Subgroups — #14269362

Order 1824.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₂₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#90696	C₂	1	4	yes	maximal, complemented
4	C₄×Dic₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#10597320	—	3	1	no	maximal, Hall
6	C₂²×D₅₇	C₂²	1	2	yes	—
7	C₂²×C₃×D₁₉	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	D₂₂₈	—	2	2	no	—
10	C₂×Dic₃×C₁₉	C₂²	1	2	yes	—
11	C₃×D₇₆	—	2	2	no	—
12	#90696	—	2	8	no	—
13	C₂×D₇₆	—	3	4	no	—
14	C₂×D₇₆	—	3	1	no	—
15	C₂×D₇₆	D₃	1	1	yes	characteristic, complemented
16	C₄²×C₁₉	—	3	1	no	—
17	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
18	C₂×D₅₇	—	2	4	no	—
19	C₂×D₅₇	—	2	2	no	—
20	C₂×C₃×D₁₉	—	2	4	no	—
21	C₂×C₃×D₁₉	—	2	2	no	—
22	C₃×C₄×C₁₉	D₄	1	2	yes	complemented
23	Dic₃×C₁₉	D₄	1	4	yes	complemented
24	C₂²×D₁₉	—	3	2	no	—
25	C₂²×D₁₉	C₂×D₃	1	2	yes	—
26	C₂×C₄×C₁₉	—	3	2	no	—
27	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
28	D₇₆	—	2	2	no	—
29	D₇₆	—	6	8	no	—
30	D₇₆	—	6	2	no	—
31	C₂×C₃×C₁₉	C₂×D₄	1	2	yes	—
32	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
33	D₅₇	—	4	2	no	—
34	C₃×D₁₉	—	4	2	no	—
35	#940	—	19	1	no	maximal, Hall
36	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
37	C₂×D₁₉	—	2	4	no	—
38	C₂×D₁₉	—	2	2	no	—
39	C₂×D₁₉	—	6	4	no	—
40	C₂×D₁₉	—	6	2	no	—
41	C₄×C₁₉	—	3	4	no	—
42	C₄×C₁₉	#67	1	2	yes	complemented
43	C₃×C₁₉	#127	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×D₄	—	19	1	no	—
45	C₂×#67	—	19	4	no	—
46	C₂×D₁₂	—	19	1	no	—
47	C₄×Dic₃	D₁₉	1	1	yes	characteristic, complemented
48	C₂×C₁₉	D₃×D₄	1	2	yes	—
49	C₂×C₁₉	C₂×#67	1	1	yes	characteristic
50	D₁₉	—	4	2	no	—
51	D₁₉	—	12	2	no	—
52	#127	—	57	1	no	Sylow
53	C₂³×C₃	—	19	2	no	—
54	C₂²×D₃	—	19	2	no	—
55	C₃×D₄	—	38	2	no	—
56	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
57	#67	—	38	8	no	—
58	C₂×Dic₃	C₂×D₁₉	1	2	yes	—
59	D₁₂	—	38	2	no	—
60	C₁₉	#940	1	1	yes	characteristic, complemented, Sylow
61	C₂×D₄	—	19	1	no	—
62	C₂×D₄	—	57	4	no	—
63	C₂×D₄	—	57	1	no	—
64	C₄²	—	3	1	no	—
65	C₂²×C₃	—	38	4	no	—
66	C₂²×C₃	—	38	2	no	—
67	C₂²×C₃	C₂²×D₁₉	1	1	yes	characteristic
68	C₂×D₃	—	38	2	no	—
69	C₂×D₃	—	38	4	no	—
70	C₃×C₄	D₇₆	1	2	yes	complemented
71	Dic₃	D₇₆	1	4	yes	complemented
72	C₂³	—	19	2	no	—
73	C₂³	—	57	2	no	—
74	D₄	—	38	2	no	—
75	D₄	—	114	8	no	—
76	D₄	—	114	2	no	—
77	C₂×C₄	—	3	2	no	—
78	C₂×C₄	D₃×D₁₉	1	1	yes	characteristic
79	C₂×C₃	—	76	2	no	—
80	C₂×C₃	C₂×D₇₆	1	2	yes	—
81	C₂×C₃	C₂×D₇₆	1	1	yes	characteristic
82	D₃	—	76	2	no	—
83	C₂²	—	38	4	no	—
84	C₂²	—	38	2	no	—
85	C₂²	—	114	4	no	—
86	C₂²	—	114	2	no	—
87	C₂²	C₂×D₃×D₁₉	1	1	yes	characteristic
88	C₄	—	3	4	no	—
89	C₄	#90696	1	2	yes	complemented
90	C₃	#10597320	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	76	2	no	—
92	C₂	—	228	2	no	—
93	C₂	D₃×D₇₆	1	2	yes	—
94	C₂	C₂×#90696	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×D₃×D₁₉
commutator, socle, cosocle	C₂²×C₃×C₁₉	C₂³
Fitting	C₂×C₃×C₄×C₁₉	C₂²
hypercenter	C₂×C₄	D₃×D₁₉
hypocenter	C₃×C₁₉	#127
LCS	G ▷ C₂²×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₂₂₈	C₂	semidirect
2. C₂×C₃×D₇₆	C₂	semidirect
3. C₂×#90696	C₂	semidirect
4. C₄×Dic₃×C₁₉	C₂	semidirect
15. C₂×D₇₆	D₃	semidirect
22. C₃×C₄×C₁₉	D₄	semidirect
23. Dic₃×C₁₉	D₄	semidirect
42. C₄×C₁₉	#67	semidirect
43. C₃×C₁₉	#127	semidirect
47. C₄×Dic₃	D₁₉	semidirect
60. C₁₉	#940	semidirect
70. C₃×C₄	D₇₆	semidirect
71. Dic₃	D₇₆	semidirect
89. C₄	#90696	semidirect
90. C₃	#10597320	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₂₂₈	2
C₂×C₃×D₇₆	2
C₂×#90696	2
C₄×Dic₃×C₁₉	2
#10597320	3
#940	19