Subgroups — #11929009

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₅₆	C₂	1	1	yes	maximal, characteristic
3	#10597666	C₂	1	4	yes	maximal, complemented
4	C₄×Dic₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#88201	—	3	1	no	maximal, Hall
6	C₂²×D₃₉	C₂²	1	2	yes	—
7	C₃×Q₈×C₁₃	—	2	2	no	—
8	C₂×C₃×C₄×C₁₃	C₂²	1	2	yes	—
9	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₃₉	C₂²	1	2	yes	—
11	D₁₅₆	—	2	2	no	—
12	C₂×Q₈×C₁₃	D₃	1	1	yes	characteristic, complemented
13	C₂×D₅₂	—	3	1	no	—
14	#6103	—	3	4	no	—
15	C₄×Dic₁₃	—	3	1	no	—
16	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×D₃₉	—	2	2	no	—
18	C₂×D₃₉	—	2	4	no	—
19	C₃×C₄×C₁₃	—	2	2	no	—
20	C₃×C₄×C₁₃	D₄	1	2	yes	—
21	Dic₃₉	—	2	2	no	—
22	C₂²×D₁₃	—	3	2	no	—
23	Q₈×C₁₃	—	2	2	no	—
24	C₂×C₄×C₁₃	C₂×D₃	1	2	yes	—
25	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
26	C₂×Dic₁₃	—	3	2	no	—
27	D₅₂	—	6	2	no	—
28	#947	—	13	1	no	maximal, Hall
29	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₃×C₁₃	#41	1	2	yes	—
31	D₃₉	—	4	2	no	—
32	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
33	C₂×D₁₃	—	6	4	no	—
34	C₂×D₁₃	—	6	2	no	—
35	C₄×C₁₃	—	2	2	no	—
36	C₄×C₁₃	#67	1	2	yes	—
37	Dic₁₃	—	6	2	no	—
38	C₂×C₃×Q₈	D₁₃	1	1	yes	characteristic, complemented
39	C₂×D₁₂	—	13	1	no	—
40	(C₂×D₃)⋊C₄	—	13	4	no	—
41	C₄×Dic₃	—	13	1	no	—
42	C₃×C₁₃	#124	1	1	yes	characteristic, complemented, Hall
43	#124	—	39	1	no	Sylow
44	C₂×C₁₃	#239	1	2	yes	—
45	C₂×C₁₃	C₂×#67	1	1	yes	characteristic
46	D₁₃	—	12	2	no	—
47	C₂²×D₃	—	13	2	no	—
48	C₃×Q₈	—	2	2	no	—
49	C₂×C₃×C₄	C₂×D₁₃	1	2	yes	—
50	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
51	C₂×Dic₃	—	13	2	no	—
52	D₁₂	—	26	2	no	—
53	C₂×Q₈	D₃₉	1	1	yes	characteristic, complemented
54	C₂×D₄	—	39	1	no	—
55	C₂²⋊C₄	—	39	4	no	—
56	C₄²	—	39	1	no	—
57	C₁₃	#947	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
59	C₂×D₃	—	26	4	no	—
60	C₂×D₃	—	26	2	no	—
61	C₃×C₄	—	2	2	no	—
62	C₃×C₄	C₂²⋊D₁₃	1	2	yes	—
63	Dic₃	—	26	2	no	—
64	C₂³	—	39	2	no	—
65	Q₈	—	2	2	no	—
66	D₄	—	78	2	no	—
67	C₂×C₄	—	39	2	no	—
68	C₂×C₄	C₂×D₃₉	1	2	yes	—
69	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
70	C₂×C₃	#6131	1	2	yes	—
71	C₂×C₃	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
72	D₃	—	52	2	no	—
73	C₂²	—	78	4	no	—
74	C₂²	—	78	2	no	—
75	C₂²	C₂²×D₃₉	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	78	2	no	—
78	C₄	#64625	1	2	yes	—
79	C₃	#88201	1	1	yes	characteristic, complemented, Sylow
80	C₂	—	156	2	no	—
81	C₂	#10597794	1	2	yes	—
82	C₂	C₂×#64625	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃₉
commutator, socle, cosocle	C₂²×C₃×C₁₃	C₂³
Fitting	C₂×C₃×Q₈×C₁₃	C₂
prime radical	C₂×D₁₅₆	C₂
hypercenter	C₂×Q₈	D₃₉
hypocenter	C₃×C₁₃	#124
LCS	G ▷ C₂²×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×Q₈×C₁₃	C₂	semidirect
3. #10597666	C₂	semidirect
4. C₄×Dic₃₉	C₂	semidirect
12. C₂×Q₈×C₁₃	D₃	semidirect
38. C₂×C₃×Q₈	D₁₃	semidirect
42. C₃×C₁₃	#124	semidirect
53. C₂×Q₈	D₃₉	semidirect
57. C₁₃	#947	semidirect
79. C₃	#88201	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×Q₈×C₁₃	2
C₂×D₁₅₆	2
#10597666	2
C₄×Dic₃₉	2
#88201	3
#947	13