Subgroups — #14546008

Order 2176.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763912	C₂	1	2	yes	maximal
2	C₄⋊#63241	C₂	1	1	yes	maximal, characteristic
3	C₄×#63241	C₂	1	2	yes	maximal
4	C₄×#63241	C₂	1	1	yes	maximal, characteristic
5	#11763858	C₂	1	1	yes	maximal, characteristic
6	C₂×#63241	C₂²	1	2	yes	—
7	C₂×#63241	C₂²	1	1	yes	characteristic
8	C₂×#63241	C₂²	1	1	yes	characteristic
9	#10587573	C₄	1	1	yes	characteristic
10	#10587544	C₄	1	2	yes	—
11	C₄⋊#3624	C₄	1	1	yes	characteristic
12	C₄×#3624	C₂²	1	1	yes	characteristic
13	C₄×#3624	C₂²	1	2	yes	—
14	C₂×Dic₃₄	C₈	1	1	yes	characteristic
15	C₂×#3624	C₂×C₄	1	2	yes	—
16	C₂×#3624	C₂×C₄	1	1	yes	characteristic
17	C₂×#3624	C₂³	1	1	yes	characteristic
18	#63241	—	2	2	no	—
19	#63241	—	2	1	no	—
20	#63241	Q₈	1	2	yes	complemented
21	C₄⋊C₄×C₁₇	C₈	1	1	yes	characteristic
22	#63225	C₈	1	2	yes	—
23	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₁₇	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₁₇	C₂×C₈	1	2	yes	—
26	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
27	C₂×Dic₁₇	C₂×C₈	1	1	yes	characteristic
28	C₂×Dic₁₇	C₂×C₈	1	2	yes	—
29	C₂×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
30	Dic₃₄	C₁₆	1	4	yes	complemented
31	#3624	—	2	2	no	—
32	#3624	—	2	1	no	—
33	#3624	C₂×Q₈	1	1	yes	characteristic
34	#3624	#41	1	1	yes	characteristic
35	Q₈×C₁₆	—	17	1	no	maximal, Sylow
36	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
37	C₄×C₁₇	—	2	2	no	—
38	C₄×C₁₇	C₂×C₁₆	1	2	yes	—
39	Dic₁₇	—	2	1	no	—
40	Dic₁₇	C₂×C₁₆	1	4	yes	—
41	Dic₁₇	C₄×Q₈	1	1	yes	characteristic
42	Dic₁₇	#131	1	1	yes	characteristic
43	C₈×Q₈	—	17	1	no	—
44	C₄⋊C₁₆	—	17	1	no	—
45	C₄⋊C₁₆	—	17	2	no	—
46	C₄×C₁₆	—	17	1	no	—
47	C₄×C₁₆	—	17	2	no	—
48	C₂×C₁₇	C₈×Q₈	1	1	yes	characteristic
49	C₂×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
50	C₂×C₁₇	#504	1	1	yes	characteristic
51	C₄×Q₈	—	17	1	no	—
52	C₂×C₁₆	—	17	1	no	—
53	C₂×C₁₆	—	17	2	no	—
54	C₂×C₁₆	—	17	1	no	—
55	C₄⋊C₈	—	17	1	no	—
56	C₄⋊C₈	—	17	2	no	—
57	C₄×C₈	—	17	1	no	—
58	C₄×C₈	—	17	2	no	—
59	C₁₇	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	—	17	1	no	—
61	C₂×C₈	—	17	1	no	—
62	C₂×C₈	—	17	2	no	—
63	C₂×C₈	—	17	1	no	—
64	C₄⋊C₄	—	17	2	no	—
65	C₄⋊C₄	#3633	1	1	yes	characteristic
66	C₄²	—	17	2	no	—
67	C₄²	—	17	1	no	—
68	C₁₆	—	17	2	no	—
69	C₁₆	—	34	2	no	—
70	C₁₆	—	34	1	no	—
71	Q₈	—	17	4	no	—
72	C₂×C₄	—	17	1	no	—
73	C₂×C₄	—	17	2	no	—
74	C₂×C₄	—	17	1	no	—
75	C₂×C₄	C₂×#3633	1	2	yes	—
76	C₂×C₄	C₂×#3633	1	1	yes	characteristic
77	C₈	—	17	1	no	—
78	C₈	—	17	1	no	—
79	C₈	—	34	2	no	—
80	C₈	—	34	1	no	—
81	C₂²	C₂²×#3633	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	17	1	no	—
84	C₄	—	17	1	no	—
85	C₄	—	17	4	no	—
86	C₄	—	34	1	no	—
87	C₄	#10587665	1	2	yes	—
88	C₂	Q₈×#3633	1	1	yes	characteristic
89	C₂	C₂×#10587665	1	1	yes	characteristic
90	C₂	#11763930	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#3633
commutator	C₂×C₁₇	C₂²×C₁₆
Fitting	C₄⋊C₄×C₁₇	C₈
socle, prime radical	C₂²×C₁₇	C₂²×C₈
cosocle	C₂×#3624	C₂³
hypercenter	C₄⋊C₄	#3633
hypocenter	C₁₇	Q₈×C₁₆
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
20. #63241	Q₈	semidirect
30. Dic₃₄	C₁₆	semidirect
59. C₁₇	Q₈×C₁₆	semidirect

Maximal subgroups

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

subgroup	index
#11763912	2
C₄⋊#63241	2
C₄×#63241	2
#11763858	2
Q₈×C₁₆	17