Subgroups — #11926702

Order 1216.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₃₈	C₂	1	1	yes	maximal, characteristic
2	#10597370	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₇₆	C₂	1	2	yes	maximal, complemented
4	C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
5	#10597273	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₁₉	—	2	1	no	—
8	C₂×Dic₃₈	—	2	1	no	—
9	C₂×Dic₃₈	—	2	4	no	—
10	C₂×Dic₃₈	C₂²	1	1	yes	characteristic
11	C₂×Dic₃₈	C₂²	1	2	yes	—
12	C₂×C₈×C₁₉	C₂²	1	2	yes	—
13	C₂²⋊Dic₁₉	—	2	1	no	—
14	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	Dic₁₉⋊C₄	—	2	1	no	—
16	Dic₇₆	—	2	4	no	—
17	C₂³×C₁₉	D₄	1	1	yes	characteristic
18	C₂×C₄×C₁₉	—	2	2	no	—
19	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×Dic₁₉	—	2	4	no	—
22	C₂×Dic₁₉	—	2	2	no	—
23	C₂×Dic₁₉	—	2	1	no	—
24	C₂×Dic₁₉	—	2	1	no	—
25	Dic₃₈	—	2	4	no	—
26	Dic₃₈	—	2	2	no	—
27	Dic₃₈	—	2	2	no	—
28	Dic₃₈	D₄	1	4	yes	—
29	C₈×C₁₉	—	2	2	no	—
30	C₂²×C₁₉	—	2	1	no	—
31	C₂²×C₁₉	—	2	1	no	—
32	C₂²×C₁₉	Q₁₆	1	2	yes	complemented
33	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₄×C₁₉	—	2	1	no	—
35	C₄×C₁₉	C₂×D₄	1	2	yes	—
36	Dic₁₉	—	2	4	no	—
37	Dic₁₉	—	4	1	no	—
38	Dic₁₉	—	4	1	no	—
39	#451	—	19	1	no	maximal, Sylow
40	C₂×C₁₉	—	2	2	no	—
41	C₂×C₁₉	#120	1	1	yes	characteristic
42	C₂×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
43	C₂×C₁₉	#137	1	1	yes	characteristic
44	C₂²×Q₈	—	19	1	no	—
45	C₂×Q₁₆	—	19	2	no	—
46	C₂²⋊Q₈	—	19	1	no	—
47	#103	—	19	2	no	—
48	C₂²⋊C₈	D₁₉	1	1	yes	characteristic
49	C₁₉	#451	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₈	—	19	2	no	—
51	C₂×Q₈	—	19	1	no	—
52	C₂×Q₈	—	38	4	no	—
53	C₂×Q₈	—	38	1	no	—
54	C₂²×C₄	—	38	1	no	—
55	C₂²×C₄	C₂×D₁₉	1	1	yes	characteristic
56	Q₁₆	—	38	4	no	—
57	C₂×C₈	C₂×D₁₉	1	2	yes	—
58	C₄⋊C₄	—	19	1	no	—
59	C₄⋊C₄	—	38	1	no	—
60	C₂²⋊C₄	—	38	1	no	—
61	C₂³	D₇₆	1	1	yes	characteristic
62	Q₈	—	19	4	no	—
63	Q₈	—	38	4	no	—
64	Q₈	—	38	2	no	—
65	Q₈	—	38	2	no	—
66	C₂×C₄	—	2	2	no	—
67	C₂×C₄	—	38	4	no	—
68	C₂×C₄	—	38	2	no	—
69	C₂×C₄	—	38	1	no	—
70	C₂×C₄	—	38	1	no	—
71	C₂×C₄	D₇₆	1	1	yes	characteristic
72	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
73	C₈	—	2	2	no	—
74	C₂²	—	2	1	no	—
75	C₂²	—	2	1	no	—
76	C₂²	Dic₇₆	1	2	yes	complemented
77	C₂²	C₂×D₇₆	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	—	38	4	no	—
80	C₄	—	76	1	no	—
81	C₄	—	76	1	no	—
82	C₄	D₄×D₁₉	1	2	yes	—
83	C₂	—	2	2	no	—
84	C₂	#10597328	1	1	yes	characteristic
85	C₂	C₂×Dic₇₆	1	1	yes	characteristic
86	C₂	#10597355	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₁₉×C₂²⋊C₈	C₂
socle	C₂²×C₁₉	C₂×D₄
prime radical	C₂³×C₁₉	D₄
hypercenter	C₂²⋊C₈	D₁₉
hypocenter	C₁₉	#451
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
3. C₂×Dic₇₆	C₂	semidirect
5. #10597273	C₂	semidirect
32. C₂²×C₁₉	Q₁₆	semidirect
49. C₁₉	#451	semidirect
76. C₂²	Dic₇₆	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₃₈	2
#10597370	2
C₂×Dic₇₆	2
C₁₉×C₂²⋊C₈	2
#10597273	2
#451	19