Subgroups — #14563237

Order 2432.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926917	C₂	1	1	yes	maximal, characteristic
2	#11926894	C₂	1	2	yes	maximal, complemented
3	#11926892	C₂	1	2	yes	maximal
4	C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#498	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₂×#64516	—	2	2	no	—
8	#10597320	C₂²	1	1	yes	characteristic
9	#10597315	C₂²	1	1	yes	characteristic
10	C₁₉×#106	—	2	2	no	—
11	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	#10597292	—	2	4	no	—
13	#10597266	—	2	4	no	—
14	C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
15	C₂×Q₈×C₁₉	—	2	2	no	—
16	C₂×D₇₆	—	2	2	no	—
17	C₂×D₇₆	—	2	1	no	—
18	C₂×Dic₃₈	—	2	1	no	—
19	C₂×C₈×C₁₉	D₄	1	2	yes	—
20	C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₄⋊C₄×C₁₉	—	2	2	no	—
22	C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₁₉	—	2	2	no	—
24	C₂×C₁₉⋊C₈	D₄	1	4	yes	—
25	#64516	—	4	4	no	—
26	C₂²×D₁₉	—	4	1	no	—
27	Q₈×C₁₉	—	4	4	no	—
28	C₂×C₄×C₁₉	—	4	2	no	—
29	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
30	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₁₉	—	4	1	no	—
32	D₇₆	—	4	2	no	—
33	D₇₆	—	4	4	no	—
34	Dic₃₈	—	4	2	no	—
35	C₈×C₁₉	SD₁₆	1	4	yes	—
36	C₁₉⋊C₈	—	2	4	no	—
37	#1708	—	19	1	no	maximal, Sylow
38	C₂²×C₁₉	#127	1	1	yes	characteristic
39	C₂×D₁₉	—	8	1	no	—
40	C₂×D₁₉	—	8	2	no	—
41	C₄×C₁₉	—	8	2	no	—
42	C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
43	C₄×C₁₉	#135	1	4	yes	—
44	Dic₁₉	—	8	1	no	—
45	#498	D₁₉	1	1	yes	characteristic, complemented
46	#492	—	19	1	no	—
47	#487	—	19	2	no	—
48	#486	—	19	2	no	—
49	C₈²	—	19	1	no	—
50	C₂×C₁₉	#492	1	1	yes	characteristic
51	C₂×C₁₉	#495	1	2	yes	—
52	D₁₉	—	16	1	no	—
53	C₂×SD₁₆	—	38	2	no	—
54	C₄⋊Q₈	—	19	1	no	—
55	C₄⋊Q₈	C₂×D₁₉	1	2	yes	—
56	#127	—	19	1	no	—
57	#106	—	2	2	no	—
58	#103	—	38	4	no	—
59	#102	—	38	4	no	—
60	C₄×C₈	—	19	2	no	—
61	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
62	C₁₉	#1708	1	1	yes	characteristic, complemented, Sylow
63	C₂×Q₈	—	2	2	no	—
64	C₂×Q₈	—	38	1	no	—
65	C₂×D₄	—	38	2	no	—
66	C₂×D₄	—	38	1	no	—
67	SD₁₆	—	76	4	no	—
68	C₂×C₈	—	19	4	no	—
69	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
70	C₄⋊C₄	—	2	2	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	38	2	no	—
73	C₄²	C₂²×D₁₉	1	1	yes	characteristic
74	C₂³	—	76	1	no	—
75	Q₈	—	4	4	no	—
76	Q₈	—	76	2	no	—
77	D₄	—	76	2	no	—
78	D₄	—	76	4	no	—
79	C₂×C₄	—	4	2	no	—
80	C₂×C₄	—	76	1	no	—
81	C₂×C₄	D₄×D₁₉	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
83	C₈	—	38	4	no	—
84	C₈	#64527	1	4	yes	—
85	C₂²	—	152	1	no	—
86	C₂²	—	152	2	no	—
87	C₂²	#10597386	1	1	yes	characteristic
88	C₄	—	8	2	no	—
89	C₄	—	152	1	no	—
90	C₄	#10597362	1	4	yes	—
91	C₄	C₂×#64527	1	2	yes	—
92	C₂	—	304	1	no	—
93	C₂	#11926918	1	1	yes	characteristic
94	C₂	#11926925	1	2	yes	—

	subgroup	G/H
center	C₂²	#10597386
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#498	C₂
socle	C₂²×C₁₉	#127
prime radical	#10597320	C₂²
hypercenter	#498	D₁₉
hypocenter	C₁₉	#1708
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

Complements

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

N	H ≅ G/N	type
2. #11926894	C₂	semidirect
4. C₈×C₁₉⋊C₈	C₂	semidirect
5. C₁₉×#498	C₂	semidirect
45. #498	D₁₉	semidirect
62. C₁₉	#1708	semidirect

Maximal subgroups

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

subgroup	index
#11926917	2
#11926894	2
#11926892	2
C₈×C₁₉⋊C₈	2
C₁₉×#498	2
#1708	19