Subgroups — #14521324

Order 1984.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#131	C₂	1	1	yes	maximal, characteristic
2	#11758528	C₂	1	2	yes	maximal
3	C₂×Dic₁₂₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#11758412	C₂	1	2	yes	maximal, complemented
5	#11758407	C₂	1	1	yes	maximal, characteristic, complemented
6	#41×C₃₁	C₂²	1	1	yes	characteristic
7	C₂×Dic₆₂	C₂²	1	2	yes	—
8	M₁₆×C₃₁	—	2	1	no	—
9	M₁₆×C₃₁	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₃₁	—	2	1	no	—
11	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
12	#92482	—	2	2	no	—
13	#92480	—	2	2	no	—
14	#92474	C₂²	1	2	yes	—
15	Dic₁₂₄	—	2	1	no	—
16	Dic₁₂₄	—	2	1	no	—
17	Q₈×C₃₁	D₄	1	1	yes	characteristic
18	D₄×C₃₁	—	2	1	no	—
19	D₄×C₃₁	D₄	1	1	yes	characteristic
20	C₂×C₄×C₃₁	—	2	1	no	—
21	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
22	C₂×Dic₃₁	—	2	2	no	—
23	Dic₆₂	—	2	2	no	—
24	Dic₆₂	—	2	2	no	—
25	C₈×C₃₁	—	2	1	no	—
26	C₈×C₃₁	D₄	1	1	yes	characteristic
27	C₈×C₃₁	D₄	1	1	yes	characteristic
28	C₃₁⋊C₈	—	2	2	no	—
29	C₂²×C₃₁	—	2	1	no	—
30	C₂²×C₃₁	#41	1	1	yes	characteristic
31	C₄×C₃₁	—	2	1	no	—
32	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
33	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
34	Dic₃₁	—	4	2	no	—
35	#473	—	31	1	no	maximal, Sylow
36	C₂×C₃₁	—	2	1	no	—
37	C₂×C₃₁	—	4	1	no	—
38	C₂×C₃₁	#121	1	1	yes	characteristic
39	#137	—	31	2	no	—
40	C₂×Q₁₆	—	31	1	no	—
41	#131	D₃₁	1	1	yes	characteristic
42	#108	—	31	1	no	—
43	#101	—	31	2	no	—
44	C₃₁	#473	1	1	yes	characteristic, complemented, Sylow
45	#41	C₂×D₃₁	1	1	yes	characteristic
46	C₂×Q₈	—	31	2	no	—
47	Q₁₆	—	62	2	no	—
48	Q₁₆	—	62	1	no	—
49	Q₁₆	—	62	1	no	—
50	SD₁₆	—	62	2	no	—
51	M₁₆	—	2	1	no	—
52	M₁₆	—	31	2	no	—
53	M₁₆	C₂×D₃₁	1	1	yes	characteristic
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
56	Q₈	—	62	2	no	—
57	Q₈	—	62	2	no	—
58	Q₈	D₁₂₄	1	1	yes	characteristic
59	D₄	—	2	1	no	—
60	D₄	D₁₂₄	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	62	2	no	—
63	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
64	C₈	—	2	1	no	—
65	C₈	—	62	2	no	—
66	C₈	C₂²⋊D₃₁	1	1	yes	characteristic
67	C₈	C₂²⋊D₃₁	1	1	yes	characteristic
68	C₂²	—	2	1	no	—
69	C₂²	#92495	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	124	2	no	—
72	C₄	C₂×D₁₂₄	1	1	yes	characteristic
73	C₄	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	4	1	no	—
76	C₂	#11758507	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11758507
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×#131	C₂
socle	C₂×C₃₁	#121
prime radical	#41×C₃₁	C₂²
hypercenter	#131	D₃₁
hypocenter	C₃₁	#473
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131

Complements

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

N	H ≅ G/N	type
3. C₂×Dic₁₂₄	C₂	semidirect
4. #11758412	C₂	semidirect
5. #11758407	C₂	semidirect
44. C₃₁	#473	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#131	2
#11758528	2
C₂×Dic₁₂₄	2
#11758412	2
#11758407	2
#473	31