Subgroups — #17948409

Order 4352.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543814	C₂	1	2	yes	maximal
2	#14528400	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#63216	—	2	2	no	—
4	#11763212	—	2	2	no	—
5	#11763189	C₄	1	1	yes	characteristic
6	C₈×#3622	C₂²	1	1	yes	characteristic
7	C₁₇×#494	C₄	1	1	yes	characteristic
8	C₂×Q₁₆×C₁₇	—	4	1	no	—
9	C₁₇×C₄⋊Q₈	—	2	1	no	—
10	C₂×Dic₆₈	—	4	1	no	—
11	#10587555	—	2	1	no	—
12	C₂×#63216	—	4	2	no	—
13	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
14	#10587478	—	4	2	no	—
15	#10587478	—	4	2	no	—
16	C₄×#3622	D₄	1	2	yes	—
17	C₂×Q₈×C₁₇	—	4	1	no	—
18	C₂×Dic₃₄	—	4	1	no	—
19	Q₁₆×C₁₇	—	8	2	no	—
20	C₂×C₈×C₁₇	—	2	1	no	—
21	C₄⋊C₄×C₁₇	—	4	2	no	—
22	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₄⋊Dic₁₇	—	4	2	no	—
24	C₂×#3622	D₈	1	2	yes	—
25	C₂×#3622	SD₁₆	1	2	yes	—
26	Dic₆₈	—	8	2	no	—
27	#63216	—	8	2	no	—
28	#7098	—	17	1	no	maximal, Sylow
29	Q₈×C₁₇	—	8	2	no	—
30	C₂×C₄×C₁₇	—	8	1	no	—
31	C₂×C₄×C₁₇	#100	1	1	yes	characteristic
32	C₂×C₄×C₁₇	#102	1	2	yes	—
33	C₂×Dic₁₇	—	8	1	no	—
34	Dic₃₄	—	8	2	no	—
35	C₈×C₁₇	—	2	2	no	—
36	#3622	—	2	2	no	—
37	#3622	SD₃₂	1	2	yes	—
38	#3622	Q₃₂	1	2	yes	—
39	#1713	—	17	1	no	—
40	#1370	—	17	2	no	—
41	C₂²×C₁₇	#331	1	1	yes	characteristic
42	C₄×C₁₇	—	2	1	no	—
43	C₄×C₁₇	—	16	1	no	—
44	C₄×C₁₇	#358	1	2	yes	—
45	C₄×C₁₇	#362	1	2	yes	—
46	Dic₁₇	—	16	1	no	—
47	#500	—	34	2	no	—
48	#494	—	17	1	no	—
49	#494	#595	1	1	yes	characteristic
50	C₄⋊C₁₆	—	34	2	no	—
51	C₈²	—	17	1	no	—
52	C₂×C₁₇	#1357	1	1	yes	characteristic
53	C₂×C₁₇	#1362	1	2	yes	—
54	C₂×Q₁₆	—	4	1	no	—
55	C₂×Q₁₆	—	68	1	no	—
56	C₄⋊Q₈	—	2	1	no	—
57	C₄⋊Q₈	—	34	1	no	—
58	C₂×C₁₆	—	68	2	no	—
59	#107	—	68	2	no	—
60	#107	—	68	2	no	—
61	C₄×C₈	—	17	2	no	—
62	C₄×C₈	C₂×#595	1	1	yes	characteristic
63	C₁₇	#7098	1	1	yes	characteristic, complemented, Sylow
64	C₂×Q₈	—	4	1	no	—
65	C₂×Q₈	—	68	1	no	—
66	Q₁₆	—	8	2	no	—
67	Q₁₆	—	136	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	17	2	no	—
70	C₂×C₈	—	17	2	no	—
71	C₄⋊C₄	—	4	2	no	—
72	C₄⋊C₄	—	68	2	no	—
73	C₄²	C₂²⋊#595	1	1	yes	characteristic
74	C₁₆	—	136	2	no	—
75	Q₈	—	8	2	no	—
76	Q₈	—	136	2	no	—
77	C₂×C₄	—	8	1	no	—
78	C₂×C₄	—	136	1	no	—
79	C₂×C₄	#10587547	1	2	yes	—
80	C₂×C₄	#10587553	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	17	2	no	—
83	C₈	—	17	2	no	—
84	C₈	—	34	2	no	—
85	C₂²	#11763667	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	16	1	no	—
88	C₄	—	272	1	no	—
89	C₄	#11763722	1	2	yes	—
90	C₄	#11763728	1	2	yes	—
91	C₂	#14543792	1	1	yes	characteristic
92	C₂	#14543799	1	2	yes	—

	subgroup	G/H
center	C₂²	#11763667
commutator	C₄×C₈×C₁₇	C₂×C₄
Frattini	C₄×C₈	C₂×#595
Fitting	C₁₇×#494	C₄
socle, prime radical	C₂²×C₁₇	#331
cosocle	C₈×#3622	C₂²
hypercenter	#494	#595
hypocenter	C₁₇	#7098
LCS	G ▷ C₄×C₈×C₁₇ ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
63. C₁₇	#7098	semidirect

Maximal subgroups

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

subgroup	index
#14543814	2
#14528400	2
#7098	17