Subgroups — #14543828

Order 2176.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587538	C₂	1	2	yes	maximal
2	C₂×C₄×#3622	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₁₇	C₄	1	1	yes	characteristic
4	C₂²×#3622	C₄	1	1	yes	characteristic
5	C₂²×#3622	C₂²	1	1	yes	characteristic
6	#10587538	—	2	2	no	—
7	#10587538	C₄	1	4	yes	complemented
8	C₂×#63216	—	2	2	no	—
9	C₄×#3622	—	2	2	no	—
10	C₂²×C₄×C₁₇	—	2	1	no	—
11	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₄²×C₁₇	—	2	1	no	—
13	C₄²×C₁₇	C₈	1	2	yes	—
14	C₂×#3622	—	2	1	no	—
15	C₂×#3622	—	2	1	no	—
16	C₂×#3622	C₈	1	2	yes	—
17	C₂×#3622	C₂×C₄	1	2	yes	—
18	C₂×#3622	D₄	1	1	yes	characteristic
19	C₂×#3622	D₄	1	2	yes	—
20	C₂×#3622	Q₈	1	1	yes	characteristic
21	#63216	—	2	4	no	—
22	C₂³×C₁₇	M₁₆	1	1	yes	characteristic
23	C₂×C₄×C₁₇	—	2	4	no	—
24	C₂×C₄×C₁₇	—	2	2	no	—
25	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₁₇	M₁₆	1	1	yes	characteristic
31	#3622	—	2	2	no	—
32	#3622	C₂²⋊C₄	1	2	yes	—
33	#3622	C₄⋊C₄	1	2	yes	—
34	#1376	—	17	1	no	maximal, Sylow
35	C₂²×C₁₇	—	2	2	no	—
36	C₂²×C₁₇	#97	1	1	yes	characteristic
37	C₂²×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
38	C₂²×C₁₇	C₄⋊C₈	1	1	yes	characteristic
39	C₄×C₁₇	—	2	4	no	—
40	C₄×C₁₇	#95	1	1	yes	characteristic
41	C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
42	C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
43	C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
44	C₂×M₃₂	—	17	2	no	—
45	C₂×C₄×C₈	—	17	1	no	—
46	C₂×C₁₇	—	2	1	no	—
47	C₂×C₁₇	—	2	1	no	—
48	C₂×C₁₇	#336	1	1	yes	characteristic
49	C₂×C₁₇	#364	1	2	yes	—
50	C₂²×C₈	—	17	1	no	—
51	C₂²×C₈	—	17	1	no	—
52	C₂×C₄²	#595	1	1	yes	characteristic
53	M₃₂	—	17	4	no	—
54	M₃₂	—	34	2	no	—
55	C₂×C₁₆	—	34	2	no	—
56	C₄×C₈	—	34	2	no	—
57	C₁₇	#1376	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	—	2	1	no	—
59	C₂²×C₄	C₂×#595	1	1	yes	characteristic
60	C₂×C₈	—	17	2	no	—
61	C₂×C₈	—	17	1	no	—
62	C₂×C₈	—	17	1	no	—
63	C₂×C₈	—	17	2	no	—
64	C₂×C₈	—	17	2	no	—
65	C₂×C₈	—	34	1	no	—
66	C₂×C₈	—	34	1	no	—
67	C₄²	—	2	1	no	—
68	C₄²	#3624	1	2	yes	—
69	C₁₆	—	34	4	no	—
70	C₂³	#63247	1	1	yes	characteristic
71	C₂×C₄	—	2	4	no	—
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	#63242	1	1	yes	characteristic
74	C₂×C₄	#63243	1	1	yes	characteristic
75	C₂×C₄	C₄×#595	1	1	yes	characteristic
76	C₂×C₄	C₄⋊#595	1	1	yes	characteristic
77	C₂×C₄	C₂×#3624	1	1	yes	characteristic
78	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
79	C₈	—	17	2	no	—
80	C₈	—	17	2	no	—
81	C₈	—	34	2	no	—
82	C₂²	—	2	2	no	—
83	C₂²	#10587542	1	1	yes	characteristic
84	C₂²	#10587544	1	1	yes	characteristic
85	C₂²	C₂²⋊#3624	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	C₄×#3624	1	1	yes	characteristic
88	C₄	C₄⋊#3624	1	1	yes	characteristic
89	C₄	#10587543	1	1	yes	characteristic
90	C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	#11763675	1	1	yes	characteristic
94	C₂	#11763732	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄⋊#595
commutator	C₄×C₁₇	C₄×C₈
Frattini	C₂²×C₄	C₂×#595
Fitting	C₂×C₄²×C₁₇	C₄
socle	C₂²×C₁₇	C₄⋊C₈
prime radical	C₂³×C₁₇	M₁₆
cosocle	C₂²×#3622	C₂²
hypercenter	C₂×C₄²	#595
hypocenter	C₁₇	#1376
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
7. #10587538	C₄	semidirect
57. C₁₇	#1376	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10587538	2
C₂×C₄×#3622	2
#1376	17