Subgroups — #14545116

Order 2176.

172 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	C₄⋊#63216	C₂	1	4	yes	maximal, complemented
3	C₂×C₄×#3622	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄²×C₁₇	C₄	1	1	yes	characteristic
5	C₂²×#3622	C₄	1	1	yes	characteristic
6	C₂²×#3622	C₂²	1	1	yes	characteristic
7	#10587538	—	2	4	no	—
8	C₂×#63216	C₂²	1	4	yes	—
9	C₄×#3622	C₄	1	2	yes	—
10	C₄×#3622	C₂²	1	2	yes	—
11	C₂²×C₄×C₁₇	C₈	1	2	yes	—
12	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₄²×C₁₇	C₈	1	1	yes	characteristic
14	C₄²×C₁₇	C₈	1	1	yes	characteristic
15	C₄²×C₁₇	C₂×C₄	1	2	yes	—
16	C₂×#3622	—	2	2	no	—
17	C₂×#3622	C₂×C₄	1	2	yes	—
18	C₂×#3622	C₂×C₄	1	1	yes	characteristic
19	C₂×#3622	D₄	1	2	yes	—
20	C₂×#3622	Q₈	1	2	yes	—
21	C₂×#3622	C₂³	1	1	yes	characteristic
22	#63216	—	2	4	no	—
23	C₂³×C₁₇	C₂×C₈	1	1	yes	characteristic
24	C₂×C₄×C₁₇	—	2	4	no	—
25	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₁₇	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₁₇	C₂×C₈	1	2	yes	—
29	C₂×C₄×C₁₇	M₁₆	1	2	yes	—
30	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
31	#3622	—	2	2	no	—
32	#3622	C₄⋊C₄	1	2	yes	—
33	#3622	C₂×D₄	1	1	yes	characteristic
34	#3622	C₂×Q₈	1	1	yes	characteristic
35	#2150	—	17	1	no	maximal, Sylow
36	C₂²×C₁₇	—	2	2	no	—
37	C₂²×C₁₇	C₄⋊C₈	1	2	yes	—
38	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₁₇	—	2	2	no	—
40	C₄×C₁₇	C₄⋊C₈	1	2	yes	—
41	C₄×C₁₇	M₃₂	1	4	yes	complemented
42	C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
44	C₂×M₃₂	—	17	2	no	—
45	C₂×C₄×C₈	—	17	1	no	—
46	C₄⋊C₁₆	—	17	4	no	—
47	C₂×C₁₇	—	2	2	no	—
48	C₂×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
49	C₂×C₁₇	C₂×M₃₂	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	—	34	4	no	—
54	C₂×C₁₆	—	17	4	no	—
55	C₄×C₈	—	17	2	no	—
56	C₄×C₈	—	17	2	no	—
57	C₁₇	#2150	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	#3624	1	2	yes	—
59	C₂²×C₄	C₂×#595	1	1	yes	characteristic
60	C₂×C₈	—	17	2	no	—
61	C₂×C₈	—	17	2	no	—
62	C₂×C₈	—	17	1	no	—
63	C₂×C₈	—	17	1	no	—
64	C₂×C₈	—	17	2	no	—
65	C₂×C₈	—	34	2	no	—
66	C₄²	#3624	1	1	yes	characteristic
67	C₄²	#3624	1	1	yes	characteristic
68	C₄²	C₂×#595	1	2	yes	—
69	C₁₆	—	34	4	no	—
70	C₂³	C₂×#3624	1	1	yes	characteristic
71	C₂×C₄	—	2	4	no	—
72	C₂×C₄	#63243	1	2	yes	—
73	C₂×C₄	C₄⋊#595	1	2	yes	—
74	C₂×C₄	C₂×#3624	1	2	yes	—
75	C₂×C₄	C₂×#3624	1	2	yes	—
76	C₂×C₄	C₂×#3624	1	1	yes	characteristic
77	C₂×C₄	C₂²×#595	1	1	yes	characteristic
78	C₈	—	17	1	no	—
79	C₈	—	17	2	no	—
80	C₈	—	17	1	no	—
81	C₈	—	34	2	no	—
82	C₂²	—	2	2	no	—
83	C₂²	C₄⋊#3624	1	2	yes	—
84	C₂²	C₂²×#3624	1	1	yes	characteristic
85	C₄	—	2	2	no	—
86	C₄	#10587538	1	4	yes	complemented
87	C₄	C₄⋊#3624	1	2	yes	—
88	C₄	C₂×#63243	1	1	yes	characteristic
89	C₄	C₂×C₄⋊#595	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×C₄⋊#3624	1	1	yes	characteristic
92	C₂	C₂×#10587538	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂²×C₈
Fitting	C₂×C₄²×C₁₇	C₄
prime radical	C₂³×C₁₇	C₂×C₈
cosocle	C₂×#3622	C₂³
hypercenter	C₂×C₄²	#595
hypocenter	C₁₇	#2150
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₄⋊#63216	C₂	semidirect
41. C₄×C₁₇	M₃₂	semidirect
57. C₁₇	#2150	semidirect
86. C₄	#10587538	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
C₄⋊#63216	2
C₂×C₄×#3622	2
#2150	17