Subgroups — #11928476

Order 1248.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6127	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597592	C₂	1	2	yes	maximal, complemented
5	C₃⋊C₈×D₁₃	C₂	1	2	yes	maximal, complemented
6	#88161	—	3	1	no	maximal, Hall
7	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₃×C₂²⋊D₁₃	C₄	1	2	yes	—
9	C₃×D₅₂	C₄	1	1	yes	characteristic
10	C₃×C₄×D₁₃	C₂²	1	2	yes	—
11	C₃×Dic₂₆	C₄	1	1	yes	characteristic
12	C₃⋊#1055	C₂²	1	1	yes	characteristic
13	C₃⋊#1055	C₂²	1	1	yes	characteristic
14	C₁₃×C₃⋊C₈	C₂²	1	2	yes	—
15	#6127	D₃	1	1	yes	characteristic
16	C₁₃×M₁₆	—	3	1	no	—
17	C₂×#1055	—	3	1	no	—
18	#6094	—	3	2	no	—
19	C₈×D₁₃	—	3	2	no	—
20	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₃×D₁₃	C₂×C₄	1	2	yes	—
22	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₃×Dic₁₃	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
26	C₂²⋊D₁₃	Dic₃	1	2	yes	—
27	D₅₂	Dic₃	1	1	yes	characteristic
28	C₄×D₁₃	C₂×D₃	1	2	yes	—
29	Dic₂₆	Dic₃	1	1	yes	characteristic
30	C₈×C₁₃	—	3	2	no	—
31	#1055	—	3	1	no	—
32	#1055	—	3	1	no	—
33	#948	—	13	1	no	maximal, Hall
34	C₂×C₃×C₁₃	—	2	1	no	—
35	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₃×D₁₃	—	2	2	no	—
37	C₂²×C₁₃	C₂×Dic₃	1	1	yes	characteristic
38	C₂×D₁₃	C₂×Dic₃	1	2	yes	—
39	C₄×C₁₃	C₂×Dic₃	1	1	yes	characteristic
40	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
41	Dic₁₃	C₂×Dic₃	1	2	yes	—
42	C₃×#41	—	13	1	no	—
43	#208	—	13	2	no	—
44	#208	D₁₃	1	1	yes	characteristic, complemented
45	C₂×C₃⋊C₈	—	13	1	no	—
46	C₂×C₃⋊C₈	—	13	2	no	—
47	C₃×C₁₃	#131	1	1	yes	characteristic, complemented, Hall
48	#131	—	39	1	no	Sylow
49	C₂×C₁₃	—	2	1	no	—
50	C₂×C₁₃	C₂²×Dic₃	1	1	yes	characteristic
51	D₁₃	—	2	2	no	—
52	C₃×Q₈	—	13	1	no	—
53	C₃×D₄	—	13	2	no	—
54	C₃×D₄	—	13	1	no	—
55	C₂×C₃×C₄	—	13	2	no	—
56	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
57	C₃⋊C₈	—	13	1	no	—
58	C₃⋊C₈	—	13	1	no	—
59	C₃⋊C₈	C₂×D₁₃	1	2	yes	—
60	#41	—	13	1	no	—
61	M₁₆	—	3	1	no	—
62	M₁₆	—	39	2	no	—
63	C₂×C₈	—	39	2	no	—
64	C₂×C₈	—	39	1	no	—
65	C₁₃	#948	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₃	—	13	2	no	—
67	C₂²×C₃	C₄×D₁₃	1	1	yes	characteristic
68	C₃×C₄	—	13	2	no	—
69	C₃×C₄	C₄×D₁₃	1	1	yes	characteristic
70	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
71	Q₈	—	13	1	no	—
72	D₄	—	13	2	no	—
73	D₄	—	13	1	no	—
74	C₂×C₄	—	13	2	no	—
75	C₂×C₄	D₃×D₁₃	1	1	yes	characteristic
76	C₈	—	3	2	no	—
77	C₈	—	39	1	no	—
78	C₈	—	39	1	no	—
79	C₂×C₃	—	2	1	no	—
80	C₂×C₃	—	26	2	no	—
81	C₂×C₃	C₂×C₄×D₁₃	1	1	yes	characteristic
82	C₂²	—	13	2	no	—
83	C₂²	Dic₃×D₁₃	1	1	yes	characteristic
84	C₄	—	13	2	no	—
85	C₄	Dic₃×D₁₃	1	1	yes	characteristic
86	C₄	C₂×D₃×D₁₃	1	1	yes	characteristic
87	C₃	#88161	1	1	yes	characteristic, complemented, Sylow
88	C₂	—	2	1	no	—
89	C₂	—	26	2	no	—
90	C₂	C₂×Dic₃×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂×D₃×D₁₃
commutator, socle	C₂×C₃×C₁₃	C₂²×C₄
Fitting	C₂×C₃×C₄×C₁₃	C₂²
prime radical	C₃×#6127	C₂
cosocle	C₃×C₄×C₁₃	C₂³
hypercenter	C₂×C₄	D₃×D₁₃
hypocenter	C₃×C₁₃	#131
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃⋊#1055	C₂	semidirect
3. C₁₃×#208	C₂	semidirect
4. #10597592	C₂	semidirect
5. C₃⋊C₈×D₁₃	C₂	semidirect
44. #208	D₁₃	semidirect
47. C₃×C₁₃	#131	semidirect
65. C₁₃	#948	semidirect
87. C₃	#88161	semidirect

Maximal subgroups

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

subgroup	index
C₃×#6127	2
C₂×C₃⋊#1055	2
C₁₃×#208	2
#10597592	2
C₃⋊C₈×D₁₃	2
#88161	3
#948	13