Subgroups — #14274113

Order 1904.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745751	C₂	1	1	yes	maximal, characteristic
2	C₇⋊#3624	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3624	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₁₉	C₄	1	1	yes	characteristic
5	C₇×Dic₁₇	C₂²	1	1	yes	characteristic
6	C₁₇×Dic₇	C₄	1	1	yes	characteristic
7	#63243	—	7	1	no	maximal, Hall
8	C₂×C₇×C₁₇	C₂×C₄	1	1	yes	characteristic
9	D₁₁₉	—	2	1	no	—
10	C₄×D₁₇	—	7	1	no	—
11	#3624	—	7	1	no	—
12	#3624	D₇	1	1	yes	characteristic, complemented
13	C₇×C₁₇	M₁₆	1	1	yes	characteristic, complemented, Hall
14	#1131	—	17	1	no	maximal, Hall
15	C₂×D₁₇	—	7	1	no	—
16	C₄×C₁₇	—	7	1	no	—
17	Dic₁₇	C₂×D₇	1	1	yes	characteristic
18	C₄×D₇	—	17	1	no	—
19	C₇×C₈	—	17	1	no	—
20	C₇⋊C₈	—	17	1	no	—
21	C₂×C₁₇	C₄×D₇	1	1	yes	characteristic
22	D₁₇	—	14	1	no	—
23	C₂×D₇	—	17	1	no	—
24	C₄×C₇	—	17	1	no	—
25	Dic₇	#595	1	1	yes	characteristic
26	C₁₇	#1131	1	1	yes	characteristic, complemented, Sylow
27	M₁₆	—	119	1	no	Sylow
28	C₂×C₇	C₂×#595	1	1	yes	characteristic
29	D₇	—	34	1	no	—
30	C₂×C₄	—	119	1	no	—
31	C₈	—	17	1	no	—
32	C₈	—	119	1	no	—
33	C₇	#63243	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	119	1	no	—
35	C₄	—	7	1	no	—
36	C₄	—	17	1	no	—
37	C₂	—	238	1	no	—
38	C₂	D₇×#595	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇×#595
commutator, Fitting, socle	C₂×C₇×C₁₇	C₂×C₄
prime radical	C₂×D₁₁₉	C₄
cosocle	C₇×Dic₁₇	C₂²
hypocenter	C₇×C₁₇	M₁₆
LCS	G ▷ C₂×C₇×C₁₇ ▷ C₇×C₁₇
UCS	C₁ ◁ C₂

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.