Subgroups — GO⁺(4,𝔽₂)⋊C₄ #64193

Order 288.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×GO⁺(4,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₂×AGL(1,𝔽₉)	C₂	1	1	yes	maximal, characteristic, complemented
3	#3777	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃²	—	2	1	no	—
5	C₂×#157	—	2	1	no	—
6	C₂×#157	C₂²	1	1	yes	characteristic
7	GO⁺(4,𝔽₂)	—	2	1	no	—
8	GO⁺(4,𝔽₂)	C₄	1	2	yes	complemented
9	AGL(1,𝔽₉)	—	2	1	no	—
10	C₂×C₃⋊D₃	D₄	1	1	yes	characteristic
11	C₂×C₃×D₃	—	4	1	no	—
12	D₃²	—	2	2	no	—
13	D₃²	—	4	1	no	—
14	#157	—	4	1	no	—
15	#157	C₂×C₄	1	1	yes	characteristic
16	#157	D₄	1	1	yes	characteristic
17	#102	—	9	1	no	maximal, Sylow
18	C₂²×D₃	—	12	1	no	—
19	C₂×C₃²	SD₁₆	1	1	yes	characteristic
20	C₃⋊D₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₃⋊D₃	D₈	1	1	yes	characteristic
22	C₃×D₃	—	4	2	no	—
23	C₂×D₄	—	9	1	no	—
24	C₂×C₈	—	9	1	no	—
25	C₄⋊C₄	—	9	1	no	—
26	C₂²×C₃	—	12	1	no	—
27	C₂×D₃	—	4	1	no	—
28	C₂×D₃	—	12	1	no	—
29	C₂×D₃	—	12	2	no	—
30	C₂×D₃	—	12	2	no	—
31	C₃²	#102	1	1	yes	characteristic, complemented, Sylow
32	C₂³	—	18	1	no	—
33	D₄	—	9	2	no	—
34	D₄	—	18	1	no	—
35	C₂×C₄	—	9	1	no	—
36	C₂×C₄	—	18	1	no	—
37	C₈	—	18	1	no	—
38	C₂×C₃	—	4	1	no	—
39	C₂×C₃	—	12	2	no	—
40	D₃	—	4	2	no	—
41	D₃	—	12	1	no	—
42	D₃	—	12	1	no	—
43	C₂²	—	9	1	no	—
44	C₂²	—	12	1	no	—
45	C₂²	—	18	2	no	—
46	C₂²	—	36	1	no	—
47	C₄	—	9	1	no	—
48	C₄	—	9	1	no	—
49	C₄	—	36	1	no	—
50	C₃	—	4	1	no	—
51	C₂	—	9	1	no	—
52	C₂	—	9	1	no	—
53	C₂	—	12	2	no	—
54	C₂	AΓL(1,𝔽₉)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	AΓL(1,𝔽₉)
commutator	#157	C₂×C₄
Fitting, socle	C₂×C₃²	SD₁₆
prime radical	C₂×GO⁺(4,𝔽₂)	C₂
cosocle	C₂×#157	C₂²
hypocenter	C₃²	#102
LCS	G ▷ #157 ▷ C₃⋊D₃ ▷ C₃²
UCS	C₁ ◁ C₂

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.