Subgroups — C₂×#11763738 #14545139

Order 2176.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587536	C₂	1	2	yes	maximal
2	#11763738	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#63243	—	2	2	no	—
5	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
6	#10587536	—	2	2	no	—
7	#10587536	C₂²	1	4	yes	—
8	C₂×C₁₆×C₁₇	C₄	1	1	yes	characteristic
9	C₂×#63214	C₄	1	1	yes	characteristic
10	C₁₆×D₁₇	C₄	1	2	yes	—
11	C₁₆×D₁₇	C₂²	1	2	yes	—
12	C₂×C₄×D₁₇	D₄	1	1	yes	characteristic
13	C₂×#3624	—	4	2	no	—
14	#63243	—	2	4	no	—
15	#63243	—	4	2	no	—
16	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×#3622	Q₈	1	1	yes	characteristic
18	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
19	C₈×D₁₇	D₄	1	1	yes	characteristic
20	C₈×D₁₇	Q₈	1	1	yes	characteristic
21	C₈×D₁₇	C₂³	1	1	yes	characteristic
22	C₁₆×C₁₇	C₂×C₄	1	2	yes	—
23	#63214	C₂×C₄	1	2	yes	—
24	C₂²×D₁₇	Q₁₆	1	1	yes	characteristic
25	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
26	C₂×Dic₁₇	D₈	1	1	yes	characteristic
27	C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
28	C₄×D₁₇	D₈	1	1	yes	characteristic
29	C₄×D₁₇	Q₁₆	1	1	yes	characteristic
30	C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
31	#3624	—	4	4	no	—
32	C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
33	C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
34	#3622	C₄⋊C₄	1	1	yes	characteristic
35	#3622	C₂×Q₈	1	1	yes	characteristic
36	C₂×#368	—	17	1	no	maximal, Sylow
37	C₂²×C₁₇	#107	1	1	yes	characteristic
38	C₂×D₁₇	—	2	2	no	—
39	C₂×D₁₇	#107	1	1	yes	characteristic
40	C₂×D₁₇	C₂×Q₁₆	1	1	yes	characteristic
41	C₄×C₁₇	#107	1	1	yes	characteristic
42	C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
43	Dic₁₇	#107	1	1	yes	characteristic
44	Dic₁₇	C₂×D₈	1	1	yes	characteristic
45	C₂²×C₁₆	—	17	1	no	—
46	C₂×#108	—	17	2	no	—
47	#368	—	17	4	no	—
48	C₂×C₁₇	#368	1	2	yes	complemented
49	C₂×C₁₇	C₂×#107	1	1	yes	characteristic
50	D₁₇	—	2	1	no	—
51	D₁₇	—	2	1	no	—
52	C₂×M₁₆	—	34	2	no	—
53	C₂²×C₈	—	17	1	no	—
54	C₂×C₁₆	—	17	1	no	—
55	C₂×C₁₆	—	17	2	no	—
56	C₂×C₁₆	—	17	2	no	—
57	C₂×C₁₆	#595	1	1	yes	characteristic
58	#108	—	17	4	no	—
59	#108	—	34	2	no	—
60	C₁₇	C₂×#368	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₄	—	17	1	no	—
62	M₁₆	—	34	4	no	—
63	M₁₆	—	68	2	no	—
64	C₂×C₈	—	17	1	no	—
65	C₂×C₈	—	17	1	no	—
66	C₂×C₈	—	17	1	no	—
67	C₂×C₈	—	17	1	no	—
68	C₂×C₈	—	17	1	no	—
69	C₂×C₈	—	68	2	no	—
70	C₂×C₈	C₂×#595	1	1	yes	characteristic
71	C₁₆	—	17	2	no	—
72	C₁₆	C₂×#595	1	2	yes	—
73	C₂³	—	17	1	no	—
74	C₂×C₄	—	17	1	no	—
75	C₂×C₄	—	17	1	no	—
76	C₂×C₄	—	17	1	no	—
77	C₂×C₄	—	17	1	no	—
78	C₂×C₄	—	17	1	no	—
79	C₂×C₄	C₄⋊#595	1	1	yes	characteristic
80	C₈	—	17	1	no	—
81	C₈	—	17	1	no	—
82	C₈	—	68	4	no	—
83	C₈	C₄⋊#595	1	1	yes	characteristic
84	C₈	C₂²×#595	1	1	yes	characteristic
85	C₂²	—	17	1	no	—
86	C₂²	—	17	1	no	—
87	C₂²	—	34	2	no	—
88	C₂²	#10587534	1	1	yes	characteristic
89	C₄	—	17	1	no	—
90	C₄	—	17	1	no	—
91	C₄	#10587534	1	1	yes	characteristic
92	C₄	C₂×C₄⋊#595	1	1	yes	characteristic
93	C₂	—	34	1	no	—
94	C₂	—	34	1	no	—
95	C₂	#11763738	1	2	yes	direct product factor
96	C₂	C₂×#10587534	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10587534
commutator	C₈×C₁₇	C₂²×C₄
Frattini	C₈	C₂²×#595
Fitting	C₂×C₁₆×C₁₇	C₄
socle	C₂²×C₁₇	#107
prime radical	C₂²×D₁₇	Q₁₆
cosocle	C₈×D₁₇	C₂³
hypercenter	C₂×C₁₆	#595
hypocenter	C₁₇	C₂×#368
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #11763738	C₂	direct (N × H)
48. C₂×C₁₇	#368	semidirect
60. C₁₇	C₂×#368	semidirect
95. C₂	#11763738	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×#10587536	2
#11763738	2
C₂×C₁₆×D₁₇	2
C₂×#368	17

Subgroups — C2×#11763738 #14545139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11763738 #14545139