Subgroups — #5426

Order 192.

79 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#859	C₂	1	2	yes	maximal, complemented
3	#417	—	3	1	no	maximal, Sylow
4	#41⋊C₃	C₄	1	2	yes	complemented
5	C₂×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₃	—	4	1	no	maximal
7	C₂×#41	D₃	1	1	yes	characteristic
8	C₂×M₁₆	—	3	1	no	—
9	C₂×C₄⋊C₄	—	3	1	no	—
10	#103	—	3	2	no	—
11	#102	—	3	2	no	—
12	C₂×C₃×C₄	—	4	1	no	—
13	C₂×Dic₃	—	4	2	no	—
14	SL(2,𝔽₃)	C₂×C₄	1	1	yes	characteristic, complemented
15	#41	—	3	2	no	—
16	#41	Dic₃	1	2	yes	complemented
17	C₂×Q₈	C₂×D₃	1	1	yes	characteristic
18	C₂×D₄	—	3	1	no	—
19	C₂²×C₄	—	3	1	no	—
20	C₂²×C₄	—	6	1	no	—
21	M₁₆	—	6	2	no	—
22	C₂×C₈	—	3	2	no	—
23	C₄⋊C₄	—	3	2	no	—
24	C₄⋊C₄	—	6	1	no	—
25	C₂²×C₃	—	4	1	no	—
26	C₃×C₄	—	4	2	no	—
27	Dic₃	—	8	2	no	—
28	C₂³	—	3	1	no	—
29	Q₈	—	3	1	no	—
30	Q₈	C₂×Dic₃	1	1	yes	characteristic
31	D₄	—	3	2	no	—
32	D₄	—	6	1	no	—
33	C₂×C₄	—	3	1	no	—
34	C₂×C₄	—	3	2	no	—
35	C₂×C₄	—	3	2	no	—
36	C₂×C₄	—	6	2	no	—
37	C₂×C₄	—	12	2	no	—
38	C₂×C₄	S₄	1	1	yes	characteristic
39	C₈	—	6	2	no	—
40	C₂×C₃	—	4	1	no	—
41	C₂×C₃	—	4	1	no	—
42	C₂×C₃	—	4	1	no	—
43	C₂²	—	3	2	no	—
44	C₂²	—	6	1	no	—
45	C₂²	—	6	1	no	—
46	C₂²	C₂×S₄	1	1	yes	characteristic
47	C₄	—	3	1	no	—
48	C₄	—	3	1	no	—
49	C₄	—	12	2	no	—
50	C₄	SL(2,ℤ/4)	1	2	yes	—
51	C₃	—	4	1	no	Sylow
52	C₂	—	6	2	no	—
53	C₂	#984	1	1	yes	characteristic
54	C₂	#986	1	1	yes	characteristic
55	C₂	C₂×SL(2,ℤ/4)	1	1	yes	characteristic

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.