Subgroups — #11926798

Order 1216.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₅₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#64515	C₂	1	1	yes	maximal, characteristic, complemented
3	#10597341	C₂	1	2	yes	maximal, complemented
4	C₁₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
5	#10597266	C₂	1	2	yes	maximal, complemented
6	C₂×D₇₆	—	2	2	no	—
7	C₂×D₇₆	C₂²	1	2	yes	—
8	C₂×C₄×D₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
11	(C₂×D₁₉)⋊C₄	—	2	2	no	—
12	C₂×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	D₁₅₂	—	2	2	no	—
14	#64515	—	2	2	no	—
15	C₂²×D₁₉	—	2	2	no	—
16	C₂²×D₁₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₉	—	2	2	no	—
18	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₁₉	D₄	1	1	yes	characteristic
20	D₇₆	—	2	2	no	—
21	D₇₆	—	2	2	no	—
22	D₇₆	—	4	4	no	—
23	C₄×D₁₉	—	2	1	no	—
24	C₄×D₁₉	—	2	1	no	—
25	C₈×C₁₉	D₄	1	2	yes	complemented
26	C₁₉⋊C₈	—	2	1	no	—
27	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
28	C₂×D₁₉	—	2	1	no	—
29	C₂×D₁₉	—	2	2	no	—
30	C₂×D₁₉	—	4	2	no	—
31	C₂×D₁₉	—	4	2	no	—
32	C₂×D₁₉	—	4	2	no	—
33	C₄×C₁₉	—	4	2	no	—
34	C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₄×C₁₉	#41	1	1	yes	characteristic
36	Dic₁₉	—	2	1	no	—
37	#469	—	19	1	no	maximal, Sylow
38	C₂×C₁₉	#121	1	1	yes	characteristic
39	C₂×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
40	D₁₉	—	4	1	no	—
41	D₁₉	—	8	2	no	—
42	C₂×D₈	—	19	1	no	—
43	C₂×M₁₆	—	19	1	no	—
44	#121	—	19	2	no	—
45	#106	D₁₉	1	1	yes	characteristic, complemented
46	#102	—	19	2	no	—
47	C₁₉	#469	1	1	yes	characteristic, complemented, Sylow
48	C₂×D₄	—	19	2	no	—
49	C₂×D₄	—	38	2	no	—
50	C₂²×C₄	—	19	1	no	—
51	D₈	—	38	2	no	—
52	M₁₆	—	38	2	no	—
53	C₂×C₈	—	19	1	no	—
54	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
55	C₄⋊C₄	C₂×D₁₉	1	2	yes	—
56	C₂²⋊C₄	—	38	2	no	—
57	C₂³	—	19	1	no	—
58	C₂³	—	38	2	no	—
59	D₄	—	38	2	no	—
60	D₄	—	38	2	no	—
61	D₄	—	76	4	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	19	1	no	—
64	C₂×C₄	—	38	1	no	—
65	C₂×C₄	—	38	1	no	—
66	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
67	C₈	—	38	1	no	—
68	C₈	D₇₆	1	2	yes	complemented
69	C₂²	—	38	1	no	—
70	C₂²	—	38	2	no	—
71	C₂²	—	76	2	no	—
72	C₂²	—	76	2	no	—
73	C₂²	—	76	2	no	—
74	C₂²	D₄×D₁₉	1	1	yes	characteristic
75	C₄	—	4	2	no	—
76	C₄	—	38	1	no	—
77	C₄	C₂×D₇₆	1	1	yes	characteristic
78	C₄	#64545	1	1	yes	characteristic
79	C₂	—	76	1	no	—
80	C₂	—	152	2	no	—
81	C₂	#10597341	1	1	yes	characteristic
82	C₂	#10597360	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₁₉×#106	C₂
socle	C₂²×C₁₉	C₂×D₄
hypercenter	#106	D₁₉
hypocenter	C₁₉	#469
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₅₂	C₂	semidirect
2. C₂×#64515	C₂	semidirect
3. #10597341	C₂	semidirect
4. C₁₉×#106	C₂	semidirect
5. #10597266	C₂	semidirect
25. C₈×C₁₉	D₄	semidirect
45. #106	D₁₉	semidirect
47. C₁₉	#469	semidirect
68. C₈	D₇₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₅₂	2
C₂×#64515	2
#10597341	2
C₁₉×#106	2
#10597266	2
#469	19