Subgroups — #16949038

Order 4352.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14531036	C₂	1	4	yes	maximal
2	#14528402	C₂	1	1	yes	maximal, characteristic
3	C₈×#63214	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#1713	C₂	1	1	yes	maximal, characteristic
5	C₂×#10587500	—	2	8	no	—
6	#11763214	—	2	2	no	—
7	#11763189	C₂²	1	2	yes	—
8	C₄×#63214	C₂²	1	2	yes	—
9	C₁₇×#500	—	2	2	no	—
10	C₁₇×#494	C₂²	1	2	yes	—
11	C₈²×C₁₇	C₂²	1	1	yes	characteristic
12	C₂×Q₁₆×C₁₇	—	2	4	no	—
13	C₁₇×C₄⋊Q₈	—	2	2	no	—
14	C₂×Dic₆₈	—	2	4	no	—
15	#10587555	—	2	2	no	—
16	C₁₇×#107	—	4	4	no	—
17	C₄×C₈×C₁₇	D₄	1	2	yes	—
18	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
19	#10587500	—	4	16	no	—
20	#10587489	—	4	4	no	—
21	C₂×#63214	D₄	1	4	yes	—
22	C₂×Q₈×C₁₇	—	4	2	no	—
23	C₂×Dic₃₄	—	4	2	no	—
24	Q₁₆×C₁₇	—	4	8	no	—
25	C₂×C₈×C₁₇	D₈	1	4	yes	—
26	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
27	C₄⋊C₄×C₁₇	—	4	4	no	—
28	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
29	C₄⋊Dic₁₇	—	4	4	no	—
30	Dic₆₈	—	4	8	no	—
31	#63214	D₈	1	8	yes	—
32	#12516	—	17	1	no	maximal, Sylow
33	Q₈×C₁₇	—	8	4	no	—
34	C₂×C₄×C₁₇	—	8	2	no	—
35	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
36	C₂×C₄×C₁₇	C₂×D₈	1	2	yes	—
37	C₂×Dic₁₇	—	8	2	no	—
38	Dic₃₄	—	8	4	no	—
39	C₈×C₁₇	Q₃₂	1	8	yes	complemented
40	C₈×C₁₇	C₂×D₈	1	4	yes	—
41	#2247	—	17	4	no	—
42	#1713	—	17	1	no	—
43	#1713	D₁₇	1	1	yes	characteristic
44	C₈×C₁₆	—	17	1	no	—
45	C₂²×C₁₇	#493	1	1	yes	characteristic
46	C₄×C₁₇	—	16	2	no	—
47	C₄×C₁₇	#493	1	2	yes	—
48	C₄×C₁₇	C₂×Q₃₂	1	4	yes	—
49	Dic₁₇	—	16	2	no	—
50	C₂×Q₃₂	—	34	8	no	—
51	#500	—	2	2	no	—
52	#500	—	34	2	no	—
53	#494	—	17	2	no	—
54	#494	C₂×D₁₇	1	2	yes	—
55	C₄×C₁₆	—	17	2	no	—
56	C₈²	C₂×D₁₇	1	1	yes	characteristic
57	C₂×C₁₇	#1712	1	1	yes	characteristic
58	C₂×C₁₇	#2247	1	2	yes	—
59	C₂×Q₁₆	—	2	4	no	—
60	C₂×Q₁₆	—	34	4	no	—
61	C₄⋊Q₈	—	2	2	no	—
62	C₄⋊Q₈	—	34	2	no	—
63	Q₃₂	—	68	16	no	—
64	C₂×C₁₆	—	17	4	no	—
65	#107	—	4	4	no	—
66	#107	—	68	4	no	—
67	C₄×C₈	C₂²⋊D₁₇	1	2	yes	—
68	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
69	C₁₇	#12516	1	1	yes	characteristic, complemented, Sylow
70	C₂×Q₈	—	4	2	no	—
71	C₂×Q₈	—	68	2	no	—
72	Q₁₆	—	4	8	no	—
73	Q₁₆	—	68	8	no	—
74	C₂×C₈	#63228	1	4	yes	—
75	C₂×C₈	D₄×D₁₇	1	2	yes	—
76	C₄⋊C₄	—	4	4	no	—
77	C₄⋊C₄	—	68	4	no	—
78	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
79	C₁₆	—	17	8	no	—
80	Q₈	—	8	4	no	—
81	Q₈	—	136	4	no	—
82	C₂×C₄	—	8	2	no	—
83	C₂×C₄	—	136	2	no	—
84	C₂×C₄	C₂×#63228	1	2	yes	—
85	C₂×C₄	#10587626	1	1	yes	characteristic
86	C₈	#10587500	1	8	yes	complemented
87	C₈	D₈×D₁₇	1	4	yes	—
88	C₂²	#11763185	1	1	yes	characteristic
89	C₄	—	16	2	no	—
90	C₄	—	272	2	no	—
91	C₄	#11763184	1	2	yes	—
92	C₄	C₂×#10587500	1	4	yes	—
93	C₂	#14528398	1	1	yes	characteristic
94	C₂	#14531036	1	2	yes	—

	subgroup	G/H
center	C₂²	#11763185
commutator, cosocle	C₄×C₈×C₁₇	C₂³
Frattini	C₄×C₈	C₂²×D₁₇
Fitting	C₁₇×#1713	C₂
socle, prime radical	C₂²×C₁₇	#493
hypercenter	#1713	D₁₇
hypocenter	C₁₇	#12516
LCS	G ▷ C₄×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1713

Complements

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

N	H ≅ G/N	type
39. C₈×C₁₇	Q₃₂	semidirect
69. C₁₇	#12516	semidirect
86. C₈	#10587500	semidirect

Maximal subgroups

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

subgroup	index
#14531036	2
#14528402	2
C₈×#63214	2
C₁₇×#1713	2
#12516	17