Subgroups — #4625

Order 192.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#120⋊C₃	C₂	1	1	yes	maximal, characteristic
2	AΣL(1,𝔽₁₆)	—	3	1	no	maximal, Sylow
3	C₂²⋊A₄	C₄	1	1	yes	characteristic, complemented
4	SL(2,ℤ/4)	—	4	1	no	maximal
5	#120	D₃	1	1	yes	characteristic
6	#100	—	3	1	no	—
7	#99	—	3	1	no	—
8	C₂×A₄	—	4	1	no	—
9	C₂⁴	Dic₃	1	1	yes	characteristic, complemented
10	C₂×D₄	—	3	1	no	—
11	M₁₆	—	6	1	no	—
12	C₂²⋊C₄	—	3	1	no	—
13	C₂²⋊C₄	—	6	1	no	—
14	A₄	—	4	1	no	—
15	A₄	—	16	1	no	—
16	Dic₃	—	16	1	no	—
17	C₂³	—	3	1	no	—
18	C₂³	—	12	1	no	—
19	C₂³	S₄	1	1	yes	characteristic
20	D₄	—	12	1	no	—
21	C₂×C₄	—	3	1	no	—
22	C₂×C₄	—	12	1	no	—
23	C₈	—	12	1	no	—
24	C₂×C₃	—	16	1	no	—
25	C₂²	—	4	1	no	—
26	C₂²	—	6	1	no	—
27	C₂²	—	6	1	no	—
28	C₂²	—	12	1	no	—
29	C₂²	—	12	1	no	—
30	C₂²	SL(2,ℤ/4)	1	1	yes	characteristic
31	C₄	—	6	1	no	—
32	C₄	—	24	1	no	—
33	C₃	—	16	1	no	Sylow
34	C₂	—	3	1	no	—
35	C₂	—	4	1	no	—
36	C₂	—	12	1	no	—

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

N	H ≅ G/N	type
3. C₂²⋊A₄	C₄	semidirect
9. C₂⁴	Dic₃	semidirect

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