Subgroups — C₂³×#88036 #16807429

Order 3328.

542 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88036	C₂	1	14	yes	maximal, direct product factor
2	C₂³×#6090	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₈×C₁₃	C₄	1	1	yes	characteristic
4	C₂²×#6090	C₄	1	7	yes	—
5	C₂²×#6090	C₂²	1	7	yes	—
6	C₂×#88036	C₂²	1	28	yes	direct product factor
7	C₂³×C₄×C₁₃	C₈	1	1	yes	characteristic
8	C₂²×C₈×C₁₃	C₈	1	7	yes	—
9	C₂²×C₈×C₁₃	C₂×C₄	1	7	yes	—
10	C₂×#6090	C₂×C₄	1	21	yes	—
11	C₂×#6090	C₂³	1	7	yes	—
12	#88036	C₂³	1	8	yes	direct product factor
13	C₂³×C₃₂	—	13	1	no	maximal, Sylow
14	C₂⁴×C₁₃	C₁₆	1	1	yes	characteristic
15	C₂²×C₄×C₁₃	C₁₆	1	7	yes	—
16	C₂²×C₄×C₁₃	C₂×C₈	1	7	yes	—
17	C₂×C₈×C₁₃	C₂×C₈	1	21	yes	—
18	C₂×C₈×C₁₃	C₂²×C₄	1	7	yes	—
19	#6090	C₂²×C₄	1	7	yes	—
20	#6090	C₂⁴	1	1	yes	characteristic
21	C₂³×C₁₆	—	13	1	no	—
22	C₂²×C₃₂	—	13	14	no	—
23	C₂³×C₁₃	C₃₂	1	8	yes	complemented
24	C₂³×C₁₃	C₂×C₁₆	1	7	yes	—
25	C₂×C₄×C₁₃	C₂×C₁₆	1	21	yes	—
26	C₂×C₄×C₁₃	C₂²×C₈	1	7	yes	—
27	C₈×C₁₃	C₂²×C₈	1	7	yes	—
28	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
29	C₂³×C₈	#261	1	1	yes	characteristic
30	C₂²×C₁₆	—	13	7	no	—
31	C₂²×C₁₆	—	13	7	no	—
32	C₂×C₃₂	—	13	28	no	—
33	C₂²×C₁₃	C₂×C₃₂	1	28	yes	complemented
34	C₂²×C₁₃	C₂²×C₁₆	1	7	yes	—
35	C₄×C₁₃	C₂²×C₁₆	1	7	yes	—
36	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
37	C₂³×C₄	#1057	1	1	yes	characteristic
38	C₂²×C₈	#1057	1	7	yes	—
39	C₂²×C₈	C₂×#261	1	7	yes	—
40	C₂×C₁₆	—	13	7	no	—
41	C₂×C₁₆	—	13	21	no	—
42	C₃₂	—	13	8	no	—
43	C₂×C₁₃	C₂²×C₃₂	1	14	yes	complemented
44	C₂×C₁₃	C₂³×C₁₆	1	1	yes	characteristic
45	C₂⁴	#6092	1	1	yes	characteristic
46	C₂²×C₄	#6092	1	7	yes	—
47	C₂²×C₄	C₂×#1057	1	7	yes	—
48	C₂×C₈	C₂×#1057	1	21	yes	—
49	C₂×C₈	C₂²×#261	1	7	yes	—
50	C₁₆	—	13	1	no	—
51	C₁₆	—	13	7	no	—
52	C₁₃	C₂³×C₃₂	1	1	yes	characteristic, complemented, Sylow
53	C₂³	#88036	1	8	yes	direct product factor
54	C₂³	C₂×#6092	1	7	yes	—
55	C₂×C₄	C₂×#6092	1	21	yes	—
56	C₂×C₄	C₂²×#1057	1	7	yes	—
57	C₈	C₂²×#1057	1	7	yes	—
58	C₈	C₂³×#261	1	1	yes	characteristic
59	C₂²	C₂×#88036	1	28	yes	direct product factor
60	C₂²	C₂²×#6092	1	7	yes	—
61	C₄	C₂²×#6092	1	7	yes	—
62	C₄	C₂³×#1057	1	1	yes	characteristic
63	C₂	C₂²×#88036	1	14	yes	direct product factor
64	C₂	C₂³×#6092	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₈	#261
commutator, hypocenter	C₁₃	C₂³×C₃₂
Frattini	C₈	C₂³×#261
Fitting	C₂³×C₈×C₁₃	C₄
socle, prime radical	C₂⁴×C₁₃	C₁₆
cosocle	#6090	C₂⁴
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×#88036	C₂	direct (N × H)
6. C₂×#88036	C₂²	direct (N × H)
12. #88036	C₂³	direct (N × H)
23. C₂³×C₁₃	C₃₂	semidirect
33. C₂²×C₁₃	C₂×C₃₂	semidirect
43. C₂×C₁₃	C₂²×C₃₂	semidirect
52. C₁₃	C₂³×C₃₂	semidirect
53. C₂³	#88036	direct (N × H)
59. C₂²	C₂×#88036	direct (N × H)
63. C₂	C₂²×#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×#88036	2
C₂³×#6090	2
C₂³×C₃₂	13

Subgroups — C23×#88036 #16807429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#88036 #16807429