Subgroups — #11928143

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₃₉	C₂	1	2	yes	maximal
3	#88071	—	3	1	no	maximal, Hall
4	C₂³×C₃×C₁₃	C₂²	1	1	yes	characteristic
5	C₂×C₃×C₄×C₁₃	—	2	2	no	—
6	C₂×C₃×C₄×C₁₃	C₄	1	2	yes	complemented
7	C₂×Dic₃₉	—	2	2	no	—
8	C₂×Dic₃₉	—	2	2	no	—
9	C₂×Dic₃₉	C₄	1	4	yes	complemented
10	C₂²×C₄×C₁₃	D₃	1	1	yes	characteristic
11	C₂²×Dic₁₃	—	3	2	no	—
12	C₂²×C₃×C₁₃	C₂×C₄	1	2	yes	—
13	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₃×C₁₃	D₄	1	1	yes	characteristic
15	C₂²×C₃×C₁₃	D₄	1	2	yes	—
16	C₂²×C₃×C₁₃	Q₈	1	1	yes	characteristic
17	C₃×C₄×C₁₃	—	2	2	no	—
18	Dic₃₉	—	2	4	no	—
19	C₂³×C₁₃	C₂×D₃	1	1	yes	characteristic
20	C₂×C₄×C₁₃	—	2	2	no	—
21	C₂×C₄×C₁₃	Dic₃	1	2	yes	complemented
22	C₂×Dic₁₃	—	3	4	no	—
23	C₂×Dic₁₃	—	6	2	no	—
24	C₂×Dic₁₃	—	6	2	no	—
25	C₃⋊#95	—	13	1	no	maximal, Hall
26	C₂×C₃×C₁₃	C₄²	1	1	yes	characteristic
27	C₂×C₃×C₁₃	C₂²⋊C₄	1	2	yes	—
28	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₃×C₁₃	C₄⋊C₄	1	2	yes	—
30	C₂×C₃×C₁₃	C₄⋊C₄	1	1	yes	characteristic
31	C₂²×C₁₃	Dic₆	1	1	yes	characteristic
32	C₂²×C₁₃	C₄×D₃	1	2	yes	—
33	C₂²×C₁₃	D₁₂	1	1	yes	characteristic
34	C₂²×C₁₃	C₂×Dic₃	1	1	yes	characteristic
35	C₂²×C₁₃	#67	1	2	yes	—
36	C₄×C₁₃	—	2	2	no	—
37	Dic₁₃	—	6	4	no	—
38	C₂²×C₃×C₄	D₁₃	1	1	yes	characteristic
39	C₂²×Dic₃	—	13	2	no	—
40	C₃×C₁₃	#95	1	1	yes	characteristic, complemented, Hall
41	#95	—	39	1	no	Sylow
42	C₂×C₁₃	C₄×Dic₃	1	1	yes	characteristic
43	C₂×C₁₃	Dic₃⋊C₄	1	2	yes	—
44	C₂×C₁₃	C₄⋊Dic₃	1	1	yes	characteristic
45	C₂×C₁₃	(C₂×D₃)⋊C₄	1	2	yes	—
46	C₂×C₁₃	#217	1	1	yes	characteristic
47	C₂³×C₃	C₂×D₁₃	1	1	yes	characteristic
48	C₂×C₃×C₄	—	2	2	no	—
49	C₂×C₃×C₄	Dic₁₃	1	2	yes	complemented
50	C₂×Dic₃	—	13	4	no	—
51	C₂×Dic₃	—	26	2	no	—
52	C₂×Dic₃	—	26	2	no	—
53	C₂²×C₄	—	39	2	no	—
54	C₂²×C₄	D₃₉	1	1	yes	characteristic
55	C₁₃	C₃⋊#95	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₃	Dic₂₆	1	1	yes	characteristic
57	C₂²×C₃	C₄×D₁₃	1	2	yes	—
58	C₂²×C₃	D₅₂	1	1	yes	characteristic
59	C₂²×C₃	C₂×Dic₁₃	1	1	yes	characteristic
60	C₂²×C₃	C₂²⋊D₁₃	1	2	yes	—
61	C₃×C₄	—	2	2	no	—
62	Dic₃	—	26	4	no	—
63	C₂³	C₂×D₃₉	1	1	yes	characteristic
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	39	4	no	—
66	C₂×C₄	—	78	2	no	—
67	C₂×C₄	—	78	2	no	—
68	C₂×C₄	Dic₃₉	1	2	yes	complemented
69	C₂×C₃	C₄×Dic₁₃	1	1	yes	characteristic
70	C₂×C₃	#6101	1	2	yes	—
71	C₂×C₃	C₄⋊Dic₁₃	1	1	yes	characteristic
72	C₂×C₃	#6103	1	2	yes	—
73	C₂×C₃	C₂²⋊Dic₁₃	1	1	yes	characteristic
74	C₂²	Dic₇₈	1	1	yes	characteristic
75	C₂²	C₄×D₃₉	1	2	yes	—
76	C₂²	D₁₅₆	1	1	yes	characteristic
77	C₂²	C₂×Dic₃₉	1	1	yes	characteristic
78	C₂²	#64625	1	2	yes	—
79	C₄	—	2	2	no	—
80	C₄	—	78	4	no	—
81	C₃	#88071	1	1	yes	characteristic, complemented, Sylow
82	C₂	C₄×Dic₃₉	1	1	yes	characteristic
83	C₂	#10597664	1	2	yes	—
84	C₂	C₄⋊Dic₃₉	1	1	yes	characteristic
85	C₂	#10597666	1	2	yes	—
86	C₂	#10597671	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂×D₃₉
commutator	C₂×C₃×C₁₃	C₄²
Fitting	C₂²×C₃×C₄×C₁₃	C₂
socle, prime radical, cosocle	C₂³×C₃×C₁₃	C₂²
hypercenter	C₂²×C₄	D₃₉
hypocenter	C₃×C₁₃	#95
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
6. C₂×C₃×C₄×C₁₃	C₄	semidirect
9. C₂×Dic₃₉	C₄	semidirect
21. C₂×C₄×C₁₃	Dic₃	semidirect
40. C₃×C₁₃	#95	semidirect
49. C₂×C₃×C₄	Dic₁₃	semidirect
55. C₁₃	C₃⋊#95	semidirect
68. C₂×C₄	Dic₃₉	semidirect
81. C₃	#88071	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄×C₁₃	2
C₂²×Dic₃₉	2
#88071	3
C₃⋊#95	13