Subgroups — #14545835

Order 2176.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763914	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈×#3633	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763853	C₂	1	1	yes	maximal, characteristic
4	#10587680	—	2	1	no	—
5	C₄×#3633	—	2	1	no	—
6	#10587666	—	2	1	no	—
7	#10587605	C₄	1	1	yes	characteristic
8	#10587550	—	2	1	no	—
9	#10587536	C₄	1	1	yes	characteristic
10	C₈×#595	C₂²	1	1	yes	characteristic
11	C₂×#3633	—	2	2	no	—
12	#63256	—	2	1	no	—
13	C₄×#595	D₄	1	1	yes	characteristic
14	#63243	—	2	1	no	—
15	#63243	—	4	1	no	—
16	#63242	—	4	1	no	—
17	#63242	D₄	1	1	yes	characteristic
18	#63241	—	4	1	no	—
19	Q₁₆×C₁₇	C₈	1	1	yes	characteristic, complemented
20	#63230	—	2	1	no	—
21	D₁₃₆	C₈	1	1	yes	characteristic, complemented
22	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
23	C₂×#595	—	2	1	no	—
24	#3633	—	2	4	no	—
25	Q₈×C₁₇	—	2	1	no	—
26	D₆₈	—	2	1	no	—
27	D₆₈	—	4	1	no	—
28	C₄×D₁₇	—	4	1	no	—
29	C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
30	#3624	—	4	1	no	—
31	#3624	D₈	1	1	yes	characteristic
32	#3624	SD₁₆	1	1	yes	characteristic
33	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
34	#3622	M₁₆	1	1	yes	characteristic
35	#1335	—	17	1	no	maximal, Sylow
36	C₂×D₁₇	—	4	1	no	—
37	C₂×D₁₇	#104	1	1	yes	characteristic
38	#595	—	2	2	no	—
39	C₄×C₁₇	—	4	1	no	—
40	C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
41	Dic₁₇	#102	1	1	yes	characteristic
42	#443	—	17	1	no	—
43	#364	—	17	1	no	—
44	C₈²	—	17	1	no	—
45	C₂×C₁₇	D₄⋊C₈	1	1	yes	characteristic
46	D₁₇	—	2	1	no	—
47	D₁₇	—	8	1	no	—
48	#135	—	17	1	no	—
49	#131	—	34	1	no	—
50	M₃₂	—	34	1	no	—
51	#108	—	17	1	no	—
52	#104	—	34	1	no	—
53	C₄×C₈	—	17	1	no	—
54	C₄×C₈	—	34	1	no	—
55	C₁₇	#1335	1	1	yes	characteristic, complemented, Sylow
56	#41	—	34	1	no	—
57	Q₁₆	#3633	1	1	yes	characteristic, complemented
58	SD₁₆	—	34	1	no	—
59	D₈	—	17	1	no	—
60	M₁₆	—	34	1	no	—
61	M₁₆	—	68	1	no	—
62	C₂×C₈	—	17	1	no	—
63	C₂×C₈	—	17	1	no	—
64	C₂×C₈	—	34	2	no	—
65	C₂×C₈	—	68	1	no	—
66	C₄²	—	17	1	no	—
67	C₁₆	—	68	1	no	—
68	Q₈	—	2	1	no	—
69	D₄	—	34	1	no	—
70	D₄	—	68	1	no	—
71	C₂×C₄	—	17	1	no	—
72	C₂×C₄	—	34	1	no	—
73	C₂×C₄	—	68	1	no	—
74	C₈	—	17	1	no	—
75	C₈	—	17	1	no	—
76	C₈	—	17	1	no	—
77	C₈	—	34	4	no	—
78	C₈	—	68	1	no	—
79	C₈	C₂×#3633	1	1	yes	characteristic
80	C₂²	—	17	1	no	—
81	C₂²	—	68	1	no	—
82	C₄	—	4	1	no	—
83	C₄	—	17	1	no	—
84	C₄	—	34	2	no	—
85	C₄	C₂²⋊#3633	1	1	yes	characteristic
86	C₂	—	34	1	no	—
87	C₂	—	136	1	no	—
88	C₂	D₄⋊#3633	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄⋊#3633
commutator	C₈×C₁₇	C₂×C₈
Frattini	C₈	C₂×#3633
Fitting	Q₁₆×C₁₇	C₈
socle	C₂×C₁₇	D₄⋊C₈
prime radical	#10587605	C₄
cosocle	C₈×#595	C₂²
hypercenter	Q₁₆	#3633
hypocenter	C₁₇	#1335
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #11763914	C₂	semidirect
2. C₈×#3633	C₂	semidirect
19. Q₁₆×C₁₇	C₈	semidirect
21. D₁₃₆	C₈	semidirect
55. C₁₇	#1335	semidirect
57. Q₁₆	#3633	semidirect

Maximal subgroups

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

subgroup	index
#11763914	2
C₈×#3633	2
#11763853	2
#1335	17