Subgroups — C₂×C₁₇⋊#11725071 #44472580

Order 29988.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#89205	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇⋊#11725071	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇×D₃₅₇	—	3	1	no	maximal
4	C₁₇×#89205	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₃₅₇	—	3	2	no	—
6	C₂×C₃×C₇²×C₁₇	D₃	1	1	yes	characteristic
7	C₂×C₇×D₁₁₉	—	9	1	no	Hall
8	C₃×C₇²×C₁₇	C₂×D₃	1	1	yes	characteristic
9	C₂×C₁₇×C₇⋊C₉	—	14	1	no	—
10	C₂×#11725071	—	17	1	no	maximal, Hall
11	C₂×C₇²×C₁₇	D₉	1	1	yes	characteristic, complemented
12	C₇×D₁₁₉	—	9	2	no	—
13	C₂×D₃₅₇	—	3	1	no	—
14	C₂×C₇×D₅₁	—	21	1	no	—
15	C₁₇×C₇⋊C₉	—	14	1	no	—
16	C₂×#89205	D₁₇	1	1	yes	characteristic, complemented
17	#11725071	—	17	2	no	—
18	C₇²×C₁₇	C₂×D₉	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₇×C₁₇	—	2	1	no	—
20	C₂×C₃×C₇×C₁₇	—	6	1	no	—
21	C₂×C₃×C₇×C₁₇	—	6	1	no	—
22	D₃₅₇	—	3	2	no	—
23	C₇×D₅₁	—	21	2	no	—
24	C₂×D₁₅₃	—	49	1	no	maximal, Hall
25	C₂×C₇×D₂₁	—	51	1	no	—
26	C₂×D₁₁₉	—	9	1	no	—
27	C₂×C₇×D₁₇	—	63	1	no	—
28	#89205	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
29	C₃×C₇×C₁₇	—	2	1	no	—
30	C₃×C₇×C₁₇	—	6	1	no	—
31	C₃×C₇×C₁₇	—	6	1	no	—
32	C₂×C₉×C₁₇	—	98	1	no	—
33	D₁₅₃	—	49	2	no	—
34	C₂×C₃×C₇²	D₅₁	1	1	yes	characteristic
35	C₇×D₂₁	—	51	2	no	—
36	C₂×C₇×C₁₇	—	2	1	no	—
37	C₂×C₇×C₁₇	—	3	1	no	—
38	C₂×C₇×C₁₇	—	6	1	no	—
39	D₁₁₉	—	9	2	no	—
40	C₇×D₁₇	—	63	2	no	—
41	C₂×D₅₁	—	21	1	no	—
42	C₂×C₇×D₇	—	153	1	no	Hall
43	C₉×C₁₇	—	98	1	no	Hall
44	C₃×C₇²	C₂×D₅₁	1	1	yes	characteristic
45	C₂×C₇⋊C₉	—	14	1	no	—
46	C₇×C₁₇	—	2	1	no	—
47	C₇×C₁₇	—	3	1	no	—
48	C₇×C₁₇	—	6	1	no	—
49	C₂×C₃×C₁₇	#64418	1	1	yes	characteristic
50	D₅₁	—	21	2	no	—
51	C₂×C₇²	D₁₅₃	1	1	yes	characteristic, complemented
52	C₇×D₇	—	153	2	no	—
53	C₂×D₂₁	—	51	1	no	—
54	C₂×D₃×C₇	—	357	1	no	—
55	C₂×D₁₇	—	63	1	no	Hall
56	C₇⋊C₉	—	14	1	no	—
57	C₃×C₁₇	C₂×#64418	1	1	yes	characteristic
58	C₇²	C₂×D₁₅₃	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃×C₇	—	2	1	no	—
60	C₂×C₃×C₇	—	6	1	no	—
61	C₂×C₃×C₇	—	6	1	no	—
62	D₂₁	—	51	2	no	—
63	D₃×C₇	—	357	2	no	—
64	C₂×D₉	—	833	1	no	Hall
65	C₂×C₁₇	#11725071	1	1	yes	characteristic, complemented
66	D₁₇	—	63	2	no	—
67	C₂²×C₇	—	1071	1	no	—
68	C₂×D₇	—	153	1	no	—
69	C₃×C₇	—	2	1	no	—
70	C₃×C₇	—	6	1	no	—
71	C₃×C₇	—	6	1	no	—
72	C₂×C₉	—	98	1	no	—
73	D₉	—	833	2	no	—
74	C₁₇	C₂×#11725071	1	1	yes	characteristic, complemented, Sylow
75	C₂×C₇	—	2	1	no	—
76	C₂×C₇	—	3	1	no	—
77	C₂×C₇	—	6	1	no	—
78	C₂×C₇	—	1071	2	no	—
79	D₇	—	153	2	no	—
80	C₂×D₃	—	357	1	no	—
81	C₉	—	98	1	no	Sylow
82	C₇	—	2	1	no	—
83	C₇	—	3	1	no	—
84	C₇	—	6	1	no	—
85	C₂×C₃	C₁₇⋊#64418	1	1	yes	characteristic
86	D₃	—	357	2	no	—
87	C₂²	—	1071	1	no	Sylow
88	C₃	C₂×C₁₇⋊#64418	1	1	yes	characteristic
89	C₂	—	1071	2	no	—
90	C₂	C₁₇⋊#11725071	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₁₇⋊#11725071
commutator, cosocle, hypocenter	C₁₇×#89205	C₂²
Frattini	C₃	C₂×C₁₇⋊#64418
Fitting, socle	C₂×C₃×C₇²×C₁₇	D₃
LCS	G ▷ C₁₇×#89205
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#89205	C₂	semidirect
2. C₁₇⋊#11725071	C₂	direct (N × H)
4. C₁₇×#89205	C₂²	semidirect
11. C₂×C₇²×C₁₇	D₉	semidirect
16. C₂×#89205	D₁₇	semidirect
18. C₇²×C₁₇	C₂×D₉	semidirect
28. #89205	C₂×D₁₇	semidirect
51. C₂×C₇²	D₁₅₃	semidirect
58. C₇²	C₂×D₁₅₃	semidirect
65. C₂×C₁₇	#11725071	semidirect
74. C₁₇	C₂×#11725071	semidirect
90. C₂	C₁₇⋊#11725071	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×C₁₇×#89205	2
C₁₇⋊#11725071	2
C₂×C₇×D₃₅₇	3
C₂×#11725071	17
C₂×D₁₅₃	49

Subgroups — C2×C17⋊#11725071 #44472580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇⋊#11725071 #44472580