Subgroups — #5404

Order 192.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#985	C₂	1	1	yes	maximal, characteristic
2	#131⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	GU(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	#443	—	3	1	no	maximal, Sylow
5	#41⋊C₃	C₂²	1	1	yes	characteristic
6	GL(2,𝔽₃)	C₄	1	1	yes	characteristic, complemented
7	#226	C₄	1	1	yes	characteristic, complemented
8	D₃×C₈	—	4	1	no	maximal
9	#135	—	3	1	no	—
10	#131	—	3	1	no	—
11	#131	D₃	1	1	yes	characteristic, complemented
12	#108	—	3	1	no	—
13	#104	—	3	1	no	—
14	#104	—	3	1	no	—
15	C₄×C₈	—	3	1	no	—
16	C₄×D₃	—	4	1	no	—
17	SL(2,𝔽₃)	C₂×C₄	1	1	yes	characteristic
18	C₃×C₈	—	4	1	no	—
19	C₃⋊C₈	—	4	1	no	—
20	#41	—	3	1	no	—
21	#41	C₂×D₃	1	1	yes	characteristic
22	Q₁₆	—	3	1	no	—
23	SD₁₆	—	3	1	no	—
24	SD₁₆	—	3	1	no	—
25	D₈	—	3	1	no	—
26	M₁₆	—	3	1	no	—
27	M₁₆	—	3	1	no	—
28	M₁₆	—	6	1	no	—
29	C₂×C₈	—	3	1	no	—
30	C₂×C₈	—	3	1	no	—
31	C₂×C₈	—	6	1	no	—
32	C₄²	—	3	1	no	—
33	C₂×D₃	—	4	1	no	—
34	C₃×C₄	—	4	1	no	—
35	Dic₃	—	4	1	no	—
36	Q₈	—	3	1	no	—
37	Q₈	C₄×D₃	1	1	yes	characteristic
38	D₄	—	3	1	no	—
39	D₄	—	3	1	no	—
40	D₄	—	6	1	no	—
41	C₂×C₄	—	3	1	no	—
42	C₂×C₄	—	6	1	no	—
43	C₂×C₄	—	6	1	no	—
44	C₈	—	3	1	no	—
45	C₈	—	3	1	no	—
46	C₈	—	3	1	no	—
47	C₈	—	6	1	no	—
48	C₈	S₄	1	1	yes	characteristic
49	C₂×C₃	—	4	1	no	—
50	D₃	—	4	2	no	—
51	C₂²	—	3	1	no	—
52	C₂²	—	6	1	no	—
53	C₄	—	3	1	no	—
54	C₄	—	6	2	no	—
55	C₄	—	6	1	no	—
56	C₄	C₂×S₄	1	1	yes	characteristic
57	C₃	—	4	1	no	Sylow
58	C₂	—	6	1	no	—
59	C₂	—	12	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.