Subgroups — #14521316

Order 1984.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#11758509	C₂	1	2	yes	maximal, complemented
3	#11758478	C₂	1	1	yes	maximal, characteristic, complemented
4	#11758421	C₂	1	2	yes	maximal, complemented
5	#11758407	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₃₁	C₂²	1	2	yes	—
7	#92495	C₂²	1	1	yes	characteristic
8	D₈×C₃₁	—	2	1	no	—
9	D₈×C₃₁	—	2	1	no	—
10	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
11	#92480	—	2	2	no	—
12	#92479	—	2	2	no	—
13	#92474	C₂²	1	2	yes	—
14	#92474	C₂²	1	1	yes	characteristic
15	#92469	—	2	1	no	—
16	C₈×D₃₁	—	2	1	no	—
17	C₂³×C₃₁	—	2	2	no	—
18	D₄×C₃₁	—	2	2	no	—
19	D₄×C₃₁	—	2	2	no	—
20	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
21	C₂²⋊D₃₁	—	2	1	no	—
22	D₁₂₄	D₄	1	1	yes	characteristic
23	C₄×D₃₁	—	2	1	no	—
24	Dic₆₂	D₄	1	1	yes	characteristic
25	C₈×C₃₁	D₄	1	1	yes	characteristic
26	C₈×C₃₁	D₄	1	1	yes	characteristic
27	C₃₁⋊C₈	—	2	1	no	—
28	C₃₁⋊C₈	—	2	2	no	—
29	C₂²×C₃₁	—	4	2	no	—
30	C₂²×C₃₁	—	8	2	no	—
31	C₂²×C₃₁	#41	1	1	yes	characteristic
32	C₂×D₃₁	—	2	1	no	—
33	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
34	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
35	Dic₃₁	—	2	1	no	—
36	#472	—	31	1	no	maximal, Sylow
37	C₂×C₃₁	—	2	1	no	—
38	C₂×C₃₁	—	8	2	no	—
39	C₂×C₃₁	#121	1	1	yes	characteristic
40	D₃₁	—	4	1	no	—
41	AGL(1,ℤ/8)	—	31	2	no	—
42	C₂×D₈	D₃₁	1	1	yes	characteristic, complemented
43	#131	—	31	1	no	—
44	#108	—	31	1	no	—
45	#100	—	31	2	no	—
46	C₃₁	#472	1	1	yes	characteristic, complemented, Sylow
47	#41	—	31	1	no	—
48	C₂×D₄	C₂×D₃₁	1	2	yes	—
49	SD₁₆	—	62	2	no	—
50	D₈	—	2	1	no	—
51	D₈	—	2	1	no	—
52	D₈	—	62	2	no	—
53	M₁₆	—	31	1	no	—
54	M₁₆	—	31	2	no	—
55	M₁₆	—	62	1	no	—
56	C₂×C₈	—	62	1	no	—
57	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
58	C₂³	—	2	2	no	—
59	Q₈	—	31	1	no	—
60	D₄	—	2	2	no	—
61	D₄	—	2	2	no	—
62	D₄	—	31	1	no	—
63	D₄	—	62	1	no	—
64	C₂×C₄	—	62	1	no	—
65	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
66	C₈	—	62	2	no	—
67	C₈	—	62	1	no	—
68	C₈	C₂²⋊D₃₁	1	1	yes	characteristic
69	C₈	C₂²⋊D₃₁	1	1	yes	characteristic
70	C₂²	—	4	2	no	—
71	C₂²	—	8	2	no	—
72	C₂²	—	62	1	no	—
73	C₂²	#92497	1	1	yes	characteristic
74	C₄	—	62	1	no	—
75	C₄	D₄×D₃₁	1	1	yes	characteristic
76	C₄	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	—	8	2	no	—
79	C₂	—	124	1	no	—
80	C₂	#11758515	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11758515
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₂×D₈×C₃₁	C₂
socle	C₂×C₃₁	#121
hypercenter	C₂×D₈	D₃₁
hypocenter	C₃₁	#472
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₈×C₃₁	C₂	semidirect
2. #11758509	C₂	semidirect
3. #11758478	C₂	semidirect
4. #11758421	C₂	semidirect
5. #11758407	C₂	semidirect
42. C₂×D₈	D₃₁	semidirect
46. C₃₁	#472	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₈×C₃₁	2
#11758509	2
#11758478	2
#11758421	2
#11758407	2
#472	31