Subgroups — #5071

Order 192.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#127	C₂	1	1	yes	maximal, characteristic
2	#870	C₂	1	1	yes	maximal, characteristic, complemented
3	#832	C₂	1	4	yes	maximal, complemented
4	#803	C₂	1	1	yes	maximal, characteristic, complemented
5	#490	—	3	1	no	maximal, Sylow
6	C₂×C₃×D₄	—	2	2	no	—
7	C₂×C₃×D₄	C₂²	1	2	yes	—
8	C₃×C₄²	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₃	C₂²	1	2	yes	—
10	Dic₃⋊C₄	—	2	2	no	—
11	C₂×C₃⋊C₈	C₂²	1	2	yes	—
12	#127	D₃	1	1	yes	characteristic
13	#125	—	3	1	no	—
14	#102	—	3	4	no	—
15	#97	—	3	1	no	—
16	C₂³×C₃	—	2	2	no	—
17	C₃×D₄	—	2	4	no	—
18	C₃×D₄	—	4	4	no	—
19	C₂×C₃×C₄	D₄	1	2	yes	—
20	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
21	C₂×Dic₃	—	2	2	no	—
22	C₃⋊C₈	—	2	2	no	—
23	C₂×D₄	—	2	2	no	—
24	C₂×D₄	C₂×D₃	1	2	yes	—
25	C₂×C₈	—	3	2	no	—
26	C₄⋊C₄	—	3	2	no	—
27	C₄⋊C₄	—	6	2	no	—
28	C₄²	C₂×D₃	1	1	yes	characteristic
29	C₂²×C₃	—	4	2	no	—
30	C₂²×C₃	—	4	4	no	—
31	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
32	C₃×C₄	—	2	2	no	—
33	C₃×C₄	#41	1	2	yes	—
34	Dic₃	—	4	2	no	—
35	C₂³	—	2	2	no	—
36	D₄	—	2	4	no	—
37	D₄	—	4	4	no	—
38	C₂×C₄	—	6	2	no	—
39	C₂×C₄	#67	1	2	yes	—
40	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
41	C₈	—	6	2	no	—
42	C₂×C₃	—	8	2	no	—
43	C₂×C₃	#124	1	1	yes	characteristic
44	C₂×C₃	AGL(1,ℤ/8)	1	2	yes	—
45	C₂²	—	4	4	no	—
46	C₂²	—	4	2	no	—
47	C₂²	C₂×#67	1	1	yes	characteristic
48	C₄	—	2	2	no	—
49	C₄	—	12	2	no	—
50	C₄	#237	1	2	yes	—
51	C₃	#490	1	1	yes	characteristic, complemented, Sylow
52	C₂	—	8	2	no	—
53	C₂	#932	1	2	yes	—
54	C₂	#936	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.