Subgroups — #11929186

Order 1248.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6129	C₂	1	1	yes	maximal, characteristic
2	#10597728	C₂	1	2	yes	maximal, complemented
3	C₂×C₃⋊#1057	C₂	1	2	yes	maximal, complemented
4	#10597724	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#88238	—	3	1	no	maximal, Hall
7	C₃×D₄×C₁₃	C₄	1	1	yes	characteristic
8	C₃×C₂²⋊D₁₃	C₄	1	2	yes	—
9	C₂×C₃×Dic₁₃	C₂²	1	2	yes	—
10	C₃×C₄×D₁₃	C₂²	1	1	yes	characteristic
11	C₃×Dic₂₆	C₄	1	1	yes	characteristic
12	C₃⋊#1057	C₂²	1	1	yes	characteristic
13	C₃⋊#1057	C₂²	1	1	yes	characteristic
14	C₃⋊#1057	C₂²	1	2	yes	—
15	#6129	D₃	1	1	yes	characteristic
16	#6122	—	3	2	no	—
17	C₂×#1057	—	3	2	no	—
18	#6118	—	3	1	no	—
19	D₁₃⋊C₈	—	3	1	no	—
20	C₂²×C₃×C₁₃	C₂×C₄	1	2	yes	—
21	C₂×C₃×D₁₃	C₂×C₄	1	1	yes	characteristic
22	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₃×Dic₁₃	C₂×C₄	1	2	yes	—
24	C₃×Dic₁₃	C₂³	1	1	yes	characteristic
25	D₄×C₁₃	Dic₃	1	1	yes	characteristic
26	C₂²⋊D₁₃	Dic₃	1	2	yes	—
27	C₂×Dic₁₃	C₂×D₃	1	2	yes	—
28	C₄×D₁₃	C₂×D₃	1	1	yes	characteristic
29	Dic₂₆	Dic₃	1	1	yes	characteristic
30	#1057	—	3	1	no	—
31	#1057	—	3	1	no	—
32	#1057	—	3	2	no	—
33	#948	—	13	1	no	maximal, Hall
34	C₂×C₃×C₁₃	—	2	2	no	—
35	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₃×D₁₃	—	2	1	no	—
37	C₂²×C₁₃	C₂×Dic₃	1	2	yes	—
38	C₂×D₁₃	C₂×Dic₃	1	1	yes	characteristic
39	C₄×C₁₃	C₂×Dic₃	1	1	yes	characteristic
40	Dic₁₃	C₂×Dic₃	1	2	yes	—
41	Dic₁₃	C₂²×D₃	1	1	yes	characteristic
42	C₃×#41	—	13	1	no	—
43	#208	—	13	1	no	—
44	#208	—	13	2	no	—
45	C₂×C₃⋊C₈	—	13	1	no	—
46	C₂×C₃⋊C₈	—	13	2	no	—
47	C₃×C₁₃	#131	1	1	yes	characteristic, complemented, Hall
48	#131	—	39	1	no	Sylow
49	C₂×C₁₃	—	2	2	no	—
50	C₂×C₁₃	C₂²×Dic₃	1	1	yes	characteristic
51	D₁₃	—	2	1	no	—
52	C₃×Q₈	—	13	1	no	—
53	C₃×D₄	—	13	2	no	—
54	C₃×D₄	#261	1	1	yes	characteristic
55	C₂×C₃×C₄	—	13	2	no	—
56	C₂×C₃×C₄	—	13	1	no	—
57	C₃⋊C₈	—	13	1	no	—
58	C₃⋊C₈	—	13	1	no	—
59	C₃⋊C₈	—	13	2	no	—
60	#41	—	13	1	no	—
61	M₁₆	—	39	1	no	—
62	M₁₆	—	39	2	no	—
63	C₂×C₈	—	39	1	no	—
64	C₂×C₈	—	39	2	no	—
65	C₁₃	#948	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₃	—	13	1	no	—
67	C₂²×C₃	C₂×#261	1	2	yes	—
68	C₃×C₄	—	13	1	no	—
69	C₃×C₄	—	13	2	no	—
70	C₃×C₄	C₂×#261	1	1	yes	characteristic
71	Q₈	—	13	1	no	—
72	D₄	—	13	2	no	—
73	D₄	C₃⋊#261	1	1	yes	characteristic
74	C₂×C₄	—	13	2	no	—
75	C₂×C₄	—	13	1	no	—
76	C₈	—	39	1	no	—
77	C₈	—	39	1	no	—
78	C₈	—	39	2	no	—
79	C₂×C₃	—	2	2	no	—
80	C₂×C₃	—	26	1	no	—
81	C₂×C₃	C₂²×#261	1	1	yes	characteristic
82	C₂²	—	13	1	no	—
83	C₂²	C₂×C₃⋊#261	1	2	yes	—
84	C₄	—	13	2	no	—
85	C₄	—	13	1	no	—
86	C₄	C₂×C₃⋊#261	1	1	yes	characteristic
87	C₃	#88238	1	1	yes	characteristic, complemented, Sylow
88	C₂	—	2	2	no	—
89	C₂	—	26	1	no	—
90	C₂	C₂²×C₃⋊#261	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×C₃⋊#261
commutator, socle	C₂×C₃×C₁₃	C₂²×C₄
Fitting	C₃×D₄×C₁₃	C₄
prime radical	C₃×#6129	C₂
cosocle	C₃×Dic₁₃	C₂³
hypercenter	D₄	C₃⋊#261
hypocenter	C₃×C₁₃	#131
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
2. #10597728	C₂	semidirect
3. C₂×C₃⋊#1057	C₂	semidirect
4. #10597724	C₂	semidirect
5. D₁₃⋊(C₃⋊C₈)	C₂	semidirect
47. C₃×C₁₃	#131	semidirect
65. C₁₃	#948	semidirect
87. C₃	#88238	semidirect

Maximal subgroups

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

subgroup	index
C₃×#6129	2
#10597728	2
C₂×C₃⋊#1057	2
#10597724	2
D₁₃⋊(C₃⋊C₈)	2
#88238	3
#948	13