Subgroups — #11927272

Order 1216.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	#10597390	C₂	1	2	yes	maximal
3	#10597335	C₂	1	4	yes	maximal
4	#10597333	C₂	1	2	yes	maximal
5	#10597316	C₂	1	2	yes	maximal
6	#10597315	C₂	1	1	yes	maximal, characteristic
7	C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic
8	C₄×Dic₃₈	C₂	1	2	yes	maximal
9	C₂×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₃₈	C₂²	1	2	yes	—
11	C₂×Dic₃₈	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₄²×C₁₉	C₂²	1	2	yes	—
16	C₄⋊Dic₁₉	C₂²	1	2	yes	—
17	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
18	C₄⋊Dic₁₉	C₂²	1	2	yes	—
19	Dic₁₉⋊C₄	C₂²	1	4	yes	—
20	Dic₁₉⋊C₄	C₂²	1	4	yes	—
21	Dic₁₉⋊C₄	C₂²	1	2	yes	—
22	Dic₁₉⋊C₄	C₂²	1	4	yes	—
23	C₄×Dic₁₉	C₂²	1	2	yes	—
24	C₄×Dic₁₉	C₂²	1	4	yes	—
25	Q₈×C₁₉	—	2	2	no	—
26	C₂×C₄×C₁₉	C₂³	1	2	yes	—
27	C₂×C₄×C₁₉	C₂³	1	2	yes	—
28	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×Dic₁₉	C₂³	1	2	yes	—
32	C₂×Dic₁₉	C₂³	1	4	yes	—
33	C₂×Dic₁₉	C₂³	1	2	yes	—
34	Dic₃₈	—	2	4	no	—
35	Dic₃₈	Q₈	1	4	yes	complemented
36	C₂²×C₁₉	C₂⁴	1	1	yes	characteristic
37	C₄×C₁₉	—	2	2	no	—
38	C₄×C₁₉	—	2	2	no	—
39	C₄×C₁₉	—	2	1	no	—
40	C₄×C₁₉	C₂×Q₈	1	2	yes	—
41	C₄×C₁₉	#41	1	2	yes	—
42	Dic₁₉	—	2	4	no	—
43	Dic₁₉	—	2	2	no	—
44	Dic₁₉	C₂×Q₈	1	4	yes	—
45	#557	—	19	1	no	maximal, Sylow
46	C₂×C₁₉	C₂²×Q₈	1	1	yes	characteristic
47	C₂×C₁₉	C₂×#41	1	1	yes	characteristic
48	C₂×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
49	C₄⋊Q₈	—	19	2	no	—
50	C₄⋊Q₈	—	19	1	no	—
51	#125	—	19	4	no	—
52	#125	—	19	2	no	—
53	C₄×Q₈	—	19	2	no	—
54	C₄×Q₈	—	19	2	no	—
55	C₄×Q₈	—	19	1	no	—
56	C₄×Q₈	D₁₉	1	1	yes	characteristic
57	C₁₉	#557	1	1	yes	characteristic, complemented, Sylow
58	C₂×Q₈	—	19	1	no	—
59	C₂×Q₈	—	19	2	no	—
60	C₂×Q₈	C₂×D₁₉	1	1	yes	characteristic
61	C₄⋊C₄	—	19	2	no	—
62	C₄⋊C₄	—	19	4	no	—
63	C₄⋊C₄	—	19	4	no	—
64	C₄⋊C₄	—	19	4	no	—
65	C₄⋊C₄	—	19	1	no	—
66	C₄⋊C₄	—	19	2	no	—
67	C₄⋊C₄	—	19	2	no	—
68	C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
69	C₄⋊C₄	C₂×D₁₉	1	2	yes	—
70	C₄²	—	19	4	no	—
71	C₄²	—	19	2	no	—
72	C₄²	C₂×D₁₉	1	2	yes	—
73	C₄²	C₂×D₁₉	1	1	yes	characteristic
74	Q₈	—	2	2	no	—
75	Q₈	—	19	4	no	—
76	Q₈	—	38	4	no	—
77	C₂×C₄	—	19	2	no	—
78	C₂×C₄	—	19	2	no	—
79	C₂×C₄	—	19	4	no	—
80	C₂×C₄	C₂²×D₁₉	1	2	yes	—
81	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
82	C₂×C₄	C₂²×D₁₉	1	2	yes	—
83	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
84	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
85	C₂²	C₂³×D₁₉	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	2	2	no	—
88	C₄	—	2	1	no	—
89	C₄	—	19	4	no	—
90	C₄	—	38	4	no	—
91	C₄	—	38	2	no	—
92	C₄	#64541	1	2	yes	—
93	C₄	Q₈×D₁₉	1	2	yes	—
94	C₂	C₂×#64541	1	1	yes	characteristic
95	C₂	C₂×Q₈×D₁₉	1	1	yes	characteristic
96	C₂	#10597436	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂²×C₁₉	C₂⁴
Fitting	C₄×Q₈×C₁₉	C₂
hypercenter	C₄×Q₈	D₁₉
hypocenter	C₁₉	#557
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
35. Dic₃₈	Q₈	semidirect
57. C₁₉	#557	semidirect

Maximal subgroups

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

subgroup	index
C₄×Q₈×C₁₉	2
#10597390	2
#10597335	2
#10597333	2
#10597316	2
#10597315	2
C₄×Dic₃₈	2
#557	19