Subgroups — C₂×#11744823 #14269278

Order 1824.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₁₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₇₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#11744823	C₂	1	4	yes	maximal, direct product factor
5	C₂×#64516	—	3	1	no	maximal, Hall
6	C₂²×C₃×D₁₉	—	2	1	no	—
7	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×Dic₅₇	—	2	1	no	—
9	Dic₁₁₄	—	2	1	no	—
10	Dic₁₁₄	C₂²	1	2	yes	complemented
11	C₃×D₇₆	—	2	1	no	—
12	C₃×D₇₆	C₂²	1	2	yes	—
13	C₁₉×C₃⋊C₈	C₂²	1	2	yes	complemented
14	C₂×D₇₆	D₃	1	1	yes	characteristic
15	C₂×Dic₃₈	—	3	1	no	—
16	C₂×C₈×C₁₉	—	3	1	no	—
17	#64516	—	3	4	no	—
18	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₃×D₁₉	—	2	2	no	—
20	C₂×C₃×D₁₉	—	4	2	no	—
21	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	Dic₅₇	—	2	2	no	—
24	C₂²×D₁₉	—	2	1	no	—
25	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
26	C₂×Dic₁₉	—	6	1	no	—
27	D₇₆	—	2	1	no	—
28	D₇₆	C₂×D₃	1	2	yes	—
29	Dic₃₈	—	3	2	no	—
30	Dic₃₈	—	6	1	no	—
31	C₈×C₁₉	—	3	2	no	—
32	C₂×C₃×C₁₉	SD₁₆	1	2	yes	complemented
33	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₃×D₁₉	—	4	2	no	—
35	C₂×#214	—	19	1	no	maximal, Hall
36	C₂²×C₁₉	#67	1	1	yes	characteristic
37	C₂×D₁₉	—	2	2	no	—
38	C₂×D₁₉	—	4	2	no	—
39	C₄×C₁₉	#67	1	1	yes	characteristic
40	C₄×C₁₉	C₂²×D₃	1	1	yes	characteristic
41	Dic₁₉	—	6	2	no	—
42	C₃×C₁₉	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
43	C₂×C₃×D₄	—	19	1	no	—
44	C₂×Dic₆	—	19	1	no	—
45	#214	—	19	4	no	—
46	C₂×C₃⋊C₈	D₁₉	1	1	yes	characteristic, complemented
47	C₂×C₁₉	#214	1	2	yes	complemented
48	C₂×C₁₉	C₂×#67	1	1	yes	characteristic
49	D₁₉	—	4	2	no	—
50	C₂×SD₁₆	—	57	1	no	Sylow
51	C₂³×C₃	—	38	1	no	—
52	C₃×D₄	—	19	2	no	—
53	C₃×D₄	—	38	1	no	—
54	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
55	C₂×Dic₃	—	38	1	no	—
56	Dic₆	—	19	2	no	—
57	Dic₆	—	38	1	no	—
58	C₃⋊C₈	C₂×D₁₉	1	2	yes	complemented
59	C₁₉	C₂×#214	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	—	57	1	no	—
61	C₂×D₄	—	19	1	no	—
62	SD₁₆	—	57	4	no	—
63	C₂×C₈	—	3	1	no	—
64	C₂²×C₃	—	38	2	no	—
65	C₂²×C₃	—	76	2	no	—
66	C₂²×C₃	D₇₆	1	1	yes	characteristic
67	C₃×C₄	D₇₆	1	1	yes	characteristic
68	C₃×C₄	C₂²×D₁₉	1	1	yes	characteristic
69	Dic₃	—	38	2	no	—
70	C₂³	—	38	1	no	—
71	Q₈	—	57	2	no	—
72	Q₈	—	114	1	no	—
73	D₄	—	19	2	no	—
74	D₄	—	38	1	no	—
75	C₂×C₄	—	114	1	no	—
76	C₂×C₄	D₃×D₁₉	1	1	yes	characteristic
77	C₈	—	3	2	no	—
78	C₂×C₃	—	76	2	no	—
79	C₂×C₃	#64516	1	2	yes	complemented
80	C₂×C₃	C₂×D₇₆	1	1	yes	characteristic
81	C₂²	—	38	2	no	—
82	C₂²	—	76	2	no	—
83	C₂²	#90696	1	1	yes	characteristic
84	C₄	—	114	2	no	—
85	C₄	#90696	1	1	yes	characteristic
86	C₄	C₂×D₃×D₁₉	1	1	yes	characteristic
87	C₃	C₂×#64516	1	1	yes	characteristic, complemented, Sylow
88	C₂	—	76	2	no	—
89	C₂	#11744823	1	2	yes	direct product factor
90	C₂	C₂×#90696	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#90696
commutator, cosocle	C₃×C₄×C₁₉	C₂³
Frattini	C₄	C₂×D₃×D₁₉
Fitting	C₂×C₃×C₄×C₁₉	C₂²
socle	C₂²×C₃×C₁₉	D₄
prime radical	C₂×C₃×D₇₆	C₂
hypercenter	C₂×C₄	D₃×D₁₉
hypocenter	C₃×C₁₉	C₂×SD₁₆
LCS	G ▷ C₃×C₄×C₁₉ ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₁₁₄	C₂	semidirect
3. C₂×C₁₉×C₃⋊C₈	C₂	semidirect
4. #11744823	C₂	direct (N × H)
10. Dic₁₁₄	C₂²	semidirect
13. C₁₉×C₃⋊C₈	C₂²	semidirect
32. C₂×C₃×C₁₉	SD₁₆	semidirect
42. C₃×C₁₉	C₂×SD₁₆	semidirect
46. C₂×C₃⋊C₈	D₁₉	semidirect
47. C₂×C₁₉	#214	semidirect
58. C₃⋊C₈	C₂×D₁₉	semidirect
59. C₁₉	C₂×#214	semidirect
79. C₂×C₃	#64516	semidirect
87. C₃	C₂×#64516	semidirect
89. C₂	#11744823	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×Dic₁₁₄	2
C₂×C₃×D₇₆	2
C₂×C₁₉×C₃⋊C₈	2
#11744823	2
C₂×#64516	3
C₂×#214	19

Subgroups — C2×#11744823 #14269278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11744823 #14269278