Subgroups — #11928953

Order 1248.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₃₉	C₂	1	2	yes	maximal
3	C₄⋊Dic₃₉	C₂	1	1	yes	maximal, characteristic
4	#10597664	C₂	1	2	yes	maximal
5	C₄×Dic₃₉	C₂	1	1	yes	maximal, characteristic
6	#88144	—	3	1	no	maximal, Hall
7	C₂×C₃×C₄×C₁₃	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₃₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₃₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₃₉	C₂²	1	2	yes	—
12	C₁₃×C₄⋊C₄	D₃	1	1	yes	characteristic
13	C₄⋊Dic₁₃	—	3	2	no	—
14	C₄⋊Dic₁₃	—	3	1	no	—
15	#6101	—	3	2	no	—
16	C₄×Dic₁₃	—	3	1	no	—
17	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
18	C₃×C₄×C₁₃	—	2	2	no	—
19	C₃×C₄×C₁₃	Q₈	1	2	yes	—
20	Dic₃₉	—	2	1	no	—
21	Dic₃₉	—	2	1	no	—
22	Dic₃₉	—	2	2	no	—
23	C₂×C₄×C₁₃	C₂×D₃	1	2	yes	—
24	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
25	C₂×Dic₁₃	—	3	1	no	—
26	C₂×Dic₁₃	—	3	1	no	—
27	C₂×Dic₁₃	—	3	2	no	—
28	#890	—	13	1	no	maximal, Hall
29	C₂×C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₃×C₁₃	#41	1	1	yes	characteristic
31	C₂×C₃×C₁₃	#41	1	1	yes	characteristic
32	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
33	C₄×C₁₃	—	2	2	no	—
34	C₄×C₁₃	Dic₆	1	2	yes	—
35	Dic₁₃	—	6	1	no	—
36	Dic₁₃	—	6	1	no	—
37	Dic₁₃	—	6	2	no	—
38	C₃×C₄⋊C₄	D₁₃	1	1	yes	characteristic
39	C₄⋊Dic₃	—	13	2	no	—
40	C₄⋊Dic₃	—	13	1	no	—
41	Dic₃⋊C₄	—	13	2	no	—
42	C₄×Dic₃	—	13	1	no	—
43	C₃×C₁₃	#125	1	1	yes	characteristic, complemented, Hall
44	#125	—	39	1	no	Sylow
45	C₂×C₁₃	C₂×Dic₆	1	1	yes	characteristic
46	C₂×C₁₃	#237	1	1	yes	characteristic
47	C₂×C₁₃	#239	1	1	yes	characteristic
48	C₂×C₃×C₄	C₂×D₁₃	1	2	yes	—
49	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
50	C₂×Dic₃	—	13	1	no	—
51	C₂×Dic₃	—	13	1	no	—
52	C₂×Dic₃	—	13	2	no	—
53	C₄⋊C₄	—	39	2	no	—
54	C₄⋊C₄	—	39	2	no	—
55	C₄⋊C₄	—	39	1	no	—
56	C₄⋊C₄	D₃₉	1	1	yes	characteristic
57	C₄²	—	39	1	no	—
58	C₁₃	#890	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
60	C₃×C₄	—	2	2	no	—
61	C₃×C₄	Dic₂₆	1	2	yes	—
62	Dic₃	—	26	1	no	—
63	Dic₃	—	26	1	no	—
64	Dic₃	—	26	2	no	—
65	C₂×C₄	—	39	1	no	—
66	C₂×C₄	—	39	1	no	—
67	C₂×C₄	—	39	2	no	—
68	C₂×C₄	C₂×D₃₉	1	2	yes	—
69	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
70	C₂×C₃	C₂×Dic₂₆	1	1	yes	characteristic
71	C₂×C₃	#6129	1	1	yes	characteristic
72	C₂×C₃	#6131	1	1	yes	characteristic
73	C₂²	C₂²×D₃₉	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	78	1	no	—
76	C₄	—	78	1	no	—
77	C₄	—	78	2	no	—
78	C₄	Dic₇₈	1	2	yes	—
79	C₃	#88144	1	1	yes	characteristic, complemented, Sylow
80	C₂	C₂×Dic₇₈	1	1	yes	characteristic
81	C₂	#10597792	1	1	yes	characteristic
82	C₂	#10597794	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃₉
commutator, socle, prime radical, cosocle	C₂²×C₃×C₁₃	C₂³
Fitting	C₃×C₁₃×C₄⋊C₄	C₂
hypercenter	C₄⋊C₄	D₃₉
hypocenter	C₃×C₁₃	#125
LCS	G ▷ C₂²×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
43. C₃×C₁₃	#125	semidirect
58. C₁₃	#890	semidirect
79. C₃	#88144	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₃×C₄⋊C₄	2
C₄⋊Dic₃₉	2
#10597664	2
C₄×Dic₃₉	2
#88144	3
#890	13