Subgroups — C₂²×#11718037 #16791495

Order 3328.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718037	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#88034	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
4	C₂×#88034	C₄	1	3	yes	—
5	C₂×#88034	C₂²	1	3	yes	—
6	#11718037	C₂²	1	4	yes	direct product factor
7	C₂²×C₈×C₁₃	C₈	1	1	yes	characteristic
8	C₂×C₁₃×C₁₆	C₈	1	3	yes	—
9	C₂×C₁₃×C₁₆	C₂×C₄	1	3	yes	—
10	#88034	C₂×C₄	1	3	yes	—
11	#88034	C₂³	1	1	yes	characteristic
12	C₂²×C₆₄	—	13	1	no	maximal, Sylow
13	C₂²×C₄×C₁₃	C₁₆	1	1	yes	characteristic
14	C₂×C₈×C₁₃	C₁₆	1	3	yes	—
15	C₂×C₈×C₁₃	C₂×C₈	1	3	yes	—
16	C₁₃×C₁₆	C₂×C₈	1	3	yes	—
17	C₁₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
18	C₂²×C₃₂	—	13	1	no	—
19	C₂×C₆₄	—	13	6	no	—
20	C₂³×C₁₃	C₃₂	1	1	yes	characteristic
21	C₂×C₄×C₁₃	C₃₂	1	3	yes	—
22	C₂×C₄×C₁₃	C₂×C₁₆	1	3	yes	—
23	C₈×C₁₃	C₂×C₁₆	1	3	yes	—
24	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
25	C₂²×C₁₆	#261	1	1	yes	characteristic
26	C₂×C₃₂	—	13	3	no	—
27	C₂×C₃₂	—	13	3	no	—
28	C₆₄	—	13	4	no	—
29	C₂²×C₁₃	C₆₄	1	4	yes	complemented
30	C₂²×C₁₃	C₂×C₃₂	1	3	yes	—
31	C₄×C₁₃	C₂×C₃₂	1	3	yes	—
32	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
33	C₂²×C₈	#1057	1	1	yes	characteristic
34	C₂×C₁₆	#1057	1	3	yes	—
35	C₂×C₁₆	C₂×#261	1	3	yes	—
36	C₃₂	—	13	1	no	—
37	C₃₂	—	13	3	no	—
38	C₂×C₁₃	C₂×C₆₄	1	6	yes	complemented
39	C₂×C₁₃	C₂²×C₃₂	1	1	yes	characteristic
40	C₂²×C₄	#6092	1	1	yes	characteristic
41	C₂×C₈	#6092	1	3	yes	—
42	C₂×C₈	C₂×#1057	1	3	yes	—
43	C₁₆	C₂×#1057	1	3	yes	—
44	C₁₆	C₂²×#261	1	1	yes	characteristic
45	C₁₃	C₂²×C₆₄	1	1	yes	characteristic, complemented, Sylow
46	C₂³	#88036	1	1	yes	characteristic
47	C₂×C₄	#88036	1	3	yes	—
48	C₂×C₄	C₂×#6092	1	3	yes	—
49	C₈	C₂×#6092	1	3	yes	—
50	C₈	C₂²×#1057	1	1	yes	characteristic
51	C₂²	#11718037	1	4	yes	direct product factor
52	C₂²	C₂×#88036	1	3	yes	—
53	C₄	C₂×#88036	1	3	yes	—
54	C₄	C₂²×#6092	1	1	yes	characteristic
55	C₂	C₂×#11718037	1	6	yes	direct product factor
56	C₂	C₂²×#88036	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₁₆	#261
commutator, hypocenter	C₁₃	C₂²×C₆₄
Frattini	C₁₆	C₂²×#261
Fitting	C₂²×C₁₃×C₁₆	C₄
socle, prime radical	C₂³×C₁₃	C₃₂
cosocle	#88034	C₂³
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#11718037	C₂	direct (N × H)
6. #11718037	C₂²	direct (N × H)
29. C₂²×C₁₃	C₆₄	semidirect
38. C₂×C₁₃	C₂×C₆₄	semidirect
45. C₁₃	C₂²×C₆₄	semidirect
51. C₂²	#11718037	direct (N × H)
55. C₂	C₂×#11718037	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×#11718037	2
C₂²×#88034	2
C₂²×C₆₄	13

Subgroups — C22×#11718037 #16791495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11718037 #16791495