Subgroups — #17960441

Order 4352.

350 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545007	C₂	1	3	yes	maximal
2	#14544995	C₂	1	3	yes	maximal
3	#14528540	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587538	C₂²	1	3	yes	—
5	C₂²×#63216	C₂²	1	1	yes	characteristic
6	#11763702	C₄	1	12	yes	complemented
7	#11763698	C₄	1	6	yes	complemented
8	#11763695	C₄	1	6	yes	complemented
9	#11762767	C₂²	1	3	yes	—
10	#11762566	C₄	1	3	yes	—
11	C₁₇×#338	C₄	1	1	yes	characteristic
12	C₂×M₁₆×C₁₇	C₂×C₄	1	3	yes	—
13	#10587612	C₂×C₄	1	3	yes	—
14	C₂²×#3622	C₂³	1	1	yes	characteristic
15	#10587538	C₂×C₄	1	12	yes	—
16	C₂×#63216	C₂×C₄	1	3	yes	—
17	C₂×#63216	C₂×C₄	1	3	yes	—
18	C₂×#63216	C₂×C₄	1	6	yes	—
19	#10587486	C₂×C₄	1	6	yes	—
20	C₈×Dic₁₇	C₂×C₄	1	6	yes	—
21	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
22	M₁₆×C₁₇	—	2	6	no	—
23	C₂×C₈×C₁₇	C₄²	1	6	yes	—
24	C₂²⋊Dic₁₇	—	2	3	no	—
25	C₄⋊Dic₁₇	—	2	3	no	—
26	C₄×Dic₁₇	C₄²	1	6	yes	—
27	C₂×#3622	C₂²×C₄	1	3	yes	—
28	C₂×#3622	C₂²×C₄	1	3	yes	—
29	#63216	C₄²	1	1	yes	characteristic
30	#63216	C₄²	1	3	yes	—
31	#63216	C₄²	1	12	yes	—
32	#12542	—	17	1	no	maximal, Sylow
33	C₂³×C₁₇	#131	1	1	yes	characteristic
34	C₂×C₄×C₁₇	C₂×C₄²	1	3	yes	—
35	C₂×C₄×C₁₇	#131	1	3	yes	—
36	C₂×Dic₁₇	—	2	6	no	—
37	C₈×C₁₇	—	2	6	no	—
38	#3622	C₂×C₄²	1	1	yes	characteristic
39	#3622	C₂×C₄²	1	3	yes	—
40	#2110	—	17	3	no	—
41	#2108	—	17	3	no	—
42	#1747	—	17	1	no	—
43	C₂²×C₁₇	—	4	1	no	—
44	C₂²×C₁₇	#405	1	3	yes	—
45	C₄×C₁₇	C₄³	1	1	yes	characteristic
46	C₄×C₁₇	#405	1	3	yes	—
47	Dic₁₇	—	4	6	no	—
48	C₂×M₃₂	—	17	3	no	—
49	C₂²×C₁₆	—	17	1	no	—
50	#405	—	17	3	no	—
51	#347	—	17	12	no	—
52	#346	—	17	6	no	—
53	C₄×C₁₆	—	17	6	no	—
54	#338	#595	1	1	yes	characteristic
55	H(3,ℤ/4)	—	17	3	no	—
56	C₂×C₁₇	—	2	3	no	—
57	C₂×C₁₇	#1726	1	1	yes	characteristic
58	C₂×M₁₆	C₂×#595	1	3	yes	—
59	C₂²×C₈	—	17	1	no	—
60	#117	—	17	3	no	—
61	M₃₂	—	17	12	no	—
62	C₂×C₁₆	—	17	3	no	—
63	C₂×C₁₆	—	17	6	no	—
64	C₂×C₁₆	—	17	3	no	—
65	#97	—	17	6	no	—
66	C₄×C₈	—	17	6	no	—
67	C₁₇	#12542	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
69	M₁₆	—	2	6	no	—
70	C₂×C₈	—	17	3	no	—
71	C₂×C₈	—	17	3	no	—
72	C₂×C₈	C₄×#595	1	6	yes	—
73	C₄⋊C₄	—	34	3	no	—
74	C₂²⋊C₄	—	34	3	no	—
75	C₄²	—	17	6	no	—
76	C₁₆	—	17	1	no	—
77	C₁₆	—	17	3	no	—
78	C₁₆	—	17	12	no	—
79	C₂³	#10587680	1	1	yes	characteristic
80	C₂×C₄	—	34	6	no	—
81	C₂×C₄	C₂×C₄×#595	1	3	yes	—
82	C₂×C₄	#10587678	1	3	yes	—
83	C₈	—	2	6	no	—
84	C₈	—	17	1	no	—
85	C₈	—	17	3	no	—
86	C₂²	—	4	1	no	—
87	C₂²	#11763774	1	3	yes	—
88	C₄	—	68	6	no	—
89	C₄	C₄²×#595	1	1	yes	characteristic
90	C₄	#11763773	1	3	yes	—
91	C₂	—	2	3	no	—
92	C₂	#14544441	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄²×#595
commutator	C₄×C₁₇	C₄³
Frattini	C₂²×C₄	C₂²×#595
Fitting	C₁₇×#338	C₄
socle	C₂×C₁₇	#1726
prime radical	C₂³×C₁₇	#131
cosocle	C₂²×#3622	C₂³
hypercenter	#338	#595
hypocenter	C₁₇	#12542
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
6. #11763702	C₄	semidirect
7. #11763698	C₄	semidirect
8. #11763695	C₄	semidirect
67. C₁₇	#12542	semidirect

Maximal subgroups

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

subgroup	index
#14545007	2
#14544995	2
#14528540	2
#12542	17