Subgroups — #11928383

Order 1248.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic
2	#10597728	C₂	1	2	yes	maximal, complemented
3	#88121	—	3	1	no	maximal, Hall
4	C₂³×C₃×C₁₃	C₄	1	1	yes	characteristic
5	C₂²×C₃×D₁₃	C₄	1	1	yes	characteristic
6	C₃×C₂²⋊D₁₃	—	2	2	no	—
7	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
8	C₃⋊#1057	—	2	2	no	—
9	C₂×C₂²⋊D₁₃	D₃	1	1	yes	characteristic
10	#6122	—	3	2	no	—
11	C₂²×C₃×C₁₃	—	2	1	no	—
12	C₂²×C₃×C₁₃	—	4	1	no	—
13	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₃×D₁₃	—	2	1	no	—
15	C₂×C₃×D₁₃	—	4	1	no	—
16	C₃×Dic₁₃	D₄	1	2	yes	—
17	C₂³×C₁₃	Dic₃	1	1	yes	characteristic
18	C₂²×D₁₃	Dic₃	1	1	yes	characteristic
19	C₂²⋊D₁₃	—	2	2	no	—
20	C₂×Dic₁₃	C₂×D₃	1	1	yes	characteristic
21	#1057	—	6	2	no	—
22	#833	—	13	1	no	maximal, Hall
23	C₂×C₃×C₁₃	—	2	1	no	—
24	C₂×C₃×C₁₃	—	4	1	no	—
25	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₃×D₁₃	—	4	1	no	—
27	C₂²×C₁₃	—	2	1	no	—
28	C₂²×C₁₃	—	4	1	no	—
29	C₂²×C₁₃	C₂×Dic₃	1	1	yes	characteristic
30	C₂×D₁₃	—	2	1	no	—
31	C₂×D₁₃	—	4	1	no	—
32	Dic₁₃	#67	1	2	yes	—
33	C₂×C₃×D₄	—	13	1	no	—
34	#208	—	13	2	no	—
35	C₃×C₁₃	#100	1	1	yes	characteristic, complemented, Hall
36	#100	—	39	1	no	Sylow
37	C₂×C₁₃	—	2	1	no	—
38	C₂×C₁₃	—	4	1	no	—
39	C₂×C₁₃	#217	1	1	yes	characteristic
40	D₁₃	—	4	1	no	—
41	C₂³×C₃	—	13	1	no	—
42	C₂³×C₃	#261	1	1	yes	characteristic
43	C₃×D₄	—	26	2	no	—
44	C₂×C₃×C₄	—	13	1	no	—
45	C₃⋊C₈	—	26	2	no	—
46	C₂×D₄	—	13	1	no	—
47	M₁₆	—	39	2	no	—
48	C₁₃	#833	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₃	—	2	1	no	—
50	C₂²×C₃	—	4	1	no	—
51	C₂²×C₃	—	26	1	no	—
52	C₂²×C₃	—	52	1	no	—
53	C₂²×C₃	C₂×#261	1	1	yes	characteristic
54	C₃×C₄	—	13	2	no	—
55	C₂³	—	13	1	no	—
56	C₂³	C₃⋊#261	1	1	yes	characteristic
57	D₄	—	26	2	no	—
58	C₂×C₄	—	13	1	no	—
59	C₈	—	78	2	no	—
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	4	1	no	—
62	C₂×C₃	—	52	1	no	—
63	C₂×C₃	C₂²⋊#261	1	1	yes	characteristic
64	C₂²	—	2	1	no	—
65	C₂²	—	4	1	no	—
66	C₂²	—	26	1	no	—
67	C₂²	—	52	1	no	—
68	C₂²	C₂×C₃⋊#261	1	1	yes	characteristic
69	C₄	—	13	2	no	—
70	C₃	#88121	1	1	yes	characteristic, complemented, Sylow
71	C₂	—	2	1	no	—
72	C₂	—	4	1	no	—
73	C₂	—	52	1	no	—
74	C₂	#10597729	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10597729
commutator	C₂²×C₃×C₁₃	C₂×C₄
Frattini	C₂²	C₂×C₃⋊#261
Fitting	C₂³×C₃×C₁₃	C₄
socle	C₂×C₃×C₁₃	C₂²⋊C₄
prime radical	C₂×C₃×C₂²⋊D₁₃	C₂
cosocle	C₂×C₃×Dic₁₃	C₂²
hypercenter	C₂³	C₃⋊#261
hypocenter	C₃×C₁₃	#100
LCS	G ▷ C₂²×C₃×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂³

Complements

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

N	H ≅ G/N	type
2. #10597728	C₂	semidirect
35. C₃×C₁₃	#100	semidirect
48. C₁₃	#833	semidirect
70. C₃	#88121	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₂²⋊D₁₃	2
#10597728	2
#88121	3
#833	13