Subgroups — D₁₇×C₂²⋊D₇ #14274152

Order 1904.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₇×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊D₁₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#11745753	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745752	C₂	1	1	yes	maximal, characteristic, complemented
7	Dic₇×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₇×C₁₇	C₂²	1	1	yes	characteristic, complemented
9	C₂×D₁₁₉	C₂²	1	1	yes	characteristic, complemented
10	C₂×D₇×C₁₇	C₂²	1	1	yes	characteristic, complemented
11	C₂×C₇×D₁₇	—	2	2	no	—
12	C₂×C₇×D₁₇	C₂²	1	1	yes	characteristic
13	C₂×C₇×D₁₇	C₂²	1	1	yes	characteristic, complemented
14	D₇×D₁₇	—	2	2	no	—
15	Dic₁₁₉	C₂²	1	1	yes	characteristic, complemented
16	C₁₇×Dic₇	C₂²	1	1	yes	characteristic, complemented
17	D₄×D₁₇	—	7	1	no	maximal, Hall
18	C₂×C₇×C₁₇	—	2	1	no	—
19	C₂×C₇×C₁₇	C₂³	1	1	yes	characteristic
20	D₁₁₉	—	2	1	no	—
21	C₇×D₁₇	—	2	1	no	—
22	C₇×D₁₇	D₄	1	2	yes	complemented
23	D₇×C₁₇	—	2	1	no	—
24	C₂²×D₁₇	—	7	1	no	—
25	C₂²×D₁₇	D₇	1	1	yes	characteristic, complemented
26	D₄×C₁₇	—	7	1	no	—
27	C₂²⋊D₁₇	—	7	1	no	—
28	C₂²⋊D₁₇	—	7	1	no	—
29	D₆₈	—	7	1	no	—
30	C₄×D₁₇	—	7	1	no	—
31	C₇×C₁₇	C₂×D₄	1	1	yes	characteristic, complemented, Hall
32	C₂×C₂²⋊D₇	—	17	1	no	maximal, Hall
33	C₂²×C₁₇	—	7	1	no	—
34	C₂²×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented
35	C₂×D₁₇	—	2	2	no	—
36	C₂×D₁₇	—	7	1	no	—
37	C₂×D₁₇	—	14	2	no	—
38	C₂×D₁₇	C₂×D₇	1	1	yes	characteristic
39	C₂×D₁₇	C₂×D₇	1	1	yes	characteristic, complemented
40	C₄×C₁₇	—	7	1	no	—
41	Dic₁₇	—	7	1	no	—
42	C₂³×C₇	—	17	1	no	—
43	C₂²×D₇	—	17	1	no	—
44	C₂²⋊D₇	—	17	1	no	—
45	C₂²⋊D₇	—	17	1	no	—
46	C₂²⋊D₇	—	17	1	no	—
47	C₂²⋊D₇	D₁₇	1	1	yes	characteristic, direct product factor
48	C₂×Dic₇	—	17	1	no	—
49	C₂×C₁₇	—	2	1	no	—
50	C₂×C₁₇	—	14	1	no	—
51	C₂×C₁₇	C₂²×D₇	1	1	yes	characteristic
52	D₁₇	—	2	1	no	—
53	D₁₇	—	14	1	no	—
54	D₁₇	C₂²⋊D₇	1	2	yes	direct product factor
55	C₂²×C₇	—	17	1	no	—
56	C₂²×C₇	—	17	1	no	—
57	C₂²×C₇	—	34	2	no	—
58	C₂²×C₇	C₂×D₁₇	1	1	yes	characteristic, complemented
59	C₂×D₇	—	17	1	no	—
60	C₂×D₇	—	34	2	no	—
61	C₂×D₇	C₂×D₁₇	1	1	yes	characteristic, complemented
62	Dic₇	—	17	1	no	—
63	Dic₇	C₂×D₁₇	1	1	yes	characteristic, complemented
64	C₁₇	C₂×C₂²⋊D₇	1	1	yes	characteristic, complemented, Sylow
65	C₂×D₄	—	119	1	no	Sylow
66	C₂×C₇	—	2	1	no	—
67	C₂×C₇	—	17	2	no	—
68	C₂×C₇	—	34	1	no	—
69	C₂×C₇	C₂²×D₁₇	1	1	yes	characteristic
70	D₇	—	2	1	no	—
71	D₇	—	34	1	no	—
72	C₂³	—	17	1	no	—
73	C₂³	—	119	1	no	—
74	D₄	—	7	1	no	—
75	D₄	—	119	1	no	—
76	D₄	—	119	1	no	—
77	D₄	—	119	1	no	—
78	C₂×C₄	—	119	1	no	—
79	C₇	D₄×D₁₇	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	7	1	no	—
81	C₂²	—	17	1	no	—
82	C₂²	—	17	1	no	—
83	C₂²	—	34	2	no	—
84	C₂²	—	119	1	no	—
85	C₂²	—	238	2	no	—
86	C₂²	D₇×D₁₇	1	1	yes	characteristic, complemented
87	C₄	—	7	1	no	—
88	C₄	—	119	1	no	—
89	C₂	—	2	1	no	—
90	C₂	—	14	1	no	—
91	C₂	—	17	2	no	—
92	C₂	—	34	1	no	—
93	C₂	—	238	1	no	—
94	C₂	C₂×D₇×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₇×D₁₇
commutator, socle, cosocle	C₂×C₇×C₁₇	C₂³
Fitting	C₂²×C₇×C₁₇	C₂²
hypercenter	C₂²	D₇×D₁₇
hypocenter	C₇×C₁₇	C₂×D₄
LCS	G ▷ C₂×C₇×C₁₇ ▷ C₇×C₁₇
UCS	C₁ ◁ C₂ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×D₁₇	C₂	semidirect
2. C₂×D₇×D₁₇	C₂	semidirect
3. C₂²⋊D₁₁₉	C₂	semidirect
4. C₁₇×C₂²⋊D₇	C₂	semidirect
5. #11745753	C₂	semidirect
6. #11745752	C₂	semidirect
7. Dic₇×D₁₇	C₂	semidirect
8. C₂²×C₇×C₁₇	C₂²	semidirect
9. C₂×D₁₁₉	C₂²	semidirect
10. C₂×D₇×C₁₇	C₂²	semidirect
13. C₂×C₇×D₁₇	C₂²	semidirect
15. Dic₁₁₉	C₂²	semidirect
16. C₁₇×Dic₇	C₂²	semidirect
22. C₇×D₁₇	D₄	semidirect
25. C₂²×D₁₇	D₇	semidirect
31. C₇×C₁₇	C₂×D₄	semidirect
34. C₂²×C₁₇	C₂×D₇	semidirect
39. C₂×D₁₇	C₂×D₇	semidirect
47. C₂²⋊D₇	D₁₇	direct (N × H)
54. D₁₇	C₂²⋊D₇	direct (N × H)
58. C₂²×C₇	C₂×D₁₇	semidirect
61. C₂×D₇	C₂×D₁₇	semidirect
63. Dic₇	C₂×D₁₇	semidirect
64. C₁₇	C₂×C₂²⋊D₇	semidirect
79. C₇	D₄×D₁₇	semidirect
86. C₂²	D₇×D₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₇×D₁₇	2
C₂×D₇×D₁₇	2
C₂²⋊D₁₁₉	2
C₁₇×C₂²⋊D₇	2
#11745753	2
#11745752	2
Dic₇×D₁₇	2
D₄×D₁₇	7
C₂×C₂²⋊D₇	17

Subgroups — D17×C22⋊D7 #14274152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇×C₂²⋊D₇ #14274152