Subgroups — #14565505

Order 2432.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₅₂	C₂	1	1	yes	maximal, characteristic
2	#11926638	C₂	1	2	yes	maximal
3	#11926347	C₂	1	2	yes	maximal
4	#11926319	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#367	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₇₆	C₂²	1	2	yes	—
7	#10597333	—	2	2	no	—
8	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#107	C₂²	1	2	yes	—
10	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
12	#10597267	—	2	2	no	—
13	Dic₁₅₂	C₄	1	4	yes	complemented
14	C₂×Dic₃₈	—	2	2	no	—
15	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
16	C₄⋊C₄×C₁₉	—	2	2	no	—
17	Dic₁₉⋊C₄	—	4	2	no	—
18	C₄×Dic₁₉	—	4	2	no	—
19	C₄×Dic₁₉	D₄	1	1	yes	characteristic
20	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
21	Dic₇₆	—	2	2	no	—
22	Dic₇₆	C₂×C₄	1	4	yes	—
23	C₁₆×C₁₉	C₂×C₄	1	2	yes	—
24	C₁₉⋊C₁₆	—	2	1	no	—
25	C₂×C₄×C₁₉	—	4	2	no	—
26	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₁₉	—	4	2	no	—
28	C₂×Dic₁₉	D₈	1	2	yes	—
29	Dic₃₈	—	2	4	no	—
30	Dic₃₈	—	4	2	no	—
31	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₁₉	#41	1	1	yes	characteristic
33	C₁₉⋊C₈	—	2	1	no	—
34	#2176	—	19	1	no	maximal, Sylow
35	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
36	C₄×C₁₉	—	8	2	no	—
37	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
38	C₄×C₁₉	#135	1	1	yes	characteristic
39	Dic₁₉	—	2	2	no	—
40	Dic₁₉	—	4	4	no	—
41	C₂×Q₃₂	—	19	1	no	—
42	C₄×Q₁₆	—	19	2	no	—
43	#367	D₁₉	1	1	yes	characteristic
44	#358	—	19	2	no	—
45	#346	—	19	1	no	—
46	C₂×C₁₉	C₄×D₈	1	1	yes	characteristic
47	C₂×C₁₉	#510	1	2	yes	—
48	C₂×Q₁₆	—	19	2	no	—
49	C₄×Q₈	—	38	2	no	—
50	Q₃₂	—	19	4	no	—
51	C₂×C₁₆	—	19	1	no	—
52	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
53	#107	C₂×D₁₉	1	2	yes	—
54	#103	—	38	2	no	—
55	C₄×C₈	—	19	1	no	—
56	C₁₉	#2176	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	—	38	2	no	—
58	Q₁₆	—	19	4	no	—
59	Q₁₆	—	38	2	no	—
60	C₂×C₈	—	19	1	no	—
61	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
62	C₄⋊C₄	—	2	2	no	—
63	C₄⋊C₄	—	76	2	no	—
64	C₄²	—	19	1	no	—
65	C₄²	—	76	2	no	—
66	C₁₆	—	38	1	no	—
67	C₁₆	C₄×D₁₉	1	2	yes	—
68	Q₈	—	38	4	no	—
69	Q₈	—	76	2	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	—	19	2	no	—
72	C₂×C₄	—	76	2	no	—
73	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
74	C₈	—	38	1	no	—
75	C₈	C₂×C₄×D₁₉	1	1	yes	characteristic
76	C₈	#64545	1	1	yes	characteristic
77	C₂²	D₈×D₁₉	1	1	yes	characteristic
78	C₄	—	8	2	no	—
79	C₄	—	38	2	no	—
80	C₄	—	76	4	no	—
81	C₄	#10597339	1	1	yes	characteristic
82	C₄	#10597365	1	1	yes	characteristic
83	C₂	#11926626	1	1	yes	characteristic
84	C₂	#11926983	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₁₉
commutator	C₈×C₁₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#367	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₈
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	#367	D₁₉
hypocenter	C₁₉	#2176
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

Complements

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

N	H ≅ G/N	type
13. Dic₁₅₂	C₄	semidirect
56. C₁₉	#2176	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₅₂	2
#11926638	2
#11926347	2
#11926319	2
C₁₉×#367	2
#2176	19