Subgroups — #5406

Order 192.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#986	C₂	1	1	yes	maximal, characteristic
2	#984	C₂	1	1	yes	maximal, characteristic, complemented
3	#131⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#471	—	3	1	no	maximal, Sylow
5	#41⋊C₃	C₂²	1	1	yes	characteristic
6	GL(2,𝔽₃)	—	2	1	no	—
7	#226	—	2	1	no	—
8	#204	—	4	1	no	maximal
9	#137	—	3	1	no	—
10	AGL(1,ℤ/8)	—	3	1	no	—
11	C₂×SD₁₆	—	3	1	no	—
12	#131	D₃	1	1	yes	characteristic, complemented
13	#108	—	3	1	no	—
14	#101	—	3	1	no	—
15	#100	—	3	1	no	—
16	D₁₂	—	4	1	no	—
17	Dic₆	—	4	1	no	—
18	SL(2,𝔽₃)	D₄	1	1	yes	characteristic
19	C₃×C₈	—	4	1	no	—
20	#41	C₂×D₃	1	1	yes	characteristic
21	C₂×Q₈	—	3	1	no	—
22	C₂×D₄	—	3	1	no	—
23	Q₁₆	—	6	1	no	—
24	SD₁₆	—	6	1	no	—
25	SD₁₆	—	6	1	no	—
26	SD₁₆	—	6	1	no	—
27	SD₁₆	—	6	1	no	—
28	D₈	—	6	1	no	—
29	M₁₆	—	3	1	no	—
30	M₁₆	—	3	1	no	—
31	M₁₆	—	3	1	no	—
32	C₂×C₈	—	3	1	no	—
33	C₂×D₃	—	8	1	no	—
34	C₃×C₄	—	4	1	no	—
35	Dic₃	—	8	1	no	—
36	C₂³	—	6	1	no	—
37	Q₈	—	6	1	no	—
38	Q₈	—	6	1	no	—
39	Q₈	D₁₂	1	1	yes	characteristic
40	D₄	—	3	1	no	—
41	D₄	—	6	1	no	—
42	D₄	—	6	1	no	—
43	C₂×C₄	—	3	1	no	—
44	C₂×C₄	—	6	1	no	—
45	C₈	—	3	1	no	—
46	C₈	—	6	1	no	—
47	C₈	—	6	1	no	—
48	C₈	S₄	1	1	yes	characteristic
49	C₂×C₃	—	4	1	no	—
50	D₃	—	16	1	no	—
51	C₂²	—	3	1	no	—
52	C₂²	—	12	1	no	—
53	C₂²	—	24	1	no	—
54	C₄	—	3	1	no	—
55	C₄	—	12	1	no	—
56	C₄	C₂×S₄	1	1	yes	characteristic
57	C₃	—	4	1	no	Sylow
58	C₂	—	6	1	no	—
59	C₂	—	24	1	no	—
60	C₂	C₄⋊S₄	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.