Subgroups — #11928423

Order 1248.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₂₆	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₃₉	C₂	1	1	yes	maximal, characteristic
3	C₁₃×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
4	#10597611	C₂	1	2	yes	maximal
5	Dic₃×Dic₁₃	C₂	1	2	yes	maximal
6	#88141	—	3	1	no	maximal, Hall
7	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×Dic₃₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₃₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₃×C₁₃	C₂²	1	2	yes	—
11	C₂×C₃×Dic₁₃	C₂²	1	2	yes	—
12	C₃×Dic₂₆	C₄	1	4	yes	complemented
13	C₂×Dic₂₆	D₃	1	1	yes	characteristic
14	C₁₃×C₄⋊C₄	—	3	1	no	—
15	#6101	—	3	2	no	—
16	C₄×Dic₁₃	—	3	1	no	—
17	C₄×Dic₁₃	—	3	2	no	—
18	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
19	C₃×C₄×C₁₃	C₂×C₄	1	2	yes	—
20	Dic₃₉	—	2	1	no	—
21	Dic₃₉	Q₈	1	2	yes	complemented
22	C₃×Dic₁₃	C₂×C₄	1	4	yes	—
23	Dic₃×C₁₃	—	2	2	no	—
24	C₂×C₄×C₁₃	—	3	2	no	—
25	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
26	C₂×Dic₁₃	—	3	1	no	—
27	C₂×Dic₁₃	—	3	1	no	—
28	C₂×Dic₁₃	C₂×D₃	1	2	yes	—
29	Dic₂₆	Dic₃	1	4	yes	complemented
30	Q₈×Dic₃	—	13	1	no	maximal, Hall
31	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₃×C₁₃	#41	1	1	yes	characteristic
34	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
35	C₄×C₁₃	—	6	2	no	—
36	C₄×C₁₃	C₂×Dic₃	1	2	yes	—
37	Dic₁₃	—	3	2	no	—
38	Dic₁₃	—	6	1	no	—
39	Dic₁₃	C₂×Dic₃	1	4	yes	—
40	C₂×C₃×Q₈	—	13	1	no	—
41	C₄⋊Dic₃	—	13	2	no	—
42	C₄⋊Dic₃	D₁₃	1	1	yes	characteristic
43	C₄×Dic₃	—	13	1	no	—
44	C₄×Dic₃	—	13	2	no	—
45	C₃×C₁₃	C₄×Q₈	1	1	yes	characteristic, complemented, Hall
46	C₄×Q₈	—	39	1	no	Sylow
47	C₂×C₁₃	D₃×Q₈	1	1	yes	characteristic
48	C₂×C₁₃	#239	1	1	yes	characteristic
49	C₂×C₁₃	C₂²×Dic₃	1	1	yes	characteristic
50	C₃×Q₈	—	13	4	no	—
51	C₂×C₃×C₄	—	13	2	no	—
52	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
53	C₂×Dic₃	—	13	1	no	—
54	C₂×Dic₃	—	13	1	no	—
55	C₂×Dic₃	C₂×D₁₃	1	2	yes	—
56	C₂×Q₈	—	13	1	no	—
57	C₄⋊C₄	—	3	1	no	—
58	C₄⋊C₄	—	39	2	no	—
59	C₄²	—	39	2	no	—
60	C₄²	—	39	1	no	—
61	C₁₃	Q₈×Dic₃	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
63	C₃×C₄	—	13	4	no	—
64	C₃×C₄	C₄×D₁₃	1	2	yes	—
65	Dic₃	—	2	2	no	—
66	Dic₃	—	13	2	no	—
67	Dic₃	—	26	1	no	—
68	Q₈	—	13	4	no	—
69	C₂×C₄	—	3	2	no	—
70	C₂×C₄	—	13	2	no	—
71	C₂×C₄	—	39	1	no	—
72	C₂×C₄	—	39	1	no	—
73	C₂×C₄	D₃×D₁₃	1	1	yes	characteristic
74	C₂×C₃	C₂×C₄×D₁₃	1	1	yes	characteristic
75	C₂×C₃	#6129	1	1	yes	characteristic
76	C₂×C₃	Q₈×D₁₃	1	1	yes	characteristic
77	C₂²	C₂×D₃×D₁₃	1	1	yes	characteristic
78	C₄	—	6	2	no	—
79	C₄	—	13	4	no	—
80	C₄	—	39	2	no	—
81	C₄	—	78	1	no	—
82	C₄	Dic₃×D₁₃	1	2	yes	—
83	C₃	#88141	1	1	yes	characteristic, complemented, Sylow
84	C₂	#10597734	1	1	yes	characteristic
85	C₂	D₃₉⋊Q₈	1	1	yes	characteristic
86	C₂	C₂×Dic₃×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×D₃×D₁₃
commutator	C₂×C₃×C₁₃	C₂²×C₄
Fitting	C₂×C₃×C₄×C₁₃	C₂²
socle, prime radical, cosocle	C₂²×C₃×C₁₃	C₂³
hypercenter	C₂×C₄	D₃×D₁₃
hypocenter	C₃×C₁₃	C₄×Q₈
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
12. C₃×Dic₂₆	C₄	semidirect
21. Dic₃₉	Q₈	semidirect
29. Dic₂₆	Dic₃	semidirect
45. C₃×C₁₃	C₄×Q₈	semidirect
61. C₁₃	Q₈×Dic₃	semidirect
83. C₃	#88141	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×Dic₂₆	2
C₄×Dic₃₉	2
C₁₃×C₄⋊Dic₃	2
#10597611	2
Dic₃×Dic₁₃	2
#88141	3
Q₈×Dic₃	13