Subgroups — #11928218

Order 1248.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#64601	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊#1057	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#1057	C₂	1	1	yes	maximal, characteristic, complemented
4	#88111	—	3	1	no	maximal, Hall
5	C₂²×D₃₉	C₄	1	1	yes	characteristic
6	C₂×Dic₃×C₁₃	C₄	1	1	yes	characteristic
7	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
8	#64601	—	2	1	no	—
9	#64601	—	2	1	no	—
10	C₃⋊#1057	—	2	1	no	—
11	C₃×#1057	—	2	1	no	—
12	C₂×C₄×D₁₃	—	3	1	no	—
13	C₂×#1057	—	3	1	no	—
14	C₂×#1057	D₃	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×D₃₉	—	2	1	no	—
17	C₂×D₃₉	—	2	1	no	—
18	C₂×D₃₉	C₈	1	2	yes	complemented
19	C₃×Dic₁₃	D₄	1	1	yes	characteristic
20	C₃×Dic₁₃	D₄	1	1	yes	characteristic
21	Dic₃×C₁₃	—	2	1	no	—
22	C₂²×D₁₃	—	3	1	no	—
23	C₂×C₄×C₁₃	—	3	1	no	—
24	C₂×Dic₁₃	C₂×D₃	1	1	yes	characteristic
25	C₄×D₁₃	—	6	1	no	—
26	C₄×D₁₃	—	6	1	no	—
27	#1057	—	2	1	no	—
28	#1057	—	6	1	no	—
29	(C₂×D₃)⋊C₈	—	13	1	no	maximal, Hall
30	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₃×C₁₃	C₂×C₈	1	1	yes	characteristic
32	C₂×C₃×C₁₃	M₁₆	1	1	yes	characteristic
33	D₃₉	—	2	2	no	—
34	C₂²×C₁₃	C₄×D₃	1	1	yes	characteristic
35	C₂×D₁₃	—	3	2	no	—
36	C₂×D₁₃	—	6	1	no	—
37	C₂×D₁₃	—	6	1	no	—
38	C₄×C₁₃	—	6	1	no	—
39	Dic₁₃	D₁₂	1	1	yes	characteristic
40	Dic₁₃	#67	1	1	yes	characteristic
41	C₂×C₄×D₃	—	13	1	no	—
42	C₂×C₃×C₈	—	13	1	no	—
43	C₂×C₃⋊C₈	—	13	1	no	—
44	C₃×C₁₃	C₂²⋊C₈	1	1	yes	characteristic, complemented, Hall
45	C₂²⋊C₈	—	39	1	no	Sylow
46	C₂×C₁₃	D₃×C₈	1	1	yes	characteristic
47	C₂×C₁₃	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
48	C₂×C₁₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
49	D₁₃	—	6	2	no	—
50	C₂²×D₃	—	13	1	no	—
51	C₂×C₃×C₄	—	13	1	no	—
52	C₂×Dic₃	#261	1	1	yes	characteristic
53	C₄×D₃	—	26	1	no	—
54	C₄×D₃	—	26	1	no	—
55	C₃×C₈	—	26	1	no	—
56	C₃⋊C₈	—	26	1	no	—
57	C₂²×C₄	—	39	1	no	—
58	C₂×C₈	—	13	1	no	—
59	C₂×C₈	—	39	1	no	—
60	C₁₃	(C₂×D₃)⋊C₈	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₃	C₂×#261	1	1	yes	characteristic
62	C₂×D₃	—	13	2	no	—
63	C₂×D₃	—	26	1	no	—
64	C₂×D₃	—	26	1	no	—
65	C₃×C₄	—	13	1	no	—
66	C₃×C₄	—	13	1	no	—
67	Dic₃	—	2	1	no	—
68	C₂³	—	39	1	no	—
69	C₂×C₄	—	3	1	no	—
70	C₂×C₄	—	13	1	no	—
71	C₂×C₄	—	78	1	no	—
72	C₂×C₄	—	78	1	no	—
73	C₈	—	26	1	no	—
74	C₈	—	78	1	no	—
75	C₂×C₃	D₁₃⋊C₈	1	1	yes	characteristic
76	C₂×C₃	#6118	1	1	yes	characteristic
77	C₂×C₃	C₂²⋊#261	1	1	yes	characteristic
78	D₃	—	26	2	no	—
79	C₂²	—	39	2	no	—
80	C₂²	—	78	1	no	—
81	C₂²	—	78	1	no	—
82	C₂²	D₃×#261	1	1	yes	characteristic
83	C₄	—	6	1	no	—
84	C₄	—	13	1	no	—
85	C₄	—	13	1	no	—
86	C₃	#88111	1	1	yes	characteristic, complemented, Sylow
87	C₂	—	78	2	no	—
88	C₂	(C₂×D₃)⋊#261	1	1	yes	characteristic
89	C₂	#10597691	1	1	yes	characteristic
90	C₂	#10597693	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₃×#261
commutator	C₂×C₃×C₁₃	C₂×C₈
Fitting, socle	C₂²×C₃×C₁₃	C₂×C₄
prime radical	C₂²×D₃₉	C₄
cosocle	C₂×C₃×Dic₁₃	C₂²
hypocenter	C₃×C₁₃	C₂²⋊C₈
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. C₂×C₃⋊#1057	C₂	semidirect
3. C₂×C₃×#1057	C₂	semidirect
14. C₂×#1057	D₃	semidirect
18. C₂×D₃₉	C₈	semidirect
44. C₃×C₁₃	C₂²⋊C₈	semidirect
60. C₁₃	(C₂×D₃)⋊C₈	semidirect
86. C₃	#88111	semidirect

Maximal subgroups

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

subgroup	index
C₂×#64601	2
C₂×C₃⋊#1057	2
C₂×C₃×#1057	2
#88111	3
(C₂×D₃)⋊C₈	13