Subgroups — C₂×Q₁₆×C₆₉₁ #36348694

Order 22112.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₆₉₁	C₂	1	2	yes	maximal
2	Q₁₆×C₆₉₁	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×C₆₉₁	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₆₉₁	—	2	2	no	—
5	Q₈×C₆₉₁	C₂²	1	4	yes	—
6	C₂×C₄×C₆₉₁	—	2	2	no	—
7	C₂×C₄×C₆₉₁	C₂²	1	1	yes	characteristic
8	C₈×C₆₉₁	C₂²	1	2	yes	—
9	C₂²×C₆₉₁	D₄	1	1	yes	characteristic
10	C₄×C₆₉₁	—	2	4	no	—
11	C₄×C₆₉₁	D₄	1	1	yes	characteristic
12	C₄×C₆₉₁	C₂³	1	1	yes	characteristic
13	C₂×C₆₉₁	Q₁₆	1	2	yes	direct product factor
14	C₂×C₆₉₁	C₂×D₄	1	1	yes	characteristic
15	C₆₉₁	C₂×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×Q₁₆	C₆₉₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×Q₈	C₂×C₆₉₁	1	2	yes	—
18	Q₁₆	C₂×C₆₉₁	1	4	yes	direct product factor
19	C₂×C₈	C₂×C₆₉₁	1	1	yes	characteristic
20	Q₈	—	2	2	no	—
21	Q₈	C₂²×C₆₉₁	1	4	yes	—
22	C₂×C₄	—	2	2	no	—
23	C₂×C₄	C₂²×C₆₉₁	1	1	yes	characteristic
24	C₈	C₂²×C₆₉₁	1	2	yes	—
25	C₂²	D₄×C₆₉₁	1	1	yes	characteristic
26	C₄	—	2	4	no	—
27	C₄	D₄×C₆₉₁	1	1	yes	characteristic
28	C₄	C₂³×C₆₉₁	1	1	yes	characteristic
29	C₂	Q₁₆×C₆₉₁	1	2	yes	direct product factor
30	C₂	C₂×D₄×C₆₉₁	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₆₉₁	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₆₉₁
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₉₁ ◁ C₂×C₄×C₆₉₁ ◁ 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.