Subgroups — #14528958

Order 2176.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587493	C₂	1	4	yes	maximal
2	#11762833	C₂	1	1	yes	maximal, characteristic
3	C₂×#10587474	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#423	C₂	1	1	yes	maximal, characteristic
5	C₂×M₁₆×C₁₇	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
7	C₂×#63223	C₂²	1	2	yes	—
8	C₂²×#3622	C₂²	1	2	yes	—
9	C₁₇×C₄⋊C₈	—	2	2	no	—
10	#10587493	—	2	8	no	—
11	C₄⋊#3622	—	2	2	no	—
12	#10587474	C₄	1	4	yes	—
13	C₂²×C₄×C₁₇	Q₈	1	2	yes	—
14	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
15	M₁₆×C₁₇	—	2	4	no	—
16	C₂×C₈×C₁₇	—	2	2	no	—
17	C₄²×C₁₇	C₂×C₄	1	2	yes	—
18	C₄²×C₁₇	D₄	1	2	yes	—
19	#63223	—	2	4	no	—
20	C₂×#3622	—	2	2	no	—
21	C₂×#3622	C₂×C₄	1	4	yes	—
22	C₂×#3622	D₄	1	4	yes	—
23	C₂×#3622	Q₈	1	4	yes	—
24	C₂³×C₁₇	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₄×C₁₇	—	4	2	no	—
26	C₂×C₄×C₁₇	C₄⋊C₄	1	4	yes	—
27	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₇	C₂×D₄	1	2	yes	—
29	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₁₇	C₂×Q₈	1	2	yes	—
31	C₈×C₁₇	—	4	2	no	—
32	#3622	—	4	2	no	—
33	#3622	C₄⋊C₄	1	8	yes	—
34	#1849	—	17	1	no	maximal, Sylow
35	C₂²×C₁₇	—	2	2	no	—
36	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₂²×C₁₇	C₄⋊Q₈	1	2	yes	—
38	C₄×C₁₇	—	2	4	no	—
39	C₄×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
40	C₄×C₁₇	#127	1	1	yes	characteristic
41	C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
42	C₂×#108	—	17	4	no	—
43	#423	—	17	1	no	—
44	#423	D₁₇	1	1	yes	characteristic
45	C₂×#97	—	17	1	no	—
46	C₂×C₁₇	—	2	2	no	—
47	C₂×C₁₇	#384	1	1	yes	characteristic
48	C₂×C₁₇	#430	1	2	yes	—
49	C₂×M₁₆	—	17	2	no	—
50	C₂×M₁₆	C₂×D₁₇	1	2	yes	—
51	C₂²×C₈	—	17	2	no	—
52	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
53	#108	—	34	8	no	—
54	C₄⋊C₈	—	2	2	no	—
55	C₄⋊C₈	—	34	2	no	—
56	#97	—	17	4	no	—
57	C₁₇	#1849	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	Dic₃₄	1	2	yes	—
59	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
60	M₁₆	—	2	4	no	—
61	M₁₆	—	34	4	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	17	4	no	—
64	C₂×C₈	—	17	4	no	—
65	C₂×C₈	—	17	4	no	—
66	C₂×C₈	—	34	2	no	—
67	C₄²	C₄×D₁₇	1	2	yes	—
68	C₄²	C₂²⋊D₁₇	1	2	yes	—
69	C₂³	C₂×Dic₃₄	1	1	yes	characteristic
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	#63225	1	4	yes	—
72	C₂×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
73	C₂×C₄	D₄×D₁₇	1	2	yes	—
74	C₂×C₄	Q₈×D₁₇	1	2	yes	—
75	C₂×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
76	C₈	—	4	2	no	—
77	C₈	—	17	8	no	—
78	C₈	—	68	2	no	—
79	C₂²	—	2	2	no	—
80	C₂²	#10587574	1	2	yes	—
81	C₂²	C₂×#63225	1	1	yes	characteristic
82	C₄	—	2	4	no	—
83	C₄	C₄⋊C₄×D₁₇	1	2	yes	—
84	C₄	#10587626	1	1	yes	characteristic
85	C₄	#10587630	1	1	yes	characteristic
86	C₂	—	2	2	no	—
87	C₂	#11762678	1	1	yes	characteristic
88	C₂	#11762857	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₇
commutator	C₂×C₄×C₁₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₇
Fitting	C₁₇×#423	C₂
socle	C₂²×C₁₇	C₂×C₄⋊C₄
prime radical	C₂³×C₁₇	C₂×Q₈
cosocle	C₂²×C₄×C₁₇	C₂³
hypercenter	#423	D₁₇
hypocenter	C₁₇	#1849
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
57. C₁₇	#1849	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10587493	2
#11762833	2
C₂×#10587474	2
C₁₇×#423	2
#1849	17