Subgroups — C₄×C₇×C₃₂ #11725762

Order 896.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₃₂	C₂	1	2	yes	maximal
2	C₄×C₇×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×C₁₆	C₄	1	1	yes	characteristic
4	C₂×C₇×C₁₆	C₂²	1	1	yes	characteristic
5	C₄×C₇×C₈	C₄	1	1	yes	characteristic
6	C₇×C₃₂	C₄	1	4	yes	direct product factor
7	C₄×C₃₂	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂×C₇×C₈	C₈	1	1	yes	characteristic
9	C₂×C₇×C₈	C₂×C₄	1	1	yes	characteristic
10	C₄²×C₇	C₈	1	1	yes	characteristic
11	C₇×C₁₆	C₈	1	2	yes	—
12	C₇×C₁₆	C₂×C₄	1	2	yes	—
13	C₂×C₃₂	C₂×C₇	1	2	yes	—
14	C₄×C₁₆	C₂×C₇	1	1	yes	characteristic
15	C₂×C₄×C₇	C₁₆	1	2	yes	—
16	C₂×C₄×C₇	C₂×C₈	1	1	yes	characteristic
17	C₇×C₈	C₁₆	1	2	yes	—
18	C₇×C₈	C₄²	1	1	yes	characteristic
19	C₇×C₈	C₂×C₈	1	1	yes	characteristic
20	C₂×C₁₆	C₄×C₇	1	1	yes	characteristic
21	C₂×C₁₆	C₂²×C₇	1	1	yes	characteristic
22	C₄×C₈	C₄×C₇	1	1	yes	characteristic
23	C₃₂	C₄×C₇	1	4	yes	direct product factor
24	C₂²×C₇	C₂×C₁₆	1	1	yes	characteristic
25	C₄×C₇	C₃₂	1	4	yes	direct product factor
26	C₄×C₇	C₄×C₈	1	1	yes	characteristic
27	C₄×C₇	C₂×C₁₆	1	1	yes	characteristic
28	C₂×C₈	C₇×C₈	1	1	yes	characteristic
29	C₂×C₈	C₂×C₄×C₇	1	1	yes	characteristic
30	C₄²	C₇×C₈	1	1	yes	characteristic
31	C₁₆	C₇×C₈	1	2	yes	—
32	C₁₆	C₂×C₄×C₇	1	2	yes	—
33	C₂×C₇	C₄×C₁₆	1	1	yes	characteristic
34	C₂×C₇	C₂×C₃₂	1	2	yes	—
35	C₂×C₄	C₇×C₁₆	1	2	yes	—
36	C₂×C₄	C₂×C₇×C₈	1	1	yes	characteristic
37	C₈	C₇×C₁₆	1	2	yes	—
38	C₈	C₄²×C₇	1	1	yes	characteristic
39	C₈	C₂×C₇×C₈	1	1	yes	characteristic
40	C₇	C₄×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²	C₂×C₇×C₁₆	1	1	yes	characteristic
42	C₄	C₇×C₃₂	1	4	yes	direct product factor
43	C₄	C₄×C₇×C₈	1	1	yes	characteristic
44	C₄	C₂×C₇×C₁₆	1	1	yes	characteristic
45	C₂	C₄×C₇×C₁₆	1	1	yes	characteristic
46	C₂	C₂×C₇×C₃₂	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₁₆	C₂²×C₇
socle, prime radical	C₂²×C₇	C₂×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₇×C₃₂	C₄	direct (N × H)
7. C₄×C₃₂	C₇	direct (N × H)
23. C₃₂	C₄×C₇	direct (N × H)
25. C₄×C₇	C₃₂	direct (N × H)
40. C₇	C₄×C₃₂	direct (N × H)
42. C₄	C₇×C₃₂	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×C₇×C₃₂	2
C₄×C₇×C₁₆	2
C₄×C₃₂	7

Subgroups — C4×C7×C32 #11725762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×C₃₂ #11725762