Subgroups — C₄×C₄⋊C₄ #378

Order 64.

97 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄	C₂	1	2	yes	maximal
2	C₂×C₄²	C₂	1	2	yes	maximal
3	C₂×C₄²	C₂	1	1	yes	maximal, characteristic
4	#95	C₂	1	2	yes	maximal
5	C₂²×C₄	C₂²	1	1	yes	characteristic
6	C₂²×C₄	C₂²	1	4	yes	—
7	C₂²×C₄	C₂²	1	1	yes	characteristic
8	C₂²×C₄	C₂²	1	1	yes	characteristic
9	C₄⋊C₄	C₄	1	8	yes	direct product factor
10	C₄²	—	2	4	no	—
11	C₄²	C₄	1	4	yes	complemented
12	C₂³	C₂³	1	1	yes	characteristic
13	C₂×C₄	—	2	4	no	—
14	C₂×C₄	—	2	2	no	—
15	C₂×C₄	—	2	4	no	—
16	C₂×C₄	C₂×C₄	1	2	yes	—
17	C₂×C₄	C₂×C₄	1	8	yes	—
18	C₂×C₄	C₂×C₄	1	2	yes	—
19	C₂×C₄	C₂×C₄	1	4	yes	—
20	C₂×C₄	C₂×C₄	1	2	yes	—
21	C₂×C₄	D₄	1	2	yes	—
22	C₂×C₄	Q₈	1	2	yes	—
23	C₂²	C₂²×C₄	1	1	yes	characteristic
24	C₂²	C₂²×C₄	1	2	yes	—
25	C₂²	C₂×D₄	1	1	yes	characteristic
26	C₂²	C₂×Q₈	1	1	yes	characteristic
27	C₂²	#41	1	2	yes	—
28	C₄	—	2	2	no	—
29	C₄	—	2	8	no	—
30	C₄	C₄²	1	4	yes	complemented
31	C₄	C₄⋊C₄	1	4	yes	direct product factor
32	C₂	C₂×C₄²	1	1	yes	characteristic
33	C₂	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₂	#117	1	1	yes	characteristic
35	C₂	C₄×D₄	1	2	yes	—
36	C₂	C₄×Q₈	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²
commutator	C₂	C₂×C₄²
Frattini, socle, prime radical, cosocle	C₂³	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ G
LECS	G ▷ C₂³ ▷ C₁

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.