Subgroups — C₂×#10597605 #11928511

Order 1248.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₇₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₂₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#10597605	C₂	1	4	yes	maximal, direct product factor
5	C₂×Dic₅₂	—	3	1	no	maximal, Hall
6	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×Dic₃₉	—	2	1	no	—
8	Dic₇₈	—	2	1	no	—
9	Dic₇₈	C₂²	1	2	yes	—
10	C₂×C₃×Dic₁₃	—	2	1	no	—
11	C₃×Dic₂₆	—	2	1	no	—
12	C₃×Dic₂₆	C₂²	1	2	yes	—
13	C₁₃×C₃⋊C₈	C₂²	1	2	yes	—
14	C₂×Dic₂₆	—	3	1	no	—
15	C₂×Dic₂₆	D₃	1	1	yes	characteristic
16	C₂×C₈×C₁₃	—	3	1	no	—
17	Dic₅₂	—	3	4	no	—
18	C₂²×C₃×C₁₃	D₄	1	1	yes	characteristic
19	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
20	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
21	Dic₃₉	—	2	2	no	—
22	C₃×Dic₁₃	—	2	2	no	—
23	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
24	C₂×Dic₁₃	—	2	1	no	—
25	C₂×Dic₁₃	—	6	1	no	—
26	Dic₂₆	—	2	1	no	—
27	Dic₂₆	—	3	2	no	—
28	Dic₂₆	—	6	1	no	—
29	Dic₂₆	C₂×D₃	1	2	yes	—
30	C₈×C₁₃	—	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	#67	1	1	yes	characteristic
36	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
37	Dic₁₃	—	2	2	no	—
38	Dic₁₃	—	6	2	no	—
39	C₂×C₃×Q₈	—	13	1	no	—
40	C₂×Dic₆	—	13	1	no	—
41	#216	—	13	4	no	—
42	C₂×C₃⋊C₈	D₁₃	1	1	yes	characteristic
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	—	13	2	no	—
48	C₃×Q₈	—	26	1	no	—
49	C₂×C₃×C₄	—	26	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	C₂×D₁₃	1	2	yes	—
55	C₂×Q₈	—	13	1	no	—
56	C₂×Q₈	—	39	1	no	—
57	Q₁₆	—	39	4	no	—
58	C₂×C₈	—	3	1	no	—
59	C₁₃	C₂×#216	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₃	D₅₂	1	1	yes	characteristic
61	C₃×C₄	—	26	2	no	—
62	C₃×C₄	D₅₂	1	1	yes	characteristic
63	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
64	Dic₃	—	26	2	no	—
65	Q₈	—	13	2	no	—
66	Q₈	—	26	1	no	—
67	Q₈	—	39	2	no	—
68	Q₈	—	78	1	no	—
69	C₂×C₄	—	26	1	no	—
70	C₂×C₄	—	78	1	no	—
71	C₂×C₄	D₃×D₁₃	1	1	yes	characteristic
72	C₈	—	3	2	no	—
73	C₂×C₃	Dic₅₂	1	2	yes	complemented
74	C₂×C₃	C₂×D₅₂	1	1	yes	characteristic
75	C₂²	#64603	1	1	yes	characteristic
76	C₄	—	26	2	no	—
77	C₄	—	78	2	no	—
78	C₄	#64603	1	1	yes	characteristic
79	C₄	C₂×D₃×D₁₃	1	1	yes	characteristic
80	C₃	C₂×Dic₅₂	1	1	yes	characteristic, complemented, Sylow
81	C₂	#10597605	1	2	yes	direct product factor
82	C₂	C₂×#64603	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#64603
commutator, cosocle	C₃×C₄×C₁₃	C₂³
Frattini	C₄	C₂×D₃×D₁₃
Fitting	C₂×C₃×C₄×C₁₃	C₂²
socle, prime radical	C₂²×C₃×C₁₃	D₄
hypercenter	C₂×C₄	D₃×D₁₃
hypocenter	C₃×C₁₃	C₂×Q₁₆
LCS	G ▷ C₃×C₄×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
4. #10597605	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	Dic₅₂	semidirect
80. C₃	C₂×Dic₅₂	semidirect
81. C₂	#10597605	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×Dic₇₈	2
C₂×C₃×Dic₂₆	2
C₂×C₁₃×C₃⋊C₈	2
#10597605	2
C₂×Dic₅₂	3
C₂×#216	13

Subgroups — C2×#10597605 #11928511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10597605 #11928511