Subgroups — #14569741

Order 2432.

844 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597320	C₂	1	3	yes	maximal, complemented
2	C₂×#10597321	C₂	1	3	yes	maximal, complemented
3	#11926454	C₂	1	8	yes	maximal, complemented
4	C₁₉×#376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₇₆	C₂²	1	3	yes	—
6	C₂²×D₇₆	C₂²	1	12	yes	—
7	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₁₉	C₂²	1	3	yes	—
9	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	12	yes	—
10	#10597321	—	2	12	no	—
11	#10597320	—	2	12	no	—
12	C₁₉×#95	C₂²	1	4	yes	—
13	C₂³×D₁₉	C₂³	1	6	yes	—
14	C₂²×C₄×C₁₉	C₂³	1	6	yes	—
15	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
16	C₂²×Dic₁₉	C₂³	1	2	yes	—
17	C₂×D₇₆	—	2	24	no	—
18	C₂×D₇₆	—	2	12	no	—
19	C₂×D₇₆	—	2	6	no	—
20	C₂×D₇₆	—	4	24	no	—
21	C₂×Dic₃₈	—	2	6	no	—
22	C₄²×C₁₉	D₄	1	12	yes	complemented
23	(C₂×D₁₉)⋊C₄	—	2	24	no	—
24	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
25	C₂²×D₁₉	—	2	6	no	—
26	C₂²×D₁₉	—	2	12	no	—
27	C₂²×D₁₉	—	2	24	no	—
28	C₂×C₄×C₁₉	—	2	12	no	—
29	C₂×C₄×C₁₉	C₂×D₄	1	12	yes	—
30	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
31	C₂×Dic₁₉	—	2	6	no	—
32	D₇₆	—	4	48	no	—
33	D₇₆	—	4	12	no	—
34	Dic₃₈	—	4	4	no	—
35	#2657	—	19	1	no	maximal, Sylow
36	C₂²×C₁₉	C₂²×D₄	1	3	yes	—
37	C₂²×C₁₉	H(5,𝔽₂)	1	4	yes	—
38	C₂×D₁₉	—	4	6	no	—
39	C₂×D₁₉	—	4	24	no	—
40	C₂×D₁₉	—	4	12	no	—
41	C₄×C₁₉	—	2	12	no	—
42	C₄×C₁₉	#127	1	4	yes	—
43	Dic₁₉	—	4	2	no	—
44	C₂×#127	—	19	3	no	—
45	C₂×#124	—	19	3	no	—
46	#392	—	19	8	no	—
47	#376	D₁₉	1	1	yes	characteristic, complemented
48	C₂×C₁₉	C₂×#127	1	1	yes	characteristic
49	C₂×C₁₉	#535	1	6	yes	—
50	D₁₉	—	8	6	no	—
51	C₂²×Q₈	—	19	1	no	—
52	C₂²×D₄	—	19	3	no	—
53	C₂²×D₄	—	19	12	no	—
54	#127	—	38	12	no	—
55	#124	—	38	12	no	—
56	C₂×C₂²⋊C₄	—	19	12	no	—
57	C₂×C₄²	C₂×D₁₉	1	3	yes	—
58	#95	C₂×D₁₉	1	4	yes	—
59	C₁₉	#2657	1	1	yes	characteristic, complemented, Sylow
60	C₂⁴	—	19	6	no	—
61	C₂×Q₈	—	38	6	no	—
62	C₂×D₄	—	38	6	no	—
63	C₂×D₄	—	38	24	no	—
64	C₂×D₄	—	38	12	no	—
65	C₂×D₄	—	76	24	no	—
66	C₂²×C₄	—	19	2	no	—
67	C₂²×C₄	C₂²×D₁₉	1	6	yes	—
68	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
69	C₂²⋊C₄	—	38	24	no	—
70	C₄²	D₇₆	1	12	yes	complemented
71	C₂³	—	38	6	no	—
72	C₂³	—	38	12	no	—
73	C₂³	—	38	24	no	—
74	C₂³	C₂³×D₁₉	1	1	yes	characteristic
75	Q₈	—	76	4	no	—
76	D₄	—	76	48	no	—
77	D₄	—	76	12	no	—
78	C₂×C₄	—	2	12	no	—
79	C₂×C₄	—	38	6	no	—
80	C₂×C₄	C₂×D₇₆	1	12	yes	—
81	C₂×C₄	C₂×D₇₆	1	6	yes	—
82	C₂²	—	76	6	no	—
83	C₂²	—	76	24	no	—
84	C₂²	—	76	12	no	—
85	C₂²	C₂²×D₇₆	1	3	yes	—
86	C₂²	#10597435	1	4	yes	—
87	C₄	—	2	12	no	—
88	C₄	—	76	2	no	—
89	C₄	#10597320	1	4	yes	—
90	C₂	—	152	6	no	—
91	C₂	C₂×#10597320	1	1	yes	characteristic
92	C₂	#11927113	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#376	C₂
hypercenter	#376	D₁₉
hypocenter	C₁₉	#2657
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #376

Complements

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

N	H ≅ G/N	type
1. C₂×#10597320	C₂	semidirect
2. C₂×#10597321	C₂	semidirect
3. #11926454	C₂	semidirect
4. C₁₉×#376	C₂	semidirect
22. C₄²×C₁₉	D₄	semidirect
47. #376	D₁₉	semidirect
59. C₁₉	#2657	semidirect
70. C₄²	D₇₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597320	2
C₂×#10597321	2
#11926454	2
C₁₉×#376	2
#2657	19