Subgroups — #14269727

Order 1824.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₁₄	C₂	1	2	yes	maximal
2	C₃×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₅₇	C₂	1	1	yes	maximal, characteristic
4	#11744887	C₂	1	2	yes	maximal
5	C₄×Dic₅₇	C₂	1	1	yes	maximal, characteristic
6	#10597334	—	3	1	no	maximal, Hall
7	C₂×C₃×C₄×C₁₉	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₅₇	C₂²	1	2	yes	—
10	C₂×Dic₅₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₅₇	C₂²	1	1	yes	characteristic
12	Dic₁₁₄	—	2	4	no	—
13	C₂×Dic₃₈	—	3	2	no	—
14	C₄⋊C₄×C₁₉	D₃	1	1	yes	characteristic
15	C₄⋊Dic₁₉	—	3	1	no	—
16	Dic₁₉⋊C₄	—	3	2	no	—
17	C₄×Dic₁₉	—	3	1	no	—
18	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
19	C₃×C₄×C₁₉	—	2	2	no	—
20	C₃×C₄×C₁₉	Q₈	1	2	yes	complemented
21	Dic₅₇	—	2	2	no	—
22	Dic₅₇	D₄	1	2	yes	—
23	Dic₅₇	Q₈	1	2	yes	complemented
24	C₂×C₄×C₁₉	C₂×D₃	1	2	yes	—
25	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
26	C₂×Dic₁₉	—	3	1	no	—
27	C₂×Dic₁₉	—	3	1	no	—
28	C₂×Dic₁₉	—	3	2	no	—
29	Dic₃₈	—	6	4	no	—
30	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₂×C₃×C₁₉	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₃×C₁₉	C₂×Q₈	1	1	yes	characteristic
33	#888	—	19	1	no	maximal, Hall
34	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
35	C₄×C₁₉	—	2	2	no	—
36	C₄×C₁₉	Dic₆	1	2	yes	complemented
37	Dic₁₉	—	3	2	no	—
38	Dic₁₉	—	3	2	no	—
39	Dic₁₉	—	6	2	no	—
40	C₃×C₁₉	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
41	C₂×Dic₆	—	19	2	no	—
42	C₃×C₄⋊C₄	D₁₉	1	1	yes	characteristic
43	C₄⋊Dic₃	—	19	1	no	—
44	Dic₃⋊C₄	—	19	2	no	—
45	C₄×Dic₃	—	19	1	no	—
46	C₂×C₁₉	C₂×Dic₆	1	1	yes	characteristic
47	C₂×C₁₉	D₃×D₄	1	1	yes	characteristic
48	C₂×C₁₉	D₃×Q₈	1	1	yes	characteristic
49	C₄⋊Q₈	—	57	1	no	Sylow
50	C₂×C₃×C₄	C₂×D₁₉	1	2	yes	—
51	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
52	C₂×Dic₃	—	19	1	no	—
53	C₂×Dic₃	—	19	1	no	—
54	C₂×Dic₃	—	19	2	no	—
55	Dic₆	—	38	4	no	—
56	C₁₉	#888	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	—	57	2	no	—
58	C₄⋊C₄	—	57	2	no	—
59	C₄⋊C₄	—	57	1	no	—
60	C₄⋊C₄	D₅₇	1	1	yes	characteristic
61	C₄²	—	57	1	no	—
62	C₂²×C₃	C₂²×D₁₉	1	1	yes	characteristic
63	C₃×C₄	—	2	2	no	—
64	C₃×C₄	Dic₃₈	1	2	yes	complemented
65	Dic₃	—	19	2	no	—
66	Dic₃	—	19	2	no	—
67	Dic₃	—	38	2	no	—
68	Q₈	—	114	4	no	—
69	C₂×C₄	—	57	1	no	—
70	C₂×C₄	—	57	1	no	—
71	C₂×C₄	—	57	2	no	—
72	C₂×C₄	C₂×D₅₇	1	2	yes	—
73	C₂×C₄	C₂×D₅₇	1	1	yes	characteristic
74	C₂×C₃	C₂×Dic₃₈	1	1	yes	characteristic
75	C₂×C₃	D₄×D₁₉	1	1	yes	characteristic
76	C₂×C₃	Q₈×D₁₉	1	1	yes	characteristic
77	C₂²	C₂²×D₅₇	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	57	2	no	—
80	C₄	—	57	2	no	—
81	C₄	—	114	2	no	—
82	C₄	Dic₁₁₄	1	2	yes	complemented
83	C₃	#10597334	1	1	yes	characteristic, complemented, Sylow
84	C₂	C₂×Dic₁₁₄	1	1	yes	characteristic
85	C₂	D₄×D₅₇	1	1	yes	characteristic
86	C₂	Q₈×D₅₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₅₇
commutator, socle, prime radical, cosocle	C₂²×C₃×C₁₉	C₂³
Fitting	C₃×C₄⋊C₄×C₁₉	C₂
hypercenter	C₄⋊C₄	D₅₇
hypocenter	C₃×C₁₉	C₄⋊Q₈
LCS	G ▷ C₂²×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
20. C₃×C₄×C₁₉	Q₈	semidirect
23. Dic₅₇	Q₈	semidirect
36. C₄×C₁₉	Dic₆	semidirect
40. C₃×C₁₉	C₄⋊Q₈	semidirect
56. C₁₉	#888	semidirect
64. C₃×C₄	Dic₃₈	semidirect
82. C₄	Dic₁₁₄	semidirect
83. C₃	#10597334	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₁₄	2
C₃×C₄⋊C₄×C₁₉	2
C₄⋊Dic₅₇	2
#11744887	2
C₄×Dic₅₇	2
#10597334	3
#888	19