Subgroups — C₃³×C₇×Q₈ #13094881

Order 1512.

336 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×C₇	C₂	1	3	yes	maximal
2	C₃²×C₇×Q₈	C₃	1	13	yes	maximal, direct product factor
3	C₂×C₃³×C₇	C₂²	1	1	yes	characteristic
4	C₃²×C₄×C₇	C₂×C₃	1	39	yes	—
5	C₃³×Q₈	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃³×C₇	Q₈	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇×Q₈	C₃²	1	13	yes	direct product factor
8	C₂×C₃²×C₇	C₂²×C₃	1	13	yes	—
9	C₃³×C₄	C₂×C₇	1	3	yes	—
10	C₃×C₄×C₇	C₂×C₃²	1	39	yes	—
11	C₃²×Q₈	C₃×C₇	1	13	yes	direct product factor
12	C₃²×C₇	C₃×Q₈	1	13	yes	direct product factor
13	C₇×Q₈	C₃³	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃³	C₂²×C₇	1	1	yes	characteristic
15	C₂×C₃×C₇	C₂²×C₃²	1	13	yes	—
16	C₃²×C₄	C₂×C₃×C₇	1	39	yes	—
17	C₄×C₇	C₂×C₃³	1	3	yes	—
18	C₃³	C₇×Q₈	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×Q₈	C₃²×C₇	1	13	yes	direct product factor
20	C₃×C₇	C₃²×Q₈	1	13	yes	direct product factor
21	C₂×C₃²	C₂²×C₃×C₇	1	13	yes	—
22	C₂×C₇	C₂²×C₃³	1	1	yes	characteristic
23	C₃×C₄	C₂×C₃²×C₇	1	39	yes	—
24	C₃²	C₃×C₇×Q₈	1	13	yes	direct product factor
25	Q₈	C₃³×C₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₇	C₃³×Q₈	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	C₂²×C₃²×C₇	1	13	yes	—
28	C₄	C₂×C₃³×C₇	1	3	yes	—
29	C₃	C₃²×C₇×Q₈	1	13	yes	direct product factor
30	C₂	C₂²×C₃³×C₇	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂×C₃³×C₇	C₂²
commutator, Frattini, cosocle	C₂	C₂²×C₃³×C₇
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃³×C₇ ◁ G

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.