Subgroups — #11929312

Order 1248.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×D₃₉	C₂	1	2	yes	maximal, complemented
3	#10597792	C₂	1	6	yes	maximal, complemented
4	#10597790	C₂	1	3	yes	maximal, complemented
5	C₂×Dic₇₈	C₂	1	3	yes	maximal, complemented
6	#88257	—	3	1	no	maximal, Hall
7	C₃×Q₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₃×D₄×C₁₃	C₂²	1	3	yes	—
9	C₂×C₃×C₄×C₁₃	C₂²	1	3	yes	—
10	#64625	C₂²	1	6	yes	—
11	C₂×Dic₃₉	C₂²	1	6	yes	—
12	D₁₅₆	C₂²	1	1	yes	characteristic
13	C₄×D₃₉	C₂²	1	6	yes	—
14	Dic₇₈	C₂²	1	3	yes	—
15	Dic₇₈	C₂²	1	6	yes	—
16	C₁₃×#41	D₃	1	1	yes	characteristic, complemented
17	Q₈×D₁₃	—	3	2	no	—
18	#6129	—	3	6	no	—
19	#6127	—	3	3	no	—
20	C₂×Dic₂₆	—	3	3	no	—
21	C₂²×C₃×C₁₃	C₂³	1	3	yes	—
22	C₂×D₃₉	C₂³	1	2	yes	—
23	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₃×C₄×C₁₃	C₂³	1	3	yes	—
25	Dic₃₉	C₂³	1	6	yes	—
26	Q₈×C₁₃	C₂×D₃	1	1	yes	characteristic
27	D₄×C₁₃	C₂×D₃	1	3	yes	—
28	C₂×C₄×C₁₃	C₂×D₃	1	3	yes	—
29	C₂²⋊D₁₃	—	3	6	no	—
30	C₂×Dic₁₃	—	3	6	no	—
31	D₅₂	—	3	1	no	—
32	C₄×D₁₃	—	3	6	no	—
33	Dic₂₆	—	3	3	no	—
34	Dic₂₆	—	3	6	no	—
35	#1010	—	13	1	no	maximal, Hall
36	C₂×C₃×C₁₃	—	2	3	no	—
37	C₂×C₃×C₁₃	C₂⁴	1	1	yes	characteristic
38	D₃₉	—	2	2	no	—
39	C₂²×C₁₃	C₂²×D₃	1	3	yes	—
40	C₂×D₁₃	—	3	2	no	—
41	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
42	C₄×C₁₃	C₂²×D₃	1	3	yes	—
43	Dic₁₃	—	3	6	no	—
44	C₃×#41	D₁₃	1	1	yes	characteristic, complemented
45	D₃×Q₈	—	13	2	no	—
46	#237	—	13	6	no	—
47	#235	—	13	3	no	—
48	C₂×Dic₆	—	13	3	no	—
49	C₃×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Hall
50	2₋¹⁺⁴	—	39	1	no	Sylow
51	C₂×C₁₃	—	2	3	no	—
52	C₂×C₁₃	C₂³×D₃	1	1	yes	characteristic
53	D₁₃	—	6	2	no	—
54	C₃×Q₈	C₂×D₁₃	1	1	yes	characteristic
55	C₃×D₄	C₂×D₁₃	1	3	yes	—
56	C₂×C₃×C₄	C₂×D₁₃	1	3	yes	—
57	#67	—	13	6	no	—
58	C₂×Dic₃	—	13	6	no	—
59	D₁₂	—	13	1	no	—
60	C₄×D₃	—	13	6	no	—
61	Dic₆	—	13	3	no	—
62	Dic₆	—	13	6	no	—
63	#41	—	39	6	no	—
64	#41	—	39	3	no	—
65	#41	D₃₉	1	1	yes	characteristic, complemented
66	C₂×Q₈	—	39	2	no	—
67	C₂×Q₈	—	39	3	no	—
68	C₁₃	#1010	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₃	C₂²×D₁₃	1	3	yes	—
70	C₂×D₃	—	13	2	no	—
71	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
72	C₃×C₄	C₂²×D₁₃	1	3	yes	—
73	Dic₃	—	13	6	no	—
74	Q₈	—	39	6	no	—
75	Q₈	—	39	3	no	—
76	Q₈	C₂×D₃₉	1	1	yes	characteristic
77	D₄	—	39	6	no	—
78	D₄	—	39	1	no	—
79	D₄	C₂×D₃₉	1	3	yes	—
80	C₂×C₄	—	39	6	no	—
81	C₂×C₄	—	39	6	no	—
82	C₂×C₄	C₂×D₃₉	1	3	yes	—
83	C₂×C₃	—	2	3	no	—
84	C₂×C₃	C₂³×D₁₃	1	1	yes	characteristic
85	D₃	—	26	2	no	—
86	C₂²	—	39	2	no	—
87	C₂²	C₂²×D₃₉	1	3	yes	—
88	C₄	—	39	6	no	—
89	C₄	C₂²×D₃₉	1	3	yes	—
90	C₄	C₂²×D₃₉	1	1	yes	characteristic
91	C₃	#88257	1	1	yes	characteristic, complemented, Sylow
92	C₂	—	2	3	no	—
93	C₂	—	78	2	no	—
94	C₂	C₂³×D₃₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×D₃₉
commutator, socle, cosocle	C₂×C₃×C₁₃	C₂⁴
Fitting	C₃×C₁₃×#41	C₂
hypercenter	#41	D₃₉
hypocenter	C₃×C₁₃	2₋¹⁺⁴
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ #41

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×#41	C₂	semidirect
2. Q₈×D₃₉	C₂	semidirect
3. #10597792	C₂	semidirect
4. #10597790	C₂	semidirect
5. C₂×Dic₇₈	C₂	semidirect
16. C₁₃×#41	D₃	semidirect
44. C₃×#41	D₁₃	semidirect
49. C₃×C₁₃	2₋¹⁺⁴	semidirect
65. #41	D₃₉	semidirect
68. C₁₃	#1010	semidirect
91. C₃	#88257	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₃×#41	2
Q₈×D₃₉	2
#10597792	2
#10597790	2
C₂×Dic₇₈	2
#88257	3
#1010	13