Subgroups — C₂×#10597670 #11929007

Order 1248.

120 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
2	C₂×Dic₇₈	C₂	1	1	yes	maximal, characteristic
3	#10597670	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃⋊#1055	C₂	1	1	yes	maximal, characteristic
5	C₂×#6107	—	3	1	no	maximal, Hall
6	C₃×Q₈×C₁₃	—	2	1	no	—
7	C₃×Q₈×C₁₃	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₁₃	—	2	1	no	—
9	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₃₉	—	2	1	no	—
11	Dic₇₈	—	2	1	no	—
12	Dic₇₈	C₂²	1	2	yes	—
13	C₃⋊#1055	C₂²	1	2	yes	—
14	C₂×Q₈×C₁₃	D₃	1	1	yes	characteristic
15	C₂×Dic₂₆	—	3	1	no	—
16	#6107	—	3	4	no	—
17	C₂×#1055	—	3	1	no	—
18	C₂²×C₃×C₁₃	D₄	1	1	yes	characteristic
19	C₃×C₄×C₁₃	—	2	2	no	—
20	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
21	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
22	Dic₃₉	—	2	2	no	—
23	Q₈×C₁₃	—	2	1	no	—
24	Q₈×C₁₃	C₂×D₃	1	2	yes	—
25	C₂×C₄×C₁₃	—	2	1	no	—
26	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
27	C₂×Dic₁₃	—	6	1	no	—
28	Dic₂₆	—	3	2	no	—
29	Dic₂₆	—	6	1	no	—
30	#1055	—	3	2	no	—
31	C₂×#216	—	13	1	no	maximal, Hall
32	C₂×C₃×C₁₃	Q₁₆	1	2	yes	complemented
33	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₁₃	#67	1	1	yes	characteristic
35	C₄×C₁₃	—	2	2	no	—
36	C₄×C₁₃	#67	1	1	yes	characteristic
37	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
38	Dic₁₃	—	6	2	no	—
39	C₂×C₃×Q₈	D₁₃	1	1	yes	characteristic
40	C₂×Dic₆	—	13	1	no	—
41	#216	—	13	4	no	—
42	C₂×C₃⋊C₈	—	13	1	no	—
43	C₃×C₁₃	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
44	C₂×Q₁₆	—	39	1	no	Sylow
45	C₂×C₁₃	#216	1	2	yes	complemented
46	C₂×C₁₃	C₂×#67	1	1	yes	characteristic
47	C₃×Q₈	—	2	1	no	—
48	C₃×Q₈	C₂×D₁₃	1	2	yes	—
49	C₂×C₃×C₄	—	2	1	no	—
50	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
51	C₂×Dic₃	—	26	1	no	—
52	Dic₆	—	13	2	no	—
53	Dic₆	—	26	1	no	—
54	C₃⋊C₈	—	13	2	no	—
55	C₂×Q₈	—	39	1	no	—
56	C₂×Q₈	D₃₉	1	1	yes	characteristic
57	Q₁₆	—	39	4	no	—
58	C₂×C₈	—	39	1	no	—
59	C₁₃	C₂×#216	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₃	C₂²⋊D₁₃	1	1	yes	characteristic
61	C₃×C₄	—	2	2	no	—
62	C₃×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
63	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
64	Dic₃	—	26	2	no	—
65	Q₈	—	2	1	no	—
66	Q₈	—	39	2	no	—
67	Q₈	—	78	1	no	—
68	Q₈	C₂×D₃₉	1	2	yes	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	78	1	no	—
71	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
72	C₈	—	39	2	no	—
73	C₂×C₃	#6107	1	2	yes	complemented
74	C₂×C₃	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
75	C₂²	#64625	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	78	2	no	—
78	C₄	#64625	1	1	yes	characteristic
79	C₄	C₂²×D₃₉	1	1	yes	characteristic
80	C₃	C₂×#6107	1	1	yes	characteristic, complemented, Sylow
81	C₂	#10597670	1	2	yes	direct product factor
82	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, prime radical	C₂²×C₃×C₁₃	D₄
hypercenter	C₂×Q₈	D₃₉
hypocenter	C₃×C₁₃	C₂×Q₁₆
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
3. #10597670	C₂	direct (N × H)
32. C₂×C₃×C₁₃	Q₁₆	semidirect
43. C₃×C₁₃	C₂×Q₁₆	semidirect
45. C₂×C₁₃	#216	semidirect
59. C₁₃	C₂×#216	semidirect
73. C₂×C₃	#6107	semidirect
80. C₃	C₂×#6107	semidirect
81. C₂	#10597670	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×Dic₇₈	2
#10597670	2
C₂×C₃⋊#1055	2
C₂×#6107	3
C₂×#216	13

Subgroups — C2×#10597670 #11929007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10597670 #11929007