Subgroups — #14521328

Order 1984.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758470	C₂	1	1	yes	maximal, characteristic
2	#11758465	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	#11758409	C₂	1	1	yes	maximal, characteristic
5	Dic₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#11758397	C₂	1	1	yes	maximal, characteristic
7	#11758395	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₁₂₄	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₃₁	—	2	1	no	—
10	C₂×Dic₆₂	—	2	1	no	—
11	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
14	(C₂×D₃₁)⋊C₄	—	2	1	no	—
15	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
16	Dic₃₁⋊C₄	—	2	1	no	—
17	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
18	C₂×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×D₃₁	—	2	1	no	—
20	C₂×C₄×C₃₁	—	2	1	no	—
21	C₂×C₄×C₃₁	—	2	1	no	—
22	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
23	C₂×Dic₃₁	—	2	1	no	—
24	C₂×Dic₃₁	D₄	1	1	yes	characteristic
25	C₂×Dic₃₁	D₄	1	1	yes	characteristic
26	D₁₂₄	—	2	1	no	—
27	D₁₂₄	Q₈	1	2	yes	complemented
28	C₄×D₃₁	—	4	2	no	—
29	Dic₆₂	—	4	2	no	—
30	C₈×C₃₁	—	2	1	no	—
31	C₃₁⋊C₈	—	2	1	no	—
32	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
33	C₂×D₃₁	—	2	2	no	—
34	C₂×D₃₁	—	4	1	no	—
35	C₂×D₃₁	—	4	1	no	—
36	C₄×C₃₁	—	4	1	no	—
37	C₄×C₃₁	—	4	1	no	—
38	C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
39	C₄×C₃₁	#41	1	1	yes	characteristic
40	Dic₃₁	—	2	1	no	—
41	Dic₃₁	—	4	1	no	—
42	Dic₃₁	D₈	1	2	yes	—
43	#474	—	31	1	no	maximal, Sylow
44	C₂×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
45	C₂×C₃₁	C₂×D₈	1	1	yes	characteristic
46	C₂×C₃₁	#137	1	1	yes	characteristic
47	D₃₁	—	4	2	no	—
48	C₄⋊Q₈	—	31	1	no	—
49	C₄×D₄	—	31	1	no	—
50	#107	—	31	1	no	—
51	#107	D₃₁	1	1	yes	characteristic, complemented
52	C₄⋊C₈	—	31	1	no	—
53	#102	—	31	1	no	—
54	#102	—	31	1	no	—
55	C₃₁	#474	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₈	—	62	1	no	—
57	C₂×D₄	—	31	1	no	—
58	C₂²×C₄	—	62	1	no	—
59	C₂×C₈	—	31	1	no	—
60	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
61	C₄⋊C₄	—	31	1	no	—
62	C₄⋊C₄	—	62	1	no	—
63	C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic
64	C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic
65	C₂²⋊C₄	—	62	1	no	—
66	C₄²	—	31	1	no	—
67	C₂³	—	62	1	no	—
68	Q₈	—	124	2	no	—
69	D₄	—	31	2	no	—
70	D₄	—	62	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	31	1	no	—
74	C₂×C₄	—	31	1	no	—
75	C₂×C₄	—	62	1	no	—
76	C₂×C₄	—	124	2	no	—
77	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	62	1	no	—
80	C₂²	—	62	2	no	—
81	C₂²	—	124	1	no	—
82	C₂²	—	124	1	no	—
83	C₂²	D₄×D₃₁	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	31	2	no	—
87	C₄	—	62	1	no	—
88	C₄	—	124	1	no	—
89	C₄	#92495	1	1	yes	characteristic
90	C₄	Q₈×D₃₁	1	1	yes	characteristic
91	C₂	—	124	2	no	—
92	C₂	#11758473	1	1	yes	characteristic
93	C₂	D₈×D₃₁	1	1	yes	characteristic
94	C₂	#11758495	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₁
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×#107	C₂
socle	C₂²×C₃₁	C₂×D₄
prime radical	C₂×D₁₂₄	C₂²
hypercenter	#107	D₃₁
hypocenter	C₃₁	#474
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
2. #11758465	C₂	semidirect
3. C₃₁×#107	C₂	semidirect
5. Dic₃₁⋊C₈	C₂	semidirect
7. #11758395	C₂	semidirect
27. D₁₂₄	Q₈	semidirect
51. #107	D₃₁	semidirect
55. C₃₁	#474	semidirect

Maximal subgroups

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

subgroup	index
#11758470	2
#11758465	2
C₃₁×#107	2
#11758409	2
Dic₃₁⋊C₈	2
#11758397	2
#11758395	2
#474	31