Subgroups — #11928221

Order 1248.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#64604	C₂	1	1	yes	maximal, characteristic
2	#10597728	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#6122	C₂	1	1	yes	maximal, characteristic, complemented
4	#88121	—	3	1	no	maximal, Hall
5	C₂²×D₃₉	C₄	1	1	yes	characteristic
6	C₂²×D₃×C₁₃	C₄	1	1	yes	characteristic
7	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
8	#64604	—	2	1	no	—
9	#64604	—	2	1	no	—
10	C₃⋊#1057	—	2	1	no	—
11	C₃×#1057	—	2	1	no	—
12	C₂×C₂²⋊D₁₃	—	3	1	no	—
13	#6122	—	3	1	no	—
14	#6122	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	—	4	1	no	—
18	C₂×D₃×C₁₃	—	2	1	no	—
19	C₂×D₃×C₁₃	—	4	1	no	—
20	C₃×Dic₁₃	D₄	1	1	yes	characteristic
21	C₃×Dic₁₃	D₄	1	1	yes	characteristic
22	C₂³×C₁₃	—	3	1	no	—
23	C₂²×D₁₃	—	3	1	no	—
24	C₂²⋊D₁₃	—	6	1	no	—
25	C₂²⋊D₁₃	—	6	1	no	—
26	C₂×Dic₁₃	C₂×D₃	1	1	yes	characteristic
27	#1057	—	2	1	no	—
28	#1057	—	6	1	no	—
29	#823	—	13	1	no	maximal, Hall
30	C₂×C₃×C₁₃	—	2	1	no	—
31	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
32	D₃₉	—	4	1	no	—
33	D₃×C₁₃	—	4	1	no	—
34	C₂²×C₁₃	—	6	1	no	—
35	C₂²×C₁₃	—	12	1	no	—
36	C₂²×C₁₃	C₄×D₃	1	1	yes	characteristic
37	C₂×D₁₃	—	6	1	no	—
38	C₂×D₁₃	—	12	1	no	—
39	Dic₁₃	D₁₂	1	1	yes	characteristic
40	Dic₁₃	#67	1	1	yes	characteristic
41	C₂×D₁₂	—	13	1	no	—
42	C₃×M₁₆	—	13	1	no	—
43	#208	—	13	1	no	—
44	C₃×C₁₃	#100	1	1	yes	characteristic, complemented, Hall
45	#100	—	39	1	no	Sylow
46	C₂×C₁₃	—	2	1	no	—
47	C₂×C₁₃	—	12	1	no	—
48	C₂×C₁₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
49	D₁₃	—	12	1	no	—
50	C₂²×D₃	—	13	1	no	—
51	C₂²×D₃	#261	1	1	yes	characteristic
52	C₂×C₃×C₄	—	13	1	no	—
53	D₁₂	—	26	1	no	—
54	D₁₂	—	26	1	no	—
55	C₃×C₈	—	26	1	no	—
56	C₃⋊C₈	—	26	1	no	—
57	C₂×D₄	—	39	1	no	—
58	M₁₆	—	13	1	no	—
59	M₁₆	—	39	1	no	—
60	C₁₃	#823	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₃	C₂×#261	1	1	yes	characteristic
62	C₂×D₃	—	2	1	no	—
63	C₂×D₃	—	4	1	no	—
64	C₂×D₃	—	26	1	no	—
65	C₂×D₃	—	52	1	no	—
66	C₃×C₄	—	13	1	no	—
67	C₃×C₄	—	13	1	no	—
68	C₂³	—	3	1	no	—
69	C₂³	—	39	1	no	—
70	D₄	—	78	1	no	—
71	D₄	—	78	1	no	—
72	C₂×C₄	—	13	1	no	—
73	C₈	—	26	1	no	—
74	C₈	—	78	1	no	—
75	C₂×C₃	—	2	1	no	—
76	C₂×C₃	C₂²⋊#261	1	1	yes	characteristic
77	D₃	—	4	1	no	—
78	D₃	—	52	1	no	—
79	C₂²	—	6	1	no	—
80	C₂²	—	12	1	no	—
81	C₂²	—	78	1	no	—
82	C₂²	—	156	1	no	—
83	C₂²	D₃×#261	1	1	yes	characteristic
84	C₄	—	13	1	no	—
85	C₄	—	13	1	no	—
86	C₃	#88121	1	1	yes	characteristic, complemented, Sylow
87	C₂	—	2	1	no	—
88	C₂	—	12	1	no	—
89	C₂	—	156	1	no	—
90	C₂	(C₂×D₃)⋊#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂	(C₂×D₃)⋊#261
commutator, Fitting	C₂²×C₃×C₁₃	C₂×C₄
Frattini, hypercenter	C₂²	D₃×#261
socle	C₂×C₃×C₁₃	C₂²⋊C₄
prime radical	C₂×#64604	C₂
cosocle	C₂×C₃×Dic₁₃	C₂²
hypocenter	C₃×C₁₃	#100
LCS	G ▷ C₂²×C₃×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. #10597728	C₂	semidirect
3. C₃×#6122	C₂	semidirect
14. #6122	D₃	semidirect
44. C₃×C₁₃	#100	semidirect
60. C₁₃	#823	semidirect
86. 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×#64604	2
#10597728	2
C₃×#6122	2
#88121	3
#823	13