Subgroups — #5247

Order 192.

506 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#217	C₂	1	6	yes	maximal, complemented
3	#379	—	3	1	no	maximal, Sylow
4	C₂⁴×C₃	—	2	12	no	—
5	C₂⁴×C₃	C₄	1	4	yes	complemented
6	C₂⁴×C₃	C₂²	1	3	yes	—
7	C₂²×Dic₃	C₂²	1	4	yes	complemented
8	#217	—	2	12	no	—
9	C₂⁵	D₃	1	1	yes	characteristic
10	C₂×C₂²⋊C₄	—	3	6	no	—
11	C₂³×C₃	—	2	32	no	—
12	C₂³×C₃	—	2	24	no	—
13	C₂³×C₃	—	2	12	no	—
14	C₂³×C₃	C₂×C₄	1	6	yes	—
15	C₂³×C₃	D₄	1	12	yes	—
16	C₂³×C₃	C₂³	1	1	yes	characteristic
17	C₂×Dic₃	—	2	12	no	—
18	C₂⁴	—	2	12	no	—
19	C₂⁴	Dic₃	1	4	yes	complemented
20	C₂⁴	C₂×D₃	1	3	yes	—
21	C₂²×C₄	—	3	4	no	—
22	C₂²⋊C₄	—	6	12	no	—
23	C₂²×C₃	—	2	32	no	—
24	C₂²×C₃	—	2	12	no	—
25	C₂²×C₃	—	2	24	no	—
26	C₂²×C₃	C₂²⋊C₄	1	12	yes	complemented
27	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₃	C₂×D₄	1	6	yes	—
29	Dic₃	—	4	4	no	—
30	C₂³	—	2	32	no	—
31	C₂³	—	2	24	no	—
32	C₂³	—	2	12	no	—
33	C₂³	C₂×Dic₃	1	6	yes	—
34	C₂³	#67	1	12	yes	—
35	C₂³	C₂²×D₃	1	1	yes	characteristic
36	C₂×C₄	—	6	12	no	—
37	C₂×C₃	—	2	12	no	—
38	C₂×C₃	C₂×C₂²⋊C₄	1	3	yes	—
39	C₂×C₃	#120	1	4	yes	—
40	C₂²	—	2	32	no	—
41	C₂²	—	2	12	no	—
42	C₂²	—	2	24	no	—
43	C₂²	#217	1	12	yes	complemented
44	C₂²	C₂²×Dic₃	1	1	yes	characteristic
45	C₂²	C₂×#67	1	6	yes	—
46	C₄	—	12	4	no	—
47	C₃	#379	1	1	yes	characteristic, complemented, Sylow
48	C₂	—	2	12	no	—
49	C₂	C₂×#217	1	3	yes	—
50	C₂	#953	1	4	yes	—

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.