Subgroups — #14543913

Order 2176.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763718	C₂	1	1	yes	maximal, characteristic
2	#11763716	C₂	1	1	yes	maximal, characteristic
3	#11763201	C₂	1	1	yes	maximal, characteristic
4	C₁₇×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
5	C₂×#63231	—	2	1	no	—
6	C₂×#63230	—	2	1	no	—
7	#10587561	C₂²	1	1	yes	characteristic
8	#10587545	—	2	1	no	—
9	#10587539	—	2	1	no	—
10	#10587474	C₄	1	1	yes	characteristic, complemented
11	C₂×Q₈×C₁₇	—	2	1	no	—
12	C₂×D₆₈	D₄	1	1	yes	characteristic
13	C₂×Dic₃₄	D₄	1	1	yes	characteristic
14	C₂²⋊#595	—	4	1	no	—
15	#63247	—	4	1	no	—
16	C₄⋊C₄×C₁₇	—	4	1	no	—
17	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
18	#63231	—	4	2	no	—
19	#63230	—	4	2	no	—
20	#63227	—	4	1	no	—
21	C₂×#3622	—	2	1	no	—
22	C₂²×D₁₇	—	2	1	no	—
23	C₂×#595	—	8	1	no	—
24	Q₈×C₁₇	—	4	1	no	—
25	Q₈×C₁₇	—	4	1	no	—
26	C₂×C₄×C₁₇	—	2	1	no	—
27	C₂×C₄×C₁₇	—	4	1	no	—
28	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×Dic₁₇	—	2	1	no	—
30	D₆₈	—	4	1	no	—
31	Dic₃₄	—	4	1	no	—
32	#3624	—	8	1	no	—
33	#3622	—	2	2	no	—
34	#1407	—	17	1	no	maximal, Sylow
35	C₂²×C₁₇	#99	1	1	yes	characteristic
36	C₂×D₁₇	—	4	1	no	—
37	C₂×D₁₇	—	8	1	no	—
38	#595	—	16	1	no	—
39	C₄×C₁₇	—	2	1	no	—
40	C₄×C₁₇	—	4	1	no	—
41	C₄×C₁₇	—	8	1	no	—
42	Dic₁₇	—	4	1	no	—
43	#497	—	17	1	no	—
44	#355	—	17	1	no	—
45	#354	—	17	1	no	—
46	C₂×C₁₇	—	2	1	no	—
47	C₂×C₁₇	#353	1	1	yes	characteristic
48	D₁₇	—	8	1	no	—
49	C₂×Q₁₆	—	34	1	no	—
50	C₂×SD₁₆	—	34	1	no	—
51	C₄⋊Q₈	#595	1	1	yes	characteristic, complemented
52	#124	—	17	1	no	—
53	#101	—	34	1	no	—
54	#99	—	34	1	no	—
55	#97	—	17	1	no	—
56	C₁₇	#1407	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	—	2	1	no	—
58	C₂×Q₈	—	17	1	no	—
59	C₂×D₄	—	17	1	no	—
60	Q₁₆	—	68	2	no	—
61	SD₁₆	—	68	2	no	—
62	M₁₆	—	68	1	no	—
63	C₂×C₈	—	34	1	no	—
64	C₄⋊C₄	—	4	1	no	—
65	C₂²⋊C₄	—	68	1	no	—
66	C₂²⋊C₄	—	68	1	no	—
67	C₄²	C₂×#595	1	1	yes	characteristic
68	C₂³	—	34	1	no	—
69	Q₈	—	4	1	no	—
70	Q₈	—	4	1	no	—
71	Q₈	—	68	1	no	—
72	D₄	—	68	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	4	1	no	—
75	C₂×C₄	—	34	1	no	—
76	C₂×C₄	—	136	1	no	—
77	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
78	C₈	—	34	2	no	—
79	C₈	—	136	1	no	—
80	C₂²	—	68	1	no	—
81	C₂²	—	136	1	no	—
82	C₂²	#10587551	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	8	1	no	—
86	C₄	—	272	1	no	—
87	C₄	—	68	1	no	—
88	C₂	—	2	1	no	—
89	C₂	—	136	1	no	—
90	C₂	#11763713	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11763713
commutator	C₄²×C₁₇	C₂×C₄
Frattini	C₄²	C₂×#595
Fitting	C₁₇×C₄⋊Q₈	C₄
socle	C₂×C₁₇	#353
prime radical	C₂×D₆₈	D₄
cosocle	#10587561	C₂²
hypercenter	C₄⋊Q₈	#595
hypocenter	C₁₇	#1407
LCS	G ▷ C₄²×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
4. C₁₇×C₄⋊Q₈	C₄	semidirect
10. #10587474	C₄	semidirect
51. C₄⋊Q₈	#595	semidirect
56. C₁₇	#1407	semidirect

Maximal subgroups

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

subgroup	index
#11763718	2
#11763716	2
#11763201	2
#1407	17