Subgroups — C₂²×#88036 #13131254

Order 1664.

120 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	C₂×#88036	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₈×C₁₃	C₄	1	1	yes	characteristic
4	C₂×#6090	C₄	1	3	yes	—
5	C₂×#6090	C₂²	1	3	yes	—
6	#88036	C₂²	1	4	yes	direct product factor
7	C₂²×C₄×C₁₃	C₈	1	1	yes	characteristic
8	C₂×C₈×C₁₃	C₈	1	3	yes	—
9	C₂×C₈×C₁₃	C₂×C₄	1	3	yes	—
10	#6090	C₂×C₄	1	3	yes	—
11	#6090	C₂³	1	1	yes	characteristic
12	C₂²×C₃₂	—	13	1	no	maximal, Sylow
13	C₂³×C₁₃	C₁₆	1	1	yes	characteristic
14	C₂×C₄×C₁₃	C₁₆	1	3	yes	—
15	C₂×C₄×C₁₃	C₂×C₈	1	3	yes	—
16	C₈×C₁₃	C₂×C₈	1	3	yes	—
17	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
18	C₂²×C₁₆	—	13	1	no	—
19	C₂×C₃₂	—	13	6	no	—
20	C₂²×C₁₃	C₃₂	1	4	yes	complemented
21	C₂²×C₁₃	C₂×C₁₆	1	3	yes	—
22	C₄×C₁₃	C₂×C₁₆	1	3	yes	—
23	C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
24	C₂²×C₈	#261	1	1	yes	characteristic
25	C₂×C₁₆	—	13	3	no	—
26	C₂×C₁₆	—	13	3	no	—
27	C₃₂	—	13	4	no	—
28	C₂×C₁₃	C₂×C₃₂	1	6	yes	complemented
29	C₂×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
30	C₂²×C₄	#1057	1	1	yes	characteristic
31	C₂×C₈	#1057	1	3	yes	—
32	C₂×C₈	C₂×#261	1	3	yes	—
33	C₁₆	—	13	1	no	—
34	C₁₆	—	13	3	no	—
35	C₁₃	C₂²×C₃₂	1	1	yes	characteristic, complemented, Sylow
36	C₂³	#6092	1	1	yes	characteristic
37	C₂×C₄	#6092	1	3	yes	—
38	C₂×C₄	C₂×#1057	1	3	yes	—
39	C₈	C₂×#1057	1	3	yes	—
40	C₈	C₂²×#261	1	1	yes	characteristic
41	C₂²	#88036	1	4	yes	direct product factor
42	C₂²	C₂×#6092	1	3	yes	—
43	C₄	C₂×#6092	1	3	yes	—
44	C₄	C₂²×#1057	1	1	yes	characteristic
45	C₂	C₂×#88036	1	6	yes	direct product factor
46	C₂	C₂²×#6092	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₈	#261
commutator, hypocenter	C₁₃	C₂²×C₃₂
Frattini	C₈	C₂²×#261
Fitting	C₂²×C₈×C₁₃	C₄
socle, prime radical	C₂³×C₁₃	C₁₆
cosocle	#6090	C₂³
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#88036	C₂	direct (N × H)
6. #88036	C₂²	direct (N × H)
20. C₂²×C₁₃	C₃₂	semidirect
28. C₂×C₁₃	C₂×C₃₂	semidirect
35. C₁₃	C₂²×C₃₂	semidirect
41. C₂²	#88036	direct (N × H)
45. C₂	C₂×#88036	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
C₂×#88036	2
C₂²×C₃₂	13

Subgroups — C22×#88036 #13131254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#88036 #13131254