Subgroups — #14269729

Order 1824.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₅₇	C₂	1	2	yes	maximal
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	#10597336	—	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	1	yes	characteristic
10	C₂×Dic₅₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₅₇	C₂²	1	2	yes	—
12	C₄⋊C₄×C₁₉	D₃	1	1	yes	characteristic
13	C₄⋊Dic₁₉	—	3	2	no	—
14	C₄⋊Dic₁₉	—	3	1	no	—
15	Dic₁₉⋊C₄	—	3	2	no	—
16	C₄×Dic₁₉	—	3	1	no	—
17	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
18	C₃×C₄×C₁₉	—	2	2	no	—
19	C₃×C₄×C₁₉	Q₈	1	2	yes	—
20	Dic₅₇	—	2	1	no	—
21	Dic₅₇	—	2	1	no	—
22	Dic₅₇	—	2	2	no	—
23	C₂×C₄×C₁₉	C₂×D₃	1	2	yes	—
24	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
25	C₂×Dic₁₉	—	3	1	no	—
26	C₂×Dic₁₉	—	3	1	no	—
27	C₂×Dic₁₉	—	3	2	no	—
28	C₂×C₃×C₁₉	C₂×Q₈	1	1	yes	characteristic
29	C₂×C₃×C₁₉	#41	1	1	yes	characteristic
30	C₂×C₃×C₁₉	#41	1	1	yes	characteristic
31	#890	—	19	1	no	maximal, Hall
32	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
33	C₄×C₁₉	—	2	2	no	—
34	C₄×C₁₉	Dic₆	1	2	yes	—
35	Dic₁₉	—	6	1	no	—
36	Dic₁₉	—	6	1	no	—
37	Dic₁₉	—	6	2	no	—
38	C₃×C₁₉	#125	1	1	yes	characteristic, complemented, Hall
39	C₃×C₄⋊C₄	D₁₉	1	1	yes	characteristic
40	C₄⋊Dic₃	—	19	2	no	—
41	C₄⋊Dic₃	—	19	1	no	—
42	Dic₃⋊C₄	—	19	2	no	—
43	C₄×Dic₃	—	19	1	no	—
44	C₂×C₁₉	C₂×Dic₆	1	1	yes	characteristic
45	C₂×C₁₉	#237	1	1	yes	characteristic
46	C₂×C₁₉	#239	1	1	yes	characteristic
47	#125	—	57	1	no	Sylow
48	C₂×C₃×C₄	C₂×D₁₉	1	2	yes	—
49	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
50	C₂×Dic₃	—	19	1	no	—
51	C₂×Dic₃	—	19	1	no	—
52	C₂×Dic₃	—	19	2	no	—
53	C₁₉	#890	1	1	yes	characteristic, complemented, Sylow
54	C₄⋊C₄	—	57	2	no	—
55	C₄⋊C₄	—	57	2	no	—
56	C₄⋊C₄	—	57	1	no	—
57	C₄⋊C₄	D₅₇	1	1	yes	characteristic
58	C₄²	—	57	1	no	—
59	C₂²×C₃	C₂²×D₁₉	1	1	yes	characteristic
60	C₃×C₄	—	2	2	no	—
61	C₃×C₄	Dic₃₈	1	2	yes	—
62	Dic₃	—	38	1	no	—
63	Dic₃	—	38	1	no	—
64	Dic₃	—	38	2	no	—
65	C₂×C₄	—	57	1	no	—
66	C₂×C₄	—	57	1	no	—
67	C₂×C₄	—	57	2	no	—
68	C₂×C₄	C₂×D₅₇	1	2	yes	—
69	C₂×C₄	C₂×D₅₇	1	1	yes	characteristic
70	C₂×C₃	C₂×Dic₃₈	1	1	yes	characteristic
71	C₂×C₃	#64543	1	1	yes	characteristic
72	C₂×C₃	#64545	1	1	yes	characteristic
73	C₂²	C₂²×D₅₇	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	114	1	no	—
76	C₄	—	114	1	no	—
77	C₄	—	114	2	no	—
78	C₄	Dic₁₁₄	1	2	yes	—
79	C₃	#10597336	1	1	yes	characteristic, complemented, Sylow
80	C₂	C₂×Dic₁₁₄	1	1	yes	characteristic
81	C₂	#11744987	1	1	yes	characteristic
82	C₂	#11744989	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	#125
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
38. C₃×C₁₉	#125	semidirect
53. C₁₉	#890	semidirect
79. C₃	#10597336	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄⋊C₄×C₁₉	2
C₄⋊Dic₅₇	2
#11744887	2
C₄×Dic₅₇	2
#10597336	3
#890	19