Subgroups — #14521438

Order 1984.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₄₈	C₂	1	2	yes	maximal, complemented
2	C₂×#92470	C₂	1	2	yes	maximal, complemented
3	#11758452	C₂	1	1	yes	maximal, characteristic, complemented
4	#11758451	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₂₄	—	2	2	no	—
7	C₂×D₁₂₄	C₂²	1	2	yes	—
8	C₂×D₁₂₄	C₂²	1	1	yes	characteristic
9	C₂×Dic₆₂	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₃₁	C₂²	1	2	yes	—
11	C₄²×C₃₁	C₂²	1	1	yes	characteristic
12	(C₂×D₃₁)⋊C₄	—	2	2	no	—
13	D₂₄₈	—	2	4	no	—
14	#92470	—	2	4	no	—
15	C₂²×D₃₁	—	2	1	no	—
16	C₂²×D₃₁	—	2	2	no	—
17	C₂×C₄×C₃₁	D₄	1	2	yes	—
18	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
19	C₂×Dic₃₁	—	2	1	no	—
20	D₁₂₄	—	2	2	no	—
21	D₁₂₄	—	2	2	no	—
22	D₁₂₄	—	2	2	no	—
23	D₁₂₄	—	4	4	no	—
24	Dic₆₂	—	2	2	no	—
25	C₈×C₃₁	D₄	1	4	yes	complemented
26	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
27	C₂×D₃₁	—	4	2	no	—
28	C₂×D₃₁	—	4	1	no	—
29	C₂×D₃₁	—	4	4	no	—
30	C₂×D₃₁	—	4	2	no	—
31	C₄×C₃₁	—	2	2	no	—
32	C₄×C₃₁	C₂×D₄	1	2	yes	—
33	Dic₃₁	—	4	1	no	—
34	#496	—	31	1	no	maximal, Sylow
35	C₂×C₃₁	#127	1	1	yes	characteristic
36	C₂×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
37	D₃₁	—	8	2	no	—
38	D₃₁	—	8	1	no	—
39	C₂×SD₁₆	—	31	2	no	—
40	C₂×D₈	—	31	2	no	—
41	#127	—	31	1	no	—
42	#124	—	31	1	no	—
43	#97	D₃₁	1	1	yes	characteristic, complemented
44	C₃₁	#496	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₈	—	31	1	no	—
46	C₂×D₄	—	31	1	no	—
47	C₂×D₄	—	31	2	no	—
48	C₂×D₄	—	62	2	no	—
49	SD₁₆	—	62	4	no	—
50	D₈	—	62	4	no	—
51	C₂×C₈	C₂×D₃₁	1	2	yes	—
52	C₂²⋊C₄	—	62	2	no	—
53	C₄²	C₂×D₃₁	1	1	yes	characteristic
54	C₂³	—	62	1	no	—
55	C₂³	—	62	2	no	—
56	Q₈	—	62	2	no	—
57	D₄	—	62	2	no	—
58	D₄	—	62	2	no	—
59	D₄	—	62	2	no	—
60	D₄	—	124	4	no	—
61	C₂×C₄	—	62	1	no	—
62	C₂×C₄	D₁₂₄	1	2	yes	—
63	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
64	C₈	D₁₂₄	1	4	yes	complemented
65	C₂²	—	124	1	no	—
66	C₂²	—	124	2	no	—
67	C₂²	—	124	4	no	—
68	C₂²	—	124	2	no	—
69	C₂²	C₂×D₁₂₄	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	124	1	no	—
72	C₄	C₂×D₁₂₄	1	2	yes	—
73	C₂	—	248	2	no	—
74	C₂	—	248	1	no	—
75	C₂	#11758451	1	1	yes	characteristic
76	C₂	#11758485	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₂₄
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×#97	C₂
socle	C₂²×C₃₁	C₂×D₄
hypercenter	#97	D₃₁
hypocenter	C₃₁	#496
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
1. C₂×D₂₄₈	C₂	semidirect
2. C₂×#92470	C₂	semidirect
3. #11758452	C₂	semidirect
4. #11758451	C₂	semidirect
5. C₃₁×#97	C₂	semidirect
25. C₈×C₃₁	D₄	semidirect
43. #97	D₃₁	semidirect
44. C₃₁	#496	semidirect
64. C₈	D₁₂₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₂₄₈	2
C₂×#92470	2
#11758452	2
#11758451	2
C₃₁×#97	2
#496	31