Subgroups — C₄×#17986953 #32912118

Order 18228.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17986953	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#17986953	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇²×C₃₁	C₂×C₃	1	1	yes	characteristic
5	C₄×#10620252	—	7	8	no	maximal
6	C₇²×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×#10620252	—	7	8	no	—
8	C₄×C₇×C₃₁	ΓL(1,𝔽₈)	1	8	yes	complemented
9	#10620252	—	7	8	no	—
10	C₄×#3861	—	31	1	no	maximal, Hall
11	C₂×C₇×C₃₁	C₂×ΓL(1,𝔽₈)	1	8	yes	—
12	C₄×C₃₁⋊C₃	—	49	1	no	Hall
13	C₂×#3861	—	31	1	no	—
14	C₇×C₃₁	C₄×ΓL(1,𝔽₈)	1	8	yes	complemented
15	C₄×C₇²	C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃₁⋊C₃	—	49	1	no	—
17	#3861	—	31	1	no	Hall
18	C₄×C₃₁	#3861	1	1	yes	characteristic, complemented, Hall
19	C₂×C₇²	C₂×C₃₁⋊C₃	1	1	yes	characteristic
20	C₃₁⋊C₃	—	49	1	no	Hall
21	C₄×ΓL(1,𝔽₈)	—	217	8	no	—
22	C₂×C₃₁	C₂×#3861	1	1	yes	characteristic
23	C₇²	C₄×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×ΓL(1,𝔽₈)	—	217	8	no	—
25	C₃₁	C₄×#3861	1	1	yes	characteristic, complemented, Sylow
26	C₄×C₇	#10620252	1	8	yes	complemented
27	ΓL(1,𝔽₈)	—	217	8	no	—
28	C₂×C₇	C₂×#10620252	1	8	yes	—
29	C₃×C₄	—	1519	1	no	Hall
30	C₇	C₄×#10620252	1	8	yes	complemented
31	C₂×C₃	—	1519	1	no	—
32	C₄	#17986953	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	—	1519	1	no	Sylow
34	C₂	C₂×#17986953	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.