Subgroups — C₂×#11745755 #14274151

Order 1904.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×Dic₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×Dic₁₇	C₂	1	1	yes	maximal, characteristic
4	#11745755	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₇×C₁₇	C₂²	1	1	yes	characteristic
6	Dic₁₁₉	C₂²	1	2	yes	—
7	C₇×Dic₁₇	C₂²	1	2	yes	—
8	C₁₇×Dic₇	C₂²	1	2	yes	—
9	C₂×Dic₃₄	—	7	1	no	maximal, Hall
10	C₂×C₇×C₁₇	Q₈	1	2	yes	complemented
11	C₂×C₇×C₁₇	C₂³	1	1	yes	characteristic
12	C₂×C₄×C₁₇	—	7	1	no	—
13	C₂×Dic₁₇	—	7	1	no	—
14	C₂×Dic₁₇	D₇	1	1	yes	characteristic
15	Dic₃₄	—	7	4	no	—
16	C₇×C₁₇	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
17	C₂×Dic₁₄	—	17	1	no	maximal, Hall
18	C₂²×C₁₇	C₂×D₇	1	1	yes	characteristic
19	C₄×C₁₇	—	7	2	no	—
20	Dic₁₇	—	7	2	no	—
21	Dic₁₇	C₂×D₇	1	2	yes	—
22	C₂×C₄×C₇	—	17	1	no	—
23	C₂×Dic₇	—	17	1	no	—
24	C₂×Dic₇	D₁₇	1	1	yes	characteristic
25	Dic₁₄	—	17	4	no	—
26	C₂×C₁₇	Dic₁₄	1	2	yes	complemented
27	C₂×C₁₇	C₂²×D₇	1	1	yes	characteristic
28	C₂²×C₇	C₂×D₁₇	1	1	yes	characteristic
29	C₄×C₇	—	17	2	no	—
30	Dic₇	—	17	2	no	—
31	Dic₇	C₂×D₁₇	1	2	yes	—
32	C₁₇	C₂×Dic₁₄	1	1	yes	characteristic, complemented, Sylow
33	C₂×Q₈	—	119	1	no	Sylow
34	C₂×C₇	Dic₃₄	1	2	yes	complemented
35	C₂×C₇	C₂²×D₁₇	1	1	yes	characteristic
36	Q₈	—	119	4	no	—
37	C₂×C₄	—	7	1	no	—
38	C₂×C₄	—	17	1	no	—
39	C₂×C₄	—	119	1	no	—
40	C₇	C₂×Dic₃₄	1	1	yes	characteristic, complemented, Sylow
41	C₂²	D₇×D₁₇	1	1	yes	characteristic
42	C₄	—	7	2	no	—
43	C₄	—	17	2	no	—
44	C₄	—	119	2	no	—
45	C₂	#11745755	1	2	yes	direct product factor
46	C₂	C₂×D₇×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₇×D₁₇
commutator, cosocle	C₂×C₇×C₁₇	C₂³
Frattini	C₂	C₂×D₇×D₁₇
Fitting, socle, prime radical	C₂²×C₇×C₁₇	C₂²
hypocenter	C₇×C₁₇	C₂×Q₈
LCS	G ▷ C₂×C₇×C₁₇ ▷ C₇×C₁₇
UCS	C₁ ◁ C₂²

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #11745755	C₂	direct (N × H)
10. C₂×C₇×C₁₇	Q₈	semidirect
16. C₇×C₁₇	C₂×Q₈	semidirect
26. C₂×C₁₇	Dic₁₄	semidirect
32. C₁₇	C₂×Dic₁₄	semidirect
34. C₂×C₇	Dic₃₄	semidirect
40. C₇	C₂×Dic₃₄	semidirect
45. C₂	#11745755	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×Dic₁₁₉	2
C₂×C₁₇×Dic₇	2
C₂×C₇×Dic₁₇	2
#11745755	2
C₂×Dic₃₄	7
C₂×Dic₁₄	17

Subgroups — C2×#11745755 #14274151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11745755 #14274151