Subgroups — #14545005

Order 2176.

160 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	#11763701	C₂	1	4	yes	maximal, complemented
3	#11762765	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#117	C₄	1	1	yes	characteristic
5	C₂×#63223	C₄	1	1	yes	characteristic
6	C₂²×#3622	C₂²	1	1	yes	characteristic
7	#10587538	C₄	1	4	yes	complemented
8	#10587538	C₂²	1	4	yes	—
9	C₂×#63216	C₄	1	4	yes	complemented
10	#10587474	C₂²	1	2	yes	—
11	C₄×#3622	C₄	1	2	yes	—
12	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₄⋊C₄×C₁₇	—	2	1	no	—
14	C₂²⋊C₄×C₁₇	—	2	1	no	—
15	C₄²×C₁₇	C₂×C₄	1	2	yes	—
16	#63223	—	2	2	no	—
17	C₂×#3622	C₂×C₄	1	2	yes	—
18	C₂×#3622	C₂×C₄	1	1	yes	characteristic
19	C₂×#3622	C₂×C₄	1	2	yes	—
20	C₂×#3622	C₂×C₄	1	2	yes	—
21	C₂×#3622	C₂³	1	1	yes	characteristic
22	#63216	C₂×C₄	1	8	yes	—
23	C₂³×C₁₇	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₁₇	—	2	2	no	—
25	C₂×C₄×C₁₇	C₄²	1	2	yes	—
26	C₂×C₄×C₁₇	M₁₆	1	2	yes	—
27	C₂×C₄×C₁₇	M₁₆	1	1	yes	characteristic
28	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
29	#3622	—	2	2	no	—
30	#3622	C₄²	1	1	yes	characteristic
31	#3622	C₄²	1	1	yes	characteristic
32	#3622	C₂²×C₄	1	2	yes	—
33	#2110	—	17	1	no	maximal, Sylow
34	C₂²×C₁₇	—	4	1	no	—
35	C₂²×C₁₇	#97	1	2	yes	—
36	C₂²×C₁₇	C₂×M₁₆	1	1	yes	characteristic
37	C₄×C₁₇	—	4	2	no	—
38	C₄×C₁₇	#97	1	2	yes	—
39	C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
40	C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
41	C₂×M₃₂	—	17	2	no	—
42	#405	—	17	1	no	—
43	#347	—	17	4	no	—
44	C₂×C₁₇	—	2	1	no	—
45	C₂×C₁₇	—	2	2	no	—
46	C₂×C₁₇	C₂×#97	1	1	yes	characteristic
47	C₂×M₁₆	—	17	1	no	—
48	C₂²×C₈	—	17	1	no	—
49	#117	#595	1	1	yes	characteristic
50	M₃₂	—	17	4	no	—
51	M₃₂	—	17	4	no	—
52	C₂×C₁₆	—	17	4	no	—
53	#97	—	17	2	no	—
54	C₄×C₈	—	17	2	no	—
55	C₁₇	#2110	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₄	C₂×#595	1	1	yes	characteristic
57	M₁₆	—	34	2	no	—
58	C₂×C₈	—	17	2	no	—
59	C₂×C₈	—	17	2	no	—
60	C₂×C₈	—	17	1	no	—
61	C₂×C₈	—	17	1	no	—
62	C₂×C₈	—	17	2	no	—
63	C₄⋊C₄	—	2	1	no	—
64	C₂²⋊C₄	—	2	1	no	—
65	C₄²	C₂×#595	1	2	yes	—
66	C₁₆	—	17	8	no	—
67	C₂³	#63247	1	1	yes	characteristic
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	#63243	1	2	yes	—
70	C₂×C₄	C₄×#595	1	2	yes	—
71	C₂×C₄	#63247	1	1	yes	characteristic
72	C₂×C₄	C₂²×#595	1	1	yes	characteristic
73	C₈	—	17	2	no	—
74	C₈	—	17	1	no	—
75	C₈	—	17	1	no	—
76	C₈	—	34	2	no	—
77	C₂²	—	4	1	no	—
78	C₂²	#10587542	1	2	yes	—
79	C₂²	C₂×#63247	1	1	yes	characteristic
80	C₄	—	4	2	no	—
81	C₄	#10587542	1	2	yes	—
82	C₄	C₂×#63243	1	1	yes	characteristic
83	C₄	C₂×C₄×#595	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	2	2	no	—
86	C₂	C₂×#10587542	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×C₄×#595
commutator	C₄×C₁₇	C₂×C₄²
Frattini	C₂×C₄	C₂²×#595
Fitting	C₁₇×#117	C₄
socle	C₂×C₁₇	C₂×#97
prime radical	C₂³×C₁₇	M₁₆
cosocle	C₂×#3622	C₂³
hypercenter	#117	#595
hypocenter	C₁₇	#2110
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
2. #11763701	C₂	semidirect
7. #10587538	C₄	semidirect
9. C₂×#63216	C₄	semidirect
55. C₁₇	#2110	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
#11763701	2
#11762765	2
#2110	17