Subgroups — #11928931

Order 1248.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₇₈	C₂	1	2	yes	maximal
2	C₃×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₃₉	C₂	1	4	yes	maximal
4	#88123	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₁₃	C₂²	1	2	yes	—
7	C₂×Dic₃₉	C₂²	1	4	yes	—
8	Dic₇₈	—	2	4	no	—
9	C₂×Dic₂₆	—	3	2	no	—
10	C₄²×C₁₃	D₃	1	1	yes	characteristic
11	C₄⋊Dic₁₃	—	3	4	no	—
12	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
13	C₃×C₄×C₁₃	D₄	1	2	yes	—
14	C₃×C₄×C₁₃	Q₈	1	4	yes	complemented
15	Dic₃₉	—	2	4	no	—
16	C₂×C₄×C₁₃	C₂×D₃	1	2	yes	—
17	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
18	C₂×Dic₁₃	—	3	4	no	—
19	Dic₂₆	—	6	4	no	—
20	#869	—	13	1	no	maximal, Hall
21	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
22	C₂×C₃×C₁₃	C₂×Q₈	1	2	yes	—
23	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
24	C₄×C₁₃	Dic₆	1	4	yes	complemented
25	C₄×C₁₃	D₁₂	1	2	yes	—
26	Dic₁₃	—	6	4	no	—
27	C₂×Dic₆	—	13	2	no	—
28	C₃×C₄²	D₁₃	1	1	yes	characteristic
29	C₄⋊Dic₃	—	13	4	no	—
30	C₃×C₁₃	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
31	C₄⋊Q₈	—	39	1	no	Sylow
32	C₂×C₁₃	C₂×Dic₆	1	2	yes	—
33	C₂×C₁₃	C₂×D₁₂	1	1	yes	characteristic
34	C₂×C₃×C₄	C₂×D₁₃	1	2	yes	—
35	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
36	C₂×Dic₃	—	13	4	no	—
37	Dic₆	—	26	4	no	—
38	C₂×Q₈	—	39	2	no	—
39	C₄⋊C₄	—	39	4	no	—
40	C₄²	D₃₉	1	1	yes	characteristic
41	C₁₃	#869	1	1	yes	characteristic, complemented, Sylow
42	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
43	C₃×C₄	Dic₂₆	1	4	yes	complemented
44	C₃×C₄	D₅₂	1	2	yes	—
45	Dic₃	—	26	4	no	—
46	Q₈	—	78	4	no	—
47	C₂×C₄	—	39	4	no	—
48	C₂×C₄	C₂×D₃₉	1	2	yes	—
49	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
50	C₂×C₃	C₂×Dic₂₆	1	2	yes	—
51	C₂×C₃	C₂×D₅₂	1	1	yes	characteristic
52	C₂²	C₂²×D₃₉	1	1	yes	characteristic
53	C₄	—	78	4	no	—
54	C₄	Dic₇₈	1	4	yes	complemented
55	C₄	D₁₅₆	1	2	yes	—
56	C₃	#88123	1	1	yes	characteristic, complemented, Sylow
57	C₂	C₂×Dic₇₈	1	2	yes	—
58	C₂	C₂×D₁₅₆	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃₉
commutator, socle, prime radical, cosocle	C₂²×C₃×C₁₃	C₂³
Fitting	C₃×C₄²×C₁₃	C₂
hypercenter	C₄²	D₃₉
hypocenter	C₃×C₁₃	C₄⋊Q₈
LCS	G ▷ C₂²×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
14. C₃×C₄×C₁₃	Q₈	semidirect
24. C₄×C₁₃	Dic₆	semidirect
30. C₃×C₁₃	C₄⋊Q₈	semidirect
41. C₁₃	#869	semidirect
43. C₃×C₄	Dic₂₆	semidirect
54. C₄	Dic₇₈	semidirect
56. C₃	#88123	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₇₈	2
C₃×C₄²×C₁₃	2
C₄⋊Dic₃₉	2
#88123	3
#869	13