Subgroups — #4565

Order 192.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	#819	C₂	1	1	yes	maximal, characteristic
3	#812	C₂	1	1	yes	maximal, characteristic
4	#362	—	3	1	no	maximal, Sylow
5	C₂×C₃×Q₈	—	2	1	no	—
6	C₃×Q₁₆	—	2	1	no	—
7	C₃×Q₁₆	C₄	1	2	yes	—
8	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
9	#208	—	2	1	no	—
10	C₃⋊C₁₆	—	2	1	no	—
11	C₂×Q₁₆	D₃	1	1	yes	characteristic
12	M₃₂	—	3	1	no	—
13	#108	—	3	1	no	—
14	C₃×Q₈	—	2	2	no	—
15	C₃×Q₈	—	4	1	no	—
16	C₂×C₃×C₄	—	4	1	no	—
17	C₂×C₃×C₄	D₄	1	1	yes	characteristic
18	C₃×C₈	C₂×C₄	1	1	yes	characteristic
19	C₃×C₈	D₄	1	1	yes	characteristic
20	C₃⋊C₈	—	4	1	no	—
21	C₂×Q₈	—	2	1	no	—
22	Q₁₆	—	2	1	no	—
23	Q₁₆	Dic₃	1	2	yes	—
24	M₁₆	—	6	1	no	—
25	C₂×C₈	C₂×D₃	1	1	yes	characteristic
26	C₁₆	—	6	1	no	—
27	C₂²×C₃	SD₁₆	1	1	yes	characteristic
28	C₃×C₄	—	4	2	no	—
29	C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
30	C₃×C₄	D₈	1	1	yes	characteristic
31	Q₈	—	2	2	no	—
32	Q₈	—	4	1	no	—
33	C₂×C₄	—	4	1	no	—
34	C₂×C₄	#67	1	1	yes	characteristic
35	C₈	—	12	1	no	—
36	C₈	C₂×Dic₃	1	1	yes	characteristic
37	C₈	#67	1	1	yes	characteristic
38	C₂×C₃	—	2	1	no	—
39	C₂×C₃	#102	1	1	yes	characteristic
40	C₂²	#214	1	1	yes	characteristic
41	C₄	—	4	2	no	—
42	C₄	#213	1	1	yes	characteristic
43	C₄	#217	1	1	yes	characteristic
44	C₃	#362	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	2	1	no	—
46	C₂	#832	1	1	yes	characteristic

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

N	H ≅ G/N	type
44. C₃	#362	semidirect

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