Subgroups — #16950726

Order 4352.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14526862	C₂	1	6	yes	maximal
2	C₁₇×#1726	C₂	1	1	yes	maximal, characteristic
3	C₂²×#63214	C₂²	1	4	yes	—
4	C₂×C₁₇×#97	C₄	1	3	yes	—
5	C₂×C₄×C₈×C₁₇	C₂²	1	3	yes	—
6	C₁₇×#376	C₄	1	1	yes	characteristic
7	C₂²×C₈×C₁₇	C₂×C₄	1	3	yes	—
8	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
9	C₂×C₄²×C₁₇	C₂×C₄	1	3	yes	—
10	C₁₇×#97	—	2	6	no	—
11	C₄×C₈×C₁₇	—	2	6	no	—
12	C₁₇×#95	C₈	1	4	yes	—
13	C₂×#63214	—	2	12	no	—
14	C₂²×C₄×C₁₇	C₂×C₈	1	6	yes	—
15	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₇	—	2	3	no	—
17	C₂×C₈×C₁₇	—	2	3	no	—
18	C₂×C₈×C₁₇	M₁₆	1	6	yes	—
19	C₂×C₈×C₁₇	#41	1	6	yes	—
20	C₄²×C₁₇	—	2	3	no	—
21	C₄²×C₁₇	—	2	3	no	—
22	#63214	—	4	4	no	—
23	#12895	—	17	1	no	maximal, Sylow
24	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
25	C₂×C₄×C₁₇	—	2	6	no	—
26	C₂×C₄×C₁₇	—	2	12	no	—
27	C₂×C₄×C₁₇	#117	1	3	yes	—
28	C₂×C₄×C₁₇	C₂×M₁₆	1	3	yes	—
29	C₈×C₁₇	—	2	6	no	—
30	C₈×C₁₇	#126	1	4	yes	—
31	#1726	D₁₇	1	1	yes	characteristic
32	#1374	—	17	6	no	—
33	C₂²×C₁₇	#431	1	3	yes	—
34	C₂²×C₁₇	#504	1	4	yes	—
35	C₄×C₁₇	—	4	6	no	—
36	C₄×C₁₇	#383	1	1	yes	characteristic
37	C₄×C₁₇	#432	1	3	yes	—
38	C₂²×C₁₆	—	17	4	no	—
39	C₂×#97	Dic₁₇	1	3	yes	—
40	C₂×C₄×C₈	C₂×D₁₇	1	3	yes	—
41	#376	Dic₁₇	1	1	yes	characteristic
42	C₂×C₁₇	#1839	1	1	yes	characteristic
43	C₂×C₁₇	#2164	1	6	yes	—
44	C₂²×C₈	C₂×Dic₁₇	1	3	yes	—
45	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
46	C₂×C₄²	C₂×Dic₁₇	1	3	yes	—
47	C₂×C₁₆	—	34	12	no	—
48	#97	—	2	6	no	—
49	C₄×C₈	—	2	6	no	—
50	#95	#3622	1	4	yes	—
51	C₁₇	#12895	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₄	C₂×#3622	1	6	yes	—
53	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
54	C₂×C₈	—	2	3	no	—
55	C₂×C₈	—	2	3	no	—
56	C₂×C₈	#63223	1	6	yes	—
57	C₂×C₈	#63252	1	6	yes	—
58	C₄²	—	2	3	no	—
59	C₄²	—	2	3	no	—
60	C₁₆	—	68	4	no	—
61	C₂³	C₂²×#3622	1	1	yes	characteristic
62	C₂×C₄	—	2	12	no	—
63	C₂×C₄	—	2	6	no	—
64	C₂×C₄	C₂×#63223	1	3	yes	—
65	C₂×C₄	#10587612	1	3	yes	—
66	C₈	—	2	6	no	—
67	C₈	#10587562	1	4	yes	—
68	C₂²	#11762862	1	3	yes	—
69	C₂²	#11763226	1	4	yes	—
70	C₄	—	4	6	no	—
71	C₄	#11762677	1	1	yes	characteristic
72	C₄	#11762866	1	3	yes	—
73	C₂	#14528927	1	1	yes	characteristic
74	C₂	#14530591	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₁₇
commutator, socle, prime radical	C₂³×C₁₇	C₂²×C₈
Fitting	C₁₇×#1726	C₂
cosocle	C₂²×C₈×C₁₇	C₂³
hypercenter	#1726	D₁₇
hypocenter	C₁₇	#12895
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₈ ◁ #1726

Complements

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

N	H ≅ G/N	type
51. C₁₇	#12895	semidirect

Maximal subgroups

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

subgroup	index
#14526862	2
C₁₇×#1726	2
#12895	17