Subgroups — C₂×#10597669 #11929005

Order 1248.

136 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	#10597669	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#6106	—	3	1	no	maximal, Hall
6	C₂²×D₃₉	—	2	1	no	—
7	C₃×Q₈×C₁₃	—	2	1	no	—
8	C₃×Q₈×C₁₃	C₂²	1	2	yes	complemented
9	C₂×C₃×C₄×C₁₃	—	2	1	no	—
10	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
11	D₁₅₆	—	2	1	no	—
12	D₁₅₆	C₂²	1	2	yes	—
13	C₃⋊#1055	C₂²	1	2	yes	complemented
14	C₂×Q₈×C₁₃	D₃	1	1	yes	characteristic, complemented
15	C₂×D₅₂	—	3	1	no	—
16	#6106	—	3	4	no	—
17	C₂×#1055	—	3	1	no	—
18	C₂²×C₃×C₁₃	D₄	1	1	yes	characteristic
19	C₂×D₃₉	—	2	2	no	—
20	C₂×D₃₉	—	4	2	no	—
21	C₃×C₄×C₁₃	—	2	2	no	—
22	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
23	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₂²×D₁₃	—	6	1	no	—
25	Q₈×C₁₃	—	2	1	no	—
26	Q₈×C₁₃	C₂×D₃	1	2	yes	complemented
27	C₂×C₄×C₁₃	—	2	1	no	—
28	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
29	D₅₂	—	3	2	no	—
30	D₅₂	—	6	1	no	—
31	#1055	—	3	2	no	—
32	C₂×#215	—	13	1	no	maximal, Hall
33	C₂×C₃×C₁₃	SD₁₆	1	2	yes	complemented
34	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
35	D₃₉	—	4	2	no	—
36	C₂²×C₁₃	#67	1	1	yes	characteristic
37	C₂×D₁₃	—	6	2	no	—
38	C₂×D₁₃	—	12	2	no	—
39	C₄×C₁₃	—	2	2	no	—
40	C₄×C₁₃	#67	1	1	yes	characteristic
41	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
42	C₂×C₃×Q₈	D₁₃	1	1	yes	characteristic, complemented
43	C₂×D₁₂	—	13	1	no	—
44	#215	—	13	4	no	—
45	C₂×C₃⋊C₈	—	13	1	no	—
46	C₃×C₁₃	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
47	C₂×SD₁₆	—	39	1	no	Sylow
48	C₂×C₁₃	#215	1	2	yes	complemented
49	C₂×C₁₃	C₂×#67	1	1	yes	characteristic
50	D₁₃	—	12	2	no	—
51	C₂²×D₃	—	26	1	no	—
52	C₃×Q₈	—	2	1	no	—
53	C₃×Q₈	C₂×D₁₃	1	2	yes	complemented
54	C₂×C₃×C₄	—	2	1	no	—
55	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
56	D₁₂	—	13	2	no	—
57	D₁₂	—	26	1	no	—
58	C₃⋊C₈	—	13	2	no	—
59	C₂×Q₈	D₃₉	1	1	yes	characteristic, complemented
60	C₂×D₄	—	39	1	no	—
61	SD₁₆	—	39	4	no	—
62	C₂×C₈	—	39	1	no	—
63	C₁₃	C₂×#215	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₃	C₂²⋊D₁₃	1	1	yes	characteristic
65	C₂×D₃	—	26	2	no	—
66	C₂×D₃	—	52	2	no	—
67	C₃×C₄	—	2	2	no	—
68	C₃×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
69	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
70	C₂³	—	78	1	no	—
71	Q₈	—	2	1	no	—
72	Q₈	C₂×D₃₉	1	2	yes	complemented
73	D₄	—	39	2	no	—
74	D₄	—	78	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
77	C₈	—	39	2	no	—
78	C₂×C₃	#6106	1	2	yes	complemented
79	C₂×C₃	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
80	D₃	—	52	2	no	—
81	C₂²	—	78	2	no	—
82	C₂²	—	156	2	no	—
83	C₂²	#64625	1	1	yes	characteristic
84	C₄	—	2	2	no	—
85	C₄	#64625	1	1	yes	characteristic
86	C₄	C₂²×D₃₉	1	1	yes	characteristic
87	C₃	C₂×#6106	1	1	yes	characteristic, complemented, Sylow
88	C₂	—	156	2	no	—
89	C₂	#10597669	1	2	yes	direct product factor
90	C₂	C₂×#64625	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#64625
commutator, cosocle	C₃×C₄×C₁₃	C₂³
Frattini	C₄	C₂²×D₃₉
Fitting	C₂×C₃×Q₈×C₁₃	C₂
socle	C₂²×C₃×C₁₃	D₄
prime radical	C₂×D₁₅₆	C₂
hypercenter	C₂×Q₈	D₃₉
hypocenter	C₃×C₁₃	C₂×SD₁₆
LCS	G ▷ C₃×C₄×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ 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. #10597669	C₂	direct (N × H)
4. C₂×C₃⋊#1055	C₂	semidirect
8. C₃×Q₈×C₁₃	C₂²	semidirect
13. C₃⋊#1055	C₂²	semidirect
14. C₂×Q₈×C₁₃	D₃	semidirect
26. Q₈×C₁₃	C₂×D₃	semidirect
33. C₂×C₃×C₁₃	SD₁₆	semidirect
42. C₂×C₃×Q₈	D₁₃	semidirect
46. C₃×C₁₃	C₂×SD₁₆	semidirect
48. C₂×C₁₃	#215	semidirect
53. C₃×Q₈	C₂×D₁₃	semidirect
59. C₂×Q₈	D₃₉	semidirect
63. C₁₃	C₂×#215	semidirect
72. Q₈	C₂×D₃₉	semidirect
78. C₂×C₃	#6106	semidirect
87. C₃	C₂×#6106	semidirect
89. C₂	#10597669	direct (N × H)

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
#10597669	2
C₂×C₃⋊#1055	2
C₂×#6106	3
C₂×#215	13

Subgroups — C2×#10597669 #11929005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10597669 #11929005