Subgroups — #11926933

Order 1216.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₅₂	C₂	1	2	yes	maximal, complemented
2	C₂×#64516	C₂	1	2	yes	maximal, complemented
3	#10597321	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597320	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₇₆	—	2	2	no	—
7	C₂×D₇₆	C₂²	1	2	yes	—
8	C₂×D₇₆	C₂²	1	1	yes	characteristic
9	C₂×Dic₃₈	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₁₉	C₂²	1	2	yes	—
11	C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	(C₂×D₁₉)⋊C₄	—	2	2	no	—
13	D₁₅₂	—	2	4	no	—
14	#64516	—	2	4	no	—
15	C₂²×D₁₉	—	2	1	no	—
16	C₂²×D₁₉	—	2	2	no	—
17	C₂×C₄×C₁₉	D₄	1	2	yes	—
18	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₁₉	—	2	1	no	—
20	D₇₆	—	2	2	no	—
21	D₇₆	—	2	2	no	—
22	D₇₆	—	2	2	no	—
23	D₇₆	—	4	4	no	—
24	Dic₃₈	—	2	2	no	—
25	C₈×C₁₉	D₄	1	4	yes	complemented
26	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
27	C₂×D₁₉	—	4	2	no	—
28	C₂×D₁₉	—	4	1	no	—
29	C₂×D₁₉	—	4	4	no	—
30	C₂×D₁₉	—	4	2	no	—
31	C₄×C₁₉	—	2	2	no	—
32	C₄×C₁₉	C₂×D₄	1	2	yes	—
33	Dic₁₉	—	4	1	no	—
34	#496	—	19	1	no	maximal, Sylow
35	C₂×C₁₉	#127	1	1	yes	characteristic
36	C₂×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
37	D₁₉	—	8	2	no	—
38	D₁₉	—	8	1	no	—
39	C₂×SD₁₆	—	19	2	no	—
40	C₂×D₈	—	19	2	no	—
41	#127	—	19	1	no	—
42	#124	—	19	1	no	—
43	#97	D₁₉	1	1	yes	characteristic, complemented
44	C₁₉	#496	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₈	—	19	1	no	—
46	C₂×D₄	—	19	1	no	—
47	C₂×D₄	—	19	2	no	—
48	C₂×D₄	—	38	2	no	—
49	SD₁₆	—	38	4	no	—
50	D₈	—	38	4	no	—
51	C₂×C₈	C₂×D₁₉	1	2	yes	—
52	C₂²⋊C₄	—	38	2	no	—
53	C₄²	C₂×D₁₉	1	1	yes	characteristic
54	C₂³	—	38	1	no	—
55	C₂³	—	38	2	no	—
56	Q₈	—	38	2	no	—
57	D₄	—	38	2	no	—
58	D₄	—	38	2	no	—
59	D₄	—	38	2	no	—
60	D₄	—	76	4	no	—
61	C₂×C₄	—	38	1	no	—
62	C₂×C₄	D₇₆	1	2	yes	—
63	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
64	C₈	D₇₆	1	4	yes	complemented
65	C₂²	—	76	1	no	—
66	C₂²	—	76	2	no	—
67	C₂²	—	76	4	no	—
68	C₂²	—	76	2	no	—
69	C₂²	C₂×D₇₆	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	76	1	no	—
72	C₄	C₂×D₇₆	1	2	yes	—
73	C₂	—	152	2	no	—
74	C₂	—	152	1	no	—
75	C₂	#10597320	1	1	yes	characteristic
76	C₂	#10597354	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₁₉×#97	C₂
socle	C₂²×C₁₉	C₂×D₄
hypercenter	#97	D₁₉
hypocenter	C₁₉	#496
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₅₂	C₂	semidirect
2. C₂×#64516	C₂	semidirect
3. #10597321	C₂	semidirect
4. #10597320	C₂	semidirect
5. C₁₉×#97	C₂	semidirect
25. C₈×C₁₉	D₄	semidirect
43. #97	D₁₉	semidirect
44. C₁₉	#496	semidirect
64. 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×#64516	2
#10597321	2
#10597320	2
C₁₉×#97	2
#496	19