁₃	Q₁₆	1	1	yes	characteristic
24	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
27	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
28	C₂×C₄×C₁₃	Q₁₆	1	1	yes	characteristic
29	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
30	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
31	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
32	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
34	#1055	—	4	4	no	—
35	C₂²×C₁₆	D₁₃	1	1	yes	characteristic
36	C₂×#108	—	13	2	no	—
37	#368	—	13	4	no	—
38	C₂²×C₁₃	—	2	2	no	—
39	C₂²×C₁₃	#107	1	1	yes	characteristic
40	C₂²×C₁₃	#107	1	1	yes	characteristic
41	C₂²×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
42	C₄×C₁₃	#107	1	1	yes	characteristic
43	C₄×C₁₃	#107	1	1	yes	characteristic
44	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
46	C₂×M₁₆	—	26	2	no	—
47	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
48	C₂×C₁₆	Dic₁₃	1	2	yes	—
49	C₂×C₁₆	Dic₁₃	1	2	yes	—
50	C₂×C₁₆	C₂×D₁₃	1	2	yes	—
51	#108	—	13	4	no	—
52	#108	—	26	2	no	—
53	C₂×C₁₃	—	2	1	no	—
54	C₂×C₁₃	—	2	1	no	—
55	C₂×C₁₃	#368	1	2	yes	complemented
56	C₂×C₁₃	C₂×#107	1	1	yes	characteristic
57	C₂²×C₄	D₅₂	1	1	yes	characteristic
58	M₁₆	—	26	4	no	—
59	M₁₆	—	52	2	no	—
60	C₂×C₈	—	52	2	no	—
61	C₂×C₈	Dic₂₆	1	1	yes	characteristic
62	C₂×C₈	Dic₂₆	1	1	yes	characteristic
63	C₂×C₈	D₅₂	1	1	yes	characteristic
64	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
65	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
66	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
67	C₁₆	C₂×Dic₁₃	1	4	yes	—
68	C₁₃	C₂×#368	1	1	yes	characteristic, complemented, Sylow
69	C₂³	Dic₅₂	1	1	yes	characteristic
70	C₂×C₄	D₁₀₄	1	1	yes	characteristic
71	C₂×C₄	D₁₀₄	1	1	yes	characteristic
72	C₂×C₄	Dic₅₂	1	1	yes	characteristic
73	C₂×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
74	C₂×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
75	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
76	C₈	—	52	4	no	—
77	C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
78	C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
79	C₈	C₂×Dic₂₆	1	1	yes	characteristic
80	C₈	C₂²×Dic₁₃	1	1	yes	characteristic
81	C₂²	—	2	2	no	—
82	C₂²	#88058	1	1	yes	characteristic
83	C₂²	#88058	1	1	yes	characteristic
84	C₂²	C₂×Dic₅₂	1	1	yes	characteristic
85	C₄	#88058	1	1	yes	characteristic
86	C₄	#88058	1	1	yes	characteristic
87	C₄	C₂×D₁₀₄	1	1	yes	characteristic
88	C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
89	C₂	—	2	1	no	—
90	C₂	—	2	1	no	—
91	C₂	#11718098	1	2	yes	direct product factor
92	C₂	C₂×#88058	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₀₄
commutator	C₈×C₁₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₂²×C₁₃×C₁₆	C₂
socle	C₂²×C₁₃	#107
prime radical	C₂³×C₁₃	Q₁₆
cosocle	C₂×C₈×C₁₃	C₂³
hypercenter	C₂²×C₁₆	D₁₃
hypocenter	C₁₃	C₂×#368
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
3. #11718098	C₂	direct (N × H)
55. C₂×C₁₃	#368	semidirect
68. C₁₃	C₂×#368	semidirect
91. C₂	#11718098	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×C₁₃×C₁₆	2
C₂×#88059	2
#11718098	2
C₂×#368	13

Subgroups — C2×#11718098 #13116628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11718098 #13116628