Subgroups — #11928988

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	#10597671	C₂	1	2	yes	maximal
3	C₄⋊Dic₃₉	C₂	1	2	yes	maximal, complemented
4	C₄×Dic₃₉	C₂	1	2	yes	maximal, complemented
5	#88180	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄×C₁₃	C₄	1	4	yes	complemented
8	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₃₉	C₂²	1	4	yes	—
11	C₂²×C₄×C₁₃	D₃	1	1	yes	characteristic
12	C₂²⋊Dic₁₃	—	3	2	no	—
13	C₄⋊Dic₁₃	—	3	2	no	—
14	C₄×Dic₁₃	—	3	2	no	—
15	C₂²×C₃×C₁₃	—	2	2	no	—
16	C₂²×C₃×C₁₃	C₂×C₄	1	2	yes	—
17	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
18	C₃×C₄×C₁₃	C₂×C₄	1	2	yes	—
19	C₃×C₄×C₁₃	C₂×C₄	1	2	yes	—
20	Dic₃₉	—	2	4	no	—
21	C₂³×C₁₃	C₂×D₃	1	1	yes	characteristic
22	C₂×C₄×C₁₃	Dic₃	1	4	yes	complemented
23	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
24	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
25	C₂×Dic₁₃	—	3	4	no	—
26	#926	—	13	1	no	maximal, Hall
27	C₂×C₃×C₁₃	—	2	2	no	—
28	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₃×C₁₃	#41	1	2	yes	—
30	C₂²×C₁₃	—	2	2	no	—
31	C₂²×C₁₃	C₂×Dic₃	1	2	yes	—
32	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
33	C₄×C₁₃	C₂×Dic₃	1	2	yes	—
34	C₄×C₁₃	C₂×Dic₃	1	2	yes	—
35	Dic₁₃	—	6	4	no	—
36	C₂²×C₃×C₄	D₁₃	1	1	yes	characteristic
37	#217	—	13	2	no	—
38	C₄⋊Dic₃	—	13	2	no	—
39	C₄×Dic₃	—	13	2	no	—
40	C₃×C₁₃	#117	1	1	yes	characteristic, complemented, Hall
41	#117	—	39	1	no	Sylow
42	C₂×C₁₃	—	2	2	no	—
43	C₂×C₁₃	#235	1	2	yes	—
44	C₂×C₁₃	C₂²×Dic₃	1	1	yes	characteristic
45	C₂³×C₃	C₂×D₁₃	1	1	yes	characteristic
46	C₂×C₃×C₄	Dic₁₃	1	4	yes	complemented
47	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
48	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
49	C₂×Dic₃	—	13	4	no	—
50	C₂²×C₄	D₃₉	1	1	yes	characteristic
51	C₄⋊C₄	—	39	2	no	—
52	C₂²⋊C₄	—	39	2	no	—
53	C₄²	—	39	2	no	—
54	C₁₃	#926	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₃	—	2	2	no	—
56	C₂²×C₃	C₂×Dic₁₃	1	2	yes	—
57	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
58	C₃×C₄	C₂×Dic₁₃	1	2	yes	—
59	C₃×C₄	C₂×Dic₁₃	1	2	yes	—
60	Dic₃	—	26	4	no	—
61	C₂³	C₂×D₃₉	1	1	yes	characteristic
62	C₂×C₄	—	39	4	no	—
63	C₂×C₄	Dic₃₉	1	4	yes	complemented
64	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
65	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
66	C₂×C₃	—	2	2	no	—
67	C₂×C₃	#6127	1	2	yes	—
68	C₂×C₃	C₂²×Dic₁₃	1	1	yes	characteristic
69	C₂²	—	2	2	no	—
70	C₂²	C₂×Dic₃₉	1	2	yes	—
71	C₂²	C₂²×D₃₉	1	1	yes	characteristic
72	C₄	—	78	4	no	—
73	C₄	C₂×Dic₃₉	1	2	yes	—
74	C₄	C₂×Dic₃₉	1	2	yes	—
75	C₃	#88180	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	2	2	no	—
77	C₂	#10597790	1	2	yes	—
78	C₂	C₂²×Dic₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃₉
commutator	C₂×C₃×C₁₃	C₂²×C₄
Frattini	C₂²	C₂²×D₃₉
Fitting	C₂²×C₃×C₄×C₁₃	C₂
socle, cosocle	C₂²×C₃×C₁₃	C₂³
prime radical	C₂³×C₃×C₁₃	C₂²
hypercenter	C₂²×C₄	D₃₉
hypocenter	C₃×C₁₃	#117
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
3. C₄⋊Dic₃₉	C₂	semidirect
4. C₄×Dic₃₉	C₂	semidirect
7. C₂×C₃×C₄×C₁₃	C₄	semidirect
22. C₂×C₄×C₁₃	Dic₃	semidirect
40. C₃×C₁₃	#117	semidirect
46. C₂×C₃×C₄	Dic₁₃	semidirect
54. C₁₃	#926	semidirect
63. C₂×C₄	Dic₃₉	semidirect
75. C₃	#88180	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄×C₁₃	2
#10597671	2
C₄⋊Dic₃₉	2
C₄×Dic₃₉	2
#88180	3
#926	13