Subgroups — C₃×C₄₃×#5997 #38760536

Order 25284.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#5997	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇²×C₄₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
5	C₇²×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×D₇×C₄₃	—	14	4	no	—
7	C₃×C₇×C₄₃	—	2	4	no	—
8	D₇×C₄₃	—	14	4	no	—
9	C₃×#5997	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₄×C₄₃	—	49	1	no	maximal, Hall
11	C₇×C₄₃	—	2	4	no	—
12	C₃×C₇⋊D₇	C₂×C₄₃	1	1	yes	characteristic
13	C₂×C₃×C₄₃	—	49	1	no	—
14	#5997	C₃×C₄₃	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₄₃	—	49	1	no	Hall
16	C₃×C₇²	C₄×C₄₃	1	1	yes	characteristic, complemented, Hall
17	C₃×C₄₃	#5997	1	1	yes	characteristic, direct product factor, Hall
18	C₇⋊D₇	C₂×C₃×C₄₃	1	1	yes	characteristic
19	C₂×C₄₃	—	49	1	no	—
20	C₇²	C₃×C₄×C₄₃	1	1	yes	characteristic, complemented, Sylow
21	C₄₃	C₃×#5997	1	1	yes	characteristic, direct product factor, Sylow
22	C₃×D₇	—	14	4	no	—
23	C₃×C₇	—	2	4	no	—
24	D₇	—	14	4	no	—
25	C₃×C₄	—	49	1	no	Hall
26	C₇	—	2	4	no	—
27	C₂×C₃	—	49	1	no	—
28	C₄	—	49	1	no	Sylow
29	C₃	C₄₃×#5997	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	49	1	no	—

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.