Subgroups — C₂×#126⋊C₃ #5442

Order 192.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#126⋊C₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₄²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#126	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₂²×A₄	—	4	1	no	maximal
5	C₄²⋊C₃	C₂²	1	1	yes	characteristic, complemented
6	#126	—	3	2	no	—
7	#126	C₂×C₃	1	2	yes	complemented
8	C₂×C₄⋊C₄	—	3	1	no	—
9	C₂×C₂²⋊C₄	—	3	1	no	—
10	C₂×C₄²	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×A₄	—	4	1	no	—
12	C₂×A₄	—	4	2	no	—
13	C₂⁴	A₄	1	1	yes	characteristic
14	C₂²×C₄	—	3	1	no	—
15	C₂²×C₄	—	3	1	no	—
16	C₄⋊C₄	—	3	2	no	—
17	C₄⋊C₄	—	3	2	no	—
18	C₂²⋊C₄	—	3	2	no	—
19	C₂²⋊C₄	—	3	2	no	—
20	C₄²	—	3	1	no	—
21	C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
22	C₂²×C₃	—	16	1	no	—
23	A₄	—	4	1	no	—
24	C₂³	—	6	1	no	—
25	C₂³	—	6	1	no	—
26	C₂³	C₂×A₄	1	1	yes	characteristic
27	C₂³	C₂×A₄	1	2	yes	—
28	C₂×C₄	—	3	1	no	—
29	C₂×C₄	—	3	1	no	—
30	C₂×C₄	—	3	2	no	—
31	C₂×C₄	—	6	1	no	—
32	C₂×C₄	—	6	1	no	—
33	C₂×C₄	—	6	1	no	—
34	C₂×C₄	—	6	1	no	—
35	C₂×C₃	—	16	2	no	—
36	C₂×C₃	—	16	1	no	—
37	C₂²	—	3	1	no	—
38	C₂²	—	3	1	no	—
39	C₂²	—	4	1	no	—
40	C₂²	—	6	2	no	—
41	C₂²	—	12	1	no	—
42	C₂²	C₂²×A₄	1	1	yes	characteristic
43	C₄	—	6	1	no	—
44	C₄	—	6	1	no	—
45	C₄	—	6	2	no	—
46	C₃	—	16	1	no	Sylow
47	C₂	—	3	1	no	—
48	C₂	—	3	1	no	—
49	C₂	—	4	2	no	—
50	C₂	#126⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#126⋊C₃
commutator, cosocle, hypocenter	C₄²	C₂²×C₃
Frattini	C₂²	C₂²×A₄
Fitting	C₂×#126	C₃
socle	C₂³	C₂×A₄
LCS	G ▷ C₄²
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.