Subgroups — #14545154

Order 2176.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763731	C₂	1	2	yes	maximal, complemented
2	#11763705	C₂	1	2	yes	maximal
3	#11763702	C₂	1	2	yes	maximal, complemented
4	M₁₆×Dic₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂×M₁₆×C₁₇	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₁₇	C₄	1	1	yes	characteristic
7	C₂×#63223	C₂²	1	1	yes	characteristic
8	#10587538	C₂²	1	4	yes	—
9	#10587486	C₄	1	1	yes	characteristic
10	#10587486	C₂²	1	1	yes	characteristic
11	C₈×Dic₁₇	C₄	1	1	yes	characteristic
12	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
14	C₂²×Dic₁₇	—	2	1	no	—
15	M₁₆×C₁₇	—	2	2	no	—
16	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₁₇	—	2	1	no	—
19	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
20	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
21	#63223	—	2	2	no	—
22	C₂×#3622	C₂×C₄	1	1	yes	characteristic
23	C₂×#3622	C₂³	1	1	yes	characteristic
24	#63216	—	2	4	no	—
25	C₂³×C₁₇	M₁₆	1	1	yes	characteristic
26	C₂×C₄×C₁₇	—	2	1	no	—
27	C₂×C₄×C₁₇	—	2	1	no	—
28	C₂×C₄×C₁₇	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₁₇	—	2	1	no	—
31	C₂×Dic₁₇	—	2	1	no	—
32	C₂×Dic₁₇	—	4	2	no	—
33	C₈×C₁₇	—	2	1	no	—
34	C₈×C₁₇	M₁₆	1	2	yes	—
35	#3622	—	2	1	no	—
36	#3622	#41	1	2	yes	—
37	#2165	—	17	1	no	maximal, Sylow
38	C₂²×C₁₇	—	2	1	no	—
39	C₂²×C₁₇	—	4	1	no	—
40	C₂²×C₁₇	C₂×M₁₆	1	1	yes	characteristic
41	C₄×C₁₇	—	2	1	no	—
42	C₄×C₁₇	#117	1	1	yes	characteristic
43	C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
44	Dic₁₇	—	2	2	no	—
45	Dic₁₇	—	4	1	no	—
46	C₄×M₁₆	—	17	1	no	—
47	#364	—	17	2	no	—
48	#349	—	17	2	no	—
49	#347	—	17	2	no	—
50	C₂×C₁₇	—	2	1	no	—
51	C₂×C₁₇	—	4	1	no	—
52	C₂×C₁₇	#432	1	1	yes	characteristic
53	C₂×M₁₆	—	17	1	no	—
54	C₂×M₁₆	#595	1	1	yes	characteristic
55	C₂×C₄²	—	17	1	no	—
56	M₃₂	—	17	4	no	—
57	#97	—	17	1	no	—
58	#97	—	17	1	no	—
59	C₄×C₈	—	17	1	no	—
60	C₄×C₈	—	17	1	no	—
61	C₁₇	#2165	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₄	—	34	1	no	—
63	C₂²×C₄	C₂×#595	1	1	yes	characteristic
64	M₁₆	—	2	2	no	—
65	M₁₆	—	34	2	no	—
66	C₂×C₈	—	17	1	no	—
67	C₂×C₈	—	17	1	no	—
68	C₂×C₈	C₂×#595	1	1	yes	characteristic
69	C₂×C₈	C₂×#595	1	1	yes	characteristic
70	C₄²	—	17	1	no	—
71	C₄²	—	17	1	no	—
72	C₄²	—	34	1	no	—
73	C₁₆	—	34	4	no	—
74	C₂³	#63243	1	1	yes	characteristic
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	34	1	no	—
78	C₂×C₄	—	34	1	no	—
79	C₂×C₄	—	68	2	no	—
80	C₂×C₄	#63243	1	1	yes	characteristic
81	C₂×C₄	C₂²×#595	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	17	2	no	—
84	C₈	—	34	1	no	—
85	C₈	#63247	1	2	yes	—
86	C₂²	—	2	1	no	—
87	C₂²	—	4	1	no	—
88	C₂²	C₂×#63243	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	34	2	no	—
91	C₄	—	68	1	no	—
92	C₄	#10587677	1	1	yes	characteristic
93	C₄	C₂×#63247	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	4	1	no	—
96	C₂	#11763830	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10587677
commutator	C₂×C₄×C₁₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×#595
Fitting	C₂×M₁₆×C₁₇	C₄
socle	C₂×C₁₇	#432
prime radical	C₂³×C₁₇	M₁₆
cosocle	C₂×#3622	C₂³
hypercenter	C₂×M₁₆	#595
hypocenter	C₁₇	#2165
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. #11763731	C₂	semidirect
3. #11763702	C₂	semidirect
61. C₁₇	#2165	semidirect

Maximal subgroups

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

subgroup	index
#11763731	2
#11763705	2
#11763702	2
M₁₆×Dic₁₇	2
#2165	17