Subgroups — #73042

Order 384.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#5403	C₂	1	2	yes	maximal
2	#504⋊C₃	C₂	1	1	yes	maximal, characteristic
3	#2222	—	3	1	no	maximal, Sylow
4	#984	—	2	2	no	—
5	#131⋊C₃	C₂²	1	1	yes	characteristic
6	Dic₂₄	—	4	1	no	maximal
7	C₂×Q₃₂	—	3	1	no	—
8	#504	D₃	1	1	yes	characteristic
9	#473	—	3	2	no	—
10	#368	—	3	1	no	—
11	#362	—	3	2	no	—
12	#41⋊C₃	D₄	1	1	yes	characteristic
13	#226	—	4	2	no	—
14	Dic₁₂	—	4	2	no	—
15	C₃×C₁₆	—	4	1	no	—
16	#137	—	6	2	no	—
17	C₂×Q₁₆	—	3	2	no	—
18	#131	C₂×D₃	1	1	yes	characteristic
19	Q₃₂	—	6	1	no	—
20	Q₃₂	—	6	1	no	—
21	M₃₂	—	3	1	no	—
22	C₂×C₁₆	—	3	1	no	—
23	#108	—	3	2	no	—
24	#101	—	6	2	no	—
25	Dic₆	—	8	2	no	—
26	SL(2,𝔽₃)	D₈	1	1	yes	characteristic
27	C₃×C₈	—	4	1	no	—
28	#41	D₁₂	1	1	yes	characteristic
29	C₂×Q₈	—	6	2	no	—
30	Q₁₆	—	6	2	no	—
31	Q₁₆	—	6	2	no	—
32	Q₁₆	—	12	2	no	—
33	SD₁₆	—	12	2	no	—
34	M₁₆	—	3	1	no	—
35	M₁₆	—	6	2	no	—
36	C₂×C₈	—	3	1	no	—
37	C₁₆	—	3	1	no	—
38	C₁₆	S₄	1	1	yes	characteristic
39	C₃×C₄	—	4	1	no	—
40	Dic₃	—	16	2	no	—
41	Q₈	—	12	2	no	—
42	Q₈	—	12	2	no	—
43	Q₈	D₂₄	1	1	yes	characteristic
44	D₄	—	3	1	no	—
45	C₂×C₄	—	3	1	no	—
46	C₂×C₄	—	12	2	no	—
47	C₈	—	3	1	no	—
48	C₈	—	12	2	no	—
49	C₈	C₂×S₄	1	1	yes	characteristic
50	C₂×C₃	—	4	1	no	—
51	C₂²	—	3	1	no	—
52	C₄	—	3	1	no	—
53	C₄	—	24	2	no	—
54	C₄	C₄⋊S₄	1	1	yes	characteristic
55	C₃	—	4	1	no	Sylow
56	C₂	—	6	1	no	—
57	C₂	#5402	1	1	yes	characteristic

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