Subgroups — #11928369

Order 1248.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅₂	C₂	1	1	yes	maximal, characteristic
2	#10597729	C₂	1	2	yes	maximal, complemented
3	#88107	—	3	1	no	maximal, Hall
4	C₂²×C₃×D₁₃	C₄	1	1	yes	characteristic, complemented
5	C₂²×C₃×D₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₃⋊#261	—	2	2	no	—
7	C₂×C₃×C₄×C₁₃	C₄	1	1	yes	characteristic, complemented
8	C₃×D₅₂	—	2	2	no	—
9	C₂×D₅₂	D₃	1	1	yes	characteristic
10	C₂²⋊#261	—	3	2	no	—
11	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×D₁₃	—	2	1	no	—
13	C₂×C₃×D₁₃	—	4	1	no	—
14	C₂×C₃×D₁₃	—	4	1	no	—
15	C₂×C₃×D₁₃	D₄	1	2	yes	—
16	C₃⋊#261	—	4	2	no	—
17	C₃×C₄×C₁₃	—	2	1	no	—
18	C₂²×D₁₃	Dic₃	1	1	yes	characteristic, complemented
19	C₂²×D₁₃	C₂×D₃	1	1	yes	characteristic
20	C₂×#261	—	6	2	no	—
21	C₂×C₄×C₁₃	Dic₃	1	1	yes	characteristic, complemented
22	D₅₂	—	2	2	no	—
23	#834	—	13	1	no	maximal, Hall
24	C₂×C₃×C₁₃	—	2	1	no	—
25	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₃×D₁₃	—	2	2	no	—
27	C₃×D₁₃	—	4	1	no	—
28	C₂²×C₁₃	C₂×Dic₃	1	1	yes	characteristic
29	C₂×D₁₃	—	2	1	no	—
30	C₂×D₁₃	—	4	1	no	—
31	C₂×D₁₃	—	4	1	no	—
32	C₂×D₁₃	#67	1	2	yes	—
33	#261	—	12	2	no	—
34	C₄×C₁₃	—	2	1	no	—
35	C₂×C₃×D₄	—	13	1	no	—
36	#217	—	13	2	no	—
37	C₃×C₁₃	#99	1	1	yes	characteristic, complemented, Hall
38	#99	—	39	1	no	Sylow
39	C₂×C₁₃	—	2	1	no	—
40	C₂×C₁₃	#217	1	1	yes	characteristic
41	D₁₃	—	2	2	no	—
42	D₁₃	—	4	1	no	—
43	C₂³×C₃	—	13	1	no	—
44	C₂³×C₃	—	13	1	no	—
45	C₃×D₄	—	26	2	no	—
46	C₂×C₃×C₄	#261	1	1	yes	characteristic, complemented
47	C₂×Dic₃	—	26	2	no	—
48	C₂×D₄	—	13	1	no	—
49	C₂²⋊C₄	—	39	2	no	—
50	C₁₃	#834	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₃	—	13	2	no	—
52	C₂²×C₃	—	26	1	no	—
53	C₂²×C₃	—	52	1	no	—
54	C₂²×C₃	—	52	1	no	—
55	C₂²×C₃	C₂×#261	1	1	yes	characteristic
56	C₃×C₄	—	2	1	no	—
57	Dic₃	—	52	2	no	—
58	C₂³	—	13	1	no	—
59	C₂³	—	13	1	no	—
60	D₄	—	26	2	no	—
61	C₂×C₄	—	78	2	no	—
62	C₂×C₄	C₃⋊#261	1	1	yes	characteristic, complemented
63	C₂×C₃	—	2	1	no	—
64	C₂×C₃	—	26	2	no	—
65	C₂×C₃	—	52	1	no	—
66	C₂×C₃	C₂²⋊#261	1	1	yes	characteristic
67	C₂²	—	13	2	no	—
68	C₂²	—	26	1	no	—
69	C₂²	—	52	1	no	—
70	C₂²	—	52	1	no	—
71	C₂²	C₂×C₃⋊#261	1	1	yes	characteristic
72	C₄	—	2	1	no	—
73	C₄	—	156	2	no	—
74	C₃	#88107	1	1	yes	characteristic, complemented, Sylow
75	C₂	—	2	1	no	—
76	C₂	—	26	2	no	—
77	C₂	—	52	1	no	—
78	C₂	#10597729	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10597729
commutator	C₂²×C₃×C₁₃	C₂×C₄
Frattini	C₂²	C₂×C₃⋊#261
Fitting	C₂×C₃×C₄×C₁₃	C₄
socle	C₂×C₃×C₁₃	C₂²⋊C₄
prime radical	C₂×C₃×D₅₂	C₂
cosocle	C₂²×C₃×D₁₃	C₂²
hypercenter	C₂×C₄	C₃⋊#261
hypocenter	C₃×C₁₃	#99
LCS	G ▷ C₂²×C₃×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. #10597729	C₂	semidirect
4. C₂²×C₃×D₁₃	C₄	semidirect
7. C₂×C₃×C₄×C₁₃	C₄	semidirect
18. C₂²×D₁₃	Dic₃	semidirect
21. C₂×C₄×C₁₃	Dic₃	semidirect
37. C₃×C₁₃	#99	semidirect
46. C₂×C₃×C₄	#261	semidirect
50. C₁₃	#834	semidirect
62. C₂×C₄	C₃⋊#261	semidirect
74. C₃	#88107	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₅₂	2
#10597729	2
#88107	3
#834	13